Production Efficiency in Domesday England, 1086 (Routledge Exploration in Economic History, 7)

Production Efficiency in Domesday England, 1086

This fascinating study uses Domesday Book data and management science methods to examine manorial production efficiency in medieval Essex in 1086. Production Efficiency in Domesday England, 1086 reveals unexpected facts about economic history. Some of the issues discussed in this study include: • Which tenants-in-chief ran efficient estates? • How was productivity affected by soil type, the size of the estate, the tenancy agreement, the institutional framework of the time and the proximity of a market centre? • Which inputs made the major contribution to the net value of output? • Did slaves make a greater contribution to the manorial lord’s net income than peasants? • What was the effect of feudal and manorial systems, which discouraged mobility of inputs, on the system of production, input productivities and total output produced? • Given technology and the institutional framework, were estates run efficiently? Contrary to the view that Normans ran their estates haphazardly according to local custom, the efficiency analysis shows that Domesday estates were run at similar efficiency levels to comparable production units in more modern economies. Nevertheless, the calculations indicate that the feudal and manorial systems imposed a substantial economic cost. This book is a remarkable contribution to economic history and medieval studies; it will be of great interest to economists, management scientists, medievalists and anyone involved with Domesday studies. John McDonald is Professor of Economics at Flinders University of South Australia. He has published widely in economics, economic history, statistics and population studies and is the author, with Graeme Snooks, of Domesday Economy: A New Approach to Anglo-Norman History.

Routledge Explorations in Economic History 1. Economic Ideas and Government Policy Contributions to Contemporary Economic History—Sir Alec Cairncross 2. The Organization of Labour Markets Modernity, Culture and Governance in Germany, Sweden, Britain and Japan—Bo Stråth 3. Currency Convertibility in the Twentieth Century The Gold Standard and Beyond—Edited by Jorge Braga de Macedo, Barry Eichengreen and Jaime Reis 4. Britain’s Place in the World Import Controls 1945–1960—Alan S.Milward and George Brennan 5. France and the International Economy From Vichy to the Treaty of Rome—Frances M.B.Lynch 6. Monetary Standards & Exchange Rates—Edited by M.C.Marcuzzo, L.H.Officer and A.Rosselli 7. Production Efficiency in Domesday England, 1086—John McDonald

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND, 1086 John McDonald

London and New York

First published 1998 by Routledge 11 New Fetter Lane, London EC4P 4EE This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 © 1998 John McDonald All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data McDonald, John Production efficiency in Domesday England, 1086/John McDonald. p. cm.—(Routledge explorations in economic history; 7) Includes bibliographical references and index. 1. Labor productivity—England—Essex—History. 2. Great Britain—History—Norman period, 1066–1154. 3. Domesday book. I. Title. II. Series. HC257.E85M38 1997 331. 11′8′09426709021–dc21 97–12877 ISBN 0-203-07419-X Master e-book ISBN

ISBN 0-203-21726-8 (Adobe eReader Format) ISBN 0-415-16187-8 (Print Edition)

To Pamela Maggie and John and in memory of Timothy

CONTENTS

List of figures

ix

List of tables

xi

Preface 1

xiii

INTRODUCTION AND BACKGROUND

1

1.1

Introduction

1

1.2

Background

3

1.3

The survey and Domesday Book

5

1.4

Economic analysis of Domesday production data

9

2

MEASURING EFFICIENCY Theoretical ideas

12

2.1

Introduction

12

2.2

Brief description of the method

12

2.3

Measuring inefficiency: the case of the competitive firm

15

2.4

Measuring inefficiency: the Domesday estate

19

2.5

Technological assumptions: scale

25

2.6

Strong and weak free disposability of resources

29

2.7

A decomposition into scale, congestion and technical inefficiency components

30

ALGEBRAIC METHODS Linear programming

34

3.1

Introduction

34

3.2

Basic characteristics of linear programming problems

34

3.3

The dual

36

3.4

The substitutability of resources in production

38

3.5

Calculating estate efficiency measures

39

3.6

A theorem on shadow prices

46

EFFICIENCY ANALYSIS OF DOMESDAY ESSEX LAY ESTATES

48

3

4

vii

4.1

Introduction

48

4.2

Domesday Essex

48

4.3

The annual values and manorial resources

52

4.4

The data used in the study

53

4.5

Manorial efficiency analysis: the efficiency calculations

56

4.6

Manorial efficiency analysis assuming constant returns to scale, strong disposability of 57 resources (CS) technology

4.7

Factors associated with efficiency: descriptive analysis

65

4.8

Factors associated with efficiency: statistical analysis

80

4.9

Resource shadow prices and slack resources

92

Efficiency results for four technologies compared

95

4.10 5

AN ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

100

5.1

Introduction

100

5.2

A review of methods of estimating efficiency

100

5.3

The effect of ancillary factors on production: a parametric production function approach

104

EXTENSIONS, COMPARISONS AND CONCLUSIONS

114

6.1

Introduction

114

6.2

Were Domesday estates run efficiently? The structural efficiency of production on Essex lay estates in 1086

114

6.3

On the economic cost of the feudal and manorial systems

120

6.4

The incidence of beneficial hidation: introduction

123

6.5

Frontier considerations

124

6.6

Beneficial hidation in Essex in 1086

126

6.7

Statistical analysis of factors affecting beneficial hidation

131

6.8

Conclusion

134

Linear programming input algorithms

138

Table 1

Essex lay estates, 1086: CS technology measures

142

Table 2

Essex lay estates, 1086: by CS technology efficiency category

158

6

APPENDIX 1 APPENDIX 2

viii

APPENDIX 3

Efficiency measures (u) of estates assuming CS, VS, CW and VW technologies: Essex lay estates, 1086

174

APPENDIX 4

Beneficial hidation indexes (BHI) for Essex lay estates, 1086

190

Notes

206

Bibliography

215

Index

222

FIGURES

1.1 The main roads and boroughs of Domesday England 1.2 The Domesday survey circuits 1.3 Sample entry from Essex folios: Almesteda, a manor of Suen held by Siric 2.1 Resource levels and annual values of three estates 2.2 Technical inefficiency 2.3 Two inputs: isoquants and cost contours 2.4 Measuring technical and input allocative inefficiency 2.5 Scale inefficiency 2.6 Producible output combinations: the production possibility set 2.7 Producible output and value of net output contours 2.8 Measuring inefficiency of a Domesday manor 2.9 Production possibility sets and inefficiency measures 2.10 The production possibility set implied by variable returns to scale technology 2.11 Production possibility sets implied by variable, non-increasing and constant returns to scale technologies 2.12 Weak and strong free disposability of resources 3.1 The optimal feasible solution to Example 1 3.2 Resource levels and annual values of three estates 3.3 Production possibility sets implied by variable, non-increasing and constant returns to scale technologies 4.1 Domesday Essex regions 4.2 Domesday Essex hundreds 4.3 Distribution of CS technology efficiency measure (u): Essex lay estates, 1086 4.4 Distribution of CS technology efficiency measure (u), by large tenants-in-chief: Essex lay estates, 1086 4.5 English translations of Domesday entries for eleven estates 4.6 Distribution of CS technology efficiency measure (u), by tenants-in-chief with small, medium and large number of estates: Essex lay estates, 1086 4.7 Distribution of CS technology efficiency measure (u), by hundred: Essex lay estates, 1086 4.8 Hundreds categorised by CS efficiency measure (u): Essex lay estates, 1086 4.9 Location of Rochford estates by efficiency category: Essex lay estates, 1086 4.10 Distribution of CS technology efficiency measure (u), by geographical (soil) region, influence of towns and size of estate: Essex lay estates, 1086 4.11 Location of estates surrounding Colchester and Maldon 4.12 Distribution of CS technology efficiency measure (u), by grazing/arable category, tenure and ancillary resources: Essex lay estates, 1086 4.13 Comparison of CS, VS, CW and VW efficiency measures (u): Essex lay estates, 1086

6 6 9 13 15 16 18 19 21 22 23 24 26 28 30 36 40 43 50 50 58 58 63 70 72 73 73 76 79 81 96

x

4.14 Distribution of VS technology efficiency measure (u), by grazing/arable category, tenure and ancillary resources: Essex lay estates, 1086 6.1 Box Plot of distribution of CS u−1 efficiency: Essex lay estates, 1086 6.2 Alternative tax frontiers 6.3 Tax assessment frontier: Essex lay estates, 1086 6.4 Beneficial hidation index (BHI) histogram: Essex lay estates, 1086

96 117 125 127 129

TABLES

2.1 Example 1: efficiency measures for producing units A, B and C 31 2.2 Measuring scale and congestion inefficiency components by two decompositions 33 2.3 Example 2: three units A, B and C, two inputs, R1 and R2, production efficiency measures for C 32 with different technologies 4.1 Summary statistics for data used in the study of 577 Essex lay estates, 1086 55 4.2 CS efficiency analysis, Essex lay estates, 1086: production on eleven selected estates 61 4.3 Tenants-in-chief, Essex lay estates, 1086: CS technology efficiency 67 4.4 Tenants-in-chief by number of estates and CS technology efficiency: Essex lay estates, 1086 69 4.5 Hundreds and CS technology efficiency: Essex lay estates, 1086 71 4.6 CS technology efficiency and various factors affecting production: Essex lay estates, 1086 75 4.7 CS technology, summary of tests of significance of various factors affecting production: Essex lay 82 estates, 1086 4.8 CS technology probit analysis, various factors affecting production: Essex lay estates, 1086 84 4.9 CS technology efficiency of estates of tenants-in-chief held in demesne and by sub-tenants: Essex 85 lay estates, 1086 4.10 Estate CS efficiency by hundred: Essex lay estates, 1086 88 4.11 CS technology, multivariate regressions of efficiency index (u−1) on estate characteristics: Essex 90 lay estates, 1086 4.12 Shadow prices (in shillings) for 577 Essex lay estates, 1086: CS technology 92 4.13 Slack resources: CS technology, Essex lay estates, 1086 93 4.14 Shadow prices (in shillings) for estates with both labour resources: CS technology, Essex lay 94 estates, 1086 4.15 VS technology, summary of tests of significance of various factors affecting production: Essex lay 96 estates, 1086 4.16 VS technology, multivariate regressions of efficiency index (u−1) on estate characteristics: Essex 99 lay estates, 1086 5.1 Constant Elasticity of Substitution production function for Essex lay estates, 1086: non-linear least 104 squares estimates, main resources 5.2 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least105 squares estimates, tenant-in-chief effects 5.3 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least106 squares estimates, hundred effects 5.4 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least107 squares estimates, effect of ancillary factors 5.5 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least108 squares estimates, effect of ancillary resources

xii

5.6 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least111 squares estimates, multivariate ancillary resource and factor effects 6.1 Comparison of structure of efficiency of Domesday estates and American surface coalmines in the 119 Midwest and West 6.2 Shadow prices (in shillings) for 577 Essex lay estates, 1086: CS technology 122 6.3 Beneficial hidation index (BHI) frequencies: Essex lay estates, 1086 128 6.4 Characteristics of estates with beneficial hidation index (BHI) of one: Essex lay estates, 1086 128 6.5 Characteristics of selected estates that received beneficial hidation: Essex lay estates, 1086 130 6.6 Mean BHI of estates of eighteen largest tenants-in-chief: Essex lay estates, 1086 131 6.7 Mean BHI of estates by hundred: Essex lay estates, 1086 132 6.8 Multivariate regressions of BHI on estate characteristics: Essex lay estates, 1086 133

PREFACE

This book examines the production efficiency of Essex Domesday estates. It continues the study of the economy of England in 1086 based on the Domesday survey, begun with Graeme Snooks, and described in the book Domesday Economy and a series of research articles. The focus is to discover which estates were run relatively efficiently, and why. Manorial production is analysed in more detail than in the earlier studies. The idea for the book was conceived after attending a seminar given by Knox Lovell, in late 1989, surveying the production efficiency literature. Knox, together with Shawna Grosskopf and Rolf Färe, has subsequently enthusiastically supported the project, providing many useful suggestions. I am greatly in their debt, and thank them most warmly for their help. I am also indebted to Dicky Damania, John Hatch, Mary Luszcs, David Pope, Jonathan Pincus, T.K.Rymes, Ralph Shlomowitz, John Skinner, Graeme Snooks, Deane Terrell, Norman Thomson and Peter Wagstaff for their valuable comments and support; Jane Priestley for doing such a magnificent job typing the manuscript; Marie Baker, Jody Fisher, Debra Hackett, Debbie Kuss, Ann Smith and Sonja Yates for their typing and computing assistance; and Maggie and John Cowie for their generous hospitality while writing the book in England. Most of the analysis was done jointly with Eva Aker (which is why, throughout, the personal pronoun ‘we’ rather than ‘I’ is used). Eva’s contribution was invaluable at all stages of the project and production of the book; and on a number of occasions she made most helpful suggestions based on her considerable knowledge of data processing, statistics, and the history of the Domesday period. I was extraordinarily fortunate to have the assistance of such a capable person, and thank her accordingly. The book was mainly written during periods of leave in England funded by the Flinders University of South Australia. This leave enabled me to undertake valuable fieldwork. Flinders University supported the project with URB grants during 1990, 1992 and 1997 and the Australian Research Council funded the project during 1991 and 1993–5. This assistance is most gratefully acknowledged. Also, I thank Cambridge University Press for permission to use (in Figures 4.1 and 4.2) material from H.C.Darby, The Domesday Geography of Eastern England; Phillimore for permission to reproduce (in Figure 1.3) entry 24:64 Elmsted, from Domesday Book, Essex, Volume 32; and the Institute of Historical Research, University of London, for permission to reproduce Domesday extracts (in Figures 1.3 and 4.5) from the Victoria History of Essex, Volume I, pp. 462–4, 491, 493, 511, 524–5, 530, 547, 549 and 561, by permission of the General Editor.

xiv

Researchers interested in using frontier methods to analyse the Domesday economy are very welcome to contact me. Email: [email protected]. au; fax: 618 8201 5071; address: Economics, Flinders University, GPO Box 2100, Adelaide S.A. 5001, Australia. John McDonald September 1997

1 INTRODUCTION AND BACKGROUND

1.1 INTRODUCTION Twenty years after invading England, at the meeting of the Great Council held at Gloucester at Christmas 1085, William the Conqueror ordered that a survey of his land be carried out. The results of the survey were later compiled into what has become known as Domesday Book. Domesday Book provides invaluable detailed information on production in eleventh-century rural England, including the resources used in production and the net incomes (or annual values) of most estates or manors. As with many modern surveys, the data were compiled from answers to questionnaires; but, unlike most contemporary censuses, answers were not given in confidence but were scrutinised publicly in local courts. In many ways the checks on the accuracy of the data were more stringent than those for currently compiled official data. The data are also unusual in that they refer to individual production units (manors or estates) rather than to aggregates. Domesday Book is a truly remarkable document providing comprehensive and detailed information on the Anglo-Norman agricultural economy of England. In the book Domesday Economy (written with Graeme Snooks), using modern economic theory and statistical methods, an initial attempt was made to reconstruct some of the central economic relationships of Domesday England.1 We investigated the fiscal system, the principles upon which taxation was based; and whether manorial tax assessments were related to capacity to pay as measured by the incomes and resources of estates. Other issues involved the process of production. An attempt was made to identify and model the key features of manorial production, explain how the relatively fixed endowments of estates could be employed effectively in production by substituting between production processes and outputs, measure the substitutability of resources in production, and establish if there were economies of scale in production. This work is technical in nature and, although readily accepted by economists, has been less well understood by medievalists. Nevertheless, an appreciation of the manorial production system is of critical importance if we are to comprehend how the Domesday economy operated; and to this end, in this volume, methods that will enable a detailed analysis of the economy and fiscal system to be undertaken are explored. The key concept used is the frontier. The production frontier allows us to assess the production performance of individual estates, and the taxation frontier, whether estate tax assessments were ‘beneficial’, reasonable or excessive. Although taxation issues are touched on in Chapter 6, the main focus of the book is manorial production efficiency. The production frontier can be used to calculate a measure of production efficiency for each

2

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

estate in a county. These, and other measures generated by the analysis, allow us to determine how successful individual estates were in transforming inputs into outputs, compare production performance on different estates, and isolate factors associated with production efficiency. County wide studies of manorial production efficiency will help to answer such questions as: Which estates were run efficiently and with high productivity? Which tenants-in-chief ran efficient estates? How did tenancy arrangements affect efficiency? How was productivity affected by soil type and the size of the estate? What was the effect of proximity of a market centre on production? What other factors were associated with high efficiency and productivity? Which inputs made the major contribution to the net value of output? Did slaves make a greater contribution to the manorial lord’s net income than peasants? Given technology and the institutional framework, were estates run efficiently? And what was the effect of the feudal and manorial systems, which discouraged mobility of inputs, on the system of production, input productivities, and total output produced? These questions complement those addressed in Domesday Economy, and are of greater interest to many economists and historians. Hopefully, by attempting to answer them, we shall obtain a much better understanding of the process of agricultural production in eleventh-century England. The book begins this research programme. It explains how efficiency measures can be calculated, and how factors associated with efficiency can be discovered. It illustrates the methods by applying them to the lay estates of Essex in 1086, and a comparison of the production performance of some of the estates is carried out—but much more needs to be done. A more extensive study of the production performance of Essex manors would be valuable, and the analysis should be extended to other Domesday counties—but medievalists and economic historians are much better placed to do this than we are. For medievalists and economic historians, this volume and Domesday Economy help to fill a gap in Domesday studies by focusing on neglected economic issues. Although historians have acknowledged that the Normans were effective as administrators and in mobilising the army, there has been a presumption, implicit or explicit, that the economy was poorly organised, that the taxation system was ‘artificial’ or arbitrary, and that the Normans ran their estates in a haphazard way according to local custom and tradition. This presumption was based on an anecdotal, rather casual reading of the evidence, and it is our argument that a more careful examination of the record does not support the contention. Instead, a picture is emerging of a more rationally organised economic system with tax assessments largely based on a capacity-to-pay principle and, given the constraints of technology, and the institutional setting, estates carefully managed. It is argued (Chapter 6) that the structure of efficiency of manorial production was similar to that of more modern economies.2 Nevertheless, it seems that the feudal and manorial systems imposed a substantial economic cost. The arrangements, whereby land was held from the king by feudal lords in return for military service, thereby providing a structure to maintain an army but also limiting the power of feudal barons, and peasants and slaves were tied to the manorial estate, thus making it easier for the lord to maintain control over them, provided considerable economic, political and social advantages for the feudal hierarchy. They also inhibited trade in inputs. The efficiency analysis enables us to estimate the output loss resulting from the adoption of these practices, and suggests that it was considerable. For economists, the study will be of interest because it helps to advance our knowledge of the production process by applying recently developed production efficiency methodology to an unusually high quality data set relating to individual units. The efficiency methodology and key economic arguments are described in simple terms, without resort to advanced mathematics; different approaches are reviewed, and the study compares production frontier-based approaches to measuring efficiency with a statistically orientated approach.

INTRODUCTION AND BACKGROUND

3

Efficiency and production frontier analyses exist already in the economic history literature. In particular, much work has been undertaken on the efficiency of slavery in the antebellum South (of the United States of America) and plantation production in the period following emancipation. Most studies have not used a production frontier methodology, but are based on statistically estimated production functions or more informal procedures (examples are David et al, 1976; David and Temin, 1979; Field, 1985; Fogel and Engerman, 1974a, 1974b, 1977 and 1980; Schaefer and Schmitz, 1979; and Wright, 1979). An exception is the pioneering work of A.R.Hall (1975), who used some of the earlier ideas of Farrell (Farrell, 1957, and Farrell and Fieldhouse, 1962) to measure the efficiency of postbellum Southern agriculture. Since Hall wrote his thesis, considerable advances in theory have occurred, and we have been able to take advantage of these developments in this analysis of Domesday estates. 1.2 BACKGROUND Following a dispute over succession to the throne, William of Normandy (later called the Conqueror) invaded England in the autumn of 1066. During the previous century the Normans, who were of Danish origin, had greatly extended their land and influence in France. There had been Viking settlements in Normandy since 911 when Rollo obtained a grant of land from the French king. In the subsequent years, by military aggression, marriage, and action in the courts, further land was acquired so that by 1066 William was amongst the most powerful French nobles. William himself was a formidable leader. Often referred to in French history as ‘William the Bastard’, because his father, Robert the Magnificent, Duke of Normandy, and mother, Herleva, were married in the Danish manner rather than in the customary Christian ceremony, he succeeded to the duchy when 7 or 8 years old. During his minority, civil war reigned in Normandy, and it was not until he was 19 that his faction was able to establish firm control. There followed several campaigns against the Count of Anjou and William’s suzerain, Henry, King of France. William was extremely successful, extending his influence into Maine and Britanny. By all accounts, William was an outstanding soldier and military leader. His French campaigns, his organisation of the invasion expedition to England and the subsequent victory testify to this. He was also, at times, quite ruthless. Following seizure of the crown of England, he vigorously put down a series of rebellions, his actions including the infamous ‘Devastation of the North’ during the winter of 1069–70. Although king of England, William remained Duke of Normandy and attended to his duties and responsibilities in France as well as in England. After 1072, William spent a greater part of his time expanding his influence in France and was eventually killed on campaign in France in 1087. Prior to the Norman invasion, from 1016 to 1035, England was ruled by the Danish king Cnut. During this period, Cnut removed many of the existing English nobility and replaced them with English lords more favourable to his rule. Cnut was succeeded briefly by his sons, Harold and Harthacnut, but they left no male heirs, and the throne went to Edward (later called the Confessor) in 1043. Edward had mixed English and Norman parentage, and during Cnut’s reign had received asylum in Normandy. During Edward’s reign, Norman influence increased at the English court, but also several of the English theigns became more powerful, especially the Wessex house of Godwine. On Edward’s death in January 1066, England faced a threat of invasion from Norway. Edward had no male heirs, and Harold, son of Godwine, the most powerful theign, was hastily elected king by the Great Council. Harold’s position was compromised by the fact that he was not of royal blood, and he did not have the support of all the English aristocracy, in particular the support of the northern lords. Also William was a

4

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

rival contender to the throne. William laid claim to the throne through Emma of Normandy, who had married Cnut; and also because he claimed that Edward had made him his heir, and Harold had subsequently sworn allegiance to him. Harold faced threats from Normandy, from Norway and from within England. In September, the King of Norway, Hardrada, landed in Yorkshire where he was joined by some disaffected English lords including one of Harold’s younger brothers. Harold marched north and won a great battle at Stamfordbridge. A few days later William landed in Kent. Harold quickly marched south to London, collecting fresh forces, then marched south to block William’s advance. A major battle took place near Hastings in Sussex (the battlefield at Battle Abbey, Battle, is preserved as a national monument). Harold was killed and William victorious. William marched eastwards, and then north-west to the Thames, eventually entering London where he was crowned king on Christmas Day 1066. Subsequently, William faced a number of rebellions until 1075, including a major campaign in the north during 1069–70, during which he employed a ‘scorched-earth’ policy, killing all who opposed him and laying waste the land. By William’s death in 1087, the Norman control of England was secure, and was further consolidated by his sons, particularly the youngest, Henry, who reigned from 1100 to 1135. William seized perhaps the wealthiest country in Northern Europe, with an economy based on wool, fisheries and agriculture. England was divided into shires which were sub-divided into ‘hundreds’ consisting of several parishes. The shire administration included the earl, the bishop and the sheriff (or shirereeve); royal orders could be transmitted via the shire and hundred courts, and an effective taxcollection system was in place. After his coronation, William redistributed land to his supporters, dispossessing the English aristocracy and creating a powerful political and military machine. The lands of over four thousand English lords were confiscated and passed to less than two hundred Norman barons. Most of the old aristocracy was eliminated, killed, dispossessed or exiled. In exchange for supplying knights and military support when required, Norman barons held nearly half the land of England, with most land being in the hands of just ten men. Holding chief estates on the borders, the barons protected the country from attack from without; and, by holding dozens of other estates scattered through the counties, they consolidated William’s rule. To safeguard the realm the Normans built a network of castles, initially simple motte-and-bailey constructions but later great stone monuments at Chepstow, Ludlow, Richmond, the White Tower in London, and elsewhere. The building boom was not confined to military strongpoints. Most of England’s great cathedrals and abbeys began their life in the half-century after the Conquest. Winchester Cathedral, St Albans Abbey, Durham, Norwich and many others were begun in the period, and many smaller churches and chapels commenced. The Church was a dominant institution. William invaded England with the papal banner, and many of his strongest supporters were ecclesiastics. The Church was the repository of knowledge, the source of literacy, and provided the bureaucracy of government and a hospital and welfare facility, as well as spiritual leadership. Prior to the Conquest, feudalism and manorialism were dominant influences on the political and economic arrangements. According to feudal theory, the king was charged with the duty of administering the land of the realm. He did this by appointing tenants-in-chief, both lay and ecclesiastical, who held land in return for provision of military support. Tenants-in-chief might grant the use of land to sub-tenants in return for rents or services. The tenants provided protection for bonded peasants and slaves in return for goods and services. Broadly speaking, the unfree peasants worked part of the week for the lord and the remaining time on land allocated to them by the lord, producing food and shelter for themselves; whilst the slaves only worked for the lord who fed and clothed them. All had a prescribed place in society; peasants

INTRODUCTION AND BACKGROUND

5

and slaves usually remained on a particular estate, were tied to a lord and did not offer their services to others. William refined this system, codifying the distinctions and duties of each class, but also restrained the system. He strengthened local government through his agent, the sheriff, and the shire court to maintain central control and prevent powerful lords from ignoring his wishes or acting too independently. Domesday Book records 112 boroughs, most small walled towns ministering to local trade or local needs such as providing services to castle garrisons (as at Windsor), an abbey (as at Bury St Edmunds), or pilgrims visiting shrines. Some were fishing ports, and there was a number of trading ports on the south coast. Winchester, London, Norwich and York were larger centres of a few thousand inhabitants. Fishing was important, and there was some industry; salt-panning (salt was used to preserve meat), some leadmining and stone-quarrying, and iron was produced in Corby in Northamptonshire. Nevertheless, England in the eleventh century was predominantly a farming country, with 7–8 million acres tilled in 1086, some 80 per cent of the acreage under cultivation at the beginning of this century. Stock-rearing was of prime importance in the south-west, and arable farming more important in the east and in the Midlands. The main grain crops, wheat, oats, barley and rye, were cultivated in large open fields sometimes divided into strips. These were usually ploughed by oxen ploughteams and the corn ground in local watermills. Vegetables were grown in abundance, chickens kept for eggs, goats for milk, and bees for honey. Pigs were the main source of meat, but sheep were by far the most common livestock, with the wool industry being of great importance and wool a major export to the Continent.3 1.3 THE SURVEY AND DOMESDAY BOOK Although there has been some dispute on the matter, it is now generally agreed that the Domesday survey had both a fiscal and a feudal purpose. It provided valuable information to revise tax assessments and also documented the feudal structure—who held what and owed what to whom; and was in later years used extensively to solve disputes over land ownership. The general view is that Domesday Book was compiled between Christmas Day 1085 and the death of William in September 1087, a period of only twenty months. One factor facilitating the speed of work was the availability of Anglo-Saxon hidage, or tax lists. For the purpose of the survey, the counties of England were grouped into circuits, probably seven in number. Stephenson (1954: 184–205) lists them as: I Kent, Sussex, Surrey, Hampshire, Berkshire II Wiltshire, Dorsetshire, Somersetshire, Devonshire, Cornwall III Middlesex, Hertford, Buckingham, Cambridge, Bedford IV Oxford, Northampton, Leicester, Warwick V Gloucester, Worcester, Hereford, Stafford, Shropshire, Cheshire VI Huntingdon, Derby, Nottingham, Rutland, York, Lincoln VII Essex, Norfolk, Suffolk The counties and circuits are mapped in Figure 1.2. Each circuit was visited by a team of commissioners, bishops, lawyers and lay barons who had no material interests in the area. The commissioners were responsible for circulating a list of questions to landholders, for subjecting the responses to a review in the county court by the hundred juries, often consisting of half Englishmen and half Frenchmen, and for supervising the compilation of county and circuit returns. The circuit returns were then sent to the Exchequer in Winchester where they were summarised, edited and compiled into Great Domesday Book.

6

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Figure 1.1 The main roads and boroughs of Domesday England

It is thought that the list of questions answered by the landholders was similar to that contained in the text of Inquisitio Eliensis, a record of the survey of the estates of the Abbey of Ely in six eastern counties. Hamilton (1876:97) translates the questions as: What is the manor called? Who held it in the time of King Edward? Who holds it now? How many hides? How many ploughs on the demesne? How many men? How many villeins? How many cottars? How many slaves? How many freemen? How many socmen? How much wood? How much meadow? How much pasture? How many mills? How many fish ponds? How much has been added or taken away? How much, taken together, was it worth and how much now? How much each freeman or socman had or has? All this at three dates, to wit, in the time of King Edward and when King William gave it and as it is now. And if it is possible for more to be had than is had.

INTRODUCTION AND BACKGROUND

7

Figure 1.2 The Domesday survey circuits

An idea of the kind of information available in the circuit returns can be gained by examining a sample entry from the Domesday Book record for Essex. Figure 1.3 reproduces the entry for Almesteda, a holding of Suen, Sheriff of Essex, in the Hundred of Tendringe, or Tendring. In the upper part of the figure, the entry, in an abbreviated form of medieval Latin, is reproduced (in a printed form) from the Domesday parchment. Below, a translation of the entry from the Victoria County History volume for Essex is displayed. The land area of Almesteda is the site of the modern village of Elmstead. The entry indicates that the manor was held by Robert Fitz Wimarc at the end of Edward the Confessor’s reign, 1066. The entry then indicates that Suen was the tenant-in-chief in 1086, that Siric was his sub-

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PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

tenant, and that in 1086 the manor was assessed for geld (tax) at eight hides. The peasants, who worked on the demesne or home farm in return for protection and the use of small plots of land, numbered fourteen villeins and thirty-one bordars in 1066. Villeins, or villans, tended to have a higher status and larger plots of land than bordars. There were also six serfs, or slaves, who worked on the demesne, probably in association with the ploughteams. In 1086 manpower on the estate was thirteen villans, thirty-six bordars and just one serf. In 1066, twenty-two ploughteams worked the arable land, three of which only worked the demesne and nineteen also the land allocated to the peasants. In 1086, there were four ploughteams only working the demesne and eighteen also working the peasants’ plots. Woodland on the estate in 1086 was measured in terms of the number of swine it could carry, and pasture by the number of sheep that could graze on it. In both 1066 and 1086 there was one mill and one saltpan. There follows a list of livestock and beehives, ‘then’ referring to 1066 and ‘now’ to 1086. A rouncey is a horse, and beasts oxen. Finally, we see that in 1086 the annual value of the manor (the net income accruing to Siric) was 10 pounds (or 200 shillings), and in 1066 the annual value was 9 pounds. It is perhaps worth emphasising that, in contrast to today, the collection of data was a public rather than a private event, society seeing no need for such information to be kept confidential. Questionnaire data were scrutinised in the county court by a jury consisting of local tenants both French and English. As the jurymen possessed knowledge of the area, they were able to assess the information read out to them in court. Concern to obtain a true record is reflected in evidence of disputes between jurors over whether or not rents paid actually reflected the income performance of manors. As a further safeguard the king sent out agents to ensure that the commissioners were carrying out their duties according to his instructions. Domesday Book consists of two volumes: Great (or Exchequer) Domesday and Little Domesday. Little Domesday is a detailed original survey circuit return of circuit VII, Essex, Norfolk and Suffolk. Great Domesday is a summarised version of the other circuit returns sent to the king’s treasury in Winchester. (It is thought that the death of William occurred before Essex and East Anglia could be included in Great Domesday.) The two volumes contain information on the income, tax assessments and resources of most manors in England in 1086, information for 1066, and sometimes for an intermediate year. The data are recorded county by county and within each county on a feudal basis, with the estates of the king followed by those of his ecclesiastical tenants-in-chief and, finally, estates of greater and lesser lay tenants-in-chief. After William’s death, Domesday Book was extensively used to resolve disputes over land. The manuscript refers to itself as the ‘Discriptio’, and it was only in this later period referred to as ‘Domesday Book’, the book of last judgement, for in land disputes there was no appeal beyond its pages—land rights could be traced to Domesday Book but no earlier. Today the original manuscript, together with early summaries of it, can be viewed in the Public Record Office, Chancery Lane, London. Copies and translations are readily available. A printed transcript in Latin, generally known as the Farley text, was published in 1783 (Farley, 1783); and a photozincographic facsimile edition published complete in 1863 (Ordnance Survey Office, 1863). English translations of many counties are contained in the Victoria County History, and in 1975 the so-called Phillimore edition was published (see Morris, 1975). This contains a facsimile of the Farley text together with a popular English translation. To mark the 900th anniversary of the document, Alecto Historical Editions in conjunction with the Public Record Office published, in a number of volumes, the first facsimile of Great Domesday Book and Little Domesday Book in full colour, together with commentaries, translations, maps and appendices (see Williams, 1987).4

INTRODUCTION AND BACKGROUND

9

Figure 1.3 Sample entry from Essex folios: Almesteda, a manor of Suen held by Siric Source: Domesday Book: Vol. II, fo. 48a (Latin from Phillimore edition, English translation Victoria History of Essex: Vol. I, p. 491)

1.4 ECONOMIC ANALYSIS OF DOMESDAY PRODUCTION DATA Production on the Domesday estate Interpretation of the Domesday data requires some notion of the way agricultural production was organised. Although there were local variations and complications, the production system can be characterised as follows. Land was held from the king by tenants-in-chief. With the land came other resources, including peasants, slaves and livestock. A tenant-in-chief might work the resources himself (through a bailiff) or, in exchange for feudal service, grant the land and resources to a sub-tenant, who then became the immediate lord.

10

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

The immediate lord either worked the resources himself or leased all or some of the resources out for a rent (which we might reasonably suppose reflected the resources’ earning capacity). We shall refer to the holdings, interchangeably, as holdings, manors or estates, and the immediate lord in control of the resources as the lord. The annual value of the holding or estate was the annual (net) income accruing to the lord from working the estate, including rents received, and minor income from jurisdiction and other seigneurial perquisites. Agricultural production was carried out on the manor or estate, which was divided into two parts: the lord’s demesne, land used to produce output for the lord; and the peasants’ land, used to maintain the peasants and their ploughteams. Domesday Book provides no information on output from the peasants’ land, but does list the annual value of the estate. In output terms, the annual value can be interpreted as the value added per annum in demesne production, that is the net output (gross demesne production less goods produced to maintain manorial resources) that accrued to the lord from working the estate or, if the estate was leased out, the rent obtained. There is also information on the inputs or resources employed on the demesne. These were essentially fixed in supply in the short run. Although manorialism was less developed in England than in some other parts of Europe, it nevertheless had a strong influence on agricultural production. The manorial system bound bordars and villans, the bulk of the peasantry (freemen and sokemen enjoyed a freer status), to their lord and the manor, the manor being worked by a resident rather than outside workforce of unfree peasants and slaves. The standard contract between lord and peasants involved a given amount of week work (working an agreed number of days a week on the demesne throughout the year) and boon work (occasional services such as ploughing and harvesting, due at the appropriate season). Although some cash transactions occurred, a labour market, as we understand it, was largely nonexistent. Similarly, the various types of land and capital (mainly ploughteams) were relatively fixed in the short run, breeding new ploughteams or clearing available land being a lengthy process. The goods produced on the manorial demesne (such as cereals, vegetables, cheese, meat, wool and honey) were tradeable goods, some of which were traded in local and overseas markets in return for commodities not produced on the estate (such as agricultural tools, military hardware, glass, lead and other building materials, finely crafted furniture, textiles and fine clothing). While the peasants and slaves consumed what they produced, the lord consumed many outside goods. Also, sufficient output needed to be sold to pay the geld—a heavy burden on the manor representing about 15 per cent of the annual value in 1086. In Domesday Economy (section 6.2), Snooks and I attempted to characterise the behaviour of a rational economic agent faced by this production situation. It was argued that a rational manorial lord would have attempted to organise production in a technically efficient way, chosen outputs so as to maximise the net value of goods produced on the demesne, and then traded to maximise utility from consumption.5 Economic analysis of the production data This characterisation of production suggests that, given that producers experienced similar output prices, the relationship between the annual values and resources of estates traces out the technical conditions of production—the annual value being a value added output measure, while the resources indicate the inputs available. In Domesday Economy, constant elasticity of substitution and flexible functional form production functions were estimated, which showed there existed a high degree of substitutability of inputs and outputs in production, and slightly increasing, but close to constant, returns to scale.

INTRODUCTION AND BACKGROUND

11

Two important features of the estimated production functions are, first, that inputs and outputs are relatively easy to measure (in particular, measuring capital, by the number of ploughteams, presents few problems) and, second, as the inputs were fixed in supply, there is no simultaneity estimation problem (as often occurs because usually firms determine both input and output levels: see Domesday Economy, chapter 10). Both of these features aid estimation and interpretation of the empirical production functions.6 The purpose of the current study is to delve deeper into the production relationship and investigate the more interesting question of efficiency in production. The analysis is undertaken at a greater level of detail than in the earlier work; statistical production functions are estimated, but the main focus is a production frontier analysis. An outline of the book is as follows. Efficiency measurement concepts and production frontier theory are reviewed in Chapter 2. Algebraic methods for calculating estate efficiency measures, shadow prices and slack are described in Chapter 3. Chapter 4 contains the frontier efficiency analysis of Essex lay estates, and Chapter 5 provides a review of the efficiency literature and an alternative statistically based efficiency analysis. In Chapter 6, the question of how efficient Domesday manorial production was, given the technology of the period and institutional setting, is examined. The institutional setting, the feudal and manorial systems, inhibited the mobility of inputs (particularly labour). An estimate of the economic cost of this is made. Chapter 6 also contains a preliminary study of beneficial hidation of Essex lay estates using a tax assessment frontier. Finally, the main conclusions of the work are summarised.7 Readers familiar with the efficiency literature may find they only need to read Sections 2.1 and 2.2 of Chapter 2, and can then skip directly to the applications in Chapters 4, 5 and 6. Those less familiar with efficiency theory but not interested in the details of the calculations should read Chapter 2 but skip Chapter 3. Although the issue is dealt with in more detail in Chapter 2, it is perhaps useful to state briefly here that we see the efficiency analysis mainly as a useful way of gaining insights into the production process. The efficiency classification of estates identifies those estates that appear to have transformed resources into net income most effectively, and thus provides a starting-point in the search for reasons why some estates appear to produce more from their endowment of resources than others. We can then examine individual estates; question the production data relating to them and similar estates; question our knowledge about the production process and the assumptions we have made about it; and ask if ancillary information about the estate can throw light on the matter. Rather as a map is a useful tool in the analysis of spatial relationships, we see the efficiency measures as a useful tool for gaining understanding about production relationships.

2 MEASURING EFFICIENCY Theoretical ideas

2.1 INTRODUCTION In this chapter, a method of measuring the efficiency of Domesday estates is developed. The method involves assuming some simple propositions about production technology and generating a production frontier from input and output data. The frontier is then used to assess the efficiency of each production unit. Efficient units are those on the frontier. Inefficient units lie inside the frontier, the degree of efficiency (or inefficiency) of a unit being measured by its distance from the frontier. The exposition draws heavily on Grosskopf’s excellent (1986) article, which builds on the work of Debreu (1951), Farrell (1957), Farrell and Fieldhouse (1962), Shephard (1970, 1974), Afriat (1972), Koopmans (1977), and Färe, Grosskopf and Lovell (1983, 1985).1 Readers familiar with this literature may only need to read the next section, which briefly describes the procedure when the preferred technological assumptions (constant returns to scale and strong disposability of resources and output) are made. Others may be interested to know what economic theory says about measuring efficiency (Sections 2.3 and 2.4); and what alternative (scale and disposability) technological assumptions can be made (Sections 2.5 and 2.6). A related approach to measuring efficiency (the decomposition proposed by Byrnes, Färe, Grosskopf and Lovell, 1988) is described in Section 2.7; and algebraic methods for generating the frontier and measuring efficiency (which are required when there are many resources and estates) are reviewed in Chapter 3. 2.2 BRIEF DESCRIPTION OF THE METHOD Grosskopf (1986) showed how a production frontier can be constructed from observed input and output data given different assumptions about production technology. The assumptions relate to the scale characteristics of production and disposability of inputs. The scale assumptions include variable, non-increasing and constant returns to scale (CRS).2 As a characterisation of the Domesday situation, the CRS assumption appears attractive. This is because production usually involved applying essentially the same process in different multiples, and in these situations output typically increases by approximately the same multiple. As an example, arable agriculture was based on applying oxen ploughteams with their complement of manpower to the land; and it seems reasonable to expect that roughly twice as much land was ploughed in a day with two ploughteams as with

MEASURING EFFICIENCY: THEORETICAL IDEAS

13

Figure 2.1 Resource levels and annual values of three estates

one. Empirical evidence also supports the CRS assumption. Constant elasticity of substitution and flexible form production functions estimated from Domesday production data suggest slightly increasing but close to CRS (see McDonald and Snooks 1986: chapter 10, and Chapter 5 of this book). The method of constructing the frontier can be illustrated by considering the simple example depicted in Figure 2.1. Estate A generates an annual value (V) of 1 pound using 10 units of resource R1 (it produces at point A in the figure), estate B generates V=3 pounds using 20 units of R1 (it produces at B), and estate C generates V=2 pounds using 30 units of R1 (it produces at C). Assuming CRS, estate B is judged to be efficient, and the production frontier is the ray from 0 through B. This can be deduced because, with CRS, when twice as much R1 is employed with estate B’s production procedure, annual value is doubled (so it is possible to produce at B2, where R1=40 and V=6) and, when half as much R1 is employed, annual value is halved (so it is possible to produce at B1/2 where R1=10 and V=1. 5). By employing more or less R1, other points on the ray from 0 through B can be attained; in particular, by using 30 units of R1 an annual value of 4.5 pounds can be generated. A point lying below the ray from 0 through B can be attained with B’s production procedure by disposing of some output or leaving some units of the resource idle. For example, point A can be attained with B’s production procedure by using 10 units of R1 and disposing of two-thirds of the output, or using 10 units of R1 and leaving the resource idle for one-third of the time. The set of all attainable production points is called the production possibility set (PPS). If there is free disposability of the resource and output, it is the frontier and the area below and to the right of the ray from 0 through B.

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The efficiency of an estate can be measured by the ratio of the maximum annual value that can be obtained with CRS technology to the annual value actually obtained. Denoting this ratio by u, estate B’s uvalue is 1, estate A’s u-value 1.5/1=1.5, and estate C’s u-value 4.5/2=2.25.3 With several inputs or resources, there is a choice of disposability assumptions. Two assumptions that have been proposed are strong and weak disposability of resources. Strong disposability of resources requires that, when any resource level (or several resource levels) is increased, technology is such that it is possible to produce the same, or greater, annual value. Congestion, with some resources hampering the production process, is ruled out. Weak disposability of resources requires only that, when all resource levels are increased proportionally, it is possible to produce the same output. The weak disposability assumption severely reduces the production possibility set in places (bringing the frontier in towards the origin) and, despite the fact that some costs may have been incurred to maintain idle resources, the strong disposability assumption would seem to give a closer approximation to agricultural production in 1086. (Disposability assumptions are discussed further in Section 2.6.) With a single resource, as we have seen, a simple two-dimensional diagram can be used to construct the frontier and calculate efficiency values for production units. With two resources a third dimension would be needed, and the frontier would be a hyperplane in two dimensions (rather than a line). With several resources the graphical method becomes non-operational, and algebraic methods must be used. Chapter 3 indicates how the frontier can be constructed and efficiency values calculated using linear programming methods. The linear programming procedure also allows us to calculate resource ‘shadow’ prices and discover if there were ‘slack’ resources on the estates. (A resource shadow price can be interpreted as the increase in annual value that could be achieved by an efficient estate when an extra unit of the resource is made available, and the existence of slack resources indicates that it was possible to produce the same annual value with fewer resources; see Section 2.5 and Chapter 3 for details.) An advantage of this general approach to measuring efficiency is that the frontier is not forced to conform to a simple functional form involving a few parameters (as is often the case with regression methods). The frontier is non-parametric, consisting of a number of hyperplanes connecting a sub-set of the estate observations (the sub-set being the estates judged efficient). In theory, all estates are perceived to share exactly the same frontier, and variation in performance from the frontier is due to inefficiency. In practice, however, measured inefficiency may be due to a number of factors, so efficiency measures must be interpreted with care. The factors include those under the control of the lord or bailiff (such variation being most closely linked to the concept of efficiency); others (including luck, unusual weather and disease) partially or totally outside their control; special production characteristics on individual estates (including variations in the quality of resources, and working arrangements of various classes of labour and peasants’ ploughteams on different estates); and data errors. A disadvantage of the method is that it is likely to be more sensitive to data measurement errors than statistical procedures such as regression. (Hence the great care with which we screen the data; see Chapter 4.) A section of the frontier can be distorted by a few unusual observations resulting from measurement error or special production conditions; and distortion may occur if, in the sample, there are no well-organised estates with a particular resource mix. Despite the limitations, the method provides a useful tool for analysing production, discovering which production units were more successful in transforming inputs into outputs, and gaining insights into why some units appear more efficient than others.

MEASURING EFFICIENCY: THEORETICAL IDEAS

15

Figure 2.2 Technical inefficiency

2.3 MEASURING INEFFICIENCY: THE CASE OF THE COMPETITIVE FIRM The next two sections review what economic theory says about production efficiency. This section deals with the standard case of a competitive firm maximising profit subject to given input and output prices, and the next with the situation faced by a Domesday estate. We begin, then, with the simple case of a firm (or production organisation) producing a single output, subject to fixed input and output prices (that is, these prices are determined by market conditions beyond the firm’s control), with the firm attempting to maximise profit, and investigate how the firm may be inefficient. (a) Technical inefficiency Technical inefficiency is due to excessive input usage. It occurs when a firm produces below its production frontier. The production frontier gives the maximum output that can be produced from prescribed quantities of inputs, the frontier being determined by the technology available to the firm. Consider a simple situation depicted in Figure 2.2. The figure shows how a firm’s output varies with the amount of the single input used in production. The output, y1, is measured up the vertical axis and the input, R1, along the horizontal. The graph indicates that if 3 units of input are used the maximum output that can be produced is 7 units; and if 6 units are used the maximum output is 10 units. If we observe a firm using 6 units of input and only producing 8 units of output (as indicated by point A), then the firm is said to be technically inefficient. A

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Figure 2.3 Two inputs: isoquants and cost contours

measure of the technical inefficiency of the firm is given by the ratio of the maximum output that can be produced to the firm’s observed output: that is, 10/8 (or, alternatively, the reciprocal of this ratio, 8/10). (b) Input allocative inefficiency This is due to using inputs in proportions that are sub-optimal relative to input prices and, consequently, not minimising the costs of production. To illustrate the concept, let us now suppose that the firm uses two inputs, R1 and R2, to produce output, y1. Also, suppose the output can be sold at a fixed price, $1 per unit, and the inputs purchased at fixed prices, $2 (for R1) and $1 (for R2) per unit. Figure 2.3 depicts the situation. R1 is measured along the horizontal and R2 up the vertical axis. Point E represents the activity of a firm that maximises profit. It produces 10 units of output, using 2 units of R1 and 2 units of R2. The y1=10 isoquant has been drawn through E. The isoquant locates all combinations of R1 and R2 that can produce (a maximum of) 10 units of output. If a firm operates with input levels corresponding to a point on the contour and produces 10 units of output, it is technically efficient. For the firm operating at E to be maximising profits, it must be technically efficient. In addition, it must be minimising the cost of producing its output. To see how this condition is depicted in the figure, we have constructed cost contours, which locate input combinations costing the same amount of money. Two cost contours, denoted c=6 and c=8, have been drawn. The $6 cost contour, or c=6 contour, was constructed as follows.

MEASURING EFFICIENCY: THEORETICAL IDEAS

17

First, it was noted that, since the inputs cost $2 and $1 per unit, the cost (c) of R1 units of the first and R2 units of the second input is c=2R1+1R2. Setting c=6 gives 2R1+1R2=6, which, in Figure 2.3, is represented by a line. Setting R1=0 in the equation gives 2(0)+1R2=6, or R2=6; so the c=6 contour passes through the point R1=0, R2=6, that is the point on the vertical axis where R2=6. Setting R2=0, we see that the contour passes through the point R1=3, R2=0, that is the point on the horizontal axis where R1=3. The c=6 contour is the line through these points. Similarly, the c=8 contour is the line through R2=8 on the vertical axis and R1=4 on the horizontal axis. Clearly, costs are reduced by moving in the direction of the arrows drawn at right angles to the contours. It follows that the cost of producing 10 units of output will be minimised at the point on the y1=10 isoquant located as far as possible in this direction. The point occurs at E. Now, suppose we observe a firm producing 10 units of output using 1.5 units of R1 and 6 units of R2 (that is, producing at A in Figure 2.4). This firm (firm A) is technically inefficient, because technology is such that less of both inputs can be used to produce 10 units of output. The y1=10 isoquant (reflecting technology) indicates that a technically efficient firm can produce 10 units of output using 1.1 units of R1 and 4.4 units of R2 (by operating at B). Firms producing at A and B use inputs in the same proportions, 1 to 4 (in the figure this is indicated by A and B both lying on the same ray, 0A, through the origin), but the firm producing at B is technically more efficient. Nevertheless, firm B is producing at higher cost than the profit-maximising firm producing at E. (Cost for firm B is 2(1.1)+1(4.4)=$6.6, and for firm E cost=$6.) Cost can be reduced by using the inputs in

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Figure 2.4 Measuring technical and input allocative inefficiency

different proportions. Note that a firm producing at D is on the c=6 cost contour, and so incurs the same cost as the profit-maximising firm producing at E. One way of measuring the technical inefficiency of firm A is by the ratio of the distances 0B to 0A. 0A is a measure of the inputs actually used by the firm, and 0B is a measure of the minimum inputs that could be used to produce the same output, given that inputs are used in the same proportions. Also the input allocative inefficiency of firm A can be measured by the ratio of the distances 0D to 0B, since the distance 0B reflects the cost incurred by a technically efficient firm producing with firm A’s input proportions and 0D the cost of a technically and allocatively efficient firm producing the same output. (This follows because the cost of producing at D is the same as producing at E.) Hence 0B/0A is a measure of the technical inefficiency of firm A, and 0D/0B a measure of its input allocative inefficiency. (c) Scale inefficiency Not all firms that minimise production costs maximise profit. Figure 2.5 illustrates that the scale of production is also important. The firm producing at F produces 11 units of output and produces this output at minimum cost. The cost of production is $8, and since output sells for $1 per unit the firm’s profit is 1(11) −8=$3. The profit-maximising firm producing at E produces 10 units of output at a cost of $6, so its profit is 1(10)−6=$4. The firm achieves a higher profit by producing at the optimal output level—it is scale efficient. Firm F, although technically and allocatively efficient, is scale inefficient. It produces too much output, receiving less revenue from the last unit produced ($1) than the cost of that unit ($2).

MEASURING EFFICIENCY: THEORETICAL IDEAS

19

Figure 2.5 Scale inefficiency

From this discussion, it is clear that for a firm to be maximising profits (and hence totally efficient) it must be technically, allocatively and scale efficient. Also, for a firm to be minimising the cost of producing its output, it must be both technically and allocatively efficient, although not necessarily scale efficient.4 2.4 MEASURING INEFFICIENCY: THE DOMESDAY ESTATE In Chapter 1, the Domesday estate was characterised as operating with an essentially fixed endowment of resources (or inputs). With this, the lord attempted to maximise the value of net output by choosing which outputs to produce, and organising production in a technically efficient way. A major difference between this production situation and that faced by the competitive firm is the absence of input markets. To begin the discussion of inefficiency in Domesday production, it will be useful to consider the following hypothetical example of manorial production. (a) A hypothetical example of manorial production A Domesday manor has a fixed endowment of resources which cannot be augmented in the short run. Two outputs (y1 and y2) can be produced on the demesne using three production processes. Using process 1 only, after allowing for maintenance of resources, a maximum of 4 units of y2 (and no units of y1) can be produced per year. Using process 2 alone, technology is such that at most 2 units of y1 and 3 units of y2 can

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PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

be produced per annum; and using only process 3 a maximum of 3 units of y1 and 1 of y2 can be produced per year. When two or more processes are used, output varies in proportion to the time spent working each process. Finally, the (net) output can be sold in the local market at 2 pounds per unit for y1 and 3 pounds per unit for y2. The relevant details can be succinctly summarised in the following table. Output per annum Process 1 Process 2 Process 3 Price (pounds)

y1 0 2 3 2

y2 4 3 1 3

The lord attempts to maximise the value of net output by choosing the quantities of outputs to produce, or, equivalently, by allocating production time between the three processes. As a first step in solving this problem, let us find all output combinations that can be produced. If only process 1 is used, then 4 units of y2 and no units of y1 can be produced. This combination of outputs is represented by point A in Figure 2.6. Point B represents the maximum output that can be produced when only process 2 is used, and C the maximum output when only process 3 is used. Now, suppose process 1 is used half the time and process 2 half the time. Using process 1, 1/2(4) units of y2 can be produced; and, using process 2, 1/2(2) units of y1 and 1/2(3) units of y2 can be produced, giving a total of 1 unit of y1 and 3 1/2 units of y2. This combination is represented by point D, which lies halfway along the line between A and B. If process 1 is used for a quarter and process 2 for three-quarters of the time, maximum output is 1/4(4) units of y2 plus 3/4(2) units of y1 and 3/4(3) units of y2, or, in total, 1 1/2 units of y1 and 3 1/4 units of y2. This is represented by point E, which lies on the line between A and B; the distance from E to B being 1/4 of the total distance from A to B. This reasoning indicates that, when process 1 is used part of the time and process 2 the rest of the time, the maximum obtainable output can be represented by a point on the line AB. Similarly, when production time is shared between processes 2 and 3, the maximum obtainable output can be represented by a point on the line BC. It is also possible to use process 1 in combination with process 3. Points on the line AC correspond to maximum output combinations that can be produced. But note that these output levels are less than can be achieved by using process 1 in combination with process 2, or process 2 in combination with process 3, and so will not be chosen by an efficient producer. By an extension of this argument, production time will not be split between all three processes. If output can be disposed of without cost, or resources left idle, then other output combinations can be produced. For example, we have seen that, by using process 3 for the entire time, the lord can produce at C. If output y2 can be disposed of without using up resources (or less y2 produced by leaving some resources idle), then the lord can also produce the output combination represented by F (by disposing of, or not producing, half a unit of y2). By disposing of, or not producing, different amounts of y2, the lord can produce at any point on the vertical line from C to G on the y1-axis. Using this argument, by leaving resources idle or disposing of output, any output combination represented by a point in the region 0ABCG can be attained. The region is called the production possibility set, and the part of the boundary connecting the points A, B, C and G the production frontier.

MEASURING EFFICIENCY: THEORETICAL IDEAS

21

Figure 2.6 Producible output combinations: the production possibility set

To find which combination maximises the value of net output, we now superimpose (net) output value contours on the diagram. Since outputs sell for 2 pounds and 3 pounds respectively, the value (V) of y1 units of the first and y2 units of the second output is V=2y1+3y2. To find the V=6 contour, we set V=6, giving 2y1 +3y2=6. This is represented by the line in Figure 2.7 which passes through the points y1=0, y2=2 and y1=3, y2=0. The V=12 contour is the line passing through the points y1=0, y2=4 and y1=6, y2=0. Value increases as we move in the direction of the arrows drawn at right angles to the contours; and the point of the region 0ABCG which lies furthest in this direction is B. B represents the output combination y1=2, y2=3; and for these outputs V=2(2)+3(3)=13 pounds. A manor operating at B (manor B) is operating efficiently, given its resource endowment, its technology and the prices of outputs. Now, let us suppose we observe a second manor, manor I, with the same resource endowment, using the same technology and facing the same output prices. Manor I operates at point I in Figure 2.8, producing 2 units of y1 and 2 units of y2. It is technically inefficient because more of both outputs can be produced. Thus, with outputs produced in the same proportions (1 to 1), output of both y1 and y2 can be increased to 2 1/3 units (as indicated by point J in the figure). A measure of the technical inefficiency of manor I is given by the ratio of the distance 0J to the distance 0I. Even so, a manor producing at J would not maximise the net value of output (because V=2(2 1/3)+3(2 1/3)=11 2/3 pounds as compared with V=13 pounds, for manor B). By producing the outputs in different proportions (that is, using the processes in a different combination) the value of output can be increased. We say that manor I is output allocatively inefficient. The value of the output combination represented by point K is the same as for point B (both points lie on the V=13 contour), so a measure of the output allocative inefficiency of manor I is given by the ratio of the distance 0K to the distance 0J. Hence, the technical inefficiency of manor I is given

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Figure 2.7 Producible output and value of net output contours

by 0J/0I, and output allocative inefficiency by 0K/0J. Finally, the overall inefficiency of manor I can be measured by 0K/0I. The inefficiency measures equal one for efficient manors and are greater than one for inefficient manors; and overall inefficiency, 0K/0I, is equal to technical inefficiency, 0J/0I, times output allocative inefficiency, 0K/0J. (As can be seen by writing , and by cancelling 0J.) We see that a manor may be technically but not allocatively inefficient and vice versa, and if a manor is either technically or allocatively inefficient it will exhibit overall inefficiency. Also, notice that the inefficiency measures measure how much extra output can be produced with fixed resources. They are output-based inefficiency measures, and hence differ from the measures we considered when analysing the competitive firm in Section 2.3. (Those measures were input-based inefficiency measures. They indicated by how much inputs could be reduced yet maintain given output levels, or output cost.) Finally, notice that in the foregoing illustrative analysis of Domesday production no mention was made of input allocative inefficiency. (Recall that this occurred with the competitive firm when input levels were chosen in the wrong proportions relative to input prices.) The reason is that, although the manorial lord is able to allocate resources between processes and thus produce different outputs, in the short run total resources are in fixed supply. Hence, output allocative inefficiency is possible, but not input allocative inefficiency. Similarly, since the lord operates with a fixed resource endowment, he is not able to vary the scale of production in the short run, and so scale inefficiency is not possible. In the longer run, of course, resource levels on Domesday estates were less rigid, and both scale and resource proportions could be modified.

