Valuation methods and policy making in environmental economics

VALUATION METHODS AND POLICY MAKING IN ENVIRONMENTAL ECONOMICS

Studies in Environmental Science Other volumes in this series

1 Atmospheric Pollution 1978 edited by M.M. Benarie 2 Air Pollution Reference Measurement Methods and Systems edited by T. Schneider, H.W. de Koning and L.J. Brasser

3 Biogeochemical Cycling of Mineral-Forming Elements edited by P.A. Trudinger and D.J. Swaine

4 Potential Industrial Carcinogens and Mutagens by L. Fishbein 5 Industrial Waste Management by S.E. Jeirgensen 6 Trade and Environment: A Theoretical Enquiry by H. Siebert, J. Eichberger, R. Gronych and R . Pethig

7 Field Worker Exposure during Pesticide Application edited by W.F. Tordoir and E A.H. van Heernstra-Lequin

8 Atmospheric Pollution 1980 edited by M.M. Benarie 9 Energetics and Technology of Biological Elimination of Wastes edited by G . Milazzo

10 Bioengineering, Thermal Physiology and Comfort edited by K. Cena and J.A. Clark

1 1 Atmospheric Chemistry. Fundamental Aspects by E. MBszaros 12 Water Supply and Health edited by H. van Lelyveld and B.C.J. Zoeteman 13 Man under Vibration. Suffering and Protection edited by G. Bianchi, K.V. Frolov and A. Oledzki

14 Principles of Environmental Science and Technology by S.E. Jorgensen and I. Johnsen

15 Disposal of Radioactive Wastes by Z. Dlouhv 16 Mankind and Energy edited by A . Blanc-Lapierre 17 Quality of Groundwater edited by W. van Duijvenbooden, P. Glasbergen and H. van Lelyveld

18 Education and Safe Handling in Pesticide Application edited by E.A.H. van HeemstraLequin and W F. Tordoir

19 Physicochemical Methods for Water and Wastewater Treatment edited by 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

L. Pawlowski Atmospheric Pollution 1982 edited by M . M . Benarie Air Pollution by Nitrogen Oxides edited by T. Schneider and L. Grant Environmental Radioanalysis by H.A. Das, A. Faanhof and H.A. van der Sloot Chemistry for Protection of the Environment edited by L. Pawlowski, A.J. Verdier and W . J Lacy Determination and Assessment of Pesticide Exposure edited by M . Siewierski The Biosphere: Problems and Solutions edited by T.". VeziroQlu Chemical Events in the Atmosphere and their Impact on the Environment edited by G.B. Marini-Bettolo Fluoride Research 1985 edited by H. Tsunoda and Ming-Ho Yu Algal Biofouling edited by L.V. Evans and K.D. Hoagland Chemistry for Protection of the Environment 1985 edited by L. Pawlowski, G. Alaerts and W.J. Lacy Acidification and its Policy Implications edited by T. Schneider Teratogens: Chemicals which Cause Birth Defects edited by V. Kolb Meyers Pesticide Chemistry by G. Matolcsy, M. Nadasy and V. Andriska Principles of Environmental Science and Technology (second revised edition) by S.E. Jsrgensen Chemistry for Protection of the Environment 1987 edited by L. Pawlowski, E. Mentasti W . J . Lacy and C. Sarzanini Atmospheric Ozone Research and its Policy Implications edited by T. Schneider, S.D. Lee, G J . R . Wolters and L.D. Grant

Studies in Environmental Science 36

VALUATION METHODS AND POLICY MAKING IN ENVIRONMENTAL ECONOMICS Selected and integrated papers from the Congress "Environmental Policy in a Market Economy" Wageningen,The Netherlands, 8-1 1 September 1987

Edited by

H. Folmer and E. van lerland Vakgroep Staathuishoudkunde, Landbouwuniversiteit Wageningen, De Leeuwenborch, Hollandseweg 1, Wageningen, The Netherlands

E LSEVlER AMSTERDAM - OXFORD - NEW YORK - TOKYO

1989

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0Elsevier Science Publishers B.V., 1989 All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying. recording or otherwise, without the prior written permission of the publisher. Elsevier Science Publishers B V / Physical Sciences & Engineering Division, P 0 Box 330, 1000 AH Amsterdam, The Netherlands Special regulations for readers in the USA -This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred t o the publisher. No responsibility is assumed by the Publisher for any injury and/or damage t o persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein Printed in The Netherlands

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VII

PREFACE

Society today is confronted with environmental problems caused by continually increasing economic activities. Various side effects of production and consumption have turned out to be very harmful to the environment. The emission of toxic substances into the atmosphere, soil and water do not only cause serious forms of local toxification but also damage the environment at a gIobaZ scale. Similarly, environmental damages are often both acute and long-lasting. The external effects of economic activities have turned out to be of such importance that free market forces in the absence of environmental public policy will lead to large scale and irreversible environmental damage. In their attempts to control environmental problems public authorities are forced with the need to consider, inter alia, the valuation of the environment, risk and life; to develop instruments and frameworks of policy and to obtain insight into the costs and benefits of specific environmental projects or environmental policies. In the present volume some valuation methods and some aspects of cost benefit analysis

and policy making in environmental economics are considered in depth. The volume is made up of a set of coherent papers presented by experts at the international conference "Environmental Policy in a Market Economy" held at the Wageningen Agricultural University, the Netherlands, 8-11 September 1987. Related publications are: F.J. Dietz and W.J. Hcijman (eds.), Environmental Policy in a Market Economy, Pudoc, Wageningen, 1988 and J.J. Krabbe (ed.) Principles of Environmental Policy, Special issue, International Journal ojSociaI Economics, Vol. 15, Nrs. 314, 1988. The financial support for the meeting from the Ministry of Agriculture, the Advisory Council for Research on Nature and Environment (RMNO) and the Wageningen Agricultural Universily, as well as the financial support for this publication from the Foundation 'LEB

VIII fonds' is gratefully acknowledged. Finally, thanks are due to Adri Kooijman, Jos Michel and Ineke Lammerse for their conscientious secretarial work in organizing this volume. The book should not only appeal to students and researchers in university departments of economics and "environmental sciences" but also to those working in public organizati-

ons and associated advisory institutes which are concerned with environmental problems. We wish that this volume may contribute to better valuation techniques for non-market assets and an improvement of environmental cost benefit analysis and policy making techniques. We also wish that it may stimulate an active policy to protect the environment.

Wageningen, December 1988 HenkFolmer

Ekko van Ierland

IX

CONTENTS

PREFACE

1. VALUATION METHODS AND POLICY MAKING IN ENVIRONMENTAL ECONOMICS: RELEVANCE AND SCOPE Henk Folmer and Ekko van Ierland

Part I

1

The Valuation of Public Goods 13 2. NON-MARKET ASSET PRICES: A COMPARISON OF THREE VALUATION APPROACHES 15 Ralph C. d'Arge and Jason F. Shogren

3. VALUING PUBLIC GOODS IN A RISKY WORLD: AN EXPERIMENT 37 Per-Olov Johansson 4. RECREATIONAL VALUES, PARETO OPTIMALITY AND TIMBER SUPPLY 49 Per-Olov Johansson, Karl-Gustaf Lofgren and Karl-Goran Maler

5. ESTIMATING SOCIAL BENEFITS OF ENVIRONMENTAL IMPROVEMENTS FROM REDUCED ACID RAIN DEPOSITION A CONTINGENT VALUATION SURVEY 69 St&e Navrud Part I1

The Valuation of Health and Life 103 6. BENEFITS OF REDUCED MORBIDITY FROM AIR POLLUTION CONTROL A SURVEY 105 Mark Dickie and Shelby Gerking

7. VALUING A PUBLIC GOOD: DIRECT AND INDIRECT VALUATION APPROACHES TO THE MEASUREMENT OF THE BENEFITS FROM AIR POLLUTION ABATEMENT 123 Mordechai Shechter, Moshe Kim and Lorette Golm 8. ENVIRONMENTAL REGULATION AND THE VALUATION OF LIFE: INTERINDUSTRY MOBILITY AND THE MARKET PRICE OF SAFETY 139 Henry W. Herzog Jr. and Alan M. Schlottmann

X Part I11

Cost Benefit Analysis 159

9. DISEQUILIBRIUM COST BENEFIT RULES: AN EXPOSITION AND EXTENSION 161 Per-Olov Johansson and Karl-Gustaf Lofgren 10. MACROECONOMIC COST BENEFIT ANALYSIS O F ENVIRONMENTAL PROGRAMMES 187 Andries Nentjes

Part IV

Aspects of Policy Making 217 11. BENEFIT ESTIMATION FOR COMPLEX POLICIES 219

Alan Randall and John Hoehn 12. THE ACID RAIN GAME 231 Karl-Goran Mder

INDEX 253

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Chapter 1 VALUATION METHODS AND POLICY MAKING IN ENVIRONMENTAL. ECONOMICS: RELEVANCE AND SCOPE HENK FOLMER AND EKKO VAN IERLAND Department of General Economics, Wageningen Agricultural University, P.O. Box 8130,6700 EW Wageningen (The Netherlands) 1 INTRODUCTION

The history of economic thought shows an increasing interest in environmental issues1. First, classical and neoclassical theory did not pay attention to environmental problems except to the availability and quality of land for agriculture and for the location of various economic activities in space, as well as to the exploitation of natural resources. The interaction between the environment and the economic process in general, in particular environmental degradation, were not fully recognized. Hence, the environment was mainly viewed as a common property resource i.e. a free good with no price attached to it. Moreover, in as far as the exhaustibility of the natural resources was recognized, it

was believed that technical progress and market forces would solve the problem. Governmental intervention was considered to be superfluous or even detrimental. At the second stage, the exhaustibility of natural resources as well as the existence of external costs resulting from pollution associated with private production and consumption was recognized. Population and per capita income growth as well as the introduction of new polluting techniques were causing substantial environmental damage and a rapid depletion of natural resources. These historical events led to new developments in economic theory. The theoretical foundation for externalities was laid by Pigou (1920), Kapp (1950) and Baumol (1952). Hotelling (1931) paid attention to the optimal rate of exploitation of natural resources. In the realm of economic policy the recognition of externalities led to the imposition of various regulations with regard to production and consumption activities.

In the present paper the notion of environment includes natural resource endowments.

2

The thud stage is characterised by the recognition of the need for sustainable economic development and environmental protection as a separate target for economic policy.2 Moreover, the functions the environment fulfils for other economic activities (i.e. public consumption good3, production factor and receptacle of wastes) are being more thoroughly understood, In particular, the competition between these functions has become apparent. Finally, the (literally) perilous consequences of the neglect of the role of the environment and the enormous offers to restore environmental degradation have become clear4 The irreversibility of ecological damage is recognised as well as the danger that harmful effects, for example climatic change, will only become evident after long time lags. Also the need to preserve the natural environment for future generations is generally accepted. The recognition of environmental degradation and the incorporation of environmental preservation in the set of goals of economic policy has created an important problem to economic sciences viz. to develop methods to integrate the environment in the decisionmaking process on the allocation of factors of production and distribution of goods and services among individuals. In this respect the valuation of the environment will play an important role. The fact that the environment was viewed as a common-property resource The difference between the second and third stages can be illustrated as follows. At the second stage, impacts of economic activities on the environment were viewed as externalities and side-effects. This resulted in subordination of environmental preservation to the economic goals of full employment, stable price level, stable exchange rate, etc. This subordination found expression, irtter alia, in the economic policy of the late 1970s and 1980s which gave priority to employment growth above environmental policy. In fact, pollution control was believed to have a severe impact on the economy, making the production of goods and services more costly and slowing down economic growth, especially because of excessive costs of regulations and regulatory delays. Moreover, the positive effects of environmental policy were viewed primarily in non-environmental terms. For instance, Peskin et al (1981) argues that pollution control improves economic growth because it increases the health and productivity of the population and provides jobs in the pollution control industry that partially or fully offset losses in production. At the third stage environmental preservation is considered as a goal equal to the other goals of economic policy. It has become quite apparent that the environment satisfies basic human needs (e.g. health) and therefore is of the same order as food and shelter.

Since the late 1960s and the early 1970s it is generally recognized that the environment has become a scarce commodity which corresponds with the visions of the second and third stages distinguished above. It should be observed, however, that elements of neo-classical theory fit quite well into the environmental policies advocated at these stages. As an example we refer to the fact that incentives are viewed as more efficient instruments of environmental policy than regulations in many circumstances.

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implied a zero price for the environment. This zero price produced a discrepancy between private costs, consisting of the costs of factor inputs of the individual firm, and social costs comprising all costs (i.e. private costs and negative externalities in other sectors of the economy than the individual firm). The zero price of the environment implies that the prices of goods which are produced with a high pollution intensity do not reflect their environmental nuisance. Consequently, the prices of these goods are too low, which implies that the demand and production of the pollution-intensive goods are too high. This has three different allocation effects: (i)

The distortion of the actual relative prices leads to overproduction of pollutionintensive products.

(ii)

Environmental degradation because of the overuse of the common property resource.

(iii) Incorrect trade-off between the goals of economic policy. Summarizing, with a zero price for environmental use, the economic system does not include control mechanisms to check an overuse of the environment and a distortion of the sectoral structure. Hence, an important contribution of economics to a solution to the environmental problem would be the transformation of environmental scarcity to signals which would start off this control mechanism. As the environment is a public good, the market cannot provide ‘these signals in the form of prices. Therefore, one has to rely upon alternative methods such as the specification of a shadow price for pollutants and the public goods and property rights approaches. 5 In the present volume some aspects of the transformation of environmental scarcity into signals for the control mechanism viz. the determination of appropriate monetary values for environmental goods and services will be dealt with. Moreover, some related aspects, viz. macroeconomic cost benefit analysis and disequilibrium social cost benefit analysis, will be paid attention to. Finally, multi-component policy making and the international contestation of transfrontier air pollution will be discussed. In the next section the various chapters of this volume will be introduced. In the last section some conclusions will be drawn and some issues for further research will be presented.

For an excellent comprehensive treatment of the reduction of the divergence of private and social costs and the introduction of an institutional framework for market economies to attribute all costs of economic activities to the individual unit see Siebert (1987).

4

2 OUTLINE OF THE VOLUME

This volume is made up of four parts. The fist two parts (Part I and 11) deal with the problem of valuation of environmental goods and services. It is well-known that social welfare change may be assumed to be expressed through the willingness to pay as revealed through market prices, provided that a market exists. In the case of environmental goods and services, however, there is no market. Therefore, alternative methods to

assess the willingness to pay have been developed. The following categories can be distinguished (see also Maer (1985) and Freeman (1985)):

- Direct market values methods which derive the damages caused by environmental degradation from e.g. relocation cost, changes in productivity, loss of earnings, etc.

- Contingent valuation methods which are based on individual's responses (via questionnaires or experiments) to hypothetical exposure to environmentel changes.

- Hedonic pricing methods which analyze surrogate markets in which environmental quality is indirectly reflected.

-

Methods based on observable changes in the non-market behaviour of individuals as a consequence of environmental changes. In part I attention is paid to the valuation of public goods whereas in Part I1 the

valuation of health and life is dealt with. Moreover, various propositions derived from economic theory which form the underpinning of the contingent valuation and hedonic pricing methods are tested.6 In chapter 2 Ralph d'Arge and Jason Shogren compare three different valuation

techniques by examining an active and well defined market for water quality in the lakes region of Iowa. Differences in assessed valuations of residences at two glacial lakes are analyzed. The lakes are very similar from a visual and locational perspective, but differ markedly with regard to recreation based water quality. The three valuation techniques are:

-

A site valuation based on comparing property values between the two lakes. A market valuation by asking a sample of refitors and real estate agents in the area to

identrfy causes for the observed price differential between the lakes.

- A contingent valuation approach using a limited sample of site dwellers to estimate their

The first and fourth category of methods are not dealt with in this volume.

5

willingness to pay for improved water quality and their willingness to accept compensation for a decrease in water quality. Five measures of water quality are developed and tested. The measures are (i)

realtor’s best estimate.

(ii)

Imputed value from regression on lake frontage for each lake separately.

(iii) (iv)

Imputed value from pooled regression.7 Willingness to pay.

(v)

Willingness to accept. On the basis of economic theory five propositions concerning the measures of water

quality are derived. In most cases the propositions were confirmed, with substantial qualifications. In particular, the first three estimated measures were found to be rather close, and, as predicted by theory, to exceed the estimated willingness to pay. The willingness to accept compensation was found to be the smallest measure, contrary to expectation.8 In chapter 3 by Per-Olov Johansson two basic issues are addressed - The willingness to pay for more than a single change in the preservation of endangered

species.

- The examination of the possibilities and limitations of questionnaire techniques in determining the willingness to pay for public goods in a risky world. Five different money measures of the value of preserving endangered species are derived from economic theory. Most of the results are consistent with the theoretical predictions. In particular, the willingness to pay is increasing in the number of saved species. Moreover, an interesting difference in risk attitudes between male and female respondents turns out. For female respondents the data set suggests risk aversion with respect to the considered public good. Male respondents, on the other hand, seem to express risk aversion only if many species become extinct while they are more inclined to accept risky outcomes if just a few species are threatened. The author argues that there is also a possibility that respondents are unable to calculate ex ante compensating variation Assessed valuation by realtors was the dependent variable. Because of resistance by residents at both lakes to accept compensation, it cannot be concluded that any adequate test was indeed accomplished. For an explication of the substantial discrepancy usually found in empirical studies between willingness to pay and willingness to accept we refer to, among others, Knetsch (1984).

6

measures and therefore report some other money measure when the situation involves uncertain outcomes. When the previous two chapters consider valuation aspects as measured by the contingent valuation method, Per-Olov Johansson, Karl-Gustav Lofgren and Karl-Goran Mder in chapter 4 analyze the problem of the multiple use management of public (and private) forest land i.e. recreation and commercial exploitation by harvesting the trees. Under the assumption that the environmental services can be treated as a public good and that the general equilibrium prices for public goods are known, it is shown that the social optimization problem can be decentralized by adding an environmental component to the ordinary present value problem. Next it is shown how the augmented present value maximizing problem, containing the demand determined shadow prices of forest land in different age classes, can be solved. The properties of the present value function are derived and it is shown when and why an efficiency criterion on the intertemporal supply of timber may be violated. Finally, attention is paid to the problem how to find the

shadow or pseudo-equilibrium prices. The last chapter of Part I is a case study. Stdle Navrud presents a contingent valuation study of the expected marginal increase in the freshwater fish populations in Norway due to reduced acid depositions and a detailed description of the organization of the survey and the questionnaire that was used.

The annual social economic value of marginal increments in the freshwater fish populations in Southern Norway, due to a reduction of 30-70 per cent in the European sulphur emissions, was estimated to be 450 million 1986-NOK. This result was elicited from a national contingent valuation survey of a representative sample of more than 2,000 Norwegian households. Non-use values constituted the major part of this amount, and only 12 per cent was motivated by recreational value of fishing.

The estimate of 450 million 1986-NOK is considered to be conservative, and must be interpreted as nothing else than an approximate size of the values involved. This is due to uncertainties in the valuation method and the dose-response function used to calculate the reduced damage to the fish populations. However, the study provides evidence for the large social economic values of environmental improvements that can be achieved by reductions in long range transported air pollutants. Part I1 deals with the evaluation of health and life. Although it is a rather new field in environmental economics, this issue has increasingly been gaining interest since the physical impacts of pollution on health and life have become more evident.

7

In chapter 6 Mark Dickie and Shelby Gerking present a survey of methods to analyze benefits of reduced morbidity from air pollution control. Three methods are discussed in detail:

- The costs of illness method. - The contingent valuation method. - The averting behaviour method. The essence and the advantages and disadvantages of each method are described. Moreover, some important case studies are discussed. The valuation of morbidity reduction due to pollution abatement is studied by means of a contingent valuation method and via a hedonic pricing method by Mordechai Shechter, Moshe Kim and Lorette Golan. In the latter case measures of welfare change are derived through an expenditure function (and the associated indirect utility function, presumed to represent preferences for the various market and non-market goods), which underlie the estimated demand system. The empirical application of both approaches is based on individual household data, obtained through a large-scale household survey conducted in Israel during 1986-1987. The results indicate that both approaches yield reasonably close estimates of welfare changes, and thus may provide additional justification and support for the use of contingent valuation methods in dealing with non-market goods, such as air quality. Valuation of risk in the workplace is studied by Henry Herzog and Alan Schlottmann within the context of compensating wage differentials. The theory of compensating wages suggests that jobs with disagreeable characteristics will command higher wages, ceteris paribus. Empirical tests of this theory have found such compensation to indeed exist. Studies of compensating wage differentials attributable to risk in the workplace usually assume that workers’ willingness to pay for risk reduction is equal to the market price of providing this reduction. Hence, workers and their employers are assumed to possess perfect information regarding work hazards, the cost of providing additional safetey, etc. Thus evaluations of the wage-risk trade-off will vary to the extent that the market price diverges from workers’ willingness to pay. Via the analysis of inter-industry mobility in the U.S. the willingness to pay is shown to exceed the market price for incremental safety substantially. Part I11 deals with cost-benefit analysis. The two papers which make up this part are surprisingly complementary. Per-Olov Johansson and Karl-Gustav Lofgren derive disequillibrium social cost-benefit rules for two typical disequilibrium situations: classical and

8

Keynesianen unemployment. To derive the social cost-benefit rules, an intertemporal multisector model with endogenous private invertment is developed. Attention is also paid (probably for the first time in literature) to disequilibrium cost-benefit rules for natural resource projects. Finally, the issue of income distribution is discussed. The commonly employed assumption of a single household is abandoned. In chapter 10 Andries Nentjes presents a unified approach which combines social cost benefit analysis and macroeconomic evaluation. The strengths and weaknesses of both approaches are described. Extensive attention is paid to the definition of costs and benefits in the context of a macro economic model, to modelling the finance decision and environmental expenditure and the economic regime and opportunity costs. Finally, the potential contributions of macroeconomic cost-benefit analysis to the existing methodolo-

gy for evaluating the environmenl is discussed. Part IV deals with two important aspects of policy making. In chapter 11 Alan Randall and John Hoehn analyze benefit estimation for complex policies. Where policy has several components, the benefits of the complex policy are in general not equal to the sum of the independently-estimated benefits of its components: complementary and competitive relationships among components are ignored in independent benefit estimation. As the number of policy components grows large, the error from independent evaluation becomes systematic and benefits of the complex policy are overstated. In a general equilibrium context, it is shown that independent estimation of benefits and costs of the components leads to a systematic break-down of the benefit cost filter: some non-net-beneficial complex policies and some non-net-beneficial policy components pass the filter. Given the invalidity of benefit cost analysis of complex policies by summing independently-estimated component benefits and costs, it is important to define and operationalize valid procedures for benefit cost analysis in a complex policy environment. TWOapproaches have been developed in the paper. First, a holistic ex ante evaluation of the complex policy is valid and may be implemented via contingent valuation. Second, econometric structures have been developed that permit approximately-valid benefit cost analysis of complex policies using independent estimates of component benefits and costs as the starting point. These approximation procedures facilitate the use of estimation methods based on, for example, weak complementarity and hedonic price theory for evaluating complex policies, The last chapter by Karl-Goran Mder deals with policy-making in an international

9

incomplete information and with many players (nations) with no agreed rules of the game. Some basic concepts of game theory are described and applied in the European context. The simulations refer to the net benefits from the full cooperative solution, the Pareto dominant outcome and coalition formation.

3 CONCLUSIONS AND TOPICS FOR FURTHER RESEARCH On the basis of the various chapters in this book some important conclusions and

recommendations for further research could be formulated.

(i) In the absence of prices, the valuation of environmental goods and services is of crucial importance in the context of environmental policy making. The optimal allocation of the production factors labour, capital and environment depends on the correct valuation of the environment, given correct prices for labour and capital.

(ii) A multitude of valuation techniques has been developed and is presently available. They can be divided into four categories: direct and surrogate market methods, contingent valuation techniques and methods based on observable changes in the non-market behaviour. In terms of reliability, completeness and data requirements no unambiguous ordering of these four categories is possible. In this volume special attention has been paid to contingent valuation methods. The degree of completeness achievable by this method (e.g. user and non-user values, dimensions of the value involved) is at the disposal of the researcher and is not limited by the (given) structure of the direct or surrogate markets. However, it requires primary data collection and therefore may be costly and time consuming. It is shown in this volume that the contingent valuation method may contribute to environmental valuation. Various sources of bias, however, need to be taken into account (see chapter 5, section 2). Moreover, results may be obtained which are not consistent with economic theory. The following ways to improve the performance of the contingent valuation method suggest themselves. First, some of the sources of bias might be handled by improving the experimental setting or the design of the questionnaire. In this respect advantage should be taken of recent results obtained in psychology and sociology. Secondly, inconsistencies may not only result from inadequacies of the research methods applied but also from theoretical inadequacy. As suggested by chapter 3, where the empirical results were found to contradict standard utility theory and to be consistent

10

with the Friedman-Savage theory, inconsistencies could be removed by searching for more adequate theoretical foundations. Finally, if there is the possibility of a choice between direct or surrogate market methods on the one hand and contingent valuation on the other the former should be preferred because they suffer less from methodological weaknesses. Moreover, applying different techniques may provide insight into the

robustness of the results. (iii) In the context of cost benefit analysis the introduction of disequilibrium notions and of frameworks to handle complex policies and multiple and conflicting uses of environmental goods and services proved to be a major improvement of this technique which plays such an important role in environmental policy making. From the chapters 4, 9-10 it follows that a self-evident topic for further research is the integration of disequilibrium, multiple use and complex policies within a comprehensive theoretical framework. Moreover, empirical studies are needed in which the various theoretical issues have been operationalized. (iv) It has become generally recognized that emissions usually have an international dimension and that efficient and effective pollution abatement requires international cooperation. Various principles of international environmental policy have been developed. In spite of that, international pollution abatement is still in its infancy, partly because of insufficient insight into the international dimensions of emissions and pollution. Therefore, an important issue for further research is the analysis of the relationships between economic activities, emissions and damages in an international perspective. As shown in chapter 12 game theory may provide substantial insight into the process

of environmental policy making. Moreover, the outcomes of simulations on the basis of game theoretical notions may provide valuable information for international negations. As game theory itself is a field in rapid development an important topic for further

research will be the application of new game theoretical results in international environmental policy making. Other important research issues are made up’ by the specific problems of environmental policy makiig which are not at the core of mainstream game theory. The conclusions formulated above refer particularly to the economic valuation of the environment. We are aware of the fact that many environmental problems cannot be dealt with by mere valuation of non-market assets. For example, environmental preservation for future generations and the avoidance of dramatic climatic changes due to human action

11

require other and in particular additional methods than those discussed in this volume. For example, scenario studies and economic ecological models may contribute to a better understanding of the interactions between the economic process and the natural environment. However, we are convinced that the political process of revealing collective preferences will - and should - play an important role in environmental policy-making. For this purpose we believe the valuation methods discussed in this volume to be useful tools to provide information about the environmental preferences of the public. The obtained information should be taken into account in political decision-making, together with all other suitable information. REFERENCES Baumol, W.J., 1952. Welfare Economics and the Theory of the State. London. Freeman, A.M., 1985. Methods for Assessing the Benefits of Environmental Programs. In: Kneese, A.V. and J.L. Sweeney (Eds) Handbook of Natural Resource and Energy Economics. North Holland, Amsterdam. Hotelling, H., 1931. The Economics of Exhaustible Resources. Journal of Political Economy, 39. Kapp, K.W., 1950. The Social Costs of Private Enterprise. Spokesman, Nottingham. Knetsch, J.L., 1984. Legal Rules and the Basis for Evaluating Economic Losses. International Review of Law and Economics 4,5-13. Maler, K.G., 1985. Welfare Economics and the Environment. In: Kneese, A.V. and J.L. Sweeney (Eds), Handbook of Natural Resource and Energy Economics. North Holland, Amsterdam. Pigou, A.C., 1920. The Economics of Welfare. London. Peskin, H.M., Portney, P.R. and Kneese A.V. (Eds), 1981. Symposium on "Environmental Regulation and the U.S. Economy. Natural Resource Journal 21,441-587. Siebert, H., 1.987.Economics of the Environment. Springer, Berlin.

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part I

The Valuation of Public Goods

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Chapter 2 NON-MARKET*ASSET PRICES: A COMPARISON OF THREE VALUATION APPROACHES RALPH C. d’ARGE and JASON F. SHOGREN Department of Economics, University of Wyoming, Laramie, Wyoming, USA, 87070-3985, and Department of Economics, Appalachian State University, Boone, North Carolina, USA, 28608, respectively. 1 INTRODUCTION

With the growing research in the valuation of environmental commodities, recent studies have attempted to compare differing experiments and valuation techniques. Schulze, et al. (1981) compared six valuation experiments. However, the study was limited by relatively distinct locations and environmental attributes.

Brookshire, et al. (1982)

contrasted results from application of the contingent valuation method and the hedonic method in Los Angeles County. Although the locations were consistent in this study, the definition of the environmental commodity might have varied substantially across locations because of differences in the mix of health and aesthetic effects. Both the Desvousges, et al. (1983) and Seller, et al. (1985) comparative analyses focused on valuation techniques for water quality.

These experiments may have been hindered by only partial or

incomplete knowledge of the commodity by those revealing their environmental preferences. This paper attempts to take the comparison of valuation techniques one step further by examining an active and well-defmed market for an environmental commodity and comparing alternative measurement methods for this commodity. Three valuation techniques are examined and compared for water quality problems in the Okoboji Lakes region of Iowa. The three techniques are: 1. a site valuation based on comparing property values between two adjacent lakes, 2. a market valuation by asking a sample of realtors and real estate agents in the area to identdy causes for the observed price differential between the lakes, and 3. a contingent valuation approach using a

* The authors thank He& Folmer and Ekko van Ierland for helpful comments. Part of this research was funded through a grant to the University of Wyoming by the United States Environmental Protection Agency, No. CR808893-02-1.

16

limited sample of site dwellers to estimate their willingness to pay for improved water quality. The paper proceeds as follows. Section 2 examines the Okoboji Lakes region experiments in detail.

Section 3 introduces the theoretical framework for comparing these

valuation techniques. Section 4 discusses the methodology and empirical results. Section 5 contains our tentative conclusions. 2 SITE DESCRIPTION AND BACKGROUND The site selected for detailed analysis are the two glacial lakes called West Okoboji and East Okoboji in northwest Iowa. The lakes are connected by a shallow canal and are very similar from a visual and locational perspective. Each offers about the same mix of water based recreation activities and there is almost unlimited and costless substitution between them except for site advantages. However, they differ markedly in one group of characteristics, namely, recreation based water quality. East Okoboji is more shallow and has a relatively greater waste input from agricultural and natural runoff. Consequently, during part of the summer recreational months (typically more than 30 days) East Okoboji supports dense blooms of algae resulting in a lime green color and noticeable odor from decaying algae. Alternatively, West Okoboji rarely (less than five days) has a noticeable algae bloom with turbidity and is typically characterized as clean in the summer months. Historically, real estate development has proceeded with substantial second home development on West Okoboji commencing in the early 1900's and proceeding to current times. The development of East Okoboji has proceeded at a slower pace. The average assessed valuation per residence for West Okoboji in 1983 was $161,716 and average square feet, 2,152 per residence.

For East Okoboji, the average assessed valuation was only

$61,484 and a typical residence, 1,415 square feet. There is substantial difference in total valuation and value per square foot at the two locations. Given that East Okoboji has been a less desirable location because of water quality, land values have been lower, development occurred at a slower pace, and lower priced housing was erected. Given the historical development, substitutability between the lakes, and current community awareness, the Okoboji lake region is an active and well-defined market for an environmental commodity. A Well-defined market where the respondents are familiar with the commodity is an essential part of any environmental valuation experiment (see Brookshire and Crocker (1981)).

However, one conceptual problem with inter-lake

comDarisons is that individuals with Dreferences for hieher water oualitv have located at

17

West Okoboji while those with lesser preferences for water quality or a greater preference for a particular mix of recreation activities have located on the East lake. In consequence, the observed difference in values between the lakes may partially be determined by differences in preference. 3 THEORY AND PROPOSITIONS

This section will introduce a simple theoretical framework necessary for comparing the valuation techniques. A diagrammatical representation will be developed which yields a set of testable propositions. In order to examine preferences, a simple utility maximization model is proposed here. (1) U(C,W) is the individual utility function where c is the composite commodity presumed unrelated

to water based recreation and w a measure of water quality. It is assumed U, > 0, Uw > 0, Ucc, U,

5 0; and Ucw 2 or c 0 where subscripts denote relevant partial

derivatives. The utility function (1)is subject to the budget constraint

Y - c - R ' w 2 0,

(2)

where Y denotes disposable personal income, the price of the composite commodity is assumed to be 1, and the individual takes the rent or cost paid for water quality as given, and equal to R. Taking the fist-order Kuhn-Tucker conditions for this simple model, one obtains

8L

-

=

uc-x 5 0 ,

c 2 0 , c(aL/ac) = 0

ac

(3)

8L - = Uw -XR
dw The optimal interior solution for the maximization problem when the rental gradient is not dependent on water quality is represented by

-UW _ UC

- R,

(5)

which is a common result observed in studies on environmental quality and housing values. (See for example, Freeman (1979) and Brookshire, et al. (1982)). It states that in equilibrium, the rational purchaser of property will equate the marginal rate of substituti-

18

on between water quality and consumption with the “rent gradient” associated with locations differentiated by a unique level of water.

The rent gradient reflects the

individual’s marginal implicit price for water quality in the housing market. (See Rosen (1974) for a complete discussion of rent gradients.) In this case the rent gradient will be linear since the individual’s purchase of improved water quality (by purchases of a new site) has no impact on the housing market equilibrium with respect to water quality or other housing characteristics. Figure 1 illustrates this simple model, and is a simplified modifcation of the graphical representation in Brookshire, et al. (1982). Let line aa represent the rent gradient where the quantity of the composite commodity c is on the abscissa and the level of water quality w is on the ordinate. Point A is the equilibrium point suggested by equation (5). The individual utility curve U, is tangent to the budget constraint or the rent gradient, line aa. However, if R is a rent gradient for property which depends on water quality (net of effects from other characteristics of housing) and the individual can adjust by changing

Commodity

AC

uW

2

/T=Rf A

AR2

ARI

1

-b

W

2

Fig. 1. Rent gradient and comDensating surdus.

W

1

a’

a

Water Q u a l i t y

w

19

location, then R w needs to be rewritten as R(w) and (4) changes to aL

- = Uw - XRw 2 0,

w 1 0, w(aL/&)

= 0,

aw and equation (5) changes to

UW

- = .,R

(7)

UC In equation (7), the purchaser, by his actions in the housing market, influences the "price" of water quality as reflected by the rent gradient. The purchaser could influence the "price" (1) if the individual decides to purchase more water quality by locating or relocating at the cleaner lake, he will shift demand for the water quality upward, thereby raising its price, and (2) given a small or "thin" property market, the buyer may make an offer below the seller's price, thereby pressuring the "price" downward. In a relatively small residential market such as the Lake Okoboji area, single sales may in fact influence housing prices, especially for relatively high priced vacation homes (there are less than

100 high-priced vacation homes on both lakes). If the purchaser can influence the "price" then the appropriate rent gradient would be concave downward such as line aa' in Figure 1. Given the purchaser may or may not influence the "price" of water quality, and if the market for housing has typical characteristics in terms of supply and demand, the rent gradient (budget constraint) shall be either linear (line aa) or concave downward (line aa'). Consider now the two rent gradients in terms of a change in water quality. Using the theoretical framework and Figure 1, a set of five testable propositions are developed. First, in Figure 1, Acl measures the income loss (in commodity terms) that would leave the individual at the same utility level as before the change in water quality (Awl), the AR1 measures the changes in rent along the rent gradient involved by a change in water quality Awl. As demonstrated by Schulze, et al. (1981), among others, AR1 > Acl if the typical properties of indifference curves hold and the rent gradient is not somehow extremely distorted. This result also holds if the rent gradient is concave downward (aa'). Therefore, we would anticipate that observed prices paid or inferred from assessor's valuations for higher water quality derived from a hedonic price equation would normally

20

exceed estimates of marginal willingness to pay. Alternatively, amounts of compensation ( A d necessary to maintain individual utility with reduced water quality (Awd would substantially exceed estimates derived from the rental gradient ( A R d or property value differentials. The relationship between the linear rent gradient (line aa) and individual valuations can be described by Proposition 1. Given the assumptions of the model, (a) a decrease in water quality

Propositionl.

&plies an individual's minimum willingness to accept compensation exceeds or equals the implicit price as reflected by a linear rent gradient.

(b) An increase in water quality implies an individual's

maximum willingness to pay is exceeded by or equals the implicit price of the linear rent gradient. a) Ac, 2 AR2 and b) AR1 2 Acl Second, note further that in Figure 1 for improvements in water quality (Awl), if the purchaser does influence the rent gradient through inducing a higher "price" for water quality, or if the "price" of water quality increases as one moves to a cleaner and A

clearer site (AR I), the resulting observed hedonic rent estimates will overstate willingness A

to pay by even more than if the gradient were linear (AR1). In symbols, AR

> AR1.

The bias for rent gradients (hedonic prices) to overestimate marginal willingness to pay is thereby even greater when individual purchasers may influence the demand for an environmental attribute, or where the "price" of water quality is not constant.

This

relationship is described by Proposition 2. PropOsition2.

Given the assiunptions of the model, water quality improvements imply the implicit price derived from the concave downward rent gradient exceeds the implicit price A ,:

derived from

the

linear

rent gradient,

> AR1.

Third, in the case of water quality losses (Awd, it can also be noted that if the A

purchaser does influence the rent gradient (AR 9, the observed hedonic rent estimates will understate compensation by more than a linear rent gradient (AR2). Proposition3.

Given the assumptions of the model, water quality decrements imply the implicit price derived from the linear rent gradient exceeds the implicit h

price derived from the concave downward rent gradient, AR2 > AR 2.

21

Fourth, and finally, due to differences in residential characteristics, a distinct rent gradient can be proposed for each lake. The residents of West Okoboji typically have higher incomes, greater environmental preferences, and a steeper budget line (rent gradient). The residents of East Okoboji typically have a lower income, perhaps less of a preference for water quality, and may confront a less steep budget line (or rent gradient). If we assume that line aa in Figure 1 is the rent gradient for West Okoboji, and given the assumptions stated above, then the rent gradient for East Okoboji would have to lie totally inside line aa and at a less steep angle.

Given the distinct rent gradients, for

small changes in water quality, we would anticipate that the rental gradient would approximate compensation or marginal willingness to pay for each lake. And through competition, at the margin, we would anticipate that the "price" differential between lakes would approximate differences in utility levels of the residents. If this were not the case, individuals could relocate thereby increasing utility in a relatively lumpy housing market. Therefore, we anticipate that the marginal willingness to pay by residents of West Okoboji Lake will exceed that of the residents of East Okoboji. These relationships are described in the following propositions. Proposition 4.

Given the assumptions of the model, for improvements in water quality the marginal willingness to pay by residents of West Okoboji Lake will exceed the marginal willingness to pay by residents at East Okoboji Lake.

Proposition5.

Given the assumptions of the model, the implicit price implied by the rent gradient of West Okoboji will exceed the implicit price implied by the rent gradient of East Okoboji.

These five propositions are partially tested and reported on in Section 4.

Before

proceeding one can make some general inferences about the magnitudes derived from the methods outlined in the introduction. The site valuation method can be biased upward or downward depending on the degree of difference between preferences, income, and rent Sradients confronting the different residents.

The contingent valuation method will be

relatively unbiased if problems of sampling, strategic behavior, information bias, and hypothetical bias are not substantive.

Finally, the market valuation method will be

unbiased unless there are noncompetitive, information, or other natural distortions 3perating on this market.

22

4 THE OKOBOJI EXPERIMENT 4.1 Methodolorn Basic date were collected during the summer and fall of 1984 in the Okoboji Lakes region.

Data was collected for (i) housing assessed valuations,

(ii>

the contingent

valuation experiment, and (iii) realtors and real estate agents response survey (referred to as data (i), (ii), and (iii), respectively). The sample size for the experiment was relatively small, 66 for housing assessed valuation (about 10% of the residences in the Lakes region), 20 for the contingent valuation experiment (3% of households), and 17 realtors and real

estate agents (15% of total agents).’

For data (i) and @), only residences actually

located on one of the lakes were examined. That is, each residence selected had some amount of actual lake frontage?

By only including “residents“, we omit consideration of

individuals forced to relocate because of higher prices, i.e., a “choke“ price. The problem of establishing “choke” price does not arise as it does with travel cost models if our sample adequately reflects all dimensions of the resident population. Therefore, we can avoid the problem of truncation and censoring that lead to biased parameter estimates using ordinary least squares (OM) (see Smith, et al. (1984)). 4.2 Rent Gradient and Willinmess to Pay Results

The three data sources revealed three estimates of the rent gradient associated with different locations differentiated by a unique level of water quality, and two compensating surplus measures of consumer surplus for differences in value per square foot of housing attributable to water quality. Consider each implicit price estimate. First, one measure of the rent gradient is the realtors’ best estimate of price differentials between East and West Okoboji residences. Table 1 illustrates the realtors’ prorated response sheet to the observed difference in water quality between East and West Okoboji. The realtors attributed 46 percent of the difference in housing between

Whether these are adequate samples to represent the area is unclear. Using a single power test suggests that sample size for the contingent valuation method should be 22 (with R2 = .30, number of variables 5, and significance level .OS). For estimating precise benefits of water quality improvements rather than examining methodologies and experimental approaches, probably a larger sample would need to be taken for accuracy in application of the contingent valuation method. Actual frontage ranges from 33 to 150 linear feet.

23

/ABLE 1 tealtors' Prorated Response Data (Percentage of East and West Okoboji Housing Differen:esAttributable to Characteristic). Water Quality Neighborhood and Social Class Beach Access Road Access Nearness to Town Visual Beauty Water Activity Seclusion Other

1%

Total

100%

46% 24% 6% 2% 2% 9% 8% 2%

17 respondents 11.76 average years experience

!ast and West Okoboji to water quality. The next largest percentage was neighborhood Ind social class accounting for 24 percent.

The remaining 30 percent were divided

between beach and road access, nearness to town, visual beauty, water activity, and eclusion. By and large, water quality dominates the differential in housing between East Ind West Okoboji. The realtors' best estimate of rent gradient was estimated as follows. Data (i) was :ollected on most recent sales of private residences on both East and West Okoboji Lake. *he assessed valuation per square foot on West Okoboji Lake (in 1983) was $75.15 and for last Okoboji Lake, $43.483

The average difference in housing square foot assessed

raluation between the lakes was therefore, $31.67. One of the central questions in this )aper is to what extent water quality contributed to this observed differential. According

o the survey of realtors and real estate agents (Data (G)) in the Okoboji area, water

Note, we have used assessed valuation rather than reported sales prices in the iomputation. The reason was that there are likely to be substantial errors in reporting of ales prices for the Okoboji area both because of tax avoidance and the method of eporting. The raw correlation coefficient between assessed valuation and reported sales rices was less than 0.25. Thus, a more accurate measure of "actual" selling price was hought to be assessed valuation.

24

quality differences between the lakes accounted for about 46 percent of this difference.4 From the realtors' perspective, the dominant factor affecting housing prices (adjusted for square footage) was the known difference in water quality.

The realtors' (averaged)

estimate of the losses in valuation due to water quality is 46 percent of $31.67, or $14.57 per square foot for lake front property. Second, a rent gradient was estimated by comparing imputed lake frontage prices. Hedonic types of equations were estimated for West and East Okoboji Lakes separately, see Table 2.

The difference in regression coefficients of feet of lake front equalled

$1,009 per square foot. Using the average measure of lake front, housing square feet, and TABLE 2 Regression Estimates for Property Value Study Experiment: Assessed Valuation.

Dependent Variable

Independent Variables House Age Feet Number Square Total of ofLake Other Constant Feet Rooms House Frontage Bldgs

Assessed Valuation 1983-West Okoboji

44,845 (2.02)*

14.30 (1.80)

3,178 (0.99)

-853 (-3.83)

1,373 (5.18)

10,327 (0.88)

23.20

1,734

17.60 (2.79)

4,623 (2.09)

-457 (-1.97)

364

1,389 (0.23)

12.46 .75

Assessed Valuation 1983-East Okoboji

(.12)

(2.00)

F Stat R2

.78

* Numbers in parentheses are "t" statistics Number of observations was 39 for West Okoboji and 27 for East Okoboji. Degrees of freedom was 33 for West Okoboji and 21 for East Okoboji.

The raw correlation matrix indicates that realtors in the Okoboji area perceive some significant effects on housing prices other than water quality, especially social class, miles to town, and scenic beauty. They tended to increase the share of value allocated to these substantially when decreasing the share to water quality. Thus, there appears to be some substitution between very broad attributes associated with a site in that some realtors place a greater emphasis on characteristics other than water quality in establishing site value and they are negatively related. Interestingly, the longer the realtor was in real estate, the more value that was placed on water quality.

25

realtor's average proportions allocated to water quality, this implies a valuation loss of $12.83 per square foot of dwelling.

Third, a rent gradient was estimated through a pooled estimate based on assessed valuation of differences in housing characteristics, see Table 3. For assessed valuation as a measure of price, the pooled regressions had significant coefficients for square feet of housing, age of house, feet of lake frontage, and most importantly, whether the property was located on East or West Okoboji. An $84,189 difference was observed net of basic housing characteristics.

This amounts to a $39.12 per square foot difference, which is

higher than the $31.67 actual average difference in the sample, but close enough to appear to be reasonable. The pooled regression equation does contain socio-economic variables reflecting neighborhood effects, visual beauty of the site, etc. in the EastWest dummy variable.

In order to account for these factors, the gross difference in terms of the

pooled regression is adjusted yielding a net difference of $29.52. Applying the 46 percent estimate by realtors to the net difference from the pooled regression yielded a square foot valuation of water quality of $13.58, which is very close to realtors' own best estimate ($14.57). It is only slightly higher than the reported value ($12.83) from the differences in lake frontage values. However, all three of the rent gradient estimates are dependent

on the realtor's average allocation of value to water quality attributes. TABLE 3 Pooled Regression Estimates, East and West Okoboji. Independent Variables

Dependent Variable Constant

East or West House Age Feet Number of ofLake Other F West=1 Square Total Rooms House Frontage Bldgs Stat East=O Feet

Assessed Valuation -20,657 (1983) (-1.09)*

84,189 (10.09)

15.93 (2.76)

3,836 (1.83)

-850 1,037 (-5.21) (5.79)

* Numbers in parentheses are "t"statistics. Number of observations was 66. Degrees of freedom: 59.

1,600 (0.22)

66.42

R2

.87

26

The final two measurements of the analysis are based on a limited application of the contingent valuation method (see Durden and Shogren (1988)). A questionnaire utilizing the water quality "ladder" was employed5 Both willingness to pay and willingness to be compensated measures of consumer surplus were elicited from a stratified random sample of residents at both lakes. The willingness to pay measure is equivalent to the compensating surplus measure of consumer surplus, since we are asking how much income the individual will give up (increased property tax) to obtain a specified water quality improvement (see Freeman (1979) and Just, et al. (1982)). Alternatively, they were asked how much they would need in minimum compensation (i.e., reduced property taxes) to be as well off as before given a symmetrical water quality decrease. This is also a compensating surplus since utility is unchanged in either case.

Neither measure is likely to

coincide with equivalent surplus, the "best welfare measure of benefits" (see McKenzie and

The water quality "ladder" was developed by W. Vaughan for Resources For The Future, Inc. (see Vaughan (1981)). The "ladder" is a form of anchoring surveys and is used extensively in water quality benefit analysis. A partial experiment was developed to test whether the water quality "ladder" is a valid approach without serious inherent economic bias. The possible bias arises since accurate value responses from subjective indexes implies that these indices contain distinct and separable activities. This separability allows say, for exact measures of value for an improvement in water quality from "boatable" to "fishable". However, if the indices are not separable, but perceived as complements or substitutes, the response may not accurately measure benefits of water quality improvements. Complementarity or substitutability may bias the willingness to pay response in a downward or upward direction, respectively. A modified ladder was developed that attempts to incorporate the possibility of complementarity and substitutability into the willingness to pay response. Several attempts were made to experiment with the modified ladder and also to test whether the various water based recreation activities identified on the ladder tend to be complementary, substitutes, or neutral. Most individuals responded to identifying whether various water based recreation activities were neutral, substitutes, or complements to them personally. Fishing and boating were highly complemental, while potable water and boating were strongly neutral. It appears the pairs of swimminglffihing, drinkinglswimmiug, and swimminghoating were either complements, substitutes, or neutral depending on the individual. These results are suggestive that as one moves up the water quality ladder, there is at first complementarity (between fishinfloating), then substitution (between swimmingkishing), and fiially, either complementarity or neutrality (between drinking/swimming or swimminghoating). Bids across activity pairs tended to indicate greater neutrality across activities than the questions on identification of how individuals compare pairs of activities. However, the preliminary results are suggestive that the assumption of neutrality in applications of the water quality ladder needs to be either verified through repeated trials or that modifications must occur prior to its use for adequate benefits estimates to be forthcoming. (For more specific results, see d'Arge (1985)).

