Developments in dual system estimation of population size and growth

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Developments in Dual System Estimation of Population Size and Growth

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Developments in Dual System Estimation of Population Size and Growth Edited by KarolJ.Krotki

The University of Alberta Press 1978

First published by The University of Alberta Press Edmonton, Alberta, Canada 1978 This book has been published with the help of a grant from the Humanities Research Council of Canada, using funds provided by the Canada Council. Copyright © 1978 The University of Alberta Press Canadian shared cataloguing in Publication Data Main entry under title Developments in dual system estimation of population size and growth Includes bibliographies. ISBN 0-88864-017-X 1. Demography - Methodology - Addresses, essays, lectures. 2. Population forecastingAdresses, essays, lectures. I. Krotki, Karol J. HB881.D49 301.32 C77-002073-9

All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means, electronic mechanical, photocopying, recording or otherwise without the prior permission of the copyright owner. Design: P. Bartl, Dept. of Art and Design Cover design: P. Bartl, Chi Lee Printed in Canada by Printing Services of The University of Alberta iv

Contents

Acknowledgments xiii Preface xiv by W. Parker Mouldin, Acting President, the Population Council, New York Introduction xvi Chapter 1 The Role of PGE/ERAD/ECP Surveys Among the Endeavours to Secure More and Improved Demographic Data 1 by Karol J. Krotki 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

The need for improved demographic data 1 An overview of the available techniques 2 The theory behind the PGE/ ERAD/ ECP technique 8 The PGE handbook and some essential PGE/ERAD/ECP features 10 An ideal PGE/ ERAD/ ECP exercise 12 An overview of the world uses of the PGE/ERAD/ECP technique 13 Modes of securing the advantages of the technique 25 Inadvertent modes of destroying the advantages of the technique 27 1.8.a Matters affecting independence 27 l.S.b Matters affecting matching procedure 27 l.S.c Matters affecting samples 28 l.8.d Matters affecting organization 28 1.9 Quasi PGE/ ERAD/ ECP estimates 29 1.10 The paucity and importance of costing data 29 1.11 The past history and the probable future of the technique 48 Discussion by Lee L. Bean 49 Chapter 2 The State of the Art in Dual Systems for Measuring Population Change 53 by H. Bradley Wells and Daniel G. Horvitz 2.1 2.2

Introduction 53 Sample design 54 2.2.a Some general sampling considerations 54 2.2.b The need for realistic parameters 55 2.2.c Rotation designs 56 V

2.2.d Some aids to improved estimation 56 2.3 The data collection elements of the dual collection system 57 2.3.a The essential elements of a dual collection system 57 2.3.b The continuous recording procedure 58 2.3.c The household survey procedure 61 2.3.d Matching procedures 63 2.3.e Field identification procedures and other factors common to both collection procedures 64 2.4 Conclusion 69 Discussion by Ivan P. Fellegi 69 Chapter 3 Dual Estimation in Demography Employing Time Series and Cross Section Data 74 by P. Krishnan 3.1 3.2 3.3 3.4

Introduction 74 Pooling cross section and time series data 74 Best estimator 75 Suggested estimation strategies 75 Estimator 1 75 Estimator 2 76 Estimator 3 77 An appendix to chapter 3: Correlation pattern in Canadian data on births and deaths 79 Discussion by Eli S. Marks 79

Chapter 4 Dual System Estimators Based on Multiplicity Surveys 81 by Monroe G. Sirken 4.1 4.2 4.3 4.4 4.5 4.6 4.7

Introduction 81 Counting rules 81 Multiplicity estimators 82 Dual system multiplicity estimators 83 Variance of sample estimators 84 Relative precision of different rules 84 Conclusion 86 Appendix A to chapter 4: Variance of DSM sample estimators 87 Appendix B to chapter 4: Simplification of Hr 87 Discussion by Ivan P. Fellegi 89

Chapter 5 The Collection of Demographic Data in Francophone Africa and Liberia Using the PGE/ERAD/ECP System 92 by Francois Pradel de Lamaze 5.1 5.2 5.3 5.4 5.5 5.6 5.7 vi

Dual collection 92 Some observations 92 Some undertakings in Madagascar 94 The Tunisian experiment 95 The case of Senegal and Cameroun 96 An endeavour in Algeria 96 Morocco: an extended experiment 97

5.8 Dual collection in Liberia 99 Discussion by William Seltzer 100 Chapter 6 The Egyptian Study to Measure Vital Rates: Some Estimates by Dual Collection 104 by K. E. Vaidyanathan 6.1 6.2 6.3 6.4 6.5

Introduction 104 Study design 104 Findings of the study 106 An evaluation of the estimates 108 Conclusion 109 Discussion by William Seltzer 110

Chapter 7 Some Practical Problems Suggested by the Application of the PGE/ERAD/ECP System in Morocco 113 by Mohamed Rachidi 7.1 7.2 7.3 7.4 7.5 7.6

Moroccan demography 113 The periodic household survey and its rotating objective 114 Cluster size and some consequences 114 The efficiency of personnel: resident and outside 115 The numbering of structures 116 Organization in the field 117 7.6.a Interval between two household surveys 117 7.6.b Relation between rounds in periodic surveys 117 7.6.c Events in medical institutions 117 7.6.d The problem of supervision in the field 118 Discussion by Charles Nobbe 119

Chapter 8 PGE/ERAD/ECP Matching Experiences in Morocco 122 by El Arbi Housni, Frances Notzon, and Marie-Daniele Picket 8.1 8.2 8.3 8.4 8.5

Features of field work most relevant to matching 122 The purpose of matching 123 Experimental matching: procedure used 124 Experimental matching: problems encountered 126 Production matching 128 8.5.a Vital rates 129 8.5.b Field verification 132 8.6 Conclusion 133 8.7 An appendix to chapter 8: The use of and experimental study for reaching decisions on matching rules 135 by Gad Nathan 8.A.I General 135 8. A.2 Data available from an experimental matching study 135 8. A.3 The variances of the estimator and its estimation 137 8. A.4 Comparison of matching rules 139 8. A.5 A proposal for a decision process 141 vii

Chapter 9 The PGE/ERAD/ECP System of Data Collection in Africa and a Comparison of its Results With Those of Analytic Techniques 145 by Roderic P. Beaujot 9.1 Introduction 145 9.2 Some African experiences with the PGE/ERAD/ECP 145 9.3 Analytic techniques 148 9.4 Some African experiences with analytic techniques 150 Discussion by Ansley J. Coale 153 Chapter 10 The Role of Dual System Estimation in Census Evaluation 156 by Eli S. Marks 10.1 The importance of publishing a census evaluation 156 10.2 Methods of census evaluation and their biases and variances 157 10.3 Internal and external consistency analysis 158 10.4 Dual system estimation 159 10.5 The two types of PES (post-enumeration survey) 161 10.6 A PES with a PGE/ ERAD/ ECP approach 162 10.7 Out-of-scope error in a PES 164 10.8 Widening the available options for census evaluation 165 Discussion by William Seltzer 166 PGE/ERAD/ECP issues 166 Census evaluation issues 167 General survey research issues 167 An appendix to chapter 10: PGE/ERAD/ECP evaluation of the Korean and Paraguayan results 168 10.A.I Introduction to the Korean and Paraguayan results 168 10.A.2 Overall results: Korea 170 10.A.3 Overall results: Paraguay 171 10. A.4 Differences in completeness between migrants and non-migrants 173 10.A.5 Differences in completeness between types of area 173 10.A.6 Completeness differences correlated with sex and age 174 10.A.7 Differences in completeness related to household composition and migration status 181 10.A.8 Post-stratification 185 10. A.9 Handling of migrants with "insufficient information for matching" 186 Chapter 11 The 1974 Post-Enumeration Survey of Liberia—A New Approach 189 by Eli S. Marks and John C. Rumford 11.1 11.2 11.3 11.4 11.5 11.6 11.7 viii

The traditional PES approach 189 Dual system estimation 191 Independence 193 Other biases 196 Handling of migrants 197 Use of one-way matching 198 Elimination of field verification 199

11.8 PES results 199 11.9 Some defects of the Liberian PES 200 11.10 Conclusion 202 Chapter 12 The Problem of Independence and Other Issues 205 12.1 12.2

C. Scott on Sources of error in the dual system approach 205 V.H. Muhsam on The bias of the PGE/ERAD/ECP estimates due to overenumeration 208 Discussion by Eli S. Marks 210

Appendix International Association of Survey Statistians Meeting, Vienna, 1973: Organizer's Report 215 Glossary 218 About the Authors 229 References 235 Index 248

ix

List of Tables

1.1 1.2 1.3 1.4 1.5 2.1 4.1 4.2 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 7.1 8.1 8.2 8.3 8.4 8.5 X

An overview of the known world involvement of PGE/ERAD/ECP techniques 14 Summary of world involvement in PGE/ERAD/ECP 25 Survey costs divided by office/field and by primary/secondary units 30 Total and proportionate survey costs 37 Costs with varying types of surveys 42 Estimated completeness rates and crude birth rates by area, periods under different recording operations, switch-back trial; Colombia, 1971-73 62 Estimates of 6,0,0,and fl based on alternative counting rules for enumerating deaths 85 Proportion of deaths that were missed by type of housing unit in the survey experiment, Los Angeles, July-October 1969 86 Estimated completeness rates in two Madagascar dual collections, 1967-70 94 Estimated completeness rates in two dual collection Sheikhdoms of Tunisia, 1968-69 95 Estimated completeness rates in dual collection allowing for delayed registration, two Sheikhdoms of Tunisia, 1968-69 96 Vital rates in Liberia, 1969 100 Migrants found by the procedures of a PGE/ ERAD/ ECP enquiry. Liberia: District of Voinjama, 1969 100 Dual collection estimation of vital events in the Lower Egypt Survey, 196566 106 Estimated vital rates from the two dual system procedures and the percentage completeness, the Lower Egypt Survey, 1965-66 107 A comparison of the dual collection vital rates with those of civil registration 109 Results of matching 1972 births and deaths in Morocco 119 Experimental matching of birth documents by characteristics and tolerance limits in the CeRED region of Morocco, 1972-73 127 Experimental matching of death documents by characteristics and tolerance limits in the CeRED region of Morocco, 1972-73 128 Matching outcomes of combinations of characteristics for birth documents in the CeRED region of Morocco, 1972-73 129 Matching outcomes of combinations of characteristics for death documents in the CeRED region of Morocco, 1972-73 130 Production matching of vital events in the CeRED region of Morocco, 197273 131

8.6 Crude vital rates per 1,000 population in the CeRED region of Morocco, 197273 131 8.7 PGE/ ER AD/ ECP estimates of vital events in the CeRED region of Morocco, 1972-73 according to various homogeneous groupings 132 8.8 The outcome of field verification of vital events reported in the urban and rural parts of the CeRED region of Morocco, 1972-73 133 9.1 Background information of PGE/ERAD/ECP studies conducted in seven African countries 146 9.2 Estimated completeness of reported births and deaths for each collection procedure in six African studies 147 9.3 Percentage distribution of estimated total births, by PGE/ ERAD/ ECP category for six African studies 148 9.4 Percentage distribution of estimated total deaths, by PGE/ ERAD/ ECP category, for six African studies 149 9.5 Stable population and PGE/ERAD/ECP estimates for Egypt 150 9.6 Stable population estimates for Morocco, 1960, 1965, 1971 151 9.7 Analytic and PGE/ ERAD/ECP estimates for Liberia 152 10.1 Estimates of completeness in the 1972 census of Paraguay 169 10.2 Estimates of completeness in the 1970 census of Korea 170 10.3 Completeness of census enumeration by age, sex, and area for Paraguay 1972 PES 175 10.4 Estimated census completeness by relationship to household head for Paraguay 1972 PES 182 10.5 Estimated census completeness by migration status for Paraguay 1972 PES 184 11.1 Persons recorded in both the census and the post-enumeration survey by age and sex: Liberia, 1974 190 11.2 Persons recorded in the post-enumeration survey by age and sex: Liberia, 1974 190 11.3 Estimated completeness of the census by age and sex: Liberia, 1974 191

xi

List of Figures

1.1 1.2 2.1 2.2 2.3 2.4 2.5 4.1 7.1 8.1 8.2 8.3 8.4 8.5 8.6 11.1

xii

Schematic presentation of the categories of events obtained by a dual collection system 6 Hypothetical examples of the outcome of three sets of matching rules: average, strict, relaxed 7 The four types of registration procedure 59 Minimum questionnaire content for record keeping and matching operations 64 Relative differences in average number of children ever born and proportion surviving for self and proxy reporters, ever married women, urban and rural areas, Mindanao Center for Population Studies, July 1972 66 Estimated completeness rates by reported month of birth, recording, and survey procedures, by area, Dual Record Study, Mindanao Center for Population Studies, January-June 1972 68 Interrelations between error and sample size for different types of survey 70 Counting rules tested in a multiplicity survey experiment for enumerating deaths, Los Angeles, July-October 1969 85 Summary results of most useful personnel by area and type of event, Morocco, July 1971-December 1972 116 Characteristics and tolerance limits used in experimental matching of birth records 125 Characteristics and tolerance limits used in experimental matching of death records 126 Events with reports in both sources by matching status in each source 137 Breakdown of reports by matching status 138 Hypothetical example: data on matching rules 143 Hypothetical example: relationship between rule A(l) and A(2) 144 The questionnaire used in the Liberian post-enumeration survey, Form PES2 194

Acknowledgements

The first thanks are due to Dr. Ivan P. Fellegi, Assistant Chief Statistician of Canada who, in his capacity as organizer of the first meeting of the International Association of Survey Statisticians in Vienna, August 1973, invited the editor of this book to organize a session on dual system estimation in demography. The original four contributors of invited papers, the two authors of contributed papers, and the four discussants, were happy to be joined later by eight other contributors and four discussants. We were all united in our interest in producing high quality data and obtaining the greatest possible analytic use from them. We may have disagreed in the pursuit of this objective, but we can only hope that in the process we helped to clarify some of the issues. Mr. Benson Morah, then a graduate student at the University of Alberta, acted as assistant editor for all the parts of the book. Miss A. Candace Fedoruk, then a graduate student at the University of Alberta and currently a Civil Servant in Ottawa, translated chapters 5 and 7 from their original French. Mr. Khalid Siddiqui, a graduate student at the Population Studies Center of the University of Michigan, worked out the tables in chapter 1. Figures 2.3, 2.4 and 2.5 were produced in the Population Research Laboratory at the University of Alberta by Mrs. Ilze Hobin. William Seltzer edited chapter 7. Finally, the appreciation of the whole international community of statisticians and demographers is expressed to the countless field workers in all five continents who laboured, often under trying conditions, to obtain more and better demographic data and in this manner increased our understanding of and knowledge about humanity, its present, and future.

xin

Preface W. Parker Mauldin

Many countries of the world do not have statistical systems that generate reasonably accurate data on population size and rate of population growth. Censuses are often one-time affairs with no continuing professional growth for planning and supervising data collection and subsequent analysis. Even so, data on population size are generally thought to be moderately good, in spite of the fact that we do not know the population of Nigeria within a figure of 10 million persons, nor that of China within 50, or possibly 100, million. But there has been an appreciable improvement in census data during the past 25 years and there is enough interest to ensure that further improvements are likely. But much time is yet to pass before adequate attention is given to systematic and scientific assessment of the accuracy of census data. Vital statistics systems are less complete and far less well maintained than are censuses. Most current estimates of the numbers and rates of births and deaths and of natural increase in less developed countries are based on sample surveys or are derived from censuses; they are not based on actual counts of births and deaths. The prospects for upgrading vital statistics systems to a moderately high level within a decade or so are not promising and, therefore, we shall continue to be dependent on census data and surveys. During the past decade or two there have been a number of promising new theories and techniques backed with some empirical data for the collection of vital statistics by one-time sample surveys. Indeed, the largest effort in man's history to collect current information on levels of and changes in fertility, the World Fertility Survey, is based on a single survey in each of about 40 less developed countries with about 19 of the more developed countries also participating in this important undertaking. Such surveys have been the norm for almost 40 years, and with recent improvements and with the care that is going into this massive effort, undoubtedly a great deal of useful information will be generated. This book explores a different philosophy, a different approach: that of collecting vital statistics and estimating population size by two independent systems, and comparing the results on a name-by-name basis. Such systems are more complicated than single systems, and typically are more costly. They are subject to a number of problems. But they have one striking advantage for the statistician who seeks certainty of knowledge as to the accuracy of results. If the two systems give somewhat different results, the statistician knows that there are deficiencies in at least one of the systems, and a field check will disclose whether the deficiencies are confined to one system or if they exist in both systems. Such a result is not comforting but it reveals xiv

the need for further improving the systems. Sometimes technicians are acutely aware that there are problems with a single system, but less rigorous technicians often do not see or understand the existence and nature of such defects. This book discusses a number of theoretical issues related to dual systems of data collection, practical problems that arise in carrying out such systems, reports in detail on selected surveys (particularly in Africa where vital statistics systems are notably weak), and summarizes actual surveys as well as the state of the art. It is an important and timely book because as the world seeks a new economic order it must have basic information about population as well as about the economy in order to measure changes, and to judge the process of progress. New York, N.Y. January 1976

W. Parker Mauldin Acting President The Population Council

XV

Introduction

The ink was not yet dry on the final draft of the PGE handbook (Population Growth Estimates: A Manual of Vital Statistics Measurement, Marks et al., 1974) when the organizer of the first conference of the International Association of Survey Statisticians, Vienna, August 1973, set up a session on dual system estimation. Five of the 12 chapters in this book were presented at the conference (Wells and Horvitz, Sirken, Pradel, Vaidyanathan, and Marks); two were presented orally in general outline (Krotki and Scott-Muhsam-Marks); and five were invited after the conference (Krishnan, Rachidi, Housni et al., Beaujot, and Marks-Rumford) to complete the subject matter. An important appendix has also been added (Nathan). The purpose of this collection of 12 chapters is to present the next stage in the development of the vastly expanding field of dual system estimation. The previous stage was wound up with the publication of the PGE handbook. At various points, but particularly at the end of chapter 1 and throughout chapters 3 (Krishnan), 4 (Sirken), and 10 (Marks), we attempt to glean an indication of future developments that are likely to take place in this field. A further purpose is to continue the clarification required to preserve the advantages of the method. The broth of the PGE method [as it is known among English-speaking professionals for Population Growth Estimation, ERAD among francophones (Estimation du Rhythme d'Accroissement Demographique), ECP among Spanish speakers (Estimation del Crecimiento de la Poblacion)] runs the risk of being spoiled by too many cooks itching to interfere with the ideal recipe and unable to buckle down to producing a superior but standard product. For example, several well documented errors have been committed in the practice of social surveying when lists of households (of increasing staleness) were used as the sampling frame instead of area samples. The PGE/ERAD/ECP technique counsels the numbering of structures as an extension and strengthening of the detailed mapping required by area sampling. Yet the critical distinction between structures and households is blurred, and alleged "refinement" is proposed in the form of listing of families and individuals (Scott, 1973b: 412). The 12 chapters fall conveniently into three groups. After the background information and articulation of some of the critical issues posed before collectors of demographic data in chapter 1, the next three chapters picture the present and some possible developments in the future state of the art in the field. The middle four chapters (five through eight) report on recent empirical evidence and actual experiences. The four final chapters deal with particularly topical and troublesome issues, on the solution of which much of the future development of the method will xvi

Introduction depend. They also report some practical application of the innovative techniques suggested theoretically in other parts of the book. Not all the topics covered in this book are of equal importance, nor have all the contributors been brainwashed by the PGE/ERAD/ECP gospel to the same extent. Consequently not all the chapters have the same status and not all of them have been included with the same degree of editorial imprimatur. However, we thought that there would be a distinct advantage in assembling declared partisans of the technique, sceptical spectators, partisans of other techniques who are downright hostile to dual estimation, and also those who tend to walk off at a tangent while professing sympathy; the latter kind is likely in the process to destroy the essence of the technique, but may — who knows — stumble into further fruitful developments. The content of the 12 chapters can be conveniently summarized. First the background story is given and the key issues are highlighted in chapter 1 — in a somewhat partisan fashion for the sake of brevity of presentation. In chapter 2, Wells and Horvitz state carefully some of the more recent results achieved and indicate some of the work being done in the area that will, it is hoped, show some promise. In chapter 3 (Krishnan) the classical textbook approach is taken of aiming at the minimum variance and/or maximum likelihood. The focus on variance is at variance with a principle PGE handbook concern to worry at all times about biases as well. The mathematics will be of no immediate utility to demographers and statisticians but they suggest some interesting possibilities in the future, and the emphasis on regression techniques in combining past and present data is innovative. Chapter 4 (Sirken) continues the well-known work of the author in multiplicity estimators and takes up their role in dual systems. The four chapters on the general review of francophone Africa and Liberia (5: Pradel), on Egypt (6: Vaidyanathan), the detailed report on Moroccan fieldwork (7: Rachidi), and the presentation of the matching procedures worked out for Morocco (8: Housni et al.) give some data that were never published in accessible sources, some data that were never published in anglophone media, and much experience and many conclusions based on actual endeavours in the field. The empirical derivation of matching rules of the Moroccan practitioners in the field reported in chapter 8 is sharply contrasted in the appendix (Nathan) with the complex and demanding principles of such a derivation based on theoretical requirements and experimental consideration. Chapter 9 (Beaujot) continues these contributions with rare data and rare experiences but, more importantly, poses a problem quite critical for the future of the PGE/ERAD/ECP: how far can we hope to go with analytic techniques while using grossly imperfect data in the estimation of vital rates. In chapter 10 Eli Marks makes a contribution in the all important field of census evaluation. As stated in section 10.4 "the theory and practice of dual system estimation for census evaluation has exhibited very little development during the past 10 to 15 years" even though increasingly competent exercises were carried out, particularly in Canada and the United States. For purposes of census evaluation all single methods of evaluation have weaknesses and a combination of dual system evaluation with demographic techniques is proposed. In an appendix to chapter 10 and in chapter 11 (Marks and Rumford) practical applications of some of the new advances carried out in Korea, Paraguay, and Liberia are reported upon and supported with original data not otherwise generally available, and not otherwise conveniently accessible. Chapter 12 concludes, somewhat unsatisfactorily, with some fireworks that are, we hope more illuminating than heat generating. Some of the issues are left hanging in the air but they will not go away. They will stay with us for a long time, until they are solved. This unsatisfactory state of the technique, and for that matter of much of the field of data collection, or rather the incomplete state of the art, has consequences. xvii

Introduction Many of our pages read like papers at an unfinished series of seminars at a university, but they cannot be finished seminar-like through further theoretical clarification. They can only be clarified through further field work on the basis of the issues defined in this volume and in the previous writings. What the editor did attempt was to clarify the avowed differences of opinions and differences of experiences among the contributors either in the form of additional endnotes in chapters or through direct textural intervention (sanctioned in each case by the contributor concerned). One non-negotiable textual intervention concerned terminology. This editor is not an academic prima donna and tries to follow previous examples whenever possible, but the situation is difficult. The POPLAB dictionary (Chanlett, 1974) does not follow the terminology of the PGE handbook. Not all POPLAB writers follow the POPLAB dictionary. French language literature tempts the reader with expressive words like "exploitation" for analysis and "confrontation" for matching, but one resists these temptations for the sake of uniformity. Our choices are given in the glossary. They fall halfway between the PGE handbook and the POPLAB dictionary. It might be useful at the outset to admit the necessity for certain peculiarities essential to the PGE/ERAD/ECP success. One of them, unreasonable to an outsider on commonsense grounds, is the insistence on not correcting data, especially not in the field. Hence the insistence on separating supervision from evaluation, on allowing no reconciliation, etc. In section 10.7 we suggest that even in census evaluation "Reconciliation is not necessary with the newer PES techniques" (post-enumeration survey). We, therefore, note with some concern that Parker Mauldin in the preface hopes that field checks "will disclose whether deficiencies are confined to one system or if they exist in both systems." He knows much about PGE/ ERAD/ ECP — that is why he was invited to write the preface — and he must remember that this is a sure way to invite collaboration between the two systems. Some of the elaborations proposed by previous writers in this field have since been found to be either empirically or, on further reflection, not very fruitful pursuits in the practical world. While in theory (Chakraborthy, 1963; Das Gupta, 1964) there is no difference between matching documents from two sources or from three and more sources, there seems to be no actual advantage in using more than two sources (Marks et al., 1974: 401-402). Probably the largest PGE/ERAD/ECP enquiry ever undertaken is that of the Indian Sample Registration Scheme. Falling under the incomplete type of a dual system enquiry discussed in section 1.8 it raises the fundamental question of how to evaluate such incomplete PGE/ ERAD/ ECP enquiries. The objection to the complete exercise apparently, is that not all biases can be removed (there is always some lingering suspicion that some biases remain). The reasoning then continues that it is better in such circumstances not to remove any. Neither the PGE handbook nor the present volume pretend to be definitive works. "Such a work could only be attempted after many of the design alternatives discussed had been systematically tested" (Marks et al., 1974: 5). When clean and definite progress has been made in almost every direction in the field of population studies and in an understanding of their problems, one segment refuses stubbornly to yield: that of vital statistics registration. It is different from the others inasmuch as for results it requires a sustained effort. PGE/ERAD/ECP also requires sustained attention and long nursing, but being more selective, and operating on a more reduced scale, it provides a viable alternative. Ann Arbour, Michigan, January 1975

xvin

KJK

Chapter 1 The Role of PGE/ ERAD/ ECP Surveys Among Endeavours to Secure Improved Demographic Data Karol J. Krotki

1.1 The need for improved demographic data The inadequacy of demographic data for the majority of humanity owing to the paucity and recency of population censuses, and even more to the non-existence or incompleteness of the registration of vital events, has caused much ingenious searching for substitute data. Another stimulus to such a search is given by the need for data required by formulators of population policies, and by designers and evaluators of family planning programmes. Both groups have been brought into existence because of the emergence of the so-called "population problem" in precisely those countries with inadequate demographic data. Demographers, particularly those working under the auspices of the United Nations, have made important contributions to the development of analytic techniques (e.g. United Nations Population Studies, 39 and 42) for the assessment and correction of faulty and unreliable data. Such assessment has often resulted in an estimation of demographic parameters, possibly and probably closer to reality than the reported data. While we are very much interested in and in sympathy with these endeavours, we show in chapter 9 the strong subjective element that enters into the estimation process and which throws into question these analytic techniques when in untried hands. There is no substitute for real data. Hence the ingenuity in the development of new analytic techniques aimed at increasing the usefulness of such unreliable data as are made available traditionally, was paralleled by ingenuity in the collection of new types of data and new methods of collecting data. The sources of demographic data for purposes of population studies can be grouped in four categories: (i) the population census, often combined with a census of housing, sometimes agriculture, occasionally fertility or some other specific, population-related topics; (ii) civil registration of vital events, such as births, deaths, stillbirths, adoptions, marriages, divorces, separations; (iii) various kinds of demographic and socio-economic surveys, either sample censuses, if this contradiction in terms can be permitted, or intensive enquiries to fill in gaps left by insufficient content of census questionnaires; (iv) recent and often unorthodox attempts to obtain demographic data in the absence of traditional data or to meet new needs usually involving special surveys, particular record keeping, and new observational techniques. This chapter is concerned with the last category, but it does not deal with such sources as electoral lists, poll-tax lists, administrative records with a demographic content, or health records.1 The chapter deals with surveys or other related arrangements specifi1

/./

Karol J. Krotki

cally made to secure more and improved demographic data. It ignores situations where demographic data become available as a by-product of other activities. Among the many new survey and non-survey sources of data, several distinct groups have become important in recent years: the service statistics from family planning programmes, KAP surveys (knowledge, attitude, practices in family planning), a group of intensive and expensive population observations, usually out of reach of underdeveloped countries (such as the national and local fertility surveys in the United States, Canada, Great Britain, and other countries, often involving panels of women pursued for years in the quest for data); highly specialized surveys such as those based on photogrammetry, called by some writers sociogrammetry; multiround surveys employing retrospective questions; multiround surveys employing the household change technique; and finally PGE/ ERAD/ ECP surveys which are the subject of this book. 1.2 An overview of the available techniques At the conclusion of the previous section in the listing of types of surveys we did not mention the single round survey. Although the most popular and most frequently used kind of survey, it has become by now somewhat discredited and it is common ground among many professionals working in the field that it should be used only in exceptional circumstances. As a rule the results are of such quality that it is probably better not to have them. One is less misled in their absence. The main reason why single round surveys give unsatisfactory results when evaluated is the unreliability of human recollection. Events of interest to the survey are forgotten or the most relevant respondents are no longer there or the events are placed in the wrong time scale. These disadvantages are compounded by the ease with which such a survey can be launched. Even when there is the weakest statistical organization, the smallest sum of money, when the purpose is not clearly understood, some kind of survey can be put together, some kind of group of interviewers can be trained and let loose onto the population. It is true that the particularly dismal results obtained from single round surveys, which will be quoted later in this section, are made to look particularly bad because of this compounding aspect. Let it, therefore, be repeated that they suffer from an inherent disadvantage, irrespective of the organization; namely the frailty of the human memory, unchecked and unsupported in conditions of a single round survey. The single round survey is also called ad hoc with the slightly pejorative implication of the phrase. "It is generally accepted that this cannot give reliable information on births and deaths" (Scott and Coker, 1971: 253). "Single retrospective surveys cannot be depended upon to provide valid or reliable estimates of births and deaths" (Mauldin, 1966: 652). "On the basis of evidence a number of those with wide experience in the developing world have concluded that single ... [round] household surveys using simple retrospective questions on births are particularly vulnerable to error" (Seltzer, 1973: 23). Similar experiences have been reported from francophone Africa. "L'humilite est certes necessaire car les difficultes sont considerables et inedites; il semble en particulier que les resultats obtenus se pretent difficilement a un traitement d'ensemble; Fimportance et la diversite des erreurs d'observation qui paraissent les effecter rendent d'autre part fort illusoire toute tentative d'adjustement general" (Blanc, 1964: 85). The first Population Growth Estimation seminar held at the Population Council offices in New York on 23 January, 1969 gathered a group of international experts and practitioners together to consider the matter. Its conclusion was that "a single system is unsatisfactory in the present state of the art in underdeveloped countries; a balanced 2

Role of PGEI ERA D/ ECP surveys

1.2

dual system is essential" (Mauldin and Bean, 1969). The language of numerous reports emanating from or through the United Nations is often diplomatic, but unequivocal is the ultimate meaning that single round surveys with retrospective questions are no good (e.g. United Nations, 1971: 157). A carefully sifted collection of evidence for the purposes of the PGE handbook (Marks et al., 1974: 54, table 2.11) has shown that the completeness of reporting deaths in single rounds in a large number of Asian surveys is hardly higher on the average (51 percent) than that of the official civil registration (49.5). It is precisely because of the inadequacy of the civil registration system that the need for alternative sources of data arises. What is the use of the alternatives if they cannot do better? For births the completeness seems to be better (67 percent) than in registration (56 percent). The range of reported completeness in the instances for which data are available is markedly wider for single round surveys than in civil registration. The reported range was 68 and 67 percentage points for the completeness of births and deaths respectively in single round surveys as against 43 and 49 percentage points in civil registration. In other words, not only was the completeness virtually the same as in the unsatisfactory civil registration, but the "product" was of a more uneven standard. "An attempt was made during the 1960 census of Morocco to obtain information on births and deaths in the last twelve months. An examination of a number of census returns suggested to census officials that these data were very incomplete" (Sabagh and Scott, 1967: 760, note 2).2 In endnote 8 to our chapter 9, the survey in North Carolina is recalled where among 3,000 households selected from birth and death registrations, only 92 percent reported to the survey the previously registered births and only 83 percent the previously registered deaths (Horvitz, 1966).3 Still, our evidence suggests that some single round surveys do less poorly than others. In other words, by trying hard some better results can be obtained in spite of the disadvantages inherent in the single rounds. At the end of section 10.5 we discuss the meaning, effectiveness, and operationality of doing a "better" job, selecting "best" enumerators, giving them "intensive training," and "reconciliation" of confusing answers and the like. This belief in the ultimate improvement of human endeavour is, of course, endearing, but less realistic than the approach of using all sources and a readiness to live in error, but measure it. To go back again to the end of the previous section, the choice between methods of collecting more and improved data for demographic purposes is, thus, limited to multiround surveys employing retrospective questions, multiround surveys employing household change technique, and the PGE/ ERAD/ ECP surveys. Multiround surveys with retrospective questions collect data more than once from the same and/ or from rotating households; their main advantage stems from the long term commitment of the organizers and the consequent cumulation of experiences and presumably gradual improvement in data. Multiround surveys recording household changes collect data at least twice from the same households; their main advantage lies in the record of household structures from the earlier round being available to the interviewers during the more recent round. The PGE/ ERAD/ ECP surveys consist of two independent means of collecting data, hence "dual collection system" and a case-by-case comparison of the reports collected; these surveys are unique in having a built-in means of evaluating the completeness rates of each of the two procedures in the dual system and, consequently, the joint omissions in both procedures. The corollary of the advantage of multiround surveys (accumulated experience and increased quality) is the risk of losing with time the financial and administrative support necessary for continuing existence. This disadvantage does not affect the consideration because, if the commitment is really that light, then the results are probably not worth having. The advantage of experience on the other hand is considered essential in countries where the evaluation of quality of data is taken seriously. 3

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KarolJ. Krotki

Statistics Canada was told in the early 1970s to augment in size and content its monthly survey at the cost of — it is said — $8 million (Canadian). It was thought necessary to take many monthly rounds before the survey would be ready and public data released. In the context of our interest, such surveys have also the advantage of overlapping recall periods when taken sufficiently frequently. For example, during the original Pakistan PGE exercise, the periodic survey was taken quarterly with a recall period of 12 months. Thus each vital event had the theoretical chance of being reported four times. The "extra" information was useful in getting a solid grip on the household and helping in the matching operations (about which more later). Some of this additional value might have been due to the frequency of the survey rounds as opposed to the number of times the same event was reported. The Pakistan exercise had the benefit of two tricks of trade, small but important, as will be argued later: for three of each four visits the interviewer had the benefit of the household composition as reported at previous interviews, but not the records of the reported vital events; every fourth interview the chain was broken and a virgin listing of households and their composition had to be started. The National Sample Survey (NSS) of India tried for a long time to obtain retrospectively data on births and deaths. When each survey was taken as a "stand alone" survey, then their results were not different from the discouraging results elsewhere in the world with single round surveys. As elsewhere, the reported rates were so low that arbitrary adjustments had to be made so that published data would not offend too much against commonsense.4 In the 7th, 14th, and 15th rounds of the NSS interesting innovations were attempted (Som, 1973). The interviews were held monthly with a reference period of one year: each vital event thus had a chance of being reported 12 times, and 12 monthly consecutive interviews produced 144 observations. Each month of the year was represented 12 times. The averaging proceeded by the 12 months for which the recall period was one month, for which the recall period was two months, for which the recall period was three months and so on. An estimate of memory decay was in this way obtained, the celebrated-in-literature "Som curve" was created, and the events with "zero" recall period were estimated. The experiment was extended into a two-year recall period so that data became available for "last year" and "the year before last". If one believes that some respondents tend to advance the dates of vital events, that is, bring events from the 13th and 14th month into the 12th month then the Som curve is underestimating memory decay; and vice versa if respondents stretch out the recall period and put events further back. The two examples of Pakistan and India highlight two uses to which multiround surveys can be put usefully: strengthening the grip of the survey organization on the population, and multiplying the amount of data available for averaging purposes. A third legitimate use, matching events reported during different rounds for the purposes of the PGE/ ERAD/ ECP technique, will be discussed later on in this section. The attempt to collect data through the household change technique in multiround surveys raises other questions. The faith in this method rests on the list of members of households collected during the first round and the changes recorded in this list during subsequent rounds. It is clear that the method reduces some omissions. Persons who have died since the previous round, even the smallest babies, should be reported as having died, without fail, provided they were entered onto the list of members of the household during the previous round. The method also reduces some of the problems of dating. For some of the events that have taken place between visits the error of dating can be at most equal to the length of the interval between rounds.5 It is clear that a method "in which the enumerator merely has to check a list of names provided, obviously offers a strong temptation to the enumerator who is less than fully conscientious" (Scott, 1973: 7). Actually the problems with the household change 4

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technique are more fundamental than merely tempting lazy enumerators. The first complaint is that it ties the survey to the listed households and their composition as reported at the time of the first round.6 Partly for this reason, and partly because of the interviewer's tendency to take the list of members of the household seriously, the survey works with a "panel". Such a panel starts as a not very representative sample (most samples suffer some selective omissions) and gradually becomes less and less representative of the current, live population. The problem of the de facto and the de jure definitions and their application to mobile members of the society are severe whatever the procedure adopted, but the household change technique is probably more clumsy in dealing with them than others. Similarly the reason for rotating a sample and avoiding staleness arises in all methods, but the household change technique has the additional disadvantage of "tying" the interviewer to whatever happens to have been listed in the first round. The problem is not the development of "significant respondent resistance" (Scott, 1973:7) with repeated calls on the same household. The technique tends to bias the sample, in place of throwing freely and probabilistically the enumeration net onto the population and its vital events in each round afresh. The long history of unsatisfactory results delivered by the household change technique (India, 1958-59; Cambodia, 1958-59; Brazil, 1961; Morocco, 1961-62; Indonesia, 1961-62; Nigeria, 1965-66; Tunisia, 1968-69) was not sufficiently discouraging and it was further applied in Algeria, 1970; Senegal, 1970-71; Lesotho, 1971-72; Haiti, 1972; Honduras, 1972; and Saudi Arabia, 1972. For countries where reports are available the experience was no different.7 For a probably atypical experience of overenumeration, more significant than underenumeration in births and deaths reporting, see the Moroccan multi-purpose survey of 1961-62 (Sabagh and Scott, 1967: 768). The experience is most sobering in that it dissects the complexities and unreliability of retrospective reporting, whatever the method.8 The high priest of the household change technique tried at the last moment to rescue something of it by suggesting that the changes between rounds could be done actually "in the blind" (Scott, 1973: 7).9 Having then obtained two or more listings of household members these are matched on a case-by-case basis, that is individual by individual, not just totals. However, the suggestion that the PGE/ ERAD/ ECP technique has "something in common with multiround surveys" is dismissed after a page of thinking aloud as "generally... impracticable" (ibid). The technique, should there ever be a field worker and researcher unrealistic enough to try it, involves "reconciliation" in the field. Obviously the differences between the two rounds: the original and the "blind" could not be accepted at the face value. They could merely be differences of recording and not real differences. As will be shown in sections 1.7 and 1.8 of this chapter reconciliation is a dirty word in PGE/ ERAD/ ECP parlance. For this and for other reasons the change of household technique can have nothing in common with a true PGE/ ERAD/ ECP survey. The fact that some PGE/ ERAD/ ECP surveys used the three months round is "analagous to the multiround surveys" (Scott, 1973:6) using the household change approach formally but without much expectation of meaning. We come now to the PGE/ ERAD/ ECP technique proper. Its arithmetical justification is given in the next section of this chapter. Some of its underlying principles are explained in other sections, particularly section 1.4 that summarizes the PGE handbook (Marks et al., 1974). Its history is sketched in section 1.11. Here we limit ourselves to an introduction comparable to the introductions of the other methods. Briefly, the technique consists of two procedures of collecting data and a case-bycase comparison of individual reports. From this comparison or matching of records, three kinds of records result. There are records in respect of events reported by both procedures (two records for each event, one from each procedure); records for events reported by one procedure only (one record for each event, all from one procedure);

5

Karol J. Krotki

1.2

and records for events reported by the other procedure only (one record for each event, all from the other procedure). Provided that the two procedures and sets of events were independent of each other we are then justified, in accordance with section 1.4, in making an estimate of events with regard to which neither procedure produced a record. This picture is summarized in figure 1.1. Figure 1.1 Schematic presentation of the categories of events obtained by a dual collection system Procedure R (- continuous recording) Events observed

Events not observed

All events

N(RS) = M

U(S)

N(S)

Events not observed

U(R)

U(R)U(S)/M = Z

V(S)

All events

N(R)

V(R)

N

Events observed

Independence between the lines and independence between the columns implies the following relationships: For procedure R Pr(R) = N(R)/N = M/N(S) = U(R)/V(S) For procedure S Pr(S) = N(S)/N = M/N(R) = U(S)/V(R) In short, the probability of inclusion is the same whether one talks about all events, or events caught by the other procedure, or events omitted. The problem of independence is sounded repeatedly throughout this chapter and in fact throughout all the other chapters. Particularly in sections 1.6 and 1.7 we show how simple devices can increase independence, and in section 1.8 how easily thoughtlessness can destroy it. Pradel in chapter 5 seems to be less convinced of the possibilities of ensuring independence and right to the very end of chapter 12 we are concerned with it. The matching problem is simpler and is negotiable. It is obvious that if we work with very strict matching rules we will end up with few cases in the first category, many in the other two categories, and consequently with a large estimate of the fourth category. On the other hand, if we set up lax matching rules, we will finish with a large first category, two small lots in the second and third category, and consequently a small estimate for the fourth category. The outcome of a hypothetical case with three sets of matching rules has been summarized in figure 1.2. Many features of carrying out a survey are applicable to PGE/ ERAD/ ECP surveys in the realm of sampling theory, sampling practice, questionnaire design, field work, office procedure and the like. The two needs of high independence and matching rules with a zero net error are peculiar to this technique. For that price, we obtain a method that is selfchecking. None of the others are. While further features of the PGE/ ERAD/ ECP technique are elaborated in other sections of this chapter and, indeed, in other chapters, it will be useful at this stage to return to the question of matching between rounds. The PGE handbook presents in chapter 4, and in some detail, three alternative systems. One of these is a comparison between two field procedures very similar to each other, namely single round surveys. 6

1.2

Role of PGEI ERA D/ ECP surveys

Figure 1.2 Hypothetical examples of the outcome of three sets of matching rules: average, strict, relaxed. (One procedure observed 840 events, the other 850) Average Recording

Observed Not observed

Observed

Not observed

790

60

50

4

estimate of N = 904 (± 4 at 95%) Strict Recording

Observed Not observed

Observed

Not observed

750

100

90

12

estimate of N = 952 (± 8 at 95%) Relaxed Recording

Observed Not observed

Observed

Not observed

820

30

20

1

estimate of N = 871 (± 2 at 95%) Single round surveys follow each other at, say, every six months with a recall period of, say, twelve months. In this manner, each vital event should be reported twice, once in each of two neighbouring surveys. Other combinations of frequencies and recall periods are possible as long as sufficient overlaps occur. The question then arises, why are single round surveys acceptable in this case? Why is not the sauce of the goose of PGE/ ER AD/ ECP good enough for the gander of the "stand alone" single round survey or at least for the household change technique? Primarily, the third example of the PGE handbook leans over backwards in stressing the need for independence and suggesting innumerable tricks of the trade to achieve it (Marks et a/., 1974, e.g. 250253,425-428). Even so, between-round comparisons in the Pakistan PGE would not have been worthwhile because of the lack of independence between the rounds of the survey.10 In fact, we do not have enough experience in the world to talk with confidence about such an approach (survey with survey). The frequent and popular examples of 7

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Karol J. Krotki

PGE/ ERAD/ ECP systems combine typically survey with civil registration (first example in the PGE handbook: 227-228) or survey with special registration (second example in the PGE handbook: 238-250). The Director-General of the next Central Statistical Office that will undertake a PGE/ ERAD/ ECP survey, can perform a real service to the international fraternity of statisticians, and probably to himself and his country, by trying a really well-founded third example suggested in the PGE handbook. We are aware of many other possible approaches in the field of measuring vital events. Those particularly hurtful are taken up in section 1.8. There is merit in others, but for the given outlay per hour of time and per unit of money they repay less than a correct PGE/ ERAD/ ECP survey. Among other approaches handicapped from the start we would list the following: pregnancy histories, expensively elaborate in their interview dynamics and resulting in longitudinal data unwieldy for traditional methods of analysis which are mostly cross sectional (Bogue and Bogue, 1967; Bogueand Bogue, 1970); maternity histories, less troublesome and somewhat more realistic than pregnancy histories, but also resulting in data surplus to available means of analysis; sample registrations following civil registration principles (Hauser, 1954; Cavanaugh, 1963) because of the basic incompatibility between the type of personnel, attitudes, finance, and a host of other considerations relevant to the establishment of a legal system and a statistical system (Linder, 1971); and panels of respondents (Vaidyanathan, 1973) because of the staleness of the sample increasing with time. 1.3 The theory behind the PGE I ERAD I ECP technique The comparative novelty of the PGE/ ERAD/ ECP technique does not lie in a new principle. In fact, the technique is based on a proposition in probability that has been with us for a long time. If two events take place independently of each other then the probability that they will take place simultaneously is equal to the probability of one of the events happening multiplied by the probability of the other event happening. In terms of the notation used in figure 1.1, if R takes place independently of S then the probability of R and S both taking place simultaneously is equal to R times S. The algebraic formulations are well known (e.g. Krotki, 1969; Krotki, 1971): the probability of (R and S) = probability of R times probability of S (1.1) where probability of R = R/(R + non R) (1.2) probability of S = S/(S + non S) (1.3) Let it be recalled once more that equation (1.1) is true on the condition that the occurrence and frequency of R has no effect on the occurrence and frequency of S and vice versa. Equation (1.1) can then be rewritten as follows: Pr(R) = [Pr(R and S)]/[Pr(S)] (1.4) The three terms of equation (1.4) can be redefined as follows: Pr
Role of PGE/ ERA D/ ECP surveys

1.3

M = number of events observed by both procedures. The notation from equation (1.4) can now be replaced by the new notation from equations (1.6) and (1.7) and we obtain: Pr(R) = ( M / N ) / (Ns/N) = M/N S (1.8) Supposing we could obtain through field work the exact value of M and N (or Ns), a subject with which most of this book is concerned, equation (1.8) would give us the completeness rate of procedure R. Combining algebraically equations (1.5) and (1.8) we obtain:

NR/N = M/N S

Carrying out the same exercise for the other procedure we obtain:

N S /N = M/NR

(1.9) (i.io)

The left hand sides of equations (1.9) and (1.10) give the completeness rate of procedures R and S respectively (indicated in the numerator). The completeness rate (see: Glossary) of a procedure is the proportion of all events (births or deaths) that were reported by the given procedure. The right hand side of the two equations gives the match rate of procedures S and R respectively (indicated in the denominator). The match rate (see: Glossary) is the proportion of events (births or deaths) reported by one procedure that were also reported by the other procedure. Equations (1.9) and (1.10) show, then, that the match rate of one procedure in the PGE"/ ERAD/ ECP system is equal to the completeness rate of the other procedure. More generally, in a dual collection system, the match rate of either procedure is equal to the completeness rate of the other procedure.11 Clearly a loss of independence will increase the match rate and consequently increase and overestimate the completeness rate. With full loss of independence when, for example, the records of one procedure are copied for the purposes of the other procedure, all records will be matched and the estimated completeness will be 100 percent. From the two equations (1.9) and (1.10), that give the completeness rate for either procedure, we can obtain, through a minor transformation, an estimate of the total number of all events: N' = (N R N S )/M (1.11) where NR, Ns, and M have the same values as defined for the purposes of equations (1.5), (1.6), and (1.7) and where N' = estimate of all events (or N) Equation (1.11) is an old friend and has been with us not only for the last two pages of discussion but more generally for centuries in the field of probability. It is popular and has been used for many different purposes. In order to respond to the special needs of PGE/ERAD/ECP estimation we have introduced into figure 1.1 some new notation: N R = M + UR

(1.12)

Ns = M + Us (1.13) where NR, Ns, and M continue to carry their earlier meanings, while UR = events observed by procedure R only; Us = events observed by procedure S only. One can now rewrite equation (1.11) in terms directly suitable for the PGE/ ERAD/ ECP technique: N'= [(M + UR) (M + Us)] / M (1.14) By simple transformation we obtain: N' = (M 2 + U R M + U S M + U R U S ) / M (1.15) N ' = M + U R + Us + (U R U s )/M (1.16) Equation (1.16) carries a clear message. It is couched in terms of the celebrated four 9

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KarolJ. Krotki

categories of the PGE/ ERAD/ ECP estimation process. The four categories are: (i) events caught by both procedures, (ii) events caught by one procedure but not by the other, (iii) events caught by the other procedure but not by the first one, and finally (iv) events missed by both procedures. The last category is the proverbial "fourth category" of the PGE/ ERAD/ ECP literature. The four categories have been shown schematically in figure 1.1. The estimate of N, which is N' as defined in equation (1.14), experiences sampling variations. The variance of the estimate, as a first approximation, can be estimated as follows: aN2 = N{[l -Pr(R)][l -Pr(S)]}/[Pr(R)Pr(S)] = (NZ)/M (1.17) where Pr(R), Pr(S), N, M have been defined earlier and where Z is the "fourth category" defined in equation (1.16). It is clear that the variance will be smaller and the estimate of N will be more precise the nearer to unity are the values of Pr(R) and Pr(S). The smaller the fourth category the smaller the variance, until in the limiting case when the fourth category dwindles to zero the variance disappears altogether. For this to happen, the second and third category will also tend to disappear. In other words, the reliability of the sample is inversely proportionate to the completeness rate and the match rate of both procedures. 1.4 The PGE handbook and some essential PGE I ERAD I ECP features The PGE handbook has been written to provide a solution to the inadequacy of registration data and retrospective surveys data. While the PGE/ ERAD/ ECP technique itself might use retrospective survey data, it does not rely on them exclusively. It uses them merely as one component in a system of other procedures that crosscheck and evaluate each other. It is recognized that other techniques and approaches are available. Some are analytic and require no collection of data(e.g. United Nations Population Studies 42), but they cannot function when data are subject to more than maximally acceptable margins of error. Some are directed towards the correction of errors on the basis of a taxonomy of errors arising traditionally (e.g. ibid; or Som, 1973), but they are subject to the uncertainty as to which feature is correcting which and the possibility that in some societies the anthropological reasons causing a typical set of error patterns work the other way round. Some rely on intensive concentration of effort either at the interview (e.g. Bogue and Bogue, 1967) or in the setting up of the field work (e.g. Arretx and Somoza, 1965). Those with disappointing experiences in field work might find this faith in the efficacy of human effort quite touching. Some of the suggestions rest more on assertion than actual experience. Until tried under difficult conditions they are no more than postulates. In any case, every one of these approaches is, in comparison with the PGE/ ERAD/ ECP technique, short of the built-in measure of reliability that works automatically when set up properly. It is because of this unique feature that the 500-page handbook has been written. However, this unique feature is not a robust panacea. It can be fully useful only if put into wider context with other important and underlying principles. These were seven in number (Marks et al., 1974:7): i. No one design is optimal, either theoretically or practically, for all situations; ii. Certain underlying principles of good design exist and can be specified; iii. A theoretically sound design is worthless if it is either impractical to implement or likely to be implemented improperly; iv. No matter how carefully a study is designed, its execution will be flawed—in other words, no set of data will be error free; 10

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v. Producers of statistical data have an obligation to investigate and report on the amount of error that may be present in the data they collect; vi. Any given design, good or bad, can be improved on the basis of administrative experience and the statistical evaluation of results; vii. Any given study is a system of interrelated parts, and an improvement of one feature of the design without considering its effect on the balance of the design is wasteful and undesirable. The last principle, in particular, led to another feature in the handbook: the careful balancing of errors rather than their elimination. To realize that one lives in an error-full world is not a characteristic requirement of the PGE/ ER AD/ ECP approach alone, but with PGE we have an increased chance and actual means of doing something about it. With regard to sample design, the continuing concern to balance errors leads to the realization that ceterisparibus, increasing the number of primary sampling units (psu), will have two counterbalancing effects: it will decrease the sampling errors of the estimates; it will also, ordinarily, increase the nonsampling errors of these estimates. It is the manager's responsibility to decide whether at the end he will be better off or worse with a larger number of psu's. In other words, a sample designer thinking in terms of the sampling errors will tend to have many, small clusters. A sample designer impressed with nonsampling errors will tend to have fewer and larger clusters. We give a relevant example including some cost considerations in section 1.10. An empirical investigation of the impact of cluster size in Liberia showed the interrelatedness of the statistical considerations with the question of independence so critical to the PGE/ ERAD/ ECP approach. The completeness rate of reported births, deaths, and infant deaths decreased with cluster size in the sample (Rumford, 1971) but the estimated values increased with cluster size. There is no reason to think that the smaller areas had smaller fertility, mortality, and infant mortality. Either matching was more difficult in larger areas and the same matching rules produced an overestimate of the events or there were losses of independence in small areas that resulted in an underestimate of events. A comparison with analytic results suggests the latter. Pradel in chapter 5 shows that the correlation leading to loss of independence is of two kinds: correlation due to the nature of the population and correlation due to communication between the two procedures. An example of the first one would be field workers of two religious groups tending to work in the households of their coreligionists. An example of the second would be field workers of the two procedures comparing notes in the evening or using the same faulty map. The religious separation would result in an overestimate of events, the communication between the field workers in an underestimate of events (though the faulty map could work either way, depending on whether the estimating personnel at headquarters worked under the same misapprehension). One somewhat unusual feature of the PGE/ ERAD/ ECP type of matching is that it need not get each match "right" as is necessary, for example, in the case of matching purposes of record linkage in administrative tasks. There is no harm if document AI is matched with document 82 and document A2 is matched with Bi, where letters of the alphabet refer to events and subscripts to PGE/ ERAD/ ECP procedures, but one would not like to have too many such gross errors even if resulting in zero net error. High gross errors, even if balancing, probably increase variances and give an uncomfortable feeling about the reliability of the whole operation. It could be that the discussant's unhappiness with this approach to matching in chapter 2 is traceable to the responsibilities he carries in his professional life, which are different from those of PGE/ ERAD/ ECP workers in less developed countries whose task is to fill in some of the demographic lacunae.12 11

1.4

KarolJ. Krotki

Much of this section may have appeared to the uninitiated in PGE/ ERAD/ ECP mysteries, as confidential exchanges between members of a close fraternity. For this reason, in the next section, a brief outline of an "ideal" PGE/ ERAD/ ECP exercise is provided. It is a highly abridged and systematized picture. It is not intended for reading by experts familiar with the issues.

1.5 An "ideal" PGE I ERAD I ECP exercise It will be based on a national sample. The dearth of data, and even more crucial, the shortage of personnel capable of carrying out reliable exercises, is such, that it is wasteful to engineer experimental investigations and local enquiries. The additional cost of carrying out a nationally representative sample is usually marginal. Often, the most expensive parts of the population need not be included in the sampling frame, because their exclusion is unlikely to affect the national estimate. For this reason, the Chittagong Hills in East Pakistan(now Bangladesh) and Baluchistan in West Pakistan were excluded from the Pakistan PGE (Pakistan, 1968). Similarly, the Saharan fringe in Morocco could be excluded (Fellegi, 1973) without loss to the estimation procedure and with considerable savings in terms of personnel and money. A national sample will secure continuing support from such clients of national data as the State Planning Commission, the Central Statistical Office, the Ministry of Finance, and the Department of Health and Welfare. If there is genuine desire for experimentation with new approaches, new techniques, or new questions, these can usually be drafted onto the main exercise in the form of rotating questions and the like. The sample will be drawn by a specialist in the field (e.g. Fellegi, 1974). Meticulous attention will be paid to the mapping, with various scales required for unambiguous field operations (e.g. Cooke, 1970). All structures in the sample areas, whether inhabited or not, will be numbered through the PGE headquarters regardless of the fact that in some parts some local "addresses" might exist (Markset al., 1974:173-177). No money or effort will be saved on these three counts. In all other respects, and with regard to lesser considerations, the PGE handbook will be followed closely unless there are clear indications to the contrary. No departures from its recommendations and experiences will be taken in ignorance. Typically the two procedures might involve a specially-set-up registration by residents or visiting recorders who continuously (once a month or every fortnight) enquire about vital events. Their rounds are highly structured so that the frequency of their visits does not depend on their zeal. The other pf ocedure might be a household survey every six months with an overlapping recall period of 12 months. The two procedures are organizationally independent of each other, except through the Director-General at the headquarters. Their documents are different, the emphasis of their enquiries is different (vital events in the case of recording, and household structure in the case of the survey), even the order of the questions on similar topics is different. The recorder's documents are withdrawn just before the survey visit, so that even if collusion was intended it is not possible. However, the main point of the organization should be that collusion is not worth anybody's while. Not only are the two procedures almost entirely different, but the results from one are not used to correct the others, even less used to "improve" the steps of the other procedure. There is as elaborate a system of supervision within each procedure as sound principles of management might require. There is complete separation between supervision under the procedure director (correcting the mistakes found and redoing the whole job if sequential quality control so demands) and evaluation 12

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1.5

(when errors are measured, but not corrected), the latter exclusively under the impartial Director-General. The case-by-case comparison is done through objective matching rules and, incidentally, always by hand (the heaps of documents for matching are never high enough to justify mechanical matching). A complete PGE/ ERAD/ ECP estimate is arrived at and published with all the attendant data swiftly. The managers will think in terms of total cost and total errors. They will seldom agree to a sample very different from 100,000 persons; a smaller sample would not give enough vital events and a larger one is unwieldy administratively and is unnecessary from the point of view of estimating annual vital rates of any typical population. They will seldom have clusters smaller than 1,000 persons, however much the highly skilled and highly paid statistical expert talks about intraclass correlations, because consideration of Mean Square Error would warn them against it. They would seldom, if ever, have sample clusters greater than 5,000, however attractive that might be administratively, because with larger clusters the intraclass correlation might truly become important. They would also be anti-intellectual in the sense that they would frown on overelaborate suggestions and requests for experimenting, when perfectly commonsensical and well-tried approaches are available. They would probably come out against subsampling of one procedure by the other.13 They would be impatient with elaborate matching procedures suggested by egg-headed back room boys and they could well afford much impatience if all the structures in their clusters were meticulously numbered.

1.6 An overview of the world uses of the PGE I ERAD I ECP technique In chapter 2 of the PGE handbook a summary of the uses of the PGE type of estimation has been provided up to and including the time when it was necessary to lock up the draft. Since then, further information has become available from the POPLAB survey in Morocco reported in our chapters 7 and 8; new data from the sister surveys in Colombia and the Philippines are presented in chapter 2; an African overview with some new African data and references is given in chapter 5; an Egyptian exercise is reported in chapter 6; some Malawi and Madagascar data are given in chapter 9. In table 1.1 we present a world summary of such involvement in the PGE/ ERAD/ ECP approach, country by country, as it was possible to identify on the basis of data available. Needless to say, the data are not strictly comparable as the large number of footnotes to the table testifies. Any PGE/ ERAD/ ECP involvement, however marginal, secured a country a place in table 1.1. When countries are excluded that never had a national PGE/ ERAD/ ECP exercise, then the proportion of regional populations given in table 1.1 dwindle in the manner summarized in table 1.2. Another reason for exclusion from the imposing proportions in table 1.1 would be national endeavours undertaken in the PGE/ ERAD/ ECP spirit, but then not followed through for one reason or another. For example, in the 1969-70 Algerian national sample for the purposes of a PGE/ ERAD/ ECP exercise 27 clusters were selected, but only in nine was the field work necessary for ERAD estimation started (Algeria, 1971: 624-27, 76-89). No report on the exercise is available. On the other hand, and to use the same country as an example, matching was carried out between the three rounds of the national enumeration through a re-copying procedure (ibid., 91) so that administrative control could increase the grip of the survey organization on its population, and possibly to establish longitudinal household data without, however, following the ERAD requirements. 13

Table 1.1 An overview of the known world involvement in PGE/ERAD/ECP techniques Study name and area within country (3)

Main purpose of the study (4)

Description of first procedure

Description of second procedure

Approx. population covered

References to reports published

(5)

(6)

(7)

(8)

Continent and country

Period covered

(1)

(2)

AFRICA Algeria

1969-70

Etude Statistique Nationale de la Population

a

Egypt

1965-66

Study undertaken by Cairo Demographic Centre and Egyptian Central Agency for Public Mobilization and Statistics-rural lower Egypt

b

Three semi-annual surveys

Continuous recording

100,000

Kenya

1973-76 (?)

Study by Demographic Studies Unit — seven contiguous districts

c

Semi-annual and annual surveys

Continuous recording

93,000

Bahri, 1969

Chapter 6 of this book

Estimated 1972 population in thousands (9) 364,000 15,270

34,839

Myers and Lingner 12,067 1973

Liberian Fertility Survey, round one — * whole country

a

Semi-annual survey Monthly survey by by staff supervisor local part-time recorders

Madagascar 1967-78 1969-70

Study by Service Statistique de Madagascar (INSRE)— Ambinanitelo (commune), Ankazoabo (prefecture)

b

Multiround survey

Malawi

1971-72

Malawi Population Change Survey1*

a

Morocco

1972-73

Study by Centre de Recherches et d' Etudes Demographiques — Northern Morocco coast to desert

a

Rural

c

Liberia

Tanzania

1969-70

Urban 20,000 Rural 50,000

Rumford, 1970 and 1972; Liberia, 1971a, 1971b, and 1971c

1,571

38,000

Chapter 5 of this book

6,750

Semi-annual survey Recording

30,000

Blacker, 1971 Kazeze, 1974

4,666

Serni-annual survey

84,000

Myers and Lingner, 1973; Chapter 7 of this book

15,286

Marks et al., 1974: 48

13,996

Civil registration

Continuous recording

X

Table J.I Continent and country

Period covered

(1)

(2)

Tunisia

1968-69

AMERICA, NORTH Barbados 1960

Study name and area within country (3)

Main purpose of the study (4)

Description of first procedure

Description of second procedure

Approx. population covered

References to reports published

(5)

(6)

(7)

(8)

Civil registration

5,000

Tunisia, 1970; Vallin, 1971

Estimated 1972 population in thousands (9) 5,377

Enquete Nationale Demographique — Oued el Khatef and Goraa (Cheikhats)2

a

Household survey of three rounds

Study in association with 1960 Eastern Caribbean population census — *

b

1960 census special Civil registration schedules for infants under 3 months of age

Byrne, 1966

233,000 240

21,848

Canada

1931

Canadian birth registration study3. All provinces excluding two territories

b

Census enumeration Civil registration enumeration of 1931 of infants under 1 year of age

Tracey, 1941

Dominica

1960

Study in assoc. with 1960 Eastern

b

1960 census special Civil registration schedules for infants

Byrne, 1966

73

Caribbean population census—*

under 3 months of age

Study in assoc. with 1960 Eastern Caribbean population census — *

b

1960 census special Civil registration schedules for infants under 3 years of age

Byrne, 1966

115

Trinidad 1960 and Tobago

Study in assoc. with 1960 Eastern Caribbean population census — Tobago

b

1960 census special Civil registration schedules for infants under 3 years of age

Byrne, 1966

1,043

United States

1936

Study conducted by Bureau of the Census —26 counties of Georgia4

b

One time retrospec- Civil registration tive household survey

Hendrich et al, 1939

208,841

1936

Study conducted by Bureau of the Census —26 counties of Georgia

b

Mail-out /mail-back postal survey

Civil registration

Hendrich et al, 1939

1937

Study conducted by Bureau of the Census- Maryland

b

One time retrospec- Civil registration tive household survey

Hendrich et a/., 1939

St. Lucia

1960

Table LI Continent and country

Period covered

(1)

(2)

Study name and area within country (3)

December 1939March 1940

United States birth registration Study — * 48 states and District of Columbia

Jan.March 1950

Description of first procedure

Description of second procedure

Approx. population covered

References to reports published

(5)

(6)

(7)

(8)

b

Census reports of infants less than 4 months old

Civil registration

Grove 1943

Infant Enumeration Study—* 48 states and District of Columbia

c

Census reports of infants less than 3 months old

Civil registration

U.S. Bureau of the Census, 1953

Jan.March 1950

United States birth registration test study* —48 states and District of Columbia

b

Census reports of infants less than 3 months old

Civil registration

Shapiro, 1954

1965

Study by the Research Triangle Institute—seven counties of North Carolina

c

Household survey with two recall periods5

Civil registration

Horvitz, 1966

Main purpose of the study (4)

Estimated 1972 population in thousands (9)

1965

AMERICA, SOUTH 1967Chile 1968 Colombia

1971

ASIA Bangladesh9 Jan. 1962 Dec. 1965

Study conducted in areas with poor registration in 1950-* sample universe consisted of 50 states and District of Columbia

b

Household surveys (CPS and HIS)6

Civil registration

Koons, 1971

Valdivia pilot study Valdivia commune7

b

Multiround household survey

Civil registration

Tacla, 1969

Pilot study for the Colombian Pop lab — one of Colombia's 16 departments

e

Retrospec-survey

Monthly household 60,000* canvass in some areas and continuous recording in other areas

Colombia, '71; Chapter 2 of this book, CIMED, 1973

Population Growth Estimation (PGE)-*

a

Continuous Household survey every three months recording with one year overlapping recall periods

42,000

Pakistan, 1968 Farooqui and Farooq, 1971

300,000 10,045

22,491

2,154,000 60,675

Table 1.1 Description of first procedure

Description of second procedure

Approx. population covered

References to reports published

(5)

(6)

(7)

(8)

Continent and country

Period covered

(1)

(2)

India

1945

Singuar Health Centre, Bengal

e

One time household Civil registration survey with approximately 2 year recall

64,000

Chandrasekaran and Deming, 1949

1946

Singuar Health Centre, Bengal

e

One time household Civil registration survey with approximately 1 year recall

64,000

Chandrasekaran and Deming, 1949

1950-

Mysore Population study, three rural zones

d

One time household Civil registration survey with recall period varying from about 1 to 2 years

23,300

United Nations, 1961

1950-

Mysore Population study, Bangalore city

d

One time household One time fertility survey with recall attitude survey with period varying from female interviewer about 1 to 2 years

1,011

United Nations, 1961

1964

Gujarat Sample

e

Household survey

36,000

Merita and

Study name and area within country (3)

Main purpose of the study (4)

Special registration

Estimated 1972 population in thousands (9) 563,490

registration scheme (pilot) — rural

conducted by supervisor every 6 months

by local resident part-time registrar

Shah, 1966 and 1968

19641966

Vaso (pilot) — urban Gujarat

e

One time household Civil registration survey with recall period of up to 28 months

19631966

Mehrauli pilot study. Five villages in Mehrauli block, South Delhi

e

Household survey conducted every 6 months by female interviewer

Special registration 5,582 by part-time non-resident registrar

Murty and Jain, 1967

1965

Kerala sample registration scheme

e

Household survey every 6 months by supervisor

Special registration by local resident as part-time registrar

260,000

Kerala, 1967 and 1968

Korea

19631965

Taeduck Gun matching project

b

One time household Civil registration survey with recall period of up to 2 years

100,000

Choe, 1967 and 1968

32,527

Pakistan10

19621965

Population Growth Estimation (PGE)*

a

Continuous recording 42,000 Household survey conducted every 3 by full-time recorder months with 1 year living in the area overlapping recall periods

Pakistan, 1968, Farooqui and Farooq, 1971

56,065

9,480

Mehta, 1967; Mehta and Shah 1968

Table 1.1 Continent and country

Period covered

(1)

(2)

Philippines

1972

Mindanao Center for Population Studies — two research areas

Thailand

19641965

Turkey

19651966

Description of first procedure

Description of second procedure

Approx. population covered

References to reports published

(5)

(6)

(7)

(8)

e

Periodic household survey

Continuous recording

Survey of Population Change (SPC)*

a

Household survey conducted every 3 months

Civil registration

Turkish Demographic Survey (TDS)-*

a

Household survey conducted every 6 months by staff supervisor

Continuous recording by part-time local recorder

Study name and area within country (3)

Region 1, urban Region 1, rural Region 2, urban Region 2, rural Ankara City Istanbul City Izmir City

Main purpose of the study (4)

Estimated 1972 population in thousands (9)

46,000

Madigan, 1973

39,040

172,000

Thailand, 1967

36,286

Rumford et al., 1968 Turkish Demographic Survey, 1967 and 1970

37,010

32,500 38,100 29,700 37,600 24,900 15,600 13,400

U.S.S.R. U.S.S.R.

1939

Vostrikova 1963

1959

Study by Central Statistical Board

b

Ten percent Civil registration systematic sample of village Soviets

1970"

ditto

b

ditto

ditto

Dmitrieva 1969

Column (3) *. Sample intended to be nationally representative. Codes used in column (4) a. To estimate basic demographic parameters. b. To assess completeness of civil registration. c. To assess completeness of reporting of enumeration procedure. d. To investigate interrelationship between population and economic and social change. e. Demonstration or pilot project to establish system for estimation of missing demographic data. Footnotes 1. 2. 3.

for various columns Sample design used was inappropriate to local conditions (Blacker, 1971). Non-randomly selected Cheikhats. Somewhat different sampling and matching procedures were used in various provinces, and precise details of certain aspects of the study are not available. 4. Sample under the household survey was not probability sample due to budgetary constraints. 5. This study was designed to test accuracy of retrospective questions on births and deaths in survey and also to compare two recall periods. 6. CPS = Current Population Survey; HIS = Health Information Survey.

247,459 247,459

7. 8. 9. 10. 11.

Civil registration records were available only for three-quarters of 191 sampled villages, so that estimates were biased. A guestimate by the author. No figure given in CIMED, 1973. Formerly West Pakistan. Formerly East Pakistan. It was announced that procedure of 1959 study would also be employed in connection with 1970 census. (Dmitrieva, 1969.)

1.6

Role of PGEI ERA D/ ECP surveys Table 1.2 Summary of world involvement in PGE/ERAD/ECP Population of countries who ever had a PGE study on national basis

%

(4)

(5)

(6)

1,447,115

38

405,542

11

109,822 232,160 32,536 825,097

30 100 11 38 0 0 100

6,237 209,269

2 90 0 9 0 0 0

Region

Population of region

Population of % countries who ever had a PGE study

(1)

(2)

(3)

World

3,787,700

Africa Northern America Latin America Asia Europe Oceania U.S.S.R.