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Figure 2.8 Measuring inefficiency of a Domesday manor

(b) Generalising the results The example of manorial production just considered has many features typical of Domesday production. It is, of course, a simplification of the situation. For example, there are only two outputs, the expositional advantage of this being that the production decision problem can be analysed graphically. Algebraic analysis (see Chapter 3) indicates that the results readily generalise to situations with more than two outputs. Also, a particular technology (the three production processes) was specified. This was done to show how the production frontier and production possibility set are determined. The analysis of efficiency does not require that technology be of this special form. Whatever the nature of technology, it and the resource endowment will determine a production possibility set similar to that in the example, although the set may not be bounded by lines (or linear segments). For example, it may have a curved production possibility boundary such as the curve AD in Figure 2.9. Another possibility is that part of the boundary is a curved and part is a linear segment, as the curve from A to B, the linear segment or line BC, and the curve CD (in Figure 2.9). If an estate is not producing on its production frontier, then it is technically inefficient. The prices of the outputs (and demand conditions generally) determine the output mix that maximises the value of net output. For example, in Figure 2.9, if the production possibility set is the set with a curved frontier AD, and prices are such that FG is a net output value contour, the lord will maximise the value of net output by producing at E (that is, produce E1 units of y1 and E2 units of y2). If the estate in fact produces at I (producing I1 units of

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Figure 2.9 Production possibility sets and inefficiency measures

y1 and I2 units of y2), then its technical inefficiency is measured by 0J/0I, its output allocative inefficiency by 0K/0J, and overall inefficiency by 0K/0I. In the example, it was assumed that the manor could sell outputs at fixed prices. This may be a reasonable assumption; however, for large Domesday estates it is possible that output prices were affected by the amounts sold. The lord would have needed to take this into account when choosing which output levels to produce. Another complicating factor is that the average prices at which outputs were sold may have varied a little between the market centres of Essex, so that the output mix that maximised the net output value for an estate selling at one centre was not exactly the same as that selling at another. Finally, the Domesday estate has been characterised as having resources absolutely fixed in supply in the short run. This is a simplification of the situation. Some opportunities for altering input proportions existed (see Section 6.3); so, although estate overall inefficiency measures mainly consist of technical and output allocative inefficiency, they also contain a component of input allocative inefficiency.5 (c) Applying efficiency concepts to Domesday data Having theoretically developed a method of measuring inefficiency, we now examine how these concepts can be applied to Domesday data. The first observation is that we do not have detailed information on the production processes available to Domesday estates. Nevertheless, much is known about the general nature of agricultural production, and (as

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was shown in Section 2.2) by making assumptions about the general characteristics of production and using the available input/output data a frontier can be constructed. Unfortunately, the limited nature of the data precludes us from obtaining separate measures of technical and allocative inefficiency. Although Domesday Book contains information on the value of net output and resources, there is no information on the quantities of outputs produced or the prices of outputs. Consequently, it will only be possible to obtain estimates of the overall inefficiency of estates, the estimates being a mixture of technical and allocative inefficiency. Moreover, when interpreting the inefficiency measures (or, as they will be called, efficiency measures) it is important to bear in mind that we do not have complete information on the production situation faced by estates. (Such information was implicitly assumed in the previous discussion.) There may be data errors. Input and net output information may not be entirely accurate; and, in any event, information is incomplete. We have no information on resource quality. Doubtless, some peasants were better workers than others, livestock were not of uniform quality, and there were variations in the productive capacity of pasture and woodland. Although there was some uniformity within the county, across estates there were variations in working arrangements of the various classes of labour and how peasants’ ploughteams were employed on the demesne. Also other factors, some not recorded, may have affected the productivity of resources. Examples of such factors are tenancy arrangements, ease of transportation and variation in output prices across market centres in the county. Because of this, care must be taken when interpreting efficiency measures. If our analysis indicates that an estate was inefficient, this will not necessarily imply that the value of net output could have been increased by operating the resources more effectively. Instead it may indicate that not all resources have been recorded; or the estate had poor quality resources, or unfavourable production or marketing conditions; or a misfortune (such as disease), which was partially or totally beyond the control of the lord, occurred.6 The analysis will provide a classification of estates into efficient and inefficient estates in this general sense, with each estate being assigned an efficiency measure. The next stage is to explain why some estates appear more efficient than others. This will be done by relating the estate efficiency measures to factors affecting production and marketing, such as soil type, tenancy arrangement, the size of the estate, whether agriculture was predominantly arable or grazing, who was the tenant-in-chief, and which town the nearest market centre. 2.5 TECHNOLOGICAL ASSUMPTIONS: SCALE Returning to the illustrative example of production on three Domesday estates (A using R1=10 to generate V=1, B using R1=20 to generate V=3, and C using R1=30 to generate V=2; see Figure 2.1), we now consider alternative scale assumptions to constant returns to scale (CRS). Recall that, with CRS, B is the only efficient estate, the frontier is the ray from 0 through B, and the production possibility set (PPS) the area below and to the right of the frontier. A’s u-value is 1.5 and C’s uvalue 2.25. An alternative way of generating the frontier (suggested by Afriat, 1972) is to argue that it is reasonable to suppose that technology was such that any estate could have operated in the same way as the observed estates, or operated using one estate’s procedure for part of the time and another’s for the remainder of the time. This technology is referred to as variable returns to scale (VRS) technology because returns to scale can vary at different points on the frontier.

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Figure 2.10 The production possibility set implied by variable returns to scale technology

It is useful to think of the way an estate operated as being a production process. If an estate operated using estate A’s production procedure or process, it would operate at A in Figure 2.10; if it used B’s process, at B; and, if it used C’s process, at C. Now consider an estate using A’s process for half of the time and B’s process for the remainder. Using A’s process half of the time 5 units of R1 would be used to generate V=0.5 pounds, and using B’s process half the time 10 units of R1 would be used to generate V=1.5 pounds. In total, 15 units of R1 would be used to generate V=2 pounds, locating D halfway along the line from A to B. It is easy to show that, if A’s process is used a quarter of the time and B’s three-quarters of the time, the point along the line halfway between A and D is located; and hence deduce that, by using A’s process for part of the time and B’s for the remainder, any point along the line AB can be attained. With free disposability of output any point below a point on the line AB can be attained (such points include, for example, F and E), and with free disposability of R1 (that is, R1 can be left idle without cost) any point to the right of a point on AB can be attained (including the points on the horizontal line from B). With free disposability of V and R1, any point to the right and/or below a point on AB can be attained. The frontier consists of the line segments A to B and the horizontal line from B. The PPS is the shaded area in the diagram. (Notice that, by using A’s process some of the time and C’s process the remainder, any point along the line AC can be attained; and, by splitting time between B’s and C’s processes, any point on the line BC attained, but these points lie below the frontier and do not enlarge the PPS.) With VRS technology, estates A and B are efficient, and C inefficient with a u-value of 3/2.7 The frontier indicates that the maximum annual value that can be generated by an estate with C’s resource level (R1=30) is V=3. This is the same annual value generated by estate B using only 20 units of

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R1. For an efficient estate producing with R1=30, there is said to be ‘slack’ in R1. The amount of slack is the amount of R1 available less the smallest amount of R1 that will generate an annual value of 3 pounds (that is, 30–20=10 units of R1). Positive slack in a resource indicates that with less of the resource the same annual value could have been generated. It does not necessarily mean that some of the resource was actually idle, but it does indicate that, at the margin, the resource made no contribution to annual value. (When this is the case, the resource shadow price is zero; see Sections 3.3 and 3.6.) The VRS frontier, at a particular resource level, is more reliant on the production experience of estates with similar resource levels than the CRS frontier. When generating the CRS frontier a global scale condition (CRS) was imposed, so the frontier at any resource level may be generated by an estate with a much different resource level. With VRS it is the observed estates in the locality of the resource level that determine the frontier. In this sense it can be said that the VRS frontier is ‘locally determined’, whereas the CRS frontier is more ‘globally determined’. Also, it can be argued that the VRS frontier is more ‘empirically determined’ (influenced more by the data) and less by technological assumptions. It is sometimes said that the CRS technology is a more ‘restrictive’ technology than VRS, in that it is based on more restrictive technological assumptions. Whilst we can interpret production at D as being achieved by using A’s process half the time and B’s process the remainder, this interpretation should not be taken too far. There may be a much simpler way of describing production at D in terms of the underlying simple production processes. For example, it may be that at A two simple production processes were used to produce wheat and wool, at B a single process was used to produce barley, and production at D was achievable by using the simple processes in combination. It may not have been necessary literally to produce in the same way as estate A for half the time and the same way as B the remainder. Other methods of generating a frontier are based on the idea that it is reasonable to suppose that, when resources are decreased proportionally from an observed production point, the same proportion of output (or annual value) can be generated. Estate B generates V=3 with R1=20. If R1 usage is halved to R1=10, then, it is argued, technology will be such that half the original annual value can be generated, that is, G, where R1=10, V=1.5 is in the PPS (see Figure 2.11). G is achieved by using B’s process, but at a reduced scale. Similarly, production at H, where R1=5 and V=0.75, is possible. Given this assumption about technology, the frontier is the ray from 0 to B and the horizontal line from B; and the PPS is the frontier and the points below and to the right of the frontier. B is the only efficient estate. A’s u-value is 1.5/1=1.5 and C’s u-value 3/2=1.5. This method of generating the frontier was suggested by Färe, Grosskopf and Lovell (1983), and is referred to as a non-increasing returns to scale (NIRS) frontier, because on some points of the frontier (for example, at G) there are CRS, and at others (for example, at K) decreasing returns to scale, but nowhere increasing returns to scale. An alternative NIRS frontier has been proposed by Koopmans (1977). He argued that it is reasonable to suppose that technology is such that points such as I, J, K and L can be generated. I is generated by using resources to produce in the same way as at A and B (at A, R1=10, V=1; at B, R1=20, V=3; and, at I, R1=10 +20=30, V=1+3=4); K is generated by using resources to produce in the same way as at A and C; L by using resources to produce in the same way as at B and C; and J by using resources to produce in the same way as at A, B and C. The frontier consists of the line segments, the ray from 0 to B, the line from B to I, the line from I to J, and the horizontal line from J. The PPS is the frontier and the points below and to the right of the frontier. B is the only efficient estate, A’s u-value is 1.5, and C’s u-value is now 4/2=2.

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Figure 2.11 Production possibility sets implied by variable, non-increasing and constant returns to scale technologies

Four ways of deriving a frontier have been described. From Figure 2.11, we can infer that, as we move from the CRS frontier to Koopmans’ NIRS frontier, to Färe, Grosskopf and Lovell’s NIRS frontier, and then to the VRS frontier, parts of the frontier contract to the origin and the PPS is reduced. Consequently, for any estate, its u-value will tend to be smaller as we move from the CRS through to the VRS frontier. (It will tend to be smaller in the sense that the u-value will either be the same, or smaller, but not larger.) Put another way, when CRS is assumed, an estate’s u-value will be greater than or equal to the u-value obtained when Koopmans’ NIRS technology is assumed. This u-value will be greater than or equal to that obtained when Färe, Grosskopf and Lovell’s NIRS technology is assumed, which in turn will be greater than or equal to the u-value obtained when VRS technology is assumed. As higher u-values are associated with greater inefficiency, the estate will tend to appear less inefficient (more efficient) as we progress from the CRS to VRS technology. In the empirical analysis reported in Chapter 4, the focus is on efficiency as determined by CRS technology. There are three main reasons for this. First, the nature of agricultural production suggests that CRS is a plausible assumption (production on larger estates tended to involve using the same basic processes as on smaller estates, but in larger multiples—an example being the use of ploughteams). Second, empirical evidence from estimated production functions indicates close to CRS (see Chapter 5). And, third, the CRS frontier is a simple and easily interpreted standard against which to assess efficiency (whereas the other frontiers are more complex). The CRS efficiency analysis is complemented by an analysis assuming VRS —this is the most empirically based (and least restrictive) frontier, lying at the other extreme of the spectrum from CRS. By

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undertaking the efficiency analysis using alternative technological assumptions, an idea of the sensitivity of the results to different assumptions can be obtained. Because the true technology is not known with certainty, it is sometimes difficult to discriminate between competing hypotheses. As an example, the efficiency analysis of Domesday Essex estates described in Chapter 4 indicates that, when CRS technology is assumed, larger estates tend to be more efficient. This result can be interpreted in several ways. First, the CRS assumption may be accepted and the inference made that larger estates were more efficient. A second interpretation is that larger estates were possibly not more efficient but the true frontier had mildly increasing returns to scale, the estimated CRS frontier being regarded as a slight misspecification of the true efficient production situation. A third possibility is that both hypotheses, larger estates more efficient and mildly increasing returns to scale, are true. If in reality this was the case, we would expect to find larger estates more efficient when CRS technology is assumed, and both larger estates more efficient and mildly increasing returns to scale when VRS is assumed.8 2.6 STRONG AND WEAK FREE DISPOSABILITY OF RESOURCES When more than one resource is used in production, the condition that there is free disposability of resources can be formulated in a number of ways. One possibility is strong free disposability of resources, which requires that when any resource level (or several resource levels) is increased technology is such that it is possible to produce the same, or a greater, annual value. Strong free disposability of resources rules out congestion, with some resources hampering the production process. A second possibility is weak free disposability of resources which only requires that when all resource levels are increased proportionally (for example, all resource levels are doubled) it is possible to produce the same or a greater annual value. Clearly, strong free disposability of resources is a stronger condition, and if technology is such that it holds, then weak free disposability of resources must hold; but weak free disposability of resources does not imply strong free disposability. Figure 2.12 illustrates the difference between the concepts. There we have assumed that estates operated with two resources, R1 and R2. Suppose we know that an estate operated at A, using 2 units of R1 and 2 units of R2, to generate 6 units of V. If technology allowed strong free disposability of resources, then we can infer that it was possible for an estate operating at B, where R1=2 and R2=3, to generate at least 6 units of V. Hence, if in fact an estate operated at B and generated only 5 units of V, then this estate is revealed to be inefficient. Also, with strong free disposability of resources technology, estate A’s production implies that an estate operating at C with 4 units of R1 and 4 units of R2 could have generated at least 6 units of V. If an estate operated at C and generated only 5 units of V, then that estate was inefficient. Notice that if, instead, technology only allowed weak free disposability of resources, then we would not be able to infer that the estate producing at B was inefficient (because resource levels have not increased proportionally); however, we would still be able to infer that the estate producing at C was inefficient.9 If strong rather than weak free disposability of resources is assumed, the production possibility set will be larger, and estate u-values tend to be larger (in the sense that for any estate the u-value may be the same, or larger, but not smaller). Estates will tend to appear more inefficient. Some Domesday estates operated with several resources, but most estates were endowed with only a few. In this circumstance, the production possibility set assuming weak disposability of resources is very much smaller than that assuming strong disposability. As a consequence, although there may have been instances of congestion, the strong disposability assumption would appear to give a better approximation to the Domesday situation.

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Figure 2.12 Weak and strong free disposability of resources

In the empirical work reported in Chapter 4, we focus on the efficiency analysis of Essex lay estates assuming constant returns to scale, strong disposability of resources technology. (This is referred to as CS technology.) We also describe in some detail results using variable returns to scale, strong disposability of resources technology (or VS technology) and summarise those using constant returns to scale, weak disposability of resources (CW) technology and variable returns to scale, weak disposability of resources (VW) technology.10 From the above discussion it is clear that, for any estate, its u-value when CS technology is assumed must be greater than or equal to its u-value when CW technology is assumed. Also, the u-value when VS technology is assumed must be greater than or equal to that when VW technology is assumed; the u-value when CS technology is assumed must be greater than or equal to that when VS technology is assumed, and the u-value when CW technology is assumed greater than or equal to that when VW technology is assumed.10 2.7 A DECOMPOSITION INTO SCALE, CONGESTION AND TECHNICAL INEFFICIENCY COMPONENTS In (1988) Byrnes, Färe, Grosskopf and Lovell (BFGL) advocate using a decomposition of inefficiency into scale, congestion and technical components, arguing that ‘Identification of these three components provides an aid to management in its search for the sources of, and remedies for, productivity gaps’.11 While this may often be the case, the decomposition can give misleading results when applied to a constant returns to scale economy. Indeed, the interpretation of the decomposition depends critically on the

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(true) nature of the technology, so that what is labelled scale inefficiency or inefficiency due to congestion may in fact be technical inefficiency. This can be shown by considering two simple examples. The first involves one input (resource) and three producing units (for example, estates); and the second two inputs and three units.12 One input With just one input, measuring efficiency (or productivity) by BFGL’s method is simplified because then there can be no congestion and there is no distinction between weak and strong disposability of inputs. Refer again to the example discussed in Section 2.5 involving three estates operating at A, B and C, with a single resource R1 (see Figure 2.11). Recall that when variable returns to scale (VRS) technology (with free disposability of output, measured by annual value, and free disposability of the resource, R1) is assumed the production frontier is the line segments, A to B, and the line from B through K. The production possibility set is the shaded area. With Färe, Grosskopf and Lovell non-increasing returns to scale (NIRS) technology, by reducing the scale of output by some proportion, output (annual value) is reduced in proportion, so the frontier is 0B and the line from B through K. With constant returns to scale (CRS), the frontier is the ray from 0 through B. BFGL advocate first measuring efficiency (productivity) relative to the most restrictive technology, CRS. The efficiency measures they use are defined a little differently from the measures we have used. For any producing unit, BFGL’s efficiency measure, K(V,R1), is defined as the actual output divided by the maximum output that can be obtained with the CRS technology. Thus, for estate A K(V,R1)=2/3, because actual output is 1 unit, but extending the vertical line from the R1 axis through A to the ray 0B we see that with CRS 1.5 units can be produced. BFGL’s efficiency measures are simply the reciprocals of the measures we have used. Table 2.1 gives the efficiency measures under CRS, NIRS and VRS for all three estates (or producing units) A, B and C. W*(V,R1) and W(V,R1), the efficiency measures under, respectively, NIRS and VRS, are similarly defined as the ratio of the actual to the maximum output that can be obtained with that technology. Table 2.1 Example 1: efficiency measures for producing units A, B and C

CRS: NIRS: VRS: S(V,R1)=K(V,R1)/W(V,R1) Returns to scale

R1 V max V K(V,R1) max V W*(V,R1) max V W(V,R1)

A

B

C

10 1 3/2 2/3 3/2 2/3 1 1 2/3 IRS

20 3 3 1 3 1 3 1 1 CRS

30 2 9/2 4/9 3 2/3 3 2/3 2/3 DRS

BFGL define a measure of scale efficiency, S(V,R1)=K(V,R1)/W(V,R1). It follows that K(V,R1)=S(V,R1).W (V,R1) and K(V,R1) can be decomposed into scale, S(V,R1), and technical W(V,R1) efficiency. They argue that a producing unit exhibits CRS, if S(V,R1)=1=W(V,R1), increasing returns to scale (IRS), if S(V,R1)<1 and K(V,R1)=W*(V,R1), and decreasing returns to scale (DRS), if S(V,R1)<1 and K(V,R1)<W*(W,R1).

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Now, suppose the true technology is CRS, such that V=0.15R1 for all R1>0. It follows that B is efficient, but A and C are technically inefficient. None of the units is scale inefficient—indeed, technology is such that there are no advantages or disadvantages in producing at one scale level rather than another. Nevertheless, BFGL’s measures indicate that A is scale, but not technically, inefficient, and locally there are increasing returns to scale. C is both scale and technically inefficient, with locally decreasing returns to scale. The measures provide misleading (incorrect) information; the problem is one of technical inefficiency, not that the units are run at wrong scale levels. If the true technology is NIRS, but not CRS (so the frontier is 0B and the line from B through K), again B is efficient. A is technically inefficient, but not scale inefficient; and C is both technically and scale inefficient. BFGL’s measures reflect the true situation for B and C, but not A. (The measures indicate scale, but not technical inefficiency, for A.) Only if the true technology is VRS, but not NIRS, are the measures useful, correctly decomposing inefficiency into scale and technical inefficiency components, and indicating whether scale should be increased or decreased. For other technologies there is a tendency for the measures to inflate scale inefficiency at the expense of technical inefficiency. Correct interpretation depends critically on the nature of the true technology. Several inputs: further problems With several inputs congestion is possible, and the problem is compounded. Again BFGL’s decomposition of inefficiency (now into scale, congestion and technical components) is only sensible if the least restrictive technology (now VRS, weak disposability of inputs) is true, and more restrictive technologies are not. Even then there is a further complication because there are two possible decompositions into scale and congestion components. The first decomposition (described by BFGL) is to define the scale component by comparing efficiency measures calculated assuming CRS, strong disposability of inputs (or CS) technology and VRS, strong disposability of inputs (VS) technology. (The scale component equals the efficiency measure assuming CS technology divided by the efficiency measure assuming VS technology.) The congestion component is obtained by comparing efficiency measures for VS technology and VRS, weak disposability of inputs (VW) technology. (It equals the efficiency measure assuming VS technology divided by the measure assuming VW technology.) The Table 2.2 Measuring scale and congestion inefficiency components by two decompositions Decomposition 1

Decomposition 2

Compare efficiency measures assuming CS and VS technologies. Result: Scale component Compare efficiency measures assuming VS and VW technologies. Result: Congestion component

Compare efficiency measures assuming CS and CW technologies. Result: Congestion component Compare efficiency measures assuming CW and VW technologies. Result: Scale component

second decomposition is to define the congestion component first, by comparing efficiency measures for CS and CRS, weak disposability of inputs (CW) technologies, and then the scale component by comparing CW and VW efficiency measures (see Table 2.2). It is easy to construct examples for which scale and congestion components depend on the decomposition used. Consider Example 2, with three producing units A, B and C, inputs R1 and R2, and production as

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indicated in Table 2.3. The table indicates efficiency measures for C under different technological regimes. Under Decomposition 1, scale and congestion inefficiencies are, respectively, 1 and 3/4; but, under Decomposition 2, 3/4 and 1 respectively.13 In conclusion, although BFGL’s decomposition may seem to hold promise of a valid method of measuring efficiency independent of technological assumptions, this is not the case. The decomposition into scale, congestion and technical inefficiencies is somewhat arbitrary, and for many technologies can give Table 2.3 Example 2: three units A, B and C, two inputs R1 and R2, production efficiency measures for C with different technologies R1 R2 V

A

B

C

1 1 2

2 1 4

2 2 3

Efficiency of C, assuming different technologies: CS VS CW VW

3/4 3/4 3/4 1

(compare C with A or B) (compare C with B) (compare C with A)

Components

Scale

Congestion

Decomposition 1 Decomposition 2

1 3/4

3/4 1

misleading information. Scale and congestion components tend to be inflated at the expense of the technical inefficiency component. Nevertheless, if little is known about the (true) technology, it can be a valuable tool for analysis. Example 1 indicates that, if the true technology is CRS, the decomposition can be misleading. Consequently, as there are strong theoretical and empirical reasons for suspecting that the Domesday technology was close to CRS, the decomposition was not employed in the efficiency analysis of Essex lay estates described in Chapter 4.

3 ALGEBRAIC METHODS Linear programming

3.1 INTRODUCTION Some basic characteristics of linear programming problems are reviewed in the next section, and the dual problem in Section 3.3. Section 3.4 shows that there can be substitution between resources, even if production processes employ resources in fixed proportions. Section 3.5 indicates how the problem of measuring the efficiency of an estate, given different technological assumptions, can be formulated as a linear programming problem, and the last section clarifies the interpretation of resource shadow prices and slack values. 3.2 BASIC CHARACTERISTICS OF LINEAR PROGRAMMING PROBLEMS In a linear programming (LP) problem a linear function in some variables is optimised, subject to a set of linear (inequality or equality) constraints relating the variables, and a set of non-negativity conditions on the variables. An example is: Example 1.

(3.1)

(3.2)

(3.3)

The linear function (3.1) that is maximised is called the objective function. It is maximised by choosing values of the variables x1 and x2 which satisfy the linear constraints (3.2) and non-negativity conditions (3. 3). A set of values of the variables that satisfy the constraints and the non-negativity conditions is called a feasible solution, and a feasible solution that maximises the objective function an optimal feasible solution (OFS). For any problem, there may be no OFS, a unique OFS or several OFSs. When the variable values that constitute an OFS are substituted in the objective function, the optimal value of the objective function is generated. In the above LP problem (as we shall see) there is a unique OFS, x1=2, x2=8. The optimal value of the objective function is V=3(2)+4(8)=38.

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In Example 1, the objective function is maximised, but in some LP problems the objective function is minimised. Also, sometimes the constraints are linear equalities or ‘≥’ inequality constraints or a mixture of equality and inequality constraints. In terms of solving LP problems, however, the format of the example is more general than might be supposed. This is because a ‘≥’ inequality can be rewritten as a ‘≤’ inequality constraint by multiplying both sides by −1 (for example, 4x1+2x2≥6 is equivalent to (−1)(4x1+2x2)≤(−1)6, or −4x1–2x2≤−6), and an equality constraint can be rewritten as two inequality constraints (for example, 4x1+2x2=6 is equivalent to the two inequalities 4x1+2x2≥6 and 4x1+2x2≤6). Also, the OFS to a minimisation problem can be found by maximising the same objective function multiplied by −1. (For example, the OFS to the problem:

is x1=2, x2=8, identical to the OFS in the example. The optimal value of the objective function is V*=−3(2) −4(8)=−38, which is the optimal value in the maximisation problem multiplied by −1.) Example 1 can be readily solved by graphical methods. In Figure 3.1, x1 is measured along the horizontal and x2 up the vertical axis. First, the set of feasible solutions, called the feasible region, is determined. It consists of all pairs of x1, x2 values satisfying (3.2) and (3.3). The non-negativity conditions, x1≥0 and x2≥0, restrict the feasible region to the positive quadrant (points on or to the right of the vertical axis and on or above the horizontal axis). The constraint, x1≤4, restricts the feasible region to points on or to the left of a vertical line through D, the point on the horizontal axis corresponding to x1=4, and the constraint, x2≤8, to points on or below the horizontal line through A, the point on the vertical axis corresponding to x2=8. Finally consider the inequality, 2x1+x2≤12. The equation 2x1+x2=12 can be represented by a line through the points F on the horizontal axis and G on the vertical axis. (At F, x1=6 and x2=0, so the equation is satisfied, 2(6)+0=12; and at G, x1=0 and x2=12, so again the equation is satisfied, 2(0)+12=12. Similarly at any other point on the line the values of x1 and x2 satisfy the equation.) Also, for any point to the left of the line, the x1, x2 values are such that 2x1+x2<12 (for example, at the origin, the point where x1=0 and x2=0, 2 (0)+0<12). It follows that the inequality 2x1+x2≤12 restricts the feasible region to points on or to the left of the line through F and G. Imposing all restrictions on the feasible region, it is clear it consists of the shaded area 0ABCD. To find the feasible solution that maximises the objective function we super-impose a contour of the objective function on the diagram. The V=6 contour is generated by setting the objective function equal to 6, that is, 3x1+4x2=6. The contour passes through the point J where x1=0 and x2=1.5 (because 3(0)+4(1.5) =6) and the point K where x1=2 and x2=0 (because 3(2)+4(0)=6). The higher V=12 contour is generated by setting 3x1+4x2=12. It passes through E and D and so is parallel with the V=6 contour but above and to the right of it. The OFS is found by moving in the direction (indicated by the arrows) at right angles to the contours until the boundary of the feasible region is reached. This occurs at B, where x1=2 and x2=8. These values of x1 and x2 generate the optimal objective function value, V=3(2)+4(8)=38. In Example 1 there is a unique OFS, but some LP problems have no OFS. Thus, if in the example, in addition to the restrictions (3.2) and (3.3) there had been a further constraint x1≤−1, the feasible region would be empty, and an OFS would not exist. Sometimes there are several OFSs. For example, if the objective function to Example 1 had been V=2x1 +x2, then the contours would be parallel with the line through B and C associated with the constraint 2x1 +x2≤12. Now, when we move in the direction at right angles to a contour, the boundary of the feasible

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Figure 3.1 The optimal feasible solution to Example 1

region we reach is the line segment BC, so any of the x1, x2 values corresponding to points on this line segment (including the values x1=2, x2=8 at B and x1=4, x2=4 at C) is an OFS. When there are more than two variables, solving LP problems by graphical methods becomes difficult, if not impossible. Fortunately, more complex problems can be solved by algebraic search procedures. One well-known procedure is the simplex method, originated by Dantzig (see Wood and Dantzig, 1951; and Dantzig, 1951a, b, c, d). This method utilises a property of OFSs illustrated above: namely that if an OFS exists, then it will lie on the boundary of the feasible region, and even if there are several OFSs at least one will be a corner or extreme point such as B. A number of computer programs are available to solve LP problems, including LINDO (see Schrage, 1989), and the LP problem is discussed in many textbooks. Chiang (1984) is a fairly elementary treatment, and Allen (1959), Gale (1960), Gass (1964), Hadley (1962), Koopmans (1951) and Lancaster (1968) are more advanced. 3.3 THE DUAL For any LP problem, there is a second, associated problem called the dual problem, or the dual. In relation to the dual, the original problem is referred to as the primal problem, or the primal. One way in which the

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primal and dual problems are related is that, if they have an OFS, the optimal value of the objective function in the primal is equal to the optimal value of the objective function in the dual. The primal and dual problems have a number of other mathematical properties, but of particular interest is an economic interpretation in terms of imputed or shadow prices that can sometimes be placed on the dual solution. This interpretation is best-discussed by example. Consider the following hypothetical production problem faced by a manorial lord. The lord can produce wool or grain using capital (including land) and labour. An amount of wool that contributes a pound to the annual value (or net income) of the manor requires the use of 4 units of capital (denoted R1)and 2 units of labour (denoted R2). Grain can be produced by working the land with more or less labour. The relatively labour-intensive method requires 1 unit of capital and 4 units of labour to produce sufficient grain to contribute a pound to the annual value of the manor; and the relatively capital-intensive method uses 2 units of capital and 3 units of labour to produce an amount of grain that adds a pound to the manor’s annual value. The lord’s objective is to maximise the annual value of the manor subject to available resources; and there are 12 units of capital and 12 units of labour available. This problem can be formulated as an LP problem. The lord is able to use three production processes. The first produces wool, the second grain using a labour-intensive method, and the third grain using a capital-intensive method. Let V1 be the annual value contributed by the first process, V2 by the second and V3 by the third. The process characteristics can be summarised as follows: Process 1:1 unit of V1 requires 4R1 and 2R2. Process 2:1 unit of V2 requires 1R1 and 4R2. Process 3:1 unit of V3 requires 2R1 and 3R2. The objective of the lord is to maximise V1+V2+V3=V. In doing this he is restricted by the resources available to him. In total 12 units of R1 are available. As process 1 uses 4 units of R1 to produce a unit of V1, process 2 uses 1 unit of R1 to produce a unit of V2, and process 3 uses 2 units of R1 to produce a unit of V3, the following restriction on the use of R1 must be satisfied: 4V1+V2+2V3≤12. The resource constraint relating to R2 is: 2V1+4V2+3V3≤12. Hence the problem faced by the lord (which will be referred to as Example 2) is:

Using LINDO or some other computer program, it can be shown that the OFS is V1=1.5, V2=0, V3=3. Process 1 is used to generate 1.5 pounds of annual value, process 3 produces 3 pounds and process 2 is not used at all. The optimal value of the objective function is V=1.5+0+3=4.5, so the total annual value generated is 4.5 pounds. In the OFS all of the available resources are used. From the first constraint we see that R1 usage is 4(1.5) +0+2(3)=12, the amount of R1 available. The constraint is satisfied exactly. From the second constraint we see that all of R2 is used (2(1.5)+0+3(3)=12). It is said there is no ‘slack’ in R1 or R2. When a resource is not fully utilised at an OFS, it is said that there is slack in the resource, the amount of slack being equal to the total amount available less the amount used in the OFS. The dual to the lord’s LP problem is:

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Notice there are three constraints in the dual, corresponding to the three processes in the primal; and two variables, corresponding to the two constraints in the primal. The coefficients (the numbers 4 and 2) relating to the first process appear in the first dual constraint, the coefficients (1 and 4) relating to the second process in the second dual constraint and the coefficients (2 and 3) relating to the third process in the third dual constraint. The coefficients (1, 1 and 1) on the right-hand side of the dual constraints are the coefficients in the primal objective function; and the coefficients (12 and 12) in the dual objective function are the coefficients on the right-hand side of the primal constraints. Finally, the dual objective function is minimised and the constraints are ‘≥’ inequalities. The OFS to the dual is z1=1/8, z2=1/4 and the optimal value of the objective function, =12(1/8)+12(1/4) =4.5, the same value as for the primal. To understand the economic interpretation of the dual, it helps to relate each of the dual constraints to a production process, the first to process 1, the second to process 2, and so on. z1 and z2 can be interpreted as imputed valuations or shadow prices. They are the opportunity costs of R1 and R2, that is, what must be forgone by not using the last unit of the resources. For example, if only 11 units of R1 were available (rather than 12), then it can be shown that the OFS to the resulting dual LP problem is the same as before, but the optimal value of both primal and dual objective functions is 4 3/8, that is 1/8 pound less than before. Hence, the manorial annual value forgone, by not using the last unit of R1, is 1/8 of a pound, the shadow price, z1, of R1. (With only 11 units of R1 available, in the primal, the only change is the first constraint, which becomes 4V1+V2+2V3≤11, and, in the dual, the only change is the objective function, which becomes =11z1+12z2. At the OFS to the dual, =11(1/8)+12(1/4)=4(3/8).) Similarly, we can show that the manorial annual value forgone, by not using the last unit of R2 is 1/4 of a pound, or the shadow price, z2, of R2. A qualification is that this interpretation of shadow prices is only valid if, when the last unit of R1 or R2 is not used, the shadow prices remain unchanged (that is, the OFS to the dual is unchanged). We have interpreted the opportunity cost of R1 and R2 as what must be forgone by not using the last unit of the resources, but we could instead have thought in terms of what would be gained by using an additional unit of the resources. Considered in this way, the shadow price, z1, can be interpreted as the increase in the value of the objective function that can be achieved by relaxing the first primal constraint so that 13 rather than 12 units of R1 are available. Similarly, z2 can be interpreted as the increase in the value of the objective function resulting from a relaxation in the second primal constraint so that an extra unit of R2 is available in production. (Again, this interpretation is only valid if the shadow prices remain unchanged at the new OFS.) Note that, at the OFS, R1 and R2 are fully utilised, hence there is a positive opportunity cost associated with using R1 and R2, and z1 and z2 are positive. However, if at the OFS R1 had not been fully utilised (so there was positive slack in R1), z1 would be zero, indicating a zero opportunity cost of using R1. 3.4 THE SUBSTITUTABILITY OF RESOURCES IN PRODUCTION Besides illustrating the shadow price concept, Example 2 also illustrates an important characteristic of production. This is that, even though production may consist of using processes that employ resources in fixed proportions, it is still possible to substitute between resources, by using the processes in different

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proportions. This can be seen by focusing on processes 1 and 2. Process 1 requires 4 units of R1 and 2 units of R2 to generate a pound of annual value. Resources are used in the ratio 4/2=2. Process 2 requires 1 unit of R1 and 4 units of R2 to generate a pound of annual value. For process 2, the resource ratio is 1/4. By varying the proportions in which the processes are used in production, it is possible to vary the ratio between these limits, as is shown below. Process 1 proportion Resource ratio (R1/R2)

1 2.00

0.9 1.68

0.8 1.42

0.7 1.19

0.6 1.00

0.5 0.83

0.4 0.69

0.3 0.56

0.2 0.44

0.1 0.34

0 0.25

3.5 CALCULATING ESTATE EFFICIENCY MEASURES (a) CRS, one resource Consider again the simple example (referred to in Section 2.2) of three Domesday estates A, B and C generating annual value V by employing a single resource (see Figure 3.2). For estate A, R1=10, V=1, for B, R1=20, V=3 and for C, R1=30, V=2. Assuming constant returns to scale (CRS) technology, the frontier is the line from 0 through B, and the production possibility set (PPS) is the region consisting of the frontier, and the area below and to the right of the frontier. Because annual value is positive for all estates, we can further

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Figure 3.2 Resource levels and annual values of three estates

restrict the PPS to points on or above the R1 axis. Estate B is efficient. Its efficiency value, denoted u, is 1. A’s u-value is 1.5 and C’s u-value 2.25. To calculate estate u-values algebraically, the first step is to derive an expression for the frontier. The frontier (the ray from 0 through B) is generated by using B’s production process at different intensity levels. Introducing an intensity variable, z, which indicates the intensity with which B’s production process is used, the frontier can be described by the two equations

To see this, set z=1, then the equations become V=3 and R1=20, which locate point B; set z=2, then V=6 and R1=40, which locate point B2, and set z=0.5, then V=1.5 and R1=10, which locate B1/2. Clearly, by setting z equal to a suitable positive value, any point on the ray from 0 through B is located. The PPS can be described by the two inequalities (3.4) This is so because any point on the frontier is located by setting z equal to a suitable positive value and setting the ‘≤’ and ‘≥’ inequalities to equalities. But, with z set equal to that value and at least one of the ‘≤’ and ‘≥’ inequalities not set as equalities, (3.4) locates points below and to the right of the point on the frontier (including points directly below or to the right of the frontier point). For example, z=1 locates B on

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the frontier, and, with z=1, the inequalities become V≤3 and R1≥20, which locate points below and to the right of B (an example is C, where V=2 and R1=30). Although (3.4) succinctly locates the PPS, to form the expression (3.4) we needed to know which estates were efficient—information that will usually be unknown until the u-values have been derived. Fortunately, an alternative expression, not requiring this information, locates the PPS. Introducing three intensity variables, z1 relating to estate A, z2 to B and z3 to C, the PPS is located by (3.5) The coefficients (1, 3 and 2) on z1, z2 and z3 in the first inequality are the V-values of estates A, B and C, and the coefficients (10, 20 and 30) on z1, z2 and z3 in the second inequality their R1-values. (3.5) locates the PPS because: (i) Setting z1=z3=0 in (3.5), gives (3.4) (with z redefined as z2), and (3.4) locates the PPS (points on or below the ray from 0 through B and on or above the R1 axis). (ii) Setting z2=z3=0 in (3.5) gives

which locates points on or below the ray from 0 through A and on or above the R1 axis. These points lie in the PPS. Similarly setting z1=z2=0 in (3.5) locates points on or below the ray from 0 through C and on or above the R1 axis. (iii) If z1, z2 and z3 are all non-zero (or two zs are non-zero), (3.5) locates a point lying between the two (extreme) rays from 0 through B and 0 through C and all points below and to the right of it (for example, setting z1=z2=z3=0.5, (3.5) becomes V≤1(0.5)+3(0.5)+ 2(0.5) or V≤3 and R1≥10(0.5)+20(0.5)+30(0.5) or R1≥30, which locates M and all points below and to the right of M, and on or above the R1 axis). Again, all these points lie in the PPS. We can now discover, by algebraic methods, if the PPS is such that an estate with estate A’s resource level (R1=10) could have produced a greater annual value than estate A in fact achieved. First, note that V would be greater if V>1 (1 is the V-value actually generated by estate A) or, alternatively, V=1u, where u>1. The value of u must, however, be such that the estate operated in the PPS, so setting R1=10, V=1u in (3.5), the requirement is (3.6) (Note that u≥0, ensures V≥0.) We need to know the largest value u can take yet V=1u be such that the estate operated in the PPS, so the problem is to maximise u subject to (3.6). This is an LP problem, with variables z1, z2, z3 and u. The OFS can be shown to be z1=z3=0, z2=0.5, u=1.5 and the optimal value of the objective function is u=1.5, which is estate A’s u-value. To calculate estate B’s u-value, set V=3u (3 is the annual value generated by B) and R1=20 in (3.5), to give

and maximise u subject to these conditions.

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The OFS to this LP problem is z1=z3=0, z2=u=1. Estate B’s u-value is 1. To calculate estate C’s u-value, set V=2u and R1=30 in (3.5), and maximise u subject to the resulting conditions. The OFS to the LP problem is z1=z3=0, z2=1.5, u=2.25. C’s u-value is 2.25. More generally, if we rename estate A, estate 1; estate B, 2 and estate C, 3; and denote the ith estate’s annual value and resource levels, Ri and Vi, respectively, the ith estate’s u-value can be calculated by solving the LP problem:

(b) VRS—one resource Figure 3.3 shows the frontier and PPS when variable returns to scale (VRS) technology is assumed. The frontier is the line segments A to B, and the line from B through K. The PPS is the shaded area. A and B are efficient estates with u-values equal to 1, and C’s u-value is 1.5 (see Section 2.5). To obtain an algebraic expression for the PPS, first obtain an expression for a point on the line between the efficient estates A and B. Such points represent production using A’s process some of the time and B’s process the remainder of the time. Introducing intensity variables, as before, points on the line can be expressed by the two equations

For example, setting z1=1, z2=0, the equations give V=1, R1=10, locating point A; setting z1=0, z2=1, they give V=3, R1=20, locating B; and setting z1=0.5, z2=0.5, they give V=1(0.5)+3(0.5)=2, R1=10(0.5)+20(0.5) =15, locating D. By choosing other positive values for z1 and z2, such that z1+z2=1, other points on the line are located. Points in the PPS are points on the line AB, and points below and to the right of points on AB, so the PPS can be expressed by the two inequalities (3.7) To see this, first note that points on the vertical line below A are included in the set, because setting z1=1, z2=0, the inequalities become V≤1, R≥10, so, for example, the point on the R1 axis where R1=10 (where V=0, R1=10) is included. Also, a point such as K (where V=3, R1=40) on the horizontal part of the frontier is included, because by setting z1=0, z2=1, the inequalities give, V≤3, R≥20, which includes K. Finally, a point inside the frontier is included because it lies below and to the right of a point on the line AB. As an example N, where V=1 and R1=20 is below and to the right of D. Setting z1=0.5, z2=0.5 in the inequalities gives V≤2, R1≥15, which includes N. Note that the condition that the zs sum to one excludes points such as G. G at V=1.5, R1=10 is generated by setting z1=0, z2=0.5—and the zs do not sum to one.

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Figure 3.3 Production possibility sets implied by variable, non-increasing and constant returns to scale technologies

Forming (3.7) requires knowledge of which estates are efficient (which will usually be unknown until estate u-values have been derived), but the following alternative expression (not requiring this information) also locates the PPS: (3.8) To calculate estate B’s u-value (as an example), set V=3u, R1=20 in (3.8), and maximise u subject to the resulting conditions. (c) NIRS—one resource With Färe, Grosskopf and Lovell’s non-increasing returns to scale (NIRS) technology, by reducing the scale of output by some proportion, output is reduced in proportion, so the frontier is 0B, and the line from B through K. Points such as G are now in the PPS, so we must allow the sum of the zs to be less than or equal to one. The PPS can be expressed:

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With Koopmans’ NIRS technology, the frontier is the line segments 0B, BI, IJ, and the horizontal line from J. Points such as I, J and L are in the PPS. For the algebraic expression to locate these points in the PPS, no restriction is required on the sum of the zs but each z must be restricted to be less than or equal to one. Hence the PPS can be expressed:

(d) Several resources: strong and weak disposability of resources When more than one resource is used in production, free disposability of resources can be formulated in a number of ways. Strong free disposability of resources requires that when any resource level (or several resource levels) are increased it is possible to produce the same, or a greater, annual value. Consider again the example described in Section 2.6. The example involved production on three estates (A, B and C), using two resources (R1 and R2) to generate annual value, V. The key features can be summarised in the following table (which indicates, for example, that estate A generated V=6 using R1=2 and R2=2). Estate V R1 R2

A 6 2 2

B 5 2 3

C 5 4 4

Assuming strong disposability of resources technology, it is easy to see that A is the only efficient estate (B and C generate less V but use at least as much R1 and R2 as A). Since A is the only efficient estate, its production alone determines the frontier. If CRS technology is also assumed (so CS technology is assumed), the PPS can be expressed

where z1 is the intensity variable relating to estate A. These inequalities do indeed indicate that B and C lie below the frontier in the PPS, and hence are inefficient (setting z1=1 in the inequalities, we see that at B’s resource level, R1=2, R2=3, V=6 on the frontier, but B produces V=5; setting z1=2 in the inequalities we see that at C’s resource level, R1=4, R2=4, V=12 on the frontier, but C produces V=5). Introducing three intensity variables, z1, z2 and z3, the PPS can also be expressed

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(Notice that the coefficients in the inequalities correspond to the row entries in the table above.) To calculate (for example) estate B’s u-value, set V=5u, R1=2 and R2=3 in the above inequalities, and maximise u subject to the resulting conditions. Weak free disposability of resources only requires that when all resource levels are increased proportionally it is possible to produce the same, or a greater, annual value. If weak free disposability of resources and CRS technology (that is, CW technology) is assumed, the PPS can be expressed

(3.9)

To see this, first note that (3.9) indicates that estate A is in the PPS (because, setting z1=1, z2=z3=0 and w1=1 in (3.9), gives V≤6, R1=2, R2=2, which includes estate A at V=6, R1=2, R2=2). Weak free disposability of resources requires that the same annual value can be generated when resources are increased proportionally, so, for example, when resource levels are doubled to R1=4, R2=4, V=6 can be generated. The production point where R1=4, R2=4, V=6 is indeed in the PPS, because, setting z1=1, z2=z3=0 and w1=2 in (3.9), gives V≤6, R1=4, R2=4, which includes the point. We can confirm that when resources are increased by a factor other than two V=6 can be generated, by setting z1=1, z2=z3=0 and w1 equal to the factor of proportionality (w1≥1). Also, the zs can be set equal to other admissible values, and by using a similar argument it can be shown that when resource levels are increased proportionally the same annual value can be generated. Notice, however, that when resources are increased non-proportionally it may not be possible to generate the same annual value. For example, estate A generates V=6 with R1=2 and R2=2; but, on the frontier when R1=2 and R2=3, V=5. (The frontier value for V when R1=2 and R2=3 is obtained by setting z2=1, z1=z3=0 and w1=1 in (3.9).) With CW technology, A and B are efficient with u-values equal to one, and C is inefficient with a u-value of 12/5 (when R1=4, R2=4, on the frontier V=12, as can be seen by setting z1=2, z2=z3=0 and w1=1). To determine algebraically estate A’s u-value (for example), set V=6u, R1=2, R2=2 in (3.9), and solve the resulting programming problem:

Setting w2=1/w1, the first resource equation can be rewritten 2w2=2z1+2z2+4z3 and the second 2w2=2z1+3z2+4z3. The restriction w1≥1 implies that w2>0 and w2≤1, so the programming problem can be re-expressed as:

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(3.10)

If we omit the constraint w2>0, we have an LP problem; and, usually, an OFS to the LP problem will be an OFS to the programming problem (3.10). If, however, in all OFS to the LP problem, w2=0, then an OFS to problem (3.10) can be obtained from the LP problem consisting of (3.10), with w2>0 omitted, and the constraint w2≥w*, where w* is a very small positive number, introduced. 3.6 A THEOREM ON SHADOW PRICES When CRS, strong disposability of resources (CS) technology is assumed, to establish if the ith estate was efficient (given there are m estates and n resources), the following linear programming problem is solved:

where Vi is the annual value of the ith estate and Rij the amount of the jth resource available on the ith estate. The last n constraints relate to the n resources, and, as we have seen, in these situations the corresponding dual variables can be interpreted as resource shadow prices. The interpretation of the shadow prices is particularly interesting in the related problem where Viu (rather than u) is maximised subject to the same n +1 constraints and non-negativity conditions. In this problem, the optimal value of Viu is the maximum annual value that can be produced with CS technology, using estate i’s resource endowment. Consequently, in the dual problem, a resource shadow price can be interpreted as the increase in annual value that can be achieved by an efficient estate operating at estate i’s resource level, when an extra unit of the resource is made available. (The result requires that the shadow price remains unchanged at the new optimal feasible solution, and is only approximately true otherwise.) Below it is proven that these shadow prices can be obtained by multiplying the shadow prices of the original problem (when u is maximised) by Vi. This particular shadow price interpretation appears to be novel and has not been exploited before. Also, note that an efficient estate will have positive slack in the jth resource if the primal constraint corresponding to the jth resource is a strict inequality when evaluated at the z-values of the optimal feasible solution. The amount of slack is the amount of the resource available less the amount used, that is,

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If an efficient estate has positive slack in a resource, this indicates that with less of the resource the same annual value could have been generated, and, consequently, at the margin, the resource made no contribution to annual value. It follows that the resource shadow price is zero. To prove the theorem on shadow prices, first express any LP problem in the form: (3.11) where c is a 1×n vector of constants, x is an n×1 vector of variables, A is an m×n matrix of constants and b is an m×1 vector of constants (see Lancaster, 1968: ch. 3). Now consider a second LP problem with the same constraints but an objective function k times that of the first, where scalar k>0, namely: (3.12) Next we prove that, if x* is an optimal feasible solution to (3.11), it is an optimal feasible solution to (3.12). If x* is the optimal feasible solution to (3.11), then Ax*≤b, x*≥0 and cx is maximised when x=x*. Hence if x=x* the constraints and non-negativity conditions in (3.12) are satisfied, and since k>0 the value of x that maximises kcx, maximises cx. Proven. Now define the dual to problem (3.11) as:

where y is a 1×m vector of variables; and the dual to (3.12) as:

where y° is a 1×m vector of variables. Finally we prove that if y* is the optimal feasible solution to the dual of (3.11), then ky* is the optimal feasible solution to the dual of (3.12). The optimal value of the objective function in the primal is equal to the optimal value of the objective function of the dual, so for problem (3.11) (3.13) and for problem (3.12) where y°* is the optimal feasible solution to the dual of (3.12), but from (3.13) Hence by setting y°=ky* the objective function of the dual to (3.12) takes its optimal value. As y°=ky* also satisfies the constraints and non-negativity conditions of the dual to (3.12), it is an optimal feasible solution. Proven.

4 EFFICIENCY ANALYSIS OF DOMESDAY ESSEX LAY ESTATES

4.1 INTRODUCTION The theoretical concepts developed in Chapters 2 and 3 are now applied to assess the production efficiency of Essex lay estates. Section 4.2 summarises general information available on Domesday Essex. In Section 4.3, more specific information on the annual values and manorial resources is described. Then the details and main characteristics of the data set used in the efficiency analysis are described in Section 4.4. Section 4.5 explains how the efficiency measures were calculated; and Section 4.6 contains the basic results of the manorial efficiency analysis when constant returns to scale, strong disposability of resources (CS) technology is assumed, and shows how the efficiency results can be used to compare production on estates. In Sections 4.7 and 4.8, questions such as which tenants-in-chief ran efficient estates; whether predominantly arable or grazing estates were more efficient; the geographical distribution of efficient and inefficient estates; the influence of a local market and urban centre on efficiency; and the relationships between efficiency and the size of the estate, and the existence of ancillary resources, are examined. Then in Section 4.9 the characteristics of resource shadow prices and slack resource variables are described. Finally, in Section 4.10, the results of efficiency analyses assuming constant returns to scale, weak disposability of resources (CW) technology, and both variable returns to scale, strong and weak disposability of resources (VS and VW) technologies are briefly reviewed. 4.2 DOMESDAY ESSEX The Norman Conquest was achieved by an élite, and did not result in a mass movement of people. It came after the Anglo-Saxons and Scandinavians had firmly established themselves in England; and, whilst the Normans brought new institutions and practices, these were superimposed on an existing order. Consequently, although the Domesday survey took place only twenty years after the Conquest, the pattern of production was well established. Our analysis relates to production in the county of Essex. Essex, situated in south-east England, is bordered by the Thames in the south, the North Sea in the east, with the northern boundary following the River Stour, and the western boundary the Lea Valley. Domesday Essex boundaries were very similar to those of the modern county. Minor changes were made to the boundary with Cambridgeshire (Great and Little Chishall and Heydon were transferred to Cambridgeshire in the nineteenth century) and near Sudbury

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(Ballingdon and Brundon being transferred to Suffolk); and more recently Essex has lost land to London; but, otherwise, the county remains the same. The entries for Domesday Essex appear in Little Domesday Book (along with Norfolk and Suffolk), and are more detailed than for counties described in the main Domesday volume. In particular, they contain information on livestock on the demesne (but not on peasant land). Curiously, no markets are mentioned in the Essex folios and only a few churches. Essex had a strong Saxon heritage, and tax assessments are stated in hides; whereas Norfolk and Suffolk, more subject to Scandinavian influences, had a more complex system. A few Essex estates form part of the land of the Abbey of Ely, and hence are described in Inquisitio Eliensis. A translation of the Essex Domesday folios accompanied by an excellent introduction has been made by J.H.Round, who was native to the county. They appear in the Victoria County History of Essex (1903). An earlier translation was made by Chisenhale-Marsh (1864). Darby has extensively examined the geography of the county, comparing it with the rest of Domesday England (Darby, 1952, 1977). Other useful references include Darby (1934), Reaney (1935), Rickwood (1911, 1913), Round (1900) and Finn (1964, 1967). As well as the Thames, Stour and Lea, the rivers Crouch, Blackwater, Pant, Chelmer and Colne run southeastwards to the sea, and the Stort and the Cam flow in the north-west. There were also many minor rivers and streams. Darby (1952: 259–63) divided Domesday Essex into three regions, largely based on soil; the Boulder Clay Plateau in the north-west, the London Clay Area in the south, and the Tendring-Colchester Loam Area in the east (see Figure 4.1). The Boulder Clay Plateau is mostly two to three hundred feet above sea level; with numerous villages in the valleys, often with meadow land; and a reasonable density of population, ploughteams and sheep. The area contained much woodland. The London Clay Area is lower-lying land, and the clay less easy to work. The density of population and ploughteams was lower; there was little meadow; and woodland was extensive, but sparser towards the south-east coast. Many sheep grazed on the marshy coastlands. Salt-making was important around the Blackwater and Colne estuaries, and fisheries existed in the Blackwater estuary, along the Thames and the Lea Valley. The low-lying Tendring and Colchester Loam Area contained fertile soils conducive to arable farming. Sheep were also in evidence, but not much meadow land. Some woodland is documented, and fisheries and saltpans are listed. The hundreds of the county are mapped in Figure 4.2. About 440 settlements are listed in the Essex Domesday folios. They are fairly evenly distributed, except in the south-west where the forests of Epping and Hainault lay and some areas along the coast which would have been marshy in 1086. Essex was fortunate in that little devastation occurred in the county either during the Conquest or during the period of consolidation that followed. According to Darby’s count (1952:225), Domesday Book records a population for the county in 1086 of 14,564. The rural population was 13,908, of which 6,969 (or 50 per cent) were bordars, 4,018 (or 29 per cent) were villans, 1,789 (or 13 per cent) were slaves, 1,032 (or 7 per cent) were freemen or sokemen and 100 were otherwise described—mainly rentpayers (censores), men (homines) or priests. The boroughs of Colchester and Maldon had recorded populations of 478 and 243 persons, respectively (some of these had rural occupations and are included in the rural count). It is thought that the recorded numbers indicate heads of households. To obtain the actual population Maitland (1897:437) suggested multiplying by five; others have suggested lower numbers (for example, Russell, 1948:38, suggests three and a half). Multiplying the recorded county population by five gives an actual population of 72,820. (If three and a half is used, it is 50, 974.)

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PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Figure 4.1 Domesday Essex regions

The percentage of freemen and sokemen is lower in Essex than in Norfolk and Suffolk. The proportion of bordars is high, and their numbers increased from 1066 to 1086 at the expense of villans, slaves and the free population. There was also a general increase in the total number of peasants over the twenty-year period. The county was more densely populated in the north-west, with about twelve (recorded) people per square mile. Winstree hundred, south of Colchester, had a similar density. The southern hundreds of Rochford and Waltham had only six inhabitants per square mile.