27

Pierce (1982)). However, for commodities (such as the water quality at the two lakes) that enter regularly, if indirectly, in a market we can presume they would be reasonable close (see Willig (1976)). Average bids by location and pooled across residents were converted to housing value equivalents by using the average residence sue on each lake and a 5 percent real rate of discount6 The adjusted bids by location are shown in Table 4. The bids were requested in dollars per $1,000 assessed valuation. The bids and compensation referenced the same

units as the hedonic regression equations. The mean bids pooled across both East and West Okoboji residents was $6.29 per $1,000 assessed valuation. Average square feet for houses on both lakes equalled 1,851, and the average assessed valuation on both lakes

rABLE 4 Average Imputed Bids or Compensation by Location, Present Value per Square Foot of Housing'. Location of Residence

WTPAl

WPB2

wTPC3

West Okoboji Lake

6.26

3.03

4.69

East Okoboji Lake

6.01

4.31

7.02

*

Presumes a 5 percent real rate of interest (net of inflation) and the appropriate square feet of housing is 2,152 for West Okoboji and 1,425 for East Okoboji, and the average assessed valuation (1983) for West Okoboji is $161,716, and for East Okoboji, $61,484. Willingness to pay in increased property taxes for improved water quality. (From B to A on ladder.) Amount of compensation in reduced property taxes for a decrease in water quality. (From B to C on ladder.) Amount of compensation in reduced property taxes for a decrease in water quality. (From B to D on ladder.) VOTE: Because of differences in weights (average assessed valuation, average square 'eet, sample size) between East and West Okoboji, these estimates are different from hose derived over the pooled sample and reported in Table 5.

Executive order #12291 requires the use of a 10 percent discount rate, but offers he option of using other rates if they can be justified. We just@ the use of a 5 iercent real rate of discount based on the recommended 10 percent discount adjusted for ipercent inflation.

28

equalled $120,700. The average bid per square foot in present value terms for both lakes can be found in Table 5 and is calculated as follows: (Bid/$1,000) * (Average assessed valuation in $1000) = (6.29)(120.7) = $8 20 (r)

'

(Average number of square feet)

(0.05)(1851)

The average bid per square foot is $8.20.7 The willingness to pay measure (compensating surplus) is estimated to be about 56 percent of the realtors' best estimate ($14.57) and approximately 60 percent of the traditional "hedonic" price derived from a pooled OLS regression ($13.58). This is consistent with other researchers' fmdings and the discussion earlier that the rental gradient should exceed marginal willingness to pay (see Feenburg and Mills (1980)). The average compensation bid per square foot was determined in the same fashion as equation (8). The average compensation per square foot, in present value terms, for both lakes equalled $4.34.

Note that the magnitude of compensation is not consistent with

Proposition 1 established earlier. Estimated compensation is less than both the estimated rent gradient and willingness to pay, the exact reverse of Proposition 1. However, it is unlikely that this compensation estimate represents an accurate one. This is due to a 60 percent refusal rate by respondents to be compensated.

Whether this was due to

questionnaire design or inherent problems in eliciting responses for compensation is unclear8 The true estimate is probably at least several times the $4.34 calculated here. We base this statement on the experimental fmding of willingness to accept versus willingness to pay disparities (see for example Knetsch and Sinden (1984)).

This result

also confirms Cummings, et al.'s (1986) argument to use willingness to pay measures, not willingness to accept, when eliciting valuations in contingent markets.

'

This figure presumes the life of the house to be indefinitely large but the contribution to value beyond 100 years is marginal at a 5 percent discount rate. Most of the non-respondents were from the West Lake, while individuals from the East Lake were more prone to provide an estimate. The majority of non-respondents indicated a very large compensation initially or indicated that reduction in water quality was "totally unacceptable", or "ungodlike", or something harmful enough to call in the "National Guard.

29

Table 5 summarizes the results from the comparative analysis. It can be seen that marginal willingness to pay is less than the rental gradient, as is predicted by Proposition 1, but not substantially so. For the Los Angeles experiment, marginal willingness to pay

was only 34 percent of the rent gradient estimate for the sample (see Brookshire, et al. (1982)). Also, the three estimates of the rental gradient are reasonably close together

with the realtors' estimate being the highest. This might be anticipated "ex ante", since realtors would have a strategic incentive to overvalue characteristics of the commodity they are selling. Second, ex ante, we should anticipate these estimates to be relatively close, given that the "commodity" is well defined to residents and has been for at least 30 years. In consequence, residents in the Lake Okoboji area have had a very long history of experience with a distinct and identifiable water quality difference which has not varied substantially over many years. TABLE 5 Comparison of Valuation Benefits. Estimate Derived From

Difference In Value per square foot of Housing

Percent of Percent of Observed Average Realtor's Housing Value Estimate

(1983 $ per sq foot)

(Percent)

(Percent)

Realtors' Best Estimate

14.57

23

Imputed Value from Regression on Lake Frontage*

12.83

20

88

Pooled Regression Estimate Coupled with Realtors' Valuation

13.58

21

93

Imputed Willingness to Pay (Average across Lakes)

8.20

13

56

Imputed Willingness to Accept Compensation (Average across Lakes)

4.34

7

30

* Adjusted for realtors' proportion attributed to water quality.

30

Again, considering Table 4, several tentative observations can be made?

First, the

average marginal willingness to pay for improved water quality by West Okoboji residents exceeds that for East Okoboji residents.

This would be expected since West Okoboji

residents have paid more via the rent gradient for higher water quality. The difference between the two is very small, on the order of 4 percent.

It can be argued that this

result should also be observed. If residents of the cleaner lake were willing to pay much less at the margin for cleaner water than those of the less clean lake, we would expect some degree of relocation between lakes which, according to realtors, has not occurred. This result was not confirmed by an OLS regression applied to the limited contingent valuation experiment, see Table 6.

Given the East-West Dummy variable in the first

equation, the sign of the EOW coefficient indicated that East Okoboji residents’ Willingness to pay is higher than West Okoboji residents’. However, given the low t-statistic, EOW is not a statistically si&icant

predictor of willingness to pay. Judgement should be

weighted accordingly. Finally, observed willingness to be compensated is substantially higher for East Okoboji residents than for those on the West Lake which is consistent with the concept of diminishing marginal utility.

However, the magnitude of compensation is less than

marginal willingness to pay for both lakes which makes no sense from the standpoint of diminishing marginal utility, and is probably indicative that the compensation measures are biased downward as was expected given the lack of replies of the respondents discussed earlier. 4.3 Interpretation of Results Five propositions were proposed in the earlier part of this paper.

Proposition 1

indicated that marginal willingness to pay should be observed to be less than the rental gradient and this was the case, for all measurements of the rental gradient.

However,

the second part of the proposition proposed that the marginal compensation measure should exceed the rental gradient. This was not observed. However, because of resistance by residents at both lakes to accept compensation, it cannot be concluded that any adequate test of this part of the proposition was indeed accomplished.

Because of the small number of observations, these average estimates must be viewed only as illustrations of the magnitudes of marginal compensation and willingness to nav hilt not an definite and nrecine meawren

31

TABLE 6 Ordinary Least Squares Regression Estimates For Experimental Survey. Constant EOW** S A W

SATE NACT

F INCOME STAT R2

WTPA

-4.40 (-.45)*

-3.96 (-1.30)

2.71 (1.68)

0.57 (0.33)

0.62 (0.30)

.0005 (0.34)

1.09

.41

WTPB

-5.12

-3.21 (-2.33)

1.01 (1.46)

0.57 (0.65)

1.48 (1.39)

.0003

1.87

.44

(-.93)

-9.61 (-1.06)

-5.12 (-2.24)

1.88 (1.64)

0.97 (0.65)

2.68 (1.52)

-.00006 (-.04)

1.96

.45

Dependent Variable

WTPC

(0.32)

* Numbers in parentheses are "t" statistics. ** East = 0, West = 1. Number of observations was 20 and included all observations including zero bids and no response recorded as zero. Degrees of freedom is 14 for all regressions. Definition of Variables WTP A

Amount the individual would be willing to pay (in higher property taxes) per year for a designated improvement in water quality.

WTP B

Amount the individual would accept in compensation (in lower property taxes) per year for a designated small reduction in water quality.

WTPC

Amount the individual would accept in compensation (lower property taxes) per year for a designated -reduction in water quality.

EOW

East or West Okoboji Lake; 0 = East, 1 = West.

SAT W

Perceived level of water quality, West Okoboji,

SAT E

Perceived level of water quality, East Okoboji.

NACT

Number of water based activities the individual participate in.

INCOME

Household annual income before taxes.

32

The second proposition was that if individual sales influenced real estate prices, that the actual rental gradient would be steeper than one based on hedonic estimate. If we

take the realtors’ best estimate as the most likely to be close to the actual rental gradient and compare it with the hedonic estimate, we observe then in fact the proposition is accepted.

best estimate.

That is, the hedonic measure of water quality is less than the realtors’ Whether this observation will continue if a true marginal estimate from

realtors was obtained cannot be ascertained given the evidence obtained. Thus, Proposition 2 is accepted, but with substantial caution.

Proposition 2 for water quality reductions.

Proposition 3 was the mirror image of

Since such reductions have not occurred

historically, we are unable to make inferences from the results as to its probable outcome. Proposition 4, that marginal willingness to pay of West Okoboji residents would exceed that of East Okoboji, was observed, both in higher taxes and imputed willingness to pay on housing per square foot basis (rent gradient). Thus, this proposition appears to be

substantially confirmed.

The reverse of this proposition with respect to magnitude of

willingness to be compensated is not supported by the findings of this experiment, but again, may be due to the unreliability of responses to compensation questions. The fifth proposition on rent gradients being substantially different between the two lakes was observed utilizing three distinct methods of estimation.

The first was by

solicitation of estimates from realtors. The second was through imputation of differences in the value of lake frontage between lakes, and the third imputed from the results derived from a pooled regression across both lakes. AU of these measures were reasonably close together which would be expected, ex ante, where water quality had become an accepted and valued commodity.

5 CONCLUSIONS This study developed a comparative analysis of various measures of the benefits from water quality improvements. The experiments are applied in a field context developed for the Lake Okoboji region of Iowa.

These glacial lakes offer a relatively unique set of

characteristics for experimentation since they are connected and have about the same amenities except water quality. Five measures of water quality value are developed and tested including:

realtors’ best estimate, comparison of imputed lake frontage prices, a

pooled regression estimate based on assessed valuation, willingness to pay, and willingness to be compensated; the last two derived utilizing the contingent valuation method on a very limited sample.

As might be expected, the values derived from the‘ different

33

approaches were similar in magnitude, except for the compensation measure. Problems with obtaining valid estimates of compensation were encountered.

However, the other

values might be expected to be similar since an active "implicit" market for water quality through residence site selection has been operating for over 30 years. Five propositions were also tested to find out whether the empirical observations conformed to theoretical expectation. In most cases, the propositions were confiied, with substantial qualificati-

ons. In conclusion, there are four final points to address. First, the valuation experiment in Okoboji examined only user values.

So called nonuser values were not explicitly

examined. Example of nonuser values include option value - the risk premium paid above expected consumer surplus to secure future provision of a desirable environmental state (see Bishop (1982)), existence value - the value individuals place on knowing that some good exists in the environment (kutilla (1967)), and bequest value - the desire of current generations to ensure future generations have access to environmental goods. To obtain a complete ex ante measure of benefits both user and nonuser values should be considered. Our goal was not to obtain a complete ex ante valuation of water quality, rather it was to compare the direct method of the contingent valuation method with the indirect method

of rent gradients.

The direct method can construct hypothetical markets, thereby

capturing nonuser values. Indirect methods, however, do not capture nonuser values since the method is based on current consumption. Therefore, the comparison is based on only user values. Second, the results obtained in the Okoboji experiment arise due to a highly active and an unusually well-defined market for water quality.

Residents have over 30 years

experience in dealing with an environmental commodity with a readily accessible substitute. Given historical development and community awareness, the Okoboji region offers a unique opportunity to examine non-market valuation techniques.

Having said that,

generalizing these site-specific results to other situations of water quality are tentative at best. What needs to be developed is a generalized model that incorporates this and other water quality studies. Such a model would account for more information on si&icant relationships between environmental attributes and implicit or explicit prices that could then be transferred to other sites, local or regional. Third, consider the application of the non-market valuation techniques to other goods. When choosing between non-market valuation techniques, one must recall that all methods make three basic underlying assumptions (d'Arge (1985)). First, all methods assume the

34

underlying axioms of welfare economics are valid or closely approximated.

Second, all

methods presume that the willingness to pay bid is not unique, but can be generalized over time, space, and environmental characteristics.

Third, all methods assume to be

scientifically valid with no potentially damaging biases. How well a method satisfies these assumptions should dictate their acceptance by a cost-benefit practitioner and policy makers. The first assumption is relatively better satisfied by the contingent valuation method for one primary reason.

All methods estimate consumer surplus; the indirect methods

such as rent gradient estimate a Marshallian measure while the direct methods estimate Hicksian equivalent and compensating measures. Recently, economists have preferred the Hicksian equivalent surplus measure since it is a money equivalent of a utility change induced by provision; the closest quantitative measure of changes in utility. If this is the case, then the direct method of contingent valuation would seem to have the advantage. In defense of rent gradient measures, the Marshallian surplus measure will closely approximate the equivalent and compensation measures if the income effect is small (Willig (1976)).

Willig’s argument fails, however, if the provision of improved water

quality induces large implicit price changes, thereby inducing potentially large differences in welfare measures. The second assumption is relatively better satisfied by direct methods due to its greater flexibility. The contingent valuation method can structure the hypothetical market such that time and space are the exact dimensions of the problem at hand.

The rent

gradient, however, is restricted to the time and spatial dimensions of the current sale. Extrapolating beyond those current dimensions is difficult, often leading to oversimplification. The direct method can estimate the nonuser values that capture the individual’s willingness to pay for guaranteed future access by themselves or others.

Although all methods have bias problems, the third assumption is arguably better satisfied by indirect methods.

The biggest asset of rent gradients is its use of actual

market data, while the biggest detraction to contingent valuation is its hypothetical data. Since every environmental good is unique, the valuation technique selected depends on how one ranks the relative importance of these three underlying assumptions. Finally, although tentative, results obtained and presented in Table 5 suggest that from 13 to 23 percent of the residence value (per square foot) is accounted for by water

quality improvements.

This would yield a sizable benefit if it could be translated to

35

the information obtained for jushfying policy decisions. As stated earlier, rather than being a complete ex ante measure of benefits, the importance of the Okoboji experiment to policy makers is the examination of the robustness of techniques to value a non-market commodity such as water quality.

REFERENCES Bishop, R. 1982. Option value: an exposition and extension. Land Economics, 58 p. 115. Brookshire, D. and Crocker, T., 1981. The advantages of contingent valuation methods for benefit-cost analysis. Public Choice, 36(2): 235-252. Brookshire, D., Thayer, M., Schulze, W., and d’Arge, R.C., 1982. Valuing public goods: a comparison of survey and hedonic approaches. American Economic Review, 72(Mar): 165-177. Cohen, J., 1977. Statistical Power Analysis for the Behavior Sciences. New York: Academic Press. Cummings, R., Brookshire, D., and Schulze, W., 1986. Valuing Environmental Goods: A n Assessment of the Contingent Valuation Method. Totowa, NJ: Rowman and Allanheld. d‘Arge, R.C., 1985. Benefit research for environmental quality: an assessment of research needs and a limited quantitative experiment, part 11. Washington, D.C.: US. Environ mental Protection Agency, draft final report. Desvousges, W.H., Smith, V.K., and McGivney, M.P., 1983. A comparison of alFernative approaches for estimating recreation and related benefits of water quality improve ments. Washington, D.C.: U.S. Environmental Protection Agency. Durden, G. and Shogren, J., 1988. Valuing non-market recreation goods: an evaluative survey of the travel cost and contingent valuation methods. The Review of Regional Studies, 18(fall), forthcoming. Feenburg, D. and Mills, E., 1980. Measuring the Benefits of Water Pollution Abatement. New York: Academic Press. Freeman, 111, A.M., 1979. The Benefits of Environmental Improvement: Theory and Practice. Baltimore: The Johns Hopkins University Press for Resources For The Future, Inc. Just, R., Heuth, D., and Schmitz, A., 1982. Applied Welfare Economics and Public Policy. Englewood Cliffs, NJ: Prentice-Hall. Knetsch, J. and Sinden, J., 1984. Willingness to pay and compensation demanded experimental evidence of an unexpected disparity in measure of value. Quarterly Journal of Economics, 99, pp. 507-521. Krutilla, J., 1967. Conservation reconsidered. American Economic Review, 57, pp. 777786. McKenzie, G.W. and Pierce, I.F., 1982. Welfare measurement - a synthesis. American Economic Review, 72(Sept): 669-682. Rosen, S., 1974. Hedonic prices and implicit markets: product differentiation in pure competition. Journal of Political Economy, 82(JanlFeb): 34-55. Schulze, W., d’Arge, R.C., and Brookshire, D., 1981. Valuing environmental commodities: some recent experiments. Land Economics, 57(May): 151-172.

36

Seller, C., Stoll, J.R., and Chavas, J.C., 1985. Validation of empirical measures of welfare changes: a comparison of nonmarket techniques. Land Economics, 61(May): 156-175. Smith, V.K., Desvousges, W., and Fisher, A., 1984. A comparison of direct and indirect methods for estimating benefits. Vanderbilt University: Department of Economics and Business Administration, working paper, 83-W32. Vaughan, W.H., 1981. The water quality ladder. In: R.C. Mitchell and R.T. Carson (Editors), An Experiment in Determining Willingness to Pay for National Water Quality Improvements. Washington, D.C.: Resources For The Future, Inc., draft report. W a g , R.D., 1976. Consumer’s surplus without apology. American Economic Review, 66(Sept): 589-597.

37

Chapter 3

VALUING PUBLIC GOODS IN A RISKY WORLD: A N EXPERIMENT* PER-OLOV JOHANSSON Department of Forest Economics, Swedish University of Agricultural Sciences, S-901 83 Ume% (Sweden) 1 INTRODUCTION Most studies aimed at determining the willingness to pay for public goods consider a single change in the provision of such goods, for example, from a low to a high level of supply. It is perhaps not too surprising that such studies generally report a positive and realistic average willingness to pay; see e.g. Schulze et a1 (1981). After all, one expects people to be willing to pay out of their limited incomes for something that contributes to utility. Therefore, further attempts to validate willingness to pay measures seem to require that respondents are asked to express their willingness to pay for more than a single change in the provision of the considered public good. In addition, many public sector programmes involve various elements of uncertainty. For example, the outcome of a particular programme may be uncertain. One of the current frontiers in valuation studies is associated with modeling and measuring benefits in such cases. In particular, the recent discussion between Mitchell and Carson (1985) and Greenley et a1 (1985) highlights that the implications of uncertainty with regards to the formulation and interpretation of willingness to pay questions remain unclear; see the aforementioned authors and also Brookshire et a1 (1983) for details. Therefore, it seems to be an important task to examine the possibilities and the limitations of questionnaire techniques in determining the willingness to pay for public goods in a risky world. The present paper reports some preliminary results from an attempt to shed some light on the possibility of estimating money measures in a risky world. As a by-product the paper also reports some results on the consistency of willingness to pay measures when respondents are asked to express their willingness to pay for more than a single change in the provision of a public good. The study is based on a questionnaire completed by 122 Swedes', who were told

* I would like to thank the participants in a seminar at the University of Stockholm and two referees for their helpful and stimulating comments on an earlier version of this paper. 1 The questionnaire was mailed to a random sample of 200 Swedes, i.e. 61 per cent completed the questionnaire. Just one bid was recognized as a protest bid. This bid by a male respondent (on the CVA-question to be defined below) has been deleted; out of the remaining bids there is one bid on SEK 20.000 (E $3 000) while the rest of the bids fall short of SEK 8 100. The reader should also note that in this paper we are not interested in the absolute level of the willingness to pay for a commodity but in the ranking of different measures. The ranking is the same whether or not the two extreme bids mentioned above are included or excluded.

38

that there are about 300 endangered species (animals, birds, and flowers) living in Swedish forests. The respondents were asked of their willingness to pay for four different programmes which would save some or all of the species. In particular, the outcome of one of the programmes was uncertain; it would save all species with a probability of'one-half and every second species with a probability of one-half. The remaining programmes would save 50 per cent, 75 per cent, and 100 per cent of the species, respectively. The design of the questionnaire enables us to test several hypotheses. Firstly, using attitude questions, we can examine if and why respondents attribute an existence value to endangered species. Secondly, the data set can be used to calculate five different willingness to pay measures. Economic theory is used to generate hypotheses concerning the relative magnitudes of these money measures, and the hypotheses are tested on the empirical material. The paper is structured in the following way. Section 2 presents various reasons for attributing an existence value to a species, and reports some results from the questionnaire. In Section 3, a set of hypotheses regarding the relative sizes of different money measures is derived, while Section 4 reports an attempt t o test these hypotheses. Section 5 contains some concluding remarks. The paper ends with an appendix containing some of the derivations needed for establishing the hypotheses presented in Section 3. 2 THE MODEL A typical feature of many environmental resources is that they provide many different values. Following Boyle and Bishop (1985) one may distinguish between four more or less distinct values. First of all, there are consumptive use values such as fishing and hunting. Secondly, some resources provide non-consumptive use values. For example, some people enjoy bird watching, while others gain satisfaction from viewing wildlife. Thirdly, a resource may also provide services indirectly through books, movie pictures, television programmes, and so on. Finally, people may derive satisfaction from the pure fact that a h,tbitat or species exists. The present study is concerned with 300 endangered species. One would expect to find people who attribute different values to the preservation of the considered species. This is confirmed by the results of the questionnaire. For example, more than 50 per cent of the respondents claim that they themselves would benefit from the preservation of endangered species, possibly because this requires a shift to soft cutting technologies. in Sweden it is widely believed that today's forestry is performed in such a way that outdoor recreation is adversely affected. In this section we will concentrate on existence values. For this reason, the following simple specification of the indirect utility function is employed:

where p is a vector of prices of private goods, z is a public good, and y is fixed annual income. For reasons which will become apparent in the next section, the utility function is assumed to be cardinal.

39

In equation (l), z is interpreted as the number of species saved. It is assumed that aV/& 2 0, i.e. the individual's welfare is a nondecreasing function of the number of species saved. (Alternatively, z is interpreted as a 1 x 300 vector with aV/aZk 2 0 for k = 1, ...., 300.) An individual may derive satisfaction from a public good such as z on the narrow grounds of self-interest, i.e. through use values and indirect service$. The individual may also derive satisfaction from the preservation of endangered species, i.e. a larger z, m,irrespective of whether he himself has any narrow advantage from this. In general, this kind of an existence value is motivated by altruistic behaviour. Boyle and Bishop (1985, p. 13), following Bishop and Heberlein (1984), suggest the following five altruistic motives for existence values. (i) "Bequest motives. As Krutilla (1967) argued many years ago, it would appear quite rational to will an endowment of natural amenities as well as private goods and money to one's heirs. The fact that future generations are so often mentioned in debates over natural resources is one indication that their well-being, including their endowments of natural resources, is taken seriously by some present members of society. (ii) Benevolence toward relatives and friends. Giving gifts to friends and relatives may be even more common than making bequests of them. Why should such goals not extend to the availability of natural resources? (iii) S g ~ p a t ~for g people and animals. Even if one does not plan to personally enjoy a resource or do so vicariously through friends and relatives, he or she may still feel sympathy for people adversely affected by environmental deterioration and want to help them. Particularly for living creatures, sympathy may extend beyond humans. The same emotions that lead us to nurse a baby or stop to aid a run*ver cat or dog may well induce us to pay something to maintain animal populations and ecosystems. (iv) Environmental linkages. A better term probably exists here. What we are driving at is the belief that while specific environmental damage such as acidification of Adirondack lakes does not affect one directly, it is symptomatic of more widespread forces that must be stopped before resources of direct importance are also affected. To some extent this may reflect a simple "you've-got-to-stop'em-somewhere" philosophy. It may also reflect the view that if "we" support "them" in maintaining the environment, "they" will support us. (v) Environmental responsibilitg. The opinion is often expressed that those who damage the environment should pay for mitigating or avoiding future damage. In the acid rain case, there may be a prevalent feeling that if "my1' use of electricity is causing damage to ecosystems elsewhere, then "1" shouId pick up part of the costs reducing the damage." In the present study, the respondents were asked if and why they themselves would gain from a programme that contributes to the preservation of the considered endangered species.

A change in z may affect some prices p, possibly including travel costs to recreation sites, and hence demand for these goods and services. However, in order t o be able to derive some simple and useful results prices are held constant throughout, implying that we overlook changes in use values due to changes in prices. See Johansson (1987) and Smith (1987) for models includine such effect,s. 2

40

About 60 per cent claimed that the programme contributes t o their own welfare because it will give others an opportunity to enjoy the species. Referring back to Boyle and Bishop's classification, motives (if and (ii) come to mind. Moreover, 75 per cent claimed that they would benefit from the programme because in their opinion every living species has a right to exist, a motive which resembles Boyle and Bishop's motive (iii). Finally, 45 per cent of the respondents mentioned both of the reasons discussed above. These empirical results lend some support to the hypothesis that many people attach a welldefined existence value to endangered species. Some further evidence is reported in Section 4 below. 3 WILLINGNESS T O PAY MEASURES

The respondents were told that about 300 endangered species - animals, birds, and flowers - are living in Swedish forests. If no measures are taken, e.g. a ban of forestry in some areas and the introduction of soft cutting technologies in other areas, all the considered species may become extinct. Therefore, the respondent was asked to make (once and for all) contributions towards programmes that would save some or all of the species. Four different programmes that would save some or all of the species were suggested. First of all, the respondent was asked about his willingness to pay for a programme - denoted Programme C below - which would save 50 per cent of the species. The respondent was then asked t o contribute to programmes - Programme B and Programme A - that would save 75 per cent and 100 per cent of the species, respectively. Finally, the respondent was asked to pay for a programme Programme D - designed in such a way that the probability is 0.5 that the programme saves all species and 0.5 that it saves 50 per cent of the species. In the case of Programmes A to C, the willingness to pay measure follows from:

where CV. is the compensating variation, i.e. the maximum (once and for all) payment the J respondent is willing to make to secure the change, j = A, B, C, a subscript 0 refers to the initial or no-programme case, Eo is the expectations operator, r; is the probability that species survive in the no-programme case, and Vo is the expected level of utility attained in the no-programme case. The reason for taking expectations in the no-programme case is that the respondents were told that all species may (but need not) become extinct. Therefore, the respondent is assumed to use his own subjective probability distribution in order to calculate the expected utility of the no-programme case. By assumption, no such uncertainty surrounds the final, i.e. with-programme, situation. If utility is strictly increasing in z (and t.he household is not satiated), it is trivially true that: ProDosition 1

CVA > CVB > cvc.

41

Recall that Programme A saves all species, Programme B saves 75 per cent and Programme C saves 50 per cent of the species. The set of strict inequalities in Proposition 1 constitutes the first hypothesis to be tested in Section 4. Turning next to Programme D, the respondent faces uncertainty in both the initial and final situations. This is because the respondents were asked to contribute to a programme which saves all the species with a probability of one-half and saves every second species with a probability of one-half. The resulting money measure is called the ex ante compensating variation:

where AP is the ex ante compensating variation, E is the expectations operator associated with the final (programme) situation, z1 = 300 with a probatility of one-half and z1 = 150 with a probability of one-half. Thus, AP is a uniform ex ante or state-independent (once and for all) payment such that the expected utility with the programme is equal to the expected utility without the programme. One purpose of the study was to examine whether respondents actually calculate the AP measure or if they misinterpret the valuatioi, question and report some other money measure. Fortunately, theory suggests certain relationships between the measures, which will give us a clue to this issue as well as to the question whether or not people have risk aversion. These relationships are summed up in Proposition 2. ProDosition 2

If the utility function is increasing and strictly concave in z, then CVA > CVB > AP

> CVc.

In order to prove these claims, we use the fact that for a strictly concave utility function, Jensen' s inequality asserts that:

where Z.= E(z'), i.e. Z is the expected value of z. In other words, if the consumer is risk-averse with respect to risk in z, he gains from having z stabilized at its mean value. For Programme D, the expected value of z is 0.75. Now, recall that the respondent also was asked to pay for a programme (Programme B) which would save 75 per cent of the endangered species. Using the fact that all money measures considered refer to one and the same level of initial utility, (2)-(4) can be used to show that: V(p, Z, y - AP) > E[V(p, z', y - AP)] = Vo = V(p, Z, y - CV,)

(5)

42

Since the left hand side expression exceeds the right hand side expression, it must be true that CVB > AP. Thus, if the household is risk-averse, the willingness to pay for a programme which stabilizes z at i exceeds the willingness to pay for a "stochastic" programme with as the expected outcome. Obviously, it holds in addition that CVA > CVB > AP > CVc, provided utility is increasing and strictly concave in z. This set of strict inequalities constitutes the second hypothesis to be tested in the next section. It enables us to provide a simple test of whether consumers have risk-aversion with respect to z. Moreover, it provides an indication of whether the respondents really calculated an AP measure. However, it is possible that respondents actually calculated an expected consumer surplus measure. In the present context this measure is defined as: E(CV) = 0.5CVA

+ 0.5CVc

(6)

i.e. E(CV) is a weighted average of the willingness to pay for the preservation of all species and the willingness to pay for a preservation of 50 per cent of the species. Proposition 3 relates the expected consumer surplus measure to the ex ante compensating variation AP and the willingness to pay CVB for having z stabilized a t z = 0.75. ProDosition 3

If the household is risk-averse with respect to risk in z,then AP

$ E(CV).

Moreober, if the expenditure function is strictly convex in z, then CVB > E(CV). In general, AP # E(CV). To prove this claim, the intermediate value theorem is applied t o obtain:

where the derivative V' is evaluated a t some intermediate point y i such that Y yi €(y-AP, y-CVi), i.e. V i = aV(p, zi, yi)/h'yi. Taking expectations, rearranging terms, and

Y

invoking a familiar theorem from mathematical statistics, one obtains:

AP = E(ViY

*

CVi)/E(V:)

= E(CV)

+ COV(V:,

CVi)/E(Vi) Y

(8)

where we have used the fact that the expectation of the product of two stochastic variables is equal to tbe product of their expected values plus their covariance, as is shown in e.g. Johansson (1987). Thus, AP # E(CV), unless the covariance term is equal to zero, i.e. V' is Y

43

independent of zi and income. Nevertheless, if the empirical data reveals a difference between the two measures and there are no systematic errors of measurement, it follows that the respondents did not calculate an expected consumer surplus measure. Therefore, the third hypothesis to be tested reads: AP # E(CV). To prove the second claim of Proposition 3, we use Jensen's inequality, assuming that the expenditure function is strictly convex in z. Then it must be the case that:

where e( .) is the expenditure function yielding the minimum expenditure necessary to realize the initial utility level when prices p and the public good z take on specified levels. According to (9), the level of expenditure necessary in order for the household t o attain the prespecified utility level is lower if z is stabilized at Z than if z is stochastic with expected value Z. Substitution of the following definitions:

i Vi)] ' and VA = V(p, zA, y), into (9) establishes that CVB where y = Eo[e(p, zo,

> E(CV). It

should be mentioned that the inequality can also be produced by an indirect utility function that is strictly concave in z and income. This result is derived in the appendix at the end of the paper. In any case, CVB > E(CV) is the final hypothesis to be tested. EMPIRICAL RESULTS In this section, we will present a test of the hypotheses generated in Section 3. However, before turning to this test, another consistency test of the empirical material is reported. In principle, the classification of values discussed in Section 2 can be used to design simple consistency tests of willingness to pay measures. For example, one sample of respondents can be asked to pay for use values while another sample is asked to pay for use values plus existence values (although it is far from trivial to provide stringent definitions of these concepts, as is shown in e.g. Bishop and Heberlein (1984), Johansson (1987), and Smith (1987)). Obviously, if agents behave in accordance with the predictions of economic theory, the average willingness to pay for use values plus existence values should be a t least as large as the willingness to pay for use values (ceteris paribus). Unfortunately, the sample of respondents considered here was only questioned regarding its total willingness to pay for various programmes aimed at the pregervation of endangered species. For this reason, it is not possible to calculate use values and existence values for the individual respondent. However, Table 1 reports an attempt to isolate various values provided 4

44

by Programme A (i.e. the preservation of all 300 endangered species). Each ("paying") respondent was asked to specify why he was willing to contribute to the programme. A few respondents, group 1 in the table, claimed that they would benefit only through use values and indirect services provided by the considered programme. A second small group of respondents, in addition to use values, attributed value to the fact that the programme would give others an opportunity to "consume" the saved species (benevolence in the table). The third group of respondents in Table 1 mentioned both of the aforementioned motives and also argued that every species has a right to exist (sympathy for animals in the table). TABLE 1 Willingness to pay (WTP in SEK; a SEK x $ 0.15 (U.S.)) for Programme A as a function of the stated motives for paying for the programme. Motive

Average W T P

Use values (group 1) Use values benevolence (group 2) Use values benevolence sympathy for animals (group 3)

+ +

+

300 500 2 300

Table 1 is based on an extremely low number of observations (4, 5, and 37 observations, respectively; many respondents state combinations of motives that do not fall in any of the "groups" defined in the table). The results are shown merely to indicate the possibility of using attitude questions to obtain rough estimates of different values/services provided by a nPtural resource. The ranking of the three willingness to pay measures in the table is the one predicted by economic theory, but further investigation involving much larger samples seems to be necessary before one can draw any definite conclusions about the appropriateness of the approach. Turning to the willingness to pay for various programmes, some results based on 120 observations are reported in Table 2. A glance at the table shows that most of the results are consistent with the hypotheses generated in Section 3. Not surprisingly, the more species saved, the higher the willingness to pay, i.e. CVA > CVB > CVc. The ex ante compensating variation AP, associated with a programme that saves all species with a probability of onehalf and every second species with a probability of one-half, falls short of the willingness t o pay CVB for a programme which saves 75 per cent of the species. This result is consistent with a utility function which is strictly concave in the number of species saved z; i.e., people have risk-aversion with respect to changes in z. Also, AP is different from the expected compensating variation E(CV), the suggested interpretation being that the average respondent did not calculate his expected compensating variation when he was asked of his ex

45

ante compensating variation.

TABLE 2 Average willingness to pay measures (SEK), where subscripts A, B, and C, refer to programmes which save 100 per cent, 75 per cent, and 50 per cent of the species, respectively. Average

CVA 1275 775 CVB 555 CVC AP 655 E(CV) 915

Female

Male

780 670 505 560 645

1830 895 610 770 1220

All these results are consistent with the hypotheses generated in the previous section. However, according t o Table 2 , E(CV) exceeds CV,, indicating an expenditure function that is strictly concave in z, and not strictly convex as expected. Moreover, it is seen that E(CV) > CVB > AP. This set of inequalities is not easily explained3. For example, an indirect utility function which is globally strictly concave or convex in z and income cannot produce E(CV) > CVB > AP, as is shown in the appendix at the end of the paper. It seems reasonable to suspect that the unexpected result under consideration reflects a difference in risk attitudes between "poor" and "rich" people. However, the inequality E(CV) > CVB > AP is obtained for low income earners as well as for high income earners. The inequality is also "robust" with respect to the stated motives for "paying" for the preservation of endangered species4. On the other hand, there is a striking difference between men and women according to Table 2. For women one obtains the ranking CVB > E(CV) > AP. This ranking suggests that women are risk-averse with respect to uncertainty in z; compare Propositions 2 and 3 in Section 3. For male respondents, on the other hand, the Friedman-Savage (1948) type of diagram depicted in Figure 1 comes into mind. That is, the indirect utility function is concave in z for low z-levels and convex in z for sufficiently high z-levels. This kind of indirect utility function can, but need not necessarily, produce the inequality5 E(CV) > CVB > AP reported in Table 3 Note that it does not make sense to test if "mean" values are statistically different since there is just a single population, i.e. all respondents were asked to pay for each of the four different programmes considered. 4 These results are not shown in Table 2 but can be obtained from the author on request. 5 We refrain from presentin a formal proof that utility functions such as the one depicted in Figure 1 can generate E ( C 4 > CVB > AP since such a proof is space consuming and adds very little to the understanding of the problem under consideration.

46

2. The interpretation being that male respondents have risk aversion when many species are threatened, i.e. when z takes on low values, while they are more inclined to accept risks when z exceeds some critical level. Utilr

t

I I

Z'

I

-ZI

I

I

z2

7

Figure 1. Diagram showing the relationship between utility and the number of species saved when the indirect utility function is concave in z for low z-levels and convex in z for sufficiently high z-levels. Note: The broken line in Figure 1 shows that the consumer prefers a stochastic programme with expected outcome to a non-stochastic programme with outcome This is just to indicate that the ranking of various programmes is sensitive to the curvature properties of the utility function as well as the z-level.

z

z.

In closing, i t should be mentioned that the aforementioned difference between male and female respondents confirms earlier Swedish Gallup polls according to which Swedish women are more negative to environmental risks than Swedish men. 5 CONCLUDING REMARKS This paper has reported preliminary results from an attempt to estimate willingness to pay measures for public goods in a risky world. Most of the results are consistent with the predictions generated by economic theory. For example, the willingness to pay is increasing in the number of saved species, which is the "public good" under consideration. According to the data, there is an interesting difference in risk attitudes between male and female respondents. The data set suggests that female respondents have risk aversion with respect to the considered public good. Male respondents, on the other hand, seem to have risk aversion only if many species become extinct while they are more inclined to accept risky outcomes if just a few species are threatened. Besides these explanations of the observed behavior, there is also the possibility that respondents are unable to calculate ex ante compensating variation measures and therefore report some other money measure when the situation involves uncertain outcomes. However, there is no strong case for the suspicion that the respondents calculated and reported an expected compensating variation measure instead of an ex ante compensating variation

41

measure. Nevertheless, it is trivially true that even if a data set happens to confirm all of the hypotheses generated in Section 3 of the paper, this is no ultimate proof that the respondents did calculate one or the other money measure. In addition, the sample of respondents used in this study is very small, implying that some or all of the results may be due to random factors that a sufficiently large sample would cause to net out. In any case, an implication of the research reported in this paper is that further attempts to validate the survey technique are in order. For example, such techniques can be used to let respondents identify additional points along what Graham (1981) calls the willingness-to-pay locus, i.e. all pairs of state dependent payments that leave the respondent's expected utility level unchanged. The two measures considered in this paper, the ex ante compensating variation and the expected compensating variation, represent just two out of possibly an infinite number of benefit measures (payment schemes) along the willingness-to-pay locus. A related issue that seems to deserve additional attention is what benefit measure is the appropriate one in situations involving uncertaintys. Obviously, for cost-benefit analysis of public sector programmes in a risky world to be possible and meaningful, it is necessary to have correct definitions of benefits and costs as well as reliable methods for their calculation. APPENDIX: USING THE INDIRECT UTILITY FUNCTION TO DERIVE SOME RESULTS DISCUSSED IN SECTION 4 In order to show that CV, > E(CV) when the indirect utility function is (strictly) concave in (z, y), a variation of the mean value theorem is used to obtain:

+x

*

2 D V(p,

- Z,

y)

* X I / ~

where DV is the gradient, i.e. a vector of first partial derivatives evaluated at the point (p, Z, - y - CV,), D2V is a 2-by-2 matrix of second partial derivatives evaluated at a point z, y such

-

.

z)

and y ~ ( -y CVi, y - CV,), x = (z' - 5, CV, - CVi), and a prime denotes a that z E(z', transposed vector. Taking expectations of (A.l), noting that E[V(p, zi , y - CV,)] = V(p, z, y - CV,) = Vo, and

i

= E(z ), one obtains:

A recent, although in the present author's eyes not completely convincing, discussion of this issue c m be found in Cory and Saliba (1987). The basic reference is Graham (1981).

6

48

E(CV) - CVB = E[x

*

D2V(p, Z,- y)

* X I ] / ~

*

Vy

where V = N ( p , Z, y - CV,)/&. The indirect utility function is strictly concave in z, y if Y D2V(.) is negative definite. Then x D2V(.) . x' < 0 implying that E(CV) < CVB. See Turnovsky (1976) for a slight extension of this result. Replacing CVi in ( A . l ) by AP, it is straightforward to show that the considered indirect utility function produces AP < CVB. Finally, if the indirect utility function is strictly convex in z, y, then D 2V ( . ) is positive definite in (A.2) implying that CVB < E(CV) and CVB < AP.

REFERENCES Bishop, R.C. and Heberlein, T.A., 1984. Contingent valuation methods and ecosystem damages from acid rain. Universitv of Wisconsin-Madison. DeDt. of Agricultural Econgmics. Staff paper no. 217. Boyle, K.J. and Bishop, R.C., 1985. The total value of wildlife resources: Conceptual and emDirical issues. Invited DaDer. Association of Environmental and Resource Economists Workshop on Recreationai Demand Modeling. Boulder, Colorado, 17-18 May 1985. Brookshire, D.S., Eubanks, L.S. and Randall, A., 1983. Estimating option prices and existence values for wildlife resources. Land Economics, 59: 1-1 5. Cory, D.C. and Saliba, B.C., 1987. Requiem for option value. Land Economics, 63: 1-10, Friedman, M. and Savage, L.J., 1948. The utility analyses of choices involving risk. Journal of Political Economy, 56: 279-304. Graham, D.A., 1981. Cost-benefit analysis under uncertainty. American Economic Review, 71: 715-725. Greenley, D.A., Walsh, R.G. and Young, R.A., 1985. Option value: Empirical evidence from a case study of recreation and water quality: Reply. Quarterly Journal of Economics, 100: 292-299. Johansson, P.-O., 1987. The economic theory and measurement of environmental benefits. Cambridge University Press, Cambridge, X + 223 pp. Mitchell, R.C. and Carson, R.T., 1985. Option value: Empirical evidence from a case study of recreation and water quality: Comment. Quarterly Journal of Economics, 100: 291-294. Schulze, W.D., D'Arge, R.C. and Brookshire, D.S., 1981. Valuing environmental commodities: Some recent experiments. Land Economics, 57: 151-172. Smith, V.K., 1987. Nonuse values in benefit cost analysis. Southern Economic Journal, 54: 19-26. Turnovsky, S.J., 1976. The distribution of welfare gains from price stabilization: The case of multiplicative disturbances. International Economic Review, 17: 133-148.

-

49

Chapter 4 RECREATIONAL VALUES, PARETO OPTIMALITY AND TIMBER SUPPLY PER-OLOV JOHANSSON, KARL-GUSTAF LOFGREN AND KARL-GORAN MALER Department of Forest Economics, the Swedish University of Agricultural Sciences, S-901 83 Ume5 (Sweden) and Stockholm School of Economics, Box 6501, S-113 83 Stockholm (Sweden)

1 INTRODUCTION Recently, there has been an increasing awareness of the fact that a forest fulfills many functions besides producing commercial timber. Very often, one would expect forest land to provide not only different, but also conflicting services. The classical example is a wilderness it can be area, which can be left unspoiled and used for various recreational purposes commercially exploited by harvesting the trees. Similarly, the attractiveness of the environment may depend on the age (distribution) of trees, implying that the "socially" optimal rotation period need not coincide with the Faustmann rotation period. In a recent paper, Johansson and Lofgren (1988), money measures were introduced of the total value of a forest supplying many different and possibly conflicting services. Such money measures are, in principle, possible to estimate by using, for example, questionnaire techniques. In this context it was pointed out that the externality in consumption created for agents with preferences regarding the environmental services provided by the forest, but no direct control over the management of the trees, must be dealt with through "special methods" in a market economy. This is because the optimal provision of environmental services normally conflicts with commercial management practices. The point is that present value maximizing forest owners must be induced to manage the forest in a manner that is consistent with Pareto optimality. AS we will demonstrate, this goal can, under certain conditions, be accomplished by a system of individually based shadow prices (pseudoequilibrium prices) which creates relative "timber prices" that are consistent with a welfare optimum. This was first shown in a more general environmental context by Maler (1974)l. It means that we can decentralize the social optimization problem by adding an environmental component to the ordinary present value problem. A special point being that this component is linear in the stand variables. In other words, the problem mentioned by Hartman (1976) that "For many plots of forest land which could reasonably be taken as unit for making cutting decisions, what happens on one plot will

1

Similar results are found in Foley (1970) and Milleron (1972). See also Maler (1985).

50

cleady affect the value of a standing forest on other units", is automatically solved by the information provided by the pseudoequilibrium prices and decentralized present value maximization. Bowes' and Krutilla's (1985) concern that "it would seem most unrealistic to assume that a single stand could be considered independently of the condition of adjacent stands" is understandable, but this is also taken care of by the pseudoequilibrium prices. Since the equilibrium is also a Pareto optimum, there cannot exist any arbitrage possibilities which, if present, would improve the situation for at least one individual, the arbitrator2. In other words, all interactions are already reflected in the prices. The practical relevance of the management problem cannot be exaggerated. For example, the Forest and Rangeland Renewable Resource Planning Act of 1974, as amended by the National Forest Management Act of 1976, "imposes" on the US-Forest Service a legislation mandate to conduct forest management under both commercial and broader environmental considerations. The analytical results derived in this paper pertain to a FORPLAN3 solution under perfect foresight and known shadow prices of environmental services. This is indeed an ideal situation, but this does not obliterate the need for theoretical information on the properties of the optimal harvesting program. Moreover, recent progress in the economic theory and measurement of environmental benefits has been considerable (for a survey, see Johansson (1987)). Thus a meaningful practical application of the approach may not be too far fetched, since even incomplete information on environmental benefits combined with qualitative theoretical information can be used to improve welfare. For example, the (qualitative!) information that the value of the environmental services provided by a forest stand increases with the age of the stand, combined with the qualitative theoretical information on the direction in which this changes the optimal rotation period4 can be used to conclude that a rotation period greater than the commercial rotation period is welfare improving. The remaining part of this paper is structured as follows: In section 2 we show, within a very simple text-book model of a small open economy with two agents, one a forest owner deriving (indirect) utility only from the commercial services of the forest, and the other a worker deriving utility also from the environmental services of the forest, how a welfare optimizing system of shadow prices (or prices for environmental services) can be designeds. The idea is to give the reader an intuitive feeling for how things would work in a more general

Compare the Value Additivity Theorem in financial economics, which states that: If no arbitrage possibilities exist, then the price of a security whose pay-offs are a linear combination of other assets must be given by the same linear combination of the prices of the other assets. See e.g., Varian (1987). 3 The US-Forest Service planning model. See also Bowes and Krutilla (1985). See e.g. Bowes and Krutilla (1985) or Hite et al (1987). 5 A considerably more comprehensive analysis can be found in Maler (1974). 2

51

setting. In Section 3 we turn to the microeconomics of the management problem. We show how the augmented present value maximizing problem, containing the demand determined shadow prices of forest land in different age classes (from Section 2), can be solved. In particular, we derive the properties of the present value function and show when and why an efficiency criterion on the intertemporal supply of timber may be violated. Section 4 contains a discussion of how the pseudoequilibrium prices can be approximated without making system wide calculations, and how forest management can be induced to converge towards the neighborhood of a socially optimal program. One idea is to use a steady state estimate of the pseudoequilibrium prices in "the normal forest"6 to generate a cutting policy that will asymptotically approach the social optimum. 2 THE ENVIRONMENTAL VALUE OF TREES AS AN EXTERNALITY IN CONSUMPTION In order to highlight the economic problems created in a situation where agents derive utility from the environmental services produced by the forest, as well as from the commercial values obtained through the timber harvest, we will introduce a very simple general equilibrium model. It contains two ordinary goods, a consumer good, x, and timber, c. Both goods can be sold in a n international market a t prices p and P, respectively. Timber is produced through the input of environmental services e and labor 1. The price of labor, w, is determined in a competitive labor market, while environmental services are unpriced7. There are two representative agents in the economy, a forest owner, and a worker. The forest owner produces timber and consumes food and derives no satisfaction from the environmental services of the forest. His optimization problem can be formulated in the following manner:

!

d d v x P, ,w) = Max {u(xl) 1 Pc(e, 1 ) -pxl - wl = 0) [l( d X1,l ,e where Pc(e, 1d )

pxl - w 1d = 0 is his budget constraint. Pcfe, 1d ) can be interpreted as the present value of all future timber rotations, while pxl and wld are the cost of food and the labor input, respectively. This formulation is implied by a perfect capital market. Finally, -

1

xl(P, p, w) is the so+alled indirect utility function with properties:

6 The normal or "syncronized" forest is defined ;19 a forest with stands of equal area and exactly one stand in each age class up to the optimal rotation period. Such a steady state means that the same area and volume - assuming a constant biotechnology - will be cut every year. 7 An alternative way to set up the problem would be to assume that the supply of environmental services is a function of the labor input.

52

where A(P, p, w) can be interpreted as the marginal utility of income. In other words, the demand for food and labor, and the supply of timber can be derived (except for sign) by differentiating the indirect utility function with respect to the respective price and dividing by the marginal utility of income. The supply of timber and environmental services as well as the demand for labor are determined from the maximization of the present value of the income from forestry. The first order conditions are: d Id = 1 ( P , w )

P ai qJ-w=OI

b =>

(3)

which mean that the intensity in forestry depends only on the price of timber and the wage rate and not on the price of consumer goods. This is a consequence of the perfect capital market assumption, and the resulting separation property is often referred to as the "Fisherian separation theoremlls. The optimization problem of the worker is formulated as: V(p, w, e) = Max {U(x2, lS, e)

1

wlS -px2 = 0)

(4)

X2,lS where wls is labor income from supplying 1' hours of work. The derivatives of the indirect utility functions are:

where p(e, p, w) is the worker's marginal utility of income. The prices of timber ( P ) and food (p) are determined in the international market, while the wage rate is determined by the market clearing condition in the labor market.

8

For its origin see Fisher (1930).

53

Note also that prices appear in the marginal utility of environmental services, since Is and x2 in optimum depend on prices. The first six equations now determine the market equilibrium. However, due to the externality in consumption created by the fact that the environmental services are imposed on the worker, the market equilibrium is not necessarily a Pareto optimum. In order to see this, assume that aLJ # 0 in the market equilibrium, say that it is positive; meaning that a (small) increase in the supplies of environmental services will improve the worker's situation. Moreover, since Pxdc = 0 in equilibrium, a small increase in the value of e will leave the income and utility of the forest owner unaffected. Hence, welfare can be improved according to the Pareto criterion. This potential improvement is not materialized in the market solution, since there is no formal way for the worker to communicate a willingness to buy additional environmental services (au E> O)9. How would we achieve a Pareto optimum? The firm's marginal willingness to pay for environmental services is given by:

The argument e in the wage function is a consequence of treating e as a parameter in the optimization problems, which in turn implies that the equilibrium wage determined in (6) will be a function of e. The worker's marginal willingness t o pay for the environmental services in monetary terms is given by:

The total marginal willingness to pay is hence given by the sum of the expressions in equations (7) and (8), respectively, which if equalized to zero enables us to solve for the optimal provision of environmental services. (Note that P and p are exogenously given.)