364,000 233,000 300,000 2,154,000 469,000 20,200 247,500

247,500

190,036

N.B. Population totals are in thousands and refer to 1972. Source: 1. Col. (2): United Nations, 1973. 7972 Demographic Yearbook, New York, United Nations 2. Cols (3) and (5) are summaries from table 1.1 Finally, to increase the meaning of table 1.1 one would have to provide similar tabulations for single round surveys (14), multiround surveys with retrospective questions (1), multiround questions with the household change technique (3), and possibly other surveys, such as panels (2). This would be a formidable task and would result in a bulky product. However, a rough indication may be provided by the summary of literature. In a random search, during the time necessary to find at least one reference for each type of survey mentioned above (in parentheses are given the numbers actually found), no less than 14 references were found for the single round survey. Presumably all types of surveys are beaten for the first place and by many lengths by the least reliable, least elegant, often useless type of survey, namely the single round survey. 1.7 Modes of securing the advantages of the technique In this section are listed such tricks of the trade as are particularly applicable to the PGE/ ERAD/ ECP technique. Some are merely elaborations of the "ideal" presented in section 1.5. They centre mainly on the two outstanding features of the technique: the need for independence and the requirements of matching. However, several other pointers relevant not exclusively to the PGE/ ERAD/ ECP technique are also added. Some of these points, and their counterpoints in the next section would necessarily find their way to a minimum qualifying list for a PGE/ ERAD/ ECP franchise.14 1.7.a With regard to the need for independence the following comments can be offered: i. The first and fundamental requirement is that the two procedures in the dual system estimation be as independent of each other as possible; the principle has already been indicated in sections 1.3 and 1.5 and a long list of suggestions, practicable and in 25

1.7.a

KarolJ. Krotki

most cases well-tried, are given in the PGE handbook; the whole book is shot through with these concerns so no particular page reference can be given, but one section is particularly devoted to this topic (7.F; pp. 425-428). ii. In the next section we give examples of how independence can be destroyed, some hypothetical, most from actual practice. There is one positive suggestion that can be made: the two procedures in any one PGE/ ERAD/ ECP system should have no common organization, no common supervisors (except the Director-General at the top), no mutual checking arrangements or reward systems. 1.7.b A separate manual could be written for matching, but some principles deserve to be pointed out even in a brief chapter. i. There should be articulate matching rules. Experience has shown that commonsense checking ("Surely this is the same birth/ death"), leads to errors that are systematic, non-random, and biasing the results in an unknown direction. ii. Experience has shown repeatedly that dwelling numbers (better still structure numbers irrespective of whether inhabited or uninhabited, whether inhabitable or uninhabitable) are the matching item with the strongest discriminating power. As reported in section 7.5 it is poor economy to try to use existing administrative numbers in such parts of the sample as might already have numbers. iii. The emphasis on matching and the amount of resources devoted to matching should be related to the degree of the completeness of the reporting of vital events. With full completeness no matching would be necessary: all events would fall into the first category and none into the second and the third categories; consequently, the estimate of the fourth category would be zero. The importance of the net matching error increases with the degree of omissions (Fellegi, 1974: 21). iv. Field follow-up of matching decisions or matching doubts are necessary, not so much to avoid or cut down gross errors, but to check empirically that matching rules result in zero or near-zero net error and that there has been no change since the rules were established. 1.7.c Then there are arrangements that differentiate good field work and superior office organization from poor field work and sloppy office organization, not necessarily peculiar to the PGE/ ERAD/ ECP approach, but important probably in most types of surveys. They may read simplistically, but experience has proven their critical importance. i. There should be a structured routine round for field workers, so that they know at any given time in which part of their area they should be working; their supervisors would then know where to find them. ii. A very considerable amount of managerial time and of the monetary budget will be spent on mapping. The senior levels of maps at least, will be based on topographical maps or aerial photographs, though junior maps may be based on the senior maps produced for the purposes of PGE/ ERAD/ ECP. iii. There will be a routine for the orderly recording of changes on maps and other documents in the organization that have been produced in quantity. iv. One of the procedures will usually require frequent calls on the respondent. Within the taxonomy suggested in figure 2.1 this will be the "active" seeking of events. To avoid respondent fatigue and in circumstances where social ties are strong and social cohesion considerable (read: "predilection to gossip mongering high") every second or third household only need be called upon at every round, but which household during which round acted as the informant for its small neighbourhood should be explicit. It is likely that in most urban areas calls on all households will be desirable.

26

Role of PGE I ERA D/ ECP surveys

/. 8

1.8 Inadvertant modes of destroying the advantages of the technique This section is devoted to the listing of arrangements that with the best of intentions are bound to destroy the fundamental or ancillary advantages of a PGE/ ERAD/ ECP system. Some are based on illogicality or ignorance. Some of them, for ease of identification, have been given geographical labels. Often this is to the great credit of the respective organizers, because they reported their findings so that others could avoid the same pitfalls. 1.8.a Matters affecting independence i. Field workers of one of the procedures being charged with supervisory responsibilities in the other procedure (the early Indian procedure). ii. Verification of documents in the field to make certain that they do or that they do not cover the same event. This is permissible, provided it is done by a third party to the two main procedures. It is not permissible to reconcile details of characteristics for differences on the two types of documents. The distinction may be talmudic, but it makes a world of difference to the preservation of independence between the two procedures. The suggestion for the improvement of one method through the other made by the discussant of chapter 2 is, therefore, no less than sabotage of the pure PGE/ ERAD/ ECP technique. iii. Subsampling.'5 This could become the thin edge of the wedge of destruction of the main PGE/ ERAD/ ECP concept. Having obtained the completeness rate through the subsampled procedure, the "natural" corollary—it might occur to the managers — would be to apply the result as means of calibrating and "improving" the other procedure. As we repeatedly argue in this chapter and elsewhere, "improving" a PGE/ ERAD/ ECP procedure through the other one is the kiss of death for the whole system. iv. The preaching of hard work, careful work, high completeness ("100 percent completeness" — indeed!) and the like. Cases were known in the history of survey taking when crude birth rates of 100 per thousand were obtained through preaching and propaganda (Sudan, 1958). The vital events recorded then cease being a reflection of the demographic processes of a given society and become a result of the persuasive process. The field procedures should be neutral in their effect and such that the reporting of vital events does not depend on the temporary zeal of any field worker. v. Implicit faith in any one part of the work being greater than in another. It is unjustified and dangerous to see in the so-called base line survey or base line study anything more than the first of many endeavours. It is not particularly better than others, and is probably poorer than subsequent ones. Like "reconciliation", the faith in "base line" discloses the tendency to improve matters. Such a tendency is destructive in itself for PGE/ ERAD/ ECP. We preach instead the more realistic tendency to live in sin and error, but to evaluate both and arrive at improved estimates. Within this spirit the basic register described in section 5.8 is not in the spirit of a true PGE/ ERAD/ ECP pursuit. 1.8.b Matters affecting the matching procedure i. Cutting the size of clusters more and more in the hope that coupled with frequent rounds the burden of matching will disappear (and as a by-product the sampling error of cluster sampling will dwindle to the level of simple random sampling). By zeroing in on one or two vital events in this manner we abstract from all those in between that escape the net of any one procedure either through their own peculiarities or the disadvantages of the procedure. 27

1.8 b

Karol J. Krotki

ii. Rushing into using the civil registration system as one of the procedures for a PGE/ ERAD/ ECP system, without ascertaining first that the civil registration bookkeeping justifies and makes possible comparisons with the size of clusters one usually draws for sampling purposes. Typically the books of civil registration are kept for areas much larger than those required for PGE/ ERAD/ ECP. iii. Making the recall period 15 months long with half yearly rounds should the next study be so adventurous as to try two periodic household surveys as the two procedures with an overlapping recall period.16 The field procedure would confuse the respondent, exasperate the field worker, and confound the analyst. iv. Offering prizes to field workers for discovering vital events not discovered by the other field worker (the Liberian case). They will surely find a way to share the bounty equitably in line with the allegedly Chinese proverb: "Two officials think up a law; two million members of the public think of ways of getting round it; who will get the upper hand?" In Liberia the field workers must have taken to dividing fifty-fifty all their vital events and estimating rates must have rocketed sky high. (We are thus in disagreement with the suggestion made in section 7.6.d.) The organizational effort required by prizes and bonuses is better spent on structuring supervision. 1.8.c Matters affecting samples i. Having a bizzare sampling design such as covering a country in five annual lots (with none of the fifths being selected probabilistically to boot) and attempting to design suitable de facto and dejure definitions (Upper Volta). Or covering one-tenth in the first year, two-tenths in the second year, three-tenths in the third year and so on, until the whole territory is covered in the tenth year (the five countries of UDEAC). While it must be hoped that no analyst worth his salt would just lump all these questionnaires together without regard to their temporal origin, any successful office treatment would require arrangements of considerable complexity. ii. Having enormous clusters such as the 20,000 they had in Cameroun. Any minimal homogeneity must result in intraclass correlations so large that the few clusters that can be enumerated do not justify the expenditure. Furthermore, it is likely that even from the standpoint of nonsampling errors, 20,000 is well beyond an optimum. iii. Using a list of households as a sampling frame, from an old census to boot (Tunisia, 1970). Such a list ties the sample to a stale population and institutionalizes old errors. In particular it excludes newly created households. l.S.d Matters affecting organization i. Hitching the PGE/ERAD/ECP survey onto a multipurpose survey (Maroc, 1967). For a discussion of the disadvantages of multipurpose surveys see Mauldin, 1966: 652. ii. Wasting time on such frills as asking females "Are you pregnant now?" (Scott, 1973: 6), in the hope that the disappearance of pregnancy at the next round will lead to the sure reporting of a birth. This Liberian initiative is like catching fish with a net whose holes are larger than the fish. iii. Having calls other than six monthly in the periodic survey procedure. Few organizations will have the stamina to carry out the quarterly matching (Pakistan, 1961-65) and yearly intervals result in too much memory loss and too great a burden on the second and third PGE/ ERAD/ ECP category (see figure 1.1). iv. Throwing out all of the data because part of them are not available or are faulty. This may arise when seemingly important parts of the sample drop out because of insufficient response or for other reasons. This may be the case when the number of areas affected is large with matching between rounds. In such a case, interround 28

Role of PGEIERAD/ECP surveys

L8.d

tabulations for the clusters for which two correct data sources are available should be printed separately from the tabulations for all the clusters. In this manner a bridge might be created between the two kinds of tabulations. v. Taking the trouble and expense of mounting an operation without seriously considering the possibility of making it nationally representative. This error can arise either through quota sampling or through concentrating the whole field work in one area for "experimental" purposes (the Philippines, 1971-75). 1.9 Quasi PG EI ERA DI ECP estimates There are instances where the PGE/ ERAD/ ECP approach is taken in all essentials except that the fourth category is not estimated (for the example of India see Ramabhadran, 1971). This is understandable when the quality and outcome of the matching rules is so uncertain that a large net error in either direction is expected. But then we must have no faith in the second or third category either (see figure 1.1) and the survey must be restructured. The sampling error is neutral either way and provides no reason for ignoring the fourth category. The possibly inadequate independence between the two procedures remains. All known examples of correlation are positive and one would be hard put to think of examples of negative correlation. One would be the bizzare case suggested in section 1.8.b iv, the case when the two field workers carved up the vital events in the area between them in order to share fairly and to the maximum the prize offered. In all more realistic cases the likelihood of the three categories being underestimated is markedly greater than overestimated. It makes no sense, as in the Indian case, to undergo the expense of matching and then only partly use the results. It would be valid to say that the expense of matching is not worthwhile to undertake because of insufficient independence, particularly should there exist a better set of data with which to match. This would be consistent with the attitude taken in this chapter and in the PGE handbook that matching between rounds of the same multiround survey is seldom worthwhile because of their dependence on the same type of procedure. It is only when extreme steps have been taken to ensure independence in conformity with the PGE handbook (Marks et a/., 1974:250-253,425428) that matching is justifiable. Once justifiable, the fourth category is valid. 1.10 The paucity and importance of costing data Table 1.3 assembles such data on expenditure on social surveys as became easily available. One of the reasons why little data on financing social surveys are published is that most social surveys are financed not only by their own budget but also by the provision of services and assistance from sources not easily identifiable for accounting purposes. There is a need to direct some effort to identifying these sources in particular cases and suggesting imputed figures in order to arrive at real, economic costs, not only the financial costs of a social survey. This is important for two reasons: to assess the total costs of an endeavour in order to compare it with the benefits of the endeavour or with the costs of an alternative way of reaching the same objective; the second is the impact that cost items have on the survey design. With regard to the first reason, international comparisons would be particularly interesting. The strong feeling of the present writer is that relative to the average national income, social surveys in underdeveloped countries are more expensive than in developed countries by a factor of three or four. In Canada the annual salary of a 29

Table 1.3 Survey costs divided by office/field and by primary/secondary units

Survey

Currency

Total

Office

Field

(1)

(2)

(3)

(4)

(5)

Algeria 1966 Algeria 1969 Anon 1967(?) Burundi 1970/71 Cameroon 1971/82 Cameroon (?) Canada-GAFS 1973 Congo 1971/82 Dahomey 1961 Gabon 1960/61 Gabon 1969 Gabon 1971/82 Guyana 1974 Ivory Coast 1970 Madagscar (?) Malawi 1970/71 Mauritania 1974 Morocco 1961/62 Morocco 1972/73 (macro) ' ' Morocco 1972/73 (micro)12 Morocco 1972 (recording)

D.A.1 D.A.1

20,493,000 6,350,000 432,000 345,600 86,400 2,822,000 357,100,000 31,500 39,879 14,281 117,089,000 18,000,000 33,000,000 20,950,000 86,959,000 268,630 416,000,000 46,000 71,000 178,950,000 46,840 3,350,000 1,600,000'°1, 750,000 516,000

u.s.s

FiBu3 F CFA5 pao Can4 FCFA 5 FCFA 6 F CFA6 FCFA5 F CFA5 G7 FCFA5 F8

u.s.s

F CFA5 D.H.9 D.H.9 D.H.9 D.H.9

303,000 285,330

Field costs: (5) as % for for of (3) PSUs SSUs (6) (7) (8)

20

43,200

43,200

average cost per one PSU SSU Cost ratio 9/10 (9) (10) (11)

0.32?

36

0.026

561

3.213

175

Morocco 1972 (household) Morocco — project Pakistan 1962/65 R.C.A. 1971/82 Senegal: Sine-Saloum 1963/65 Senegal: Khombol Thienaba Senegal: Pikine 1967/69 Senegal 1970/71 Sudan 1953 Sudan 1955/56 Tchad 1971/82 Tunisia (?) USA-GAF 1955 USA-GAF 1960

D.H.9

350,637

D.H.9

u.s.s

130,000 122,880,000

F CFA5

F19

160,000

p20

46,000

F21

16,000 75,000,000 14,880 469,939 350,832,000 1,500,000

F CFA5 L.E.22 L.S.22

FCFA 5 F23

Algeria 1966

Orstom, 1973, p. 370 Orstom, 1973, p. 370 Seltzer, 1971, p. 101 Orstom et al., 1971, p. 277 Orstom, 1973, p. 374

Burundi 1970/71 Cameroon 1971/82

12,005 375,519

2,875 94,420

2317

19 20

9,000

1,063 69,220

1,288 20,700

50018

912 26,200

17.8 6.7

3.214 40215 0.21 '6 2,380

0.015 1,187 0.014 479

40,990 58,823

(3)

Anon 1967(?)

215,000 29,700

U.S.$ U.S.S

Sources

Algeria 1969

100,300

(4)

(5)

(7)

(8)

(9)

arbitrary arbitrary arbitrary arbitrary

(10)

24

(4)

Sources

(3)

Cameroon (?)

Orstom, 1973, p. 373

Canada-GAFS 1973

25

Congo 1971/82

Orstom, p. 374 Orstom, p. 369 Orstom, p. 370 Orstom, p. 370 Orstom, p. 385 Orstom, p. 374 Guyana,, p. 21 Orstom, p. 369 Orstom, p. 373 Blacker,

Dahomey 1961 Dahomey 1966 Gabon 1960/61 Gabon 1969 Gabon 1971/82 Guyana 1974 Ivory Coast 1970 Madagascar (?) Malawi 1970/71 Mauritania 1974 Morocco 1961/62 Morocco 1972/73 (macro)

25

1973, 1973, 1973, 1973, 1973, 1973, 1974, 1973, 1973,

1970

Orstom, 1973, p. 368 Orstom et al., 1970, p. 262 10 Fellegi, 1971a, letter of 6 April

(5)

(7)

(8)

(9)

(10)

Morocco 1972/73 (micro)

Fellegi, 1973, p.ll

Morocco 1972 (recording) Morocco 1972 (household) Morocco-project (?)

Orstom, 1973, p. 385 Orstom, 1973, p. 385

Pakistan 1962/65

Seltzer, 1971 p. 101 Orstom, 1973, p. 374

R.C.A. 1971/82 Senegal: Sine-Saloum 1963-65 Senegal: Khombol Thienaba

(?)

Senegal: Pikine 1967/69 Senegal 1970/71 Sudan 1953 Sudan 1955/56 Tchad 1971/82 Tunisia (?)

ibid., p.ll ibid., p.ll

Fellegi, 1973

ibid., p. 4 ibid., p. 4

26

27

ibid., p. 78 ibid., p. Ill

ibid., p. 124 ibid., p. 1ll derived

Orstom, 1973, p. 373 Orstom, 1973 p. 373 Orstom, 1973 p. 373 Orstom, 1973, p. 369 Krotki, 1955, p. 78 Sudan, 1958, p. 87: 444,544, p. Ill: 25,395 Orstom, 1973, p. 374 Orstom, 1973, p. 372

Sources USA-GAF 1955 USA-GAF 1960

1

(3)

(4)

(5)

(7)

(8)

(9)

(10)

SRC, ISR Ann Arbor verbal SRC, ISR Ann Arbor verbal

Multiply all values by 0.2026 to bring them to U.S.: dollars It is believed that there was more than one single visit in the survey. Following footnote 18, a division by 4 is suggested ($0.08). 3 Multiply all values by 0.0114 to bring them to U.S. dollars 4 Multiply all values by 1.0016 to bring them to U.S. dollars. 5 Multiply all values by 0.0036 to bring them to U.S. dollars. 6 Multiply all values by 0.0041 to bring them to U.S. dollars. 7 Multiply all values by 0.50 to bring them to U.S. dollars. 8 Multiply all values by 0.1813 to bring them to U.S. dollars. 9 Divide all values by 4.6 to bring them to U.S. dollars. 10 The office expenditure in column (4) is a minimal estimate relating to office treatment of questionnaires, i.e. it excluded all overheads, etc. 11 The "macro" estimate for Morocco of 1972/73 was derived for budgetary purposes prior to the exercise in global terms. 12 The "micro" estimate for Morocco of 1972/73 was derived for analytic purposes after the exercise on the basis of assumed "per household" performance. 13 On the assumption of 5 persons per each of the 17,000 households in the Moroccan PGE/ERAD/ECP study. 14 On the assumption of 5 persons per each of the 9,600 households in the proposed national PGE/ERAD/ECP survey in Morocco. 15 The Moroccan-project cost ratio in column (11) rises to 805 when only one survey is considered. 16 Average annual figures are quoted for the 4-year Pakistan study. 17 High ratios due to some overheads spread over 4 years (Seltzer, 1971:101). 18 In any one year there were 3 multi-visits and equivalents of 6 longitudinal registrations. To compare with single visits, divide by 9 ($56 and $0.023). 2

19

Multiply all values by 0.2041 to bring them to U.S. dollars. Multiply all values by 0.1813 to bring them to U.S. dollars. Multiply all values by 0.2021 to bring them to U.S. dollars. 22 Multiply all values by 2.8 to bring them to U.S. dollars. 23 Multiply all values by 0.20 to bring them to U.S. dollars. 24 On the assumption of 5 persons per each of the 27,000 households (in the "anon" country). 25 The cost estimates were based on the revised 1973 budget. 26 On the assumption of 18 recorders, 18 interviewers, 9 supervisors, at U.S.S790 annually. 27 4/5 of the time of the 18 recorders and 18 interviewers. 20 21

7.70

Karol J. Krotki

field worker will be twice the national income per capita, but in a typical underdeveloped country it will be six or eight times higher, though rather extreme variations in similar and neighbouring countries will occur. With regard to the second reason, it is probably even more difficult to obtain details of the expenditure unless very good care is taken by the accountant to post each item of expenditure to the heading most relevant analytically, which is not necessarily the same as for accounting purposes. For example, travel and subsistence while away from one's place of residence might be one accounting heading, but the expenses of the interviewers will affect the size of clusters and other design aspects differently from the expenses of their supervisors. Fortunately we need not depend on actual monetary values. One can use substitutes in the form of time possibly multiplied by the fraction by which the salaries of supervisors and their other emoluments exceed those of the interviewers. There were not enough data to pursue this alternative but an attempt has been made in table 1.4 to ensure some international comparability by bringing all reported costs to the 1975 price level and expressing them in the most convenient international currency, namely the U.S. dollar. The table has the same blanks as table 1.3, but we consider the effort worthwhile if it will encourage a wider reporting of cost items. The available information has been pushed to further limits in table 1.5 where the cost per unit of contact was calculated in order to show the variability between countries and between types of survey. The data are still so limited that we will leave any verbalization that the table might deserve to the reader. In a discussion of PGE/ ERAD/ ECP costs and those of a multiround survey it has been shown that with three rounds in a multiround survey annually, the PGE/ ERAD/ ECP system begins to be less expensive and wins on the grounds of costs alone, not to mention the built-in feature of self evaluation (Seltzer, 1971). The two procedures of a PGE/ ERAD/ ECP system and the costs of matching are under some circumstances less than the cost of three rounds of a multiround survey. In the course of the work on tables 1.3,1.4, and 1.5 certain simple principles of accounting for analytic purposes occurred and it might be useful for future reference to spell them out: i. Have own costs posted into at least three ledger headings: overheads, costs tied to primary sampling units, and costs tied to secondary sampling units; ii. Impute costs covered from external budgets, and put these under the same three ledger headings; iii. Unusual costs (international or subsidized) should be identified and some indication given of what the normal local cost would be; iv. Indicate changes in the local price index when the survey spreads over a sufficiently long period of time; v. Indicate the rate of exchange with one or two major international currencies, particularly when changes in exchange rates are taking place in the course of the survey (consider an average between official and black-market rates if relevant); vi. State the starting or average salary of a field worker and those of a supervisor; state their employment in terms of person-years or person-months; vii. Give sources of the data meticulously, if necessary in tabular form, separately for each column, not unlike those in tables 1.3,1.4 and 1.5; viii. Publish the cost data. The person-years or person-months substitutes are not always a complete answer to the problem. Only rarely are the totals of the "time on the job" a direct reflection of all the costs. In organizational circumstances when field workers spend only a small proportion of their time on the job and the rest "just hanging around" the time-andmotion measured cost may actually be misleading and only a very small proportion of 36

Table 1.4 Total and proportionate survey costs Survey

Currency reported

Total costs

(1)

(2)

(3)

Algeria 1966 Algeria 1969 Anon 1967 (?) Burundi 1970/71 Cameroon 1971/82 Cameroon (?) Canada-GAFS 1973 Congo 1971/82 Dahomey 1961 Dahomey 1966 Gabon 1960/61 Gabon 1969 Gabon 1971/82 Guyana 1974 Ivory Coast 1970 Madagascar (?) Malawi 1970/71 Mauritania 1974 Morocco 1961/62 Morocco 1972/73 (macro)8 Morocco 1972/73 (micro)

D.A. D.A.

20,493,000 6,350,000 432,000 86,400 2,822,000 357,100,000 31,500 14,281 39,879 117,089,000 18,000,000 60,000,000 33,000,000 20,950,000 86,959,000 268,630 416,000,000 46,000 71,000 46,840 178,950,000 3,350,0007 1,750,000 516,000

0.2026 0.2026 1.0000 0.0114 0.0036 0.1813 1.0016 0.0036 0.0041 0.0036 0.0041 0.0036 0.0036 0.5000 0.0036 0.1813 1.0000 0.0036 0.2400 0.2200

1.623 1.435 1.578 1.328 1.300 1.300 1.624 1.300 1.760 1.623 1.778 1.806 1.300 1.300 1.356 1.300 1.328 1.300 1.751 1.300

303,000

0.2200

1.300

u.s.s

FiBu FCFA F Can FCFA FCFA FCFA FCFA FCFA FCFA G FCFA F U.S.S FCFA D.H. D.H. D.H.

Field Multipliers used to Total cost costs bring costs (3) & (4) in US $ of 1975 to US$ (3)X(5) to 1975 X(6) (4) (5) (6) =(7) 6,736,912 1,845,705 681,696 359,036 1,671,635 7,424 46,425 548,110 128,337 350,653 237,691 98,070 406,968 17,461 2,031,241 10,842 94,288 873,486 1,407,804

Field cost in US $ of 1975 (4)X(5) X(6) =(8)

No. of households

(9)

Avg. cost per household in US $ of 1975 Total Field costs costs (7):(9) (8):(9) -(10) -(11)

136,339

70,000' 27,000

26.37 25.25

5.05

16,613

3,0002 1,045

2.47 44.42

15.90

14,0003

9.17

104,0004

2.29

5,000 19,0005 5,0006 10,000

34.92 106.91 2.17 9.43

735,420 147,576

66,000 16,000

21.33

86,658

17,000

219 11.14 9.22

5.10

Table 1.4 Survey

Currency reported

Total costs

0)

(2)

(3)

D.H. Morocco 1972 (recording) Morocco 1972 D.H. (household) D.H. Morocco-project (?) Pakistan 1962/65 U. S.S F CFA R.C.A. 1971/82 Senegal: Sine-Saloum F 1963/65 F Senegal: Khombol Thienaba (?) Senegal: Pikine 1967/69 F F CFA Senegal 1970/71 L. E. Sudan 1953 Sudan 1955/56 L. S. Tchad 1971/82 F CFA F Tunisia (?) USA-GAF 1955 U. S.S USA-GAF 1960 U. S.S

Field Multipliers used to Total cost costs bring costs (3) & (4) in US $ to US$ of 1975 (3)X(5) to 1975 X(6) (6) =(7) (4) (5)

Field cost in US $ of 1975 (4)X(5) X(6) =(8)

No. of households

(9)

Avg. cost per household in US I f of 1975 Total Field costs costs (7):(9) (8):(9) =(10) -(11)

285,330

0.2200

1.300

81,604

16,000'°

5.10

350,637

0.2200

1.300

100,282

1 6,00010

6.27

0.2200 1.0000 0.0036 0.2041

1.300 1.707 1.300 1.697

221,910 575,219 55,412

46,000

0.1813

1.356

16,000 75,000,000 14,800 469,939 350,832,000 1,500,000

0.2021 0.0036 2.8000 2.8000 0.0036 0.2000 1.0000 1.0000

130,000 122,880,000 160,000

215,000 29,700

2,875 94,420 40,990 58,823

61,490 50,698

9,600 20,000

11.10

10,600"

5.23

11,309

2,500'2

4.52

1.514 4,896 1.356 366,209 1.968 81,995 1.953 2,569,814 1.300 1,642,294 1.514 454,200 1.967 1.778

15,842 516,326

80013 100,00014 10,000 376,600

6.12 3.66 8.20 6.82

28,000 15 2,913 3,322

16.22

80,627 104,587

6.41 2.53

1.58 1.37 27.68 31.48

Sources (1)

(3)

Algeria 1966

Orstom, 1973, p.370

Algeria 1969

Orstom, 1973, p.370

Anon 1967(?)

Seltzer, 1971, p. 101

Burundi 1970/71 Cameroon 1971/82

Orstom et al, 1971,p.277 Orstom, 1973, p.374

Cameroon (?)

Orstom, 1973, p.373

Canada-GAFS 1973

16

Congo 1971/82

Orstom, 1973, p.374

Dahomey 1961

Orstom, 1973 p.369

Dahomey 1966

Orstom, 1973 p.370

Gabon 1960/61

Orstom, 1973, p.370

Gabon 1969

Orstom, 1973, p.385

Gabon 1971/82

Orstom, 1973, p.374

Guyana 1974

Guyana, 1974, p.21

Ivory Coast 1970

Orstom, 1973, p.369

(4)

16

(5)

(6)

Derived from exchange rate reported in IMF, 1971, p.43 Derived from exchange rate reported in IMF, 1971, p.43

U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973

Derived from exchange rate reported in IMF, 1972, p.73 Derived from exchange rate reported in IMF, 1972, p.373 Derived from exchange rate reported in IMF, 1972, p. 143 Derived from exchange rate reported in IMF, 1974, p.77 Derived from exchange rate reported in IMF, 1972, p.373 Derived from exchange rate reported in IMF, 1964, p.241 Derived from exchange rate reported in IMF, 1972, p.373 Derived from exchange rate reported in IMF, 1964, p.241 Derived from exchange rate reported in IMF, 1972, p.373 Derived from exchange rate reported in IMF, 1972, p.373 Derived from exchange rate reported in IMF, 1972, p. 165 Derived from exchange rate reported in IMF, 1972, p.373

(9)

Orstom, 1973, p.370 Seltzer, 1971, p.101

Orstom, 1973, p.373

Orstom, 1973, p.385

Guyana, 1974, p. 6 Orstom, 1973, p.369

Sources (1)

(3)

Madagascar (?)

Orstom, 1973, p.373

Malawi 1970/71

Blacker, 1970

Mauritania 1974

Orstom, 1973, p.368 Orstom et a/., 1971, p.262

Morocco 1961/62 Morocco 1972/73 (macro) Morocco 1972/73 (micro) Morocco 1972 (recording) Morocco 1972 (household) Morocco-project (?) Pakistan 1962/65 R.C.A. 1971/82 Senegal: Sine-Saloum 1963/65 Senegal: Khombol Thienaba (?) Senegal: Pikine 1967/69

(4)

(5) Derived from exchange rate reported in IMF, 1972, p. 143

ibid., p.368

Derived from exchange rate reported in IMF, 1972, p.373

Fellegi, 197 la letter of 6 April, 1971 Fellegi, 1973, p.ll Orstom, 1973 p.385 Orstom, 1973, p.385 Fellegi, 1973, p.4 Seltzer, 1971, p.101 Orstom, 1973, p. 374 Orstom, 1973, p.373 Orstom, 1973, p.373 Orstom, 1973, p.373

Derived from exchange rate reported in IMF, 1972, p.373 Derived from exchange rate reported in IMF, 1971, p. 140 Derived from exchange rate reported in IMF, 1971, p. 143 Derived from exchange rate reported in IMF, 1971, p. 146

(6) U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973

(9) Orstom , 1973, p.373

Fellegi, 1973, p.39 Fellegi, 1973, p.ll Orstom, 1973, p.385 Orstom, 1973, p.385 Fellegi, 1973, p.4

Orstom, 1973, p.373 Orstom, 1973, p.373 Orstom, 1973, p.373

Senegal 1970/71

Orstom, 1973, p.369

Sudan 1953

Krotki, 1955, p.78

Sudan 1955/56 Tchad 1971/82

Sudan, 1958 p.87:444,544 p.l 11:25,395 Orstom, 1973, p.374

Tunisia (?)

Orstom, 1973, p.372

USA-GAF 1955 USA-GAF 1960 1

SRC, ISR Ann Arbor verbal SRC, ISR Ann Arbor verbal

Derived from exchange rate reported in IMF, 1972, p.373

U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973

Derived from exchange rate reported in IMF, 1972, p.373 Derived from exchange rate reported in IMF, 1972, p. 143

U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973 U.S. Dept. of Commerce, 1973

Orstom, 1973, p .369

Orstom, 1973, p. 372

SRC, ISR Ann Arbor verbal SRC, ISR Ann Arbor verbal

On the assumption of 5 persons per household, the number of households was derived from dividing the reported 350,000 individuals by 5. Following footnote 1, the reported number of 15,000 individuals was divided by 5. 3 Following footnote 1, the reported number of 70,000 individuals was divided by 5. 4 Following footnote 1, the reported number of 520,000 individuals was divided by 5. 5 Following footnote 1, the reported number of 95,000 individuals was divided by 5. 6 Following footnote 1, the reported number of 25,000 individuals was divided by 5. 7 The total cost in Morocco of 1961/62 included only minimal office expenditure relating to the office treatment of questionnaires, i.e., it excluded all overhead. 8 The "macro" estimate for Morocco of 1972/73 was derived for budgetary purposes prior to the exercise in global terms. 9 The "micro" estimate for Morocco of 1972/73 was derived for analytic purposes after the exercise on the basis of assumed "per household" performance. 10 Following footnote , the reported number of 80,000 individuals was divided by 5. 11 Following footnote , the reported number of 53,000 individuals was divided by 5. 12 Following footnote , the reported number of 12,500 individuals was divided by 5. 13 Following footnote , the reported number of 40,000 individuals was divided by 5. 14 Following footnote , the reported number of 500,000 individuals was divided by 5. 15 Following footnote , the reported number of 140,000 individuals was divided by 5. 16 The cost estimates were based on the revised 1973 budget. 2

Table 1.5 Costs varying with types of surveys

Survey

Number of households

(1)

(2)

Avg. annual cost per household in US$ of 1975 Total cost Field cost (3) (4)

70,000' 27,000

26.37 25.25

Algeria 1966 Algeria 1969 Anon 1967 (?) Burundi 1970/71 Cameroon 1971/82 Cameroon (?) Canada-GAFS 1973 Congo 1971/82 Dahomey 1961 Dahomey 1966 Gabon 1960/61 Gabon 1969 Gabon 1971/82 Guyana 1974 Ivory Coast 1970 Madagascar (?) Malawi 1970/71 Mauritania 1974 Morocco 1961/62 Morocco 1972/73 (macro)7

3,0002 1,045

44.42

14,0003

9.17

104,0004

2.09

5,000 19,0005 5,0006 10,000 66,000 16,000

Number of contacts

(5)

(6)

Avg. field cost per contact (4): (6) -(7)

National survey National statistical study on population 4

5.05

15.90

106.91 9.43 21.33

Type of survey

11.14 9.22

Regional project on population Pilot for fertility study KAP and fertility Regional project on population National survey Regional survey National survey National census Regional project on population Fertility survey GFS/WFS National survey Pilot for fertility survey PGE/ERAD/ECP National census Multi-purpose PGE/ERAD/ECP

1.26

5 1

15.90

1 4 3 6

3.71 1.54

Morocco 1972/73 (micro)8 Morocco 1972 (recording) Morocco 1972 Morocco-project (?) Pakistan 1962/65 R.C.A. 1971/82 Senegal: Sine-Saloum 1963/65 Senegal: Khombol Thienaba (?) Senegal: Pikine Senegal 1970/71 Sudan 1953 Sudan 1955/56 Tchad 1971/82 Tunisia (?) USA-GAF 1955 USA-GAF 1960

17,000 16,0009

5.10

16,0009 9,600 20,000

6.27 11.10

10,60010

5.23

5.10

PGE/ERAD/ECP

6

0.85

6.41 2.53

PGE/ERAD/ECP PGE/ERAD/ECP Regional project on population Pilot for a fertility survey

6 8

1.07 0.32

Pilot for a fertility survey

6

Pilot for a fertility survey National survey Pilot for a national census National sample population census Regional project on population National survey KAP and fertility KAP and fertility

3

2,500 11 80012 100,00013 10,000 376,600 28, 00014 2,913 3,322

6.12 3.66 8.20 6.82

1.58 1.37 27.68 31.48

4

1 1

1.58 1.37

3 1 1

27.68 31.48

Sources N.B. Cols (2), (3), (4) are copied from cols (9), (10), (11) of table 1.4.

(1) Algeria 1966 Algeria 1969 Anon 1967 (?) Burundi 1970/71 Cameroon 1971/82 Cameroon (?) Canada-GAFS 1973 Congo 1971/82 Dahomey 1961 Dahomey 1966 Gabon 1960/61 Gabon 1969 Gabon 1971/82 Guyana 1974 Ivory Coast 1970 Madagascar (?) Malawi 1970/71 Mauritania 1974 Morocco 1961/62 Morocco 1972/73 (macro) Morocco 1972/73 (micro)

(2)

Orstom, 1973, P- 370 Seltzer, 1971, P- 101 Orstom, 1973, P- 373 Orstom, 1973, P- 369 Orstom, 1973, P- 385 Guyana,, 1974.. P.21 Orstom, 1973, P- 369 Orstom, 1973, P- 373 Maroc, 1967, P- 111 Fellegi, 1973 Fellegi, 1973, P- 11

(6)

(5)

Orstom, 1973, p. 370 ibid., p. 370 Orstom, 1973, p. 374 ibid., p. 373 Orstom, 1973, ibid., p. 369 Orstom, 1973, Orstom, 1973, ibid., p. 385 Orstom, 1973, ibid., p. 1 ibid., p. 369 ibid., p. 373

ibid., P .370 arbitrary ibid., P- 373

p. 374 p. 370 p. 370 p. 374

Orstom, 1973, p. 368 ibid.

ibid., P . 2 1 ibid., P .373 ibid., P . Ill 2 visits annually by recorders are 2 visits annually by recorders are

by interviewers and assumed that the 12 visits equivalent of 4 visits by interviewers and assumed that the 12 visits equivalent of 4 visits

Morocco 1972 (recording) Morocco 1972 (household) Morocco-project (?)

Orstom, 1973, p. 385

Pakistan 1962/65

Seltzer, 1971, p. 101

Orstom, 1973, p. 385 Fellegi, 1973, p. 4

R.C.A. 1971/82 Senegal: Sine-Saloum Orstom, 1973, p. 373 1963/65 Senegal: Khombol Orstom, 1973, p. 373 Thienaba (?) Senegal: Pikine 1967/69 Orstom, 1973, p. 373 Orstom, 1973, p. 369 Senegal 1970/71 Krotki, 1955, p. Ill Sudan 1953 Sudan, 1958, p. Ill Sudan 1955/56 Tchad 1971/82 Orstom, 1973, p. 372 Tunisia (?) SRC, ISR Ann Arbor USA-GAF 1955 verbal USA-GAF 1960 SRC, ISR Ann Arbor verbal

2 visits annually by interviewers and assumed that the 12 visits by recorders are equivalent of 4 visits 3 visits annually by interviewers and assumed that the 12 visits by recorders are equivalent of 5 visits Orstom, 1973, p. 374 ibid., p. 373

ibid., p. 373

ibid., p. 373

ibid., p. 373

ibid., p. 373 ibid., p. 369 ibid. ibid. Orstom, 1973, p. 374 ibid., p. 372

ibid., p. 373 ibid., p. 369

ibid., p. 372

1

2 3 4 5 6 7 8

9 10 11 12 13 14

On the assumption of 5 persons per household, the number of households was derived from dividing the reported 350,000 individuals by 5. Following footnote 1, the reported number of 15,000 individuals was divided by 5. Following footnote 1, the reported number of 70,000 individuals was divided by 5. Following footnote 1, the reported number of 520,000 individuals was divided by 5. Following footnote 1, the reported number of 95,000 individuals was divided by 5. Following footnote 1, the reported number of 25,000 individuals was divided by 5. The "macro" estimate for Morocco of 1972/73 was derived for budgetary purposes prior to the exercise in global terms. The "micro" estimate for Morocco of 1972/73 was derived for analytic purposes after the exercise on the basis of assumed "per household" performance. Following footnote , the reported number of 80,000 individuals was divided by 5. Following footnote , the reported number of 53,000 individuals was divided by 5. Following footnote , the reported number of 12,500 individuals was divided by 5. Following footnote , the reported number of 40,000 individuals was divided by 5. Following footnote , the reported number of 500,000 individuals was divided by 5. Following footnote 1, the reported number of 140,000 individuals was divided by 5.

Role of PGEI ERA D/ ECP surveys

1.10

the total cost. The field workers may work very hard when on the job (reports of one hundred household interviews with pretty hefty interview schedules are not uncommon) precisely because they know that they can loaf afterwards.17 In such cases the neat arithmetical exercise that allots time proportionately to the variance in stratified sampling or to intraclass correlation in cluster sampling becomes rather pointless, or rather baseless. The need for accurate cost coefficients can be illustrated by the choice of cluster size for estimating birth rates with the proposed Moroccan national dual collection sample (Fellegi, 1973). It was assumed (a) that fulltime resident recorders would be used for the continuous recording procedure, (b) that all the clusters selected for continuous recording would also be subjected to the periodic household survey and that there would be no subsampling of one procedure by the other procedure; in other words, that in terms of the notation used in 2.2.b, ki = k2 and h = H, (c) that the periodic surveys will be conducted by survey teams travelling from cluster to cluster and (d) that the continuous recording cost component CR = O (see 2.2.b), since the data collection budget was not to be charged to the resident recorder costs. The last assumption reduced the problem to one of determining the appropriate cluster size for the periodic survey procedure. The cost for the two surveys to be conducted each year was estimated to be (in terms of person-days): C= 1288 k2+ 1.6 k2 H, (1.18) where 1288 represents the cost per cluster for initial delineation and travel costs18 between two clusters and 1.6 is the per person enumeration cost with two surveys per annum. From formula (1.18) we express k2 k2 = C/(1288 + 1.6H) (1.19) The classical formula for the variance of a cluster sample is Variance of an estimated total = N2 (a 2 /k 2 H) (1 + Hd) (1.20) where a2 = pq p = birth rate q= 1 -p N = total population size k2 = the number of selected clusters H = the number of persons per cluster minus 1 (Kish, 1966: 216) d = intraclass correlation. The empirical intraclass correlation for births was reported to be 0.0008. Substituting the values from (1.19) into (1.20) we obtain: Var (B) = (a 2 /k 2 H)(l+0.0008 H) (1.21) = (a 2 /C) [(1288 + 1.6H)/H](1 + 0.0008H) (1.22) = (a21C) [(1288/H) + 0.00128 H + 2.6304] (1.23) where B = total births. Taking the derivative of var (B) with respect to H and setting it equal to O, we obtain (1288/H 2 ) = 0.00128 (1.24) Therefore, we have the following optimal cluster size for the estimation of births Hop, = 1000 (1.25) Thus, for a simple random sample of clusters and intracluster correlation of .0008 for births, the optimal cluster size H is 1,000 persons. This result is interesting from two standpoints. First, it is based on "no subsampling" assumptions, although the actual cost ratio C R /C S = 1.420/4.322 for a national sample of 50,000 or 100,000 persons suggests subsampling of one of the procedures may, in fact, be worthwhile.19 Second, H = 1000 is on the lower side of the limits suggested in section 1.5 but is 47

1.10

Karol J. Krotki

still larger than those found in other African countries. Scott and Coker (1971) report household survey cost coefficient ratios of 80 to 300 for team enumeration under African conditions as compared to the Moroccan ratio in equation (1.18) above of 1288/1.6 = 805. This suggests possible overestimation of the cluster cost coefficient (1288) or underestimation of the within cluster cost coefficient (1.6). It points up the need for accurate determination of variable cost components for specification of optimum or nearly optimum dual collection designs.20 Other considerations enter into the choice of cluster size than merely that value of H which, together with appropriate choices of ki, k2 and h, minimizes the relvariance of the estimated number of births (or the estimated birth rate) for a given survey budget, but the example is illuminating.

1.11 The past history and the probable future of the technique It is satisfying to a Canadian writer to report that an early example of case-by-case matching occurred in Canada. The occasion was the 1931 population census and the PGE technique was used as means of evaluating the quality of the civil registration. The impressive series of monographs resulting from the 1931 census must have been facilitated by the ease with which the then Dominion Bureau of Statistics could recruit at that time of high unemployment university graduates at cut rates. The test was a oneway match from the census data to the civil registration. No attempt was made to test the completeness of census enumeration of young children by searching among census records for children registered as born in the years immediately preceding the census. This was to come years later when, particularly after the censuses of 1961,1966, and 1971, the so-called reverse record check (RRC) was used in order to assess the quality of census enumeration. For RRC sources other than birth registrations were also used to build up the control list. As we indicated in section 1.2 there are many uses of dual collection and dual comparison, but for our purposes at least two other characteristics are required: a caseby-case comparison (not a comparison to totals) and an estimate of omission by one or either procedure. Table 1.1 gives an overview of the world involvement in PGE/ ER AD/ ECP surveys. Some background history is presented in chapter 2 of the PGE handbook, brought up to date in some chapters of this book. In this connection the relation of the PGE/ ERAD/ ECP approach with the "capture/ tag/ recapture" (C-TR) techniques may be noted. What of the future? In the main, progress can be expected because of increasing disillusionment with unsatisfactory types of surveys. Presumably more and more countries will use the one method that, when properly conducted, gives a built-in estimate of omissions. Another possible development is in the direction of estimating the denominator of vital rates through dual collection of data on all persons at risk that should be entering the denominator. A suggestion to that effect has been made by Deming and Keyfitz, 1965. Their suggestion can be adapted to an enumeration of nomads. Nomads are usually enumerated through administrative efforts of "getting at them" (e.g. Brenez, 1971). A cross of the C-T-R technique and what was to become the Deming-Keyfitz suggestion has been used to enumerate the nomads of Sudan (Krotki, 1955). Our own chapter 10 elaborates the possibility of making the traditional PES (post-enumeration survey) less dependent on the original survey through adopting PGE/ ERAD/ ECP features. The field is wide and the possibilities are many, but the greatest and most immediate benefit is likely to accrue through the pursuits of orthodox — dare one say so of 48

Role of PGEI ERA D/ ECP surveys

1.11

this still new to some — technique, following the principles explained in the PGE handbook and brought up to date in the present volume.

Discussion by Lee L. Bean

Faced with the problem of generating or evaluating valid and reliable demographic information, administrators and researchers are faced with the problem of selecting from among various methodologies. The distinction between generating and evaluating data is an important one because various discrete methods of research, often in combination with others, are used for the same process. Whether particularly methodological elements in various combinations, however, produce equally acceptable results for generation and evaluation is an important issue. PGE/ ERAD/ ECP utilizes, in part, techniques which have been standard for years in the evaluation of demographic data. The concept of matching records from two sources—both independent and correlated (such as cohorts in successive censuses adjusted for mortality and migration) is central to much demographic analysis as A.J. Jaffe(1951: 85) has argued on the basis of the "principle of comparison". PGE/ERAD/ ECP, thus, builds upon well-established demographic methods which are widely accepted. Why then must one begin a volume of this type with a defence of the "role of PGE/ ERAD/ ECP surveys relative to other endeavours to secure more and improved demographic data",—the title of Krotki's chapter? Obviously because the PGE/ ERAD/ ECP method has yet to be accepted as the appropriate alternative to other methods. Krotki deals at some length with various alternative methods, particularly single round and multiround surveys, but the chapter provides much more than simply an evaluation of PGE/ ERAD/ ECP relative to other "endeavours to secure more and improved demographic data". There are discussions of ideal models of PGE systems, what one can do to maximize the "pay-off, and how one might destroy this fragile creature. The reader is provided with a concise, coherent treatment of PGE/ ERAD/ ECP, but not so systematically that one is able to weigh the evidence related to all issues that an administrator or a demographer may wish to consider in selecting PGE or some other method. Indeed, by focusing on the "closest competitors" to PGE/ ER AD/ ECP—single and multiround surveys—some important questions are ignored. The chapter is seemingly based upon an important assumption. That is, PGE/ ERAD/ ECP (and other survey methods) are an alternative to a fullblown, accurate vital statistics system.21 Should it be? Particularly if one is concerned with the development of demographic data in the Third World, that assumption is worth some reflection. At the time the PGE program in Pakistan was being discussed at the beginning of the 1960s, many demographers, including several associated with the Pakistan PGE project, argued that PGE was the right method at the right time because of the immediate need for demographic data to stimulate population policy and to provide a system by which family planning programs could be evaluated as they would begin to force down birth rates. The rationale for the adoption of PGE reflected an element of expediency: the data were needed then and in the short run; developing a vital statistics system which would generate accurate statistics would take at least 20 years. In spite of the fact that Pakistan operated a most efficient PGE system, Pakistan lacks a vital statistics system, current demographic data, and a system to generate data. One wonders, 15 years later, whether one should not take the long view. If one had said invest all available resources in developing an efficient vital statistics system, would we now be five years away from having such a system in Pakistan instead of being at least, still, 20 years away from such a state?22

49

Discussion

Lee L. Bean

Perhaps there were not enough resources available in Pakistan in the 1960s to begin a comprehensive vital registration system, but what resources are required for such a program relative to PGE/ ERAD/ ECP? Indeed another important element not covered in Krotki's discussion is the question of resource utilization. I mean not solely costs (which Krotki treats, noting we need more information) but also human resources. Given that the question of accuracy of the data may clearly override some cost and manpower considerations, particularly evident in the comparison of single round and PGE/ ERAD/ ECP systems, for long-term planning purposes one needs to know what types of skills and how many individuals will be required for one program versus another. Ignoring that particular question, I submit, is largely responsible for the breakdown of the elegantly designed Algerian ERAD experiment. In most developing countries the lack of trained manpower is critical, and how does PGE/ ERAD/ ECP stack up relative to developing a vital registration system, using single round or multiround surveys? We don't know. Demographic data which refer to one point in time are almost completely useless. The strength and importance of a full-blown vital statistics system (or the continuous registration system of selected European countries) is its continuity. Certainly that continuity can be achieved by other systems. A PGE/ ERAD/ ECP system which remains in operation, using exactly the same techniques, over a series of years would constitute an important and reasonable alternative to a vital registration system. In evaluating PGE/ ERAD/ ECP relative to other systems, what is its record of continuity? That issue is not treated systematically by Krotki, but there is some evidence. Using the more generous definition of what has constituted a PGE system (see table 1.1) 26 PGE studies covered one year,23 seven covered two years, three ran for three years and only one was operated for as long as five years. We do not have comparative data for competitive systems, but the evidence suggests lack of continuous support for PGE/ ERAD/ ECP and unless one can generate such support, is it worth the manpower, money, and effort to mount a PGE/ ERAD/ ECP exercise? There are many factors which one must consider in determining the selection of PGE/ ERAD/ ECP relative to other methods if one is interested in securing more and improved demographic methods, and Krotki does deal efficiently and directly with many of these issues: the benefits in terms of accuracy and efficiency through use of independent systems and matching problems of determining cluster size and so on. Often, however, these arguments are presented in such a fashion as to reflect the continuation of an intellectual debate between Kr6tki and certain other statisticians and demographers.24 And it appears that such arguments may ignore more important issues and may actually result not in progress but rather in retrogression in the generation of demographic data in the developing countries which continue to face the problem of poor quality demographic data. The important questions are not size of cluster or two versus three rounds per year, but can PGE or any other survey method receive such a degree of commitment from a government that it will support—providing the resources in terms of manpower first, and then money—such a system for not one or two years, but rather five, 10 or 15 years and do so without changing elements of the methods so often that observed changes cannot be attributed to nonmethodological factors? Is PGE/ ERAD/ ECP worth doing for five, 10 or 15 years, or should the limited manpower and financial resources be devoted to developing more classical systems? Those are some of the questions which I believe remain to be answered as one attempts to fully assess the "role of PGE/ ERAD/ ECP surveys among the endeavours to secure more and improved demographic data".

50

Role of PG El ERA Dj ECP surveys

Endnotes

Endnotes to Chapter 1 1. Among health records, data on epidemics are worth mentioning because of their historical importance, at least for the time being. When used for demographic purposes they seldom give good results, because of uncertain completeness, sometimes even uncertain coverage. 2. Under exceptional circumstances, here and there, even single round surveys will report what appear to be reliable, high quality data on small areas consistent with commonsense (Goldberg and Adlakha, 1968); death reports in the example quoted. 3. With this evidence accumulated over the years, the United Nations, the International Union for the Scientific Study of Population, and the International Statistical Institute decided to base the World Fertility Survey (WFS) on single round surveys. There are, of course, also other purposes in front of the WFS than measuring birth rates and the high mobilization of talent in the WFS headquarters will presumably justify this flying in the face of world opinion and evidence. If not, then the world might obtain intricate answers to sophisticated questions on fertility and reproductive practices and attitudes, but still not know how much of its population is being born and how much is dying. 4. Arbitrary adjustments have now been with us for a long time and are likely to remain if the stream of data flowing from the World Fertility Survey conforms to the experience with single round surveys in the collection of vital rates. (That is, without prejudice to the other more sophisticated ratio measures at which the WFS is aiming.) 5. This error statement abstracts from other sources of error such as interviewers' mistakes in writing down dates, especially soon after the beginning of a new calendar year, errors in transcribing dates between different types of calendar, punching errors, coding errors, and a host of others. For the sake of brevity, the need to refer repeatedly to these ceteris paribus conditions is largely ignored in this chapter. 6. A "reform" has been proposed for the structure numbering required as addresses for PGE/ ERAD/ ECP surveys. These numbers are, it must be repeated, addresses or structures, not codes for housholds. The reform suggests that not only structures should be listed, but also households and individual persons (Scott, 1973: 412). In this manner the original sin of the household change technique would become an acquired sin of the PGE/ ERAD/ ECP. The "reform" would also assist in institutionalizing the Tunisian error described in l.S.c iii. 7. For an example of an arbitrary correction in Cambodia on the basis of what the figures "should" be, see Kannisto, 1973: 397. Even after the correction, four out of 14 provinces were found to show a fertility "too low". They were further upped. For Indonesia the crude death rates had to be similarly and arbitrarily, though "cautiously" doctored. The birth rates were beyond repair and had to be estimated from age distributions (ibid., 400). It is curious to note that both in Cambodia and Indonesia the deaths caused less trouble, that is less under-reporting, than births. It could be that the anthropology of these two countries is different from the rest of the world; or that there were some peculiar features in the two surveys. 8. The allegedly over-reported birth rates are below long term estimates derived from a painstaking analysis of three consecutive censuses (Krotki and Beaujot, 1975). 9. In Pakistan a match has been attempted between the households as reported during the last or fourth round of a series of survey rounds and the first of the next series of four rounds. With the resources available, and they were considerable, this proved an impossible task. The matching task was just too great. 10. Matching in the Pakistan PGE has been carried out between the documents collected by the continuous recorders and the documents of one of the four surveys. 11. Algebraically, equations (1.9) and (1.10) look like simple inversions and as such 51

Endnotes

Karol J. Krdtki

hardly deserve being written out fully. Also, in PGE/ ERAD/ ECP surveys with two way matching (see: Glossary) either formula will do. However, it is worthwhile to write out both of them because in one way matching(see: Glossary) only one of the formulae is operational. 12. It is less certain what is the correct PGE/ ERAD/ ECP attitude in this regard when it comes to using PGE/ ERAD/ ECP techniques to evaluate national censuses in the manner proposed in our chapter 10. 13. We offer a discussion of subsampling in section 2.2.a. For additional reviews of the subject see Fellegi, 1974: 15,23,24 and Markset a/., 1974: 388-400. 14. At a Paris seminar, when all sorts of outlandish suggestions had been made which disregarded the need to preserve the essential features of a PGE exercise, the possibility was advanced that three prestigious government agencies should appoint themselves a court that would grant the ERAD franchise only to proposals that met minimum ERAD requirements (Krotki, 1972). 15. Subsampling is dealt with again in section 1.10 in connection with costing. Briefly, instead of including the whole of each sample area in both procedures, only a proportion (say, a third) are included in one of the procedures, but all the area in the other procedure. This will pay if the cost of carrying out the work under one procedure is markedly higher than under the other procedure and provided that savings are possible in the former procedure, though this will seldom occur to the full extent of the cut in proportion. 16. The possibility of using two household surveys as the two procedures for a PGE/ ERAD/ ECP system is indicated towards the end of section 1.4 and in subsection l.Sb.iii. 17. The two rows for Morocco 1972-73 (macro and micro) in table 1.5 seem to provide some evidence consistent with this observation. When watched individually, the field workers give field costs about similar to those reported from Pakistan. However, when the actual and total expenditure is considered then they almost double for the same unit of output. 18. Presumably, all these initial overheads were charged to one year. For a different allocation of the initial costs see section 7.4. 19. It should be noted that the PGE handbook came out rather unfavourably disposed towards the idea of subsampling (Marks et a/., 1974: 338-399). Nevertheless, the matter is not yet closed. 20. The many blanks and the wide variations in the cost ratio shown in column (11) of table 1.3 reinforce the need for more data, if practising statisticians are to suggest to demographers realistically optimum designs. Furthermore, it will be noted that the empirical intraclass correlation available to us was lower than the lowest suggested schematically in an overview of African samples (Scott, 1968: table 2) and the empirical cost ratio available to us was higher than the highest in the same overview. Both considerations move the optimum cluster size away from the alleged 300 in Africa towards our 1,000 and above it. And, the discussion has not yet taken into account the nonsampling components of the total error as defined by the mean square error. 21. Here I am assuming that only the matching of two independent operational systems — census and vital statistics, for example — and the use of estimation techniques as outlined by Krotki do not constitute a PGE/ ERAD/ ECP system. 22. The discussant made a notable contribution to numerous attempts to evaluate the quality of Pakistan demographic data (e.g. Bean, 1974). [Editor's note.] 23.1 am assuming dates such as 1966-67 refer to fiscal years and have therefore counted these as one year. 24.1 personally find that the personalized references, such as referring to Christopher Scott as the "high priest of the household change technique" detract from the argument. 52

Chapter 2 The State of the Art in Dual Systems for Measuring Population Change H. Bradley Wells and Daniel G. Horvitz 2.1 Introduction During the 1960s, major national trials of different dual collection designs have been carried out in Pakistan, India, Thailand, Turkey, Liberia, (Wells, 1971; Marks et al., 1974) and the Philippines (Philippines, 1973). The largest of these, the Indian Sample Registration System, was started with pilot studies in 1963 and is now firmly established as the major source of current vital statistics data for the country (India, 1972). The original Pakistani, Thai, and Turkish systems have been deactivated but plans are being made to establish new systems in both Pakistan and Turkey. The Liberian system has been in operation since 1969. The Philippines system (not to be confused with the Mindanao Center for Population Studies) is the newest and is in the third year of operation. Morocco is planning to expand its current program to a national system. These national systems were developed in an effort to meet demands of social and economic planners for basic population data, especially birth, death, and growth rates. Some have succeeded to a large extent in meeting those needs — some have failed, for various reasons. All have encountered difficulties both administrative and technical. Many of the difficulties were of the type that occur in the implementation of any new statistical program. Other problems were due to the need for co-ordinating the two procedures so that the collection of records, processing, and matching could be done with acceptable levels of accuracy. Considerable effort in these ongoing programs is devoted to methods research in dual collection systems. Many other studies utilizing the dual collection system approach have been carried out for areas smaller than a country. These include the experimental field trials conducted in Colombia, Kenya, Morocco, and Northern Mindanao by collaborating institutions in the International Program of Laboratories for Population Statistics (POPLAB) under the direction of Dr. Forrest E. Linder at the University of North Carolina. Much more research is still being done in single than in dual system methodology, but a great deal of that is also pertinent to dual systems. Detailed reviews of many of the single system studies, as well as all of the country systems and early historical developments of dual collection systems, may be found elsewhere(Mauldin, 1966; Wells, 1971; Marks etal., 1974). Our aim in this chapter is to review systematically some of the major methodological issues in the design and management of dual collection systems and attempt to describe procedures for making rule of thumb decisions. Because of space limitations the amount of detail will necessarily be restricted. We make no claim that the ideas and 53

2. /

H. Bradley Wells and Daniel G. Horvitz

recommendations are new, indeed most of them have been described and advocated by others. In particular, for a much more detailed and comprehensive discussion of the problems and alternatives in designing dual systems the Population Council Handbook for Population Growth Estimation Studies (PGE handbook) by Eli Marks, William Seltzer, and Karol Krotki (1974) is highly recommended. Dual collection systems are without question more complex to design and administer than two single systems but their accuracy in terms of mean square error may more than offset the added cost in well executed dual systems. Unlike a single system, a dual system includes nonsampling error detection and correction procedures as an integral component and this is the unique feature that distinguishes the dual system and makes it potentially more cost effective than most single systems. Thus the dual system is a logical extension of the usual sample survey model in that it includes measurement of an adjustment for nonsampling as well as sampling error components. In spite of the general conclusion that dual systems are more efficient, in the statistical sense, there is a great need for detailed data about design parameters and cultural variations in order to develop optimal or nearly optimal design in given situations. We will largely limit our considerations to the three essential components of the dual collection system: (i) a continuous recording procedure; (ii) a periodic survey procedure; and (iii) procedures for matching of records from the two sources. Some sample design questions will be discussed first. We assume that the sampling frame will consist of clusters of households located in geographic areas with identifiable boundaries.

2.2 Sample design 2.2.a Some general sampling considerations A major advantage of probability samples is that the data collected can be used to assess the magnitude of the sampling error in estimates of population means and totals derived from the same data. The usual formulae for computing the error variance for complex sample designs, when measurement errors and other nonsampling errors are also present in the data, will include their contribution to the total error of estimates, provided these measurement errors are uncorrelated and have expectation zero. In this situation no special modification to the sample design is necessary. Steps should be taken, of course, to reduce the added component of variance due to the nonsampling errors if that component seriously affects the total error. This may be accomplished by improving the measurement process with tighter statisticial control, or by merely increasing the sample size. This not too unhappy circumstance does not obtain when the errors of measurement are correlated, in which case the usual variance formulae are biased and increasing the sample size will not significantly reduce the contribution of this component to the total error variance. Finally, if the measurements on all observation units in the sample are subject to an unknown systematic error component or bias, then estimates computed from the sample will be subject to this same bias. There is little doubt that sample household surveys designed to measure vital rates suffer from measurement errors which are correlated and which contain systematic components. Since these errors and biases, in fact, seriously affect the accuracy of vital rates estimates, it is essential that surveys concerned with demographic measurement be so designed that a proper balance is achieved between the magnitude of the sampling and nonsampling error components of the total error of estimate (measured by the mean square error). Dual data collection systems for measuring population change offer not only an excellent opportunity to accomplish a significant increase in the 54

State of the art

2.2. a

accuracy of estimates of vital events, but also to achieve this more efficiently through appropriate allocation of resources (Marks, 1971). 2.2. b The need for realistic parameters When dual collection systems for collecting data on vital events were first introduced, there was but limited knowledge concerning the most appropriate choices to make among the large number of design parameters under the control of the investigator. Information of specific value in judging or assessing the relative efficiency of alternative dual system data collection procedures was just not available. For example, completeness rates for active registration with local recorders or for quarterly household surveys versus annual surveys were unknown. And there was little if any accumulation of data on variances, covariances, intracluster correlations, biases (e.g. due to reporting of out-of-scope events, temporal or geographic), costs and other indices essential to a cost effective evaluation of alternative dual collection systems. Although still far from ideal, the situation is much improved today to the point that serious consideration can be given to choosing parameters which will tend to optimize a dual collection system, in the sense of minimizing the total error of estimated vital events or vital rates for a given data collection budget. It should be recognized, of course, that the optimal design for estimating total births will not necessarily be optimal for estimating the birth rate or any other measures such as total deaths or death rates. Some guidance in the choice of more efficient designs has been provided by Marks (1971) and Marks et al. (1974), with initial emphasis on the number of sample clusters or subclusters to select for each procedure which will minimize the relvariance of the dual system estimate of the adjusted number of births (or deaths) for a given cost with a simple random sample of clusters. The design parameters to be specified are: ki = the number of sample clusters to select for continuous recording; k2 = the number of sample clusters to select for periodic surveys; the k2 clusters are either identical to or a subsample of the ki clusters, i.e., fc^k,;1

H = the size of the sample clusters in terms of the number of subclusters of households for continuous recording; h = the number of sample subclusters to select at random in each cluster for the periodic surveys, i.e., h ^ H. The usual dual collection system for estimating the number of births (or number of deaths) will have k2 = ki and h = H = 1. These are not necessarily the optimum design choices. Under the assumptions (i) that the intraclass correlation within clusters is the same for Ni, N2 and M (as defined in Marks et al. Chapter 2), (ii) that the match rate for each procedure is independent of the number of events reported by that procedure, (iii) that the number of vital events occurring in a cluster per unit of time is a Poisson variate, and (iv) that the two procedures are in fact independent, Marks (1971) shows (for h = H) that the optimum subsampling rate for k2 is given by: where P1 and P2 are the probabilities that the vital events of interest will be reported by the respective procedures, CR and Cs are the respective variable costs per sample subcluster and the total variable cost is C = CakiH + Csk2h. If Pi = P2 = -7, selecting a subsample of the ki sample clusters for coverage by the periodic survey would only be more desirable than surveying all ki if Cs were somewhat greater than CR. For P\ > P2 > .8, it still might be advisable to select a subsample of the ki clusters for the periodic survey even if CR = Cs. 55

2.2.b

H. Bradley Wells and Daniel G. Horvitz

The optimum subsampling rate f = h/ H (within clusters) for the periodic survey is also given by the right side of equation (2.1) above, under the additional assumptions that k2 = ki, that full-time resident recorders must be used with the continuous recording procedure in order to reduce costs and to maintain better statistical control, and that the intracluster correlation is zero. The effect of a positive intracluster correlation is to reduce the optimum within cluster subsampling rate for the periodic surveys. For PI = P2 = .7, equation (2.1) suggests that within cluster subsampling would be desirable if Cs is somewhat larger than CR (when k2 = ki). The gain in precision brought about by subsampling within clusters and using the savings to increase the number of clusters should be weighed against the added design complexity. The above results, while providing some guidance, are still restricted to particular parameter combinations (i.e., h = H in the first instance and k2 = ki in the second) and therefore yield only locally optimum designs. For countries or cultures for which estimates of the variances and covariances for Ni, N2 and M for one or more cluster sizes are available, and for which an appropriate cost function and reasonably accurate variable cost coefficients are known, unconditional solutions for the optimum combination of the design parameters ki, k2, h and H should be computed. Other considerations enter into the choice of cluster size than merely that value of H which, together with appropriate choices of ki, k2 and h minimizes the relvariance of the estimated number of births (or the estimated birth rate) for a given survey budget. The cluster size must be such that boundaries for the area containing the cluster can be specified and easily identified in the field. As H decreases, the boundary identification problem increases. This can lead to the inclusion of events which do not belong to sample clusters and to the exclusion of events which do belong. Also migration or local moves can become a significant factor for small clusters. Further, the variation in the adjusted number of events n may be somewhat greater for small clusters since the number matched M, might then be too small for stable estimates of N resulting in a larger ratio bias. Thus, dual collection systems for estimating vital events and vital rates require somewhat larger cluster sizes than would ordinarily be appropriate in household surveys. 2.2.c Rotation designs An important objective in most national vital event dual collection systems is to be able to detect changes in fertility and mortality, as well as to estimate their magnitude accurately. If an estimate of change from the preceding year were the only objective, then the same sample of clusters should be used for both years. If an estimate of average level for each of the two years were the only objective, then a fresh sample of clusters should be selected for the second year. Since there is interest in both change and level, a rotation sample in which some clusters are retained and other clusters are dropped each year would be most appropriate. The argument for some rotation of sample clusters is strengthened further by the need to minimize respondent conditioning effects and respondent fatigue, both of which can lead to unknown biases of response (Marks et al., 1974,396 and 397). 2.2.d Some aids to improved estimation Despite a sound sample design and appropriate field procedures with adequate controls for quality, the dual system estimate of the number of vital events may still be subject to unknown biases. Correlation bias occurs when the two procedures are not operating independently. Completeness bias occurs when vital events are included or 56

State of the art

2.2.d

excluded erroneously in either or both procedures due to errors in reporting the time of the event or the geographic location of the event. When completeness of reporting is decidedly different for subgroups of the population for both procedures, correlation bias will result. This can be reduced by dividing the sample into appropriate groups (post-stratification), such as by age of mother or type of event (i.e. infant death and non-infant death) and estimating the number of events separately for each group. This procedure will reduce the correlation bias provided that each group is homogeneous with respect to completeness of reporting. Care should be taken that the groups are not so small as to increase the ratio bias substantially (Chandrasekaran and Deming, 1949). Completeness bias can be reduced in a similar fashion, that is by grouping the population or the events into homogeneous strata with respect to the probability of out-of-scope errors, preparing separate estimates for each group, and then combining the group estimates. For example, to adjust for boundary errors, events reported for households in areas on or near the boundaries of the cluster, or events reported in the first and last months of the reference period can be classified into a single stratum for events with a "high probability of out-of-scope error" and the remaining events into a second stratum. The usual matching and adjusted estimate can be computed for the latter stratum. The estimate for the first stratum would not be based on matching, but rather on an average of the events observed by the two procedures. Rules for classifying out-of-scope events are necessary, such that the number included in the first stratum balances (approximately) the estimated number of in-scope omissions (Marks et a/., 1974). Completeness bias may be introduced by migration. The continuous recording procedure may miss births which occurred to in-migrants prior to moving to the sample cluster, but during the survey period. The periodic survey may pick up such births, but miss births to out-migrants that the continuous recording picked up. In order to obtain an improved estimate, the sample population is divided into two groups. Those households which resided in a sample cluster for the entire period are placed in the first group. All migrant households are placed in the second stratum. Again, the usual dual system estimate n is computed for the first stratum. Births (Nn) for the households that moved out of the cluster can be estimated by multiplying the number reported by the reciprocal of the completeness rate for the periodic survey for the non-migrant households (i.e. N2/ M). Births (N22) for the households that moved into the cluster can be estimated by multiplying the number reported by the reciprocal of the completeness rate for the continuous recording procedure for the non-migrant households (i.e. Ni/M). The average of these latter two estimates for the migrant households is used for the second stratum estimate.