51

Figure 4.2 Domesday Essex hundreds

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

Domesday Book contains no description of London and only incidental references to Winchester. The description of Colchester is long but difficult to understand. It mainly consists of a list of holders of houses and plots of land, and is discussed by Round (1903:193). The entries suggest that the town had a population of over 2,000. Little emerges of the activities of the burgesses. No market is mentioned, though it is inconceivable that one did not exist. One thing that is clear is that, as well as commerce and industry, the inhabitants engaged in agricultural activities. The other borough in the county, Maldon, was also partly an

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PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

urban and partly an agricultural settlement. The population was probably greater than 1,000 people. In addition to Colchester and Maldon within the county, London (population over 10,000), Southwark in Surrey, Sudbury and Clare in Suffolk, and Stanstead Abbots in Hertfordshire lay on the border. 4.3 THE ANNUAL VALUES AND MANORIAL RESOURCES The important production variables are the manorial annual values, measuring the (net) income of the lord or value added in demesne production, and the main resources or inputs. These were the various kinds of manpower, slaves, villans, bordars, freemen and sokemen; the land types, meadow land, pasture and woodland; and the capital, ploughteams (which also give an indication of the amount of arable land) and livestock. In addition, there were a number of ancillary resources including fisheries, saltpans, mills, beehives and vineyards. Below we briefly review how Domesday Book recorded these variables, and their main characteristics in Domesday Essex. A tenant-in-chief held land directly from the king. He could either make a grant of the land to a feudal sub-tenant in return for feudal services, lease it to a sub-tenant (or mesne-tenant) for a negotiated rent, or work the demesne himself. If he granted the land, he ceased to be the immediate lord and surrendered his right to receive the rent or revenue accruing to the estate, but if he leased out the estate he retained both the lordship and the right to renegotiate the lease periodically. The annual values (valets) are the (net) incomes of lords. They were sometimes rents (reddits) received for leasing all or part of the estate, but usually the net revenue gained from directly working the manorial demesne. Darby (1952:228) states: ‘The valuation of estates in Essex seems to have been carried out with care and detail.’ The values are given in pounds and shillings. The annual value of some large estates changed by just a few shillings from 1066 to 1086; others changed markedly. The values show considerable variation across estates. For Essex lay holdings in 1086, they varied from zero to 1,200 shillings (60 pounds). The mean value was 94.6 shillings, the median 60 shillings and the mode 20 shillings. The distribution is skewed with a long tail to the right. There is also a tendency for the values to take on numbers that are multiples of 10 or 100 shillings, suggesting that many values have been rounded. In comparison with other counties, Essex rated highly both in terms of value per square mile and value per (recorded) person. Darby (1973: 90–3) calculates the average value per square mile for Essex at 67 shillings, just over twice as great as the average for all counties, and exceeded only by Oxfordshire (78 shillings), Wiltshire (69 shillings) and Dorset (68 shillings). Value per man in Essex was 8 shillings, as against 6 shillings per man for the average of all counties. Six other counties, Wiltshire (11 shillings), Dorset (10 shillings), Gloucestershire (10 shillings), Oxfordshire (10 shillings), Buckinghamshire (9 shillings) and Kent (9 shillings), had greater values per man; and four others, Cambridgeshire, Surrey, Hampshire and Somerset, the same. These calculations show Essex to be a productive county, particularly in terms of value per acre. Domesday Book distinguishes between ploughteams of the lord, which were used to work the demesne, and the peasants’ ploughteams. The latter were used to work the peasants’ plots and also the demesne when the peasants fulfilled their work obligations to the lord. For some counties, Domesday Book records ploughlands which are thought to be the amount of arable land that could be ploughed. This information is, however, not available for Essex. The density of ploughteams averaged between two and a half and three and a half per square mile in the Boulder Clay Plateau and Tendring and Colchester Loam Area, and about two per square mile in the London Clay Area.

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53

Essex was a heavily wooded county. Woodland was widely spread over both the Boulder and London Clay areas, being most dense in the west. The extent of woodland on an estate was usually indicated in terms of the number of swine which it could support. The number on the lay estates ranged from just a few to over two thousand. Woodland was important both for the animals it could support and for the wood that could be cut. It should not be confused with forest, which was a legal term denoting land outside common law, subject to special laws that safeguarded the king’s hunting. Meadow was measured in acres. There was much more meadow in the north and west (particularly for villages on the rivers and streams that flow south-eastwards across the Boulder Clay upland) than in the south and east. Pasture, on the other hand, was measured in terms of the number of sheep that could graze on it. Pasture was recorded for some other counties but rarely measured this way. Pasture denoted land available throughout the year for feeding cattle and sheep; meadow denoted land bordering a stream, liable to flood and producing hay. The villages with pasture lay in a belt along the coast, the pasture being on the Essex marshes. Little Domesday Book records information about livestock on the demesne land. Darby (1952:255) counts 46,095 sheep, 13,171 swine, 3,576 goats, 4,005 beasts or oxen (animalia), cows and calves, and several hundred horses and rounceys. Most livestock were widely distributed. Sheep were more numerous along the coastal marshes. Most recorded fisheries lay along the coast, especially the Thames estuary and the estuary of the Blackwater. These were probably saltwater fisheries. Some freshwater fisheries lay along the Lea, Chelmer, Pant and Stour. In all, fisheries are listed for 1086 at twenty-seven places. (The number of fisheries is stated but not the value of the fishery.) It seems that many fisheries were not recorded. Thus, Darby (1952:246) states: ‘All these can hardly have been the total number of coastal and river fisheries in eleventh-century Essex.’ Salt was used extensively to preserve meat and fish, and saltpans are recorded for 1086 at twenty-two villages. Except for a pan at Wanstead in the south-west, all pans lay within the hundreds of Tendring, Winstree and Thurstable. Again, it is questionable that all saltpans are listed. ‘What of the coastal hundreds of Dengie and Rochford to the south, to say nothing of those along the Thames estuary?’ asks Darby (1952: 247–8). The grain was ground in watermills. Mills are recorded for 151 of the 440 Domesday settlements in 1086. Usually the number of mills only is recorded, but sometimes also the value. Again it seems likely that some mills were not recorded. Beehives and vineyards are also recorded. Honey was used to produce mead. The number of hives is listed. Darby (1952:258) counts the number recorded for 1086 as 599, and says: ‘All the entries can scarcely represent the total number of hives in the county.’ There are nine listings of vineyards. Except in one case they are measured in arpents, a French measure. Round (1903: 382–3) claimed that the Normans reintroduced viticulture into England, citing the French arpent measure and the fact that most vineyards were on estates run by Norman tenants-in-chief as evidence. Darby (1973:58) disputes the claim, referring to Ordish (1953: 20–1) for evidence of English vineyards from the eighth through to the tenth centuries. 4.4 THE DATA USED IN THE STUDY Considerable care was taken in the collection, verification and compilation of the Domesday data. Impartial commissioners were selected to organise the survey, evidence was reviewed publicly under oath in the county

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courts, and William dispatched agents to ensure that his instructions were carried out. With landholders from the hundreds aware of local conditions scrutinising evidence, falsification would not have been easy; and, since the information was given under oath, penalties for perjury were probably severe. Despite these precautions, either by accident or by design, errors appear in the document. Of course, in such a large body of data, errors are bound to exist, and it has been popular for scholars to reveal them and caution about the problems inherent in the record. A more balanced statement is made by Harvey (1980: 130–1): DB certainly contains deficiencies and gaps, but these are often due to its orientation to certain objectives, a consideration surely common to all sources…. Certainly arguments from Domesday silence are invalid…. But of the positive evidence, what is gratifying is that many curiosities, given enough further information, are found to be accurate and explicable. …What is present in DB is highly reliable. About what may be absent there is still room for discussion and demonstration. Round (1895:30), despite being able to detect many minor inaccuracies and omissions, regarded the data as a whole to be reliable although subject to individual errors. He stated ‘if we find that a rule of interpretation can be established in an overwhelming majority of cases examined, we are justified…in claiming that the apparent exceptions may be due to errors in the text’. Finn (1971: 14, 245) had a similar opinion, arguing that ‘Long study of them [the values] convinces me that over the vast range of statistics serious misapprehension is unlikely’ and ‘The entries…are so numerous that incorrect interpretation of the doubtful passages probably does not appreciably affect the results’. Darby, Maitland and others have also noted occasional errors in the record, but have been willing to analyse and make conclusions from large bodies of data. For Essex, Darby (1952: 209–11) notes that the descriptions of the Essex estates in Inquisitio Eliensis agree with those in Little Domesday Book, but claims some discrepancies in a few duplicate entries which appear in the Essex folios of the Book. Our assessment is that, over all, the data on the values and main resources appear reliable, but some entries are subject to clerical or other errors. Variables such as the number of peasants and ploughteams denoted in physical terms were easily measured, but the annual values and variables described in more conceptual terms (such as woodland measured in terms of the number of swine that could graze on it) less so. Some of the data, including the values, were clearly subject to rounding error. We have less confidence in data relating to the ancillary resources (fisheries, saltpans, mills, beehives and vineyards). The suggestion is that these resources were sometimes overlooked. In addition, a point that has some significance for our analysis is that it is unclear whether the returns from these resources were included in the manorial annual values. For example, there are doubts about mill renders. Darby (1973:210) assumes mill renders were included, but Finn (1971: 11) assumes they were not.1 Our strategy has been to examine each manorial entry and delete from the analysis those that appear incomplete or implausible. Upon examining the entries, we developed the general rule of thumb that only entries for which (1) the annual value is positive, (2) either ploughteams or livestock entries are positive (or both), and (3) there is a positive entry of at least one of the four labour variables (freemen and sokemen, villans, bordars, and slaves) be retained for analysis. A further five estates whose entries satisfied these conditions were deleted. They are large estates with many resources but inexplicably no entry for either ploughteams or alternatively livestock. They are Phincingefelda, a manor of Count Alan in the hundred of Hinckford (no livestock); Staplefort, a manor of Suen of Essex in the hundred of Ongar (no ploughteams); Toleshunta, a manor of Suen in the hundred of Thurstable (no ploughteams); an unnamed estate of Geoffrey de Mandeville in the hundred of Barstable (no

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livestock); and Taindena, a manor of Peter de Valognes in the half-hundred of Thunreslau (no ploughteams). Finally, medievalists have been unable to locate geographically two estates (Niuetuna, a small estate of Ralf de Limesi, and Scilcheham, the manor of William Levric). As a consequence, certain features of the estates (such as geographic region and hundred) cannot be determined, so they were deleted from the study. In total 118 of the 695 Essex lay estate entries were discarded. A list of the 577 estates used in the study is given in Appendix 2, Table 1.2 Because of the problems surrounding the ancillary resources, it was decided to undertake the efficiency analysis using the main resources only, and then see if the existence of ancillary resources helped to explain the efficiency measures of the estates. The main resources were defined as the demesne ploughteams (denoted R1), the peasants’ ploughteams (R2), livestock (R3), freemen and sokemen (R4), villans (R5), bordars (R6), slaves (R7), woodland (R8), meadow (R9) and pasture (R10). All livestock, other than horses, were combined into one variable, using market values. Horses were excluded because they were used largely for non-productive military and leisure purposes. It was not until the thirteenth and fourteenth centuries that ploughing with horses became common.3,4 Table 4.1 lists summary statistics for the variables. Notice that the mean annual value is 108.5. This is against a mean of 94.6 for all Essex lay estates, indicating that the entries of smaller estates have tended to be discarded. The median and mode are also larger, and the distribution remains skewed, as are the distributions for the resources. For demesne ploughteams, only 9 estates had no ploughteams, and 78 per cent two or less; 216 estates had no entry for peasants’ ploughteams, 73 listed one, 56 two, 44 three and 23 four ploughteams. Not all ploughteam numbers are integers. Ploughteams were sometimes shared between the lord and the peasants, or between estates. About 60 per cent of the estates had some livestock. For the manpower variables, 508 estates had no freemen or sokemen, but 60 per cent had villans, 93 per cent bordars and 62 per cent slaves. Some woodland and meadow was present on about three-quarters of the estates, but pasture is recorded for one in five estates. Beehives and mills were recorded on about 20 per cent of the estates, but only sixteen estates had fisheries and nineteen had saltpans. Some estates had several fisheries, mills or saltpans, and sometimes the number was given as a fraction. On occasions the resources were shared between Table 4.1 Summary statistics for data used in the study of 577 Essex lay estates, 1086 Variable

Minimum

Maximum

Mean

Median

Mode

Standard deviation

annual values demesne ploughteams peasants’ ploughteams livestock freemen and sokemen villans bordars slaves woodland

3.0

1,200

108.5

65

60

131.8

0

10

1.9

2

1

1.3

0 0 0

37.5 3,816 37

2.3 542.4 0.6

1 388 0

0 0 0

4.1 656.3 2.8

0 0 0 0

72 79 20 1,500

4.1 8 2.2 105.9

1 5 1 30

0 3 0 0

7.3 9.1 2.8 189

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PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Variable

Minimum

Maximum

Mean

Median

Mode

Standard deviation

meadow 0 120 12.2 6 0 16.2 pasture 0 1,100 28.3 0 0 88.6 beehives 0 30 0.9 0 0 2.7 fisheries 0 4 0.1 0 0 0.3 mills 0 8 0.2 0 0 0.6 saltpans 0 5 0.1 0 0 0.6 vineyards 0 10 0.1 0 0 0.6 Notes: Annual values are in shillings. Livestock is a weighted sum of cows, swine, sheep and goats (see note 3). Woodland is measured in terms of the number of swine and pasture in terms of the number of sheep that could be supported. Meadow and vineyards are in acres. The other variables are measured by a count of their number.

estates; but an entry of, say, half a fishery may indicate that the value of fish taken was about half that expected from a normal-size fishery. All nine vineyards recorded in Essex are included in our sample. The entries list productive vineyards measured in arpents or acres. 4.5 MANORIAL EFFICIENCY ANALYSIS: THE EFFICIENCY CALCULATIONS Denoting the annual value of the ith estate by Vi, and the amount of the jth (main) resource available on the ith estate by Rij(i=1…577, j=1…10), efficiency measures for the estates were calculated in the following way. When constant returns to scale, strong disposability of resources (CS) technology was assumed, to establish if the ith estate was efficient, the following linear programming problem was solved:

With variable returns to scale, strong disposability of resources (VS) technology, to find if the ith estate was efficient, the above linear programming problem, with the additional constraint z1+z2+…+z577=1, was solved. When constant returns to scale, weak disposability of resources (CW) technology was assumed, the linear programming problem solved was:

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When variable returns to scale, weak disposability of resources (VW) technology was assumed, the constraint z1+z2+…+z577=1 was added to the (CW) technology linear programming problem. The linear programming problems can be solved using a computer program such as LINDO (see Schrage, 1989). Notice, however, that each linear programming problem involves more than 500 variables and more than ten constraints, and there are four times 577 problems to solve. Clearly, it would take a considerable time to specify manually the input instructions to solve the more than 2,000 linear programming problems. Fortunately, the input specification can also be computerised. Algorithms that do this task are listed in Appendix 1.5 4.6 MANORIAL EFFICIENCY ANALYSIS ASSUMING CONSTANT RETURNS TO SCALE, STRONG DISPOSABILITY OF RESOURCES (CS) TECHNOLOGY The results of the efficiency analysis assuming constant returns to scale, strong disposability of resources (CS) technology are now described. Many simple agricultural economies exhibit constant returns to scale, and the production analysis of Essex lay estates described in Chapter 5 suggests close to constant returns to scale. Both constant returns to scale and strong disposability of resources are plausible and easily interpreted technological assumptions; and, although they may be only approximately true, more useful insights are likely to be gained from this analysis than when less restrictive assumptions that constrain the data only marginally are imposed (see Sections 2.5 and 2.6). The results of efficiency analyses assuming weaker technological assumptions are summarised later in the chapter. The CS efficiency results (summarised in Figure 4.3) indicate that 96, or 17 per cent, of the estates were efficient (u=1); 159, or 28 per cent, were relatively efficient having u-values between 1 and 1.5; and 116, or 20 per cent, were less efficient with u-values between 1.5 and 2. This leaves 206 inefficient estates (36 per cent of the total) with an efficiency value of 2 or more. For these estates, with CS technology and efficient use of available resources, it would have been possible to double the accrued annual value. Of the inefficient estates, 149 (26 per cent) had u-values between 2 and 3 and are categorised inefficient, and 57 (10 per cent) were very inefficient with u-values of 3 or more.6 The percentages of estates in the five efficiency categories (efficient, u=1; relatively efficient, 1
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Figure 4.3 Distribution of CS technology efficiency measure (u): Essex lay estates, 1086

Notes: Bars giving percentages of efficient, relatively efficient, less efficient, inefficient and very inefficient estates for tenants-in-chief with most estates in Essex (percentage of estates held by tenant-in-chief above bar, tenant-in-chief identification code below bar). 1=Count Eustace. 2=Suen of Essex. 3=Geoffrey de Magna Villa. 4=Robert Greno. 5=Richard son of Count Gilbert. 6=Ranulf Peverel. 7=Ralf Baignard. 8=Eudo dapifer. 9=William de Warene. 10=Ranulf brother of Ilger. Figure 4.4 Distribution of CS technology efficiency measure (u), by large tenants-in-chief: Essex lay estates, 1086

chief of the estate, the efficiency value (u) for the estate, and the list of non-zero intensity variables (zi) and non-zero slack variables (si) in the optimal linear programming solutions.7 As an example, the first estate, Fobbing, was an estate of the tenant-in-chief coded 1. The note at the end of the table indicates that this is Count Eustace (of Boulogne). The efficiency value for the estate is 1.042. In the linear programming optimal solution, the non-zero intensity variables were 59, 193, 205, 399 and 502. This indicates that, with CS technology and the available resources, a (linear) combination of the activities

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of the estates with these codes generated an annual value (V) 1.042 times greater than that of Fobbing. The non-zero slack variables in the optimal solution were 2, 3, 8 and 10. The note to Table 1 indicates that 2 refers to the peasants’ ploughteams, 3 to livestock, 8 to woodland, and 10 to pasture. The non-zero slack values indicate that not all the amounts available of these four resources were used in the optimal solution (see Sections 2.5, 3.3 and 3.6). Table 2 of Appendix 2 lists the estates by efficiency category. To illustrate how the efficiency results can be used to compare production on estates, we focus attention on about a dozen estates. Pebmarsh (identification code 502), Lawling (190), Maldon (181), Easton (283), Michaelstow (357) and Down (392) are examples of efficient estates; Witham (10) was relatively efficient (u=1.104); Shortgrove (19) less efficient (u=1.998); Blunts Hall (9) inefficient (u=2.500); and East Donyland (559, u=5.143) and Paglesham (488, u=6.286) very inefficient. Table 4.2 lists the main production characteristics of the estates. (For simplicity, we have selected estates without ancillary resources.) Pebmarsh, in the hundred of Hinckford, was held by a sub-tenant (Garenger) of the tenant-in-chief, Roger Bigot. Bigot had seven estates in Essex. We have grouped tenants-in-chief into three groups according to the number of estates they had in Essex: small (S), one to four estates; medium (M), five to nineteen estates; and large (L), greater than nineteen estates. Bigot falls in the medium group. Pebmarsh, an efficient estate, was in the Boulder Clay Plateau geographical (soil) region and was remote from the major towns of Colchester and Maldon (so the ‘Influence of towns’ entry in Table 4.2 is 0). We have categorised estates by size, based on the single best indicator of economic size, the annual value, V, of the estate. The categories are very small (VS), V lies in the lowest 10 per cent for estates in the sample; small (S), V lies in the 10–35 per cent range; medium (M), V lies in the 35–65 per cent range; large (L), V lies in the 65–90 per cent range; and very large (VL), V lies in the top 10 per cent. Pebmarsh, with an annual value of 80 shillings, is in the medium category. The estate had one and a half demesne ploughteams, one bordar, woodland for eight swine, and three and a half acres of meadow in 1086. An index of whether production was mainly arable or grazing is given by the grazing/arable ratio, defined as livestock less cattle and beasts (which were required for ploughing) divided by the number of ploughteams on the estate.8 Pebmarsh had no livestock, so the grazing/arable ratio is zero. Estates for which this is the case are categorised as mainly arable (A). The remaining estates were divided into two roughly equal categories: mixed (M), grazing/arable ratio less than 150; and mainly grazing (G), ratio greater than 150. A translation of the Domesday Book entry for Pebmarsh is contained in Figure 4.5, and the estate’s location is marked on the map, Figure 4.2. The entry indicates that the annual value doubled between 1066 and 1086. The annual value of Lawling also increased (from 3 to 4 pounds) between 1066 and 1086, this despite there being (marginally) fewer resources on the estate at the later date. Lawling, also an efficient estate, lay in the hundred of Dengie, at the foot of Lawling Creek which runs into the Blackwater estuary. It was held by a subtenant of Eudo dapifer, a tenant-in-chief with a large number of holdings in Essex. Located in the London Clay Area near Maldon, the estate had one demesne ploughteam, one bordar, three slaves and sixty-three sheep in 1086. The entry for Maldon suggests that some dues were received by the king and some by Suen, the tenant-inchief. (Round discusses the reference to the king’s dues in the introduction to the Victoria County History translation, 1903:386, remarking that its construction may be open to question.) The estate was run by a subtenant (Guner) of Suen. With one demesne ploughteam and a bordar, the annual value was one pound. Compared with Pebmarsh and Lawling (which admittedly had more resources) this may seem a little low. Nevertheless, the CS efficiency analysis classifies Maldon as an efficient estate.

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Witham was a relatively efficient estate (u=1.104). Held by a sub-tenant of Count Eustace, it was situated near Maldon adjacent to the road linking Colchester to London. With one demesne ploughteam, one bordar and two and a half acres of meadow, the annual value of Witham was the same as at Maldon (with the same number of demesne ploughteams and bordars but no meadow), and 10 shillings less than at Easton (an estate held by a sub-tenant of Geoffrey de Magna Villa in the hundred of Dunmow with the same number of demesne ploughteams and bordars but twelve acres of meadow9). Assuming CS technology, Easton’s production process can be used at Witham just over one-fifth of the time to generate an annual value of 6.24 (=0.208×30) shillings, and the Maldon production process about four-fifths of the time to generate 15.84 (=0.792×20) shillings, thus giving a total annual value of 22.08 shillings, 1.104 times greater than was actually generated. (Notice that the Easton process requires meadow in the proportion: one ploughteam, one bordar, twelve acres of meadow; and Witham’s endowment of meadow is exhausted when the process is used for just over one-fifth of the time: 0.208×12=2.5.) The degree of inefficiency at Witham was very small, and may have resulted simply from a rounding down of the annual value from 22 shillings to 20 shillings. Shortgrove is an example of a less efficient estate (u=1.998). Held by Adelolf de Merc, a sub-tenant of Count Eustace, it was located in the hundred of Uttlesford in the Boulder Clay Plateau Area. The estate had two demesne ploughteams, three bordars, three beasts, eleven swine, ninety sheep and nine acres of meadow, and an annual value of 2 pounds. Considerably less annual value was generated on Shortgrove than on the estates of Michaelstow and Down which had similar resources, although Michaelstow had slightly more livestock and Down twice as many bordars. (Michaelstow was an estate of Ralf Baignard, run by a sub-tenant in Tendring, in the Tendring and Colchester Loam Soil Area.

Table 4.2 CS efficiency analysis, Essex lay estates, 1086: production on eleven selected estates

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES 61

Notes: For each estate, the identification code is given, CS efficiency measure, non-zero intensity variables and slack variables in the linear programming optimal solution (values in parenthesis), the annual value and resources of the estate, the name of the tenant-in-chief, the hundred and geographical (soil) region in which the estate was located (B=Boulder Clay Plateau Area, L=London Clay Area, T/C=Tendring and Colchester Loam Area), whether the estate was located close to a town (M, if within approximately 6-mile radius of Maldon; C, if within approximately 6-mile radius of Colchester; 0 otherwise), the grazing/arable ratio (ratio of livestock less cattle and beasts to the number of ploughteams), and grazing/arable category (A, if ratio=0; M, if ratio greater than zero and less than 150; G, if io rat greater than 150), and tenure (1 sub=1 sub-tenant, Demesne=held in demesne). Tenants-in-chief are grouped by number of holdings in Essex (S=1–4 holdings; M=5–19 holdings; L=more than 19 holdings) and estates categorised by size, based on annual value, V (VS, V lies in the lowest 10 per cent for estates the in sample; S, V lies in the 10–35 per cent range; M, V lies in the 35–65 per cent range; L, V lies in the 65–90 per cent range; VL, V lies in the top 10 per cent). None of the estates had ancillary resources (beehives, fisheries, mills, saltpans or vineyards).

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63

Figure 4.5 English translations of Domesday entries for eleven estates Source: Victoria History of Essex, vol. I

Table 4.2 continued Down was held in demesne by Ranulf Peverel and was located in the hundred of Dengie, near the Blackwater estuary, in the London Clay Area.)

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The Michaelstow production process can be used almost all the time to generate 79.36 (0.992×80) shillings, 1.984 times greater than the annual value generated at Shortgrove. Two bordars and five acres of meadow will be idle. Technically it is possible to increase slightly the annual value generated at Shortgrove by using the Down process for the remainder of the time. Switching to the Down process for so short a period of time seems impractical, but this description of the process should not be taken too literally. The annual value of 79.92 shillings (1.998 times what was actually generated) may well be obtained by using a single simple process rather than by switching. Switching between the two processes is only one way of achieving the result. It is quite possible that it can be achieved in a simpler way with CS technology (see Section 2.5). An example of an inefficient estate (with u=2.500) is Blunts Hall. Blunts Hall was held in demesne by Count Eustace. Located in the hundred of Witham, near the estate of Witham, it had one demesne ploughteam, one bordar and six acres of meadow. Its annual value, 10 shillings, was half that generated at Maldon with fewer resources, and 20 shillings less than at Easton with twice as much meadow. If Easton’s production process is used half of the time and Maldon’s process half the time, all resources are exhausted and the annual value is increased two and a half times to 25 shillings. It is notable that, although resource levels at Blunts Hall appear to have been no greater in 1066 than in 1086, the annual value fell from 20 to 10 shillings. An annual value of 20 shillings in 1086 would have given Blunts Hall an efficiency value of 1. 25, putting it in the relatively efficient category. Two examples of very inefficient estates are East Donyland (u=5.143) and Paglesham (u=6.286). East Donyland was held in demesne by Ilbodo. In Lexden hundred, in the Tendring and Colchester Loam Area, it was located within 6 miles of Colchester. It had one demesne ploughteam, three bordars, and two acres of meadow, but an annual value of only 7 shillings. Down had a very much greater annual value, although more demesne ploughteams and bordars. Using Down’s process, but at a resource level only four-tenths of that used at Down (thus exhausting East Donyland’s demesne ploughteam endowment), annual value can be increased 5.143 times to 36 shillings. Not all of the time of one bordar is used, and none of the meadow. It may well have been possible to increase the annual value further by using these resources. Paglesham in the hundred of Rochford was held by a sub-tenant of Robert son of Corbutio. Its annual value was very low compared with estates with similar resources. In particular, if Maldon’s and Down’s processes are each used half of the time, but both at a scale level roughly one-quarter that used on the respective estates, the annual value can be increased to 31.43 shillings (31.43 is approximately (0.286×20)+ (0.286×90)). Both the ploughteams and bordar resources at Paglesham are fully utilised (ploughteam usage is (0.286×1)+(0.286×2.5)=1 and bordar usage (0.286×1)+(0.286×6)=2); and 31.43 shillings is 6.286 times the annual value actually generated at Paglesham. In a footnote to the entry (1903:547), Round says: ‘Here, if the figures are correct, is a fall in value to one-eighth, with absolutely nothing to account for it. There is a gap between “modo” and “v” 5) in the MS.’ If in fact there is a clerical error, and the annual value was 25 shillings (corresponding to the entry being xxv), the efficiency value for Paglesham would have been 1.257, putting it in the relatively efficient category; if the annual value was 35 shillings (corresponding to xxxv), Paglesham would have been an efficient estate. We have attempted to keep the preceding discussion as simple as possible by choosing estates with few resources. As a result the inefficient estates can easily be seen to be inefficient by comparing their production characteristics with just one or two other (efficient) estates. For many estates, however, it is only by comparing their production characteristics with several other estates that it can be discovered if they are efficient or inefficient, and, if inefficient, by how much annual value can be increased.

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65

For example, the annual value of Fobbing, the estate referred to earlier, can be increased by using its resources in a combination of the activities of five other estates. As a second example, Elmstead, the subject of the sample entry from Domesday Book described in Chapter 1, is an inefficient estate with u=2.930. This can be determined by using its resources in a combination of the activities of seven estates. The entries in Table 1 of Appendix 2 indicate that such cases are quite usual. As was indicated earlier, the fact that the annual value can be increased by employing resources in a combination of activities of several estates does not necessarily mean that the production process has to be complex. Employing the combination is just one way of generating the annual value. It may well be possible, with CS technology, to obtain the result much more simply. The efficiency results can be used to analyse production on any estate in the county and compare production on different estates. The efficiency values and other information provide an aid to understanding, analogous to the way maps provide an aid to understanding spatial relationships. An extensive analysis is left to others. Medievalists with access to detailed local knowledge are much better placed to carry out the analysis than an economist (and a geographer) living 12,000 miles away in Australia. We have, however, attempted to discover the main factors associated with efficient production. This is the subject of the next section. 4.7 FACTORS ASSOCIATED WITH EFFICIENCY: DESCRIPTIVE ANALYSIS Some Essex lay tenants-in-chief were ranked amongst the greatest barons of the realm. They included Geoffrey de Magna Villa (or Geoffrey de Mandeville), Richard son of Count Gilbert (Richard Fitzgilbert), William de Warene and Count Alan (of Brittany). Geoffrey de Magna Villa was Sheriff of Middlesex and held estates in ten counties. Lord of Pleshey (where there was a castle), his descendants became Earls of Essex. Richard son of Count Gilbert, one of William’s inner circle of advisers, acted as co-regent. Also known as Richard of Clare, he held almost 100 estates in Suffolk, as well as land in seven other counties. William de Warene, Lord of Lewis (which had a castle) and Earl of Surrey, held land in eleven counties; and Count Alan, the King’s son-in-law and leader of the Breton community in England, was tenant-in-chief of 400 estates in twelve counties. In Essex itself, though, Count Eustace of Boulogne held most lay estates (he also had major holdings in Hertfordshire and elsewhere), and the Sheriff of Essex, Suen, the second-largest number of holdings (Suen also had estates in Suffolk). We ask: Were the estates of some tenants-in-chief more efficiently run than others? And were the estates of larger tenants-in-chief more efficiently run than those of smaller tenants-inchief? Table 4.3 lists the number of estates held in Essex by each tenant-in-chief. It also gives the number of estates included in the 577 estates analysed in this study and, of these, the number of efficient estates. The final five columns give the percentages of estates falling into the five efficiency categories: efficient, relatively efficient, less efficient, inefficient and very inefficient. The last entry gives the percentages for all 577 estates. As an example, we see that Count Eustace had eighty-one estates in Essex, of which seventy-two are in our sample; and of these twenty-one estates, or 29 per cent, were efficient. This percentage is considerably greater than the average for all estates (17 per cent). Count Eustace had a slightly lower than average percentage of relatively efficient estates (22 per cent compared with 28 per cent), and the average percentage of very inefficient estates (10 per cent).

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Comparisons can more easily be made by comparing bar diagrams. Figure 4.4 displays bars giving percentages of estates in the five efficiency categories for all estates and the ten largest tenants-in-chief in the county. (The percentage of estates held by the tenant-in-chief is given above the bar and tenant-in-chief identity code below the bar.) We see that the estates of Suen (identification code 2) conform quite closely to the average of all estates. Geoffrey de Magna Villa (code 3) had rather more relatively efficient estates and fewer inefficient estates than average, Richard son of Count Gilbert (code 5) rather more less efficient estates than might be expected, and William de Warene (code 9) a large proportion of relatively efficient estates and no very inefficient estates. Notice that the last four bars indicate that Ralf Baignard (code 7), Eudo dapifer (code 8), William de Warene (code 9) and Ranulf brother of Ilger (code 10) all had no very inefficient estates. From Table 4.3, we see that Count Alan’s estates were relatively inefficient as compared with the average. Others with a relatively large number of more inefficient estates include Robert Greno, Peter de Valognes and Roger de Ramis. Ranulf Peverel, Eudo dapifer, Sasselin and Henry de Ferrariis were amongst

Table 4.3 Tenants-in-chief, Essex lay estates, 1086: CS technology efficiency

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES 67

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EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

69

Table 4.3 continued those with a relatively large number of more efficient estates. For the smaller tenantsin-chief, with only a few estates, the percentages must be interpreted with care because one estate constitutes a high percentage of the total. Clearly some tenants-in-chief had relatively more efficient estates than others, but there is no obvious division between tenants-in-chief with mainly efficient estates and others with inefficient estates. In Table 4.4 and Figure 4.6 we give percentages when the estates are grouped into those held by tenantsin-chief with a small number of estates (one to four), those with a medium number (five to nineteen), and those with a large number of estates (twenty or more). The percentage of efficient and relatively efficient estates for small tenants-in-chief is a little higher than average; and, for those with a medium number of estates, a little lower; but again there is no clear pattern. Was efficiency associated with spatial location? And were efficient estates more concentrated in some hundreds than in others? Table 4.5 and Figure 4.7 provide the relevant information. For Barstable (code 1), the percentage of estates in the relatively efficient category is a little low, but otherwise the percentages are similar to those for all estates. For the other hundreds with a reasonable number (more than fifteen) estates, Dengie (code 5), Rochford (14), Tendring (15) and Uttlesford (16) estates tended to be relatively more efficient (28 per cent of the estates in Rochford and 31 per cent of the estates in Tendring were efficient), and Clavering hundred and half-hundred (7), Harlow (9), Lexden (12), Ongar (13), Witham (19) and Thurstable (22) estates less efficient (26 per cent of the estates in Lexden were very inefficient and 59 per cent of the estates in Thurstable either very inefficient or inefficient). Of the hundreds with fewer estates, Becontree (code 2, with nine estates) and Chafford (code 3, with twelve) both had 33 per cent efficient estates. Were hundreds with relatively more efficient estates located adjacent to each other or scattered through the county? On the map, Figure 4.8, we have identified the hundreds with more than 50 per cent of estates efficient or relatively efficient, hundreds with 25–49 per cent of estates efficient or relatively efficient, and hundreds with less than 25 per cent of estates efficient or relatively efficient. There are two bands running north to south of hundreds in the first (more than 50 per cent) group. Tendring, Winstree, Dengie and Rochford on the coast, and Uttlesford, Dunmow and Chafford in the west. Three hundreds, Waltham, Witham and Thurstable, are in the last (less than 25 per cent) group. Witham and Thurstable are adjacent to each other in the east, and Waltham (with only four estates) is on the western boundary of the county. Within a county were efficient estates bunched together or scattered? Figure 4.9 provides information relating to Rochford hundred (which had more than 50 per cent of estates efficient or relatively efficient). The vills of Rochford are located by dots (and numbered), and the estates of the vills by letters which denote their efficiency category. Some vills consisted of several estates. For example, Pudsey Hall (numbered 2) located just south of Bridgemouth Island in Table 4.4 Tenants-in-chief by number of estates and CS technology efficiency: Essex lay estates, 1086 Number of estates Percentages Small number of estates (1–4 estates) Medium number of estates (5– 19 estates) Large number of estates (20 or more estates) All estates analysed

efficient

relatively efficient less efficient inefficient very inefficient

59

20

29

17

25

8

131

11

23

21

29

15

387

18

29

20

25

8

577

17

28

20

26

10

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Notes: Bars giving percentages of efficient, relatively efficient, less efficient, inefficient, and very inefficient estates for tenants-in-chief with a small number of estates (1–4), a medium number of estates (5–19) and a large number of estates (20 or more) (percentages of estates in category above bar). Figure 4.6 Distribution of CS technology efficiency measure (u), by tenants-in-chief with small, medium and large number of estates: Essex lay estates, 1086

the River Crouch (which marks the northern boundary of the hundred) consisted of four estates in our sample (all called Pudsey, with identification codes 158, 160, 162 and 163). Two of the estates were efficient, one relatively efficient and one less efficient. There are clusters of efficient and relatively efficient estates in the hundred. We have divided the hundred into four groups (vills 1, 2 and 3 in the north, vills 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13 just south, vills 17 and 22, and the rest of the vills in the south) containing estates in similar efficiency categories. There is

Table 4.5 Hundreds and CS technology efficiency: Essex lay estates, 1086

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Notes: Bars giving percentages of efficient, relatively efficient, less efficient, inefficient and very inefficient estates for each hundred (percentage of estates above bar hundred code below). Hundred code: 1=Barstable. 2=Beacontree. 3=Chafford. 4=Chelmsford. 5=Dengie. 6=Dunmow. 7=Clavering hundred and half-hundred. 8=Freshwell half-hundred. 9=Harlow. 10=Harlow half-hundred. 11=Hinckford. 12=Lexden. 13=Ongar. 14=Rochford. 15=Tendring. 16=Uttlesford. 17=Waltham. 18=Winstree. 19=Witham. 20=Maldon half-hundred. 21= Thunreslau half-hundred. 22=Thurstable. Figure 4.7 Distribution of CS technology efficiency measure (u), by hundred: Essex lay estates, 1086

some uniformity within the groups, but also some exceptions. The method of grouping is, of course, subjective. Others may see different patterns. An alternative spatial classification is according to geographical (soil) region (see Table 4.6 and Figure 4.10). A slightly larger proportion of estates in the London Clay Area are in the efficient category than on average, and a slightly smaller proportion in the very inefficient category. For the Tendring and Colchester Loam Area estates, there are more efficient and very inefficient estates than on average; and for the Boulder Clay Plateau fewer efficient estates and more relatively efficient estates than average. The towns provided a market centre and demand for the output of estates. For local estates, transport and selling costs would perhaps be less and local demand could have lifted output prices marginally, both having the effect of increasing measured efficiency. We ask: Were estates close to the urban centres of Colchester and Maldon more efficient? To answer this we have located the estates that lie within a 6-mile radius (with some allowance for topography) of Colchester and Maldon. The estates are listed in the notes to the map, Figure 4.11; their location being given on the map itself. From Table 4.6 and Figure 4.10, we see that there are more efficient estates than average for the estates proximate to Colchester (24 per cent against 17 per cent), but there are also fewer relatively efficient estates and more very inefficient estates than would be expected. For the estates close to Maldon, there are fewer efficient and relatively efficient estates than on average, and more

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

Figure 4.8 Hundreds categorised by CS efficiency measure (u): Essex lay estates, 1086

73

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Notes: E=efficient. R=relatively efficient. L=less efficient, I=inefficient. V=very inefficient. Numbers are vill codes. Vill codes (with estate identification codes in parenthesis): 1=South Fambridge (569). 2=Pudsey Hall (158, 160, 162, 163). 3=Canewdon (150). 4=Hockley (145, 159). 5=Plumberow (157). 6=Ashingdon (164). 7=Paglesham (99, 363, 488). 8=Hawkwell (165, 194). 9=Rayleigh (143, 144). 10=Rochford (152). 11=Gt Stambridge (153). 12=Sutton (156, 161, 562). 13=Eastwood (146, 166). 14=Shopland (72). 15=Barrow Hall (128). 16=Lt. Wakering (155). 17=Littlethorpe (151). 18=Gt Wakering (147). 19=Leigh (402). 20=Prittlewell (148). 21=N. and S. Shoebury (149, 154). 22=Thorpehall (444). Figure 4.9 Location of Rochford estates by efficiency category: Essex lay estates, 1086

inefficient but fewer very inefficient estates. ‘Other estates’ constitute 82 per cent of all estates, so it is not surprising that its category percentages are similar to those for all estates. It seems that there is no clear evidence that estates close to urban centres tended to be more efficient.

Table 4.6 CS technology efficiency and various factors affecting production: Essex lay estates, 1086

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Notes: Bars giving percentages of efficient, relatively efficient, inefficient and very inefficient estates for geographical (soil) region, influence of towns and size of estate (percentage of estates above bar).

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77

Location of Colchester and Maldon estates Location of Colchester estates by efficiency category Notes: The estates lie within a 6-mile radius (with some allowance for topography) of Colchester or Maldon. In lower map: E=efficient. R=relatively efficient. L=less efficient. I=inefficient. V=very inefficient. Figure 4.10 Distribution of CS technology efficiency measure (u), by geographical (soil) region, influence of towns and size of estate: Essex lay estates, 1086

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Location of Colchester estates by efficiency category Notes: The estates lie within a 6-mile radius (with some allowance for topography) of Colchester or Maldon. In lower map: E=efficient. R=relatively efficient. L=less efficient. I=inefficient. V=very inefficient.

In the lower map in Figure 4.11, we have marked estates in the Colchester area according to their efficiency category to see if there are clusters of like estates or any other pattern. No obvious pattern is evident. The best single indicator of the economic size of an estate is its annual value. Did larger estates tend to be more efficient? Were there economies of scale? The evidence from estimated production functions (based on Essex lay estates data) is that there were mildly increasing returns to scale. Is this also apparent from the efficiency analysis? On the basis of the estate’s annual value (V), we have placed estates in one of five size categories (very small, V lies in the lowest 10 per cent for estates in the sample; small, V lies in the 10–35 per cent range; medium, V lies in the 35–65 per cent range; large, V lies in the 65–90 per cent range; very large, V lies in the top 10 per cent). From Table 4.6 and Figure 4.10, we see there is a clear tendency for large estates to be more efficient. For example, comparing the very small and very large estates, we see that only 9 per cent of estates in the very small category were efficient and 5 per cent relatively efficient, but 47 per cent very inefficient. In contrast, 29 per cent of very large estates were efficient, 51 per cent relatively efficient, no estates very inefficient, and only 3 per cent inefficient. These results are consistent with the hypothesis that larger estates tended to be more efficient, and/or mildly increasing returns to scale at the frontier (see Section 2.5). Although it is difficult to discriminate between these hypotheses, efficiency calculations made when the VS, variable returns to scale, technology was assumed suggest both that larger estates tended to be more efficient and returns to scale were very mildly increasing (see Section 4.10). Some estates relied on arable farming, others had significant numbers of livestock (mainly sheep). Was efficiency associated with arable or grazing activity? For each estate, we calculated a grazing/arable ratio defined as livestock less cattle and beasts (which were involved in arable agriculture) divided by the number of ploughteams on the estate. We categorised estates with a zero ratio (no livestock), mainly arable;

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

Figure 4.11 Location of estates surrounding Colchester and Maldon

79

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and divided the remaining estates into two roughly equal categories: mixed, grazing/arable ratio less than 150; and mainly grazing, ratio greater than 150. For estates in the mainly arable category, there are more very inefficient and fewer inefficient and relatively efficient estates than on average (see Table 4.6 and Figure 4.12). The mixed category contains more relatively efficient and fewer very inefficient estates than on average; and, for the mainly grazing estates, there are more inefficient estates and fewer efficient and very inefficient estates than on average. For all three categories, however, deviations from the average are quite small. Tenure arrangements could affect efficiency. Were estates held in demesne by tenants-in-chief or those run by sub-tenants more efficient? Referring again to Table 4.6 and Figure 4.12, we see that estates held in demesne tended to be more efficient, both the efficient and relatively efficient categories being higher than average, and the less efficient and inefficient categories being smaller. For estates, held by one sub-tenant, there are fewer efficient and relatively efficient estates than on average, and more less efficient and inefficient estates. Estates with several sub-tenants tended to be small. There are only four in our sample, two being efficient and two relatively efficient. The existence of ancillary resources (beehives, fisheries and so on) might be expected to increase the annual value, and hence tend to reduce the efficiency measure of the estate (making it appear more efficient). The situation is, however, somewhat more complex because ancillary resources were probably under-reported, and it is possible that their returns were not included in the estate’s annual value. If the latter was the case, and other estate resources (such as manpower) were used to work the ancillary resource, annual value might actually be less than without the resource, and the estate appear more inefficient. For most estates we would expect the influence of ancillary resources on production to be small. Beehives and mills were reported on about 20 per cent of the estates in the sample. Estates with beehives and mills had a smaller proportion of efficient estates than on average, but the proportion of estates with beehives in the relatively efficient group is high. Only 2 or 3 per cent of estates had fisheries, saltpans or vineyards. Estates with saltpans did not tend to be more efficient, but those with fisheries and vineyards did: 31 per cent of estates with fisheries were efficient and none very inefficient; and 78 per cent of estates with vineyards relatively efficient and none inefficient or very inefficient. 4.8 FACTORS ASSOCIATED WITH EFFICIENCY: STATISTICAL ANALYSIS The analysis of the previous section is descriptive and rather subjective in nature. Here we provide a more objective analysis based on statistical tests. Statistical tests are used to test the significance of the association of estate efficiency with factors affecting production. (a) Testing for independence of cross-tabulations The cross-tabulations of efficiency and factor categories can be used to test for independence of efficiency and the factor. We used Pearson’s contingency table test (see Freund, 1971: 334–7), adjusting categories so that the expected number in each cell was approximately five (or more) and no cells had zero frequencies.10 The results (summarised in column 1 of Table 4.7) indicate that the hypothesis of independence was accepted when the efficiency categories were cross-tabulated against the estates of the ten largest tenants-inchief, the grouping of estates according to whether they were held by a tenant-in-chief with a small, medium or large number of estates, when estates were grouped according to proximity to Colchester and Maldon,

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81

Notes: Bars giving percentages of efficient, relatively efficient, less efficient, inefficient and very inefficient estates for grazing/arable category, tenure and ancillary resources (percentage of estates above bar). Figure 4.12 Distribution of CS technology efficiency measure (u), by grazing/arable category, tenure and ancillary resources: Essex lay estates, 1086

and the grazing and arable categories. The independence hypothesis was rejected at the 5 per cent significance level

Notes: Chi(60), F(60,516) and t(575) refer to the distribution of the test statistic under the null hypothesis (degrees of freedom given in parenthesis), t ratios are signed according to the sign of the factor effect. * indicates significant at the 5 per cent level, and ** significant at the 1 per cent level. For the Pearson tests for independence, to increase cell numbers and ensure non-zero frequencies, some categories were adjusted and cells amalgamated. For the tenant-in-chief test only data for the estates of the ten largest tenants-in-chief were used and the inefficient and very inefficient categories amalgamated; for hundreds, only data for hundreds with more than twenty-two estates were used, and the inefficient and very inefficient categories amalgamated; for tenure, the sub-tenant categories were amalgamated; and for the estates grouped by size independence test the large and very large categories were amalgamated.

Table 4.7 CS technology, summary of tests of significance of various factors affecting production: Essex lay estates, 1086

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EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

83

for efficiency and geographical (soil) region; and rejected at the 5 and 1 per cent levels for efficiency and the size of estate, hundred location, and tenure. These independence tests, whilst suggestive, can be adversely affected by the categorisation of variables and amalgamation of cells, and cannot be applied directly to quantitatively measured factors. (b) Factors associated with fully efficient estates If we focus on whether or not an estate was fully efficient and seek to determine factors significantly associated with an estate being efficient, techniques, such as probit analysis, are available that do not suffer from these deficiencies; and, moreover, if a factor is significant, the nature of the association can be estimated. Table 4.8 contains the results of some probit analyses. In the upper part of the table, some key statistics for the probit analysis relating estate efficiency to hundred location are listed (the explanatory variables consisted of a set of binary variables, one for each hundred, taking the value one, when the estate was located in the hundred, zero otherwise). Because most estates were not efficient (481 of 577) and the dependent variable was set to one for an efficient estate and zero when not efficient, the probit coefficient estimates are mainly negative. Estimated probabilities of an estate in each hundred being efficient are given under the coefficient t ratios. The probabilities correspond to the proportions of efficient estates in the hundreds; higher probabilities being associated with larger estimated coefficients. The Count R2 value is 0. 834, corresponding to just over 83 per cent of predictions being correct.11 The probit analysis allows us to test the null hypothesis that all hundred probit coefficients are equal, against the alternative that they are not equal. (Equal coefficients imply that the probability that an estate was efficient was the same irrespective of hundred location, or, put another way, that efficiency did not depend on hundred location.) The test statistic, asymptotically distributed as a Chi-square distribution with 21 degrees of freedom when the null hypothesis is true, takes a value of 38.965. The hypothesis of equal coefficients is rejected at conventional significance levels, suggesting that efficiency did depend on the spatial location of the estate. The results for the analysis relating efficiency and geographical (soil) regions seem to confirm this. The hypothesis that the efficiency probability of an estate depended on its geographical region location is accepted at the 1 per cent level. On the other hand, there is no significant association between efficiency and proximity to the towns of Colchester and Maldon. Economic size of the estate is also a significant correlate with efficiency. The probit analysis (see Table 4.8) indicates that there is a significantly larger probability of larger estates being efficient. The result is confirmed in two ways: by an analysis of the estates grouped by size and by a direct probit analysis of efficiency against (the logarithm of) estate annual value. Column 2 of Table 4.7 summarises the results of the foregoing and other probit tests. The first row indicates that, at conventional significance levels, the efficiency probability did not depend on who the tenant-in-chief was. Because the coefficient estimates for tenants-in-chief with a few estates are imprecise, this test has low power, so it is more interesting to test if the coefficients of each tenant-in-chief with a reasonable number of estates (say, ten or more) and the rest grouped together are equal. The second row of the table indicates that this hypothesis is also accepted at the 5 and 1 per cent levels; as is the hypothesis of equal probit coefficients for the grouping of tenants-in-chief into those with a large, medium and small number of estates in Essex (see row 4).