9 Note that the public good property of environmental services means that in an economy with more than one agent caring about the environment the "marginal willingness to pay" of different agents has to be added. See below.

54

This "Lindahl equilibrium"10 volume of environmental services, e ' , means that the worker has gained at the expense of the forest owner. The former would, however, be willing to pay a(e ) dollars for the last unit of the environmental good and this amount would exactly compensate the latter's loss from producing it. In other words, a policy that promised the forest owner * a ( e ) dollars per unit of the environmental good, would induce him to produce11 the optimal * * amount e . The lump-sum of money a(e ) . e is also the minimum amount of money that would accomplish this, and that the worker would be willing to pay, since12 a(e) > a(e ), for e * * < e . In other words, given a ( e ) the consumer demands e . If we introduce many consumers of the environmental services, the optimal allocation problem can be solved by adding the respective marginal willingness to pay functions, oi( .), i = 1,

n

...., n,

and using the sum in (9) to solve for e

*

. The

firm's shadow price becomes

a = C ai(e*), and the costs t o consumers are allocated according to the principle that each i=l

* *

agent pays (or receives if ai < 0) ai(e )e . The above is a sketchy and simplified treatment of a general allocation problem involving public goods. The existence of a Lindahl equilibrium, which is crucial for the analyses to follow, was first dealt with thoroughly in Milleron (1972). Maler (1974) solved a corresponding problem13 with explicit reference to environmental services. In this general setting a and e would be vectors, and environmental services can, of course, be dated, so we can apply the model to an economy where trees are produced, and where forest stands, as such, produce environmental services. A Lindahl equilibrium means that all markets are cleared and all consumers demand the same amount of environmental services. It is also possible to show, in the spirit of Arrow-Debreu, that this equilibrium is a Pareto optimum and that every Pareto optimum can be represented as an equilibrium. Loosely speaking, t h e , necessary and sufficient condition for the validity of this general theorem is that each producer is limited to a convex production set, and that each consumer is guided by a convex preference ordering. Under these assumptions the aggregate production and consumption sets can be separated by a price-hyperplane. Some strong arguments have been given against assuming that the aggregate production, set under the existence of detrimental externalities, is convex. Nonconvexities would prevent the establishment of optimal prices in voluntary exchange. However, it would not prevent

10 11

See Lindahl (1919), Foley (1970), and Milleron (1972). The first order condition for present value maximum

*

P Y , P , P, e 1 + a ( e = 0 would be fulfilled. 12 Certain regularity conditions are implicitly assumed to hold. 13 An "unimportant" difference being that Mller introduces an environmental agency that supplies the environmental services to the consumers. The existence of Lindahl equilibrium is also discussed by Hart and Kuhn (1975).

55

the efficiency properties of taxes representing the social marginal benefits of environmental services14. Whether nonconvexities are also crucial for the production of the recreational services of the forest must be the topic of another paper. Here we will proceed as if an intertemporal equilibrium exists. 3 THE MICROECONOMICS OF FORESTRY IN THE PRESENCE O F ENVIRONMENTAL SERVICES Having established the existence of a price vector, including prices for environmental services, which clears all markets and creates Pareto optimality, we will redo the Hartman (1976) rotation analysis in a more general and appropriate setting. The model we introduce is a variation of the Berck-Johansson - Lofgren15 linear and nonlinear forest management model. This has been augmented with an extra term in the goal function which contains a valuation of the age distribution of the forest's. The assumption being that an age class has given environmental attributes which can be priced. Time has now come to introduce the technology of the forestry firm. Let = the number of acres of land occupied

at the end of period t by trees in age

class i = [XtO'

...

7

Xtnl

= the number of acres of land with trees of age class i cut in period t - [Ctl' -.-,Ctnl = the total amount of forest land = the amount in m3 that can be harvested from one acre of land with trees in age class i

- kl'

gnl of one m3 of timber from trees in age class i at time t = the price of timber from trees on one acre with trees in age class i at time t, i.e., . g .1' q ti = r ti '"I

= the price

- [ q t p .'.I 9tnl

= the interest rate in the perfect capital market = the cost of cutting [ctl1 ..., ctn] in period t = the net social benefits in period t from having an age distribution

of the forest

given by xt at the end of period t.

This is shown by Starret (1972). 15 See Berck (1976) and Johansson and Lofgren (1985). To give the model a name is a little pretentious, since a t least the linear version is a standard LP-model of a multiple stand forest. 16 The model is also in its non-linear version a generalization of Bowes-Krutilla (1985), who take the problem considerably further than Hartman (1976) and Strang (1983). Another difference compared with earlier models is that we interpret prices as corrected general equilibrium prices that create Pareto optimality, through a well defined market induced mechanism. In other words, multiple use forestry is married to the Malerian general equilibrium approach. 14

56

The basic dynamics of the growth of the forest is given by the following equations: n

C xoi = M i=O n

t = 1, ...,T

c.=o i = l tl

Xt0-C

t = 1, ...,T i = 1, ...,n - 1 X

t-1 n-1

+

't-1

n - 'tn - Xtn = O

-

t = 1, ...,T i = 0,

xoi - xoi = 0

...,n

where we have assumed that a tree that has reached age class n will stay there forever unless it is cut. A feasible cutting policy must also satisfy the inequalities cti, xti L 0 for all t. The net social benefits in period t can be written:

The present value of all the future benefits is then:

The optimal management of the forest in the face of the environmental considerations is defined as the cutting policy that maximizes the present value. In order to characterize such an optimal policy, the Kuhn-Tucker conditions will be used. The Lagrangian of the optimization problem is: n

T

L=

c t=l

([qtct - Kt(ct)

+ Et(xt)] [l + ,Ipt) +i=OC (Xoi[Foi - x0J)

T t = 1Xtn[xt-l n-1

+

Xt-ln - Ctn - Xtnl

The necessesary conditions for a maximum are:

57

If the cost functions are convex these conditions will also be sufficient. The Lagrange multipliers At = [Ato, ..., Atn] (the royalties) can be interpreted as the net present value of standing trees at time t , given that the stands are managed according to the optimal program. Roughly speaking (18 i ) tells us that if it is optimal to cut a stand at t (cti > 0), then the net marginal revenue from the last acre plus the value of newly seeded land (Ato) coincides with the royalty (Ati). If some of the trees are saved, xti > 0, then the present value of the marginal recreational value will coincide with the difference between the royalty in period t and the corresponding royalty of the same stand in a later period. Since the recreational value is positive this means that the royalty will fall over time. It is easily seen that if t = 1, ..., T i = 1, ... n

(19)

are considered constant psedoequilibrium prices along the optimal trajectory, then the same optimal management plan of the forest would be obtained if p t i x t i is substituted for Et(xt) in the objective function. Assuming for the moment that the psedoequilibrium prices are known and that we are dealing with a linear version of (17), which is obtained if we drop the cost functions, and reinterpret the price vector as consisting of net present values. By manipulating the KuhnTucker conditions (18), which are both necessary and sufficient in the LP-case, it is easy to prove the following three propositions (defining qti(l+r)-t = pti and ati r = a,ti(l+r)-t).

58

The royalties of the combined present value LP-problems can be found by using the algorithm

ProDosition 1

A ti = m a x [ A t + l i + l

Pti

+

+

'to]

for all t (starting with t=T) and all i < n. For i = n the right hand side r should be written Max [At+ln atn, ptn Ate].

+

+

The modification that has to be made in comparison with a pure present value program is that the value of saving the trees consists not only of the royalties in the next period, but also the demand price of the environmental services consumed during the period ( a:i). From the way in which the solution in Proposition 1 is obtained, part (a) of the following proposition is obviously true, provided that the algorithm in Proposition 1 can be started with scrap values that are independent of xo. (a) The royalties Xti are independent of the initial endowments

ProDosition 2

-

(:oo> ..-,X&J. (b) .The royalties are non-decreasing functions of the price vectors p l , p2, ..., pT (which contain the coefficients of the production function r r r gl, g2, ..., gn), and the psedoequilibrium price vectors al, a2, ...,

a;r.

Part (b) of Proposition 2 is intuitively true17. If prices increase in the future, the value of a unit of forest land today cannot decrease. On the other hand, only prices in the future matter. Yesterday's prices (timber or prices of environmental services) cannot affect the combined value of a unit of today's forest land. Moreover, a better production function cannot, ceteris paribus, decrease the combined value of forest land. Intuition also suggests that the stand may be profitably cut if

i.e. if the value of the cut plus the value of the seed or a unit of forest land is worth not less than the royalty of the same unit of forest land at time t + l plus the value of the environmental services supplied during period t. A more formal argument, making use of the Lagrangian of the forest management problem and the Kuhn-Tucker condition, reveals tlial intuition is indeed correct, i.e.: ProDosition 3

~~~

'7

The cutting (saving) rules of the combined present value LP-problem arc the following

~

The second part of the claim can be demonstrated by an induc-tion argument.

59

(a) Timber of age class i is cut at time t if 'to

+

Pt+l i+1> 't+l i+l

+

4i

(b) It may be saved or cut at time t if

(c) Timber is saved if

Since the cutting rules do not depend on the composition of the initial endowment, we have the following Corollary: Corollarv 1

The optimal management of a forest stand in the combined present value problem, does not depend on the size and composition of To.

One can say that Corollary 1 is the theoretical justification for the practice, emerging from Hartman (1976), of treating the combined present value maximization problem stand by stand. Things are more complicated if we take account of the cost functions. For example, if the cutting technology exhibits increasing or decreasing returns to scaleis, it may be profitable to merge cuttings together, and optimal harvesting decisions can no longer be taken stand by stand. Note, however, similar problems do not enter into the environmental part of the combined present value function. Since everyone consumes environmental services in the same quantities (the public good property), and the environmental prices by assumption are sums of individual Pareto-supporting valuations in the same sense as competitive timber prices, they can be used as ordinary competitive prices. In other words, even if the consumers value forest land as a whole, with age composition mattering for the aggregate value, this is implicit in the environmental prices. Like competitive equilibrium prices, they pick up all the interactions of the economy. Let r r c Y = [a1, o2 ...

41

c' = [cl, c2,

..., CT)

x' = [XI'

X2'

..., XT]

C = {c, x ( c , x satisfy eqs (10) - (14))

18 Economics of scope, a restricted form of sub-additivity, would create a similar deviation from a stand by stand treatment. See Baumol, Panzar and Willig (1982) ch. 4.

60

Moreover, we introduce a more explicit cutting technology by letting the labour input19 in period t be a function of the cutting program ct.

Finally, we introduce the input vector and the input price vector:

where wi is the present value of the cost of a unit of labor in period t , and a feasible set F such that:

We are now ready to define a "combined present value function".

The fundamental properties of the combined present value function are summed up in the following proposition. ProDosition 4

(a)

The combined present

value function is convex in prices (I-A) r( ell) 2 - ~ (X ),0 where X is a scalar

+ 0 < X < 1, and 8x = XB' + (I-A) 6' = (p, w,

(b) (c)

i.e. Xr(8')

(Y),

6'". It is homogeneous of degree one in prices, i.e., p ~B)( = ~(pb'),for p > 0. It is subadditive in prices, i.e.,

.(el)

+

.(ell)

2

T(el

+

ell).

Claims (a)-(c) are also properties that are held by the profit function in neoclassical theory, and the proofs are standard20 and therefore omitted. Convexity means, among other things, that. the function is continuous and almost everywhere twice continuously differentiable on the positive orthtant. Homogeneity means that a doubling of all prices doubles the profit, and homogeneity and convexity implies subadditivity, but a direct proof of the subadditivity claim is also easy.

19 A more general input vector would not cause any additional problems. Note that the cost function Kt( .) is defined as Min{wt$ = ft(ct)} = wtft( ct See e.g. Johansson and Lofgren (1985).

14

a).

61

Convexity also means that the quadratic form of the function is negative semidefinite and homogeneity of degree one means that the derivative of the function is homogeneous of degree zero. The usefulness of these properties will be more evident after we have introduced Proposition 5. Subadditivity has, so far, been a less useful property than the other two, but Lofgren (1987) uses it together with convexity to provide upper and lower bounds on the change in the value of forest land when land value is evaluated at any two different price vectors. x) the combined present value function can be written If we define y = (c, 4, ~ ( 8= ) Max [By Y

1 y 6 C n F]

The following proposition can now be proved. ProDosition 5

For an interior solution, 0 >> 0, it is true that Dr(8) = y(B), when the derivatives exist (where Dn(8) is the gradient of the profit function).

Proof

Define a function h(0) = By' - ~ ( 8 ) where y' maximizes n(8) for 8 = 8'. This function will, by definition, have a maximum for 8 = 8', and since it is an interior maximum it holds that

Since this is true for all 8' the claim is proved. Decomposing y we find, c(B), the timber supply vector, x(Q), the environmental supply vector of standing timber and, -l(0), the labor demand vector. Now since a(0) is convex, the matrix Dzr(0) = D y(8) is a symmetric and positive semidefinite matrix. For the case when there are only two periods and two age classes we have

62

I: ap,,

........

........

A10

&lo

axlo

aa,,

a P 2 2 T aX22

Gaw,

........

'*.*

axlo sol,,

* * . *

aol,,

ax22

From the semidefiniteness of the quadratic form it follows that:

6)

acti axti The own supply effect is nonnegative + (,2 0). ti @ti

(ii)

The own demand effect is nonpositive (= . 2 - 0).

a

-ati

1

(e

dxlk

ac..

(iii) The crossprice effects are symmetric

=

Olk

or the element ij equals

IJ

the element ji). Claims (i) and (ii) tell us that the elements along the main diagonal are positive, meaning, for example, that an increase in the price of an environmental service or timber in a certain age class in a particular period increase the supplies of these services. Claim (iii) means, for example, that an increased demand price for a stand in age class 2 in period 2, (a2B), has the same effect on timber supply in age class 1, as an increase in the price of timber in age class 1 in period 1 has on the supply of environmental services in age class 2 in period 2 %l h22 (r =F). Qi2 11

Finally, from Proposition 5 and the properties of homogeneous functions it follows that the supply and demand functions are homogeneous of degree zero in prices, i.e., c(p0) = c(O), x ( p 0 ) = x(B), and l(pB) = t(0). In other words, only relative prices matter for the firm's supply and demand decisions.

63

Let us now introduce the following definition of efficiency. A feasible program (ct, -EL, xi), t = 1, ..., T dominates another feasible Definition: program if gc; 2 gct and 4;2 -Et for all t with at least one strict inequality. A program is production efficient if it is feasible and there is no dominating program. A dominated program is called inefficient. It is fairly well known, since the classical paper by Malinvaud (1953), that if the planning horizon is infinite the present value maximizing program will not necessarily be efficient. However, as soon as the planning horizon is finite the present value maximizing program is efficient . It is equally well known that the maximization of combined present value function under both a finite and infinite planning horizon may involve an inefficiency in production. In the infinite time horizon case this has been shown by Strang (1983), and in the finite time horizon case it is obvious from the solution algorithm in the linear case that every time trees are saved in the final period there is an inefficiency in production. What can easily be shown for the combined present value problem with a finite planning horizon is that the optimal program is efficient if it is present value maximizing. The reverse statement is, however, not in general true. 4 HOW T O FIND THE PSEUDOEQUILIBRIUM PRICES?

The points made so far would only be of pure theoretical interest, if it is necessary to make systemwide calculations in order to find the pseudoequilibrium prices. The problem of finding the correct shadow prices for the environmental services may seem almost insurmountable. We will, in this section, discuss three approaches to a search for these prices, one of which we consider to be a promising possibility. (i) A particularly simple case would be if the function Et(xt) is linear, i.e. the willingness to pay for a hectar of land in a certain age class is independent of the total number of hectars in this age class, and also of the age of trees in surrounding stands. As has been pointed out by among others, Bowes and Krutilla (1985) this is hardly a reasonable case. (ii) Another possibility would be if other similar forests exist, and the willingness to pay for the recreational services of trees in a certain age class depends on the total number of hectars in the age class. Formally, this can be written as:

where Xt is the aggregate area of all other forests. The marginal willingness to pay for trees of age class i would be

64

and if xti is small compared to Xti (the total number of hectares in age class i), it is reasonable to assume that the marginal willingness to pay is approximately independent of xt. This would correspond to the case when a mountain valley is going to be cut, a t the same time as there exist a number of similar valleys. The marginal willingness to pay for preserving trees of a certain age class would, in this case, be determined by the valuations of the age distributions in all other valleys. Thus, when there exist substitutes for the forest under consideration it may be reasonable to assume constant and given shadow prices, which could be estimated by contingent valuation methods. (iii) However, quite often it is not possible to find "substitute" forests. It may still be possible to argue that there exists a vector of constant shadow prices which would approximately generate the same management plan as would the willingness to pay function. These are the steady state prices. If we let the planning horizon approach infinity, it is easily seen that there may be two different steady states. The first one is a state with no cutting and with all trees in the highest age class n. This will also be the optimal steady state if the willingness to pay for environmental services is such that old trees are very highly valued compared with younger trees. The other possible steady state is the normal or synchronized forest. It corresponds to the existence of an integer N' 5 n such that trees of age less than N' are not cut, while all trees of age N' are cut. This would correspond to a situation where the general public wants a variety of stands with trees in different age classes. It is this steady state that will be considered below. The normal forest is a traditional concept in forest economics, and it would not be unfair to say that foresters have had an intuitive feeling for the potential asymptotic optimality of the normal forest. The formal theorems are, however, very recent. Mitra and Wan (1986) show the following theorem. Theorem:

When future profits are undiscounted, and the profit function is strictly concave in the cut, the optimal program from any initial situation will converge to a unique optimal stationary program (the normal forest). The yearly cut along the optimal stationary program will be equal to the maximum sustainable yield.

In other words, if the interest rate is zero and the marginal profit (utility) of the last cubic meter of the harvest is decreasing, the composition of the forest land will eventually reach the normal forest. The intution behind the result is to some extent clarified by Figure 1.

t

y'i

0

I

I I

c2

C,+C*

2

,

65

I I

~

I I I

c

c = cut

1

Figure 1. Cutting patterns under a strictly concave profit function. Let c1 and c2 be the harvests today and tomorrow, respectively, under an uneven cutting

c12

+

pattern generated by a nonuniform age distribution. Moreover, let = (cl c2)/2 represent the yearly cut under an even cutting pattern resulting from a uniform age distribution. Obviously, the uniform cutting pattern is preferred (re > 7rUe) to the nonuniform, indicating that it pays to gradually smooth the age distrbution of the forest. Loosely speaking, when profits are undiscounted the total gain from a transformation to a more smooth cutting pattern is unbounded, while the total loss along a path towards the normal forest is bounded. No wonder that the solution converges towards the normal forest. It can, however, be shown by a counter example that the above theorem is no longer valid if profit is discounted21. The intuitive reason is that a positive interest rate means that both the gain from the normal forest and the loss from a path towards it are bounded. If the adjustment loss is higher than the gains from smoothness, there will be no convergence towards the optimal stationary program. An analoguous theorem can be proved in a case when there are recreational values present. What has to be done is to reinterpret the production function so it includes the production of not only commercial values, but also recreational values. In other words, the results in Mitra and Wan (1985, 1986) are transferable, although not directly, to our formulation of the Groblem. See Appendix. Hence, if the interest rate is "small enough" one might conjecture22 that the solution for

T i m will converge to a unique normal forest, x(q,

z,

r), and a unique vector of

See Mitra and Wan (1985). The conjecture is supported by e.g., numerical analyses in Kemp and Moore (1979), but has not yet been formally proved.

21

22

66

pseudoequilibrium prices 5.Given that we by, say, contingent valuation methods, can find the relevant steady state pseudoequilibrium prices (or a good approximation of them) we can use these in the origional problem together with timber prices and the interest rate, and hope that the problem, so modified, will converge to the same steady state. Clearly, if the steady state is unique as a function of prices and the interest rate, a convergence as such would do the job. We would, however, need information on the rotation period in the (maximum sustainable yield) steady state. Accurate quantitative information is of course difficult to obtain, but there are qualitative information on the shape of the normal forest in the presence of environmental services. More precisely, if the environmental benefits are increasing, constant or decreasing as a function of the age of the stand, then the commercial steady state rotation will be shorter, equal to or longer than the rotation period that solves t h e problem in the presence of environmental services (the socially optimal steady state rotation period). A non-technical "proof" runs like this: if the environmental yearly benefit is independent of the age of the standing trees - say equal to a constant Vo - its present value equals the value of a perpetuity yielding Vo dollars/year, or Vo/r, where r is the interest rate. Clearly this expression is independent of the rotation age, and the commercial rotation period coincides with the socially optimal rotation period. If the environmental benefits increase with the age of the stand, the extra value created by older trees can only be realized by a lengthening of the commercial rotation. The opposite is obviously true if the benefits are decreasing with the age of the trees. For a formal proof see Hite et.al. (1987) or Johansson and Lofgren (1988a), where it is easily seen that the above result holds also for the case when r = 0. 5 CONCLUSION The intention of this paper is to apply results from the theory of Lindahl equilibria in economies with public goods to the multiple use management of public (and private) forest land. We show that, given that we can treat the environmental services of standing trees as public goods and that we know the general equilibrium prices for public goods, we can then decentralize the social optimization problem by adding an environmental component to the ordinary present value problem. One point being that this component is linear in the case of stand variables, and the problem that the valuation of one stand depends on the states of others is automatically solved by the general equilibrium prices. We use the theoretical knowledge on the existence of these prices in a microeconomic analysis of the multiple use management problem. The results are far from surprising, since they are analogous to similar results from neoclassical theory, but are, nevertheless, worth stating. A very difficult and essentially unsolved practical problem is to find the pseudoequilibrium prices. We suggest three "methods" to approximate these prices; the third being the most interesting. Here we use the theoretical convergence properties of the management problem to support an idea that people should be asked about how they value stands in a regulated forest. These valuations can then be used to generate a cutting pattern not too far from the "first

GI

best optimum". Under ideal conditions the cutting pattern would asymptotically converge to the optimal steady state. Some of the forests which should be completely saved from the start - such as virgin forests -would probably be possible to pinpoint by less subtle methods. APPENDIX Let f(t) be the production function of a stand on one acre of land, where t denotes time. Moreover, let g(s) 2 0 for s 0 be the environmental benefit function of a stand of age s. Over

>

a short interval ds, the total environmental benfit is g(s)ds, and its present value is e-rsg(s)ds (this entity corresponds to our *ki:s, and {f(l), f(2), ..., f(n)} corresponds to our vector g). When the interest rate is zero the Hartman problem can be shown to transform into the maximization of the sustainable combined yield, i.e.,

M a x i [f(t) t

+

g(s)ds] 0

If we define t

f(t)

+ J g(s)ds = F(t) 0

and H(t) = F(t)t-' all the results in Mitra and Wan (1986) will follow, if we invoke on F(t) and H(t) all the properties of the "Mitra and Wan"-commercial production function. In particular, the optimal program will, from any initial state, converge toward a normal forest, if the production function is strictly concave in the cut. Note that the cut is now valued both for its timber content, and its accumulated environmental values. REFERENCES Baumol, W.J., Panzar, J.C. and Willig, R.D., 1982. Contestable Markets and the Theory of Industry Structure, Harcourt Brace Jovanovich Inc., New York. Bowes, M, and Krutilla, J., 1985. Multiple Use Management of Public Forest Land. In: A. Kneese and J. Sweeney, (Editors), Handbook of Natural Resource Economics, Vol. 11, North Holland Publishing Company, Amsterdam. Fisher, I., 1930. The Theory of Interest. Macmillan, London. Foley, D., 1970. Linda111 Solutions and the Core of an Economy with Public Goods. Econornetrica 38, 66-72, Hart, O.D. and Kuhn, H.W., 1975. A Proof of the Existence of Equilibrium without the Free Disposal Assumption. Journal of Mathematical Economics 5, 335-348.

68

Hartman. R., 1976. The Harvestine: Decision when a Standinn - Forest has Value. Economic Inquiry 14, 466-92. Hause, J.C., 1975. The Theory of Welfare Cost Measurement. Journal of Political Economy 83, 1145-82. Hite, M., Johansson, P.O. and Lofgren, K.G., 1987. On Optimal Rotations when a Standing Forest has Value. Swedish University of Agricultural Sciences, Department of Forest Economics, Umel. Report 70. Johansson, P.O., 1987. The Economic Theory and Measurement of Environmental Benefits. Cambridge University Press, Cambridge. Johansson. P.O. and Loferen. K.G.. 1985. The Economics of Forestrv and Natural Resources. Basil Blackwell, Oxf&d. ' Johansson, P.O. and Lofgren, K.G., 1988. Money Measures of the Total Value of Forest Lands. Forthcomintz in EuroDean Review of Aericultural Economics. Johansson, P.O. and fofgren, K.G., 1988a. Where's the Beef?: A Reply to Price. Journal of Environmental Management 26, forthcoming. Kemp, M.C. and Moore, E.J., 1979. Biological Capital Theory: A Question and a Conjecture. Economic Letters 4, 141-144. Lindahl, E., 1919. Die Gerechtigkeit der Besteuerung. Gleerup, Lund. Lofgren, K.G., 1987. A Fundamental Inequality for the Assessment of Forest Land Values. Canadian Journal of Forest Research 17, 1309-131 1. Malinvaud, E., 1953. Capital Accumulation and Efficient Allocation of Resources, Econometrica 21, 233-268. Milleron. J.C.. 1972. Theorv of Value with Public Goods: A Snrvev Article. Journal of Economic Theory 5, 419377. Mitra, T. and Wan, Jr, H.Y., 1985. Some Theoretical Results on the Economics of Forestry. Review of Economic Studies 52. 263-282. Mitra, T. and Wan, Jr. H.Y., 1986. On the Faustmann Solution to the Forest Management Problem. Journal of Economic Theory 40, 229-249. Maler, K.G.. 1974. Environmental Economics: A Theoretical Inauirv. Johns HoDkins " University Press, Baltimore. Maler, K.G., 1985. Welfare Economics and the Environment. In A. Kneese and 1. Sweeney (Editors), Handbook of Natural Resource Economies, Vol I. North Holland Publishing Company, Amsterdam. Strang, W.J., 1983. On the Optimal Forest Harvesting Decision. Economic Inquiry 21, 576-83. Starret, D., 1972. Fundamental Non-Convexities in the Theory of Externalities. Journal of Economic Theory 4, 180-199. Varian, H., 1987. The Arbitrage Principle in Financial Economics. Economic Perspectives 1, 55-72. Y

69

Chapter 5 ESTIMATING SOCIAL BENEFITS OF ENVIRONMENTAL IMPROVEMENTS FROM REDUCED ACID DEPOSITIONS: A CONTINGENT VALUATION SURVEY STALE NAVRUD* Agricultural University of Norway, Department of Forest Economics, P.O.Box 44, N-1432 L-NLH (Norway) 1INTRODUCTION

In Scandinavia, fish kills in connection with acidic waters have been observed since the turn of the century (Overrein et al. 1980). Populations of atlantic salmon (Salmo salar) were first affected, followed by brown trout (Salmo trutta) and other freshwater species.

By 1980 fish populations throughout an area of 33,000 km2 had been affected in Norway (see also map in Appendix 1).Today, although there has been no increase in annual acid depositions, the fish losses in acidified areas of Southern Norway continue and are spreading to the western coast (Rosseland, Skogheim & Sevaldrud 1986, Sevaldrud & Skogheim 1986). Most European countries have now committed themselves to reducing their sulphur emissions by 30 % before 1993 (using 1980 as the reference year). International negotiations on further reductions in sulphur dioxide and other long range transported air pollutants are also in progress. In Norway, which imports about 90-95 % of its annual sulphur depositions of 191,000 metric tons (1985) (NMI 1983, reduced sulphur depositions are predicted to have a very positive effect on water chemistry and freshwater fish populations (Muniz et al. 1984, Seip et al. 1986). This paper presents some results of a survey estimating the Norwegian population’s willingness-to-pay (WIT) for these predicted increments in freshwater populations.’ This

* This research has been supported by grants from the Norwegian Ministry of Environment. I wish to thank the Ministry‘s representative Petter Talleraas for valuable comments, Dr. Nils Christophersen and Dr. Hans Martin Seip (Center of Industrial Research) for descriptions, calculations and diagrams of the effects from reduced acid depositions on fish populations, and my colleagues at the Department of Forest Economics for advice and comments. Special thanks go to Grethe Delbeck for word processing. A recent nationwide survey of 1,005 lakes (NEMP 1987) supports these forecasts.

70

survey is the core of an empirical follow-up study based on a methodological "package" proposed in a pilot project (Navrud 1985). This package also includes a regional WTP-sur-

vey of a sample of 573 households in the most heavily affected area: Sorlandet (i.e. the four southernmost counties Telemark, AustAgder, Vest-Agder and Rogaland). Both these surveys use the Contingent Valuation Method (CVM) to estimate the social benefits of increased freshwater fish populations.

In addition, a mail survey of anglers in the River Vikedalselv in Southwestern Norway was carried out autumn 1987. Here, both the CVM and the Travel Cost Method (TCM) were employed. The Viedalselv, once a prime sea trout and salmon river, is now recovering after being on the verge of losing its salmon stock. Sea trout, which is less sensitive to low pH-levels, has become more abundant. This situation is very similar to the expected development in restored salmon rivers in Southern Norway after reductions in acid depositions. The results from this case-study can be used as a consistency check of values extracted from the national and regional surveys. Large scale liming in this river started in 1987, and the mail survey together with annual recreation participation data collected since 1979 (before the effects of acidification became obvious), can also give important information on how different levels of acidification affect the recreational value of fishing. Similar surveys over the next few years will enable us to estimate the effects of liming on fish populations and their recreational value. The total economic value to society of a marginal increase in this non-market environmental good (freshwater fish populations in Norway), can be estimated as the aggregate, maximum, total WTP for all people affected by this environmental improvement. They are here defined as all of the 1.52 million households in Norway (Central Bureau of Statistics 1987). This estimated value constitutes a very significant part of the welfare improvement

to the Norwegian population obtainable through reductions in long range transported air pollutants. 2 METHOD AND DATA 2.1 Contingent Valuation Method

During the past two decades economists have applied a variety of echniques

J

reveal

individual preferences for non-market environmental commodities. These can be divided into two major groups; indirect and direct methods. The indirect methods assume either that private goods are complementary to environmental goods, or that the environmental quality is incorporated in the private good. The

71

value of the environmental good can thus be calculated from the demand for the private good. The two most important of these methods are the Travel Cost Method (TCM), based on travel costs to visit a recreational area, and the Hedonic Price Method (HPM), usually based on property values. The direct methods use interview techniques to make individuals express their subjective evaluation of the good explicitly in constructed hypothetical markets. The most promising of these methods is the Contingent Valuation Method (CVM). The CVM is used in this study and will therefore be described in more detail. The essence of this survey method is succinctly expressed by Randall et al(1983, p. 637) as follows: "Contingent valuation devices involve asking individuals, in survey or experimental settings, to reveal their personal valuations of increments (or decrements) in unpriced goods by using contingent markets. These markets define the good or amenity of interest, the status quo level of provision and the offered increment or decrement therein, the institutional structure under which the good is to be provided, the method of payment, and (implicitly or explicitly) the decision rule which determines whether to implement the offered program. Contingent markets are highly structured to confront respondents with a well-defined situation and to elicit a circumstantial choice contingent upon the occurrence of the posited situation. Contingent markets elicit contingent choices".

In the CVM, individuals are asked neither about their opinions nor about their attitudes, which may be poor predictors of actual behaviour. Rather, they are asked about their contingent valuation (If "this" happened, what would you be willing to pay?). While questions posed in the CVM are (arguably) not attitudinal, the "market", or the commodity and payment, as they appear in the CVM, are hypothetical. Because of this hypothetical nature, several potential biases may occur. The major types of biases are: (1) strategic bias, i.e. depending on how respondents perceive the consequences of the hypothetical experiment, they may behave strategically and not reveal their true preferences (by acting as "free riders"); (2) information bias - potential biases induced by lack of, or type of, information given to the consumer in the contingent market, including: (a) instrument bias

- introduced by the process or procedures employed

to discover preferences (e.g. bidding games, payment card); (b) starting point bias, i.e. the mean final bid may differ with different starting points in bidding games; (c) vehicle bias, i.e. different forms of payment elicit different bias and the vehicle should therefore correspond reasonably well to how people actually would pay for the environmental improvement; (d) commodity specifcation bias, i.e. not explaining the commodity to be valued in a detailed way understandable to the respondents can distort the result; (3) hypothetical bias - the potential error induced by confronting the individual with an

72

imaginary situation i.e. would people behave the same way in an actual market?; (4) constant budget bias, which originates from the hypothesis that each individual has a type of mental budget for environmental goods, i.e. an idea of how much money they want to spend on environmental quality. If they are asked about one particular environmental good they tend to give up all or a very large part of their environmental account; and (5) sampling, interviewer or nonrespondent bias. In addition, disparities have been observed in empirical studies between using "willing-

ness-to-pay" (WTP) e.g. for reduced air pollution and "willingness-to-accept" (WTA) compensation to accept that the pollution continues, i.e. the disparity between Equivalent Variation (EV) and Compensating Variation (CV). This is contrary to expectations from conventional welfare theory. However, experimental evidence supports an interpretation of the observed disparity in payment and compensation-based measures as both red and psychologically meaningful (Knetsch & Sinden 1984, Gregory 1986, d'Arge & Shogren 1988).

In this study WTP was choosen as the appropriate measure. Clearly, asking someone what they will do or pay a priori is not the same as confronting them with a recognized and wellunderstood market and observing what they actually pay. However, two recent state-of-the-art assessments of the CVM, which review the majority of empirical applications of the method, alternative methods, experiments with actual payments (auctions) and laboratory experiments, conclude that carefully constructed surveys give meaningful values for environmental goods (Cummings et al. 1986, Mitchell & Carson 1986). For well defined recreational goods with little uncertainty and with which people have had valuatiodchoice experience, CVM using WTP-measures appears to give value estimates with an accuracy of

* 50 %. Cummings et al. (1986) consider this accuracy

to be sufficient to give an approximate size of the values involved. Using CVM to measure the benefits of less familiar goods such as air quality improvements or risk reductions of various kinds is more difficult. However, provided the respondents can be motivated to carefully follow the contingent market described in the scenario and find it sufficiently plausible, CV-surveys offer the possibility of obtaining meaningful information about consumer preferences for all nonmarket amenities (Mitchell & Carson 1986). CVM may in many cases also be the only way to estimate the value of an environmental asset. However, I agree with Mitchell & Carson (1987) when they say that we still have much of importance to learn about the CVM and that. it is vulnerable to misuse. They assume that new methodologies progress along a learning curve consisting of several stages. Although the CVM has passed the experimental prototype stage, it is not

73

understood well enough to have reached the routine application stage. Field applications should therefore always be combined with methodological research. The principal challenge facing the CV researcher is to make the scenario sufficiently understandable, plausible, and meaningful to respondents so that they can and will give valid and reliable values despite their lack of experience with one or more of the scenario's dimensions. Provided a representative sample of all the affected individuals is used, CVM can potentially elicit both use and non-use values, held by people today. By use vahe we mean the value of actually using the environmental good; e.g. the recreational value of fishing. The non-use values include option-, existence- and bequest value. Option value is the value or "insurance premium" an individual would pay to ensure the existence of fish populations so that hefshe could have the option of fishing in the future, even if helshe does not do so now. Existence value is the value people place on the simple existence of the fish populations. Their valuation of being able to deliver this existence to future generations is termed the bequest value. The different parts of the non-use values can often be difficult to separate. Both the use and the non-use values are needed to estimate the total WTP for an environmental good. Empirical evidence indicates that a large part of the WIT is due to other motives than recreational use of the good (Strand 1981, Greenly et al. 1981, Walsh et al. 1984). Therefore it is very important to include the non-use values, This may be particularly important in this study. In situations with a large degree

of uncertainty (which characterizes the dose-response relationships between acid depositi-

ons and freshwater fish populations), large non-use values motivated by risk-averted behaviour can be expected. Large non-use values in this acid rain case may also be expected because non-users vastly outnumber users. To conclude this short presentation of the CVh4 and to state the importance of valuing environmental goods, I would like to quote Schultze et al. (1981,p. 170). From a review of four CV-studies where alternative methods were also used, they concluded as follows:

"In many cases decision makers quite simply have no idea as to the economic value of preserving environmental quality. All evidence obtained to date suggests the most readily applicable methodologies for evaluating environmental quality - hedonic studies of property values or wages, travel cost and survey techniques - all yield values well within one order of magnitude in accuracy. Such information in our view is preferable to complete ignorance".

74

2.2 SamuIing method and auestionnaire construction

This CV-survey consists of two independently drawn random samples from the Norwe.@an population, each of about 1,000 individuals over 15 years of age. The total survey sue was 2,032 persons, each representing one household. They were interviewed in-person by interviewers from a professional opinion poll agency (Gallup/NOI). Both samples were tested against socioeconomic data of the Norwegian population and found to be representative. The interviews were made in April and June 1986. This period began before the Chernobyl accident of April 26th and ended before the large media coverage of the radiation effects on fish populations and the following recommended consumption limits and prohibition of sale of freshwater fish from affected areas in July. Furthermore, differences between the results from interviews made in April and June were insignificant. This incident therefore seems to have had no systematic influence on the results of the survey. Respondents were asked to reveal their WTP for various intensities of lime application to the acidified water bodies. These intensities were described as enabling different increments in the freshwater fish populations in Southern Norway. These increments corresponded to the expected effects of 30, 50 and 70 % reduction in sulphur emissions in Europe (compared to 1980 levels). Different subsamples were confronted with different increments, and each respondent was asked about only one specific increment, In this way the respondents were not aware of the other possible improvements. This was done to avoid overwhelming the respondent with information during the relatively short interview. However, this can introduce biases. People may have difficulties in perceiving different marginal changes in environmental quality, and this problem may be exacerbated if not all of the possible improvements are presented. Paired comparison may therefore reduce this bias. (Paired comparisons of 30 and 50 % emissions reductions were used in the regional survey). Division into subsamples was also used to test for instrumental bias. Payment cards may provide a lower, more conservative estimate of value than the bidding games technique. To test for starting point bias in bidding games six subsamples were given different starting bids, which they could accept or reject. Depending on the answer the next bid presented to the respondent was higher or lower. This procedure was repeated until their highest bid on the scale was found. (The different bidding schemes are shown in Table 1.) Then they

TABLE 1 Description of payment instrument and emission reduction used in the nine subsamples. Subsample no,

Percent reduction in

Payment instrument1 sulphur emissions B.G. B.G. B.G. P.C. B.G. B.G. B.G. P.C. P.C.

30 30

30 30 50 50 50 50 70

- f.b.

NOK 200

- f.b. = NOK 500 - f.b. = NOK 1O , OO - f.b. = NOK 200 - f.b. = NOK 500 - f.b. = NOK 1,OOO

1a) B.G.(Bidding Games) - different biddine. schemes

First bid (f.b.)

NOK 500

Bid sequence

\ 200

b) P.C. (Payment Card) (originallv all amounts were on the sameline1 0

10

20

50

100

200

300 400

500

700

1,000 1,200 1,500 1,700 2,000 3,000 4,000 5,000 10,OOO

76

were asked the maximum, annual WTP for their household. The bidding technique was used only to establish a "learning process'' for the respondents about their subjective valuation of this non-market good. The remaining three subsamples were shown a payment card with amounts ranging from 0 to 10,000 NOK (1 NOK = US $ 0.16) and were asked to pick the amount that reflected their maximum WTP. Table 1 gives an overview of the different payment schemes and marginal changes in sulphur emissions used in the nine subsamples. Because statistical analysis limits the possibility of using split samples, corrections were made in construction of the WTP-questions in an attempt to avoid other potential methodological biases. These WTP-questions for subsample no. 5 and a review of the background information collected is reproduced in Appendix 1. The corresponding questions in the other subsamples are identical except for payment scheme, degree of emission reduction and the resulting effect on freshwater fsh.

In the following I wiU comment on the questionnaire and the potential biases involved. The contingent market was designed to be as realistic and credible as possible. A map of acidification damages to freshwater f s h in Southern Norway in 1980 was shown (see Appendbi 1). At the same time information was given about this pollution problem, its origin, and international commitments to emission reductions. To most Norwegians this environmental problem is well-known through widespread media coverage. Nevertheless it is important to give all respondents the same minimum amount of objective information. Then it was stated that Norwegian authorities were considering starting large scale liming of the affected water bodies as a necessary first aid action while waiting for the effects of the international agreements on emissions reductions. This liming was assumed to have the same effects on the fsh populations as emission reductions. This description was used to try to avoid "protest bids", i.e. people stating a WTP lower than their actual value because they believe the "Polluter-Pays-Principle"should be used. The setting was also realistic and appropriate since liming was already in progress and government grants for this purpose were (and are) very limited. Next, diagrams of improvement in the brown trout stocks corresponding to reduced sulphur emissions, together with a verbal description of the effects on the atlantic salmon stocks were introduced. The diagrams are shown in Appendix 2. Originally both

the map and the diagrams were in colour, different colours corresponding to different fshery conditions. These simple descriptions are based on the expected value of the improvements. Alternatively a probability distribution of different increments in the fish

77

stocks based on experts' "best guesses" could have been used. However, no such data was available. Also, this more complicated, detailed and more uncertain delphi-technique does not guarantee a more perfect assessment, considering the low level of information about the dose-response relationship (Crocker 1985). Based on comments from the interviewers it seems the map and the diagrams were understood by the respondents and that the presentation in general worked well. The wording of the question may be seen as a reasonable compromise to avoid both the hypothetical and strategic bias. To put the described situation into a "decision framework",

it was stated that the answers to the questions would influence the decision to lime or not. This was done to motivate respondents to think carefully through their valuation of the environmental improvement, and to make the constructed scenario less hypothetical. A more realistic situation may, however, increase the possibility of strategic answers. The provision at the end of the question (that all Norwegian households would pay, and according to their income), was introduced to minimize the strategic bias. If respondents gave biased WTP responses, visual inspection of the frequency distribution may show bimodal clustering of values at abnormally high and/or low levels. This was not observed, suggesting there may be little or no strategic bias in the results. However, without knowledge of the true underlying values, visual inspection does not constitute a completely satisfactory test of strategic bias. To avoid respondents basing their WTP on the actual costs of liming, these were said to be unknown. Such statements could have had the same anchoring effect as first bids. The period of payment was also made uncertain. In this way, the value estimate elicited can be assumed to approximate the annual WTP per household for all time to come. The payment was to be collected as an annual income tax to a federal liming fund. Tax was used for two reasons. First, this is a just payment vehicle, i.e. everybody pays according to their income. Second, the results can be compared directly to the total WTP for all the freshwater fish in Norway estimated as increased income tax in a previous CV-study (Strand 1981). Paying into a special fund, to be used exclusively for the purpose of liming and restocking acidified lakes and rivers, is recommended as a relatively neutral method of payment (Water Resources Council 1979). Respondents not willing to pay for increments in the fish population were asked a question designed to determine why (Appendix 1, question no. 3). This made it possible to find out how many of these individuals stated zero WTP because they rejected the payment vehicle or hypothetical market, although their "real" WTP was not zero (i.e.

78

"protest zero-bids"). To distinguish between use and non-use values, respondents were asked to estimate how large a portion of their stated amount was due to different motives (see Appendix 1,question no. 4).

To control for the "constant budget''-bias, the respondents were asked their maximum WTP for improvements in the qualitylquantity of all the public goods affected by acid rain. A verbal description of the effect on these goods was given (see Appendix 1, question no. 5). This description is very rough due to the lack of empirical studies and large uncertainty about the dose-response functions. This accuracy should be sufficient to test for the specific bias, but one should be careful in interpreting the resulting value estimate as the social economic value of the total environmental improvements from reduced acid depositions.The question was not constructed for this purpose. In addition to the above described WTP-questions, data on relevant predictor variables

was collected (see Appendix 1 for a complete fist). They were used to develop an appropriate econometric model of the WTP for increments in the fish stocks. One of these explanatory variables is of particular interest. It is reasonable to assume that people will have less difficulty in describing how their behaviour would change in response to an environmental improvement, than in placing an economic value on the same improvement. Thus, all respondezts, both anglers and non-anglers, were asked how many additional days they would fish in freshwater habitats each year as a result of the described increments in fish stocks. The statement of intended behavioural change, together with information on the recreational value per angler day (RVD)(collected from rivers and lakes of the same quality that can be expected in the restored water bodies), can be compared to the recreational value derived from question no. 4 in the survey (Appendix 1). This comparison provides a consistency check of the recreational value. However, of the

rivers in Norway where the TCM has been used to derive RVD-estimates, none have the same quality as can be expected in restored rivers. Therefore the previously mentioned case study of the River Vikedalselv has to be completed before the consistency check can be carried out. 3 RESULTS AND DISCUSSION In this chapter, I will fust present the value estimates derived from the WTP-questions

and discuss how the potential biases inherent in the CVM may have influenced these results. In the second section multiple regression is used to find those explanatory variables that are important in predicting the respondents' WTP. In the last section

79

benefits per household are aggregated to produce total social benefits for the described increments in the freshwater fuh stocks. This estimate is compared with benefit estimates from other studies, and with the costs of liming and re-stocking, which are first-aid actions to achieve this environmental improvement.

3.1 Benefit estimates and Dotential biases Table 2 shows some statistical characteristics of the WTP-results for the different subsamples. Let us first discuss the results for the increments in fish stocks. A very high response rate to these questions and relatively low and constant zeroresponse indicate reliable and valid results. The 95 % confidence interval for the mean value of the WTP for different subsamples was also constant around

rt

15-25 %. The mean values vary from 278 to 603 NOK in the

different subsamples. The payment card tends to give the lowest estimates, and the largest first bid the highest. Mean WTP increases as the first bid increases. One way classification analysis of variance was used to test for starting point bias. The results showed that the mean final bids corresponding to different starting bids in the bidding game for 30 % emission reduction were significantly different at the 0.05 confidence level. This statistical difference could not be observed in the 50 % emission reduction bidding game. For the 70 % reduction the starting point bias could not be tested, because only one subsample was shown a payment card. This was due to the survey’s budget restrictiOm.

In spite of the highest, but still relatively small, zero responses, the payment card generally seems to work better than the bidding schemes. The payment card also produces more conservative value estimates. The median values for WTP range from 100 to 300 NOK/household/year. This would be

an important predictor of the maximum WTP that could be adopted if an actual referendum on this subject was taken. However, this is not common practice in Norway. Nonetheless, the median values show the maximum amount 50 % of the respondents are willing to support. Comparisons of mean and median values show that the frequency distribution of the WTP is skewed towards the left, i.e. the lowest bids. A comparison of the mean WTP for the increments in fish stocks with the correspon-

ding estimate for the total increment in all the affected public goods (fsh included), shows that 59-91 % of the latter is due to the fsh stock improvements. The percentage seems to be lowest and most stable for subsamples using the payment card. The generally

TABLE 2 Maximum, annual willingness-to-pay ( W T P ) of Norwegian households for improvement in the freshwater fish populations (WTP-fish) and all public goods in Norway affected (WTP-public goods) by reduced European sulphur emissions. ( I n 1986-NOK). ( 1 N O K = U S $ 0.16 - exchange rate April 1988).

Subsample no. (emission reductions) 1

N o . of observations 288

Response rate fish/pubiic

First bid

goods

98/97

WTP - f i s h / household/year Mean M e d i a n S t d . Dev .

200

278

200

338

J T P - p u b l i c goods/ household /y e a r dean M e d i a n S t d . Dev I

375

200

652

Mean WTP-fish Mean WTP-publ i c goods

VTP-f i s h ? e r c e nt cero- b i d

(%)

74

23

270

97/95

500

455

200

826

537

200

1003

85

18

238

99/96

1000

603

300

712

700

250

1285

86

23

239

97/99

335

100

514

478

100

1130

70

29

206

99/96

200

366

200

660

617

200

1324

59

23

206

98/98

500

578

200

1036

793

300

1883

73

17

204

97/97

1000

192

98/98

189

98/97

0-10000 (payment card )

597

200

796

656

200

962

91

23

0-10000 (payment card)

291

100

492

444

150

998

66

28

0-10000

387

200

648

603

200

1274

64

27

(payment card )

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high percentage can be viewed as reasonable due to the fact that the current damage to public goods by acid rain in Norway is largest for the freshwater fish populations. However, this result may also be due to the sequencing and the constant budget bias. The respondents were fist asked their WTP for fish without being aware or thinking of the other public goods affected. They therefore could have overestimated their WTP for

this particular environmental good. This would have given them less of their "environmental budget" to spend on the other public goods affected by acid rain. This bias could have been avoided if the respondents had been provided the opportunity to reconsider and adjust their bids for the fish stock increments. Results from the regional survey where such reconsideration was provided, showed that only 13 % of the respondents adjusted their bids and that the mean WTP for fish should be reduced by 6-13 76 to correct for this bias. A CV-study of the WTP for increments in the fish population in Oslomarka (the recreational area surrounding Oslo), showed a 35-50 % reduction of the mean WTP for this good when environmental policy items other than acid rain were introduced (Amundsen

1987). This local CV-study used the same question format as the national survey, and was constructed with this comparison and transferance of results in mind. These results correspond well with the results obtained by Schultze et al. (1983). They found a tendency

for the WTP for one separate environmental good to decrease by 10-40 % when other environmental goods were introduced. Figure 1 illustrates the variation of mean WTP with different emission reductions and the corresponding increments in the fish populations. (Note that the dose-response relationship utilized is assumed to be linear). No emission reduction and no environmental improvements are assumed to give zero WTP, and the curves therefore pass through the origin. When looking at the mean of subsamples using bidding games the WTP appears to increase (but at a decreasing rate) with increasing improvements in the fish populations and for all affected public goods. This corresponds well with general welfare theory. However, the observed tendency is not statistically signtficant, and the same tendency can not be observed for the subsamples using payment cards. This indicates that the respondents have difficulties in perceiving the differences between the environmental improvements. The reason for this could be that the differences are so small that they are difficult to distinguish or that each respondent was asked about only one particular improvement. Results from the regional survey, where each respondent received descriptions of the effects of both 30 and 50 % reduction in the sulphur emissions, indicate that the

82

Mean WTP/household/ Year (1986 NOK)

100

600

500

400

300

200

100

Percentage reduction in the number of lakes devoid of brown trout in "S~rlandet".Corresponding percentage reduction in the sulphur emissions in Europe in parentheses.

FIGURE 1 Mean, annual willingness-to-pay (WTP) of the Norwegian households for environmental improvements due to different reductions in sulphur emissions. Key to symbols:.- d subsamples with bidding games MWTP for fish 0--Q WTP for all affected environmental goods

- subsamples with payment card MWTP for fah 0-- -0 WTP for all affected environmental goods

*At these levels of sulphur emission reductions the salmon rivers in "Sarlandet" could also recover reproducing fah stocks.

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latter explanation is more likely.2 Respondents not willing to pay for increments in the freshwater fish populations were asked a question designed to determine why. From Table 3 it can be determined that rejection of the payment vehicle or hypothetical market (i.e. "protest zero-bids") represented 14.5 % of the total sample of 2,032 households. This is within the 15 % limit recommended in the guidelines for CV-studies by the Water Resources Council (1979). These individuals may actually place an economic value on the described environmental improvement, but object to the construction of the question. Therefore the aggregated, total WTP for all households estimated may understate the total value to society. TABLE 3 Frequency distribution of the most important reasons for stating zero willingness-to-pay for increments in freshwater fish populations at different emission reductions. (Results from question no. 3, see Appendix 1). Emission reductions

Reason for zero bid

30 %

50%

70%

28%

23%

31%

58 % 14 %

69 % 8%

61 % 8%

Sum

100 %

100 %

100 %

No. of observations of zero bids

237

183

52

1,035

808

189

A. "Real zero-bids" (1.Don't fish; 2. Can't afford it; 3. Other things are more important) B. "Protest zero-bids" (4. I pay too much tax already; 5. The polluters should pay) C. Other reasons

Total sample size

An approximated Student's t-test (Welch 1947) was used to test the hypothesis Ho: Mean WTP (30%) = mean WTP (50 %) versus Ha: Mean WTP (30%) # mean WTP (50 %). Ho was rejected at the 0.01 confidence level.

84

The respondents asked about the 50 and 70 % emission reductions who stated a positive WTP were asked to distribute this amount among different motives. Table 4 shows how the aggregate, total WTP for all respondents was distributed between use and non-use values. As hypothesized, a very large part (88 %), of the total WTP was due to non-use values, and only 12 % was motivated by recreational use (angling). This is due to the fact that even the anglers, who constituted 27 % of the respondents, were also motivated largely by non-use values: only 27 5% of their total WTP was due to recreational value. In addition the mean WTP stated by anglers was higher and differed significantly (at the 0.01 level) from the corresponding value for non-anglers (non-users). The decomposition of use and non-use values used here, may be subject to bias due to people’s difficulties in dividing their total WTP between these two categories. However, this strategy is considered preferable to describing each individual type of value to the respondents and then ask them separate questions about their WTP for the good motivated by use and non-use. In that way separate values for use and non-use are obtainedduectly, and total WTP is estimated by simply adding the values (Mitchell & Carson 1987). Greenly et al. (1981) has used this latter strategy to obtain a use value comprising 39.8-51.9 % of the total WTP for preservation of existing water quality in the South Platte River Basin, USA. Strand (1981) used a third strategy to find a use value comprising 40 % of the total WTP for preserving all freshwater fish in Norway. He estimated the total WTP by using a TABLE 4

Frequency distribution of aggregated, total willingness-to-pay (WTP) for increment in freshwater fish populations on different motives.* Motives for WTP

Percentage of total WTP

(%I ~~

Recreational value Option value Bequest- and Existence value

12 12 76

Sum

100

No. of observations

733

* (Results from question no. 4; see Appendix 1. This question was used only in the subsamples asked about 50 and 70 % emission reductions).

85

nationwide CV-survey. This estimate was compared to a use value estimate derived from a TC-study of one river assumed to be representative of all rivers in Norway. Clearly, this

is a strict and not very plausible assumption. Both these studies result in a higher use value than our study. This may be due to the different strategies used to separate use and non-use values. A comparison with results from a study using the decomposition strategy (Strand 1985) supports this hypothesis. Strand (op.cit.) concluded

that most of the

non-use values of the Norwegian population's WTP for improved air quality from automobile pollution abatement was due to uncertainty about current and future effects of air pollution. A strategy of treating the WTP amounts given by the non-users as a relatively pure

expression of non-use values and assigning all of the users' WTP amounts to use value has been suggested as a method of giving a lower boundary for non-use values (Fisher 8c Raucher 1984). Using the strategy in this study suggests a minimum non-use value of 63 % of the total WTP. Clearly, regardless of the strategy used, non-use values constitute the major part of the total WTP. 3.2 Multble regressions

Multiple regression was used to produce statistical WTP functions. W P for increments

in the freshwater fish stocks due to emission reduction j for household unit i, was estimated as: WTPij = f(1, S,F, B, S,A, P) where I = household income, S = socioeconomicvariables, F = freshwater angling activity, B = intended behavioural changes in freshwater angling, S = substitute activity, i.e.

saltwater angling, A = attitude towards environmental preservation and P = payment instrument. Previous empirical research (Strand 1981) and theoretical welfare economics served as a guide in preselecting these explanatory variables. Table 5 illustrates the relationship between annual WTP and household income and other predictor variables thought to be important. The estimations are carried out separately for 30 % and 50 % emission reductions. Ordinary Least Square (OM) regressions are estimated. Due to uncertainties inherent in the method and the fact that statistical estimation will therefore provide a very uncertain picture of the true preferences in the

86

population, it seemed unnecessary to use more advanced statistical methods (e.g. generalized non-linear regression models). The multiple regressions (no 2 and 4) are based on less observations than the corresponding simple regressions (no. 1 and 3) because some respondents did not answear

all the questions. The simple linear regressions between WTP and household income (regression no. 1 and 3) show that the WTP increases with increasing household income. The regression coefficient is significant at the 0.01 level and is about the same size for TABLE 5 Regression estimates of total willingness-to-pay (WTP) for increments in freshwater fish populations in Southern Norway due to 30 and 50 % sulphur emissions reductions a. Variables

Regression coefficients 30 % emis. red. 50 % emis. red. 1 2 3 4

. Income (1,OOONOK)

- household income .&

- 15-29 - 30-44 - 45-59

.Number of angler days in

1.464**

1.107** 1.447**

0.835**

140.21** 49.18 -40.12

176.98* 123.48 -25.35

-22.00 66.99 128.43

182.40* 157.58 328.18*

14.38 186.27** 353.87**

36.12 60.96 92.90

691.88

544.59

337.68** 193.17 111.93

427.71** 174.99 18.89

freshwater in 1985

- 1-9

-

10-29 - 30 + , Number of additional ander dayslyear - 1-4 - 5-10 - 11 + .Attitude towards environmental preservation - active in environmental issues - greatly concerned about environmentalissues - less concerned - little concerned

(TABLE 5 - continued) Regression coefficients

Variables

30 % emis. red. 1

Pavment instrument - first bid = 500 NOK - first bid = 1,000NOK - paymentwd Education (years) - 10-12 - 13 + Recreational fishinq in saltwater in 1985 - yes Place of residence - Oslo - Bergen - Trondheim - town with more than 2,000inhabitants - town with less than 2,000inhabitants Living in "Sarlandet" - yes Sex - man Constant term

3

4 194.47** 236.70** -53.02

129.57** 319.27** 71.68 60.87 54.49

15.46 162.65

87.79*

86.16

-17.55 150.01* 482.02**

-154.05 260.32* 563.91** 88.00

160.55** 16.87

-77.98

115.04*

185.22*

161.94**

39.9 -355.94* *

-115.78* 169.75** -208.02

0.05 51.47

0.25 11.98

0.04 33.06

0.18 6.65

0.0001 966 968

O.Oo0 1

0.0001 751 753

0.0001 653 681

-

Adjusted R2 F-value Significance level of F-value Degrees of freedom Number of observations

2

50 % emis. red

843 871

a Regression coefficients significantly different from zero at the 0.01 and 0.05 confidence level are denoted respectively ** and *.

WTP for effects from 30 % and 50 % emission reductions. These simple regressions are

used to calculate the gross effect of income on WTP, i.e. not considering the effects of other explanatory variables. The Engel elasticity for freshwater fish populations, here defined as the relationship between the households WTP (as an expression of the demand for the good) and their money income, is estimated to be in the range l.447 - 1.464.This

88

means that the demand for this non-market good increases by 1.45 to 1.46 % when income increases by 1 %. This is in agreement with Biarn & Jansen (1982, Table 7.7), who estimated the Engel elasticity for recreational goods to be 1.260, This estimate was based on cross-section data on consumer demand in Norwegian households in the period 1975-77 (from the Central Bureau of Statistics). In USA Thompson & Tinsley (1978) found an Engel elasticity for recreational fishing of 1.39. However, both these studies are based on real expenditures and estimate the Engel elasticity of only the recreational part of the environmental goods. In addition these studies are also based on the gross effect of income, and are therefore subject to specification error. Inclusion of other important explanatory variables would give a more correct estimate of the Engel elasticity for freshwater fish populations. The lower Engel elasticity of 0.835-1.107 derived from regression no. 2 and 4 in Table 5 should therefore be used. In

these regressions the pre-selected explanatory variables considered most important are included. With the exception of income, binary predictor variables are used. For the binary variables, the regression coefficients show the difference in WTP compared to the reference alternatives. The reference alternatives are defined as following:

- Age = 60 4 - Number of angler days in freshwater in 1985 = 0

- Number of additional angler days/year = 0 - Attitude towards environmental preservation

= Thinks there has been too much environ-

mental preservation

- Payment scheme = First bid equal to 200 NOK

- Education = 9 years or less - Recreational fishing in saltwater in 1985 = No - Place of residence = Rural area with less than 2,000 inhabitants in a cluster - Living in "S~rlandet"= No - Sex = Woman The youngest age group was found to be willing to pay 140-177 NOK more than those over 60 years of age. This difference was statistically significant for both 30 % and 50 % emission reductions. For the 50 % emission reduction the WTP stated by anglers was higher than for the reference group that did not fish. This difference was significant only for those anglers that fished 1-9 or more than 30 days during the year before the survey was conducted. Such significant relationships were not found for the 30 % emission reduction. However, regression no. 2 shows that those stating they would fish an

89

additional 5 days or more per year were willing to pay 186-354 NOK more than the reference group, who would not change their angling activity. This difference was significant at the 0.01 level. The pattern was the same for the 50 % emission reduction, but no significant differences were found. Those greatly concerned about environmental issues stated a significantly higher WTP than those who felt environmental preservation had gone too far already. The results from the payment instrument variable provide evidence of instrument bias in subsamples for both emission reductions. The respondent's education was found to have a small positive, but not significant, effect on the WTP. Participation in saltwater recreational fishing, considered a substitute activity to freshwater recreational fishing, seems to have a positive effect on the WTP. This effect was significant only in the 30 % emission reduction case. Residents in the large cities Bergen and Trondheim have significantly larger WTP than those living in rural areas. For Oslo, the capital and the largest town in Norway, the picture seems to be the opposite. This difference is, however, not statistically significant. People residing in "Seirlandet", the area most heavily affected by fish losses, were willing to pay 115-185 NOK more than those living in other parts of the country (a significant difference). The results also indicate that women state a higher WTP than men do. In general, the relationships described above seem reasonable in regards to expectations

from economic theory and a previous study of the WTP for all freshwater fish populations in Norway (Strand 1981). R2 adjusted for degrees of freedom for regression 2 and 4 indicates that respectively,

25 and 18 % of the total variation in WTP can be explained by the variables included in the functions. This is the same level that has been obtained in other Norwegian CVstudies using data from a cross section survey of households (Strand 1981, Hervik et al.

1987). The F values of the equations were significant at the 0.0001 level. The mean, annual, total WTP per household to achieve marginal increments in the freshwater fsh stocks due to 30-70 % reductions in the sulphur emissions was found to be

in the range of 278-603 NOK (see Table 2). One way classification analysis of variance was used to test the hypothesis of no difference between the mean WTP. for the three different environmental improvements. The hypothesis could not be rejected at the 0.01 level. Thus, one mean WTP-estimate for all the different increments in the fish stocks was calculated. This estimate was then multiplied by the total number of Norwegian house-

90

holds, to produce an approximation of the total social economic value of these effects of reduced sulphur emission. Because of the observed starting point bias in subsamples using "bidding games", and because the payment card seemed to have the smallest "constant budget"-bias, gave conservative estimates and worked best in general, this latter method was used to produce a reasonable, least biased mean value estimate of 300 NOWhouseholcUyear (US$48). 3.3 Benefit amenation and ComDarison with costs

The estimate of 300 NOK/household/year aggregates to a social economic value of 456

million 1986-NOK per year. This is the value of achieving reproducable brown trout stocks in 567-928 lakes (larger than 5 ha) in "S@rlandet",recovering "some atlantic salmon" or

reproducable stocks in the same area, and halting further geographical spreading of the fish losses. This .estimate can be compared to the social economic value of preserving all freshwa-

ter fsh populations in Norway from extinction. In 1980 Strand (1981) used a CV-survey of 4,400 persons over the age of 15 to estimate a mean annual WTP of 800 1980-NOK per

person. This was considered a conservative estimate from the calculated interval 750-1,200. Adjusted by the consumers' price index and multiplied by the number of inhabitants over

15 years of age, this corresponds to an annual social economic value of 4,350 million 1986-NOK. This means that the economic value of the marginal change in freshwater f s h populations from reduced acid depositions is about 10 percent of the value of all freshwater fish. However, both the number and the area of lakes and rivers restored as a result of the emission reductions seem to be much less than 10 percent of the total (Central Bureau of Statistics 1981, 1983). The unproportionally large value of the marginal increment in the

f s h stock is assumed to be due to the fact that these fish losses are concentrated in an area where more than l/3 of the Norwegian population lives. This effect may, however, be partly offset by methodological differences between the two surveys. Because Strand (1981) asked about the WTP to avoid extinction while in our survey WTP to recover fish populations was stated, loss aversion and the drastical extinction threat may have "biased"

Strand's estimate upwards. To my knowledge there have been no similar studies of the total WTP for marginal increments in freshwater fish populations due to reduced acid depositions. However, two Travel Cost (TC)-studies of the reduced recreational value of fishing due to acidification

91

in the Adirondack Mountains in the state of New York, USA should be mentioned. Both studies (Mullen & Mentz 1985 and Violette 1986) are based on the New York Anglers Survey 1976-77. Mullen & Mentz (1985) found that if 5 % of the water acreage was devoid of f s h this would reduce the annual recreational value of fshing to the New York resident anglers by 3.4 %. If the damaged water acreage increased to 10 %, the corresponding reduction in the recreational value was found to be 5.5 %. Thus, the incremental reduction in the recreational value was less than that associated with the initial habitat

loss. This was found to be due to the increased importance of substitution as additional angling sites were lost. Mullen & Mentz op.cit. conclude that these estimates probably understate the loss in recreational value because of uncertainties about the assumptions made in the TC-model and the extent of the current acidification damages. Violette (1986) uses a different TC-model not including any "substitution variables", because it might be argued that these threatened, high altitude brown trout ponds provide a relatively unique recreation experience with no perfect substitutes. Violette op.cit. tried

to incorporate the uncertainty of the acidification damages by constructing four different scenarios. The results approximated those found by Mullen & Mentz (1985). Because these studies reflect changes only in use value from decrements in the fsh stocks they cannot be directly compared to the results from my study. In addition the scale of the problem is much larger in Norway. Due to these differences, it is difficult to draw any unambiguous conclusions from this comparison. The benefit estimate of 456 million 1986-NOK per year for the increments in the Norwegian fsh stocks from reduced acidification can also be compared to the costs of liming and re-stocking. From Matzow (1984) the annual costs of liming the run-off from the entire acidified area in Southern Norway can be calculated to be approximately 300

million 1986-NOK. Thus, this estimate can be viewed as the liming costs corresponding to a 100 % reduction in sulphur emissions. However, this estimate does not include labour costs, because current liming operations are voluntarily carried out by land owners and members of the local hunting and fishing organizations. In addition to the liming costs come the costs of re-stocking those rivers and lakes devoid of fish. No estimates of these costs exist, but it is reasonable to assume that they are not larger than the additional liming costs corresponding to the difference between 70 and 100 % reduction in emissions. Due to the lack of cost estimates, present values of these liming and re-stocking efforts can not be calculated. However, the existing information and the considerable size of the benefit estimate indicate a positive net present value.

92

Liming and re-stocking of water bodies are fust aid actions, and only large international emission reductions can provide a final solution to this pollution problem. Thus, since Norway is a net-importer of long range transported air pollutants and the Polluter-Pays-Principle is internationally accepted, the benefit estimate should be used to document the economic value of repairing the currently most important environmental damage from acid rain in Norway. 4 CONCLUSION

The annual social economic value of marginal increments in the freshwater fish populations in Southern Norway due to a 30-70 % reduction in sulphur emissions, is estimated to be approximately 450 million 1986-NOK (or about US $ 72 million). This is 0.009 % of the Norwegian GDP in 1986 (Central Bureau of Statistics 1987). The value estimate illustrates the size of the welfare improvement to the Norwegian population, expressed as their aggregated subjective, total willingness-to-pay (WTP) for this environmental improvement. A Contingent Valuation (CV) survey of two independently drawn random samples of the Norwegian population, each of about 1,000 households, was employed to derive this estimate. The potential biases of the Contingent Valuation Method are addressed, and the CV survey was designed to control for the most important biases. The results indicate that this CV-design worked reasonably well. Nevertheless, there remain uncertainties in the

method and the damage estimates on which the valuation is based. In addition, the derived value is based on two important assumptions. First, the valuation is based upon present income distribution and the welfare change induced is assumed not to influence this distribution. Second, WTP of people today is assumed to reflect the value of the change in the environmental good, because unborn future generations can not be asked. The WTP for environmental improvements may, however, vary substantially with potential changes in the income distribution, and change over time as preferences for environmental goods change and new information becomes available. Using the conservative estimate of 450 million NOK reduces the possibility of overestimation. But due to the above described uncertainties, this estimate should be interpreted only as an approximation of the values involved. This is especially true since it is difficult to control the accuracy of the large non-use values observed. However, this study indicates that the economic value of environmental improvements due to reduced acid depositions is large. For the Nordic countries, as net-importers of

93

sulphur dioxide and other long range transported air pollutants, it is important to document these values and use them in negotiations about further emission reductions. To compensate for the lack of data and empirical studies on this subject, Navrud (1988) proposes and describes a Nordic research program on valuation of public goods affected by long range transported air pollutants. Such studies should, however, also be done in cooperation with other countries, which are differently affected by acidification damages. This would produce comparable results of considerable interest to policy makers. REFERENCES Amundsen, B.-T., 1987: Recreational value of the fish population in Oslomarka. In Norwegian. Masters thesis, Department of Forest Economics, Agricultural University of Norway, 89 pp. Biern, E. & E.S. Jansen, 1982 Econometrics of incomplete cross-section/time series data: Consumer demand in Norwegian households 1975-1977. Social economic studies no. 52, Central Bureau of Statistics of Norway, Oslo-Kongsvinger, 307 pp. Central Bureau of Statistics, 1981 Salmon and sea trout fisheries 1980. Central Bureau of Statistics of Norway, Oslo-Kongsvinger. Central Bureau of Statistics, 1983 Environmental Statistics 1983. Natural Resources and Pollution. Central Bureau of Statistics of Norway, Oslo-Kongsvinger. Central Bureau of Statistics, 1987: Statistical Yearbook 1987. Central Bureau of Statistics of Norway, Oslo-Kongsvinger, Crocker, T., 1985: Acid Deposition Control Benefits as Problematic. Journal of Energy Law & Policy 6(2):339-356. Cummings, R.G., D.S. Brookshire & W.D. Schultze, 1986: Valuing Environmental Goods. An Assessment of the Contingent Valuation Method. Rowman & Allanheld Publishers, New Jersey, USA, 270 pp. d'Arge, R.C. & J. Shogren, 1988 Non market asset prices: A comparison of three Valuations (this volume). Fisher, A. & R. Raucher, 1984: Intrinsic Benefits of Improved Water Quality: Conceptual and Empirical Perspectives. In Advances in Applied Economics, ed. V. Kerry Smith, (Greenwich, CT.,JAI Press). Greenley, DA., R.G. Walsh, & R.A. Young, 1985: Option Value: Empirical Evidence from a Case Study of Recreation and Water Quality. Reply. The Quarterly Journal of Economics 1985295-299. Gregory, R., 1986: Interpreting Measures of Economic Loss Evidence from Contingent Valuation and Experimental Studies. Journal of Environmental Economics and Management, 13:325-337. Hervik, A., M. Risnes & J. Strand, 1987: The value of river preservation in Norway. A Contingent Valuation Study. In Norwegian. NTNF-report. 78 pp. Knetsch, J.L. & J.A. Sinden, 1984: Willingness to pay and Compensation Demand: Experimental Evidence of an Unexpected Disparity in Measures of Value. The Quarterly Journal of Economics, 1984507-521. Matzow, D., 1984 Acid water. A situation report with cost estimates for liming actions with main emphasis on the county of Aust-Agder. In Norwegian. County Governor of Aust-Agder, Department of Environment. Working paper. 17 pp.

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Mitchell, R.C. & R.T. Carson, 1986: Using Surveys to Value Public Goods: The Contingent Valuation Method. Final Draft. Resources for the Future (RfF'), Washington D.C., USA. Mitchell, R.C. & R.T. Carson, 1987: How far along the learnhg curve is the Contingent Valuation Method? Discussion paper QE 87-07. Resources for the Future, 32 pp. Mullen, J.K. & F.C. Mentz, 1985 The Effect of Acidification Damages on the Economic Value of the Adirondack Fishery to New York Anglers. Am. J. Agr. Econ. 67:112-119. Munitz, F.P., H.M. Seip & L.H. Sevaldrud, 1984: Relationship between fish populations and pH for lakes in Southernmost Norway. Water, Air & Soil Pollution 239-113. Navrud, S., 1985: Increased social economic value of freshwater fish populations in Norway by reductions in sulphur emissions. In Norwegian. Report no. 830501-1 from the Center of Industrial Research, Oslo, 80 pp. Navrud, S., 1988: Valuation of public goods in the Nordic countries affected by acid rain. Report to the Nordic Council of Ministers. In Norwegian with an abstract in English. NMR-report. 109 pp. In press. NEMP, 1987 1000 lake survey 1986 Norway. The National Environmental Monitoring Programme (NEMP). Report no. 283/87 from the Norwegian State Pollution Control Authority. 33 pp. M I , 1987: Sulphur budgets for Europe for 1979-1985. The Norwegian Meteorological Institute. EMEPNSC-W, Note 4/87,17 pp. Overrein, L.N., H.M. Seip & A. Tollan, 1980 Acid precipitation-effects on forest and fEh. Final report of the SNSF-project 1972-1980. Research Report FR 19/80 (SNSF-project, MSK, 1432As-NLH, Norway). Randall, A,, J.P. Hoehn & D. Brookshire, 1983: Contingent Valuation Surveys for Evaluating EnvironmentalAssets. Natural Resources Journal 23(3):635-648. Rossland, B.O., O.K. Skogheim & I.H. Sevaldrud, 1986: Acid deposition and effects in Nordic Europe. Damage to fsh population in Scandinavia continue to apace. Water, Air & Soil Pollution, 30:65-74. Schultze, W.D., R.G. Cummings, D.S. Brookshire, M.H. Thayer, R.L. Whitworth and M. Rahmatian, 1983 ExperimentalApproachesto valuing EnvironmentalCommodities: Volume II. Draft final report for Methods Development in Measuring Benefits from Environmental Improvements, USEPA Grant CR 808-893-01, July 1983. Schultze, W.D., R.C. d'hge & D.S. Brookshire, 1981: Valuing Environmental Commodities: Some Recent Experiments. Land Economics, 61:156-175. Seip, H.M., N. Christophersen & S. Rustad, 1986: Changes insstreamwater chemistry and fshery status following reduced sulphur deposition: Tentative predictions based on the Birkenes model. Proceedings from "Workshopon Reversibility of Acidification",Grimstad, Norway, June 9-11,1986,Commission of European Communities:177-184. Sevaldrud, I.H., I.P. Muniz & S. Kalvenes, 1980: Loss of fish populations in Southern Norway. Dynamics and magnitud of the problem. In Drablgs, D. & Tollan, A. (eds.): "Ecological impact of Acid precipitation":350-351,SNSF-project. Sevaldrud, I.H. & 0.K Skogheim 1986: Changes in fish populations in Southernmost Norway during the last decade. Water, Air & Soil Pollution, 3031-386. Strand, J., 1981: Economic valuation of freshwater fish populations as a public good in Norway. Results from an interview survey. In Norwegian with summary in English. Department of Economics, University of Oslo, 111pp. Strand, J., 1985 Valuation of Reduced Air Pollution from Automobiles in Norway. In Norwegian. Department of Economics, University of Oslo, Memorandum no. 1-1985, 89 PP. Thompson, C.S. & A.W. Tinsley 1978: Income Expenditure Elasticities for Recreation: Their

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Estimation and Relation to Demand for Recreation. Journal of Leisure Reserch, 10:26S270. Violette, D.M., 1986: A Model Estimating the Economic Impacts of Current Levels of Acidification on the Recreational fishing in the Adirondack Mountains. EPA-report no. 230-32-86-021, September 1986. Walsh, R.G., J.B. Loomis & R. G h a n 1984 Valuing Option, Existence and Bequest Demands for Wilderness, Land Economics 60(1):14-29. Water Resources Council, 1979 Procedures for evaluation of national economic development benefits and costs in water resources planning. Federal Register 44,24272950-72965. Welch, B.L., 1947 The generalization of Students problem when several different population variances are involved. Biometrica 3428-35.

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APPENDIX 1 QUESTIONAIRE - NATIONAL SURVEY, SUBSAMPLE NO. 5 (Instructions to interviewers in parentheses) Question 1 JShow maD1 This map shows the acidification damages to our freshwater fish populations. This acidification is largely due to long range transported air pollution from other countries in Europe. To reduce this acidification most of the European countries have agreed to reduce their sulphur emmissions by 30 % within 1993, and negotiations on further reductions have started. In anticipation of these reductions, the Norwegian govern ment is now considering large scale liming of our water bodies. The lime will neutrahze acid depositions. This liming, together with re-stocking of lakes and rivers devoid of fish, is a necessary fustaid action to maintain fisheries in the damaged areas and prevent spreading of acidification damages to other vulnerable water bodies. (Show diagrams) These diagrams show the considerable increase in trout populations in the four southernmost counties (Telemark, AustAgder, Vest-Agder and Rogaland) that can be achieved by lime applications corresponding to a 50 % reduction in acid depositions. Similar effects could be expected in the rest of the affected area. This liming will also have a positive effect on salmon rivers. AU of the rivers in the four southernmost counties, where salmon are now nonexistent, can be re-stocked and will again give rise to good salmon fishing. This liming would also stop fish losses from spreading north along the western coast of Norway, where there are still rich salmon rivers. The costs of any liming and re-stocking program must be paid by the Norwegian society (i.e. taxpayers). The government is therefore interested in determining the value the Norwegian population places on the described increase in fish populations and on preventing the further spread of fish losses. An important question is whether this value outweighs the costs of liming and re-stocking. One way to measure this value is the people’s willingnessto-pay to achieve this environmental improvement. The answers to the following questions may therefore affect the decision to undertake these actions. We don’t know exactly how much these actions will cost, or how many years it will be necessary to lime.

91

Suppose that the costs will be distributed among all households in Norway by payment of a special, annual tax to a federal liming fund. If all households pay equally in relation to their income, and this tax was NOK 200 each year for an average household in the years to come, would you then be willing to support these actions?

(Bidding scheme)

Question 2 What is the largest amount your household is willing to pay annually, if that should be neccessary to implement the liming program? NOKQuestion 3 (To those that answered NOK 0 to question 2 ask:)

What is your primary reason for answering NOK O? JShow card with these alternatives1 1.I don’t fish and therefore see no reason to pay for increased fish populations. 2. My living costs are already too high; I can’t afford it.

3. Other things are more important; e.g. hospitals, schools etc. 4. I think I pay too much tax already.

5. I think that those countries that produce the pollutants causing the damage, also should pay for actions taken to repair these damages. 6. Other reasons:

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Question 4 People are willing to pay for this increase in the fish populations for different reasons. How large a portion (7% of 100) of the amount you stated would you say is motivated by these different reasons? JShow card with these alternatives): 1. I am an angler myself and pay to continue

this recreational activity.

%

2. I am not an angler, but I will pay to secure

the option to fish in the future.

%

3. Payment to preserve the freshwater fish popu-

lations due to other reasons than being an angler or wanting to keep the option to fish in the future; i.e. payment to preserve the existence of freshwater fish, and being able to deliver this existence to future generations.

-%

Total.

100 %

Question 5 If acid depositions were reduced by 50 % in Norway, this would also entail other environmental improvements. In addition to effects on freshwater fish this would reduce the danger of forest dieback, the accumulation of toxics in plants and animals, the corrosion of historical buildings and monuments and the possibility of long term effects on people’s health and wellbeing. The government is also interested in finding the value the people place on this total environmental improvement. One way of measuring this value is the people’s willingness-to-payto get this improvement. Suppose that all households pay the same amount in relation to their income. What is the highest amount your household is willing to pay annually to achieve this environmental improvement?

total

99

OTHER INFORMATION COLLECTED: 1.Recreational fishing activity

a) No. of angler days in freshwater habitats in 1985 (divided into salmon fishing and fishing for other freshwater fish species) b) No. of additional days in freshwater habitats if we achieved the described increase in the fish populations; even if you do not

fish today (i.e. intended behavioural

change) c) No. of angler days in saltwater in 1985 (i.e. substitute activity) 2. Attitudes towards environmental issues in general

3. Socioeconomicvariables:

a) Personal income

b) Household income c) No. of persons in household

d) Sex e) Age f ) Marital status g) Place of residence h) Education

i

A

m

S \<-

101

AppENDM 2

THE CONDITION OF BROWN TROUT POPULATIONS IN THE LAKES IN THE FOUR SOUTHERNMOSTCOUNTIESOF NORWAY (TELEMARK,AUST-AGDER,VEST-AGDER AND ROGALAND) UNDER DIFFERENT REDUCTIONS IN ACID DEPOSITIONS. (a) Reference situation (1980).

Y

44 %

1800

:1600 u.4 0

1400

n2 1200

5 1000

z

800 600

400 200 0

Good

s t r o n g l y affected

Ext m c t

(b) The situation after a 30 Dercent reduction in acid depositions.

2000 Y

2

1800 1600

u.4

o 1400

y D 9

1200 1000

z 800 600 400 200 0

Good

S t r o n g l y affected

Extinct

I

102

(c) The situation after a 50 percent reduction in acid depositions.

2200 2000

1

5 1 '8

u)

1800 rl W

1600

0

1400

y

1200

z5

1000

e

30 %

800 600 400

200 0 Good

Strongly affected

Extinct

(d) The situation after a 70 percent reduction in acid depositions.

2600 2400

63 %

2200 2000 v)

2 2 4%

0

y

1800 1600

1400 1200

e

5 2

1000 800

600 400 200 0 Good

S t r o n g l y affected

Extinct