2.3 The data collection elements of a dual collection system The first three essential data collection elements of a dual collection system are: 2,3.a The essential elements of a dual collection system i. A (continuous) recording procedure. This is the first source for recording births and deaths and it may be an existing record source such as civil registration. More commonly it is a special procedure somewhat different in nature from either the civil registration system or the usual sample survey. ii. A (periodic) survey procedure. This almost always is designed specifically as the second source of data to be matched with the recordingprocedure. This may be a single

57

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H. Bradley Wells and Daniel G. Horvitz

visit survey but more often it will be a longitudinal periodic (multiple visit) household survey. iii. Procedures for the matching of recording and survey events. These will include designs for record flow, data processing, and matching of records from both procedures as well as procedures for field recheck or verification of unmatched and doubtfully matched events. The dual system of data collection for measuring births and deaths is much more complex than the simple sum of the complexities due to two single procedures producing the same reports. It requires co-ordinating the design, definitions, training of field and office staff, scheduling of field work, and at the same time maintaining as much independence as is practicable between the two procedures. In designing data collection procedures for each of the procedures, a number of basic questions must be answered bearing in mind the objectives and the cost factors in relation to the precision required. These include questions concerning the content of event records and interview schedules; the wording of items; the field procedures, including frequency of visits to informants or households; the use of full-time versus part-time staff (part-time continuous or full-time intermittent employment); staff qualifications in terms of education and experience; residency of the field staff (local or non-local residents); training and supervisory procedures; and the flow of records and reports. Clearly the answers to these questions are interrelated. They are also related to sample design factors including cluster size, subsampling, and whether the sample is fixed or rotating, and to the levels of literacy of the survey population, and to the availability of qualified persons to staff the system at all levels. Whether or not subsampling is used, a relatively fool-proof field identification system is required as a fourth essential element in a dual collection system. iv. Field identification procedures. These are necessary in order that the sample units can be consistently and unambiguously located by field workers of either procedure. In the event that only a single survey is to be conducted for identifying events to be matched with a recording procedure that already exists (for example, measuring the completeness of civil registration), the field identification procedure must be capable of correctly assigning records from either procedure to the same (small) geographic areas in the matching process. Field identification procedures are crucial in minimizing the biases that can result if area boundaries of the two procedures do not correspond. Even when a good field identification system has been developed there will be errors in using it. See Cooke (1971) for a general description and Madigan et al. (1974) for a specific illustration of approaches to the field identification system. 2.3.b The continuous recording procedure The major objective of a recording procedure is to obtain as complete a list as possible of births and deaths in the sample population. Recording procedures can encompass a wide range but may generally be classified into four groups based upon the combination of legal status and effort required of field staff as depicted in figure 2.1. Most civil registration systems fall into group i. Examples of dual collection efforts related to this are the U.S. birth registration tests of 1940,1950, and 1968; Thailand, 1964-66; Singur 1946-47; and Vaso Town 1966-68 (Marks et al., 1974). We are not aware of any recording procedures in group ii nor of purely group iii procedures. Dual systems in which active efforts by field staff to supplement the usual passive civil registration are relatively few but are illustrated by the Peruvian effort (Cavanaugh, 1963) and a large national system now operated in the Philippines by the Bureau of Census and Statistics.2 Such efforts are a combination of i and iii. 58

State of the art

2.3.b

Figure 2.1 The four types of registration procedure Effort of Field staff Passive Active

Legal status Civil registration Special registration i iii

ii iv

Most recording procedures, including the current Indian system and the early Pakistan and Turkish efforts, fall into group iv. The dual collection systems being tested by POPLAB use group iv recording procedures. There are two important variations in the activities followed in recording procedures of group iv. These two recording variations can also be used together, resulting in three types ranked in terms of the intensity of recording contact with households: i. Informant or "routine round contact" procedure (contact household only if vital event is reported). Pakistan and early Indian experience were based upon this method. ii. Periodic household visits (whether or not vital event is reported). The early Turkish and the Liberian efforts were of this type. iii. Combination of i and ii. The POPLABs at Xavier University in Mindanao and Kenya are experimenting with this approach and India is now using it in some states. The recording procedure based on routine round (RR) contact must at a minimum include the following four activities by the recorder designed specifically to minimize household visits: i. Setting up a group of local persons (routine round contacts) who are expected by virtue of their professional or social status to be aware of vital events occurring in the sample area and who are willing to report them to the recorder. ii. Visiting the RR contacts on a regular basis (weekly or bi-weekly) and asking about families which experienced vital events. iii. Visiting those families for which events are reported and completing a detailed vital event report for each event. iv. Transmitting individual vital event reports to headquarters. In addition the recorder might optionally be required to maintain a special register of vital events, update a household listing,3 and up-date maps periodically. The recording procedure based upon repeated household visits is, in effect, a periodic survey since every household is supposed to be contacted at intervals, whether or not they have had a vital event. The household visit approach requires that the recorder, at a minimum: (i) visit each household at specified intervals and inquire directly about whether any vital events have occurred; (ii) complete a vital event report for each reported event; (iii) transmit the reports to headquarters. In addition the recorder may, as in the informant system, be required to maintain a register of vital events, and up-date household listings, maps, dwelling lists, and the numbering system. The recorder may also be required to report migrations, for example, as in Turkey and Liberia. In India, after the same sample units had been covered for a number of years, estimated completeness rates for the informant-based recording procedure began to decline. Recorders are now required to conduct quarterly household visits in addition to their usual visits to informants (India, 1972).

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Preliminary results from part of a rather complicated experiment done in the Colombian POPLAB (table 2.1) show higher recording completeness rates in both rural and urban samples for household visits than for the informant system. Overall birth rates are also higher where the recording procedure used household visits. This suggests a lack of independence between the recording and survey procedures. The results are difficult to interpret since survey completeness was better than recording completeness when household visits were used in the first period, but poorer than recording completeness when household visits were used in the second period. There was an overall decline in survey completeness in the second period which was expected, since two three-month surveys were used in period I and one six-month survey in period II. On the other hand overall recording completeness increased in the second period. Taken at face value these preliminary Colombian results are disturbing because the estimated birth rates vary so greatly with the different factors and combination of factors. It is possible that unknown correlations may be responsible for the observed differences. If this is borne out in the more detailed analyses now underway it would suggest that more intensive efforts are required to develop data collection and estimation techniques appropriate for quasi-independent procedures rather than continuing to use the independence assumption.

Table 2.1 Estimated completeness rates and crude birth rates by area, periods under different recorder operations, switch-back trial*, Colombia, 1971-72.

Area and procedure

Sequence of recorder activities and period Household visits Period I, Informants Period I, informants Period II household visits Period II Period Period I II Change I II Change Completeness rates (percent)

Rural area Recorder Survey Urban area Recorder Survey

81 86

88 68

+7 -18

68 73

90 65

+22 -8

76 82

77 60

+1

-22

62 70

87 70

+25 0

41 29

58 33

+ 17 +4

Crude birth rates per 1.000 Rural area Urban area

53 28

42 25

-11 -3

* At the end of Period I recorders in sample areas where monthly household visits had been used were trained to use the informant system in Period II and vice versa for the other half of the sample areas. Note: Period I is 1 October, 1971 - 31 March, 1972; Period II is 1 April, 1972 - 30 September, 1972. Source: Adapted from data in table 4 shown by permission of Departmento Administrative National de Estadistica in Myers and Lingner (1973). 60

State of the art

2.3.c

2.3.c The household survey procedure Experience with survey techniques and procedures for measuring population phenomena is much more widespread and well known than experience with the recording procedure. There are, however, a much wider variety of survey options which can be used as a component in a dual collection system. The first objective of the survey procedure is to obtain reports of a high proportion of the vital events which occurred in the sample during a time period which overlaps completely with that of the recording procedure. Except in instances where the population base for vital rates is obtained from an outside source, such as a census, the second objective of the survey is to provide the population base. When the household survey is repeated periodically, a third objective can be to collect substantive data of special interest and this content may be varied from time to time.4 A major feature of any survey design is the frequency of interview. This can be crucial in a periodic multiround survey. On the one hand frequent interviewing may cause respondent conditioning and/ or fatigue. On the other hand, interviews spaced too far apart may result in many survey households being lost because of migration and in under-reporting due to recall lapse about events of interest. A dual collection system requires a minimum of one survey to collect vital event reports for the same period prior to interview for which events were covered by the recording procedure. Theoretically there is no limit to the maximum frequency of survey interview, but the practical constraints of costs and respondent fatigue force limits to be set. The optimum survey frequency is not known, either for dual collection systems or for single surveys. Furthermore, what is optimal for one country may be less than optimal in another. The most popular survey frequency in continuing dual collection studies has been six months, although Pakistan and Thailand used three-month intervals. Experimental testing of three, six and 12 month survey frequencies with nonoverlapping recall periods has been carried out in the Colombia POPLAB. Preliminary results are shown in table 2.2. Three-month frequencies were investigated only in Santander. With the exception of period II survey results for births in Santander (lines d and e) the results support the conclusion that survey coverage is more complete for more frequent visits; two three-month surveys are more complete than one six-month survey, and similarly two six-month surveys are more complete than one twelve-month survey. Differences are more marked for deaths than for births. Also the estimated completeness rates in Santander increased rather markedly from period I to period II, perhaps due to better training and practice or to increasing dependence between procedures or to a combination of these. It is also possible that the frequency of survey results have been confounded with other factors in the design (see table 2.1 and the discussion in section 2.3.b). The effect of using different frequencies with overlapping recall periods is being tested in India and in several other POPLABs. A closely related question is the length of the recall period for which respondents are asked to report vital events. A recall period which is longer than the interval between repeated interviews is called an overlapping period. In Pakistan interviews were conducted every three months but respondents at each interview were asked to report all events for the previous 12 months. Thus each event had four chances to be reported in the survey. In Turkey and Liberia interviews were done at six-month intervals, in January and July. The July interview used a non-overlapping recall period of only six months while the January interview used a recall period of 12 months, a sixmonth overlap.5 A major virtue of overlapping reference periods in a single system periodic multiround survey is that it minimizes the effects of time telescoping of events, provided 61

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2.3.c

Table 2.2 Estimated completeness rates for births and deaths by recording and survey procedures by period and frequency of survey, Santander and Bolivar, Colombia, 1971-73. Study period and dates

Number and frequency ofsurvey(s)

Births Recorder Survey

Births Recorder Survey

Santander Period I Oct. 1971 to March 1972 Period II April 1972 to March 1973

a) Two 3-month b) One 6-month

71 77

85 73

68 58

65 41

c) One 6-month, Oct. 1972 to March 1973 d) Two 6-month e) One 12-month

83

82

83

53

84 85

75 76

81 85

58 54

81 80

77 65

83 75

58 46

Bolivar Period II April 1972 to March 1973

f) Two 6-month g) One 12-month

Source: Data adapted from Colombia Departmento Administrativo National De Estadistica, 1973, "Primeros Resultados del Estudio ERED". Centro de Investigaciones en Metodos Estadisticos Para Demographia, Bogota, Junio 1973.

records from different rounds are matched and duplicates are eliminated. It is not clear that this virtue of a single system multiround survey will be desirable in a dual collection system. If it is used, the record keeping and matching operation within the survey itself increases in volume and quite likely in complexity. A compromise approach uses the overlapping recall period for the interview and then processes only those event records which are reported in the most recent nonoverlapping reference period of interest. This approach may improve time reporting and will minimize the number of reports for processing. Further research on the value of overlapping periods in a dual collection system is needed. Measurement bias is a major consideration in determining optimal survey frequency and length of recall periods. The manner in which recall lapse, telescoping errors, respondent fatigue, respondent conditioning, and the changing composition of the sample over time influence measurement errors, has not been systematically studied in dual collection systems, nor indeed in single systems, for measuring population change. As indicated by Marks el al. (1974) the range of choices for survey procedure designs depends so directly upon the recording procedure that it is unwise to make recommendations without considering a fairly wide range of feasible alternatives. If the objectives of the survey are to provide both birth and death events for matching and population data for the denominator, we would be inclined to recommend six-month survey intervals, provided the budget can support them.

62

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2.3.d

2.3.d Matching procedures The objective of the matching operation in a dual collection system is to yield minimum matching bias and matching variance as defined by Seltzer and Adlakha (1974), and in Marks et al. (1974). On the basis of experience to date Marks et al. (1974) recommend, and we agree, that matching be done by hand rather than machine or computer even in a large scale, country-wide dual collection system, especially in the developmental stages. It is also considered essential that matching procedures be developed specifically for the two field procedures as they actually operate in a given setting. A set of vital reports whose "true" match status is known is required to assess the value of using different characteristics in alternative matching rules. This is essentially a "boot-strap" operation as recommended by Marks et al. (1974) and summarized as follows by Madigan and Wells (1973). "Developing matching procedures for a new dual collection system involves a number of steps: i. Select or create a sample of 300-600 reports of births or deaths from each of the two procedures; these could come from a pretest or from the first stages of an actual collection program. The completed reports would of course have to contain the characteristics which are to be considered in developing the matching rules. Different characteristics will usually be required for deaths than for births. ii. Match the events from the two procedures as accurately and carefully as possible. At this stage all information on the reports, and knowledge of cultural characteristics, and interviewing procedures should all be utilized implicitly in arriving at decisions as to what constitutes a match. It is recommended that this be done independently by three junior or senior professionals. After the three have independently agreed on a match or a non-match these are considered as 'true or correct'. If only two of the three agree on a report then all are asked to reconsider. After reconsideration the remaining reports on which the three disagree as well as the non-matches are sent back to the field for verification or additional information.6 After the field check some outof-scope events may be eliminated and final decisions are made regarding the 'true' match status of the remaining reports thus creating the standard against which alternative matching rules can be judged. iii. Erroneous matches and non-matches for individual matching characteristics are then compared over the feasible range of tolerance limits by matching only on single characteristics. The sum of erroneous matches and erroneous non-matches is defined as the gross matching error and their difference is defined as the net matching error for a characteristic. iv. The data on gross and net matching error as an aid in choosing the characteristic set or subsets and the corresponding weight for each characteristic which will become the basis for the matching rules either explicit or implicit to be applied in the subsequent matching operation. There are usually an extremely large number of possible characteristic sets but a reasonably good explicit matching procedure can usually be developed by examination of the gross errors of individual characteristics. For an individual characteristic gross error shows the relative ability of a specific cutting point or tolerance limit to place an event in the correct class and tolerance limits should be chosen to minimize gross matching error for the characteristic. Net error, taking account of sign, indicates the direction of bias for the individual characteristic and therefore helps determine the relative weight which should be given to a match or nonmatch on that characteristic and vice versa for a variable which yields a high erroneous match rate". One approach to choosing a set of characteristics with minimum net matching error is to rank the individual characteristics (at chosen tolerance limits) from low to 63

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H. Bradley Wells and Daniel G. Horvitz

high in terms of erroneous matching error (reverse of discriminating power) and consider the first, the first two, and first three, etc. in combination and choose the set which minimizes net matching error for low gross matching error. Another approach is to assign different weights to the different characteristics so as to achieve the same goal. Weights may be based upon judgement and empirical evidence, i.e. the gross and net errors, and can be derived approximately without considering all possible characteristic sets. Alternatively, weights may be derived through statistical methods such as discriminant or cluster analysis, ideally by considering all combinations of characteristics and cutting points through computer analysis. Although the above procedures have been proposed, no application has yet been reported in which these procedures have been compared within the same study against alternative rules. Madigan and his co-workers are conducting such studies (Madigan and Wells, 1973). Myers and Lingner (1973) described the characteristics and tolerance limits being used for matching in the various POPLABs and there were few similarities other than the use of names of decedents and newborns and their parents. There is great need for studies in which results of such "approximate" rules are compared with "optimum" rules based upon consideration of all combinations of characteristics. 2.3.e Field identification procedures and other factors common to both collection procedures Several other factors which influence the design of interview, editing, and supervisory procedures are relevant. These all relate more or less directly to the content of one or both collection procedures. For convenience we include them in this section although most are discussed only briefly. Individual vital event reports in each procedure must, as a minimum, include sufficient detail to determine whether the event matches or corresponds to an event for the same time period in the other procedure. If the survey is repeated periodically the same basic detail would be required in each round to match within the survey and eliminate duplicate survey event reports. Elimination of duplicate survey events is especially critical when there are overlapping reference periods for the survey (Sabagh and Scott, 1967). Minimum essential items for event reports in any survey which is part of a dual Figure 2.2 Minimum questionnaire content for record keeping and matching operations Content

Survey only Household schedule

Survey and recorder Birth Death report report

Geographic identification Details on household members Births in report period Deaths in report period Place event occurred Particulars: infant /decedent Mother /father Fat her /wife

X X X X

X

64

X X

X

X X X X

X X X X

State of the art

2.3.e

collection system to provide reports of births and deaths and denominator data for estimation of vital rates are shown in figure 2.2. Abernathy and Lunde (1972) described the record content in dual collection systems in India, Pakistan, Turkey, and Liberia. Marks et al. (1974) include a detailed checklist of suggested items for inclusion and an indication of how useful each item is for the different purposes of matching, demographic analyses, and survey control. Decisions must be made at the outset regarding counting rules for the numerator events, birth or death, and for the denominator, total population or women exposed to risk. Two common ways of calculating vital rates are: (i) on the basis of residence (de jure} i.e. events to residents during the year divided by the number of persons residing in the area at midyear, and (ii) on the basis of occurrence (de facto) i.e. events which occur in the area during the year divided by the number of persons occupy ing (living in) the area at midyear. Usually the denominators for crude rates, the total populations at midyear are not very different for the two rates; however, for age specific rates or sex-age specific rates "residents" and "occupants" might differ more in some groups than others, depending upon migration rates and the definitions of migrants. Further, when vital events and population data are from civil registration and census (or projections of the census) respectively, the denominators often are identical in either case. Dual collection systems usually collect data for both numerator and denominator because they attempt to follow residents/ occupants in sample areas over time. Migration, changes in household composition, and travel outside the sample area for delivery of an infant or for hospitalization before death create special problems. Decisions must also be made on handling vital events which occur to inmates of institutions such as prisons, hotels, and long-term hospitals. The continuous recording procedure, especially if it relies upon RR contacts, is more likely than the periodic survey procedure to find and record events occurring to non-residents or visitors in the sample area. The periodic survey on the other hand is perhaps more likely to find events which occurred elsewhere to newcomers or to residents temporarily absent; it also is more likely to miss early infant deaths, or deaths which caused the breakup and migration of a family which has been resident in the area. The de facto approach was used in the Pakistan country system (Marks et al., 1974), Philippines dual collection system, and in the Moroccan POPLAB. India and the MCPS collect both de facto and dejure vital events but after matching and field verification,7 analysis is based upon dejure events. The Turkish Demographic Survey, the Liberian, the Colombian, Kenyan, and the proposed new Turkish systems use the dejure approach to counting vital events. Determination of "residence" classification for the population requires at a minimum that a question on "usual" residence be asked for each individual at the time of survey. It is possible to ask a whole series of additional questions to establish residence more accurately, such as split places of abode, student status, intent to reside here, and duration of stay here. It is recommended however that the simplest counting rules consistent with the usual statistical definitions of the country be used by both procedures. Both defacto or dejure approaches should yield the same result for a representative country-wide sample. In either case it is usually best to use other means to measure vital events occurring to the institutional population. In the pre-test phases of developing a system it would be wise to test procedures for collecting both de facto and dejure events and to develop and test matching and field reverification procedures which would assist in arriving at "the most probable" 65

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H. Bradley Wells and Daniel G. Horvitz

classification status of each questionable event. This would provide a basis for deciding whether analysis should be based upon a dejure or a de facto approach. Whatever approach is used the procedures and subject matter content must be designed to include questions in sufficient detail to permit residence classification of an event or a person. It should also minimize possible multiple counting of events for those who move within the sample area. Some POPLABs are collecting data on children ever born and children surviving, in addition to children born last year, so that estimates of fertility obtained by stable population or Brass estimation procedures (United Nations Population Studies 42) can be compared with dual collection estimates. Data on children ever born and children surviving can be obtained in a number of ways. As a minimum, for each woman (or ever married woman) age 15 years to some age beyond childbearing, two questions must be asked: (i) How many live births have you (she) had, and (ii) how many are still alive? At the other extreme, the data can be obtained by reconstructing a complete pregnancy history for each woman in the childbearing ages. The timing of each live birth from puberty onward should be asked for and the subsequent survival status of each live birth. As well, there should be an accounting for any long interlive birth intervals by probing for the use of contraceptives or foetal death. Because there may be differential levels of completeness in reporting births by sex, survival status, and whether the child is living in the home, it is sometimes recommended that three bits of data be collected separately by sex of offspring for each woman: children born alive and (i) living here; (ii) living elsewhere; (iii) now dead. Because of concern with reporting errors Madigan and Herrin(1973) also recorded whether or not the data on children ever born and children surviving were self or proxy reported. Some results are shown in figure 2.3.

Figure 2.3 Relative differences in average number of children ever born and proportion surviving for self and proxy reporters, ever married women, urban and rural areas, Mindanao Center for Population Studies, July 1972 66

State of the art

2.3.e

Selfreporting ever married women in the urban area reported higher average numbers of children ever born at every age than proxy reported women. The differences between self and proxy reporters were greatest between 20-29 years of age, somewhat lower under age 20, and decreased to roughly less than 10 percent at ages 40 and above. For rural women a similar age trend in differences in the average of children ever born was observed, but the relative differences between self and proxy reporters were quite a bit lower than the urban ratios at every age above 20 years. For rural women above age 40 there were no clear cut differences between self and proxy reporters. Ratios of the proportion of children surviving show much smaller differences between self and proxy reporters. Considered as a whole these ratios decline with age for both urban and rural women. At almost every age the ratio of self to proxy reports of the proportion surviving is lower for urban than rural women. Taken at face value it would appear that something more than simple proxy under-reporting of children born and children surviving may be responsible for such results. One can speculate that: i. Under-reporting is related to familial relationship and the degree of association of proxy reporters and the women for whom they report. These would be closer in the rural than urban areas. ii. Cultural factors, such as reluctance to report deaths, might also be related to the age of the respondent. Proxy respondents would tend to be older for young mothers and younger for old mothers; for example daughters might report more often for women over age 40. This might be a possible explanation of the decline with age in the reported survival rates. Further research into the possible effects of proxy versus selfreporting should be conducted because this obviously has potential for introducing bias into any survey regardless of the method of analysis used. Additional interesting preliminary results provided by Madiganef a/., (1973) from the Philippine POPLAB experience shown in figure 2.4 illustrate negative correlation. In almost every month, both for rural and urban areas, the completeness rates for one procedure increases while the rates for the other decreases. Baseline household listings were done in the summer of 1971 and the continuous recording procedure was started immediately thereafter. Retrospective surveys were conducted in January/ February 1972 with a recall period from time of interview to Christmas 1970, and again in July/August 1972 using essentially a non-overlapping recall period from date of interview to Christmas 1972. Hence events reported in the January/ February survey had a second chance of being reported again in the July/ August survey. In addition, the recorder or interviewer who first reported an event was paid a bonus. Recorders were instructed not to make calls in their area during the period when survey interviewers were in the field. Analysis and matching, however, were based upon the period 1 January - 30 June, 1972. Events reported as occurring outside of this period were excluded. The fall and rise in survey completeness and the rise and fall of recording completeness over the reference period suggests that the observed changes occur because of what happens near the end points of the reference period. Taking the estimated completeness rates at face value the survey pattern might well be due to a combination of double coverage in January and the recall lapse phenomenon. The low completeness levels for the recorder at the start and end of the period may be due to a combination of the incentive effect and time delays in reporting. Similar analyses in studies without incentives, for different interview frequencies, overlapping recall periods and for informant based recording procedures will help to throw light upon the influence of some of these factors. 67

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H. Bradley Wells and Daniel G. Horvitz

Figure 2.4 Estimated completeness rates by reported month of birth, recording and survey procedures, by area, Dual Record Study, Mindanao Center for Population Studies, JanuaryJune 1972

Innovative advances in single system survey methods for measuring population change have also been made in recent years. Procedures developed are useful also in dual collection systems for control of field work and processing records from the two procedures. Sabagh and Scott (1967) describe the results and limitations of the multiple round 1961-63 Moroccan survey. The matching and reconciliation procedures followed in that survey are recommended reading for anyone faced with the task of designing field and office procedures for matching and maintaining household and individual records for multiple-round periodic surveys, whether or not they are part of a dual collection system. Similar procedures are described for the Population Growth Survey in Liberia (Liberia, 1969). The longitudinal periodic survey and person-years of exposure accounting procedures for denominators developed by CELADE (Arretx and Somoza, 1965), and applied on a national scale in Honduras (1972), bear further investigation as an alternative or supplementary approach to the usual periodic survey component in dual collection systems. Further study, through analytical and simulation models, is needed to explore the magnitude of possible biases in various estimation procedures such as Brass, and other stable population procedures, and Chandrasekaran-Deming in the presence of different types of nonsampling errors such as age-misreporting, telescoping of vital events in time and space (location), memory lapse or biases in reporting of children born alive but now dead, and differential reporting by sex or other characteristics. 68

State of the art

2.4

2.4 Conclusion We have attempted to examine some of the inherent limitations as well as problems yet to be solved in the design of dual collection systems. It certainly was not a profound discussion. In all fairness we probably have devoted more effort to the strong or potentially strong features of dual collection system than we have to enumerating the difficulties. On balance we do feel that some form of the dual collection approach is essential to cope adequately with measurement errors in population surveys. Although concrete results are indeed sparse, the upsurge in the use of the method to obtain substantive demographic data, coupled with the increased interest in experimental testing of the method, would seem to indicate that the dual collection era is either here or is just around the corner. The dual collection system movement certainly appears to be growing in popularity very rapidly. Nevertheless, the state of the art probably should still be characterized as developing. In spite of our optimism about its potentials, we are very much aware of the practical difficulties in achieving the degree of technical and administrative control that is absolutely essential in operating a dual collection system. Other proponents of the dual collection are also well aware of these difficulties (Krotki, 1972, Marks et al., 1974). The basic question, for which there probably is a long list of possible answers, is: How good do the data have to be? It seems clear that dual collection systems are making significant contributions in helping to determine how good the data are. Discussion by Ivan P. Fellegi

The authors have to be congratulated for their bravery in agreeing to undertake a brief review of the "state of the art" relating to a topic as broad as dual collection systems. It is just recently that Marks, Seltzer, and Krotki have written a book of several hundred pages covering the same topic; and it is only recently that I, in commenting on that book, found myself writing well over 100 pages in discussion. The present discussion will be much shorter. I will start with some general comments on dual collection systems, prompted by the present paper but not exclusively related to it. At several places in the paper sweeping statements are made about the superiority of estimates derived from dual collection systems over those obtained from single source surveys. For example, the statement has been made, without qualification, that "while the variances may be greater for the PGE estimates the mean square error will be less". It is a fact [shown in Marks (1971) and Fellegi (1974)] that the variance of PGE estimates will be greater than the corresponding estimate derived from the survey alone. However, this result is derived without taking into account the fact that if the survey was conceived of as a "stand-alone" operation, rather than one part of a dual collection system, it would have available to it a significantly larger budget, it would be free of some significant design constraints (e.g. it could typically utilize considerably smaller clusters, leading to increased sampling efficiency), and thus a stand-alone survey at the same budget (rather than same sample size) as that of a corresponding PGE survey would probably have its sampling variance reduced by a factor of up to two or three. Of course, it would be subject to the well known biases of under-reporting. This discussion highlights some important points: i. One is not justified in assuming that under all circumstances the best strategy is to trade off the variance in favour of reducing the bias. This should be the result of a deliberate examination of the likely parameters of any given situation. If the budget is 69

Discussion

Ivan P. Fellegi

small, resulting in very small sample sizes, the improvement of the sampling variance may outweigh the potential reduction in bias. ii. Even where the overall strategy calls for the PGE approach, the estimates derived from the survey alone have a smaller sampling error. At the national level (or other large aggregation) the PGE estimate, because of its smaller bias, presumably has a smaller mean squared error (otherwise we should not have designed a dual collection system), so the PGE estimate would be preferred. As we pass to more detailed disaggregations, the variance will inevitably increase while the order of magnitude of the bias will remain more or less the same. There must be a cross-over point beyond which the variance begins to dominate the bias and therefore the survey estimate alone, or better still the average of survey and recorder estimates, is preferable to the PGE estimate. The argument is illustrated in figure 2.5 (assuming that the PGE estimate is unbiased): clearly for higher aggregates (to the right of the "cross-over point") the PGE estimate is to be preferred; for finer disaggregations the single source or average estimates are preferred. iii. The "best of both worlds" might prevail if we could use the single source estimate but reduce its bias through means other than the PGE estimate. It is not inconceivable that using a dual collection system, but using it differently from the usual PGE estimation, such an "ideal" could be approximated. What I have in mind is the use of the recording procedure as a direct quality control activity with feedback to the survey, rather than an independent operation. This would involve a careful analysis of the types of vital events uncovered by continuous recorders but missed by the survey interviewers, tightening the periodic survey operations accordingly, pointing out to survey interviewers the specific vital events they missed and analysing the reasons, etc. Clearly, using the continuous recording procedure in this way would introduce a positive correlation between continuous recording and the periodic survey data but probably (although generally not known) positive correlations exist anyway (except in

Figure 2.5 Interrelations between error and sample size for different types of survey 70

State of the art

Discussion

situations involving some specific incentive system, such as that reported in the discussion centering on figure 2.4 regarding the experience in the Philippines). In connection with point (iii) above, the material in table 2.1 is very instructive. Let us denote by Pr the overall completeness rate of continuous recording, by Pr|s the completeness rate of continuous recording of those vital events which are also covered (i.e., not missed) by the household survey. Then the expected value of the PGE estimate is (approximately) equal to (Pr/Pr|s)X

(2.2)

where x is the number of vital events. If Pr = Pr|s then registration and survey are independent. More often (and at least in the case of the Colombian experience reported in table 2.1) some positive correlation exists, in which case Pr
(2.3)

so that (Pr/P,|.)
Discussion

Ivan P. Fellegi

The problem of reporting vital events for migrants at the end of section 2.2.c is treated in something of a cookbook fashion. The proposed solution is a plausible one, but it clearly is not unbiased and its use should not be prescribed without at least some cautionary notes. In the discussion centering on table 2.2, the use of overlapping reference periods is questioned in the context of a dual collection system operation — presumably on the basis of the unstated premise that to the extent the survey completeness might be reduced without the use of overlapping reference periods, the PGE/ ERAD/ ECP estimate will correct for it anyway. This would be a dangerous assumption. For one thing, it is known that the variance of the estimate will be increased if the completeness of either procedure is reduced — even apart from biases. However, as the earlier discussion indicates, the bias may also well be increased if the completeness of either procedure is poor — unless one is willing to assume away the correlation between the two data collection procedures. The higher the completeness of the survey, the less dependent one is on the PGE/ ERAD/ ECP correction and all of its built-in assumptions and problems. The question raised by the authors would be more valid if they put it in the context of cost-benefit considerations; if overlapping reference periods are the source of significant costs, can those costs be more usefully expended in other directions? The discussion on matching follows Marks et al., (1974). I disagree with the proposed procedure. If the choice of matching characteristics is carried out by considering the gross error of individual characteristics, one will be unlikely to arrive at an optimal matching strategy: for example, one would never use "sex" as a matching variable because it has an obviously high gross matching error — yet everybody intuitively knows that sex is a very useful matching variable. One has to consider variables from two points of view: their contribution to confirming as "matched" those records which refer to identical events and their (negative) contribution to disproving the match status of those vital event reports which refer to different events. It can be shown that variables with a high discrimination (i.e. which create fine code classes) are ideal from the first point of view; variables with a low frequency of reporting errors (e.g. sex) are ideal from the second point of view. A set of matching variables can then be combined into a matching rule through the use of weights: agreement on a characteristic contributes a positive weight to the overall matching weight (test statistic), the size of the positive weight being dependent on the discrimination of the given variable (agreement on a rare characteristic obviously carries a higher positive weight); disagreement on a characteristic contributes a negative weight whose absolute value is larger if the characteristic has a low error reporting rate (disagreement on a very reliably reported characteristic has a high value in disproving the match status of records). Finally, alternative sets of matching characteristics are compared to one another as follows: one sets the decision point(i.e. the value above which the combined matching weight would indicate "match", below which it would indicate "no match") for each set of matching characteristics at a level for which the net matching error is zero (this can always be done!); one then compares the gross matching error for the alternative set of matching characteristics and chooses the one for which it is the smallest. For more detail the audience is referred to the paper by Fellegi and Sunter (1969). In conclusion, let me congratulate the authors once again for a thoughtprovoking paper. My specific criticisms are all attributable to a tendency of the paper to deal with complex issues in a somewhat simplified fashion. For this reason my review is, almost by definition, unfair: it can only deal with the paper as it is and not as it would be had the authors had less severe constraints of time and space. 72

State of the art

Endnotes

Endnotes to Chapter 2 1. For clarity of exposition the case k2 < ki is stipulated. Obviously, and depending on the cost functions of any actual empirical situation, sub-sampling might become worthwhile in the case where k2 > ki. [Editor's note.] 2. The National Philippine sample consists of 600,000 persons in 470 census enumeration districts for which detailed maps are prepared, special incentives are paid to the local civil registrar and to local officials to augment the report to the legal system, and periodic annual surveys are conducted by regional personnel of the Bureau of Census and Statistics. (Philippines, 1973.) 3. It is clear that extending the duty of the continuous recorder to obtaining the household composition is making it alike to the duties of the periodic survey interviewer. The consequent contribution to the loss of independence must be weighed against the alleged advantage of structuring the duty of the continuous recorder in this manner. [Editor's note.] 4. However, for a discussion of the disadvantages of multipurpose surveys, see Mauldin, 1966:652. [Editor's note.] 5. A clear distinction must be made between data collection by survey interviewers inquiring about events during a recall period without reference to a list of residents at some previous time, and data collection by follow-up surveys in which a list of persons present at some previous time is checked. See Scott's discussion of this in chapter 11. 6. There are no PGE/ ERAD/ ECP objections to field verification during the experimental matching for purposes of establishing matching rules. [Editor's note.] 7. There are strong PGE/ ERAD/ ECP objections to field verification during production matching. As argued repeatedly in chapter 1 and elsewhere, such verification advances the possibility of competitiveness between procedures. [Editor's note.]

73

Chapter 3 Dual Estimation in Demography Employing Time Series and Cross Section Data P. Krishnan 3.1 Introduction One of the primary aims of statistical estimation theory is to provide the best estimator (to be defined in some sense) of a population parameter. Toward this end, estimators of the same parameter by different procedures, or from different sources, are prepared and combined to obtain a more (or most) efficient one. In demographic research this strategy has found an application in what is called the PGE/ ERAD/ ECP technique, employed in some countries to estimate fertility, mortality, and natural increase in the absence of reliable data, and in some others to estimate the completeness of the civil registration system. Examples were cited in chapters 1 and 2. The different techniques suggested to date with regard to dual estimation in demography do not consider demographic theories, or make use of other available prior information for improving the estimators. In this chapter an attempt is made to suggest some strategies in that direction by integrating demographic theories and statistical theory of estimation with a view to deriving best estimators in the minimum variance sense. 3.2 Pooling cross section and time series data In countries that have a good civil registration system, the researcher can lay hands on a time series of the data of interest. The sample survey for the particular year under consideration provides a cross section. In the regular PGE/ ERAD/ ECP technique one does not make use of the past data (prior information). Matching is done and the sources are combined to secure the PGE/ ERAD/ ECP estimator in accordance with chapter 1. Suppose one wishes to make the best use of the prior information supplied by the time series. However poor the civil registration system, it has some information to offer and that has to be exploited for improving the estimator. Econometricians have developed several procedures for pooling cross section and time series data. There is voluminous literature in this area. Some of the recent developments can be found in Maddala (1971) and Swamy (1971). Most of the work done by econometricians is not of immediate relevance to the problem at hand despite its similarity to the pooling issue in econometrics. The attempt here is to integrate 74

Time series and cross section data

3.2

demographic and statistical estimation theories for the development of improved estimation procedures. The different strategies are discussed in section 3.4. 3.3 Best estimator If the best estimator of a parameter is defined in the minimum variance sense, and if TI and Ta are two independent unbiased estimators of the parameter, then Let the variances be denoted by One can secure a more efficient estimator by combining TI and T2. If a linear combination is considered, it is shown (see Rao, 1970: 137) that is more efficient than TI and Ta. It is also clear that This logic can be exploited to some extent with regard to the problem at hand. 3.4 Suggested estimation strategies Estimator 1: Combining a time series regression estimator with the PGE estimator. For the year under consideration, one can find the PGE estimator, say Ni, for the events under consideration. The variance of the PGE estimator is given by > where p = the probability of detecting the ith source (i = 1, 2), NI = the actual number of events in the universe. If ft is the rate of incidence of the events, then where P is the base (risk) population of choice. P may be estimated or known from a census or other sources. We shall assume that P is not estimated. An estimate of /3, say /3, is

When we regress the number (or incidence) of the events at time t on the number (or incidence) at time t-1, t-2, t~3, . . . linearly, we obtain an autoregressive predictor. Working with the Canadian data on births and crude birth rates, it was seen that a second order auto-regression equation is a good predictor (see appendix). Furthermore, the Canadian data revealed that the correlation pattern existing between the different auxiliary variables is approximated by the geometric pattern ptt+ k = pk (k = 1, 2, . . . ). We hope that this pattern would hold for other countries as well. Under this pattern, let Na be the predicted number of events for time t (the year under consideration). Then

3.4

P- Krishnan

where a2 is the variance of the error term, C the row vector of the coefficients of the predictor, ft the column vector of regression coefficients, and X the matrix of observations (Johnston, 1972: 126, 153). If the geometric pattern does not hold true, where R2 is the square of the multiple correlation coefficient of the dependent variable on the independent variables. The advantage one can reap with the geometric pattern is that only one independent variable js needed for prediction. Equation (3.11), in conjunction with the PGE estimate NI yields the best estimator N of the number of events under consideration employing time series and cross section, viz V(N) is given by equation (3.4). Since ai 2 , a-i are unknown, the sample estimates can be substituted in (3.14). Estimator 2: Combining time series and cross section under rigorous assumptions with regard to error term. Estimator 1 is rather simplistic with regard to the composition of the error term. The "matching" part need not be of concern to us at this stage. Depending on whether an estimate of the extent of under- (over) registration is required or not, matching need or need not be done. We shall consider only the time series and the cross section data. Let the time series and cross section models be

where Y t ( 1 ) = the number of events at time t in the macro unit; Pt = population at time t in the macro unit; Yi (2) = the number of events in the ith micro unit; Pi = population of the ith micro unit; and /u t , Vj = error (disturbance) terms. ft is assumed to remain the same throughout this period. Let us further assume that the disturbance terms have zero mean and finite variance, and are serially uncorrelated.1 Then we have: estimate of ft from cross section data only

estimate of ft from time series only Case I: Let V(M.) = a,2 = V(vi) = a22 = a2 (say) Under this condition, we treat cross section and time series as one set yielding the pooled estimator

Now let us compare the variances ot'/J, ft, ft.

76

Time series and cross section data

3.4

It is clear from (3.20), (3.21), and (3.22) that (3)—the pooled estimator—is the most efficient of the three. Case II: o-i = k 2 ai 2 (k known) The pooled estimate (3) in this case is:

For k = 1, (3.23) reduced to (3.22). Under large sample assumptions, the variance of (3.23) follows from Cramer's result on the asymptotic normality of maximum likelihood estimators (MLE), (see Rao, 1970: 158). Case III: <5,Va 2 2 The likelihood function of the parameters is

The MLEs of o2, oi2 and ft are obtainable on solving equations (3.25), (3.26), and (3.27) simultaneously.

An iterative procedure yields the MLEs. Usually the cross section sample is large and assuming that the time series also is large, the large sample estimates of oi2 and a22 can be employed in (3.27) to arrive at a large sample estimate of ft. Cramer's theorem yields the variance of the MLE of ft. Estimator 3: An integrated estimator from demographic and statistical theories. Demographers have tried to develop a theory of fertility based on the influences of social, economic, psychological, and biomedical factors. There is no need to enumerate here the various contributions to the sociology of fertility. At family (individual) level, duration of marriage, knowledge and effective use of contraception, infant mortality, desired family size, present parity, family income, schooling, etc. are all known to be predictors of fertility. At societal level, it has been noted that literacy, age at marriage, infant mortality rate, degree of urbanization, per cent population in non-agricultural activities, extent of female labour force participation, income per capita etc. are all associated with fertility. A similar set of socio-economic correlates are available for mortality prediction also. Since the demographic journals are replete with empirical regression applications, there is no need to refer to specific studies here. The PGE/ ERAD/ ECP technique has not exploited these auxiliary variables for improving the estimates of fertility and/ or mortality. At micro (family/ individual) level, data on the relevant auxiliary variables can be collected at the time of the survey without adding much to the cost. 77

P. Krishnan At macro (societal) level, the data are available from censuses, or from other reliable official sources. Hence, the methodology discussed in the following paragraph does not present any difficulty as such in the generalization of the PGE/ ERAD/ ECP technique. Let be the time series model, where Z t (1) = rate of events under consideration Xit = ith auxiliary variable (i = 1, 2, . . . k) 7, = ith regression coefficient (i = 1, 2, . . . k) Ut = disturbance term with E(u,) = 0, E(u.u.+s) The auxiliary variables may be lagged over time to suit the demographic theories. The least squares predictor of Z t (1) given X;t (i = 1, 2, . . . k) is Variance of Z t (1) is given by the standard formula available in Johnston (1972: 153). Suitable modifications are necessary if the problems of multicollinearity, heteroscedasticity etc. are present in the regression set up. Let the cross section model be where

The cross section predictor is with V(Z(2)) = o22 (say). (3.29) and (3.31) can be combined now to arrive at the best estimator of the rate(s) under consideration. Large sample estimates of ai2 and oi2 may be applied in the estimation strategy. No illustrations are presented here to show how this pooling technique works. The main aim of this chapter has been to indicate that, if suitable time series and cross section data are available, the pooling technique could be employed to improve the PGE estimator.

78

Time series and cross section data

Appendix

An appendix to Chapter 3

Correlation pattern in Canadian data on births and CBRs Canadian data on crude birth rates (CBR) and total number of births from 1948 through 1970 yielded the following results: CBR Matrix of Correlation Coefficients time t t-1 t-2 t 1 .985 .953 t-1 1.000 .977 t-2 1.000

Mean Maximum Minimum Standard deviation

Total No. of Births Matrix of Correlation Coefficients t t-1 t-2 1 .948 .827 1.000 .942 1.000

Crude Birth Rates t 24.8 28.5 17.4 4.02

t-1 25.3 28.9 17.6 3.77

t-2 25.7 28.9 17.6 3.39

Statistical testing reveals that the geometric pattern holds here. Discussion by Eli S. Marks

Section 3.1 of this chapter notes that: "The different techniques suggested to date with regard to dual estimation in demography do not consider demographic theories, or make use of other available prior information for improving the estimators." This statement is somewhat misleading since the role of PGE/ ERAD/ ECP estimation is to try to reduce the biases in the data, and a number of the references in the PGE/ ERAD/ ECP field have emphasized the desirability of combining demographic analysis with dual system estimates. However, the point that one needs to use other available information to improve dual system estimates is very important and cannot be overstressed. We badly need some concrete examples of how PGE/ ERAD/ ECP can be used to improve the results of some of the recognized techniques of demographic analysis, and we also need specific suggestions of new ways of using other available data to improve PGE/ERAD/ECP results.2 Unfortunately the chapter misses the major problem. That is, in "integrating demographic theories and statistical theory of estimation" the goal is to minimize the mean square error (rather than the variance) of our estimates. Thus Krishnan presents quite adequately the standard statistical theory for combining two independent unbiased estimators to get a third estimator having a lower variance than either of the originals; but the real problem is to combine two methods which produce (different) biased estimators to get results having lower mean square errors than the results of other methods used alone. It is true, however, that, because PGE/ ERAD/ ECP methods usually involve the use of small samples, some of the dual system estimates will have high variances and one must look for means to reduce those variances. But we must guard against reducing the variance by increasing the bias unduly. For example, the use of time series or of relationships derived from previously observed data can be very useful if (i) 79

Discussion

Eli S. Marks

PGE/ ERAD/ ECP techniques or some other methods have been used to reduce the bias in both the current and past data to manageable levels and (ii) the relationships used in the time series model are stable over time. Thus, for example, one can use estimates of fertility and mortality rates by age from previous years to reduce the variance of our estimates of current mortality and fertility rates and of the growth rate and the current age-sex structure. But we will have to correct past mortality and fertility rates for under-reporting biases (by using dual system estimates or some other means) just as we need to correct the current mortality and fertility rates for these biases. Furthermore, we cannot use a model which assumes stable age-specific rates unless there is reasonable evidence that the rates have been stable over time. And, even with such evidence, it would be rather foolhardy to use fertility rates which project past trends, if the objective of our estimates is to measure the effectiveness for reducing fertility of a national family planning program. In general, the use of past relationships will be best accomplished by using a specific model rather than the generalized linear regressions presented by Krishnan. For example, due to high variance, the PGE/ ERAD/ ECP estimate of the death rate in Thailand in 1964-67 was higher for females 1-4 than for males-a most unlikely situation. The civil registration for this period shows a masculinity ratio more in line with demographic expectations. A model which assumes that the ratio of deaths of males 1-4 to females 1-4 is that given by the civil registration will probably give lower mean square errors than one based on the regression of the observed death rates on age and sex. However, we will still need to use PGE to correct the general level of fertility. One minor point is the assumption that "the variance of the PGE/ ERAD/ ECP estimator" is given by Krishnan's equation (3.5): V(N,) = ( N , q i q 2 ) / ( p i p 2 ) This equation only applies if (i) one has reports for the whole population in both sources (or uses only simple random samples or some other type of fixed size sample with zero intraclass correlations); and (ii) reporting errors are truly independent in both systems. In a well designed and well executed PGE/ERAD/ECP system, the second condition will obtain approximately but the first condition (having data for the whole population in both sources or using only simple random samples) is rather rare.3 While the limitations on equation (3.5) are not a major point, it is mentioned because the misunderstanding is rather common and people assume that equation (3.5) is "the" variance of a dual system estimate. More general variance formulas are given in chapter 7 of Marks, Seltzer and Krotki (1974). Endnotes to Chapter 3 1. For a detailed description of serial or auto-correlated disturbance terms, see Johnson, 1970:243-66. 2. We are suggesting one such approach in our chapter 9. [Editor's note.] 3. In the 1940 and 1950 U.S. birth registration tests, both sources (civil registration and census) did try to obtain reports for all members of the population.

80

Chapter 4 Dual System Estimators Based on Multiplicity Surveys Monroe G. Sirken

4.1 Introduction We are concerned with the problem of improving the reliability of dual system estimators of vital statistics derived from single retrospective sample surveys. Our objective is to investigate the effect of alternative counting rules in single retrospective surveys on the sampling errors of dual system estimators of vital statistics, especially mortality statistics. In addition to the sample design itself, there are several other factors that affect the accuracy of the survey statistics over which the statistician exercises control in designing single retrospective surveys. These design factors include, for example, the length of the reference period and the kind of respondent rule adopted in the survey. The former defines the calendar period for which vital events are reported retrospectively. The latter designates who may serve as eligible respondents in the survey. Another design factor which had received no attention until recently (Sirken, 1970, 1972a, 1972b) is the counting rule. In single retrospective surveys, this design factor designates the housing units where the vital events that occurred during the reference period are eligible to be enumerated. Clearly, the distribution of the vital events among the housing units is a function of the counting rule. By changing the counting rule, the statistician modifies this distribution and thereby alters also the sampling distribution of the survey statistics. The counting rule strategy is to select the rule that minimizes the variance of the sampling distribution. 4.2 Counting rules We differentiate between conventional and multiplicity rules in single retrospective surveys. The conventional counting rule distributes the vital events that occurred during the reference period among the housing units such that every event is uniquely linked to and hence eligible to be enumerated at only one housing unit. In household surveys, conventional counting rules are often referred to as residence rules. For instance, the de jure residence rule links vital events that occurred during the reference period to the usual places of residence of the individuals who experienced the event. For most vital events the usual place of residence would be the housing unit where the person who experienced the event was residing when the 81

4.2

Monroe G. Sirken

survey was conducted. In the event of death, however, the usual place of residence would be the housing unit where the person resided at death. A multiplicity rule distributes vital events among the housing units such that every event is linked to one or more housing units where it is eligible to be enumerated. Multiplicity rules have been proposed that would link persons who experienced vital events to the residences of their relatives. For instance, one of these rules links adults who died during the reference period to the residences of their surviving spouse, siblings, and children. Another rule links children who died during the reference period to the residences of their mother, grandparents, aunts, and uncles. 4.3 Multiplicity estimators Several unbiased estimators have been proposed (Birnbaum and Sirken, 1965) for estimates based on surveys using multiplicity rules. We will use one of these, the socalled multiplicity estimator, to estimate N, the number of persons that died during the reference period specified by the survey. Denote the L housing units in the population by Hi, . . . , Hi, . . . , HL, and the N deaths that occurred to persons who resided in the L housing units during the reference period by Ii, . . . , Ia, • • • , IN. Let the indicator variable, r 6 a ,i, specify the links between the L housing units and the N deaths based on counting rule r. Thus,

A multiplicity estimator of N is

where = the multiplicity of I<*(a = 1, . . . , N), that is, the number of housing units linked to Ia by the rule r. This estimator assumes that all deaths are reported by the housing units which are eligible to report them, and that deaths are not reported by housing units ineligible to report them. It is an unbiased estimator if the counting rule links every death to at least one housing unit, that is, if sa> 1 (a = 1, . . • , N). The unbiased sample estimator of Nr, is

where ii, . . . , ij, . . . , i^ represent the indices of the Chousing units selected in the sample. It will be noted that the estimator Nr requires the multiplicity of every death enumerated in the sample housing units. We are proposing (Sirken, 1970) to obtain the multiplicities from the housing units where deaths are enumerated in the survey. Suppose the counting rule stated that decedents are linked to the housing units of their surviving spouse, children, and siblings. A death would be enumerated at a sample housing unit whenever a surviving spouse, child, or sibling of the decedent lived in the unit. The multiplicity of an enumerated death would be ascertained by asking the housing units which reported a death also to report the number of other housing units which contained either a surviving spouse, child, or 82

Multiplicity surveys

4.3 A

sibling of the decedent. If Nr were based on a conventional rule, however, it would be unnecessary for the survey to obtain the multiplicities of the enumerated deaths since by definition sa = 1 (a = 1, . . . , N). Thus, the estimator based on a multiplicity rule requires the collection of supplementary information which is not needed by a conventional rule. 4.4 Dual system multiplicity estimators Typically, deaths are grossly underenumerated in single retrospective surveys (Seltzer, 1969). This appears to occur because deaths are not enumerated at the housing units to which they are linked by the counting rule (Sirken and Royston, 1970). Therefore, the estimator Nr understates N. Hence we consider an alternative estimator, rj,, which we refer to as a dual collection estimator of N based on rule r. The estimator rjr involves matching the deaths enumerated in the survey with the file of deaths recorded by the registration system. We will assume that deaths are incompletely registered as well as incompletely enumerated. Otherwise, there would be no need to conduct the household survey. Before defining rjr we introduce some notations. Let the indicator variable r/u 0,1 identify the deaths that are enumerated in a survey based on rule r, where 1 i f I a ( a + 1 , . . . , N ) is linked to as well as enumerated at rua,i

Hi(i + 1, . . . , L) 0 otherwise

The biased estimator of N based on the deaths actually enumerated in the survey using counting rule r, is

where

denotes the weighted number of deaths enumerated at

Hi (i = 1, . . . , L). We assume that the multiplicities are not subject to measurement errors so that A one way match of deaths enumerated in the survey is made against the complete file of registered deaths. Let the indicator variable ,i>a,i specify the enumerated deaths that are matched with registered deaths, where 1 if Ia(a +1, . . . , N) is linked to as well as enumerated at Hi(i + 1, . . . , L) and matched with a registered death rua,i 0 otherwise The number of registered deaths enumerated in the survey based on counting rule r, is

where

denotes the weighted number of deaths enumerated

at Hi (i = 1, . . . , L) that were matched with registered deaths. The dual system multiplicity estimator of N is where pr = N r / X r and X is the number of registered deaths. The sample estimate of rjr is 83

4.4

Monroe G. Sirken

The sample estimators of Xr and Nr based on a simple random sample of £ housing units are

where i i , . . . , i j , . . ., i& represent the indices of the sample housing units. Despite the fact that the survey underenumerates deaths and the registration system fails to record some deaths, r)r is an unbiased estimate of N if Xr/ X = Nr/ N. 4.5 Variance of sample estimators Assuming a simple random sample of £ housing units selected without replacement, the sampling variance of ij, is The derivation of V(»7r), presented in appendix A to this chapter, assumes no more than one death is linked to a housing unit. The parameter, T =X/ L is the proportion of housing units that was a de jure residence of a registered death. Two parameters depend on rule r. , = Xr/ X is the proportion of registered deaths that are enumerated in the survey, and 0r = (1 - l/p r ) r Ex + (l/p r ) r EN-X where and

respectively are based on the multiplicities of registered and unregistered deaths enumerated in the survey. Since 0 < r ^ 1 and 0 < 6 ^ 1, it follows that Hr = 6,1$, > 0 and thus Hr serves well as a measure of the sampling efficiency of counting rule r. The efficiency of counting rule r is inversely proportional to flr. If the survey is based on a conventional counting rule, flc = 1/<£ C since cEx = C£N-X = 1, and it follows that the sampling variance of i If the survey is based on a multiplicity rule, the estimator is and from (4.7) and (4.8) we have Assuming pc = pm, it follows that If 0C = 0m, formula (4.10) implies that 4.6 Relative precision of different rules The effect of counting rule r on the variance of the dual system sample estimator of N, is shown by formula (4.7) to depend on the parameter Hr = 0r/ r. Survey experiments are needed to estimate 0r and t for different counting rules. In this section, we describe the design of such a survey experiment and present findings that compare the sampling precision of selected counting rules. The findings are considered provisional and they are presented for illustrative purposes only. A small experiment (Sirken and Royston, 1970) investigated the counting 84

Multiplicity surveys

4.6

Figure 4.1 Counting rules tested in a survey experiment for enumerating deaths, Los Angeles, July - October, 1969 Rule

Statement of rule

1 2

Decedents are linked to their former housing Decedents are linked to their former housing surviving children Decedents are linked to their former housing surviving siblings Decedents are linked to their former housing surviving children and siblings

3 4

units units and to units of their units and to units of their units and to units of their

rules listed in figure 4.1. Rule 1 is a conventional rule and rules 2, 3, and 4 are multiplicity rules. Each of the multiplicity rules links the decedents to their former housing units and thereby guarantees that every death is linked to at least one housing unit. Should it be established empirically that virtually all decedents have at least one surviving close relative, it would be sufficient to link deaths to housing units of these relatives. The experiment was based on a small sample involving 142 noninstitutionalized white adults who died in Los Angeles during the four month period, July/October 1969. The sample deaths were selected from the files of the Los Angeles County Department of Health. The survey was conducted during the three month period January/March 1970. First, interviews were conducted at the sample decedent's former housing units as identified from the address listed as the usual place of residence on the death record. Subsequently, interviews were conducted at housing units of the surviving relatives of the sample deaths, who were living in Los Angeles County. These relatives were identified in interviews completed at the decedents' former housing units. Household respondents were asked the same question in the first and second stage interviews. Screening questions identified the deaths that occurred during the preceding 12 month period to persons who either formerly lived in the housing unit or to persons who had a surviving child or sibling living in the housing unit. Whenever a death was screened, its multiplicity was ascertained by asking a series of questions about the location of the decedent's former residence and the locations of the residences of his surviving children and siblings. The estimates Hr = 0 r /0 r derived from the survey experiment are shown in table 4.1. The estimates of Hr range from about .54 for rule 4 to about 1.6 Table 4.1 Estimates of 6,
1 2 3 4

1.00 .61 .59 .38

.63 .70 .63 .70

1.59 .87 .94 .54 85

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for conventional rule. In other words, for fixed sample size the variance of the estimated number of deaths based on either rule 2 or 3 would be about three-fifths as large as the variance based on the conventional rule. Limitations of the survey experimental design forced us to make a number of assumptions in order to estimate r and 6,. On the basis of these assumptions, which are discussed in Appendix B to this chapter, the estimate of 6, is where x is the number of registered deaths in the experiment that were enumerated at the decedents' former residence and rsa is the multiplicity of LXa = 1, . . . , x) based on rule r as reported by the household residing at L's former residence. The estimate of r is where qc = proportion of sample deaths that were not reported at their former residences = proportion of sample deaths that were not reported by surviving relatives. The estimates of qc and rqm based on the survey experiment are presented in table 4.2. Thus, qc = .37 and rqm is equal to .38, .20, and .26 respectively for housing units of surviving siblings, surviving children, and surviving children or siblings. It is apparent from table 4.2, however, that qc and rqm would have been smaller had more resources been available to reduce the noninterview rate. Had we estimated qc and rqm solely on the basis of the missed deaths in completed interviews, we would have qc = .23 and rqm = .29, .08, and .15 respectively for housing units of surviving siblings, surviving children, and surviving children or siblings. Table 4.2 Proportion of deaths that were missed by type of housing unit in the survey experiment, Los Angeles, July - October 1969 Units formerly occupied by key deaths Sample size Deaths enumerated Deaths missed Interview completed Interview not completed

142

Other units occupied by relatives Total Siblings Children

46 .63 .37 .19 .18

16 .74 .26 .13 .13

30 .62 .38 .25 .13

.80 .20 .07 .13

4.7 Conclusion We have investigated the effect of different counting rules in single retrospective surveys on the sampling errors of dual system estimators of vital statistics. First we derived an expression for the variance of the survey estimates which contains a parameter that serves as an index of the sampling efficiency of the counting rule. Then, we presented estimates of this index for several different counting rules for linking persons who died during the reference period to housing units where they are

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eligible to be enumerated in the survey. These estimates, though provisional, being based on the findings of a small survey experiment, indicate that the counting rule would have a decided effect on the sampling errors of dual system estimators of the number of deaths in the United States. Further experiments are needed to substantiate these findings. Since counting rules are culture bound, survey experiments to test alternative counting rule strategies in single retrospective surveys are needed particularly in countries lacking viable registration systems. In limiting the scope of this report to the effect of counting rules on the sampling errors of dual system estimators, we did not consider the effect of counting rules on the bias of these estimators. It has been shown (Sirken, 1973b), that the counting rule has a substantial effect on the number of deaths that are missed in the survey, and there can be little doubt that the bias of the dual system estimators would vary considerably depending on the counting rule adopted in the survey, although this remains to be confirmed experimentally.

Appendix A to chapter 4 Variance of DSM sample estimators In a prior paper (Sirken, 1973b), we derived the sampling variance of Pr = X r /N r , which is the dual system multiplicity estimator of vital registration completeness. The derivation assumed that counting rule r links no more than one vital event to a housing unit. We apply that prior result here to derive the sampling variance of rj r , the dual system multiplicity estimator of the number of vital events. Since it follows that Assuming a simple random sample of £ housing units is selected with replacement, we showed (Sirken, 1973b) that where 0r = (1 - P r ) r E x + (P r )rE N =x. Substituting (4.14) into (4.13), noting that Pr = l/p r , we have where Appendix B to chapter 4 Simplification of Hr The measure of samoline efficiency of rule r is where

and We assume that rEx = r E N -x so that (4.18) reduces to (4.19) Additional assumptions were made in order to facilitate estimating 6T and r on the 87

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basis of the restricted information collected in the survey experiment. These assumptions are described below. We assume that counting rule r links every decedent to his former de jure residence, and to the residences of specified surviving relatives. Let 1 if a registered death is enumerated at its de jure residence, reai 0 otherwise and 1 if a registered death is enumerated at a linked housing unit other than its de jure residence, r f ai 0 otherwise. We assume also that r c a ,i and r fo,i are binomial random variables with expected values: E(rca,i) = (1 - qc) = probability the registered death is enumerated at its de jure residence and E(rf a ,i) = (1 ~ r q m ) = probability the registered death is enumerated at a relative's residence, other than the decendent's de jure residence. With these assumptions, 6, = 8', and r = 'r become random variables. The expected value of 6', is

{ {

where and

Since every Ia(a = 1, . . . , N) is linked to its de jure residence by rule r, each Itt is also linked to exactly ( r s a - 1) other residences of relatives. Thus, we have

and

Substituting (4.21) and (4.22) in (4.20) we have V

Y

since R is generally a negligible quantity. If sa = s, R = 0. From (4.21) and (4.23), it follows that the expected value of 0'r is

Now if we assume that a random sample of x registered deaths were enumerated in the experiment, we have 88

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Discussion by Ivan P. Fellegi The development of multiplicity counting rules for rare events can justifiably be considered as one of the few genuinely original developments in household survey methodology during the last 10 years. I am very glad indeed that Sirken has attempted to take the step of marrying the multiplicity counting rule technique with dual system estimation. The first technique is primarily a variance reduction device (most valuable for rare events which, therefore, are subject to high variances), the second is designed to reduce biases due to non-reporting. If the combination of techniques can successfully be made to work, a major step forward in measuring population change may well have been accomplished. Like all ingenious ideas, the concept of multiplicity counting rules is very simple. It can be illustrated in the context of an oversimplified example as follows. Suppose the proportion of deaths in a population is to be estimated from a simple random sample of n persons (living or dead). The usual estimate, p, is unbiased and is the sample mean of the counting process whereby we associate a 1 with every person who died in the reference period and a 0 with all other persons. The variance of p is approximately given by where S2 = p(l-p) If, now, with every person who died in the reference period we can associate another (k - 1) persons uniquely (e.g. their surviving siblings or children), then we can change the counting rule to associate 1 / k with every person who died in the reference period or who is associated with one who died. We can expect in the sample nkp observations of 1/k and n(l - kp) observation of O's (instead of np observations of 1 and the remainder O's). The number k is the "multiplicity". The estimate will clearly be unbiased still, but the dispersion of the observations is significantly reduced resulting in a reduced variance: where Sk2 = p ( l / k - p ) so long as kp ^ 1 If p is small, the variance will be reduced (in comparison with the traditional counting rule) by a factor of k. This oversimplified presentation of the principle underlying the concept of multiplicity counting might be useful because it illustrates not only how the rule reduces the variance of an estimate but also because it indicates another phenomenon at work: from a pure variance point of view it would clearly be advantageous to increase k without limit. A problem arises, however, because a high multiplicity can only be achieved by defining the rule of association in terms of increasingly tenuous relationships (surviving children, surviving children or siblings, surviving first cousins, second cousins, etc.). Since the counting rule must be one that can be understood by respondents, it must be defined in terms of relationships meaningful to the respondent. Thus the multiplicity (as in the examples above) is not a predetermined constant but varies with the particular death involved, and thus it must be reported in the survey by the respondents. Clearly, the more tenuous the rule of association, the more likely it is that respondents will under-report the number of persons they are defined by the counting rule to be in association with. Since this number enters the denominator of the estimate Nr (based on a single survey), an upward bias may 89

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well result. The bias is likely to increase as the multiplicity increases. So the variance reduction may well be accompanied by an increase in the bias of the estimates. At some (a priori unknown) level of multiplicity an optimal balance may be reached. The matter is further complicated by the fact that the likely upward bias due to multiplicity counting rules may at least partially be offset by the traditional underreporting of rare events. Still further complication is introduced by the fact that the estimated multiplicity is subject not only to bias, but also to response variance. The variance of the resulting multiplicity estimates is likely to be higher, therefore, than one would guess on the basis of the chapter's assumed error-free reporting of the estimated multiplicity. Worse yet, if the reported multiplicity is subject to response variance, given the generally small magnitude of the estimated multiplicities, the resulting multiplicity estimates may be subject to a not insignificant ratio estimate bias. Moving to dual system multiplicity estimation, the author considers a case where the first collection procedure is a census (100 percent registration) and the second a survey. In order to assess the proposed estimator, a variety of other biases have to be considered. Since the probable upward bias of the single source multiplicity estimation will, in the dual system estimator, appear both in the numerator and in the denominator, this particular source of bias may partially cancel out. There may well be additional biases, however. In particular, an essential aspect of all dual system estimators is related to matching between two data sources. Clearly, the quality of matching is fundamentally dependent on the identification of the events which are to be matched (in the case of deaths, information such as name, last address, age, etc. of the deceased). The more tenuous the "association" between the person reporting the death and the deceased, the more error-prone the matching information will be. This will probably result, other things being equal, in an understatement of the number of matched cases and hence an overstatement of the dual system multiplicity estimator. At any rate, as the author himself indicates, the proportion of missed events may well be affected by the counting rule (it may be reduced to the point where dual system estimators become unnecessary); also the correlation between the two sources may be affected in an unpredictable fashion. Ascending even further in this presentation of escalating difficulties, the author does not treat the case where both registration and survey are based on samples—by far the most frequent situation in developing countries. No doubt, the consideration of the different trade-offs between biases and variances would be even more complex in this case. In particular, if the continuous recording is also based on a sample, it has to collect information using the same counting rule as that of the survey (otherwise matching would not be possible—the proposed post facto reconstruction of the multiplicity estimator based on the events matched between the survey using a multiplicity rule and the registration using traditional counting is predicated on the fact that the register is a complete census, rather than the result of a sample survey). The value of data collection for the registration would, therefore, be substantially altered since a more than usual amount of information would have to be collected. This, in turn, would quite possibly affect the correlation between registration and survey. Of course, there would be other possibilities also worth exploring: such as collecting the registration information using the traditional counting rule, collecting the survey information in such a way as to facilitate the compilation of a survey estimate using both the traditional and the multiplicity counting rule, and compiling a "hybrid" estimate in which Nr is the multiplicity estimate from the survey, X is the "traditional" registration estimate, M is the

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estimate based on the matched events (using only those deaths in the survey which correspond to the "traditional" counting rule): As can be seen, the chapter presents a new technique with exciting possibilities. The author himself is well aware of the fact that much further exploration of the behaviour of the mean square error of the proposed estimates is required before the technique can be said to be ready for large scale applications. The present discussion attempts to focus future experimentation on some specific sources of bias. The intention is not to indicate a long list of problems with a view to discouraging potential users of the technique, but rather to encourage the profession to accumulate the necessary empirical evidence. The technique is of major potential pay-off: by significantly reducing the sampling variance of estimates of births and deaths, it may permit a major reduction of sample sizes and hence costs. However, a significant initial investment in the form of experimentation is required before we can expect to begin to reap the dividends.