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PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Although tenants-in-chief may have influenced, to some degree, how the estates of their sub-tenants were run, their prime concern would have been the performance of the estates they held in demesne. It is arguable, then, that a more interesting breakdown is in terms of estates held in demesne by each of the larger tenants-in-chief (say those with at least ten estates in Essex), those held in demesne by other tenantsin-chief, and estates held by mesne-tenants. Row 3 of the table indicates that the efficiency probability varied significantly (at the 5 per cent level) for estates in these groups; the probability being greater for estates held in demesne. A direct test that tenure affected the efficiency probability (reported in column 2 alongside ‘tenure’) also suggests that tenure (that is, whether or not an estate was held in demesne) was a significant factor. Column 2 of Table 4.7 also gives details of tests when the efficiency probability is linked to the grazing/ arable ratio and grazing/arable categories. A significant relationship is detected in the first case but not in the second. The grouping is, perhaps, too crude a reflection of the mix of agriculture under-taken. Finally, the probit method was applied to assess the relationship between estate efficiency and the existence of ancillary resources. The analysis was carried out in two ways: the qualitative effect of the resource being available on the estate was examined (the number, one, was entered for the explanatory variable when the resource was available; zero, otherwise), and also the quantitative effect (the number of units of the resource available was entered). The results are similar in both cases. The t ratios indicate that for all ancillary resources neither effect is significant at the 5 per cent level. (c) Factors significantly associated with estate efficiency index values If an estate is not fully efficient, it may operate very close to full efficiency or be very inefficient. The efficient/not efficient dichotomy just considered obscures this fact, and for many purposes it is more useful to focus on the estate u-efficiency index, which numerically indicates both whether an estate is efficient and (when not efficient) the degree of inefficiency. In Table 4.9 u-efficiency measures are used to investigate further the effect of estates being held in demesne on efficiency. Mean estate efficiency for each tenant-in-chief is listed, and a breakdown into those held in demesne and those Table 4.8 CS technology probit analysis, various factors affecting production: Essex lay estates, 1086 Hundred code

1

estimate t ratio efficiency probability

−1.068 −0.431 4.1** 1.0 0.14 0.33

code

2

12

13

3

4

−0.431 1.2 0.33

−0.812 −0.792 4.0** 3.6** 0.21 0.21

14

estimate −0.989 −1.049 −0.589 t ratio 3.7** 4.0** 2.6** efficiency 0.16 0.15 0.28 probability Chi-square test statistic (21)=38.965**

5

6

7

−1.258 −5.723 5.2** 0.0 0.10 0.00

15

16

−0.489 2.6** 0.31

−1.020 −5.723 4.2** 0.0 0.15 0.00

Count R2=0.834

8

17

18

9

10

−1.565 −1.221 3.2** 3.1** 0.06 0.11

19

−0.842 −1.786 2.3* 4.0** 0.20 0.04

11

−5.723 −1.042 0.0 5.8** 0.00 0.15

20

21

22

0.000 0.0 0.50

−5.723 −5.723 0.0 0.0 0.00 0.00

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

85

Geographical (soil) region

London Clay Area Tendring/Colchester Loam Area Boulder Clay Plateau

estimate t ratio efficiency probability Chi-square test statistic (2)=11.510**

−0.825 8.6** 0.21 Count R2=0.834

−0.623 3.6** 0.27

−1.186 12.5** 0.12

Colchester/Maldon influence

Colchester

Maldon

Other

estimate t ratio efficiency probability Chi-square test statistic (2)=1.61 1

−0.712 3.4** 0.24 Count R2=0.834

−1.040 5.5** 0.15

−0.985 14.2** 0.16

Table 4.8 continued Estates grouped by size

Very small

Small

Medium

Large

Very large

estimate t ratio efficiency probability Chi-square test statistic (4)=11.370*

−1.335 5.6** 0.09 Count R2=0.834

−1.145 7.2** 0.13

−0.894 8.6** 0.19

−1.064 8.7** 0.14

−0.547 3.3** 0.29

Economic size indicator estimate 0.225 t ratio 3.6** Count R2=0.834 Notes: Entries consist of probit parameter estimates, t ratios and the estimated probability of an estate being efficient. Hundred codes: 1=Barstable, 2=Beacontree, 3=Chafford, 4=Chelmsford, 5=Dengie, 6=Dunmow, 7=Clavering and Clavering half-hundred, 8=Freshwell half-hundred, 9=Harlow, 10=Harlow half-hundred, 11=Hinckford, 12=Lexden, 13=Ongar, 14=Rochford, 15=Tendring, 16=Uttlesford, 17=Waltham, 18=Winstree, 19=Witham, 20=Maldon half-hundred, 21=Thunreslau half-hundred, 22=Thurstable. The Chisquare test statistic (with degrees of freedom in parentheses) is used to test that all factor parameters are zero. (* indicates significant at the 5 per cent level, ** significant at the 1 per cent level.) Table 4.9 CS technology efficiency of estates of tenants-in-chief held in demesne and by sub-tenants: Essex lay estates, 1086 Code

Tenant-inchief

Number of

estates in Essex

estates analysed

estates held in demesne

estates held by subtenants

all estates estates held in demesne

estates held by subtenants

1

Count Eustace Suen of Essex

81

72

25

47

1.700

1.543

1.784

65

57

16

41

1.734

1.288

1.908

2

Mean efficiency (u)

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PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Code

Tenant-inchief

Number of

estates in Essex

estates analysed

estates held in demesne

estates held by subtenants

all estates estates held in demesne

estates held by subtenants

3

Geoffrey de Magna Villa Robert Greno Richard son of Count Gilbert Ranulf Peverel Ralf Baignard Eudo dapifer William de Warene Ranulf brother of Ilger Hugh de Montfort Hamo dapifer Peter de Valognes Aubrey de Ver Robert son of Corbutio Count Alan Roger de Ramis John son of Waleram Walter the deacon Moduin Tithel the Breton Roger Bigot Sasselin Henry de Ferrariis Robert Malet

57

42

6

36

1.666

1.608

47 44

44 29

11 9

33 20

2.332 1.832

2.484 2.281 1.325 2.060

39

37

12

25

1.760

1.289

1.986

32

29

7

22

1.755

1.534

1.826

25 25

24 18

8 6

16 12

1.495 1.609

1.519 1.483 1.883 1.472

23

17

5

12

1.826

1.548

1.942

20

18

7

11

1.901

1.472

2.174

19 16

15 14

2 7

13 7

1.660 2.485

1.759 1.644 2.904 2.066

16

16

6

10

1.931

1.877

1.963

14

11

1

10

2.388

1.000

2.527

13 13

9 12

3 10

6 2

2.155 2.725

2.613 1.926 2.713 2.783

10

8

1

7

2.166

1.000

9

9

4

5

1.768

1.693 1.829

8 8

5 8

5 6

0 2

1.806 1.868

1.806 − 1.500 2.674

7 7 5

7 4 5

1 4 4

6 0 1

2.066 1.570 1.278

1.463 2.167 1.570 − 1.177 1.683

5

3

1

2

2.268

3.087

4 5

6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Mean efficiency (u)

1.676

2.333

1.859

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

Code

Tenant-inchief

Number of

estates in Essex

estates analysed

estates held in demesne

estates held by subtenants

all estates estates held in demesne

estates held by subtenants

26

Roger de Otburville Ilbodo

5

5

5

0

1.388

1.388

–

4

4

4

0

3.065

3.065

–

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Thierri Pointel Walter de Doai Hugh de Gurnai Ralph de Limesy Roger de Poitou Roger ‘God save the ladies’ Hugh de St Quintin Adam son of Durand Countess of Aumale Edmund son of Algot Grim Matthew of Mortagne William Peverel Robert son of Roscelin William de Scohies Ralf de Toesni Ulveva Walter the cook William the deacon Count of Ou Frodo brother of the abbot Gilbert son of Turold Gonduin Goscelin the lorimer John nephew of Waleram Countess Judith Otto the goldsmith Ralf Pinel Rainald the crossbowman Robert son of Gobert Stanard Robert de Toesni Turchill

Mean efficiency (u)

4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

3 3 3 3 2 2 3 2 2 2 1 2 2 1 2 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 3 0 2 2 2 3 2 2 2 1 2 1 1 1 0 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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

1.665 1.219 1.484 1.706 2.286 2.099 1.822 2.826 1.395 1.726 2.150 1.447 1.331 1.251 1.947 1.325 1.583 1.149 1.300 1.593 1.161 1.542 2.500 1.000 2.416 1.000 1.211 1.454 1.000 2.125 3.333 1.446 2.000

1.426 1.219 − 1.359 2.286 2.099 1.822 2.826 1.395 1.726 2.150 1.447 1.000 1.251 1.395 − 1.583 1.149 1.300 1.593 1.161 1.542 2.500 1.000 2.416 1.000 1.211 1.454 1.000 2.125 3.333 1.446 2.000

2.143 − 1.484 2.400 − − − − − − − − 1.663 − 2.500 1.325 − − − − − − − − − − − − − − − − −

87

88

61

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

William son of Constantine All estates analysed

1

1 577

1 223

0 354

1.442 1.844

1.442 1.728

− 1.918

held by sub-tenants given. The estates of Count Eustace tended to be more efficient than average. The mean u-efficiency index value for all his estates was 1.700 against the overall estate mean of 1.844. For estates held in demesne by Count Eustace, the mean index value was 1.543 against 1.728 for all estates held in demesne; and the mean index value for estates held by the Count’s subtenants was 1.784 against the overall mean for sub-tenant estates of 1.918. Similar results are obtained for the other tenants-in-chief holding the largest number of estates in Essex. Of the ten tenants-in-chief with the largest number of estates, the mean index value for all estates held is less than the overall mean in all but one case; and, for estates held in demesne, the mean is less than average in eight of the ten cases. Usually estates held in demesne by a tenant-in-chief were more efficient than those held by sub-tenants. Of the twenty-seven tenants-in-chief who held some estates in demesne and some not in demesne, the mean u-index value for estates held in demesne was less in twenty cases. Moreover, the mean index value for estates held in demesne was significantly smaller (indicating greater efficiency) than for those not in demesne.12 Tenants-in-chief who held a reasonable number of estates in demesne (four or more) and organized them relatively efficiently include Suen of Essex (mean u-efficiency 1.288), Richard son of Count Gilbert (1.325), Ranulf Peverel (1.289), Hugh de Montfort (1.472), Henry de Ferrariis (1.177) and Roger de Otburville (1. 388). Those of Robert Greno (2.484), Peter de Valognes (2.904) and Roger de Ramis (2.713) were relatively inefficient. Table 4.10 gives a breakdown of u-efficiency measures by hundred. Maldon half-hundred has the highest average efficiency (1.006), but only two estates were located in its area. Others with high average efficiency are Chafford hundred (1.271), Dengie (1.445), Harlow half-hundred (1.422), Rochford hundred (1.653) and Winstree (1.664). Those with more inefficient estates were Lexden hundred (2.384), Thurstable (2.303), Waltham (2.301), Clavering hundred and half-hundred (2.195), Witham hundred (2.099), Ongar (1.908) and Harlow hundred (1.905). The third column of Table 4.7 lists the results of tests of significance when the estate efficiency index was regressed on the factors affecting production. The measure u−l rather than u was used as the dependent variable in the regressions as this transformation resulted in more homoskedastic disturbances.13 (Note that, as u−l is the dependent variable, factors that have a positive effect in the regressions are associated with greater efficiency.) In most cases factors significant in the regressions were those significant in the probit analyses. The grouping of estates according to whether they were held in demesne by tenants-in-chief, the hundred influence, the size of estates, the grazing/arable ratio and tenure variables were all significant; and the grazing/arable categories, Colchester/Maldon influence and ancillary resources not significant. Some differences with the probit results were that in the efficiency index regressions the classification of estates according to tenant-in-chief, and the grouping by Table 4.10 Estate CS efficiency by hundred: Essex lay estates, 1086 Hundred

Mean u efficiency Standard deviation of mean

Deviation from overall Number of estates in mean sample

Barstable Beacontree Chafford

1.895 1.824 1.271

0.051 −0.020 −0.573

0.126 0.300 0.099

35 9 12

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

Hundred

Mean u efficiency Standard deviation of mean

Deviation from overall Number of estates in mean sample

Chelmsford Dengie Dunmow Clavering hundred and half-hundred Freshwell half-hundred Harlow Harlow half-hundred Hinckford Lexden Ongar Rochford Tendring Uttlesford Waltham Winstree Witham Maldon half -hundred Thunreslau halfhundred Thurstable

1.882 1.445 1.692 2.195

0.115 0.071 0.100 0.239

0.038 −0.399 −0.153 0.351

48 42 48 10

1.795 1.905 1.422 1.877 2.384 1.908 1.653 1.869 1.716 2.301 1.664 2.099 1.006 1.880

0.200 0.157 0.195 0.099 0.224 0.132 0.167 0.156 0.117 0.247 0.195 0.139 0.006 0.502

−0.049 0.061 −0.422 0.033 0.540 0.064 −0.191 0.025 −0.128 0.457 −0.180 0.254 −0.838 0.036

17 18 3 74 31 34 36 48 39 4 15 27 2 3

2.303

0.198

0.459

22

89

the number of estates the tenants-in-chief held in Essex were significant, but the geographical (soil) region grouping was not. (d) Multivariate Analysis The preceding analysis should be seen as exploratory in nature, a search to discover which factors influenced CS u-efficiency. We have assessed bivariate relationships between efficiency and a single factor. This would be entirely satisfactory if the effects of other factors were held constant, as in a controlled experimental situation, but may be misleading if, as in the Domesday sample, several factors vary as we move from one estate to another. In these circumstances, the bivariate relationship between efficiency and a factor may appear significant because of changes in a third variable. (For example, in the bivariate probit analysis, the factor, geographical (soil) region, may appear to affect significantly the probability of an estate being fully efficient, but this may be because more efficient tenants-in-chief happened to hold estates in particular soil regions.) Similarly, the influences of other factors may result in a bivariate relationship appearing insignificant, even though the factor does significantly influence efficiency. (For example, a negative bivariate relationship between estate efficiency and the existence of a mill on the estate may be obscured by an association of mills with more

90

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

efficient tenants-in-chief.) If the influence of the other factors is controlled for, the (true) bivariate relationship would be revealed. A technique that allows us to (partially) control for the influence of extraneous factors when assessing the relationship between variables is multivariate regression. Table 4.11 displays the main results of two interesting multivariate regressions. In the preferred specification, the tenant-in-chief in demesne effect was modelled by binary variables indicating whether an estate was held in demesne by one of the eighteen tenants-in-chief with ten or more estates in Essex, held in demesne by one of the remaining tenants-in-chief, or held by a sub-tenant. This effect was significant at the 5 per cent level, as was the hundred effect (modelled by binary variables indicating the hundred location of an estate). The estate economic size indicator (the logarithm of the estate’s annual value) and the kind of agriculture effect (modelled by the estate’s grazing/arable ratio) were also significant, larger estates and estates with relatively more grazing being more efficient. Proximity to Colchester and Maldon and the Table 4.11 CS technology, multivariate regressions of efficiency index (u−l) on estate characteristics: Essex lay estates, 1086

Tenant-in-chief in demesne effect Tenant-in-chief effect Tenure effect Hundred effect Colchester/Maldon influence Economic size indicator Kind of agriculture effect Geographical (soil) region effect Beehives Fisheries Mills Saltpans Vineyards

Preferred specification Test Alternative specification statistic Test statistic

Distribution on null

1.883*

F(19,525)

1.583* 0.748

1.646* 0.3 1.473 0.619

F(18,525) t(525) F(21,525) F(2,525)

10.4** 2.4* 1.512

10.3** 2.4* 1.466

t(525) t(525) F(2,525)

−1.9 −1.5 t(525) −1.0 −0.4 t(525) −2.6** −2.8** t(525) −1.9 −2.1* t(525) 0.4 0.1 t(525) 0.282 0.274 Notes: * indicates significant at the 5 per cent level and ** significant at the 1 per cent level. The efficiency measure u−l (rather than u) was used as the dependent variable, because this resulted in more homoskedastic disturbances; indeed, no significant heteroskedasticity was detected in a battery of tests. For example, for the preferred specification when the squared residuals were regressed on the (dependent variable) predicted values, the Chi-square test statistic (with one degree of freedom) was 2.881 (not significant at the 5 or 1 per cent levels). is the coefficient of determination adjusted for degrees of freedom.

estate’s geographical (soil) region were not significant influences. It is interesting that in the multivariate regression (where the influences of third variables are controlled for) the impact of some ancillary resources (including beehives, mills and saltpans) on efficiency is negative, the mills effect being significantly

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

91

negative. This is consistent with the returns from these resources not being included in the estate annual values and other estate inputs (particularly labour) having been used to work the ancillary resources. Even so, the quantitative effect of the ancillary resources on efficiency is quite small. The adjusted coefficient of determination, , equals 0.282, so a little over a quarter of the variation in the efficiency measure (u−1) is explained by movements in the explanatory variables.14 Similar statistical results were obtained in the alternative multivariate regression specification, in which binary variables were introduced to indicate the tenant-in-chief of the estate, and a separate binary variable used to indicate whether or not the estate was held in demesne. The tenant-in-chief effect was significant, but not the tenure effect; suggesting that this way of modelling tenant-in-chief and tenure is less appropriate. Although the hundred effect is not significant at the 5 per cent level, it is at the 9 per cent level. As in the preferred specification, the economic size indicator and kind of agriculture effect were significant, and the Colchester/Maldon influence variables and geographical region effects not significant. As before, the existence of beehives, mills or saltpans on the estates was associated with lower efficiency, the effects for mills and saltpans being significant.15 To summarise, the estimated estate bivariate relationships suggested a number of factors associated with estate efficiency. The multivariate regressions (which control for third variables influencing the efficiency relationship) indicated that CS efficiency was influenced by whether an estate was held in demesne by the tenant-in-chief (estates being held in demesne tending to be more efficient) and who the tenant-in-chief was, the hundred location, economic size of the estate (larger estates being more efficient) and the kind of agriculture carried out on the estate (estates with relatively more grazing being more efficient). Estates with beehives, mills or saltpans tended to be less efficient, perhaps because the returns from these resources were not included in the estate annual values but labour and other estate inputs were used to work the resources. Commenting on these results, we note that economists would expect some variation in efficiency across tenants-in-chief. A tenant-in-chief fulfilled an entrepreneurial role, and it might be expected that he would have operated his various estates using organisational methods that reflected his abilities, experience and entrepreneurial flair. Turning to other multivariate results, sub-tenants usually only operated one or two estates. This may have disadvantaged them and hence may explain why estates held in demesne tended to be more efficient. The significant hundred location effect indicates the importance of spatial factors; production at some locations was more favourable than at others. It is perhaps surprising that location close to an urban centre was an insignificant factor. One might have thought that estates located near towns would have enjoyed lower transport costs to market and demand would have raised output prices in larger markets. On the other hand, the effect of competition amongst suppliers may have offset these factors. The geographical (soil) region classification was also an unimportant determinant of efficiency. The classification (into three regions) is very broad, and it may be that the effect of soil on efficiency is captured by the finer hundred spatial classification. The relative efficiency of estates involved in grazing probably reflects the profitability of the wool trade. Sheep were the dominant livestock in Essex with Domesday Book listing large numbers of sheep on the Essex marshlands. Snooks (1995:39) describes Domesday England as a major supplier of raw wool to Europe, the lush pastures of England providing a comparative advantage in raw wool production. Wool was produced for domestic consumption but much wool was exported overseas, especially to Flanders. Finally, interpretation of the higher efficiency of larger estates is deferred until the efficiency analyses assuming other technologies are described (see Section 4.10).16

92

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

4.9 RESOURCE SHADOW PRICES AND SLACK RESOURCES Shadow prices can be calculated from the linear programming problems that generated the estate efficiency measures (u). In Section 3.6, it was shown that the shadow prices, multiplied by the estate’s annual value, generate a further set of shadow prices, with the following interesting productivity interpretation: An estate’s resource shadow price equals the increase in annual value that can be achieved by an efficient estate, operating at the estate’s resource level, when an extra unit of the resource is made available. (This result requires that the shadow price remains unchanged at the new optimal feasible solution, and is only approximately true otherwise.) Information on shadow prices with this interpretation is summarised in Table 4.12. For each resource, the mean, standard deviation, coefficient of variation and interquartile range of the shadow prices for all 577 estates analysed are displayed. For demesne ploughteams, the mean shadow price is 43.1 shillings, so, on average, an addition (or subtraction), at the margin, of one demesne ploughteam would have added (subtracted) about 43 shillings to (from) the annual value of the estate. The shadow price varied quite considerably with the estate’s resource mix. Three measures of dispersion are given: the standard deviation (17.7 shillings), coefficient of variation (0.4) and interquartile range (18.2 shillings). (The coefficient of variation is the ratio of the standard deviation to the mean of the variable, so it is a dispersion measure that allows for the average size of the variable; the interquartile range is the difference between the third and first quartiles.) The contribution made by peasants’ ploughteams was far less (mean value 7.4 Table 4.12 Shadow prices (in shillings) for 577 Essex lay estates, 1086: CS technology Demesne ploughteams Peasants’ ploughteams Livestock Freemen and sokemen Villans Bordars Slaves Woodland Meadow Pasture

Mean

Standard deviation

Coefficient of variation

Interquartile range

43.1 7.4 0.2 2.8 8.2 5.5 12.5 1.3 3.1 0.6

17.7 12.0 0.3 5.3 11.1 10.6 13.2 2.3 8.5 0.4

0.4 1.6 1.7 1.9 1.4 1.9 1.1 1.8 2.8 0.7

18.2 11.4 0.2 3.8 10.0 6.7 11.9 1.3 2.8 0.5

shillings). The peasants’ ploughteams were used to cultivate the peasants’ strips and occasionally on the demesne, and we might expect that the arrangement would have varied between estates. The statistics (standard deviation 12.0, coefficient of variation 1.6, and interquartile range 11.4) are consistent with this. The contribution from livestock appears rather high (for example, an additional sheep added, on average, about nine pence to the annual value of an efficient estate). Again, there was considerable variation in productivity across estates. Of the labour resources, slaves had the highest mean shadow price (12.5 shillings), villans and bordars 8. 2 and 5.5 shillings respectively, and freemen and sokemen a rather lower price (2.8 shillings). As slaves worked full-time on the demesne, villans and bordars for only part of the week, and freemen and sokemen

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

93

made a small (but variable) contribution, these prices seem plausible. A unit of woodland (that ‘could support one swine’) had a mean shadow price of 1.3 shillings, an acre of meadow a mean shadow price of 3.1 shillings, and pasture that ‘could support one sheep’ 0.6 shillings. Meadow was clearly a valuable resource. Most resources, including land and livestock, had relatively high valuations on efficient estates. For all resources there were major variations in shadow prices across estates, as is evident from the wide interquartile ranges and high standard deviations and coefficients of variation. Table 4.13 indicates one reason for the large variation in shadow prices—the widespread existence of slack resources. Positive slack in a resource indicates that with less of the resource the same annual value could have been generated (had the estate been run efficiently). It does not necessarily mean that some of the resource was actually idle, but it does indicate that, at the margin, the resource made no contribution to annual value. Only 1 per cent of estates with demesne ploughteams had positive slack in demesne ploughteams. Slack in slaves was also relatively less common (21 per cent of estates with slaves had positive slack in slaves). For other resources the percentages were in the region Table 4.13 Slack resources: CS technology, Essex lay estates, 1086

Demesne ploughteams Peasants’ ploughteams Livestock Freemen and sokemen Villans Bordars Slaves Woodland Meadow Pasture

Number of estates with resource

Number of estates with positive slack

Percentage Mean of estates positive with slack values resource with positive slack

Median positive slack value

Standard deviation

Coefficient of variation

568

5

1

1.0

0.5

1.1

1.1

361

157

43

1.6

0.8

2.3

1.4

348 69

153 44

44 64

535 3.1

389 1.4

482 3.5

0.9 1.1

346 534 359 428 426 116

122 211 77 177 204 49

35 40 21 41 48 42

2.4 3.8 1.5 103 9.4 103

1.8 2.7 1.0 45.4 5.3 60.0

3.0 5.4 1.2 147 11.7 124

1.2 1.4 0.8 1.4 1.2 1.2

of 40 per cent, rising to 64 per cent for freemen and sokemen. On many estates the amount of the resource that was slack was quite large as can be seen from the mean positive slack values. For example, for bordars the mean slack value for the 211 estates with positive slack in the resource was 3.8 bordars (the fractional part, 0.8, can be interpreted as 8/10 of a bordar’s work-time). Notice that the median is considerably smaller (2.7 bordars), which indicates that the distribution has a long tail to the right (corresponding to high values). This is common to the other resources. We have already briefly compared the shadow prices of the different classes of labour. We now analyse them in more detail. We have argued that the resources of the estate were relatively fixed in the short run. Over time there were opportunities for varying them. For example, livestock could be bred and the amount of pasture increased by clearing. One possibility was to change the contractual arrangement with labour—

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perhaps freeing slaves or forming a villan-contract with a bordar. Social and political factors, as well as economic factors, would be important if such a change was made. The Domesday record indicates that in Essex between 1066 and 1086 the number of bordars increased relative to the number of villans and slaves. Was there an economic incentive to change the status of villans and slaves in 1086? From Table 4.12 we see that the mean shadow price of bordars (5.5 shillings) was less than that for villans (8.2 shillings) and considerably less than that for slaves (12.5 shillings). This suggests that there was no economic incentive. Nevertheless, there was considerable variation across estates, and it may be that on a class of estates (for example, large estates with both bordars and villans) the shadow price for bordars was greater. Table 4.14 helps to answer the question. For all estates with villans and bordars, the mean shadow price for both classes of labour was considerably less (4.4 shillings for villans and 3.6 shillings for bordars) than for all 577 lay estates. (This is not surprising because on average these estates have more bordars and villans relative to other resources, and it is to be expected that productivity will fall as relatively the number of units of a resource increases.) Although the villan mean shadow price was 1.19 times that for bordars, the means are not statistically significantly different. On larger estates (with an annual value in the top 35 per cent of all estates), the mean shadow prices for villans and bordars were very similar (4.4 and 4.2 shillings respectively), and on smaller estates the mean shadow price difference greater (4.3 and 2.6 shillings, this difference being significant at the 5 per cent level). When an estate had both bordars and slaves, the slave mean shadow price was considerably greater, although the difference was less marked on larger estates; and, when an estate had both villans and slaves, the mean slave shadow price was again considerably greater with the difference less marked on larger estates. (All these differences are significant at the 5 per cent level.) The evidence, then, suggests that on most estates in 1086 there was no Table 4.14 Shadow prices (in shillings) for estates with both labour resources: CS technology, Essex lay estates, 1086 All estates Number of estates

Larger estates Mean price

Number of estates

Smaller estates Mean price

Number of estates

Mean price

Villans 4.4 4.4 4.3 Bordars 3.6 4.2 2.6* Ratio 326 1.19 204 1.05 122 1.61 Bordars 3.8 4.0 3.6 Slaves 7.3** 6.8** 7.9** Ratio 334 0.52 181 0.59 153 0.46 Villans 4.5 4.3 4.9 Slaves 7.1** 6.5** 8.1* Ratio 246 0.64 167 0.67 79 0.60 Notes: Smaller estates are estates with an annual value that lies in the lowest 65 per cent of all estates, and larger estates those with an annual value in the top 35 per cent. * indicates mean prices significantly different at the 5 per cent level, ** significantly different at the 1 per cent level.

economic incentive to free slaves or give a bordar-contract to a villan, although on the larger estates the return from bordars and villans was very similar.17

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

95

In this section, we have focused on shadow price mean values, but the dominant feature of the resource shadow prices is their variability. Why did resource productivities vary so much? Why was there so much slack in resources? What are the implications of this for the efficiency of Domesday agricultural production? These issues are discussed in Chapter 6. 4.10 EFFICIENCY RESULTS FOR FOUR TECHNOLOGIES COMPARED In Appendix 3, efficiency measures (u) for each estate assuming constant and variable returns to scale technologies are listed. The identification code for the estate is given followed by efficiency measures assuming: constant returns to scale, strong disposability of resources (CS) technology; variable returns to scale, strong disposability of resources (VS) technology; constant returns to scale, weak disposability of resources (CW) technology; and variable returns to scale, weak disposability of resources (VW) technology. Estates tend to have higher efficiency measures (tend to be more inefficient) under constant returns rather than variable returns technologies, and under strong disposability rather than weak disposability of resources technologies. More precisely, for any estate, the u-value assuming CS technology is greater than or equal to that under the other technologies, the u-value under CW technology is greater than or equal to that under VW technology, and the u-value assuming VS technology is greater than or equal to that assuming VW technology. Figure 4.13 contains bar charts giving percentages in the five efficiency categories, for all 577 estates in the sample, assuming different technologies. Under CS technology, about one-sixth of estates are efficient. This proportion increases to about one-third assuming VS technology, just over one-half under CW technology and almost three-quarters under VW technology. In our view the CS technology assumptions give the closest approximation to production reality in Essex in 1086, so we have emphasised the CS efficiency results. VS technology gives the next-closest approximation, and the influences of the various production factors on VS efficiency tend to be similar to those on CS efficiency. To illustrate this, consider the distribution of the VS efficiency measure u by grazing/arable category, tenure and ancillary resources described in Figure 4.14. Turning to the grazing/arable categories first, we see that the mainly arable efficiency category percentages are very similar to the average, with the very inefficient percentage slightly greater than average and the inefficient percentage slightly less than average. This reflects the situation for CS efficiency (see Figure 4.12). For the mixed category, under VS technology, the relatively efficient category percentage is slightly greater than average, and the inefficient and very inefficient percentages down; and, for the mainly grazing category, the inefficient percentage above, and the efficient and very inefficient percentages below, average. Similar results were obtained under CS technology. The tenure and ancillary resources results also indicate broad similarities for the two technologies. Table 4.15 summarises the results of significance tests of the various factors on VS efficiency. The results are again broadly similar to those for CS technology. On the Pearson Chi-square tests for independence the only difference in test results is that, with VS efficiency, independence was rejected at the 5 per

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Notes: Bars give percentages of efficient, relatively efficient, less efficient, inefficient and very inefficient estates, for all estates, assuming different technologies. Figure 4.13 Comparison of CS, VS, CW and VW efficiency measures (u): Essex lay estates, 1086 Table 4.15 VS technology, summary of tests of significance of various factors affecting production: Essex lay estates, 1086 1. Pearson Chi-square tests for independence Tenants-inchief: All Tenants-inchief: Largest Tenants-inchief: In demesne Tenants-inchief: Grouped Hundred Geographical (soil) region Colchester/ Maldon influence Estates grouped by size Economic size indicator Grazing/arable ratio Grazing/arable categories Tenure Beehives: Qualitative

41.473*

Chi(24)

−

2. Probit analyses: Probability estate efficient

3. Efficiency measure (u−1) regressions

75.576

Chi(60)

1.418*

F(60,516)

36.739**

Chi(18)

3.168*

F(18,558)

48.183**

Chi(19)

3.753**

F(19,558)

10.170

Chi(8)

80.058*

Chi(2)

3.630*

F(2,574)

62.219** 19.420*

Chi(30) Chi(8)

45.058** 9.552**

Chi(21) Chi(2)

2.811* 1.455

F(21,555) F(2,574)

11.131

Chi(8)

0.279

Chi(2)

0.426

F(2,574)

135.676**

Chi(9)

60.036**

Chi(4)

32.753**

F(4,572)

−

6.1**

t(575)

12.00**

t(575)

−

1.7

t(575)

1.8

t(575)

9.689

Chi(8)

0.464

Chi(2)

0.729

F(2,574)

16.956** −

Chi(4)

2.8** −1.1

t(575) t(575)

3.9** −0.5

t(575) t(575)

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

97

Notes: Bars giving percentages of efficient, relatively efficient, less efficient, inefficient and very inefficient estates for grazing/arable category, tenure and ancillary resources (percentage of estates above bar). Figure 4.14 Distribution of VS technology efficiency measure (u), by grazing/arable category, tenure and ancillary resources: Essex lay estates, 1086

Quantitative

1. Pearson Chi-square tests for independence

2. Probit analyses: Probability estate efficient

3. Efficiency measure (u−1) regressions

−

1.5

1.7

t(575)

t(575)

98

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

1. Pearson Chi-square tests for independence

2. Probit analyses: Probability estate efficient

3. Efficiency measure (u−1) regressions

Fisheries: − 1.5 t(575) 1.1 t(575) Qualitative Quantitative − 1.6 t(575) 0.9 t(575) Mills: − −0.9 t(575) −0.1 t(575) Qualitative Quantitative − 0.7 t(575) 1.0 t(575) Saltpans: − 0.1 t(575) −1.0 t(575) Qualitative Quantitative − −0.8 t(575) −1.4 t(575) Vineyards: − 0.1 t(575) 1.9 t(575) Qualitative Quantitative − 0.5 t(575) 1.3 t(575) Notes: Chi(60), F(60,516) and t(575) refer to the distribution of the test statistic under the null hypothesis (degrees of freedom given in parenthesis), t ratios are signed according to the sign of the factor effect. * indicates significant at the 5 per cent level, and ** significant at the 1 per cent level. For the Pearson tests for independence, to increase cell numbers and ensure non-zero frequencies, some categories were adjusted and cells amalgamated. For the tenant-in-chief test only data for the estates of the seven-largest and ninth- and tenth-largest tenants-in-chief were used, and the inefficient and very inefficient categories amalgamated; for hundreds, only data for hundreds with more than twenty-two estates were used, and the inefficient and very inefficient categories amalgamated; for tenure, the subtenant categories were amalgamated; and for the estates grouped by size independence test the large and very large and inefficient and very inefficient categories were amalgamated.

cent level when tenant-in-chief was cross-tabulated with efficiency. (With CS efficiency, independence was rejected at the 5.1 per cent level, test statistic p-value, 0.0509, but not the 5 per cent level, so the difference is quite minor.) Comparing the probit analyses, the main differences were that under VS technology the efficiency probability varied significantly with the grouping of estates by (largest) tenants-in-chief and the grouping into tenants-in-chief with a small, medium and large number of estates in Essex, and the grazing/arable ratio was not significant at the 5 (but was at the 10) per cent level. (Under CS technology, these tenant-in-chief variables were not significant and the grazing/ arable ratio was.) In the u−l efficiency measure regressions, the main difference was that the grazing/arable ratio was not significant at the 5 per cent level in the VS regression, but was significant at that level in the CS regression. (The grazing/arable ratio was significant at the 8 per cent level in the VS regression.) In the multivariate regressions, the results were again similar (see Table 4.16). As under CS technology, in the preferred specification the tenant-in-chief in demesne effect, hundred effect and the economic size indicator variable were significant, the Colchester/Maldon influence and geographical region effect not significant, and beehives, mills and saltpans associated with less efficient estates. (The beehives and saltpans estimates were significant.) A difference is that the grazing/arable ratio was not significant. Similar results were obtained in the alternative specification. The tenant-in-chief, hundred, economic size and saltpans effects were significant and, again, the grazing/arable ratio not significant (as were the tenure, Colchester/Maldon influence and geographical region effects). It is, perhaps, not surprising that the VS frontier tends to exhibit very slightly increasing, but close to constant, returns to scale. The returns to scale vary with input proportions and scale. An impression of

EFFICIENCY ANALYSIS OF ESSEX LAY ESTATES

99

average returns to scale can be obtained by observing how the ratio of frontier annual value to the key ploughteams input varied with the number of ploughteams working the estate. Ploughteams were by far the most productive inputs (see the shadow prices listed in Table 4.12), so an approximation to input use is given by the weighted sum of an estate’s demesne and peasants’ ploughteams (with weights determined by mean shadow prices). If the frontier annual value/ploughteams ratio is constant as the number of ploughteams on the estate increases, this suggests constant returns to scale; and, if it increases, increasing returns to scale. A regression of the ratio on the number of ploughteams in use indicates very mildly increasing but very close to constant returns to scale. The frontier annual value/ploughteams ratio increased by about one and a half (shillings per unit of the ploughteams variable) for each extra unit of ploughteams, an increase which is not significantly different from zero.18 It is particularly interesting that, when VS technology is assumed, larger estates tend to be more efficient. This result was also obtained with CS technology. In that case the interpretation was confused by the problem that the result could have occurred because larger estates were indeed more efficient, or Table 4.16 VS technology, multivariate regressions of efficiency index (u−l) on estate characteristics: Essex lay estates, 1086

Tenant-in-chief in demesne effect Tenant-in-chief effect Tenure effect Hundred effect Colchester/Maldon effect Economic size indicator Kind of agriculture effect Geographical (soil) region effect Beehives Fisheries Mills Saltpans Vineyards

Preferred specification Test Alternative specification statistic Test statistic

Distribution on null

9.610**

F(19,525)

2.306** 1.180 9.6** 1.1 1.098

2.337** 0.6 2.234** 1.112 9.9** 1.0 1.404

F(18,525) t(525) F(21,525) F(2,525) t(525) t(525) F(2,525)

−2.8** −1.8 t(525) −0.7 0.6 t(525) −1.2 −1.3 t(525) −2.4* −2.3* t(525) −0.7 −0.5 t(525) 0.268 0.282 Notes: * indicates significant at the 5 per cent level and ** significant at the 1 percent level. The efficiency measure u−l (rather than u) was used as the dependent variable, because this resulted in more homoskedastic disturbances; nevertheless, diagnostic tests detected some heteroskedasticity, and, consequently, all test statistics are heteroskedasticity-consistent test statistics (see H.White, 1980). is the coefficient of determination adjusted for degrees of freedom.

because the constant returns to scale assumption is not strictly correct (technology in fact allowing slightly increasing returns to scale). VS technology does allow for possible increasing returns to scale, and yet we find larger estates still tend to be more efficient. This gives greater credibility to the hypothesis that larger estates were (on average) more efficient.

5 AN ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

5.1 INTRODUCTION In earlier chapters we focused on one approach to measuring efficiency. Given plausible technological assumptions, mathematical programming methods were used to locate an estate relative to a production possibility frontier. An estate operating on the frontier was judged efficient and one below the frontier inefficient, the distance from the frontier being a measure of its inefficiency. This method, sometimes referred to as data envelopment analysis, or DEA, has been used extensively in the economics, management science and operations research fields. (For examples, see Section 6.2, and the references cited there; Nunamaker, 1985, Silkmans,1986, and Epstein and Henderson, 1989, discuss the use of DEA in management science and operations research.) Economists have suggested other ways of generating production frontiers, and hence measuring efficiency. The articles of Førsund, Lovell and Schmidt (1980), Schmidt (1986), Seiford and Thrall (1990), and Bauer (1990) provide excellent surveys of this literature. (Additional references are Dogramaci and Färe, 1988; Sueyoshi, 1991; Fried, Lovell and Schmidt, 1993; Färe, Grosskopf and Lovell, 1994; and Charnes, Cooper, Lewin and Seiford, 1994.) In Section 5.2, the alternative approaches, their advantages and disadvantages, are briefly reviewed in a non-technical way. The review draws on the production theory and statistical ideas discussed in Domesday Economy, chapters 8, 9 and 10. Non-frontier approaches to measuring efficiency also exist. It is argued that a particular non-frontier method appears to be a promising way of analysing the efficiency of the Essex Domesday estates. This analysis is the subject of the remainder of the chapter. 5.2 A REVIEW OF METHODS OF ESTIMATING EFFICIENCY Førsund, Lovell and Schmidt (1980) refer to the mathematical programming approach to generating the frontier as a deterministic, non-parametric method. The frontier is non-parametric in the sense that it is not a simple functional relationship linking annual value to the resources and involving a few parameters (such as the Cobb-Douglas function, described below). Instead it consists of a number of lines (or hyperplanes) connecting a sub-set of the manorial observations (the sub-set being the manorial observations judged efficient).

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It is deterministic because all estates share exactly the same frontier, with all variations in performance relative to the frontier attributed to manorial efficiency. Some of the variation in performance was due to factors that the manorial lord or bailiff had control over, but some (such as luck, unusual weather and disease) were partially or totally outside his control. Also, some factors affecting production were not allowed for when generating the frontier; for example, some minor activities were ignored, and, presumably, all resources were not of equal quality. Moreover, it is inevitable that there would have been some measurement errors in the data. Clearly when all performance variations relative to the frontier are labelled inefficient, efficiency is given a wide meaning. It is certainly an advantage that the frontier was not forced to conform to a parametric function, which would inevitably be an approximation to reality. Disadvantages of the method include the wide interpretation that must be placed on the efficiency measures; the fact that technological assumptions (about returns to scale and disposability of resources) must be made; and the problem that, since the frontier depends on a sub-set of the sample, it can be distorted by a few erroneous observations. An attempt was made to minimise these problems. We clarified the meaning of efficiency by relating the efficiency measures to factors affecting production; technological assumptions that appear plausible on the basis of theory, and empirical evidence from this and other studies were adopted; and considerable care was taken to delete suspicious observations from the analysis. Now let us consider other methods that have been used to analyse efficiency. A deterministic, parametric function has been estimated by Aigner and Chu (1968) (thereby implementing a suggestion of Farrell, 1957). Their method can be explained by reference to the Cobb-Douglas function involving two resources, where V represents the estate’s annual value, R1 and R2 are the amounts of the two resources available, and A, β1 and β2 are coefficients or parameters. Taking logarithms, and adding a random disturbance, ε, we have, where β0=lnA (see Domesday Economy: 188, 212). Aigner and Chu forced the Cobb-Douglas function to be a frontier by imposing the condition that all disturbances be less than or equal to zero, so that all observations lie on or below the Cobb-Douglas function. The unknown parameters β0, β1 and β2 were estimated by mathematical programming methods. (For example, when they were estimated by minimising the sum of the absolute values of the residuals, subject to the negative of each residual being greater than or equal to zero, the linear programming method was used.) The disturbance, ε, associated with each estate measures the inefficiency of the estate. The residual associated with the estate provides an estimate of the disturbance, and hence the estate’s inefficiency. This method can be applied with functional relationships other than the Cobb-Douglas function. Usually the method will only allow a very few observations to be efficient, and, if some of these are in error, very distorted results may be obtained. To guard against this, Timmer (1971), exploring an idea suggested by Aigner and Chu, examined the effect of discarding efficient observations until deletions resulted in little change in parameter estimates. Because no statistical assumptions are made about the disturbance or explanatory variables (lnR1 and lnR2), statistical properties for the parameter estimates cannot be determined. Others (for example Afriat, 1972; Richmond, 1974; and Schmidt, 1976) have made such assumptions. Typically, it is assumed that the explanatory variables are independent of the disturbance, the disturbance drawings are independent drawings from a common distribution, and a distribution (such as the gamma distribution) is chosen for the

102

ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

disturbance. It is then possible to use the maximum likelihood method (see Domesday Economy: 157–9) to estimate the β-parameters. The maximum likelihood estimates have attractive properties (such as consistency and minimum variance) when the sample size is large (although the usual regularity conditions are violated; see Greene, 1980). Alternatively, as Richmond (1974) showed, a corrected least squares method can be used to obtain consistent β-estimates. The least squares method (see Domesday Economy: 127–57) gives consistent estimates of β1 and β2 but not the intercept, β0 (because the disturbance has a non-zero mean). A consistent estimate of the intercept can be obtained by shifting the function up until no residual is positive and one is zero (Gabrielson, 1975; Greene, 1980), or, when a specific distribution for the disturbance is assumed, by adding on a function of the residuals (Richmond, 1974). Shifting the function up in this way clearly makes the procedure susceptible to errors in extreme observations, while Richmond’s approach does not guarantee that all residuals will indeed be less than or equal to zero. The methods just described generate deterministic frontiers (and so all variations in individual performance are attributed to variations in efficiency), and the frontiers have the disadvantage of being simple parametric functions of the resources (and hence may be fairly crude approximations to reality). Aigner, Lovell and Schmidt (1977), and Meeusen and van den Broeck (1977) have suggested a way of generating a stochastic frontier. This is an attempt to allow for ‘statistical noise’ present in all empirical relationships, due to measurement error and minor influences that affect the relationship but have not been specified explicitly. The idea is that the disturbance is composed of two independent parts. The first is a symmetric component, allowing for statistical noise, random variation of the frontier across estates and random shocks beyond the lord’s or bailiff’s control; and the second a component, which takes values less than or equal to zero, that measures inefficiency. When the probability distributions of the components are specified, maximum likelihood and corrected least squares estimates of the β-parameters can be obtained, and Jondow, Lovell, Materov and Schmidt (1982) show how efficiency estimates for the individual production units can be made. Kopp and Mullahy (1990) propose an alternative estimation procedure that does not require knowledge of the distributions of the components, although the components are required to be independent of one another, and the symmetric component symmetric about zero. Even these are strong assumptions; in particular, it is not clear why statistical noise, random variation of the frontier and random shocks beyond the manorial lord’s control should give rise to a symmetric component or a component with a zero mean. Consequently, it is not surprising that in practice the composed disturbance is often asymmetrical in the wrong direction. Indeed, this was the case when the method was applied to the Essex Domesday data. The computer program LIMDEP (see Greene, 1992), was used to estimate the relationship. Unfortunately, the residual distribution was positively skewed, implying that the asymmetric component took values which were greater than or equal to zero.1 Methods have been developed to measure both technical and allocative efficiency. They use so-called dual theory and require input (or resource) price data. As such data are unavailable for the Domesday estates, the methods cannot be applied to our sample, and are not discussed here. There have also been attempts to modify the deterministic programming techniques to allow for statistical noise. Varian (1985) and Banker (1988) introduced two-sided deviations to allow for random noise, whilst Desai and Schinnar (1987) and Land, Lovell and Thore (1988) have shown how the chanceconstrained programming method, originally introduced by Charnes, Cooper and Symonds (1958), and Charnes and Cooper (1959), can be used for this purpose. Unfortunately, the information requirements are too demanding for the methods to be applied to our study. (Other approaches involve resampling techniques, Boland (1990), N’Gbo (1991) and Simar (1992), or using semi-parametric methods, Härdle (1990) and

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Pinkse (1993).) A more promising way of developing a stochastic framework for programming (DEA) techniques is discussed in Banker’s seminal paper (1993) (referred to in Chapter 2, note 8). Further research needs to be undertaken to assess the value of this interesting approach. There are also non-frontier methods of measuring efficiency. Some require price data, and hence are not relevant to our situation, but one provides a promising method of analysis. It lends itself to our situation because, in addition to the basic information on the main inputs and the value of output, we possess ancillary information on Domesday production relating to factors influencing relative production performance, or efficiency. The idea is to estimate a parametric production function (such as the Cobb-Douglas function) linking annual value to the main resources. This can be done using a standard econometric procedure such as least squares. The estimated relationship can be thought of as giving the average relationship between annual value and the resources, and also the distribution of annual value for given resource levels. If an estate produces such that its observation lies on the function (that is, it has a zero residual), we can think of it as producing with average efficiency—where efficiency has a wide meaning, including the effect of factors beyond the lord’s control, statistical noise, and so on. Estates that have positive residuals can be regarded as producing with above average efficiency, and those with negative, below average. The next stage is to try to clarify the meaning of efficiency by asking why some estates appear to perform better than others. This can be done by regressing the residuals on factors, such as ancillary activities of estates, variables measuring variation in soil, tenancy arrangements, and so on; or alternatively introducing these factors directly into the relationship determining manorial annual value. This approach is recommended by Schmidt (1986: 317–18). See also Lau and Yotopoulos (1971), Timmer (1971), Pitt and Lee (1981), and Huang and Bagi (1984). With this approach we still have a reference or standard for measuring the relative efficiency of estates, although it is not a frontier but an average relationship. Because the average is used as a reference, and because efficiency effects are parameterised rather than aggregated into a component of the disturbance, standard econometric methods can be used. These methods are less sensitive to outliers than frontier estimation procedures. They may also lead to different results either because the methods are based on different assumptions (which may, to a degree, be violated) or because the reference behaviour is systematically different. Efficient production units may well tend to make some (but perhaps not all) decisions more effectively, thereby creating a divergence between frontier and average behaviour. The method is a deterministic, parametric method. The parametric function is an approximation to reality, and all deviations in performance from the average relationship are attributed to efficiency, interpreted in a broad sense. We then attempt to discover the factors associated with efficiency, thus reducing our ignorance. When choosing the parametric function, we can either enter all the main resources separately and use a form such as the Cobb-Douglas that has just one or two parameters associated with each resource, or aggregate the resources into a few categories (such as land, labour and capital) and use a flexible functional form that requires several parameters per resource. The advantage of using a flexible functional form is that it often provides a better approximation to the true functional relationship (see Domesday Economy: chapter 9, for a discussion of economic production functions). On the other hand, aggregating the resources inevitably results in a less adequate representation of production. For the Domesday situation, with resources being fixed endowments and with no price information, the problem of appropriately aggregating the resources is serious. Our preference was not to aggregate the data, but to estimate a reasonably simple parametric function involving all the main resources. The

104

ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

Constant Elasticity of Substitution function, which is somewhat more general than the Cobb-Douglas form (see Domesday Economy. 190–7), was chosen for this purpose. The results of this analysis are described in the remaining section of the chapter.2 5.3 THE EFFECT OF ANCILLARY FACTORS ON PRODUCTION: A PARAMETRIC PRODUCTION FUNCTION APPROACH In econometric analysis, relationships are often approximated by linearisation. This simplifies the mathematics and computations. When linearisation is inappropriate, Box and Cox (1964) suggested transforming variables by power transformations and then relating the transformed variables linearly. In Domesday Economy: 217–25, it was shown that a particular Box-Cox functional relationship could be interpreted as a Constant Elasticity of Substitution production function. The following Box-Cox relationship between annual value (V) and (for simplicity) a single resource (R1), (5.1) where λ, μ, β0 and β1 are parameters and ε is a random disturbance, can be written as (5.2) where Equation (5.2) is in the form of a Constant Elasticity of Substitution production function linking V to R1 (see Domesday Economy: 9.7). The equivalent Box-Cox form (5.1) is useful for computational purposes. λ and μ can be estimated by a grid search, and β0 and β1 estimated by ordinary least squares. Since the estimates of β0 and β1, so obtained, are conditional on the values of λ and μ obtained from the grid search, the standard errors for the least squares estimates of β0 and β1 are conditional on these values. The standard errors will not reflect the fact that λ and μ have been estimated, and hence are subject to sampling error. Nevertheless, a nonlinear least squares procedure (allowing for the Jacobian of the transformation) does allow for the sampling error, and provides appropriate standard errors for all parameters. Excellent starting values for the nonlinear least squares procedure are obtained by undertaking the grid search and least squares estimation of β0 and β1. Details of the method are described in Box and Cox (1964) and Domesday Economy: 162–76 and 217–27. Estimates of the Constant Elasticity of Substitution production function (5.2) linking annual value to the ten main resources of estates are listed in Table 5.1. The estimates are similar to those reported in Domesday Economy: Table 10.2, regression 1, the small differences being attributed to the different data used.3 Table 5.1 Constant Elasticity of Substitution production function for Essex lay estates, 1086: non-linear least squares estimates, main resources Parameter λ μ β0 β1

Explanatory variable

Demesne ploughteams

Parameter estimate

t ratio

Elasticity

0.445 1.437 0.753 1.025

9.4** 13.2** 3.5** 4.9**

0.47

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Parameter

Explanatory variable

Parameter estimate

t ratio

Elasticity

β2

Peasants’ ploughteams Livestock Freemen and sokemen Villans Bordars Slaves Woodland Meadow Pasture

0.404

3.9**

0.20

0.014 0.093 0.220 0.101 0.180 0.011 0.051 0.031

4.0** 2.0* 3.7** 2.9** 3.5** 2.0* 2.9** 3.7**

0.08 0.02 0.14 0.08 0.09 0.03 0.05 0.04 1.20

β3 β4 β5 β6 β7 β8 β9 β10 Σ

105

0.862 Notes: The elasticities are partial output elasticities, evaluated at the sample mean of the resources.Σ is the sum of the output elasticities, that is, the elasticity of scale evaluated at the resource means. is the coefficient of determination allowing for degrees of freedom. * indicates significantly different from zero at the 5 per cent level, ** significantly different at the 1 per cent level.

Σ, the elasticity of scale estimate, is 1.20. This indicates slightly increasing, but close to constant returns to scale. The qualitative effect of estates operating in, for example, different soil regions, can be estimated by adding binary variables to the equations. For example, two binary variables: D1, defined as D1=1, if the estate was located in the London Clay Area; 0, otherwise; and D2, defined as D2=1, if the estate was located in the Boulder Clay Plateau region; 0, otherwise; can be added to (5.1) and (5.2) as follows:

where , and ε* are related to β0, β1 and ε as before, and and give the effects of the estates being located in, respectively, the London Clay region and the Boulder Clay Plateau region as compared with being located in the Tendring and Colchester Loam Area.4 Tables 5.2, 5.3, 5.4 and 5.5 give the estimated effects of the various factors affecting manorial production, such as tenancy arrangements, soil, tenant-in-chief, and ancillary resources. The effect of there being ancillary resources on the Table 5.2 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least squares estimates, tenant-in-chief effects Tenant-in-chief effect code

1

2

3

4

5

6

7

8

9

estimate t ratio

0.091 1.2

−0.151 −1.6

0.058 0.7

−0.344 −2.7**

0.102 1.0

0.005 0.1

−0.060 −0.6

0.276 2.1*

0.069 0.6

106

ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

code

10

11

estimate −0.089 −0.074 t ratio −0.7 −0.6 F test statistic (18, 546)=3.551**

12

13

14

15

16

17

18

−0.052 −0.4

−0.240 −1.6

−0.164 −1.2

−0.208 −1.3

−0.309 −1.8

−0.424 −2.4*

−0.099 −0.6

Effect of grouping estates according to number of estates tenant-in-chief held in Essex estimate t ratio F test statistic (2, 562)=4.161*

5–19 estates

20 or more estates

−0.162 −1.8

−0.034 −0.15

Effect of tenants-in-chief holding estates in demesne code

1

2

3

4

5

6

7

8

9

10

estimate t ratio

0.292 2.0*

0.237 1.6

0.121 0.6

−0.408 −2.2*

0.297 1.6

0.479 2.4*

0.116 0.6

0.521 2.2*

−0.030 −0.1

0.005 0.1

16

17

18

19

code

11

12

13

14

15

estimate 0.105 −0.027 −0.429 −0.309 −0.398 −0.429 −0.343 0.502 0.132 t ratio 0.6 −0.1 −1.9 −1.4 −0.8 −1.4 −1.9 1.0 1.8 F test statistic (19, 545)=3.008** Notes: Entries consist of non-linear least squares parameter estimates and (signed) t ratios. Tenant-in-chief effect codes: 1=Count Eustace. 2=Suen of Essex. 3=Geoffrey de Magna Villa. 4=Robert Greno. 5=Richard son of Count Gilbert. 6=Ranulf Peverel. 7=Ralf Baignard. 8=Eudo dapifer. 9=William de Warene. 10=Ranulf brother of Ilger. 11=Hugh de Montfort. 12=Hamo dapifer. 13=Peter de Valognes. 14=Aubrey de Ver. 15=Robert son of Corbutio. 16=Count Alan. 17=Roger de Ramis. 18=John son of Waleram. (Others accounted for by intercept.) Effect of grouping estates according to number of estates tenant-in-chief held in Essex: 1–4 estates group accounted for by intercept. Effect of tenants-in-chief holding estates in demesne: Codes 1 to 18 as for tenant-in-chief effect (but with estate held in demesne by the tenant-in-chief), code 19= estate of other tenant-in-chief held in demesne. (Estates not held in demesne accounted for by intercept.) The F test statistics (degrees of freedom in parenthesis) were used to test for the (joint) significance of the effects. * indicates significant at the 5 per cent level, ** significant at the 1 per cent level. Table 5.3 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least squares estimates, hundred effects Hundred effect code

1

2

3

4

5

6

7

8

9

10

11

estimate t ratio

0.188 1.4

0.043 0.2

0.586 2.5*

0.384 2.4*

0.541 3.0**

0.429 2.5*

0.056 0.3

0.436 2.3*

0.203 1.3

0.420 1.5

0.330 2.3*

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

code

12

13

14

15

16

17

18

19

20

107

21

estimate 0.055 0.298 0.373 0.311 0.298 −0.060 0.472 0.127 0.685 0.086 t ratio 0.4 1.9 2.4* 2.2* 2.0* −0.3 2.4* 1.0 1.8 0.3 F test statistic (21, 543)=3.192** Notes: Entries consist of non-linear least squares parameter estimates and (signed) t ratios. Hundred codes: 1=Barstable. 2=Beacontree. 3=Chafford. 4=Chelmsford. 5=Dengie. 6=Dunmow. 7=Clavering and Clavering half-hundred. 8=Freshwell half-hundred. 9=Harlow. 10=Harlow half-hundred. 11=Hinckford. 12=Lexden. 13=Ongar. 14=Rochford. 15=Tendring. 16=Uttlesford. 17=Waltham. 18=Winstree. 19=Witham. 20=Maldon half-hundred. 21=Thunreslau half-hundred (Thurstable accounted for by intercept). The F test statistic (degrees of freedom in parenthesis) was used to test for the (joint) significance of the hundred effects. * indicates significant at the 5 per cent level. ** significant at the 1 per cent level. Table 5.4 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least squares estimates, effect of ancillary factors Geographical (soil) region Boulder Clay Plateau

London Clay Area

estimate 0.054 t ratio 0.7 F test statistic (2, 562)=0.510

0.068 1.0

Colchester/Maldon influence estimate t ratio F test statistic (2, 562)=1.413

Colchester

Maldon

−0.127 −1.4

−0.039 −0.6

Grazing/arable ratio estimate 0.0005 t ratio 3.1** Grazing/arable categories estimate t ratio F test statistic (2, 562)=1.271

Mixed

Mainly grazing

−0.038 −0.4

0.057 0.5

Tenure Held in demesne estimate t ratio F test statistic (2, 562)=2.385

0.081 1.6

108

ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

Tenure Held in demesne Notes: Entries consist of non-linear least squares parameter estimates and (signed) t ratios. Geographical (soil) region: Tendring and Colchester Loam Area accounted for by intercept. Colchester/Maldon influence: Other estates category accounted for by intercept. Grazing/arable ratio: Mainly arable category accounted for by intercept. Tenure: Estates not held in demesne accounted for by intercept. The F test statistics (degrees of freedom in parenthesis) were used to test for the (joint) significance of effects. * indicates significant at the 5 per cent level, ** significant at the 1 per cent level.

estate was measured in two ways: first, the qualitative effect was estimated (in the same way that the soil region qualitative effect was estimated); and, second, the quantitative measure of the ancillary resource was used, the ancillary resource being treated in the Constant Elasticity of Substitution production function in the same way as the main resources. The effect of the grazing/arable ratio on production was measured by introducing a term, α1G, into the Constant Elasticity of Substitution production function of form (5.1), where G is the ratio. When written in the form (5.2), . In all estimations, the estimates for μ, λ, and were similar to those reported in Table 5.1, and so are not recorded. Table 5.2 reports the estimated effects of the tenant-in-chief being one of the larger tenants-in-chief (with ten or more estates in Essex) as compared with Table 5.5 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least squares estimates, effect of ancillary resources Qualitative effect

Quantitative effect

Beehives estimate −0.072 −0.032 t ratio −1.2 −0.9 Fisheries estimate 0.076 0.104 t ratio 0.6 0.7 Mills estimate −0.182 −0.263 t ratio −2.3* −2.5* Saltpans estimate −0.317 −0.370 t ratio −2.1* −2.4* Vineyards estimate −0.132 −0.067 t ratio −0.7 −0.5 Notes: Entries consist of non-linear least squares parameter estimates and (signed) t ratios. * indicates significantly different from zero at the 5 per cent level, ** significantly different at the 1 per cent level.

being a tenant-in-chief with less than ten estates. Estates of Robert Greno (code 4) and Roger de Ramis (17) had significantly smaller annual values than those of the smaller tenants-in-chief, while the estates of Eudo

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

109

dapifer (8) were, on average, significantly larger. Others with relatively small annual values were Suen (2), Peter de Valognes (13), Aubrey de Ver (14), Robert son of Corbutio (15) and Count Alan (16). Those with larger values included Count Eustace (1), Geoffrey de Magna Villa (3), Richard son of Count Gilbert (5) and William de Warene (9). The size of these effects in shillings depends on the resources on the estate. As an example, for an estate with one demesne ploughteam and two bordars, the average effect of Roger de Ramis being the tenant-in-chief (rather than a tenant-in-chief with less than ten estates) was to reduce the annual value by about five shillings. For an estate with five demesne ploughteams and ten bordars, the annual value was reduced by about 15 shillings. The F test statistic tests the null hypothesis that the eighteen tenants-in-chief coefficients are zero against the alternative that some are not—in other words, that the joint effect for the eighteen large tenants-in-chief is statistically significant. The joint effect is significant at the 1 per cent level.5 Table 5.2 also indicates that the tenant-in-chief grouping (according to the number of estates in Essex) was significant at the 5 per cent level. The estimate for the group with five to nineteen estates (−0.162) gives the effect of the tenant-in-chief having a medium number of estates (five to nineteen estates) compared with having a small number (one to four estates). For an estate with one demesne ploughteam and two bordars this corresponds to a reduction in annual value of about two shillings. For a larger estate with five ploughteams and ten bordars, the reduction is about six shillings. The lower section of Table 5.2 displays estimated effects of tenants-in-chief holding estates in demesne as compared with estates not being held in demesne. (The effects for tenants-in-chief with most estates in Essex are given under codes 1–18. Under code 19, the average effect for all other tenants-in-chief is listed.) Tenants-in-chief (with four or more estates in demesne) who generated a relatively high annual value from their demesne estates include Eudo dapifer (8), Ranulf Peverel (6), Richard son of Count Gilbert (5), Count Eustace (1) and Suen of Essex (2). (John son of Waleram (18) generated a high annual value, but held only one estate in demesne.) Those who produced relatively low annual values include Peter de Valognes (13), Robert Greno (4), Roger de Ramis (17) and Aubrey de Ver (14). (Count Alan (16) and Robert son of Corbutio (15) produced lower annual values but held, respectively, only three and one estates in demesne.) The average performance of estates held in demesne by the latter tenants-in-chief was inferior to that of subtenants. As an example of the size of the effects, the average effect of Peter de Valognes holding an estate with one demesne ploughteam and two bordars in demesne (compared with the estate not being held in demesne) was to decrease the estate’s annual value by about five shillings. For an estate with five ploughteams and two bordars, the reduction was about 15 shillings. The joint tenant-in-chief in demesne effect was significant at the 1 per cent level. Comparing the tenant-in-chief and tenant-in-chief in demesne effects, it can be seen that estates held in demesne by Suen generated a considerably better return than those of his sub-tenants. The hundred location effects were also jointly significant at the 1 per cent level (see Table 5.3). The estimates measure the effect of an estate being located in each hundred compared with being located in Thurstable. For most hundreds the effect is positive, being largest for Chafford (code 3), Dengie (5), Dunmow (6), Freshwell half-hundred (8), Harlow half-hundred (10), Winstree (18) and Maldon halfhundred (20). Estates located in Thurstable (intercept) and Waltham (17) had, on average, lowest annual values. In monetary terms, for an estate with one demesne ploughteam and two bordars, the effect of being located in Chafford rather than Thurstable was to add about 11 shillings to the annual value. For an estate with five ploughteams and ten bordars the effect increased to about 29 shillings. Table 5.4 indicates that the geographical (soil) region effects, the influence of location close to Colchester or Maldon, the grazing/arable category effects, and the effects of different tenure arrangements

110

ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

were not significant. The grazing/ arable ratio was significant, however (at the 1 per cent level). Estates with a higher ratio (relatively more grazing activity) tended to have higher annual values. For a small estate (with one demesne ploughteam and two bordars) the effect of the ratio being 1,000 rather than zero was to add about 9 shillings to the annual value, and for a larger estate (with five ploughteams and ten bordars) about 24 shillings.6 Turning to the ancillary resources—beehives, fisheries, mills, saltpans and vineyards—except for fisheries, the effects are negative (see Table 5.5). The qualitative and quantitative effects of beehives, fisheries and vineyards were not significant, but both the qualitative and quantitative effects of mills and saltpans were significantly negative. For estates with one demesne ploughteam and two bordars, the mills effect reduced annual value by about 2 shillings and the saltpans effect by 3 1/2 shillings. For an estate with five ploughteams and ten bordars the mills effect amounted to a reduction of around 7 shillings and the saltpans effect a reduction of about 11 shillings. One explanation for these results is that the annual value of the estate did not include returns from these ancillary activities but resources of the estate (particularly manpower) were expended on the activities. Table 5.6 displays estimates when the ancillary resources and selected ancillary factors were added jointly to the basic Constant Elasticity of Substitution production function. These multivariate estimations can be compared with the multivariate regressions of efficiency measures on estate characteristics described in Chapter 4 (see Tables 4.11 and 4.16). In the preferred specification, the ancillary resources were measured quantitatively and binary variables were used to measure the effect of estates being held in demesne by different tenants-in-chief, the effect of hundred location, proximity to the towns of Colchester and Maldon, and location in different soil regions. The kind of agriculture effect was modelled by the grazing/arable ratio.7 The estimates for λ and μ were both a little lower than when only the main resources were entered as explanatory variables (see Table 5.1), and the ratio μ/λ remained fairly constant. The parameter estimates and t ratios for the main resources are similar in Tables 5.6 and 5.1, and the effects of the minor resources and other factors affecting production similar when estimated jointly and individually. The elasticities (calculated at resource mean values) show the dominant influence of the ploughteams variables in explaining production. The manpower variables (villans, bordars and slaves) were also important. The influence of non-arable activities is captured jointly by the livestock and non-arable landtype variables (woodland, meadow and pasture). Because non-arable activities were indicated in this way, but arable activities measured by ploughteams alone (the amount of arable land on the estate not being recorded), the livestock elasticity is low (as compared with the ploughteams elasticities). The influences of the ancillary resources and factors were relatively small. The elasticity of scale (the sum of the elasticities of the resources) was 1.18, indicating close to constant, but slightly increasing returns to scale. The beehives, mills and saltpans effects were negative, but not significant at the 5 per cent level (although the mills effect was significant at the 8 per cent level). The effect of estates being held in demesne by different tenants-in-chief, the hundred location effect and the kind of agriculture effect were significant at the 1 per cent level, and the effect of an estate being located close to Colchester or Maldon and the geographic (soil) region effect not significant. The goodness of fit coefficient, , was 0.883. This indicates that about 88 per cent of variation in annual value is explained by variation in the explanatory variables. When only the main resources were entered as explanatory variables in the production function, was 0.862, so about 15 per cent of the variation not explained by the main resource variables is explained by the ancillary resources and other factors affecting production.