~~~~

part II

_____

The Valuation of Health and Life

This Page Intentionally Left Blank

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Chapter 6 BENEFITS OF REDUCED MORBIDITY FROM AIR POLLUTION CONTROL A SURVEY MARK DICKIE and SHELBY GERKING School of Social Sciences, University of Texas at Dallas, Richardson, Texas, 75083-0688; Department of Economics, University of Wyoming, Laramie, Wyoming, 82071-3985 (United States)

1 INTRODUCTION

Estimating human health benefits from reduced air pollution is important both to policymakers and academics. In the United States, the Clean Air Act and its subsequent amendments direct the U.S. Environmental Protection Agency to establish primary standards to protect human health, with special emphasis on the health of particularly sensitive population groups. Additionally, Executive Order # 12291 requires Regulatory Impact Assessments of major federal rules and regulations, making benefit-cost analysis of health oriented standards an important practical issue.

From an academic viewpoint,

valuation of improved health and other nonmarket commodities is a key aspect of applied welfare and environmental economics.

Yet, until recently, methods used to compute

benefits of reduced morbidity and mortality often have not been based on a measure of

willingness to pay.

As a consequence, there now is considerable interest in developing

theoretically defensible and empirically feasible methods for valuing these benefits. These two sources of interest in estimating the benefits of improved health have motivated a considerable volume of research. Relatively more research has been devoted to the mortality effects of air pollution and, more generally, to estimating the marginal value of safety. One reason for this emphasis is that death is more easily measured than illness or injury. Death is a one dimensional event, while there are varying degrees of illness and injury. However, benefits of reduced morbidity are equally important to obtain

in light of the need to evaluate the reduction of nonfatal hazards. This paper critically reviews methods for estimating benefits of reduced morbidity and suggests directions for future research.

A corresponding recent survey of methods for

estimating the marginal value of safety or "value of life" may be found in Fisher et al. (1986).

Additionally, a somewhat older but still useful survey of morbidity benefit

106

estimation has been prepared by Chestnut and Violette (1984). This review of morbidity benefit estimation surveys three methods. Section 2 surveys the cost of illness method and Section 3 surveys the contingent valuation method. The averting behavior method is discussed in Section 4.

The averting behavior method is given the greatest attention

because it is the least well known of the three methods. More extensive evaluations of the cost of illness and contingent valuation methods may be found, respectively, in Hu and Sandifer (1981) and Cllmmings et al. (1986). Implications and conclusions are presented in Section 5. 2 THE COST OF ILLNESS METHOD The cost of illness (COI) method estimates the total cost which morbidity imposes on society.

Total cost is defined as the sum of direct and indirect costs.

Direct costs

measure the value of resources devoted to the treatment of illness including (1) hospital care, (2) nursing home care, (3) home health care, (4) services of physicians, dentists, and other health specialists, (5) drugs, and (6) eye glasses. Indirect costs measure the value of lost productivity due to illness.

Indirect costs usually are estimated by the wage

multiplied by the time lost from work, often with some adjustment for the value of homemaker services.

Losses associated with disutility of illness, such as for pain and

suffering, are not included in cost of illness estimates. Total costs may be estimated on either a prevalence or an incidence basis.

The

prevalence of a disease is the number of existing cases of the disease in a given time period. Prevalence based costs, then, are all costs associated with all cases of the disease in that time period. The incidence of a disease is the number of new cases of the disease that occur in a given time period.

Incidence based costs are all discounted costs

associated with new cases of the disease, from the onset of illness until recovery or death occurs. Prevalence and incidence are nearly identical for short term illnesses. Cooper and Rice (1972) provide widely used prevalence based illness cost estimates which update the earlier estimates of Rice (1966). Hartunian et al. (1980) argue that prevalence based costs are more relevant for analyzing programs that would reduce the severity of existing cases of disease, while incidence based costs should be used for programs that involved prevention of additional cases of disease.

As Chestnut and Violette (1984) point out, air pollution may be

associated both with increased severity of existing diseases and increased incidence of illness. Thus, both prevalence and incidence based costs are relevant to pollution control

107

questions. Prevalence-based costs are more available, however, and hence are used more often in COI studies. To use the COI to value the impact of air pollution on morbidity, a two-step procedure often is employed.

In the first step, the marginal effect of air pollution on health is

derived from a physical damage function which relates a particular health effect to measures of air quality and a set of sociodemographic, medical, and perhaps lifestyle variables. In the second step, total direct and indirect costs attributable to air pollution are computed by applying COI estimates of the medical expenses and the value of time lost from work associated with the health response to air pollution. Seskin's (1979) paper is an important example of the two-step damage function approach.

At least two

important variations to this two-step procedure have been used by economists studying air pollution and morbidity. One variation is to define the dependent variable in the damage function in monetary units; for example, medical expenses could be regressed on air pollution and other variables to estimate the impact of air pollution on direct costs. The work of Jaksch and Stoevener (1974) and Bhagia and Stoevener (1978) illustrates the method of defining the damage function in value terms. The second variation on the twostep procedure is to estimate only the damage function without attempting to value the damage. Examples of damage function estimates without a valuation procedure may be found in Ostro (1983) and Portney and Mullahy (1983,1986). A fundamental criticism of the COI approach is that it does not estimate a theoretically correct measure of the benefits of improved health. In economic theory, the benefit of a good is measured as the amount of money which would make an individual indifferent between consuming and not consuming the good. When an individual's health improves, then, the economic benefit he enjoys may be measured as the maximum amount of money he is willing to pay for the increase in health. When his health worsens, the economic damage he suffers may be measured as the minimum amount of money he is willing to accept for the decrease in health.'

While other measures of benefit or "value" could be

proposed, perhaps of a philosophical or ethical nature, this review takes as given the notion that benefit estimates for policy evaluation and design should be willingness to pay (WTP) or willingness to accept (WTA) measures.

The benefit measures discussed in the text are "compensating variation" measures. Alternative measures of economic benefit or damage are provided by the "equivalent variation". The equivalent variation values a gain as the minimum willingness to accept to forego the gain; it values a loss as the maximum willingness to pay to avoid the loss.

108

The cost of illness measures neither WTP nor WTA. Harrington and Portney (1987) argue that the WTP exceeds COI because the latter accounts neither for the disutility effects of disease nor defensive expenditures for goods other than medical care. Additionally, in a recent theoretical analysis, Berger et al. (1987) rigorously show that COI underestimates WTP in all but a special case.

As a consequence, alternative benefit

estimation methods, including the contingent valuation method have received considerable attention. 3 THE CONTINGENT VALUATION METHOD In applying the contingent valuation method (CVM),survey respondents are presented

with a hypothetical situation describing how a change in morbidity will be accomplished and how payment would be made.

Payment mechanisms include the use of iterative

bidding, payment cards, and "referendum" questions. Regardless of which mechanism is adopted, however, the respondents are asked for their maximum willingness to pay for a specific reduction in morbidity or for their minimum willingness to accept for a specific increase in morbidity.

In contrast to the COI, the CVM attempts to measure the

appropriate theoretical quantity. However, data to implement the CVM must be obtained from primary rather than secondary sources. CVM benefit estimates are subject to a number of possible biases which are discussed

at length by Cummings et al. (1986) and in the paper by Navrud in this volume. One source of bias in data drawn from hypothetical situations, which is most relevant when dealing with public goods, is the strategic misrepresentation of preferences. For instance, a respondent who has a strong desire for a good may over-report his true willingness to pay if he feels that his bid will influence the good's provision, but that he will never actually have to pay this amount. This potential problem suggests that CVM studies in the morbidity area should focus on valuing changes in private health attributes rather than on valuing changes in environmental hazards. If private health attributes are valued, then the benefits stemming from environmental changes can be obtained by linking the CVM bids to dose-response or damage functions. Additional biases in the CVM benefit

estimates may result if the individual is unfamiliar with the commodity or if the commodity is intangible or complex. As a consequence, more accurate bids may result when the

respondent is asked to focus on health outcomes experienced in the very recent past rather than on outcomes experienced in the past year, or worse yet, on diseases which are a complex bundle of health attributes.

Still other sources of bias include vehicle bias,

109

where the method of payment may influence the results, and starting point bias, where an initial price suggested by the interviewer may influence the final value reported by the respondent. Even in situations where these potential biases either can be avoided or minimized, the CVM bids obtained across all respondents frequently display an uncomfortably large

dispersion. The mean bid sometimes is exceeded by its standard error. Moreover, the bids often display a marked skewness with the mean bid as much as five to ten times higher than the median bid (see Green et al., 1978 for examples of this phenomenon). In specific cases, this skewness may be at least partially accounted for by a few very large bids from respondents who either did not understand the question or were protesting the fact that it was asked. Detecting these bids, however, is difficult because very large bids also may be obtained from individuals in poor health who have been unable to find treatments which effectively improve their health.

Two main approaches have been used to apply the CVM to value air pollution-morbidity relationships. The first approach assesses WTP for health improvements; the resulting morbidity valuation can be related to air pollution with a separately estimated doseresponse or damage function. Representative studies which focus on health improvements include Loehmin et al. (1979)) Loehman and De (1982)) Berger et al. (1987), Rowe and Chestnut (1984)) and Dickie et al. (1987). The second approach is to use the CVM to value reductions in air pollution directly.

In this approach, respondents are given

information on the health effects of air pollution prior to being asked the valuation question. The second approach assumes that respondents can implicitly estimate their own dose-response functions. Examples of the second approach may be found in the work of Brookshire et al. (1979), Loehman et al. (1984)) and Schulze et al. (1983). While the CVM is an improvement over the COI technique in the sense that the

CVM

estimates WTP, many economists and policymakers question the accuracy of contingent valuation estimates because of all the potential sources of bias which plague the technique.

As a consequence, economists have begun to develop an alternative method of

estimating the benefits of improved health, namely the averting behavior method. 4 THE AVERTING BEHAVIOR METHOD The averting behavior method provides estimates of willingness to pay for health improvements based on individual's revealed preferences for health and health related goods.

Unlike the cost of illness and contingent valuation approaches, the averting

110

behavior method is based on an explicit model of consumer choice. The model has three key features. First, good health is assumed to be a direct source of satisfaction to the individual.

Thus the method can, in principle, account for the disutility, or "pain and

suffering" associated with ill health. Second, health is considered a determinant of time available both for work and for leisure activities. As a result, the model provides a basis for valuing time lost from both employment and nonemployhent activities. Third, health is endogenous in the averting behavior model; that is, the individual can choose his state of health subject to relevant biological and economic constraints. Health is produced by a

number of exogenous inputs, such as air pollution, as well as some endogenous inputs, such as medical care. The model predicts that, in response to a change in some exogenous input, the individual will adjust his consumption of the endogenous inputs in order to

maximize the benefit (minimize the loss) he obtains from the exogenous change. Thus the model directly accounts for behavioral responses to air pollution changes. 4.1 Theoretical Considerations Averting behavior models have a common underlying structure, subject to a few variations. This structure is U = U(X,H) H = H(V,a) I = rXX

+ rvV

where U denotes utility, X represents a composite good (or composite expenditures if r x =

l), and H denotes the household output of interest, such as health or the cleanliness

of the home.

This output is produced in eqn. (2) by an averting behavior, V (which

might be medical care in the case of health or the frequency of cleaning in the case of home cleanliness), and an exogenous variable or vector of exogenous variables a,which might be measures of air pollution.

Equation (3) is a budget constraint where I is

income and ri is the price of good i, i = X, V. Often V is defined as averting expenditure with r v = 1. A few variations to this structure have been made.

To analyze home cleanliness,

Harford (1984) and Watson and Jaksch (1985) write r v as a function of V and a,thus incorporating a tradeoff between the frequency of cleaning, V, and its intensity, measured by its unit price r v To analyze health issues, the budget constraint may be generalized

111

to incorporate the value of time, as in Gerking and Stanley (1986). Another extension in the health area, made by Harrington and Portney (1987) and Berger et al. (1983, is to define a function M(H) giving medical and possibly other costs of illness as a function the health stock.

Berger et al. further generalize the model to an uncertainty framework

which accounts for health risks.

Finally, Bartik (1988) focuses on the function V(H,)

giving the amount of averting expenditure necessary to achieve output H given pollution a, rather than the primal production function H(V,a). An interesting point about the averting behavior model is its close connection to hedonic price models, Bartik (1988) points out that in the averting behavior model, the household’s opportunity locus is determined by pollution levels and the averting technolo-

gy. In hedonic price models, this locus is determined by demand and supply equilibrium. In this averting behavior model, the individual is assumed to maximize utility in eqn. (1) subject to the production function (2) and some variant of the budget constraint, (3).

By totally differentiating the utility function with respect to pollution while holding utility constant at the constrained maximum, the following marginal WTP expression can be derived2

WTP = -(rV/HV)Ha.

(4)

The WTP for a reduction in air pollution is the income change that holds utility constant despite the air pollution change, i.e. WTP = d I / a a subject to dU/da = 0.

Two of the first order conditions, namely UX-XrX = 0 UHUV - XrV = 0, when substituted into dU/da = 0 hold utility constant at the constrained maximum, yielding upon rearrangement rx(dx/dor)

+ rV(aV/8a)

=

-(UH/X)H,.

Substituting this result into aI/da and using - UH/A = conditions leaves eqn. (4).

-

rv/Hv from the first order

112

This expression states that the marginal benefit of a reduction in pollution is equal to the marginal cost of achieving the same improvement in health through the use of V. More specifically, six aspects of this benefit expression are worth noting. First, WTP is higher, the higher the full price and the lower the marginal productivity of the averting input V. This may explain why some contingent valuation surveys have found a negative association

between health insurance and W T P

insurance lowers the full price of medical care.

Second, if the marginal damage of air pollution (Ha)is higher (more negative) for those in poor health, then WTP would be higher as well. This would explain the finding in CVM studies that poor health is associated with higher WTP.

Third, despite the fact that

health enters the utility function, no utility terms appear in the WTP expression, making estimation of eqn. (4) relatively straightforward. Fourth, the WTP for health improvements can be obtained from the WTP for air pollution reductions simply by dividing both sides of eqn. (4) by Ha, an operation which results in - rv/Hv as the measure of the marginal benefit of health improvements3 Fifth, the WTP expression involves partial derivatives of the health production function rather than parameters from a reducedform dose-response or damage function. A key difference between the dose-response and the health production approaches is the treatment of V.

The averting behavior model

treats V as a choice variable while in the dose-response approach, H is specified as a function of a variety of variables (possibly including averting inputs such as medical care),

all of which are treated

as exogenous. This distinction is important since most estimates

of benefits of improved air quality are based on the two-step dose-response approach described in section 2. The sixth point to note about the benefit expression in eqn. (4) concerns its interpretation in terms of standard microeconomic theory. To simplify the exposition, interpret a as a measure of the air quality rather than of air pollution, so that 01

is a good.

WTP is simply the price the individual would be willing to pay, at the

margin, per unit of air quality. Let ra denote this price. Now suppose that a market existed for air quality, with units of air quality traded at price rO1. The individual is assumed to choose X, V, and constraint I =

01

to maximize utility in eqn. (1) subject to the budget

f i x + VrV + oxO1.

The WTP for marginal health improvements is the marginal rate of substitution between health and hcome: - UH/X, where X is the marginal utility of income. The results in the previous footnote include - U,/X = - rv/Hv, as in the text.

113

It is clear that whatever level of health is chosen in the utility maximization process must be produced at minimum cost. If the chosen level of health could be produced at lower cost, then more of the good X could be purchased while maintaining the same consumption of health, which would increase utility and violate the hypothesized utility maximization. The cost-minimizing producer of health facing given prices ra and r v would choose the levels of a and V so that the marginal rate of technical substitution between these two inputs was equated to their price ratio:

This familiar tangency between an isoquant and an isocost line is illustrated in Fig. 1.

0

ao

Fig. 1. Cost-minimkhg production of health. The cost minimizing health producer who faced a market for air quality would equate the slope of an isoquant to the slope of an isocost line. When no market for air quality exists, cost minimizing production can be used to infer ra. In reality, no market exists for air quality, and the individual faces a given quantity of 01

rather than a given price ra.

Given some quantity a ' , the individual's chosen level of

V, Vo, determines a point on an isoquant. Knowledge of the production function then allows determination of the slope of the isoquant at that point.

Finally, observing the

price r v allows the willingness to pay for air quality, ra, to be inferred. Algebraically,

114

the WTP expression in eqn. (4) can be obtained by multiplying both sides of the costminimizing tangency condition in eqn. (5) by - r v Thus, the ABM allows inference of WTP through knowledge of the production function and prices. Four additional issues have arisen in deriving WIT expression from averting behavior models: (1) the relationship between an individual’s WTP and his expenditures on averting goods, (2) the relationship between an individual‘s WTP and his COI, (3) extending the model to nonmarginal welfare are analysis, and (4) extending the model to arbitrary numbers of averting goods and home produced commodities. Courant and Porter (1981) and Berger et al. (1987) have demonstrated that under plausible conditions, averting expenditure will be lower bound on marginal WTP. The Berger et al. comparison was made in the context of uncertainty and hence is not directly relevant here. The Courant and Porter comparison involved calculating averting expenditure while holding utility constant and hence is of limited empirical relevance. Bartik (1988) has shown that the change in averting expenditure will always be a lower bound to WTP, but the bound is not necessarily tight. Harrington and Portney (1987) and Berger et al. developed theoretical comparisons of individual COI and WTP. Both groups of authors concur that under plausible conditions, COI is a lower bound on WTP. For example, Harrington and Portney demonstrated for the model above that WTP 2 COI provided W d a < 0 and a V / a a > 0. That is, COI is a lower bound on WTP provided the total effect of pollution on health is negative and averting behavior increases with pollution. Both these conditions are plausible, but neither is a theoretical requirement of the model. The partial effect of pollution on health H, presumably negative, but the total effect =/da

is

might be positive if increases in pollution

resulted in more than offsetting increases in averting behavior.

The sign of W/aa

similarly depends on the nature of the health production function.

Thus it is likely

although not certain that WTP 2 COI. The work of Bockstael and McConnell (1983) and Bartik (1988) extends the marginal welfare analysis presented above to the case of nonmarginal welfare changes. Bockstael and McConneIl show that changes in the consumer’s surplus area behind the demand curve for a necessary input can be used to approximate the WTP for pollution reductions. In the context of the model presented above, changes in a would shift the demand curve for V. If V is necessary to produce H, then the change in the area behind the demand curve

for V approximate the consumer’s WTP for reductions in a.