91

Chapter 5 The Collection of Demographic Data in Francophone Africa and Liberia Using the PGE/ ERAD/ ECP System Francois Pradel de Lamaze 5.1 Dual collection The insufficient findings in the various demographic surveys, as well as underenumeration—obvious but difficult to quantify—in the registration of vital statistics of third world countries, led in Africa (among other attempts) to the reciprocal verification between two a priori independent operations (the PGE/ ERAD/ ECP technique). In the cases known to us, the use of this method has a pedestrian goal: the precise determination of the number of births and deaths. These in turn permit by reference to the population, obtained at the same time or otherwise, the calculation of the rate of natural increase. To the best of our knowledge the technique has not been used in Africa for other reasons: rectification of the age pyramid, measurement of the completeness of a census, etc.' No doubt the difficulties encountered even when a relatively simple objective is chosen would increase considerably with more difficult objectives. Most experiments with dual collection have been done on samples, and the method has sometimes been condemned because of sampling problems. The method may be put to work on a total area, even a very large one. Nevertheless, because the cost is considerable, it is expedient — at least in African circumstances — to work with samples. The general problems presented by a sample design are the same as for an ordinary survey, but with the added difficulty that the two samples should coincide exactly. The "slips" that are almost always produced in a survey (poor boundaries, non-responses, absences, etc.) then have an even greater significance. Finally, note that "dual collection" as usually presented in Africa is a matching of two types of operations: (i) a continuous recording of vital events analogous in principle to the civil registration, but distinct from the corresponding administrative operation; (ii) a survey of vital events in households, in retrospect, taken with the same recall as that of the continuous recording. But this schema is not immutable and diverse variations can be used: comparison of the civil registration and a survey, comparison of two retrospective surveys, comparison of one retrospective survey and a multiround survey, etc. 5.2 Some observations The application of the PGE/ ERAD/ ECP technique presupposes the total independence of the two operations. Two aspects of this independence should be considered. 92

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The first is operational independence: it is essential that the field workers participating in the household survey completely ignore those engaged in continuous recording. Good organization can resolve this problem. The second is causal independence: this problem appears to be more difficult to resolve. The PGE/ ERAD/ ECP formula used supposes, in effect, that within each procedure of observation, each event has an equal probability of being reported, and that this probability is not affected by the existence of the other procedure. In practice, there will not be an equal probability of collection for all events within a procedure. Thus, for example, births in young families in which the heads of the households are educated have presumably a greater chance of being correctly reported than those happening in older families in which the heads are illiterate. Similarly, deaths of isolated individuals are more easily omitted than those occurring in normal families. The problem can be resolved by stratification, whether a priori — stating the principle causes of omissions elsewhere—or a posteriori—stating omissions as a function of the characteristics of the events. The final estimation is the sum of the strata estimates. Note that, in so far as it is otherwise possible to estimate adequately the corresponding populations for each strata, this eventally permits the calculation of differential rates, though with variable precision. Even more serious is the fact that a connection will be established, in a quasiautomatic way, between the two procedures during the surveys. The probability of a household already surveyed by one of the procedures declaring an event in the other procedure, depends strongly on its previous response. Because of the fact that an interviewer has already arrived, asked judicious questions, and has been able to revive the memories of the household, the recorder following him some days later will certainly obtain a similar response. If, as is often the case, one of the procedures carries out frequent visits to the households, at a certain time the two procedures will give nearly identical results, but be hampered by the same systematic errors and omissions. These problems for which we see no suitable solution, handicap all operations of too long a duration, and leave suspect operations which are too short. Then there are the problems of matching. When an event is reported in both procedures, the difficulty arises of ascertaining, with sufficient certainty, whether the two documents refer to the same single event. In African reality, and this problem is even more difficult when the two sources are really independent, the characteristics given are rarely coherent. The given and family names are often unstable, the ages or birth dates are poorly determined and a fortiori even more so, more remote characteristics such as the age of the parents or the occupation. In chapter 1 it has been shown that very strict matching rules tend to underestimate the quantity M in figure 1.1 (events observed in both procedures) and consequently, to overestimate the quantities Ui (events observed only by the first procedure), U2 (events observed only by the second procedure), and Z (events not observed in either procedure). If, on the other hand, the matching rules are too lax, M will be overestimated and the other quantities will be underestimated. In conditions of African uncertainty and changeability the striking of matching rules close to a zero net matching error might be particularly difficult and frustrating. The PGE/ ERAD/ ECP technique is of Anglo-Saxon origin and has been applied so far mainly to the territories formerly part of the British Empire. Abundant literature, most often in English, describes the more important operations. Francophone countries have usually displayed a certain reluctance to take the full plunge. This reluctance might explain some of the mediocrity of the results. The only experience of a respectable magnitude is the field exercise started by the Moroccan CeRED, which we have described to the extent required by this chapter. The fuller findings of the Moroccan PGE/ ERAD/ ECP enquiry are presented in chapters 7 and 8. 93

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5.3 Two undertakings in Madagascar Having decided to undertake a large national demographic survey, the statistical service of Madagascar (INSRE) launched two successive pilot studies, one in 1967-68 on the Ambinanitelo Commune2 (approximately 14,000 inhabitants), and the other in 1969-70 on the subprefecture of Ankazoabo (population 24,000) (ORSTOM et al, 1971: 154-158). In the two cases the dual collection system was applied by comparing the documents arising out of the survey (repeated enumerations) with those of the civil registration. The concordance between the administrative boundaries permitted the use, without difficulty, of the existing registration data. The two procedures were independent of each other. There were, however, some difficulties in boundary interpretations between the two procedures. There were difficulties over time. The fact that many events were not registered until after a significant delay required the use of a longer period of registration, rectified according to the declared dates of the events, so as to ensure coverage of duration equal to that of the survey. The registration being permanent, this procedure did not present difficulties in collection. There were difficulties over space. The problem of de facto and dejure populations and events has arisen. Because the survey observed dejure events it was necessary to "retrieve" the events that occurred in neighbouring communes, but which concerned families residing in the survey area. This necessitated, theoretically, the analysis of the entire civil registration because at least some of the vital events were registered de facto in the "foreign" communes. In practice only the registration for communes neighbouring to the survey area was analyzed. The matching of events was done according to diverse matching rules as much for theoretical reasons (that is, stratification) as to permit analyses of: births and deaths by village births and deaths by month births by sex births by age of mother deaths by sex and age. On the whole, the declarations of sex and place of residence were consistent between the two sets of documents. This was not so for ages and dates of birth. As a result, the stratification that could have been the most useful (age) was the most difficult in terms of matching. The gain in precision given by a good stratification was thus counterbalanced by the mediocrity of the matching. In addition, numerous uncertainties about family and given names made the manual work difficult. The results are shown in table 5.1. It seems, then, that the quality of the household survey was appreciably the same as that of the civil registration. It was possible to Table 5.1 Estimated completeness rates in two Madagascar dual collections, 1967-70 Procedure

Births

Deaths

Household survey Civil registration Estimated completeness in the absence of survey Estimated crude rates per 1,000 pop.

81% 77% 73% 55

72% 74% 66% 18 '

Source: Orstom et al., 1971: 157 94

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estimate than an improvement in civil registration was produced by the fact of the household survey: under "normal operation" the completeness of the civil registration would only have been 73 percent for births and 66 percent for deaths. The measurement of this amelioration was obtained from a comparison of the results month by month, the completeness increasing rapidly during the period of the household survey. It is evident that this loss of independence calls into question the final result (raw total births and deaths), but it does not weaken a certain number of observations that could be made: lower declaration of female births and deaths lower declaration of births to young women (or overestimation of age) poor appreciation of dates, ages and so on. The Madagascar experience confirms, then, the importance of the risks incurred by a mechanical application of the PGE/ ERAD/ ECP technique: the probability of noting an event varies quite strongly over time (a problem that can be resolved by a "stratification"), but this variation results from the interaction of the two procedures. The prolonged application of the PGE/ ERAD/ ECP technique risks leads to a convergence of results, and nothing indicates that this convergence would be produced without systematic omission of the same events by both procedures. 5.4 The Tunisian experiment The national demographic survey conducted in Tunisia in 1968-69 put priority on the measurement of the rate of natural increase. After having adopted the principle of a multiround survey, the problem of eventually measuring omissions was raised. The survey plan chosen (surveying a sample of households in very small clusters) did not lend itself to the application of a dual collection system. After some fruitless attempts to double survey households it was decided to modify the survey plan, in two reduced zones, in such a way that comparison with the civil registration would be possible.3 Two sheikhdoms were chosen, Goraa and Oued el Kharef, in which the survey was extended to the total population coterminous with the population of the civil registration offices, and then the events reported in the household survey were compared to those recorded at the civil registration. The results are shown in table 5.2. It can be seen that, contrary to the case in Madagascar, the quality of the household survey was largely superior to that of the civil registration/ A motivational survey done in "non-registering" households established that in most cases the non-registrants ignored the civil registration or did not see it as useful. The improvement of the civil registration which has taken place as a result of delayed registration has been estimated. The results after the survey are shown in Table 5.2 Estimated completeness rates in two dual collection Sheikhdoms of Tunisia, 1968-69

Household survey Civil registration

Births

Deaths

%

%

97 79

88 62

Source: Tunisia, 1973: 77

95

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table 5.3. The estimated vital rates of table 5.3 are lower than the implied estimated vital rates of table 5.2 by the extent of late registration. Table 5.3 Estimated completeness rates in dual collection, allowing for delayed registration, two Sheikhdoms of Tunisia 1968-69

Survey Registration Estimated crude rates Goraa Oued el Khatef

Births %

Deaths %

97 86.4

88 64.5

40.5 47.0

20.5 15.6

Source: Tunisia, 1973: 39 and 78.

5.5 The case of Senegal and Corner oun During the years 1965 to 1970 various pilot studies were done in Senegal (Cantrelle, 1969) and Cameroun(Podlewski, 1970). The common idea in all these experiments was to establish permanent observation of vital events. To start with, a basic register of individuals was created, and then kept up to date by repeated surveys. In order to check this updating, another source, usually a village notable, was asked to keep a book in which the principle events were noted. It is not really possible, then, to speak of a dual collection operation but rather simply of a checking mechanism. To our knowledge, the use of the PGE/ ERAD/ ECP formula for estimation of omissions, though possible, has not yet been attempted in these two countries. 5.6 An endeavour in Algeria In 1969-70, Algeria undertook a large multiround household survey very close in its conception to the Tunisian study. The sampling design, by clusters of approximately 500 persons, lent itself very well to the setting up of the dual collection system. The size of the sample was too large (about 700 clusters) for a dual collection system. A subsample was chosen of about 80 clusters (distributed within 20 communes, that is four clusters per commune) for which continuous recording was set up, independent of the household survey itself; The procedure of matching the vital event reports from the continuous recording and the periodic household survey was thus possible for a sample of nearly 40,000 people. Essentially the goal of the sub-sample was to measure the eventual under-reporting during the national survey intended to cover about one-third of a million persons (Pradel, 1970). For several reasons this operation was not continued: i. Difficulty in recruiting field personnel for the continuous recording was experienced. Though it was possible, at the start, to find suitable candidates in all 20 communities, most were not able or did not wish to continue the work for the 18 months during which the dual collection was to take place. Many reasons were given as 96

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the causes for their abandoning the work: an apparent lack of interest in a job which in practice duplicated the civil registration, limited proposed remuneration, travel difficulties (small motorcycles had been considered but proved to be unsuitable), etc. ii. Insufficient supervision: those directing the implementation, having sufficient problems with the main survey, were apt to neglect the continuous recording, which was considered secondary. iii. Difficulties in the exploitation of results: in spite of the preceding difficulties, the continuous recording functioned satisfactorily in five or six communes where the personality of the continuous recorder was fairly strong.5 The exploitation of the results of the main survey had been difficult enough because of changes among planners, and this led to the operation of matching events being considered secondary even in the 20 or 24 clusters where it was possible. An important lesson may be gained from the Algerian project. The decision to start a dual collection system must not be taken if it is not certain to be carried to term. It must not be an auxiliary operation lest it is neglected and unusable in the end. 5.7 Morocco: an extended experiment The CeRED (Centre de Recherches et d'Etudes Demographiques) is an organization which, located in Rabat, Morocco, has as one of its main purposes the implementation of a dual collection system. In so far as the PGE/ ERAD/ ECP technique relates to CeRED's essential mission, it can be expected that, contrary to the Algerian experience just cited, this organization will be concerned with the resolution of problems that may be posed by a dual collection system. The results which it will obtain will furnish valuable lessons. Morocco has at its disposal some experience in the collection of a demographic data, having brought to successful conclusion two censuses and a multiple-purpose survey, and having planned a civil registration which was obligatory, though far from universal in coverage and less in completeness. In this context, the role of the CeRED was facilitated by a number of elements: the presence of competent personnel at all levels, an administration already favourable to statistical operations, and a receptive population. On the other hand, the clearly experimental character of the operations undertaken in the framework of the dual collection system freed the officials from the worry and restraints of immediate and productive "pay offs". A sample of experimental areas was chosen, the initial object not being national estimation. The CeRED region, equal to about a quarter of the country, constituted a field of experimentation with differing problems. Out of this region a sample of some 84,000 people was drawn, 48,000 in rural areas and 36,000 in towns. Meanwhile, certain adjustments were made in such a manner that the results could eventually be extrapolated from the CeRED region to the level of national estimates. The definition of areas of observation took into account several criteria: i. The necessity of constituting clusters of a size such that the effect of the cluster (intracluster correlation) would not be too awkward. In the particular case, the choice of large clusters would not have posed estimation problems since it was not representativeness which was being sought. However, in order to maintain the value of the exercise as a test, it was necessary to take into account the needs of the eventual national system. The clusters finally adopted generally had a population in the order of 300 households. ii. The necessity of easily definable boundaries. In order to take two observations

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of the same population it was necessary that the territorial limits be sufficiently clear that neither field worker might over-run them. iii. The possibility of a subdivision into "daily rations". In order to be able to justify permanent work, and eventually to permit fairly strict controls, it was necessary that the continuous recorder determine each day, his intended work area. Given the topographical conditions, the number of visits possible in a day (to search for new events only) was estimated to be between 50 and 80 households. A cluster thus could be covered by a continuous recorder in four or five days. Assuming the desirability of touring households monthly, either one continuous recorder could be devoted fulltime to the observation of four clusters, or the employment of part-time recorders had to be considered, each to be employed for a week during each month. After having chosen, as a function of these diverse criteria, areas of observation (often corresponding to the census districts), the creation of a detailed map permitted clear identification of structures and, through them, households. Large scale plans were made and each structure was numbered on the sketch and also in the field, by means of a number painted on the door. Several particular cases should be mentioned: the presence of moveable dwellings (tents) in certain districts, a complex habitat of several households in the same building, and the appearance of new buildings in the course of the study. These do not appear to have presented major problems, the "CeRED number" having been rapidly adopted by the non-mobile population in the study zone. The de facto convention was adopted in the periodic survey and in continuous recording. An exception was made for births taking place in specialized institutions (hospitals, maternity clinics) which were counted at the place of residence of the mother. This exception was justified by the importance of this phenomenon, particularly in the city of Rabat. The two procedures, continuous recording and periodic survey, were operated by distinct and separate teams, in principle without any contact. The continuous recording requires frequent information from each household. Each event occurring between two interviews is noted with its characteristics. For each event a separate questionnaire is made out in triplicate, one copy of which is left in the home. In urban areas all households are visited monthly in a systematic way, whereas, in rural milieux the continuous recorder has chosen a number of "routine round contacts" (see Glossary) or information points and only visits those households for which he has obtained "first intelligence" (see Glossary) that an event has taken place. The periodic survey is of the multi-round interview type, normally with six-month intervals between rounds. In practice it does not seem that the exact constancy of the interval can be respected. At each round the survey interviewers fill out a complete household questionnaire and also a separate document for each vital event. The periodic household survey and the continuous recording are strictly controlled, as much to ensure their own quality as to avoid contacts between the field workers which might be prejudicial to the independence of the two procedures.6 All the questionnaires corresponding to the vital events are then entrusted to a third team, working in the headquarters office, who are charged with the case-by-case matching. Returns to the field to verify cases in doubt are foreseen, but it is not yet specified whether these will be done by the third group. The dual collection system having been established late in 1971 and gone on for only a few years, few data are as yet available. They are presented in chapter 7. However, already several general remarks may be made: i. Resolutely organized and using the necessary means, this operation appears to have a more serious chance than others to lead to important results. ii. The existence of statistical and census operations as well as of civil registration 98

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in the same areas risk prejudicing the dual collection system: a certain confusion must develop in the population between all these operations, and the tendency to furnish every field worker with the same responses becomes more convenient, more especially since appropriate reference documents have been created and distributed to respondents. Thus, even though the independence of the field workers appears effectively assured, the independence of their observations seems to be contestable.7 iii. Such matching experiences as are available suggest and will suggest subtle problems, the reported characteristics of events varying enormously: spelling of family (or Kounia) and given names, age of the deceased, ages of parents, etc.8 It seems that, in the final analysis, the only element in the two questionnaires which can almost certainly be matched is the date of the event. But this element is one of the most susceptible to the risk of non-independence. A fuller report on the matching experience is given in chapter 8. 5.8 Dual collection in Liberia Started in 1969, the Liberian Population Growth Survey was based entirely on the principles of a dual collection system. It had as its objectives the provision not only of estimates of births and deaths, but migration as well. The operation, carried out by means of a survey using a sample of about 70,000 people (one-twentieth of the total population of the country) is conducted in a manner similar to that of Morocco's: the monthly recording of events by a continuous recorder, who is resident in the PGE area; and an independent, periodic household survey, twice yearly, by outside interviewers. At the start, an overview of the population is conducted by field workers of both procedures together, who have also jointly prepared the necessary geographic maps. During this overview every household is visited and a household list is drawn up without enquiries about vital events. It is only after this baseline survey that the two teams become independent.9 The continuous recorders then visit each household on a monthly basis, recording events and keeping the household's list up to date. The survey interviewers, in groups of three, visit the households after six months, prepare a new list, and ask about events that have taken place in the meantime. Note that the continuous recorders are also equipped with a fertility questionnaire, allowing them to note pregnant women. The originality of the Liberian system lies in its utilization of various methods of motivation, for the field workers of both procedures designed to enhance their behaviour as well as to insure that they remain independent. To this end "encouragement bonuses" are given to each continuous recorder who records a subsequently verified event, and to the survey interviewer for each event uncovered by him and omitted by the interviewer. In this way continuous recorders have it in their best interests to record a maximum number of events, while the survey interviewers will try to find as many omissions as possible.10 Obviously, careful controls are needed to avoid the creation of fictitious events. This system appears to have been satisfactory in this regard. Encouragement is not restricted to field workers alone, but is also directed to the population by means of letters of congratulation for births and condolences for deaths. These techniques also help to implement the controls. For the first survey period (May to October 1969) results concerning births and deaths were analyzed in total and by strata. The criteria of stratification, chosen a priori, were as follows. For births: age of mother, sex of infant, and birth order. For deaths: age and sex of deceased. It did not appear that greatly different results were 99

5.5

F. Pradel de Lamaze

Table 5.4 Vital rates in Liberia, 1969.

Rural areas Urban areas Liberia

Population

Birth rate

1,123,380 399,670 1,523,050

50 52 51

Death rate

Infant mortality rate per 1,000 pop per 1,000 pop per 1,000 live births 18 12 16

158 82 131

Source: Quesnel, 1972. obtained as a result of stratification.11 Order of birth appeared to be important, and it was noted that male deaths were more likely to be omitted than female deaths and conversely female births were more difficult to detect than male births. Also, infant mortality appeared to be under-reported by mothers at their peak fertility. For the period reviewed, vital rates were obtained and are presented in table 5.4. The Liberian method seems to be satisfactory on the basis of table 5.4 for births and deaths, even though the causal independence may be questionable.12 Not so with migration, which is decidedly recorded with a serious bias.13 Though one may assume equal probability of observing a birth within each procedure of observation, the hypothesis is definitely unsupported for migrations. The results of the migration question in one district are summarized in table 5.5 It is evident from table 5.5 that such discordant results raise doubts not so much in the application of the dual collection system as such, as in the possibility of serious study of migration through this system. Table 5.5 Migrants found by the procedures of a PGE/ ERAD/ ECP enquiry, Liberia: District of Voinjama, 1969 District of Voinjama

1 May to 31 October, 1969 Number of migrants

Findings Findings Findings Findings

196 186 141 149

by both procedures by monthly survey alone by 6-month survey alone by checking

Source: Quesnel, 1972. Discussion by William Seltzer

To start with, I would like to express my deep appreciation to Pradel de Lamaze for presenting results from the dual collection studies conducted in Madagascar. Many of us have heard something about the existence of this study, but what we heard provided 100

Francophone Africa and Liberia

Discussion

a vague and sometimes conflicting picture of the nature of the study. Indeed, as the years went by, I had all but abandoned hope of learning more about it. Pradel de Lamaze has performed a notable service to the international statistical community by making the results and experience of the study generally available.14 None of the detailed comments that follow should be seen as detracting from an overriding sense of gratitude to the author for his noteworthy contributions. With regard to the specifics of the chapter, I have two comments to offer. First, I think Pradel de Lamaze might wish to supplement his present discussion of the errors introduced into PGE/ ERAD/ ECP estimates by lack of independence between the two procedures, by considering how the ratio of the dual system estimate of events to a comparable single system estimate behaves as independence is reduced. (You will see at the end of the next chapter how while pondering over the Egyptian exercise, by considering a ratio myself, I recovered from an attack of "correlation bias syndrome".) Pradel de Lamaze is properly worried about positive response correlation, and it is certainly true that the ratio of the PGE/ ERAD/ ECP estimate of events to the single procedure estimate will decrease as independence is reduced. However, with positive correlation between two procedures the ratio will never decline below one. Therefore, even in the face of substantial lack of independence, one would prefer the dual collection estimate of the number of events to the comparable single procedure estimate, unless cost or other sources of error indicate another choice. Secondly, closing section 5.2, Pradel de Lamaze observes that the dual collection method is of "Anglo-Saxon origin" and the use of this method "has been confined so far mainly to the territories formerly part of the British Empire". As long as we do not forget the word mainly, and as long as we confine ourselves to vital statistics measurement, I would agree with the correctness of this observation. The question then becomes, are we observing an historical accident — that is, a sort of variance — so that with time we can expect that both the Anglophone and Francophone literature will be equally rich; or are we observing a bias of some sort? Pradel de Lamaze implies that there is, indeed, a "certain resistance" against the technique in Francophone countries. If this is really so, I am deeply saddened. After all we owe much of the foundations of probability theory to the brilliant formulations of French rationalism. I am sure, were he alive today, that Laplace would be among those strongly advocating the use of PGE/ ERAD/ ECP methods. For the dual collection estimate, where the match rate of one procedure is the completeness estimate of the second procedure, is nothing more than an application of the calculus of probabilities to a particular class of problems. Indeed, I would not be at all surprised to hear that Laplace, in some forgotten paragraph, did in fact suggest such a dual system. But whether the dual collection system is referred to as the ChandrasekaranDeming technique or as the Laplace technique, I do hope that survey statisticians in all countries will consider it an available tool by which imperfectly collected data can be improved. Endnotes to Chapter 5

1. The historical survey in chapter 2 of the PGE handbook (Marks et al., 1974) shows that the PGE/ ERAD/ ECP technique has been used in many countries and with a variety of purposes long before its more recent application to vital events. In our chapter 10 a method of estimating census completeness is suggested through the use of the PGE/ERAD/ECP technique. [Editor's note.] 2. A commune is the smallest territorial division, approximately equal to a parish. 101

Endnotes

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3. In the PGE handbook (Marks et al., 1974: 250-253) special attention is paid to the possibility of using two household surveys as the two procedures of a PGE system. Until somebody tries thoroughly and competently there will be no empirical evidence concerning the validity of this suggestion. [Editor's note.] 4. In the original report on the Tunisian exercise the suggestion is made that perhaps the civil registration is less incomplete than the PGE/ ERAD/ ECP evaluation indicates, because there were delayed registrations of which the matching process was ignorant (Tunisia, 1973:77). On the assumption of even flow such delayed registrations do not lower the reported vital rates, except in the trivial sense that there is population growth. Any one period deprived of its own delayed registrations is compensated by delayed registrations from the preceding period. The effect on the estimated vital rates of the recovery of delayed registrations is less certain: in terms of the categories given in figure 1.1 the first category probably increases and the second category correspondingly decreases; in consequence the fourth category, always rather small, decreases very slightly; on the other hand, the third category might increase with consequential increase in the fourth category. On balance there is probably a very slight decline in the overall estimate in any actual case. [Editor's note.] 5. The continuous recorders were called in Algeria "enregistreurs permanents". [Editor's note.] 6. As argued in section 1.6 the independence between the two procedures is achieved not by strictly controlling the absence of contacts between the field workers of the two procedures, but by structuring all aspects of the two procedures in such a manner that contacts do not occur and that neither side sees any benefit in them occurring. [Editor's note.] 7. Pradel would be even more concerned with the independence of the observable events if he knew that a proportion of households in Morocco have booklets of vital events and like to reply to questions concerning vital events by reference to these booklets. There is no denying the critical importance of the independence for a PGE/ ERAD/ ECP system. [Editor's note.] 8. An informal survey conducted by the editor among Moroccan acquaintances (n = 37) suggested that 54 percent of Moroccans have no Kounia. Moreover, the variability among the Kounia available seems to be as limited as that of family names among the old timers of Quebec. CeRED has now thousands of Kounias collected and could provide a definitive answer to the usefulness and the strength of the discriminating power of this characteristic. [Editor's note.] 9. It will be noted that in terms of the argument of chapter 1, common field work between the field workers of the two procedures is an offence against the desirability of separation. Furthermore, it should be noted that the continuous recorders in Liberia were called interviewers, which is a neutral description, but the survey interviewers were called supervisors, implying invitation to interfere with the continuous recording. In PGE/ ERAD/ ECP parlance this is known as the "Turkish error" where it was committed for the first time. India introduced it on a large scale. [Editor's note.] 10. In fact, if the continuous recorder and the survey interviewer are co-operative, they can divide the events evenly among themselves and maximize in this manner their respective encouragement bonuses. As we repeatedly argue in this volume, quality checks in the field tend to destroy the benefits of PGE/ ERAD/ ECP. If the administrative capacity to operate the bonus is available, it should be devoted to furthering the true purposes of PGE/ERAD/ECP. [Editor's note.] 11. There are few reports available that would show the benefits of such stratification. In fact, the only one that springs readily to mind is the experience reported in the original Chandrasekaran-Deming article (1949). [Editor's note.] 102

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Endnotes

12. Either the stratification carried out in Liberia has not been done on the most relevant variables, or the indirect dependence which Pradel points out so consistently, does not amount to much. [Editor's note.] 13. Pradel does not say on what bases he considers the Liberian migration underreported, and we do not take up this matter in this volume, but it is noticeable that in section 6.5 the migration reported from the Egyptian survey is apparently excessive. 14. Actually the data for Madagascar and details on the features of the mode of collecting data were available, at least in a bilingual country such as Canada, since 1969 (Gendreau) and 1971 (ORSTOM et a/.), but there is no denying that the sources quoted are difficult to come by. [Editor's note.]

103

Chapter 6 The Egyptian Study to Measure Vital Rates: Some Estimates by Dual Collection1 K.E. Vaidyanathan 6.1 Introduction The dual collection principle was incorporated in a large demographic survey carried out jointly by the Cairo Demographic Centre and the Egyptian Central Agency for Public Mobilization and Statistics during 1965-66. The study, sponsored and funded by the United States National Center for Health Statistics, aimed at deriving vital rates for the rural areas of Lower Egypt. The enquiry consisted of three parts: (i) a complete survey enumeration of all households in the selected villages at three dates six months apart; (ii) a continuous recording of vital events; and (iii) a fertility history schedule (Vukovich, 1965; Vaidyanathan, 1971;Zaghloul, 1971). The analysis presented here is based on matching events reported in the household survey with those recorded in the continuous recording. This is one of the earliest studies incorporating the dual collection principle and a brief description of the study design will be in order for its methodological interest. 6.2 Study design The survey design was one of stratified random sampling. The villages of the eight provinces of Lower Egypt were grouped according to population size into three strata, namely, (i) less than 2,000; (ii) 2,000 to 4,999; and (iii) 5,000 and more inhabitants. The 1960 census of Egypt provided the figures for the above stratification. The sample covered approximately 100,000 persons or about one percent of Lower Egypt's population. The number of villages to be sampled from each stratum was determined by dividing one percent of the population of the stratum concerned by the population of the median village in each stratum (which were 1,200,3,200 and 7,000 respectively). The number of villages required for each stratum sample to provide equal sampling fractions came to eight in the first stratum, 11 in the second, and six in the third. Three household surveys of the sample villages were carried out on a dejure basis on November 30, 1965, May 31, 1966, and November 30,1966. In the first survey the following information was elicited through a household schedule: (i) relation to head of household; (ii)sex; (iii) age based on date of birth; (iv) marital status; (v) religion; (vi)educational attainment; (vii) place of birth; (viii) duration of residence in the village; (ix) employment status; (x) present occupation; (xi) previous occupation; (xii) industry; and (xiii) the number of children ever born(for ever married females only). It 104

The Egyptian study

6.2

was also noted whether the individual was present or absent at the time of the enumeration. The second survey was carried out exactly six months after the first one. The schedule used this time was the schedule of the 1966 Sample Census of Egypt, which elicited more information concerning women who had married more than once. The third survey was carried out exactly twelve months after the first one using a schedule similar to that of the second survey, with an additional question regarding the vital events that had occurred during the preceding 12 months. The second procedure, namely, the recording of vital events, was carried out on a continuous basis beginning from the date of the first survey (30 November, 1965) until the date of the third and final survey (30 November, 1966). The continuous recorders (who were lady health visitors) were posted for a group of two or three villages and were expected to record the vital events irrespective of whether they were registered by the civil registration authority. The vital events occurring each month were recorded on six separate forms pertaining to births, deaths, marriages, divorces, in-migration, and out-migration. These records also included the usual questions regarding the characteristics of the parents in the case of births and the characteristics of deceased persons in the case of deaths. A copy of the household schedule completed during the first survey was supplied to the continuous recorders to provide the basis for their enquiries.2 The recorders were also required to utilize the services of informants to elicit information regarding vital events. The third part of the enquiry concerned the fertility history of ever married women and was included in the first survey. The questionnaire consisted of two parts. The first part elicited information on the number of marriages and their duration, pregnancy history, and the characteristics of the ever married women. The second part of the schedule included questions on knowledge, attitude, and practices of family planning. The fertility questionnnaire was completed over a period of six months in order not to overload the main survey schedules, and also to enable the survey interviewers to establish rapport with the household members before embarking upon the delicate questions included in the fertility history schedule. The field operations for the surveys were carried out by the staff of the Egyptian Central Agency for Public Mobilization and Statistics, while the continuous recording of vital events and the canvassing of the fertility history schedules were carried out by the female health workers. The supervision of the entire operation was entrusted to the staff of the Central Agency who had considerable experience in such work. They were given training in the filling up of the survey schedules, their scrutiny for internal consistency, and in the matching operations. The separation of the twin tasks of periodic surveys and the continuous recording of vital events was done with a view to avoiding violation of the independence of the two procedures. The survey interviewers were men drawn from the statistics department and were stationed in the field headquarters. The continuous recorders of vital events were women drawn from the health department and stationed in the villages. Thus the staff of the two procedures were kept physically and functionally separated from each other. The item-by-item matching of the vital events as reported in the third survey and the vital event records were done on the basis of three criteria: address, name, and sex. The difficulties of matching would have been enormous if an additional variable like age were involved. Since the matching was done at the field office, it was possible for the inspectors in charge of matching to visit the households concerned to verify any unmatched events, which were fewer than the matched cases. The field operations, supervision, and matching were done in an exemplary manner, and it may be assumed that the number of false matches will probably offset the number of false non-matches.

105

6.3

K.E. Vaidyanathan

6.3 Findings of the study The study provided valuable data on population characteristics as well as the components of population change in rural Lower Egypt (Zaghloul, 1971; Vaidyanathan, 1971). This section is limited to the findings of the matching between the two independent data procedures. In this analysis, the reports on births, deaths, marriages, and divorces obtained in the vital event continuous recording were matched with the events in the survey year gathered through the third periodic survey on 30 November, 1966 in order to determine which were reported by both and which by either procedure alone. This information provided the basis for the estimation, under certain conditions, of the extent of completeness of each procedure and the proportion of events missed by the two procedures. The PGE/ ERAD/ ECP estimation procedures, as elaborated in the introductory chapter by Krotki, were adopted and are therefore not repeated here. What bears repeating is that these estimations are valid subject to the condition that the two procedures are statistically independent. Despite all the precautions taken to preserve the independence of the two procedures, it is not unlikely that some common discrepancies and other built-in interdependencies could have crept into the two procedures. This aspect has to be borne in mind while interpreting the results of the matching shown in tables 6.1 and 6.2.

Table 6.1 Dual collection estimation of vital events in the Lower Egypt Survey, 1965-66

Records Survey and only survey C Births Stratum 1 Stratum 2 Stratum 3 Total

428 1522 1501 3451

Record only

122 467 414

35 192 249 476

1003

66 246 264 576

PGE/ERADTotal reported in / ECP Estimate Survey Record S\ 82 Si S2 C

463

550

594

1714 1750 3927

1989 1915 4454

2240 2232 5066

174 622 536

219 775 690

249 912 868

1332

1684

2029

Deaths Stratum 1 Stratum 2 Stratum 3 Total

1108

21 93 110 224

Marriages Stratum 1 Stratum 2 Stratum 3 Total

107 387 321 815

7 31 56 94

33 128 124 285

114 418 377 909

140 515 445

149 556 522

1100

1227

Divorces Stratum 1 Stratum 2 Stratum 3 Total

32 86 63 181

2 8 12 22

9 27 22 58

34 94 75 203

41 113 85 239

44 124 101 269

106

153 529 426

6.3

The Egyptian study

Table 6.2 Estimated vital rates from two dual system procedures and the percentage completeness, the Lower Egypt Survey 1965-66

PGE estimate

Rate per 1000 persons Survey

Recording

Percent completeness2 Survey Recording

Births Stratum 1 Stratum 2 Stratum 3 Total

48.0 47.2 46.4 46.9

37.4 36.1 36.3 36.3

44.4 41.9 39.8 41.2

78.0 76.5 78.4 77.5

92.5 88.8 85.8 87.9

Deaths Stratum 1 Stratum 2 Stratum 3 Total

20.1 19.2 18.1 18.8

14.1 13.1 11.2 12.3

17.7 16.3 14.4 15.6

70.0 68.2 61.8 65.6

87.8 84.9 79.4 82.9

Marriages Stratum 1 Stratum 2 Stratum 3 Total

12.0 11.7 10.9 11.4

9.2 8.7 7.8 8.4

11.3 10.8 9.3 10.2

76.8 75.2 72.3 74.0

94.1 92.6 85.3 89.6

Divorces Stratum 1 Stratum 2 Stratum 3 Total

3.6 2.6 2.1 2.5

2.7 2.0 1.6 1.9

3.3 2.4 1.8 2.2

77.2 75.6 74.1 75.4

93.1 91.0 84.1 88.8

Note: 1. The denominator for the computation of these rates is the population as recorded in the second survey on 31 May, 1966 which corresponds with the mid-point of the reference period. 2. Completeness of each procedure is expressed as a percentage of the PGE/ERAD/ECP estimate. An examination of the estimates presented here indicate that by far the larger number of vital events were recorded in the continuous recording than in the periodic survey. The continuous recording of vital events, despite its inherent limitations, appears to be a more efficient procedure, if the kind of supervision exercised in the Lower Egypt study is present. The continuous residence of the recorder in the villages permits a greater rapport with the populace and facilitates the establishment of an informant system.3 Equally, this demonstrates the limitation of the retrospective household survey as the basis for deriving vital rates. The common problems were recall lapse and boundary effects, despite the fact that the temporal boundaries of the reference period were clearly defined by the first and last survey. Secondly, the match rates between the two procedures are consistently high, indicating, in the absence of collusion, that the two procedures have functioned as well as they could. There are variations in the extent of completeness of the two procedures in the different strata and for different events. From the last two columns of table 6.2 it appears that, barring a few exceptions, the procedures have worked better in the 107

6.3

K.E. Vaidyanathan

smaller localities (stratum 1) than in the larger ones (stratum 3). This may be a reflection of the large distances involved in the larger localities, which probably inhibit close contacts between the field worker and respondents. Thirdly, in both the procedures involved, the continuous recording of births, marriages, and divorces has fared better than the continuous recording of deaths. The ratio of omission rate for deaths (100 minus the completeness rate) to the omission rate for births varied between the strata; for all strata it was slightly over 1.5.4 As in the case of births and deaths the completeness of marriage and divorce reporting was better in the continuous recording procedure than in the periodic survey. Within each procedure, the completeness of marriages and divorces was nearly of the same order, about 75 percent in the periodic survey and 89-90 percent in the continuous recording procedure. It is of interest to examine the vital rates derived by the dual collection matching with those obtained from each procedure. As one might expect, the vital rates derived from the dual collection approach are higher than those derived from each of the two procedures involved. The estimate of the birth rate was 46.9 against 36.3 from the periodic survey and 41.2 from the continuous recording; the estimated death rate was 18.8 in the dual collection while it was 12.3 and 15.6 according to the periodic survey and continuous recording respectively. The estimated marriage rate was 11.4 as against 8.4 and 10.2. Likewise, the estimated divorce rate was 2.5 as against 1.9 in the survey and 2.2 in the continuous recording. Indeed the dual collection estimates are closer to reality (see section 6.4) than those provided by the two individual procedures. Another observation that emerges from table 6.2 is the consistent downward trend in the vital rates with the increase in the population size of villages. For instance, a difference of three to five percent between the first and third strata appears to be a common feature, and in the case of divorce rates the difference is even larger. Five possible explanations could be offered for this: (i) sampling fluctuations; (ii) genuine variations in the fertility, mortality, and nuptiality patterns of different strata; (iii) differences in the completeness of vital events reporting in the different strata;' (iv) compositional differences in the population of the three strata; (v) positive response correlations greater in stratum 3. It is probable that all the five factors are confounded in the estimates derived. 6.4 An evaluation of the estimates An evaluation of the estimates derived in this chapter can be attempted by making a comparison of these estimates with those derived from civil registration (Capmas, 1970). The comparison is attempted in table 6.3. The dual collection estimates of birth and death rates (46.9 and 18.8 respectively) are higher than those yielded by civil registration (41.3 and 15.0 respectively). It is known that civil registration is nearly complete in Egypt, but it is more complete in rural areas with health bureaux than in those without health bureaux (Valaoras, 1972). The crude birth and death rates for rural areas with health bureaux (42.3 and 17.5 respectively) are lower than the estimates derived in this study. The same can be said of the marriage and divorce rates. It appears that the vital rates derived by the dual collection system are slightly overestimated, probably because the number of false non-matches exceeds the number of false matches. This is likely to be the case where more than one recording procedure is involved, because the same individual may report two different names or ages for each procedure. Further, as repeatedly pointed out in this book, the assumption of independence between the probabilities of recording a valid event in the two procedures may be less than complete.6 The error in the 108

The Egyptian study

6.4

Table 6.3 A comparison of the dual collection vital rates with those of civil registration Vital rate

PGE estimate"

Vital statistics2

Crude Crude Crude Crude

46.9 18.8 11.4 2.5

41.3 15.0 9.8 2.1

birth rate death rate marriage rate divorce rate

Source: 1. Table 6.2 2. Capmas, 1970. derived estimates will therefore comprise two kinds of errors: the sampling errors and the dual estimation error. These two kinds of errors are likely to be differently related to sample size. Where sample size is small, the sampling error is likely to be large and the matching error small, and vice versa.

6.5 Conclusion The dual collection system enables the derivation of vital rates that are closer to reality than those provided by any single system. Its added advantages are that only serious social investigators are likely to undertake it, that they are likely to carry out field work of high quality, and that it yields an estimate of the degree of completeness of the two procedures. In the Lower Egypt study, a question on the vital events of the preceding one-year period was asked only in the third survey. The results might have been better if a prospective element had been incorporated by asking in the second and third surveys a question on the vital events that occurred since the previous visit. By making the recall period shorter (six months), the errors due to recall lapse and boundary effects could be lowered.7 This would also have facilitated comparisons between the vital rates for the two half-year periods. Another aspect that deserves mention in the light of the experience in this study concerns the value of the dual collection procedure for estimating migration. The data gathered in this study (not presented in the chapter) gave rise to high in- and outmigration rates, which cannot be explained by the socio-economic circumstances in the selected villages. It appears likely that there are « jme inherent limitations in the application of this approach for estimating migration. Further research is needed on this aspect. The organization and administration of a dual collection system is more expensive and complex than the running of any single system. For a country such as Egypt, which has a very nearly complete recording of vital events, the gain is not commensurate with the cost and effort involved. However, such a dual system is necessary and more dependable for countries (such as India) that face an uphill task in developing a more complete civil registration system. The potentiality of the dual collection method for deriving demographic measures in African countries is indeed great. The Lower Egypt study can serve as a basic model for African countries. Such a model must, of course, be modified to suit the conditions of individual countries. 109

Discussion

William Seltzer

Discussion by William Seltzer With respect to the details of Vaidyanathan's contribution, I have two questions and then three comments. First, my questions: i. Would the author provide us with more detailed information about the basic data collection procedures used in the continuous recording system? Perhaps in a paper for a methodological journal? In particular, were reports of events obtained by an "active" or "passive" procedure? If the former, who was contacted and at what frequency? And how was the system supervised? ii. Similarly, would Vaidyanathan provide more details about how the matching was carried out and the results of the field follow-up procedure? For example, I assume from his paper the matching was done on the basis of implicit matching rules. Is this assumption a correct one? Who actually did the matching? What was their training? How were they supervised? When was the matching done and how long did it take? How many out-of-scope reports were identified during the field follow-up? How much variability was there among the various field offices in the match rates, the rates of field follow-up, and the proportions of reports found to be out-of-scope? Now for my comments: In his discussion of table 6.2 at the end of section 6.2, Vaidyanathan observes that there is a "consistent downward trend in the vital rates with the increase in the population size of villages" and indicates four possible "explanations." My first thoughts were to suggest that a fifth factor, correlation bias, should be added to the four factors listed by VaidyanathanJ (The notion being that the observed inverse relationship between the PGE/ ER AD/ ECP estimates of the vital rates and the size of the sample areas might be due, in part, to the two vital events reporting procedures functioning in a less independent manner in the larger areas than the smaller ones.) However, on more thoughtful reflection I think it is apparent that I fell victim to "correlation bias syndrome". This is a common malady afflicting those evaluating any set of PGE/ ERAD/ ECP estimates for the first time, in which the perceived impact of correlation bias on the estimates becomes so irrationally swollen that there arises a blindness to the existence of all other sources of error. Fortunately, although attacks are very common, the condition need not last long. In the present case, recovery occurred as soon as I noticed that the ratios of the stratum 1 to the stratum 3 dual system estimates were closer to unity than were the comparable ratios for either of the single system estimates. Of course, this did not rule out the possibility that correlation was affecting the PGE/ ERAD/ ECP estimates in some modest way, but it did serve to remind me of a number of other unlisted factors that should be considered as potential sources of error. With respect to the PGE/ ERAD/ ECP estimates, four other sources of error have been identified in the literature: (i) net matching error; (ii) out-of-scope reports; (iii) ratio bias; and (iv) errors in the base population count. If one asks which if any of these factors could be responsible for raising vital rate estimates (for both births and deaths) in small villages relative to those in large villages and doing so in at least as pronounced a fashion for single system estimates as for dual system estimates one must conclude that only the last factor could, by itself, produce the observed pattern. Based on this reasoning, I would suggest that Vaidyanathan add to his list of five factors, a sixth, "differential errors, by size of sample area, in the base populations used to calculate the vital rates". Of course, like Vaidyanathan, I believe that "it is probable that all t h e . . . factors are confounded in the estimates ..." (section 6.3). My second comment relates to Vaidyanathan's attempt to explain why early in section 6.3 "by far the largest number of vital events were recorded in the continuous 110

The Egyptian study

Discussion

recording than in the periodic survey". Quite correctly he focuses on a number of differences in the characteristics of the two collection procedures. A difference not mentioned in this context, and perhaps an important one, is that the survey interviewers were men and the continuous recorders were women. I believe there is some sketchy evidence from India indicating that in gathering reports of vital events women do better than men, particularly when the respondent is also a woman.' Clearly, this is an area that needs more research since the use of female interviewers will entail higher field costs in a number of countries. In order to determine whether these added costs are justified by improvements in quality, comparative data on costs and performance, by sex of field workers, will have to be compiled. Finally, Vaidyanathan remarks that "a dual collection system is more expensive and complex t h a n . . . any single system. For a country such as Egypt, which has a very nearly complete recording of vital events, the gain is not commensurate with the cost and effort involved" (section 6.5). I would fully agree with the conclusion that a dual collection system is not necessary for the purposes of vital statistics estimation for a country with a complete and current system of civil registration. However, I would argue that some sort of registration completeness test is in order to determine whether, in fact, the civil registration system is as complete as one hopes it to be. Based on the data presented in table 6.3 I would say that, although the civil registration system in Egypt is moving close to satisfactory completeness, the system still has some distance to go. Of course, dual collection systems have frequently been used to test the completeness of civil registration and to adjust the resulting vital statistics for incompleteness. Indeed, it is my understanding that the Government of the Arab Republic of Egypt is now undertaking a test of birth and death registration completeness using the PGE/ ERAD/ ECP approach. Endnotes to Chapter 6

1. The author is grateful to Dr. M.A. El-Badry and Dr. M.N. Murthy for their helpful comments. The author is alone responsible for the views expressed in the chapter. 2. It will be observed that normally handing over the survey documents to the continuous recorders would be a severe breach of the requirements of independence between the two procedures. There might have been in Egypt features of the operations that made this breach less severe. [Editor's note.] 3. A difference in principle, and probably in effectiveness, should be drawn between informal informants, however formally appointed, and the routine round contacts (RRC: see Glossary) established as part of the structured duties of continuous recorders. [Editor's note.] 4. See section 9.2 for a comparison with other African PGE/ ERAD/ ECP results and an average result for Asia. [Editor's note.] 5. If the PGE/ ERAD/ ECP technique were applied properly then the differences in the completeness of vital event reporting between strata would not affect the estimate. The second, third, and fourth categories would be simply greater, and the first category would be smaller. In fact the estimates were lower, but so were those for deaths, marriages, and divorces, which rules out the plausibility of explanation (iv) and partly (i) and (ii). Could it be that the loss of independence was more pronounced and effective in stratum 3? In any case, as pointed out later on by the discussant, the problem is less severe than in the corresponding values from the single system estimates. [Editor's note.] 6. It need not be pointed out at this point when we are so far into this volume that 111

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the existence of such indirect dependence would underestimate the rates derived. [Editor's note.] 7. Twelve months are easier to ask about ("same season last year"). The PGE/ ERAD/ ECP formula is powerful enough to look after memory lapses greater in the earlier six months than in the more recent six months. [Editor's note.] 8. In the version published in this book the author added the fifth possible source of error but not the others suggested further on in the discussion. [Editor's note.] 9. During a fertility survey in Edmonton in 1975 female interviewers established such excellent rapport with female respondents that on a number of sensitive questions they obtained the same answers as answers collected under the protection of the randomized response technique, e.g. proportion engaged in premarital sex 61 and 62 percent respectively (Krotki and Fox, 1974), though there are limits to what even women can achieve. Less than one-third of abortions have been admitted in direct conversation in comparison with the answers obtained through the randomized response technique. With regard to the cost of female interviewers demanded by the discussant later on, it can be reported that during the First Population Census of Sudan 1955/ 56 females were used in the PES at a cost about double that of male enumerators, not so much because they commanded high rates of pay, but more so because in the circumstances of an orthodox Moslem society they had to be carted long distances between their headquarters and place of work. Their sleeping accommodation had to be specially sought and protected.[Editor's note.]

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Chapter 7 Some Practical Problems Suggested by the Application of the PGE/ ERAD/ ECP System in Morocco M. Rachidi

1.1 Moroccan demography The population of Morocco has been characterized by rapid growth over the last 40 years. It has grown from 6,600,000 in 1935 to 8,600,000 in 1952, attaining 11,100,000 in 1960 and 15,150,000 in 1971 (Maroc, 1965; Maroc, 1972). At the present rate of growth, the Moroccan population will be approximately 20 million by 1978. This increase in the population is a consequence of a continuing high level of fertility and rapidly falling mortality (Maroc, 1967). It is estimated that the birth rate is about 50 per thousand, the mortality rate is in the order of 15 per thousand, resulting in an annual rate of natural growth in the order of 3 to 3.5 percent. The overall growth rate is alleviated somewhat by emigration. This particularly high growth rate leads to an unfavourable demographic situation, not only in terms of the general rhythm of growth but also because of the age structure of the population. Individuals under 15 years of age represent more than half of the total population.' It is important to realize that an age structure such as this presents an enormous strain economically and socially (Maroc, 1968). The existing demographic data are, for the most part, based on the population census of 1960, a multiple purpose survey done in 1962, and the census of 1971. These sources provide a fragmentary and largely out-of-date base on which population projections can be made and the demographic phenomena of the country can be studied. Knowledge of the rate of natural increase of the population and its composites, natality and mortality, constitutes an indispensible base for all economic and social planning. It is in this frame of reference that the dual collection system is applied to Morocco (Krotki and Rachidi, 1971). The principle purpose is to determine the rate of demographic growth and its composites. The application of the method also has methodological objectives: to test a number of practical and organizational questions relevant generally to any demographic inquiry and particularly to the PGE/ ERAD/ ECP technique. The primary purpose of this chapter is not to describe the dual collection system in the CeRED region, but to present some reflections concerning various aspects and issues based on the experience of the Moroccan exercise with the PGE/ERAD/ECP technique. The purposes and general outline of the CeRED study have been given in section 5.7.

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1.2 The periodic household survey and its rotating objective The surveys had two permanent objectives: (i) to obtain reports of vital events; (ii) to provide the population base necessary for the calculation of vital rates; and one rotating objective, which during the first survey was (iii) to collect data on marriage and childbearing. The survey was to be taken every six months with a one-year recall period. During the first round, between July and December 1972, information was collected about parent survival.2 In the second round we collected information on age at marriage, divorce, and birth history. An attempt was made to determine ages on the basis of a societal, historical calendar. The third objective, because it was very ambitious, created some difficulties and increased interview time and costs. With regard to the frequency of surveying, we followed the preferences expressed in section 2.3.c in favour of six-month intervals between rounds. Frequency must also be related to other considerations such as the size of the clusters, distance between clusters, and the types of personnel available (permanent or part-time). 7.3 Cluster size and some consequences The cluster size in the Moroccan sample was 1,500 persons, that is, approximately 300 households. In the rural areas the boundaries of the clusters were fixed by our staff, ensuring approximately the desired cluster size. The national census, which was organized a few months before we began our dual collection system, had divided urban areas into "districts" containing about 1,200 persons. These districts were originally taken as clusters for our dual system, but when the boundaries of the clusters were fixed, it was found that the average urban cluster size was only about 900 persons. To obtain the desired cluster size, we combined randomly two neighbouring census "districts" to form one cluster. This was done for 12 out of the 28 urban clusters. The boundaries of the clusters were verified using district maps from the 1971 census. Revised maps were then drawn up. We attempted to determine the optimal cluster size with regard to local conditions, and as dictated by the cost of field work, and other costs. We followed in this respect the principles discussed in section 2.2.d of this book. Each urban and rural cluster was divided into five smaller areas called "laches journalieres" or "daily rations" (see Glossary). This concept is described in section 5.7. We tested for the variance involved when one, two, three, four, or all five daily rations in each PGE area were used in the estimation of the total vital events. It will be remembered from section 5.7 that the total sample was about 84,000 people, of which 36,000 are in urban areas. Although the sample includes strata that cover diverse population groups in Morocco, it is not a national probability sample. However, we are now considering extension of the dual collection system to a national sample. Regarding the constitution of clusters in rural areas, the method used consisted of forming new units in the sampling frame out of the administrative communes. These are called enlarged communes and statistical communes. The boundaries of a statistical commune should have limits recognizable in the field, and the mathematical expectation of their population size should be equal to that of the corresponding administrative commune (Fellegi, 1971; Fellegi and Krotki, 1972).3 In certain statistical communes we had mixed clusters; that is, those having a part of their population belonging to the chosen administrative commune and another part belonging to neighbouring

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communes. A majority of such clusters had a large proportion of their population coming from the chosen administrative commune. This situation demonstrates the fact that the choice of clusters was not independent of the choice of communes. Had it been independent, one would have found as many mixed clusters with a large proportion of their population coming from the chosen administrative commune as clusters with a small proportion. But in practice, the resulting error must have been unimportant. Perhaps it would be better to use boundaries in the field corresponding very closely to administrative communes or to any other administrative unit usable for the dual collection (CeRED, 197 Ib). It is often difficult for the field worker to determine whether or not an event has taken place within a cluster. This may occur when the family found in the cluster has reported an event which has recently taken place, but at a place "not very far away". The point "not very far away" may or may not be inside the cluster. In the case where the household can provide a structure number for the place of occurrence, the solution is simple. But where the household can give no structure number, there is only one solution for the field worker, and that is to go with a member of the family to the place where the event took place to determine whether or not this was inside the sampled cluster. Sometimes a family that was a member of the cluster during the previous survey moved between two surveys and is now present again at the next survey. Young mothers in Morocco frequently return to their mother's home at the time of confinement, especially for the first birth. If the field worker does not pay close attention he may register such a birth as having taken place in the cluster. The continuous recorders are better able to avoid errors of this type. After several periodic surveys, a worker from outside also begins to know his cluster well. 7.4 The efficiency of personnel: resident and outside In the continuous recording, two types of personnel were used, "resident" personnel and personnel from "outside" (CeRED, 1971a). Resident personnel consisted of part-time personnel working, in general, five days per month in either urban or rural clusters (28 clusters in all). In the course of the 17 months of the dual collection, 40 people had been involved in continuous recording. The resident recorder was relatively young, with an average age of 23.4 years. Farmers were the most dependable recruits and worked an average of 16.2 months out of the period of 17 months. The previously unemployed were the least stable recruits. They accepted PGE/ ERAD/ ECP work, but when they found permanent employment or higher remuneration elsewhere, they left the job. The category "other" included especially the "fkihs", that is, the teachers in Muslim schools, and other employees who knew how to read and write. These categories together made up 20 percent of the strength of the "resident" recorders. Outside personnel were used full-time in the dual collection. They were generally of secondary school level and very young (average 18 years). For the continuous recording they were used in about half of the clusters (14) in urban as well as rural areas. As they worked full-time and as they had to serve as many clusters as the "resident" workers there were one-fourth as many outside personnel as residents. It is our experience that the "residents" were as effective as those from "outside" and this was equally true in urban and rural milieux. However, there are two qualifications to this rule and the conclusion drawn from these exceptions are summarized in figure 7.1. 115

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Figure 7.1 Summary of results for most useful personnel by area and type of event Personnel to use Births Deaths Urban Rural

Outsiders Residents

Residents Outsiders

i. In urban areas the "outsiders" are more effective than the "residents" in uncovering births, but for deaths, the "residents" were more effective. ii. In rural areas the "residents" were more efficient for births and "outsiders" for deaths. The resident personnel are the less expensive. This is an argument in their favour. But there is an argument against the utilization of this group: the fact that it is always necessary to have a list of potential candidates. In the case of a resignation it is necessary to rush someone to the area to find a replacement and to train him in two or three days. There is also the possibility that a worker may leave without notice. If the supervisor does not visit the sample areas relatively frequently, such absences may go unnoticed for a long period.4 7.5 The numbering of structures It is clear that the numbering systems used to identify housing units can differ from one place to another. In effect, one may number all structures, inhabited or not, which are found in the sample clusters. This is what was done in the case of Morocco. One can equally well number only dwellings where there are families. Experimentally, not only dwellings but also families could be numbered, leaving aside uninhabited structures. In all cases it is necessary to adopt a decimal numbering system that permits the numbering of new structures in the future and the insertion of the new numbers into the old sequence. There is no experience yet on which to determine frequency of renumbering. In the majority of urban clusters, dwellings were not all numbered by the municipality. Houses which had no number at all received a PGE/ ERAD/ ECP number. Those which had one supplied by the municipal authorities retained that number. This situation has sometimes created some confusion, especially during the matching. We recommend, agreeing with section 5.7.iii, that all housing should receive dual collection numbers irrespective of the fact that such structures may have municipal numbers. The added cost of renumbering already numbered structures is more than repaid at the matching stage and, even more, by reducing the need for field followup. There is also the problem of buildings holding several households (apartment blocks). It would be best to number all the doors inside the building rather than assigning a single number to the entire building. When faced with several families in the same dwelling unit, the problem is more delicate. It is difficult to assign a number to each part of the same residence occupied by a different family.5 Mobile homes (for example the tents of nomads) and seasonal migration have often made the implementation of a numbering system difficult. In some sample areas 116

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such factors may require re-numbering every four months; an expensive and timeconsuming task. Despite these problems, it is our firm finding that numbering constitutes an indispensible tool for regular supervision and for verification of some cases of matching. It contributes to more complete reporting in both procedures by encouraging the continuous recorder and the survey interviewer to visit all households, even if this is not always possible, especially for isolated structures during periods of heavy rain or snow. It also permits the field workers in the continuous recording as well as in the periodic household survey to work in an orderly way (see section 2.3 a. iv).

7.6 Organization in the field 7.6.a Interval between two household surveys At the start of the demographic research it was thought that an interval of 12 months between survey rounds could be used. It was quickly found that this duration was too long and was the source of many errors in the reporting of vital events. A period of six months is more suitable. But if the mobility of the population is very great it may be preferable to take an interval of three months. As time passes, certain categories of events tend to be omitted more frequently than others. Deaths of infants only a few days old, of elderly individuals who do not have close relatives, and of domestics who are not considered part of the family seem to be particularly prone to omission. It would perhaps be better to do surveys every three months and thus detect a larger portion of these events. 7.6.b Relation between rounds in periodic surveys There may or may not exist a relation between the collection of information in successive survey rounds. For example, in the course of the first round of a survey, the family members of the cluster may be listed and only verified in the course of the second round. In such a case, there is a risk of only households noted in the first round being visited and of laziness in reporting changes of any kind. In effect the interviewer having at his disposal an initial list of families can transform a survey based on an area sample into a survey based on a fixed and soon out-dated list of families. According to our Glossary, such a link between two survey-rounds is called "household change technique". To avoid this difficulty inherent to the household change technique, it is necessary to have very close supervision and permanent verification in the field. Of course the advantage of a "household change" link between two survey rounds is that it permits the determination of population movements and hence certain categories of vital events. The population can be divided into three categories: those who are present at the first and second rounds, those who are present at the first round but absent at the second (deaths or out-migrants), and those who are only present at the second round (births or in-migrants). To ensure valuable results, the field work of the two rounds must be of the same quality, that is, they must have the same coverage and completeness. Furthermore, some types of vital events can not be identified in this way. These events (for example, the birth and death of a newborn baby occurring between survey rounds) can only be obtained by retrospective questions. 7.6.c Events in medical institutions The great majority of vital events in rural areas take place at home; moreover, in the CeRED region the proportion of deaths taking place in hospitals or clinics is smaller 117

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than the proportion of births. Most medical institutions serve a population living in a large area and few of the events occurring in these institutions refer to the population resident in the cluster in which the institution is located. It is necessary to separate out the few events relating to the actual population resident in the cluster. Thus, only events that occur in private dwellings and institutional events pertaining to the population of the cluster are considered. The issue is a complex one whether we use the notion of de jure residence or the notion of de facto occurrence inside the cluster. Without doubt we must include in the numerators of vital rates some institutional events that concerned non-residents merely because they had relatives in the cluster. In urban clusters, an estimated 46 per cent of all births occurred in medical institutions. In rural clusters this percentage was slightly less than 12 percent. In urban areas, 13 percent of all deaths occurred in hospitals while in rural areas, 4 percent were in hospitals. We distinguished between two states regarding the residence status of mothers giving birth: (i) residence of the mother was in the cluster; (ii) residence of the mother was outside the cluster. The proportion of mothers whose residence was outside the cluster was about one percent in urban areas and 0.5 percent in rural areas. The proportion of persons who died outside the cluster in which they lived was two percent in both rural and urban areas (Rachidi, 1973). 7.6.d The problem of supervision in the field6 As in the case of a single source collection system, the supervision in the field of the dual collection workers is a very important operation. In addition to his other duties related to providing administrative and technical guidance to the field workers under his control, the supervisor in a dual collection system must be alert to actions that tend to compromise the independence of the two systems.7 Concerning the completeness of events, the supervisor of the continuous recorders must see that all dwellings are visited and that all the events are noted. The supervisor visits a different worker every day. He cannot check more than a part of the questionnaires completed. The choice of the field inspectors for the survey and of the supervisors for continuous recording must be made from among the best workers, from those who have already worked several months as survey interviewers or as continuous recorders. They must have had much experience in field work. They do not have to be well educated, but must like their work and be able to direct and supervise. The principal role of the supervisor of continuous recording consists of visiting certain categories of dwellings (dwellings on the boundaries of the cluster, those far away, those difficult to reach in rural areas, etc.) in order to achieve the highest possible rate of completeness of events. For this it may be necessary to find a system of bonuses for the supervisor who reveals events not picked up by the continuous recorder and penalties for the continuous recorder who misses these events. The same system could be applied in the periodic survey.8 It is certain that the educational level of the workers in supervising the dual collection is not a problem but the time it takes for them to gain experience in the field is. Whether or not there should be a bonus system is also a problem.9 For births, the continuous recording yielded 71 percent of the events estimated by the dual collection system, and the periodic surveys gave 74 percent. The results are slightly better in urban than in rural areas. The percentage of births missed by both procedures is about 7.5 percent for the whole sample, eight percent in rural areas, and seven percent in urban areas. For deaths, the completeness of the continuous recording is 62 percent whereas for the household survey the completeness is 74 percent. The proportion of deaths missed by both procedures represents 16 percent, but with a 118

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Table 7.1 Results of matching 1972 births and deaths in Morocco* % of events missed

% of events Total events observed or from one estimated source Births Deaths Births Deaths Births Deaths

Events missed by two sources Births Deaths

— — —

— — —

74.2 76.6 72.9

52.7 56.8 57.4

3,494 1,236 2,258

849 275 574

— — —

— —

Continuous recording — Urban — Rural —

— — —

70.8 71.4 70.5

61.9 54.5 65.5

3,334 1,152 2,182

919 264 655

— — —

— —

16.2 19.2 14.7

— — —

— — —

4,707 1,612 3,095

1,484 484 1,000

354 107 247

241 95 147

Household survey Urban Rural

Dual collection Urban Rural

7.5 6.6 8.0

* The matching was done between events of 1972 as revealed by the recording and by two surveys (first survey started in July 1972 and second survey started in January 1973 with a retrospective period of one year each time). higher percentage in urban areas (19) than in rural areas (15). For a summary see table 7.1. The matching rate for births is about 41.8 percent and about 35.4 percent for deaths. Some deaths of young infants are reported by field workers only as deaths and not as births. This category represented about 2 to 3 percent of the births in 1972 for the periodic survey and 1.5 percent for the continuous recording. It is recommended that verification of such events be done before matching is undertaken (Rachidi, 1973).

Discussion by Charles Nobbe The application of the PGE/ ERAD/ ECP system to Morocco provides a further opportunity to reflect upon some of those methodological problems encountered in implementing such an undertaking in this part of the world. A review of similar exercises carried out elsewhere in diverse cultural settings around the globe indicates that there are certain fundamental methodological principles to which all such exercises must adhere if the objective of achieving reliable data on vital events is to be realized. Two of those principles are singled out for comment in this section: principles of sampling and principles of independence. In the presentation which follows an effort is made to discuss some of the practical problems encountered in the Morocco exercise within the broader framework of these two principles. This review is necessarily critical especially with regard to omissions. Principles of sampling. Whenever possible, PGE/ ERAD/ ECP studies should be based on probability samples of national scope. In the Moroccan instance, no nationally representative sample was undertaken and no rationale for this omission was provided. Certainly the inclusion of such a sample would have entailed little additional cost and would have considerably augmented the utility of vital events data from a national planning point of view.

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Charles Nobbe

Regarding the selection of rural clusters through the forming of statistical communes, it was noted that the degree of correspondence between such units and administrative communes was remarkably high. Is there a lesson to be learned from such experimentation; viz. that less elaborate sampling procedures will yield approximately similar results at substantially less cost and expenditure of manpower? Principles of independence. The PGE handbook recommends that all structures should be assigned a unique and unambiguous identifying number in accordance with some rationally devised plan. This principle appears to have been adhered to with the exception of particular households in urban areas which retained the numbers assigned to them by municipal authorities. Although the author is evidently aware of the difficulties that obtain from the standpoint of matching, it is equally important to note that failure to correct this deficiency also results in some reduction in the independence between the two systems in the reporting of vital events. Furthermore, the PGE handbook repeatedly emphasizes that the supervision of the field operations must be distinctly organized and managed separately from the statistical evaluation if the two procedures in the dual system estimation are to achieve maximum independence. Unfortunately, insufficient details are given to permit assessment of the independence of the two procedures. The discussion in 7.6.d, however, gives the impression that the author has not fully grasped the operational importance of distinguishing between the supervisory and evaluative functions. Moreover, it would have been more informative had the author pursued the discussion of "efficiency of personnel" (7.4) within the context of independence between the two systems. Instead we are treated to a rather mundane discussion of the different efficiency levels of "resident" and "outside" workers in rural and urban areas. The discussion is all the more frustrating since we are offered no explanation for the findings that were uncovered at the end of section 7.4 (see i and ii).

Endnotes to Chapter 7 1. Some of this unusually high proportion under 15 mustbeafreak of the enumeration procedure. It is virtually impossible for a human population to have "more than half of the total population" under 15. There would not be enough percentage points left for the women of reproductive ages to produce the required children under 15. [Editor's note.] 2. Since this chapter has been written, the question on the survival of parents, or the orphanage question as some like to call it, has been put to good use. Life tables based on these questions have been calculated and published (CeRED; Abou-Gamrah, 1975). [Editor's note.] 3. The original sampling frame in Morocco consisted of the administrative communes. These, however, were not clear territorial units having considerable ethnic and tribal elements in them. The references cited in the text describe a procedure invented by Fellegi where through the creation of "enlarged communes" emerge "statistical communes", which are territorial units and unbiased equivalents of the administrative communes. In the end it was found that the problem was less severe than feared at the beginning; the conterminancy between the administrative units and the statistical units was quite close.[Editor's note.] 4. Supervision with small clusters and part-time workers is a complex task of synchronising the movements of the supervisor with the working days of the continuous recorder. It becomes more complex if it is desired to inject an element of surprise into the visits by the field inspector.[Editor's note.]

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5. The suggestion of numbering families and households as distinct from dwellings or structures runs the risk of repeating the Tunisian experience when the census list of households became the sampling frame. For the consequences of such a reliance see chapter 1. [Editor's note.] 6. See endnote 4 to this chapter. [Editor's note.] 7. The supervisor should supervise the routine work of the field worker. If he worries about the loss of independence, he will bring such a loss about. [Editor's note.] 8. As repeatedly stressed in the PGE handbook (Marks et al., 1974) and at all relevant points in this book, combining the three functions of supervision, evaluation, and correction as suggested here, is the surest way to lose the main advantages of PGE/ ERAD/ ECP. [Editor's note.] 9. See endnote 10 to chapter 5 on the destructiveness of bonuses. [Editor's note.]

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Chapter 8 PGE/ ERAD/ ECP Matching Experiences in Morocco El Arbi Housni, Samuel Notzon, Marie-Daniele Picket 8.1 Features of field work most relevant to matching The African content of the Moroccan exercise has been described in chapter 5 where, particularly in section 5.7, the extensive nature of the experiment and its implications for the quality of data obtained have been discussed. Chapter 7 presents some of the practical problems experienced when a rigorous exercise is launched under difficult circumstances. In this chapter one of the key elements of a successful PGE/ ERAD/ ECP exercise is reported upon: the determination of the matching rules and their application.1 The importance of the chapter lies in detailing the objective manner in which the matching rules were determined. While much matching has been done in the past by various practitioners in the field, much of it has been carried out somewhat commonsensically. This is one of the few examples where the principles recommended in the PGE handbook (Marks et al., 1974: 111-122, 195-220) have been applied.2 The numbering of structures as a key element in the CeRED system of field work has already been stressed in chapter 7. Let it be added here that the dwelling numbers proved to be a powerful discriminator during the matching process. As in many countries, determination of the occurrence of events in time is difficult in Morocco. To assist both the recorders and interviewers in this task, a historical calendar was devised, including parallels of Muslim and Gregorian calendars and special events. This calendar made it easier to determine an individual's age in completed years. The quality of information varied with the source from which the data were obtained, so did the probability of a successful match. Sociocultural factors and the spatial arrangement of dwelling units determined certain initial decisions concerning the type of recording used. In this connection it is important to note that only the house-to-house monthly visit procedure was followed in urban areas, whereas in rural areas either the house-to-house or the routine round contact (RRC: see Glossary) procedure was followed. In certain instances even a combination of the two was used. In the case of dispersed dwelling units in rural areas, the recorder selected certain community contact points in each daily ration. In general these consisted of one community contact for each three dwellings. On each visit he would ask for information on events that had occurred in the three dwellings since the last visit. When the community contact informed him of a birth or death having occurred in one of the neighbouring households, the recorder would then visit that household and take down the necessary information. There were two types of community contacts: (i) regular 122

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points, called RRCs, and (ii) special informants, such as beauty parlours, headmen, coffee shops, midwives, or grocery stores. In general the recorder was in touch first with special informants. As can be seen from the tabular summary below, these points turned out to contribute almost a tenth of the information leads. In the case of clustered dwelling units, the recorder tended to use the house-to-house visit procedure. In the course of the visit, he would also ask for information on the neighbours in the event they were absent at the time of the visit. When he could obtain no information at all he was required to make a second call. Because of the frequency of visits to these points, the recorder instituted a rotation system, i.e. the households visited during the month of September were not the same as those visited during the month of August. Sources of information on live births and still-births as recorded during 1972 in the rural and urban areas Source of Information Percentage Rural Urban Households where events had occurred 36 87 Neighbours 15 6 Households in the same daily ration 31 6 Households from other daily rations 9 1 Special informants: headmen, grocers, midwives, etc. 9 0 Total 100 100 Here one can see the important role played in rural areas by those outside the household; 64 percent of the birth events were reported from that source. In the urban areas, as already indicated, recorders used only the house-to-house procedure. It can be observed that information regarding births originated primarily within the household where the events occurred; it was in fact the case for 87 percent of the births. In an informal manner, certain self-styled community contacts also played a part: 13.4 percent of the births were accounted for through the spontaneous and unscheduled collaboration of persons outside the household. The survey procedure was entirely different and there were no procedural points of contact between the survey and recording. The survey interviewers entered a cluster only after the local authorities had been consulted. The supervisor would visit the "Caid" or the "Khalifa" (local authorities) with a letter which explained clearly the purpose of the survey. Upon arrival in the cluster the supervisor would assign a subcluster (daily ration) to each of the five interviewers. A predetermined supervisory program prescribed the number of times the supervisor would attempt to cover a maximum number of interviewer's visits, particularly those of the weaker ones, in order to correct their errors. 8.2 The purpose of matching Matching, the key element in the dual collection system, is here described as it was developed in the experimentation of the system by CeRED. The initial and essential stage of the matching process is the experimental phase. It permits the determination of the rules for the matching of birth and death records taken from the two sources of collection, survey and recording. Throughout the process of determining the matching rules the aim is to minimize the number of errors. 123

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El Arbi Housni, Samuel Notion and Marie-Daniele Picket

Once determined on an experimental batch of records the rules are applied to all the records. During the matching operation the records are divided into matched, nonmatched coming from the survey, non-matched coming from the recording, and outof-scope. The "true" number of vital events is then estimated from the matched and nonmatched events yielded by one and the other procedure of the PGE/ ER AD/ ECP system (eq. 1.11). As a third stage, CeRED proceeded to an a posteriori field verification to detect on the one hand certain errors committed by the data collectors and on the other hand, errors in the matching process at the office. 8.3. Experimental matching:procedure used The experimental matching was carried out on the vital events of 22 "daily rations" (subdivisions that represent a fifth of a cluster) selected both from urban and rural areas. The first phase consisted of establishing the "true matching status" of each form. Towards this end, two teams worked independently: after an attentive reading of each form and making use of their own judgment each team determined the matching status of the form. Next, they confronted their opinions and after an exchange of views certain forms were declared "matched" and the letter "C" (for couple—matched in French) was stamped on the back of the forms. The out-of-scope forms for reasons of time or space were left aside. The remaining records consisted of two kinds: "nonmatched" or "doubtful matches" and were sent to the field. During the field verification some of the "out-of-scope" has been assigned to "non-matches" or "doubtful matches". The remaining forms, as a result of the supplementary information gathered in the field, were definitively declared either as "matched" and marked with the letter "C" or "non-matched" and marked "NC". The second phase of the experiment consists of deciding on what sort of information or characteristic should be compared in order to establish a match. For births, it was decided that the sex of the child, place of birth, and residence of the mother should at any rate agree so that there be a "match". On the other hand, due to extensive errors and lack of precise answers, the following four characteristics were discarded since they do not have enough discriminating power: date of birth, profession of the father, relation to the head of household, and relation to the informer. The eight characteristics that appear in figure 8.1 were chosen for births; each characteristic was tested with different rigidity levels or tolerance limits. For deaths, the four characteristics shown in figure 8.2 were chosen and tested with the different tolerance limits. It is then possible to compare the "true matching status" of the records as determined through the attentive consideration of all the information in the records by the initial teams of matchers with the different matching status obtained from a comparison of the records based on different characteristics with different tolerance limits. For every tolerance limit in each characteristic one thus determines the correct matches and non-matches and the erroneous matches and non-matches. The erroneous matches are records that should not have been matched according to their "true status", but were matched within the given tolerance limit of the given characteristic. Erroneous nonmatches are records that should have matched according to their "true status", but were not matched within the given tolerance limit of the given characteristic. The results of this operation and the gross matching error in each case appear in tables 8.1 and 8.2.3 The tolerance limits are classified according to their decreasing discriminating power, while the number of erroneous matches increases inversely to the erroneous

124

Matching experiences in Morocco

8.3

Figure 8.1 Characteristics and tolerance limits used in experimental matching of birth records CeRED, Morocco, 1973 Characteristic

Tolerance limit

1. Name and first name of the newborn

a. b. c. d. e.