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

111

In the alternative specification (see Table 5.6), binary variables were used to indicate the estate’s tenantin-chief and a separate binary variable used to indicate whether or not the estate was held in demesne.8 The estimates of λ and µ, and the main resource coefficient estimates and elasticities were very similar. (The elasticity of scale estimate was 1.19.) The fisheries effect was again positive, but insignificant; and the other minor resource effects negative, with the mills effect significant at the 8 but not 5 per cent level. The tenantin-chief, hundred and kind of agriculture effects were significant (the tenant-in-chief and kind of agriculture effects at the 1 per cent level, and the hundred effect at the 2 per cent level). The tenure, Colchester/Maldon and geographical (soil) region effects were not significant. Estates with negative residuals in these production function estimations produced a below-average annual value (given their resource levels) which cannot be explained by ancillary resources and factors. In the preferred specification, Elmstead (code 182, its Domesday Book entry was described in Chapter 1), had the largest negative residual (−3.58). In terms of the CS technology analysis it was classified as an inefficient estate, with u=2.930. Most other estates with large negative residuals also had large u-values. For example, Ardleigh (269), an estate of Geoffrey de Magna Villa in Tendring, had a residual value of −3.38 and CS uvalue of 3.506. Others include Dikeley (code 333, residual −3.34, CS u-value 3.306), Wivenhoe (code 319, residual −3.23, CS u-value 6.198) and Little Bentley (code 79, residual −3.20, CS u-value 3.333), all of which were classified as very inefficient estates in terms of CS technology. Weeley (205), an estate held in demesne by Eudo dapifer in Tendring, had the largest positive residual (5. 28). In common with most other estates with large positive residuals, it was categorised as efficient (u=1) in the CS technology analysis. Others include Bircho (59), an estate of Count Eustace in Tendring (residual value 4.08), Pebmarsh (code 502, residual value 3.75) described in Chapter 4, and Lawford (code 61, residual value 3.30). On the other hand, Polhey (92), an estate of William de Warene in Hinckford, had a residual value of 4.19 and CS u-value of 1.419 (and hence was relatively efficient). A feature common to some estates with very large positive residual values was a large increase in annual value between 1066 and 1086 which cannot be explained in terms of increases in resources. Hence Weeley’s annual value rose Table 5.6 Constant Elasticity of Substitution production functions for Essex lay estates, 1086: non-linear least squares estimates, multivariate ancillary resource and factor effects Preferred specification

Test statistic Alternative specification

Elasticity

Estimate

Elasticity

Estimate

λ μ β0 Demesne ploughteams Peasants’ ploughteams Livestock Freemen and sokemen Villans

0.414 1.372 0.362 1.141

0.51

8.5** 12.5** 0.9 5.0**

0.417 1.388 0.413 1.097

0.473

0.23

4.1**

0.010 0.120

0.04 0.03

0.192

0.12

Test statistic Distribution of test statistic on null

0.50

8.8** 12.9** 1.1 5.1**

t(494) t(494) t(494) t(494)

0.485

0.24

4.3**

t(494)

2.5* 2.4*

0.009 0.118

0.04 0.03

2.4* 2.4*

t(494) t(494)

3.3**

0.187

0.12

3.4**

t(494)

112

ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS

Preferred specification

Test statistic Alternative specification

Elasticity

Estimate

Elasticity

Estimate

Bordars Slaves Woodland Meadow Pasture Beehives Fisheries Mills Saltpans Vineyards Tenant-inchief in demesne effect Tenant-inchief effect Tenure effect Hundred effect Colchester/ Maldon effect Kind of agriculture effect Geographical (soil) region effect Σ

0.121 0.156 0.017 0.086 0.031 −0.032 0.019 −0.155 −0.128 −0.070

0.10 0.07 0.04 0.08 0.04 −0.01 0.00 −0.04 −0.02 −0.01

3.1** 3.3** 2.4* 3.3** 3.2** −0.9 0.1 −1.8 −0.9 −0.5 2.211**

2.646**

F(18,494)

1.857**

0.4 1.743*

t(494) F(21,494)

1.939

2.495

F(2,494)

3.0**

3.0**

t(494)

0.085

0.171

F(2,494)

0.121 0.141 0.017 0.084 0.027 −0.021 0.159 −0.149 −0.135 −0.092

0.10 0.07 0.04 0.08 0.04 −0.01 0.02 −0.04 −0.02 −0.02

Test statistic Distribution of test statistic on null 3.2** 3.2** 2.4* 3.5** 3.0** −0.6 1.0 −1.8 −1.0 −0.7

t(494) t(494) t(494) t(494) t(494) t(494) t(494) t(494) t(494) t(494) F(19,494)

1.18 1.19 0.883 0.884 Notes: The elasticities are partial output elasticities, evaluated at the sample mean of the resources. Σ is the sum of the output elasticities, that is, the elasticity of scale evaluated at the resource means. is the coefficient of determination allowing for degrees of freedom. * indicates significant at the 5 per cent level, ** significant at the 1 per cent level. The grazing/arable ratio was used to model the kind of agriculture effect.

from eight pounds to ninteen pounds 15 shillings, Bircho from 3 pounds to 4 pounds 7 shillings, Polhey from 10 pounds to 14 pounds 16 shillings, and Pebmarsh from 2 to 4 pounds.9 The increase may point to errors in the record, or may simply indicate more efficient practice in 1086. How do the Constant Elasticity Production function analysis results compare with the CS efficiency results? First, let us consider the statistical significance of production factor effects.

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

113

The single factor results reported in Tables 5.2, 5.3, 5.4 and 5.5 can be compared with those in column 3 of Table 4.7, and the multivariate results in Table 5.6 with those in Table 4.11. The production function and CS efficiency results are remarkably similar. Comparing the results when a single factor was estimated (Tables 5.2–5.5 and 4.7), in both cases the various tenant-in-chief effects, the hundred effect and the grazing/arable ratio were judged significant, and the geographical (soil) region effect, Colchester/Maldon effect and grazing/arable categories effect not significant. The estimated effects for the minor resources were broadly similar, but a different result was found for the tenure effect. (In the CS efficiency study it was significant, but not in the production function study.) Turning to the multivariate studies (Tables 5.6 and 4.11), in the preferred specification the results were again very similar. For both, the tenant-in-chief in demesne, hundred and kind of agriculture effects were significant, and the Colchester/Maldon and geographical region effects not significant. The estimated minor resource effects were broadly similar. In the alternative specification, in both studies, the tenant-in-chief and kind of agriculture effects were significant and the tenure, Colchester/Maldon and geographical region effects not significant. Broadly similar estimates were obtained for the ancillary resources. In the production function study the hundred effect was significant at the 5 per cent level. It was significant at the 9 per cent level in the CS efficiency study. Not only was the assessment of the significance of factor effects similar, but broadly similar individual effects were obtained in the studies. For example, referring to the tenant-in-chief effects, in both studies the estates of Eudo dapifer, Count Eustace, Geoffrey de Magna Villa and William de Warene tended to be more efficient (or generate above-average annual value), and those of Robert Greno, Roger de Ramis, Peter de Valognes, Aubrey de Ver, Robert son of Corbutio and Count Alan less efficient. With respect to the grouping of tenants-in-chief, for both, estates of tenants-in-chief with one to four estates were, on average, most efficient, and those with five to nineteen estates least efficient; for both, estates held in demesne by Suen of Essex, Richard son of Count Gilbert and Ranulf Peverel tended to be more efficient, and those of Robert Greno, Peter de Valognes and Roger de Ramis less so, and, in both cases, estates in the hundreds of Chafford, Dengie, Dunmow, Harlow half-hundred, Winstree and Maldon half-hundred tended to be more efficient, and those of Thurstable and Waltham less efficient. Both studies suggested estates with high grazing/arable ratios were on average more efficient. There is also a close correspondence between the CS efficiency value of an estate and its production function residual value. CS u efficiency values were calculated by comparing the annual value generated from the main resources (ignoring minor resources and ancillary factors). The corresponding production function results are those reported in Table 5.1. Were the estates with very large positive residuals CS efficient estates; and those with large negative residuals CS inefficient estates? In effect we have already answered the question, because the estates with extreme residuals in the basic production function estimation reported in Table 5.1 were (in the main) also the estates with extreme residuals in the multivariate estimation reported in Table 5.6. These residuals were examined earlier. The examination indicated that there was a close correspondence between estates having very large negative residuals and being categorised as inefficient or very inefficient in the CS analysis, and estates having large positive residuals and being efficient. Further inspection of the residuals of the regression reported in Table 5.1 shows that 89 per cent of the CS efficient estates had positive residuals (the mean residual value for CS efficient estates being 1.63); and all the CS very inefficient estates had negative residuals (the mean residual value being −1.97). Because the u efficiency values are effectively truncated at u=1, the correlation between the residuals and u-values is not an entirely satisfactory way of measuring their association; even so, the correlation coefficient between the two, a value of −0.73, indicates a reasonably strong association.10,11

6 EXTENSIONS, COMPARISONS AND CONCLUSIONS

6.1 INTRODUCTION The statistical analysis of production performance in Essex described in the previous chapter confirms the main findings of the CS efficiency analysis of Chapter 4. There are some minor differences, but broadly similar results were obtained in the two studies. In this chapter (Section 6.2) we ask: Were the Domesday Essex estates run efficiently? The structure of CS efficiency of the estates is compared with that of modern economies. The dominant institutional conditions, the feudal system and manorialism, induced a degree of factor immobility and discouraged the development of factor markets. This is mainly responsible for the wide variation in shadow prices and considerable slack in manorial resources reported in Section 4.9. The economic cost of this factor immobility is investigated in Section 6.3. The next few sections (6.4–6.7) show how frontier methods can be used to investigate beneficial hidation; who and which estates received favourable tax assessments—a matter often alluded to by Domesday scholars. Finally, the last section contains a summary and some concluding comments on the study as a whole. 6.2 WERE DOMESDAY ESTATES RUN EFFICIENTLY? THE STRUCTURAL EFFICIENCY OF PRODUCTION ON ESSEX LAY ESTATES IN 1086 Were Domesday estates efficiently run? One way of answering this question is to examine the structure of efficiency, to see how less efficient inefficient estates were, relative to efficiently run estates, and measure the average level of efficiency. As long as at least some estates were well organised and effective (that is, best practice was good practice), this will be a useful exercise. If, as some medievalists would have us believe, many estates were run haphazardly and ineffectively, the dispersion of efficiency measures will be considerable and average efficiency low. Comparisons can be made with more modern economies.1 Efficiency measures are calculated relative to the contemporary technology and institutional setting, and so the measured structure of efficiency of Domesday estates is conditional on these factors. Clearly, with modern technology, output would be much greater. But absolute efficiency is not the issue. More interesting questions are: Given the contemporary technology and institutions, how efficient was Domesday agricultural production? How does the Domesday structure of efficiency compare with other economies and industries? The impact of institutional factors on Domesday production is considered in the next section.

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A large number of efficiency studies have been reported in the literature. Some are general surveys. For example, Leibenstein (1966) cites evidence of substantial inefficiencies in studies carried out throughout the world in a broad range of industries. Others are individual case-studies of particular industries or economies. An example is the study of Seale (1985), who reports on the efficiency of floor-tile firms operating in the Fayoum region in Egypt. The firms made floor tiles using a fairly simple technology: sand, cement and water were mixed and pressed into tiles, which were dried in the sun. Three kinds of tile were made, and no other outputs produced. Capital consisted of mixers, electric presses and polishers. The age of the machines did not seem to be important. There were two distinguishable skill-categories of labour. Seale aggregated the basic data into measures of output, labour and capital, and estimated a Cobb-Douglas production function. A production unit’s efficiency was measured as the ratio of actual to maximum output, expressed as a percentage. Measures of technical efficiency for production units ranged from 73 to 100 per cent. A second example is contained in the seminal paper of Farrell (1957). The study is of the agricultural output of forty-eight American states in 1950. Output is the dollar value of receipts plus the value of home consumption, and the inputs: land (ignoring woodland) in acres; labour on farms (including unpaid family workers); materials, expenditure on food, livestock and seed, expressed in dollars; and capital, the value of implements and machinery, in dollars. The data were compiled by the United States Department of Agriculture. Farrell calculated efficiency measures which are essentially the reciprocals of the CS u-values of the Domesday study. Expressing these measures as percentages, efficiency ranged from 58 per cent for Vermont to 100 per cent for nine states. Mean efficiency was 82 per cent and the standard deviation 12 per cent. Another agricultural study is that of Bagi and Huang (1983). They estimated a stochastic frontier with a composed error term (using a translog function). The data related to 115 crop farms and seventy-eight mixed farms in West Tennessee in 1974. Output was measured in dollars. The five inputs were land area, hours of labour used, value of capital, value of fertiliser and other chemicals, and livestock expenses. Average efficiency measures were in the order of 66 to 77 per cent. Seitz (1971) investigated the effectiveness of 181 new steam-electric generating plants constructed during 1947–63 in the United States. Output and inputs (capital, labour and fuel used) were expressed in dollar terms. Input price data were also available. A frontier was calculated using programming methods and measures of technical efficiency, price (or allocative) efficiency and economic (or overall) efficiency (given scale) calculated. Mean overall efficiency (given scale) was about 80 per cent. More recently Ferrier and Lovell (1990) have used both statistical production function and mathematical programming methods to investigate cost efficiency in banking. Data were available for 575 banking institutions. Five outputs and three inputs were measured, together with information on input prices and twelve environmental variables. The production function estimates indicated that on average banks operated at costs 26 per cent above frontier costs. The mathematical programming estimate was 21 per cent. Further examples of studies of agriculture include farms in Northwest India (Huang and Bagi, 1984), 208 groups of farms in England and Wales (Farrell and Fieldhouse, 1962), 83 farms in Kansas (Thompson et al., 1990) and Indian rice farming (Kalirijan, 1981). Mathematical programming frontier methods have been used to investigate programme and managerial efficiency in educational programmes (Charnes, Cooper and Rhodes, 1981), evaluate the comparative efficiency of schools (Bessent and Bessent, 1980), study hospital production (Banker, Conrad and Strauss, 1986), investigate the administrative efficiency of courts (Lewin, Morey and Cook, 1982), the efficiency of commercial banking (Charnes, Cooper, Huang and Sun, 1990), Kansas farming (Thompson et al., 1990), the electricity power generating industry (Kopp and Mullahy, 1990; and Greene, 1990) and American airlines (Cornwell, Schmidt and Sickles, 1990).

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Other areas of study include American primary metals (Aigner, Lovell and Schmidt, 1977), French manufacturing (Meeusen and van den Broeck, 1977), Norwegian pulp firms (Førsund and Jansen, 1977), Brazilian manufacturing (Lee and Tyler, 1978), Swedish dairy plants (Førsund and Hjalmarsson, 1979), Indonesian weaving firms (Pitt and Lee, 1981), and public and private sectors in Iraq (Levy, 1981). Numerous further examples are contained in the references to the articles in the two survey volumes edited by Aigner and Schmidt (1980) and Lewin and Lovell (1990), the survey of Schmidt (1986) and the bibliography of Seiford (1990). Clearly, there is a great diversity of case-studies, and it is to be expected that measures of structural efficiency will vary considerably depending on the method used to measure efficiency, the production activity examined and the level of aggregation of the production units. Other factors, usually of lesser importance, are the number of observations (production units), the number of inputs and outputs, and the way in which inputs and outputs are measured.2 It would be sensible to compare the structure of Domesday estate production efficiency with the structure of industries or economies with similar characteristics. Comparisons with case-studies for which the individual establishment is the unit, unsophisticated primary production is the activity, and mathematical programming frontier methods are used to measure efficiency would be most appropriate. These considerations suggest three studies as particularly useful comparisons with the Domesday study. The first is A.R.Hall’s (1975) study of agriculture in the post-bellum American South. The farm is the production unit, and CS efficiency measures are calculated. It is particularly interesting that, as with the Domesday study, the data refer to a period about two decades following invasion and major disruption to society (the American Civil War and the abolition of slavery). The second is B.F.Hall and E.P.LeVeen’s (1978) efficiency analysis of seventy-five small Californian farms based on a modern survey. Efficiency was measured using the mathematical programming frontier method. The final study is Byrnes, Färe, Grosskopf and Lovell’s (1988) study of American surface coalmines. The activity, although not agriculture, is simple primary production, and the mine establishment the production unit. A particularly useful feature of this study is that, as well as CS efficiency measures, VS and VW measures were calculated. The structure of Domesday efficiency Aspects of the structure of Domesday CS efficiency were described in Chapter 4. Figure 4.3 gives a histogram of the CS u measures. The measures ranged from 6.286 for Paglesham to 1 for ninety-six estates. Mean efficiency was 1.844, and the standard deviation 0.851. An interesting structural measure is the increase in annual value that would be achieved if all estates were run efficiently. The increase is 51.0 per cent.3 For the three comparison studies, efficiency is measured as the ratio of actual to maximum output, that is, the reciprocal of the u measures. Denoting these measures u−1, for the Domesday study u−1 ranged from 0. 159 to 1; the first quartile was 0.435, the median 0.626 and the third quartile 0.861. This information can be usefully displayed in a Box Plot diagram (see Figure 6.1). The ‘box’ length corresponds to the interquartile range, and the distance between the ends of the ‘whiskers’ to the range. The distribution of u−1 is slightly skewed with a longer tail on the left (corresponding to inefficient estates). Mean u−1 efficiency was 0.643, and the standard deviation 0.243.

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Figure 6.1 Box Plot of distribution of CS u−1 efficiency: Essex lay estates, 1086

Agriculture in the American South, 1879–80 A.R.Hall’s excellent (1975) study is based on 2,117 farms in the American South during 1879–80. The American Civil War, 1861–5, was followed by the abolition of slavery in 1865. During the war substantial destruction of railroad and manufacturing capital occurred, but by the 1870s the railroads and much of the devastated manufacturing capital had been restored. Even allowing for Sherman’s march from Atlanta to the sea and his pursuit of Johnston, the direct effect of the war on agriculture was small. (Most campaigns were fought in northern Virginia and western Tennessee and Kentucky, areas outside or on the periphery of the great staple agricultural regions of the South.) Nevertheless, the abolition of slavery redefined labour contracts and was a major shock to the production system; and the postbellum period was a period of stagnation in Southern agriculture. Hall was (amongst other things) concerned with the reasons for this stagnation. The principal agricultural outputs were cotton and corn. Hall measured cotton in bales less the value of fertiliser (converted to units of cotton bales) and corn in bushels. The inputs were labour, measured physically in full-time equivalents; workstock, the number of horses, asses, mules and working oxen; the value of implements; total farm acres (used to measure the contribution to final output of land not actually producing crops); and a land quality index. Inputs and outputs were standardised by dividing them by the number of acres of the farm planted in cotton and corn. CS u−1 efficiency measures of technical efficiency, overall price (or allocative) efficiency and price (or allocative) efficiency of the cotton-corn choice were calculated. Unfortunately, because the efficiency values themselves are not available, the information on the structure of efficiency that can be gleaned from Hall’s published results is limited. Mean technical efficiency was 0.419, with standard deviation 0.203. The bulk of the sample had estimated technical

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efficiency measures between 0.10 and 0.50. The smallest technical efficiency value was less than 0.08, and values between 0.10 and 0.30 were common. Fifty-seven farms were efficient. Mean overall price efficiency (resulting from input and output allocation decisions) was 0.291, with standard deviation 0.155. One farm was efficient. Mean output price (or output allocative) efficiency was 0. 854, with standard deviation 0.121, and 118 farms were efficient. Comparing with the Domesday study, recall that Domesday estates were able to allocate resources between the production of different outputs, but had little choice over resource levels. The Domesday CS u−1 efficiency measures are of overall efficiency, which is mainly technical and output price (or output allocative) efficiency. Mean postbellum Southern agriculture technical efficiency was only 42 per cent with a standard deviation of 20 per cent, which is lower than mean overall Domesday efficiency (64 per cent, with standard deviation of 24 per cent). An estimate of mean postbellum Southern agriculture technical and output price efficiency is given by the product of mean technical and mean output price efficiencies. This is 36 per cent. The corresponding estimate for mean overall efficiency is 12 per cent. These figures indicate that Domesday estates had a more favourable structure of efficiency—relative to best practice they were, on the whole, more efficient. Agriculture in California, 1977 B.F.Hall and E.P.LeVeen’s (1978) paper is concerned with farm size and efficiency, and includes a casestudy of the efficiency of a sample of relatively small (less than 100 acres) Californian fruit and vegetable farms in the 1970s. It is based on a smaller sample (seventy-five farms) than A.R.Hall’s study and the Domesday study. Mathematical programming frontier methods were used to calculate farm CS u−1 efficiency measures. Output was the value of aggregate agricultural production and the inputs: acres of land, man-days of family labour, the dollar-value of hired labour, physical capital and material expenses. Average economic (or overall), technical and price (or allocative) efficiencies are reported. Mean technical efficiency was 0.665, mean allocative efficiency 0.413, and mean overall efficiency 0.275. Price or allocative efficiency relates to allocative decisions relating to both input and output prices. Domesday mean overall efficiency (64 per cent) is similar to Californian farm mean technical efficiency (67 per cent) and considerably greater than mean overall efficiency (28 per cent). American surface coalmines 1975–8 In the final comparison study, by Byrnes, Färe, Grosskopf and Lovell (1988), the authors report VS and VW efficiency measures as well as CS measures. Although the production activity is not agriculture, it is unsophisticated primary production. The efficiency of American surface coalmines is analysed. The data relate to eighty-four midwestern American mines in 1978; and sixty-four Western mines over all or part of 1975–8, providing a sample of 113 observations. Surface mining involves three procedures: first, removal of overburden, the earth covering coal seams, using bulldozers, power shovels, wheel excavators and draglines; second, coal extraction, using drills, power shovels, front end loaders and trucks; and, third, land reclamation, using bulldozers, motor graders and carry-all scrapers. Production conditions differ in the Midwest and West (owing to thicker coal seams and less overburden in the West), so separate frontiers were estimated for the two regions. Output was measured as annual coal produced in tons. The inputs were: miner hours, the number of draglines and power shovels with each of four different bucket capacities, the number of coal drills, front-

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end loaders and brooms weighted by value, and the number of scrapers, dozers and graders weighted by value. For each region (Midwest and West), the authors disaggregated the efficiency results by the union status of the miners. The three status categories are non-union, Union of Mine Workers of America (UMWA) and other (that is, unionised with UMWA affiliation). The results are summarised in Table 6.1. All measures are of overall efficiency. (Unfortunately, only these summary statistics are reported; individual production unit efficiency measures are not given.) The Domesday mean CS, VS and VW efficiencies and standard deviations are similar to the corresponding American mining figures. Domesday mean CS efficiency (64 per cent) is a little higher than for the American mines (Midwest and West, both 61 per cent). The Domesday mean VS efficiency (74 per cent) is also a little higher than for the American mines (Midwest 68 per cent, West 66 per cent). For VW efficiency, the Domesday mean (91 per cent) lies between the Midwest mean (92 per cent) and the West mean (86 per cent). In summary, the comparisons of the structure of the efficiency of Domesday production with the casestudies indicate that the structure of efficiency was more favourable for Domesday estates than for postbellum Southern agriculture and the small Californian farms—that is, relative to best practice, Domesday estates were on average more efficient. For the third comparison, mean efficiencies for Domesday estates and American mines were very similar when calculated under different technological assumptions. In comparative terms, the evidence suggests that Domesday estates were efficiently run. Table 6.1 Comparison of structure of efficiency of Domesday estates and American surface coalmines in the Midwest and West Efficiency measures CS Number of observations

mean

VS standard deviation

mean

VW standard deviation

mean

standard deviation

Midwest Non-union 22 0.486 0.231 0.675 0.304 0.923 0.204 Other 8 0.917 0.136 0.944 0.106 0.977 0.066 UMWA 54 0.612 0.261 0.638 0.256 0.911 0.200 Total 84 0.608 0.268 0.677 0.272 0.920 0.192 West Non-union 12 0.301 0.290 0.341 0.317 0.895 0.330 Other 42 0.498 0.244 0.536 0.268 0.757 0.309 UMWA 59 0.752 0.217 0.806 0.200 0.950 0.115 Total 113 0.611 0.282 0.656 0.291 0.863 0.247 Domesday Total 577 0.643 0.243 0.742 0.241 0.905 0.188 Notes: The American mining efficiency statistics are reported in Byrnes et al. (1988:1,047). The Domesday efficiency statistics relate to the 577 Essex lay estates in 1086 analysed in Chapter 4.

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6.3 ON THE ECONOMIC COST OF THE FEUDAL AND MANORIAL SYSTEMS Why was there such a wide variation in resource shadow prices on Domesday estates? And why was there so much resource slack? What effect did institutional factors have on manorial efficiency? The two dominant institutional factors affecting agricultural production were feudalism and manorialism. The feudal arrangements prescribed that all land in England belonged to the king and all who held land did so as his tenants. Most tenants, both lay and ecclesiastical, held land by military service, their lands being fiefs. Some ecclesiastical land was held by the service of prayer and some land held by sergeanty, the performance of some specific service such as huntsman or cook, but these tenures were of relatively small importance. Tenants-in-chief held land directly from the king usually in return for supplying, in times of need, a fixed quota of fully equipped knights. The knights were sometimes maintained in the tenant-in-chief’s own household, or he could sub-enfeoff them, granting them land on which they could support themselves. If land was granted, then the knight became a mesne-tenant or sub-tenant. On occasions men held some land as tenants-in-chief and some as sub-tenants. Domesday Book often records the terms on which land was held. Although a variety of expressions are used to describe tenure, it is thought that most refer to bookland, which, in effect, conferred perpetual tenure of the estate with free right of disposition. With the land came resources, principally labour, ploughteams and livestock. An essential feature of manorialism was the demesne or home farm upon which the peasants worked in return for protection, housing and the use of land to cultivate their own crops. Labour services consisted of week-work, due on an agreed number of days a week throughout the year; and seasonal boon-work, ploughing, mowing and reaping, as the season required. The peasants were tied to the lord and the manor, and the lord enforced his rights over the peasants in the manorial court. With this system the opportunities for varying the inputs to production on the manor were limited. The demesne was worked by a resident labour force, and the contract between lord and peasant fixed the number of hours worked. Feudalism inhibited trade in land, and breeding could only gradually increase the numbers of ploughteams and livestock. When granted an estate, a lord received a fixed set of endowments which could not be easily varied in the short run. Although feudalism and manorialism had a pervasive influence on rural life and the organisation of agriculture in Domesday England, the systems existed there in a modified form. Slaves also worked the demesne, there were freemen and sokemen (with a freer status than the bonded bordars and villans), and some wage labour occurred. Some livestock trading took place. There is evidence of loanland (land granted temporarily by holders of bookland with revision to the grantor) and farms (the renting of land either for a fixed annual sum or a lump payment). These modifications had the effect of partially freeing up input proportions; nevertheless, Domesday agriculture suffered from poorly developed factor markets and considerable immobility of inputs.4 Input productivity The productivity of a resource depends greatly on the amounts of the other resources it works with in production. With fixed resource endowments and widely different resource mixes on estates, it might be expected that the productivity of resources would exhibit great variation across estates. The argument, however, ignores the possible effects of resource substitution in production and trade in outputs.

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If the resources are perfectly substitutable, then the mix is irrelevant, because the resources effectively operate as a single resource in production. Even with outputs being produced with fixed input proportions— which is probably a closer approximation to Domesday production—because the manorial production unit produced several outputs, opportunities for substitution still existed. Providing the different outputs were obtained by using resources in different proportions, the proportions in which resources were used on the manor could be varied by varying the mix of outputs. If the outputs could be produced by using different processes, further opportunities for substitution existed (see Section 3.4). These resource substitution possibilities, in conjunction with trading in the outputs, could result in similar resource productivities across estates, despite the immobility of resources. This idea is the basis for an important argument in international trade theory: the Factor Price Equalization Theorem advanced by Heckscher and Ohlin (see Woodland, 1982: 70–9, for a statement of the theorem). The theorem states that, under certain conditions, trading in outputs will lead to an equalization of resource marginal productivities and prices across trading groups, even though the resources themselves are not traded. The conditions required for equalization are strict, and include: no barriers to trade, zero transport costs, competition in output markets, constant returns to scale, no joint production and factor mobility within trading groups.5 These conditions were certainly not satisfied in Domesday England; nevertheless, there was considerable trading in outputs, and this may have had an effect in reducing disparities in resource productivities across estates. Estates in close proximity to a common market centre or town had the greatest opportunities for trading with each other. Did productivities vary less for estates surrounding a large market town than in the county generally? Comparing ‘urban’ and rural shadow prices Colchester and Maldon were the major urban centres in Essex. The resource shadow prices examined in Section 4.9 are measures of resource productivities when production is efficient. Table 6.2 gives a breakdown of shadow prices by estates close (within about 6 miles) to Colchester (forty-two estates), those close to Maldon (sixty-seven estates) and the other estates in the sample (468 estates). The statistics for the ‘other’ group are very similar to those for all estates examined earlier in Section 4.9. Mean shadow prices vary a little between the three groups; for example, for demesne ploughteams, the Colchester estates mean is about 6 shillings greater than the ‘other’ group, and the mean for Maldon estates about 10 shillings less. For most resources, although the standard deviation for Colchester estates is usually a little smaller than for the ‘other’ group, the standard deviation is often greater for the Maldon estates. There is little evidence to suggest that estates near towns had more similar shadow prices. A statistical test of the null hypothesis, that the resource shadow price variance for the Colchester (or Maldon) estates is equal to that for the ‘other’ group, against the alternative, that the variance for the Colchester (or Maldon) estates is smaller, only occasionally leads to rejection of equality of variances. From the last column of Table 6.2, we see that equality of variance is rejected in six of the twenty possible cases at the 5 per cent significance level, and four cases at the 1 per cent level. This evidence suggests that trading in outputs did not greatly reduce productivity disparities. The cost of factor immobility If the productivity of a resource was higher on one estate than on another, there was potential to increase total output by increasing employment of the resource on the more productive estate and reducing employment on the less productive estate. The greater the difference in productivity on the estates, then the

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greater the possible increase in total output, and the greater the economic cost of an institutional arrangement that discouraged mobility of resources. An idea of the magnitude of the economic cost of factor rigidity induced by the feudal and manorial institutional arrangements can be obtained by estimating the total annual value had all estates been run efficiently at the frontier, and comparing this total with the total annual value achievable had production been at the frontier and input mixes variable. The former is estimated by Σ Viui, where ui is the u-value for the ith estate, and the latter by calculating the maximum annual value obtainable on an estate with resource endowments equal to the totals for the 577 estates. Given constant returns to scale, the scale of production implied by the latter estimate does not present a problem; nevertheless, the comparison is based on partial rather than general equilibrium reasoning as, for example, no adjustment is made for the effects of increased output on relative or absolute output prices. Table 6.2 Shadow prices (in shillings) for 577 Essex lay estates, 1086: CS technology Mean Standard deviation Coefficient of variation Test H0: Variance equal against H1: C/M variance smaller Demesne ploughteams Maldon Other Peasants’ ploughteams Maldon Other Livestock Maldon Other Freemen and sokemen Maldon Other Villans Maldon Other Bordars Maldon Other Slaves Maldon Other Woodland Maldon Other Meadow Maldon Other

Colchester 33.4 43.6 Colchester 11.2 7.2 Colchester 0.1 0.2 Colchester 2.5 2.8 Colchester 7.0 8.0 Colchester 6.6 5.5 Colchester 14.4 12.4 Colchester 1.4 1.3 Colchester 6.1 2.7

49.7 19.2 17.3 3.7 18.6 10.9 0.2 0.2 0.3 2.6 3.7 5.4 12.7 9.0 11.3 3.7 9.4 10.9 11.3 13.9 13.3 0.7 2.3 2.4 2.5 7.2 8.9

17.0 0.5 0.4 9.6 1.7 1.5 0.3 1.7 1.6 6.2 1.5 1.9 11.5 1.3 1.4 7.6 1.4 2.0 11.0 1.0 1.1 2.0 1.6 1.8 4.5 1.2 3.3

0.3 Accept equal

Accept equal

2.6 Accept equal

Accept equal

2.1 Reject at 1%

Accept equal

2.4 Reject at 1%

Accept equal

0.9 Reject at 5%

Accept equal

2.0 Accept equal

Reject at 1%

1.0 Accept equal

Accept equal

2.7 Accept equal

Accept equal

1.8 Reject at 5%

Reject at 1%

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Mean Standard deviation Coefficient of variation Test H0: Variance equal against H1: C/M variance smaller Pasture Maldon Other

Colchester 0.7 0.5 0.4 0.6 0.4

0.4 0.8 0.6

0.5 Accept equal

Accept equal

A great advantage in using the frontier to produce these estimates is that estate inefficiency and the special production characteristics of individual manors are, to a degree, controlled for (see Sections 2.4 and 2.5). The measure is of potential rather than actual output change. The calculation indicates that total annual value could have been increased by 40.1 per cent. This potential loss in output is considerable. It can be compared with the loss resulting from estates being run inefficiently. In the previous section it was calculated that the increase in output (over actual output) that could have been achieved had all estates been run efficiently (at their resource levels) was 51.0 per cent. The loss in output due to factor rigidities is smaller, but of a similar order of magnitude.6 In eleventh-century England, the feudal and manorial systems provided considerable economic, political and social advantages for the feudal hierarchy. Feudalism provided a structure to maintain the military might of the kingdom yet helped to limit the power of feudal barons; and manorialism tied peasants to the manorial estate, both making it easier for lords to maintain control over them and diminishing labour’s bargaining power. These institutional arrangements also inhibited trade in resources. The calculations made here indicate that the economic cost of input inflexibility was substantial. It is not surprising, then, that in the twelfth and thirteenth centuries, as Norman rule was consolidated and security became a less severe problem, input rigidities tended to break down (see Britnell and Campbell, 1995). 6.4 THE INCIDENCE OF BENEFICIAL HIDATION: INTRODUCTION Domesday Book entries include tax assessments. Often there are assessments for both 1066 and 1086, but when an assessment is only given for 1066 the general presumption is that the assessment was the same for 1086. The tax was referred to as the geld, a non-feudal tax, thought to be levied annually, at least by the end of William’s reign. It originated from the Danegeld, which was introduced by King Ethelred in 911 to provide finance to bribe or fight the Danes. In 1086 the geld was one of a number of public revenue sources and probably contributed about a quarter of the total public purse. It was a significant impost on landholders. The rate struck in 1083–4 of 6 shillings to the hide implies that the tax amounted to about 15 per cent of the annual value of the average Essex lay manor. The tax assessment was measured in hides and fiscal acres, and is often referred to as hidage. Further information and references are contained in chapter 4 of Domesday Economy. Domesday scholars have written extensively about the tax assessments. Round (1895) considered the assessments to be ‘artificial’, in the sense that they were imposed from above with little or no consideration of the capacity of an individual estate to pay the tax. Other issues include whether the basis of assessment was the hundred or the vill rather than the manor; whether vills were grouped in multiples of five hide units within the hundred; more recently, the existence of a five-hide pattern in the assessments of individual estates; and the significance of the Domesday Book ‘ploughlands’ entries. These matters have important implications

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for the way shire and local government were organised, and the effectiveness of government administration in general. Snooks and I argued (1985a, 1986) that, contrary to Round’s hypothesis, the tax assessments were based on a capacity-to-pay principle, subject to some politically expedient tax concessions. Similar tax systems operate in most modern societies and reflect an attempt to collect revenue in a politically acceptable way. There is empirical support for the hypothesis, using regression methods. We showed, for example, that for Essex lay estates about 65 per cent of variation in the tax assessments could be attributed to variations in either manorial annual value or resources, two alternative ways of measuring capacity to pay. Similar results were obtained for other counties. Capacity to pay explains from 64 to 89 per cent of variation in individual estate assessment data for the counties of Buckinghamshire, Cambridgeshire, Essex and Wiltshire, and from 72 to 81 per cent for aggregate data for twenty-nine counties. (See McDonald and Snooks, 1987a, 1990a, 1990b, Hamshere, 1987a, 1987b, and Leaver, 1988, for details, and a lively debate on the implications of the results.) Although capacity to pay seems to explain most variation in tax assessments, some variation remains. Who was treated favourably? Which estates received a beneficial hidation? And what factors were associated with beneficial hidation? Answers to these questions would throw light on the hypothesis advanced by Snooks and myself (1987a: 259–61) that differences in assessment rates between counties may be due to beneficial hidation granted to powerful tenants-in-chief (who were located unevenly across counties). Clearly, a first step in addressing these issues is to develop a measure of beneficial hidation. A simple and appealing measure is based on the idea that an estate has received beneficial hidation if it has a lower tax assessment than another estate with the same or lower annual value (annual value or net income being a measure of capacity to pay). More formally, the beneficial hidation index (BHI) for estate i is defined as the ratio of the maximum tax assessment of all estates with the same or a lower annual value than estate i to the actual tax assessment of estate i. A BHI value of one corresponds to no beneficial hidation, and a value greater than one to some beneficial hidation. 6.5 FRONTIER CONSIDERATIONS The beneficial hidation index is one of several possible measures that can be employed. This can be seen from Figure 6.2, using the frontier methodology. A, B, C, D and E indicate the tax assessments and annual values of five (fictitious) manors (manor A, for example, has an annual value of 5 shillings and tax assessment of four fiscal acres). In the upper diagram, the line segments 0A, AB, and B extended through D, give one plausible tax frontier. This frontier, Frontier 1, would be reasonable if the underlying tax regime was one of multiple constant, positive marginal tax rate schedules, with some beneficial hidation. Starting from 0, the frontier connects points representing manors by line segments so long as the slope of the segment is positive (corresponding to a positive marginal tax rate). Thus, 0 is connected to A and A to B, because the line segments have positive slopes; but B is not connected to C by a segment, and D not connected to E, because the slopes of the lines would not be positive. (These segments would imply zero or negative marginal tax rates.) Once a frontier has been determined a beneficial hidation index can be defined for each estate. For example, for estate i, it may be defined as the ratio of the maximum tax assessment consistent with the frontier for an estate with estate i’s annual value, to the actual tax assessment of estate i. Estates A, B and D have a BHI of one, the index for C is two, and for E two and a half.

EXTENSIONS, COMPARISONS AND CONCLUSIONS

125

Figure 6.2 Alternative tax frontiers

Notice that for Frontier 1, from A, the manor on the frontier with the smallest annual value, a line segment is drawn to the origin, 0. Also, the line segment BD is extended through D, the manor on the frontier with

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the largest tax assessment. An alternative way of dealing with the end values is to drop a line vertically from A to the V-axis (using the argument that estates with very low annual value may have been tax exempt), and to draw a horizontal line from D (because estates with income greater than D should have paid at least as much tax, but perhaps paid no more); the frontier then becomes the dashed line from the V-axis to A, AB, BD, and the dashed horizontal line from D. This frontier, Frontier 2, can be described algebraically as:

where T is the tax assessment and V the annual value of an estate, and z1, z2, z3, z4 and z5 are intensity variables. As before, we may define a beneficial hidation index for estate i as the ratio of the maximum tax assessment consistent with the frontier divided by the actual tax assessment of estate i. If Ti is the tax assessment for the ith estate, the index value for estate i can be found algebraically by setting T=Tiu in the first inequality and maximising u subject to the two inequalities, the equation, and the non-negativity conditions. This is, of course, a linear programming problem. The index value is the maximum value of u. For manors A, B and D the index value is one, for manor C two, and for E one and a half. In the lower diagram of Figure 6.2 a third frontier is drawn. Frontier 3 consists of the ‘steps’, 0 to the point vertically below A, that point to A, the horizontal line from A to the point vertically below B, and so on. This frontier would be appropriate if the tax regime was one of constant tax assessment over annual value intervals, with some beneficial hidation. The frontier generates the beneficial hidation index defined at the end of the previous section. Manor E has a BHI value of one and a half, all other manors have a BHI value of one. Unfortunately, we do not know the details of how the tax assessments were formulated, so we do not know which is the most appropriate frontier and hence beneficial hidation index. Can we, using empirical methods, determine which is the ‘true’ frontier? For example, is the true frontier the frontier that gives the closest fit to the data points? Unfortunately, this is not necessarily so. Casual inspection of Figure 6.2 indicates that Frontier 3 must always fit the data better (in the sense that the distances of data points from the frontier cannot be greater and will sometimes be smaller) than the other two, whether or not it is the true frontier (that is, whether or not the true tax regime is essentially one of constant tax assessment over annual value intervals). In practice, if we have many observations reasonably well distributed over the annual values, all three frontiers will be similar. We focus on Frontier 3. An attractive property of this frontier is that it measures beneficial hidation more conservatively than the others. If an estate exhibits beneficial hidation when measured against this frontier, it will also do so when measured from the other frontiers. 6.6 BENEFICIAL HIDATION IN ESSEX IN 1086 Tax assessments for 1086 for three of the estates in our sample of Essex lay estates were not available. They were 5 White Notley, 221 Estoleia and 502 Pebmarsh. These estates were deleted from the analysis, reducing the sample to 574 estates. Eighteen estates had a BHI of one, and so formed the tax frontier, which is graphed in Figure 6.3. The numbers on the frontier are the identification codes of the estates that form the frontier (for example, 1

EXTENSIONS, COMPARISONS AND CONCLUSIONS

127

Figure 6.3 Tax assessment frontier: Essex lay estates, 1086

refers to Fobbing with an annual value of 720 shillings and a tax assessment of 2,445.5 fiscal acres). All other estates can be represented by points below the frontier. Some examples are 31 Boxted (BHI 2.00), 241 Stambourne and Toppesfield (BHI 9.88), 374 Fairsted (BHI 15.27), 247 Tiltey (BHI 18.02) and 453 Stevington End (BHI 25.44). BHIs, tax assessments, frontier tax assessments and the annual values of all 574 estates are listed in Appendix 4. Table 6.3 lists frequencies for BHI intervals, and Figure 6.4 is the BHI histogram. The BHI distribution is concentrated on values between one and five. Index values tend to be much larger than CS u efficiency values. Only 3 per cent of estates have values of one, almost one-quarter of estates have BHI values of five or more, 11 per cent values of eight or more, seven estates have values of twenty or more, and 195 Boxted has the largest value of 71.11. Table 6.4 provides summary information about the eighteen estates lying on the frontier. No obvious patterns are evident for the estates with a BHI of one. Some tenants-in-chief were major magnates such as Count Eustace, Count Alan, Suen and Geoffrey de Magna Villa, but several estates had tenants-in-chief who were less significant lords. In terms of tenancy, nine estates were held in demesne and nine had a single subtenant. Five of the frontier estates were in the hundred of Dengie, three in Uttlesford, two in Barstable, Lexden and Tendring, and one in each of Rochford, Beacontree, Chelmsford and Thurstable. The estates seem to be well distributed over the hundreds.

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Turning to the estates with very high beneficial hidation indexes (greater than 18), from Table 6.5 it can be seen that they range from 395 Prested with a small annual value of only 12 shillings to a relatively large estate 247 Tiltey with an annual value of 140 shillings (140 shillings exceeds the annual value of more than three-quarters of the estates in the sample). Of the nine estates with a BHI greater than eighteen, most have minor lords as tenants-in-chief, six are subtenancies and three held in demesne, three estates were in Hinckford hundred, two in Dunmow, two in Freshwell half-hundred, and the others in Tendring and Lexden hundreds. Table 6.3 Beneficial hidation index (BHI) frequencies: Essex lay estates, 1086 Beneficial hidation index (BHI) value

Frequency

Per cent

Cumulative per cent

1 1
18 132 121 92 82 31 23 14 9 11 34 7

3 23 21 16 15 5 4 2 2 2 6 1

3 26 47 63 78 83 87 89 91 93 99 100

Table 6.4 Characteristics of estates with beneficial hidation index (BHI) of one: Essex lay estates, 1086 Estate

BHI Tax assessment

Frontier assessment

Annual value Tenant-inchief

1

Fobbing

1

2,445.5

2,445.5

720

50

Tolleshunt Guines Elmdon

1

1,081

1,081

110

1

1,680

1,680

400

79 Lt. Bentley 138 Wickford 219 Purleigh

1 1 1

42.5 1,200 840

42.5 1,200 840

3 180 100

250

Woodham Ferrers 288 Stow Maries

1

1,680

1,680

560

1

637

637

65

289

1

3,120

3,120

1,000

66

Saffron Walden

Tenancy

Count demesne Eustace Count 1 sub-tenant Eustace Count 1 sub-tenant Eustace Count Alan 1 sub-tenant Suen of Essex demesne Hugh de demesne Montfort Henry de demesne Ferrariis Geoffrey de 1 sub-tenant Magna Villa Geoffrey de demesne Magna Villa

Hundred Barstable Thurstable Uttlesford Tendring Barstable Dengie Chelmsford Dengie Uttlesford

EXTENSIONS, COMPARISONS AND CONCLUSIONS

Figure 6.4 Beneficial hidation index (BHI) histogram: Essex lay estates, 1086

Estate

BHI Tax assessment

Frontier assessment

Annual value Tenant-inchief

Tenancy

Weneswic

1

640

640

80

1 sub-tenant Dengie

319 Wivenhoe 384 Debden

1 1

625 1,980

625 1,980

46 600

390

Down

1

1,680

1,680

260

393

Stangate

1

1,140

1,140

160

451

Ardleigh

1

195

195

17.67

481

Leyton

1

540

540

20

488

Paglesham

1

90

90

5

293

559

Geoffrey de Magna Villa Robert Greno Ranulf Peverel Ranulf Peverel Ranulf Peverel Ranulf brother of Ilger Robert son of Corbutio Robert son of Corbutio Ilbodo

East 1 188 188 7 Donyland Notes: Tax assessments are measured in fiscal acres and annual values in shillings.

Hundred

1 sub-tenant Lexden demesne Uttlesford demesne

Dengie

1 sub-tenant Dengie 1 sub-tenant Tendring

demesne

Becontree

1 sub-tenant Rochford demesne

Lexden

129

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Table 6.5 Characteristics of selected estates that received beneficial hidation: Essex lay estates, 1086 Estate

BHI

Tax assessment

Frontier assessment

Annual value Tenant-inchief

Tenancy

Hundred

31

Boxted

2.00

600

1,200

240

demesne

Lexden

241

9.88

170

1,680

280

demesne

Hinckford

374

Stambrn/ Toppesfld Fairsted

15.27

55

840

100

247

Tiltey

18.02

60

1,081

140

115

How Hall

19.23

43.6

625

50

25.44

42.5

1,081

115

25.60

453

Stevington End 500 Sibil Hedingham 28 Toppesfield

25

640

80

36.00 15

540

20

207

36.00 15

540

30

36.00 15 37.60 5

540 188

20 12

Radwinter

555 Tendring 395 Prested

Count Eustace Hamo dapifer Ranulf Peverel Henry de Ferrariis Richard son of C.Gilbert Tithel the Breton Roger Bigot Count Eustace Eudo dapifer

Moduin Ranulf Peverel 195 Broxted 71.11 9 640 80 Eudo dapifer Note: Tax assessments are measured in fiscal acres and annual values in shillings.

1 sub-tenant Witham demesne

Dunmow

1 sub-tenant Hinckford demesne

Freshwell HH 1 sub-tenant Hinckford 1 sub-tenant Hinckford 1 sub-tenant Freshwell HH demesne Tendring 1 sub-tenant Lexden 1 sub-tenant Dunmow

In footnotes to the Victoria County History entries for Essex (1903) Round commented that four of the nine estates with very high beneficial hidation indexes had abnormal or nominal assessments. Thus, in footnote 1, page 450, he noted that 195 Broxted (BHI 71.11) was ‘assessed at 9 acres and valued at 4 pounds, which makes the assessment nominal’. Of 247 Tiltey’s assessment (BHI 18.02) he said (footnote 3, page 503), ‘This is an almost nominal assessment’; 28 Toppesfield’s assessment (BHI 36.00) was described as abnormal (footnote 4, page 502), and of 500 Sibil Hedingham (BHI 25.60) he said, ‘This low assessment should be noted’ (footnote 4, page 549). Round also commented on the low assessment of estates with smaller beneficial hidation indexes. These include the assessments of 374 Fairsted (BHI 15.27) described as ‘strangely low’ (footnote 4, page 527), 571 Gestingthorp (BHI 8.00) also referred to as ‘strangely low’ (footnote 9, page 564), 241 Stambourne and Toppesfield (BHI 9.88) described as ‘an almost nominal amount’ (footnote 4, page 502), and 273 High Easter (BHI 3.26) ‘a very low hidation’ (footnote 4, page 509). On the other hand, the low assessments of 115 How Hall (BHI 19.23), 453 Stevington End (BHI 25.44), 207 Radwinter (BHI 36.00), 555 Tendring (BHI 36.00) and 395 Prested (BHI 37.60) are not commented on (although he does note that the annual value for Radwinter tripled from 1066 to 1086 ‘with nothing to account for the rise’ (footnote 10, page 495). Round’s comments are rather unsystematic. By calculating beneficial hidation indexes for each estate it is possible to identify estates with low or abnormal assessments in a more comprehensive fashion.

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131

6.7 STATISTICAL ANALYSIS OF FACTORS AFFECTING BENEFICIAL HIDATION In the previous section the characteristics of estates with extreme BHI values were examined. Do formal statistical analyses throw further light on factors that were associated with high or low beneficial hidation? Tables 6.6, 6.7 and 6.8 provide the evidence. Table 6.6 lists the mean BHI of estates of the eighteen largest tenants-in-chief (those that had more than ten estates in Essex). Eudo dapifer has the largest mean value (7.87). The deviation of this value from the overall mean (4.35) is 3.52. Notice, however, that the standard deviation of Eudo dapifer’s mean BHI is large (3.09). The high mean value is largely due to the high BHIs of two of Eudo dapifer’s estates: 195 Broxted (BHI=71.11) and 207 Radwinter (BHI=36.00). Richard son of Count Gilbert also has a high mean BHI (7.27), which is significantly greater than the overall mean. Roger de Ramis and John son of Waleram also had high mean BHIs (5.66 and 5.34 respectively). Those who were not leniently treated include Robert son of Corbutio (mean BHI=2.06), Robert Greno (mean BHI=2.73), Ralf Baignard (mean BHI=2.87), Ranulf brother of Ilger (mean BHI=2.94) and Hugh de Montfort (mean Table 6.6 Mean BHI of estates of eighteen largest tenants-in-chief: Essex lay estates, 1086 Tenant-in-chief

Mean BHI Standard deviation of mean

Deviation from overall mean

Number of estates in sample

Count Eustace Suen of Essex Geoffrey de Magna Villa Robert Greno Richard son of Count Gilbert Ranulf Peverel Ralf Baignard Eudo dapifer William de Warene Ranulf brother of Ilger Hugh de Montfort Hamo dapifer Peter de Valognes Aubrey de Ver Robert son of Corbutio Count Alan Roger de Ramis John son of Waleram Others

4.25 4.19 3.55 2.73 7.27

0.56 0.48 0.31 0.29 0.88

−0.10 −0.16 −0.80 −1.62 2.92

71 57 42 44 29

4.26 2.87 7.87 3.93 2.94 2.97 4.33 4.76 4.76 2.06 4.50 5.66 5.34 4.77

1.03 0.37 3.09 0.46 0.41 0.47 0.66 1.31 0.82 0.35 1.13 1.17 1.14 0.51

−0.09 −1.48 3.52 −0.42 −1.41 −1.38 −0.02 0.41 0.41 −2.29 0.15 1.31 0.99 0.42

37 29 24 18 17 17 15 14 16 11 9 12 8 104

BHI=2.97). There is a clear tendency for the tenants-in-chief with the largest number of estates in Essex to have less favourable assessments. Ten of the twelve largest tenants-in-chief have a mean BHI below the

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overall mean. A robust statistical test of the null hypothesis that the mean BHIs for the tenants-in-chief are equal resulted in rejection of the null at the 5 and 1 per cent significance levels.7 Estate index values vary with tenant-in-chief. Table 6.7 gives a breakdown of mean BHI by hundreds. A statistical test indicates that the BHI varied significantly (at the 5 and 1 per cent levels) with hundred location.8 Hundreds for which estates received milder assessments included Freshwell half-hundred (mean BHI=8.94), Hinckford (mean BHI= 7.43), Dunmow (mean BHI=6.60), Lexden (mean BHI=5.57) and Maldon half-hundred (mean BHI=5.40). Those less well treated were Beacontree (mean BHI=1.55), Dengie (mean BHI=2.34), Clavering hundred and halfhundred (mean BHI=2.37), Winstree (mean BHI=2.38), Waltham (mean BHI=2.39), Chafford (mean BHI=2.43), Chelmsford (mean BHI=2.52) and Barstable (mean BHI=2.55). In most tax systems, certain groups or activities receive concessions and the administrative process induces unevenness in the assessments. Details of the implementation of the hidage system are now largely unknown, so it would be interesting to see if there is empirical evidence indicating whether particular Table 6.7 Mean BHI of estates by hundred: Essex lay estates, 1086 Hundred

Mean BHI Standard deviation of mean

Deviation from overall mean

Number of estates in sample

Barstable Beacontree Chafford Chelmsford Dengie Dunmow Clavering hundred and half-hundred Freshwell half -hundred Harlow Harlow half-hundred Hinckford Lexden Ongar Rochford Tendring Uttlesford Waltham Winstree Witham Maldon half-hundred Thunreslau half-hundred Thurstable

2.55 1.55 2.43 2.52 2.34 6.60 2.37

0.21 0.10 0.39 0.14 0.25 1.44 0.33

−1.80 −2.80 −1.92 −1.83 −2.01 2.25 −1.98

35 9 12 48 41 48 10

8.94 3.61 2.97 7.43 5.57 5.09 4.10 3.74 2.90 2.39 2.38 4.83 5.40 3.30 2.89

2.18 0.88 0.77 0.67 1.21 0.51 0.57 0.74 0.27 0.80 0.26 0.75 3.60 0.72 0.36

4.59 −0.74 −1.38 3.08 1.22 0.74 −0.25 −0.61 −1.45 −1.96 −1.97 0.48 1.05 −1.05 −1.46

17 18 3 73 31 34 36 48 39 4 15 26 2 3 22

groups or activities received special treatment, and, given these special considerations, whether the assessments were evenly distributed over the county.