115

Dickie et al. (1987) extend the ABM to arbitrary numbers of home-produced commodities and averting goods. In the utility function of eqn. (l), H now represents a vector of n health attributes HI, H2,

..., H,.

In the budget constraint of eqn. (3), V now repre-

sents a vector of m averting goods V1, V2,

..., Vm, while

r v represents a vector of the m

prices rl, 9, ..., rm. Equation (2) is replaced by the n household production functions Hi =

Hi(V1, V2, ...,Vm; a),i = 1,...,n. The complications introduced by this generalization' of the model are not trivial

because of joint production. Joint production occurs whenever an averting good enters several production functions simultaneously. Several authors, notably Pollak and Wachter (1975), Hori (1975), and Bockstael and McConnell (1983), have demonstrated that the interpretation of the household production model in both positive and normative contexts is severely complicated by joint production. Dickie et al. consider whether the averting behavior model with joint production still yields a WTP expression which is a function only of prices and production function parameters. In the extended averting behavior model, the WTP for a reduction in air pollution is

where Ui is the marginal utility of health attribute i, A is the marginal utility of income, and Hi, is the marginal product of air pollution in the ith production function. If WTP is

to be expressed as a function only of market prices and production parameters, it must be possible to eliminate the utaty ratios (U;/A) from eqn. (6). Dickie et al. consider the m irst order conditions for the Vj shown in eqn. (7).

~1

2

(7)

.

'm

-

where Hij is the marginal product of the jth averting good in the ith production function.

This system of linear equations has a unique solution for the Ui/A if and only if the rank of the system equals the number of unknowns (n). The system has rank n if the

116

rank of the health technology matrix is n, which occurs if (1) m 2 n and (2) n of its rows are linearly independent. That is, there must be at least as many averting goods as health attributes, and there must be no linear dependence among the health production functions.

This theoretical review yields several ideas important for applying the ABM to estimate

WTP. First, under plausible conditions, an individual's averting expenditures and his cost of illness both are lower bounds on his willingness to pay. Second, the ABM works best when the number of averting goods is at least as great as the number of home produced commodities affected by pollution. In this case, calculation of WTP is relatively straightforward because the WTP expression can be reduced to a function of market prices and production function parameters which are in principle observable or estimable. Even when the number of averting goods is at least as great as the number of health attributes, however, the method fails to yield an easily estimable WTP expression if the rows of the household technology matrix are linearly dependent. Statistical tests of the rank of the matrix should be performed prior to estimating WTP. Third, the ABM may be incapable of estimating separate values for a comparatively large number of detailed health attributes, particularly if the attributes are highly correlated. In such a case it is likely either that the number of health attributes will exceed the number of averting goods, or that the correlation among health attributes will result in linear dependence in the household technology matrix. Finally, Dickie et al. point out possibly the most serious limitation to the averting behavior model

the assumption that averting goods are not a direct source of utility.

This problem is important because of the difficulty in identifying private goods that are purchased but do not enter the utility function. If some of the averting goods directly affect utility, then WTP reduces to a function of market prices and production function parameters only if the number of averting goods

not entering

the utility function is at

least as great as the number of health attributes. 4.2 Empirical evidence

Economists have pursued two lines of empirical research related to averting behavior. One line of research, exemplified by the work of Smith and Desvousges (1986), Berger et

al. (1987), and Rowe and Chestnut (1984) examines the existence and nature of averting responses to pollution. On the basis of these three studies, it appears that individuals attempt to mitigate the effects of air and water pollution in at least three ways: (1) by

117

making expenditures on durable goods such as air purifiers and water filters, (2) by making expenditures on nondurables such as bottled water, and (3) by changing their daily schedule to avoid pollution exposure. None of the three studies incorporated both durable and nondurable expenditures and scheduling changes in the analysis, nor did they examine the price to effectiveness ratio of these averting activities. A second line of research attempts to use the averting behavior model to make benefit estimates.

There have been relatively few such studies; one reason for this

outcome is that the simplicity and intuitive appeal of averting behavior WTP expressions are not achieved without cost. Chestnut and Violette (1984), for example, correctly argue that the model implicitly: (1) values the individual's time at his wage rate, (2) considers only private, as opposed to total, social costs of medical care, (3) allows for no interdependence of utility among friends and family members, and (4) considers only small (marginal) changes in pollution and health. Additionally, as noted by Gerking and Stanley (1986), the ultimate averting behavior, moving from an area to avoid exposure to environmental toxins, is not adequately captured in existing ABM approaches.

Finally,

from an implementation viewpoint, the ABM requires special primary data collection. This subsection surveys three recent attempts to use the ABM to estimate WTP; the work of Cropper (1981), Gerking and Stanley (1986), and Dickie et al. (1987). Cropper treats health as a pure investment good which individuals desire only to reduce time spent ill and hence increase income. Since health is assumed to have no direct effect on utility, the model's WTP expression measures only consumer valuations of the effect of pollution on time lost from work.

Cropper uses data from the Michigan

Panel Study in Income Dynamics for three years during the 1970s. Cropper estimates that the average worker in the 1976 sample, who earned $6.00 per hour, would be willing to pay about $7.00 annually for a 10 percent reduction in annual average sulfur dioxide pollution.

Cropper's work is noteworthy as an early attempt to incorporate behavioral

adjustments to pollution into a benefit estimation technique.

Her model provides a

theoretical justification for using work loss days as a basis for estimating WTP, but the model suffers from the serious deficiency of not allowing health to affect utility directly. The Gerking and Stanley model is similar to the one presented in section 4.1,where medical care is the averting good considered. The model generalizes Cropper's approach by allowing health to affect utility directly and by considering the time lost from both work and leisure activities. Gerking and Stanley estimate that fully employed individuals in a sample of households in St. Louis, Missouri during 1977-1980 would be willing to pay

118

between $18 and $25 for a 30 percent reduction in ambient mean ozone levels. The work by Gerking and Stanley is important for at least two reasons. First, their work illustrates the derivation and estimation of a simple WTP expression when health is a direct source of utility. Second, their estimation method accounts for the simultaneity of medical care and health. The most serious problem with the paper is the inconsistency of the data and the model.

The health effects measured were the existence and duration of chronic

illness, while the pollution variables measured only recent exposure. If recent pollution is not representative of lifetime exposure, pollution coefficients may be biased, particularly if

ill health induces migration to less polluted environments. Dickie et al. (1987) model two health attributes, respiratory and nonrespiratory symptoms, and consider four durable averting goods:

home and car air conditioning,

home air purifying, and cooking with some fuel other than natural gas. The sample is split into two groups, one group including subjects with chronic respiratory impairment and the other including subjects with normal respiratory function. Each subsample has two averting goods which are correctly signed and statistically significant at conventional levels in the two health production functions. Thus, the number of averting goods equals the number of health attributes.

The authors then test the null hypothesis that the

determinant of the household technology matrix is zero.

The hypothesis cannot be

rejected at conventional significance levels, suggesting that joint production may pose a serious problem for using the averting behavior model to estimate WTP.

Despite the

negative outcome of the hypothesis test, Dickie et al. make WTP calculations indicating that the value of avoiding a symptom for one day is quite small, around $1 per day. The Dickie et al. work is important in extending the averting behavior model to account for joint production, the most serious limitation of the work is the likely fact that the averting goods considered are direct sources of utility.

5 COMPARISON OF THE THREE METHODS This paper has reviewed three methods for estimating the monetary damages associated with the adverse effects of air pollution on health

the cost of illness method, the

contingent valuation method, and the averting behavior method.

The three methods

differ greatly with respect to the theoretical assumptions which underlie them.

This

section will briefly summarize these issues. First, however, it should be noted that there is at least one major difficulty shared by all three methods, namely, the estimation of the physical damage or health production function.

119

The estimation of such a function, whether for morbidity or mortality, involves a great deal of specification and measurement uncertainty. Specification uncertainty enters because the functional form of the relationship between air pollution and health and the proper set of explanatory variables are unknown. Additionally, some variables which might explain the relationship between air pollution and health are subject to the control of individuals, introducing the possibility of simultaneous equation bias. A key example of measurement error is in the measurement of pollution exposure. Individuals normally are matched to a pollution monitoring station somewhere in the vicinity of their residence, but the pollution levels measured at this station may be a poor indicator of actual exposure. For a more complete discussion of specification and measurement difficulties in estimating the health effects of air pollution, see Crocker et al. (1979) and Gerking and Schulze (1981). Returning to the comparison of the three damage function estimation techniques, consider first the theoretical differences among them.

The COI approach effectively

assumes that individuals are ignorant of the health damages of air pollution and/or are unable to adjust their behavior to mitigate these damages. As Lave (1972) indicates, it is this assumption of individual ignorance that justifies the two-step approach of (1) estimating a physical damage function, and (2) simple multiplication of this damage function by some price schedule. In contrast, the ABM assumes that individuals rationally adjust their behavior to minimize the value of air pollution losses. Cropper (1981) argues that this process of rational adjustment does not require that individuals be fully aware of the effects of air pollution on health; rather, it need only be assumed that individuals adjust their behavior when they perceive some change in their health.

The marginal

conditions of the model, which require optimal adjustment to infinitesimal changes in pollution, however, seem more consistent with an assumption of complete knowledge on the part of individuals. As a practical matter, people must have at least some knowledge of an association between air pollution and ill health if averting behaviors such as

spending less time outdoors and reducing indoor air pollution are to be used to produce benefit estimates. The CVM, when applied to measures of morbidity, does not require any knowledge at all on the part of respondents of the link between air pollution and health. Subjects value the health effect, and the association to air pollution is made by the analyst.

If the CVM is applied to air pollution directly, however, it is assumed that

respondents know their own damage function.

120

In addition to the degree of knowledge assumed, the three techniques differ in their

treatment of behavioral responses to air pollution. The COI method and the CVM tend to ignore averting behavior; only the ABM directly accounts for behavioral adjustments to mitigate pollution effects. Perhaps the most important distinction between these techniques is the interpretation of the values they produce, The COI estimates the monetary costs which illness imposes on society.

It does not estimate WTP, nor does it &elude values for the disutility of

illness. Both the CVM and the ABM, on the other hand, estimate individuals’ WTP, and the WTP value includes the monetary value of the disutility of illness.

The CVM

estimates WTP on the basis of expressed preferences, while the ABM estimates WTP on the basis of revealed preferences. A comparison of WTP and COI is complicated by the fact that COI values tend to be for society as a whole, while WTP values are for individuals. This is significant because 68 percent of all health-related expenditures are made by third parties such as insurance companies (Chestnut and Violette, 1984). Thus, the costs faced by individuals do not reflect social costs. A Final, and perhaps the most practical, distinction between these three methods is

the cost of implementing each. The COI approach seems the least costly to implement, since no primary data collection effort is required. Damage functions can be estimated from existing data sets and the Cooper and Rice cost estimates can be applied. The CVM is more costly to apply in that primary data collection on WTP and other economic variables is required.

The ABM is the most costly, since the primary data collection

effort must extend to the prices and quantities of averting behaviors. A tradeoff emerges, then, between the costs of obtaining estimates of the value of air

pollution damages and the type of estimates obtained. The COI is the least costly, but does not cover the disutility of illness and does not measure WTP. The CVM and the ABM are more costly because of the primary data collection efforts they require, but

they do estimate WTP. The incremental cost of the ABM over the CVM is the price paid for revealed values, which some economists and policymakers would prefer to the expressed values produced by the CVM. REFERENCES Bartik, T., 1988. Evaluating the benefits of non-marginal reductions in .pollution using information on defensive expenditures. Journal of Environmental Economics and Management, 15: 111-127.

121

Berger, M.C., Blomquist, G.C., Kenkel, D., and Tolley, G.S., 1987. Valuing changes in health risks: A comparison of alternative measures. Southern Economic Journal, 53: 967-984. Bhagia, G.S., and Stoevener, H., 1978. Impact of Air Pollution on the Consumption of Medical Services, EPA-600/5-78-002. National Technical Information Service, Springfield, Virginia, USA. Bockstael, N., and McConnell, R., 1983. Welfare measurement in the household production framework. American Economic Review, 73: 806-814. Brookshire, D., d'Arge, R., Schulze, W.D., and Thayer, M.A., 1979. Experiments in Valuing Non-Market Goods: A Case Study of Alternative Benefit Measures of Air Pollution Control in the South Coast Air Basin of Southern California, Vol. 11, Methods Development for Assessing Air Pollution Control Benefits, EPA-600/5-79-001b, National Technical Information Service, Springfield, Virginia, USA. Chestnut, L. and Violette, D., 1984. Estimates of Willingness to Pay for Pollution-Induced Changes in Morbidity: A Critique for Benefit Cost Analysis of Pollution Regulation, EPA-68-01-6543. National Technical Information Service, Springfield, Virginia, USA. Cooper, B.S. and Rice, D.P., 1976. The economic cost of illness revisited. Social Security Bulletin, 3 9 21-36. Courant, P.N., and Porter, R.C., 1981. Averting expenditure and the cost of pollution. Journal of Environmental Economics and Management, 8: 321-329. Crocker, T.D., Schulze, W.D., Ben-David, S., and Kneese, A.V., 1979. Methods Development for Assessing Air Pollution Control Benefits, Vol. I, Experiments in the Economics of Epidemiology, EPA-600/5-79-001a. National Technical Information Service, Springfield, Virginia, USA. Cropper, M.L., 1981. Measuring the benefits from reduced morbidity. American Economic Review, 71: 235-240. Cummings, R.G., Brookshire, D.S., and Schulze, W.D., 1986. Valuing Environmental Goods: An Assessment of the Contingent Valuation Method. Rowman & Allenheld, Publishers, Totowa, New Jersey, USA. Dickie, M., Gerking, S., Schulze, W., Coulson, A., and Tashkin, D., 1987. Value of symptoms of ozone exposure: An application of the averting behavior method, vol. 11. In Improving Accuracy and Reducing Costs of Environmental Benefit Assessments, final report, US. Environmental Protection Agency, Cooperative Agreement #CR-81205401-2 (unpubl.). Fisher, A., Chestnut, L, and Violette, D., 1986. New information on the value of reducing risks, Energy and Resource Consultants, Boulder, Colorado, USA (unpubl.) Gerking, S., and Schulze, W., 1981. What do we know about benefits of reduced mortality from air pollution? American Economic Review, 71: 228-334. Gerking, S., and Stanley, L., 1986. An economic analysis of air pollution and health The case of St. Louis. Review of Economics and Statistics, 6 8 115-121. Green, A., Berg, S., Loehman, E., Shaw, M., Fahien, R., Hedinger, R., Arroyo, A., and De, V., 1978. An interdisciplinary study of the health, social, and environmental economics of sulfur dioxide pollution in Horida. Interdisciplinary Center for Aeronomy and (Other) Atmospheric Sciences, University of Horida, Gainesville, Florida, USA (unpubl.). Harford, J.D., 1984. Averting behavior and the benefits of reduced soiling. Journal of Enviromental Economics and Management, 11:296-302 Harrington, W., and Portney, P.R., 1987. Valuing the benefits of health and safety regulation. Journal of Urban Economics, 2 2 101-112. Hartunian, N., Smart, C., and Thompson, M., 1980. The incidence and economic costs of cancer, motor vehicle injuries, coronary heart disease, and stroke: A comparative analysis. American Journal of Public Health, 7 0 1249-1260

122

Hori, H., 1975. Revealed preference for public goods. American Economic Review, 65: 947954. Hu, T., and Sandifer, F., 1981. Synthesis of Cost of Illness Methodology. National Center for Health Services Research, Department of Health and Human Services, Washington, DC, USA. Jaksch, J., and Stoevener, H.,1974. Outpatient Medical Costs Related to Air Pollution in Portland, Oregon Area, EPA-600/5-84-017. National Technical Information Service, Springfield, Virginia, USA. Lave, L., 1972. Air Pollution Damage: Some Difficulties in Estimating the Value of Abatement. In A. Kneese and B. Bower (Editors), Environmental Quality Analysis. Johns Hopkins University Press for Resources for the Future, Baltimore. Loehman, E., and De, V., 1982. Application of stochastic choice modeling to policy analysis of public goods. A case study of air quality improvements. Review of Economics and Statistics, 64.474-480. Loehman, E.T., Boldt, D., and Chaikin, K., 1984. Measuring the benefits of air quality improvement in the San Francisco Bay area. U.S. Environmental Protection Agency, Contract #R805059010, SRI Project No. EPD-8962 (unpubl.). Loehman, E., Berg, S., Arroyo, A., Hedinger, R., Schwartz, J., Shaw, M., Fahien, R., De, V., Fishe, R, Rio, D., Rossley,, W., and Green, A., 1979. Distributional analysis of regional benefits of cost of air quality control. Journal of Environmental Economics and Management, 6: 222-243. Navrud, S., 1988. Estimating social benefits of environmental improvements from reduced acid depositions: a contingent valuation survey. This volume. Ostro, B., 1983. The effects of air pollution on work loss and morbidity. Journal of Environmental Economics and Management, 103 371-382. Pollak, R.A., and Wachter, M.L., 1975. The relevance of the household production function approach and its implications for the allocation of time. Journal of Political Economy, 83: 255-277. Portney, P., and Mullahy, J., 1983. Ambient Ozone and Human Health: An Epidemiological Analysis. Resources for the Future, Washington, DC, USA. Portney, P.R., and Mullahy, J., 1986, Urban air quality and acute respiratory illness. Journal of Urban Economics, 20: 21-38. Rice, D., 1966. Estimating the Cost of Illness, Health Economics Series No. 6, U.S. Department of Health Education and Welfare, U.S. Government Printing Office, Washington, DC, USA. Rowe, R., and Chestnut, L., 1984. Oxidants and Asthmatics in Los Angeles: A Benefit Analysis. Energy and Research Consultants, Inc., report to EPA, EPA-230-07-85-010. National Technical Information Service, SpImgfield,Virginia, USA. Schulze, W., Cummings, R., Brookshire, D., et al., 1983. Experimental approaches for valuing environmental commodities, Vol. 11. In Methods Development in Measuring Benefits of Environmental Improvements. U.S. Environmental Protection Agency, Grant #CR808-893-01 (unpubl.). Seskin, E., 1979, Pollution and health in Washington, D.C. Journal of Urban Economics, 6 275-291. Smith, V.K., and Desvousges, W., 1986, Averting behavior: Does it exist? Economics Letters, u):291-296. Watson, W., and Jaksch, J., 1982. Air pollution: Household soiling and consumer welfare losses. Journal of Environmental Economics and Management, 9 248-262. Watson, W., and Jaksch, J., 1985. Production of household cleanliness in polluted environments. Mimeograph (unpubl.).

123

Chapter 7 VALUING A PUBLIC GOOD: DIRECT AND INDIRECT VALUATION APPROACHES TO THE MEASUREMENT OF THE BENEFITS FROM POLLUTION ABATEMENT*

MORDECHAI SHEGRTER, MOSHE KIM and LORMTE GOLAN Department of Economics, University of Haifa, Haifa 31999 (Israel) 1 INTRODUCTION

Air

pollution

Pollutants

in

agricultural negative

is

the

known air

productivity,

ecological

to

cause

increase damage

impacts,

cause

visibility). Converting these

of

data has

recently

specifically

with

health

and

environment.

morbidity;

they

also

(mainly

aesthetic the

by

money

effects

affect

corrosion),

damage

damages into

shown that

contributing perhaps 90% of

to

and

materials

and

reduced US.

damages

mortality

(mainly

values,

on health

an

are

have through analysis

dominant,

total damages (Freeman, 1982). This paper deals

estimating

the

economic

benefits

of

reducing

air

pollution-induced morbidity. The public good attribute of

environmental

quality

requires that

approaches to those customarily employed in market-goods Two

basic

approaches

indirect methods

have

such

been

usually

as hedonic price

employed.

models.

In

different

studies be adopted.

The

first

encompasses

principle these infer

the

implicit value of a public good from the observable demand for some private good

associated

approach method

is

with

based

(CVM).

attribute

to

state-of-the-art

it on

These the

(e.g., direct

elicit

public

air

quality

methods,

directly good

from

in

a

and

housing

principally

the

values). The contingent

individuals the market-like

value

second

valuation

they

environment

would

(on

the

of CVM, see Cummings, et al., 1986).

in this paper both approaches are applied to the valuation of benefits from the reduction of mmpared. obtained

The through

morbidity associated with air empirical a

analysis

large-scale

is

based

household

pollution

and

on

individual

survey

conducted

1986. Unlike most treatments of the subject using

the

results are

household in

Israel

data, during

the indirect approach,

the

present study employed primary, individual household data. This enabled us to apply both approaches t o the same data base, and compare them. The results indicate that both approaches yield reasonably

close estimates of

the welfare

changes associated with improved air quality and improved health.

* This work was supported by a grant from the U.S.-Israel Binational Science Foundation. We would like to thank E. Loehman. L. Lave. D. Shefer. and E. Mills for helpful suggestions and advice.

124

INDIRECT APPROACH

2 AN

2.1 Market good

-

TO PUBLIC GOOD VALUATION

p u b l i c good r e l a t i o n s h i p

Two basic methods, each using an indirect approach, are usually invoked to derive measures of welfare change. The first

begins by estimating an observed

market demand function for a market good, specifying some type of demand interdependence

between

interrelationship

is

the

reflected

public

in

the

good change

observed variations in the quantity of associated

with

these

variations

and in

the

market

market

good

good.

demand

This

due

to

the public good. The consumer surplus

measures

the

corresponding

welfare

change.

However, as is well known (cf. Just, et al. 1982)) this yields an approximate value of the potential welfare change. The second method specifies a demand system in terms of the parameters of an

underlying

or

direct

expenditure function,

indirect

money

or

utility

function.

metric utility,

is

then

The used

corresponding

to

calculate

the

welfare changes. In this case, a theoretically exact measure

monetary value of

--

of the welfare change involved is obtained

the compensating and equivalent

variations. In the study presented here we began with a translog approximation to any arbitrary

indirect

utility

function,

and

then

proceeded

to

derive

the

implied

demand system in the form of budget share equations. Here we deal with two market goods, housing services and medical services, both of which are related to

the

public good,

as

well

as

air

quality.

expenditures on 1 effect of pollution on health.

Clearly,

preventive

air

and

quality

medical

affects housing

care

associated

prices,

with

the

2.2 I n d i r e c t v a l u a t i o n : Exact w e l f a r e m e a s u r e s Assume individual preferences are defined over a vector of‘ market goods X and a public good y, by U(X,y), where U is a well defined utility [unction.

U ( , ) there exists an

Dual to

indirect utility

function, V(P,M,y), -

which

solves

Max[U(.)IP.X
on

on

X, -

prices

conditional

indirect

normalized

prices,

non-negative,

and and

m the

utility.

P*=P/M.

non-increasing,

money

is

level The

of

a

function

The

income.

The

public

good

can

conditional

also

indirect

be

indirect

has

utility

also

defined utility

function

been

termed

terms

of

function

is

in

and convex in P* for fixed y, and oon-decreasing

and concave in y for fixed P*. It is also positively linearly homogenous in P* for given y.

1

This is related to MLler’s (1974) weak complementary condition, or Bradford and Hildebrandt’s (1977) demand interdependence condition, which arc required in order to solve Ihe public good demand in terms of the underlying ntility function.

125 The

expenditure

the inverse of

function,

p,

which

relates

income

and

utility

(strictly,

the indirect utility

function), is defined as the minimum sum 0 0 necessary to maintain a given level of utility, U , at a given price P : p ( P0, U 0 ) = Min [P0X:

U(X) = U(X0 ) ]

X

is the Hicksian compensated demand function. For a given set of

where

reference prices, the function serves as a money index of utility -- a money metric utility (see, Varian, 1984, ch. 3; McKenzie and Pearce, 1982). If utility

and

a

of

function,

(Bradford good

quantity

the

a

public

corresponding

Hildebrandt,

(ap/ay
good,

yields

a

y,

is

now

expenditure

function

1977). Its

derivative

with

marginal

willingness

to

compensated demand function, for the public good, measures

-

included

can

respect pay

in

the

indirect

be

defined

to

the

schedule,

public

or

the

from which exact welfare

compensating and equivalent variations associated with

the change

in y - may be calculated. In this case, compensating variation (CV) is defined

as the income change which offsets the change in utility induced by a change in the level

of

y,

holding utility

( U ) constant at its orzginal level. CV can

2 therefore be defined in terms of the expenditure function as:

Analogous to this,the equivalent variation (EV) for the nou-market

good is the

change in income equivalent to the utility gain induced by a change in the non-market good, holding utility at its subsequent level.

If y 1>y 0, the CV measure is interpreted as the the maximum amount of money a consumer

would

pay

as a lump sum to obtain the specified

increase,

Ay

(following Randall and Stoll, 1980). It is a measure of a willingness to pay 1 0 rather than a willingness to accept, and it is denoted here as W P C . If y
analysis,

however,

involves

only

a

subset

of

commodities

from

the

consumer's total consumption space. As noted by Hanemann and Morey (1987), the

CV and EV measures calculated from a partial demand system are not identical to those calculated from a full system. The CV is a lower bound on the conventional CV, and the EV can be greater than, less than, or equal to the

Strictly, it is defined in terms of the Compensation function, or the money metric utility, which is identical to the expenditure function for fixed y (cf. Varian, 1984, pp. 123-125).

126

conventional EV.

3

3 APPLICATION 3.1 The s u r v e y

The

household

survey

was

based

a

on

stratified, cluster

area

probability

sample of about 2,000 household in the metropolitan area of Haifa in northern Israel.4 The saniple was drawn

from 137 Census Statistical Areas which were

classified into four socioeconomic groups on the basis of data from the latest (1983) Census. pollution.

They

were

Seventeen

neighborhood) blocks were sampling

were

chosen

randomly in

classified

areas

to

(each

represent

into

three

the

of

the

strata.

a

Heads

of

of

ambient

different

(3x4) sampling

12

sampled within each stratum, with

each

levels

approximating

urban

strata.

City

approximately equal

household

(either spouse)

within each block were interviewed. The survey was carried out

over a period

of

ratios

further

statistical

six months, from April 1986 through August 1987. Each

repetitively sampled over the entire period, so that

neighborhood was

every household

in each

neighborhood had an approximately equal chance of being sampled a t any time. This was Haifa

in

area.

interview,

order The

lasting

to capture data

were

about 30

the seasonality collected

effect

during

minutes. The

of

the

air

pallution in

course

of

a

the

structured

overall response rate was

8196,

9%

refused to be interviewed, and another 10% could not be reached even after a second

visit.

Descriptive

statistics

of

the

relevant

variables

of

interest

utility

function

appear in Appendix A.

3.2 Model s p e c i f i c a t i o n and e s t i m a t i o n The

translog

form

(Christensen et.al., of

a

utility indirect

second-order

was

chosen

1975). The local

function,

represent

the

function

is

approximation

function (Just, et al., utility

to

translog

we

to

any

indirect

a general,

flexible

twice-differentiable

form

indirect

1982, Appendix B). Given the properties of

the

have

the

specified

the

following

function

for

empirical application:

where

V = V(P*,y,h) h represents

a

vector

of

individual household

(4) characteristics employed

In order for the partial system to represent preferences satisfactorily, it must be assumed that the group of commodities for which data exist is separable in consumption from the group of all other commodities (see Hanemann and Morey, 1987).

*theThecountry. Haifa Bay Its

area is considered to be one of the most polluted regions in topography, meteorological conditions, and concentration of heavy industry create conditions which are often conducive to high ambient pollution levels, especially high SO2 and TSP concentrations, in residential areas,

127 here

as

control

conditional

obtained

by

utilizing

For

three-good,

the

An

variables.

differentiable,

indirect

the partial

approximation utility

function

translog

specification

demand

system,

to

an

arbitrary,

specified

by

( Christensen,

the translog

twice

( 4 ) , can et

al.,

be

1975).

approximation

takes

the following form:

p;) [421hl t @2zh2

t

@2sh3

@2dh4

@55h5

@26h61

where

P1 - housing prices; index of medical services price;

P2

-

M

- annual household expenditure on both goods;

P;

=

1

P;

=

1

hl

-

h2

-

h3 h4

p2 smoking habits (head of household); respiratory illness symptoms (head of household);

- respiratory illness symptoms (other household members); respiratory diseases (head of household); -

h5 -

respiratory diseases (other household members);

h6 -

net household income from all sources.

Housing prices were represented by

annual municipal tax assessements, the

rates of which generally reflect the socio-economic

status of

the neighborhood

and the quality and size of the dwelling. This variable was used imputed

rental

values

housing

prices

by

service

prices

clinics

and

is

because

there

neighborhood based

on

hospitalization

these are merely rough

are

no

reliable,

published

and

housing

quality.

The

reported

national

average

estimates

costs.

figures for

As

no

better

statistics

instead of statistics

index

of of

were

all illnesses combined. However,

on

medical visits

to

available, we

also

128 obtained out-of-pocket

doctor and medication expenditure from the ~ u r v e y .The ~

survey also provided information on implied and reported consumption levels of housing (dwelling size and locational quality are the two parameters local property tax quality,

y,

information perceived

indicates was

the

affecting

assessments), and the consumption of

perceived

the

obtained

pollution

from

level

in

of

level

the

medical services. Air 6 neighborhood pollution . This

respondents

their

who

neighborhood.

were They

asked were

they

how

requested

to

indicate this on a severity scale of 1 to 6. The h s are the health attributes k of the respondents (head of household), or the other household members, that are associated with air pollution (with the except of smoking which, in and by itself,

induces

similar

illnesses).

The

illness

symptoms

include

coughing,

wheezing, sputum emission, and shortness of breath; diseases refer to asthma, bronchitis,

pneumonia,

and

other

lower

respiratory

tract

diseases.

The

sixth

attribute, h6, is a proxy far socioeconomic status. Two

distinguishing features

of

out. One is the introduction of translog

function,

pollution Varian,

related 1984,

equations

and 126-7)

and

to

expenditure

logarithmic form

of

constraints

were

imposed

integrability

of

namely:

inclusion

symptoms

p.

into

the

the

share

specification in

(5),

share

of

relevant

illnesses. and

7

( 5 ) should

be

Applying

equations

for

equations to

be

below,

eq. demand

p ij--p..J1 6ij--6..Jland 41k=-42k

(6)

individual

transforming

in

posited

eq.

pointed

a public good as a quality parameter in the

system

Roy's the is

to

Christensen,

the

Symmetry

ensuring et

(cf.

demand

goods,

obtained.

equivalent

(cf.

identity

resulting

market

the

estimated

characteristics

al,

the 1975),

for all k. This causes the characteristics

variables (the hks) to drop out of D, as is shown below:

f

2(pij+6..eny)enP* 1 + 'J J

It should be noted that most of the population subscribes to one of several public health insurance schemes, and do not pay directly for medical services except for a monthly insurance premium. However, paying for private medical visits and medications in order to receive faster, and often better quality, treatment is rather common. Thus, the opportunity cost of time invoIved in obtaining medical treatment cannot be overlooked, too.

On the appropriateness of level

in

using perceived rather than measured such circumstances, see Zeidner and Shechter(1988).

pollution

The inclusion of characteristics in a translog utility function was first introduced by Woodbury (1983), in connection with a model describing labor compensation by either wage or fringe benefits. The characteristics were variables describing the worker or the workplace. Morey (1985) incorporated personal and site characteristics into a demand system for ski resorts.

129

where

*

*

D

( " i t y i C n y ) t ( c r . t y . e n y ) t (piitGiitny)enPi t (p..tG..tny)enP. t J J JJ JJ J

=

From consumer theory it is known that the budget share equations should be

of

homogenous

degree

zero.

A

customary

constraint on the demand system is

normalization

5I Si--1,

equation) can be determined from the m-1 (SAS,

1985)

non-linear regression 8 parameter estimates. It

is

instructive

For

function.

up"

restriction

which

with to

check

example,

the

iterative

estimation

it

consumer

the SAS SYSNLIN

minimization

technique.

properties of

differentiating

of

budget shares equations (our first ( 6 ) we employed

combines

OLS

this

equation (our second

implying that the parameter of the m-th

equation). T o estimate the share equation procedure

imposes

Cor.=-l (cf., e.g., Christensen and Manser, I 1

1977). The system should also satisfy the "adding theory,

which

with

Table

the

1

estimated

respect

to

for

displays

the

indirect

prices,

*

methods

*

utility

income

and

the public good, and evaluating a t the point of means of PI, P2, and y, the following is obtained: WnV m* < 0 (=-0.058)

< 0 (=-0.303)

Thus,

the

estimated

- for i=l

(housing)

-

(medical

for i=2

(indirect) utility

care)

function

exhibits

decreases with a rise in the (normalized) prices of services, and

rises

with

the level of

money

the

housing

correct and

expenditures, and

signs.

It

medical care

with

the level

of the public good - air quality. It can also be shown that the estimated function

is

concave.

Moreover,

corresponding

share

*

perceived

Respondents'

elasticites,

the which

estimated are

air quality levels were

observation i the independent variable is yi/y, where

share

equation

closely

used

7 is

related

fo;

yields to

y. Specifically,

the sample mean.

the

income

for

130

TABLE 1 Parameter estimates of the budget share equation Parameter

-0.155 (-16.28) 0.258 (-22.44) -1.346 (-35.71) -0.029 -( 11.73) 0.0147 (3.61) -0.153 (-27.91) -0.0269 (-11.92) -0.0197 (-9.25) -0.243 (-33.83)

71 y2

41 4 2 p22 *11

5 2 *22

*

Parameter

Estimate

"1

* Estimate -0.0038 (-5.20) 0.0036 (5.53) 0.0055 (7.49) 0.005 (7.49) 0.0055 (7.68) 8.4~10-~ (3.83)

411 1' 2 '13 1' 4 1' 5 1 '6

2

R = 0.31 N = 2234

Asymptotic t statistics in parentheses.

elasticities interest

(cf.,

in

the

example,

for

present

Christensen

context

is

the

and

Manser,

elasticity

with

Of

1977).

respect

to

special variations

in the level of air quality:

aenS "iy

=

=

0.113 (for i=l, the housing share)

= -0.023 (for i=2, the medical care share)

Thus, these elasticities bear the sign expected. On average, spend 1.3% more improvement respective

in

on housing air

quality

neighborhoods.

and levels

Such

0.2% less

from

results

on

levels

may

individuals would

medical care given currently

clearly

have

perceived

a

in

significant

10%

their policy

implications for setting ambient air quality standards. 3.3 Computing w e l f a r e change m e a s u r e s

The expenditure function corresponding to (5) is given in Appendix B.

In

the survey respondents were asked to state their W P for a *50% change in currently

perceived

air

quality

levels.

Accordingly,

the

calculations

of

CV

and EV associated with a such a change are presented. WTPc and WTPe as functions of y - the Bradford (1970) bid curves - are computed from eq. ( B l ) in Appendix B, as shown in eqs. ( 2 ) and (3). These calculations yielded values

131 9 30.1 and 130.6 New Israeli Shekels (NIS) , respectively, per household,

of

per

year.

4 A

DIRECT APPROACH TO PUBLIC GOOD VALUATION

In

this

section

several

salient

results

use of

regarding

changes

in

air

framework. The

questionnaire included

pay

to

in

the

survey

are

presented.

In the household survey respondents were asked t o state their

CVM.

preferences

from

of the environmental good, through the

These deal with the direct valuation

order

prevent

a

quality

in

one question

worsening

contingent

a

eliciting a

present

of

(specifically, a 50% increase

in ambient pollution levels)

also a question relating to

the respondent's

willingness

valuation

willingness

air

quality

to

levels

WTPe. There wa.s

-

to

pay

in order

to

present pollution levels -

achieve a 50% improvement through a reduction of

WTPc.lo The payment vehicle was the municipal tax, and the interviewee was asked to indicate WTP in terms of a percentage increase in his or her currrent tax payment (the percentage change categories were listed on a card shown to the

respondent

by

the

interviewer). Respondents

were

also

asked

about

the

reasons for refusing to pay any sum at all. Mean sample values of WTPc and WTPe for air quality changes are presented in Table 2. For the purpose of the analysis, neighborhoods were divided into the th'ree pollution levels. With regard to W P C , it was assumed that a 50% improvement

roughly

implies

that

a

neighborhood

with

would be upgraded into one with good air quality,

i.e.,

moderate

air

quality

a (relatively) clean

one, and that a "bad" neighborhood would move into the "moderate" category. Similarly, with respect to WTPe, a 50% deterioration in pollution levels would imply a downgrading of a relatively clean neighborhood to one with moderate levels, and so on.11 Thus, on average, an individual living in a moderately polluted neighborhood (according to his or her perception) would be willing to contribute a yearly sum of NIS 37.9 towards improving air quality, and a sum of NIS 40 in order to prevent a worsening of present levels. Both wTpc and WTPe

increase

significant

with

pollution

(non parametric

levels,

and

the

between-group

median test). The two-sample

differences

mean

tests

are

indicate

that although WTPe and WTPc differ significantly, WTPC>WTPe in one case (poor neighborhood respondents), but the reverse holds for moderate neighborhoods. The variables found to be significant in explaining the variation

'(USA), The exchange rate approximately.

in WTPc

of the NIS during the survey period was 1.5 NIS to $1

lo A visual stimulus, presenting respondents with polluted and a clear day in the Haifa area, was provided.

photographs

depicting

a

Note that the neighborhood marked "Very poor" in Table 2 is a fictitious neighborhood, created by hypothetically downgrading the "poor" neighborhood category.

132

TABLE 2

*

Direct (CVM) valuations of perceived air quality changes Present pollution level

.

Pollution level after change Good

Moderate

Poor

Very poor

(a) me Mean = 26 Median = 15 N =847

Good

Moderate

( b ) WTPc

(c) WTpe

Mean = 37.9 Median = 28 N =750

Mean Median

= 40 = 28

N

=749

Poor

( d ) WTPc

(el W T P ~

Mean = 47.2 Median = 40 N =192

Mean Median

N

42.7 32 =192 = =

*

Values in table refer to means and medians of the indicated sample air quality stratum, and stated in NIS per household per year. S i g n i f i c a n c e Levels: Nonparametric median test for 2 samples:

Ho: WTPc (cell b) = WTPc (cell d )

H~W : T P ~(cell a)

0.015

= W T P ~(cell c) =

me(cell e )

0.001

Paired t-test for means ( 2 tailed):

Ho: WTPc (cell b ) = WTPe (cell c)

0.001

We (cell e )

0.049

Ho: WTPc (cell d )

and WTPe multiple

(using a stepwise OLS procedure) are presented

regressions

significantly status-related

=

affects

support both

the

WTP

finding variables.

in Table 3. The

in

Table

2

that

It

should

be

noted

air

variables did not enter the regressions, whereas they

the shale equations. However, it was found that

pollution

that

health

did enter

these variables did explain

some of the variation in WTP when "untrue" zero answers were excluded from the 12 analysis .

12' These refer to zero payments, while the reasons given for it indicate that the respondent does value the public good but either objects to the vehicle (tax) or believes that the "authorities" or the "polluter" should pay. Also note the importance of question order on WTP. This result supports earlier arguments by Tversky and Kahenman (1981) and others, concerning the influence of framing and sequence of questions on decision.

133

TABLE 3 Willingness to pay regression coefficients. Regress ion coefficients Explanatory variable

WTpe

WTPC -

Demographic and s o c i o e c o n o m i c v a r i a b l e s : Age of respondent * Education Self-employed Blue collar worker Number of children Size of apartment Apartment size squared Net household income Age x income Number of children x income Annual municipal taxes

-0.39" 0.43d 2.8Zd -7.4 -4.1" 0.22b -0.002"

-0.34" -7.37b -1.77b 0.5" -0.002' 0.009"

0.0002a 0.002c

0.05"

0.045"

Attitudional variables: Perceived exposure to pollution at work* Perceived neighborhood pollution (log)** Believes budget share allocated to pollution abatement too high* Pollution induces defensive actions by respondent*

4.58' 8.78"

4.53' 18.4aa

-7.66"

-8.76"

6.77b

Q -uestionnaire structure: Health questions before WTP questions* Intercept

R2 F

** a b c

d

0.23

0.25 40.14" (14, 1770)

d.f.

*

-5.67b -1.35

-3.75c 12.51

36.88" (13, 1770)

A binary variable On an ordinal severity scale (1 to 6 ) Significance level = 0.0001 Significance level = 0.001 Significance level = 0.01 Significance level = 0.1

5 CONCLUDING REMARKS

A uniform primary data set - household survey data study

-

was employed in this

to obtain implicit and explicit valuations of an environmental good -

air quality. Two approaches were applied, an indirect, market good related approach, and a direct, nonmarket good valuation approach. On the one hand, direct

valuation

relies

survey data composed

exclusively of

on

direct

individual responses

question are

techniques.

therefore

Primary

essential for

its

application. Market demand systems, on the other hand, are normally estimated from aggregate, secondary market data. However, the information gathered in the present study made it possible to

134

apply

these

two

different

approaches

to

the

same

data,

and

comparable valuations pertaining to exactly the same set of

thus

obtain

data. Since both

approaches are supposed to measure the same thing - the implicit demand for a public good, this

paper

they we

could

have

be

expected,

attempted

to

priori, . t o yield

a

test

this

similar

proposition. The

results.

welfare

In

change

measures obtained under these two approaches are presented in Table 4. TABLE 4 Direct and indirect valuations (NLS per household per year). Indirect approach

Direct approach

WTPC

30.1

32.6

WTPe

130.6

33.4

These

results

could

be

viewed

as

modest

a

addition

to

the

efforts

of

environmental economists to establish CVM as an appropriate valuation tool. It should be noted that the comparisons essentially are made bctween ex post and ex

ante measures. The closeness of the two WTPc values, however, must hearten

CVM

practitioners.

support

to

and

They

are encouraging

increase

contingent valuation method.

the

and

profession's

seem,

at

confidence

least in

to

the

ub,

use

to

add

of

the

13

In investigating further the "robustness" of CVM, we have recently analysed results from closed-ended questions (referendum-style), binary response questions . These questions demand "yes" or "no" responses to a glven, randomly assigned payment level. This form of eliciting WTP response has been recently advocated by several CVM practitioners (e.g. Loehman and De, 1982; llanemann, 1984, Cameron and James, 1987). Prelimifiary results indicate that this variant of the direct approach yields values comparable to those giver1 in Table 4.

135 REFERENCES Bradford, D.F., 1970. Benefit-cost analysis and demand for public goods, Kyklos, 23, Fasc. 4: 775-791. Bradford, D.F. and Hildebrandt G.G., 1977. Observable preferences for public goods. Journal of Public Economics, 8: 111-131. Cameron, T.A., and James, M.D., 1987. Efficient estimatiopn methods for ”closed-ended” contingent valuation surveys. Review of Economics and Statistics, 77: 269-276. Chestnut L.G. and Violette D.M., 1984. Estimates of Willingness to Pay for Pollution -Induced Changes in Morbidity: A Critique For Benefit-Cost Analysis of Pollution Regulation. U S . Environmental Protection Agency, Washington, D.C. Christensen, L.R., Jorgenson, D.W., and La1 L.J., 1975. Transcendental logarithmic utility functions. American Economic Review, 65: 367-383. Christensen, L.R., and Manser, M.E., 1977. Estimating U.S. consumer preferences for meat with flexible utility function. Journal of Econometrics, 5: 37-53. Cummings, R.G., Brookshire P.S. and Schulze W.D., 1986. Valuing Environmental Goods - An assessment of the Contingent Valuation Method. Rowman & Allanheld, Totowa, N.J. Freeman, A.M., 1982. Air and Water Pollution Control A Benefit-Cost Assessment. Wiley, New York. Hanemann, M , 1984. Welfare evaluations in contingent valuation experiments with discrete responses. American J. of Agricultural Economics, 66:332-341. Hanemann, M. and Morey, E., 1987. Separability, partial demand systems and consumer’s surplus measures. University of California, Berkeley (unpubl. ) Just, R.E., D.L. Hueth, and A. Schmitz ,1982. Applied Welfare Economics and Public Policy. Prentice-Hall, Englewood Cliffs, N.J. Loehman, E. and De, V.H., 1982. Application of stochastic choice modeling to policy analysis of public goods: A case of air quality improvements. Review of Economics and Statistics, 64:474-480. Loehman E., 1986. Measures of welfare for nonmarket goods: some conceptual and empirical issues. Department of Agricultural Economics, Purdue University (unpubl.). Maler, K.G., 1974. Environmental Economics: A Theoretical Inquiry. John Hopkins University Press, Baltimore. McKenzie, G.W. and Pearce, 1982. Welfare measurement - a synthesis. American Economic Review, 72: 669-682. Morey, E.R., 1985. Characteristics, consumer surplus, and new activities. Journal of Public Economics, 26: 221-236. Randall, A. and Stoll, J.R., 1980. Consumer’s surplus in commodity space. American Economic Review, 70: 449-455. SAS/ETS User’s Guide, 1985. Version 5 Edition. SAS Institute Inc., Cary, N.C. Shapiro, P. and Smith, T., 1981. Preferences for nonmarket goods revealed through market demands. In: K.V. Smith (Editor), Advances in Applied Microeconomics, 1. JAI Press, Greenwich, Conn. Tversky A. and Kahenman, D., 1981. The framing of decisions and the psychology of choice. Science, 211 (January 30). Varian, H.R., 1984. Microeconomic Analysis. Norton, New York. Woodbury S.A., 1983. Substitution between wage and non-wage benefits. American Economic Review, 73: 166-182. Zeidner, M. and Shechter, M., 1988. Psychological responses towards air pollution: Some personality and demographic correlates. Natural Resource and Environmental Research Center, University of Haifa. Mimeo.

136 APPENDIX A: Descriptive Statistics. Variable

Mean

81.5

Apartment area (m')

Standard Deviation 25.4

Physician visits per year

7.69

8.76

Annual tax rate (NIS*per m2)

6.01

2.54

Annual rent proxy (NIS)

464

253

Annual medical outlay (NIS)

938

400

1402

518

Total annual expenditure, M (NIS)

**

Cigarette smoking, h l

0.29

0.45

Respiratory illness symptoms of head of household, h2

0.65

0.47

Respiratory illness symptoms of all other members of household, h3

0.54

0.49

Respiratory illness of head of household, h

0.19

0.39

Respiratory illness of all other members of household, h5

0.28

0.45

Net household monthly income from all sources, in NIS, h6

1174

Perceived air quality level [Scale: 1 - (bad) - 6 (good)]

4.06

589 1.5

N = 2277

* **

NIS = New Israeli Shekel. The average exchange rate of the NIS during the survey period was 1.5 NIS to $1 (USA). Variables hl through h5 are binary

APPENDIX B: The expenditure function and bid curve. The function

expenditure

function

corresponding

1 ,

t b24nPlCnP2 where

to

indirect

(5) has the following form (in terms of the log of M):

+

1 2 Zb3(tnP2) - CnVo

utility

137 p = 1nM

a = a fl+Cny 0

6

6

d2=

Z'$ h 2k k

k=l

The utility

expenditure function function

(5),

in

is

terms

derived by of

given

solving

for M

(initial) prices

of

from

the

indirect

the

two

market

goods, quantity of the public good (perceived neighborhood air quality), and a given level of

utility. Ln

v"

was computed by inser ting the sample mean

values of yo, Po, and hks in eq. ( 5 ) . Differentiation

of

the

expenditure

function

(B.1)

with

respect

to

the

public good, y, yields the marginal bid function, or the (compensated) demand 0

0

price function for air quality, -dp(y,P ,U )/Oy. It can be shown that for our parameter estimates (Table l ) , with y.

-ap/ay>O

(cf. Loehman, 1986), and it decreases

This Page Intentionally Left Blank

139

Chapter 8 ENVIRONMENTAL REGULATION AND THE VALUATION OF LIFE:* INTERINDUSTRY MOBILITY AND THE MARKET PRICE OF SAFETY HENRY W. HERZOG Jr. and ALAN M. S C H L 0 " N Department of Economics, The University of Tennessee Knoxville, TN 37996 (USA)

1 INTRODUCTION

Environmental policy in both Europe and the United States has increasingly become associated with the necessity to value costs and benefits of proposed regulations. This growing emphasis on "cost-benefit" analysis is particularly acute for health and safety hazards (and regulations) that are difficult to measure and involve relatively small probabilities. In these instances the fundamental question is how to measure the benefits of a regulation that saves a human life. As indicated in Table 1, current methods of assigning a dollar value to human life by government agencies in the United States indicate a wide variance. The use of these estimates of human life in setting environmental regulations can be controversial. As discussed by Waldman (1988), in a 1986 suit against OSHA the Public Citizen Litigation Group charged that cost-benefit analysis was used to weaken regulation of ethylene oxide, a sterilizing agent that may cause cancer and spontaneous abortions. Similarly, the continuing controversy over EPA draft rules which appeared initially in 1984 phasing in a ban on asbestos has often centered on the proper discounted value of life. These examples clearly indicate that environmental policy and the valuation of life are becoming increasingly intertwined. Economists have often approached the issue of determining the value of life from the perspective of compensating wage differentials.

The theory of compensating wage

differentials, attributable to Adam Smith, suggests that jobs with disagreeable characteristics will command higher wages, ceteris paribus. Most empirical tests of this theory with hedonic wage equations have addressed the job-related risks of death or serious injury,

* The authors wish to thank the editors of this volume for valuable comments. Partial suport for this study was provided by the Waste Management Research Institute, The University of Tennessee. Microdata employed in the study was acquired under a past grant to the authors from the National Science Foundation.