2. Name and first name of the mother

As in characteristic 1.

3. Name and first name of the father

As in characteristic 1.

4. Name and first name of head of household

a. b. c. d.

5. Age of mother

a. Complete agreement. b. Five years of difference or less. c. Two groups: less than 30 years, 30 years and over.

6. Age of father

a. Complete agreement. b. Five years of difference or less. c. Two groups: less than 30 years, 30 years and over.

7. Rank of birth

a. Complete agreement. b. One birth plus or minus. c. Two categories: 1, 2 or 3 births; 4 births or more.

8. Address

a. Complete agreement, CeRED number. b. Complete agreement, CeRED number or municipal number.

Name, complete agreement within the order. Name, complete agreement regardless of order. First name, complete agreement. First name, agreement in the two first letters. First name, agreement in the first letter.

Name, complete agreement regardless of order. First name, complete agreement. First name, agreement in the two first letters. First name, agreement in the first letter.

non-matches. The tolerance limit chosen is the one that minimizes the gross matching error. The last stage of the experiment consists of combining the different characteristics with the previously selected tolerance limits. When assembling the number of characteristics to be taken into account for matching, the number of erroneous matches should decrease, the cumulative matching criteria becoming stricter with each addition. The erroneous non-matches will for the same reason increase. The best combination of characteristics is that which gives the smallest net matching error.4 On the level of this error depend the bias and the variance of the total number of events estimated according to equation 1.11. It is important, however, not 125

8.3

El Arbi Housni, Samuel Notion and Marie-Daniele Picket

Figure 8.2 Characteristics and tolerance limits used in experimental matching of death records CeRED, Morocco, 1972 Characteristic

Tolerance limit

1. First name of deceased a. Complete agreement. b. Agreement in the first two letters. c. Agreement in the first letter. 2. Address

a. Complete agreement, CeRED number. b. Complete agreement, CeRED number or municipal number.

3. First name of father of the deceased

a. Complete agreement. b. Agreement in the first two letters. c. Agreement in the first letter.

4. First name of head of household

a. Complete agreement. b. Agreement in the first two letters, c. Agreement in the first letter.

to lose sight of the gross matching error, whose value influences the variance of the net error. For births as well as deaths, the best results in Moroccan circumstances came from the combination of three characteristics, and agreement on any two characteristics was found to be sufficient to assert a match. The combination of characteristics considered are shown in tables 8.3 and 8.4.

8.4. Experimental matching:problems encountered One of the principal problems was the choice of the characteristics to be employed. From the beginning, data related to dates had to be eliminated from matching because of their lack of precision. Likewise data related to ages were inexact. Other characteristics, such as the sex of the child,5 or the residence or occupation of the father, have an insufficient discriminating power to be themselves criteria for matching. With regard to names, the first difficulty is the fact that certain names are extremely common, others are very similar to each other. Furthermore, a great number of names, in Moroccan circumstances, begin with the same letter or letters. The tolerance limits requiring an agreement among the first two letters or the first letter do not give adequate results. The best results for matching are the outcome of agreement established after reading aloud, in Arabic, the name or first name on the records considered.6 A second point to be noted is the evidence of the important role played by the subjective judgment of those in charge of matching, and given by the way the best combination of birth characteristics was chosen. In effect, the best combination according to which two out of three characteristics should agree, had not been tested during the experiment, and matching was at the beginning carried out through three characteristics. Thereafter, during the application of rules arrived at experimentally for the purposes of production matching, it was found commonsensically that if two 126

8.4

Matching experiences in Morocco

Table 8.1 Experimental matching of birth documents by characteristics and tolerance limits in the CeRED region of Morocco, 1972-73 Matching status Errors Code of the Matched NonNonErroneous Erroneous Gross characteristic and matched: matched: matches nonmatching tolerance limit1 recording survey matches error (1)

(2)

(3)

(4)

(5)

(6)

(7)

1. a b c d e 2. a b c d e 3. a b c d 4. a b c d 5. a b c 6. a b c 7. a b c 8. a b

93 94 148 150 152 68 69 154 159 161 131 155 159 164 88 147 153 159 98 168 166 66 151 169 139 164 174 122 146

109 108 54 52 50 134 133 48 43 41 71 47 43 38 114 55 49 43 104 34 36 136 51 33 63 38 28 80 56

121 120 66 64 62 146 145 60 55 53 83 59 55 50 126 67 61 55 116 46 48 148 63 45 75 50 40 92 68

1 1 17 19 31 0 1 17 29 42 7 26 34 44 1 22 38 49 32 63 58 20 51 59 40 64 67 1 3

137 135 43 41 49 186 185 31 37 44 67 38 38 38 145 52 54 53 158 51 48 210 71 43 84 58 41 89 33

138 136 602 60 80 186 186 482 66 86 74 642 72 82 146 742 92 102 190 114 1062 230 122 1022 124 122 1082 90 362

1 For an explanation of codes used see figure 8.1 2 The tolerance limit with the smallest gross error for each characteristic.

out of three characteristics agree, it is clearly the best way of matching records. Let us recall that the three characteristics kept for births were: number of residence, first name of the mother, and first name of the newborn child. It occurred with some frequency, that the child's first name had not been reported on one or both records in the case of birth or infant death, either because the child had not yet been given a first name or because the informer, a neighbour or another person not belonging to the household, had not been able to furnish this information. The other two characteristics agreeing and an examination of the records strongly suggesting a match, it is evident that the rule should be loosened and a match should be declared even when only two 127

8.4

El Arbi Housni, Samuel Notzon and Marie- Daniele Picket

Table 8.2 Experimental matching of death documents by characteristics and tolerance limits in the CeRED region of Morocco, 1972-73 Errors Matching status Code of the Matched NonNonErroneous Erroneous Gross matching characteristic and matched: matched: matches nontolerance limit' recording survey matches error (5) (6) (7) (1) (2) (3) (4) 1. a b c 2. a b 3. a b c 4. a b c

36 48 48 24 34 32 32 35 35 35 35

29 29 37 31 31 33 33 30 30 30 30

13 13 12 25 15 17 17 14 14 14 14

0 1 4 0 0 1 3 7 0 2 2

6 7 6 30 10 15 15 15 8 10 10

62 8 10 30 102 162 18 22 82 12 12

1 For an explanation of codes used see figure 8.2 2 The tolerance limit with the smallest gross error for each characteristic. out of three characteristics agree. Other cases may occur: a change in the first name of the child, the dwelling number is omitted, or the household has moved within the cluster. Once this was realized, the matches resulting from the combination of two out of three characteristics were compared to the true matching status of the experimental records. Since the results were conclusive this solution was finally adopted (table 8.3). 8.5 Production matching1 The characteristics and limits of tolerance selected during experimental matching were then used to carry out the matching of all the forms from the survey and recording. This matching was undertaken in respect of the entire period under review, from January 1, 1972, to the end of the second round of the survey in each cluster by daily ration. The forms of the two procedures were first confronted at the daily ration level. Records remaining as non-matched from all the daily rations were confronted at cluster level. The matching status of every form determined in either of these steps was inscribed on its back in the manner already explained. The results of production matching are summarized in table 8.5. For births, the number of events omitted by both methods represent 5 percent of the total number estimated. The percentage omitted for deaths is greater 10 percent of the estimated number. The survey yielded a greater percentage of the total number of events than the recording, with the exception of deaths in rural areas. Nevertheless, the rates of completeness of both systems are relatively weak.

128

8.5

Matching experiences in Morocco

The following tabular summary gives the rates of completeness (in percentages): Survey Recording All Urban Rural All Urban Rural Births 79 82.5 76.9 76 78.8 75.1 Deaths 67 69.8 66.3 70 65.8 71.3 Source: Housni, 1975:26; CeRED, 1975:29 and 31

Table 8.3 Matching outcomes of combinations of characteristics for birth documents in the CeRED region of Morocco, 1972-73 Matching status

Errors

Charac- MatchedNonteristics matched: used1 recording (1) (2) (3)

NonErroneous Erroneous Gross matched: matches nonmatching survey matches error (4) (5) (6) (7)

146 .2 129 .3 128 125 2.3 .2.3 138 .2.5 123 .3.5 126 2.3.5 127 .2.3.4 127 .2.3.5 130 .2.3.4.5. 123 .2x32 156

68 85 86 89 76 91 88 87 87 84 91 58

56 73 74 77 64 79 76 75 75 72 79 46

3 0 0 1 0 0 1 0 0 0 0 0

33 64 66 73 46 76 71 68 68 62 76 10

36 64 66 74 46 76 72 68 68 62 76 10

Net matching error (8)

30 64 66 72 46 76 70 68 68 62 76 10

1 Characteristics used, in each instance with full agreement 1. structure number or municipal address 2. mother's first name 3. infant's first name 4. father's first name 5. first name of head of household 2 Matching was accepted when at least one of the following combinations was realized: 1.2 or 1.3 or 2.3. 8.5.a Vital rates The total number of births and deaths estimated in table 8.5 represents the events which occurred amongst the population in an average period of approximately 15 months. These totals must be adjusted to a 12 month period and divided by the base population in order to obtain crude death and birth rates. The base population was determined by the de facto population in the first round of the survey, which was taken to represent the average population of the period considered. The calculated rates appear in table 8.6 cols. (2) and (4). One could say that these rates do not seem plausible, especially the crude birth rates: the urban rate appears underestimated and the rural rate seems to be greatly overestimated. A possible explanation for the overestimation of a rate is the underenu129

El Arbi Housni, Samuel Notzon and Marie-Daniele Fichet

8.5. a

Table 8.4 Matching outcomes of combinations of characteristics for death documents in the CeRED region of Morocco, 1972-73 Errors Matching status Net Erroneous Erroneous Gross NonChara- Matched Nonnonmatched: matched: matches matching matching teristics error error matches recording survey used1

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

1.2 1.3 1.4 1.2.3 1.2.4. 1.3.4. 2.3.4. 1.2.3.4 1.2x32 1.2x43 1.2.x3.x 44

35 34 28 30 29 27 29 26 39 38 38

14 15 21 19 20 22 20 23 10 11 13

30 31 37 36 36 38 36 39 26 27 29

0 0 0 0 0 0 0 0 0 0 0

8 10 22 18 20 24 20 26 0 2 6

8 10 22 18 20 24 20 26 0 2 6

8 10 22 18 20 24 20 26 0 2 6

1 Characteristics used, in each instance with full agreement 1. structure number or municipal address 2. first name of deceased 3. first name of head of household 4. first name of father of deceased 2 Matching was accepted when at least one of the following combinations was realized: 1.2 or 1.3 or 2.3 3 Matching was accepted when at least one of the following combinations was realized: 1.2 or 1.4 or 2.4 4 Matching was accepted when at least three of the four characteristics were the same in the two procedures. meration of the base population. Nevertheless, we do not have an independent estimate of this population. A possible solution is to adjust the numerator instead of the denominator of the rate; that is to say, to eliminate the observed events through the recording which do not belong to the population yielded by the survey. After this operation, we shall have the total number of events referring strictly to the population yielded by the survey. In our case this means eliminating a certain percentage of events non-matched in the recording, which results in a reduction in the estimated number of events. The results of this operation show that this adjustment has not eliminated much of the suspected bias. In both areas, the rates have been slightly reduced, but the rural rates still appear overestimated and the urban rates still underestimated [table 8.6, cols. (3)and(5)].8 Another possible cause of bias affecting the rate estimates is the tendency of both procedures to omit the same type of events. The existence of this type of bias will end in an underestimation of the total number of events, and hence of the rate itself. In our case, this problem might explain the underestimation of the urban rates, but not that of rural rates. 130

8.5. a

Matching experiences in Morocco

Table 8.5 Production matching of vital events in the CeRED region of Morocco, 1972-73

Urban

Deaths Rural Whole region

(4)

(5)

(6)

(7)

2277

3540

262

636

898

753 683

1093

951

136 113

256 323

392 436

226

294

59

130

190

3939

5878

570

1345

1916

77% 75%

79% 76%

70% 66%

Matching status

Urban

Births Rural Whole region

(1)

(2)

(3)

1263 Matched Non-matched Survey 340 Recording 340 Events omitted by both ("fourth category") 268 PGE/ ERAD/ ECP estimate of all events ' 1943 Completeness rate Survey2 83% 79% Recording2

66% 71%

67% 70%

1 Estimated according to equation 1.11 2 Estimated according to equation 1.9 and 1.10 respectively.

Table 8.6 Crude vital rates per 1,000 population in the CeRED region of Morocco, 1972-73

(1)

Births Deaths Before After Before After correction to the numerator correction to the numerator (2) (3) (4) (5)

Urban Rural Whole region

41.3 61.7 54.61

38.1 58.2 51.2'

12.1 21.1 18.01

10.9 20.2 16.3'

1 Calculated as weighted averages applying proportions urban/rural for the whole of Morocco, 1971.

A possible solution is to match by homogeneous groups. This method consists in dividing the events into homogeneous groups according to some related criteria: age, sex, etc., and to calculate the total number of events separately for each group. For example, if both procedures are more inclined to omit infant deaths than non-infant deaths, we have an instance of lack of independence between the two procedures. By treating real homogeneous groups separately the dependence is theoretically reduced and better results are obtained when using the PGE formula with infant and non-infant deaths separately. This correction has been applied to the first results of matching, before correction has been made for the recording of events without a corresponding household in the

131

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El Arbi Housni, Samuel Notzon and Marie-Daniele Picket

Table 8.7 PGE/ ERAD/ ECP estimates of vital events in the CeRED region of Morocco, 1972-73 according to various homogeneous groupings

Homogeneous grouping

Urban

(1)

(2)

Births Rural Whole region (3) (4)

1943 1965 1940 1943 1944

3934 3983 3979 3950 3940

1955 1943

3936 3938

Estimates without sub-divisions Daily ration Cluster Stratum Sex of the infant/deceased Sex of the infant/deceased and age of the mot her/deceased Place of event

(5)

Deaths Rural Whole region (6) (7)

5878' 5950 5921 5893 5884

570 556 571 567 569

1345 1383 1356 1347 1346

1916' 1939 1927 1914 1915

5891 5881

570 570

1354 1346

1924 1916

Urban

1 Calculated through the application of the PGE/ERAD/ECP formula to the results of matching in the region as a whole. survey. The results of matching by homogeneous groups (table 8.7) show that this method has not eliminated the suspected sources of bias: the greatest difference between the total number of events before and after the division into homogeneous groups is less than 3 percent and in most cases, there is practically no change. It then seems that, either the independence of both systems is relatively well preserved, or an adequate division into homogeneous groups was not applied. 8.5.b Field verification A field verification of the results of matching was organized after production matching. A sample of 1/5 of available records was selected, representative of all the categories: matched, non-matched and out-of-scope. This sample covered 19 rural and 23 urban clusters, which represented all the strata within the study area. The work of the verifiers consisted of finding and questioning the households corresponding to the selected forms in order to determine whether the data gathered by the survey and the recording of these households were correct. Following the first phase of the work in the urban area, the information from the verification interviews was studied and the matching error (bias) was calculated.9 The results show that all out-of-scope forms did not change the estimate of the total number of events drawn from verification. Accordingly, it was decided to eliminate the out-of-scope forms from verification in rural areas. The results for both the urban and rural areas are given in table 8.8. After this stage of verification, two types of forms were studied in greater detail: forms that changed their matching status after verification (6 percent of the sample); forms remaining non-matched after verification. The forms that changed matching status were examined in order to determine the reasons for this change. The conclusions drawn from this work could be utilized to improve future field work. Likewise, non-matched forms were studied in order to 132

8.5.b

Matching experiences in Morocco

Table 8.8 The outcome of field verification of vital events reported in the urban and rural parts of the CeRED region of Morocco, 1972-73 No verification

(1) Urban % of sample verified Bias in the PGE/ERAD/ECP estimate Births Deaths Rural % of sample verified Bias in the PGE/ERAD/ECP estimate Births Deaths

(2)

0

+ 14.1% +3.30% 0

+9.4% +4.9%

Verification of all the forms: matched, non-matched, out-of-scope1 (3)

100

0.0 0.0 1

1 1

Verification of forms: matched and non-matched only

Verification of forms: non-matched only

(4)

(5)

77

61

0.0 -0.8

0.0% -6.7%

82

40

0.0 0.0

+0.1% -3.6%

1 Forms out-of-scope were not verified in rural areas. improve data collection, and especially to determine the reasons of the inability of both procedures to record the same event.10 The most important reasons for the change in matching status are the following: (i) the date of the event has been wrongly reported by the field worker; (ii) the place of the event has been wrongly determined; (iii) the first names of the members of a household (head of household, mother, dead, newborn) are badly written or incomplete; (iv) the matching clerks have committed mistakes during matching. For the majority of non-matched forms (74 percent for the survey, 63 percent for the recording), no reason has been identified which can explain why survey alone or recording alone have reported the event. The most frequent reasons for the rest of non-matched forms are the following: (i) the family has moved; (ii) a birth followed by a death, which causes either the death not to be reported or both events to be omitted by the field workers; (iii) frequent summer absences in the family (particularly in the survey); (iv) the event concerns a person in transit (not residing within the cluster). 8.6. Conclusion In this chapter we have summarized all the stages in the matching process, including experimental matching, production matching, estimation of rates and the corrections used, and field verification. The rates, calculated from the results, show that in spite 133

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El Arbi Housni, Samuel Notzon and Marie-Daniele Picket

of all the efforts to eliminate errors in matching, there still remain serious problems. Nevertheless, the difficulties found in the different stages of matching suggest certain changes for the improvement of future work, both at desks and in the field.

Endnotes to Chapter 8 1. This chapter has been compiled by the editor with the agreement of the co-authors. It draws heavily on their writings, particularly in Housni, 1975 and Notzon and Fichet, 1975. For a more complete report on Moroccan matching see CeRED, 1975, which enlarges upon and supersedes with adjusted data an earlier report (Rachidi, 1974). [Editor's note.] 2. For a rare example of a detailed report on matching see PIDE, 1968. For a still more rare example of reported objective determination of matching rules see Srinivasan and Muthiah, 1968. [Editor's note.] 3. In table 8.1 the number of errors reported in columns 5 and 6 is often higher than the number of corresponding events in columns 2,3, and 4, at first sight a seemingly impossible situation. The co-authors explain that some events involved more than one error. [Editor's note.] 4. The net matching error is equal to the difference between erroneous matches and erroneous non-matches, (e.g. Marks et al. 1974: 26,87,102,196,205,442). 5. Discriminating power is not a symmetrical concept. The same sex on two records is a poor proof that the record refers to the same person. A different sex on two records is a strong proof that the records do not refer to the same person. [Editor's note.] 6. It will be noted that Moroccan practitioners found application of an objective system of evaluating names, suchasSoundex(Markse/a/., 1974: 116,211-212,448) too cumbersome. [Editor's note.] 7. Production matching is called mass matching in Housni, 1975: 26. Production matching is preferred as a distinction from experimental matching, because mass matching runs the risk of confusion with matching in social science experimentation where groups (cells) as a whole are matched with each other on several characteristics. The case-by-case matching remains the distinctive feature of PGE/ ERAD/ ECP work. [Editor's note.] 8. Since the co-authors completed their work for this chapter, an independent estimate of vital rates for Morocco has been produced based largely on demographic analysis (Krotki and Beaujot, 1975). It compares as follows with the rates given in table 8.6 (per 1,000 population):

PGEI ERAD I ECP rates before correction in the numerator after correction in the numerator Demographic analysis estimates high estimate low estimate

Crude birth rates

Crude death rates

54.6

18.0

51.2

16.3

49.5 44.0

20.5 16.0

9. The bias was determined in the following manner: the total number of events was calculated before and after the verification of all the categories of forms. The difference between the two estimates was divided by the total number of events estimated on the basis of the field verification. An estimate of bias has also been obtained from the

134

Matching experiences in Morocco

Endnotes

comparison of verified events, when only non-matched events were verified. 10. Interest in reasons for the omission of events in a PGE/ ERAD/ ECP system is dangerous. It may generate a desire to improve matters, determine causes, apportion blame, correct field work, and throw the two types of field workers into each other's arms. It is better to live in error and to measure it. In the process of correcting error, one may miss both it and the ability to measure it. [Editor's note.]

An appendix to Chapter 8 The Use of an experimental study for reaching decisions on matching rules

by Gad Nathan 8.A.I General The importance of the matching process in the PGE study and of the reduction of matching bias by good decisions on matching rules has been extensively dealt with by Marks, Seltzer and Krotki (1974: 101-122, 195-220, 286-302). The crucial position of an experimental matching study in reaching decisions on matching rules is also emphasized. Since the experimental study may require a relatively large investment, it is of the utmost importance to attain maximal utilization of all the information obtainable from the experimental study. The design and analysis of an experimental matching study involve many factors: the initial determination of a feasible set of characteristics for matching and tolerance limits for each of them; the design of a sample large enough to allow comparisons of different matching rules and ensuring replication, as far as possible, of real PGE conditions (e.g. samples of complete geographical areas, within which matching is to be carried out); testing feasibility and costs of different matching rules; and the use of the experimental data, with appropriate criteria, as a basis for decisions on the matching rules to be used in the full study. These are all discussed by Marks et al. (1974). In the following, discussion will concentrate on further elaboration and development of the last stage, i.e. full utilization of the data obtainable from an experimental matching study and the criteria for reaching decisions on matching rules. It must be emphasized that concentration on this aspect and the proposed mechanistic decision process is somewhat artificial and that practical considerations of feasibility and costs must be taken into account in reaching decisions on matching rules. These, however, vary considerably according to the specific conditions and are different to quantify. Furthermore, since the set of all possible matching rules (defined by combinations of matching characteristics and their tolerance limits: see Glossary) will, in general, be very large, it is most advisable to take the practical considerations into account at an early stage, in order to reduce the set of matching rules for consideration. For instance, if initial considerations can rule out certain characteristics for matching because of extensive response errors (e.g. exact date of birth), it may be well to exclude the collection of data on these characteristics already in the design of the experimental study. 8.A.2 Data available from an experimental matching study On the basis of the assumptions and notation of Marks et al. (1974), modified as necessary, consider first the data which are independent of a specific matching rule. The experimental study is assumed to be based on n "true" events, ni of which are 135

8.A.2 Appendix

Gad Nathan

recorded in source 1 and n2 in source 2. An "ideal" matching procedure, based on all possible information, is assumed so as to determine which records truly relate to the same event, i.e. are "true matches". Assuming each event is reported by at least one source, the number of "true matches" is then: mt = ni + n2 - n (8.1) The experimental matching study is assumed to ensure that the relevant sample proportions are unbiased estimates of the population probabilities, i.e. E(n 1 /n) = P1 = probability of an event being reported in source 1 E(n 2 /n) = P2 = probability of an event being reported in source 2 E(m t /n) = Pn = probability of an event being reported in both sources Thus from (8.1): P1 + P 2 - P 1 2 = 1. (8.2) Consider next the data specific to a given matching rule. For each report in each of the sources, the matching rule determines if the report is considered as matched or non-matched. Let m be the number of matched reports (in each of the sources), so that n1 - m is the number of non-matched reports from source 1 and n2 - m the number of non-matched reports from source 2. If: Pm = E(m/n); Pc = P12 - Pm, (8.3) then the relative bias of the PGE estimate, due to matching error, is: Bm = P C /(P 12 + PC) (8.4) and the measurement of mt and of m is sufficient to provide an unbiased estimator of PC - the relative net error: PC = n c / n = ( m t - m ) / n (8.5) Since only Pc in (8.4) depends on the matching rule, the rule which minimizes the absolute value of Pc is to be sought. However since Pc is a sample estimate whose variance is not necessarily a monotonic function of | Pc |, the minimization of | Pc | is not sufficient to reach an optimal matching rule. As will be shown in the following, further analysis of the data from the experimental matching study is necessary for estimating the variance of Pc. By comparing the matching decision for each report with its true status, a determination can be made if the matching decision is correct or erroneous. Let nu, n2a denote the number of erroneous matches in source 1 and 2, respectively and nib, n2b the number of erroneous non-matches in source 1 and 2, respectively. Then from the relationship: m = mt + nia - n1a = mt + n2a - n2b, (8.6) n1b and n2b are functions of previously defined parameters: n1b = mt + n1a - m; n2b = mt + n2a - m (8.7) Thus the observations of the variables m, n1a, n 2a , dependent on the matching rule, completely determine the subdivision of reports from each source into the following groups; TOTAL Matched—total —correctly matched —erroneously matched Non-matched—total —correctly non-matched —erroneously non-matched 136

Reports in Source 1 n, m m - n1a n1a

Reports in Source 2 n2 m m - n2a n2a

ni - m ni - mt - n1a m, + n1a - m

n2 - m n2 - mt - n2a mt + n2a - m

Matching experiences in Morocco

Appendix 8. A.2

If P1a, P2a, P1b, P2b denote the expected values of n 1a /n, n 2a /n, n 1b /n, n 2 b/n, respectively, then the above observations are sufficient to estimate unbiasedly the gross error probabilities: P1d = P1a + P1b = 2Pla + PC P2d = P2a + P2b = 2P2a + PC

and their average: Pd =

P1a +

(8.8)

P2a + PC,

by means of: Pid = (2n la + n c )/n P2d = (2n2a + n c )/ n (8.9) Pd = (ni a + n2a + n c )/n However, as will be shown in the next section, the variance of Pc depends on an additional parameter, not estimable from the above. For this it is necessary to break down the mt events with reports in both sources by their joint distribution according to the matching status (correctly matched or erroneously non-matched) of their reports in both sources. Let me be the number of events (with reports in both sources) for which both reports are correctly matched (not necessarily with each other since mis-matches are not considered in this analysis) and let Pe = E(me/n). Events with reports in both sources are then broken down as shown in figure 8.3. Figure 8.3 Events with reports in both sources by matching status in each source

Source 2 report: Total Correctly matched Erroneously non-matched

Total

nit m— n2a nit+n2a—m

Source 1 report: Correctly Erroneously matched non-matched

m—nia me m-n 1a- nie

m1+m2-m

m-n2a-me mt+nia+n2a-2m+me

The complete breakdown of reports by matching status is illustrated in figure 8.4. Thus, in addition to the values of n, ni, n2 and mt, which are independent of the matching rule, the outcome of the experimental matching is completely specified for a given matching rule by the values of m, ni a , n2a and me. The variance of this estimate of the net error probability will be shown to depend on the values of Pn, Pm, Pu, ?2a and Pe, all of which are estimable from the above observed values. 8. A.3 The variance of the estimator and its estimation In order to evaluate the variance of the estimator Pc (8.5) of the net error rate, consider the following breakdown of the n events in the experimental study into mutually exclusive and exhaustive subsets:

137

KEY: 0

Both reports matched

(5)

Source 1 report matched; Source 2 report non-matched

(3)

Source 2 report matched; Source 1 report non-matched

(4)

Both reports non-matched

Figure 8.4

Breakdown of reports by matching status

Matching experiences in Morocco

Appendix 8. A.3

Subset Number of events Probability Erroneously matched: na = n1a + n2a Pa = P1a + P2a Both reports erroneously non-matched: nA = mt + na - 2m + me PA One report erroneously non-matched: nB = 2m - 2me— na PB Other events: n - na - nA - nB 1 - Pa - PA - PB Note that: PA = P12 + Pa - 2Pm + Pe, PB = 2Pm - 2Pe - Pa,

(8.10) (8.11)

and: nPc = nc = m, - m = (l/2)(2n A + nB - na). (8.12) For this subdivision, (na, nA, nB, n - na - HA - na) can be assumed to be multinomially distributed with parameters (n; Pa, PA, PB, 1 - Pa - PA - PB) Denoting: the variance of Pc is given by:

Noting that: Pc = (l/2)(2P A + P B -Pa), Pd = Pa + Pc = ( 1 / 2 ) ( 2 P A + PB + Pa)

and: P m - P e = ( l / 2 ) ( P B + Pa),

(8.14)

The variance of Pc can be written as: This can obviously be estimated by: As pointed out above, the estimate of Pc in itself is not a sufficient criterion for deciding that a matching rule is associated with a truly small matching bias. However, taken together with the estimate of its variance, the closeness to zero of the confidence interval for the net error rate can be used as a criterion if the interval is sufficiently small. Thus for a given significance level o and maximal length of confidence interval L we might require that the approximative confidence interval covers zero, and that its length does not exceed L, i.e.: where Z1-a/2is the upper a/2 critical value of the normal distribution. However, a more reasonable criterion would be that the ends of the approximative confidence interval are no further from zero than some pre-assigned value Ro, i.e.: R = max Note that (8.17) implies (8.18) if L = R0. 8.A.4 Comparison of matching rules The statistic R defined by (8.18) can be used as a criterion for comparing matching rules and a matching rule with a smaller value of R should obviously be preferred to one with a larger one. However, the computation of R for all feasible matching 139

8.A.4 Appendix

Gad Nathan

rules will, in general, be a rather formidable task. A matching rule is defined by some combination of characteristics (e.g. name, age, address), each with its tolerance limit (e.g. agreement on first four letters of name). For each characteristic several alternative tolerance limits may be considered. Subsets of characteristics may be combined by intersection (i.e. the matching rule requires agreement, within the given tolerance limits, for all characteristics in the subset) or by union (i.e. the matching rule requires agreement within the given tolerance limits for at least one characteristic in the subset). Consider a very simple case with three feasible characteristics (denoted by A, B and C), each with only 2 possible tolerance limits (denoted by subscripts 1 and 2, e.g. Ai, B2). There are then 6 possible rules based on a single characteristic; 6 pairs of unions or intersections of characteristics each with 4 possibilities of combinations of tolerance limits provide 24 rules (e.g. Ai fl B2, A2 U C1, where D denotes intersection and U denotes union); and 8 triplets of characteristics (assuming a characteristic is checked at only one tolerance limit) each with 8 combinations of tolerance limits provide 64 different rules [e.g. A1 ("I B2 H C1, A1 fl (B2 U C2) etc.]. Thus a total of 94 different rules would have to be evaluated even for this simple case. In order to reduce the number of different rules which have to be considered, a partial ordering on matching rules can be defined as follows: Matching rule X is defined as stricter than matching rule Y (Y > X) if all pairs of records matched by rule X are also matched by rule Y (i.e. pairs of records non-matched by Y are also non-matched by X). Not all pairs of matching rules are comparable by this criterion. Thus some tolerance limits for the same characteristic may be comparable (e.g. for date of event, "exact agreement—month and year" is stricter than "exact agreement on year") while others are not (e.g. "exact agreement on month" and "agreement within 30 days"). The ordering is obviously transitive and the following relationships hold: XU UY Y >>XX>>XxUn Y Y .. (8.19) In examining the relationships between the parameters of two matching rules X and Y, where Y > X, it is sufficient to consider the relationship between the basic observations m, n1a, n 2a , me (or the respective probabilities Pm, P1a, P2a, Pe) for the two rules. Denoting by primed letters the values for the stricter rule X and by unprimed letters those for Y, the following relationships are obvious from the definition of the strictness ordering:

Also: Thus the stricter rule will always have a not larger (algebraic) net matching error than the less strict rule: The difference in gross matching error may be negative or positive but is no greater in absolute value than the absolute value of the difference in net matching error: Although the above relationships do not ensure that the variance of the estimate Pc will be smaller than that of P'c, when Pc and P'c are positive (or larger when PC and P'c are negative), it is clear from (8.16) that for a large enough 140

Matching experiences in Morocco

Appendix 8.A.4

sample, the difference between Pc and P'c will dominate the difference in standard errors in the expression for R (8.18). Thus, in general, R' (for the stricter rule) will be smaller than R, if both Pc and P'c are positive and larger than R, if both PC and P'c are negative. Adopting the value of R (8.18) as a criterion for comparing matching rules, a matching rule will be termed inadmissable (i.e. need not be considered), if some other matching rule has a smaller value of R. From the above it can be seen that, to a good approximation, any matching rule which is less strict than a matching rule with a positive value of Pc should be considered inadmissable. Similarly, a stricter rule than one with a negative value of Pc is to be considered inadmissable. This implies, by (8.19), that unions of inadmissible rules with at least one positive value of Pc and intersections of admissible rules with at least one negative value of Pc are also inadmissible. However, intersections of inadmissible rules with positive values of PC (and unions of inadmissible rules with negative values of Pc) must still be considered. The above considerations may be modified by taking into account the absolute size of the difference Pc - P'c and testing whether the difference is significant. 8. A. 5 A proposal for a decision process The above considerations may be used to determine a decision process which eliminates the necessity to check all possible matching rules, by determining which rules are inadmissible. Define S(l) as the set of basic rules determined by single characteristics at various tolerance limits and let S(k) be the set of all rules determined by unions and intersections of no more than k basic rules. Thus S(2) is obtained by adding to S(l) all intersections and unions of rules in S(l). Assuming that a rule based on a larger number of characteristics is more expensive in operation than one based on a smaller number of characteristics, the decision process aims at determining those rules in S(k) with the smallest value of k for which (8.18) holds. The choice between these rules can be made on the basis of the value of R or on the basis of practical considerations. For a rule X we denote X > 0, 0 > X if the value of Pc is positive or negative, respectively (if Pc = 0, X can be included arbitrarily in either case) and denote by R(X) the value of the R statistic defined by (8.18). A rule X will be termed acceptable if R(X) < Ro. For any set of matching rules, order chains are defined as subsets of rules for which any pair of rules are comparable by the strictness ordering. X and Y will be termed adjacent, within a given order chain, if X > Y and the relationship X > Z > Y does not hold for any other rule Z. Finally, define S+(k) as the subset of S(k) for which X > 0 and S~(k) as a subset of S(k) for which X < 0. At any stage of the process, denote by I(k) the subset of S(k) recognized as inadmissible and A(k) = S(k) - I(k). The decision process utilizes the strictness relationships and (8.19) in order to determine all the admissible rules A(k) based on k or less characteristic and only for admissible rules checks whether they are acceptable. The process is defined as follows: Set A(l) = S(l); 1(1) = 0 and k = 1, 2, . . . : 1. Determine order relations among the rules of A(k). 2. For an adjacent pair X > Y determine: 2.1 IfY>0: Add X and all less strict rules in S(k) to I(k) and to S+(k). Add Y to S+(k). Proceed to step 2 for comparison of Y and adjacent stricter rule(s), if any (if none, proceed to step 3). 2.2 IfO > X: Add Y and all stricter rules in S(k) to I(k) and to S"(k). Add X 141

8. A.5 Appendix

Gad Nathan

to S"(k). Proceed to step 2 for comparison of X and adjacent less strict rule(s), if any (if none, proceed to step 3). 2.3 If X > 0 > Y: Add all less strict rules than X in S(k) to I(k) and to S+(k). Add X to S+(k). And all stricter rules than Y in S(k) to I(k) and S"(k) and add Y to S"(k). Check if X and/ or Y are acceptable (i.e. if R(X) < R0 and R(Y) < R0). Proceed to step 3. 3. Redefine A(k) = S(k) - I(k). If an order chain in A(k) has not been checked by step 2, proceed to step 2 for the next order chain. If all order chains have been checked and acceptable rules found, stop. Otherwise, proceed to step 4. 4. Define A*(k) = S(k) - I(k) and define A(k + 1) as A*(k), together with all unions of pairs of values of S~(k), provided they include exactly k characteristics and are not intersections of any rule in S"(k), and all intersections of pairs of rules of S+(k), provided they include exactly k characteristics and are not unions of any rule in S+(k). Define I(k + 1) = S(k + 1) - A(k + 1) and proceed to step 1 for k + 1. To illustrate the operation of this decision process consider a hypothetical example with matching rules based on three feasible characteristics A, B, C, each at two possible tolerance limits. Thus the rules based on a single characteristic are: A(l) = S(l) = [Ai, A2, B1, B2, Ci, C2]. Assume that the tolerance limit denoted by subscript 2 is stricter than that denoted by 1. Thus for k = 1 the following three order chains have to be checked: A, > A2; B, > B2; C, > C2. (8.27) On the basis of the hypothetical data in figure 8.5 it is seen that A, > A2 > 0; Bi > 0 > B2; O > d > C2. (8.28) Note that to establish these relationships only the data on m (number matched) in column (2) is needed, for comparison with mt. The value of R has to be computed only for Bi and B2 (.043 and .079, respectively). Taking R0 = .025, no acceptable rule is thus found, based on a single characteristic. From (8.28), Ai and Ci are established as inadmissible, so that A*(l) = [A2, Bi, B2, Ci] and: S+(l) = [A,, A2, Bi]; S"(l) = [B2, C,, C2]. (8.29) + Intersections of rules in S (l) involving two characteristics are Ai D Bi, A2 fl Bi (since Ai > A2,+ Ai (~1 A2 = A2 need not be considered) and unions of rules in S"(l) are B2 U Ci, B2 U C2. Thus: The order relationships between members of A(2) are given in figure 8.6 [together with those of A(l)]. Note that at this stage only relationships not previously checked (denoted by double lines) have to be checked. From the data in figure 8.6 the following relationships are found:

Note that the last relationship need not be checked since B2 U Ci was previously found inadmissible and that only 3 additional values of M have to be computed. For Ro = .025 the rule B2 U C2 is thus acceptable and the process would stop at this point. It should be noted that the acceptable rule involves C2, even though C2 is inadmissible. Even if a lower value of Ro than .022 is required, it is easy to check that, in addition to:

142

Figure 8.5 Hypothetical Example: Data on Matching Rules Source 1 reports: ni = 2,090; Source 2 reports: n2 = 1,597; Truly matched: mt = 1,158; [Total events: n = 2,529] Matching rule

(1) A, A2 B, B2 C, C2 A1 n B, A2n B1 B2 U C1 B2 U C2

Erroneously matched Source 1

Source 2

m

n1aa

n2a

Correctly matched in both sources me

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

1300 1229 1312 1097 893 873 1258 1056 1321 1175

581 563 622 476 527 512 572 432 624 535

324 281 413 219 236 197 296 211 347 225

711 537 685 413 360 339 638 523 643 441

+.0562 +.0281 +.0609 -.0241 -.1048 -.1127 +.0395 -.0403 +.0644 +.0067

.3017 .3056 .3484 .2989 .4065 .3930 .3036 .2945 .3195 .2938

.0085 .0082 .0093 .0080 .0107 .0104 .0084 .0086 .0085 .0077

.073 .044 .079 .040 .126 .133 .056 .057 .081 .022

Matched

Estimated relative net error Pc

Estimated relative gross error Pd

Estimated standard error of Pc a(Pc)

Value of R

8.A.5 Appendix

Gad Nathan

Figure 8.6 Hypothetical example: relationship between rules A(l) and A(2)

A(3) includes only 18 unions and intersections involving three characteristics [e.g. A1 n (B, U Ci), B1 n (A2 U C1), B2 U (A1 n C2), C2 U (A2 n B2)]. Thus at the most an additional 18 rules would have to be checked. In practice far less will have to be checked since many of them will be ruled as inadmissible at an early stage. Considering that there is a total of 94 different rules, the decision rule proposed can obviously provide substantial savings in effort.

144

Chapter 9 The PGE/ ERAD/ ECP System of Data Collection in Africa and A Comparison of Its Results With Those of Analytic Techniques Roderic P. Beaujot 9.1 Introduction In attempting to overcome the problems of inadequate data, demographers have taken two general approaches: using novel collection procedures, and using novel analysis techniques. This chapter first summarizes some African experiences, or such fragments as could be identified, with the PGE/ ERAD/ ECP system of data collection. We will then consider results obtained through two analytic techniques: stable population and Brass techniques. The purpose of the chapter is essentially to compare the results of the dual collection system with those of analytic techniques. 9.2 Some African experiences with

PGE/ERAD/ECP

Background data on the PGE/ ERAD/ ECP studies of seven African countries are presented in table 9.1. This table provides information about the area covered by the studies, the coverage period, the two collection procedures, the approximate population covered, and the proportion of the population of the area thus represented. While Asian experience goes back to 1945 (Seltzer, 1969: 396), the African studies quoted have all taken place within the last decade. The studies in Liberia and Morocco are initial results of ongoing systems of dual data collection. No results are yet available for Kenya. It can be seen that the first procedure is typically a semi-annual household survey while the second is a continuous recording. The population covered varies from 100,000 for Egypt to 5,000 for Tunisia. In Madagascar and Tunisia the whole population of small areas has been covered, but otherwise the population covered is a sample of the population of the country or of an area within the country. Estimates of completeness by collection procedure for each study are shown in table 9.2 for births and deaths. The variations in the completeness estimates shown reflect true differences in completeness as well as the sources of bias mentioned in earlier chapters. The correlation bias (lack of independence) will usually lead to an overestimate of completeness, matching bias to either over or underestimate completeness, and out-of-scope bias (spurious reports) to underestimate completeness. The completeness estimates for births range from 54 to 97 percent and for deaths from 49 to 88 percent. The median completeness for the household surveys is 79 percent for births and 69 percent for deaths; for the continuous recording these medians are 74 and 66 percent respectively. Completeness is consistently lower for deaths. The median com145

Table 9.1 Background information on PGE/ERAD/ECP studies conducted in seven African countries Country and period covered

Study name

Area within country

First procedure

Second procedure

(1)

(2)

(3)

(4)

(5)

1. Egypt 1965/66

4. Liberia 1969/70

Project undertaken by Cairo Rural lower Egypt Demographic Centre and Egyptian Central Agency for Public Mobilization and Statistics Study by Service Statistique de Ambinanitelo (comMadagascar (INSRE) mune), Ankazoabo (sous-prefecture) Enquete Nationale Demographique Oued el Khatef and Goraa (cheikhats) Liberian Fertility Survey, Round 1 Whole country

5. Malawi 1971/72

Malawi Population Change Survey

2. Madagascar 1967/68, 69/70 3. Tunisia 1968/69

6. Morocco 1972/73 Study by Centre de Recherches et d'Etudes Demographiques Study by Demographic Studies Unit 7. Kenya

1. 2. 3. 4.

Vaidyanathan, 1973 Pradel de Lamaze, 1973 Republique Tunisiene, INS, 1970: 5-6; Vallin, 1971 Rumford, 1972

Whole country Northern Morocco coast to desert Seven contiguous districts

Continuous Three semiannual surveys recording

Approx. pop. covered (6)

%of pop. of area (7)

100,000

1%

38,000

100%

Multi-round survey

Normal vital registration

Multi-round survey Semi-annual survey Semi-annual survey Semi-annual survey Semi-annual and annual survey

Normal vital registration Monthly survey

5,000

100%

70,000

5%

Recording

30,000

5%

Continuous recording Continuous recording

84,000

2%

93,000

2.6%

5. Blacker, 1971; Kazeze, 1974 6. Myers and Lingner, 1973; Rachidi, 1973 7. Myers and Lingner, 1973.

Data collection in Africa—a comparison

9.2

Table 9.2 Estimated completeness of reported births and deaths for each collection procedure in six African studies

Country

1. Egypt 2. Madagascar 3. Tunisia 4. Liberia 5. Malawi 6. Morocco Range Median

Procedure 1 Household survey Births Deaths (1) (2)

Procedure 2 Continuous recording Births Deaths (3) (4)

77.5 81 97 64 80.6 74.2

65.6 72 88 49 81.6 57.2

87.9 77 78 54 66.7 70.8

82.9 74 60 64 68.1 61.9

64-97 79

49-88 69

54-88 74

60-83 66

For sources see table 9.1. pleteness rate for births is about 15 percent higher than that for deaths. For births, the household survey has a higher completeness than the continuous recording in every country except Egypt.1 For deaths, the recording procedure has a higher completeness than the survey procedure in every country except Tunisia and Malawi. Giving equal weighting to births and deaths, the completeness of the recording and survey procedures are within three percentage points of each other in Madagascar, Liberia, and Morocco. In Egypt the continuous recording has better "overall" completeness, while in Tunisia and Malawi the household survey is better. The central tendency of the Asian experience summarized by Seltzer (1969) is remarkably similar to that presented here. The medians of the completeness rates for all procedures were 77 and 69 percent for births and deaths respectively in Asia, as compared to 77 and 67 percent respectively in Africa. The ratios of the omission rate for deaths (i.e. one minus the completeness rate) to the omission rate for births are in the order of 1.8 or less except in the multi-round survey of Tunisia. The medians of these ratios are 1.5 for the household surveys, 1.3 for the continuous recording, and 1.4 for both procedures (compared to 1.3 in Asia). Despite the higher omission rates for deaths compared to those for births, the unadjusted estimates of natural increase taken directly from the household surveys or from the continuous recording would be too low. This will be the case as long as the ratio of births to deaths (or of the birth rate to the death rate) in the population under study is greater than the ratio of omission rate for deaths to the comparable omission rate for births (Seltzer, 1969:402). Since the ratio of births to deaths in African populations has an average of 2.2,2 rates of natural increase will be underestimated whenever the omission rates for deaths are less than about 2.2 times those for births. Since these ratios of omission rates are less than 2.2 and since they tend to be higher for the household survey procedure as compared to the continuous recording procedure, a survey taken alone would come closer to the true growth rate than a continuous recording with a baseline count. Another way of looking at completeness is to examine the proportion of the estimated total number of events that are covered by both procedures, covered by the household survey only, covered by the continuous recording only, and missed by both

147

9.2

Roderick P. Beaujot

Table 9.3 Percentage distribution of estimated total births, by PGE/ERAD/ECP category, for six African studies

Country

Estimated total births (1)

1. 2. 3. 4. 5. 6.

5066

Egypt Madagascar Tunisia Liberia Malawi Morocco

580* 3691** 4707

Medians

Percentage distribution Caught Survey Recording Missed by Estimated by both only only both pro- total procedures cedures (2) (3) (4) (5) (6)

9.4

19.8 14.6

68.1 62.4 75.7 34.6 53.8 52.5

18.6 21.3 29.4 26.8 21.7

19.4 13.0 18.3

58

22

16

2.3

2.7 4.4 0.7 16.6 6.5 7.5

100 100 100 100 100 100

5

For sources see table 9.1 with the following transformations: 1. calculated on the basis of frequencies 2., 3., 4., 5., 6. calculated from table 9.2 using C = S i S 2 / N * This is the number of births found in three passages of the survey ** This is the "number of events analyzed". procedures; that is, to distribute the estimated total into the four PGE/ ERAD/ ECP categories (Seltzer, 1969: 404). This breakdown, presented in table9.3 for births and in table 9.4 for deaths, is essentially a different way of presenting the same information that was available in table 9.2. The proportions estimated as missed by both procedures is relatively small — medians five and seven percent for births and deaths (Asia five and nine percent). The median proportion covered by both procedures is 58 percent for births and 53 percent for deaths (Asia 56 and 44 percent). The remaining events were caught by only one of the two procedures employed. Though the fourth category tends to be small, it still remains true that PGE/ ERAD/ ECP increases completeness over a single system. The second procedure has of course already found many of the events missed by what would otherwise be a single system. 9.3 Analytic techniques A second general approach to the problems of estimating vital rates on the basis of inadequate data is to combine information, check for consistency, and rely on those parts of the data that are most trustworthy for a particular purpose and in a given population. Stable population procedures and Brass techniques are the prime examples of this analytic approach. Stable population models have been developed in such a way as to reflect empirical consistencies that are found to hold among various population factors. In the Coale-Demeny (1966) models, for instance, age specific mortality rates were first regressed on life expectancy at age 10 for countries with accurate data. The model life tables thus derived were then merged with various growth rates in order to obtain a series of model stable populations covering the range of human experience. If the 148

9.3

Data collection in Africa—a comparison

Table 9.4 Percentage distribution of estimated total deaths, by PGE/ERAD/ECP category, for six African studies.

Country

Estimated total deaths (0

1. 2. 3. 4. 5. 6.

2029

Egypt Madagascar Tunisia Liberia Malawi Morocco

Medians

183* 1030** 1484

Percentage distribution Caught Survey Recording Missed Estimated by both only only by both total procedures procedures (2) (3) (4) (5) (6)

54.6 53.3 52.8 31.4 55.6 35.4

11.0 18.7 35.2 17.6 26.0 21.8

28.4 20.7 7.2 32.6 12.6 26.5

53

20

24

6.0 7.3 4.8 18.4 5.9 16.2

100 100 100 100 100 100

7

For sources see table 9.1 with the following transformations: 1. calculated on the basis of frequencies 2., 3., 4., 5., 6. calculated from table 9.2 using C = SiS 2 /# * This is the number of deaths found in three passages of the survey ** This is the "number of events analyzed". assumptions of a stable population hold for the data under consideration,3 these models have been found useful for making estimates of vital rates. The procedure essentially involves using "reliable" parameters in a given population (typically the growth rate and the proportionate age distribution) in order to identify a model that most closely resembles the population under study. Other parameters of the model, particularly the vital rates, are then taken as estimates of those of the given population (see U.N. Population Studies 42). The Brass techniques make use of survey data especially on children born in the last year, children ever born, and children surviving. It has been suggested that a major problem with data on children born in the last year is that an incorrect reference period may be used. On the other hand, a major deficiency of data on children ever born is that of the possible omission of children who have moved away from home or who have died. Arguing that younger women are less liable to give erroneous information about children who died, and that women of different ages still use a similar reference period, Brass (1968) used data on children born in the last year to establish the shape of the fertility schedule and data on children ever born to younger women to establish the level of fertility (see U.N. Population Studies 42). Analytic techniques have the basic advantage of being able to detect and correct errors and biases through internal comparisons and through reference to model relations. It is then possible to rely on those parts of the information which are most robust for a particular purpose (Brass, 1971). If the use of alternative parameters produces similar estimates, the confidence in the results is increased. The basic problem with these techniques is that estimates are dependent on the particular model and parameters chosen. One is never sure which is the most appropriate model, how closely the chosen model reflects the given population, or which parameters are the most trustworthy. Stated more simply, results are somewhat de149

Roderick P. Beaujot

9.3

pendent on the decisions which the researcher makes in arriving at the estimates. As Brass (1971: 400) himself notes: "One problem in assessing the accuracy of the estimates for these analyses is that they are not automatic but require judgment between alternatives and work better for some types of errors and biases than for others." He goes on to say that, with adequate information, they give good results at least for fertility and child mortality.

9.4 Some African experiences with analytic techniques In view of the criticism noted above, a useful manner by which to appraise these analytic techniques is to compare results obtained by different researchers. An attempt was made to locate relevant material on the same countries as considered earlier. Estimates for Egypt, Kenya, Morocco, and Liberia are summarized below. Stable population estimates for Egypt refer to dates between 1907 and 1960 (see table 9.5). In spite of this wide span in reference periods, the variation in estimated crude birth rates (CBR) is only from 40 to 47, with the preferred estimates being between 42 and 45. The crude death rates (CDR) estimated in 1960 have more variation (11 to 21). This general consistency, particularly in the birth rates, is in spite of various assumptions regarding the onset of mortality decline, the accuracy of the 1947 census, and the appropriate stable population model.4 Coale and van de Walle(1968) and Blacker (1970) have experienced difficulty in applying the Brass technique of fertility estimation to Kenya. The straightforward application of Brass adjustments leads to estimates of total fertility rate (TFR) that these authors judge to be unacceptably high. Coale and van de Walle then proceed to Table 9.5 Stable population and PGE/ERAD/ECP estimates for Egypt Source

Method and assumptions (1)

El Badry, 1955: 302-3 Abdel-Aty, 1961:367 Khodary, 1970: 267 Schultz, 1972: 450

1907-1937 growth (because 1947 is overcount) and ages 0-9/10-19 from 1947 Life table from 1947 census and stable population Quasi-stable population, South

Reference date (2)

Estimates CBR CDR (3) (4)

1907-47

47-42

35-31

1937-46

44

32

1960

45

21

43 42 44

19 17 —

40

11

47

19

Quasi-stable population 1960 1. Mortality decline since 1946 2. Mortality decline since 1927 1960 3. Mortality decline since 1946 1960 and 5.6% overcount in 1947 1960 4. Mortality decline since 1927 and 5. 6% overcount in 1947* Vaidyanathan, PGE/ERAD/ECP 1965-66 1973: 6

* Judged to be implausible because of the low levels of death rates. 150

9.4

Data collection in Africa—a comparison

use instead the West series of stable populations to derive a TFR of 6.8 (CBR = 48, CDR = 18) for 1962. Blacker makes complex adjustments of the Brass data to arrive at a TFR of 7.6 (CBR = 50, CDR = 17) for 1969. This is a good example of what often tends to happen with analytic techniques. The researcher starts in a given direction and if he or she "judges" that the results are unacceptable, he or she makes adjustments or proceeds in an alternative direction. Though these judgments may be well based in "demographic wisdom" there is often insufficient independent control and evaluation. Parallel work on the Moroccan population has been done by Thavarajah (1970) as well as by Beaujot and Krotki (1973) and Krotki and Beaujot (1975). In all instances, stable population techniques were applied to available data. Thavarajah used the age distribution and infant mortality rate of the 1961-63 multiple-purpose survey to identify the appropriate (South) model. The female CBR varies from 43 to 53, depending on the age group chosen to reflect the population. Krotki and Beaujot made use of the inter-census growth rate and the 1960 census age distribution to identify the appropriate (West) stable population. Taking the data literally, the mortality levels reflected by the various parts of the age distribution were found to span almost the whole range of human experience.5 Extensive work was then done to adjust the growth rate and the age distribution for problems of differential completeness among censuses and age and sex selective underenumeration. Though the gross reproduction rates (GRR) and the life expectancies at birth (eo) obtained for Morocco are in reasonable agreement, the CBRs vary from 44 to 50 and the CDRs from 16 to 25 (table 9.6). In order to determine the robustness of the Moroccan results with respect to available models, Bracher Table 9.6 Stable population estimates for Morocco, 1960, 1965, 1971 Source

Method and assumptions

(1) Krotki and Beaujot, 1975

Stable populations, West ages 0-9/25+ 1. median underenumeration in 1950-52 2. high underenumeration in 1950-52 Bourgeois- Pichat, Stockholm model Bourgeois-Pichat, UN model Carrier and Hobcraft Thavarajah, Quasi-stable population, South, with IMR and age 1970 distribution Krotki and Stable populations, West Beaujot, ages 0-9/25+ Bourgeois-Pichat, 1975 Stockholm model Bourgeois-Pichat, UN model Carrier and Hobcraft

Reference Estimates date CBR CDR r GRR e0 (2) (3) (4) (5) (6) (7)

1960

45

17

2.8

3.0

1960

49

25

2.4

3.3

1960

44.0 16.0 2.8

1960

49

3.1

49

1960 1965

2.8 49.6 18.0 3.16

3.0 3.4

49 47

1971

44.5

3.0

49

1971

49.5 20.5 2.9 3.1

49

3.0

49

16.5 2.8

1971 1971

2.8

151

Roderick P. Beaujot

9.4 Table 9.7 Analytic and PGE/ ERAD/ ECP estimates for Liberia* Model used

Adjustments made

Parameters used

(1)

(2)

(3)

1. Brass techniques 2. Brass techniques 3. Brass techniques 4. Brass two parameter

eo GRR M M &F F (4) (5) (6) (7)

P 2 /F 2 , 12, masc 105 males 0-9 P 2 /F 2 , 1 2 h

33 33 34

P 2 /F 2 , 1 2

Age adjustments for r, females 0-14 migration, underenumeration and misreporting 5. Brass two General age adjust- r, males 0-14 parameter ments taking r females 0-14 seriously 6. CoaleGRR, m, C(10), Demeny West C(35) 7. CoaleGeneral adjustment GRR, mortality Demeny West of age distribution level, r, C(x) females, m = 29 8. Coaler, C(x) females Demeny West 9. Coalee0, C(15) females Demeny West 10. PGE/ERAD

35 35 37

3.7 3.8 38

34

3.7

58

3.2

45

3.7

47 42

48

3.2

37

42

3.7

Judged to be too wide to be reliable 35

3.1

51

57

2.6 3.2

* Estimates are all for 1970 except #9 which is for 1962 1. to 8. Students in a graduate seminar in demography, University of Alberta (Sociology 551, Fall 1973) 9. Coale and_van de Walle, 1968: 160, 182. The present author obtained the GRR estimate (m = 29) using the given e0 and CBR 10. Liberia, 1971:2,4,5. (1973) applied the various stable population models to the Kr6tki-Beaujot adjusted data. The results on life expectancy at birth had the range of 45 to 49: West family, females 49.5 North family, females 46.4 East family, females 46.0 South family, females 45.2 Brass, two parameter system, females 47.5 Bourgeois-Pichat, intermediate network, females 48.8 In an additional effort to study the extent to which estimates depend on the particular model chosen and on the decisions that the researcher makes in the process of arriving at the estimates, eight students in a graduate seminar in demography were asked to obtain estimates of eo and GRR on the basis of available age-sex, growth, and Brass-type data on Liberia. The estimates obtained, along with those of Coale and van de Walle (1968) and the "official" PGE/ ERAD/ ECP estimates are presented in table 152

Data collection in Africa—a comparison

9.4

9.7. This table also gives the model chosen, the preliminary adjustments made if any, and the parameters used to identify the appropriate model. The CD'S obtained by the students vary from 34 to 58 and the GRRs fro;n 3.1 to 3.8 (for 1970). The corresponding values by Coale and van de Walle are 35 and 2.6 (for 1962) and PGE/ ERAD/ ECP 54 and 3.2 (for 1970). It is immediately apparent that there is much more consistency within the Brass estimates (eo ranges from 34 to 35; GRR from 3.7 to 3.8) than within the stable population estimates.6 But the high mortality and fertility rates obtained through Brass techniques seem to be inconsistent with "official" PGE/ ERAD/ ECP estimates.? The general conclusion of this exercise is that, at least for stable population techniques, the final results do depend considerably on the researcher's decisions.8 This overview is far from being able to conclude the debate regarding the relative worth of emphasizing collection procedures versus analytic techniques in attempts to resolve problems of inadequate data. Given that we are already trying to measure "deeds" on the basis of "words" where the record is not very good,9 it would seem that the independent check provided by PGE/ ERAD/ ECP is a valuable tool by which to decrease or at least measure content and completeness error. There is no doubt that analytic techniques can deal with at least certain types of errors through checks for internal consistency and reference to models, but the errors involved may be too great to be dealt with in this manner. Brass (1968: 172), in fact, proposes that because of age errors, data for African populations cannot be analyzed by stable population means with hope of anything but accidental success. In as much as resources permit,10 it would generally seem that, given the seriousness of problems often encountered (as evidenced by completeness estimates of PGE/ ERAD/ ECP results and subjectivity of analytic results), both analytic and PGE/ ERAD/ ECP techniques should be emphasized. The former may be less costly and subject to less sampling error, but the latter is more able to estimate the error component in the results obtained.

Discussion by Ansley J. Coale

It seems to me that Beaujot has to some extent understated the potential usefulness of analytic techniques. Estimates based on age distribution and the proportion of children dying before their second birthday —2q0—are reasonably invariant with different age patterns of mortality; and if the estimates of the birth rate are based on the proportion under an early age — 5,10, or 15 — deviations of the actual population from stability do not much affect the estimates. Of course, such procedures are vulnerable to the gross age misreporting that is found in many African and Asian populations. However, age misreporting is less severe in Latin America, the Philippines, and especially in censuses of the populations in East Asia that use the Chinese calendar system. Moreover, there are indications that the second round of censuses in Africa have achieved a somewhat better reporting of age than their predecessors. The usefulness of these procedures for estimating the birth rate derives from the surprisingly good quality of estimates of child mortality by the Brass method of analyzing data on the number of children ever born and the number of these surviving. The Brass procedure of estimating fertility from tabulations of data on parity and on births during the last year is vulnerable to the massive age misreporting found in Africa, but it has shown itself quite successful in other populations such as those of Latin America. We have been experimenting in Princeton with the use of model age specific fertility schedules to estimate the level of marital fertility from tabulations of average parity by the duration of marriage.11 We then estimate overall fertility by multiplying 153

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Ansley J. Code

the proportion married at each age by estimated marital fertility. Tests with the family census in Ireland in 1911, and the census of Kuwait in 1970 show that the procedure is quite promising, whenever there is little voluntary control of fertility. The author fails to give an account of methods of estimating adult mortality from the proportion of children orphaned by age, and by the analysis of the age structure of incompletely registered deaths, both procedures recently developed by Brass.12 A weakness of most analytical procedures is that the reference period for the estimates of fertility and mortality is typically several years prior to the census or survey, and thus the methods are weak instruments for detecting changes in fertility or mortality that have just been initiated. The advantage of analytic procedures in comparison to dual systems is that they cost less and have potential for improvement in the accuracy of estimation with accumulated experience. In contrast, the dual system faces the constant danger that through repetition the requisite independence of the two procedures may be lost, and the high quality of administration required may not be sustained.

Endnotes to Chapter 9

1. See table 6.2. 2. The ratio quoted was calculated from the Population References Bureau estimates of birth and death rates for all of Africa (see the "1973 World Population Data Sheet"). 3. These assumptions are: closure to migration and fixed schedules of fertility and mortality. If the schedule of mortality is not fixed but declining, the procedure can still be used with minor adjustments (quasi-stable population). 4. We have, however, in Khodary (1970) an example of a procedural judgment with weak objective support. The stable population estimates obtained varied for CBR from 37 to 51 and for CDR from 12 to 26 depending on the age group used. The author then chooses the proportion at ages 0-9 (CBR = 48, CDR = 23) for no apparent reason: "In the case of the UAR, it was found that the estimates derived from C( 10) are to be preferred to the rest" (idem, p. 264). 5. A United Nations workshop report (1971:162) suggests a similar conclusion: "the quality of age data in Africa is so poor... that widely differing results may be obtained according to which index of the age distribution is used for matching against the models". For Niger, 1960, the gross reproduction rate is found to be 3.8 using the proportion to age 10 [C (10)] and 2.9 using C (15). "Furthermore, the basic assumptions concerning fertility, mortality and migration are not entirely valid." 6. Coale and Lorimer (1968: 165) found that in 14 out of 16 comparisons within African countries, the Brass estimates of fertility were lower than the stable population estimates. This result is not confirmed here; if anything the opposite situation occurs. 7. Madigan et al. (as quoted in Myers and Lingner, 1973: 35) found opposite results for the Philippines: The Brass birth rate was five per cent lower and death rate 29 per cent lower than their corresponding PGE/ ER AD/ ECP estimates. 8. The author is indebted to Professor Karol Krotki and the eight students in Sociology 551 (Fall 1973), University of Alberta, for the results that appear in table 9.7. Acknowledgement is also due to Mr. William Seltzer for suggesting this exercise. 9. For references in demography see Horvitz (1966), Sabagh and Scott (1965), Sirken and Sabagh (1968), and Som (1959). Horvitz, for instance, interviewed over 3,000 households selected from birth and death registration lists in seven counties in North Carolina. He found that 92 per cent of registered births and 82 per cent of registered 154

Data collection in Africa—a comparison

Endnotes

deaths were reported in the interviews. These rates were lower for certain population groups and for certain characteristics of the events (infant deaths, illegitimate births). 10. See Seltzer (1971) for an attempt to compare costs of PGE/ERAD/ ECP versus other methods of data collection. 11. For a report on these "model" fertility schedules in human populations see Coale and Trussell, 1974. [Editor's note.] 12. For a presentation of the orphanage technique of estimating mortality see Brass and Hill, 1973. [Editor's note.]

155

Chapter 10 The Role of Dual System Estimation in Census Evaluation Eli S. Marks

10.1 The importance of publishing a census evaluation The past few decades have seen rapid improvement of census-taking and other statistical methodology. Along with this development has come an increasing awareness of errors in census data on the part of both producers and users. While the initial effects have been to destroy naive faith in the absolute accuracy of a census, the long term effect has been the development of a more sound and more defensible view of censustaking in which "census evaluation" plays a central role. This newer viewpoint concedes, once and for all, that a "perfect" census is impossible; that errors will and must exist; and it goes on to emphasize that census figures that are subject to error are still valuable if the magnitude of error is known and is consistent with the major uses of the figures. That is, there are very few decisions which turn on a determination that the population of a country is exactly 21,728,516 persons, but there may be a great many that turn on the determination that it is between 21.0 million and 22.5 million and there are a large number of decisions for which knowledge that the population is between 20 and 24 million may be quite adequate. From this standpoint, knowledge of the "range of census variation" (i.e. the range within which the principal census statistics may be reasonably presumed to fall) is an essential part of the census proper. "Evaluation" of the census and wide publication of that evaluation is not only desirable, it is necessary and is the only real protection against unwarranted attacks on the accuracy of the census and the integrity and competence of its producers. Securing general public acceptance of the concept of a census as fallible but valuable will require a sustained educational campaign. For that campaign to be successful, it will be necessary to change our habits of publishing censuses and of referring to census figures. The statement on "limitations and errors" of census figures must become an integral and prominent part of any census publication. It must also become ^positive statement on the kinds of uses for which the census figures are valid. We must keep emphasizing that we do not have "exact" statistics on anything (and that any claims of the existence of such figures are suspect) but that we do have an excellent idea of the range within which the census statistics fall and that range is such that the census figures are valid for most of the important uses made of them. The last assertion requires, of course, that we be able to produce census figures which are valid for most of the important uses made of them and that we have valid 156

Role in census evaluation

1 0.1

methods for assessing the range of variation for at least the more important census statistics (i.e. valid methods of "census evaluation").

10.2 Methods of census evaluation and their biases and variances Statistical methods of evaluating census quality can be divided into three categories: i. Analysis of internal consistency — e.g. examining whether the ratio of males age 40-49 to females age 40-49 is consistent with what is known about masculinity ratios at birth and sex differentials in mortality and migration for ages 0 to 49; ii. Comparison with external (aggregate) figures — e.g. comparing the number of persons age 45 in a census taken in October 1970 with the number age 41 in a census taken in October 1966, less adjustments for deaths and migration; iii. Dual system estimation — involving the matching to the census listings of an independent listing of units (persons, households, living quarters, establishments, etc.) that should have been enumerated in the census; the independent listings are either from administrative files (resident registration, social security files, etc.) or from a separate survey, usually a household survey conducted on a sample basis subsequent to the census and therefore, referred to as a post-enumeration survey (PES). Census statistics, like other statistics, are subject to both constant and variable error. The bias or "constant" component of error is the difference between the expected value of the census statistic and the "true value" which one is trying to measure. For census statistics, variable error is due to response variance. For example, if the "true value" to be measured is the number of women aged 40 to 44 on their last birthday, the census estimate of this number may tend to have a downward bias because (i) some women aged 40 to 44 will not be enumerated in the census and (ii) the number of women aged 40 to 44 who report themselves as younger than 40 or older than 44 tends to exceed the number of women older than 44 or younger than 40 who report themselves as aged 40 to 44. However, the omission of a woman from the census is a random event.1 Also, while age may be reported in an invariant manner for some people, for others it will vary in a random fashion so that a given woman may sometimes be reported (correctly or incorrectly) as age 40 to 44 and sometimes in some other age group. The discussions of the merits of various methods of census evaluation have usually focussed on their value for estimating the biases of the census statistics. In most cases, bias is more important than variance with respect to the census statistics themselves, since the number of cases involved is large. However, the variances of estimates of census error may be a major factor because (i) they are based on sample data (e.g. in the case of dual system estimation); (ii) they involve some relatively rare phenomenon (e.g. number of births that are not registered). While the variance of dual system estimates is primarily due to sampling and tends to be relatively large, the reverse tends to be true for the other methods of census evaluation, particularly those which involve fairly elaborate demographic analyses. That is, in demographic analyses, a rare event may have a high variance even though it is estimated from data for the entire population; but this is usually of minor importance precisely because the event is rare. On the other hand, more complex methods may use the estimate of the rare event as one element of a matrix or vector in such manner that the unreliability of this single event is communicated to the result of the entire computation. It is particularly important, therefore, that we examine the more sophisticated methods of census evaluation for their sensitivity to variance (as well as bias) in the data used for the evaluation.