EXTENSIONS, COMPARISONS AND CONCLUSIONS

133

Table 6.8 lists the main results of two multivariate regressions of estate BHI on variables indicating the estate’s tenant-in-chief, the hundred location, whether or not the estate was close to an urban centre, and variables measuring the size of the estate and tenure. Activities of the estate were measured by the grazing/ arable ratio (indicating the kind of agriculture undertaken), and variables indicating the amount of meadow and the number of beehives, fisheries, mills, saltpans and vineyards. In Domesday Economy: 63–4, Snooks and I tentatively speculated that a tax deduction may have been granted on meadow (a critical resource for maintaining ploughteams and warhorses) to encourage landholders to increase the acreage. It will be interesting to reassess the evidence relating to this proposition. In the first regression (Specification A), binary variables were used to indicate whether an estate was held by one of the eighteen largest tenants-in-chief in the county, and a separate variable used to indicate whether or not the estate was held in demesne. In Specification B, binary variables were used to indicate whether an estate was held in demesne by one of the eighteen largest tenants-inTable 6.8 Multivariate regressions of BHI on estate characteristics: Essex lay estates, 1086 Specification A Test statistic Specification B Test statistic Distribution on null Tenant-in-chief in demesne effect Tenant-in-chief effect Tenure effect Hundred effect Urban centre effect Economic size indicator Kind of agriculture effect Meadow Beehives Fisheries Mills Saltpans Vineyards

1.900*

F(19,524)

1.800* F(18,524) −2.2* t(524) 5.220** 5.263** F(21,524) −3.1** −3.2** t(524) −2.9** −2.0* t(524) −0.9 −0.1 t(524) −0.8 −1.2 t(524) −1.0 −0.7 t(524) −1.7 −1.5 t(524) −1.1 −1.3 t(524) −0.5 −1.7 t(524) 1.5 1.7 t(524) 0.173 0.133 Notes: * indicates significant at the 5 per cent level and ** significant at the 1 per cent level. All test statistics are heteroskedasticity-consistent test statistics (see H. White, 1980). is the coefficient of determination adjusted for degrees of freedom.

chief, in demesne by one of the other tenants-in-chief, or by a sub-tenant. The two regressions provided very similar results.9 For Specification A, the statistics indicate that the tenant-in-chief and hundred effects remain significant when other factors are allowed to vary in the multiple regression. (Smaller tenants-in-chief, as before, tended to have more favourable assessments.) Whether the estate was close to Maldon or Colchester was also a significant factor. The BHI for estates close to these towns was, on average, 1.70 lower than for other estates. Economic size (measured by the logarithm of annual value) of the estate also significantly affected the index value. A large estate (with an annual value of 320 shillings) had an average index value 1.82 less than a small estate (with an annual value of 20 shillings). Whether or not an estate was held in demesne was

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a significant factor at the 5 per cent level. Estates held in demesne, on average, had a BHI 0.94 less than those that were sub-or mesnetenancies. None of the variables measuring estate activity were significant. In the Specification B regression, the tenant-in-chief in demesne effect was significant at the 2 per cent level and the outcome of the significance tests for the other effects and variables was the same as for Specification A.10 To summarise, although the details of the levying of the geld in 1086 are largely lost in time, the empirical evidence clearly indicates that the manorial tax assessments were based on a capacity-to-pay principle (as measured by the manor’s annual value), and the analysis of estate BHIs shows that other factors also had a significant influence. Allowing for the capacity of an estate to meet the tax, some estates were favoured above others. The results also show that some tenants-in-chief were treated more leniently than others, and, interestingly, it tended to be the tenants-in-chief holding fewer rather than more estates in the county. At the margin, the assessment system may have tended to favour the less wealthy, because it was also found that smaller estates and those held by sub-tenants received lower assessments, and urban estates (often held by the wealthy) higher assessments. The fact that there was a significant hundred assessment differential suggests that administrative factors affected the hidage system. This could have been because the assessments were made at different dates or with (slightly) more rigour in some hundreds than in others. As for concessions being given when particular activities were undertaken, the regression provides no evidence of this. The tax system did not favour arable activity over animal husbandry or vice versa; no special treatment was associated with the occurrence of beehives, fisheries, mills, saltpans or vineyards; and the evidence did not support the speculation that a tax concession was granted on meadow. The foregoing is but a preliminary analysis, but nevertheless shows how frontier methods can be used to investigate the issue of beneficial hidation, how a BHI can be employed to compare the tax situation of estates, and how factors associated with more or less favourable tax treatment can be discovered. A more comprehensive study by a medievalist would certainly be interesting. 6.8 CONCLUSION The aim of the book is to encourage detailed research of Domesday production and fiscal relationships. A technique, the frontier, which can be used to carry out the research, is explained, and illustrative studies of Essex estates described. Further studies of the Essex estates and other counties by medievalists and economic historians would be of value. The production frontier enables us to discover which estates were successful in transforming inputs into outputs. Estate efficiency measures can be used to compare production on different estates, and thereby develop a deeper understanding of Domesday manorial production relationships. Factors associated with manorial efficiency can be determined and comparisons made with other economies. The taxation frontier can be used to discover which estates received favourable tax assessments. A beneficial hidation index for each estate can be calculated and the indexes used to compare the tax situation of estates. Factors associated with favourable tax treatment can be determined. The frontier methodology was reviewed in Chapters 2 and 3, and applied to manorial production in Chapter 4. Efficiency measures (u) under the preferred technological assumptions, constant returns to scale, strong disposability of resources (CS) were calculated for a sample of 577 Essex lay estates in 1086. Ninetysix, or 17 per cent, of the estates were efficient (u=1), 28 per cent categorised as relatively efficient (1
EXTENSIONS, COMPARISONS AND CONCLUSIONS

135

5), 20 per cent less efficient (1.5 ≤u<2), 26 per cent inefficient (2≤u<3) and 10 per cent very inefficient (u≥3). The results of the efficiency analysis were used to compare production on about a dozen estates. A more extensive county wide comparison by scholars with access to detailed historical and geographical knowledge would be useful. A descriptive analysis of factors associated with efficiency indicated that Geoffrey de Magna Villa, Eudo dapifer, Ranulf Peverel, Sasselin and Henry de Ferrariis were tenants-in-chief with a relatively large number of more efficient estates. Those whose estates were relatively inefficient included Count Alan of Brittany, Robert Greno, Peter de Valognes and Roger de Ramis. Hundreds containing more efficient estates were Dengie, Rochford, Tendring and Uttlesford. Estates in Clavering hundred and half-hundred, Harlow, Lexden, Ongar, Witham and Thurstable tended to be less efficient. Other spatial characteristics of manorial efficiency were examined. Some clustering of estates with similar efficiency characteristics was noted in Rochford; and estates in the London Clay geographical (soil) region tended to be more efficient than those in the Boulder Clay Plateau region. No clear relationship between estate efficiency and proximity of the urban centres of Colchester and Maldon was evident. Efficiency and size appeared to be related, larger estates tending to be more efficient. Subsequent analysis suggested that this reflects both a tendency for larger estates to be better-managed and very mild economies of scale on the frontier. Efficiency and tenancy arrangements were examined. Estates held in demesne tended to be more efficient. Some patterns were noted in the relationship between estate efficiency and the activities of estates (as indicated by the kind of agriculture undertaken and the existence of the ancillary resources: beehives, fisheries, mills, saltpans and vineyards). A number of statistical analyses were undertaken to clarify the relationship between estate efficiency and factors affecting production. Pearson’s contingency table test was used to assess the significance of crosstabulations of efficiency categories against factor categories. Significant relationships were found for estate efficiency and geographical (soil) region, size of estate, hundred location and tenure. The probit method was used to discover factors significantly associated with fully efficient estates. Significant factors were whether the estate was held in demesne and, if so, which tenant-in-chief held the estate in demesne, the hundred location, geographical (soil) region and economic size of the estate, and the kind of agriculture undertaken. The estate efficiency indexes themselves give a more comprehensive measure of efficiency, indicating both whether an estate was fully efficient and, if not, the degree of its inefficiency. Factors significantly associated with estate efficiency index values (in bivariate regressions) were the estate’s tenant-in-chief, whether the estate was held in demesne, and, if so, who held the estate in demesne, the number of estates the tenant-in-chief held in the county, the estate’s hundred location, geographical region and economic size, and the kind of agriculture carried out. These bivariate regressions, although suggestive, do not allow for the influence of third variables in the efficiency relationship. Multivariate regressions of estate efficiency index on factors affecting production do allow for simultaneous movement in the factors, and provide more appropriate individual factor effect estimates. Two multivariate regression specifications (which model the tenant-in-chief and tenure effects differently) were estimated. Similar results were obtained for the two regressions. They indicated that CS efficiency was influenced by whether an estate was held in demesne by the tenant-in-chief (estates held in demesne tending to be more efficient) and who the tenant-in-chief was, the hundred location, economic size of the estate (larger estates were more efficient) and the kind of agriculture carried out on the estate (estates with

136

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

relatively more grazing activity were more efficient). Estates with beehives, mills or saltpans tended to be less efficient. A possible explanation for this is that the returns from these resources were not included in the estate annual values, but labour and other estate inputs were used to work the resources. Explanations for the other factors that affected efficiency were also considered. For example, that tenants-in-chief operated their estates at different efficiency levels can be explained in terms of their differential abilities and entrepreneurial skills, and the relative efficiency of estates with more grazing activity probably reflects the profitability of the wool trade (sheep being the predominant livestock). Similar results were obtained when the efficiency analysis was repeated assuming variable returns to scale, strong disposability of resources (VS) technology. The VS frontier tends to exhibit very mildly increasing but very close to constant returns to scale, and the VS efficiency measures indicated that larger estates were, on average, more efficient. When an alternative statistical (Constant Elasticity of Substitution) production function analysis was undertaken (see Chapter 5) similar factors were significant in bivariate and multivariate regressions as in the frontier studies. The signs of factor effects and individual effects were also similar (for example, the same tenants-in-chief were judged to hold more efficient estates in the two analyses) and efficiency characteristics of estates were similar (estates judged efficient in one analysis tended to be judged efficient in the other). The production function exhibited mildly increasing, but close to constant returns to scale, and about 15 per cent of variation in the regression not explained by the main resource variables was explained by the ancillary resources and other factors affecting production. From the CS frontier analysis, shadow prices can be calculated for each resource (see Chapter 4). The resource shadow prices, measures of productivity at the frontier, clearly indicated the importance of arable activity. The mean shadow price for demesne ploughteams was 43 shillings, six times that of peasants’ ploughteams; and slaves had higher mean shadow prices than villans and bordars. From 1066 to 1086, the proportion of bordars to villans and slaves increased in Essex, but on most estates in 1086 there was no economic incentive to free slaves or give a bordar-contract to a villan (although on larger estates the return from bordars and villans was very similar). Most resources, including land and livestock, had relatively high valuations on efficient estates, with meadow land being particularly valuable. A major feature of the shadow prices was the wide dispersion of prices across estates. This was associated with widespread slack in resources. In Chapter 6 the structure of Domesday efficiency was compared with that of agriculture in the American South 1879–80, small Californian farms in 1977 and surface coal-mining in America in 1975 to 1978. The structure of efficiency was more favourable for Domesday estates than for Southern agriculture and the small Californian farms—that is, relative to best practice, Domesday estates were, on average, more efficient. Mean efficiencies for Domesday estates and for American mines were very similar when calculated under different technological assumptions. This evidence suggests that in comparative terms Domesday estates were efficiently run. The wide dispersion of resource shadow prices and extensive slack in resources can be explained by input rigidities resulting from feudalism and manorialism. Output trading did not appear greatly to alleviate the situation. The economic cost of the rigidities was substantial. Potential output could have been increased by about 40 per cent had estate input mixes been variable. This compares with an increase in output of 51 per cent that could have been achieved had all estates been run efficiently (at their endowed resource levels). A tax frontier was used to measure beneficial hidation indexes for Essex lay estates in 1086. An index value of one corresponds to no beneficial hidation, and values greater than one to more lenient tax assessments. Index values tended to be larger than production efficiency values, and only eighteen estates were on the frontier (and hence had an index value of one). The tax situations of selected estates were compared.

EXTENSIONS, COMPARISONS AND CONCLUSIONS

137

Tenants-in-chief and hundreds of the county with lenient assessments were discovered, and regression methods used to assess the significance of the association of beneficial hidation with estate characteristics. Tenants-in-chief who received more favourable assessments included Eudo dapifer, Richard son of Count Gilbert, Roger de Ramis and John son of Waleram. Those less favourably treated included Robert son of Corbutio, Robert Greno, Ralf Baignard, Ranulf brother of Ilger and Hugh de Montfort. Tenants-in-chief holding the largest number of estates in Essex tended to have less favourable assessments. Hundreds in which estates received lower assessments included Freshwell half-hundred, Hinckford, Dunmow, Lexden and Maldon half-hundred. Those less well treated were Beacontree, Dengie, Clavering hundred and half-hundred, Winstree, Waltham, Chafford, Chelmsford and Barstable. Factors in the multivariate regressions significantly associated with beneficial hidation were the tenant-inchief holding the estate (hidation tended to be less beneficial for the tenants-in-chief holding a large number of estates in Essex), the hundred location, proximity to an urban centre (estates remote from the urban centres being more favourably treated), economic size of the estate (larger estates being less favourably treated) and tenure (estates held as sub-tenancies having more lenient assessments). The activities of the estates were not significant factors. At the margin, the assessment system may have tended to favour the less wealthy because tenants-inchief with fewer estates in the county, smaller estates, and those held by sub-tenants received lower assessments, and urban estates (often held by the wealthy) higher assessments. The significant hundred assessment differential suggests that administrative factors (such as assessments being made at different dates or with slightly more rigour in some hundreds than in others) affected the hidage system. The regressions provide no evidence that concessions were given when particular activities were undertaken. It is hoped that these preliminary analyses will encourage researchers to explore further the microeconomic relationships of rural Domesday England.

APPENDIX 1 Linear programming input algorithms

The following algorithm will construct the input files for the 577 linear programming problems which establish if the estates were efficient assuming variable returns to scale, weak disposability of resources (VW) technology. The algorithm must be run using the computer program SHAZAM (see White, Wong, Whistler and Haun, 1990), although only minor modifications are required for it to be run as a Fortran program. The algorithm was run with the DOS extended memory version of SHAZAM with 4 Kbytes of memory and 30 Mbytes available on the hard disk. (Notice that LINDO interprets the strict inequality z1+z2>l as the non-strict inequality z1+z2≥l.) VW TECHNOLOGY INPUT ALGORITHM sample 1 577 * data read in file 11 f1.dat format (11f7.2) read(11) v r1–r10/format * z1. . . . .z577 read in file 12 f.dat format (1x,5a4) read(12) z z1–z4/format *generate lags of v and r1–r10 genr v1=lag(v) genr v2=lag(v1) genr v3=lag(v2) genr v4=lag(v3) do#=1,10 genr r#1=lag(r#) genr r#2=lag(r#1) genr r#3=lag(r#2) genr r#4=lag(r#3) endo * text read in sample 11 format (a5,a5,a8,a8,al,a8,a3,a2,a4,a8,a8,a4,a5) read t1–t13/format

APPENDIX 1

batchtersedivert infile.datmax u stendgononzrpri n p : p>0rvrtleave format (a7, a3) read t14 t15/format w>.0005w<1 * symbols read in format (9a1) read p m u g 1 n e i w/format +−u><0=1w * write batch terse, divert Undo output to infile.dat in foxplus file 13 c:\foxplus\a format (1x,a5/1x,a5/1x,a8,a8,al) write(13) t1−t5/format * do statement for number of LP problems solved on this run do !=1,577 * write max u st format (1x, a8) write(13) t6/format * write output constraint sample 11 do #=5,575,5 sample 11 format (1x,5(a1, f7.2, a4)) write(13) p v4:# z4:# p v3:# z3:# p v2:# z2:# p v1:# z1:# p v:# z:#/format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p v:576 z:576 p v:577 z:577 m v:! u g n/format * write input constraints * 1st constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r14:# z4:# p r13:# z3:# p r12:# z2:# p r11:# z1:# p r1:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r1:576 z:576 p r1:577 z:577 m r1:! w e n/format * 2nd constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r24:# z4:# p r23:# z3:# p r22:# z2:# p r21:# z1:# p r2:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r2:576 z:576 p r2:577 z:577 m r2:! w e n/format * 3rd constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r34:# z4:# p r33:# z3:# p r32:# z2:# p r31:# z1:# p r3:# z:#/& format endo

139

140

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r3:576 z:576 p r3:577 z:577 m r3:! w e n/format * 4th constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r44:# z4:# p r43:# z3:# p r42:# z2:# p r41:# z1:# p r4:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r4:576 z:576 p r4:577 z:577 m r4:! w e n/format * 5th constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r54:# z4:# p r53:# z3:# p r52:# z2:# p r51:# z1:# p r5:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r5:576 z:576 p r5:577 z:577 m r5:! w e n/format * 6th constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r64:# z4:# p r63:# z3:# p r62:# z2:# p r61:# z1:# p r6:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r6:576 z:576 p r6:577 z:577 m r6:! w e n/format * 7th constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r74:# z4:# p r73:# z3:# p r72:# z2:# p r71:# z1:# p r7:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r7:576 z:576 p r7:577 z:577 m r7:! w e n/format * 8th constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r84:# z4:# p r83:# z3:# p r82:# z2:# p r81:# z1:# p r8#:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r8:576 z:576 p r8:577 z:577 m r8:! w e n/format * 9th constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r94:# z4:# p r93:# z3:# p r92:# z2:# p r91:# z1:# p r9:# z:#/& format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1)

APPENDIX 1

141

write(13) p r9:576 z:576 p r9:577 z:577 m r9:! w e n/format * 10th constraint do #=5,575,5 format(1×,5(a1, f7.2, a4)) write(13) p r104:# z4:# p r103:# z3:# p r102:# z2:# p r101:# z1:# p r10:# & z:#/format endo format(1×,2(a1, f7.2, a4),a1, f7.2, 3a1) write(13) p r10:576 z:576 p r10:577 z:577 m r10:! w e n/format * write vrs constraint sum zi=0 do #=5,575,5 format (1×,5(a1, a4)) write(13) p z4:# p z3:# p z2:# p z1:# p z:#/format endo format (1×,2(a1, a4),2a1) write(13) p z:576 p z:577 e i/format * write weak disposal constraint format (1×,a7/1x, a3) write(13) t14 t15/format * write end go nonz rpri n p : p>0 format(1×,a3/1×,a2/1×,a4,/1×,a8, a8) write(13) t7–t11/format endo * write rvrt leave format(1×,a4/1×,a5) write(13) t12 t13/format stop CW, VS AND CS TECHNOLOGY INPUT ALGORITHMS To construct the 577 input files for the efficiency linear programming problems corresponding to constant returns to scale, weak disposability of resources (CW) technology, simply omit the six statements following the comment statement, * write vrs constraint sum zi=0, thus omitting the constraint z1+z2+…+z577=1. The input files for the linear programming problems corresponding to variable returns to scale, strong disposability of resources (VS) technology require the following modifications: The six statements following the comment statement, * write vrs constraint sum zi=0, should be included. The last two lines of each of the ten input constraints should be changed. For the first constraint the following lines should appear: format (1×, 2(a1, f7.2, a4),a1, f7.2) write (13) p r1:576 z:576 p r1:577 z:577 1 r1:!/format For the second constraint replace r1:! by r2:!, and make a similar modification for the other constraints. Delete the two statements following the statement, * write weak disposal constraint. The final 577 input files corresponding to CS technology are obtained from the VS algorithm by omitting the six statements following the statement, * write vrs constraint sum zi=0.

APPENDIX 2

TABLE 1 ESSEX LAY ESTATES, 1086: CS TECHNOLOGY MEASURES Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables: Non-zero slack variables

1 Fobbing 2 Horndon 3 Shenfield 4 Gravesanda 5 White Notley 6 Coggeshall 7 Rivenhall 8 Rivenhall 9 Blunts Hall 10 Witham 11 Gt Parndon 12 Latton 13 Dunmow 14 Iltney 15 Plesinchchou 16 Langenhoe 17 Abberton 18 Layer 19 Shortgrove 20 Ridgewell 21 Claret

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.

1.042 3.104 1.000 1.000 1.639 1.535 1.726 3.175 2.500 1.104 1.856 1.000 2.049 1.048 3.000 1.144 1.000 1.349 1.998 1.000 1.000

59.193.205.399.502: 2.3.8.10. 160.190.495:6.9.10. 3: 4: 27. 59.117.190.205.226.502. 529:9. 27. 55. 59.117.120.321.502: 2.4.9. 20. 55. 58. 59.120.205:5.7. 9.10. 58.160.190.479.525:5.7.9. 181.283: 181.283: 27.117.286.399.502.526:8. 12: 36.120.190.415.529.540:5.9. 181.392:10. 399:7.8.9. 58. 59.190.205:2.3.7.8.10. 17: 190.306.392:3.8. 357.392:6.9. 20: 21:

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

22 Belchamp 23 Bumpstead 24 Belchamp

1. 1. 1.

2.184 1.251 2.222

Non-zero slack variables

120.138.190.202.226.252. 502:3.4. 479.495.525:2.5.6.7. 190.357:3.4.6.9.

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

25 Finchingfield 26 Finchingfield 27 Smeeton Hall 28 Toppesfield 29 Maldon 30 Gt Tey 31 Boxted 32 East Donyland 33 Gt Birch 34 East Thorpe 35 Colne Engaine 36 Stanford Rivers 37 Parva Stanford 38 Laver 39 Chipping Ongar 40 Laver 41 Lambourne 42 Fyfield 43 Fyfield 44 Newland Hall 45 Lt. Baddow 46 Runwell 47 Runwell 48 Lt. Waltham 49 Boreham 50 Tolleshunt Guines 51 Goldhanger 52 Tolleshunt 53 Tolleshunt 54 Tollesbury 55 Chiche 56 Tendring 57 Alresford 58 Frinton

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.

1.596 3.266 1.000 2.700 1.188 1.000 1.071 1.978 2.868 2.208 2.865 1.000 1.000 1.228 2.024 1.000 2.848 2.000 2.050 1.156 1.687 2.543 1.000 1.686 1.000 2.738 1.778 5.167 1.119 1.306 1.000 1.510 1.000 1.000

Non-zero slack variables

190.502.540.550:8.9. 392.502:6.9. 27: 282.502:5.8.9. 47.59.190.193.306:2.3. 30: 3.120.138.361.502:2.3.4. 59.160.399.502.540:8.9.10. 36.149.173.190.226.252. 361:2.3. 226.399.461:2.6.7.8. 399.502:2.6.7.9. 36: 37: 27.36.117.190.399.502.529: 7. 37. 55.120.399.415:3.8.9. 40: 120.226.502.529.540:2.3.9. 399:7.8.9. 27.117.321.399:6.8.9. 27.117.127.286.399:5.8. 190.502.540.550:8.9. 392.502:3.6.8. 47: 190.226.502.540:3.6.9. 49: 58. 59.160.190.193.402:3.8. 502:2.6.8.9.10. 47. 59.190.193.391:8.10. 306.392.398:8. 99.495:1.2.10. 55: 36.120.149.190.361.502:2.3. 57: 58:

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

59 Bircho 60 Lt. Holland

1. 1.

1.000 1.519

143

59: 58. 59.138.250:2.5.8.10.

Non-zero slack variables

144

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

61 Lawford 62 Tendring 63 Chreshall 64 Lt. Chishall 65 Lt. Chishall 66 Elmdon 67 Leebury 68 Crawleybury 69 Bendish Hall 70 Newenham 71 Lt. Bardfield 72 Shopland 73 Epping 74 Willingale Spain 75 Gt Canfield 76 Gerham 77 Finchingfield 78 Beauchamp Roding 79 Lt. Bentley 80 Lt. Bentley 81 Manhall 82 Housham Hall 83 Quick Bury 84 Gt Easton 85 Lt. Canfield 86 High Roding 87 Leaden Roding 88 Dunmow 89 Payton Hall 90 Halstead 91 Steeple Bumpstead 92 Polhey

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 16. 16. 16. 16. 16. 16. 16. 16. 16. 9. 9. 9. 9. 9. 9. 9. 9. 9. 9. 9.

1.000 1.481 1.456 1.913 3.310 1.000 1.000 3.310 1.373 1.013 1.548 1.000 2.158 2.100 1.167 2.238 3.600 1.800 3.333 2.000 1.000 1.084 1.423 2.228 1.456 1.068 1.075 1.000 2.527 2.531 1.994 1.419

61: 47. 67.127.526:2.5.8. 250.256.415.525:2.3.4.5.6. 190.357.525:2.3.5.9. 181.283.392: 66: 67: 181.283.392: 149.190.256.399.415: 2.4.5.7. 138.149.502.525.526.529: 5.7. 27. 36.120.190.399.479.502: 9. 72: 286.321.502:5.6.8. 27.117.127.399:5.6.8. 282.321.502:6.8.9. 399.502:6.7.9. 392:6.9. 282.321.502:6.8.9. 4.380:5.9. 4.380:5.9. 81: 36.102.173.415.529.540:2.3. 4.173.357.479.495.525:2. 120.190.226.502.529.540: 2.9. 117.120.226.529.540:2.6.9. 27. 36.120.190.399.479.502: 9. 27.120.502.529.540:3.5.9. 88: 173.322.392.536:5.6. 27. 36.120.138.190.502.529: 5. 81.190.357.502.508:6.9. 357.502:3.6.9.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

93 Kenningtons 94 West Hanningfield 95 Boreham 96 Belstead Hall

9. 9. 9. 9.

1.031 2.333 2.667 1.083

Non-zero slack variables

120.399.502:3.5.8.9. 190.193.306.399:3.8. 502:6.8.9. 40.399:9.

Non-zero slack variables

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

97 Lt. Wenden 98 Eynsworth 99 Paglesham 100 Wallbury 101 Thaxted 102 Thaxted 103 Gt Dunmow 104 Gestingthorpe 105 Finchingfield 106 Panfield 107 Gt Yeldham 108 Wickham St Paul’s 109 Finchingfield 110 Bineslea 111 Alderford 112 Ashen 113 Finchingfield 114 Bulmer 115 How Hall 116 Boyton Hall 117 Bures 118 Roding Morell 119 Lt. Bentley 120 Lt. Bromley 121 Colne 122 Fordham 123 West Bergholt 124 Langham 125 Gt Bardfield 126 Lt. Sampford 127 Hempstead 128 Barrow Hall 129 West Thorndon 130 Langdon 131 West Tilbury

9. 9. 9. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 5. 2. 2. 2.

1.473 1.577 1.000 1.333 1.132 1.595 1.723 1.510 2.500 1.002 1.870 2.667 5.000 1.449 1.783 1.029 1.635 2.465 2.795 1.557 1.000 1.529 1.130 1.000 2.667 2.667 3.000 1.737 2.249 1.096 1.000 1.000 1.537 1.179 2.165

Non-zero slack variables

81.173.392.536:6.9. 173.322.536:3.5.6. 99: 502:2.6.8.9. 36.120.190.399.415:5.7.9. 282.502:4.5.6.9. 27.117.127.399:5.6.8. 27.446.495.526:2.4.5.7. 357.502:3.6.9. 117.127.399.495:6.7.8. 399.502:2.6.7.9. 502:6.8.9. 495:6.9. 286.321.502:2.5.6. 88.502:3.6.9. 392:6.9. 495.502:6.7.9. 181.398.502:1. 190.502.540.550:6.9. 117.321.399.502:2.6.9. 117: 27.117.286.399.502:8.9. 67.321.502:5.6.8. 120: 502:4.6.8.9. 502:4.6.8.9. 399:6.7.8.9. 120.415.529:2.3.6.9. 36. 55.120.149.190.415.502: 3. 36.117.138.173.226.529:2.6. 127: 128: 3.47.138.190.250:2.4.8. 58.391.491:2.7.8.10. 58. 59.190.193:2.3.8.10.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

132 Childerditch

2.

1.580

145

160.190.193.495:8.10.

Non-zero slack variables

146

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

133 Horndon-o-t-Hill 134 Hassingbroke 135 Basildon 136 Basildon 137 Wickford 138 Wickford 139 Wickford 140 South Benfleet 141 Wheatley 142 Thundersley 143 Rayleigh 144 Rayleigh 145 Hockley 146 Eastwood 147 Gt Wakering 148 Prittlewell 149 Shoebury 150 Canewdon 151 Northorp 152 Rochford 153 Gt Stambridge 154 Shoebury 155 Lt. Wakering 156 Sutton 157 Plumberow 158 Pudsey 159 Hockley 160 Pudsey 161 Sutton 162 Pudsey 163 Pudsey 164 Ashingdon 165 Hawkswell 166 Eastwood 167 Iltney 168 Asheldham

2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.

1.819 1.868 2.800 1.632 1.469 1.000 2.500 1.250 1.338 1.984 1.368 2.080 3.871 1.855 1.000 1.169 1.000 1.000 2.351 1.760 2.000 1.077 1.348 1.427 2.000 1.143 1.313 1.000 1.200 1.598 1.000 1.571 1.571 1.800 2.558 1.896

Non-zero slack variables

190.495:2.6.7. 357.392:6.9. 190.193:3.10. 4.193.306.380.398.569:2. 120.138.361.502.529:3.6. 138: 398:8. 495:6.7.10. 160.193.392:2.10. 58. 59.190.193:2.3.8.10. 36.149.190.226.361.502:2.3. 322.392:2.3.6. 160.190.193.392:3. 59.138.149.160.173.402.502. 529:3. 147: 138.160.402.569:2.3.8. 149: 150: 58.190.193.306.402.569:3. 3.138.190.226.361.502: 2.3.4. 495:10. 138.193.322.395.402.569: 3.8. 160.193.392:2.10. 160.193.392:2.10. 3.160.193:2.3.8. 306.392:3.8. 160.193:2.3.8.10. 160: 392:3.6. 160.193.392:3. 163: 181.392:10. 181.392: 392:6. 58.190.193.306.569:2.3. 357.392:6.9.

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

169 Rivenhall 170 Notley 171 Lt. Hallingbury 172 Dunmow 173 East Mersea 174 Clavering 175 Berden 176 Asheldham 177 Horkesley 178 Theydon Mount 179 Warley Franks 180 Kenningtons 181 Maldon 182 Elmstead 183 Foulton 184 Lt. Totham 185 Gt Braxted 186 Harlow 187 Roding Morell 188 Lindsell 189 Mundon 190 Lawling 191 Steeple 192 Down Hall 193 Acleta 194 Hawkwell 195 Broxted 196 Shellow 197 Dunmow 198 Takeley 199 Pledgon 200 Boxted 201 Theydon Gernon 202 Roding Abess

2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

203 Rettendon 204 Lees

8. 8.

3.116 1.441 2.133 3.243 1.000 1.213 2.346 1.714 1.000 1.225 1.007 1.800 1.000 2.930 2.782 1.800 1.418 1.759 1.403 1.132 1.300 1.000 1.000 1.250 1.000 1.425 2.349 2.667 1.652 1.600 1.134 1.350 2.104 1.000

1.000 2.805

147

Non-zero slack variables

160.190.193.536:2.4.9.10. 120.361.502.529:3.6.9. 27.36.120.190.479.529:5.6. 190.502.540.550:8.9. 173: 117.120.138.190.226.502: 2.6. 120.138.149.415.502.529:3. 283.392:9. 177: 3. 88.120.502:2.8.9. 47. 67.502.526:2.6.8. 392:3.6. 181: 120.149.160.205.361.502. 529:2.3. 190.193.357.495:9.10. 392:6.8.10. 120.502.529:2.3.4.8.9. 88.502.540:3.8.9. 120.190.399.415.502.529: 3.9. 27.495.502.526:2.5.6. 58. 59.190.250.518.525: 2.3.4. 190: 191: 160.190.193:3.10. 193: 149.190.415.525.529.540: 2.3. 3. 47.120.138.149.190.502: 3. 502:6.8.9. 286.321.502:2.5.6. 120.399:2.3.8.9. 120.138.502.529:3.5.6. 3. 88.536:2.3.6. 66.120.149.379.502:3.5.8. 202:

203: 120.190.502.540.550:8.9.

Non-zero slack variables

148

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

205 Weeley 206 Quendon 207 Radwinter 208 Arkesden 209 Gt Hallingbury 210 Rodinges 211 Arkesden 212 Arkesden 213 Chishall 214 Downham 215 Kelvedon 216 Leyton 217 Purleigh 218 Latchingdon 219 Purleigh 220 Halesduna 221 Estoleia 222 Layer 223 Rayne Hall 224 Bradwell-on-Sea 225 Markshall 226 Sandon 227 Sandon 228 Wix 229 Lt. Totham 230 Goldhanger 231 Tolleshunt Darcy 232 Ateleia 233 Faulkbourne 234 Notley 235 Rayne 236 Gt Braxted 237 Rise-Marses 238 Dunmow 239 Roding Marci

8. 8. 8. 8. 26. 26. 26. 26. 26. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 12. 12. 12. 12. 12. 12. 12. 12.

1.000 1.477 1.697 1.347 2.176 1.126 1.104 1.081 1.451 1.510 1.273 2.359 1.400 1.093 1.554 1.167 1.444 1.286 2.116 1.048 2.670 1.000 2.394 5.366 2.372 1.500 2.667 1.250 2.000 1.000 1.083 1.713 1.429 1.667 1.425

205: 36.120.149.173.190.502.529: 3. 4. 81.190.283.357:5. 27.117.495.502.526:2.7. 120.415.502.529:3.8.9.10. 27.117.399.479.502:7.9. 120.502:3.5.6.9. 282.502:5.6.9. 120.138.149.190.415.502. 529:3. 3. 88.502:2.8.9. 27.120.190.502.529.540:5.9. 88.120.502:2.3.8.9. 3.190.250:3.5.6.8. 59.391.495:5.7.8.10. 181.392.398:10. 4.495:7.10. 4.392:5. 306.392:2.3. 36.120.173.190.361.502.529: 3. 181.392:2.10. 120.190.250:2.3.6.7.8. 226: 392.502:6.8. 282.502:5.6.8. 160.190.540:7.8.9.10. 282.399:5.6.7.8.10. 502:6.8.9. 495:1.7. 495:6.7.9. 234: 181.283: 120.190.502.540:5.6.9. 4.380:5.9. 502:6.8.9. 27.286.321.502.526:6.8.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

240 Lt. Wigborough

12.

1.140

Non-zero slack variables

58.190.491:2.3.10.

Non-zero slack variables

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

241 Stambrn/Toppesfld 242 Northey 243 Greensted 244 Kelvedon Hatch 245 Norton Mandeville 246 Gt Totham 247 Tiltey 248 Stebbing 249 Steeple 250 Woodham Ferrers 251 Butsbury 252 Marks Tey 253 Shelley 254 Abbess Roding 255 South Ockendon 256 Gt Waltham 257 Gt Waltham 258 Chatham 259 Patching 260 Broomfield 261 Chignal 262 Chignal 263 Chignal 264 Danbury 265 Legra 266 Kewton Hall 267 Moze 268 Frinton 269 Ardleigh 270 Black Notley 271 Ridley Hall 272 Lt. Hallingbury 273 High Easter 274 Newton Hall 275 Barnston

12. 12. 12. 12. 12. 12. 24. 24. 24. 24. 24. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3.

1.256 1.000 2.261 2.872 2.073 2.725 1.053 1.322 1.333 1.000 1.683 1.000 1.271 1.549 1.012 1.000 1.231 2.279 3.000 1.000 1.852 1.725 3.600 1.900 2.668 2.231 2.234 1.000 3.506 1.483 1.820 1.500 1.000 1.438 1.712

20.117.138.202.415.525.529: 4.6. 242: 117.120.138.226.529:2.6.9. 27.117.321.399.502:6.9. 37. 55.120.190.399.415:7.9. 36.117.190.525.540:2.3.6. 190.226.479.508.536:3.9. 120.138.173.226.361:2.3.6. 190:2.3.6. 250: 47. 58. 59.190.250:2.3.8. 252: 27.117.286:5.7.8.9. 282.286.321.502:8.9. 3.120.160.361.502.536: 2.4.6. 256: 392.479.495:2.5.6. 117.127.399:5.6.7.8. 399:9. 260: 27.117.479:2.5.6.7. 27.117.399.479.502:7.9. 392:6.9. 27.321.399:6.8.9. 120.138.173.190.226.361. 502:3. 190.357.479.508.536:5.9. 58.120.138.149.205.402.415. 502:3. 268: 286.321.502.569:2.5.8. 250.379.395.525:2.4.5.8. 399.502:2.6.7.9. 399:6.7.8.9. 273: 27.117.286.399:5.7.8. 27.117.286.399.502.526:8.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

276 Berners Roding

3.

1.071

Non-zero slack variables

117.286.399:7.8.9.

Non-zero slack variables

149

150

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

277 Bigods 278 Lt. Dunmow 279 Shellow Bowells 280 Shellow Bowells 281 White Roding 282 Dunmow 283 Easton 284 Lt. Canfield 285 Roding 286 Roding 287 Dunmow 288 Stow Maries 289 Saffron Walden 290 Gt Chishall 291 Manhall 292 Birchanger 293 Weneswic 294 West Thurrock 295 Ramsden 296 Ramsden 297 PowersHall Witham 298 Hubbridge Hall 299 Rivenhall 300 Matching 301 Chingford 302 West Ham 303 East Ham 304 Leyton 305 Loughton 306 Purleigh 307 East Whettenham 308 Lega 309 Salcot Verley 310 Stanstd Mtfichet 311 Takeley

3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 3. 47. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4.

1.250 1.167 2.609 1.299 1.030 1.000 1.000 1.166 1.092 1.000 2.667 1.331 1.449 1.187 1.800 3.600 1.250 1.593 3.244 2.000 1.942 3.530 2.704 1.918 2.979 1.038 1.918 3.600 2.543 1.000 1.455 2.284 1.689 2.444 2.199

27.117:5.6.7.8.9. 27.117.286.399:7.8.9. 120.190.502.550:6.8.9. 27.117.399:4.6.7.8.9. 502.545:2.5.6.9. 282: 283: 286.321.502.545:2.9. 399.502:6.7.9. 286: 502:6.8.9. 392.569:5.6.8.10. 36.117.120.138.252.502.529: 2.4. 190.502.540:3.6.8. 392:6.9. 392:6.8. 495:2.5.6.7. 58. 59.138.160.190.205.502. 529:3. 3.190.250:3.5.6.8. 3:3.5. 173.190.357.536:2.3.9. 120.361.502.529:3.6.9. 88.502.550:6.9. 88.502.550:8.9. 37. 55.120.399:5.7.8.9. 117.138.256.415.529:2.5.6. 117.120.256.273.415.529: 2.6.9. 392:6.9. 392.502:6.8. 306: 3. 47.190:2.3.8. 138.190.250:2.6.7.8. 190.392:3.6. 47.120.149.190.502:2.3.8. 120.190.226.502.529.540: 2.9.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

312 Gt Wendon

4.

1.281

Non-zero slack variables

4.190.357.479.525:2.5.

Non-zero slack variables

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

313 Benfieldbury 314 Bollington 315 Farnham 316 Manuden 317 Gt Maplestead 318 Wormingford 319 Wivenhoe 320 Lt. Birch 321 Stapleford Abbots 322 Rainham 323 South Weald 324 Frierning 325 Frierning 326 Chicknal Zoyn 327 Springfield 328 Frierning 329 Patching Hl Picot 330 Culvert 331 Gt Oakley 332 Tendring 333 Dikeley 334 Widington 335 Shortgrove 336 Arkesden 337 Elsenham 338 Tolleshunt Darcy 339 Ulting 340 Langford 341 Cold Norton 342 Cold Norton 343 Woodham Walter 344 Purleigh 345 Lt. Dunmow 346 Lt. Dunmow

4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 7. 7. 7. 7. 7. 7. 7. 7.

2.498 1.371 3.331 2.960 3.479 2.162 6.198 2.833 1.000 1.000 1.800 4.527 2.543 1.559 2.325 1.476 1.333 1.468 1.153 2.684 3.606 2.250 1.000 3.329 2.925 2.025 2.814 2.063 1.359 2.400 2.036 1.671 1.915 2.400

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

347 Wimbish 348 Barnwalden

7. 7.

1.152 1.200

Non-zero slack variables

20. 36.120.138.149.190.202. 502:4. 306.392:2.3. 120.226.399.502.540:2.8.9. 120.502.540:3.5.6.9. 120.190.226.502.529.540: 2.9. 36.120.190.226.502.529:2.3. 59.138.160.205.226.361.502. 529:6. 190.226.540:2.7.8.9. 321: 322: 392:5.6.8. 138.190.250:2.6.7.8. 392.502:6.8. 120.361.502.529:2.3.9. 120.502.529:3.5.6.9. 3.120.361.536:2.3.6. 502:2.6.8.9. 181.283.392: 36.120.138.173.190.205.525: 2.6. 3.138.361.502:2.3.6. 3.392.502:2.3.6. 173.190.525:3.6.9. 335: 190.357.495:6.9. 120.138.502.529:2.6.9. 59.120.138.190.205.449: 5.6.8. 120.138.502.529:3.5.6. 283.392.395:4. 138.306.322.402.569:3.8. 395: 37.120.399.415:3.5.8.9. 282.286.321.502.545:6. 36.117.190.529.540:5.6.9. 395.399:4.5.7.9.

Estate

120.138.529:2.5.6.9. 392:3.6.8.

151

Non-zero slack variables

152

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

349 Pentlow 350 Burnham 351 Burnham 352 Lt. Baddow 353 Lt. Baddow 354 Hanningfield 355 Lt. Oakley 356 Ramsey 357 Michaelstow 358 Michaelstow 359 Witlebroc 360 Wenden Loughts 361 Henham 362 Ashdon 363 Paglesham 364 Langford 365 Langford 366 Tolleshunt 367 Tolleshunt 368 Bowers Gifford 369 Inga 370 Hatfield Peverel 371 Hatfield Peverel 372 Blunts Hall 373 Terling 374 Fairsted 375 Chickney 376 Willingale Doe 377 Woodham Mortimer 378 Lt. Maldon

7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 7. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6.

1.074 1.600 2.384 1.833 2.946 1.000 1.699 1.101 1.000 1.200 2.083 1.223 1.000 1.326 1.800 1.768 1.800 2.159 2.900 1.208 3.600 1.719 3.500 2.044 1.933 2.450 1.239 1.265 1.962

120.252.361.502.529: 2.3.4.9. 160.193.402:2.3.10. 181.392.495:10. 4.190.399.555:3.8. 399.502:6.7.9. 354: 36. 58.190.205.256.415.525: 5.7. 120.138.190.415.525:3.5.6. 357: 395:4. 181.283: 47.127.399.495.526:5.8. 361: 120.138.322.415.502:3.4.5. 392:6.10. 120.190.502.540:5.6.9. 392:4.6. 3. 58.190.250.322:3.5.8. 392.395:4. 491:3.10. 392:6.8. 36.117.120.138.226.502.529: 2. 392.495:5. 173.190.357.479.536:3.4.9. 120.160.402.502.529: 2.3.4.10. 120.190.205.226.502.529. 540:2.9. 3. 88.502.536:2.3. 120.190.202.226.252.502. 540:3.4. 47.120.138.190.250.322.502: 3.

6.

1.011

36.138.173.190.415.525.540: 3.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

379 Hazeleigh 380 Hazeleigh 381 Layer 382 Abberton 383 Wigborough

6. 6. 6. 6. 6.

1.000 1.000 3.071 1.200 3.143

379: 380: 3.190.203.392:2.3. 300:2.6.8.9. 181.392:

Non-zero slack variables

Non-zero slack variables

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

384 Debden 385 Amberden 386 Stebbing 387 Gt Henny 388 Lammarsh 389 Lammarsh 390 Down 391 Lawling 392 Down 393 Stangate 394 Prested 395 Prested 396 Plumtuna 397 Springfield 398 Rettenden 399 Tendring 400 St Osyth 401 Frating 402 Leigh 403 Tolleshunt Darcy 404 Goldhanger 405 Gt Canfield 406 Udecheshale 407 Thunderley 408 Ugley 409 Castle Hedingham 410 Belchamp Walter 411 Hersham Hall 412 Earls Colne 413 Gt Bentley

6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 14. 14. 14. 14. 14. 14. 14. 14. 14.

1.454 1.585 1.402 2.395 1.446 1.072 1.129 1.000 1.000 1.549 1.391 1.000 2.255 2.000 1.000 1.000 2.413 1.305 1.000 3.715 2.645 2.253 2.690 1.764 1.940 1.689 1.222 4.000 1.548 1.801

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

414 Dovercourt 415 Beaumont 416 Beaumont 417 Helions Bumpstead 418 Radwinter 419 Stevington End

14. 14. 14. 14. 14. 14.

1.281 1.000 1.271 1.282 2.222 1.789

Non-zero slack variables

37. 55.120.190.399.415:7.9. 36.120.190.399.415.529:5.9. 117.127.399.495.526:2.6. 120.138.361.502.529:3.6. 120.138.361.502.529:3.6. 286.321.502:2.5.6. 59. 67.495:2.5.7.8. 391: 392: 47. 59. 67.392.495 2.6. 88.502.550:6.8. 395: 4.380:5.9. 27.120.190.226.502.529.540: 9. 398: 399: 55. 58. 59.190.205.399: 2.8.10. 3.190.226.502.540:2.8. 402: 120.138.190.205.415.502. 529:3.5. 57. 59.160.190.226.502: 4.6.8. 36.120.190.529.540:5.6.9. 36.120.190.529.540:5.6.9. 120.138.415.502.529:3.5. 36.120.226.361.502.529:2.3. 36.117.120.173.415.529.540: 2. 173.202:2.3.4.6.7.9. 502:6.8.9. 226.399.502.540:2.8.9. 47. 58.190.193.205.502: 2.3.8.

Estate

153

Non-zero slack variables

58.160.190:2.3.9.10. 415: 392.502:4.6.8. 120.138.190.415.502.529: 3.5. 27.117.399.495.502.526:7. 282.502:5.6.8.

154

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

420 Stevington End 421 Sheering 422 Latton 423 Lt. Parndon 424 Walda 425 Leyton 426 Higham Bensted 427 Loughton 428 Balingdon 429 Bineslea 430 Loughton 431 Theydon Bois 432 Theydon Bois 433 N.Weald Basset 434 N.Weald Basset 435 Inga 436 Ramsden 437 Roydon 438 Harlow 439 Gt Parndon 440 Gt Parndon 441 Walda 442 Nazing 443 Nazing & Epping 444 Thorp 445 Birdbrook 446 Bapthorne 447 Newland

14. 13. 13. 13. 13. 13. 13. 13. 13. 13. 13. 13. 13. 13. 13. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

448 Bobbingworth 449 Mountnessing 450 Mountnessing 451 Ardleigh 452 Yardley 453 Stevington End 454 Radwinter 455 Helion Bumpstead

10. 10. 10. 10. 21. 21. 21. 21.

3.143 3.219 1.049 1.996 3.000 2.248 2.249 2.667 1.552 2.865 2.667 4.348 2.667 1.531 2.732 2.000 2.671 2.052 2.490 2.485 2.424 2.606 1.800 2.267 1.645 1.422 1.000 1.667

1.265 1.000 1.250 1.000 2.881 1.158 2.467 1.998

Non-zero slack variables

181.392: 120.190.399.479.502.529: 5.9. 282.286.321.502:8.9. 190.226.399.540:2.8.9. 399:6.7.8. 120.286.415.529:2.5.9. 37.55.120.399.415:5.7.9. 502:6.8.9. 190.226.536:2.3.9. 399.502:2.6.7.9. 502:6.8.9. 339.502:1.8.9. 502:6.8.9. 37. 55.120.399:5.7.8.9. 282.502:5.6.8. 3:2.3.6.8. 190.252.399.540:2.3.4.8. 55. 58. 59.205.286.399.502. 529:9. 282.502:5.8.9. 88.502.540.550:8.9. 502:6.8.9. 120.149.379.399.415.502: 3.8. 392:5.6. 120.138.160.502.529.569: 4.9.10. 58. 59.190.193.569:2.3.8. 20. 27.138.190.446.479.502. 529:4. 446: 495:6. Non-zero slack variables

190.502.540:3.6.8. 449: 495:6.8.10. 451: 88.502.550:6.9. 190.357.495:6.9. 120.138.502.529:3.5.6. 36.120.138.190.415.502.529: 5.

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

456 Steeple Bumpstead 21. 457 Sturmer 21. 458 Sturmer 21. 459 Tilbury by Clare 21. 460 Rayne 17. 461 Rayne 17. 462 Sibil Hedingham 17. 463 Messing 17. 464 Messing 17. 465 Dedham 17. 466 Bures 17. 467 Bradfield 17. 468 Ardleigh 17. 469 Bradfield Manston 17. 470 Cliva 17. 471 Ardleigh 17. 472 Black Notley 18. 473 Gt Saling 18. 474 Lt. Maplestead 18. 475 Henny 18. 476 Bures St. Mary 18. 477 Fyfield 18. 478 High Ongar 18. 479 Aveley 18. 480 Smalland 15. 481 Leyton 15. 482 Lawling 15. 483 Hanningfield 15. 484 Waltham 15. 485 Waltham 15.

1.660 2.074 1.000 1.708 3.029 1.000 1.567 2.096 4.000 1.445 3.633 2.843 4.311 2.770 4.800 1.200 1.673 1.278 2.476 2.670 4.238 2.309 1.685 1.000 2.667 1.000 1.828 1.831 1.500 3.000

Non-zero slack variables

27.479.495.526:2.5.7. 173.190.357.479.525:3.9. 458: 4.190.335.399.415:5.7.9. 36.120.190.415.529.540:3.9. 461: 127.286.399:2.4.5.8.9. 36.117.190.226.529.540:6.9. 395:4. 36.120.190.226.502.529:2.9. 392.502:6.8. 3.138.190.250:2.3.6. 3.120.138.361.502:3.6. 399.495.502:5.6.7.10. 395:4. 395:4. 282.286.321.502.569:6.8. 27.286.399:5.7.8.9. 190.502.540.550:6.8. 190.226.399.502.540:2.9. 392.502:5.6.8. 36. 55.120.138.149.190.256. 502: 190.540.550:6.8.9. 479: 190.357:3.6.9. 481: 160.190.193.392:3. 399.495.502:6.7. 399:6.9. 395:

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

486 Sandon 487 Foulton 488 Paglesham 489 Tolleshunt Major 490 Tolleshunt Major 491 Bowers Gifford

15. 15. 15. 15. 15. 19.

1.472 1.971 6.286 3.217 1.500 1.000

155

Non-zero slack variables

3.190.226.399:2.6.8. 4. 81.190.357.495:5.10. 181.392: 58. 59.120.190.205.495: 5.6.8. 391:8.10. 491:

156

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

492 Purleigh 493 Lt. Easton 494 Purleigh 495 Stow Maries 496 Colne Engaine 497 Wix 498 Lt. Bromley 499 Lt. Chesterford 500 Sibil Hedingham 501 Sibil Hedingham 502 Pebmarsh 503 Ovington 504 Belchamp Otton 505 Lt. Henny 506 Weston 507 Stansted Hall 508 Goldingham 509 Wakes Colne 510 Moreton 511 Moreton 512 Mount Bures 513 West Bergholt 514 Liston 515 Ardleigh 516 Fordhaam 517 East Thorndon 518 Grays Thurrock 519 Brundon 520 Chigwell

19. 19. 19. 19. 19. 19. 19. 19. 22. 22. 22. 22. 22. 22. 22. 25. 25. 25. 42. 42. 32. 32. 30. 30. 30. 40. 40. 31. 31.

1.024 2.243 1.411 1.000 3.540 2.095 2.082 1.521 1.641 2.000 1.000 1.463 1.868 3.320 3.172 2.717 1.000 3.087 1.395 2.500 1.432 3.140 1.284 1.000 2.168 1.663 1.000 1.700 1.019

306.322.379.380:2.3.8. 88.120.502.540:3.6.8. 59.242.391.495:2.5.8. 495: 190.226.399.502:6.8.9. 36.120.138.173.190.540:3.6. 3.120.190.226.361:2.3.6. 120.138.190.502.529:3.5.6. 4.380.399:1.9. 260.399:5.7.8.9. 502: 4.479.495:2.5.7. 27.282.502:5.6.8. 495.502:5.7.9. 495.502:6.7.9. 30.120.226.540:2.6.7.8.9. 508: 55.117.120.138.190.399.502: 2. 120.190.226.399.540:2.8.9. 495:2.5. 36.55.117.120.138.190.502: 2. 36. 55.120.190.399.415:3.9. 283.357.536:2.9. 515: 120.138.173.190.226.502. 529:3. 3. 47. 59.190:2.3.4.8. 518: 27.117.138.190.479.525.529: 7. 286.415.502:2.5.8.9.

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

521 Chigwell 522 Cheswick Hall 523 Magdalen Laver 524 Upminster 525 Rainham 526 Holland 527 Gt Easton

31. 59. 43. 29. 29. 29. 39.

2.400 1.446 1.325 1.656 1.000 1.000 1.369

Non-zero slack variables

Non-zero slack variables

395:8.9. 286.321.502:2.5.8. 120.190.502.540:5.6.9. 36.120.138.149.190.256.415. 502: 525: 526: 36.117.190.529.540:5.6.9.

APPENDIX 2

Estate

Tenant-in-chief code Efficiency value u Non-zero intensity variables:

528 Margaretting 529 Borley 530 Manningtree 531 Walthamstow 532 Radwinter 533 Layer 534 Pinchpoles 535 Childerditch 536 Bonhunt 537 Wickham Bonhunt 538 Horndon-o-t-Hill 539 Wigborough 540 Lt. Birch 541 Horndon-o-t-Hill 542 Matching 543 Willingale 544 Horstedafort 545 Ilford 546 Elsenham 547 Peldon 548 Shalford 549 Shalford 550 Ashwell Hall 551 Wickford 552 Witham 553 Cricksea 554 Layer 555 Tendring 556 Wickford 557 Listen 558 Liston

39. 36. 36. 53. 48. 23. 23. 23. 23. 49. 34. 34. 34. 37. 37. 35. 35. 51. 52. 46. 46. 45. 45. 20. 20. 20. 20. 20. 27. 27. 27.

1.525 1.000 1.791 1.000 1.161 1.300 2.626 1.352 1.000 1.542 1.800 2.667 1.000 2.220 1.233 3.600 2.051 1.000 2.416 1.000 1.600 1.298 1.000 2.333 2.741 1.267 1.689 1.000 3.604 2.351 1.161

Non-zero slack variables

138.190.449.525:5.7.8. 529: 3.59.160.226:2.6.8.9. 531: 36.120.190.399.415.502.529: 3. 3.120.190.226.361:2.3.6. 190.357.495:6.9. 138.193.569:2.5.8. 536: 36.120.138.190.415.529:5.6. 392:3.6.8. 190:3.6. 540: 81.160.392.536.569:6.9. 120.138.149.415.502.529:5. 392:6. 502:6.8.9. 545: 55.120.149.190.502:2.3.8. 547: 502:8.9. 190.502.540:3.5.6.9. 550: 181.283: 88.502:3.6.9. 193.306:3. 190.392:3.6.8. 555: 395:4. 190.226.495.536:2.9. 392:4.6.

Estate

Tenant-in-chief code

Efficiency value u

Non-zero intensity variables:

Non-zero slack variables

559 East Donyland 560 Tilbury 561 North Fambridge 562 Sutton 563 Felsted

27. 28. 28. 28. 33.

5.143 2.143 1.333 1.519 1.333

392:6.9. 283.392:9.10. 190.250.354:2.3.6.8. 59.160.190.226.502.540:8.9. 40.399:7.9.