140

TABLE 1 Value of Life Estimates: U.S. Government Agencies. Agency

Value of Life ($)

Consumer Product Safety Commission (CPSC) Environmental Protection Agency (EPA) Federal Aviation Administration (FAA) Occupational Safety and Health Administration (OSHA)

2 million 475,000 - 8.3 million 1 million 2 million - 5 million

~~~

~~~

~~

Source: Various government publications. and, for the most part, have found such compensation to indeed exist. For examples of U. S. experience, see Dillingham (1985), Dorsey (1983), and Gegax, Gerkhg and Schulze (1986), while risk compensation in Britain and Sweden has been examined by Martin and

Psacharopoulos (1982) and Duncan and Holmlund (1983), respectively. Implicit within this literature is the assumption that workers' willingness to pay for risk reduction (safety) in the workplace through diminished wages, and market valuations of the "price" of these reductions, are

equivalent. Thus, it is generally assumed that no externalities exist in

the pricing and provision of industrial safety, and therefore that estimates of the market price of incremental safety also measure the wage-risk trade-off of workers. Our analysis below suggests that this is clearly not the case within the manufacturing sector, where willingness to pay for risk reduction exceeds the price (cost) of such reduction when measured at current levels of risk exposure.

Thus, to the extent that implicit prices

derived from (hedonic) wage equations understate worker willingness to pay for incremental safety, implied value of life estimates determined from these equations are downward biased. In the following section, risk valuation is examined within the context of compensaf i g wage differentials. A demand-side method for valuing willingness to pay for risk reduction is also proposed, and compared to that employed to generate market prices for enhanced safety in the workplace. These two methods, or models, for valuing the wagerisk trade-off are specified in Section 3 by examining their individual determinants and sources of data. Econometric estimates of these models are then presented and discussed in Section 4, and provide the basis for a comparison of the implied value of life

evaluated, alternatively, by market price and willingness to pay. Conclusions follow in Section 5.

141 2 THE VALUE OF LIFE AND RISK VALUATION

2.1 Measuring the Wave-Risk Trade Off Jobs can be characterized by many dimensions such as likelihood of injury, pace of work, and the general unpleasantness of tasks to be performed. Employees and employers negotiate a single wage at the time of hiring that reflects both underlying demand and supply functions pertinent to these and other job characteristics. Under the assumption of perfectly competitive labor markets (and thus perfect information on working conditions), an equilibrium price is established for each job attribute that is equal to its

marginal cost. Such "compensating differentials" among wages for various jobs are often examined, and empirically estimated, based upon the hedonic theory of prices as outlined by Rosen (1974). Following Rosen, consider jobs in which equilibrium quantity and value, or marketclearing implicit price, have been established for all job attributes but one, here the risk of injury, R. In order to maintain a constant level of profit, fums will supply safer jobs only at reduced wages, W, ceteris paribus.'

Again assuming that equilibrium value and

quantity have been predetermined for all job attributes other than risk, worker indifference curves representing various levels of total utility and an associated wage-risk trade-off can be determined.

In this context, with worker satisfaction held constant,

the required trade-off between wages and risk increases with the level of risk exposure. Following Rosen (1974), a "market clearing implicit price" curve can be determined, W(R). Within perfectly competitive labor markets, workers maximize utility by accepting jobs along W(R) that equate, at the margin, their willingness to "pay" for risk reduction (safety) with the wage-risk trade-off required by fvms to maintain (zero) profits. Because workers differ in their tastes for job safety, various wage-risk bundles (W,R) are selected at long-run equilibrium. Thus, as noted by Smith (1979), "workers who value safety highly tend to accept jobs with firms that can offer it most cheaply."

On the

other hand, a worker who places a lower value on safety will seek employment with a

firm offering both high relative wages and risk. The coefficient estimate on risk (or its transformation) in a hedonic wage equation can be interpreted as the slope of W(R) at the prevailing level of risk exposure, W(R).

In

addition, within perfectly competitive

For a detailed discussion of this theory see Rosen (1974). Also, see Curington (1986) on the impact of OSHA safety regulations on both workplace injuries and their frequency.

142

labor markets in long-run equilibrium,

this slope is also equal to a representative

worker's willingness to pay for risk reduction. However, there are several reasons to suspect that labor markets are not in a state of equilibrium, and therefore, that estimates of W(R) obtained from (hedonic) wage equations do not approximate the representative worker's offered wage concession for added safety at the prevailing level of risk exposure in the economy.

Conditions existing within

imperfect labor markets that likely maintain this imbalance include imperfect information, ineffective bargainin& and transactionscosts. With respect to imperfect information, Viscusi (1979) and Vicusi and O'Connor (1984) found worker quit rates to be positively augmented by job hazards; and that the imperfect nature of workers' prior information combines with the potential for learning on the job to produce this adaptive behavior. O n the other hand, ineffective collective bargaining, or any noncompetitive aspect of the contracting process, could also produce this situation. Such a case would arise if the risk component of a negotiated wage package fails to align firm and workers' wage-risk trade-offs (by a single "price"). Evidence of ineffecti-

ve labor contracting is provided by Martin and Psacharopoulos (1982) who show that collective bargaining in Great Britain actually weakens compensating differentials obtained between more and less dangerous jobs. Finally, to the extent that transactions costs of a wage-risk adjustment exceed the benefits of such an adjustment, this discrepancy will

also be maintained. (Weinberg, Friedman and Mayo (1981) have analyzed similar transactions costs incident to housing search under disequilibriumconditions.)

Thus, there is reason to suspect that the willingness to pay for risk reduction on the part of workers diverges somewhat from its market "price!'

The

direction of this

divergence is, of course, less certain, but is amenable to empirical investigation below. Based upon the above, estimates of market price and/or willingness to pay (and thus any divergence) cannot be obtained from a hedonic wage equation whose price function for job attributes such as risk describes an equilibrium relationship (and thus equality of market price and willingness to pay). In addition, both Epple (1987) and Bartik (1987) have recently shown that equilibrium conditions of the hedonic model impose surprising restrictions on the error terms of such models, restrictions that rule out many seemingly natural estimation strategies. An estimate of the implicit market price of risk at the prevailing level of risk exposure (defined above as W'(R)] will be obtained as coefficient estimate on risk (or its transformation) in a wage/earnings

the

equation with

regressors selected in accordance with Mmcer's model of schooling, experience and

143

earnings [Mincer (1974)l.

Such an equation, unconstrained by hedonic equilibrium

conditions, can be represented as W = W(H,X,R),

(1)

where W again represents wage, H and X are vectors of human capital and other controlling variables, respectively, and R is a measure of risk in the work place. Included in X are working conditions other than risk exposure. On the other hand, a demand-side, or willingness to pay, interpretation of risk evaluation must measure the slope of a representative worker's indifference curve at the present level of risk exposure. However, since worker utility can not be measured, how is one to evaluate the worker's offered concession for added safety, dW/dR, while holding such worker satisfaction constant? Under the assumption that workers in effect "vote with their feet" among jobs in various industries in response to working conditions and compensation received, then worker satisfaction (utility) is likely maintained to the degree that interindustry mob&ty is also maintained2

This mobility, here termed the likelihood of industry switching, S,

can be represented as S

=

S(H, X, R, W*),

(2)

where the vector of human capital variables, H, controls not only for mobility variation directly attributable to factors such as education and experience, but also for the "cost" of job-search as well3 estimate of W constant (dS

=

dW

S'(R)

dR

S'(W) '

When combined with equation (1) to generate a fust-stage

w*in equation (2)], and holding the likelihood of industry switching 0), note that

_- --

by the implicit-function rule. reduction departs s@icantly

(3)

To the extent that this willingness to pay for risk from W(R), the provision of safety in the work place

diverges from its "optimal" level. Tiebout (1956), of course, coined this phrase in describing household response to local government expenditures. For detailed analyses of interindustry mobility and its determinants, see Gallaway (1969), and Schlottmann and Herzog (1984).

144

3 MODELS OF WAGE DETERMINATION A N D INDUSTRY SWITCHING 3.1 Determinants

As will be explained below, equations (1) and (2) were fit to Census microdata for white-male workers employed within manufacturing.

Personal characteristics entered

within these equations to represent human capital include both age and education, as well as their interaction and squared terms4 Vocational training and work disabilities were also entered.

To the extent that such “inputs” build human capital, wages should be

augmented accordingly. Other personal characteristics of workers were included in both the wage and industry switching equations as control variables [X in equations (1) and (2)]. These include two measures of family dependency, namely marriage and the presence of school age children, as well as variables representing specific occupations. In addition, a variable representing prior migration was included in the industry switching equation to partially control for past interindustry mobility (which should augment present mobility). 5 Two other groups of variables were included as determinants of both wages

and

industry switching [and comprise X in equations (I) and ( 2 ) ] . The fist of these relate to the labor market in which each worker resides.

Economic conditions there are

represented by the local unemployment rate and growth rate of total employment, while population and its density represent unmeasurable aspects of the labor market to include job-search (transactions) and living costs as well as amenities and disamenities.

It is

expected that nominal wages will be augmented, ceteris paribus, by tight labor markets and higher costs of living (population and population density). In addition, the likelihood of industry switching should be increased somewhat within labor markets characterized by rapid job creation. Industry characteristics comprise the final group of variables relevant to the analysis. Based upon the industry of employment for each worker and data for those industries at the national level, variables representing employment growth, percent union, and the risk of fatal injury [the risk variable, R, in equations (l), (2) and (3)] were included within

both the wage and industry switching equations.

Each of these three variables is

expected to augment worker compensation, while the likelihood of industry switching These determinants were selected in accordance with Mincer’s model of schooling, experience and earnings [Mincer (1974)l. In addition, see Blinder (1976). For analyses of these interactions, see Schlottmann and Herzog (1984).

145

should be diminished and increased respectively by industry growth and risk exposure. In addition, an interaction term set equal to the product of the risk and percent union variables was included within the wage equation to examine the effect, if any, of collective bargaining on risk rewards in manufacturing. Finally, based upon equation (2), each worker's wage [predicted in equation (l)] was considered a determinant of industry switching. 3.2

Observations for the estimation of equations (1) and (2) comprise micro-data on personal characteristics (to include wages and industry switching) matched to aggregate data on both labor market of residence and industry of employment. As stated, workers were required to be white-males employed within manufacturing. In addition, workers were required to hold jobs as craftsmen, operatives or laborers in order to place them "at risk" to the job hazard variable.

Table 2 presents the distribution of these job

categories and representative occupations within each category. Based upon these and other restrictions, individuals were drawn from the 5% one-in-a-thousand Public Use Sample (PUS) of the 1970 Census (1972) in two nonexclusive groups: Group A representing workers employed within manufacturing in 1965, and Group B representing equivalent employment in 1970.6 Observations drawn from the PUS were 4,511 in Group A and 4,509 in Group B. Finally, Group A (B) observations were matched in labor market and

industry characteristics based upon residence and industry of employment in 1965 (1970), respectively.

These two samples were necessary in order to fully exploit the wage

information (see estimation below). Labor market characteristics for states were obtained from published Cen sus materials and, with the exception of employment growth, take values for 1965 (1970) when matched

Workers were also required to be the chief income recipient within the family, and of age 19-55 in 1965 (24-60 in 1970). In addition, workers were deleted from the sample if they attended college in 1965 and/or 1970, or were members of the armed forces in 1965 and/or 1970. Finally, 1970 rather than 1980 Census microdata was employed in the study since the latter provides no coding to identify interindustrymobility.

146

TABLE 2 Sample Distribution of Manufacturing Employment and Representative Occupations. ~

~~

~

~~

Category

Percent of Samplea

Craftsmen and Kindred Workers: Carpenters Cranemen, Derrickmen, and Hoistmen Electricians Heavy Equipment Mechanics Metal Job and Die Setters

40.5

Operatives, Total:

52.3

(a) Operatives (ExcludingTransport) Assemblers Cutting Operatives Textile Operatives Machine Operatives Welders

46.8

@) Transport Operatives Truck Drivers Forklift and Tow Motor Operatives Motormen in a Mine, Factory, etc.: Railroad Switchmen Bus Drivers

5.5

Laborers Construction Laborers Carpenter’s Helpers Longshoremen Warehousmen Stockhandlers

7.2

a 6,652 observations, Public Use Sample of the 1970 Census.

to Group A (B) observations. Among the industry characteristics, both employment growth and the percent union were derived from U. S. Department of Labor (1975), while the risk variable was determined on the basis of information provided in U. S. Department of Labor (1971).

In this study, workplace risk is represented by the number of on-the-job fatal injuries per million hours worked in specific three-digit StandGd Industrial Classification (SIC)

147

manufacturing industries7

Means of this "risk" in

1%9 within the Group A and B

samples are .0498 and .@I90 respectively, and range from .0019 in electronic computing equipment to ,4224 in logging.

4 ECONOMETRIC ESTIMATES 4.1 Wage (Earnings) Determination Estimates of the wage equation were obtained for both W and h(W) in equation (l), employing alternatively Group A and B data in order to examine the robustness of implied market prices of risk reduction.

In all cases, the dependent variable was

represented by weekly wage and salary earnings (or their natural logarithm) rather than by an hourly wage.8 In addition, binary independent variables were created and set equal to unity (vs. zero) for married individuals as well as those with school age children, vocational training and/ or a disability which limits work.

Also, specific manufacturing

occupations were represented by dummy variables (with laborers excluded). Ordinary least squares (OM) estimates of individual 1969 weekly earnings are provided in Table 3 for white-male workers employed within manufacturing in 1970 (Group B data) and, in addition, corresponding estimates for 1965 (Group A data). In order to facilitate our analysis, we will confine our discussion to the 1969 estimates. Coefficient estimates are shown for both earnings and the natural logarithm of earnings, the latter form implying a rising price (reward) per unit of fatal injury risk.

Notice that, with few

exceptions, estimates in both equations satisfy a priori expectations. Employing the semilogarithmic form as an example, note in Table 3 among human capital variables that both age and education significantly augment weekly earnings

Based upon U. S. Department of Labor (1971), this risk variable was determined as the product of the number of fatal or disabling injuries per million hours worked and the fraction of these injuries resulting in death. Assuming average weekly hours and weeks worked per year of 40 and 50 respectively, the annual likelihood (per worker) of a fatal injury is equal to the above number divided by 500. Information on "perceived job related accidental death risks has recently been developed by Gegax, Gerking and Schulze (1986). W in equation (1) may be obtained for individual workers in 1969 from our microdata samples by dividing annual earnings by the product of weeks and hours worked (in a year and week respectively). However, this is not advisable since both earnings and weeks worked were measured in 1969 while hours pertain to the Census reference week in the followinqyear, i.e. 1970.

148

TABLE 3 Determinants of Weekly Earnings in Manufacturing: Ordinary Least Squares Estimates for White-Malesa.

Independent Variables:

Dependent Variables (1969): Earnings Ln(Earnings)

Constant Personal Characteristics: Age Age squared Education Education squared Age x education Vocational training Disability which limits work Married School age children

4.3706

3.1183*** .0296** * -.0375*** -.0003*** -2.8108 .0609** * .2840** * -.0010* .0869* * -.0001 12.4227*** .0693** * -10.2836** * -.0886** * 12.1252** * .0773** * 9.2931*** .0414** *

Occupation: Craftsman or kindred worker Operative (except transport) Transport equipment operative

35.0363* * * .2374** * 10.1065** .0962*** 16.7834*** .1416***

Labor Market Characteristics:b Employment growth, 1965-1970 (%) Unemployment rate (%) Population (106)

1.9056

Population density (lo3) Industry Characteristics:c Employment growth, (1965-1970 (%) Percent union Fatal injury risk Fatal injury risk x percent union

3.4452* *

.0083

3

Number of observations

57.6843*** 4.16***

.4052 .0023 2.2912** * .0572** ,0133 1.9564*** 1.6392* .6448 .4235

.0001 .0219** * .0015** .0001 .0181*** .0160** .0078 .0037

4.9327* * * 3.4106*** 2.7209*

.0426** * .0291*** .0174

s597

.0044*

.0005*

-4.7798*** -.0331*** 1.9376*** .0116*** 12.1522*** .0603**

1.8102** * .0011*** .0100

.0175*** .0001* .0003

.6730*** .0054** *

.8403** *

.0095***

.5713** * 178.5870** * 2.9809***

.0054** * 1.9557*** .0311***

.4450*** .0032** * 175.9491** 1.6521** * -2.8983* -.0293* * *

F- tatistic R (adjusted)

Dependent Variables (1965): Earnings Ln(Earnings)

55.20 .20 4,509

* t-test significant at the 0.10 level. * * t-test significant at the 0.05 level. *** t-test sigtllfcant at the 0.01 level.

55.48 .20 4,509

79.15 .26 4,510

84.16 -28 4,510

149 aAll variables are defined in the text. Estimates were obtained using Group A and Group B microdata also described in the text. bBased upon state of residence in 1970. Variables represent 1970 values except where noted. 'Based upon industry of employment in 1970 and national data. Percent union and fatal injury risk represent 1968 and 1969 values, respectively. (albeit at a declining rate), and that such augmentation is also attributable to vocational training.

However, when work effort within manufacturing is limited by a disability,

earnings suffer.

On the other hand, such effort is apparently enhanced (resulting in

increased earnings) among white-male workers encumbered by family responsibility. In addition, craftsmen and kindred workers as well as operatives (both transport equipment and other) receive compensation in excess of that awarded laborers, ceteris paribus. Turning now to labor market characteristics in Table 3, note that manufacturing workers receive increased nominal compensation when employed within tight labor markets (low unemployment rates) as well as in those markets characterized by higher costs of living (high population and population density). Also, notice among industry characteristics that rapid industry expansion (employment growth), greater bargaining power of workers (percent union), and increased risk in the workplace each augment weekly earnings. Thus, compensating wage (earnings) differentials do exist within manufacturing as a reward for risk exposure. In addition, the coefficient estimates on the fatal injury risk variable in Table 3 indicate the implicit market price of additional safety at prevailing levels of risk exposure.

Finally, note the negative and signifcant interaction term between risk and percent union in Table 3.9. Two additional equations employing Group A

This result is consistent with fmdings by Martin and Psacharopoulos (1982) for collective bargaining in Great Britain. They suggest two reasons for this result. First, collective bargaining often takes place for broader groups than the occupations used here, and broad wage settlements could reduce the sensitivity of wages to risk. The second possible reason is that to the extent unions often press directly for safety improvements rather than using risk solely in wage bargaining, risk would play less of a role in earnings determination by collective bargaining. On the other hand, Thaler and Rosen (1976) find a positive interaction for the United States by employing a binary variable depresenting union affiliation. In commenting on their work, Kosters (1976) suggests that unions may be better equipped than nonunion workers to assemble reliable information on risk, and to utilize it effectively during the bargaining process.

150

data and variables equivalent to those in Table 3 were estimated utilizing weekly earnings 10 in 1965 [for use as first-stage estimates of W*in equation (2)) Although not shown in Table 3, coefficient estimates and significance levels are similar to those obtained for 1969.

For instance, for both dependent variables (1965 weekly

earnings and the natural logarithm of these earnings), signs and si&cance

levels on

industry characteristics match those in Table 3. Thus, compensating wage differentials for risk exposure within manufacturing were also detected in 1965, as was the compression of such risk rewards by increased unionization. 4.2 Interindustrv Mobility

As stated, an estimate of workers' willingness to pay for risk reduction can be obtained from an industry switching equation where the likelihood of interindustry mobility is determined, in part, by risk exposure on-the-job as well as compensation received. In this respect, equation (2) was determined from Group A microdata for white-male workers employed within manufacturing in 1965 and, thus, "at-risk to interindustry mobility over the ensuing five-year period. For each of the 4,511 observations, the dependent variable in this equation was set equal to unity (vs. zero) if a worker was employed in an industry in 1970 (manufacturing or nonmanufacturing) other than that in which employed in 1965. Based upon three-digit SIC codes, 994 manufacturing workers (22 per cent) switched industries between 1965 and 1970, some migrating interstate in the process. Binary logit estimates of the determinants

of this interindustry mobility among white-males are provided in Table 4. Based upon asymptotic t-values in the last column of Table 4, note among personal characteristics that the likelihood of industry switching is augmented by vocational training, by a disability which limits work, and by prior geographic mobility."

On the other

hand, this likelihood is diminished somewhat by increased age (an effect that also

lo However, labor market variables (representing residence in 1965) assumed 1965 rather than 1970 values. In addition, both 1965 weekly earnings and industry characteristics were based upon industry of employment in 1965.

l1 Binary independent variables are equivalent to those employed for earnings determination in Table 3. The variable representing prior migration (as of 1965) was set equal to unity (and zero otherwise) if an individual resided in a state other than his birth in 1965.

151

TABLE 4 Determinants of 1965-1970 Industry Switching For Individuals Employed in Manufacturing in 1965: Binary Logit Estimates for White-Malesa. Constant and Independent Variables: Constant Personal Characteristics: Age Age squared Education Education squared Age x education Vocational training Disability which limits work Married School age children Prior migrant Occupation: Craftsman or kindred worker Operative (except transport) Transport equipment operative

Coefficient

Asymptotic t-value

5.4349

- .1825 .0015 .0727 -.0020 -.0004 ,2205 2305 -.0192 .1133 .2036

-4.11*** 3.46* * * .58 -.46 -.23 2,34** 2.02** -.11 1.10 2.08* *

-.0458 -.1159 .3118

-.25 -.70 1.57

Labor Market Characteristicsb Employment growth, 1965-1970 (%) Unemployment rate (%) Population (106) Population density (lo3)

.1165 -.0083 .ox9 .3191

2.07** -.13 2.30**

Industry Characteristics:c Employment growth, 1965-1970 (%) Percent union Weekly earningsd Fatal injury risk

.0255 .0058 -.0309 2.8831

1.30 .57 -1.80* 2.87** *

1.46

* t-test significant at the 0.10 level. ** t-test significant at the 0.05 level. *** t-test significant at the 0.01 level. aAll variables are defined in the text. Estimates were obtained using Group A microdata (4,511 observations) also described in the text. Industry switching was based upon threedigit Standard Industrial Classification codes for industries of employment in 1965 and 1970. The log likelihood ratio test statistic was significant at the 1percent level. bBased upon state of residence in 1965. Variables represent 1965 values except where noted.

152

‘Based upon industry of employment in 1965 and national data. Percent union and fatal fjury risk represent 1968 and 1969 values, respectively. Represents W* in equation (2). Predicted 1965 values were obtained from an estimate of equation (1) employing Group A microdata. See the text. attenuates with age). In addition, industry switching is also responsive to labor market conditions, such industrial mobility being increased by rapid local job creation (employment growth) as well as compactness of local employment opportunity (population density), and thus lower search (transactions) costs. Finally, interindustry mobility among white-male manufacturing workers is augmented and diminished by risk of fatal injury in the workplace and by weekly earnings received, respectively.12

Thus, to the extent that

additional earnings provide insufficient compensation for added risk (based upon workers’ willingness to pay for risk deduction), individuals likely “vote with their feet” to fmd employment in other, less risky, industries.

4.3 The Wage-Risk Trade-off: Market Price vs. Willingness to Pav As stated above, there are reasons to suspect that the market price of risk reduction

[W(R)] diverges from workers’ willingness to pay for this reduction (dW/dR).

Thus,

safety in the workplace may quite possibly be provided in suboptimal amounts. Based upon the econometric estimates above, we are now equipped to investigate this question of market failure empirically. Notice that W(R) can be derived from coefficient estimates in Table 3 on the fatal injury risk variable and its interaction with percent union, while dW/dR can be determined by equation (3) from estimates on weekly earnings and risk in Table 4. Also note that an estimate of the total risk reward (compensatory earnings) provided workers at the prevailing level of risk exposure (say R2) is equal to W(R2) hand, workers’ willingness to pay, industrial work hazards (such that R evaluated at R213

*

R2.

On the other

through foregone earnings, for the elimination of all =

0) is equal to (dW/dR)

‘

RZ, the derivative being

Termed collectively “fatal injury risk rewards,” these terms were

l2 Weekly earnings in Table 4, W* in equation (2), represent the predicted 1965 value for each manufacturing worker obtained from an estimate of equation (1) employing Group A microdata. See the section on wage (earnings) determination below. l3 Since a “one unit” change in fatal injury risk (a fraction) is difficult to interpret, comparisons below of market price and willingness to pay for risk reduction, W(R) and dW/dR respectively, will be made on the basis of these wage-risk trade-offs

153

evaluated on the basis of estimated parameters in four earnings equations (two of which are shown in Table 1) as well as estimates from the industry switching equation. Results are listed in the first column of Table 5. Based upon estimates of the earnings equations for white-males employed within manufacturing, weekly earnings premiums for risk, evaluated at "market" prices, range from $1.91 to $3.28 (in 1965 dollars). Such "compensating differentials" comprise 1.7 -2.9 percent of weekly earnings (see column 2).

Alternatively, the estimates in the first

column in Table 5 also represent the weekly wage consession reauired of manufacturing workers to reduce risk to zero.

However, an estimate obtained from the industry

switching equation with equivalent data indicates that such workers are willine, to forgo $4.64 per week (4.0 percent of their income) to eliminate risk of fatal injury from the workplace. Thus, willingness to pay for risk reduction within manufacturing exceeds its market price (by a minimum of 41 and a maximum of 143 percent). Since willingness to pay for risk reduction exceeds the market price of providing this reduction, implied value of life estimates derived from wage/earnings (or hedonic) equations are downward biased. Examples of such estimates derived from the four wage equations are provided in the last column of Table 5.14 In addition, the fdth entry in column 3 represents implied value of life based upon willingness to pay for risk reduction (as determined from the industry switching equation). This and the other four value of life estimates were determined in accordance with accepted practice.

Assuming for an

average worker an average work week of 40 hours and an average of 50 weeks worked per year (two thousand hours), the fatal injury risk variable (fatalities per million hours worked) represents the likelihood of an adverse outcome per 500 workers. Thus, multiplication of W ( R ) or dW/dR by 500 yields the value that workers place on their life for small changes in the likelihood of death on-the-job.

In addition, this value must be

inflated by a factor of 50 to convert weekly earnings [employed in both equations (1) and

weighted by the mean risk level. See the footnotes in Table 5. Theoretically, that such an approach may overvalue (undervalue) estimates of risk compensation based upon willingness to pay (market price) has been noted by Smith (1979). l4 These estimates are consistent in magnitude with other implied value of life estimates obtained from wage/earnings equations and an equivalent job hazard variable. In this respect, see Viscusi (1978).

154

TABLE 5 Fatal Injury Risk Rewards in Manufacturing and Implied Value of Life (1965 Dollars). ~

~~

~

~~

Fatal Iniurv Risk Reward Source of Estimate:

Weekly Premium'

Relative Weekly Premiumd

Implied Value of Lifee (x 106)

Earnings Equation/ by dependent variable: 1969 Earningsa

$1.91

1.7%

$ .972

Ln (1969 Earnings)a

2.45

2.1

1.250

1965 Earnings

2.28

2.0

1.145

Ln (1965 Earnings)

3.28

2.9

1.644

4.64

4.0

2.330

Industry Switching Equation

aSee equation (1) and Table 3. 1969 earnings were deflated to 1965 dollars based upon average weekly earnings of production workers on manufacturing payrolls (deflator of .8303). For a similar procedure, see Dillingham (1985). For example, $2.45 is the product of .8303, $60.20, and the mean risk level .049. The value of $60.20 is obtained from the mean of weekly wages ($173.63), the mean union rate, and the estimated equation as mean wage times the sum of the coefficient on fatal injury risk (1.6521) and the coefficient on the interactive variable (-.0293), the latter multiplied by the mean union rate (44.55). bSee equations (2) and (3), and Table 4. Evaluated at the mean risk level. 1965 dollars. ?his premium is equal to W(R) in equation (l), or dW/dR in equation (3), multiplied by the mean fatal injury risk level. %h'is is calculated as 100 (weekly premium)/mean 1965weekly earnings. ($115.04) eThe implied value of life is determined as W(R) in equation (l), or dW/dR in equation (3), multiplied by 25,000 (which represents the conversion of the risk data per 500 workers times 50 weeks per year). For example, .972 = 25000 x (175.9491 - 2.8983 x 44.55) x .8303. (2)) to annual c ~ m p e n s a t i o n . ~Based ~ upon the mean of the fust four entries ($1.253 million dollars), implied value of life estimates obtained from wage/earnings equations and, thus, market evaluations of risk rewards, understate life's value by 46 percent. Compared to the government agencies listed in Table 1, the implied value of life from l5 Important income effects overlooked by this procedure are examined by Viscusi

(1978b).

155

the industry switching equation (when inflated to current dollars) tends to agree only with the higher values utilized by OSHA and the EPA. 5 CONCLUSIONS

Public policy debates over environmental regulations for health and safety

hazards

have often centered on cost-benefit analysis in which the critical parameter is the implied value of life.

This necessity to evaluate environmental policy affecting human

life in dollar terms is becoming increasingly common in both the United States and Europe.

For example, in the United States the FAA proposal in 1985 for all airline

manufacturers to strengthen seats depended critically on the assumed value of life estimates.

In this paper we have examined the valuation of life from the economist's

perspective of compensating wage differentials. Empirical studies of compensating wage differentials attributable to risk in the workplace assume, most often implicitly, that workers' willingness to pay for risk reduction (safety) is equal to the market

"price" of

providing this reduction. Thus, it is assumed that labor markets are observed in a state of pure competition in long-run equilibrium. In this regard, workers and their employers are believed to possess perfect information regarding work hazards, the likelihood of adverse outcomes stemming from these hazards, and the cost of providing additional safety in the work place. However, to the extent that such information is not known in its entirety, the prices at which risk is "bought" and "sold" within industrial labor markets are likely to differ. Thus, evaluations of the wage-risk trade-off will vary to the extent that the market (employer's) price diverges from workers' willingness to pay. Under the assumption that manufacturing workers "vote with their feet" among jobs in various industries in response to working conditions and compensation received (and thereby reveal their workplace preferences in the process), this willingness to pay for risk reduction was shown to exceed, by 41 to 143 percent, the market price of incremental safety. Since value of life estimates derived from wage/earnings (hedonic) equations also assume equivalence between the willingness to pay for, and market price of, added safety in the workplace, such valuations are downward biased. was placed at 46 percent.

A mean estimate of this bias

Finally, by employing workers' own wage-risk trade-offs at

prevailing levels of risk exposure within manufacturing, the implied value of life for white-male workers was shown to exceed two million (1965) dollars.

These results

156

suggest that the use of "traditional" value of life estimates in formulating environmental regulations may be too low. REFERENCES Bartik, T., 1987. The estimation of demand parameters in hedonic price models. Journal of Political Economy, 9581-88. Blinder, A. S., 1976. On dogmatism in human capital theory. Journal of Human Resources, 53~8-11. Curington, W. P., 1986. Safety regulation and workplace injuries. Southern Economic Journal, 5351-72. Dillingham, A. E., 1985. The influence of risk variable definition on value-of-life estimates. Economic Inquiry, Dk277-294. Dorsey, S., 1983. Employment hazards and fringe benefits: further tests for compensating differentials. In: John D. Worrall (Editor), Safety and the Work Force. Ithaca, New York: ILR Press, pp. 87-102. Duncan, G. J. and Holmlund, B., 1983. Was Adam Smith right after all? Another test of the theory of compensating wage differentials. Journal of Labor Economics, 1:366-379. Epple, D., 1987. Hedonic prices and implicit markets: estimating demand and supply functions for differentiated products. Journal of Political Economy, 9559-80. Gallaway, L. E., 1969. Age and labor mobility patterns. Southern Economic Journal, 36:171-180. Gegax, D., Gerking, S. and Schulze, W., 1986. Perceived risk and the marginal value of safety. Unpublished. Kosters, M., 1976. Comments on 'The value of saving a life: evidence from the labor market.' In: Nestor E. Terleckyj (Editor), Household Production and Consumption. New York: National Bureau of Economic Research, pp. 298-301. Martin, A. and Psacharopoulos, G., 1982. The reward for risk in the labor market: evidence from the United Kingdom and a reconciliation with other studies. Journal of Political Economy, 902327-853. Mincer, J., 1974. Schoolig, Experience, and Earnings. New York: Columbia University Press. Rosen, S., 1974. Hedonic prices and implicit markets: product differentiation in pure competition. Journal of Political Economy, 8234-55. Schlottmann, A. M. and Herzog, H. W., Jr., 1984. Career and geographic mobility interactions: implications for the age selectivity of migration. The Journal of Human Resources, 19:72-86. Smith, R. S., 1979. Compensating wage differentials and public policy: a review. Industrial and Labor Relations Review, 32:339-352. Thaler, R. and Rosen, S., 1979. The value of saving a life: evidence from the labor market. In: Nestor E. TerleckyJ (Editor), Household Production and Consumption. New York: National Bureau of Economic Research, pp. 265-298. Tiebout, C. M., 1956. A pure theory of local government expenditures. Journal of Political Economy, 64416-424. U.S. Bureau of the Census, 1972. Public Use Samples of Bas.ic Records from the 1970 Census. Washington, D.C.: U.S. Department of Commerce. US. Department of Labor, 1975. Handbook of Labor Statistics 1975 - Reference Edition. Bulletin 1865. Washington, D.C.: Bureau of Labor Statistics.

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, 1971. Injury Rates by Industry. Report No. 389. Washington, D.C.: Bureau of Labor Statistics. Viscusi, W. K., 1979. Job hazards and worker quit rates: an analysis of adaptive worker behavior. International Economic Review, 20:29-58. , 1978. Wealth effects and earnings premiums for job hazards. The Review of Economics and Statistics, 60:408-416. and O’Connor, C. J., 1984. Adaptive responses to chemical labeling: are workers bayesian decision makers? American Economic Review, 74942-956. Waldman, S., 1980. Putting a price on life. Newsweek, January 11. Weinberg, D. H., Friedman, J. and Mayo, S. K., 1981. Intraurban residential mobility: the role of transactions costs, market imperfections, and household disequilibrium. Journal of Urban Economics, 9:332-348.

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part 111

Cost Benefit Analysis

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Reprinted from: ValuationMethods and Policy Making in Environmental Economics, edited by H. Folmer and E. van Ierland 01989 Elsevier Science Publishers B.V.. Amsterdam - Printed in The Netherlands

Chapter

161

9

DISEQUILIBRIUM COST-BENEFIT RULES: A N EXPOSITION A N D EXTENSION* PER-OLOV JOHANSSON and KARL-GUSTAF LOFGREN Department of Forest Economics, SLU, S-901 83 Umei, (Sweden) and FIEF, Wallingatan 38,4 tr, S-111 24 Stockholm, (Sweden)

1 INTRODUCTION

This paper reviews some of the recent developments in disequilibrium cost-benefit analysis. Instead of repeating previous modelling attempts we generalize some of the results by deriving cost-benefit rules within an intertemporal multi-sectoral model of a small open economy, with endogenous private investment. We show in particular how some of the earlier results follow as special cases. Distributional issues are most often neglected by focusing on efficiency considerations, and introducing a representative household. To our knowledge the distributional problems have so far not been addressed in a disequilibrium cost-benefit setting. A special section below is devoted t o a discussion of necessary and sufficient conditions for welfare improvement in the compensation sense. The paper is structured as follows: After a short survey of the literature we introduce our general equilibrium model and show how the general equilibrium cost-benefit rules follow by differentiation of the indirect utility function of the representative household with respect to the project parameter. Next, we derive the corresponding cost-benefit rules for two typical disequilibrium situations; classical and Keynesian unemployment. We devote a special section to a discussion of cost-benefit rules for natural resource projects, and the section on distributional issues concludes the analytical part of the paper. 2 A BRIEF SURVEY O F THE LITERATURE The beginnings of cost-benefit analysis date back over a century to the work of Jules Dupuit, who was concerned with the benefits and costs of constructing a bridge; Dupuit's famous paper "On the Utility of Public Works" was published in 1844. In particular, Dupuit introduced the concept of the consumer's surplus, i.e. the fact that benefits are measured by an area under a demand curve, not by what is actually paid. The next major contribution to cost-benefit analysis seems to have appeared almost one hundred years later.

* The authors acknowledge comments from participants of the economic seminar at the Department of Economics, University of Stockholm, and the editors of this book.

162

In a well-known paper, "The General Welfare in Relation t o Problems of Railway and Utility Rates" published in 1938, Harald Hotelling, among other things, formulated the case for marginal cost pricing: "The efficient way to operate a bridge is to make it free to the public, so long at least as the use of it does not increase to a state of overcrowding" [Hotelling (1938, p. 158)]. The first attempts to apply cost-benefit analysis to empirical decision making also date back to the thirties. The United States Flood Control Act of 1936 introduced the principle that a project is desirable if "the benefits, t o whomsoever they may accrue, are in excess of the estimated costs". However, the precise meaning of a "benefit" remained unclear, and individual agencies often approached similar projects from different standpoints. This stimulated academic interest in the subject. In particular, beginning in the late fifties, an extensive literature on the foundations of cost-benefit analysis emerged; see Eckstein (1958), McKean (1958), Krutilla and Eckstein (1958), Maass (1966), Marglin (1967), Harberger (1969, 1971), Musgrave (1969), Lesourne (1975), Little and Mirrlees (1968), Dasgupta et a1 (1972), Boadway (1975), Srinivasan and Bhagwati (1978), and Diewert (1983), just to mention a few.1 Several of these works can be considered as manuals since they are concerned with many problems such as the choice of an appropriate discount rate, measuring the opportunity cost of capital withdrawal from the private sector, and the efficiency gains from public sector projects in a tax-distorted economy. Of particular interest in the present context, however, is the treatment of market imbalances in the aforementioned as well as in later contributions. For a long period of time interest has been focused on disequilibria in the labor market. The traditional way to view employment
1 Arrow and Kurz (1970), Meade (1955), and Tinbergen (1952) are examples oE related works which have influenced the development of cost-benefit analysis.

163

w ---

Figure 1. The partial equilibrium view on the employment effect of an increased demand for labor when the wage rate is fixed above the market4earing level. However, for a long period of time, cost-benefit analysts had difficulty in providing a theoretical justification for their treatment of the macroeconomic effects caused by a project. This difficulty arose because of the lack of a satisfactory link between microeconomics and Keynesian macroeconomics. Whereas public finance theory uses models based on individual optimization, it is ill-equipped to deal with non-market4earing situations which lie beyond its Walrasian equilibrium framework. Macroeconomics, on the other hand, focuses on market imbalances but its microeconomic underpinning has often been weak. This lack of microeconomic foundations has made it difficult to directly assess the welfare effects of government policies. In their seminal paper, "A General Disequilibrium Modcl of Income and Employment", Barro and Grossman (1971) provided a link between microeconomics and Keynesian macroeconomics. However, to the best of our knowledge, this link was not discovered by cost-benefit analysts until the early eighties. It turns out that the general disequilibrium approach in general produces cost-benefit rules which are very different from the partial equilibrium rules presented above. There are at least two generations of models that have been used in deriving disequilibrium cost-benefit rules and in making welfare evaluations. The early papers, e.g. Bell and Devarajan (1983), Blitzer et a1 (1981), Cuddington et a1 (1984), J.H. Dreze (1985), J.P. Dreze (1982), Fourgeaud ct a1 (1986), Johansson (1982), Maneschi (1985) and Roberts (1982), use essentially single period models with exogenous private investment. This means that a public-sector pioject has no adverse effect on the level of investment. The second generation models are intertemporal, which admit an explicit treatment of expect,ations, and

164

some of them treat private investment as an endogenous variable; see e.g. Johansson (1984), Johansson and Lofgren (1985), and Marchand et a1 (1984, 1985). Instead of reviewing this literature, we will present a model similar to the one in Neary and Stiglitz (1983) which, as other special cases, generates most, if not all, of the results found in the aforementioned literature. In addition, this approach will enable us to derive some results which we believe are new. 3 THE MODEL IN THE ABSENCE OF QUANTITY CONSTRAINTS This section considers a small open economy which can buy and sell tradeables without limit in each period at fixed foreign currency prices. Moreover, assuming perfect capital mobility and a single international traded bond, the foreign
where a superscript i = x refers to producers of traded goods and i = n refers to producers of ' p2) i is a vector of prices containing the present value price in non-traded goods, pi = (pi, period t (t = 1, 2), w is a vector of present value wage rates, yl is a vector of gross outputs of goods, Ii is a vector of investments, !is a vector of demands for labor, &.) denotes profits in all periods beyond the second period as a function of the level of investment in the second period and expectations 0' of future prices, etc, Fi(.) and Hi(.) are the twice continuously differentiable and strongly concave first-period and second-period production functions, respectively, all prices are domestic currency prices, and notation denoting transposed vectors have been suppressed. According to ( l ) , firms choose current and future employment levels. In addition, firms may invest part of the output in order to augment productivity of labor in the future. Note

165

that we "collapse" all periods beyond the second period into a single period so that 4i(.) contains the sum of the present values of expected profits in these future periods. In later sections, we will employ the envelope theorem in order to simplify the exposition; see e.g. Varian (1984) for details. For example, the effect of a ceteris paribus change in p i on the present value of profits is equal to:

where x i ( . ) is the first-period supply of commodity i, i.e. what is produced less what is invested of the commodity. Thus, by taking the partial derivative of (1) with respect to a price, we obtain the net supply of that commodity. 3.2 The Government To derive cost-benefit rules we will follow the tradition within the field and introduce (two) stateowned firms. These firms produce traded goods and non-traded goods, respectively, using labor as the sole variable input. Any profits (or losses) incurred by the state-owned firms are assumed to be disposed of (financed) by lump-sum transfers (taxes) T. Hence, the government budget constraint takes the form: n

T = C [piyi - w $1 i=x

g

g

(3)

where the g subscript denotes government output supply or labor demand, i.e. 1 i l l i i i yg = (ygl, yi2), 1; = (egl, tg2),and ygt = f'(1' ). State-owned firms hire labor at the t gt prevailing wage and sell output at the prevailing prices, i.e. these firms, like all other agents in the economy, are assumed to take prices as given. Because the level of public sector employment, by assumption, is an exogenously4etermined policy variable, the marginal revenue product of government-employed labor may exceed, be equal to, or fall short of the i i i > w for i = X, n, t = 1, 2. wage; pt(@ gt /a1gt ) < t This simple specification of the public sector allows us to concentrate on the market imbalance issue in later sections. In addition, it is the specification used in almost all papers deriving (disequilibrium) cost-benefit rules. See for example the references introduced above. 3.3 Households In order to focus on efficiency considerations while setting aside matters of equity and income distribution, the commonly employed assumption of a "representative" household is used in Sections 3 - 5, but in Section 6 we discuss distributional issues in terms of the Kaldorian compensation criterion, see Kaldor (1939). The household consumes both traded and non-traded goods and supplies labor. In addition, the household is assumed to save in

166

order to be able to consume in periods beyond the second period. This is captured by including as an argument in the utility function holdings of an asset at the end of the second period. Both borrowing and lending are allowed at the prevailing interest rate. Once the possibility of borrowing or lending at the prevailing interest rate is introduced, the issue of whether profits are distributed in the period in which they are generated or in the subsequent period becomes less important. In what follows it will be assumed that the sum of current profits from both private producers and state owned firms are distributed within the current period. The household is assumed to maximize utility subject to its budget constraint. The indirect utility function of the household is defined as: ~ ( pW, , IT

+T +M

,@

- max {U(X, C, M, - X,C,M

@)I Mo + II + T + wC-pX

- M = 0)

(4)

where p = (px, pn) is a vector of goods prices, II = IIx + IIn, Mo is initial wealth yielding the internationa1 interest rate, 0 denotes expectations of prices in periods beyond the second period, U(.) is the twice continuously differentiable and strongly quasi-concave utility function, X = (Xy, X i , X,: X i ) is a vector of demands for goods, C = ($, $) is a vector of supplies of labor, and M is end of second period wealth. According to (4), (indirect) utility is a function of all prices and wages, exogenous income, and expectations. This indirect utility function has all the properties known from textbooks on microeconomics. For example, taking the partial derivative with respect to a goods price, one obtains the corresponding demand function (multiplied by - A, where X denotes the marginal utility of exogenous income Y , i.e. av/aY). 3.4 Societv's welfare function

From the point of view of the entire economy, the profits of both private sector and public sector firms in equation (4) are functions of prices and wages, i.e. they cannot be treated as exogenous entities as in (4). In addition, public sector profits are determined by the levels of employment Ci since these are exogenously determined policy variables. Therefore, using (4) g the indirect utility function, or the social welfare function in our single household economy, can be written as:

n where Y = C IIi(pi, w, 0') i =x

2

n

+t=1 C C i=x

[pi#($ ) - w Ci ] l = ( p e") is a vector of governt gt tgt' g g' g

ment labor demands, and 6 = (0,Ox,Qn). Taking the partial derivative of (5) with respect to pk, one obtains:

since av/apt = - x and

xi, au/%

= A,

n/api ~II'/+' = t -- ani/*' t + m/api, t t

yi - I' t t - X t '

m/@f= yit.

Thus, by taking the partial derivative of (5) with respect to a price (or the wage rate), one obtains the excess supply or demand of the commodity in question (multiplied by A). =0 Obviously, if all prices and wages correspond to their market clearing levels, then in (6) for all i and t. This is a useful result which will simplify considerably the derivations of the cost-benefit rules.

4 GENERAL EQUILIBRIUM AND DISEQUILIBRIUM COST-BENEFIT RULES To obtain a monetary welfare change measure of a marginal change in the public project, we differentiate totally the welfare function (5) with respect to Ci and divide through by A, to gt obtain:

Wt

Vi, t

(7)

Dividing through by A, the marginal utility of exogenous income, converts the right-hand side expression from unobservable units of utility to observable units of money. According to the monetary welfare change measure (7), the appropriate rule for project evaluation would be to value all outputs and inputs at their domestic market-clearing (present value) prices. Using this criterion, it is clear that welfare can be increased as long as the marginal revenue product of government employed labor differs from the wage rate. This is the well-known general equilibrium rule found in the literature on cost-benefit analysis. See e.g. Boadway (1975), Harberger (1971), Lesourne (1975), and Starrett (1979). Note that a change in the level of public sector employment may affect some or all of the economy's prices. However, given the assumption of continuous market4earing prices, equation (6) ensures that any indirect effects through changed prices are equal to zero (or rather the net effect is zero). Therefore, the measure (7) is a general equilibrium measure, although it is only valid for "small" changes in C' For the problems of examining discrete gt' changes, the reader is referred to Johansson (1987), Starrett (1979), and Tsuneki (1985). The assumption of continuous market-learing prices employed above in deriving cost-benefit rules is a strong one. For practical applications it is invaluable to determine how the shadow pricing rules are changed by different kinds of market imbalances. In this section it is shown how the model can be used to derive project evaluation or cost-benefit rules for situations where there is quantity rationing due to price stickiness in markets for goods and factors2. Since the model contains several commodities and periods, it is possible to construct

For a survey of different reasons for sticky prices, the reader is referred to Cuddington et a1 (1984) and Stiglitz (1986). 2

168

a lot of disequilibrium variations, but to keep the problem tractable we will only consider two cases. The basic idea is to make the important distinction between the short run (period 1) and the medium run or long run (period 2). In the short run, the wage rate is assumed to be sticky. However, in the long run it adjusts to its market-learing level. In our opinion, this is a scenario which is close to the one often faced by policy makers, i.e. the conflict between short-run targets such as a low level of unemployment and medium or long run targets such as a high level of investment3 (growth). Two typical situations are considered. The first situation, labelled classical unemdovment, is characterized by (first period) excess supply in the labor market due to excessive real wages (and a trade balance deficit or surplus due to a fixed exchange rate). The other situation, called Keynesian unemDIovment, refers to a situation where there is unemployment due to deficient demand. Consider first classical unemployment. 4.1 Classical unemdovment The fact that there is an excess supply of labor, but no other market imbalances (quantity constraints), means that firms are still unconstrained in all markets. Hence, the maximization problems of firms are those described in Sections 3.1 and 3.2 above. On the other hand, the household maximizes its utility function subject to the budget constraint & the first period -

employment constraint tl = C1. Straightforward but tedious calculations verify that the indirect utility function ( 5 ) now can be written as:

-

+

+

c1

G1,

where C1 = $ + i.e. the household does the best possible and sells the amount of labor demanded. The main difference between the indirect utility function in (8) and the one in equation ( 5 ) is that a change in the first-period wage rate now has an income effect, but not a substitution effect. This is so because the household faces a binding constraint in the labor market in period 1, i.e. the household cannot adjust the level of employment following a change in the wage rate. Consider now a small change in the level of employment in period 1. Taking the partial -

derivative of (8) with respect to

el, one obtains:

3 In contrast, in the intertemporal model used by Marchand et a1 (1985) to derive shadow prices there is no investment or production of goods in period 2, i.e. all such activities take place in period 1 (but the goods become available for consumption in period 2).

169

where all prices and public sector output levels are being held constant, and U i refers to the 1 partial derivative with respect to the next to last argument of the indirect utility function (8). In fact, U e is the marginal disutility of work effort, evaluated at the optimal or utility 1 maximizing levels of all unconstrained household demands and supplies. In the literature, *

*

U-

X is sometimes referred to as (the negative of) the supply price or the virtual price of

ell

labor4. Equation (9) reflects the fact that there is a difference between the market wage and the marginal disutility of work effort whenever the household is unemployed/underemployed (or, for that matter, overemployed). In order to obtain cost-benefit rules to be used in the case of classical unemployment, let us assume that first-period public sector employment and production are increased. Taking the total derivative of (8) with respect to

!'gl and dividing through by X yields:

where l$) = q ( p y , wl) + q ( p nl , wl), i.e. . !denotes : private sector employment in period 1. The welfare measure in the middle expression in (10) differs from the one obtained in the & equilibrium case in that a new term reflecting the policy induced change in total employment (private plus public) is now added. This term reflects the fact that the marginal disutility of effort is less than the sticky nominal wage whenever there is unemployment. The middle expression in equation (10) provides a straightforward rule for evaluating public sector enterprises under classical unemployment. First, evaluate all outputs and inputs of state-owned enterprises at prevailing domestic market prices and assess the firms' profitability on this basis. Second, determine the total policy induced change in employment in both the private and public sectors ( d i l ) and evaluate this change a t the prevailing wage less any adjustment reflecting household disutility of increased work effort. Let us compare this rule with the traditional partial equilibrium rule found in textbooks and briefly discussed in Section 2. The partial equilibrium view, illustrated in Figure 1 in Section 2, treats all labor employed in a marginal project as coming from the unemployed, and implicitly ignores any effect of increased public sector employment on employment in the private sector. Therefore, the partial equilibrium rule corresponds to the first expression within brackets in the right-hand side expression of equation (10). This says: Value all public sector output at market prices but attribute a positive shadow price to the labor hired only to See Cuddington et a1 (1984), Neary and Roberts (1980), and Rothbarth (1940/41). A, the marginal utility of money, transforms money to units of utility.