157

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Eli S. Marks

10.3 Internal and external consistency analysis Analysis of census data for internal consistency is particularly important for the detection of error. It is, in fact, frequently necessary in evaluating the results obtained by the other methods (use of external aggregates and dual system estimation). For example, the report of the U.S. Post-Enumeration Survey of 1950 (U.S. Bureau of the Census, 1960) notes that the PES (dual system) estimates gave masculinity ratios for the age group 15-39 which were "much lower than would be expected on the basis of sex differentials in birth and mortality rates. They suggest a differential shortage of males as compared with females of about 0.9 million, as compared with the PES results which indicate net underenumeration of less than 0.1 million among males of these ages". Inconsistencies in census data indicate errors, and one can often infer the direction of the error and make a suitable correction. Of course, such inferences are open to argument. In the 1950 U.S. PES example cited, one can argue that the discrepancy is due to the fact that age misreporting tended to increase the count of females age 15-39 and to have little or no net effect on the number of males age 15-39. Nevertheless, informed statistical and demographic opinion would strongly support the conclusion of a "differential shortage of males". Comparison of census data with external aggregates frequently yields results similar to those from internal consistency analysis. For example, the results of the last previous census adjusted for intervening births, deaths and (net) migration will often be inconsistent with the current census. However, in this case, it is much more difficult to determine how much of the discrepancy is due to error in the current census and how much to error in the previous census or in the birth or death or migration statistics. Decisions on the causes of discrepancies detected by comparison with aggregates from external sources can sometimes be made on the basis of knowledge about the general demographic situation and about the enumeration process. For example, as reported by Cho (1972), the number of males age 27 enumerated in the Korean census of October 1970 was about 17 percent below the October 1966 census count of males age 23 adjusted for intervening mortality. This discrepancy might be due to differential underenumeration, to differences in age reported, to errors in the mortality estimates, or possibly, to migration. Errors in peace time mortality at this age can obviously not account for a 17 percent discrepancy. Age reporting errors in Korea tend to be small and the picture for the cohorts at adjacent ages would not support this explanation. Net migration also seems to be a very unlikely explanation. Thus, it is reasonable to attribute the discrepancy to greater underenumeration of the cohort in 1970 than in 1966. Not all decisions on the sources of an observed discrepancy can be made on the basis of general knowledge of the demographic situation and of the enumeration process. Quite often, in fact, internal consistency analyses and comparisons with external sources indicate clearly that there are errors in some or all of the statistics involved but give little or no indication of how much error should be attributed to each statistic. Also, internal consistency checks and comparison of aggregates indicate only differentials in underenumeration or age reporting. Thus, the examples cited pointed to greater underenumeration of males than females in the U.S. Population Census of 1950 and greater underenumeration in the Korean 1970 census than in the 1966 census of the cohort of males age 27 in 1970. But this does not tell us how much underenumeration there was in 1950 of U.S. females or how much underenumeration of males age 23 there was in the Korean census of October, 1966. Furthermore, if internal consistency checks and external aggregate comparisons do not reveal a discrepancy, this is not 158

Role in census evaluation

10.3

grounds for belief that there was no error in the figures but only for concluding that the error in the two figures was of the same magnitude and sign. To get at the loci and the absolute (rather than differential) magnitudes of error in internal consistency analyses and external source comparisons, we usually resort to some type of dual system estimation. Thus, the estimates of net enumeration error in the U.S. census of 1960 and 1970 made by Siegel( 1973) used the estimates of completeness of birth registration obtained by dual system methods (matching of survey or census data against birth registration files) for 1940,1950, and 1964 to 1968. Also, as indicated in Coale and Zelnik (1963), the Siegel estimates for white females aged 35 to 64 in 1970 and aged 25 to 54 in 1960 were adjusted to reflect the net incompleteness of 1.0 percent for white females age 15 to 54 shown by the 1950 PES. Thus, just as there is no error-free census statistic, so there is no error-free method of evaluating census statistics. In the controversy of evaluation of census statistics by various demographic methods versus evaluation by dual collection methods such as record checks or post-enumeration surveys, there is no uniformly best procedure. Some methods are better than others for some circumstances. A combination of methods is likely to be better than any single method. All methods need further study of their strengths and weaknesses and ways of improving them. 10.4 Dual system estimation The use of demographic techniques and dual system estimation in the evaluation of the U.S. 1970 population census illustrates very well how a combination of methods leads to acceptable results which could not be obtained by any method singly. Thus, the use of birth and death statistics (i.e. external source comparison) for evaluating the census count of the population under 35 years of age is unsatisfactory without a dual system correction for incompleteness of birth registration. For white females aged 15 to 54 in 1950, an external source comparison based on prior census data and intervening deaths gave a result (an estimated 0.4 percent overcount in the 1950 census) which was judged to be less plausible than the 1.0 percent net incompleteness estimated by the 1950 PES and the latter figure was, therefore, used. On the other hand, as noted above, the 1950 PES gave sex ratios (particularly in the age ranges 15 to 39) which were quite out of line with sex differentials in birth and death rates. The (internal consistency) check on sex ratios for the 1960 PES estimates and for the Medicare estimates of persons over 65 in 1970 also indicated that the estimates were out of line with what was known about sex differentials in birth and death rates. Therefore, estimates of expected sex ratios were applied to the external source and dual system estimates of males aged 65 and over and females aged 35 to 64 in order to estimate females aged 65 and over and males aged 35 to 64. Dual system estimation has been used about as long and about as widely for census evaluation as for vital statistics. However, the theory and practice of dual system estimation for census evaluation has exhibited very little development during the past 10 to 15 years. On the other hand, recent work in the vital statistics area has contributed enormously to our understanding of the possibilities and the limitations of dual system estimation. This development is covered in a comprehensive fashion in the recent book by Marks, Seltzer and Krotki (1974). In both census and vital statistics work, errors can be classified as relating to: (1) completeness—the erroneous omission or erroneous inclusion of vital events, persons, households, dwelling units, etc.; or (ii) content—the misreporting of the characteristics (age, sex, location, etc.) of persons, households, etc. 159

10.4

Eli S. Marks

Note that content errors do not affect the count for the total population. That is, they simply result in an increase of the count for one subgroup and a decrease in the count for some other subgroup. Completeness error refers only to omission from or inclusion in the total population count although it also affects the counts for population subgroups. One major use of dual system estimation is in separating content from completeness. With the other methods of evaluation, it is usually not feasible to measure these error components separately. For example, as already noted, a sex ratio for any census age cohort which is considerably above that expected on the basis of sex differentials in birth and death rates indicates census error; but the error can be in greater net underenumeration of males than females (completeness error) or in a male-female differential in age misreporting (content error). It is, in fact, usually necessary to resort to some form of case-by-case matching to get any clues to the causes of the discrepancies disclosed by internal consistency analyses and comparisons of census results with data from other sources. While the PES form of dual system estimation will often give valuable clues on content bias, a PES usually gives adequate measures only for the variance component of content error. That is, in spite of earlier optimism about improving reports of age or income or occupation by doing a more intensive interviewing job, PES reports of these characteristics are usually not better than census reports. To measure content bias one must use a record check against a source with demonstrably more accurate information (e.g. determine "true ages" by matching census enumerations against birth registration files) or must subtract a dual system estimate of completeness bias from an estimate of total bias obtained by other means. For example, on the basis of data on Medicare enrolments, Siegel(1973) estimates that the 1960 U.S. Population Census overestimated the number of non-white males 65 years old and over by 5.8 percent; and, as reported by Marks and Waksberg( 1966), the 1960 PES gives an estimate of net incompleteness of 6.7 percent for non-white males 65 years old and over. From the combination of the PES estimate of incompleteness and the Medicare estimate of total error, we obtain an estimated content bias of 12.5 percent over-reporting of non-white males age 65 and over—i.e. we estimate that 12.4 percent of the numerated persons classified as non-white males 65 years old or over should have been classified elsewhere (as white or as under 65). Dual system estimation does give estimates of content error variance and of completeness bias and variance. These dual system estimates must be used with caution. As illustrated above, some dual system estimates will be obviously biased, sometimes so badly as to be unusable. In other instances, the dual system estimates will be clearly superior to estimates prepared by other methods. In still other cases, information (whether pro or con) on the quality of dual system estimates will be completely lacking. Thus with respect to quality, dual system estimation is essentially no different from other forms of census evaluation except for being so much simpler that its inadequacies are glaringly obvious rather than being obscured by an elaborate mathematical superstructure. In most countries (including some with very good statistical systems), it will be necessary to resort to dual system estimation for at least part of the census evaluation. In general, this will mean a PES (with supplementary record checks where suitable record files are available). More often than not, PES results will be needed to help in evaluating other methods of census evaluation. Unfortunately, the costs of PES techniques used in the past have been much more uniform than their effectiveness. That is, for most countries the difficulties and costs of a PES have been high relative to the results obtained. 160

Role in census evaluation

10.5

10.5 The two types of PES (post-enumeration survey) Until recently, PES manuals have stressed doing a better (and more expensive) canvassing job than the census, using better qualified and better trained and supervised enumerators, and doing a "reconciliation" (third interview at considerable cost) to determine the correct value whenever the census and the PES disagree. In some cases, better qualified, better trained, and better supervised enumerators can do a better canvassing job, //one can find the better qualified enumerators and can afford to pay them and //one can find and pay well-qualified supervisors to give the better training and better supervision. Certainly, one should do the best one can to get competent enumerators and to get supervisors who are able to do a competent job of training and supervision. On the other hand, recent work in dual system data collection for vital statistics estimation casts doubts on assertions that it is desirable to use for reenumeration the "best enumerators from the census", that PES enumerators should receive "intensive training" and be paid on a basis "allowing them ample time to obtain valid replies", and that a PES should involve "reconciliation" of all discrepancies between PES and census. The earlier PES emphasis on achieving completeness and very high quality reflects a misunderstanding of the essential difference between dual system estimation and single system estimation. That is, the earliest PES designs were essentially single system estimate designs. The idea was to obtain PES estimation which would replace the census figures rather than to make an estimate based on both the census and the PES. The census results were used in the PES estimates primarily for purposes of detecting and correcting errors in the PES through "reconciliation" of discrepancies. Our understanding of the nature of dual system estimation derives from the the work in this area for vital statistics measurement. This work starts with the assumption that incompleteness is an inevitable feature of any data collection system, no matter how carefully and competently it is designed and executed. The emphasis is, therefore, placed on trying to attain independence between two incomplete procedures, rather than upon trying to get completeness in one of the procedures. Thus, the theory which has been developed for dual system estimation (Marks et al., 1974) replaced ^"completeness bias" of the estimates from the individual systems by: (i) correlation bias — due to failure to achieve complete independence between procedures; (ii) matching bias; and (iii) out-of-scope bias — due to erroneous inclusions of cases in one or both of the procedures.2 Note that incompleteness per se does not bias a dual system estimate. It is true that obtaining completeness in one of the procedures will reduce the correlation bias to zero. But the correlation bias is also zero when errors in the two procedures are independent even though neither procedure attains as much as 50 percent completeness. Independence with low completeness in one or both procedures will mean a high variance of the dual system estimate. However, for completeness of 50 percent or more in both procedures, variance can usually be reduced more effectively and more economically by increasing sample size than it can by increasing completeness.3 Usually, for a PES (as for dual system estimation in general), it is not worth increasing expenditures appreciably to increase completeness unless the improvement in completeness also means greater independence. That is, both theory and practical experience in the vital statistics field indicate that independence is much more essential to good dual system results than is greater completeness. A PES which is independent of the census but picks up only 60 to 80 percent of the population will do about as well as a PES which is independent and picks up 90 percent of the population and will do considerably better than a PES which gets 90 to 95 percent of the population but at a sacrifice of independence. 161

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Eli S. Marks

10.6/4 PES with a PGE/ERAD/ECP approach A new PES method based on the PGE/ ERAD/ ECP approach of maximizing independence has considerable promise. It involves: i. Emphasis on independence rather than quality; ii. Enumerating persons resident in the sample segments at the time of the PES, rather than trying to reconstruct the population as of the time of the census; iii. Doing a "one-way match" in which a person is searched in every location where he might have been enumerated (whether or not this was in or near a sample segment); iv. Keeping reconciliation and other expenditures aimed at improving PES accuracy to a minimum. With this approach, the job of the PES enumerator is nearly identical to that of a census taker or that of an interviewer in a single round household sample survey. He canvasses his sample area and tries to list all the households in it; he lists the persons in the households; and he completes questionnaires on the characteristics of the persons and households. For these jobs, we do not need PES interviewers who are very exceptionally qualified (and very highly paid) nor do they need training or supervision substantially in excess of that given census enumerators. Note that, while the newer technique simplifies the PES canvassing job, it does require that the PES interviewer obtain for persons who were living or staying elsewhere at the time of the census, information which can be used in searching for the person in the census listings at these other locations. Obtaining satisfactory information of this type is not easy. Address information is likely to be vague. In rural areas, one can get at best the name of the village of residence and a village may contain as many as 300 households and 10 to 15 enumeration areas (EAs). The smaller villages may not be always referred to by the same name and, if they are, the name may not be shown on maps of the district or province. In many urban areas, there is no satisfactory system of street names and house numbers. Also, very often the people are unfamiliar with the "official" name and number of the house in which they stayed a few months previously; may, in fact, not be familiar with the official number of the house in which they are currently living. In spite of these difficulties, a test of the method conducted in Paraguay indicates that it is possible to get satisfactory data for census searches of most of the PES sample persons. In any event, the likelihood of obtaining satisfactory data for searching for people in the former location seems to be considerably greater than the probability of getting a satisfactory reply from someone who recently moved into an area to the question: "Who were all of the people living here at the time of the census?" The difficulties of the questions are considerably amplified for a de facto census where one must ask about people, "who were staying here at the time of the census" (including persons who may have slept in the alley behind the house without the occupant's knowledge). After all, one can ask a person who slept in an alley where he was staying and hope to get a reasonably accurate reply; but asking the occupant of the house "who slept in the alley behind?" is likely to elicit blank stares or the glib reply "no one". Also, apart from quality of response, reports from Paraguay indicate that the enumerators find the newer techniques easier to work with, a fact which may be important in the area of costs. While the newer technique is likely to result in more independent PES listings and less correlation bias, it does increase the difficulties and costs of matching. That is, with a PES listing of persons who were living or staying in the area at the time of the census, matching is usually limited to the PES sample EA. In some cases, the search for PES sample persons may be extended to neighbouring EAs to allow for errors (by either the 162

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census or the PES enumerator) in identifying the EA boundaries. With the newer technique, it is necessary to search in the census listings of the area in which they were formerly living for persons who move between the census and the PES. In the case of a de facto census, one must search in the area where the person was staying at the time of the census. Furthermore, since people will know where they were but be vague about exact dates,4 one may have to ask about more than one previous location. It is necessary, then, to get descriptions of these former locations in order to identify the census EA where the person should have been enumerated. Since address information is frequently vague or ambiguous, one must add to the PES, questions about: i. Names of (nearby) villages, estates, etc., in rural areas and names or numerical designations of barrios or "neighbourhoods" in urban areas; ii. Names of roads, (major) streets, rivers, creeks, etc., bounding the location; and, possibly, iii. Other landmarks that might be used in locating the E A where the person might have been enumerated (e.g. "near the building where one goes for social security benefits"). A major problem of the new technique is that even with the additional data one can often not be sure of identifying the correct EA. Of course, actually finding the person in the census listing is proof that one has identified the EA correctly; but, if the person cannot be found, this may be either because he was not enumerated or because we did not search in the correct EA. To reduce the ambiguity (and errors) of enumeration area identification in matching, in Paraguay, the test of the new PES technique added to the information collected for persons who were not staying in the PES sample area at the time of the census, a listing of the names and ages and relationships of other persons in the household where the person was staying at the time of the census, and also of the names of the heads of neighbouring households. Then, when we find in the census listings the names of the other household members but not that of the PES sample person, we can be confident that we have the correct EA and this person was not enumerated. When we find the names of the neighbouring heads in the census listing but not the names of the members of the designated household, we can be confident that we have the correct E A and this household was not enumerated.5 The critical question about the proposed method is whether "reasonably correct" matching can be carried through at moderate costs. The Paraguayan test (and another test in Korea of an earlier form of the new PES technique) indicate that reasonably correct matching is feasible. The question being investigated in the Paraguayan test is whether the gains of the new technique justify its greater costs. Of course, in Paraguay we are not doing a "reconciliation" of discrepancies for either procedure. In general, reconciliation is not necessary with the newer PES technique. For post-enumeration surveys which attempt to reconstruct the population of a sample area at the time of the census, it has been customary to do a "reconciliation" of discrepancies between census and PES. In some cases, this reconciliation has included both completeness and content and, in other cases, content only. Reconciliations involve a third visit to the household6 and the costs of reconciliation will usually be greater than the costs of the additional matching required by the newer procedure. However, the gains from reconciliation are questionable. "Reconciliation" is a holdover from an earlier view of a PES as trying to do a more complete and more correct (sample) census. "Reconciliation" was therefore, undertaken to correct the PES. In all cases, it tends to increase the correlation between the census and the PES. For example, cases added to the PES enumeration by reconciliation are always cases that were included in the census, never cases that were omitted.

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Similarly, reconciliation on content always makes the PES entries more like the census entries. Usually the content changes in PES entries as a result of reconciliation do not improve the PES accuracy. That is, very often it is not possible on a reconciliation visit to determine which, if either, of the entries is correct but a decision on the "correct" entry is made anyway. Such decisions will not reduce the bias of the PES estimate but do result in an underestimate of the response variance.

10.7 Out-of-scope error in a PES Work on dual system estimation for vital statistics can also contribute to our understanding and control of the third type of bias listed above, "out-of-scope error". In vital statistics dual system estimation, it is convenient to distinguish: (i) chronological outof-scope error—i.e. the reporting of vital events which occurred outside the time reference period; and (ii) geographical out-of-scope error. In census work the "time reference period" becomes a "time reference point" (the census date and, within that date, some specific moment of time, usually midnight). Thus, in census evaluation, "chronological out-of-scope errors" are inclusions of persons who were born after or who died before the census date. In vital statistics, the term "geographic out-of-scope errors" refers primarily to errors in sample listing—i.e. the inclusion in the sample of vital events which do not pertain to the particular areas sampled. The most common causes of geographic outof-scope error are "boundary" problems (i.e. difficulties in identifying sample area boundaries) and de facto/de jure problems(i.e. listing a vital event in a dejure survey at the point where it occurred or listing a vital event in a defacto survey at the residence of the neonate or decedent). The "geographic out-of-scope error" in census evaluation is very similar to that in vital statistics work and the suggestion above for use of "one-way matching" between PES and census is the direct counterpart of one-way matching as used in vital statistics to reduce "geographic out-of-scope bias". That is, by one-way matching sample survey reports of vital events against civil registrations wherever the vital events happen to be listed in the civil registration (whether inside or outside a sample area), one reduces the effect of a sample segment or of a birth being listed at the mother's (dejure} place of residence instead of at the (de facto) place where the event occurred. One-way matching has, obviously, similar advantages in reducing the effects of geographic out-ofscope error in PES listings. Two additional types of "out-of-scope error" are given considerable attention in census evaluation but are usually ignored in vital statistics work. These are: (i) duplicate (or multiple) enumerations of the same person (or household, living quarters, etc.); (ii) enumeration of persons (households, living quarters, etc.) who should not have been included in the census at any location — fictitious persons, diplomatic personnel stationed in the country, etc. While this type of erroneous inclusion is at least theoretically possible in vital statistics, it is usually ignored as being of very small magnitude. In census work, enumeration of persons who should not have been enumerated any place is also relatively rare and, for most purposes, this kind of erroneous inclusion can be ignored in census work also.7 Duplicate enumerations may be more common in census work than in vital statistics and the magnitude of duplicate enumeration should at least be explored in a PES. Such an exploration is not feasible where PES matching is restricted to matching within the PES sample segments. That is, for this procedure we can only determine that 164

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a person was enumerated in the wrong area, and cannot determine whether this case was also enumerated in some other area. Actually, there are people in any census for whom there are difficulties in determining where the person should be enumerated even if all the information on where the person lives (or lived), "stayed", etc., is complete and is completely accurate. In Paraguay, the test of the newer procedure asked where the sample person lived on 9 July, 1972 (the census date), where he stayed on that date and where he stayed during the first half of July 1972. A search of the census listings is then made at all the locations reported. A person is classified as "erroneously omitted" only if he was not enumerated at any of the possible locations and as "erroneously included" only if he is found in the census lists at more than one location. Cases where the PES reports that the person stayed in one area on 9 July, 1972 but the census shows him only in some other area are treated as instances of content variation—i.e. a difference in geographic location between census and PES similar to differences in reports of age or other characteristics. This new procedure is called procedure B in the appendix to this chapter. The alternative PES procedure of trying to list all persons who should have been enumerated in the sample segment is being used in Paraguay in half of the sample segments.8 Here, however, we must classify as "erroneously omitted" any person who is reported as having stayed in the sample segment and who is not found in the census listings for that area, even though the person may have been enumerated in some other area. Similarly, we should classify as "erroneously included" all persons enumerated in the sample area by the census who are reported as not having stayed there on the census date. However, there will be people enumerated in a sample area for whom the PES listings provide no information on where they stayed on the census date. This bias could have been removed by doing callbacks on such persons. For Paraguay, it was decided that the cost of such "reconciliation" callbacks could not be justified by the possible bias reduction achieved. 10.8 Widening the available options for census evaluation In spite of the advantages described above for the newer PES technique, an alternative method which should be considered where there is a periodic household sample survey, is to use this survey to do a PES along the lines that have been followed in the past. In this situation, the costs of the PES will be covered in a large part by expenditures which would be undertaken in any event and consequently one does not need to look for means of reducing these costs. The interview taken immediately before the census can serve as the PES proper and can be matched to census listings. The interview immediately following the census can be used as a "reconciliation interview". Of course, there may be adverse "conditioning effects" from the fact that the sample households were interviewed prior to the census and the sample may therefore not be fully representative. However, the cost savings must be weighed against the possible biases. Furthermore, one can use the new households rotated into the household sample to do a small scale evaluation study on households not interviewed prior to the census and this will give us a measure of the "conditioning". The above is not intended as a "definitive answer" to improved census evaluation. It will be a step forward if it gives either lower PES costs or better estimates of census completeness and content error in some situations. Whether or not we achieve this limited success, we should go on to explore other possibilities. There is a great need to widen the available options on census evaluation. A method which is satisfactory in 165

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Eli S. Marks

one country, may be very unsatisfactory in another, and completely impracticable in a third. Discussion by William Seltzer

In this chapter three sets of issues are raised for the discussant, (i) those related to PGE/ ERAD/ ECP estimation directly; (ii) those related to problems of census evaluation generally; and (hi) those related to the broad field of survey research. Let me take up these topics in turn. PGE/ERAD/ECP issues I think Marks's generally excellent chapter suffers from a form of "correlation bias syndrome". He seems to be saying that we can largely ignore problems of quality in the PES as long as the census and the PES are independent. Implicit in his recommendation that "we do not need PES interviewers who are very exceptionally qualified (and very highly paid) nor do they need training or supervision substantially in excess of that given census enumerators" is a census operation carried out by adequately qualified, trained, and supervised enumerators. However, in many countries, for the next two decades at least, most of the enumeration will be in the hands of census enumerators who are poorly qualified, ill-trained, and haphazardly supervised. In such a situation an emphasis on "quality" in the PES is not a wasteful luxury but a necessary precondition for preparing census completeness estimates of minimal adequacy. In particular, low quality in the PES will almost certainly threaten the integrity of the sample design and result in frequent departures from other basic survey procedures. In short, correlation bias must be considered along with other sources of error in the design of a PES, but not to the exclusion of those other sources of error. On the other hand, Marks's insistence that the PES procedure must be viewed in the context of PGE/ ERAD/ ECP studies can only have beneficial consequences. At present, a grey cloud of disenchantment surrounds the PES as a tool for census evaluation in the statistical offices of many developing countries. Too frequently, when the PES estimate of the total population has been compared with the equivalent census count, the census figure was found to be the larger of the two. The implied finding of a census overcount was correctly disbelieved and the PES was adjudged to be a wasteful endeavour. The point behind Marks's remarks is that the waste lies not in the PES itself, but in how the information obtained in the PES is used. In earlier PES studies, he observes, "the idea was to obtain PES estimates which would replace the census figures rather than to make an estimate (of census completeness) based on both the census and the PES". Of course, if case-by-case matching is to be done for the purposes of preparing estimates of census completeness, the PES must be designed with this purpose clearly in mind, since, as Marks also notes, the matching requirements for a completeness check differ from those of a content check. Finally, all of us associated with PGE/ ERAD/ ECP estimation will do well to keep in mind the evidence that Marks cites on the increase in correlation bias attributable to using the basic PES interview to "reconcile" responses made at that time with those made in the census. Lest I am diagnosed as relapsing into "correlation bias syndrome", it should be noted that reconciliation not only increases correlation bias, but also increases the mean duration of the PES reinterview and hence increases the funds needed to carry out a PES. In other words, although one does well to avoid correlation bias syndrome, there is no reason to pay needlessly for correlation bias. 166

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Discussion

Census evaluation issues An important topic not touched on in this chapter, I fear, by PGE/ ERAD/ ECP methods, is the evaluation of census data for local administrative and political units. For many purposes, some measure of census completeness will be required for at least hundreds and perhaps thousands of local geographic areas. Clearly, neither PES nor PGE/ ERAD/ ECP procedures are sufficient for this task. By its very nature the PES is a sample survey and this implies that most of the country (and most administrative units) will not be included in the sample. The critical issue then becomes how to link aggregate estimates of completeness to numerous individual geographic areas. This resolves itself into two problems: first, the availability of supplementary data sets covering all the units for which individual adjustments are required, and second, the development of dependable methods of estimation. With regard to data sets four possibilities now seem promising. i. Information from the census itself (for example, data by age and sex, by household size, by enumerator's age), ii. Information from the previous census and civil registration statistics, iii. Other administrative data (for example, school registration data, social security systems data), and iv. Earth satellite and other remote imagery (for example, structure counts and spectral signatures). A number of estimation procedures using one or another of these supplementary data sets are now in use in different countries. In this connection, I think it is well to indicate two lines of methodological research that have received little attention so far. The first of these involves efforts to model the census enumeration as a statistical process and to use information obtained in the census itself (particularly data about census operations and personnel) to estimate the parameters of this process. In a very rough way this is what PGE/ ERAD/ ECP does, but I have in mind a somewhat more detailed model of the enumeration process (for example, one involving an assumed distribution of enumerators by the quality of their work). The other area of development I would urge on my colleagues is a very serious consideration of the new resource given us by the remote sensing capabilities of artificial earth satellites. Satellites dedicated to gathering socially-useful, scientific data are in the sky now, they are collecting an immense volume of current data for the entire planet across a wide range of frequencies, and they are close to a free resource for the government statistician or demographer. Certainly, these satellites are not a deus ex machina that will solve all the problems of demographic measurement. But so far that is not the problem, for we have regarded them as providing no useful information. This apparent "waste", it seems to me, should serve to challenge the ingenuity of applied statisticians and demographers to make use of a new tool. General survey research issues The variance, bias, mean square error model has been a powerful tool for the examination of error structures of data gathering procedures. Frequently it has been used to suggest major improvements and refinements in the design of censuses and surveys. Yet as an applied survey statistician I am troubled by some of the ways it has been used. As I understand the situation, in the simple mean square error model what is termed "bias" and what is termed "variance" depends, in part, on the expected value, which in turn depends upon the sample space considered. This means that the parti167

Discussion

William Seltzer

tioning of total error into its bias and variance components is more or less arbitrary depending upon the definition of the sample space. When discussing sampling errors alone or the theory of statistical estimators there is usually agreement about what is the appropriate sample space. On the other hand, when nonsampling errors are introduced the choice is no longer as clear cut. In fact, I think many of us have somewhat different sample spaces in mind. In many situations, no harm results from the imprecision. However, if we begin to take the terms "bias" and "variance" too seriously then problems can arise. That is, we may begin to feel that having identified the bias of a procedure we can live with it because we can adjust for it. However, we can only take such partitioning of total error into bias and variance absolutely seriously when we are talking about a process that is under statistical control. In all other situations, and specifically when we begin to generalize about problems of error in demographic measurement, the bias of yesterday and the bias of today may differ in magnitude and sometimes direction. This means that yesterday's bias adjustment may not correct for today's bias. All this is by way of saying I think it would be helpful if Marks would spend some time in clarifying the sample spaces real or hypothetical to which his frequent references to bias and variance refer. In addition, I hope that we may have at the next meeting of the International Association of Survey Statisticians, a comprehensive restatement of the response error model from the point of view of the evaluation of specific data collection procedures. Fellegi makes a strong case in a paper presented at another session of the Vienna conference (Fellegi and Sunter, 1973) that no such comprehensive model can be used to optimize a design for a specific study, but what I have in mind is something less ambitious. What is needed are rational ways of interpreting the rich, but diverse, body of information on measurement error we have available.

An Appendix to Chapter 10 PGE/ERAD/ECP Evaluation of the Korean and Paraguayan Censuses

10. A. 1 Introduction to the Korean and Paraguayan results Korea and Paraguay have led the way in the recent work done on developing improved PES techniques. The earliest attempt to use the newer PES approach (of listing people where they are at the time of the PES and inquiring about where they were at the time of the census) was in the PES of the 1970 Population Census of Korea. Lessons from the 1970 Korean PES were used in designing a test (referred to in section 10.6) of the two PES approaches in connection with the 1972 Population Census of Paraguay.9 While final results of these post-enumeration surveys(Korea 1970 and Paraguay 1972) have not yet been released for general distribution, the Bureau of Statistics (BOS) of Korea and the Direction General de Estadistica y Censos of Paraguay (DGEC) have kindly granted permission for the inclusion of some of the preliminary results in this volume.10 It must be emphasized that none of the estimates in this appendix are official estimates of the governments of Korea or Paraguay and the statistical offices of those countries accept no responsibility for the accuracy of the estimates shown here. The results shown in tables 10.1 and 10.2 represent an encouraging step forward in the art and science of census evaluation by means of dual system estimation and we are indebted to the DGEC of Paraguay and the BOS of Korea for making their pioneering work in this area available to other countries. 168

Appendix 10. A.I

Role in census evaluation Table 10.1 Estimates of completeness in the 1972 census of Paraguay

Population enumerated in census Number ( N i ) Percent Population estimates Procedure A Total (N 2 ) Non-migrants (N 2n ) Migrants (N2m) Procedure B Total (N 2 ) Non-migrants (N 2 n ) Migrants (N 2m ) Unweighted number of sample cases Procedure A Non-migrants Migrants Procedure B Total Non-migrants Migrants

Percent migrant Procedure A Procedure B Completeness of enumeration estimates Procedure A Total (wi) Non-migrants (win) Migrants (w ]m ) Procedure B Total (w,) Non-migrants (wi n ) Migrants (w ]m ) Completeness of enumeration estimates with post-stratification (w.) Procedure A Procedure B Percent of migrants with insufficient information for matching (Procedure B only)

Rural

Paraguay total

Asuncion

Other urban

2,357,955 100.0

388,958 16.5

493,387 20.9

1,475,610 62.6

1,387,875 1,353,163 34,712

325,670 301,890 23,780

255,048 254,397 651

807,157 796,876 10,281

1,602,316 1,452,735 149,581

333,165 280,742 52,423

374,638 331,520 43,118

894,512 840,473 54,039

10,056 9,790 266

2,247 2,083 164

1,318 1,311 7

6,491 6,396 95

11,507 10,496 1,011

2,234 1,882 352

1,935 1,643 292

7,338 6,971 367

%

S.D.*% %

S.D*% %

S.D.*% S.D* % %

2.5 9.3

0.4 7.3 0.9 15.7

1.3 0.3 2.2 11.5

0.3 2.4

1.3 6.0

0.3 1.0

92.6 92.8 82.4

0.7 93.1 0.7 94.3 3.3 78.1

0.9 88.3 0.8 88.3 ** 4.4

2.3 93.7 2.3 93.7 91.3

0.7 0.7 2.9

90.0 91.0 80.9

0.7 89.9 0.7 91.0 3.3 83.9

1.3 89.2 1.3 90.2 4.1 81.6

2.0 90.4 2.1 91.2 8.8 77.7

0.9 0.8 4.8

92.4 90.0

0.7 92.9 0.7 89.9

1.0 88.3 1.3 89.0

2.3 93.7 2.0 90.3

0.7 0.9

44.2

4.6 45.0

5.7 49.0

8.9 39.8

7.8

see overpage for notes

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10.A.I Appendix

Notes: 1. "Migrant" = living in different location at time of PES from where staying at time of census. 2. S.D.*of percents estimated taking into account actual stratification and clustering of observations and correlations between the enumerators and denominators of the events. 3. Migrants in Procedure B with "insufficient information for matching" were allocated proportionately among enumerated (matched in census) and not enumerated (not matched in census) * S.D. = standard deviation ** Percent not computed, less than 10 persons in base. Table 10.2 Estimates of completeness in the 1970 census of Korea Korea total Population enumerated in census Number (Ni) Per cent PES sample cases Total: Number (N 2 ) Per cent ^ Non-migrants (N 2n ) Migrants (N 2m ) Per cent migrant Completeness of enumeration estimates Total (wi) Non-migrants (wi n ) Migrants (wim) Total with poststratification (wi) Per cent of migrants with insufficient information for matching

Metropolitan

30,882,386 100.0

,339,010 27.0

62,386 100.0 59,713 2,673 4.3

17,164 27.5 15,400

Other urban

Rural

4,370,503 18,172,875 14.1 58.8

10.3

8,075 12.9 7,849 226 2.3

37,147 59.5 36,464 683 1.8

95.2 96.2 74.1

91.1 92.9 75.5

96.0 96.2 89.6

96.9 97.5 66.2

94.9

90.8

96.0

96.7

49.3

58.1

27.4

33.8

1,764

10. A.2 Overall results: Korea The overall estimate of completeness of the census enumeration (1970) is 95.2 percent for Korea (see table 10.2). The 4.8 percent estimated incompleteness for Korea contrasts with the results of earlier post-enumeration surveys done for the Population Censuses of 1960 and 1966. Jay Soo Park (1960) estimates the net incompleteness rate of the 1960 census as 1.2 percent and the (unpublished) results of the 1966 PES indicate about the same rate of incompleteness. It may be argued that the increase from 1.2 percent net omissions in the 1960 (and 1966) PES to 4.8 percent net omissions in 1970 represents a bias in the 1970 PES estimate. One could, in fact, argue that the greater difficulty in matching the "migrants" (those who move between the Census and the PES) involved in the newer approach (procedure B) used in 1970 would tend to give a larger proportion of non-matches and, hence, an overestimate of census omissions. As noted below,

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the matching and estimation techniques used are such that the reverse is probably the case (i.e. the figures in table 10.2 probably underestimate the net omission). However, even if one looks only at the non-migrants in table 10.2 (a group which is estimated to be much more completely enumerated than the migrants in both table 10.1 and table 10.2), the incompleteness estimate is 3.8 percent for 1970, probably an underestimate but still substantially greater than the 1.2 percent estimated incompleteness for 1960. It seems likely that the difference between the 1960 and 1970 PES estimates for Korea is attributable almost entirely to the downward bias of the 1960 estimate. This downward bias is due less to the use of procedure B in 1970 than it is to the failure of the 1960 PES (and the 1966 PES) to achieve satisfactory independence between census and PES. As Lee-Jay Cho (1975) states in the unpublished report from which the figures of table 10.2 are taken: "PES designs both in 1960 and 1966 were essentially single system estimate designs.... The idea was to obtain PES estimates which would replace the census figures rather than to make an estimate based on both the census and PES. The census results were used in the PES estimates primarily for purposes of detecting and correcting errors in the PES through 'reconciliation' of discrepancies".

10. A.3 Overall results: Paraguay Turning to the results for Paraguay in table 10.1, the completeness estimates for the country as a whole are quite close for the two procedures," regardless of which form of estimate (wi without "post-stratification" or Wi with "post-stratification") is used— about 92.5 percent for procedure A and 90.0 percent for procedure B. Since both of these estimates are subject to an estimated sampling error of about 0.7 percent and the estimates are independent7, the standard deviation of the difference is about 1.0 percent and the difference of 2.5 percent is "statistically significant at the 2 percent level". However, part of the difference is due to the underreporting in procedure A of "migrants" (persons living at the time of the PES in a different dwelling from the one where they stayed at the time of the census), 2.5 percent of the PES estimated population being migrant for procedure A vs. only 9.3 percent for procedure B. The difference in estimated census completeness between the two procedures is not statistically significant for the migrants and is of "borderline significance" for the non-migrants and, if procedure A had shown the same census completeness rates as it did for migrants and non-migrants (82.4 percent and 92.8 percent) but obtained the same proportion of migrants as procedure B (9.3 percent), procedure A would show an overall census coverage rate of 91.8 percent, still somewhat above the Procedure B rate of 90.0 percent (a difference about 1.8 times its standard deviation). Even for the non-migrants, procedure A tends to give a higher census completeness rate estimate than procedure B. This is true for Asuncion and for the rural areas and in both cases the difference is more than twice its standard deviation. For urban areas, procedure A gives a lower census completeness estimate for non-migrants than procedure B (88.3 percent vs. 90.2 percent) but here the standard deviation of the difference is quite high, about 3 percent. It will be noted that the PES population estimates (N2) for procedure A are lower than those for procedure B for all areas (Paraguay total, Asuncion, Other Urban, Rural) and the procedure B estimates are less than the corresponding figures (N.) for the census. While the differences between procedure A and procedure B are probably due almost entirely to the poorer PES coverage of procedure A (particularly with respect to migrants), the differences between the Nj values for procedure B and theNi 171

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values for the census are only partly attributable to poorer PES completeness. The Chaco area of Paraguay and some other sparsely settled areas where access from outside is difficult and expensive were excluded from the PES (but not, of course, from the census). For the areas that were covered by PES, the census counts are: Paraguay total Asuncion Other Urban Rural

1,880,723 374,812 392,101 1,113,810

These figures are still above the N2 values for procedure B. Some of the residual difference is due to the (purposive) omission of the institutional population from the PES coverage13 and some of it may be sampling variance. In addition, there are probably sample areas where the PES completeness was poorer than the census completeness even for procedure B. The most obvious difference between the procedure A and the procedure B results is in the PES completeness of migrants. This large (and statistically significant) difference holds for all areas. This result is not unexpected. A major reason for taking on the matching problems involved in procedure B is the difficulty encountered in listing migrants at the place where they were at the time of the census. Where the whole household has moved, the listing must be obtained from the current (at time of the PES) residents who frequently know little or nothing about their predecessors or from a neighbour who may know some of the former household members (the household head and his wife, a child who played with one of the neighbour's children) but usually does not know all of them. In the case of procedure B, one is likely to pick up the migrants since they are resident in the sample household at the time of the PES interview. Of course, it may not be possible to get a satisfactory description of the former address (in Paraguay 44.2 percent and in Korea 49.3 percent of the procedure B migrants gave "insufficient information for matching") but there is much greater probability with procedure B of listing the migrant. There may be some migrants listed in procedure B who are not identified as migrants. This may be one of the reasons for the higher number of nonmigrants and the lower census completeness estimates of procedure B—i.e. migrants erroneously identified as having been in the sample dwelling at the time of the census are, of course, added to the count of "non-migrants" and are not found enumerated at the sample address nor searched for elsewhere in the census. An alternative explanation of procedure A's higher estimate of census completeness and lower number of non-migrants reported, is that procedure A tends to get fewer listings than does procedure B of non-migrants actually missed by the census but picks up about the same number of non-migrants enumerated in the census. This might be due to the emphasis in procedure A on listing persons who were in the sample dwelling at the past date, with the PES respondents tending to be uncertain about persons who move about a good deal from one dwelling to another and therefore failing to report some who were actually at the sample dwelling location at the time of the census, but reporting "permanent residents" who have moved and those still at the sample dwelling. There is no completely convincing evidence for either the hypothesis of an upward bias in the procedure A census completeness estimate or a downward bias is the procedure B estimate. In any event, the residual difference in census completeness between the procedure, after adjusting for the lower procedure A PES completeness of migrants, appears to be relatively small and may be a matter of sampling variance. 172

Role in census evaluation

Appendix 10.A.4

10. A.4 Differences in completeness between migrants and non-migrants An interesting feature of tables 10.1 and 10.2 is the difference in census completeness between non-migrants and migrants shown by the Korean PES and both procedures of the Paraguayan PES. This difference is particularly interesting if one remembers that the "migration" involved occurred after the census. It emphasizes again that correlation is not causation and that correlation bias can be present even where there is no direct communication between the two data collection systems.14 To achieve independence, it is, of course, necessary to guard against direct communication between the two systems. It is important, for example, that the PES interviewer not be the same person who did the census enumeration in any area nor the supervisor of the census enumerator for the area.15 But eliminating direct communication, while necessary, is not sufficient to secure independence between the systems. One must also take steps to prevent the correlation that conies from the tendency of both systems to miss certain types of person.16 Thus, part of the difference shown in table 10.1 between the census completeness estimates of procedure A and procedure B may be due to higher correlation bias of procedure A because: (a) migrants have a relatively high probability of being missed in the census, and (b) procedure A has a very high probability of missing migrants. Of course, the probability of migrants being missed in the census is the same for procedure B as it is for procedure A and the difference between the procedure A estimate of 82.4 percent census completeness of migrants and the procedure B estimate of 80.9 percent is neither statistically significant nor substantively important. However, while procedure B may also miss some migrants, it does a much better job of including them than does procedure A; and the difference between the estimated 34,712 migrants picked up by procedure A and the 149,581 migrants for procedure B is statistically and substantively significant (standard deviation of the difference is 15,900).

10.A.5 Differences in completeness between types of area All differences between areas of Paraguay for migrants shown in table 10.1 are subject to such high variances that conclusions are somewhat risky. For migrants, the only difference between areas within procedure in table 10.1 that is statistically significant is that for rural areas. For Korea, the differences in omissions between areas for migrants are small and probably not statistically significant. For the total of migrants and nonmigrants, the low census completeness estimate for the metropolitan areas (91.1 percent vs. 96.0 percent for other urban areas and 96.9 percent for rural areas) is undoubtedly statistically significant, reflects a very real demographic phenomenon, and has considerable implication for census-taking in Korea (and in other countries with similar demographic changes). As shown in table 10.1, the population of Asuncion as enumerated in 1970 was nearly 400,000. In contrast, the "metropolitan" areas of table 10.2 are really in the "megalopolis class". That is, the Korean "metropolitan" areas are Taegu with about 1 million population enumerated in 1970, Pusan with nearly 2 million, and Seoul with over 5 million population. Furthermore, these Korean metropolises, and particularly Seoul, experienced a phenomenal growth during the 1960s (a population increase of over 100 percent in the case of Seoul). The predictable result has been that the population of the Korean metropolitan areas has far outgrown the housing supply. Newcomers to the cities and other persons with low incomes and no immediate family in the area, "double up" (and often "triple up" or "quadruple up") with friends or sleep in 173

10. A.5. Appendix

Eli S. Marks

makeshift quarters — in sheds, shacks or temporary shelters, in or behind stores, warehouses or factories, or anywhere else where one can snatch a few hours of rest. Trying to enumerate this type of population completely is a hopeless task. It is, in fact, amazing that the 1970 census succeeded in enumerating 75.5 percent of the metropolitan "migrants" which number probably contained a large proportion of these recent arrivals and there is probably an equally large number of relatively recent arrivals among the "non-migrants" of table 10.2, so that the 92.9 percent completeness of nonmigrants was probably achieved only by accomplishing a near 100 percent enumeration of the bulk of the population that lives in stable and well-defined residential quarters.

10. A.6 Completeness differences correlated with sex and age Table 10.3 presents estimates of the completeness of census enumeration for Paraguay by sex and age. The pattern of underenumeration by age and sex for the 1972 Census of Paraguay tends to resemble the pattern shown in chapter 11 for the 1974 Census of Liberia. That is, enumeration of children under 5 years of age tends to be less complete than enumeration of children 5-14, with completeness of census enumeration declining after age 15 to a very low level (for ages 20-24 in the Paraguayan census and ages 15-19 in the Liberian census). For ages above this point of lowest coverage, completeness of enumeration improves and reaches its maximum in the age range 35 to 59. There appears to be somewhat lower completeness of persons 60 and over, although the completeness of persons 65 and over is somewhat better than that of persons 60-64 years old for both sexes in Liberia and for males in Paraguay. While most of the individual differences between age cohorts are not statistically significant, the general pattern of underenumeration holds for both sexes and procedures and for Asuncion, Other Urban, and Rural Areas. There are, of course, minor differences in the pattern between Paraguay and Liberia and also between males and females in both censuses. There are also some differences between the age-sex pattern shown by procedure A and that shown by procedure B and some of the difference between the Liberian and Paraguayan age-sex patterns may be due to differences in the PES procedures. However, the similarity of the basic age-sex pattern as well as the major differences in pattern probably reflect similarities and differences in basic life styles—age at which people leave the parental home (to marry or seek employment) and differences between males and females and urban and rural persons in this age, age of marriage (and new household formation), metropolitan-urban-rural patterns of residential stability, etc. Thus, in addition to providing important qualifications on demographic analysis, the facts about census completeness can themselves be fruitful data inputs/or demographic analysis. Completeness of census enumeration is higher for females than for males. This difference is not statistically significant but holds for both procedures and, within procedures, for all areas except for Asuncion with procedure B. There does not appear to be any consistent pattern of sex differences associated with age. However, the differences tend to be larger in the age range 30-44; but for Other Urban areas with procedure A and Asuncion with procedure B, completeness of persons 30-44 is better for males than for females. While the evidence is confused by the high variances and biases of many of the figures, there is some support for the hypothesis that, for Paraguay, differences in census completeness between males and females are related primarily to the fact that adult females adopt a stable residential pattern at an earlier age than men. That is, women marry (or enter a "consensual union") and have children in 174

Table 10.3 Completeness of census enumeration by age, procedure., sex and area for Paraguay 1972 PES

(1)

Estimated census completeness (%) Combined Procedure Procedure B procedures A (4) (3) (2)

PES Population (N2) Procedure A Procedure B no. (000) percent no. (000) percent (8) (7) (6) (5)

Ratio of estimated A/B[(5)/(7J\ (9)

All areas both sexes 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65+

91.1 90.4 93.5 91.8 87.5 84.5 87.7 91.5 93.9 94.0 95.0 95.0 94.0 93.6 92.8

92.6 92.1 95.0 92.4 89.0 86.3 90.8 92.1 95.8 96.7 95.7 95.1 94.8 93.6 95.2

89.9 88.6 92.3 91.4 86.2 82.7 85.6 90.9 92.3 91.6 94.5 95.0 93.2 93.8 91.3

1,388 155 211 201 155 112 84 77 73 67 55 53 43 32 62

100.0 11.2 15.2 14.5 11.2 8.1 6.1 5.5 5.3 4.9 4.0 3.8 3.1 2.3 4.5

1,602 181 244 229 181 144 98 87 75 80 62 59 40 40 78

100.0 11.3 15.2 14.3 11.3 9.0 6.1 5.4 4.7 5.0 3.9 3.7 2.5 2.5 4.8

.87 .86 .86 .88 .86 .78 .86 .89 .97 .84 .89 .90 1.06 .80 .80

All areasboth sexes 0-14 15-29 30-44 45-60 60+

92.1 86.6 93.1 94.8 93.3

93.3 88.6 94.8 95.2 94.6

91.0 84.9 91.6 94.4 92.2

567 351 217 151 94

41.1 25.4 15.7 11.0 6.8

655 422 242 161 118

41.0 26.4 15.1 10.1 7.4

.87 .83 .90 .94 .80

Age

Table 10.3

Age

PES Population (N2)

Estimated census completeness (%) Combined Procedure Procedure B procedures A

Procedure A no. (000) percent

Procedure B no. (000) percent

(2)

(3)

(4)

(5)

(6)

(7)

(8)

92.3 91.8 95.3 92.8 90.0 85.4 88.1 91.5 94.1 96.7 93.4 97.4 96.8 90.2 94.0

89.2 88.0 91.1 93.1 84.4 82.9 82.7 88.1 89.9 90.8 92.6 94.7 92.5 91.6 94.5

676 81 106 105 74 53 40 35 34 34 24 26 18 15 26

100.0 12.0 15.7 15.6 10.9

7.9 5.9 5.2 5.1 5.1 3.5 3.9 2.6 2.2 3.8

757 95 126 116 84 68 47 42 32 39 29 26 19 17 31

100.0 12.3 16.2 15.0 10.9

65+

90.6 89.8 93.0 93.0 87.1 84.2 84.7 89.8 92.0 93.5 93.0 96.1 94.4 90.9 94.1

All areasmales 0-14 15-29 30^4 45-60

92.1 85.6 91.7 94.5

93.4 88.0 94.0 95.8

90.9 83.5 89.5 93.3

292 167 104 68

43.5 24.8 15.5 10.1

337 200 113 74

43.7 25.8 14.7

(1) All areasmales

0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40^4 45-49 50-54 55-59 60-64

60+

8.7 6.1 5.4 4.1 5.1 3.8 3.4 2.4 2.2 4.0

9.6

Ratio of estimated A/B[(5)/(7j] (9) .87 .85 .84 .90 .87 .78 .83 .86 1.07 .87 .82 1.01 .95 .86 .84

.87 .83 .92 .92

All areasfemales 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40^4 45-49 50-54 55-59 60-64 65+

91.6 91.0 94.0 90.6 87.9 84.8 90.5 93.1 95.5 94.4 96.7 94.1 93.7 95.8 91.9

92.9 92.5 94.7 92.1 88.2 87.2 93.3 92.7 97.3 96.7 97.5 92.9 93.4 96.6 96.0

90.6 89.3 93.6 89.7 87.8 82.5 88.3 93.6 94.1 92.4 96.2 95.2 93.7 95.5 89.2

712 74 105 96 81 59 45 41 39 33 31 27 25 17 36

100.0 10.4 14.7 13.5 11.4 8.2 6.3 5.8 5.4 4.6 44 3.8 3.5 2.5 5.1

828 86 119 113 96 76 50 45 43 41 33 33 22 23 47

100.0 10.4 143 137 116 91 61 54 52 49 40 40 26 28 5.6

86 86 88 '85 84 78 ~89 92 89 81 95 '82 116 75 J8

All areasfemales 0-14 15-29 30-44 45-60 60+

92.0 87.5 94.3 94.9 93.2

93.2 89.1 95.4 94.8 96.2

91.0 86.1 83.4 95.2 91.3

275 185 113 83 54

38.8 26.0 16.0 11.7 7.5

318 222 129 87 70

385 269 156 106 8.4

87 '83 '88 95 .77

Both sexesAsuncion 0-4 5-9 10-14 15-19 20-24 25-29

91.6 90.5 92.7 92.6 90.3 90.0 88.9

93.1 89.9 92.3 94.5 93.9 92.7 93.3

90.2 90.9 93.0 90.4 86.5 87.7 85.1

326 25 38 45 41 34 22

100.0 75 11.6 13.8 12.5 10.3 6.7

356 27 41 40 39 39 25

1000 79 ll's 115 112 112 73

.94 90 .92 1.13 1.04 .87 .87

Table 10.3 Age

PES Population (Ni)

Estimated census completeness (%)

Procedure A no. (000) percent (5) (6)

Procedure B no. (000) percent (7) (8)

Ratio of estimated A/ B [(5)/ (7)] (9)

(1)

Combined Procedure Procedure procedures A B (2) (3) (4)

30-34 35-39 40-44 45-49 50-54 55-59 60-64 65+

92.6 92.4 93.4 93.7 93.4 91.6 94.5 90.9

89.7 92.9 97.0 95.5 96.3 92.5 98.1 91.3

85.0 92.0 90.4 91.9 90.8 90.4 92.0 90.6

21 18 19 16 12 12 8 15

6.5 5.6 5.8 4.9 3.7 3.6 2.3 4.6

25 21 23 15 14 9 11 17

7.3 6.2 6.6 4.4 3.9 2.6 3.1 4.8

.84 .86 .84 1.05 .87 1.30 .70 .90

Both sexesAsuncion 0-14 15-29 30-44 45-60 60+

92.1 89.9 92.8 93.0 92.2

92.7 93.4 93.0 94.9 93.6

91.5 86.6 92.6 91.1 91.2

107 96 58 39 22

33.2 29.7 18.0 12.2 6.9

108 103 69 38 27

31.3 29.8 20.0 10.9 7.9

.99 .94 .84 1.05 .82

Both sexesother urban 0-4 1 10-14 15-19 20-24

88.8 88.3 5-9 88.2 85.6 82.1

88.3 86.3 90.5 86.3 83.2 79.1

89.2 89.3 93.1 89.4 87.5 84.0

255 22 88.9 35 31 20

100.0 8.4 35 13.9 12.1 7.8

362 40 13.9 58 40 32

100.0 11.1 56 16.0 11.0 8.8

.71 .54 .63 .61 .78 .63

25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65+

83.2 91.7 92.2 89.4 86.8 92.9 93.3 90.5 91.0

78.3 93.1 95.4 91.8 99.3 86.6 91.9 88.9 93.9

86.8 90.4 89.4 87.3 94.6 97.8 94.6 92.2 89.4

14 13 15 13 12 12 9 9 14

5.4 5.2 5.8 5.3 4.8 4.5 3.6 3.6 5.4

19 14 16 16 14 15 9 9 24

5.3 3.8 4.6 4.4 3.8 4.1 2.6 2.6 6.5

.72 .95 .91 .85 .89 .77 .99 .99 .58

Both sexesother urban 0-14 15.29 30-44 45-60 60+

89.1 83.9 91.1 94.4 90.9

88.9 80.9 93.5 92.8 91.9

89.2 86.1 89.0 95.9 90.2

92 65 42 33 23

36.2 25.4 16.3 13.0 9.0

153 91 46 38 33

42.5 25.1 12.8 10.5 9.1

.60 .71 .90 .87 .70

Both sexesrural 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64

91.8 90.7 94.8 93.0 87.1 82.0 89.2 90.9 95.6 95.9 95.1 96.7 95.5 95.0

93.7 93.8 96.2 93.5 88.8 85.2 93.3 93.0 97.3 98.4 94.3 97.9 97.3 94.3

90.1 87.9 93.4 92.6 85.7 79.5 85.4 89.0 93.8 93.9 95.7 95.5 93.7 95.6

807 109 138 121 83 58 49 43 40 35 27 30 22 16

100.0 13.5 17.1 15.0 10.3 7.2 6.0 5.3 4.9 4.3 3.3 3.7 2.7 1.9

95 114 148 132 102 73 54 48 38 41 33 31 22 20

100.0 12.8 16.5 14.7 11.4 8.1 6.0 5.4 4.2 4.6 3.7 3.4 2.5 2.3

.90 .96 .93 .92 .81 .80 .91 .89 1.06 .84 .81 .98 .99 .76

Table 10.3

Age

PES Population (N2)

Estimated census completeness (%) Procedure Procedure

Combined procedures A

Procedure A no. (000) percent

Procedure B no. (000) percent

(5)

(7)

Ratio of estimated A/ B [(5) / (7)]

(1)

(2)

(3)

B (4)

65+

95.0

97.4

92.8

33

4.1

37

4.2

.90

93.0 86.0 84.0 95.8 95.0

94.6 88.8 96.1 96.5 96.4

91.5 83.6 92.0 95.1 93.8

368 190 117 79 47

45.9 23.8 14.6

394 229 127 86 58

44.1 25.6 14.2

.93 .83 .92 .92 .82

Both sexesrural 0-14 15-29 30-44 45-60

65+

(6)

9.8 5.9

(8)

9.6 6.5

Note: The percentages shown are based on the totals of persons of all ages in the category, including a small number of persons for whom age was not reported. Consequently, the totals for the various age groups will not add to the total persons shown nor will the percentages add to 100.

(9)

Role in census evaluation

Appendix 10.A.6

their twenties. While men are usually only slightly older than women at first marriage, their period of "residential instability" may persist longer because, even after marriage, the men are still seeking jobs (and locations) which offer greater economic opportunity. There is also, in Paraguay, the fact that "consensual unions" (common-law marriages) are not necessarily permanent, even where there are children. However, women tend to settle down at an earlier age to a permanent union or to living alone or with relatives and raising their children in a permanent location. 10. A.7 Differences in completeness related to household composition and migration status In table 10.4 are given details of census completeness by relation to head of household. The household head and spouse (almost always "wife" or "concubina" in Paraguay) are best enumerated, with children of the head with somewhat lower completeness but still over 90 percent complete. Other relatives and "criadas"11 show somewhat lower completeness (about 85 percent) and that of employees (mostly domestic servants) is still lower (72.8 percent). Completeness of "other non-relatives" is 75.8 percent, falling between employees and "criadas"17 (including "other relatives") but closer to the former. For procedure B, migrants and non-migrants show about the same ranking on completeness but the "nuclear family" members (head, spouse, children) show a significantly lower completeness for the migrants, not significantly above that for migrant "other relatives" and "criadas". For procedure B, the relationship categories with the poorest completeness, employees and "other non-relatives", have the highest proportion of migrants (about 48 percent of all persons in the category) and also even poorer census completeness of non-migrants than of migrants. The latter phenomenon may be due to the fact that, for about 50 percent of the migrants in these two categories, there was insufficient information for doing the matching and determining enumeration status. The completeness rates were therefore based on the cases for whom there was sufficient matching information and these cases may well have been those in the category who were more likely to have been enumerated in the census. The proportion of migrants reported by procedure A for most relationship categories was too small to affect the estimated census completeness rates appreciably. Even where the proportions of migrants reported by procedure A are large (for employees with 33.1 percent migrant and "other non-relatives" with 14.3 percent migrant), they are well below the proportions of migrants in the categories reported by procedure B (47.7 percent for employees and 48.2 percent for "other non-relatives"). As already noted, the inclusion of migrants was less complete for procedure A than for procedure B. That is, procedure A picked up less than one-fourth the number of migrants reported by procedure B. Procedure A also reported about 7 percent fewer non-migrants than did procedure B. Taking procedure B as an approximate measure of the number of cases in a given category that should have been reported by procedure A, there are only three relationship categories ("other relatives", employees, and"criadas") for which procedure A reporting was more than 25 percent complete. These three categories are also the only three categories for which census completeness is estimated to be better by procedure A then by procedure B. Of course, the groups involved are small, the standard deviations of the differences are large and the reversals of the relationship may be coincidental. It will be noted from table 10.5 that procedure A reporting of migrants is particu181

Table 10.4 Estimated census completeness by relationship to household head for Paraguay 1972 PES Estimated census completeness (%) Relationship to household head

(1)

Combined Procedure Procedure procedures A B (2) (4) (3)

Total population Head Spouse Child Other relative Employee Criada Other non-rel.

91.1 93.6 94.7 91.8 83.8 72.8 84.4 75.8

92.6 96.3 96.5 92.3 85.2 73.6 87.1 80.3

PES Population (N2) Procedure A No. (000) percent (6) (5)

89.9 91.3 93.0 91.3 82.9 72.3 82.4 72.7

L3882 271 198 733 136 11 13 13 2

100.0 19.7 14.4 53.3

9.9 0.8 0.9

0.9

Procedure B percent1 No. (000) (7) (8) 1,602* 313 212 825 194 16 17 19

Non-migrants Head Spouse Child Other relative Employee Criada Other non-rel.

91.9 94.4 95.3 92.2 84.8 71.8 85.9 74.8

92.8 96.3 96.4 92.4 86.2 75.0 88.5 79.6

91.0 92.7 94.2 91.9 83.7 69.1 83.6 69.4

1.3S3 266 195 722 127 7 12 11

97.5 98.2 98.5 98.4 93.5 66.9 92.6 85.7

1,453' 285 195 772 164 8 14 10

Migrants Head Spouse Child Other relative

81.4 84.6 87.2 83.2 76.5

82.4 97.0 100.0 85.1 71.1

80.9 81.1 83.6 82.5 79.3

352 5 3 11 9

2.5 1.8 1.5 1.6

ISO2 28 17 53 30

6.5

Ratio of estimated AIB[(5)l(7)-\ (9)

100.0 19.6 13.3 51.1 12.1 1.0 1.1

.87 .86 .93 .89

1.2

.66

90.7 91.2 92.2 93.6 84.5 52.2 82.4 51.8

.93 .93 1.00 .94

9.3 8.8 7.8 6.4 15.5

.23 .17 .18 .22

2

.70 .67 .77

.78 .86 .87 1.10

.29

Employee Criada Other non-rel. 1

2

13.1 74.9 80.5

70.9 70.1 84.1

753 78.1 79.0

3 1 2

33.1 1.3 14.3

7 3 9

47.7 17.6 48.2

For the total population the percents are the percents in each category (excluding cases with relationship not reported that are included in the total population shown but not in the base of the percents). For non-migrants and migrants the percents are the percent that the non-migrants or migrants are of the total population reported in the category by the given procedure. Total population, total non-migrants and total migrants include some persons with relationship to household head not reported. Consequently the estimates will not necessarily sum to the totals nor the percents to 100.

.47

.32 .20

£

Table 10.5 Estimated census completeness by migration status for Paraguay 1972 PES Migration status of household members

Estimated census completeness (%)

PES Population (N2)

Ratio of cases reported Al B [(5)1 (7)] (9)

Combined procedures (2)

Procedure A (3)

Procedure B (4)

Procedure A no. (000) percent (5) (6)

Procedure B no. (000) percent (7) (8)

Total All non-migrant All migrants Some migrants Single person household

91.1 91.9 86.5 86.8

92.6 92.6 97.0 91.0

89.9 91.3 86.0 84.4

1,388 1,260 8 104

100.0 90.8 0.6 7.5

1,602 1,269 95 212

100.0 79.2 5.9 13.3

.87 .99 .08 .49

86.9

94.9

81.6

16

1.1

24

1.5

.65

Non-migrant All non-migrant Some migrants Single person household

91.9 91.9 91.6

92.8 92.6 95.5

91.0 91.3 89.4

1,353 1,260 78

100.0 93.1 5.8

1,453 1,269 162

100.0 87.3 11.2

.93 .99 .48

88.7

94.8

84.3

15

1.1

20

1.4

.77

Migrants All migrant Some migrants Single person household

81.4 86.5 73.3

82.4 97.0 77.9

80.9 86.0 67.9

35 8 27

100.0 22.4 76.4

149 95 57

100.0 63.7.08 38.1.47

.23 .08 .47

76.8

_*

70.4

0.4

1.1

3

2.5.10

.10

(1)

* Less than 10 sample cases.

Role in census evaluation

Appendix 10.A.7

larly poor (8 percent of Procedure B) when an entire multi-person household moved between the census and the PES and is relatively good (47 percent of procedure B) when only some members of a multi-person household moved. That is, a moderately good reporting of migrants could be obtained where some household members remained at the census location and could furnish information on those who moved. However, when all household members moved from the census location, information on the migrants had to be obtained from neighbours or from the new occupants of the dwelling unit and these reports are necessarily incomplete.