157

158

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Estate

Tenant-in-chief code

Efficiency value u

Non-zero intensity variables:

Non-zero slack variables

564 Gt Baddow 33. 2.865 399.502:6.7.9. 565 Theydon 61. 1.442 286.321.502:2.5.8. 566 Heydon 41. 1.251 4.190.357.415.479.525:2.5. 567 Gt Bromley 55. 1.454 117.127.495:2.6.7.8. 568 Belstead Hall 57. 2.125 495.502:6.7.9. 569 South Fambridge 56. 1.000 569: 570 Tolleshunt 50. 2.500 495:6.7. 571 Gestingthorpe 54. 1.211 49.190.226.252.399.540:2.8. 572 Bowers Gifford 38. 2.150 495.569:5.6.7.10. 573 Pitsea 44. 1.000 573: 574 Latchingdon 44. 2.167 190.306:3. 575 Walkfares 60. 2.000 399:6.8.9. 576 Wethersfield 58. 3.333 502:6.8.9. 577 Wheatley 2. 3.000 283:9. Notes: The table lists estates with their identification code, efficiency value (u) assuming CS technology, and non-zero intensity variables (zi), then after the colon non-zero slack variables (si) in the CS efficiency linear programming solution (see Chapter 4 for details). The tenant-in-chief of the estate is indicated by code: 1=Count Eustace. 2=Suen of Essex. 3=Geoffrey de Magna Villa. 4=Robert Greno. 5=Richard son of Count Gilbert. 6=Ranulf Peverel. 7=Ralf Baignard. 8=Eudo dapifer. 9=William de Warene. 10=Ranulf brother of Ilger. 11=Hugh de Montfort. 12=Hamo dapifer. 13=Peter de Valognes. 14=Aubrey de Ver. 15=Robert son of Corbutio. 16=Count Alan. 17=Roger de Ramis. 18=John son of Waleram. 19=Walter the deacon. 20=Moduin. 21=Tithel the Breton. 22=Roger Bigot. 23=Sasselin. 24=Henry de Ferrariis. 25=Robert Malet. 26=Roger de Otburville. 27=Ilbodo. 28=Thierri Pointel. 29=Walter de Doai. 30=Hugh de Gurnai. 31=Ralph de Limsey. 32=Roger de Poitou. 33=Roger ‘God save the ladies’. 34=Hugh de St Quintin. 35=Adam son of Durand. 36=Countess of Aumale. 37=Edmund son of Algot. 38=Grim. 39=Mathew of Mortagne. 40=William Peverel. 41=Robert son of Roscelin. 42=William de Scohies. 43=Ralf de Toesni. 44=Ulveva. 45=Walter the cook. 46=William the deacon. 47=Count of Ou. 48=Frodo brother of the abbot. 49=Gilbert son of Turold. 50=Gonduin. 51=Goscelin the lorimer. 52=John nephew of Waleram. 53=Countess Judith. 54=Otto the Goldsmith. 55=Ralf Pinel. 56=Rainald the crossbowman. 57=Robert son of Gobert. 58=Stanard. 59=Robert de Toesni. 60=Turchil. 61=William son of Constantine. The codes for the slack variables are: 1=demesne ploughteams, 2=peasants’ ploughteams, 3=live-stock, 4=freemen and sokemen, 5=villans, 6=bordars, 7=slaves, 8=woodland, 9=meadow, 10=pasture. TABLE 2 ESSEX LAY ESTATES, 1086: BY CS TECHNOLOGY EFFICIENCY CATEGORY Efficient estates (u=1) 3 4 12 17 20 21 27 30

Shenfield Gravesanda Latton Abberton Ridgewell Claret Smeeton Hall Gt Tey

APPENDIX 2

Efficient estates (u=1) 36 37 40 47 49 55 57 58 59 61 66 67 72 81 88 99 117 120 127 128 138 147 149 150 160 163 173 177 181 190 191 193 202 203 205 226 234 242 250 252

Stanford Rivers Parva Stanford Laver Runwell Boreham Chiche Alresford Frinton Bircho Lawford Elmdon Leebury Shopland Manhall Dunmow Paglesham Bures Lt. Bromley Hempstead Barrow Hall Wickford Gt Wakering Shoebury Canewdon Pudsey Pudsey East Mersea Horkesley Maldon Lawling Steeple Acleta Roding Abess Rettendon Weeley Sandon Notley Northey Woodham Ferrers Marks Tey

159

160

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Efficient estates (u=1) 256 260 268 273 282 283 286 306 321 322 335 354 357 361 379 380 391 392 395 398 399 402 415 446 449 451 458 461 479 481 491 495 502 508 515 518 525 526 529 531

Gt Waltham Broomfield Frinton High Easter Dunmow Easton Roding Purleigh Stapleford Abbots Rainham Shortgrove Hanningfield Michaelstow Henham Hazeleigh Hazeleigh Lawling Down Prested Rettenden Tendring Leigh Beaumont Bapthorne Mountnessing Ardleigh Sturmer Rayne Aveley Leyton Bowers Gifford Stow Maries Pebmarsh Goldingham Ardleigh Grays Thurrock Rainham Holland Borley Walthamstow

APPENDIX 2

Efficient estates (u=1) 536 540 545 547 550 555 569 573

Bonhunt Lt. Birch Ilford Peldon Ashwell Hall Tendring South Fambridge Pitsea

Relatively efficient estates (1
Panfield Warley Franks Lt. Maldon South Ockendon Newenham Chigwell Purleigh Ashen White Roding Kenningtons West Ham Fobbing Bradwell-on-Sea Iltney Latton Tiltey High Roding Boxted Berners Roding Lammarsh Pentlow Leaden Roding Shoebury Arkesden Belstead Hall Rayne Housham Hall Roding Latchingdon Lt. Sampford

1.002 1.007 1.011 1.012 1.013 1.019 1.024 1.029 1.030 1.031 1.038 1.042 1.048 1.048 1.049 1.053 1.068 1.071 1.071 1.072 1.074 1.075 1.077 1.081 1.083 1.083 1.084 1.092 1.093 1.096

161

162

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Relatively efficient estates (1
Ramsey Witham Arkesden Tolleshunt Rodinges Down Lt. Bentley Lindsell Thaxted Pledgon Lt. Wigborough Pudsey Langenhoe Wimbish Gt Oakley Newland Hall Stevington End Listen Radwinter Lt. Canfield Lt. Dunmow Gt Canfield Halesduna Prittlewell Langdon Gt Chishall Maldon Michaelstow Sutton Abberton Barnwalden Ardleigh Bowers Gifford Gestingthorpe Clavering Belchamp Walter Wenden Loughts Theydon Mount Laver Gt Waltham

1.101 1.104 1.104 1.119 1.126 1.129 1.130 1.132 1.132 1.134 1.140 1.143 1.144 1.152 1.153 1.156 1.158 1.161 1.161 1.166 1.167 1.167 1.167 1.169 1.179 1.187 1.188 1.200 1.200 1.200 1.200 1.200 1.208 1.211 1.213 1.222 1.223 1.225 1.228 1.231

APPENDIX 2

Relatively efficient estates (1
Matching Chickney Mountnessing Bigods Ateleia Weneswic South Benfleet Down Hall Bumpstead Heydon Stambn/Toppesfld Willingale Doe Bobbingworth Cricksea

1.233 1.239 1.250 1.250 1.250 1.250 1.250 1.250 1.251 1.251 1.256 1.265 1.265 1.267

Relatively efficient estates (1
Beaumont Shelley Kelvedon Gt Saling Gt Wendon Dovercourt Helion Bumpstead Liston Layer Shalford Shellow Bowells Mundon Layer Frating Tollesbury Hockley Stebbing Magdalen Laver Ashdon Stow Maries North Fambridge Steeple Patching Hl Picot Wallbury

1.271 1.271 1.273 1.278 1.281 1.281 1.282 1.284 1.286 1.298 1.299 1.300 1.300 1.305 1.306 1.313 1.322 1.325 1.326 1.331 1.333 1.333 1.333 1.333

163

164

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Relatively efficient estates (1
Felsted Wheatley Arkesden Lt. Wakering Layer Boxted Childerditch Cold Norton Rayleigh Gt Easton Bollington Bendish Hall Prested Moreton Purleigh Stebbing Roding Morell Purleigh Gt Braxted Polhey Birdbrook Quick Bury Hawkwell Roding Marci Sutton Rise-Marses Mount Bures Newton Hall Notley Theydon Estoleia Dedham Cheswick Hall Lammarsh Bineslea Saffron Walden Chishall Debden Gt Bromley East Whettenham

1.333 1.338 1.347 1.348 1.349 1.350 1.352 1.359 1.368 1.369 1.371 1.373 1.391 1.395 1.400 1.402 1.403 1.411 1.418 1.419 1.422 1.423 1.425 1.425 1.427 1.429 1.432 1.438 1.441 1.442 1.444 1.445 1.446 1.446 1.449 1.449 1.451 1.454 1.454 1.455

APPENDIX 2

Relatively efficient estates (1
Chreshall Lt. Canfield Ovington Culvert Wickford Sandon Lt. Wenden Frierning Quendon Tendring Black Notley

1.456 1.456 1.463 1.468 1.469 1.472 1.473 1.476 1.477 1.481 1.483

Less efficient estates (1.5 ≤u<2) 490 230 272 484 104 56 214 562 60 499 528 118 433 6 129 537 71 412 393 254 428 219 116 326 462 165 164

Tolleshunt Major Goldhanger Lt. Hallingbury Waltham Gestingthorpe Tendring Downham Sutton Lt. Holland Lt. Chesterford Margaretting Roding Morell N.Weald Basset Coggeshall West Thorndon Wickham Bonhunt Lt. Bardfield Earls Colne Stangate Abbess Roding Balingdon Purleigh Boyton Hall Chicknal Zoyn Sibil Hedingham Hawkswell Ashingdon

1.500 1.500 1.500 1.500 1.510 1.510 1.510 1.519 1.519 1.521 1.525 1.529 1.531 1.535 1.537 1.542 1.548 1.548 1.549 1.549 1.552 1.554 1.557 1.559 1.567 1.571 1.571

165

166

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Less efficient estates (1.5 ≤u<2) 98 132 385 294 102 25 162 198 350 548 136 113 5 500 444 197 524 456 517 238 447 344 472 251 478 48 45 409 554 309 207 355 519 459 275 236 176 370 103 262

Eynsworth Childerditch Amberden West Thurrock Thaxted Finchingfield Pudsey Takeley Burnham Shalford Basildon Finchingfield White Notley Sibil Hedingham Thorp Dunmow Upminster Steeple Bumpstead East Thorndon Dunmow Newland Purleigh Black Notley Butsbury High Ongar Lt. Waltham Lt. Baddow Castle Hedingham Layer Salcot Verley Radwinter Lt. Oakley Brundon Tilbury by Clare Barnston Gt Braxted Asheldham Hatfield Peverel Gt Dunmow Chignal

1.577 1.580 1.585 1.593 1.595 1.596 1.598 1.600 1.600 1.600 1.632 1.635 1.639 1.641 1.645 1.652 1.656 1.660 1.663 1.667 1.667 1.671 1.673 1.683 1.685 1.686 1.687 1.689 1.689 1.689 1.697 1.699 1.700 1.708 1.712 1.713 1.714 1.719 1.723 1.725

APPENDIX 2

Less efficient estates (1.5 ≤u<2) 7 124 186 152 407 364 51 111 419 530 442 180 291 323 184 538 365

Rivenhall Langham Harlow Rochford Thunderley Langford Goldhanger Alderford Stevington End Manningtree Nazing Kenningtons Manhall South Weald Lt. Totham Horndon-o-t-Hill Langford

1.726 1.737 1.759 1.760 1.764 1.768 1.778 1.783 1.789 1.791 1.800 1.800 1.800 1.800 1.800 1.800 1.800

Less efficient estates (1.5 ≤u<2) 363 166 78 413 133 271 482 483 352 261 146 11 504 134 107 168 264 64 345 300 303

Paglesham Eastwood Beauchamp Roding Gt Bentley Horndon-o-t-Hill Ridley Hall Lawling Hanningfield Lt. Baddow Chignal Eastwood Gt Parndon Belchamp Otton Hassingbroke Gt Yeldham Asheldham Danbury Lt. Chishall Lt. Dunmow Matching East Ham

1.800 1.800 1.800 1.801 1.819 1.820 1.828 1.831 1.833 1.852 1.855 1.856 1.868 1.868 1.870 1.896 1.900 1.913 1.915 1.918 1.918

167

168

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Less efficient estates (1.5 ≤u<2) 373 408 297 377 487 32 142 91 423 19 455

Terling Ugley Powers Hall Witham Woodham Mortimer Foulton East Donyland Thundersley Steeple Bumpstead Lt. Parndon Shortgrove Helion Bumpstead

1.933 1.940 1.942 1.962 1.971 1.978 1.984 1.994 1.996 1.998 1.998

Inefficient estates (2≤u<3) 157 153 233 296 396 435 575 501 42 80 39 338 343 372 13 43 544 437 340 245 457 144 498 359 497 463 74

Plumberow Gt Stambridge Faulkbourne Ramsden Plumtuna Inga Walkfares Sibil Hedingham Fyfield Lt. Bentley Chipping Ongar Tolleshunt Darcy Woodham Walter Blunts Hall Dunmow Fyfield Horstedafort Roydon Langford Norton Mandeville Sturmer Rayleigh Lt. Bromley Witlebroc Wix Messing Willingale Spain

2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.024 2.025 2.036 2.044 2.049 2.050 2.051 2.052 2.063 2.073 2.074 2.080 2.082 2.083 2.095 2.096 2.100

APPENDIX 2

Inefficient estates (2≤u<3) 201 223 568 171 560 572 73 366 318 131 574 516 209 22 311 34 541 418 24 84 266 267 76 493 425 426 125 334 405 397 243 443 258 308 477 327 551 94 175 195

Theydon Gernon Rayne Hall Belstead Hall Lt. Hallingbury Tilbury Bowers Gifford Epping Tolleshunt Wormingford West Tilbury Latchingdon Fordhaam Gt Hallingbury Belchamp Takeley East Thorpe Horndon-o-t-Hill Radwinter Belchamp Gt Easton Kewton Hall Moze Gerham Lt. Easton Leyton Higham Bensted Gt Bardfield Widington Gt Canfield Springfield Greensted Nazing & Epping Chatham Lega Fyfield Springfield Wickford West Hanningfield Berden Broxted

2.104 2.116 2.125 2.133 2.143 2.150 2.158 2.159 2.162 2.165 2.167 2.168 2.176 2.184 2.199 2.208 2.220 2.222 2.222 2.228 2.231 2.234 2.238 2.243 2.248 2.249 2.249 2.250 2.253 2.255 2.261 2.267 2.279 2.284 2.309 2.325 2.333 2.333 2.346 2.349

169

170

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Inefficient estates (2≤u<3) 557 151 216 229 351 227 387 342 346 521 400 546 440 310 374 114 454

Listen Northorp Leyton Lt. Totham Burnham Sandon Gt Henny Cold Norton Lt. Dunmow Chigwell St Osyth Elsenham Gt Parndon Stanstd Mtfichet Fairsted Bulmer Radwinter

2.351 2.351 2.359 2.372 2.384 2.394 2.395 2.400 2.400 2.400 2.413 2.416 2.424 2.444 2.450 2.465 2.467

Inefficient estates (2≤u<3) 474 439 438 313 511 570 9 105 139 89 90 325 46 305 167 441 279 534 404 430 196

Lt. Maplestead Gt Parndon Harlow Benfieldbury Moreton Tolleshunt Blunts Hall Finchingfield Wickford Payton Hall Halstead Frierning Runwell Loughton Iltney Walda Shellow Bowells Pinchpoles Goldhanger Loughton Shellow

2.476 2.485 2.490 2.498 2.500 2.500 2.500 2.500 2.500 2.527 2.531 2.543 2.543 2.543 2.558 2.606 2.609 2.626 2.645 2.667 2.667

APPENDIX 2

Inefficient estates (2≤u<3) 539 108 95 231 480 287 432 122 427 121 265 475 225 436 332 406 28 299 507 246 434 50 552 469 183 115 135 204 339 320 467 41 564 429 35 33 244 452 367 337

Wigborough Wickham St. Paul’s Boreham Tolleshunt Darcy Smalland Dunmow Theydon Bois Fordham Loughton Colne Legra Henny Markshall Ramsden Tendring Udecheshale Toppesfield Rivenhall Stansted Hall Gt Totham N.Weald Basset Tolleshunt Guines Witham Bradfield Manston Foulton How Hall Basildon Lees Ulting Lt. Birch Bradfield Lambourne Gt Baddow Bineslea Colne Engaine Gt Birch Kelvedon Hatch Yardley Tolleshunt Elsenham

2.667 2.667 2.667 2.667 2.667 2.667 2.667 2.667 2.667 2.667 2.668 2.670 2.670 2.671 2.684 2.690 2.700 2.704 2.717 2.725 2.732 2.738 2.741 2.770 2.782 2.795 2.800 2.805 2.814 2.833 2.843 2.848 2.865 2.865 2.865 2.868 2.872 2.881 2.900 2.925

171

172

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Inefficient estates (2≤u<3) 182 353 316 301

Elmstead Lt. Baddow Manuden Chingford

2.930 2.946 2.960 2.979

Very inefficient estates (u≥3) 485 123 424 15 259 577 460 381 509 2 169 513 383 420 506 8 489 421 172 295 26 68 65 505 336 315 79 576 317 371 269 298 496 263

Waltham West Bergholt Walda Plesinchchou Patching Wheatley Rayne Layer Wakes Colne Horndon Rivenhall West Bergholt Wigborough Stevington End Weston Rivenhall Tolleshunt Major Sheering Dunmow Ramsden Finchingfield Crawleybury Lt. Chishall Lt. Henny Arkesden Farnham Lt. Bentley Wethersfield Gt Maplestead Hatfield Peverel Ardleigh Hubbridge Hall Colne Engaine Chignal

3.000 3.000 3.000 3.000 3.000 3.000 3.029 3.071 3.087 3.104 3.116 3.140 3.143 3.143 3.172 3.175 3.217 3.219 3.243 3.244 3.266 3.310 3.310 3.320 3.329 3.331 3.333 3.333 3.479 3.500 3.506 3.530 3.540 3.600

APPENDIX 2

Very inefficient estates (u≥3) 77 Finchingfield 304 Leyton 369 Inga 292 Birchanger 543 Willingale 556 Wickford 333 Dikeley 466 Bures 403 Tolleshunt Darcy 145 Hockley 464 Messing 411 Hersham Hall 476 Bures St Mary 468 Ardleigh 431 Theydon Bois 324 Frierning 470 Cliva 109 Finchingfield 559 East Donyland 52 Tolleshunt 228 Wix 319 Wivenhoe 488 Paglesham Notes: Entries consist of estate identification code, estate name and u value.

3.600 3.600 3.600 3.600 3.600 3.604 3.606 3.633 3.715 3.871 4.000 4.000 4.238 4.311 4.348 4.527 4.800 5.000 5.143 5.167 5.366 6.198 6.286

173

APPENDIX 3 Efficiency measures (u) of estates assuming CS, VS, CW and VW technologies: Essex lay estates, 1086

Id code

CS

VS

CW

VW

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

1.042 3.104 1.000 1.000 1.639 1.535 1.726 3.175 2.500 1.104 1.856 1.000 2.049 1.048 3.000 1.144 1.000 1.349 1.998 1.000 1.000 2.184 1.251 2.222 1.596 3.266 1.000 2.700

1.000 2.125 1.000 1.000 1.361 1.000 1.484 3.172 2.500 1.104 1.657 1.000 1.669 1.000 1.000 1.000 1.000 1.289 1.998 1.000 1.000 2.115 1.047 2.181 1.595 2.830 1.000 2.500

1.000 2.677 1.000 1.000 1.607 1.000 1.546 1.000 2.500 1.104 1.700 1.000 1.955 1.000 1.000 1.000 1.000 1.222 1.705 1.000 1.000 1.933 1.000 1.517 1.278 3.040 1.000 2.293

1.000 1.000 1.000 1.000 1.123 1.000 1.036 1.000 2.500 1.104 1.249 1.000 1.155 1.000 1.000 1.000 1.000 1.000 1.063 1.000 1.000 1.877 1.000 1.420 1.130 2.820 1.000 2.203

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58.

1.188 1.000 1.071 1.978 2.868 2.208 2.865 1.000 1.000 1.228 2.024 1.000 2.848 2.000 2.050 1.156 1.687 2.543 1.000 1.686 1.000 2.738 1.778 5.167 1.119 1.306 1.000 1.510 1.000 1.000

1.000 1.000 1.000 1.490 2.825 2.208 2.459 1.000 1.000 1.000 1.535 1.000 2.224 2.000 1.938 1.077 1.202 2.295 1.000 1.518 1.000 1.679 1.587 4.755 1.000 1.000 1.000 1.510 1.000 1.000

1.176 1.000 1.000 1.475 2.786 1.000 1.000 1.000 1.000 1.204 1.000 1.000 2.730 1.000 1.941 1.000 1.632 1.000 1.000 1.565 1.000 2.360 1.000 1.000 1.000 1.000 1.000 1.096 1.000 1.000

1.000 Id code CS VS CW VW 1.000 1.000 1.000 2.677 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.067 1.000 1.867 1.000 1.000 1.000 1.000 1.346 1.000 1.041 1.000 1.000 1.000 1.000 1.000 1.068 1.000 1.000

Id code

CS

VS

CW

VW

59. 60. 61. 62. 63. 64. 65. 66.

1.000 1.519 1.000 1.481 1.456 1.913 3.310 1.000

1.000 1.447 1.000 1.473 1.288 1.273 2.967 1.000

1.000 1.000 1.000 1.000 1.000 1.000 3.310 1.000

1.000 1.000 1.000 1.000 1.000 1.000 2.967 1.000

175

176

APPENDIX 3

Id code

CS

VS

CW

VW

67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106.

1.000 3.310 1.373 1.013 1.548 1.000 2.158 2.100 1.167 2.238 3.600 1.800 3.333 2.000 1.000 1.084 1.423 2.228 1.456 1.068 1.075 1.000 2.527 2.531 1.994 1.419 1.031 2.333 2.667 1.083 1.473 1.577 1.000 1.333 1.132 1.595 1.723 1.510 2.500 1.002

1.000 2.967 1.000 1.000 1.316 1.000 2.025 1.506 1.167 2.200 2.000 1.000 1.000 2.000 1.000 1.080 1.340 1.979 1.400 1.000 1.018 1.000 2.456 1.239 1.000 1.000 1.000 1.270 1.067 1.083 1.469 1.542 1.000 1.200 1.000 1.000 1.599 1.200 2.479 1.000

1.000 3.310 1.270 1.000 1.507 1.000 1.559 1.769 1.000 2.067 3.556 1.709 1.000 1.000 1.000 1.000 1.223 1.765 1.155 1.051 1.033 1.000 1.000 2.528 1.956 1.256 1.000 2.286 1.415 1.000 1.255 1.000 1.000 1.000 1.064 1.312 1.363 1.328 1.000 1.000

1.000 2.967 1.000 1.000 1.074 1.000 1.540 1.000 1.000 2.002 1.000 1.000 1.000 1.000 1.000 1.000 1.081 1.384 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Id code CS VS CW VW 1.000 1.000 1.000 1.096 1.000 1.000 1.000

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140.

1.870 2.667 5.000 1.449 1.783 1.029 1.635 2.465 2.795 1.557 1.000 1.529 1.130 1.000 2.667 2.667 3.000 1.737 2.249 1.096 1.000 1.000 1.537 1.179 2.165 1.580 1.819 1.868 2.800 1.632 1.469 1.000 2.500 1.250

1.000 2.125 5.000 1.316 1.610 1.000 1.339 2.465 2.242 1.364 1.000 1.242 1.008 1.000 2.388 1.342 1.339 1.000 1.609 1.000 1.000 1.000 1.507 1.000 1.557 1.544 1.819 1.685 2.800 1.302 1.429 1.000 2.500 1.250

1.444 2.003 4.103 1.000 1.606 1.000 1.560 1.000 2.730 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.167 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.806 1.962 1.000 1.175 1.000 1.000 1.000

1.000 1.000 3.952 1.000 1.406 1.000 1.101 1.000 2.070 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.223 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.677 1.931 1.000 1.173 1.000 1.000 1.000

Id code

CS

VS

CW

VW

141. 142. 143. 144.

1.338 1.984 1.368 2.080

1.000 1.540 1.172 2.050

1.000 1.564 1.000 1.776

1.000 1.254 1.000 1.379

177

178

APPENDIX 3

Id code

CS

VS

CW

VW

145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184.

3.871 1.855 1.000 1.169 1.000 1.000 2.351 1.760 2.000 1.077 1.348 1.427 2.000 1.143 1.313 1.000 1.200 1.598 1.000 1.571 1.571 1.800 2.558 1.896 3.116 1.441 2.133 3.243 1.000 1.213 2.346 1.714 1.000 1.225 1.007 1.800 1.000 2.930 2.782 1.800

2.389 1.014 1.000 1.000 1.000 1.000 1.978 1.255 2.000 1.000 1.000 1.000 1.641 1.000 1.000 1.000 1.000 1.591 1.000 1.000 1.000 1.500 2.533 1.670 2.667 1.400 2.117 3.237 1.000 1.000 2.107 1.514 1.000 1.000 1.000 1.500 1.000 2.275 2.733 1.000

3.863 1.741 1.000 1.000 1.000 1.000 2.125 1.684 1.067 1.070 1.000 1.000 1.637 1.000 1.000 1.000 1.000 1.526 1.000 1.000 1.571 1.000 1.000 1.832 1.000 1.350 2.071 3.227 1.000 1.000 1.000 1.682 1.000 1.000 1.000 1.224 1.000 1.000 1.941 1.000

1.899 1.000 1.000 1.000 1.000 1.000 1.567 1.000 1.000 1.000 1.000 1.000 1.402 1.000 1.000 1.000 1.000 1.498 1.000 1.000 1.000 1.000 1.000 1.654 1.000 1.339 1.962 3.212 1.000 1.000 1.000 1.514 1.000 1.000 1.000 1.224 1.000 Id code CS VS CW VW 1.000 1.941 1.000

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219. 220. 221. 222.

1.418 1.759 1.403 1.132 1.300 1.000 1.000 1.250 1.000 1.425 2.349 2.667 1.652 1.600 1.134 1.350 2.104 1.000 1.000 2.805 1.000 1.477 1.697 1.347 2.176 1.126 1.104 1.081 1.451 1.510 1.273 2.359 1.400 1.093 1.554 1.167 1.444 1.286

1.168 1.629 1.214 1.108 1.000 1.000 1.000 1.194 1.000 1.269 1.835 1.262 1.574 1.000 1.109 1.333 1.918 1.000 1.000 1.219 1.000 1.379 1.696 1.232 1.704 1.071 1.058 1.026 1.450 1.500 1.150 2.020 1.093 1.007 1.000 1.167 1.444 1.250

1.064 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.320 1.791 1.277 1.261 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.249 1.680 1.000 1.000 1.043 1.000 1.000 1.000 1.000 1.026 1.000 1.000 1.000 1.525 1.000 1.190 1.000

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.826 1.221 1.277 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.588 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

179

180

APPENDIX 3

Id code

CS

VS

CW

VW

223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 244. 245. 246. 247. 248. 249. 250. 251. 252. 253. 254. 255. 256. 257. 258. 259. 260. 261. 262.

2.116 1.048 2.667 1.000 2.394 5.366 2.372 1.500 2.667 1.250 2.000 1.000 1.083 1.713 1.429 1.667 1.425 1.140 1.256 1.000 2.261 2.872 2.073 2.725 1.053 1.322 1.333 1.000 1.683 1.000 1.271 1.549 1.012 1.000 1.231 2.279 3.000 1.000 1.852 1.725

1.768 1.000 2.233 1.000 1.760 4.683 2.000 1.000 2.306 1.000 1.533 1.000 1.083 1.304 1.000 1.000 1.297 1.000 1.199 1.000 1.558 2.857 1.826 2.294 1.000 1.297 1.333 1.000 1.401 1.000 1.225 1.428 1.000 1.000 1.160 2.035 3.000 1.000 1.773 1.683

2.113 1.000 2.341 1.000 1.892 1.000 1.000 1.000 1.735 1.000 1.443 1.000 1.083 1.448 1.000 1.000 1.259 1.000 1.120 1.000 2.226 2.693 1.872 2.713 1.000 1.000 1.000 1.000 1.000 1.000 1.168 1.033 1.000 1.000 1.000 1.950 1.000 1.000 1.000 1.496

1.755 1.000 1.564 1.000 1.337 1.000 1.000 1.000 1.710 1.000 1.000 1.000 1.083 1.000 1.000 1.000 1.148 1.000 1.000 1.000 1.000 2.689 1.281 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.122 1.032 1.000 1.000 1.000 1.045 1.000 1.000 1.000 1.487

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

263. 264. 265. 266. 267. 268. 269. 270. 271. 272. 273. 274. 275. 276. 277. 278. 279. 280. 281. 282. 283. 284. 285. 286. 287. 288. 289. 290. 291. 292. 293. 294. 295. 296. 297. 298. 299. 300. 301. 302.

3.600 1.900 2.668 2.231 2.234 1.000 3.506 1.483 1.820 1.500 1.000 1.438 1.712 1.071 1.250 1.167 2.609 1.299 1.030 1.000 1.000 1.166 1.092 1.000 2.667 1.331 1.449 1.187 1.800 3.600 1.250 1.593 3.244 2.000 1.942 3.530 2.704 1.918 2.979 1.038

3.113 1.889 1.922 1.951 1.888 1.000 3.125 1.315 1.778 1.500 1.000 1.398 1.639 1.000 1.000 1.085 1.734 1.050 1.000 1.000 1.000 1.124 1.000 1.000 1.213 1.308 1.000 1.022 1.000 3.000 1.000 1.000 2.504 2.000 1.703 3.188 2.382 1.865 2.246 1.000

3.522 1.682 2.657 2.193 2.233 1.000 1.000 1.000 1.000 1.000 1.000 1.169 1.557 1.000 1.000 1.119 2.457 1.099 1.000 1.000 1.000 1.000 1.000 1.000 1.689 1.000 1.443 1.000 1.000 1.000 1.000 1.554 2.030 1.000 1.715 3.342 1.000 1.796 1.309 1.000

3.113 Id code CS VS CW VW 1.679 1.585 1.875 1.774 1.000 1.000 1.000 1.000 1.000 1.000 1.138 1.522 1.000 1.000 1.000 1.392 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.188 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.069 1.000 1.307 2.914 1.000 1.792 1.000 1.000

181

182

APPENDIX 3

Id code

CS

VS

CW

VW

303. 304.

1.918 3.600

1.474 2.000

1.890 3.308

1.000 1.000

Id code

CS

VS

CW

VW

305. 306. 307. 308. 309. 310. 311. 312. 313. 314. 315. 316. 317. 318. 319. 320. 321. 322. 323. 324. 325. 326. 327. 328. 329. 330. 331. 332. 333. 334. 335. 336. 337. 338. 339. 340.

2.543 1.000 1.455 2.284 1.689 2.444 2.199 1.281 2.498 1.371 3.331 2.960 3.479 2.162 6.198 2.833 1.000 1.000 1.800 4.527 2.543 1.559 2.325 1.476 1.333 1.468 1.153 2.684 3.606 2.250 1.000 3.329 2.925 2.025 2.814 2.063

1.150 1.000 1.292 2.134 1.667 1.753 1.844 1.000 2.107 1.200 2.703 2.321 3.369 1.781 5.572 1.950 1.000 1.000 1.500 4.404 2.252 1.399 2.114 1.353 1.200 1.400 1.016 2.469 3.561 1.875 1.000 3.250 2.685 1.724 2.102 1.896

1.000 1.000 1.000 2.161 1.000 1.000 1.854 1.000 2.498 1.000 2.766 2.850 3.408 2.123 6.132 2.460 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.468 1.000 1.000 1.000 2.119 1.000 1.000 2.117 1.340 2.677 1.770

1.000 1.000 1.000 1.648 1.000 1.000 1.714 1.000 2.089 1.000 2.620 2.208 3.136 1.151 4.493 1.064 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.142 1.000 1.000 1.000 1.440 1.000 1.000 2.008 1.000 1.612 1.584

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

341. 342. 343. 344. 345. 346. 347. 348. 349. 350. 351. 352. 353. 354. 355. 356. 357. 358. 359. 360. 361. 362. 363. 364. 365. 366. 367. 368. 369. 370. 371. 372. 373. 374. 375. 376. 377. 378. 379. 380.

1.359 2.400 2.036 1.671 1.915 2.400 1.152 1.200 1.074 1.600 2.384 1.833 2.946 1.000 1.699 1.101 1.000 1.200 2.083 1.223 1.000 1.326 1.800 1.768 1.800 2.159 2.900 1.208 3.600 1.719 3.500 2.044 1.933 2.450 1.239 1.265 1.962 1.011 1.000 1.000

1.136 1.333 1.408 1.281 1.856 2.356 1.000 1.000 1.000 1.100 1.000 1.000 2.933 1.000 1.016 1.000 1.000 1.200 2.083 1.109 1.000 1.197 1.500 1.424 1.641 2.156 2.678 1.208 3.000 1.192 1.125 1.889 1.573 2.266 1.000 1.000 1.486 1.002 1.000 1.000

1.024 2.400 1.578 1.571 1.879 1.000 1.000 1.000 1.000 1.000 1.602 1.000 2.481 1.000 1.000 1.000 1.000 1.000 2.083 1.000 1.000 1.000 1.000 1.469 1.552 1.000 2.388 1.000 1.000 1.630 3.214 1.729 1.824 2.198 1.098 1.200 1.895 1.011 1.000 1.000

1.000 1.000 1.000 1.000 1.000 Id code CS VS CW VW 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.162 1.000 1.000 1.000 1.000 1.000 2.083 1.000 1.000 1.000 1.000 1.000 1.536 1.000 1.690 1.000 1.000 1.000 1.000 1.513 1.430 1.966 1.000 1.000 1.359 1.000 1.000 1.000

183

184

APPENDIX 3

Id code

CS

VS

CW

VW

381. 382. 383. 384. 385. 386.

3.071 1.200 3.143 1.454 1.585 1.402

3.060 1.200 2.800 1.059 1.498 1.000

2.611 1.000 3.143 1.386 1.445 1.290

2.605 1.000 2.800 1.000 1.139 1.000

Id code

CS

VS

CW

VW

387. 388. 389. 390. 391. 392. 393. 394. 395. 396. 397. 398. 399. 400. 401. 402. 403. 404. 405. 406. 407. 408. 409. 410. 411. 412. 413. 414. 415. 416. 417. 418.

2.395 1.446 1.072 1.129 1.000 1.000 1.549 1.391 1.000 2.000 2.255 1.000 1.000 2.413 1.305 1.000 3.715 2.645 2.253 2.690 1.764 1.940 1.689 1.222 4.000 1.548 1.801 1.281 1.000 1.271 1.282 2.222

2.305 1.317 1.014 1.000 1.000 1.000 1.153 1.208 1.000 1.000 1.680 1.000 1.000 1.795 1.261 1.000 2.594 2.253 2.088 2.454 1.434 1.724 1.497 1.104 4.000 1.000 1.432 1.000 1.000 1.164 1.000 1.980

2.234 1.342 1.000 1.038 1.000 1.000 1.000 1.000 1.000 1.655 2.240 1.000 1.000 1.000 1.000 1.000 3.512 2.116 2.229 2.355 1.543 1.933 1.674 1.000 2.534 1.000 1.727 1.000 1.000 1.000 1.189 2.179

1.489 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.340 1.000 1.000 1.000 1.000 1.000 2.102 1.112 1.763 1.906 1.000 1.721 1.000 1.000 1.142 1.000 1.394 1.000 1.000 1.000 1.000 1.835

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

419. 420. 421. 422. 423. 424. 425. 426. 427. 428. 429. 430. 431. 432. 433. 434. 435. 436. 437. 438. 439. 440. 441. 442. 443. 444. 445. 446. 447. 448. 449. 450. 451. 452. 453. 454. 455. 456. 457. 458.

1.789 3.143 3.219 1.049 1.996 3.000 2.248 2.249 2.667 1.552 2.865 2.667 4.348 2.667 1.531 2.732 2.000 2.671 2.052 2.491 2.485 2.424 2.606 1.800 2.267 1.645 1.422 1.000 1.667 1.265 1.000 1.250 1.000 2.881 1.158 2.467 1.998 1.660 2.074 1.000

1.561 2.800 2.204 1.027 1.638 3.000 2.241 1.945 2.400 1.150 2.833 2.400 1.739 2.400 1.331 2.483 2.000 2.145 1.588 1.000 2.138 1.000 2.606 1.500 1.888 1.243 1.241 1.000 1.667 1.214 1.000 1.250 1.000 2.844 1.000 2.150 1.156 1.256 1.917 1.000

1.000 3.143 3.101 1.000 1.000 1.000 1.000 2.160 1.000 1.000 1.000 2.228 1.000 1.000 1.000 1.000 1.000 1.000 1.789 2.227 1.000 1.000 1.000 1.000 1.000 1.300 1.421 1.000 1.000 1.000 1.000 1.000 1.000 2.154 1.082 2.259 1.968 1.461 1.735 1.000

1.000 2.800 1.247 1.000 1.000 1.000 1.000 1.767 1.000 Id code CS VS CW VW 1.000 1.000 2.227 1.000 1.000 1.000 1.000 1.000 1.000 1.097 1.000 1.000 1.000 1.000 1.000 1.000 1.059 1.238 1.000 1.000 1.000 1.000 1.000 1.000 1.688 1.000 1.653 1.000 1.000 1.724 1.000

185

186

APPENDIX 3

Id code

CS

VS

CW

VW

459. 460. 461. 462. 463. 464. 465. 466. 467. 468.

1.708 3.029 1.000 1.567 2.096 4.000 1.445 3.633 2.843 4.311

1.147 2.802 1.000 1.395 1.783 4.000 1.172 1.643 2.493 4.072

1.450 1.000 1.000 1.000 2.066 2.083 1.330 1.000 2.784 3.766

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.036 3.410

Id code

CS

VS

CW

VW

469. 470. 471. 472. 473. 474. 475. 476. 477. 478. 479. 480. 481. 482. 483. 484. 485. 486. 487. 488. 489. 490. 491. 492. 493. 494. 495. 496.

2.770 4.800 1.200 1.673 1.278 2.476 2.670 4.238 2.309 1.685 1.000 2.667 1.000 1.828 1.831 1.500 3.000 1.472 1.971 6.286 3.217 1.500 1.000 1.024 2.243 1.411 1.000 3.540

2.750 4.267 1.000 1.026 1.240 2.435 2.186 1.910 1.570 1.667 1.000 2.444 1.000 1.111 1.742 1.500 3.000 1.472 1.679 5.600 2.982 1.500 1.000 1.000 1.099 1.224 1.000 2.769

2.043 1.000 1.100 1.466 1.000 1.845 1.000 1.000 2.309 1.000 1.000 1.000 1.000 1.816 1.775 1.000 3.000 1.000 1.144 6.286 2.428 1.000 1.000 1.000 1.958 1.000 1.000 3.297

1.981 1.000 1.000 1.000 1.000 1.456 1.000 1.000 1.411 1.000 1.000 1.000 1.000 1.000 1.698 1.000 3.000 1.000 1.000 5.600 2.052 1.000 1.000 1.000 1.000 1.000 1.000 2.186

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

497. 498. 499. 500. 501. 502. 503. 504. 505. 506. 507. 508. 509. 510. 511. 512. 513. 514. 515. 516. 517. 518. 519. 520. 521. 522. 523. 524. 525. 526. 527. 528. 529. 530. 531. 532. 533. 534. 535. 536.

2.095 2.082 1.521 1.641 2.000 1.000 1.462 1.868 3.320 3.172 2.717 1.000 3.087 1.395 2.500 1.432 3.140 1.284 1.000 2.168 1.663 1.000 1.700 1.019 2.400 1.446 1.325 1.656 1.000 1.000 1.369 1.525 1.000 1.791 1.000 1.161 1.301 2.626 1.352 1.000

1.585 1.750 1.497 1.000 1.537 1.000 1.100 1.282 1.358 1.163 1.937 1.000 2.241 1.000 2.500 1.353 2.574 1.160 1.000 1.849 1.167 1.000 1.624 1.000 2.400 1.298 1.143 1.490 1.000 1.000 1.314 1.418 1.000 1.597 1.000 1.067 1.024 2.500 1.329 1.000

2.036 1.000 1.274 1.000 1.000 1.000 1.000 1.693 2.795 2.814 1.998 1.000 3.035 1.291 1.000 1.410 3.059 1.000 1.000 2.168 1.000 1.000 1.690 1.000 1.000 1.000 1.000 1.656 1.000 1.000 1.352 1.179 1.000 1.000 1.000 1.136 1.240 2.482 1.000 1.000

1.274 1.000 1.274 1.000 1.000 1.000 1.000 1.124 1.000 1.000 1.000 1.000 1.871 Id code CS VS CW VW 1.000 1.000 1.344 2.462 1.000 1.000 1.797 1.000 1.000 1.403 1.000 1.000 1.000 1.000 1.436 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.449 1.000 1.000

187

188

APPENDIX 3

Id code

CS

VS

CW

VW

537. 538. 539. 540. 541. 542. 543. 544. 545. 546. 547. 548. 549. 550.

1.542 1.800 2.667 1.000 2.220 1.233 3.600 2.051 1.000 2.416 1.000 1.600 1.298 1.000

1.469 1.500 2.667 1.000 2.161 1.231 3.000 1.000 1.000 1.874 1.000 1.600 1.291 1.000

1.524 1.402 1.741 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.142 1.000

1.384 1.343 1.649 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.127 1.000

Id code

CS

VS

CW

VW

551. 552. 553. 554. 555. 556. 557. 558. 559. 560. 561. 562. 563. 564. 565. 566. 567. 568. 569. 570. 571. 572. 573. 574.

2.333 2.741 1.267 1.689 1.000 3.604 2.351 1.161 5.143 2.143 1.333 1.519 1.333 2.865 1.442 1.251 1.454 2.125 1.000 2.500 1.211 2.150 1.000 2.167

2.333 2.500 1.267 1.433 1.000 3.604 1.777 1.000 4.432 1.250 1.016 1.000 1.083 2.126 1.025 1.000 1.244 1.707 1.000 1.000 1.000 1.800 1.000 1.050

2.333 2.221 1.000 1.510 1.000 3.003 1.000 1.000 5.090 1.000 1.189 1.515 1.000 2.624 1.000 1.000 1.000 1.834 1.000 1.000 1.181 1.000 1.000 1.000

2.333 2.079 1.000 1.000 1.000 3.003 1.000 1.000 4.432 1.000 1.000 1.000 1.000 1.738 Id code CS VS CW VW 1.000 1.000 1.000 1.258 1.000 1.000 1.000 1.000 1.000 1.000

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

CS

VS

CW

VW

575. 576. 577.

2.000 3.333 3.000

2.000 1.482 3.000

1.712 1.000 1.000

1.704 1.000 1.000

189

APPENDIX 4 Beneficial hidation indexes (BHI) for Essex lay estates, 1086

Id code

BHI

Tax assessment

Frontier assessment

Annual value

1. 2. 3. 4. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

1.00 2.05 2.60 4.50 3.42 3.81 4.00 3.13 10.59 1.52 2.31 4.22 2.25 3.13 1.47 2.98 1.89 3.60 4.23 3.21 3.20 13.23 6.00 7.71 5.08 3.17 36.00 4.00

2,445.50 305.00 240.00 120.00 491.00 315.00 135.00 60.00 51.00 420.00 270.00 270.00 240.00 60.00 1,140.00 210.00 330.00 150.00 397.50 523.00 200.00 63.50 90.00 70.00 37.00 360.00 15.00 270.00

2,445.50 625.00 625.00 540.00 1,680.00 1,200.00 540.00 188.00 540.00 640.00 625.00 1,140.00 540.00 188.00 1,680.00 625.00 625.00 540.00 1,680.00 1,680.00 640.00 840.00 540.00 540.00 188.00 1,140.00 540.00 1,081.00

720.00 50.00 60.00 20.00 290.00 240.00 30.00 10.00 20.00 80.00 60.00 160.00 30.00 10.00 345.00 60.00 60.00 40.00 480.00 450.00 80.00 100.00 30.00 40.00 16.00 160.00 20.00 120.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

30.

1.82

923.00

1,680.00

440.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67.

2.00 2.65 2.25 3.72 13.50 2.15 2.70 4.67 9.50 4.70 1.95 10.80 6.75 3.00 1.80 4.50 2.25 2.31 1.15 1.00 4.00 2.20 3.48 1.74 2.50 10.42 2.16 1.78 1.78 1.33 3.64 6.10 2.28 1.44 3.13 1.00 2.80

600.00 240.00 373.00 145.00 40.00 1,140.00 200.00 360.00 120.00 40.00 320.00 50.00 80.00 360.00 600.00 120.00 480.00 270.00 988.00 1,081.00 135.00 245.00 155.00 360.00 480.00 60.00 290.00 360.00 360.00 480.00 330.00 105.00 736.00 750.00 60.00 1,680.00 300.00

1,200.00 637.00 840.00 540.00 540.00 2,445.50 540.00 1,680.00 1,140.00 188.00 625.00 540.00 540.00 1,081.00 1,081.00 540.00 1,081.00 625.00 1,140.00 1,081.00 540.00 540.00 540.00 625.00 1,200.00 625.00 625.00 640.00 640.00 640.00 1,200.00 640.00 1,680.00 1,081.00 188.00 1,680.00 840.00

240.00 65.00 100.00 30.00 40.00 805.00 40.00 400.00 160.00 10.00 60.00 30.00 40.00 140.00 120.00 20.00 120.00 60.00 160.83 110.00 30.00 20.00 30.00 60.00 230.00 60.00 60.00 90.00 87.00 80.00 220.00 80.00 301.33 120.00 10.00 400.00 100.00

191

192

APPENDIX 4

Id code

BHI

Tax assessment

Frontier assessment

Annual value

68. 69. 70. 71.

6.27 2.22 5.58 4.44

30.00 541.25 215.00 270.00

188.00 1,200.00 1,200.00 1,200.00

10.00 240.00 240.00 200.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105.

1.74 2.77 5.09 4.17 12.86 2.34 4.67 1.00 3.13 4.50 4.50 2.33 3.50 5.17 5.60 2.71 9.00 3.60 7.12 3.17 3.88 1.33 1.26 3.13 4.91 2.98 2.08 4.50 4.50 2.74 4.12 2.55 14.41 11.25

690.00 195.00 165.00 150.00 42.00 38.50 180.00 42.50 60.00 120.00 240.00 360.00 240.00 232.00 300.00 420.00 60.00 150.00 236.00 378.00 433.00 480.00 507.00 60.00 110.00 210.00 300.00 120.00 120.00 1,140.00 262.50 330.00 75.00 48.00

1,200.00 540.00 840.00 625.00 540.00 90.00 840.00 42.50 188.00 540.00 1,081.00 840.00 840.00 1,200.00 1,680.00 1,140.00 540.00 540.00 1,680.00 1,200.00 1,680.00 640.00 640.00 188.00 540.00 625.00 625.00 540.00 540.00 3,120.00 1,081.00 840.00 1,081.00 540.00

200.00 30.00 100.00 60.00 25.00 5.00 100.00 3.00 10.00 20.00 146.00 100.00 100.00 180.00 360.00 160.00 35.00 25.00 277.33 240.00 296.00 97.00 80.00 10.00 40.00 60.00 60.00 20.00 40.00 1,000.00 120.00 100.00 140.00 30.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

106. 107. 108. 109. 110. 111. 112.

5.71 6.72 7.71 4.95 4.50 17.36 5.40

210.00 125.00 70.00 38.00 120.00 36.00 100.00

1,200.00 840.00 540.00 188.00 540.00 625.00 540.00

200.00 100.00 40.00 10.00 40.00 60.00 35.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143.

17.69 6.00 19.23 5.57 13.50 7.11 5.21 9.00 5.74 4.70 5.97 5.60 3.50 2.80 3.73 3.56 1.26 1.80 3.50 3.38 2.00 3.60 4.00 1.74 2.79 1.00 1.79 2.25 1.07 1.37 2.00

36.00 90.00 32.50 115.00 40.00 90.00 120.00 60.00 94.00 40.00 31.50 300.00 480.00 600.00 450.00 180.00 665.00 600.00 240.00 160.00 270.00 150.00 135.00 360.00 224.00 1,200.00 105.00 240.00 600.00 615.00 600.00

637.00 540.00 625.00 640.00 540.00 640.00 625.00 540.00 540.00 188.00 188.00 1,680.00 1,680.00 1,680.00 1,680.00 640.00 840.00 1,081.00 840.00 540.00 540.00 540.00 540.00 625.00 625.00 1,200.00 188.00 540.00 640.00 840.00 1,200.00

65.00 22.17 50.00 88.00 30.00 80.00 50.00 40.00 20.00 10.00 10.00 300.00 320.00 340.00 320.00 80.00 100.00 120.00 100.00 40.00 30.00 20.00 25.00 60.00 50.00 180.00 10.00 40.00 80.00 100.00 200.00

193

194

APPENDIX 4

Id code

BHI

Tax assessment

Frontier assessment

Annual value

144. 145. 146. 147. 148. 149. 150. 151. 152. 153.

1.80 3.60 2.86 1.82 1.29 2.00 1.81 4.17 3.28 2.88

300.00 150.00 420.00 660.00 930.00 600.00 930.00 150.00 330.00 187.50

540.00 540.00 1,200.00 1,200.00 1,200.00 1,200.00 1,680.00 625.00 1,081.00 540.00

40.00 40.00 200.00 200.00 240.00 200.00 300.00 60.00 140.00 25.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181.

2.38 2.67 1.94 4.50 10.29 5.33 2.57 4.00 7.20 4.95 3.13 12.53 18.00 5.40 5.57 15.43 6.94 3.60 14.59 1.67 1.10 2.25 5.57 1.64 2.73 4.50 4.50 9.00

480.00 240.00 330.00 120.00 52.50 120.00 210.00 135.00 75.00 38.00 60.00 15.00 30.00 100.00 97.00 35.00 90.00 300.00 37.00 720.00 1,800.00 240.00 97.00 1,027.50 440.00 240.00 120.00 60.00

1,140.00 640.00 640.00 540.00 540.00 640.00 540.00 540.00 540.00 188.00 188.00 188.00 540.00 540.00 540.00 540.00 625.00 1,081.00 540.00 1,200.00 1,980.00 540.00 540.00 1,680.00 1,200.00 1,081.00 540.00 540.00

160.00 80.00 80.00 40.00 30.00 80.00 40.00 30.00 30.00 10.00 10.00 10.00 20.00 26.00 20.00 30.00 60.00 120.00 20.00 200.00 600.00 40.00 20.00 345.00 180.00 120.00 20.00 20.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194.

1.25 4.91 6.27 4.98 2.08 4.80 9.01 1.28 1.52 1.62 2.40 3.29 2.67

960.00 110.00 30.00 229.00 260.00 225.00 120.00 1,310.00 420.00 395.00 260.00 190.00 405.00

1,200.00 540.00 188.00 1,140.00 540.00 1,081.00 1,081.00 1,680.00 640.00 640.00 625.00 625.00 1,081.00

200.00 20.00 10.00 160.00 40.00 120.00 120.00 346.00 80.00 80.00 60.00 50.00 140.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

195. 196. 197. 198. 199. 200. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219.

71.11 3.13 7.20 8.89 1.97 4.32 3.86 3.13 2.36 2.67 2.46 4.50 36.00 3.73 2.72 3.50 5.21 5.21 1.52 1.93 2.57 1.38 2.25 1.91 1.00

9.00 60.00 75.00 135.00 580.00 125.00 166.00 383.50 270.00 240.00 683.00 240.00 15.00 225.00 398.00 240.00 120.00 120.00 420.00 280.00 420.00 390.00 480.00 440.00 840.00

640.00 188.00 540.00 1,200.00 1,140.00 540.00 640.00 1,200.00 637.00 640.00 1,680.00 1,081.00 540.00 840.00 1,081.00 840.00 625.00 625.00 640.00 540.00 1,081.00 540.00 1,081.00 840.00 840.00

80.00 10.00 40.00 200.00 160.00 45.00 81.00 240.00 70.00 80.00 395.00 120.00 30.00 100.00 120.00 100.00 50.00 50.00 80.00 40.00 140.00 40.00 140.00 100.00 100.00

195

196

APPENDIX 4

Id code

BHI

Tax assessment

Frontier assessment

Annual value

220. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236.

2.25 2.73 4.91 3.00 8.56 1.33 3.08 1.57 1.99 4.00 6.00 4.50 3.33 6.00 9.00 4.03

240.00 198.00 220.00 180.00 73.00 480.00 203.00 120.00 272.00 135.00 90.00 120.00 187.50 90.00 60.00 155.00

540.00 540.00 1,081.00 540.00 625.00 640.00 625.00 188.00 540.00 540.00 540.00 540.00 625.00 540.00 540.00 625.00

30.00 40.00 140.00 30.00 60.00 80.00 50.00 10.00 40.00 20.00 20.00 20.00 50.00 30.00 20.00 60.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

237. 238. 239. 240. 241. 242. 243. 244. 245. 246. 247. 248. 249. 250. 251. 252. 253. 254. 255. 256. 257. 258.

3.13 5.01 6.22 1.39 9.88 1.23 3.30 3.27 3.28 1.39 18.02 4.44 1.49 1.00 1.64 2.84 8.00 6.00 1.31 3.25 3.68 2.31

60.00 37.50 135.00 780.00 170.00 520.00 345.00 165.00 195.00 780.00 60.00 270.00 420.00 1,680.00 660.00 423.00 80.00 90.00 1,280.00 960.00 170.00 270.00

188.00 188.00 840.00 1,081.00 1,680.00 640.00 1,140.00 540.00 640.00 1,081.00 1,081.00 1,200.00 625.00 1,680.00 1,081.00 1,200.00 640.00 540.00 1,680.00 3,120.00 625.00 625.00

7.00 16.00 100.00 140.00 280.00 80.00 160.00 35.00 80.00 140.00 140.00 240.00 60.00 560.00 140.00 240.00 80.00 40.00 320.00 1,200.00 60.00 60.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

259. 260. 261. 262. 263. 264. 265. 266. 267. 268. 269. 270. 271. 272. 273. 274. 275. 276. 277.

2.25 2.25 4.00 3.09 4.18 1.80 2.03 2.31 2.50 1.52 2.25 4.08 3.86 3.86 3.26 2.37 3.11 3.60 2.45

240.00 480.00 135.00 175.00 45.00 300.00 315.00 270.00 480.00 420.00 240.00 265.00 140.00 140.00 750.00 270.00 270.00 300.00 490.00

540.00 1,081.00 540.00 540.00 188.00 540.00 640.00 625.00 1,200.00 640.00 540.00 1,081.00 540.00 540.00 2,445.50 640.00 840.00 1,081.00 1,200.00

20.00 120.00 45.00 40.00 10.00 40.00 90.00 60.00 180.00 80.00 40.00 120.00 30.00 40.00 860.00 80.00 100.00 140.00 200.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

278. 279. 280. 281. 282. 283. 284. 285. 286. 287. 288. 289. 290. 291. 292. 293. 294. 295. 296.

6.01 3.47 3.60 4.50 8.33 9.00 8.22 3.50 3.05 6.27 1.00 1.00 2.80 2.09 3.13 1.00 1.27 1.39 2.25

180.00 180.00 300.00 240.00 75.00 60.00 76.00 240.00 210.00 30.00 637.00 3,120.00 300.00 90.00 60.00 640.00 1,560.00 450.00 240.00

1,081.00 625.00 1,081.00 1,081.00 625.00 540.00 625.00 840.00 640.00 188.00 637.00 3,120.00 840.00 188.00 188.00 640.00 1,980.00 625.00 540.00

140.00 60.00 110.00 120.00 60.00 30.00 60.00 100.00 80.00 10.00 65.00 1,000.00 100.00 10.00 10.00 80.00 600.00 50.00 30.00

197

198

APPENDIX 4

Id code

BHI

Tax assessment

Frontier assessment

Annual value

297. 298. 299. 300. 301. 302. 303. 304. 305. 306. 307. 308. 309. 310. 311. 312. 313. 314. 315. 316. 317. 318.

1.33 1.80 9.00 4.50 1.06 1.70 1.75 1.50 4.27 2.12 3.56 1.19 3.00 1.43 2.24 1.37 1.72 2.77 2.60 1.30 10.42 2.36

480.00 300.00 60.00 120.00 600.00 990.00 960.00 60.00 44.00 255.00 180.00 540.00 180.00 840.00 375.00 834.00 630.00 195.00 240.00 480.00 60.00 484.00

640.00 540.00 540.00 540.00 637.00 1,680.00 1,680.00 90.00 188.00 540.00 640.00 640.00 540.00 1,200.00 840.00 1,140.00 1,081.00 540.00 625.00 625.00 625.00 1,140.00

80.00 40.00 20.00 30.00 70.00 480.00 360.00 5.00 10.00 30.00 80.00 80.00 30.00 220.00 100.00 160.00 140.00 25.00 50.00 60.00 60.00 160.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

319. 320. 321. 322. 323. 324. 325. 326. 327. 328. 329. 330. 331. 332. 333. 334.

1.00 2.65 2.04 1.56 4.50 1.50 3.53 2.67 2.23 1.93 1.80 3.00 1.40 5.14 3.43 1.64

625.00 235.50 306.50 540.00 120.00 360.00 153.00 240.00 280.00 331.00 300.00 180.00 1,200.00 105.00 157.50 390.00

625.00 625.00 625.00 840.00 540.00 540.00 540.00 640.00 625.00 640.00 540.00 540.00 1,680.00 540.00 540.00 640.00

46.00 60.00 60.00 100.00 20.00 20.00 20.00 80.00 60.00 80.00 40.00 30.00 320.00 30.00 20.00 80.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

335. 336. 337. 338. 339. 340. 341. 342. 343. 344. 345. 346. 347. 348. 349. 350. 351. 352. 353. 354. 355. 356. 357. 358. 359.

2.60 4.82 4.50 1.57 5.09 5.93 1.13 1.33 1.29 5.33 1.82 9.00 1.75 4.50 2.00 1.71 1.15 2.25 1.99 1.78 1.82 1.92 2.13 1.98 1.57

240.00 112.00 120.00 690.00 165.00 91.00 960.00 405.00 840.00 120.00 660.00 60.00 960.00 120.00 840.00 492.00 988.00 480.00 271.00 360.00 660.00 875.00 300.00 95.00 120.00

625.00 540.00 540.00 1,081.00 840.00 540.00 1,081.00 540.00 1,081.00 640.00 1,200.00 540.00 1,680.00 540.00 1,680.00 840.00 1,140.00 1,081.00 540.00 640.00 1,200.00 1,680.00 640.00 188.00 188.00

60.00 20.00 40.00 110.00 100.00 20.00 140.00 30.00 140.00 80.00 220.00 20.00 400.00 30.00 320.00 100.00 160.00 120.00 20.00 80.00 180.00 300.00 80.00 10.00 10.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

360. 361. 362. 363. 364. 365. 366. 367. 368. 369. 370. 371. 372.

4.00 1.04 4.47 7.20 1.52 3.00 1.70 2.78 4.50 1.34 1.45 1.29 2.03

210.00 1,610.00 255.00 75.00 420.00 180.00 368.00 194.00 120.00 140.00 1,162.00 495.00 315.00

840.00 1,680.00 1,140.00 540.00 640.00 540.00 625.00 540.00 540.00 188.00 1,680.00 640.00 640.00

100.00 400.00 163.00 20.00 80.00 20.00 60.00 20.00 40.00 10.00 400.00 80.00 80.00

199

200

APPENDIX 4

Id code

BHI

Tax assessment

Frontier assessment

Annual value

373. 374. 375. 376. 377. 378. 379. 380. 381. 382. 383. 384. 385. 386. 387. 388. 389. 390. 391. 392. 393. 394. 395. 396. 397. 398. 399. 400.