4

170

the extent that households perceive disutility from additional employment (i.e. U j < 0). 1 Unfortunately, this shadow pricing rule based on partial equilibrium analysis is in general incorrect even though the public sector hires only from the pool of unemployed workers. The reason for this is that even a marginal increase in public sector employment will affect prices and hence private sector demand for labor. This indirect dependence is captured by the second expression within brackets in equation (10). For example, if total employment decreases, i.e.

+

dli dlf < 0, the presence of the last expression within brackets in (10) implies that gl profitability calculated at producer prices - which is the general equilibrium rule derived in equation (7) above - is not sufficient to ensure that a project is socially profitable. According to the partial equilibrium rule, on the other hand, a project is always socially profitable if it is profitable when measured at producer prices. Consider next changes in future output levels. Suppose that the government announces that public-sector production of nontradeables will increase in the future, i.e. in period 2. Since all period 2 prices are allowed to adjust to their marketxlearing levels, it is quite natural to use equation (7) to assess the profitability of the project in question. However, in the present context, where there is unemployment in period 1, this is a partial or incomplete rule. TO show this, note that the increased supply of nontradeables in period 2 will drive down the equilibrium price p; of such goods. In turn, this induces private sector firms to reduce investment and hence gross production of non-traded goods in period 1; recall that less capacity is needed in period 2 due to the decrease in p;. Therefore, first period employment is reduced, thereby imposing an extra cost on the considered project. This extra cost is captured by an expression similar to the final expression within brackets in equation ( l o ) , and should be added to the project evaluation rule (7), which is valid if there is full employment in all periods. These results show that it is of utmost importance for the policy maker to try to estimate and include also the indirect or induced effects caused by a particular project. Otherwise, the policy maker may implement projects which are socially unprofitable and reject projects that are socially profitable. In particular, it shows that relief work announced to be conducted during future periods of full employment have effects in the current unemployment period. 4.2 Kevnesian unemdovment If both prices and wages are fixed such that there is excess supply of both goods and labor, one speaks of Keynesian unemployment. In this paper, however, the analysis is restricted to a situation where there is unemployment and private producers of non-traded goods face a sales constraint for their output in the short-run, i.e. in period 1. Firms producing traded goods are throughout assumed to never face quantity constraints. As before, in the long run, represented by period 2, prices and wages are flexible so that neither households nor firms are rationed.

Private firms producing non-traded goods face a sales constraint Fy = yy - I?. Adding

171

this constraint to the maximization problem (1) for i = n, yields a profit function which can be written as:

where pf' is the market price of non-traded goods in period 1, and

$ is the virtual price of

such goods in period 1. This virtual price is such that the auantitv unconstrained supply xy is equal to the quantity constraint ?;

(and all other supply and demand levels remain

unchanged). Obviously, since the firm is rationed, then p: > py. This implies that the right-hand side profit function in (11) yields a lower level of profits than the left-hand side profit function, although py is chosen in such a way that both functions produce the same optimal supply and demand levels. This explains the fact that we add the expression (py - py)?; to the right-hand side of (11).

Taking the partial derivative of (11) with respect to F,: one obtains:

n w) = ? .: According to (12), the increase in profits caused by a where ann/$ = xnl ( p^ ln, p2, small increase in sales is equal to the difference between the ruling market price and the virtual price of nontradeables, as is illustrated in Figure 2a. Roughly speaking, substituting (11) into (8) we obtain the social indirect utility function to be used in Keynesian unemployment situations. Taking the total derivative of this function with respect to the policy parameter and dividing through by the marginal utility of income, we obtain the cost-benefit rule to be used in the presence of Keynesian unemployment:

172

2;

=

x;

(by, p;,w,

Figure 2a. Illustration of the definition of a virtual price (py).

Figure 2b. Illustration of the firm's investment function. Note that (13) reduces to (10) if nontradeables firms are not rationed since then py = py in (13). However, given that the total private and public sector production of nontradeables is now demand determined, an increase in public sector employment in the firm producing non-traded goods causes a redistribution of production between the privately owned and the stateowned firms (assuming that the public sector firm gets priority in the market for nontraded goods). In order to further interpret (13), let us consider increased government production of non-traded goods. There are a t least two differences between the project evaluation rule (13) for i = n and the rule for project evaluation under Keynesian unemployment found in earlier

173

works, e.g. Cuddington et a1 (1984) and Johansson (1982). In earlier workss, based on single-period models with exogenous investment, there is a one-to-one relationship between the decrease in the level of production of privately owned firms and the level of increase of

+

production of non-traded goods by the government, i.e., dyn dFy = 0 (assuming that the gl household utility function is weakly separable in first period labor supply, an assumption which therefore is implicitly employed also here). Therefore, any change in welfare must follow from differences, if any, in the marginal productivities of labor between privately owned and state-owned firms. Welfare will increase only if state-owned firms are more efficient than private sector firms so that total employment decreases (provided that Ue < 0 as is usually assumed). This conclusion can be arrived a t by setting dxy = - d y i l and dIy = 0 in (14) below, but see e.g. Cuddington et a1 (1984) for a detailed derivation of this result. However, in the model used in this paper, private sector firms are allowed to adjust their levels of investment following a decrease in sales. In fact, in the appendix a t the end of the -n paper it is shown that demand-constrained firms increase investment if sales, i.e. x 1' decreases. The reason is, loosely speaking, that the opportunity cost of investment increases when the demand constraint is relaxed. This result, which is illustrated in Figure 2b, questions the popular belief that measures aimed at reducing unemployment in the short run tend to crowd-out private investment. In turn, this change in private investment affects employment and hence the household's income in such a way that final demand for non-traded goods increases. However, private sector firms sales are still reduced, but there is not complete crowding-out as in earlier models, i.e. 0 > &"l / d y i l > - 1 in our model. (In arriving at this result we have suppressed any induced changes in p2 and w2.) Therefore, our project evaluation rule, stated in (13), is somewhat less discouraging than the one found in e.g. Cuddington et al (1984) and Johansson (1982). Nevertheless, even in our model, a decrease in total employment is a sufficient condition for welfare to increase following an increase in government production of non-traded goods when the economy suffers from Keynesian unemployment. To prove this claim, equation (13) is written in the following way:

where we have used the fact that $dxy

= $[aFn($)/aq]d$

-

$dI;

=

wid$ - pydIy;

recall that py is such that a profit maximizing firm would supply exactly Zy if unconstrained

We refrain from a comparison with Marchand et a1 (1985) since, in their intertemporal model with endogenous investment, all production activities take place in period 1. Therefore, we believe the models are too different for a meaningful comparison of the results (given a perceived constraint on the acceptable number of pages of this paper). 5

174

in this market, implying that the marginal revenue product of labor is equal to the wage, i.e. p;6'Fn($)/dC = wl. Therefore, all "wage terms" net out. The signs below the different terms indicate whether it has a positive or a negative sign; see the discussion above. Obviously, a reduction in aggregate employment ensures that welfare increases following an increase in government production of nontradeables. A second difference between the cost-benefit rule (13) or (14) and the rule found in earlier works stems from the treatment of expectations. Most previous authors use single-period models where expectations of future prices and quantity constraints are treated as exogenous. In sharp contrast, in our model agents have rational expectations implying that they correctly foresee any changes in second period prices. Therefore, the virtual price of labor as well as private sector demands for labor and investment goods depend on future, i.e. period 2, prices. For example, period 1 demand for labor by private sector firms producing non-traded goods in (14) is = q(Zy, wl, p i , wz). Since future (market-clearing) price levels may be affected by the considered first period change in government production, the partial derivatives in (14) should be interpreted as including any induced changes in future prices. In sum, one possible formulation of the project evaluation rule for production of nontradeables under Keynesian unemployment would be: (a) evaluate the net change - private plus public - in the supply of nontradeables at the ruling market price; (b) evaluate any change in investment at the virtual price of nontradeabless; and (c) evaluate the net change in total labor demand at the virtual price of labor. It is of course also possible to use the model to examine the case when a state-owned firm supplies traded goods. Under Keynesian unemployment (and a fixed exchange rate in period l ) , increased government production of traded goods in period 1 will generate real income-induced multiplier effects in the nontraded goods sector. Due to the small open economy assumption, private sector firms' supply of traded goods is left unchanged by the considered change in government production, since the relevant relative prices are left unchanged and there is no demand constraint facing firms in this sector. Therefore, national income, i.e. profits plus wage income, increases unambiguously. Part of the new incomes are spent on non-traded goods. Since supply of such goods by assumption is demand-constrained, the usual multiplier process, well-known from textbooks on Keynesian macroeconomics, is initiated. However, also in this case our model produces slightly different results from those found in previous works. The reason being that private investment is endogenous in our model. Therefore, the cost-benefit rule reads:

6 Note that today's virtual price of the good in question contains information about conditions tomorrow.

175

If private investment is unaffected by the change in question, i.e. aIy/&Y = 0, then (15) reduces to the "textbook" Keynesian multiplier expression with py&:/a$, representing income-induced changes - multiplier effects - in the demand+!onstrained nontradeables sector; see Cuddington et a1 (1984) for a detailed derivation of the multiplier expression. However, in our model, the magnitude of the income-induced effects is reduced by the decrease in private investment; recall that aIy/&y < 0. Therefore, to the domestic market value of the direct change in tradeables output one has to add income-induced effects in the demand
176

unlimited quantities at the prevailing (world market) price. The reader interested in further details is referred to e.g. Dasgupta and Heal (1979). There are, however, important situations where one can reasonably expect quantity constraints in the markets for natural resources. Even if the economy is small in the sense that changes in domestic supply/demand have an imperceptible influence on world prices, domestic producers or consumers may face rationing if the world prices are slow to adjust to eliminate world excess supply or demand. A good example of such a situation would be a small oil-exporting nation facing a world price and sales constraint imposed by the OPEC oil cartel. Quantity constraints can also arise in situations where the country in question is small in the world market, if it imposes import quotas coupled with domestic price controls. This may result in domestic rationing, yet the country may be small in the sense that it would, in the absence of such distortionary policies, perceive perfectly elastic world supply or demand curves for these products at prevailing world prices. Even in the absence of import quotas agents may face rationing. The domestic wage may be fixed at a level which, given other prices, results in excess supply or excess demand for labor. This suggests a priori that the rules for the optimal management of natural resources in situations with rationing in the labor market are very different from the rules to be used under full employment conditions. As a point of departure for our discussion, it is assumed that the economy suffers from classical unemployment in the short-run7. Then, assuming that there are private profit maximizing extractors of a non-renewable resource as well as a state-owned firm extracting the resource, we obtain the following cost-benefit rule when the state-owned firm increases its level of extraction in period 1 (possibly in order to reduce short-run unemployment):

where the N superscript refers to (traded) non-renewable resources. The three first terms in (16) can be interpreted by referring to Hotelling's rule discussed above. In order to maximize profits, the state-owned firm should select a path of extraction such that the marginal profit is equal in both periods. (In the absence of extraction costs, the marginal profit in a period is equal to the present value price p: implying that the first term in (16) produces Hotelling's aforementioned simple extraction rule.) The reader should recall that increascd extraction in one period has to be followed by decreased extraction in the second period. Therefore, it is profitable to reallocate extraction and employment between periods as long as the marginal

7 In the general equilibrium case one derives a cost-benefit rule which exactly corresponds to t,he present value criterion. The stateawned firm's change in production is profitable provided that the present value of the change in profits is positive.

177

profit is not equal across all periods (provided such an interior solution is possible and optimal; see Johansson and Lofgren (1985) for details). If there is full employment in both the short-run and the long-run, the extraction rule stated above is also socially optimal. However, if there is unemployment in the short-run, the final term in (16) must be accounted for. In Johansson (1984) it is shown that increased extraction by the state-owned firm in period 1 causes w2 to fall. In turn, this is shown to induce private sector profit maximizing extractors to increase extraction in period 2, i.e. to reduce extraction and employment in period 1. Hence, aggregate employment in period 1, i.e.

& , / d ~ , in (16), may rise or fall. These effects suggest a priori that a reallocation of extraction by the state-owned firm from full-employment periods to unemployment periods may cause a rise or a fall in monetary welfare. Recall that the sum of the three first terms as well as the final term in (16) may be positive or negative. As this analysis has demonstrated, it is far from self-evident that the presence of unemployment changes extraction rules for an exhaustible resource in a way predictable from the traditional partial equilibrium rule. According to the partial equilibrium rule discussed in Section 4.1, production of a good should be increased as long as the marginal revenue product of labor exceeds the virtual price of unemployed laborers. In light of the discussion following equation (16), such a rule of thumb may be quite misleading when applied to natural resources. This conclusion generalizes both to the case of other disequilibrium situations than the one considered in this section and to the harvest of a renewable resource. Due to considerations of space, we resist any temptations to prove these claims, but the interested reader is referred to Johansson and Lofgren (1985) for a full treatment. 6 DISTRIBUTIONAL ISSUESS Most derivations of cost-benefit rules focus on efficiency considerations. Sentences like the one at the very beginning of Section 3c above, where a representative household is introduced, are therefore very common in the literature. Important exceptions are Boadway (1974), Harberger (197S), Just et a1 (19S2), and Weisbrod (1968). The underlying idea is that since the cost-benefit rule essentially tells us whether national income has increased or not, it should be "intuitively clear" that if income indeed has increased - the a.ggregate budget constraint has moved outwards - t h e winners are able to compensate the losers. This is true in the following limited sense. Let xf be a vector of commodities allocated to household i, where i = 1, ...., n, and say that there are I1 commodities. Moreover, n let C xi = XI be the aggregate bundle, while the vector x' = { x i , ...., x;} tells US how it is i=l

8 Note that the model in this section is not directly comparable with the above multi-sectoral model, and that the notation therefore differs slightly.

178

allocated over households. We can now define a reallocation of

XI,

n denoted X I ' , such that C xy

i=l = XI. The winners are (potentially) able to compensate the losers in the compensation sense;

i.e., x' is better than x (the initial allocation), if there is an allocation x" with Ex7 = Ex'i and x'/ +xi for all consumers i. (All households strictly prefer x" to x.) The following well-known result for the general equilibrium case can now the provedg. Proposition 1:

(i)

(ii)

If x' is preferred to x in the compensation sense it must be true that n n c px; > c pxi, i=l i=l where p is a vector of H general equilibrium prices supporting x. n n If C pxj' = pX' > pX = C pxi, and I xf - xi I is small for all i, i= 1 i=l there is a reallocation of x' - call it x" - such that everyone strictly prefers x" to x.

Since the proof is short and can be used to illuminate how things change in a disequilibrium setting we will sketch it here. To prove (i) we use the reallocation X I ' such that Cxy = Ex;, and xy kixi for all i. Since x is a general equilibrium allocation supported by p it holds n n n n that px'/ > pxi for all i. Summing over i yields C pxi > C pxi. Since C pxi = C pxf this i= 1 i=l i=l i=l establishes the necessity claim. To "prove" the sufficiency claim, (ii), we note that if I xi -xi I is small for all i , then

where DUi is the gradient of the utility function, and Xi is the marginal utility of income. In other words, the utility change can be approximated with the first order term of the Taylor series expansion. Now define X I ' by:

XI

= xi

+ -n1 (X* - X),

(18)

i.e., each household is given 1 th of the aggregate change in moving from x to x'. We now havelo

See Varian (1984), chapter 7. Note that we are assuming that preferences can be approximated by a continuously differentiable utility function, and that we are dealing with an interior solution xi. By shrinking the distance I xf -xi 1, the absolute error can be made smaller than any 6 > 0. 9

10

179

Ui(X/) - Ui(Xi) I: Aig(X' - X) > 0

(19)

for all i, since pX' > pX by assumption. Hence, loosely speaking, pX' > pX (national income increases) is both necessary and sufficient for x' to dominate x according to the compensation criterion, provided that projects are small.The term small projects here means that they are of the same magnitude as those dealt with in the previous sections. Let us next investigate how things are changed if there is disequilibrium. A little thought reveals that a similar proposition, where national income is evaluated at disequilibrium prices is not necessarily valid. The reason is, as we have just shown, that one has to use shadow prices to value the real effects from the projects under consideration. Evaluated at the ruling prices, markets can either be in excess demand or excess supply. These two cases are illustrated in Figure 3 below. Marainal valuation

PI

MV

p':

/ I Excess demand 'D S

I

I I

D

-1

XI

X

Figure 3a. Illustration of the case where price is fixed below its market-clearing level.

I I -2

X

w X?

Figure 3b. Illustration of the case where price is fixed above its market-clearing level.

180

In the excess demand case the buyers' marginal valuation of the last unit is greater than or equal to the market price, while in the excess supply case the two entities coincide. If trade is voluntary, markets are frictionless, and all consumers are net demanders in all markets, then all consumers' marginal valuations in all markets are at least as high as the market price. In other words

where pd is the disequilibrium price vector. The inequality will hold with equality for components corresponding to goods in excess supply. Assume now that pdX' > p dX, then it is tempting to use the ideas in the above sketch of the proof of (ii) to try and show that this is sufficient for x' to dominate x in the compensation sense, given that I xi - xi I is small for all i. On face then, we would like to be able to prove that if national income (measured at disequilibrium prices) increases through the project, then it is profitable in the compensation sense. This will, however, not work, since the fact that every component of the vector DUi(-) is positive and at least as large as every component of the positive vector Xipd , and Xipd (xi -xi) > 0, does not imply that DUi(xi -xi) > 0. In less formal language the problem arises because both the cost from a decreaed supply and the benefits from an increased supply are undervalued by the disequilibrium prices. The best we have been able to do in terms of sufficient conditions is the following: Proposition 2:

d If all consumer are net demanders of all goods p dX' 2 - p X, I xi -xi I is small for all i, the supply of all goods in excess demand at x is not decreased at X I , and the supply of at least one good in excess demand is strictly increased, then x' is strictly preferred to x in the compensation sense.

To understand this claim it suffices to note that since goods in excess demand are undervalued by the price vector and increase in supply, the reallocation principle used in "the proof" of (ii) in Proposition 1, will do the job also in this case. For a more formal argument see appendix. The necessity proof of claim (i) of Proposition 1 will obviously not go through under d d disequilibrium. To see this, we note that Proposition 2 tells us that p X' = p X may be sufficient for x' to strictly dominate x in the compensation sense. A simple continuity argument indicates that it may do so even if pdX' < pd X. In other words, a project can under

disequilibrium conditions improve welfare in the compensation sense, even if it decreases

181

national income measured at disequilibrium prices. The reason is, of course, that market prices underestimate the true utility gains, and this is also why shadow prices appear in the cost-benefit rules derived above. If, however, the project decreases national income at disequilibrium prices, for welfare to improve in the compensation sense, it is necessary that the project increases the supply of at least one commodity initially in excess demand (one undervalued good). Finally, it is worth reminding the reader that the compensation criterion has its flaws, e.g., that it gives no guidance in making comparisons between Pareto efficient allocations on the same utility frontier, and that it can result in paradoxical comparisons between points on different utility frontiers. Also, if winners do in fact compensate the losers, welfare will unambiguously increase in the Pareto sense. On the other hand it is not at all clear why one should regard x' better than x merely because it is potentially possible to make everyone better off by moving to a new allocation XI'. 7 CONCLUDING COMMENTS One of the main messages that follows from the recent developments of disequilibrium cost-benefit analysis is that the partial equilibrium view of disequilibrium, which has frequently been practiced in project analysis, and which e.g., under unemployment conditions assumes that labor resources are drawn from the pool of unemployed, can be very misleading. There are crowding out effects that mean that even if one assumes the individual supply price of unemployed resources to be zero, the total real opportunity cost of public sector employment may exceed the wage rate. For example, if total employment decreases, this may imply that profitability calculated at producer prices (the general equilibrium rule) is not sufficient to ensure that a project is socially profitable, while the incorrect partial equilibrium rule does not even require profitability measured at producer prices. This paper in particular shows that the intertemporal aspects may also be important. Under rational expectations a public project planned for a future full employment situation may inflict extra social costs today, through a lower future price which induces a lower private investment activity today, causing a decrease in today's employment. Intertemporal considerations are also shown to modify some of the more "counterintuitive" conclusions arrived at by earlier investigators of "atemporal" models. For example, a decreased total employment is no longer necessary for a public project in nontradeables to improve welfare under Keynesian unemployment. The reasons are that crowding out effects are smaller in an intertemporal setting, and that, interestingly enough, existing crowding out effects stimulate investment. The public projects that are discussed in this paper are financed by nondistortionary l u m p sum taxes. This has, of course, affected the exact shape of the cost-benefit rules. Under a more general tax system the rules would contain terms measuring the deadweight losses from taxation. There is, however, an interesting exception worth pointing out. A variable tax on the wage rate works like a lump-sum tax when the household is rationed in the labor market. What normally distinguishes a lump-sum tax from a tax on a good or a factor is that it has an

182

income effect but no substitution effect. However, if the household is rationed in the labor market, a change in the after-tax wage, like a lump-sum tax, will have only an income effect on the demand for unrationed goods. Needless to say, the disequilibrium paradigm can be used to study the direction of tax reform, optimal taxation, and to develop optimal shadow pricing rulesll, given restrictions on the shape of the tax system. For example, optimal shadow prices are obtained by maximizing the social indirect utility function with respect to the project parameters. To see this, if prices are market clearing, the gradient of this function with respect to prices vanishes like equation (6) tells us. These developments, however, must be relegated to another paper. Note, however, that the fact that tomorrow's policy parameters affect today's decisions imply that optimal policy rules may be time inconsistent. For example, if we evaluate the relief works mentioned in Section 4.1 in the full employment period we will be inclined to use the time consistent, but inoptimal general equilibrium evaluation rule, and, hence, wrongly neglect any extra costs in the preceeding unemployment period. See Kydland and Prescott (1977) for details. The distributional aspects of cost-benefit analysis are often dominated by more straightforward efficiency considerations. In this paper an attempt is macie to derive conditions for one state to dominate another in terms of the Kaldorian welfare criterion. It turns out that the resulting conditions are slightly more complex than under equilibrium, but that they can be expressed in ruling nonmarket clearing prices, and that they lend themselves to simple intuitive explanations. The main message is that the likelihood of welfare improvements is enhanced if the projects generate net supplies of goods in excess demand undervalued goods. In particular, profitable compensation may be possible, even if the project in question decreases national income measured at ruling disequilibrium prices, provided that it increases net supplies of goods in excess demand sufficiently. To sum up: Given the non-negligible first order induced effects of even small projects under disequilibrium conditions, it is of first order importance to find out their magnitude in relation to more obvious direct effects. Today's macroeconometric model building paired with the speed of todays computer's indicate that simulation techniques &n be used to accomplish this task. A recent attempt by Fourgeaud et a1 (1986), where shadow prices are estimated numerically for the French economy illustrates the feasibility of the approach. APPENDIX: PROOFS OF CLAIMS IN THE MAIN TEXT 1 Proof that aI/&, < 0

In order to derive the sign of aI,/&$

for a firm facing a sales constraint in period 1, the

11 See e.g. Guesnerie (1978), and Hammond (1986) for analysis of tax reform in a general equilibrium context. An interesting dual approach to the second best problem is pursued in Guesnerie and Roberts (1984), who investigate how quantity rationing can be used as an instrument to achieve optimality. Optimal policy rules and regime switching is analyzed in Cuddington et a1 (1985) and Marchand et a1 (1985).

183

profit maximization problem of the firm is written as:

-xl,

and a where we have used the fact that X1 = y1 - I1 and y1 = F($), i.e. I1 = F(C1) superscript i referring to the kind of commodity produced by the considered firm is suppressed in order to simplify the exposition. Throughout both the first-period and the second-period production functions are assumed to be strongly concave. The necessary (and sufficient) conditions for profit maximization are:

where subscripts e and .I refer to partial derivatives with respect to e and I, respectively, and Fe, He HI, @I> 0 by assumption. Tedious but straightforward calculations, using (A.2), show that:

2 2 + HIE'$Iee) > 0, and subscripts 8,etc, refer to crosswhere A = p ~ ( H I I I I $ ~- €IeIFe 2

derivatives. A is positive since, for a strictly concave production function, HIIHee - HpI > 0 and Fii, Hii < 0 for i = ,! I. Next, let us consider the following partial derivatives of the profit function (11):

BrI/apl =

x1 = y 1-11

Combining (A.3) and (A.4), one finds that, 8I/Zl < 0

2 Proof of ProDosition 2 To prove Proposition 2 in Section 7, we first note that if one person can be made strictly better off than in x by redistribution of a vector X I , and no one worseoff, we can in a norisatiated solution make everybody better off by redistributing some of the gain to the nongainers. In other words, if we can prove that there is a redistribution of x' - call it x" - such

184

that at least one household is strictly better off and no household worse off, we are through. The change in utility in moving from xi to xy can if I xy - xi I is small enough be approximated to any degree by the first order terms in the Taylor series expression of the utility function, i.e., U(xy) - U(xi) x DU(xi) (xi -xi) If we partition the vector of goods into goods in excess demand (xy - xi)e and goods in excess supply (xy - xi)s, with prices pe and ps, respectively, we can rewrite the above expression in the following manner:

U ( X ~-) U(xi) x DU(xi) (x; -xi) = DeU(xi) (x; -

+ Xips(xy - xi)s

(A.5)

where DeUi(xi) is a vector of marginal utilities corresponding to the goods in excess demand. If XI/ is defined as x!' = xi

+ n1 [(XL, Xi) - (Xe, X,)] = xi + n1 (X'

-

X)

1

(A4

we have

Since Xk - Xe

2 0 by assumption, and DeU(xi) 2 Xipe it follows that

DeU (xi) (Xk - Xe)

+

Xi PS

Xi P

d

(Xi - XS) 2 7 (X' - X) 2 -0

for all i, with strict inequality for at least one i in the first inequality, since the supply of at least one good in excess demand increases, and a t least one household must be rationed in an

excess demand market 7( au > Xi ph).

ax

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k.

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Maass, A., 1966. BenefitCost Analysis: Its Relevance t o Public Investment Decisions. Quarterly Journal of Economics 80. Maneschi, A., 1985. The Shadow Pricing of Factors in a Multicommodity Specific-Factors Model. Canadian Journal of Economics 18: 843-853. Marchand, M., Mintz, J. and Pestieau, P., 1984. Shadow Pricing of.Labor and Capital in an Economy with Unemployed Labor. European Economic Review 97: 239-252. Marchand, M., Mintz, J . and Pestieau, P., 1985. Public Production and Shadow Pricing in a Model of Disequilibrium in Labor and Capital Markets. Journal of Economic Theory 36: 237-251. Marglin, S., 1967. Public Investment Criteria: Benefit-Cost Analysis for Planned Economic Growth. Cambridge, MD: MIT Press. McKean, R.N., 1958. Efficiency in Government through Systems Analysis. New York: John Wiley & Sons. Meadc, J.E., 1955. Trade and Welfare. Oxford: Oxford University Press. Musgrave, R., 1969. Cost-Benefit Analysis and the Theory of Public Finance. Journal of Economic Literature 7: 797-806. Musgrave, R.A. and Muserave. P.B.. 1973. Public Finance in Theorv and Practice. London: McGraw-Hill. Neary, J.P. and Roberts, K.W.S., 1980. The Theory of Household Behaviour under Rationine. EuroDean Economic Review 13: 2 5 4 2 . Neary, J.P."and Stiglitz, J.E., 1983. Toward a Reconstruction of Keynesian Economics: Expectations and Constrained Equilibria. Quarterly Journal of Economics 98: (supplement), 199-228. Ohlsson, H., 1987. Cost-Benefit Rules in a Regionalized Disequilibrium Model. Scandina vian Journal of Economics 89: (forthcoming). Roberts. K.W.S.. 1982. Desirable Fiscal Policies under Kevnesian UnemDlovment. Oxford Economic Papers 34, 1-22. Rothbarth, E., 1940-1. The Measurement of Changes in Real Income under Conditions of Rationine. Review of Economic Studies 8: 100-107. Somers, G . 6 . and Wood, W.D., 1969. Cost-Benefit Analysis of Manpower Policies. Proceedings of a North American Conference, May 14-15, 1969. Kingston, Ontario: Industrial Relations Centre, Queenls University. Srinivasan, T.N. and Bhagwati, J.N., 1978. Shadow Prices for Project Selection in the Presence of Distortions: Effective Rates of Protection and Domestic Resource Costs. Journal of Political Economy 86: 96-116. Starrett, D., 1979. Second Best Welfare Economics in the Mixed Economy. Journal of Public Economics 12: 329-349. Stiglitz, J.E., 1986. Theories of Wage Rigidity. In: J. Butkiewicz, I(. Koford, and J. Miller, (Editors), Keynes' Economic Legacy. New York: Praeger. Tinbergen, J., 1952. On the Theory of Economic policy. Amsterdam: North-Holland. Tsuneki, A., 1985. On the Choice of Large Projects. Canadian Journal of Economics 18: 660-664. Varian, H.R., 1984. Microeconomic Analysis. New York: Norton. Weishrod, B., 1968. Income Redistribution Effects and Benefit-Cost Analysis. In: S.B. Chase (Editor), Problems in Public Expenditure Analysis. Washington, D.C.: Brookings Institution. "

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Chapter 10 MACROECONOMIC COST-BENEFIT ANALYSIS O F ENVIRONMENTAL PROGRAMMES

ANDRIES NENTJES Department of Economics and Public Finance, Rijksuniversiteit Groningen, P.O. Box 72, 9700 AB Groningen (The Netherlands)

1 INTRODUCTION

In the evaluation of environmental projects and programmes two traditions can be discerned. The first is the applied welfare economics of social cost-benefit analysis. The second, stemming from quite a different origin, is macroeconomic evaluation. Both approaches have their strengths and their weaknesses. In this article I shall critically survey both methods and propose a synthesis. Public investments are seldom directly profitable for the authority undertaking it. Generally financial proceeds are far below the expenditures and the investment projects do not meet the criterion that is usually applied in private economic calculations. A major reason for the growth of social cost-benefit analysis is the need for a method and a criterion that can be used to assess whether a public investment can be justified from a broader economic point of view, looking at the costs and benefits for society as a whole. In a social cost-benefit analysis welfare losses and gains to all members of society are included in the costs and benefits, no matter whether the cash flow of the public investor

is affected or not. The investment proposal is accepted if it meets the criterion that the present value of all future benefits, no matter whom they accrue to, should exceed the present value of all costs of the investment. The criterion implies that a social costbenefit analysis, narrowly defined, only covers those welfare changes that can be brought under the measuring rod of money [Pigou, 19211. Since the nineteen-thirties social-cost benefit analysis has been used in public decision-making. Originally the method of social cost-benefit analysis was applied for the assessment of public investments in economic infrastructure; e.g. flood-control dams, roads, land reclamation, airports. Since the early nineteen-seventies the analysis of monetary environmental damage and the cost-benefit analysis of projects aiming at environmental improvement and nature conservation have emerged. A body of knowledge has evolved and environmental cost-benefit analysis is growing into a flourishing branch of environ-

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mental economics. A review of the "state of the art" has been given by Freeman [1979] and by Dixon and Hufschmidt [1986]. Earlier surveys include Maler and Wijzga [1976], Pearce [1978] and Abebon [1979]. The strength of environmental cost-benefit analysis is its methodology for analyzing the details of a specific environmental improvement and the paradigm it offers for constructing shadow prices, in terms of money values, for goods and services which have no market price because no explicit markets exist for them. A major weakness is the

neglect of the macroeconomic context and its impact on the costs and benefits of environmental projects. Macroeconomic evaluation of environmental programmes goes back to the Keynesian revolution in macroeconomic policymaking. Empirical macroeconomic models were constructed to provide a scientific base for macroeconomic forecasts and for predicting the consequences (in terms of income, employment, balance of payments, government budget) of changes in fiscal policy, e.g. the impact of a rise in government expenditure, aiming at macroeconomic stabilization. From the early sixties on the simple Keynesian expenditure models have been succeeded by a class of models which include supply and cost equations. This progress in model building has made it possible to simulate specific investment programmes and to assess long-run structural impact on macroeconomic variables, next to the short-run expenditure impacts. Examples of macroeconomic evaluations are studies that are concerned with seaport industries [Vanden Beld and Middelhoek 19711, nuclear energy and energy saving. Since the early nineteen-seventies the macroeconomic evaluation of environmental programmes has been added to this list. Macroeconomic evaluations take the macroeconomic conditions into account by definition. The impacts of an environmental programme (and any other programme or project) are identified by calculating the divergences of the macroeconomic variables from a reference path of macroeconomic development that is expected to occur if the investment project is not carried out. The reference path will take account of the relevant economic regime, e.g. underemployment. A methodological weakness of the macroeconomic evaluations is that up to now the specific effects, especially the benefits of environmental investment, have been dealt with either rather cavalierly or not at all. It can be concluded from the above that both methods - social cost-benefit analysis

and macroeconomic analysis

- have their strengths and weaknesses. In section 2 they will

be discussed at length. One might ask whether a unified approach can be developed which

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combines the strengths of both methods, and excludes their weaknesses. In section 3 an attempt will be made to achieve this. The elements of a "macroeconomic cost-benefit analysis'' will be discussed. In section 4 the components will be put together. Section 5 recapitulates what such a macroeconomic cost-benefit analysis adds to the existing methodology for evaluating the environment. 2 TWO TRADITIONS IN ECONOMIC EVALUATION 2.1 Social cost-benefit analvsis

A key problem in social cost-benefit analysis is how to value the positive and negative impacts of a public investment. The conventional solution of the problem is to take the Walrasian model of general equilibrium as a point of reference. In Walras's conceptual model of a market economy all markets are in equilibrium and consumers and producers have adjusted to market prices in such a way that the welfare of each participant is maximized.1 Under these conditions the prices that prevail indicate exactly what value the economic agents attach to (marginal) increments in resources and in producible goods. Consequently market prices coincide with their social value. When a number of markets is in disequilibrium the set of existing market prices does not reflect their true social value. The cost-benefit analyst should then look for an adequate set of shadow prices.

For practical cost-benefit analysis the important question is whether in the real world, where the public investment has to be carried through, the economic situation during the lifetime of the project will correspond to Walras's blueprint of a market economy to such an extent that actual prices can be accepted as adequate indicators of marginal social value. Actually some major markets frequently are not in equilibrium. Labour markets and foreign exchange markets are the most glaring examples. The price on capital markets is heavily affected by tax distortions, causing a divergence between the demand price and supply price of capital, even if demand equals the supply of capital. But if one looks at practical cost-benefit analysis as it is actually applied in practice in the developed countries one sees that in most cases market prices are used rather uncritically in the calculations of costs and benefits. The question how the existing economic situation

Of course one should bear in mind the well-known provisos that there is perfect competition, that external economies or diseconomies and collectieve goods are absent and all property rights are fully specified.

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relates to Walras’s general economic equilibrium is not taken into consideration. It is implicitly assumed that there is a close enough correspondence between the real world and the model. This is a fortiori true of practical environmental cost-benefit analysis. The specialists working in this area are concentrating their efforts on’ valukg the environmenhl spillovers. In cases in which a market good is a close substitute for the unmarketed and unpriced environmental good the market price is generally taken as a proxy for the marginal social value of the environmental good. In consequence of the futation on the environmental aspect the environmental economist is inclined to ignore the problem that in reality the economic regime diverges from the Walrasian general equilibrium and that market prices do not reflect social values. The studies reviewed in Freeman 1979 illustrate this point. By using market prices he is implicitly assuming that a competitive general equilibrium actually prevails and will continue to exist during the lifetime of the project. In the theory of cost-benefit analysis, which should be distinguished from the practical applications discussed above, the restrictions on the use of market prices were recognized at rather an early date. Large and persistent unemployment, taxation which affects marginal valuations, price controls and imperfect competition, public goods and externalities disturb the Walrasian-Paretian conditions of general equilibrium and maximum welfare. These discrepancies between blueprint and reality are most glaringly visible in the developing countries: massive unemployment, price controls of foreign currency, to mention two outstanding examples. The theoretical literature on cost-benefit analysis of development projects has taken the lead in adapting cost-benefit analysis rules to such nonoptimum and non-equilibrium regimes [La1 1974, La1 1980, Kuyvenhoven and Mennes 1985, Unido 1972, Little and Mirlees, 19741. Progress has been slower in the literature on project analysis for the developed world. In the first stage ad hoc partial solutions were proposed to handle such problems as unemployment [Haveman and Krutilla, 19681 or distortions in capital markets [Hufschmidt

C.S.

1961, Marglin 19631. This is also the approach in modern

textbooks on cost-benefit analysis [Sugden and Williams 1978, Dasgupta and Pearce 1978, Lesourne 1975, Mishan 19821. A major weakness of the partial equilibrium approach is that it does not take into account the relations between markets which could affect shadow prices in a systematic way. A recent development is the derivation of disequilibrium cost-benefit rules in the

context of a general Walrasian framework. Johansson [1982] has developed rules for assessing the costs and benefits of investment projects under different regimes: Keynesian

191

unemployment, classical unemployment and repressed inflation. In a mathematically rigourous way he shows which corrections have to be made in market prices under different regimes of disequilibrium. In this volume [Johansson and Lofgren 19881 the general disequilibrium approach of social cost-benefit analysis is further explored.2 It surely is an important step ahead in the theory of cost-benefit analysis and it is interesting to observe that in their contribution to this volume the general disequilibrium approach is, to my knowledge, for the first time applied to an environmental project, in this case a natural resource project. In environmental cost-benefit analyses in general, however, the state of the art is such that there exists a developed body of methodological knowledge capable of being applied to evaluate the environmental dimensions of actual projects. At the same time there is a lack of applicable methods which enable us to take account of the actually existing economic regime in all those cases in which the state of the world diverges from general equilibrium. 2.2 Macroeconomic evaluation

Macroeconomic evaluation has developed from Keynesian macroeconomics and macroeconometric model building: areas of economic investigation that are far removed from welfare economics and its application in cost-benefit analysis. Macro-econometric models have been used for purposes of economic forecasting, but also and increasingly for policy simulations. The simple short-run expenditure models of the first and second generation developed into full-blown medium-term structural models, incorporating the supply side. The new generation of models offered the opportunity to progress from simulating the expenditure impacts of short-term stabilization policies to the simulation of structural policy measures, which have major impacts on the supply side by changing factor productivities, costs and other variables. During the past two decades the macroeconomic evaluation of structural policies has been extended to cover environmental programmes. National studies have been made for several countries. OECD [1978] surveys Japan, Italy, the Netherlands and the United States. The OECD 1985 publication discusses recent results for the US and the Netherlands ttnd adds Austria, Finland, France and Norway. Christainsen and Haveman's survey [I9811 See also their references to the literature on disequilibrium cost-benefit rules following Johansson's pioneering article.

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of studies concerning the impact of environmental regulation on economic growth contains a number of macrocconometric studies for the US-economy. Recently a macroeconometric analysis of an international environmental programme has been made: Klaassen et al. [1987] discuss the macroeconomic impact of a program of acid rain abatement, carried out

simultaneously by all EC-member countries. In most of these studies use has been made of existing macroeconometric models that have been adapted to capture the impacts of environmental programmes on variables such as national output and income, employment, consumption, balance of payments and balance of the government budget. These studies take a historical or 'projected' future time path of macroeconomic variables as a starting point. Then the environmental investments are inserted into the macroeconometric model and other adaptations are made to take account of the costs and other specific characteristics of the programme. Next a second model run is made. The macroeconomic impact of the environmental programme is presented by the differences between the time paths of the macroeconomic variables with and without the environmental programme.

In these macroeconomic policy simulations the actual economic regime is taken into account. When the reference time path is characterized by unemployment and excess capacity the macroeconomic impact of environmental expenditure will differ from the macroeconomic consequences that would have resulted under a regime of full employment.

In macroeconomic evaluation the state of the art is just the opposite of that in costbenefit analysis. A general economic point of view is chosen, contrary to the partial view in practical cost-benefit analysis. The relations between markets for output, labour and money are modelled. The information about the relevant economic regime is contained in the quantitative data about excess capacity and unemployment. On the other hand the macroeconomic modelling of the specific characteristics of environmental programmes and projects is hardly developed. This is especially true of the evaluation of the environmental benefits. Actually the macroeconomic benefits of reducing environmental damage have not been incorporated in the programme simulations. Only the macroeconomic consequences of the pollution control investment expenditure and of the ensuing costs of pollution control are analysed. We shall elaborate this point further in section 3.5. An additional shortcoming of macroeconomic evaluation, from the point of view of cost-benefit analysis, is that the economic impacts of the environmental investments are expressed in terms of the macroeconomic variables instead of a common measure of welfare (see section 4). The

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explanation for these deficiencies is the lack of a sound welfare economic underpinning of 'the macroeconomic evaluation technique, which again points to its Keynesian origin. ,3 ELEMENTS OF A MACROECONOMIC COST-BENEFIT ANALYSIS

Table 1 contains the gist of a comparison of the two methods of economic evaluation. The table shows that it can be interesting to investigate whether the two methods can be combined in such a way that use can be made of the strong elements of both approaches.

TABLE 1 Strenghts and weaknesses of social cost-benefit analysis and macroeconomic evaluation. cost-benefit analysis ~~~

~

~~

macroeconomic evaluation

~

modelling of the economic regime welfare economic foundation modelling of environmental characteristics

no Yes

Yes no

no

In this section an attempt will be made to accomplish such a synthesis of cost-benefit analysis and macroeconomic evaluation. I shall do this by taking macroeconomic evaluation as a starting point and by investigating: a. in what way macroeconomic evaluation can be given a welfare economic foundation (section 3.1 to 3.4); b. in what way environmental specific characteristics can be introduced in a macroeconomic evaluation based on welfare economics (section 3.5). 3.1 Measure of costs and benefits A first question concerns the definition of costs and benefits in the context of a

macroeconomic model. AU costs and benefits have to be classified in terms of the wellknown macroeconomic output aggregates: consumption, investment, government expenditure,

exports and imports. In most empirical macroeconomic models further subcategorization may be required. The costs of the (environmental) project should be conceived of as opportunity costs, that is the output foregone by allocating factors of production to the public investment project and not using them in an alternative direction. The benefits consist of the

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increase of output, e.g. additional production in agriculture resulting from an air pollution abatement programme. A second category of benefits is made up by the welfare gains, e.g. the value attached to better visibility when air pollution is reduced. As welfare can best be measured in terms of consumption it is the appropriate unit to

express all output variables. But which conversion factors should be used in converting a unit of investment into a unit of consumption? In the macroeconomic calculations of the national income the components consumption, investment and so on are added up by using their market prices. But this procedure must not be followed to calculate economic welfare if market prices do not reflect the true social value. In such cases a guilder of investment is not equivalent to a guilder of consumption in terms of the satisfaction it gives. One important reason why the shadow price of investment - that is the multiplication factor that is used to convert the value of one dollar allocated to investment into consumer goods - diverges from 1 is formed by the taxes levied on business and personal income. Because the investor receives only a part of the return on capital his rate of time preference is considerably below the rate of return on capital. In other words the value of one dollar of investment - that is the present value of the consumer goods to be produced by this dollar of investment during its lifetime - exceeds the value of one dollar of present consumption. The shadow price of investment (relative to consumption) is greater than l.3In order to be converted into consumption the value of investment has to be multiplied by the appropriate shadow price. Identifying the conversion factor for exports and imports boils down to finding a shadow price of foreign currency which truly reflects its scarcity. It is particularly relevant when the official exchange rate deviates from the rate which would have prevailed in a free competitive market for currency. By multiplying the (changes in) macroeconomic variables with their appropriate shadow prices and adding up these consumption equivalents the costs and benefits for subsequent years over the lifetime of the project can be calculated. 3.2

Modelling the frnance decision Musgrave 119691 and Feldstein [1974] have propounded the idea that the level of

opportunity costs is affected by the financing of the project. The source of finance may Zuidema (1982) calculated a shadow price of capital for the Netherlands of 4.

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be a tax increase, capital market loan, additional bank credit or a combination of these. Another possibility is that the government "finances" a project by reducing its expenditure on other items of public expenditure. In the view of the authors mentioned the financial instrument is of importance because capital market loans, for example, will reduce investment to a greater extent than a rise in income taxes. Given the different shadow prices of consumption and investment the financial instrument that is chosen will affect the level of opportunity costs. Even in a state of full employment equilibrium, iike Musgrave and Feldstein implicitly assume, such differences will be manifest. In our macroeconomic evaluation of costs and benefits it is a fortiori true that the choice of the financial instrument affects the macroeconomic variables; its ultimate impact being determined by the economic regime that is implied by the structure of the model and the numerical values of the parameters.

3.3 Modelling environmental expenditure The environmental project or programme is introduced into the model by raising the relevant expenditure variable. In a programme to abate industrial air pollution the compliance investments of industry are modelled by increasing business faed investment; if three-way catalysts are to be installed in motor-cars part of the expenditure will constitute a rise in consumption. An increase in bank credit or a rise in taxes, necessary to procure the finance for the programme, can be incorporated in most models by increasing the money supply or the tax rate. In most cases the private sector has to make the environmental investments on its own account. This asks for equations which model the impacts of pollution abatement

costs during the lifetime of the equipment. A direct impact of rising costs will be a fall in profits. This, possibly together with a rise in the rate of interest, discourages investment. The costs of pollution abatement push up prices; among them are export prices. The deterioration of international competitiveness will reduce exports. The ultimate impact of the environmental project expenditure consists of a combination of expenditure impacts during the period the environmental investments are made, and cost impacts which only carry their full weight after the completion of the investment programme. Consequently, almost all macroeconomic evaluations of environmental programmes show a rise in national output and employment during the years of investment and subsequently a decline, caused by the costs of pollution control. It should be reminded, however, that the macroeconomic results depend on the general economic state of the world.

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A weakness of macroeconomic models is the aggregative nature of the output variables

and of the technical and import coefficients attached to them. By disaggregating and adding variables the model can be adapted further. Such refinements are particularly in place when the environmental investments and costs have specific technical or import coefficients which diverge substantially from the macroeconomic average coefficients.

3.4 Economic re&e and otmortunitv costs

We pointed out that the macroeconomic impacts of an environmental programme or project, and consequently its costs and benefits, greatly depend on the economic state of the world and the financial instrument. This dependence can best be illustrated with a simple model. The appendix contains such a didactic model in which different "pure" economic regimes can be represented. A host of assumptions are made to raise the transparency of the model and its solution. The project asks for governmental expenditure only and it is finished within one period. The impacts of the benefits are not studied; only the opportunity costs of the project are analyzed. The macroeconomic model

represents a closed'economy with markets for products, labour and money4 The demand functions for consumer goods, investment, public goods and money are specified, as well as the demand for labour. The structure of output is characterized by decreasing marginal productivity of labour and increasing marginal costs of aggregate supply. From the basic model four specific models are derived for the following economic regimes: neoclassical equilibrium, neoclassical unemployment, Keynesian unemployment and Keynesian inflation. For each of these states of the world the opportunity cost formulae are calculated, taking into account the

instrument that has been used to f i a n c e the

project. By comparing the formulae it is possible to isolate the impact of the economic regime and the impact of the financial instrument on the level of opportunity costs. In a regime of neoclassical equilibrium demand equals supply in every market. Total

output is determined by the supply of labour coming forth at the equilibrium price of labour. Any increase in output would cause excess demand in the labour market. When a public investment project is undertaken full employment equilibrium can only be maintained by reducing private sector output. In the model the reduction of consumption and investment is realized by a rise in the rate of interest. When the project is fianced by taxes consumption relative to private investment will decrease to a larger extent then The model is closed with a market for securities.

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would have been the case if the financial needs had been met by capital market loans. The shadow price of investment in terms of consumption units being greater than one, tax finance will minimize opportunity costs under a regime of neoclassical full employment equilibrium. Under neoclassical unemployment, caused by downward rigidity of the real wage rate, the level of opportunity costs equals the opportunity costs in a situation of neociassical equilibrium on all markets. Total employment and the output produced by labour are fuced by the rigid wage rate. The reservoir of unemployed labour will not be used to increase output. Consequently the public investment will crowd out private sector output in quite the same way it does under a regime of full employment equilibrium. Even under a regime of Keynesian inflationary disequilibrium, with positive excess demand in the product market, the opportunity costs can be equal to the costs in neoclassical states of the world, given specific assumptions about rationing. The constraint on output set by full employment of labour causes reactions in the economic system more or less comparable to the crowding-out effects under the neoclassical regimes. The important exception is the regime of Keynesian unemployment. Opportunity costs are at a lower level than they are under the three other regimes. When a public investment is made output can be increased by absorbing unemployed labour. Consequently the working of the crowding-out mechanism is reversed. The rise in the rate of interest can be limited and consequently the decrease of private investment can be small. The increase of output and income will even induce a rise in consumption. At low levels of employment, where the elasticity of supply is high, opportunity costs can turn out to be a boon: the sum of consumption and private investment increases instead of showing a decline. In such a situation opportunity costs are not represented by output foregone but by output won. For each economic regime a least-cost financial instrument can be found. Under Keynesian unemployment bank credit gives the lowest level of opportunity costs, because it minimiies the crowding-out effects of a rise in the rate of interest. In the other states of the world a lump-sum tax is to be preferred. Such a tax decreases consumption

relative to investment to a larger degree than bank credit or a capital market loan would; with a shadow price of capital in terms of consumption units greater than 1 this implies a lower level of opportunity costs. The didactic model shows four pure regimes. Such pure forms will seldom or never be found in the real world. In practical macroeconomic cost-benefit analysis (cba) it is necessary to derive opportunity costs and benefits from an empirical macroeconomic model

198

which gives a true and quantitative picture of the existing situation in a specific economy during a specific time period. The cba analyst has to spec@ the relevant economic regime carefully; neoclassical equilibrium is only a special case. This makes the task of the cba analyst more difficult and hazardous. Fortunately it will very often not be necessary to construct completely new models because existing models can be used. Some of these models have a more or less official status (e.g. the model of the Dutch CPB, or the OECD Interlink model) and they reflect the view of policy makers on the existing economic situation and on the most relevant economic interdependencies. By taking such a model as a starting point for macroeconomic cost-benefit analysis consistency is attained between macroeconomic planning and project evaluation; nowadays such a consistency is often lacking.