10.A.8 Post-stratification To reduce the effects of correlation bias in dual system estimates it has been recommended (Marks et al., 1974) that: i. The sample data be classified ("post-stratified") into groups having very different census completion rates. ii. A separate (dual system) estimate be made of the "true" population in each class (stratum). iii. The stratum populations be added to give the overall "true" population. iv. The estimated "true" overall population be divided into the population (or population estimate) reported by a given source (census or PES) to give the estimated completion rate for the source. For the Korean and Paraguayan post-enumeration surveys, the strata were the three types of area (metropolitan, urban, rural) and the classification of "migrant" or "non-migrant". The completion estimate Wi (without post-stratification) is made by adding the matched cases over all strata and dividing by the total number of PES cases.18 This gives the estimate: where i is summed over the two migration classes (non-migrants and migrants) and h is summed over the three type-of-area classes; and = total number of PES cases in the ith migration class of the hth area class, = number of matched PES cases in the ith migration class of the hth area class, = proportion of matched in the census = estimated census completeness rate for the hith class,

The estimate of census completeness made with post-stratification is: where Ni h i = the number of cases reported in the hith class by the census; and is the dual system estimate of the "true" population in the hith class. It can be seen from Equation (10.1]i that Wi is the weighted arithmetic average of the Wihi values, using the weights [NzhJ. Correspondingly, it can be seen from Equation (10.2) that Wi is also a weighted mean of the WIHI values but a weighted harmonic mean, using the weights [Nihi]. Actually, we can only obtain from the census, the counts: 185

10.A.8 Appendix

Eli S. Marks th

Nih = number of cases reported by the census for the h area class. These appear on the line labelled "Ni" in tables 10.1 and 10.2. To estimate Niw, we assume that the proportions of migrants and nonmigrants reported in the census for an area class is approximately the same as the proportions reported for that area class by the PES. This gives: or

From Equations (10.2) and (10.4), we have where It can be seen in tables 10.1 and 10.2 that the use of post-stratification in the estimates makes practically no difference.19 That is, the value of wi and WIH (on the line labelled "wi") do not differ appreciably from the corresponding values of wi and wih (on the line labelled "wi"). 10.A.9 Handling of migrants with "insufficient information for matching" As noted above, while procedure B was successful in listing migrants and identifying them as such, considerable difficulty was encountered, both in Korea and in Paraguay, in securing enough information to do a satisfactory search for the migrant in the census. The difficulty was, of course, in locating the enumeration district containing the dwelling where the person was reported as living or staying at the time of the census. Frequently, address information was meagre — e.g. only that it was in the "Barrio Sta. Maria", an area of 5000-plus population. Of course, one could examine all the 1000-plus census schedules for the Barrio Sta. Maria and, in fact, one person was located in the census by just such a search. But this takes considerable time and requires tremendous patience and conscientiousness. Futhermore, if a search is made of all the schedules in a large area and the person is not found, how can one be certain the person was not listed but that boredom and sheer fatigue caused one to overlook the name, particularly considering the misspellings and semi-legible handwritings one is likely to encounter in any census. In both Korea and Paraguay procedure B, we were fortunate in having very competent and conscientious, semi-professional personnel assigned to do the matching of the migrants. Initially, the clerks were left free to do as extensive or limited a census search as their judgment indicated was appropriate to the particular case. If the search undertaken did not turn up a census match for the case, the clerk was to classify the case as "unmatched" or as "insufficient information for matching". The cases with insufficient information were then to be treated like other cases with information on a characteristic not available. That is, the enumeration status for the cases with insufficient information is, in fact, not available and it is appropriate to "impute" an enumeration status in the same manner as one "imputes" ages or incomes where these are not entered on a census schedule. The method of "imputation" is, of course, to assume the same distribution of the characteristic exists among the non-response cases as among the respondents.20 The imputation is sometimes improved by doing it within classes set up on the basis of characteristics having a substantial (multiple) correlation with the characteristic being computed. Further consideration of the handling of cases classified as having insufficient 186

Role in census evaluation

Appendix 10. A.8

information for matching led to the realization that this classification must be made prior to the census search rather than after it. That is, if the classification is made after the search, only the cases not found will be classified as "information not available"; and these will almost certainly have a higher proportion of persons not enumerated than would be true for those to whom an enumeration status was assigned. As a result of this, cut-offs on the number of household listings and census schedules to be searched were set; and cases which could require searching more cases than the cut-off number were classified as "insufficient information for matching" and not searched for in the census. This resulted in 49.3 percent of the Korean migrants and 44.2 percent of the procedure B migrants in Paraguay being classified as having "insufficient information for matching". While the cut-offs eliminated a major part of the original bias in handling the cases with insufficient information for matching, it is still likely that the migrants so classified contained a higher proportion of cases not enumerated in the census than was true for the migrants who were searched for in the census files. Since the cases with insufficient information constitute a large proportion (nearly half) of all migrants, they would have an appreciable effect on the completeness estimates for migrants and, in consequence, these estimates are (as suggested previously) likely to overestimate the census completeness. Endnotes to Chapter 10 1. The author is not concerned in this paragraph with sex (or age) selective omissions from the census enumeration. Nor does he deny later on in the paragraph the occurrence of age heaping. He merely describes random variations in completeness and age reporting: however large, they create no bias. [Editor's note.] 2. In the Moroccan experience reported in section 8.5.b, the out-of-scope bias does not make much difference once reasonable care has been taken about the cluster boundaries. [Editor's note.] 3. It will be recalled that that type of consideration led the discussant of chapter 2 to the rather dangerous conclusion that "if both completeness and correlation increase ... the fetish o f . . . independence ... is [not necessarily] the ... maximum payoff". [Editor's note.] 4. The vagueness on exact date is complicated by the fact that census listings do not necessarily conform to the specified "census date" i.e. they may include persons in an area at the time of the census enumerator's call even though those persons were living or staying elsewhere on the specified "census date". 5. Our confidence in the proof suggested in the text will depend on how "neighbouring" the other heads were. If not surrounding the given household entirely, a spill-over into neighbouring E As could explain the absence of the household through inclusion in a neighbouring EA. [Editor's note.] 6. An early PES, that of the 1950 U.S. Census of Population (U.S. Bureau of the Census 1960), attempted to combine "reconciliation" with the PES interview proper. It was the judgment of those involved in the PES that the procedure unduly sacrificed independence and they strongly recommended a third visit for reconciliation. This recommendation has been followed in subsequent post-enumeration surveys. 7. The paragraph about the unlikelihood of the listing of persons in a census who should not have been listed, was written before tens of millions of persons of that kind were listed in the 1973 census of Nigeria. [Editor's note.] 8. This is the A procedure. 9. Particularly important were the lessons on designing the PES forms to obtain 187

Endnotes

Eli S. Marks

additional information necessary for carrying through the search of the census listings for persons who move between the census and the PES. 10. The design and execution of these studies was the joint responsibility of Jose Diaz de Bedoya, David Vera, and Alberto Sanchez of the Direccion General de Estadisticas y Censos of Paraguay; of SunRayChoe, S. K. Chang, J. H. Bang and J. Y. Park of the Bureau of Statistics of Korea; of Lee-Jay Cho of the East-West Population Institute in Honolulu, Hawaii; and of Hans J. Muller and Eli S. Marks of the U.S. Bureau of the Census. Consulting work by the Bureau of the Census was done as part of the program of the Agency for International Development. 11. (i) In procedure A the sample consisted of persons staying in the sample segments at the time of the census (July 1972) and the matching search of the census listings was confined to the PES sample enumeration areas and in a few boundary line cases, adjacent areas, (ii) In procedure B, the sample consisted of all persons living in the sample segment at the time of the PES interviews there (May to October 1973) and the search of the census listings was of all areas where the person might have been enumerated in the census (areas where person was reported as living or staying in July 1972). 12. Sample segments were assigned randomly to procedure A or procedure B and there was no overlapping of either respondents or interviewers between procedures. 13. Coverage, rather than completeness, is the correct expression in this instance, because it refers to the intended coverage; intended by the definition of the PES population. [Editor's note.] 14. The inevitability of correlation bias has been confirmed theoretically, when it has been shown that independence can only be achieved in the unlikely case when one of the two PGE/ ERAD/ ECP sources is 100 percent efficient (or rather less rigorously, but equally unattainably, has constant incompleteness) (Greenfield, 1976). Before practitioners in the field begin entertaining suicidal thoughts let it be added quickly that these elegant refinements are relevant close to the ideal, and not within the rather wide band of uncertainty where most of us operate in real life. [Editor's note.] 15. This is confirmation of the view repeatedly expressed that using supervisors or workers from one procedure to supervise, or match, or determine doubtful cases, or sit in judgment over unmatched cases, is the denial of the PGE/ ERAD/ ECP advantages. A probably extreme case of a breach of this principle occurred in the Indian Sample Registration Scheme. [Editor's note.] 16. The attentive reader will recall that chapter 5 is shot through with the concern for this indirect dependence. [Editor's note.] 17. A "criada" is a girl who is given to some family (often friends or relatives of her own family) to be raised by them. She works as a maid in the household but is not paid and her status is usually quite similar to that of a young relative whom a family is raising. It is likely that, in some cases, distant relatives living as wards in a household are reported as "criadas". 18. For Korea, the sample was "self-weighting" so the number of matched and total PES sample cases (shown in table 10.2) was used without weighting. In Paraguay, the PES sample cases had to be weighted to allow for differential sampling probabilities. The figures N2; N2n, N2m, are the total PES sample cases weighted up on the "study universe" level. Corresponding weights were applied to estimate the matched cases for the "study universe". 19. This is not the first time that post-stratification made no difference. Literature contains several such experiences. In fact, only in the original article by Chandrasekaran and Deming(1949) did it appear to make a difference. [Editor's note.] 20. Assuming the same distribution for nonrespondents as that for respondents is, of course, the "implied imputation" where a percent distribution by age, income, etc. is based only on the respondents. [Editor's note.] 188

Chapter 11 The 1974 Post-Enumeration Survey of Liberia — A New Approach Eli S. Marks and John C. Rumford 11.1 The traditional PES approach Fifteen days after the beginning of the 1974 census of population and housing in Liberia, a post-enumeration survey was conducted. Though the short interval of time between the census and evaluation survey was unusual, what made the Liberian effort different was the simple and relatively inexpensive survey and implementation system used. In the past, post-enumeration surveys have proven difficult, time-consuming, and expensive to carry out. Because of this, many countries, particularly the developing countries, have avoided post-enumeration surveys in census evaluation planning. This is unfortunate because no census, regardless of how carefully planned and executed, is perfect. While perfection cannot be obtained, completeness of enumeration can and should be estimated. The purpose of this chapter is to outline the post-enumeration survey system used in Liberia which, when combined with the traditional methods of demographic analysis, shows promise of being developed into an effective census evaluation tool. We hope that the simplicity of the Liberian model and the success achieved in its application will encourage those countries which have not considered using a postenumeration survey, to include this important tool in their census plans. The primary purpose of a post-enumeration survey (PES), is to provide estimates of census completeness. All censuses suffer from two types of completeness errors. The first, and most frequent, is underenumeration, and the second is overcounting. Underenumeration errors are caused by such things as missing persons in enumerated living quarters, missing living quarters entirely or, in some cases, missing whole localities. Overcounting is almost always of much smaller magnitude and results from enumerators overlapping at area boundaries, reporting of persons by more than one household, and the enumeration of persons who should not have been enumerated, such as (names entered for) nonexistent individuals or persons who died before or were born after the census date.1 The traditional PES used to estimate these errors involves re-enumerating a sample of census enumeration areas (EAs) or parts of EAs several months after the census, using a specially selected, well-trained group of enumerators. These enumerators are usually provided with pre-enumeration intelligence derived from the census, and each is instructed to reconstruct the population in the evaluation area as of the census date. At the close of the re-enumeration, a case-by-case matching with the 189

11.1

Eli S. Marks and John Rumford

Table 11.1 Persons recorded in both the census and the post-enumeration survey by age and sex; Liberia, 1974 Age group

Total

Male

Female

All ages Under 1 year 1- 4 years 5- 9 years 10-14 years 15-19 years 20-24 years 25-29 years 30-34 years 35-39 years 40-44 years 45-49 years 50-54 years 55-59 years 60-64 years 65 years and over

9782 242 1129 1425 1047 876 708 775 678 678 479 499 355 262 236 393

4948 117 610 754 564 419 288 316 286 318 262 269 213 154 148 230

4834 125 519 671 483 457 420 459 392 360 217 230 142 108 88 163

Table 11.2 Persons recorded in the post-enumeration survey by age and sex; Liberia, 1974 Age group

Total

Male

Female

All ages Under 1 year 1- 4 years 5- 9 years 10-14 years 15-19 years 20-24 years 25-29 years 30-34 years 35-39 years 40-44 years 45-49 years 50-54 years 55-59 years 60-64 years 65 years and over

10990 282 1311 1613 1176 1035 803 859 752 746 516 546 383 279 263 426

5544 136 690 849 636 500 332 356 321 354 284 291 227 161 160 247

5446 146 621 764 540 535 471 503 431 392 232 255 156 118 103 179

census questionnaires is carried out, and a full field follow-up "reconciliation" is made of all non-matching persons. The principle underlying this methodology is that the PES will be much better than the census and, therefore, estimates derived from this survey are a "standard" to which the census can be compared and eventually adjusted. 190

1974 post-enumeration survey of Liberia

11.1

However, experience in the United States and elsewhere has suggested that PES estimates are not necessarily better than census results (U.S. Bureau of the Census, 1960; Marks and Waksberg, 1966; and chapter 10 in this book). Moreover, in the Liberian context, evidence existed that the techniques associated with traditional PES systems were inappropriate. This evidence was primarily the experience gained from four years of conducting the Liberian Fertility Survey, a national, multiround, household survey, that used case-by-case matching and other techniques common to traditional post-enumeration survey designs (Rumford, 1970). During this survey, it was repeatedly demonstrated that a single enumeration system, using experienced, welltrained enumerators and supervisors, failed to enumerate many persons. Moreover, it was found that, when enumerators were grouped and tested by age, experience, and education, the older, more experienced, and better educated enumerators missed about the same number of persons as did their younger and less experienced colleagues with average education (Rumford, 1972). Confronted with this evidence, it was decided to use a new PES approach in Liberia based on dual system estimation. This method was developed mainly through work in vital statistics. Techniques for applying the method to census evaluation are suggested in our chapter 10.

11.2 Dual system estimation There are four main methodological elements in this new approach as implemented in Liberia, which depart from the traditional PES method. The first is emphasis on independence between the census and PES; the second is the use of one-way matching

Table 11.3 Estimated completeness of the census by age and sex; Liberia, 1974 Age groups

Both sexes %

Male %

All ages Under 1 year 1- 4 years 5- 9 years 10-14 years 15-19 years 20-24 years 25-29 years 30-34 years 35-39 years 40-44 years 45-49 years 50-54 years 55-59 years 60-64 years 65 years and over

89.0 85.8 86.1 88.3 89.0 84.6 88.2 90.2 90.2 90.9 92.8 91.4 92.7 93.9 89.7 92.3

89.2 86,0 88.4 88.8 88.7 83.8 86.7 88.8 89.1 89.8 92.3 92.4 93.8 95.7 92.5 93.1

Female %

88.8 85.6 83.6 87.8 89.4 85.4 89.2 91.3 91.0 91.8 93.5 90.2 91.0 91.5 85.4 91.1

Standard errors are as follows: Both sexes, all ages 1.5% Male, all ages 2.2% Female, all ages 2.4%

191

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Eli S. Marks and John Rumford

to reduce "geographic out-of-scope" error; the third is providing for a very brief time interval between census and PES in order to minimize the problems of tracing migrants; and the fourth is the elimination of field verification of unmatched (census or PES) enumerations. The third and fourth features were introduced in Liberia for reasons of cost and operational feasibility. The first two features are attempts to reduce the effects of two of the three major biases of dual system estimation. The model for, and the biases of, dual system estimation are discussed in detail in Marks, Seltzer, and Krotki (1974) and in Seltzer and Adlakha( 1969). An early presentation of the model and discussion of one major type of bias is the paper by Chandrasekaran and Deming (1949) and a discussion in the PES context is given in chapter 10. As used in these references and in this chapter, "dual system estimation" involves: (i) collecting data from a sample of the target population with two independent data collection systems (in census evaluation, the census and the PES); (ii) matching the reports of the two systems to determine which of the sample individuals were reported by both systems; (iii) using the proportion matched of all cases reported in one system as an estimate of the completeness of reporting (the "completeness rate") in the other system. Thus, the proportion matched of all PES cases is used as the estimate of the completeness of the census. For PES-census dual system estimation, we have: Number of sample cases2 Reported in Census Not Reported in Census Total Reported in PES m u2 n2 Not Reported in PES u1 z n - na Total n1 nn1 n where: m = number of matched sample cases, n1 = number of sample cases reported in the census, n2 = number of cases reported in PES, U1 = number of sample cases reported in the census but missed by the PES, u2 = number of sample cases reported by PES but missed in the census, z = (unknown) number of sample cases not reported by either PES or census, n = (unknown) number of sample cases that should have been reported by the census and the PES. In dual system estimation, the proportion of PES sample persons that were also enumerated in the census; W1 = m/n 2 (H-1) is used as the estimate of the proportion of all persons enumerated in the census: P. = N,/N, where N1 = number of persons enumerated in the census, N = number of persons that should have been enumerated in the census; and the estimate of N (the "true" number of cases in the population) is: N = N 1 /w,=(N 1 n 2 )/m. (11.2) Equations (11.1) and (11.2) also apply if one wishes to estimate the completeness of reporting, P1A, and the number of persons that should have been reported, NA, for the Ath class of the population (e.g. completeness of reporting and the corrected population count of males ages 20 to 24). For this purpose, one replaces n2, m, N1 by n2A, mA, N1A defined as: n2A = number of persons reported in the PES as being in class A, mA = number of sample persons reported in class A by the PES who are matched to a census enumeration,3 N1A = number of persons reported in class A in the census. 192

7974 post-enumeration survey of Liberia The estimates are: W1A = m A /n 2 A,

11.2 (11.1A)

and NA = N 1 A /w I A = (N 1 An2A)/mA. (11.2A) Where the completeness errors (omissions) of the census and PES are independent, Ew1A = P1A = N 1 A/N A ,

so that WIA and NA are unbiased estimates of PIA and NA. The effects of correlation between census and PES errors are not absolute. The bias increases as the difference between w1A and U 1A /(n A - n2A) (and, therefore, the correlation) increases. The bias is also a decreasing function of P2A( = En 2A /NA), the probability of a sample person being reported by the PES.

11.3 Independence It will be noted that the purpose of the PES is to provide an estimate of the completeness of the census coverage. The PES estimate of census coverage will not be biased by the erroneous omission of some sample cases or by the erroneous inclusions of some nonsample eases (e.g. due to the PES enumerator getting outside the boundaries of the sample segment), provided the PES completeness errors are independent of the census completeness errors—i.e. provided the probability of a PES case being enumerated in the census is the same for the cases erroneously omitted from or erroneously included in the PES as it is for the cases correctly included. Note that independence implies nothing about causality. Obviously, whether a person is or is not reported in the PES cannot causally affect his probability of being reported in a census taken/?r/or to the PES. However, the classes of persons with low probabilities of being reported in the PES could also (apart from any direct causal connection) have lower (or higher) probabilities of being reported in the census than the classes of persons with high probabilities of being reported in the PES. There is, in fact, evidence from recent postenumeration surveys in Paraguay and Korea that persons who change their places of residence between the census and the PES tend to have lower probabilities of enumeration in both the census (taken before their change of residence) and the PES than persons who do not move between the census and the PES. (See appendix chapter 10.) Correlation between PES and census errors may be"direct" or"indirect". Indirect correlation results from the fact that the probability of certain individuals or classes of individuals being enumerated is high or is low for both census and PES.4 Direct correlation involves a causal relationship between census and PES errors — i.e. the fact of a person being enumerated or not being enumerated in the census actually changes the probability of his being enumerated in the PES.5 Since indirect correlation is an inherent feature of the population and the reporting methods, its control involves careful selection of the basic PES procedures. The newer techniques of taking PES, used in Korea and Paraguay, were developed primarily for the purpose of eliminating a major source of indirect correlation. The preservation of direct statistical independence is largely a matter of avoiding collusion between the two enumeration systems in the field. One of the steps that can be taken to do this is to postpone the selection of the sample areas until after the census enumeration is complete. In Liberia, the PES sample was selected immediately prior to national census day. However, the sample enumeration areas were not identified to the field officers until the census enumeration was completed 5 to 10 days later. When the field officers were notified, they were instructed to impound immediately the com193

Figure 11.1 The questionnaire used in the Liberian post-enumeration, Form PES-2 Republic of Liberia Ministry of Planning and Economic Affairs 1974 Census of Population and Housing 1. la. 2. 3. 4. 5.

Locality name Is locality on listing sheet Street address if available Available structure number Assigned structure number Household serial No

1 Yes 1 2

2 No

PES-2: POST ENUMERATION SURVEY QUESTIONNAIRE

(OFFICE USE ONLY) Name of usual resident of household

(6)

1. 2. 3. 4. 5. 6. 1. 8. 9. 10. 11. 12.

Sex

Age last birthday

M F (7)

1 1 1 1 1 1 1 1 1 1 1 1 If listing is continued on other page

(8)

2 2 2 2 2 2 2 2 2 2 2 2 enter "X" D.

Usual residents this locality Yes No (9)

Present 1st. February Yes No (10)

1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1

2 2 2 2 2 2 2 2 2 2 2 2

Enumerated in census Yes No (11)

2 2 2 2 2 2 2 2 2 2 2 2

1 ]

2 2 2 2 2 2 2 2 2 2 2 2

Reconciliation Condition Locality In Out (13)

(12) 1 1 1 1 1 1 1 1 1 1

3 3 3 3 3 3 3 3 3 3

1 3 4

In Out (14)

2 2 2 2 2 2 2 2 2 2

4 4 4 4 4 4 4 4 4 4

134

Serial codes Structure

]

2 2

1 1

2 2 2 2 2 2 2 2 2 2 2 2

11.3

Eli S. Marks and John Rumford

pleted census questionnaire workbooks for the EAs scheduled to be re-enumerated. These workbooks remained in custody throughout the PES enumeration. In another effort to prevent direct correlation, the PES enumerators were recruited from County Inspectors and District Supervisors. These workers were selected because they were familiar with the general census enumeration procedures, but took no active part in the census enumeration at the EA level. These PES enumerators were briefed on the PES questionnaires but they were not given any additional training nor were they provided with any pre-enumeration intelligence. Moreover, they used listing sheets and E A maps that were duplicates of those provided to the census enumerators. A time limit of 72 hours was imposed for the enumeration (the same time target prescribed for the original census enumeration) and the PES, like the census, was conducted on a dejure basis. After completing the PES enumeration, the PES questionnaire workbooks were transferred to a census regional officer. However, no review was made at regional headquarters. Instead, the original census questionnaire workbooks were transmitted to national headquarters for review and matching by a completely separate and specialized group. In spite of these elaborate precautions, and as a tribute to the ingenuity of Man, two of the 32 sample EAs were compromised and had to be eliminated. It should be stressed that although it is not sufficient for unbiased PES estimates, technical and administrative independence is essential. Without it, the Liberian PES system cannot be used.

11.4 Other biases In addition to correlation bias, dual system estimates are subject to matching bias and out-of-scope (or erroneous inclusion) bias. Matching bias is the result of "erroneous matches" and "erroneous non-matches". Erroneous matches will increase m (the number of PES cases considered to be enumerated inthe census) and will, consequently, result in w1 being an overestimate of P1 and N being an underestimate of N. Erroneous non-matches reduce m and, therefore, lead to downward bias in w1 and upward bias in N. The overall matching bias depends on the "net matching bias", which is the difference between the number of erroneous matches and the number of erroneous non-matches. (See appendix to chapter 8.) "Out-of-scope" error is the result of improper inclusion of cases in the PES or the census. Erroneous inclusions in the census are duplicate enumerations and enumerations of persons who should not have been enumerated — e.g. persons who died before or were born after the census date, diplomatic personnel or other persons excluded from the census by definition and enumeration of fictitious persons, either deliberately (i.e. enumerator "curbstoning", the completion of census entries without interviewing every household) or accidentally (e.g. entry of a dog or other household pet under the mistaken impression that it was a child).6 Erroneous inclusions in the PES include the PES enumeration of persons who should not have been enumerated in the census (as described above) and also the enumeration of non-sample persons. Enumeration of non-sample persons results from boundary difficulties (i.e. the PES enumerator enumerating households actually located outside the sample segment) and from improper handling of "migrants" (persons who move between the census and the PES). On the latter, "migrants" can be sampled either on the basis of where they were on the census date or of where they are at the time of the PES interview. These are the procedures A and B respectively of the appendix to chapter 10. Thus, an out-of-scope error occurs in a PES which samples on the basis of residence on the census date, if the PES 196

1974 post-enumeration survey of Liberia

11.4

enumerator includes someone who moved into the sample segment after the census date. For PES samples based on location at the time of the PES interview, an out-ofscope error occurs if the PES enumerator includes someone who moved out o/the sample segment before the PES date.

11.5 Handling of migrants Persons who move into or out of a sample segment between the census date and the time of the PES enumeration represent a particularly difficult problem. Prior to 1970, all PES sampling was based on the person's location on the census date. However, this tended to produce a correlation bias because (1) migrants tend to have a larger census omission rate than non-migrants and (2) persons who move away from an area prior to the PES are likely to be missed by the PES. Persons who move away tend to be omitted from the PES because (a) where a whole household moves, neighbours may be able to furnish only very incomplete information about the individual household members; and (b) if an individual moves out of a household, the remaining members of the household may be vague about the date that he left.7 The reasons for poor census enumeration are not immediately obvious. Part of the difficulty may be with the fact that census enumeration is dragged out over a long time period and, therefore, the canvass for many of the migrants occurs after the migration. However, the higher omission rates for migrants occur also in de facto censuses in areas where 80% or more of the census enumeration is actually completed on the census date. It may be hypothesized that the causal mechanism is the fact that many of the "migrants" (particularly in a de facto census) have only tenuous connections with the household where they were staying or living on the census date and are, therefore, not mentioned when the enumerator asks for "all the people staying (or living) in this household". There are two ways of reducing the correlation bias due to migrants both described in the appendix to chapter 10. One of these has been introduced only recently into PES work — in the PES of the 1970 Census of Korea and the PES of the 1972 Census of Paraguay. This method involves sampling migrants on the basis of where they are at the time of the PES interview. In Paraguay, two samples of approximately equal size were used in the 1972 PES, one asking about people in the sample segment on the census date and the other asking about people in the sample segment at the time of the PES interview. The second sample gave nearly four times as many migrants (people who moved into sample segments) as the number of migrants (people who moved out of sample segments) given by the first sample, although the number of nonmigrants was about the same (only 7 percent difference) for the two samples.8 While basing the sampling of migrants on their residence at the time of the PES will improve the reporting of migrants and thus reduce the correlation bias due to migrants, it considerably increases the difficulties (and the errors) in matching the migrants to the census. That is, in order to search for a migrant in the census files, it is necessary to have his address at the time of the census, with the kind of precision and detail that permits an accurate determination of the enumeration area (E A) in which he should have been enumerated. While people will usually know their former addresses, they frequently cannot furnish the kind of address information needed to determine the EA. The other method of reducing correlation bias due to the migrants is to reduce the number of migrants by reducing the time lag between the census and the PES. This was the method adopted for Liberia where the time lag between the Liberian census date and the PES enumeration was set at 15 days.9 This period was long enough to allow the 197

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census enumerators to canvass and clear their areas, and yet, was short enough to limit opportunities for migrations, births, and deaths to occur. The PES asked whether anyone listed on the questionnaire was born after the national census day and eliminated such persons from the tabulations. No such accommodation was considered necessary for deaths, since the rarity of this event in a ten to fifteen day period would make errors from this source negligible. However, if the period between the census and the PES is longer, a specific question on deaths may be needed. It should be pointed out that the short time period increases the danger of over-lapping the two enumeration systems in the field, if strict precautions are not taken, but the overall result of minimizing the opportunity for errors associated with migration to occur was considered worth the risk.

11.6 Use of one-way matching A second problem is control of the geographic out-of-scope errors, which occur at the boundaries of sample evaluation areas. These errors can be particularly troublesome in heavily populated urban centres where no easily identified natural or man-made boundaries exist. In these areas, it is relatively easy for a census or PES enumerator to erroneously extend his canvassing area beyond the limits of the designated sample area.'0 Because the Liberian system is based on maintaining strict independence between the census and the PES, it is not desirable to use information obtained during the actual census enumeration to help locate the EA boundaries. To minimize the effect of boundary errors, the Liberian PES used "one-way matching", with a provision for searching for cases in adjoining EAs where the possibility of boundary errors existed. One-way matching was used in Liberia primarily because of its relative simplicity and economy. The technique is most effectively employed in circumstances where one of the two data sources has records covering the entire population.11 With one-way matching, it is only necessary to determine the exact matching status of each report for one of the two record systems (the one with data for a sample only). As implemented in the Liberian Post Enumeration Survey, the PES records were compared to the census records and each person was categorized as "found" (or "matched") or "not found" in the census listings. After the initial matching within the sample EA, the unmatched PES cases were searched for in adjacent EAs. For the PES cases that were matched in an adjacent EA, an attempt was made to determine whether the error was made by the census or the PES. However, the determination of whether the error was made by the census or the PES was not very successful. In most cases, an acceptable determination of the correct E A boundaries requires a further field visit and it was not felt that the expense of such a visit was warranted since the number of cases involved was small. A major purpose of a field reconciliation is to determine whether any of the PES cases, matched or unmatched, should not have been included, either because the person was not supposed to be enumerated in the census or because the person was a nonsample case who should have been enumerated outside the sample EA boundaries. Actually, since the only purpose of the PES is to determine the estimate wi of PI (the proportion of the population enumerated in the census), the bias due to a few cases erroneously included in the PES sample is minor, provided erroneously included cases contain the same (expected) proportion of cases enumerated in the census as do the correctly included cases. Of course, there will be a bias if the cases near an EA boundary do not have exactly the same census omission rate as those in the interior of an EA. In general, cases near an EA boundary will have a somewhat higher census 198

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omission rate and, also, a somewhat higher census duplication rate. However, both the difference and the number of cases involved will be small (unless the census maps and procedures are totally inadequate) and the bias will be trivial. The important thing is to extend the search for PES cases near an EA boundary to the adjacent EAs, so that no PES case will be called unmatched because the census or PES enumerator (or both) made a mistake in locating the EA boundary. It would, of course, be desirable to search all boundary cases, matched or unmatched, in the adjacent EAs to check on duplicate census enumerations. However, such duplication is rare in practice and the bias of not searching adjacent EAs for cases matched within the sample EA is minor. 11.7 Elimination of field verification Field follow-up verification of unmatched PES and census populations has been abandoned in Liberia, primarily because the method is fairly expensive and has proven ineffective in this country and in several other developing countries as well. During the four years of the Liberian Fertility Survey, it was found that field reconciliation and verification of unmatched household populations (particularly among migrants who make up the bulk of the unmatched cases) was uncertain, unproductive, and expensive (Rumford, 1970 and 1972). Difficulties in matching migrants have also been reported in such divergent geographical and cultural settings as Pakistan (Ahmed and Krotki, 1963), Thailand (Lauriat, 1967), Turkey (Rumford, Heperkan and Fincanciogulu, 1968) and Malawi (1973). As indicated previously, the potential reconciliation case-load due to migrations was sharply reduced by the narrow time span between the census and the PES. However, this did not eliminate the problem entirely. The problem remained of differentiating between PES cases that did not match because they were recent in-migrants who should not have been enumerated and those that were simply not enumerated in the census. To help make this differentiation three questions were added to the PES questionnaire: (1) whether the person considered himself a usual resident of the locality; (2) whether the person was physically present on National Census Day; and (3) whether he was enumerated anywhere during the census. These questions were later correlated with other evidence on the questionnaire and PES and census eligibility was determined. 11.8 PES results The PES estimates of census completeness by age and sex appear in table 11.2. Overall, the 1974 Liberian census appears to have achieved 89 percent completeness. The figures for particular age-sex cells are subject to fairly high variances (and, possibly, to biases in the reporting of age). However, the overall pattern represents more than variance and, in spite of the errors in age reporting, show interesting differences from the underenumeration pattern typical of more industrialized countries. Thus, there is little or no overall difference between males and females in completeness for the 1974 Liberian census. On the other hand, the United States censuses show higher completeness of women than men largely due to the poorer enumeration of men in the age range 15 to 44, which also seems to hold for Liberia. For Liberia, the higher completeness of females 15 to 44 is balanced by the lower completeness for females under 10 and 45 plus which does not obtain for the U.S.In fact, completeness in the U.S. for females under 10 and also for females 65 and over completeness tends to be better than for males in the corresponding age groups. In the U.S. census, the com199

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pleteness of males dropped for ages 20-24 and remained low up to age 45 but no such decline appears for U.S. females ages 20 to 44. In Liberia, completeness for both sexes seems to drop off at ages 15 to 19 but then improves for ages 20 to 24 and continues to improve for males up to age 60 and females up to age 45.

11.9 Some defects of the Uberian PES A key feature of the Liberian PES system is completing the PES field work within a short interval after the census date. This is also a key weakness of the system. Having a very short interval between the census and the PES eliminates many of the serious problems associated with substantial migration between the census date and the PES date. It makes it possible to keep the PES costs down to relatively low levels and also to utilize in the PES a good part of the field and administrative structure set up on a temporary basis for the census. On the other hand, it imposes certain requirements which may be serious handicaps. One of these is the difficulty of maintaining independence and administrative control between the census and PES. As noted above, special instructions were issued that a PES enumerator not be told the location of his assignment until all of the census enumeration for the evaluation area was complete and the census schedules for the EA were in the hands of the regional supervisor. In spite of this precaution, there was a coincidence between census and PES reports for two of the 32 sample EAs which could not possibly have occurred without someone altering either the census returns to accord with the PES results or vice versa. The fact that this contamination affected only 6 percent of the Liberian PES sample reflects the great efforts which were made to preserve independence while adhering to an extremely tight time schedule. With adequate planning and supervision, five days is sufficient time for completing a census in 80 percent or more of the EAs of almost any country. Unfortunately, there are delays and slip-ups that will affect a minority of EAs in almost any country. An enumerator may have misunderstood his map (with or without the "help" of ambiguous boundaries) and failed to enumerate a whole section of his EA; or an entire EA or group of EAs may not have been assigned for enumeration; and these errors might not be detected until preliminary count figures are announced and complaints from local areas start pouring (or dribbling) in. A short time interval between census and PES imposes other restraints. The sample areas must be selected well before the census, possibly before the work of setting up the census EAs has been completed. (Note: there are always areas where some of the initial EAs are too big and must be split up and other areas where combinations of some small EAs are desirable.) Once selected, the sample EAs must be kept confidential until the census work in those EAs has been completed. Also, the short time interval usually means that the PES schedules and procedures cannot be tested and revised under actual census conditions. This is likely to be particularly harmful with respect to the matching procedures. Most countries have some experience with other census and PES operations. If not, it is possible to draw on experiences of other countries with similar conditions (e.g. in collecting and coding data on occupation and industry) or to dispense with or simplify the operation. Most developing countries (and not a few statistically advanced countries) have no directly applicable experience with modern matching methods. The matching operation is indispensable to a PES and simplification can pose very serious dangers of matching errors which raise questions about the validity of the entire PES. There were, in fact, serious defects in the design of the Liberian PES matching. In trying to keep the PES

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procedure simple and the questionnaire short, some information very useful for matching was omitted, notably relationships and alternative names. Both of these items are fairly easy to obtain and add only trivially to the total interview time. Relationship will be useful for matching in almost any culture (particularly those where most of the names are common ones and it is necessary to distinguish the Ali bin Muhammed who is Muhammed bin Muhammed's younger brother from the one who is his son). The need for alternative given names is culturally limited; and the fact that they may not be needed in the United States does not mean that they will not be needed in Liberia.12 The fact that the omission of these items was a serious (and unnecessary) defect was only evident after the matching procedures had been tried out and found wanting. Matching is a difficult and unique operation which is very sensitive to the identification information used and to the rules on "error tolerances". If the matching information is too restricted, it may not provide a unique identification for most of the population. Thus, there will be a large number of erroneous matches. On the other hand, if there are too many matching items and a requirement for agreement within narrow "tolerances" on all of them, the number of erroneous non-matches may shoot up alarmingly. In Liberia, the paucity of PES match information made it necessary to provide rather narrow tolerances to prevent substantial numbers of erroneous matches. On the other hand, the provision of narrow tolerances resulted in too many unmatched cases and the review of the matching with relaxed matching rules was instituted to try to reduce the number of erroneous non-matches. Some suggestions for setting up a more satisfactory matching system appear in Marks, Seltzer and Krotki(1974: 101-122,195-220), and the question is also discussed by Nathan in the appendix to chapter 8. Although a great deal has been done in the past 20 years to develop sound theory and practice to deal with the matching problem, much still remains to be done. The sensitivity of matching to the characteristics of the particular culture and country and the differences between matching for dual system estimation and matching for other purposes (e.g. file maintenance) makes it important that the user examine carefully the applicability of a given set of matching rules (no matter how plausible they may seem at first examination) to the particular circumstances of his own problem. One problem of the Liberian PES system is particularly acute for de facto censuses. This is the problem of visitors and the "floating population." Providing for a short time interval between PES and census is not satisfactory for dealing with the "floating population" — i.e. persons with no usual residence any place. In dejure censuses, such persons are to be enumerated on a de facto basis — i.e. where they happen to be staying on the census date. Even with a PES taken two weeks after the census date (as in Liberia), the probability is small of finding persons with no usual place of residence where they were on the census date. They may be in the same neighbourhood but, since such persons are most common in large urban centres, the PES location will frequently not be in the same EA as the census location nor in an adjoining EA. Thus, a PES of the Liberian type omits most persons with no usual place of residence. This introduces a correlation bias, since the probability of such persons being omitted from a census (and, particularly from a dejure census) is considerably higher than it is for the persons included in the PES. A further complication is the difficulty of determining whether these persons were actually in the same households on the census date. If they say they were not or cannot say they were, those that are found in the same dwelling unit in the census listings are usually counted as enumerated in the census. However, those who do not say that they were at the same location and who are not found there, are not counted as missed by the census, even though they 201

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were not enumerated anywhere. This adds to the upward bias of Wi. There is, of course, a compensating bias of counting as missed by the census, those who are reported by the PES as having been in the same location on the census date but who were actually enumerated in some other location. This compensating bias is almost always very small. Experience suggests that one may be somewhat more likely to miss persons with no usual place of residence in a dejure census than in a de facto census. However, a de facto census adds to the relatively small population with no usual place of residence, persons with a usual place of residence who temporarily stayed elsewhere on the census date. Many of these "visitors" will have left their temporary lodgings (frequently to return to their usual residence) by the time of the PES, even if the PES could be taken one week after the census date. Like the floating population, these "visitors" are very likely to be missed by both a census and by a PES that asks about them at their census date location. In general, the numbers of "floating population" and "visitors" will be trivial outside of very large and overcrowded urban centres. Where very large urban centres are not an important part of a country's population the bias of the Liberian PES system should be small. 11.10 Conclusion The Liberian system is no panacea. When the final 1974 census results become available, all the available methods of demographic analysis will be required to refine and improve the completeness estimates derived from dual system estimation. Comparisons with previous census and survey results will be necessary to fully evaluate the census. Moreover, as indicated above, the system itself has several deficiencies. Nevertheless, with some minor modifications, such as the provision of additional matching information or a small extension in the time period between census and PES (e.g. 30 days instead of 15), the Liberian PES system is applicable to and effective for countries which do a dejure census with a very short census enumeration period and also to countries with a defacto census where the matter of temporary sojourners in a location is minor (usually countries which are primarily rural and non-industrial). Where a country does a de facto census and has a substantial number of temporary "sojourners" (or persons with no usual place of residence) or where a short time interval between PES and census is not feasible, one should consider the use of a PES sample based on where the individual is at the time of the PES. (Procedure B in the appendix to chapter 10.) This requires determining for migrants the location on the census date and doing the matching search at that location. While this kind of matching can be difficult and expensive, methods for simplifying the procedures and improving the results are being explored and may provide an answer in the near future. It may also be possible to use a "hybrid" technique where the estimate of the number of migrants is determined from people who have moved into the PES sample area since the census date, but the estimate of the census omission rate for migrants is determined from those who have moved out o/the PES sample area since the census date. We can be certain that there will continue to be problems of evaluating census completeness, no matter which methods are used, and whether they involve a PES or other dual system estimation or do not. However, the need for methods of a more adequate census evaluation and correction is painfully evident for many developing 202

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countries where recent censuses have been so inconsistent with all the known demographic facts as to be completely unacceptable. No one method of census evaluation and correction provides a complete answer. However, the post-enumeration survey is a powerful technique and it should not be ignored or avoided. It is hoped that the simplicity and economy of the dual estimation system used in Liberia will help remove the post-enumeration survey from the luxury item list in census evaluation and place this important tool within reach of all census planners. It is at least a starting point from which census planners can go on to more sophisticated and more powerful (but not necessarily, more expensive) tools.

Endnotes to Chapter 11 11

1. To the causes of overenumeration listed in the text, the more recent piling up of tribal groups in Nigeria in the 1973 census and the less well documented overenumeration of ethnic groups in the 1972 census of Pakistan must be added. Demographic analysis and survey procedures are not helpless before such tendencies, but practitioners have not yet addressed themselves seriously to the problem. [Editor's note.] 2. The table and equations (11.1) and (11.2) assume self-weighting PES samples. For other types of sampling m, nz, etc. must be adjusted to allow for differentials in sampling rates. 3. PES sample cases in class A should be counted as matched even though they are reported in some other class in the census (e.g. a person reported as male, age 20-24 by the PES might be matched to a census enumeration where the age is reported as 25 years). There are estimates where PES persons in class A matched to persons in some other class are not counted as matched. These estimates attempt to correct for "classification" or "content error" as well as for "completeness error" of the census and require also an estimate of "erroneous inclusions" in class A by the census. This type of estimate may be desirable if one has reason to believe the PES gets better information than the census on characteristics like sex, age, race, occupation, etc. The estimates corrected for content and completeness error are somewhat more complex and, for the type of PES used in Liberia, the simpler estimates of equations (11.1) and (11.2) are preferable. 4. There can, in theory, be indirect negative correlation, in which individuals with a high probability of being reported in the census have a low probability of being picked up in a PES and vice versa, but no actual instances of this have been noted to date. 5. Writers in this volume are aware of the problem of direct dependence throughout and the matter received a particularly incisive airing by Pradel in chapter 5. [Editor's note.] 6. Another example of accidental inclusion (or exclusion) would be a mistake in the retention of census households for matching through the addition (or exclusion) of households outside (inside) the sample cluster. [Editor's note.] 7. Precise dating of "events" such as births, deaths, and migrations is a major problem of vital statistics measurement. It was, for example, the major reason for the development of techniques for estimating fertility which use "children ever born" (regardless of date) rather than children born during the past year. 8. See appendix to chapter 10. 9. However, cutting the time lag between the census and PES must have one disadvantageous corollary. It leaves the number of migrants available for analysis so small that there can be no proper understanding of what is happening.

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10. See endnote 4 for a source of "out of scope" error arising with census data. However, this source does not arise in one way matching.f Editor's note.] 11. One way matching is also effective when the cluster size in the census or the unit of analysis that is identifiable is so large that it becomes reasonable to subsample in the other PGE method of enumeration. [Editor's note.] 12. Section 5.7 and endnote 8 to chapter 5 both describe the importance of given names in a different cultural milieu. [Editor's note.]

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Chapter 12 The Problem of Independence and Other Issues

12.1 C. Scott on Sources of error in the dual system approach I would like to take up a number of miscellaneous points, mainly from chapter 2 by Wells and Horvitz and chapter 10 by Marks. But first, in chapter 1 discrepancy is noted between the cost ratios (clusters/ individuals) observed on the one hand by Fellegi (1973) in Morocco and on the other by myself and Coker (1971) in tropical African countries, our own ratios being three or more times smaller. Part of this discrepancy may be due to the fact that our figures were computed on a "time" rather than "cost" basis. We regrettably did not make this clear enough in the reference consulted, though in the same paper we did refer to an earlier article (Scott, 1967), in which this question is discussed more fully. The main difference between the time and cost evaluations is the inclusion of transport in the latter. This will swell the cluster costs and lead to a higher cost ratio than time ratio. The method of costing transport in African surveys varies widely. Few figures are available, and even if they were and were based on a standardized methodology, one would expect them to vary widely between surveys. However the justification given in Scott (1967) for using the time basis was that most African surveys up to that time had been constrained more by the combination of a time limit for completion and a numbers limit on available supervisory staff, which together imply a limit of man-hours of field work. This may be less true today, and if so the oft-quoted optimum cluster size for African demographic surveys of 200-300 persons should probably be raised somewhat to take account of transport costs. Some very rough estimates suggest that this modification could hardly bring the figure above 400. It should be noted that in a dual collection system the numerator and denominator come from different sources and the estimation procedure commonly used compounds any errors of completeness. In these circumstances there is a premium on accurate determination of the boundaries of area-sampling units. This will normally lead to a higher per-cluster cost in a dual collection system and this probably explains a good part of the higher ratio found by Fellegi. In any discussion of optimal cluster size in dual collection systems mention should be made of the effect of cluster size onmatching. Here there are two distinct effects. On the one hand, assuming that the cluster equals the matching batch and assuming twoway matching, it is easily seen that for a given total sample size the total number of pairs to be considered in the whole matching operation is approximately proportional to the cluster size. (The basis "for a given total sample size" is perhaps somewhat 205

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artificial; however, if we argued in terms of "a given overall sampling error", the relationship of the size of the matching load to the cluster size would be even steeper than linear). Secondly, a smaller cluster size(i.e. matching batch size) implies a smaller proportion of matching errors, other things being equal. In practice in dual collection systems, if very small clusters are used together with frequent rounds, the matching problem becomes so small that the survey office takes it in its stride, the elaborate organization, with pretesting and calibration, needed to take care of matching when large clusters are used becomes quite unnecessary. Of course there are other arguments affecting cluster size, but this one should not be overlooked. Wells and Horvitz discuss the overlapping reference periods proposal for periodic multiround surveys. A significant point that seems to be regularly overlooked when this method is under discussion is the incompatibility between the technique of overlapping reference periods and the household change technique for asking about births and deaths. In the household change technique there is essentially no fixed reference period. For deaths, we quote the name of each person listed in the preceding round and ask (i) is he still living? and if not, (ii) when did he die? We record the death whatever the date given in answer to(ii). For births, there are two possible approaches, (i) We may ask "Have you had a baby since the birth of so-and-so?" (citing the name of the woman's last recorded baby from the record made at the preceding round) and if so "when?"; or (ii) we make a list of all persons now present and, in the case of a baby not listed on the record of the preceding round, ask for its date of birth. Again, we record the birth whatever the date may be given; there is no fixed reference period, although// no error has occurred we will in fact get events only for the period since the preceding round. Thus it hardly makes sense to speak of adopting the method of overlapping reference periods in the context of the household change technique of questioning. One could say that the household change technique automatically makes the reference periods overlap once an omission has occurred: the questioning method is such that any event which has been missed will be the subject of questioning in all subsequent rounds until it is reported — or at least until another superseding event, such as emigration or another birth, is reported. Thus, other things being equal the household change technique must pick up at least all the events which would be reported by the overlapping reference periods method besides, presumably, many of those that were missed. Assuming multiround surveys, it is difficult to see any possible advantage of the method of overlapping reference periods compared with the household change technique.1 Turning now to chapter 10 by Marks, if we are concerned with estimates of absolute numbers (such as the number of vital events) it is quite correct to say that the error of completeness in the single system is replaced by the three following errors affecting the dual collection system: (i) correlation bias; (ii) matching bias;(iii) out-ofscope (spurious overcompleteness) bias. However, if we are estimating rates, with the denominator estimate coming from one part of the dual collection system (as it usually must, at least in developing countries) the situation is not so simple — nor so favourable to the dual approach. Let us begin with some simplifying assumptions. Suppose errors (i) and (ii) above are zero and suppose that the errors of over and undercompleteness in each system occur at random and independently between the two procedures. And for the moment let us suppose that the only completeness errors relate to complete omission (or erroneous inclusion) of persons, so that there are, for example, no errors of omission of births occurring to women who have been covered. Then if'u' is the omission rate andV the overcompleteness rate and if suffixes 'r' and Y refer to the continuous recording and the household survey respectively, and if the denominator estimate comes from the household survey, the following approximate results are fairly obvious: 206

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Dual collection estimate Completeness error rate, numerator: +vs + vr Completeness error rate, denominator: -us + vs If the error rates are expressed as proportions and if they are small, we obtain: Dual collection error rate for ratio: vr + us Single system estimate Completeness error rate, numerator: -us + vs Completeness error rate, denominator: -us + vs Single system error rate for ratio: 0 How far does a modification of the assumptions change the conclusions? Firstly, the completeness errors will not normally occur at random with respect to the ratio being estimated, so that there will be a bias in the single system estimate of the ratio. However, this is a second order effect which must, on any plausible assumptions, be smaller than the effects shown above—in practice generally much smaller. Secondly, and far more important, there is the effect of omission of events (the numerator) occurring to persons correctly included (the denominator). Suppose this error has a rate of'u'. There can also be overcompleteness of events occurring to persons correctly included (temporal out-of-scope events). Let this be V. We then obtain: Dual collection error rate for ratio: vr + us +v'r + v's Single system error rate for ratio: -u's + v's Summing up, the supposed advantage of the dual collection estimate rests on the assumption that the survey error u's will outweigh the three error terms vr + Us + v'r in the dual collection estimate. Even this conclusion is still too favourable to the dual collection system, for two reasons: i. We have assumed zero correlation error and matching error; ii. We have assumed that a single system would have the same errors as the survey procedure of a dual collection system; in reality it should have less, in view of the greater complexity of the dual collection system which is likely to mean lower quality organization and field work.2 (This is the same argument as that which attributes higher quality field work to surveys than censuses.) Finally a word should be said about the correlation bias. Marks's emphasis on independence rather than quality is in my view mistaken and could easily lead to a step backwards. I am not sure what he means by independence being "much more essential" than completeness. Obviously either complete independence or full completeness would suffice to give us an unbiased estimate in the conditions he assumes. If we are trying to decide whether to aim for higher completeness or greater independence we need to ask not which is the more "essential", nor even the more important, but which would give a better return on a given investment or a given effort. It may well be that, however much effort we make, the correlation cannot be reduced below a certain rather high threshold value. Possibly, the application of every conceivable measure may reduce the correlation from 0.6 to 0.5—we don't know whether or not this is the situation. Especially in the case of a census PES specifically designed, as Marks recommends, to be done in the same way as the census, there is obviously a likelihood that a substantial proportion of the errors made by one source will be repeated by the other. The source of correlation is likely to lie in large measure within the respondents and not in the elicitation procedure. In chapter 5, this problem is rightly stressed and the kind of mechanism likely to be involved is convincingly described. If this is the situation, all our efforts to achieve independence may run up against a brick wall long before we reach the stage where correlation bias has been reduced to a negligible level.3

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A reasonable strategy would surely be to attempt to measure the correlation between the sources rather than to accept a biased estimator in the blind hope that the bias may not be very large. 12.2 H.V. Muhsam on The bias of the PGE/ERAD/ECP estimates due to overenumeration Dual system estimates are usually made by the Chandrasekaran-Deming approach. This approach as well as all the other applications, modifications, and improvements of which I am aware, completely disregard the possibility of overenumeration; they deal only with underenumeration. Overenumeration, as I use the term here, includes multiple counting of cases which belong to the target universe as well as the inclusion of cases which do not belong to the universe. I do not think that this audience needs to be convinced that overenumerations do, in fact occur. It may, however, be useful to remember in this context that estimates of the amount of overenumerations in population censuses show that in this type of operation, overenumerations are of the same order of size as underenumerations: they vary, in practice, between about one-fifth to one-half of the amount of underenumerations. On the other hand, it should be admitted that similar estimates of overregistration of vital events are not known to me, but from my own experience I know that a birth is often notified to the authorities by both the father and the midwife, and if there are small divergencies in names, dates, etc., a double registration easily results. Or, a stillbirth may be erroneously counted as a livebirth. This would incidentally, lead also to a false death notification. Similarly, the death of a transient non-resident may easily be registered at his place of death, while he does not belong to the population exposed to the risk of death in this area. In order to get an idea of the bias caused by disregarding overenumerations, we can utilize a model which I proposed (Muhsam, 1960) to generalize the PGE/ ERAD/ ECP approach as follows. A universe of P elements is to be enumerated, each element having the probability p; of being enumerated at operation i (in dual collection systems i = 1,2.). In addition to this universe there is another universe of R elements which should not be enumerated but are exposed to the risk of being erroneously enumerated with a probability n. In a dual collection system, the expected numbers of elements enumerated at both occasions (£12), at the first but not the second occasion (£12), etc. are then E12 = P p1p2 + R r 1 r 2 E 12 = Pp 1 (l -p 2 ) + R r 1 ( l - r 2 ) E12 = P(l - p1)p2 + R(l - r1)r2 and E12 = P(l - p,)(l - p2) + R(l - r 1 )(l - r2) The PGE/ ERAD/ ECP estimate of P is PpGE

=

E 12 + E l2 + E 12 + (E l 2 E l 2 ) / E l 2

The estimate resulting from our model, taking overenumeration into account is: P — El2 ~ Rl2 + El2 ~ Rl2 + El2 ~ Rl2

+ [(El2 - R l 2 )(E l 2 - R l2 )]/[E 12 - R I2 ]

where R ij = Rr i r j . If for all i, j Eij > Rij, we may write approximately P = PPGE ~ ( R l 2 + R l 2 + R l 2 ) - ( E l 2 R l 2 + E l 2 R l 2 ) / E l 2

+ E l 2 E l 2 (R l 2 /E 2 I 2 ) - (El2 R l2 + E l2 R l 2 )(R l 2 /E 2 l 2 ) + (Rl2 R l 2 )/E l 2 + (R l 2 R l 2 R l 2 )/E 2 l 2 .

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Bias of estimates due to overenumeration

12-2

The correction to be made to PPGE, i.e. its bias, as we have written it here, is composed of six terms. The meaning of the first of them (Rl2 + Rl2+ Rl2) is obvious: all cases erroneously enumerated must be deducted from the PGE/ ERAD/ ECP estimate. If the number of erroneously enumerated cases is small (Rij < Eij, for all i, j) the last three terms of the bias are much smaller than the first three and may be neglected. The second and the third term deserve some discussion. They are due to the fact that a number of the cases enumerated only at one occasion do not belong to the universe to be enumerated, so that the two enumerations are, in fact, not as wrong as the PGE/ ERAD/ ECP approach assumed them to be. The estimate of the number of cases belonging to the universe and not enumerated at either occasion, as obtained by PGE/ ERAD/ ECP approach, is therefore rather weak. Whether this number is overestimated or underestimated by the PGE/ ERAD/ ECP approach depends on the relation between the ratios (ps/1 - p) of the probability of the elements of the universe to be enumerated being enumerated to that of being omitted, and the ratios (1 - ri)/ Ti of the probability of an element of the universe exposed to the risk of being erroneously enumerated. It is indeed easily seen that the contribution of these two terms to the bias will be positive, i.e. the bias of the PGE/ ERAD/ ECP estimate which is negative, will be relatively small, when (E12 E12 R12)/ E 2 12 > (E12 R12 + E12 R12)/ E12 or (E 12 /E 12 )(E 12 /E 12 ) >(E12/E12)(R12(R12) + (E12/E12)(R12-/R12) If we introduce in this inequality the PGE/ ERAD/ ECP estimates of the Ey, we obtain [P2/(1 - P2)][p 1 /(l - P1)] > [p 2 /(l - P2)][(l - r 1 )/r] + [p 1 /(l-p 1 )][(l-r 2 )/r 2 ]. This condition can be fulfilled only if (1 - r1)/ r1 for both i = 1 and 2 is small. Now it is obvious that this is so only if the n are large and, consequently, R is small, i.e. if we assume that there are only few cases which do not belong to the universe to be enumerated, and are exposed to the risk of being erroneously enumerated, and the probability of each of them to be, in fact enumerated, is relatively large. In this case, the bias of the PGE/ ERAD/ ECP estimate due to overenumeration is relatively small. Unfortunately, from the three observed quantities E12, E12 and E12 obviously only three unknown quantities can be estimated, namely, for example, P, pi and p2. But our model involves three additional unknown quantities R, n and r2. It has been pointed out that even a triad system (Muhsam, 1960) would supply only 7 observed quantities Ei 23, £123, £123, £[23, £123, £123, £123 from which the 8 unknown quantities of our model (P, R, pi, p2, p3, ri, r2, r3) cannot be estimated. Only a system based on four repetitions would supply 15 observations from which the 10 parameters can be estimated. On the other hand a triad system may prove to be of practical use, because we are not interested in estimating all the unknown quantities of our model, and, in particular neither R nor any of the H; these are, so to say, dummy variables. Thus it may be possible to make some reasonable assumption with regard to R, estimate P on this assumption and show then, that a different assumption with regard to R would have affected the ri but not very markedly the estimate of P. It would therefore appear desirable that some experimentation be made with triad systems. This does not mean that it is recommended to use triad systems in routine field work. But if some experience with triad systems were available, we would be able to form an opinion on the question, how serious the bias of the PGE/ ERAD/ ECP estimate is and with which amount of overenumeration we must count in the kind of studies to which our experiments refer.

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Discussion

Eli S. Marks

Discussion by Eli S. Marks There seems to be considerable confusion about "independence" and its significance for dual collection estimation. On this subject, I wish to offer the following observations: With respect to Muhsam's comments, "independence" in dual collection estimation is independence between the errors of the two procedures. As Muhsam suggests, it is independence of the measurements of the events and not, of course, of the events themselves. With respect to Scott's comments on independence, my emphasis on its importance was indeed in connection with the use of the PGE/ ERAD/ ECP estimator. This is the basic dual collection estimator and it was used prior to Chandrasekaran and Deming's 1949 paper—e.g. in the 1940 estimate of completeness of U.S. birth registration based on matching with the Population Census.4 It has, in fact, been used in a number of studies whose results are accepted without question by some of those who have been highly vocal in their opposition to any use of dual collection estimation. The dual collection estimator "assumes" independence only in the sense that other estimators "assume" a particular model—e.g. in the sense that the Brass estimator of fertility assumes completely accurately reporting of the number of children ever born on the part of younger women. Just as the Brass estimator is biased because, in practice, reporting of children ever born is not completely accurate, so the dual collection estimator is biased because, in practice, complete independence is not attained. The bias of the dual collection estimator, like that of most single estimators, is almost always downwards. However, to the extent that independence is attained, the bias of the dual collection estimator will be less than that of single system estimators. Independence is not an all-or-none phenomenon; neither is it something which is achieved automatically. As Wells and Horvitz indicate in chapter 2 the gains of dual collection estimation apply to "well-executed systems"—systems where efforts are made to secure a substantial degree of independence (and also to control other sources of bias). The studies which have been cited by critics as examples of the ineffectiveness of dual collection estimation have been ones in which independence was not attained—mostly because the importance of making an effort to control correlation between the errors of the two procedures was not properly appreciated by those responsible for the study design and execution. While I have stressed the importance of independence in chapter 10, it is because it is the feature of the dual collection method which is most widely misunderstood, both by the opponents of the method and also by some of those who have attempted to do studies using the method. I strongly agree with Seltzer on the need to give attention to other sources of error. As he suggests, I have probably let some recent pre-occupations with the census evaluation problems of one country (the U.S.) with a well-developed statistical system distract my attention from the problems in countries with less welldeveloped statistical systems, where the biases due to lack of independence may be considerably amplified by poor overall statistical quality. One needs a balance between emphasis on high individual system quality without concern for independence and emphasis on independence without concern for individual system quality. Scott also suggests attempting "to measure the correlation between sources rather than to accept a biased estimator in the blind hope that the bias may not be very large". As noted above, I strongly agree with Scott in rejecting "blind hope". Unless every effort is made to keep correlation low and completeness high, the bias will be large. The danger of an unwitting acceptance of large biases is the main reason for my own insistence on the need to use more than one method and not rely on dual collection

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Discussion

estimation alone or any other method alone. Internal consistency checks and external source comparisons are necessary in the evaluation of dual or single system estimates. Abnormally high or low sex ratios, widely different error rates for very similar population subgroups, discrepancies between inter-censal growth as reported by a census, and estimates of births, deaths and migration, all point to the presence of biases and the need for further investigation. In my own thinking, I do not make a major distinction between measuring correlation and reducing correlation bias. If it is feasible to measure the correlation, it will be feasible to eliminate it, either by developing a new procedure or by a statistical correction. Reducing the measurable correlation bias statistically is, in fact, the purpose of the procedure suggested in the original Chandrasekharan-Deming paper of dividing the population into strata on the basis of characteristics highly correlated with completeness of reporting and making separate estimates for each stratum. This stratification approach would apply particularly to the reduction of the biases due to "causal dependence" described in chapter 5 by Pradel de Lamaze.5 Most of the attempts to apply the Chandrasekharan-Deming stratification method have produced little or no reduction in bias. This can be due to the difficulties in measuring the correlation—(i) difficulties in identifying strata which differ substantially in completeness of reporting and (ii) the fact that, if there are strata with very low reporting probabilities for both sources, we will have too few cases (matched or unmatched) in either source to yield a reliable estimate of the completeness of reporting for the other source.6 Usually, however, the low bias reduction achieved by (post-) stratification is attributable to the fact that the correlation bias is low. It is, in fact, very difficult to construct a plausible situation with substantial response correlation bias where completeness in either procedure is high (say 80 percent or more). That is, one must postulate that there are a large number of cases with practically zero probability of being reported for both sources. While cases with zero reporting probabilities exist in any population, they are usually cases of deliberate concealment (e.g. persons engaged in illegal activities who are purposively omitted from census or survey reports, or deaths which are not reported by the family to avoid payment of death duties). Deliberate misreporting is a rare phenomenon for most properly set-up collection systems. However, where there is reason to suspect wide-spread concealment of information, dual collection estimates, like all other estimates, should be viewed with suspicion. With respect to problems other than those of independence: i. I wish to reply to Muhsam that we do not ignore overenumeration. In the vital statistics area, there is considerable discussion of the (equivalent) problem of "out-of-scope" bias—e.g. in the PGE handbook by Marks, Seltzer and Krotki (1974) and in an earlier paper by Seltzer and Adlakha (1974). The bias of overenumeration while it is real, is less than that of underenumeration. In most cases the residual underenumeration bias due to lack of independence will more than balance the overenumeration bias. In any event, one does one's best to measure overenumeration and to secure independence in one's measurement of underenumeration. ii. With respect to another point made by Muhsam, there have been several models of triple system estimation. These are presented and discussed in some detail in the PGE handbook by Marks, Seltzer and Krotki (1974). In general, such systems reduce but do not eliminate the correlation bias. In general, also, triple system estimation is a relatively expensive method of reducing correlation bias but it may have advantages in some special circumstances. iii. While Scott is correct in indicating that matching costs and the probability of 211

Discussion

Eli S. Marks

matching errors tend to increase with size of cluster, this is one of the lesser factors in the design of dual data collection systems. In census evaluation, the matching unit is the census "Enumeration Area", whose size is fixed by census design considerations which far outweigh the matching costs and difficulties. In vital statistics, the matching costs are trivial compared to the field costs. That is, one needs to consider the matching of a very small number of vital events even for segments of fairly large size. For example, with units of 5,000 population one would have less than 200 births and half that number of deaths in any given segment but would have (in a survey) to enumerate 1,000 to 1,500 households. iv. Mr. Scott raises an interesting point regarding the estimation of vital rates as distinct from number of vital events. We discuss this question at considerable length in the PGE handbook and suggest a number of ways of correcting for the bias due to underestimation of the population base. One such suggestion involves use of an independent population base derived from the census with a dual system (PES) correction. Another suggestion is to stratify the vital events into those associated with households (or peisons) reported in the survey and those associated with households (or persons) not reported in the survey and applying the dual collection estimate only to the events associated with households reported in the survey (Marks et al., 1974: 142-149,254256,314-315,321-322, 385,386). Even if one uses for vital rates a population base derived from the household survey with no correction for underenumeration, the bias of the vital rates will tend to be small. In the first place, completeness of reporting of vital events in any source is almost always poorer than completeness of reporting of persons and frequently very much poorer—a 20 to 40 percent undercount of vital events versus a 4 to 10 percent undercount of persons. In the second place, dual collection estimates of vital events rarely, if ever, achieve zero correlation bias. It is, in fact, usual for the effects of correlation bias on dual collection estimates of the number of vital events to fall somewhere between Scott's optimistic assumption of zero effect in discussing the bias of vital rates and the pessimistic assumption of a bias greater than that of single system estimates implied by the remainder of his discussion. At least for the immediate future, I would be happy to accept, in dual collection estimation, sufficient independence to reduce the undercount of the number of events in the numerator of a vital rate to about the same level as the undercount of the number of persons in the denominator of the rate. Scott's discussion does suggest one important point for further investigation—namely, the fact that errors in vital event reporting can be divided into those occurring to persons missed by the survey and those occurring to persons correctly covered by the survey. A division along these lines in the analysis of dual system reporting errors may be valuable in pointing the way to future improvements.

Endnotes to Chapter 12 1. The editor hopes that the two definitions of household change technique and overlapping reference period are stated without the ambiguity revealed by the author. In the former definition the dependence of it on retrospective questions is pointed out. [Editor's note.] 2. Contrary to what Scott is saying, it is by no means certain that censuses are, as a rule, inferior to surveys. Such technical literature as is available, suggests rather the contrary. Let it be added that such literature emanates from countries and statistical organizations where the business of evaluation is taken seriously. One can actually

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Endnotes

think of a host ofa priori reasons why ambitious and prestigious national undertakings such as decennial censuses would recruit the best people, adequate financial and administrative support, plus the interest and co-operation of the public. Similarly, there are a priori reasons why a single round survey might have an organization inferior in comparison with a PGE/ ERAD/ ECP investigation. Single round surveys could be reviewed as a matter of a last and desperate resort, when one does not know what to do or what one is doing, while the PGE/ ERAD/ ECP is a challenging endeavour that excites the best people who look forward to the possibility of breaking out of continuing ignorance and uncertainty. [Editor's note.] 3. The matter of independence versus correlation is considered at many points in this book, particularly in the discussion of chapter 2 and in section 11.3. The difficulty of the matter lies in the fact that participants in the discussion "believe" that completeness is achievable even under the difficult circumstances in which some of them work. [Editor's note.] 4. The PGE/ ERAD/ ECP technique was applied even earlier, although it was not yet named so, in Canada (Tracey, 1941). [Editor's note.] 5. As repeatedly pointed out in earlier chapters, except in the original PGE article of 1949, the stratification by degree of completeness or perceived correlation, resulted in no particular benefit. [Editor's note.] 6. Ultimately, of course, we have no measure of completeness of reporting for cases which have zero probability of being reported.

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Appendix

International Association of Survey Statisticians First Meeting in Vienna, 18-24 August 1973 Session on: Developments in Dual System Estimates Thursday, 23 August 1973

Organizer's Report

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Organizer's report Organizer and chairman:

KarolJ. Krdtki University of Alberta

In vited papers: "The State of the Art in Dual Systems for Measuring Population Change"

Bradley Wells and Daniel G. Horvitz The University of North Carolina

"La collecte de donnees demographiques en Afrique francophone par la methode PGE/ERAD/ECP"

Francois Pradel de Lamaze INSEE, Limoges, France.

"The Role of Dual System Estimation in Census Evaluation"

Eli S.Marks Bureau of the Census, U.S.A.

Contributed papers: "Dual System Multiplicity Estimators"

Monroe G. Sirken National Center for Health Statistics, U.S.A.

"The Egyptian Project for Measuring Vital Rates: Some Estimates"

K.E. Vaidyanathan U.N. Development Programme Cairo, Egypt

Invited discussants: Ivan P. Fellegi, Statistics Canada Mohammed Rachidi, CeRED, Rabat, Morocco Christopher Scott, UNESCO, Paris and World Fertility Survey, London William Seltzer, The Population Council, New York, N.Y. The session started punctually and came to an end at 1715 hrs. Including the participants named above, the number of persons present during the session varied between 44 and 52. William Edwards Deming, the co-author of the ChandrasekaranDeming formula, on which much of the work in the dual systems estimates is based, was present during the latter part of the session. Apart from authors of papers and invited discussants, three members from the floor took part in the discussion. Low attendance by colleagues from underdeveloped countries was noticable, itself a reflection of a somewhat low participation in the I ASS Meetings from LDCs. The presentation of papers and the discussion was conducted bilingually, and the chairman was ready to deal with trilingual contributions from natives, should these have been forthcoming. The chairman erred in giving too much time to authors. Discussants were all interesting, and almost all kept to their allotted time, but in the end not enough time was left for discussion from the floor. The alternative system, followed at the meeting of the IUSSP in Liege, whereby no direct presentations from authors are made, is to be preferred. All papers are summarized by a moderator. It makes for a lively discussion from the floor, which is the life blood of a good session, and the authors of papers take part in the discussion like everybody else. On the substantive side the session provided one more forum for this interest that has been topical in the last 12 years (after 12 years of silence between the appearance of

216

Organizer's report the Chandrasekaran-Deming article in 1949 and first PGE/ ERAD/ ECP field work in 1961). To put it at the lowest the session served as means of information and education, the need for which continues to be considerable as some of the discussion has shown. At a somewhat higher level, the meeting provided an opportunity for the meeting of experts in survey sampling, in dual system techniques, and in demographic techniques of analysis. One participant asked himself after the meeting the question: "I wonder whether I appear as brassly overconfident in the other two areas, as some of the participants appear to be in mine?" The substantive and new contributions in the papers presented (and the others now available, not presented to the session) have been reviewed in summary form by the Publications Committee of the Social Science Research Council of Canada. They encouraged the chairman to proceed with the editing of the proceedings from the session. The main issues raised or discussed during the session can be summarized as follows: i. A systematic examination of theoretical and practical issues and suggestions for procedures and rules of thumb for making decisions; ii. The effect of conventional and multiplicity rules on the sampling variance of dual system estimators; iii. Suggestions for the resolution of PGE/ ERAD/ ECP difficulties in Francophone Africa; iv. Reports on experiences in other parts of Africa and lessons therefrom; v. Learning from PGE/ ERAD/ ECP results in vital statistics, the future explorations in census evaluation should lie in the independence of PES and census rather than improvements in single system PES estimates. But the session also provided means for the consideration and discussion of various other related issues, such as for example, the cluster size under varying costs conditions.