3.23 15.27 3.60 6.15 1.40 1.79 1.19 6.75 5.02 2.98 3.13 1.00 2.00 4.31 1.86 2.57 3.47 1.00 1.90 1.08 1.00 3.56 37.60 6.43 1.71 3.60 6.94 3.80

335.00 55.00 300.00 195.00 600.00 670.00 540.00 80.00 107.50 210.00 60.00 1,980.00 600.00 390.00 345.00 420.00 180.00 1,680.00 335.00 594.00 1,140.00 180.00 5.00 14.00 633.00 150.00 90.00 300.00

1,081.00 840.00 1,081.00 1,200.00 840.00 1,200.00 640.00 540.00 540.00 625.00 188.00 1,980.00 1,200.00 1,680.00 640.00 1,081.00 625.00 1,680.00 637.00 640.00 1,140.00 640.00 188.00 90.00 1,081.00 540.00 625.00 1,140.00

122.50 100.00 140.00 210.00 100.00 235.00 80.00 20.00 20.00 50.00 10.00 600.00 240.00 320.00 80.00 120.00 60.00 260.00 75.00 90.00 160.00 80.00 12.00 5.00 122.00 25.00 60.00 160.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

401. 402. 403. 404. 405. 406. 407. 408. 409. 410.

2.60 7.00 1.47 1.62 4.50 4.05 1.80 1.90 4.54 3.39

240.00 120.00 570.00 332.50 240.00 158.00 600.00 600.00 370.00 495.00

625.00 840.00 840.00 540.00 1,081.00 640.00 1,081.00 1,140.00 1,680.00 1,680.00

60.00 100.00 100.00 41.67 120.00 90.00 140.00 160.00 400.00 360.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

411. 412. 413. 414. 415. 416. 417. 418. 419. 420. 421. 422. 423. 424. 425. 426. 427. 428. 429. 430. 431. 432. 433. 434. 435. 436. 437. 438. 439. 440. 441.

12.00 2.00 3.33 1.67 4.75 2.40 4.75 8.33 12.00 4.70 1.72 1.89 1.71 18.00 1.50 1.80 3.60 2.00 4.50 4.50 2.19 5.40 4.29 13.50 2.25 2.00 1.67 1.72 2.25 3.13 7.20

45.00 600.00 360.00 720.00 240.00 225.00 240.00 75.00 45.00 40.00 630.00 330.00 365.00 30.00 360.00 600.00 150.00 420.00 120.00 120.00 285.00 100.00 280.00 40.00 240.00 270.00 720.00 630.00 240.00 60.00 75.00

540.00 1,200.00 1,200.00 1,200.00 1,140.00 540.00 1,140.00 625.00 540.00 188.00 1,081.00 625.00 625.00 540.00 540.00 1,081.00 540.00 840.00 540.00 540.00 625.00 540.00 1,200.00 540.00 540.00 540.00 1,200.00 1,081.00 540.00 188.00 540.00

20.00 240.00 200.00 240.00 160.00 40.00 160.00 60.00 30.00 10.00 120.00 60.00 60.00 20.00 40.00 110.00 20.00 100.00 20.00 20.00 46.00 20.00 240.00 20.00 30.00 40.00 180.00 110.00 40.00 11.00 30.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

442. 443. 444. 445. 446. 447. 448.

4.50 1.24 3.60 4.95 4.70 2.51 4.17

120.00 675.00 300.00 242.50 242.50 215.00 150.00

540.00 840.00 1,081.00 1,200.00 1,140.00 540.00 625.00

20.00 103.00 120.00 180.00 160.00 30.00 60.00

201

202

APPENDIX 4

Id code

BHI

Tax assessment

Frontier assessment

Annual value

449. 450. 451. 452. 453. 454. 455. 456. 457. 458. 459. 460. 461. 462. 463. 464. 465. 466. 467. 468. 469. 470. 471. 472. 473. 474. 475. 476. 477. 478. 479. 480. 481. 482.

1.11 2.03 1.00 4.50 25.44 8.33 2.50 7.21 3.21 3.47 5.32 4.57 5.21 13.33 14.00 2.36 4.00 7.52 1.16 4.50 3.72 3.00 4.50 2.12 10.42 9.00 2.08 6.00 5.15 6.00 2.00 2.25 1.00 1.19

1,080.00 266.00 195.00 120.00 42.50 75.00 480.00 150.00 195.00 180.00 158.00 140.00 120.00 63.00 60.00 18.00 300.00 25.00 540.00 120.00 145.00 30.00 120.00 510.00 60.00 60.00 300.00 15.00 210.00 90.00 420.00 240.00 540.00 540.00

1,200.00 540.00 195.00 540.00 1,081.00 625.00 1,200.00 1,081.00 625.00 625.00 840.00 640.00 625.00 840.00 840.00 42.50 1,200.00 188.00 625.00 540.00 540.00 90.00 540.00 1,081.00 625.00 540.00 625.00 90.00 1,081.00 540.00 840.00 540.00 540.00 640.00

200.00 40.00 17.67 20.00 115.00 60.00 180.00 120.00 60.00 60.00 100.00 80.00 60.00 100.00 100.00 3.00 240.00 7.00 60.00 30.00 20.00 5.00 40.00 120.00 60.00 30.00 50.00 6.00 140.00 40.00 100.00 20.00 20.00 80.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

483. 484. 485. 486.

3.00 3.60 1.42 1.49

180.00 150.00 30.00 420.00

540.00 540.00 42.50 625.00

30.00 40.00 4.00 50.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

487. 488. 489. 490. 491. 492. 493. 494. 495. 496. 497. 498. 499. 500. 501. 503. 504. 505. 506. 507. 508. 509. 510. 511. 512. 513. 514. 515. 516. 517. 518. 519. 520. 521. 522. 523. 524.

1.95 1.00 4.50 1.30 2.23 1.49 4.75 1.80 2.60 7.40 2.50 2.91 1.80 25.60 12.89 4.27 5.30 3.55 3.76 2.99 4.50 7.21 8.57 12.41 5.71 2.04 7.08 2.13 4.45 2.18 2.49 3.54 1.42 3.00 3.00 5.31 1.43

320.00 90.00 120.00 482.00 280.00 420.00 240.00 600.00 240.00 73.00 480.00 220.00 600.00 25.00 48.50 150.00 158.50 176.00 170.00 362.00 240.00 150.00 140.00 43.50 210.00 306.50 90.00 300.00 243.00 385.00 482.00 305.00 846.00 30.00 180.00 120.00 800.00

625.00 90.00 540.00 625.00 625.00 625.00 1,140.00 1,081.00 625.00 540.00 1,200.00 640.00 1,081.00 640.00 625.00 640.00 840.00 625.00 640.00 1,081.00 1,081.00 1,081.00 1,200.00 540.00 1,200.00 625.00 637.00 640.00 1,081.00 840.00 1,200.00 1,081.00 1,200.00 90.00 540.00 637.00 1,140.00

50.00 5.00 40.00 50.00 48.33 60.00 160.00 120.00 50.00 40.00 200.00 80.00 120.00 80.00 60.00 80.00 100.00 64.00 80.00 122.00 120.00 120.00 200.00 20.00 220.00 60.00 68.00 80.00 140.00 100.00 255.00 120.00 200.00 5.00 40.00 70.00 160.00

Id code

BHI

Tax assessment

Frontier assessment

Annual value

525.

1.18

1,020.00

1,200.00

220.00

203

204

APPENDIX 4

Id code

BHI

Tax assessment

Frontier assessment

Annual value

526. 527. 528. 529. 530. 531. 532. 533. 534. 535. 536. 537. 538. 539. 540. 541. 542. 543. 544. 545. 546. 547. 548. 549. 550. 551. 552. 553. 554. 555. 556. 557. 558. 559. 560. 561. 562. 563. 564. 565.

2.15 2.80 1.80 4.44 2.60 1.33 11.20 1.13 4.50 3.05 2.60 2.90 3.00 2.25 2.51 1.98 4.67 3.13 12.53 1.94 2.38 2.29 10.42 10.42 10.42 3.13 4.50 4.50 2.60 36.00 1.06 6.94 3.13 1.00 4.18 1.07 2.92 6.00 3.00 3.00

780.00 600.00 600.00 270.00 240.00 1,260.00 150.00 960.00 120.00 210.00 240.00 373.00 180.00 240.00 75.00 315.00 180.00 60.00 15.00 330.00 480.00 367.00 60.00 60.00 60.00 60.00 120.00 120.00 240.00 15.00 40.00 90.00 60.00 188.00 45.00 1,010.00 390.00 90.00 180.00 280.00

1,680.00 1,680.00 1,081.00 1,200.00 625.00 1,680.00 1,680.00 1,081.00 540.00 640.00 625.00 1,081.00 540.00 540.00 188.00 625.00 840.00 188.00 188.00 640.00 1,140.00 840.00 625.00 625.00 625.00 188.00 540.00 540.00 625.00 540.00 42.50 625.00 188.00 188.00 188.00 1,081.00 1,140.00 540.00 540.00 840.00

280.00 300.00 120.00 240.00 60.00 590.00 300.00 140.00 20.00 80.00 55.00 140.00 20.00 30.00 16.00 50.00 100.00 10.00 13.00 80.00 160.00 100.00 50.00 50.00 60.00 10.00 20.00 30.00 60.00 20.00 3.33 60.00 15.50 7.00 8.00 140.00 160.00 40.00 40.00 100.00

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

Id code

BHI

Tax assessment

Frontier assessment

Annual value

566. 567. 568. 569. 570. 571. 572. 573. 574. 575. 576. 577.

1.95 2.00 2.84 2.25 1.57 8.00 2.60 1.50 1.04 4.91 6.27 3.13

615.00 540.00 220.00 480.00 120.00 150.00 240.00 720.00 615.00 110.00 30.00 60.00

1,200.00 1,081.00 625.00 1,081.00 188.00 1,200.00 625.00 1,081.00 640.00 540.00 188.00 188.00

240.00 140.00 50.00 130.00 10.00 240.00 50.00 120.00 80.00 30.00 8.00 10.00

205

NOTES

1 INTRODUCTION AND BACKGROUND 1 See also McDonald and Snooks (1985a, 1985b, 1985c, 1987a and 1987b). 2 Further discussion of the traditional and modern approaches to analysis of the economics of the Domesday period is contained in chapter 3 of Domesday Economy, McDonald and Snooks (1985a, 1985b, 1985c, 1987a and 1987b). Others, in the more recent period, who have made important contributions to our understanding of the Domesday economy include Miller and Hatcher (1978), Harvey (1983), Fleming (1983), and the contributors to the volumes edited by Aston (1987), Holt (1987), Hallam (1988), and Britnell and Campbell (1995) (especially Snooks, 1995). 3 For further background information on Domesday England, see Domesday Economy: chapters 1 and 2. More comprehensive accounts of the history of the period can be found in many works, including Brown (1984), Clanchy (1983), Loyn (1962, 1965, 1983), F.M.Stenton (1943) and D.M.Stenton (1951). Other useful references include Ballard (1906), Darby (1952, 1977), Galbraith (1961), Hollister (1965), Lennard (1959), Maitland (1897), Miller and Hatcher (1978), Postan (1966, 1972), Round (1895, 1903), the articles in Williams (1987) and references cited in Domesday Economy. 4 For more on the survey, see Domesday Economy: section 2.2, the references cited there, and the articles in Williams (1987). 5 The model of production is discussed in more detail in Domesday Economy: sections 6.2 and 10.6, and McDonald and Snooks (1987b). 6 For details, see chapters 6, 9 and 10 of Domesday Economy. 7 The data file for the analyses was compiled in 1990 by Eva Aker under the direction of John McDonald with the aid of a Flinders University research grant. The file was compiled directly from Domesday Book entries in the Victoria County History of Essex, which were checked against a facsimile of the Latin transcript and the English translation in the Phillimore edition. In the process of constructing this file a number of minor errors in the data used in the analyses described in Domesday Economy were detected. The errors do not affect those analyses in any important way.

2 MEASURING EFFICIENCY: THEORETICAL IDEAS 1 Other useful references include the excellent survey articles by Førsund, Lovell and Schmidt (1980), Schmidt (1986), and Seiford and Thrall (1990), and the references therein, Färe, Grosskopf and Lovell (1994), and the

NOTES

207

references cited in Sections 5.2 (where methods of estimating efficiency are reviewed), 6.1 and 6.2 (where some applications are discussed). 2 Returns to scale are said to be constant if, when inputs are increased proportionally, output is increased in the same proportion, so, for example, a doubling of inputs results in a doubling of output; with increasing returns to scale, output is more than doubled, and with decreasing returns to scale, less than doubled. 3 Alternatively, efficiency can be measured as the reciprocal of the u-values: that is, 1 for B, 2/3 for A and 4/9 for C. 4 An alternative way of analysing the behaviour of a profit-maximising firm is to use calculus methods (see, for example, Henderson and Quandt, 1980: ch. 4, for details). Let us denote the firm’s profit by π, the price of the output by p, the price of the inputs by w1 and w2, and fixed costs of production by b. The production frontier can be denoted y1=f(R1,R2)

where y1 is the maximum output that can be obtained when R1 and R2 units of inputs are used in production. Profit is the difference between total revenue (py1) and total cost (c): π=py1−c.

Total cost, c, is the sum of variable cost (w1R1+w2R2) and fixed cost (b): c=w1R1+w2R2+b

Substituting y1=f(R1,R2), and c=w1R1+w2R2+b in the expression for profit, π, we have π=pf(R1,R2)−w1R1−w2R2−b.

The firm attempts to maximise profit by choosing input levels R1 and R2. Calculus methods indicate that a condition for maximising the profit function is that the partial derivatives of profit with respect to both R1 and R2 (denoted π1 and π2) must be such that

where f1 and f2 are the (first) partial derivatives of the production function with respect to the inputs. These equations can be rewritten:

Since f1 can be interpreted as the marginal product of the first input, the first equation says that the value of the marginal product of the first input must equal the price of that input. A similar condition holds for the second input. These conditions require that the firm continue to employ units of an input until the level is reached at which the value of the input’s marginal product equals its price. This must be so, because profit can be increased as long as the addition to revenue from using a further unit of input exceeds its cost. Dividing the first equation by the second we have

which says that the ratio of the marginal products of the two inputs must be equal to the ratio of their prices. Technical efficiency requires that the firm produces on (that is, not below) its production frontier. Allocative efficiency requires that input proportions are such that the ratio of the marginal products of the inputs is equal to the ratio of their prices; and scale efficiency requires that input usage, and hence output produced, is such that the value of the marginal product of each input is equal to its price. Further (so-called second-order) conditions for profit maximisation are π11<0, π22<0, and π11π22−π12π21>0 where π11 is me second partial derivative of profit with respect to R1, π22 is the second partial derivative with respect to R2 and π12 the second cross partial derivative. Since π11=pf11 where f11 is the second partial derivative of the production function with respect to the first input, π11<0 requires that f11<0, that is, the marginal product of

208

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

the first input be decreasing. Similarly, since π22<0, the marginal product of the second input must also be decreasing. The calculus analysis (unlike the diagrammatic exposition in the text) can be easily generalised to allow for more than two inputs in production. 5 When the production possibility frontier is curved (for example, the frontier AD in Figure 2.9), calculus methods can be used to analyse the behaviour of an optimising estate. Suppose the estate can sell y1 and y2 at prices p1 and p2 respectively; so the value of net output is V=p1y1+p2y2.

The production frontier, AD, indicates the (maximum) net output combinations that can be produced. On the frontier, the maximum amount of y2 output that can be produced depends on the amount of y1 produced, that is, y2 is a function of y1, with the function defined by the frontier curve. Let us denote this function y2=g(y1)

where g1, the partial derivative of the function with respect to y1, is negative, reflecting the negative slope of the curve AD (which, in turn, reflects the fact that, to obtain more y2, some y1 must be given up).−g1 indicates the amount of extra y2 that is obtained when output of y1 is reduced by a (small) unit amount, and is referred to as the marginal rate of product transformation y2 for y1. Substituting y2=g(y1) in V=p1y1+p2y2 gives V=p1y1+p2g(y1).

The lord attempts to maximise V. Setting the partial derivative of V with respect to y1 (denoted V1) equal to zero gives

—g1 is the marginal rate of transformation y2 for y1, so the equation says that, at the maximising output levels, the return from a unit of y1 output (that is, p1) must equal the return from instead producing a unit less of y1, but more y2 (that is, p2(–g1)). A further condition for net value maximisation is that the second partial derivative of V with respect to y1 (denoted V11) is negative. V11=g11, and this will be negative if the production frontier is bowed away from the origin, as AD is in Figure 2.9. In mathematical terms, y2 must be a strictly concave function of y1, so that as more y2 and less y1 is produced, a decreasing amount of y2 is obtained, when a unit of y1 is given up. This analysis can easily be generalised to the case when there are more than two outputs (see Henderson and Quandt, 1980: 98–101). Calculus methods will only locate optimal points which lie on the curve between A and D. (Points where the function, y2=g(y1), is differentiable). Hence, if no optimal point is located, the value of V at the points A, D and 0 should be calculated. Note that V will be greatest at D (where only y1 is produced) if p2 is zero and p1 is positive; and V will be greatest at 0 (where no output is produced) if pl and p2 are negative. If the production frontier has a linear segment (such as the frontier ABCD in Figure 2.9), output combinations that maximise V will be represented by a point on the curves between A and B, or C and D or one of the points 0, A, B, C or D. Usually, the conditions p1=p2(–g1) will only be satisfied exactly if the optimising output combination lies on the curved parts of the frontier. However, the Kuhn-Tucker conditions of non-linear programming will be applicable. (See, for example, Henderson and Quandt, 1980: 384–6, and Lancaster, 1968: ch. 5, for a description of the optimising procedure; and Henderson and Quandt, 1980: 17–18 and 115–17, and Lancaster, 1968: ch. 8, for economic applications. Nonlinear programming can also be used to solve problems where the production possibility frontier is bowed towards the origin.) When the producer can influence output prices, prices will be determined by the interaction of the quantity supplied with the market demand function. The calculus optimising condition is, as before, that net marginal returns from using the resource endowment to produce different outputs must be equalised, but, because price is

NOTES

6

7

8

9

10

11 12

13

209

affected by the quantity offered for sale, the output prices will no longer be the marginal revenues obtained from selling a unit of the outputs (see Henderson and Quandt, 1980: ch. 7). There has been considerable discussion in the literature on the nature of efficiency and the interpretation of revealed inefficiency. A good summary is Førsund et al. (1980: 4.2). Other references include Leibenstein (1966, 1976) and Scnmidt (1986). For R1<10, the frontier can either be left undefined, or the frontier V-value set equal to zero, thus adding the horizontal line from the origin (0) to the point on the R1 axis where R1=10 to the frontier and PPS. Banker (1993) shows that the VRS frontier generates the monotone increasing function which ‘most tightly’ envelops the data. Our approach has been to analyse estate efficiency using technical assumptions which (on the basis of empirical evidence and theoretical reasoning) would seem to generate the best approximation to the true frontier, then check for sensitivity of the results to the chosen assumptions. An alternative approach is directly to test the returns to scale assumption, but this is difficult to do without a stochastic model of the data-generating process. Intuitively, the closer the generated CRS frontier is to the VRS frontier, the greater the plausibility of the CRS assumption (because the CRS assumption is not imposed when the VRS frontier is generated, yet, if the frontiers are similar, the data suggest it is valid). With a deterministic framework, however, it is difficult to assess how close the frontiers need to be to accept the CRS assumption. Banker (1993) provides a stochastic framework for a test to be carried out (see also Mukherjee and Ray, 1994), but this approach is in its early stages, and problems remain with the testing procedure. For example, the outcome of the test will depend greatly on the stochastic assumptions made. What disturbance distribution should be assumed? Should disturbance variances be assumed constant at all scale levels, or is it more reasonable for the disturbance variance to increase with scale? There is an incidental parameters problem, and little is known of the power of the test in finite samples. Unlike most tests which essentially involve estimating means, to get a good estimate of the frontier, extreme values are needed. Sample sizes required to give a good approximation, and for asymptotic test results to hold, are largely unknown. Also, if the CRS frontier is rejected, it does not necessarily follow that, with a finite sample, the VRS frontier provides a better approximation. It is quite possible for the CRS assumption to be invalid, yet, with a finite set of data, generate a better approximation to the true frontier. With CRS, free disposability of output technology and a single resource, imposing the assumption of free disposability of the resource does not increase the size of the production possibility set. Also, when there are several resources, imposing the weak free disposability of resources assumption does not increase the size of the production possibility set. Imposing strong free disposability of resources does enlarge the set, because it implies minimum values below which V cannot fall when resource levels are increased non-proportionally. If a resource is lumpy and, for example, estates are only endowed with integer amounts of the resource, the production possibility set is reduced to that part of the set corresponding to integer values of the resource (for example, in Figure 2.11, to the points in the constructed production possibility sets that lie on vertical lines drawn from the horizontal axis where R1=0,1,2,…). Efficiency measures for estates are unaffected, and can be calculated using the programming methods described in Chapter 3. The decomposition is also discussed in Färe, Grosskopf and Lovell (1994). Of course, other techniques depend for their validity on the true technology, but this is usually obvious (for example, CS efficiency measures require the true technology to be CS, or close to it). It is easy to gain the impression from the literature that the decomposition works well whatever the true technology and can be used advantageously irrespective of our knowledge of technology. This problem is discussed in McDonald (1996).

4 EFFICIENCY ANALYSIS OF DOMESDAY ESSEX LAY ESTATES 1 It is also a point of dispute as to whether profits from manorial courts were included in the annual values. Such profits were usually a small proportion of the annual value and can be thought of as part of the return extracted from the peasants.

210

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

2 Of the 118 discarded entries: twelve had no recorded annual value, one had an annual value recorded as zero, twenty no recorded resources, seventy-eight did not satisfy the three criteria, five were the large manors with implausible entries, and two could not be located geographically. 3 Horses cost more to keep than oxen because of the cost of shoeing and the need to feed them oats in winter, whereas oxen could survive on hedge clippings: see Postan (1972:80), Hallam (1981:54) and Langdon (1982). Regression estimates that support the contention that horses did not have economic significance are reported in McDonald and Snooks (1985b). The weights (based on market prices) for livestock were: cows, 24; swine, 8; sheep, 5; and goats, 4. Sources for underlying market prices include: Maitland (1897:44), Ballard (1906:27), Round (1903:367) and Raftis (1957:62). 4 In just a few instances, woodland was measured in hides and acres rather than in swine that could be supported. This occurs in our sample in ten cases. Following Fowler (1922), we converted these measures to swine that could be supported, using the formula 1.5 acres per swine. Very occasionally (there are seven cases in our sample) pasture was measured in shillings and pence, rather than in sheep that could graze on the land. The entry for Wigborough in Winstree records pasture for 100 sheep rendering 16 pence. We adopted this conversion rate. One entry (Wheatley in Barstable) has pasture measured in acres. We treated this as an error, interpreting the land as meadow. 5 The linear programming problems corresponding to CW and VW technologies were solved a second time without the constraint, w≥0.0005. On all occasions, the same optimal solution was obtained. 6 The efficiency category labels, relatively efficient, less efficient, inefficient, and very inefficient, are relative terms and have no absolute meaning. The annual value is the annual net revenue accruing to the lord from the estate and so is analogous to the annual profit of a modern company that owns its land and capital. The efficiency values therefore seem reasonable, for it is common for some companies (of a given size) to have profits two, three or even five or six times that of others. See Section 6.2 for further discussion. 7 The production frontier (and hence the efficiency measures) could be distorted by erroneous observations. To protect against this, we initially screened all observations and deleted suspicious data (see Section 4.4). As a further safeguard, we re-examined the observations that most often resulted in estates being judged inefficient. For example, the intensity variables (zi) corresponding to Pebmarsh (code 502) and Lawling (190) were most often non-zero in the linear programming optional solutions of the estates (Pebmarsh on 206 occasions, Lawling on 165 occasions). For both estates, annual value increased markedly from 1066 to 1086, but in other respects the entries for the estates appear plausible. Moreover other estates—including Michaelstow (code 357) and Down (392)—have similar annual values and resource mixes. 8 Three estates had no ploughteams. For them, the ratio was set at 2,000, the largest ratio for estates with non-zero ploughteams being 1,376. 9 The exact location of Easton is unknown, so it is not marked on the map, Figure 4.2. 10 To increase expected cell numbers and ensure non-zero frequencies, for the tenants-in-chief test only data for the estates of the ten largest tenants-in-chief were used, and the inefficient and very inefficient categories amalgamated; for hundreds, only data for hundreds with more than twenty-two estates were used and the inefficient and very inefficient categories amalgamated; for tenure, the sub-tenant categories were amalgamated; and, for the estates grouped by size independence test, the large and very large categories were amalgamated. 11 The probit method is described by Amemiya (1984), Greene (1993), Judge et al. (1985) and Maddala (1983, 1992). As Maddala (1992:332) indicates, there is a problem with the use of conventional ‘goodness of fit’ measures (such as R2 and ) when the dependent variable takes on only two values (zero or one). This is because the dependent variable predicted values are probabilities, but the actual dependent variable values either zero or one. A number of goodness of fit measures have been suggested, none of which are entirely satisfactory. We report Count R2 values, which are the proportion of correct predictions. (The predicted value is judged correct if, when the actual dependent variable value is one, the predicted value is greater than 0.5; and, when the dependent variable is zero, the predicted value is less than 0.5.) 12 The test was carried out by regressing the efficiency measure, u−l on dummy variables indicating which tenant-inchief held each estate and whether the estate was held in demesne. (The index u−1, rather than u, was used as the

NOTES

13

14

15

16 17

211

dependent variable because this resulted in more homoskedastic disturbances.) The null hypothesis was that the regression coefficients for the twenty-seven tenants-in-chief who held some estates in demesne and some not in demesne were equal. The test statistic, in large samples approximately distributed as an F distribution with 27 and 439 degrees of freedom when the null is true, took the value 2.129, significant at the 1 per cent level. Diagnostic tests indicated that the disturbances in the u−1 regressions were homoskedastic. For example, in the first regression of u−1 on binary variables indicating the tenant-in-chief of the estate, when the residuals squared were regressed on the (dependent variable) predicted values, the Chi-square test statistic (with one degree of freedom) was 0.025 (not significant at the 1 per cent level). An alternative statistical model to the u−1 regressions is the censored normal regression, or tobit, model. However, this model implicitly assumes that the relationship that determines the probability of an estate being efficient is the same as that that determines the degree of inefficiency given that the estate is inefficient: a testable hypothesis which was rejected at the 1 per cent level in all cases. (See Greene, 1993: 700–1, for details of the test.) u−l was the dependent variable in the regression. The tenant-in-chief in demesne effect was modelled by nineteen binary variables, one for each of the eighteen tenants-in-chief holding ten or more estates in Essex (the binary variables taking the value one, if the tenant-in-chief held the estate in demesne; zero otherwise) and one binary variable for the remaining tenants-in-chief (taking the value one, if one of these tenants-in-chief held the estate in demesne; zero otherwise); the intercept accounted for estates not held in demesne. The hundred effect was modelled by twenty-one binary variables, each associated with a hundred (taking the value one, if the estate was located in the hundred; zero otherwise); Thurstable hundred was accounted for by the intercept. The Colchester/ Maldon influence effect was modelled by two binary variables; the first taking the value one, if the estate was located within a 6-mile radius of Colchester; zero otherwise; and the other taking the value one, if the estate was located within a 6-mile radius of Maldon; zero otherwise. The economic size indicator was the logarithm of the estate’s annual value, and the kind of agriculture carried out was measured by the estate’s grazing/arable ratio. The geographical (soil) region effect was modelled by two binary variables, the first taking the value one, if the estate was located in the Boulder Clay Plateau region; zero otherwise; and the second taking the value one, if the estate was located in the London Clay Area; zero otherwise; the intercept accounting for the third soil region. The ancillary resources were measured quantitatively (by the number on the estate). Diagnostic tests indicated no significant heteroskedasticity in the disturbances. For example, when the squared residuals were regressed on the (dependent variable) predicted values, the Chi-square test statistic (with one degree of freedom) was 2.881 (not significant at the 5 per cent level). The statistics in Tables 4.9 and 4.10 give a good indication of the quantitative effect of the tenant-in-chief in demesne and hundred effects. The economic size indicator regression coefficient indicated that a large estate (with an annual value of 150 shillings) had, on average, a u-index value 0.543 smaller than a small estate (with an annual value of 20 shillings). Estates with relatively more grazing activity tended to be more efficient, an estate relatively specialized in grazing (with a grazing/arable ratio of 1,000, a value exceeded by only six estates) had, on average, a u-index value 0.243 less than an estate with no livestock. An estate with a mill had, on average, a u-index value 0.104 greater than an estate without a mill. u−1 was the dependent variable in the alternative specification. The tenant-in-chief effect was modelled by eighteen binary variables, one for each of the tenants-in-chief with more than ten estates in Essex (a binary variable taking the value one, if the tenant-in-chief held the estate; zero otherwise). The intercept accounted for the case when an estate was held by one of the tenants-in-chief with less than ten estates in Essex. The tenure effect was modelled by a binary variable taking the value one, if the estate was held in demesne; zero otherwise. The other effects were modelled as in the preferred specification. In this regression, there was no evidence of heteroskedasticity in the disturbances, and quantitative effects were similar to those for the preferred specification. In an alternative analysis in which information on ancillary resources was not used (see McDonald, 1997) similar conclusions were reached. Of course, the situation may have been different in 1066. Unfortunately, the coverage and quality of the 1066 data does not encourage repeating the exercise for that year.

212

PRODUCTION EFFICIENCY IN DOMESDAY ENGLAND

18 The ploughteams variable, P, was set equal to (the number of demesne ploughteams) +1/6 (the number of peasants’ ploughteams). Denoting frontier annual value by V*, V*/P was regressed on P. The intercept was 55.08 (t ratio 14.8) and slope estimate 1.60 (t ratio 1.2; not significant at the 5 per cent level). Diagnostic tests indicated no significant heteroskedasticity in the disturbances. A plot of V*/P against P indicated that the regression summarised the relationship well.

5 AN ALTERNATIVE NON-FRONTIER EFFICIENCY ANALYSIS 1 A Cobb-Douglas functional relationship was specified linking annual value to the resources. 2 This brief review of efficiency measurement methods can be supplemented by referring to the excellent survey articles of Førsund, Lovell and Schmidt (1980) and Schmidt (1986), which contain more detail on methods and applications, and an extensive list of references. Other useful surveys are Bauer (1990), Greene (1991) and Seiford and Thrall (1990); see also the other references given in Section 5.1. 3 Computational problems can arise if resource variable values are not positive, so a small number (1/6) was added to all resource values. This has a negligible effect on the results (see Mosteller and Tukey, 1977:112, for values reported relate to the Box-Cox equation (5.1) and hence discussion of this ‘starting’ procedure). The are not comparable with those given in Domesday Economy. Diagnostic tests (described in Domesday Economy: 8.12) indicated no significant heteroskedasticity in the disturbances. 4 The choice of soil region to compare the others against does not affect the test of joint significance of the soil region location effects, or, if care is taken in interpretation, other inferences. 5 The F test statistic =(RSS0−RSSA)(n-k)/(RSSA.H), where RSS0 is the residual sum of squares when the null hypothesis is imposed, RSSA the residual sum of squares when the alternative hypothesis is estimated, H(=18) the number of restrictions imposed under the null hypothesis and k(=31) the number of parameters estimated under the alternative hypothesis. When the null hypothesis is true and n is large, the test statistic distribution can be approximated by an F distribution with H(=18) and n−k(=546) degrees of freedom. 6 Since the economic size of an estate was measured by its annual value, and this is the dependent variable in the production function regression, size of the estate was not introduced as a production factor. The elasticity of scale gives an indication of how size of the estate influenced production. 7 The tenant-in-chief in demesne effect was modelled by nineteen binary variables, one for each of the eighteen tenants-in-chief holding ten or more estates in Essex (the binary variables taking the value one, if the tenant-in-chief held the estate in demesne; zero otherwise) and one binary variable for the remaining tenants-in-chief (taking the value one, if one of these tenants-in-chief held the estate in demesne; zero otherwise); the intercept accounted for estates not held in demesne. The hundred effect was modelled by twenty-one binary variables, each associated with a hundred (taking the value one, if the estate was located in the hundred; zero otherwise); Thurstable hundred was accounted for by the intercept. The Colchester/Maldon effect was modelled by two binary variables; the first taking the value one, if the estate was located within a 6-mile radius of Colchester; zero otherwise; and the other taking the value one, if the estate was located within a 6-mile radius of Maldon; zero otherwise. The geographical (soil) region effect was modelled by two binary variables, the first taking the value one, if the estate was located in the Boulder Clay Plateau region; zero otherwise; and the second taking the value one, if the estate was located in the London Clay Area; zero otherwise; the intercept accounting for the third soil region. The quantitative effects of ancillary factors and resources were similar to those reported earlier. 8 The tenant-in-chief effect was modelled by eighteen binary variables, one for each of the tenants-in-chief with more than ten estates in Essex (a binary variable taking the value one, if the tenant-in-chief held the estate in demesne; zero otherwise). The intercept accounted for the case when an estate was held by one of the tenants-inchief with less than ten estates in Essex. The tenure effect was modelled by a binary variable taking the value one, if the estate was held in demesne; zero otherwise. The other effects were modelled as in the preferred specification.

NOTES

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9 Referring to Weeley’s Domesday Book entry, Round comments in a note (Victoria History of Essex, Vol. I, p. 495): ‘This enormous rise in value seems to be unaccounted for’. And referring to the entry for Bircho he says (p. 470): ‘This is a remarkable instance of a manor on which the ploughteams had decreased from 3 to 2, while all the other livestock had disappeared, being valued nearly 50 per cent higher than it was before!’ 10 Other studies in which efficiency has been examined by using more than one technique include Banker, Charnes, Cooper and Maindiratta (1988), and Bowlin, Charnes, Cooper and Sherman (1985), both using artificial data; and Byrnes, Färe, Grosskopf and Lovell (1988), and Ferrier and Lovell (1990), who used real world data. In some studies similar results were obtained with the different techniques, in others the results were widely different. Differences may arise because one (or both) analysis is carried out unsatisfactorily (inappropriate assumptions or inferences being made). Differences can also arise because efficiency is measured from different referencepoints. For example, in the mathematical programming (DEA) analysis the reference is the frontier (generated by extreme behaviour), but in the Constant Elasticity of Substitution production function analysis it is average behaviour. Ferrier and Lovell (1990), Charnes, Cooper and Sueyoshi (1988), and Evans and Heckman (1988) discuss these issues. 11 The Constant Elasticity of Substitution production function provides estimated resource marginal products, but they are not comparable with the resource shadow prices described in Chapter 4. This is because the marginal products measure average actual productivity, while the shadow prices measure potential productivity, that is, productivity when the estates are run efficiently. For the Constant Elasticity of Substitution production function, when resource levels are equal, the ratio of resource marginal products (at a given output level) equals the ratio of the resource parameters. The parameter estimates suggest that villan and slave marginal products exceeded the bordar marginal product, but the villan marginal product was greater than the slave marginal product.

6 EXTENSIONS, COMPARISONS AND CONCLUSIONS 1 Farrell (1957:262) introduced the idea of comparing the structural efficiency of industries. 2 Farrell (1957), Schmidt (1986: esp. 318–20), Byrnes et al. (1988), and Ferrier and Lovell (1990) consider the problem of making comparisons. See also the references in Ferrier and Lovell (1990). 3 Actual total output is ΣVi=A, total output when estates are run efficiently is ΣViui=E where ui is the u-value for the ith estate. The percentage increase if all estates had been run efficiently is (E-A). 100/A. 4 Snooks (1995:41, for example) states ‘Although the commodity market was well developed by the late eleventh century, factor markets in labour, land and capital appear to have been very restricted in scope’; and again, p. 54: ‘In 1086 commodity markets were well established but factor markets were in their infancy.’ 5 Woodland (1982: 70–9) provides an excellent discussion of the Factor Price Equalization Theorem, which he states in the following terms: ‘If two or more nations have the same cost functions (technology), face the same product prices, produce the same M* products, and have their endowment vectors in the interior of the same cone of diversification, then each nation will have the same factor price vector.’ In relation to this statement, the following should be noted. First, it is assumed that the common technology has the characteristics of constant returns to scale and free disposability of factors. Second, product prices may be expected to vary if there are impediments to trade, transport costs, non-traded goods and endogenous factor supplies. Third, M* is endogenously determined, and this statement of the theorem requires the nations to produce the same products: and, fourth, the cone of diversification is the set of factor endowments that can be fully used in producing the M* products, so the theorem imposes restrictions on technology and the factor endowments that each nation has. 6 Unfortunately, as far as we are aware, similar calculations of the loss in output due to input rigidities for other economies have not been made, so empirical comparisons with other economies are not possible. Certainly, it would be incorrect to argue that a 40 per cent increase in output could have been achieved under an alternative economic system, because some input inflexibility exists in all systems. Until estimates of the cost of input inflexibility for other systems are made, we can only speculate as to what the gains might have been.

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7 The test was carried out by regressing the BHI on tenant-in-chief binary variables, taking the value one, if the tenant-in-chief held the estate; zero otherwise. Since the regression diagnostics indicated heteroskedasticity in the disturbances, H.White’s (1980) heteroskedasticity-consistent test was used. On the null, when the sample size is large, the test statistic is asymptotically distributed as an F distribution with 18 and 555 degrees of freedom. The test statistic value was 4.293, significant at the 1 per cent level. 8 The test was carried out in a similar way to the test for equality of the tenant-in-chief means (using White’s method; see previous note). The test statistic value (in large samples approximately F distributed with 21 and 552 degrees of freedom on the null) was 11.085, significant at the 1 per cent level. 9 In Specification A, the estate’s tenant-in-chief was indicated by eighteen binary variables (the ith, i=1…18, taking the value one, if the ith largest tenant-in-chief held the estate; zero otherwise; the intercept measuring the effect when none of the eighteen largest tenants-in-chief held the estate), and the hundred location by twenty-one binary variables (with the intercept measuring the effect of location in Thurstable hundred). The effect of proximity to an urban centre was measured by a binary variable, taking the value one, if the estate was in an approximate 6-mile radius of Colchester or Maldon (allowing for topography); zero otherwise. The economic size indicator was the logarithm of the estate’s annual value and the kind of agriculture effect was measured by the grazing/arable ratio. The tenure effect was measured by a binary variable taking the value one, when the estate was held in demesne; zero otherwise. In Specification B, the tenant-in-chief in demesne effect was measured by nineteen binary variables (the ith, i=1…18, taking the value one, if the ith largest tenant-in-chief held the estate in demesne; zero otherwise; the nineteenth taking the value one, if one of the other tenants-inchief held the estate in demesne; zero otherwise, the intercept measuring the effect when an estate was not held in demesne). 10 An alternative approach is to measure beneficial hidation from an estimated average tax relationship (this is analogous to the Constant Elasticity of Substitution production function approach of Chapter 5). The empirical analysis described in Domesday Economy: chapter 4 suggests a log-linear relationship between manorial tax assessments and annual values. When the logarithm of tax assessments was related to the variables of Specification A and Specification B, results similar to those described here were obtained. The logarithm of annual value, the tenant-in-chief in demesne, tenant-in-chief, tenure and urban centre effects were significant, and other variables and effects not significant. Tax assessments increased with annual value, were higher for estates held in demesne and closer to an urban centre, and similar tenant-in-chief and hundred effects were obtained, thus confirming the BHI multivariate regression results given here.

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INDEX

acreage under cultivation 6 administration 2–6, 57, 144 Afriat, S. 30, 116 Aigner, D.J. 115–16, 133 Alan of Brittany, Count 76–7, 124–5, 129, 148, 157 Alecto Historical Editions 11 algebraic search procedures 44 algorithms for input to linear programming 68, 161–6 Almesteda manor 9–10 America see United States of America American Civil War 134–5 ancillary resources 65, 92, 95, 103, 120–9 passim, 157–8 annual values of estates 1, 11–13, 48–9, 61–2, 65, 90, 103– 5, 115 arable land see grazing/arable ratio Ardleigh estate 127

Box, G.E.P. 119 Box Plot diagrams 134–5 Brazil 133 Britnell, R.H. 143 Bury St Edmunds, Abbey of 6 Byrnes, P. 15, 36–41, 134, 137 Cam, River 58 Campbell, M.S. 143 capacity-to-pay 3, 144, 155 Charnes, A. 114, 117, 133 Chelmer, River 58, 63 Chepstow Castle 5 Chiang, A.C. 44 Chisenhale-Marsh, T.C. 58 Chi-square distribution and test 94, 109 Chu, S.F. 115–16 Church, the 5 Clare (Suffolk) 61 Clare, Richard of see Richard, son of Count Gilbert clustering of estates 81, 157 Cnut, King of England 4 coalmining 134, 137–8, 159 Cobb-Douglas production function 115–19, 132 Colchester 58, 61, 85, 88–94 passim, 102–3, 125–9, 141, 155, 157 Colne, River 58 competitive firms 18–23 congestion inefficiencies 34, 36, 38–40 Conrad, R.F. 133 Constant Elasticity of Substitution function 119–21, 124, 126, 128–9, 158 constant returns to scale (CRS) 15–17, 30–40 passim, 47, 51–4, 108, 113, 141; see also CS technology; CW technology contingency table test 92, 157

Bagi, F.S. 118, 132–3 Baignard, Ralf 71, 77, 152, 159 Banker, R.D. 117, 133 banking 133 Bauer, P. 114 beehives 9, 62–6 passim, 92, 103, 112, 126, 154, 156–8 beneficial hidation index (BHI) 144–56 passim, 159–60; values of 200–14 Bessent, A. and W. 133 Bigot, Roger 70 binary variables 120, 126–7, 154 Bircho estate 127, 223n bivariate relationships 101–2 Blackwater estuary 58, 63, 71 Blunts Hall estate 75 Boland, I. 117 bookland 139–40 boon-work 12, 139 bordars 9, 12, 61, 66, 105–8, 139, 159 boroughs 6 222

INDEX

contours 20, 25, 42–3 contractual relationships 12, 107–8, 139 Cook, T.J. 133 Cooper, W.W. 114, 117, 133 Corby 6 Cornwell, C. 133 corrected least squares estimates 116–17 cost contours 20 counties see shires Cox, D.R. 119 Crouch, River 58 CS technology (Constant returns, Strong disposability) 36– 9, 47–57, 67–8, 108–9, 112, 127, 129, 134–7, 142, 156– 8, 167–91 CW technology (Constant returns, Weak disposability) 36, 39, 53–4, 57, 67, 108 dairy industry 133 Danegeld 143 Dantzig, G.B. 44 dapifer, Eudo 71, 77, 124–5, 127, 129, 152, 157, 159 Darby, H.C. 58, 61–3, 65 data envelopment analysis (DEA) 114, 117 de Ferrariis, Henry 100, 157 de Limes, Ralf 65 de Magna Villa (or de Mandeville), Geoffrey 65, 76–7, 124, 127, 129, 148, 157 de Merc, Adelolf 71 de Montfort, Hugh 100, 152, 159 de Otburville, Roger 100 de Ramis, Roger 100, 124–5, 129, 152, 157, 159 de Valognes, Peter 65, 100, 124–5, 129, 157 de Ver, Aubrey 124–5, 129 de Warene, William 76–7, 124, 127, 129 decomposition of inefficiency 36–40 decreasing returns to scale (DRS) 32, 38 demesne, estates held in see tenure demesnes 12, 139 Desai, A. 117 deterministic methods of analysis 114–15, 118 ‘Devastation of the North’ 4–5 disposability of resources 17, 115; see also strong disposability; weak disposability Dogramaci, A. 114 Domesday Book, original and copies of 10–11 Domesday Economy (book) 1–3, 12–14, 114–19 passim, 143–4, 154 Domesday survey:

223

circuits 6–8, 10; methods of collection and accuracy of data 1, 9, 62, 64–5; purposes and uses of 1, 6, 11; types of information collected and not collected 29, 63–4, 147 Down estate 71, 75 dual and primal problems 44–6, 55–6 dual theory 117 Durham Cathedral 5 East Donyland estate 75 Easton estate 71, 220n economic conditions 5–6, 11–13 economic (in)efficiency see overall (in)efficiency educational programmes, study of efficiency in 133 Edward the Confessor 4 efficiency: case studies of 132–3; descriptive analysis of factors associated with 57, 76– 92; determinants of 2, 29–30, 115, 139; historical comparisons of 136–7; input- and output-based approaches to 26; measurement of 15–37, 67, 114–17, 132–4; statistical analysis of factors associated with 92–104; structure of 131–4, 138, 159; variations in 30, 68–73; see also inefficiency efficiency analysis 13–14, 157 efficiency value see u-values Egypt 132 elasticity of substitution 13, 16 electrical power generation 133 Elmstead estate 9, 76, 127 Ely Abbey 9, 58 Emma of Normandy 4 entrepreneurial roles 103, 158 Epping Forest 61 Epstein, M.K. 114 errors in data 18, 115–16 Essex: geographical situation of 57–61; valuation of property in 61–2 Ethelred, King 143 Eustace of Boulogne, Count 68, 71, 75, 77, 100, 124–5, 127, 129, 148 Exchequer Domesday 10

224

INDEX

F-test statistic 124 facsimiles of Domesday Book 11 factor immobility 140–3, 159 Factor Price Equalization Theorem 140, 223–4n Färe, R. 15, 32–4, 36–41, 51, 114, 134, 137 Farley text of Domesday Book 11 Farrell, M.J. 3, 115, 132–3 feasible solutions 41 Ferrier, G.D. 133 feudal system 3, 5–6, 131, 139, 141, 143, 159 Fieldhouse, M. 133 Finn, R.W. 58, 64–5 fisheries 58, 62–7, 92, 126–7, 154–7 Fitz Wimarc, Robert 9 Fitzgilbert, Richard see Richard, son of Count Gilbert five-hide pattern of tax assessment 144 floor-tile making 132 Fobbing estate 68, 70, 76, 147 forest land 63 Førsund, F.R. 114, 133 France 3–4, 133 free disposability of resources see disposability freemen 12, 61, 66, 105, 107, 139 Fried, H.O. 114 frontier, concept of 2; see also production frontiers; stochastic frontiers; taxation frontiers Gabrielson, A. 116 Gale, D. 44 geld 12, 143, 155 geographical position see spatial location government see administration grazing/arable ratio 70, 90, 95, 102, 104, 109, 112, 123–9 passim, 154, 158 Great Chishall 58 Great Domesday 8, 10–11 Greene, W.H. 116, 133 Greno, Robert 100, 124–5, 129, 152, 157, 159 Grosskopf, S. 15, 32–4, 36–41, 51, 114, 134, 137 Hadley, G. 44 Hainault Forest 61 Hall, A.R. 3, 134–5 Hall, B.F. 134, 136 Hamilton, N.E.S.A. 9 Hamshere, J.D. 144 Härdle, W. 117

Hardrada, King of Norway 4 Harold I and Harold II, Kings of England 4–5 Harthacnut, King of England 4 Harvey, S.P.J. 64 Hastings, Battle of 4–5 Henderson, J.C. 114 Henry I, King of England 5 Hjalmarsson, L. 133 home farms see demesnes homoskedastic disturbances 100 horses 65–6, 219n hospital production, study of efficiency in 133 Huang, C.J. 118, 132–3 hundred location of estates 82–4, 94, 100–3, 125–9, 153– 60 hundreds 5, 60–1 increasing returns to scale (IRS) 38, 90, 112–13 India 133 Indonesia 133 inefficiency 18–30; decomposition of 36–40; see also efficiency; input-allocative (in)efficiency; overall (in)efficiency; scale economies; technical (in)efficiency input-allocative (in)efficiency 19–23, 27, 29, 133, 135 Inquisitio Eliensis 8, 58, 64 intensity variables 48–53, 146 Iraq 133 isoquants 20 Jansen, E.S. 133 John, son of Waleram 125, 159 Jondow, J. 117 juries 8, 10 Kalirijan, K. 133 Koopmans, T.C. 32–3, 44, 52 Kopp, R.J. 117, 133 labour services 12, 139 Lancaster, K. 44 Land, K.C. 117 Langemeier, L.N. see Thompson, R.G. et al. Lau, L.J. 118 Lawford estate 127 Lawling manor 71

INDEX

Lea Valley 58, 63 least squares estimates 116–17, 119 Leaver, R.A. 144 Lee, C.T. and E. see Thompson, R.G. et al. Lee, L.-F. 118, 133 Leibenstein, H. 132 LeVeen, E.P. 136 Levric, William 65 Levy, V. 133 Lewin, A. 114, 133 LIMDEP (computer program) 117 LINDO (computer program) 44, 161 linear programming (LP) 17, 41–4, 67, 115, 146 linearisation 119 Little Chishall 58 Little Domesday Book 10–11, 58, 63–4: extract from 74 livestock 219n loanland 140 London 5–6, 58, 61, 63 Lovell, C.A.K. 15, 32–4, 36–41, 51, 114, 116–17, 133–4, 137 Ludlow Castle 5 McDonald, John 144 Maitland, F.W. 61, 64 Maldon (estate) 71 Maldon (town) 61, 71, 85–94 passim, 102–3, 125–9, 141, 155, 157 manorial court profits 219n manorialism 3, 5–6, 131, 139, 141, 143, 159 manpower of estates 66, 126 manufacturing, studies of efficiency in 133 market centres 83; see also towns Materov, I.S. 117 maximization and minimization see objective functions maximum likelihood estimates 116–17 meadowland 9, 58, 63, 66, 105, 154, 156, 159 Meeusen, W. 116, 133 mesne-tenants 62, 139; see also tenure Michaelstow estate 71, 75 mills 9, 62–3, 65–6, 92, 103, 126–7, 154, 156–8 minimum-cost production 22–3 minor activities of estates see ancillary activities mobility of resources 140–3 Morey, R.C. 133 Mullahy, J. 117, 133

225

multivariate analysis 101–3, 112–13, 126, 155, 158–60 N’Gbo, A.G.M. 117 Niuetuna estate 65 ‘noise’, statistical 116–17 non-frontier methods of analysis 117 non-increasing returns to scale (NIRS) 32–4, 37–8, 51–2 non-negativity conditions 41–2, 55–6 non-parametric methods of analysis 114 Norman Conquest 3–5, 57; see also administration Norway 133 Norwich 5–6 Nunamaker, T.R. 114 objective functions 41–2 open fields 6 opportunity costs see shadow prices optimal feasible solutions (OFSs) 41–3, 54–6 Ordish, G. 64 output-allocative (in)efficiency 25–9, 136 output value contours 25 overall (in)efficiency 26, 133, 136 Paglesham estate 75–6 Pant, River 58, 63 pasture 13, 63, 66, 219n Pearson’s contingency table test 92, 157 peasants 5–6, 11–12, 61, 139 Pebmarsh manor 70, 127 Peverel, Ranulf 75, 100, 125, 129, 157 Phillimore edition of Domesday Book 11 Phincingefelda manor 65 Pinkse, C.A.P. 117 Pitt, M.M. 118, 133 ploughteams 9, 62, 104–5, 112, 126, 158, 220n; absence of 65–6 Polhey estate 127 population 61 price data 117–18 price inefficiency see input-allocative inefficiency probit analysis 94–7, 100, 112, 157, 220n production efficiency see efficiency production frontiers 2–3, 13, 15, 18, 25, 28, 30, 48, 51–3, 90, 114, 116, 156, 217–18n, 220n; empirically based 32, 34; locally and globally determined 32 production function study compared with CS efficiency study 128–31

226

INDEX

production functions 3, 13, 16; flexible form of 13; see also Cobb-Douglas; Constant Elasticity production possibility sets (PPSs) 17, 24–5, 28, 31, 33, 36, 47–53 production processes 1, 11–14; assumptions about 15, 29; characteristics of 23, 29; combinations of 30–2, 47, 76; hypothetical 23–6 productivity see efficiency productivity gap 36 profit maximisation 18, 22–3, 216–17n Public Record Office 11 pulp manufacture 133 Radwinter estate 152 rational economic agents 12 Reaney, P.H. 58 regression analysis 18, 100–3, 112–13, 118, 126, 144, 155, 158–60 rents 12, 62, 140 resampling techniques 117 returns to scale 13, 115, 158; see also constant returns; decreasing returns; increasing returns; non-increasing returns Rhodes, E. 133 Richard, son of Count Gilbert 76–7, 100, 124–5, 129, 152, 159 Richmond, J. 116 Richmond Castle 5 Rickwood, G. 58 rivers 7, 58 Robert, son of Corbutio 124–5, 129, 152, 159 Rochford hundred 61 Round, J.H. 58, 61, 64, 71, 76, 143–4, 152 Russell, J.C. 61 St Albans Abbey 5 saltpans 9, 58, 62–6, 92, 103, 112, 126, 154, 156–8 scale economies and scale efficiencies 22–3, 27, 36, 38– 40, 90; see also returns to scale Schinnar, A.P. 117 Schmidt, P. 114, 116–18, 133 Schmidt, S.S. 114

schools, study of efficiency in 133 Scilchecham manor 65 Scale, J.L. 132 Seiford, L.M. 114, 133 semi-parametric methods of analysis 117 serfs see slaves shadow prices 17, 32, 41, 44–6, 55, 57, 104–8, 141–2, 158; variation in 104–5, 108, 131, 139, 159 SHAZAM (computer program) 161 sheep 104, 158 sheriffs 5–6; see also Suen shires 5–7 Shortgrove estate 71, 75 Sickles, R.C. 133 significance tests 93, 100 Silkmans, R.H. 114 Simar, L. 117 simplex method 44 simultaneity 13 size of estates 70, 90, 94, 102–3, 112–13, 154–8, 160 ‘slack’ resources 17, 31–2, 41, 45–6, 55, 57, 105–7, 131, 139, 159 slaves 5–6, 9, 61, 66, 105, 107, 139, 158–9; freeing of 107–8, 134–5, 159 Snooks, Graeme 1, 12, 104, 144, 154 soil, effect on efficiency of 104, 125–9, 157–8 sokemen 12, 61, 66, 105, 107, 139 Southwark 61 spatial location: impact on efficiency 80–3; see also hundred location; towns Stanstead Abbots 61 Staplefort manor 65 stochastic frontiers 116, 132 Stort, River 58 Stour, River 58, 63 Strauss, R.P. 133 strong disposability of resources 15, 17, 34–6; see also CS technology; VS technology sub-tenants 62, 139; see also tenure substitution between resources 13, 16, 46, 140 Sudbury 61 Suen, Sheriff of Essex 9–10, 65, 71, 77, 100, 124–5, 129 Sueyoshi, T. 114

INDEX

Sun, D.B. 133 Sweden 133 Symonds, G.H. 117 Taindena manor 65 tax assessment 143–4, 147, 153–4, 156; favourable see beneficial hidation index tax assessment frontiers 2, 13, 144–8, 156, 159 technical (in)efficiency 18–29 passim, 36, 38, 40, 136 tenants-in-chief 5, 11, 62, 70–1, 77–81, 90–103 passim, 123–9, 139, 144, 148, 152–60 Tendring(e) 9, 58, 63, 71, 127 tenure 90, 95, 98–103 passim, 125, 129, 139, 148, 154–60 passim tests of significance 93, 100 Thames Valley 58 Thompson, R.G. et al. 133 Thore, S. 117 Thrall, R. 114; see also Thompson, R.G. et al. Thurstable estate 125, 129 Timmer, C.P. 116, 118 Toleshunta manor 65 towns, influence of nearness to 83–94 passim, 102–4, 125– 9, 140–1, 154–7, 160 trade 12, 139–41, 143, 159 Tyler, W.G. 133 u-values (ratios of maximum to actual value) 17, 32–6, 47– 54, 68, 95, 100, 108, 130, 132; associated with CS, VS, CW and VW technologies 192–9 u-1 values 134–6, 143 Union of Mine Workers of America (UMWA) 137 United States of America 3, 132–7 passim, 159 V-values see annual values of estates value added 12–13, 61 value per square mile or per person 62 van den Boeck, J. 116, 133 variable returns to scale (VRS) 30–4, 37–8, 50–1 Varian, H.R. 117 Victoria County History 9, 11, 58, 71, 152 villans 9, 12, 61, 66, 105, 108, 139, 158–9 villeins see villains vineyards 62–5, 67, 92, 126, 154, 156–7 VS technology (Variable returns, Strong disposability) 36, 38, 57, 67, 90, 108, 111, 113, 134, 137, 158

VW technology (Variable returns, Weak disposability) 36, 38–9, 57, 67, 108–9, 134, 137 Waltham (estate) 125, 129 Waltham (hundred) 61 weak disposability of resources 17, 34–6; see also CW technology; VW technology weaving industry 133 week-work 12, 139 Weeley estate 127, 223n White Tower, London 5 William the Conqueror 3–6, 11, 64 Winchester 5–6, 61 Windsor Castle 6 Winstree hundred 61 Witham estate 71 woodland 9, 58, 63, 66, 219n; see also forest land Woodland, A.D. 140 York 6 Yotopoulos, P.A. 118 z-values see intensity variables

227