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Glossary

PGE pge POPLAB poplab

taken from taken from taken from taken from

Marks et al., 1974 without changes Marks et al., 1974 with changes Chanlett, 1974 without changes Chanlett, 1974 with changes

Base population The number of people in a given area (such as a country, province, city, or sample area) to which a specific vital rate applies — for example, the denominator of the crude birth rate or the crude death rate. (PGE) Bias

A measure of the error associated with a particular method of data collection over the long run. More precisely, the bias of a particular method or procedure is equal to the difference between the expected value of the population characteristic being measured obtained from the repeated use of the procedure and the true value of the characteristic. See also sampling error and variance. (PGE) Block A convenient subdivision of a chunk in a PGE area, usually consisting of from 50 to 100 dwellings, or about 200 to 500 residents — approximately the size of a small census enumeration district. In urban areas a PGE block corresponds to one or more urban blocks. (PGE) Blocking A concept used in the technical literature on matching to describe the separation of documents, usually on the basis of geographic variables, in order to lower the quantity of documents to be matched at any one time. (PGE) Category In the PGE literature, sometimes used without further qualification to refer to one, some, or all of the four cells of the two-by-two contingency table used to demonstrate how PGE estimates are developed. By convention, when dual collection system is being used, the "first" category refers to vital events caught by both procedures, the "second" category consists of events caught by the first procedure but missed by the second procedure, the "third" category consists of events missed by the first procedure but caught by the second procedure, and the "fourth"

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Glossary category consists of events missed by both procedures. This model is directly applicable only in the case of a two-way match, (pge) Chunk A division of a PGE area, consisting of several blocks, roughly corresponding to a small village or a hamlet or subward or a small precinct, (pge) Civil registration The traditional method of registration of births and deaths, intended to be continuous and comprehensive. A civil registration system provides both legal documentation of each vital event and statistical reports for the compilation of vital statistics. It must be supplemented by information on the base population so that the necessary vital rates can be calculated. A registration system created specifically for PGE purposes is called continuous recording procedure. (pge) Cluster A group of related analysis units used as a sampling unit — for example, the households in a given city block. If all analysis units in a cluster are to be in the sample, it is referred to as an "ultimate cluster". (PGE) Community informant A person, such as a religious functionary, or an institution, such as a barber's shop, who by virtue of their position in a village are likely to know about vital events occurring there. In a properly structured PGE system a much less important source of first intelligence than the routine round contact. Completeness The proportion with which coverage has been achieved successfully. Completeness rate The proportion of the total events occurring in a population obtained through one procedure of a dual collection system; the match rate of one procedure is the estimated completeness rate of the other procedure, (poplab) Continuous recorder In the dual collection system of the International Program of Laboratories for Population Statistics, the person who collects data in the continuous recording procedure, (poplab) Correlation bias See Response correlation bias Coverage Refers to either the population or a geographic area intended for inclusion in a given study. A so-called "full-count" census has 100 percent coverage; a one-infifty 2 percent coverage. Their completeness is a matter of luck and efficiency. It is usually less than the intended coverage. Coverage bias In a PGE study, the bias arising from undetected out-of-scope reports, (pge) Daily ration A daily assignment that corresponds to the part of the PGE area to be visited on a given day of a week by the PGE continuous recorder active in continuous record-

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Glossary ing. There is one daily ration for each day of a week, and there are as many multiples of five daily rations as there are weekly rations. With a system of daily rations, the inspecting official will always know where a continuous recorder will be working on a given day. (pge) De facto population A concept under which individuals (or vital events) are attributed to the geographic area where they were (or occurred) at a specified time. (POPLAB) Dejure population A concept under which individuals (or vital events) are attributed to a geographic area by virtue of a formal belonging on the basis of residence or other legal and traditional criteria, (poplab) Demographic analysis As used in this book, a general term for a group of techniques for estimating basic demographic variables from census or household survey data on the basis of assumptions about either the nature of the population being studied or the expected relationships in the reporting of certain kinds of information. While these techniques have roots deep in the history of demography, they have been improved markedly in recent years by the technical advances associated with the work of Brass, Coale, and Demeny. (pge) Dependence bias See Response correlation bias Dual collection system A system for collecting information on vital events (especially births and deaths) and on the appropriate exposed-to-risk population. The system comprises any two procedures that, ideally, are independent of each other. See independence. In this book two procedures are assumed for the clarity of exposition: (1) ^continuous vital event recording procedure independent of the civil registration system and (2) aperiodic household interview survey procedure conducted in the same geographic area for the purpose of detecting by retrospective questions, vital events occurring in a designated time period in the past, and to obtain data on the population of the area for rate computation and for other purposes. Matching of the events reported by the two procedures provides methods of improving the estimate of the total number of vital events. Since the system is for statistical purposes, both the recording procedure and the survey procedure can accommodate variables required to compute a variety of specific rates, (poplab) Dwelling

Any inhabited structure such as a house, hut, or tent where one or more households are living. A dwelling usually has one main entrance from the outside. (PGE) Erroneous match A form of matching error in which a report of a vital event in one collection procedure is classified asamatch, but does not correspond to any report in the other procedure. (For PGE purposes, mismatches are not counted as erroneous matches.) The number of erroneous matches is calculated separately for each collection procedure and may be different for each procedure, although net matching error will be the same for both. Erroneous matches arise when the matching items used lack sufficient discriminating power, (pge) 220

Glossary Erroneous non-match A form of matching error in which a report of vital event in one collection procedure of the dual collection system is classified as a non-match, but in fact does correspond to some report from the other procedure. (POPLAB) Expected value In sampling literature, used as a synonym for "mathematical expectation". Simply put, it is the mean (average) value of all possible outcomes of a random process. See also bias. (PGE) Experimental matching A procedure which involves the use of all the information in order to match documents referring to the same event. Its purpose is to select characteristics and their tolerance limits such that would lower the cross matching error and produce a zero net matching error. Field follow-up A field procedure carried out as part of the matching operation and designed to investigate the non-matched reports further, to identify the out-of-scope reports, and, in the case of a two-way match, to match correctly some of the non-matched reports with each other. Field follow-up should always be conducted by workers not used by either of the two collection procedures — that is, by a third party. Other purposes of a field investigation are to establish the best matching rules at the early stages of the experiment, to check the base population, and to check doubtful matches. It is not the purpose of a field follow-up to discover more vital events, (pge) Field inspector In a continuous recording procedure, the person who is the immediate supervisor of the continuous recorders. He is required to inspect the work of the recorders carefully, to correct any errors they may have been making, and to set a high standard of accuracy. His job requires constant travel to PGE areas, (pge) Field workers A general term covering the entire field staff used to collect information on vital events and the base population — that is, the continuous recorders and the interviewers, (pge) First intelligence The initial indication, sometimes in the form of mere hint, that a vital event has taken place. Even if the information is very complete, it must be followed up by a visit to the household most directly concerned. (PGE) Geographic out-of-scope Reports of vital events that occurred (1) to persons whose usual residence is outside the PGE area in a dejure system or (2) outside the PGE area in a de facto system. See out-of-scope. (PGE) Gross matching error A measure of matching error equal to the sum of erroneous matches and erroneous non-matches. Gross matching error is the major component of the variance of the estimate of net matching error. However, it has no direct effect on the variance or the bias of the match rate. (PGE)

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Glossary Household change technique A method of enumerating vital events in a multiround survey by comparing the lists of household members obtained in successive survey rounds and accounting for changes in the persons listed as members in terms of vital events or migration. Not all events can be covered by this technique (for example, the births and deaths of infants who are born and die between the survey rounds will be missed); those missed by this procedure must be covered using retrospective questions, (pge) Household survey See periodic household survey Independence A statistical term used in PGE literature to mean that the probability of a given vital event being reported in one procedure in a dual collection system is the same whether or not that event is reported in the other procedure. Lack of independence leads to response correlation bias, (pge) In-scope A term used to describe reports of vital events that are properly recorded by some data collection procedure with respect to the fact, time, and place of occurrence. See also out-of-scope. (pge) Intraclass correlation coefficient As used in sampling, a measure of the homogeneity of the population with respect to some characteristic within the clusters of a sample, and as such an indication of the extent to which the use of a cluster sample increases the sampling error of an estimate. In other words, it reflects the degree to which total variance can be accounted for by within-cluster variance. The value of the intraclass correlation coefficient (6) varies depending upon the population sampled, the variable under study, and the size and nature of the clusters. When the elementary units within clusters are very similar to each other with respect to some characteristic, 8 will approach +1. On the other hand, if the elementary units within clusters are relatively heterogeneous with respect to the characteristic, 6 will approach zero or, occasionally, be a negative value. (PGE) Linkage See matching Match Two data reports, presumably referring to the same person or event, linked on the basis of a set of matching rules and the identification contained in each record, (poplab) Matching In a PGE study, the process of establishing whether two reports on vital events, each obtained by one part of a dual collection system, refer to the same or different vital events. The determination of whether or not any two reports are a match is based on a set of matching rules. The application of these rules in any given instance may lead to a correct match or to one or more different kinds of matching errors. The process can involve an attempt to match either all the reports of one of the two procedures (see one-way match) or all the reports of both procedures (see two-way match), (pge) Matching characteristic See matching item 222

Glossary Matching criteria See matching rules Matching errors The incorrect outcomes of a matching process. Specifically, either a failure to match two reports that, in fact, refer to the same vital event (an erroneous nonmatch) or the incorrect linkage of two reports which, in fact, refer to different vital events (an erroneous match). A mismatch, however, is not considered to be a matching error for PGE purposes. See also gross matching error and net matching error. (PGE) Matching item Any one of the items in a vital event report used to determine whether or not two records match. Matching items must be present on the reports of both procedures. Individual matching items have differing discriminating power. In most situations it is advisable to use a combination of matching items, (pge) Matching mode The physical means of comparing two reports of vital events to determine whether or not they match. Matching may be done by human beings, by mechanical punchcard equipment, or by an electronic computer, (pge) Matching rules A set of criteria, sometimes implicit, used to determine whether or not two records are a match — that is, whether they are to be treated as referring to the same person or event. As an intermediate step in the application of matching rules, pairs of records may be classified as doubtful matches pending further processing or filled follow-up. Matching rules, and their application also give rise to erroneous matches and erroneous non-matches, (pge) Matching status The classification of a vital event report in relation to the final outcome of a matching process — that is, whether a particular record is a match or a nonmatch. In a two-way match, the matching status of all reports from both procedures is determined, yielding the following final categories: matched (events reported by both procedures), non-matched in the first system (events reported by the first procedure and missed by the second procedure), and non-matched in the second procedure (events reported by the second procedure and missed by the first procedure). In a one-way match, the matching status of allrecords of only one of the procedures is determined. See also category and match rate, (pge) Match rate The proportion of vital event reports from a given data collection procedure that are found to match the records of another procedure. Given an independent dual collection system, the absence of ratio bias and of out-of-scope reports and zero net matching error, the match rate of either procedure is an unbiased estimate of the completeness of the other procedure. The match rate should not be confused with the proportion of events reported by both procedures (that is, the "first category"), which has the same numerator but a different denominator. In the case of the match rate, the denominator is the sum of the match and non-matched reports of a particular collection system; the proper denominator for the other proportion is all events, whether or not they were reported in either procedure. (Pge)

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Glossary Mean square error A measure of total error equal to the sum of the variance and the square of the bias. In many applications the square root of the mean square error is used and is referred to as the root mean square error, abbreviated as RMSE. (PGE) Mismatch The linkage of a vital event report from one procedure that has a partner in the other procedure (and thus should be classified as a match) with the wrong report in the second procedure. For the purposes of a PGE study a mismatch is not considered a matching error, (pge) Multiround survey One of the two types of household survey, the other being a one-time or singleround survey. In a multiround survey the same panel of sampling units are reinterviewed two or more times; either the household change technique or retrospective questions can be used to obtain reports of the vital events that occurred between each survey round. Only the latter method can be used in a singleround survey, the first round of a multiround survey, (pge) Net matching error A measure of matching error equal to the difference between the number of erroneous matches and erroneous nonmatches; by convention, erroneous matches minus erroneous nonmatches. Positive net matching error, undetected, causes an upward bias in the match rate and a downward bias in the PGE estimate; negative net matching error, undetected, causes a downward bias in the match rate and an upward bias in the PGE estimate. See also gross matching error. (PGE) Non-match In one sense, any pair of vital event reports, presumably referring to different persons or events, that do not match. In another sense, any individual report that, at the end outmatching process, has not been linked with another record. See also matching status. (pge) One-way match A matching operation that is concluded when the matching status of all the vital event reports (or a probability sample thereof) of one of the two procedures has been determined. A one-way match yields only match rate (for the procedure in which each report has a known matching status) and, hence, only one completeness estimate (for the other procedure). See also two-way match and wrong-way match, (pge) Out-of-scope Reports of vital events or of units of an enumerated population which should not be included in a given computation or tabulation because they refer to events which took place outside the time period being studied (temporal out-of-scope), events not in the study area (geographic out-of-scope), events outside the definition of the variables being studied (out-of-scope definition), or events that did not occur. (POPLAB) Overlapping reference periods Arising usually when surveys with retrospective questions are conducted more frequently than the length of the recall period. By definition, cannot be used with the household change technique when changes are recorded since the last survey. 224

Glossary Periodic household survey procedure A procedure of data collection using interviews with designated households to obtain and record responses to a specified list of questions. A household survey may involve a single interview with a given household or repeated interviews over an extended period of time. It differs from a census, the other method of enumeration, in that only a sample of households is interviewed. In a PGE study, a household survey is often one of the procedures of dual collection system used to obtain information on vital events and the base population, (pge)

PES See post-enumeration survey. PGE area The sampling unit used in a PGE study. If continuous recording is one of the collection procedures, each PGE area may be an ultimate cluster with a population of approximately 5,000 or 10,000 — providing an adequate work load for a full-time continuous recorder. Other designs may call for somewhat smaller areas. (Pge) PGE/ERAD/ECP technique A method of preparing estimates of vital statistics adjusted for omitted vital events or of estimating the completeness of reporting of a collection procedure used to gather vital data. The PGE technique has three basic features: dual collection, matching, and the use of the match rate to prepare completeness estimates. It also frequently involves the collection of data on a sample basis. (PGE) Post enumeration survey A special-purpose household survey conducted after a main enumeration activity in order to assess the quality of the original enumeration. Often abbreviated as PES. (PGE) Probable match An interim matching status assigned to a pair of reports during a matching process. It indicates that the validity of the match might be investigated should field follow-up be done for some other reason. In the absence of such a follow-up the probable match is accepted as a correct match. This classification is used most often during the early stages of a PGE study when the matching rules are being established, (pge) Probable non-match An interim matching status assigned to a pair of reports during a matching process. It indicates that the validity of a match so classified might be investigated, should there be afield follow-up. In the absence of such a verification the probable non-match is considered unmatched, (poplab) Production matching A non-research production task to divide field records into the four PGE/ ERAD/ ECP categories. It uses characteristics and tolerance limits arrived at during experimental matching. Ratio bias In PGE estimation, a source of bias that may lead to error in making estimates if the number of matched reports is very small. In such a situation the reciprocal of the match rate can become very large, yielding a PGE estimate with an upward bias. Ratio bias occurs most often when estimates are prepared separately for small population subgroups, (pge)

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Glossary Recall lapse The failure to report events or characteristics in response to retrospective questions. The degree of recall lapse varies according to the type of event and the form of the interview questions. Recall lapse is also generally observed to increase as the interval between time of occurrence of the event and the time of the survey increases. (POPLAB) Recall period The length of time between the date of enumeration and the earliest date for which information is requested in a retrospective question. See also reference period. (Pge) Recorder See continuous recorder Recording procedure See continuous recording procedure Reference period Depending upon the context, either the interval of time about which information is sought in a retrospective question or the time interval for which results are processed. Used in the first sense, the reference period is often identical to the recall period in length, occasionally shorter, and never longer. However, reference periods that do not continue to the date of enumeration generally should be avoided. Reference periods are said to "overlap" when, in a multi-round survey, the frequency of the rounds and the length of the reference period are such that information is sought about the same time interval in two or more rounds. (PGE) Registration See civil registration Relative bias A measure of the relative error of a measurement process attributable to systematic error; that is the bias of a process divided by the true value. (PGE) Relvariance A shortened form of the term "relative variance"; that is, the variance of an estimate divided by the square of \i^ expected value. The relvariance of an estimate is also equal to the coefficient of variation squared. (PGE) Respondent A person who answers questions in a census or survey or other data collection procedure. (POPLAB) Response correlation bias A source of bias in a dual collection system arising from a failure to maintain independence between the two collection procedures in the reporting of vital events. In other words, a failure to meet the condition that the probability of an event being reported by either procedure if it is covered by the other procedure is equal to the probability that it will be reported by the first procedure if it is omitted by the second. Response correlation may be due either to the nature of the population or to undue communication between the procedures. It is almost always positive, giving an upward bias to the match rate and a downward bias to the PGE estimate, (pge) 226

Glossary Response error variance A form of variable error arising from variation in the reporting of the same vital events, or some other characteristic, for a given household observed in repeated applications of the same measurement process. It can be defined as the variance of the individual observations made by the same collection procedure operating under the same general conditions around the expected value of these observations taken over a large number of conceived repetitions. (PGE) Retrospective question (s) A type of question, used primarily in enumeration, seeking information about past actions or events rather than about the present status of the respondent and his family. Responses to retrospective questions are affected by two distinct error processes: "Forgetting", a general tendency for respondents to omit events as the reference period is extended further into the past; and "telescoping", the tendency for events that occurred prior to the start of the reference period to be brought forward in time and thus reported as occurring in the period. (PGE) Root mean square error The square root of the mean square error and, like it, a measure of total error. Abbreviated as RMSE. (PGE) Routine round contact A term used in some continuous recording procedures. The routine round is an arrangement by which each sector (consisting of approximately 10 households) in a PGE area is visited once in the course of every one to four weeks by the continuous recorder. Every routine round contact (appointed informally from among the respondents of each sector by the recorder) is contacted during a routine round. He is expected to furnish/irsf intelligence on any vital event that may have occurred in the sector since the recorder's last visit. (PGE) Source of first intelligence A term sometimes used in continuous recording to indicate how the continuous recorder received his first intelligence of a particular vital event, (pge) Slippage A somewhat mysterious experience during repeated sampling surveys, when with the use of the same sampling frame, and same field and office procedures, individuals and/or households "slip" from the survey net in subsequent rounds. Some seem to be coming back with a certain periodicity. Some writers apply the term (unhelpfully) to all losses from the sampling frame, including all kinds of nonresponse and refusals. (PGE definition refers to losses of documents before summarization.) Source of report In a dual collection system, an identification item on each vital event report indicating which procedure supplied a particular report. (PGE) Structure Any inhabited or inhabitable building, shack, tent, or similar construction that can provide permanent or semi-permanent shelter for households. If it is actually inhabited at the time of determination, it is a dwelling, which may consist of one or more dwelling units. If it is inhabitable, but not inhabited at the time of determination, it is vacant. There are difficulties of definition and application at the borderline — when, for example, a road bridge over a dry river is sometimes inhabited or at least could be made habitable. (PGE)

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Glossary Structure number An identifying number, unique within a given PGE area, assigned to each structure for the purposes of the PGE study, whether or not the structure is occupied. Structure numbers are used when other possible matching items, such as names or street addresses, cannot be relied on to provide unique identification. Like a house number, a structure number is most useful when it is clearly visible as one approaches the structure from the front, (pge) Subcluster Part of a cluster, usually a half or a third or a quarter. Used in subsampling when cost differentials between the PGE/ ERAD/ ECP procedures make it advisable to include in one of the procedures only part of the cluster for the purposes of the other procedure. Survey interviewer In a dual collection system, the person who collects data in theperiodic household survey interview procedure, (poplab) Tolerance limits In matching, the range of values for a part of an identification code within which variation is disregarded—for example, considering all first names of identical origin regardless of spelling variations as the same or treating all ages in any five-year interval as the same. (PGE) Total error The difference between the estimate from a particular sample and the true value of the same characteristic. In other words, the sum of all the sources of error affecting such an estimate. For analytical purposes, total error is often divided into two components: variable error (variance) and fixed error (bias). For other purposes, some other division may be more appropriate. Mean square error and its square root, root mean square error, are often used as measures of total error, (pge) Two-way match A matching operation that is continued until the matching status of all the records in both procedures has been determined. A two-way match yields two match rates and two completeness estimates. PGE studies using continuous recording and a household survey frequently employ two-way matching. See also category, oneway match, and wrong-way match, (pge) Variance As sampling variance, a measure of the average difference between a sample estimate and its expected value for samples of a given size. As population variance, a measure of the variability of a population about its mean. (PGE) Weekly ration In a continuous recording procedure, that part of a PGE area scheduled to be visited by a continuous recorder during a given week. See also daily ration, (pge) Wrong-way match A one-way match that yields a match rate and completeness estimate irrelevant to the question being studied — for example, an attempt to estimate the completeness of birth registration by taking a 10 percent sample of registered births and matching those reports with the enumeration records for all infants included in a recent census. Such a one-way match yields an estimate of the census's completeness of infants. (PGE) 228

About the Authors

IUSSP I ASS ISI ASA AAAS

— member of the International Union for the Scientific Study of Population — member of the International Association of Survey Statisticians — member of the International Statistical Institute — member of the American Statistical Association — member of the American Association for the Advancement of Science

Bean, Lee L., B.A. 1957, M.A. (Utah) 1958, Ph.D. (Yale) 1961 IUSSP Chairman, Department of Sociology, The University of Utah. One time Associate Director, Demographic Division, The Population Council, New York. Selected publications: "Demographic review. The population of Pakistan: an evaluation of recent demographic data," Middle East Journal 28 (2): 177-184, Spring 1974 (co-authored) Population and family planning manpower and training. Occasional Paper. New York: The Population Council, 1971. Beaujot, Roderic P., M.A. (Alberta) 1972, Ph.D. (Alberta) 1974 Statistician in the Population Estimates and Projections Division, Census Field, Statistics Canada until 1976. Assistant Professor of Sociology, University of Western Ontario. Selected publications: (with Abdessetar Elamrani-Jamal), "L'observation directe sur 1'execution du recensement 1971 (ODER)," As-soukan, 1 (2): 25-44, June 1973 (with Karol J. Krotki), "La population marocaine: Reconstitution de 1'evolution de 1950 a 1971," Population (Paris) 30 (2): 335367, March-April, 1975. Coale, Ansley J., M.A. (Princeton) 1941, Ph.D. (Princeton) 1947 ISI, IUSSP (President 1974-78), ASA (Fellow) Director, Office of Population Research and Professor of Economics, Princeton University. Selected publications: The growth and structure of human populations: a mathematical investigation. Princeton, New Jersey: Princeton University Press, 1972 (co-authored) The demography of tropical Africa. Princeton, New Jersey: Princeton University Press, 1968 (with Paul Demeny) Regional model life tables and stable populations. Princeton, New Jersey: Princeton University Press, 1966. Fellegi, Ivan P., Ph.D. (Carleton), 1961 IASS, ISI, ASA (Fellow) 229

About the authors Assistant Chief Statistician of Canada; the technical advisor of the Survey Research Centre of York University, and the Centre de Sondage of the Universite de Montreal. Selected publications: "Sampling with varying probabilities without replacement," Journal of American Statistical Association, 58 (30): 183-201, March 1963 "Some sampling techniques applied by the Dominion Bureau of Statistics," Estadistica, 1963 "Response variance and its estimation," Journal of American Statistical Association, 59 (308): 1016-1041, December 1964 (with Karol J. Krotki) "The testing programme for the 1971 Census of Canada," pp. 29-38 in Proceedings of the Social Statistics Section, 1967. Washington, D.C.: American Statistical Association (with Allen Sunter) "A theory of record linkage," Journal of the American Statistical Association, 64(328): 1183-1210, December 1969 "The evaluation of the accuracy of survey data: some Canadian experiences," International Statistical Review, 41 (1): 1-14, April 1973. Fichet, Marie-Daniele, Expert demographe, Institut Demographique de 1'Universite de Paris, 1973. Researcher at the Centre des Recherches et des Etudes Demographiques in Rabat, Maroc, 1973-1975. Research Assistant at the International Program of Laboratories for Population Statistics, The University of North Carolina. Publication: (with F. Notzon) "Le couplage: 1'experience marocaine," As-soukan 3: 28-46, February 1976. Horvitz, Daniel G., Ph.D. (Iowa State) 1973 IASS, ASA (Fellow) Vice-President, Statistical Services, Triangle Research Institute, North Carolina. In 1973 Professor of Biostatistics at the University of North Carolina. Selected publications: (co-authored) "Recent developments in randomized response designs," in A survey of statistical design and linear models. Ed. by J.N. Srivastava. Amsterdam, The Netherlands: North-Holland Publishing Company. "Problems in designing interview surveys to measure population growth," pp. 245-249 in Proceedings of the Social Statistics Section, 1966, Washington, D.C.: American Statistical Association. Housni, El Arbi, Ingenieur Statisticien (Institut National de la Statistique et d'Economie Appliquee, Rabat) 1971 Director of the Centre des Recherches et des Etudes Demographiques, Rabat, Morocco, since 1974. Selected publications: Field operations of dual record tests in the CeRED POP LAB. Scientific Report Series No. 21, Laboratories for Population Statistics. Chapel Hill, N.C.: The University of North Carolina, 41 pp., June 1975 "Analyse de 1'effet de retrospection (methode Som)," As-soukan 3: 17-2, February 1975 (with S. Saidi) "Essai d'analyse de la migration marocaine internationale," Assoukan 5:38-52, July 1976. Krishnan, P., Ph.D. (Cornell) 1971 IUSSP, ASA Associate Professor and Director, Population Research Laboratory, Department of Sociology, University of Alberta, Edmonton. Selected publications: "Rotation sampling with a fixed panel: ratio estimation strategies," Paper presented at the Applied Statistics Conference, Department of Mathematics, Dalhousie University, Halifax, May 1974 230

About the authors "Preliminary report on an epidemic model approach to the propagation of family planning ideas," Socio-Economic Planning Sciences, 8 (4): 225228, 1974. Krotki, KarolJ., B.A. (Hons., Cantab) 1948: M.A. (Cantab) 1952; M.A. (Princeton) 1959; Ph.D. (Princeton) 1960 IUSSP, IASS, ASA (Fellow), AAAS, 1SI Professor of Sociology, University of Alberta, Edmonton. (Visiting Professor of Sociology, University of Michigan, 1975; Visiting Professor of Biostatistics, University of North Carolina, 1971-1973; Visiting Lecturer in Economics, University of California at Berkeley, 1967.) Selected publications: (with Nazir Ahmed) "Simultaneous estimations of population growth — the Pakistan experiment," The Pakistan Development Review (Karachi) 3(1): 3765, Spring 1963 "First report on the Population Growth Estimation experiment," International Population Conference, Ottawa, 1963. Liege, Belgium: Union Internationale pour 1'etude scientifique de la population, 1964, pp. 159-174 "Estimating population size and growth from inadequate data," International Social Science Journal (Paris). 17 (2): 246-259, 1965 (with Nazir Ahmed) "Second report on the Population Growth Estimation experiments," Indian Population Bulletin (New Delhi) 3: 97-104, 1965 (?)'"Estimation de Rythme d'Accroissement Demographique: une introduction aux PGE/ERAD/ECP techniques de mesurages duals." Estadistica (Washington, D.C.) 27 (5): 561-570, December 1969 "Estimation du Rythme d'Accroissement Demographique (ERAD)," Cahiers ORSTOM, serie Sciences humaines 8(1): 17-24, Paris: Office de la Recherche Scientifique et Technique Outre-Mer. Marks, Eli S., A.B., M.A., Ph.D. (Columbia) 1935 IUSSP, IASS, ASA (Fellow), American Psychological Association (Fellow) Chief Census Research and Technical Advisor, U.S. Bureau of the Census, Statistical Consultant to OAS, UNFAO, the Population Council and various countries in Latin America, Asia, and Africa. Relevant publications: (with W. Seltzer and K..J. Krotki), Population Growth Estimation: A handbook of vital statistics measurement; The Population Council, 1974 (with J. Waksberg) "Evaluation of coverage in the 1960 Census of Population through case-by-case checking," pp. 62-70 in Proceedings of the Social Statistics Section, 1966, Washington, D.C.: The American Statistical Association. (with H. Kappes) "Evaluation of the Chilean Censuses of 1960," Estadistica, 1962 (with W.P. Mauldin and H. Nisselson) "The post-enumeration survey of the 1950 censuses, a case history in survey design," Journal American Statistical Association, 48 (262): 220-243, June 1953. Muhsam, Helmut V., Licence-es-sciences mathematiques, Dr. Sc., Universite de Geneve, Switzerland, 1936 IUSSP Professor of Demography and Statistics, the Hebrew University, Jerusalem. Selected publications: "Enumerating the Beduin of Palestine," pp. 9-24 in Beduin of the Negev. Ed. by H. V. Muhsam. Jerusalem Academic Press, 1966, 123 pp. "Vital statistics from limited data — Moderator's introductory statement," pp. 25-46 in International Population Conference, Ottawa 1963. Liege, Belgium: International Union for the Scientific Study of Population "Population estimates based on census enumeration and coverage check," Population Studies, 8 (1): 71-86, 1961. Nathan, Gad, Ph.D. (Case Institute of Technology) 1964 Professor of Statistics, The Hebrew University, Jerusalem, Israel. 231

About the authors Selected publications: An optimal matching process. Pittsburgh: Case Institute of Technology (Ph.D. thesis), 1964 "Outcome probabilities for a record matching process with complete invariant information," Journal of the American Statistical Association 62 (318): 454469, June 1967 "Matching processes with multistage estimation," pp. 386-389 in Proceedings of the Social Statistics Section, 1972. Washington, D.C.: American Statistical Association. Nobbe, Charles, Ph.D. (Washington University) 1963 Special Population Advisor to the Canadian International Development Agency (CIDA/ACDI). In 1974/1975 Ford Foundation Population Advisor to the Census Organization, the Government of Pakistan. Selected publications: (with P.M. George and G.E. Ebanks) "Labour force participation and fertility, contraceptive knowledge, attitude and practice of the women of Barbados," Journal of Comparative Family Studies. Ed. by P. Krishnan, 7 (2): 273-284, Summer 1976, Special issue on family and demography, The University of Alberta, (with G.E. Ebanks and P.M. George) "A re-exploration of the relationship between types of sex unions and fertility: the Barbadian case," Journal of Comparative Family Studies. Ed. by P. Krishnan, 7 (2): 295-308, Summer 1976, Special issue on family and demography, The University of Alberta. Notzon, Francis, (Sam), B.A. (Texas) 1970, M.S. 1973 and M.A. (Wisconsin) 1974 North Carolina Population Center Frederiksen Fellow posted as a researcher to the Centre des Recherches et des Etudes Demographiques, Rabat, Maroc, 1973/1974. Selected publication: (Co-authored) "Table d'activite de la population marocaine, 1967," As-soukan 4: 16-32, February 1976. Pradel de Lamaze, Fran?ois, Bacc. M.D., Licence-es-sciences (Paris), 1960 IUSSP Charge de mission a PINSEE depuis mars 1970; chef du service "Etudes Demographiques" a la Dr de Lille de mars 70 a sept. 72, chef du service "Etudes" a la Dr de Limoges depuis octobre 72. Activites d'enseignement Cours d' "Economic de la region du Nord" a 1'uer de Sciences Economiques de Lille 197071-72; cours de "Collecte des donnees demographiques" a 1'Institut de Demographic de Paris (Paris I — Sorbonne) depuis 1971. Selected publications: "La population d'Algerie d'apres le recensement de 1966," Population 26 (no. special), March 1971. "Algerie—Enquete statistique nationale de la population," in Les enquetes demographiques a passages repetes INSEE-ORSTOM-INED 1971 Chapitres "Plan de sondage" et "Exploitation" in Les enquetes demographiques a passages repetes" INSEE-ORSTOM-INED 1971 Chapitres "Les recensements" et "Double collecte" in Source et analyse des donnees demographiques — INSEE-ORSTOM-INED 1973. Rachidi, Mohamed, Ingenieur Statisicien (INSEA, Rabat) 1969. Expert demographe (Paris) 1972 IUSSP First director, Centre des Recherches et des Etudes Demographiques, Rabat, Morocco. In 1977 member of the Moroccan parliament. Selected publications: Les donnees et la recherche demographiques au Maroc. Laboratories for Population Statistics, Scientific Report Series No. 12, Chapel Hill, N.C.: The University of North Carolina. "Evaluation de Recensement par Enregistrement sur Bande," As-soukan I (2): 45-47, June 1973 232

About the authors (with Karol J. Krotki) "Le Programme et les premieres experiences (PGE/ERAD) du centre demographique marocain," Bulletin de liaison: La demographic en Afrique d'expressionfran$2i\se 3: 23-25, 1972. "Quelques problemes pratiques souleves a 1'occasion de 1'application de la methode PGE/ERAD au Maroc," Jimler Mutane 1 (2). Rumford, John C, B.A. (UCLA) 1954, M.A. (Washington) 1956 IUSSP, ASA U.S. AID adviser in demographic data collection at various times to the Governments of Turkey, Malawi, Liberia, and Saudi Arabia. Selected publications: "Use of the Chandrasekaran-Deming technique in the Liberian fertility survey," Public Health Reports 85: 965-973, November 1970 "Factors that affect case finding in the Liberian fertility survey," Public Health Reports 87 (3): 247-261, 1972 "Factors influencing the casefinding of migrations in the Liberian fertility survey," Demography 9: 431-1941, 1972. Scott, Christopher, Ph.D. (Ghana) 1972 IUSSP, IASS Assistant Director (Technical) with the World Fertility Survey, International Statistical Institute, London. One time Statistician with UNESCO, Paris. In 1961-1970 Regional Adviser in Sample Surveys, UN Economic Commission in Africa. Selected publications: (with John Blacker) Manual on African demographic surveys. Addis Ababa, Ethiopia: Economic Commission for Africa, 1975 Technical problems of multiround demographic surveys. Laboratories for Population Statistics, Reprint Series No. 11, Chapel Hill, N.C.: The University of North Carolina, September 1973. "Sampling for demographic and morbidity surveys in Africa," Review of the International Statistical Institute, 33 (2): 154-171 "The dual record (PGE) system for vital rate measurement: some suggestions for further development," pp. 407-416 in Vol. 2, International Population Conference, Liege, Belgium, 1973. International Union for the Scientific Study of Population, 1973. Spanish translation forthcoming in Estadistica. Seltzer, William, B.A. (Chicago) 1956 IUSSP, IASS, ASA (Fellow), ISI Chief, Demographic and Social Statistics Branch, United Nations, Statistical Office. One time Staff Associate, Demographic Division, The Population Council, New York. Selected publications: (with A. Adlakha) On the effect of errors in the application of ChandrasekaranDeming Technique, Laboratories for Population Statistics, Reprint Series No. 14, Chapel Hill, N.C.: The University of North Carolina, April 1974. Demographic data collection: a summary of experience. New York: The Population Council, vii + 50 pp. Sirken, Monroe G., B.A. (UCLA) 1946, M.A. (UCLA) 1947, Ph.D. (Washington) 1950 IASS, ASA (Fellow) Chief Mathematical Statistician and Statistical Advisor, National Center for Health Statistics; Chief, Measurement Research Laboratory, National Center for Health Statistics. Selected publications: (with Patricia N. Royston) "Underreporting of births and deaths in household surveys of population change," pp. 412^415 in Proceedings of the Social Statistics Section 1973, Washington, D.C.; American Statistical Association, 1974 "Design of household sample surveys to test death registration completeness," 233

About the authors

Demography, 10 (3): 469-478, August, 1973 "Multiplicity estimation of proportions based on ratios of random variables," Journal of the American Statistical Association 69 (345): 68-73, March 1974. Vaidyanathan, K.E., M.A. (Shahrun) M.A. (Demography), Ph.D. (Pennsylvania), 1968 IUSSP, ISI Demographic Advisor, United Nations, Cairo Demographic Centre. Selected publications: "The household sample survey as a tool for manpower analysis," A case study of lower Egypt survey in demographic factors in manpower planning in Arab countries. Research Monograph 3. Cairo: Cairo Demographic Centre "The panel longitudinal approach in demographic enquiries," Contributed papers: 39th session of the International Statistical Institute. Vienna, August, 1973. Wells, H. Bradley, B.A. (Emory University), 1950; M.S.P.H. (1953) and Ph.D. (North Carolina, 1959) IUSSP, IASS, ASA (Fellow) AAAS (Fellow), American Public Health Association (Fellow) Professor of Biostatistics, School of Public Health, University of North Carolina. Selected publications: (with Agrawal, B.L.) "Sample registration in India," Demography, 4: 374-387, 1967 (with Joan W. Lingner) Organization and methods of the dual record system in India. Laboratories for Population Statistics, Scientific Report Series No. 9, Chapel Hill, N.C.: The University of North Carolina, 1974 Data collection systems: national dual record and related systems, Laboratories for Population Statistics, Scientific Report Series No. 15, Chapel Hill, N.C.: The University of North Carolina, 1974.

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References United States Bureau of the Census, 1953 Infant Enumeration Study 1950. Procedural Studies of the 1950 Censuses, No. 1, Washington, D.C.: United States Government Printing Office. 1960 The Post-Enumeration Survey: 1950. Technical Paper, No. 4. Washington, D.C.: U.S. Bureau of the Census. United States Department of Commerce, 1973 Business Statistics 1973: a supplement to the Survey of Current Business. Washington. Vaidyanathan, K.E., 1971 "The household sample survey as a tool for manpower analysis," Demographic aspects of manpower in some Arab countries. Research Monograph 3 (in print). Cairo: Cairo Demographic Centre. 1973 "The panel longitudinal approach in demographic enquiries," contributed papers: 39th session of the International Statistical Institute. Vienna, August, 1973. Valaoras, Vasilios, 1972 Population analysis of Egypt. Occasional Paper No. 1; Cairo: Cairo Cemographic Centre. Vallin, Jacques, 1971 "L'enquete nationale demographique tunisienne," Population (Paris) 26 (Numero special): 205-44, March. Vostrikova, A.M., 1963 Sample surveys in demographic statistics. Report prepared for a meeting of developing countries, Moscow. Vukovich, A., 1965 "The UAR project for measuring vital rates in rural areas," pp. 195-198 in Vol. 3, Proceedings of the World Population Conference, Belgrade, 1965. New York: United Nations. Wells, H.B., 1971 Dual record systems for measurement of fertility change. Working Paper No. 13. Honolulu, Hawaii: University of Hawaii, The East-West Population Institute, April. Zachariah, K.C., 1970 "The demographic measures of Arab countries: A comparative analysis," pp. 279-326 in Demographic measures and population growth in Arab countries. Research Monograph II, Cairo: Cairo Demographic Centre. Zaghloul, S., 1971 "A project for measuring vital rates in rural areas of lower Egypt," Paper presented at the UNESOB Expert Group Meeting on Traditional and New Techniques of Data Collection in Demographic Statistics, Beirut.

247

Index

Addresses, 12,26,51,58,98, 116, 117, 120, 122, 127, 162, 163, 186, 197 Administrative factors, 200, 212 communes, 120 data, 167 determination, 97, 109 records, 1 Africa, vii, x, 13, 14, 25, 147-149, 150, 154, 217 cost ratios, 205 francophone, 2, 92,217 PGE/ERAD/ECP systems, 109, 111, 145 surveys, 48, 52, 145-147 typical errors, 153 vital statistics, viii Age distribution, 113 analytic use of, 51, 120, 149, 151 Age misreporting, 68, 152, 153, 157, 158, 199, 211 analytic significance, 174 estimation (societal calendar), 114, 126 heaping, 187 Alberta, University of, 152, 154 Algeria, 102 costing, 30, 31,37, 39,42, 44 dual collection experiment, 13, 14, 50,96, 97 surveys, 5, 96, 97 Ambinanitelo 94, 146 Analytic techniques, see also: Stable population techniques and Brass estimation procedures, 1, 145, 148, 150, 151 costs, 154 vs. collection procedures, 153 weaknesses, 154 248

Ankara, 22 Ankazoabo, 94, 146 Ann Arbor, xi, 34, 41, 45 Asia, 25, 111 censuses in east Asia, 153 surveys, 3, 145, 147, 148 typical errors, 153 Asuncion, see also: Paraguay, 169, 171-174, 177,178 Baluchistan, 12 Bangalore, 20 Bangladesh, 12, 19 Barbados, 16 Baseline surveys, 27, 67, 147 as a standard, 190 in Liberia, 99 Bengal, 20 Bias, 54, 55, 125, 130, 134, 167, 168 completeness, 56, 57, 160, 161 content, 160 correlation, 56, 57, 101, 110, 145, 161, 172, 173,211 correlation . . . due to migration, 197 dual compared with single, 210, 211 in census evaluation, 157, 185 in multiplicity surveys, 90 matching, 161 negative correlation bias, 101, 112 negative indirect correlation, 203 out-of-scope, 55, 57, 161 positive correlation bias, 101 reducing, 80, 211 reduction through homogeneous groups, 131, 185, 186, 188 Birth rates, 56, 113, 129, 134, 151 crude, 149 estimation of, 55, 129, 153

Index in Colombia, 60 measuring, 51 Bogota, 62 Bolivar, 62 Bonus, see: Rewards Boundaries, spatial, 97, 107, 164, 189, 193, 197-199 and cost in PGE, 205 EA, 163 in surveys, 57, 94, 114, 115, 118 temporal, see: Recall lapse Brass estimation procedures, 66, 68, 145, 148154,210 Brazil, 5 British Empire, 93, 101 Bureau of the Census, U.S.A., 18, 158, 188, 216 Burundi, 30, 31,37,39,42,44 Caid in Morocco, 123 Cairo Demographic Centre, 104, 145, 216 Calibrating, 27, 206 Calendar, societal Chinese, 153 for age estimation, 114 for dating events, 127 Cambodia, 5, 51 Cameroon, a study registering vital events, 28, 30,32,37,39,42,44,96 Canada bilingual country, 103 census, x evaluation of census, 48, 213 social surveys, 2, 16, 29-31,37, 39,42,44 time series and cross section data, 75, 79 Cantrelle, 96 Capture-tag-recapture technique, 48 Carribean, 16, 17 Causality, 193 independence, 93, 211 Celada, 68 Census evaluation, x, xi, 156, 164, 189 affected by housing shortage, 174 bias, 157 by dual system estimation, 101, 156, 168, 197 capacity to separate content error from completeness error, 160 census completeness, rural vs. urban in Korea, 173 census process data used substantively, 167 census quality vs. survey quality, 207,212 completeness errors, 158, 159, 206 consistency analysis, 157, 158 content errors, 156, 159 data, viii, 52, 61, 65, 77, 80, 90, 97, 98,

113, 121, 167,190 decennial census, 213 enumeration, 16, 170, 172 fallacy of "best enumerators", 161, 189 methods, 157, 172, 197,212 PES census interval, 203 PGE vs. demographic methods, 159 reference date, 187 reports, 1 variances, 156, 157 Centrafricain Republic, 31, 33, 37-40, 43, 45 CeRED, see: Morocco Chaco, Paraguay, 172 Chile, 19 China, vii, 28, 153 CIMED, 19, 24 Civil registration system, 1,3,8, 15-24, 27,28, 48, 57-59, 65, 74, 92, 94, 97, 98, 102, 108, 109, 164, 167 in Egypt, 111 in Thailand, 80 test of completeness, 95, 111 Clusters, 55, 123 analysis, 64 boundaries of, determining, 54, 56, 187 cost coefficient, 48, 205 rural, 115, 120 size of, 11, 27, 28,47, 56, 58, 71, 96, 97, 114, 115,204-206,212,217 size of, and matching batch, 206 urban, 115 Colombia, 13, 19, 53, 60-62, 65 correlation bias, 71 POPLAB, 61 Columbia, District of, 18, 19 Common law marriage, 174, 181 Communes administrative, 114, 115, 120 statistical, 114, 120 Comparison, principle.of, 49 Completeness, 3, 55, 207, 210, 212 bias, 56, 57 changes over reference period, 67, 68 errors, 153, 159-161, 165, 189, 193, 203, 207 in continuous recording, median, 145, 147 in dual estimation, 111, 192, 193 in household surveys, median, 145, 147 of census by relationship to household head, 182, 183 of census enumeration, 167, 171, 187, 200, 202 of civil registration, 23, 95, 111 of reporting, 23, 26 related to household composition and migration, 173, 174, 181, 184, 185,187 249

Index Completeness rates, 3, 9-11, 27, 59-62, 67, 71, PGE vs. other data collection systems, 72,95,128, 185, 192 155 and household composition, 181-185 productivity, 52 and migration, 181-185 ratio, 47, 205 household surveys, 118 variations in, 36 in Madagascar dual collection system, 94 Counting rules, 65, 81, 85-88 precision of, 84 periodic surveys, 118 see also: Variances quarterly vs. annual household surveys, Covariances, 55, 56 55 see also: Variances recording procedures, 8, 57, 107, 118, Coverage, difference from completeness, 188 129,131 CPS, see: Current Population Survey survey procedures, 8, 107, 129, 131 Cramer's result on MLE, 77 through PGE, 148 Criada, 181-183, 188 Cross section data, pooled with time series Computer analysis, 64 data, 74, 76-78 Concubina, 181 Current population survey, 19, 23 Congo, 30, 32, 37, 39, 42, 44 Consistency, in census data internal, 157-159,211 Dahomey, 30, 32, 37, 39, 42, 44 Daily ration, 98, 114, 122-124, 128 external, 158 Data collection, 73, 92, 192 Contact points, 122, 123 active, 110 Content error, 153, 160, 165, 203 designs (techniques), 57, 58 Continuous recording procedure, 6, 14, 15, in Lower Egypt, 106 21, 22,47, 55-58, 65, 67, 70, 90, 92, 93, passive, 110 96-99,102,104,105, 107, 108, 110, 111, Dating, 4, 203 117-119, 145-147,206 Deaths personnel, 115 crude rates, 51, 129, 134, 150, 151 Conventional rules, 81, 85, 217 estimation of, 55, 82, 83 Correction procedures, 121 in U.S.A., 87 Correlation, 11, 47, 49, 54, 75, 210, 213 linking to residences, 88 between civil registration and household overestimation, 129 survey, 90 reporting of, 86 between PES and census errors, 193 bias, 56, 57, 110,145,161, 162, 173, 185, Decision process, 141, 142 188, 196, 197,201,206,207,211,212 rule, 144 bias syndrome, 101, 110, 166 De facto (occurrence) events, 66,94, 118, 129, direct, 193 162-164, 197 indirect, 193 measuring, 208 coverage, 28 multiple, 186 definition, 5, 65 negative, 67, 203 in Liberia, 201,202 pattern, 79 in Morocco, 98 positive, 29, 70, 71, 101, young mothers, 115, 118 unknown, 60 De jure (residence) events, 66, 81, 88, 94, 104, Cost factors 118, 164, 196,201,202 and errors, 13,48 coverage, 28 by sex of field worker, 11, 112 definition, 5, 65 cluster/households cost ratio, 205 Delhi, South, 21 cost effectiveness, 54 Demographic estimates, 54, 69, 74, 75, 77, 78 data on, 29, 36 analysis, 65, 78, 153, 154, 174, 189 in evaluation (Procedures A and B), 160"demographic wisdom", 151, 158 162, 186 in census evaluation, 159 in matching, 29, 36, 186 Demographic surveys, 1, 104, 134 data, 1,2,49,50,92 in national samples, 119 parameters, 23, 113 in relative terms, 36 Denominator for rates and ratios, 48,68, 110, in surveys, 30-48 114, 129,207,212 in surveys relating to national income, 29 250

Index matching, 26, 63, 72, 124, 127-130, 132,165 mean square, 13, 54, 69, 70, 79, 91, 167, 168 memory lapses, 68 non-matching, 124, 125, 127-130 non-sampling, 28, 52, 54 sampling, 29, 54, 70, 71, 86 telescoping, 62, 68 total, 13 Europe, 25 Evaluation of data, 12,49, 121 of census through PGE, 52 "statistical wisdom", 158 Events, 8, 10 matched, 132, 133 non-matched, 132, 133, 135 Family planning, 1, 2, 80 Fertility, 11,99, 150 attitude survey, 20 changes in, 56 estimates of, 66, 74, 80, 148, 149 history schedule, 104, 105 level of, 113, 149 marital, 153, 154 "model" schedule, 153-155 predictors of, 77 rates, 151, 153 shape of schedule, 149 Earth satellites, for census data, 167 theory of, 77 ECP, Estimacion Del Crecimiento De La total fertility rate, 150 Poblacion, ix Field Edmonton, fertility survey, 112 costs, 212 Egypt, x, 13, 14, 101, 103, 106, 108, 109, 111, identification procedures, 58, 64 145-150, 154 work, 6, 26 central agency, 104, 105 workers, 27, 98, 102, 115, 117 demographic survey to derive vital rates, men vs. women, 111 104 Field verification, 63, 73, 105, 117, 119, 124, 1947 census overcount, 150 132-134, 198 sample census of 1966, 105 elimination of, 192, 199 EA, see: Enumeration areas reverification, 65 Epidemics, 51 First intelligence, 98 Enumeration Fkihs, in Morocco, 115 cost per person, 47 "Floating" population, 201, 202 duplicate, 164 Follow-up, field, 26 errors, 164 "Fourth category", in PGE estimation, 6, 10, personnel, 196 26,28,29,102, 111, 131, 148 Enumeration areas, 162, 163, 187, 189, 193, Francophone countries, 93, 101, 217, 248 196-201,212 data, x in Morocco, 98 Frequency ERAD, Estimation Du Rhythme of interview, 61 d'Accroissement Demographique, ix, of survey, 62, 114, 117 52 Error variance, computing of, 54, 71 Gabon, 30, 32, 37, 39, 42, 44 Errors, 76, 117 see also: Content error and Completeness Generating data, 49 Georgia, 17 error differential reporting, 68 Goraa Cheikhat in Tunisia, 16, 95, 96, 146 interval time, see: Survey frequency adjusting numerator for population missing in the denominator, 130 PES correction, 212 Dependence, direct vs. indirect, 193, 196,203 Design factors, 10, 58 Design parameters, 55, 56 Discriminating power in matching, 26, 64, 102,122,124, 134 Divorces, 105-108, 114 Dominica, 16 Doubtfully matched events, 124 Dual collection designs, 69, 109, 192 see throughout text Dual collection systems, 3, 54, 119, 145 see individual countries Dual system estimation, viii, 83, 154, 157,161 see throughout text advantages, 207 bias, 87, 91, 206 costs, 54, 55 independence, 210 of census, 159, 192 sampling errors, 159, 192 Duplicate enumeration, see: Overcounting DSM (for Dual System Multiplicity), see: Multiplicity estimates Dwelling numbers, see: Addresses

251

Index Gossip-mongering, 26 Great Britain, 2 Growth rate, 113, 149, 151 Gujarar, 20, 21 Guyana, 30, 32, 37, 39, 42, 44 Haiti, 5 Harmonic mean, 185 Hawaii, East-West Population Institute, 188 Health Information Survey, 19, 23 Health records, 1 bureaux,108 HIS, see: Health Information Survey Honduras, 5, 68 Household change technique, 2-5, 7, 25, 51, 52, 117,212 incompatability with multiround surveys, 206 Household survey, 12, 16-21, 23, 52, 54, 5961,71,81,91,93-95,102,104,117, 122, 123, 147,206,212 completeness rates, 118 longitudinal, 13, 58 lists, 28 multiround, 19,95,96 schedule, 104, 105 semi-annual, 144 Imputation, in PES evaluation, 186 Independence, 6, 7, 11, 26, 29,49,55,58,71, 92,102,106,108,118, 135,161,162, 171, 187, 191, 193, 198, 205, 208, 210, 211,213 between census and PES, 170-173, 191, 200,217 causal, 10,93, 173, 188 evidence from Liberia, 103 in matching, 63 loss of, 9, 60, 72, 73,95, 101, 111, 131, 188 of field workers, 99 operational, 10, 25, 27, 93, 106, 120, 121 principles of, 119, 120 quasi-independent compromise, 60 steps taken in Egypt, 105 technical and administrative, 50, 98, 99, 102, 111, 120, 196,200 vs. quality, 207 India, 5, 20, 53, 59, 65, 109-111 NSS,4 POPLAB, 61 Sample Registration System, xi, 53, 188 surveys, 19, 27, 29, 53 "Turkish error", 102 Indonesia, 5, 51 Informant system, 107, 111 see also: Routine round contacts 252

Ingenuity of man, 126, 200 INSRE of Madagascar, 94, 146 Institute of Social Research, 34, 41, 45 Institutional population, 65, 98, 172 events, 98, 117 medical, 118 International Association of Survey Statisticians, v, ix, 168, 215, 216, 229 International Union for the Scientific Study of Population, 216, 229 Interviewers, female, 111, 112 Intracluster correlations, 13 intraclass correlation, 28, 47, 52, 55, 56, 80,97 Ireland, 154 ISR, see: Institute of Social Research Istanbul, 22 Ivory Coast, 30, 32, 37, 39, 42, 44 Izmir, 22 Kampochea, see: Cambodia KAP surveys, 2, 105 Kenya, 14, 53, 59, 65, 145, 146, 150 Kerala, India, 21 Khalifa, in Morocco, 123 Khombol-Thienaba, 31, 33, 38, 40 Korea, 163, 168, 170-173, 185-188, 193, 197 census, x, 158,168, 170 census personnel, 188 completeness estimates in census, 170 megalopolis: Pusan, Seoul, Taegu, 173 surveys, 21 Kounia, 99, 102 see also: Names, Matching problems Kuwait, 154 Latin America, 25, 153 Lesotho, 5 Liberia, 15, 28, 53, 59, 92, 100, 102, 103, 145150,153, 189-203,248 census, x, 174 completeness, male vs. females, 200 Liberian Fertility Survey, 15, 28, 146, 191, 199 Liberian Population Growth Survey, 10, 11,68,99 recall period, 61 record content, 65 Liege, 216 Life expectancy, 152 model, 148 tables, 120 Los Angeles, experiment, 85, 86 Madagascar, 145-149 two studies involving dual collection, 13,

Index purpose of, 13 tolerance limits, 63, 124, 125, 127, 135, 140,201 "true" matches, 124, 128, 135, 136 two-way, 52 Matching variance, 63, 72, 126, 139 causes of non-matches, 133 errors, 63, 64, 72, 124-127, 129, 130, 134136,145,161,163, 196,207 gross error, 125, 126, 128-130, 137, 140 Maternity histories, 8 Mauritania, 30, 32, 37, 40, 42, 44 MCPS, see: Mindanao Mean square error, 13, 52, 54, 69, 70, 79, 91, 167, 168 in multiplicity surveys, 91 Measurement errors, 54, 69, 71, 168 bias, 62 Medicare, 159, 160 Mehrauli, India, 21 Migration, 56, 57, 59, 72, 99, 105, 109, 113, 116, 117, 154, 158, 169, 170, 172, 183, 187,200,212 caused by death, 65 differences in procedures A and B, 173, 181.196 emigration from Morocco, 113 "floating" population without permanent addresses, 201 handling the problem of, 61,65, 72, 117, 174.197 140 in census enumeration, 181, 184, 197 through discriminant analysis, 64 in census evaluation, 157, 158, 171, 173, transitive ordering of tolerance limits, 174, 182,186 140 in Egyptian survey, 103, 109 Matching technique (procedures), x, 5, 13,25, in Liberian survey, 99, 100, 152 27,48-51,57,62-65,68,74,76, 123, migrants difficult to match, 199 128, 157, 171, 192, 198, 200, 201, 203 "migrants" in PES evaluation, 185, 186, between PES and census, 166 192, 196, 200 between rounds, 6, 29 seasonal, 116 by batches, 128 "visitors" in de facto census, 202 by homogeneous groups, ) >2 Mindanao, 22, 53, 59 cost, 162,211,212 Center for Population Study, 53, 65, 66, dependence on addresses, 1 i • 120 68 different characteristics, 63, %, 105, 124, Northern, POPLAB, 53 126, 127, 135,200,201 Xavier University, 59 difficulties, 28, 93, 120, 172, 203 Morocco, x, 12, 15, 52, 116, 119, 125-128, 130, experience with, 200 131,145-151, 187,205 experimental matching, problems of, 58, booklets of vital events, 102 63, 123, 124,126,133-135 census, 3,113 manual/mechanical, 63, 94 CeRED,93,97, 103, 113, 115, 117, 120, matching batch and cluster size, 206 122, 123, 125-134,216 matching characteristics, 135, 140 costing and output, 47, 48, 52 matching vital events, 58, 119, 127, 130, dual collection system, 15, 53, 93, 97, 99, 189 113, 119, 145 of records, 54 matching, 122 one-way, 162, 164, 191, 198, 204 multiple round survey, 61-63, 68, 113,151 15, 30, 32, 37, 40, 42, 44,94,95, 100, 103 Malawi, 13,15, 30, 32, 37,40,42,44, 146-149 migrants, 199 Mapping, 26, 59, 98, 99, 114, 196, 199, 200 Marriages, 105-108, 114 consensual unions, 174, 181 duration of, 153 Maryland, 17 Match rate, 9, 10,55, 107, 119 Matching bias, 26, 145, 161, 172, 196, 206 erroneous matches, 63 error, 26, 64, 109, 110, 132 false matches, 108, 124, 127-130, 196 false non-matches, 108, 124, 127-130, 196 gross and net error, 72, 136, 196 in multiplicity estimators, 90 Matching rules, x, 6, 7, 11, 13,26,63,72,73, 94, 110,122-124, 126,135-139, 142, 144,201 and independent jurors, 63 by intersection or by union, 140-142 doubtful matches, 124 in Morocco, 122, 126 inadmissable vs. acceptable, 140, 141 matches and non-matches, 124, 129-133, 135, 136, 196 of events, 4, 63,83,91,94, 99, 124, 132, 133 order chains, 141, 142 strictness of rules and net matching error,

253

Index out-of-scope, 187 POPLAB, 13,53,65 population growth, 113, 114, 146 Rabat, 97, 98 surveys, 5, 28, 30-34, 37, 40-45 Mortality changes in, 56 child, 150 estimates of, 11,74,77,80, 155 infant mortality rate used analytically, 151

Numbering systems, to identify housing units, 98,116, 117, 120, 121, 162 Oceania, 25 Omissions degree of, and matching error, 26 estimate of, 48, 170 events vulnerable, 117, 119 in registered deaths and its analytic use, 154

in-scope, 57 rate, 113, 148, 153, 154, of vital events, 206, 207 schedule, 154 persons vulnerable, 117 Motivation rates of, 108, 147, 198, 199 of field workers, 99 One-way matching, 52,162, 164,191, 198,204 of the population, 99 in Canada, 48 Multiplicity counting rules, 217 Optimal design, 55 for rare events, 81-86, 89, 90 Orphanage question, see: Parental survival in different cultures, 87 Oued el Khatef sheikdoms in Tunisia, 16, 95, in mortality, 82 96, 146 vs. conventional rules, 84 Out-of-scope, 55, 57, 63, 145, 204, 207 see also: Counting rules biases, field verified, 132, 133, 145, 161, Multiplicity estimators, x 187, 196,206,211 and ratio estimate bias, 90 eliminated through one-way dual system, 81,82, 87 matching, 192 Multipurpose survey, 5, 28 error, 197,204 disadvantages, 73 chronological, 109, 110, 164, 196 in Morocco, 97, 113, 151, geographical, 110, 124, 164, 196 Multiround surveys, 2-4,15,25,29,49,91,95, in PES, 164, 187 96,98,146, 191 matches, 124 costs, 36 overcounting (overenumeration), 5, 164, 189, intervals between, 117 199,203,208,209,211 Morocco, 68 overestimate events, 11, 93 single system, 62 spurious, 51, 206 Tunisia, 147 Overelaborateness, 13 Mysore, 20 Overlapping period, 72, 212 Names impossible in household change alternative given, 201, 204 technique, 206 recall, 4, 61,62,64, 67 kounia in Morocco, 99, 102 matching problems, 99, 186 Pakistan of villages and barrios, 162, 163 East, 24, see also: Bangladesh National sample, 12 migrants, 199 National Sample Survey (NSS), of India, 4 overcounting, 203 Natural increase, rate of, 92 PGE study, 4, 7, 12, 19,21,28,31-34,38, estimation of, 74, 95 40,43,45,49,50,53,59,217 Net matching error, 6, 110 productivity, 52 New York, 2, 216 Niger, 154 record content, 65 sampling in PGE study, 12 Nigeria, vii, 5, 187,203, survey frequency, 61 Nomads, enumeration of, 48, 98, 116 West, 24 Non-matches, 63, 124, 125, 129-133, 135,136, Panel surveys, 5 196 Non-sampling error Paraguay costs, 11 census, x detection, 54, 68 census evaluation, 162, 163, 165, 168-177, North Carolina, 3, 18, 53, 154, 216 180-188,193,197,203 Northern America, 25 census personnel, 188 254

Index PES, 162, 163, 173, 175-188 Parental survival technique, 114, 120, 154, 155 Paris, 52, 216 Parity, 153 Periodic household survey, 4-6,22, 28,47, 5457,59,65, 115, 117-119, 165 data, 70,71 longitudinal, 68 multiround, 61, 206 Personnel census enumerators, 162 enumerators for PES, 196 field inspection in household surveys, 118 qualifications, 120, 162, 166, 186, 191 residency, inside vs. outside, effectiveness and costs, 115, 116, 120 supervisors in continuous recording, 118 urban and rural areas, 116 Peru, 58 PES, see: Post enumeration survey PGE handbook, ix, xi, 3, 5-8, 10, 12, 13, 25, 26,29,49,52,54, 101, 102, 120-122, 211,212 franchising, 52 PGE/ERAD/ECP surveys, 2, 3, 6, see also: Dual collection best sources of information, 123 costs, 36, 50 estimates, sources of error, 75, 131 government commitment, 50 highly structured, 12 history, 48 "ideal" design, 12, 49 methodological problems, 102, 166 operation of, 50 resident vs. outside recorders, 115, 116 PGE techniques, x, xi, 4, 5, 48, see throughout text active vs. passive collection, 110 overview, 13 procedures, 12, 25, 26 system, 9, 26, 162 theory, 8 two household surveys, 102 Philippines, 13, 22, 29, 53, 58, 65, 67, 71, 73, 153, 154 Photogrammetry, 2 Pikine, 31,33, 38,40,43,45 Poll tax lists, 1 POPLAR (International Program of Laboratories for Population Statistics), 53,66, 218 Colombia, 19, 60, 61 dictionary, xi experiments, 59, 64, 66 in Morocco, 13, 65

India, 61 Northern Mindanao, 53 Population base, 61, see also: Denominator "true" population 185 Population census, vii, 1 Population change growth survey in Liberia, 68 Population characteristics, 129 Population Council, The, vii, 2, 54 Population policies, 1,49 Population reference bureau, 154 Population register (continues), 50 Post enumeration survey (PES), xx, 157, 159166, 168, 170-173, 182-187, 189-203, 207 costs, 160, 165 completeness, 172 in U.S.A., 158, 159 manuals, 161 matching, 164 PES estimates vs. census results, 191 questionnaire, 198,201 time lag between census and PES, 197 to correct for content error, 203 uses in census, 48, 157 Postal survey, 17 Post-stratification, 57, 185, 186, 188, 211 in Paraguay, 169, 171 unsuccessful in reducing correlation, 211, 213 Pregnancy histories, 8, 66, 105, 114 recording, 99 Primary sampling unit, 11 Princeton University, 153 Prizes, see: Rewards for workers Procedures A, 169,171-174,181, 187, 188,202 B, 165, 169, 170, 172-174, 181, 186-188, 202 hybrid procedures (A and B), 202 underreporting of migrants in procedures A and B, 171 Production matching, 73, 126, 128, 131-134 see also: Reconciliation Proxy reporting, 66, 67 PSU, see: Primary sampling unit Pusan,173 Quality control, 12, 102 Quebec, 102 Questionnaires, 64, 98, 99, 104, 105 books, 196 census, 190 design, 6 on fertility, 105 PES, 198, 201 255

Index Quota sampling, 29 Rabat, 97, 98 Randomized response technique, 112 Ratio estimate bias, 56, 57, 71, 90, 110 RCA, see: Centrafricain Republic Recall period, 4, 28, 109 overlaps, 62 problems, lapses, 61, 62, 107, 112 Reconciliation, 27, 68, 161, 162, 164-166, 187, 190, 198 not required by new PES, 163 wrong PES if leading to replacement, 161 Recording procedures, 12, 26, 129-131 delayed recording, 102 Registration data, 10 Regression techniques, x, 75 Relvariance, see: Variance Research Triangle Institute, 18 Residence of mothers, 118 rule, 81 Respondent conditioning, 56, 61, 62, 165 Respondent fatigue/resistance, 5, 26, 56, 61, 62

Respondent rule, 81 Retrospective questions, 2, 3, 117 reporting, 5 single survey, 81, 83 surveys, 10, 17, 18, 67, 86, 92, 107 Reverse Record Check (RRC), 48, 111, 122, 123

Rewards for workers, 26, 28, 29, 67, 73, 118, 121 for respondents, 99 in Liberia, 99, 102 Rotation samples, 12, 56, 71, 123 RR, see: Routine rounds Routine round, 26, 28, 160 contacts, 59, 65, 98, 107, 111, 122

special informants, 123 Sahara, 12 St. Lucia, 17 Sample clusters, 13, 116 Sample design, 11, 23, 63, 71, 81, 96. 135 area, ix, 97 dependence on quality of field staff, 166 probability samples, 114, 119 problems of, 92 sample size, 54, 70, 109 self-weighting, 188, 203 theory, 6, 120 Sample registration, 8 in India, 53 256

Sampling error, 11,29,70,81,85, 109, 168, 206 Sampling frame, ix, 54, 114 special problem in Morocco, 120 the "Tunisian" error, 121 Sampling problems, 28 costs, 11

frame, 12 procedures, 23 variance, 10,70,87, 172 Santander, 61 Satellite imagery as supplementary data, 167 Saudi Arabia, 5 Self reporting, 66, 67 Senegal, a study registering vital events, 5,31, 33,38,40,41,43,45,96 Seoul, 173 Sex-selective reporting in Liberia, 199,200 in U.S.A., 199,200 Sine-Saloum, 30, 33, 38, 40, 43, 45 Single evaluation methods, x Single round surveys, 2-4, 6, 7, 25, 49, 51, 69, 162,213

Single system survey, 68, 69, 118, 161, 206 Singur, 20, 58 Small area estimation, use of supplementary data, 167 Social surveys, 1 costs, 29 Socio-economic surveys, 1 Som's curve, 4 Soundex, 134 Special registration, 8, 20, 21, 59 Spurious reports, see: Out-of-scope Stable population techniques, 65, 80, 145, 148-151, 153, 154 Staff, see also: Personnel qualification, training, 58 "Stand alone" survey, see: Single round survey Statistics Canada, 4, 216 Statistical communes, 120 data, 11

estimation, 75, 157 theory, 77 Stockholm model by Bourgeois-Pichat, 151 Stratification (stratified sampling), 47, 94, 95, 100, 102-104,213 a posteriori, 93 a priori, 93, 99 in Egypt, 104 to lower correlation bias, 102 Structure numbers, see: Addresses Subsampling, 13, 27, 47, 52, 55, 58, 73, 96 Sudan,43, 45

Index costing, 31,33,38,41 enumeration of nomads, 48 First Population Census of Sudan, 112, 195 vital rates, reported, 27 Supervision, 12,97, 116, 117, 123 dangers to independence, 188 importance of, 161 in the field, 26, 118, 120, 121, 123 qualifications, 118 structured, 28, 165 unannounced, 120 vs. evaluation, xx, 120, 121 Survey costs, 30, 36-48 Survey frequency, 61, 62, 104, 114, 117 and completeness, 61 annual, 14 one-time, vii semi-annual, 14, 15, 146 Survey procedures, 2, 8, 62, 129-131, 167 control, 65 part-time vs. full-time employment, 98, 114 postal, 17 slippage, 92 types, 43 Taeduck, Gun, Korea, 21 Tanzania, 15 Tchad,31,33,38,41,43,45 Telescoping errors, 68 Tents, see: Nomads, enumeration of Thailand, 22, 53, 58, 61,80 migrants, 199 Third World, data in, 49, 92 Time factors interval between census and PES, 192 ratio, 206 reference point, 164 Time series data, 76-80 pooled with cross section data, 74 regression, 75 Tobago, 17 Tolerance limits, 125, 126, 128, 135, 142 Trinidad, 17 Triple system estimation, 209, 211 Tunisia, 16,28, 102 census, 145, 147-149 completeness rates, 96 costing, 31,33,38,41,43,45,95 demographic survey, 95 national demographic survey, 5, 16, 28, 51, 146 "Tunisian experience", 121 Turkey, 22, 53,59,61,65 demographic survey, 22, 66 migrants, 199

the "Turkish error", 102 Two-way matching, 52, 205 UDEAC, 28 Underenumeration, 92, 152, 158, 174, 188, 199,211 of base population, 130 of births followed by early deaths, 119 of deaths, 51 sex-selective, 151 Underestimation of events, 11, 93, 130 Under reporting, 96 bias, 69 of deaths, 89 of rare events, 90 UNESCO, 216 United States, 191,201 aid, 188 Bureau of the Census, 18, 158, 188, 216 census evaluation, x, 158-160, 187, 191, 200,210 civil registration evaluation, 59, 80, 210 costing, 31,34, 38,41,43,45 NCHS, 104 number of deaths, 87 social survey, 2, 17-19 U.S. dollar, 35, 36 United Nations, 3 demographic yearbook, 25 population studies, 1, 10,20,66, 149, 151 publications, 154 Upper Volta, 28 USSR, 23,25 Variance, 10,79, 160, 165, 167, 168 and counting rule, 81, 87 error, 71 in census evaluation, 157 minimum, x of total number of events, 125 of sample estimators, 47, 48, 54, 69, 70, 137,139,140,217 reduction device, 81, 89, 90, 161 relvariance, 55 response variance, 90, 157, 164 sampling, 87 test for, 114 trade-off against bias, 70 Vaso Town, 21,58 Verification in the field, 27, 58, 98 for evaluation purposes, 192, 196 for experimental purposes, 63, 73, 124, 132 for production purposes, 102, 105 Vienna, ix, 168,215 Vital events, 4, 7, 12,27 completeness, 87 257

Index measuring, 8, 114 registration of, 1, 72, 114, 146, 164, 212 "true number", 124 Vital rates, 108, 109, 129, 212 estimates of, 131, 149 Vital statistics registration system, xi, 50

258

Vital statistics system, vii, 49, 52, 81 Voinjama in Liberia, 100 World Fertility Survey, vii, 51 London, 216

Author Index

Abdel-Aty, 150 Abernathy, 65 Abou-Gamrah, 120 Adlakha, 51,63, 192,211 Ahmed, 199 Arretx, 10, 68 Bahri, 14 Bang, 188 Bean,3,49,50, 52 Beaujot, ix, x, 51, 134, 145, 151-153 Birnbaum, 82 Blacker, 15, 23, 32, 40, 146, 150, 151 Blanc, 2 Bogue, 8, 10 Bourgeois-Pichat, 151, 152 Bracher, 151 Brass, 68, 149, 150, 153, 155, 220 Brenez, 48 Byrne, 16, 17 Capmas, 108, 109 Carrier, 151

Cavanaugh, 8, 58 Chakraborthy, xi Chandrasekaran, 20, 57, 68, 101, 102, 188, 192,208,210,211,216,217 Chang, 188 Chanlett, xi,218 Cho,158, 171, 188 Choe, 21, 188 Coale, 148-150, 152-155, 159, 220 Coker, 2, 48, 205 Cooke, 12,58 Das Gupta, xi de Bedoya, 188 Demeny, 148, 152,220

Deming,20,48,57,68, 101, 102, 188, 192, 208,210,211,216,217 Dmitrieva, 23, 24 El-Badry, 111, 150 Farooq,19, 21 Farooqui, 19, 21 Fedoruk, v Fellegi, v, 11, 12, 26, 27, 32, 33, 40,44,45,47, 52,69,72,89, 114, 120, 168,205,216 Fichet, 122, 134 Fincanciogulu, 199 Fox, 112 Gendreau, 103 Goldberg, 51 Greenfield, 188 Grove, 18 Hauser, 8 Hendrich, 17 Heperkan, 199 Herrin, 66 Hill, 155 Hobcraft, 151 Hobin, v Horvitz, ix, x, 3, 53, 154, 205, 206, 210, 216 Housni, ix, x, 122, 129, 134 Jaffe, 49 Jain, 21 Johnston, 76, 78, 80 Kannisto, 51 Kazeze, 15, 146 Keyfitz, 48 Khodary, 150, 154 Kish, 47 259

Author Index Koons, 19 Krishnan, ix, x, 74, 79, 80 Krotki, ix, xi, 1, 8, 33, 41, 45, 48-52, 54, 69, 80,106, 112-114, 134, 135, 151, 152, 154. 159, 192, 199,201,211,216,248 Laplace, 101 Lauriat, 199 Under, 8,53 Lingner, 14, 15,60, 64, 146, 154 Lorimer, 154 Lunde, 65 Maddala, 74 Madigan, 22, 58, 63, 64, 66, 67, 154 Marks, ix, x, xi, 3, 5, 7, 10, 12, 15, 29, 52-58, 62, 63, 65, 72, 79, 80, 101, 102, 121, 122, 134,135,156,159-161, 166, 168, 185, 188, 189, 191, 192, 201, 206,207, 210-212,216,218 Mauldin, vii, xi, 2, 3, 28, 53, 72, 73 Mehta, 21 Morah, v Muhsam, ix, 208-211 Muller, 188 Murthy, 111 Murty, 21 Muthiah, 134 Myers, 14, 15,60,64, 146, 154 Nathan, ix, x, 135,201 Nobbe, 119 Notzon, 122, 134 Orstom, 31-33,39-41,44, 45,94, 103 Park, Jay Soo,170,188 Podlewski, 96 Pradel, ix, x, 6, 11, 92, 96, 100-103, 146, 203, 207,211,216

Rao, 75 Royston, 83,84 Rumford, ix, x, 11, 15,22, 146, 189, 190, 191 Sabagh, 3,5,64, 68, 154 Sanchez, 188 Schultz, 150 Scott, ix, 2-5, 28, 48, 52, 68, 73, 154, 205, 210212,216 Seltzer, v, 2, 31, 33-36, 39, 40, 44, 45, 54, 63, 69, 80, 83,100, 110,135,145,148,154, 155, 159, 166, 192,201,210,211,216 Shah,21 Shapiro, 18 Siddiqui, Khalid, v Siegel, 159, 160 Sirken, ix, x, 81-84, 87, 89, 154, 216 Som, 4, 10, 154 Somoza, 10,68 Srinavasan, 134 Sunter, 72, 168 Swamy, 74 Tacla, 19 Taegu, 173 Tao,77 Thavarajah, 151 Tracey, 16, 213 Trussell, 155 Vaidyanathan, ix, x, 8, 104, 110, 111, 146, 150,216 Valaoras, 108 Vallin, 16, 146 Vera, 188 Vostrikova, 23 Vukovich, 104 Waksberg, 160, 191 Walle, vande, 150, 152, 153 Wells, ix, x, 53, 63, 64, 205, 206, 210, 216

Quesnel, 100 Rachidi, ix, x, 113, 118, 119, 134, 146, 216 Ramabhadran, 29

260

Zaghloul, 104, 106 Zelnik, 159

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