3.5 Macroeconomic impacts of environmental benefits In section 3.4 I have stressed the importance of the general economic context. Environmental cost-benefit analysis which concentrates on the ecological-economic linkages really runs the risk of losing sight of the relevance the existing economic regime has for the economic values that have to be attached to the impacts of environmental projects and programmes. Having said this we shall concentrate in this section on the environmental aspects of macroeconomic environmental cost- benefit analysis. The beneficial impacts of environmental measures affect economic welfare by the following routes: a. a rise in economic performance because of reduction of environmental damage; b. technical spin-off resulting from new or larger markets for pollution abatement equipment; c. direct impact of environmental improvement on the utility of persons. A. Effects of reduction of environmental damage to output.

The valuation of environmental damage constitutes the core of practical environmental cost-benefit analysis. Detailed empirical micro studies have been made of the impact of pollution on the productivity andlor prices of crops, forests, human labour, houses and recreational fa~ilities.~ The strategic questions are how to detect the physical impact of

Compare Freeman [1979].

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pollution and how to value the quantities of goods affected. In those cases in which the goods have a market price it is usually assumed in practical benefit analysis that the price reflects the social value of the products. In this way the benefits that are expected to arise from the environmental measure are expressed in monetary units. Such a calculation, which proceeds in accordance with the established methodology in environmental benefit analysis, implicitly assumes that the growth in output will be absorbed by an equal expansion of demand. In other words the assumption is made that Say’s law - “supply creates its own demand“

-

holds true and that the economic system

reacts as if a regime of neoclassical equilibrium exists. Apparently there is a lack of studies which assess the consequences of different economic regimes for the benefits. A way to

fa

this gap is to start from a macroeconomic model and to introduce

environmental benefits. In macroeconomic models of the most simple kind the benefits of air pollution abatement (which for example improves agricultural output) could be inserted as an exogenous increase in the output of consumer goods. In more sophisticated models the productivity coefficients can be raised or the factor-input coefficients reduced. Next a

run with the macroeconomic model has to be made to pinpoint the impact of environmental improvement on output variables and on aggregate national product. Results can be refined and made more specific by disaggregating the output variables in such a way that the environmentally relevant sectors are sorted out. A rise in productivity will reduce the costs of production. This may induce reductions

in prices; exports may increase; profits will increase too, which in turn may stimulate investments. Such positive impacts on national income will be reinforced by a rise in consumption. In this way and through other linkages within the macroeconomic model, output and expenditure variables will increase. It should be noted that the increase of the national product may be above or below the level of benefits that was calculated in the separate environmental benefit analysis. The ultimate outcome wilI be largely determined by the structure and parameters of the macroeconomic model (which again express a view on the prevailing economic regime). Very

crucial is the way and the degree in which

total expenditures are assumed to react to increases in productivity. If the economic regime is such that additional output is absorbed by a corresponding rise in effective demand, the potential environmental benefits will be fully realized. But one can also imagine an economic regime of Keynesian unemployment where lack of effective demand forms a constraint on the rise in income. The increase in productivity would only increase

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the amount of unused productive resources. In "partial" environmental cost-benefit analysis this problem is overlooked. Research on the impact of environmental benefits on macroeconomic growth has been a sadly neglected area6 This lack of research interest is in stark contrast to the many sophisticated studies in partial environmental benefit analysis. B. Effects of technical spin-off Environmental programmes will increase the market for specific pollution abatement equipment; new programmes may even create completely new markets. The familiarity with national legislation and the vicinity of potential customers will give home producers a head start on foreign competitors. A growing market will stimulate "learning by doing". The increase in knowledge and experience will enable producers to reduce costs. By strengthening their competitive position

producers will have better chances to export

environmental equipment when at a later stage the same environmental policies are adopted in other countries. It should be noted that the macroeconomic impacts of technical spin-off are affected

by the economic regime. An increase in the export of environmental technology will have a powerful multiplier impact on national income when the general economic situation is one of large excess capacity and Keynesian unemployment. Under a regime of market equilibrium the increase in exports of environmental technology will have considerable crowding-out effects on other sectors and the net gain in income may be relatively modest. Examples of growth in the home market followed by a strong export position are air pollution abatement equipment in Japan and waste water treatment technologies in the Netherlands. Although technical spin-off impacts may materialize in time, their occurrence and magnitude are very uncertain. These uncertainties do not differ, however, from other uncertain benefits in conventional cost-benefit analysis and they can be dealt with in the usual way.

The only study I know of, Nentjes and Klaassen (1985) and Nentjes (1987), is rather elementary. The analysis of macroeconomic benefits is based on the assumption that a damage reduction of x billion guilders in agriculture and forestry arising from air pollution abatement will cause the export of the sectors to increase by the same amount.

201

C. Direct utility impacts In macroeconomic models the national account definitions of output and income are used. Unmarketed goods are not included in these concepts, with the exception of public sector outputs. It would be a mistake to insert a money equivalent of human satisfactions into the macroeconomic model, for example the joy of beautiful scenery, because they will not affect output and income. Only if utility impacts are assumed to affect things like labour productivity, which in turn would induce a change of income, the model should be adapted. The best way to deal with direct utility impacts is to calculate them separately; express them in terms of the macroeconomic consumer good equivalents by using a willingness-to-pay measure and add this figure to the increase of consumer goods that has been calculated with the macroeconomic model. 4 A USER’S GUIDE TO MACROECONOMIC COST-BENEFIT ANALYSIS

In section 3 the steps which have to be made in drafting a macroeconomic costbenefit analysis of environmental programmes or projects have been discussed. The logical order of the elements of the complete procedure is as follows: 1. Select an appropriate empirical macroeconomic model and calculate a reference path.

A. Cost impact 2. Calculate the expenditures of the environmental project. The expenditures are split up

into expenditure on durable equipment and expences of operating the equipment during its lifetime. Durable equipment is split up into government investment, private investment and durable consumer goods? It can be useful to divide operating expenses into wages and other factor incomes. 3. Insert the project expenditure variables in the macroeconomic model and make other

model adaptations: e.g. in the cost and price equations and in the import equations. 4. Find out from which source(s) the environmental project has to be financed.

5. Adapt the macroeconometric model to take account of the finance choice. 6. Make a model run to determine the opportunity costs of the environmental projects in

terms of foregone consumption, investments, exports and so on in subsequent years.

More refinement can be obtained by calculating the output variables, expressed in value added, with the aid of a separate input-output model.

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B. Benefit impact

7. Calculate the benefits of the damage prevented by the environmental project. Very often a detailed economic model or ecological-economic model of the sector(s) involved will be needed to make a reliable estimate of the benefits. 8. Adapt the macroeconometric model to take account of the impact of damage preventi-

on (direct environmental benefits) on macroeconometric parameters. 9. Make an estimate of the benefits of technical spin-off. 10. Adapt the macroeconometric model to take account of technical spin-off. 11. Make a model run to determine the benefits of the environmental project in terms of

additional consumption, investments, exports and so on.

C. Valuation 12. Calculate the shadow price of private investment (and of foreign currency). 13. Multiply the macroeconometric output impacts of the project expenditure with their

shadow prices and add up. 14. Multiply the macroeconometric output impact of the benefits (prevented damages and

technical spin-off) with their shadow prices and add up. 15. Calculate the direct utility impacts in terms of consumer goods.

16. Discount the opportunity cost (sub 13) and the benefits (sub 14 and 15) in successive years, using a rate of discount equal to the social rate of time preference. 17. Calculate the benefit-cost ratio.

A comparison of the above-mentioned procedure for a complete macroeconomic environ-

mental cost-benefit analysis with standard macroeconomic evaluations of environmental projects or programmes reveals that in the usual macroeconomic evaluations only parts of the total procedure are performed. Steps 1 to 6 are carried out. Next the output variables are added up, using market prices instead of shadow prices. Benefit evaluation (7 to 11) is not undertaken at all.8 Expressing costs (and benefits) in one number and in a way which satisfies the demands of welfare economics (12 to 16) has not been tried. Actually

In Nentjes and Klaassen [1985] and Nentjes [1987] steps 7 to 11 have been performed in a tentative way.

203

macroeconomic environmental project evaluation boils down to some primitive and incomplete sort of cost-effectiveness analysis in which the options of implementing and not implementing the environmental programme are compared. In such analyses the implicit assumption is made that all shadow prices are equal to 1 and a present value of the cost impacts over subsequent years is not calculated.

5 CONCLUDING REMARKS In section 3 the intention was announced to develop a full-blown macroeconomic costbenefit analysis of environmental policies by giving a welfare economic foundation to macroeconomic evaluation and by introducing the attainments of environmental benefit analysis into it. In summary the welfare economic underpinning consists of the following elements.

- All relevant impacts of the environmental programmeme are taken into account; costs as well as all benefits. -

Costs are interpreted and modelled as opportunity costs.

-

The shadow prices of capital and foreign currency are introduced to correct market prices in cases of market failure.

- (Future) costs and benefits are expressed in one unit of measurement (consumer goods) and discounted at an appropriate discount rate.

- The general economic context in which the environmental programme is carried out (the economic regime) is explicitly taken into consideration. The macroeconomic cost-benefit analysis uses the methods developed in microeconomic environmental cost-benefit analysis to estimate the direct benefits of reducing pollution. On top of that the indirect benefits of technical spin-off are taken into consideration, as well as the specific characteristics (the technical and import coefficients) of the investment in environmental equipment, and its costs. The transformation of macroeconomic policy simulation into a macroeconomic costbenefit analysis in my view adds a useful tool of analysis to the existing methods of evaluation. Its main strength compared to microeconomic cost-benefit analysis is that it offers a practical solution to the problem of how to model the impact of the economic regime on the costs and benefits of environmental programmes.

204

APPENDIX1 Opportunity cost rules under alternative economic regimes In the following it will be shown that it is possible to construct opportunity cost formulae for other states of the world than neoclassical equilibrium. First the characteristics of the economic situation have to be specified by constructing a mathematical model of the economic regime. Next the opportunity cost equation can be derived from the model. The costs will differ according to the state of the economy. Four different regimes will be modelled: - neoclassical equilibrium, with zero excess demands in all markets ; - neoclassical unemployment, arising from downward rigidity of the real wage rate; - Keynesian unemployment, arising from a lack of effective demand ; - Keynesian inflation with positive excess demand in the product markets. Under any of the four regimes the level of the alternative costs will be influenced by the way the project is financed. The following options will be considered: - issue of government bonds; - (lump sum) taxes; - bank credit; - reduction of other government expenditure items; The basic model The starting point for the construction of opportunity cost rules is a basic or trunk model from which the models for the four regimes will be derived. XD

= CD t

Xs

=

C,,

s=s(X

It G

-k S

S

t T

- T ) - ~ t a r , O ~ s < l

~ = - i r t i

, O j t < l

T=tX t T S

I thank Ide W.H. Nentjes for his assistance in working out the mathematics.

205

G = E ND

=

2 nXS

Definition of the symbols: D' I G

- demand for consumer goods = demand for capital goods = government expenditure

s = T

savings

= taxes

- demand for aggregate output D' xs - aggregate supply ND - labour demand N

S

= labour supply

wP = real wage

rate

w = money wage rate P r

= general price level = rate o f interest

% = money M

S

demand

= money- supply

206

BD

=

demand for bonds

BS

=

supply of bonds

a, i , 11, 12, n , r, s , t

are coefficients

E . f , c , 2, R, T have a predetermined value Neoclassical equilibrium model The neoclassical equilibrium model is derived from the trunk model by transforming (13) to (16) into market equilibrium conditions:

XD

=

xs

13a)

ND

=

NS

14a

MD

=

MS

15a)

From the model for the product and labour market, which consists of 11 equations (1 to 9, 13a, 14a and 11 endogenous , r) the reduced form variables ( C D' I, G, S, T, XD, Xs, ND, NS,

L

equations for consumption and investment can be derived. Aggregate output is calculated from (7). (9), (13a) and (14a). fp,5

--

n 0.5

-xD=xs

=x

From (1) and (2) it follows I = S t T (5) and ( 6 ) into this equation gives:

I

i -{(l-c)x ati

=

-

-

a at1

=

ct t

c

=

(1-s-ttst)

A

=

f

cD

t

5 t E

A} t i

(1-s)T t -{(l-c)R

-

-

G. Substituting ( 3 ) , (4).

(22)

-

A}

(23)

(1-s)T

Assume that the project is financed with bond loans. The change in government expenditure arising from a public investment project is AG. From (22) and (23) it follows:

207

In neoclassical equilibrium the opportunity cost-components are determined by the interest elasticities of the savings and investment functions. The idea, often encountered in practical cost benefit analysis, that the public investment fully crowds out private investment, holds only in the special case of a completely interest-inelastic savings equation (a = 0). If the project is financed with.lump-sum taxes AG = AT. From (22) and (23) it can be derived AI =

-

Ac

- a+i

+a

AG

sa

=

AG

-

(1-s)

AG

=

-(I- asi +i)A

If the project is financed with lump-sum taxes private investment will diminish with a smaller amount than in the case of financing with loans. Financing with bank credit is not consistent with a neoclassical model. Increasing the money supply would imply a switch of economic regime. The money market only affects the product and labour market in a situation of market disequilibrium. This case will be investigated in the context of the inflation regime. If the government decides to 'finance' the public investment project by cutting other government expenditures then the level of G is unchanged and the opportunity cost is - A G for any of the four regimes. Neoclassical unemployment model To transform the trunk model into a model generating neoclassical unemployment equations (13) and (15) have to be changed into equilibrium equations and downward rigidity of the real wage rate has to be postulated.

XD

=

xs

%

=

MS

W -

W = (-)

P P Moreover the definition of unemployment may be added. U =

NS

-

ND

(18)

The model for the product and labour market consists of 12 equations (1 to 9, 13a, 17, 18) and 12 unknowns (CD, I, G, S, T,

208

XD, X s ,

W

ND, NS, --, r, U). The endogenous variables can be solved

from this model. We shall concentrate on I and C

D' Under a regime of neoclassical unemployment the level of production is not determined by the available supply of labour, as it is under neoclassical equilibrium, but by the rigid wage rate. According to ( 7 ) and by solving X from (8) by integration we obtain

is fixed at a level above the full employment wage then X represents a level of output that is below full employment output.

-

If

P

The equations for I and C are derived in quite the same way D as was done for a regime of neoclassical equilibrium. The formulae only differ in that 2 has be to replaced by z. From these formulae we calculate the opportunity cost components A C and A I. The results are completely identical to the opportunity cost rules under a regime of neoclassical full employment equilibrium for the four financial instruments that have been distinguished. This outcome demonstrates that the existence of unemployment as such does not guarantee that public investment projects will diminish unemployment, even if the project is financed by government bonds. From ( 2 4 ) and ( 2 5 ) it follows:

Public works will not increase employment. Any increase in employment would decrease marginal productivity, which in turn asks for a lower real wage rate. The real wage rate rigidity blocks this adjustment. Total output remains constant and consequently a public investment project can only absorb workers by driving them out of their jobs in the private sector. Keynesian unemployment model The trunk model transforms into a Keynesian model with unemployment by specifying market equilibrium in the product and money market and by postulating rigidity of the money wage:

xD = xS

MD

= MS

209

-

w = w Again the unemployment equation can be added U

=

-

NS

(19)

ND

(18)

The number of equations is 15 (1 tot 11, 14, 13a, 15a, 18, 19) from which the 15 endogenous variables (CD, I, G, S , T, XD, Xs, ND, NS, w , p, r, %, MS, U) can be solved. From (1) to (6) and (13a) it follows:

and from ( 7 ) , (8) and (19) p

2nW

=

xS

Substituting the equations for r, p, (10) and (15a) in (11) gives: =

's

1 {Z 41 nw

t Y0S5}

1

By substituting X

S

in the equation for r and next the equation

for r in ( 4 ) we get: i (1-c) -(ZtY ati '41 nE

I

0*5) - A} t

= -

f

1

The reduced form equation for consumption is solved by substituting the equation for r in 13) and substituting (3) in ( 2 ) and X S (29) in that equation. C

=

C A

1-c

t

E

-

(1-s)? t

{-

a

C

(1-c1

t a +i}{-(Z

(1-c) 4 1lnw

t YO P 5 )

-

A} (31)

If the project is financed with bond loans the impacts on the opportunity cost components are calculated by differentiating (30) and (31) to G. A1

=

i AGtR-i - ati ati

AG

=

-

i

-(l-R)

ati

AG

(32)

210

Ac

=

- i+aa

AG

a

t {-ati t

C R AG 1-2

=

a - ati (I-R) A G t C 1-cRAG (33)

Compared with the results of the neoclassical model it appears that under the Keynesian unemployment regime the neoclassical (negative) cost component is compensated by a positive component (R). For consumption the positive component is larger than for investment. For plausible values of the coefficients and predetermined variables the range of R is 0 < R < 1. If R > 1-c then private sector output ( A I t A C ) will increase instead of falling off. Depending on the shadow price of investmant the opportunity cost will be negative, but very small, or even be positive. Let us consider financing with lump-sum taxes. Differentiating G and T in (30) and (31) and set gives A T equal to A G .

A1 =

si - a~i(l-R) AG

AC =

- ati -(l-R)

sa

(34)

sc

-R

bG t

1-C

A

G

-

( 1 - S )AG

(35)

In comparison with financing out of loans under Keynesian unemployment the decline in investment is smaller; the increment of consumption is smaller too. Compared with financing with taxes under neoclassical (dis)equilibrium regimes the decrease of investment is lower and consumption might even show an increase, where under neoclassical (dis)equilibrium consumption decreases. Next consider financing with bank credit. When the project is financed with bank credit AG = AM We derive from (30) and (31): i

A1

=

- i+a

ati

(1- (1 t -)R} l2

A I t A C = -

AG

1 (1 t a<) 1-c

A G t -

R AG

The results show that under a regime of Keynesian unemployment monetary financing induces a smaller reduction of investment than

2 11

would have occured if the project had been financed with bond loans; an increase of investment even is possible (if R > 0,5). Consumption increases more than under bond loan finance. Keynesian inflation model The trunk model can be extented to a Keynesian model with excess demand and inflation. The money market is in equilibrium and output is determined by the maximum of available labour:

xs

s

1 ,0,5

= -

fio,5

> X s , national labour demand is determined by the demand D for output. Equations (8) and (7) transform into:

If X

ND

nX

=

2

(7a)

D

dXD - w

dND -

p

A s in the former Keynesian model the money wage is rigid in the period concerned.

-

w = w

(19)

By definition

From the model of 15 equations (1 to 6, 7a, 8a, 9 to 11, 15a, 21) and 15 unknown variables (CD, I, G, S, T. X D , X s , NDB N S 9 P w, P, r r MS)

s,

the reduced form equations of investment and consumption can be derived by substituting the other equations in (11). t -(ati) M- } t ~ R t I

(3812

2

2

ID, Is investment demand resp. supply. Under a regime of inflation is In > Is and CD > Cs.

212

cD Q

=

=

cf t -

I5

-

(1-s)T

-

a {cf 12Q t (ati)

t A t

(ati) -

a

l2

I

2nl1GRS Consider the case of financing out of bond loans. From (30) and (31) we derive: AID

=

-i (ati)tQ12

AG

ACD

-

-a (ati)tQ1,

AG

AID t

ACD

--

-

AG

Q12 + a+i

Under a regime of Keynesian inflation the consumption demand and investment demand both decrease less than they would have done under full1 employment equilibrium or under neoclassical unemployG in ( 4 0 ) and (41) is multiplied with a ment. (Note that fraction that is smaller than in (24) and (25). Consequently private sector demand decreases less than the increase of government expenditure. Aggregate excess demand will increase and the public project financed by loans adds to inflationary pressure. The decrease of the production of investment and consumer goods can only be determined by making additional assumptions about the reactions of suppliers. It should be noted that the public investment project can only be carried out if the reduction of private sector output exceeds the reduction of private sector demand. Assuming such a rationing mechanism and assuming that the reduction in the private sector is proportional to the decrease in consumer and investment demand the resulting rationing fraction f is determined by the equation:

ACs

where

t AIs

f

=

=

1 t

-i (ati)tQ12

-

a AG (ati)tQ12

=

-

AG

-

Q12

ati

The increase in the supply of investment and consumption is i AIs = f AID = ati A G

--

(43) (44)

(45)

213

Acs

f AC,,

=

=

a - ati -

AG

Under these specific assumptions the opportunity cost equation is equal to the results obtained under a regime of neoclassical equilibrium or unemployment disequilibrium. Let us now pay attention to financing with (lump-sum) taxes. The reduction of consumption and investment demand is calculated in the usual way: AID

=

-

si atitQ12 AG

“D

=

-

sa a+i+Qr2

(47)

AG - (1-S) AG

The reduction of investment demand and of consumer demand is smaller than it would have been under a neoclassical regime (cf. ( 2 6 ) and ( 2 7 ) ) . The reduction of total private sector demand is larger than it would have been if the project had been financed through the capital market under a regime of Keynesian inflation. This is so because consumption demand shows a relative large reduction. Contrarily the investment demand reduction is smaller than it would be if the project was financed by loans. In the case of financing with bank credit changes in private sector demands are AID

=

“D

-

- i(1-Q) atitQ12

( A

M

= A

G)

the

A G

a(1-Q) A G atitQlg

1

+

2

ati

Again total demand for private output will decrease less than the increase in demand of the public sector. The demand reduction will be smaller than the demand reduction in. case the project was financed by loans under a regime of Keynesian inflation.

214

Proportional rationing of investment and consumption just enough to produce the additional government output, makes for the same result as under a neoclassical regime with loan finance i AIs - - ati AG

and

A C =~

a - ati -

A G.

From the above analysis it appears that under regimes of neoclassical equilibrium and neoclassical unemployment the lowest possible level of opportunity costs is attained if public projects are financed by raising lump-sum taxes. Under a regime of Keynesian Unemployment opportunity costs are minimized if the projects are financed with bank credit. Under Keynesian inflation the minimum opportunity cost alternative will depend on the rationing decisions of producers. If rationing is proportional t o the reduction in demand then tax finance should be preferred.

215

REFERENCES Abelson, J., Cost Benefit Analysis and Environmental Problems, Westmead, Farnborough 1979. Beld, C.A. van den and A.J. Middelhoek, Evaluation of Seaport Projects, Central Planning Bureau, The Hague 1971. Boadway, R.W., The Welfare Foundations of Cost-Benefit Analysis, Economic Journal, 35 (1974), pp. 962-993. Christainsen, G. and R. Haveman, The Contribution of Environmental Regulations to the Slowdown in Productivity Growth, Journal of Environmental Economics and Management, 8, No. 4 (1981)) pp. 381-391. Dagupta, A.K. and D.W. Pearce, Cost-Benefit Analysis; Theory and Practice (MacMillan Press), London 1978. Dixon, J., and M. Hufschmidt, eds., Economic Valuation Techniques for the Environment, Baltimore 1986. Feldstein, M.S., Financing in the Evaluation of Public Expenditures, in W.L. Smith and J.M. Culbertson, eds., Public Finance and Stabilization Policy (North Holland Publishing Company), Amsterdam 1974, pp. 13-16. -- Opportunity Cost Calculations in Cost-Benefit Analysis, Public FinancePinance Publiques, (1964), pp. 117-139. Freeman 111, A.M., The Benefits of Environmental Improvement. (John Hopkms University Press), Baltimore and London 1979. Haveman, R.H., Evaluating Expenditures under Conditions of Unemployment, in Haveman, R.H. and J. Margolis, eds., Public Expenditures and Policy Analysis (Rand Mc Nally College Publishing Company), Chicago 1970, pp. 33-347. Haveman, R.H. an J.V. Krutilla, Unemployment, Idle Capacity and the Evaluation of Public Expenditures; National and Regional Analysis, (John Hopkins University Press),Baltimore 1968. Hufschmidt, M., J. Krutilla, J. Margolis and S.A. Marglin, Standards and Criteria for Formulating and Evaluation Federal Water Resources Development, Mimeo, Report of Panel of Consultants to the Bureau of the Budget, Washington DC 1961. Johansson, P.O., Cost-Benefit Rules in General Disequilibrium, Journal of Public Economics, 18 (1982), pp. 121-137. Johansson, P.O. and K.G. Lofgren, 1988, Disequilibrium cost-benefit rules: an exposition and extension. This volume. Klaassen, G., P. Kee, A. Nentjes, W. Hafkamp, The Macroeconomic Impacts of the EC Large Combustion Plants Directive Proposal, Institute for Environmental Studies, Amsterdam Dec. 1987. Kuyvenhoven, A., and L.B.M. Mennes, Guidelines for Project Appraisal, The Hague 1985. Lal, D., Methods of Project Analysis, A Review, Baltimore 1976. -- Prices for Planning: Towards the Reform of Indian Planning, London 1980. Lesourne, J., Cost-Benefit Analysis and Economic Theory, Amsterdam 1975. Little, I.M.D., and J.A. Mirlees, Project Appraisal and Planning for Developing Countries, 1974. Maler, K.G., and R.E. Wijzga, Economic Measurement of Environmental Damage, OECD, Paris 1976. Mar+, S.A., The Opportunity Costs of Public Investment, The Quarterly Journal of Economics, 77 (1963), pp. 274-289. Mishan, E.J., Cost-Benefit Analysis, 3rd ed., London 1982.

216

Musgrave, R.A., Cost-Benefit Analysis and the Theory of Public Finance, Journal of Economic Literature, 7 (1969), pp. 797-806. Nentjes, ,A. and G. Klaassen, Macroeconomic Consequences of a Policy to Save Energy and to Abate Acid Rain Emissions in the Netherlands. Paper for the symposium "Acid Rain and the European Economy", Strassbourg, 28-30 October 1985. Nentjes, A., Creating Employment by Abating Acid Rain in the Netherlands, Informationen zur Umweltpolitiek 38, Umweltschutz und Arbeitsplatze, Institut fiir Wirtschaft und Umwelt, Wien 1987, pp. 32-53. OECD, Employment and Environment, Paris 1978. -- Macroeconomic Evaluation of Environmental Programmes, Paris, 1978. -- The Macroeconomic Impact of Environmental Expenditure, Paris 1978. Pearce, D.W., ed., The Valuation of Social Cost, London 1978. Pigou, A.C., The Economics of Welfare, 1921. Sugden, R. and A. Williams, The Principles of Practical Cost-Benefit Analysis, (Oxford University Press), Oxford 1978. Unido, Guide to Practical Project Appraisal, Social Cost-Benefit Analysis in Developing Countries, New York 1978. Zuidema, T., Een onderzoek naar de alternatieve kosten van overheidsprojecten: theorie en empirie (dissertation), University of Groningen 1982.

part IV

Aspects of Policy Making

This Page Intentionally Left Blank

219

Chapter 11 BENEFIT ESTIMATION FOR COMPLEX POLICIES ALAN RANDALL*

Department of Agricultural Economics and Rural,Sociology, The Ohio State University, Columbus, Ohio 43210-1099 (USA) JOHN HOEHN* Department of Agricultural Economics, Michigan State University, East Lansing, MI 48824 (USA)

1 INTRODUCTION While the idea and some of the analytics of benefit cost analysis have a lengthy history (e.g., Dupuit, 1844), its domain and influence have expanded in recent years. BCA has been firmly grounded in the Hicks-Kaldor compensation test and the potential Paretoimprovement (PPI) criterion.

This welfare-theoretic base permits two rather different

economic interpretations of what it means to say that a proposal passes a BC test. First, it implies that, for the affected population, the interpersonal sum of self-evaluated prospective gains and losses is positive. Second, the proposed innovation could potentially (is., in an environment of completely-specified property rights and low-friction markets) be implemented via voluntary exchange among the affected population. These economic interpretations have direct counterparts in political philosophy:

the first

implements one version of the classical utilitarian test, while the second identifies proposals that could potentially (i.e., if acceptable compensation were actually paid to those who would otherwise lose) gain unanimous consent. Both the classical utilitarian test and the test of hypothetical compensation are, of course, controversial among political philosophers. To argue that BCA has standing in political philosophy is a far cry from claiming that it is generally noncontentious. *The authors acknowledge research support from the National Science Foundation (Grant No. SES-8309157), U. S. Environmental Protection Agency (Cooperative Agreements 807768-01-0 and CR 811056-01-0),Recources for the Future, Inc. (Small Grants Program), The Ohio Agricultural Research and Development Center, and the Agricultural Experiment Stations of Kentucky and Michigan.

221

Holistic estimates will not yield component benefit estimates that would be useful in fiietuning the policy package. Arbitrary sequencing will ensure a valid aggregate BCA of the complex policy, but may be misleading with respect to benefits and costs of individual policy components. Furthermore, the valid benefit measure for complex policy does not seem to permit the use of "in isolation" benefit estimates for policy components, even where an inventory of such estimates is readily available.

In section 3 we outline a

procedure for econometrically approximating the valid welfare change measures for many configurations of complex policy using valid holistic BC estimates for a sample of such policies.

Further, we suggest a possible modification of this procedure to approximate,

roughly, the valid holistic benefit measure, using existing "in isolation" benefit estimates for individual policy components and some additional information about substitution relationships among components.

2 THEORY Consider an economy where individuals value market goods and environmental services, and the level of environmental services is controlled by policy.

Household preferences

across market goods, x, and environmental services, q, are described by a utility function,

u

= u(x,q), (where boldface characters indicate vectors) that is strictly increasing,

Continuous, and strictly quasiconcave. Given income, m, market prices, p, and access to environmental services, q, the level of well-being attained by a household is described by M indirect

u

=

utility function.

v(q,m)

=

{u: u = maxu(x,q) s.t. m

=

px}

(1)

where the constant price level, p, is left implicit in v(.). At an initial level of income, m0,and an initial level of environmental quality, q0,initial utility is uo = v(q0,m0). The household's expenditure function is e(q,u)

=

{e: e

=

min px s.t. u(x,q) 2 u}

(2)

where the constant price level is left implicit in e(.). The expenditure function is strictly decreasing and strictly convex in q. The expenditure function states the minimum expenditure on market goods that sustains a utility level u at market prices p and environmental quality q. At an initial level of environmental quality, q0, initial income is

222

just enough to maintain initial utility: mo

=

e(q0,u0). For notational simplicity, let q be a

2-element vector, q = (ql,q;?). 0 to Now we introduce a sinde-impact policv that would change the level of q1 from q1 q11 while leaving q20 unchanged. The Hicksian compensating measure of benefit, HC, is the

amount of income, paid or received, that would leave a household at a pre-policy level of well-being while enjoying the post-policy level of environmental quality. For the singleimpact policy defined above,

If the policy change is beneficial to the household, HC measures the household's willing-

ness to pay (WTP) for the change; if the policy is detrimental, HC is negative and -HC measures WTA, the compensation that the household is willing to accept. Now, consider a multipart policv that changes the levels of both elements of q. For a two-element change from q10 to q11 and q20 to q2, 1 the conventional BCA procedure would evaluate the two changes independently--perhaps in different studies conducted by independent research teams--and then aggregate the "in isolation" benefit estimates to calculate the benefits of the two-part policy.

We denote this procedure IVS, for

independent valuation and summation. For the policy change posited above, IVS would generate the benefit measure

A conceptually valid benefit evaluation design is derived directly from the defiuition of HC.. That is, HC is the amount of income paid or received that would leave an individual

household at the initial level of utility subsequent to the multiule impacts of policy. For the multipart change from q0 to q1, HC is

Equation (5) summarizes the structure of a valid benefit evaluation design. First, as the difference between initial income, mo, and the well-defined function e(.), HC is unique

223

for any multipart change in policy. There is a single measure of H C for any given policy. Second, HC encompasses the overall impact of policy in a single, one-step valuation. A contingent valuation format could be designed to value, ex ante, the multipart policy in a one-step, holistic valuation. Equation (5) can be decomposed into separate valuations of the two components of policy. To carry out this disaggregation, a sequential path of valuation is selected. The - 0 0 and that only requirement of a valid sequence of valuation is that it begin with q0 -(ql,q2) 1 2 One admissible sequence of valuation would value the change from it end at q1 = (ql,q2). 0 0 to (q1,q2) 1 0 first, and the change from (q1,q2) 1 0 to (q1,q2) 1 1 (q1,q2) second. Using this path of valuation, HC is

For expositional convenience, the multipart policy addressed above is confined to two elements. However, some complex policy packages may well impact many elements of environmental quality. For a g-impact policy, the structure of the valid HC measure of benefits would be analogous to that in equations (6). The valuation sequence would be g items long and the ith impact in g would be evaluated as though the i-lth policy component was already in place. We have elsewhere developed and proved three theorems that detail the relationships between the conventional IVS benefit measures and the valid HC measures for multipleimpact policies (Hoehn and Randall, 1986). Here, we simply state these theorems and discuss, at an intuitive level, their implications. Theorem 1: HC (as defmed in equations 5 and 6) is a valid benefit measure for multipart

policy. HC is unique for a given multipart policy. If HC is calculated by aggregating the sequenced valuations of the components of policy, H C for the multipart policy is unique; however, the valuations of individual policy components are not unique, but depend on their place in the valuation sequence. Further, HC for the multipart policy is in general not equal to IVS.

224

This result defiies a valid benefit measure for multipart policy, shows that the conventional measure is invalid, and suggests two approaches to empirical evaluation of multipart policy: first, a holistic one-shot evaluation; and, second, a sequenced valuation procedure that considers the policy components separately but in some particular sequence. For ex ante evaluation of complex policy proposals, contingent valuation has obvious advantages, deriving from the flexibility afforded the researcher in constructing and communicating scenarios. We see no insurmountable difficulties in developing contingent valuation scenarios for holistic and sequenced valuation of complex policy proposals. Opportunity exists for evaluating a number of alternative sequences, which is clearly useful if component valuations are of interest and no particular valuation sequence seems self-evident. We recognize, of course, that a variety of questions remain, concerning the susceptibility of contingent valuation to various sources of error and bias. For ex post evaluation of complex policies, the contingent valuation method is available.

In addition, hedonic price analysis may be effective for holistic valuation.

Where policy has local or regional application, multi-market, wage-rent hedonic analysis may be effective; repeat sales analysis may be serviceable, where one can obtain observations both before and after policy implementation and within and beyond the policy impact area. There may be cases in which the vector of policy components had been implemented piecewise with some considerable lags between components.

In such cases, ex vost

analyses of component benefits using hedonic or weak complementarity methods may satisfy the requirements of a valid valuation structure. More typically, we fear, there wiU be little opportunity to use these methods for ex vost evaluation of valid policy component benefits. Theorem 1 states that HC is in general not equal to IVS. If policy components are substitutes for each other, IVS would tend to overstate policy benefits, but if they are complements IVS would tend to understate the benefits of complex policy. Theorem 2 identifies a situation in which the error from IVS is systematic. Theorem 2 Let there be many potential policy components, each with positive benefits if

implemented in isolation. Then, as the number of such components included in a multipart policy grows large, the error from using IVS evaluation becomes systematic: overstates HC for the multipart policy and for at least some of its components.

IVS

225

While the frst two theorems demonstrate that IVS introduces error into the benefit estimates for complex policy, a question remains about the benefit cost ratio or net present value. Are there circumstances in which the IVS procedure would misidentify the PPI/non-PPI status of proposals?

Theorem 3 Let each policy component impose a resource cost on the economy. Then, as the number of policy components becomes large, the IVS procedure misidentifies some non-PPI complex policies as PPI and some non-PPI policy components as PPI. These results show that the conventional IVS procedure introduces errors that become systematic as the number of policy components becomes large: some non-net-beneficial policies and policy components pass an IVS BC filter. With routine use of IVS procedures, the portfolio of public policies could grow wastefully large. Two economic phenomena are involved. First, for any number of policy components, small or large, some policy components may be substitutes for or complements with others. IVS fails to consider these possibilities. Second, as the number of policy components becomes large, resource scarcity makes the error in IVS systematic. Scarcity eventually forces the dominance of substitution effects. 3 TOWARD EMPIRICAL APPLICATION

It is easy to understand the popularity of IVS.

It is convenient in application and

adaptable to all of the acceptable non-market valuation tools, and it allows the accumulation and re-use of an inventory of benefit estimates. Often, ex ante benefit estimates for a complex proposal are calculated by IVS using of component benefit values, estimated (perhaps, ex post) by independent teams of researchers using different methods. Compared with de novo empirical benefit estimates for each and every complex proposal under consideration, the savings from using IVS are obvious. However, our theoretical results demonstrate general, perhaps large, and ultimately systematic errors from IVS. Here, we explore the possibilities of designing practical methods to approximate the valid HC measure of benefits while economizing on research effort. practical problems:

We consider two

first, rather than de novo holistic benefit evaluation of each and

every conceivable complex policy configurations, a method to approximate the benefits of many complex policy packages from valid benefit estimates for a sample of packages would be helpful; and, second, it would be desirable to find ways to use an inventory of

226

component benefit estimates to calculate approximately valid benefii estimates for complex policies. We begin by developing an econometric structure for the benefits of a complex policythat changes the vector of environmental services from qo to q 1. The valid benefit measure for that policy is HC(ql;qo) = m0 - e(q1,u0).

(7)

Rearranging and taking natural logarithms, we obtain ln(mo-HC)

=

In[e(ql,uO)].

A second-order Taylor series expansion of (8) about In(m0) yields

In(m0-HC) = ln(mo)

+ ln(al)'P + In(al)'Bln(al)

(9)

(In(q:/qy), ....,h(q?q;)) is a g-element vector, p is a matrix of coefficients conformable to In(a1), and B = (bij), i, j E (1,...,g) is a g2-element symmetric matrix.

where ln(al)

=

Equation (9) is essentially a translog approximation to the expenditure function. If a 0 in the proposed policy scenario, qi policy component qi is unchanged (i.e., q! = 4;) vanishes from the right-hand side of (9). One need only consider the policy components that would be changed by the proposed policy. Equation (9) imposes no arbitrary restrictions on the degree of substitution or complementarity between policy components. Consider the problem of an agency exploring an array of combinations and permutations of multipart policy. If one had valid HC benefit estimates for a sample of multipart policies under consideration (perhaps estimated by contingent valuation), one could estimate the degree of substitution and complementarity from the sample data (Hoehn 1987). By estimating (9), one could calculate the valid HC benefit measure for any multipart policy within the sample range.

If, on the other hand, one has information on base income, mo, and an inventory of "in isolation" benefit estimates for policy components, it is possible to approximate the valid HC benefit measure for multipart policy if one is willing to impose some further restrictions on the econometric structure and if some additional data can be obtained.

assume the diagonal terms in B are zero.

First,

Second, since it can be shown that the off-

221

diagonal terms of B are functions of ,f?i/?j, assume that bij is simply proportional to that is, be. = 6,f?./3.. A positive 6 implies the qi and qj are substitutes in valuation.1 9 1 J Rearranging (9), one finds, for PI, that

where s;0! indicates that all elements of q other than q1 are unchanged. Using equation (10) to estimate the elements of

p, only the parameter, 6, remains unknown. Obviously,

the substitution parameter could be estimated in an empirical research project initiated for that purpose. Or, perhaps, previous research may yield an array of plausible values for 6.

In the worst case, a value for 6 may simply have to be assumed. This simplified version (equation 10) of the econometric structure for valid benefit estimation (equation 9) permits the use of "in isolation" component benefit estimates, e.g., 1 0. 0), to calculate an approximation of the valid benefit measure for complex HC(q1,q2,q policy. In addition to the "in isolation" component benefit estimates, one needs estimates of the base income level, and the substitution parameter. It is important to recognize that this simplification substitutes structure for informati-

on. In particdar, simplifying assumptions are imposed about the nature of the substitutiodcomplementarity relationships among policy components. In the extreme, where all offdiagonal terms in B are zero and all b- = 6/?./3.,the substitution relationships are assumed J' 1 J to be identical for all pairs of policy components. A less restrictive approach might seek to measure, in a set of demonstration projects, a vector of substitution parameters for at least the major pairs of components of environmental policy.

To verify this assertion, consider the case of a two-component policy, where both q1 and 42 are desired amenities. Equation (9) reduces to: In(mo - HC) = In mo

+ p1 In a: + /?2 In a21 + 6 In al1In a2.1

A positive 6 implie that the marginal effect of interaction between the policy components is to increase h(mb HC), i.e. to reduce HC. Thus a positive 6 implies q1 and q2 are substitutes. I

228

4 CONCLUDING COMMENTS

We have shown that conventional BCA procedures are invalid for evaluating complex policy.

Where the number of policy components under consideration is very large,

conventional IVS procedures would provide a systematically biased filter and, as a result, a wastefully large portfolio of policies may be implemented. We have, however, defined valid BCA structures that would eliminate this problem. We are conscious that the valid BCA structure is informationally demanding, allows no use of "in isolation" component benefit estimates collected from previous research, and seems poorly adapted to the use of the hedonic and weak complementarity methods that are favored by some environmental economists. Our exploratory efforts to develop flexible and simplified econometric structures for approximating the valid benefit ,measures are addressed to these difficulties. We have planned some initial empirical research along these lines, but it will be some time before the results are available. In the case where a single agency has control of a manageably-small number of policy components, an important concern raised by our work is the need to identify and properly consider substitution and complementarity among policy components.

Since Burt and

Brewer (1971), economists have been conscious that multiple recreation facilities may be substitutes for one another. However, complementary relationships may also be important. Consider forest wildland management, where water quality, scenic integrity, atmospheric visibility and ecological diversity may all be complements. For the "small numbers" case, our work focuses attention on the importance of substitution and complementarity among policy components, and suggests some strategies for empirically accounting for such relationships, more and less precisely. REFERENCES Brautigam, Ronald, and Roger G. Noll, "The Regulation of Surface Freight Transportation: The Welfare Effects Revisited," Review of Economics and Statistics, 66( 1):80-87, February, 1984. Burt, Oscar R., and D. Burwood Brewer, "Estimation of Net Social Benefits from Outdoor Recreation," Econometrica, 39:813-827,1971. Dupuit, Jules, "On the Measurement of the Utility of Public Works,"International Economic, Papers, 283-110,1952 (1844). Hoehn, John P, "An Improved Framewoik for Valuing Natural Resource Services," Staff Paper 87-7, Department of Agricultural Economics, Michigan State University, East Lansing, MI, 1987. Hoehn, John P. and Alan Randall, "Too Many Proposals Pass the Benefit Cost Test," American Economic Review (in press).

229

Lave, Lester B., "Controlling Contradictions among Regulations, "American Economic Review, 74471-476,1984. Morey, Edward R., "The Demand for Site-Specific Recreational Activities: A Characteristic Approach," Journal of Environmental Economics and Management, 8346-371,1981.

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23 1

Chapter 12 THE ACID RAIN GAME* KARL-GORAN MALER Stockholm School of Economics, Box 6501,113 83 Stockholm (Sweden)

1 INTRODUCTION During the last couple of years, the problems connected with emissions of sulfur- and nitrogen oxides and the resulting damages on eco-systems have come more and more in the focus. The death of forests in central Europe and Scandinavia have been quite important news items and rightly so, because if the European eco-systems will change so drastically there will be a substantial reduction in timber supply, that will effect not only nature conservationists but also everyday man because of the economic consequences in a conventional sense. Thus, the problems of acid rains seem to be a very important issue for economists to analyse. Moreover, it offers a fascinating multitude of intellectual challenges, one being that the information on causes and effects is very uncertain, another being that it concerns the use of a common property resource in a very asymmetric way, a third being that it is about a game with incomplete information and with many players so that problems with incompatible incentives will be at the heart, and finally, the parties involved are different nations with no agreed rules of the game. In addition to these challenges, there are of course a multitude of equally challenging empirical problems. The objective of this paper is to give a skeleton of an analytical model in which some of the above problems, and in particular the problems of international cooperation, will be analysed. However, in view of the complexities of the interactions between national

* This chapter is an outgrow of a research project on the economics of acid rains at the Stockholm School of Economics, financed by the Swedish Environment Protection Board. I am grateful to Lars Bergman for many rewarding discussions on the topics covered in this chapter and to Clas Olsson for excellent research assistance. I would also like to express my gratitude to Partha Dasgupta for teaching me game theory and in particular the concept of a strong equilibrium. Finally I would like to thank two anonymous referees as well as He& Folmer and Ekko van Ierland for many valuable suggestions which have improved the presentation very much. They are, of course, absolved from remaining errors and mistakes.

232

emissions and the resulting environmental damage, we will make a few, rather serious simpIifications. Our basic model will concentrate on national sulfur emissions in different countries in Europe. Thus, we will not look into the very relevant issue of spatial distribution of the emissions in each country. Nor will we look into the spatial distributi-

on of damages within each country. Finally, we will neglect the effects of nitrogen oxide emissions and the formation of ozone, although it seems clear that these factors are perhaps as much to be blamed as sulfur emissions for the observed damages to forests. Moreover, it should be stressed that this paper is one in a series of different papers, analysing different aspects of international cooperation in the environmental field. Thus we will discuss the following scenario. Each European country is emitting sulfur oxides, the amount of which depends on energy consumption, sulfur content in the burnt fuels, the combustion technology and stackgas cleaning technology. By switching to fuels with lower sulfur content, by changing combustion technology, by reducing energy consumption etc. it is possible to reduce the emissions of sulfur, but at a cost. Thus we will postulate a cost function for reducing the emissions. The expected control cost

function for country i will be denoted Ci(E;) where E; denotes the emission in country i. This function is, of course, decreasing in Ei, as the cost of abatement increases with abatement. We will also assume C; to be strictly convex (although in some simulation it

will be linear or piecewise linear). Moreover, we will assume it to be sufficiently smooth. The emissions will have local effects due to the resulting ambient concentrations of sulfur oxides. These local effects are health effects, corrosion to materials, damage to vegetation etc. We will for the discussion in this paper assume that we have a monetary damage function for these local effects so that we can form the net control cost function by subtracting the local damage from the control cost function.

We will in the sequel

reinterpret Ci as the expected net control cost function. The cost functions actually used in the simulations presented in this paper are, however, gross, i s . do not include local damage costs. The sulphur emitted will be transported by winds in the atmosphere and will also be transformed by chemical processes from sulfur oxides to sulphates. Ultimately, the This construction is not completely correct as the local damage from increased ambient concentrations of sulfur oxides is not directly related to the emissions but also to the height of -the stack, the location of the stack etc. We will, however, neglect those factors here.

233

sulphates will be removed from the atmosphere by direct "dry" deposition or by rains"wet" deposition. It turns out that there exists at least one meteorological model that describes this transportation and transformation and is simple enough to be used for an economic analysis of the acid rain problem and is accepted by most European countries as giving a fair description of the actual processes, namely the EMEP model. The EMEP model is based on a grid by which Europe is divided into about 700 squares. The model assumes sulfur emissions in these squares and by using observations on actual winds etc. the air package above a square is followed as it moves from one square to another. The model predicts the chemical changes w i t h the airpackage and the removal of sulfur from the package in the form of deposition. With steady state climatic conditions, the model reduces to a transfer matrix with a dimension equal to about 700 times 700. An element in the matrix gives the amount of sulfur deposition in one square, following the emission of one ton in another square. However, for the purpose of this study, the matrix is aggregated into a country times country matrix, i.e. with a dimension 28 times 28, so that a typical element in the matrix describes the deposition in one country that is due to the emission of one ton in another country!

However, Iceland has been excluded, so the

actual matrix is of order 27 times 27. Finally, as the contribution to the acid rain problem from Luxemburg is neghgible, Luxemburg has been deleted from all tables containing results from the calculations. The transfer is denoted by the matrix A. If E is the vector of emission levels in the European countries and if Q is the vector of sulfur deposition in the countries, the steady state model for the transport of sulfur is simply Q = AE. The deposition of sulfur gives rise to various environmental damages. The first environmental problems from acid rains to be observed were acidification of surface water. It was noted, mainly in Scandinavia, that the Ph-level of lakes and streams was falling, and in some cases to such low levels that further life of traditional species was inhibited.3 It soon became quite clear that even the ground water was affected and that in the long run, the growth of the forests would be reduced. These effects are now being observed both in Scandinavia and central Europe. See Binmore and Dasgupta (1986). One of the early reports on environmental damage from acid rains is to be found in the Swedish case study to the U.N. conference on human environment in Stockholm 1972.

234

However, the experts on forest ecology are not in agreement on the factors behind the damages4 There seems to be three explanations that have been put forward. According to the first, the forest damages are due to acidification of and the resulting chemical changes in the soil. The acidification of the soil is then explained by the deposition of

sulfur from the atmosphere. Another explanation gives the blame to increased ambient concentrations of nitrogen and sulfur oxides. These concentrations are very high close to the points of emissions but fall very rapidly with the distance. One of the main sources of nitrogen oxides is the automobile, and it is possible in many countries to watch dying trees close to motorways. If this would be the only explanation of forest damages, then the international aspects of the problem would be negligible and it would be almost completely a domestic issue. (Recently, research results have, however, indicated that NO, may also be transported by winds for long distances.) Finally, there is the "stress theory", which in a way integrates the two previous ones, namely that the defense to extra stress the trees can provide is reduced by pollution. Thus the explanation would consist of many different factors. It should be clear from above that there is no simple answer to the question: what are the environmental consequences from acid rains? In fact, the uncertainty is so great that one could imagine that acid rains have nothing to do with the death of forest and also that they are the main and only culprit. (It should be added that the damage from acid rains to surfwe and ground water is much more firmly established.) Because of this uncertainty, we should then talk about an expected damage function of deposition of sulfur. We, therefore, posit the existence of an expected damage function for each country which relates the deposition of sulfur to a monetary measure of damage. Assume that the deposition in country i is Q; Then we will denote the expected damage cost function (or simply damage function) by Di(Qi). For each country we thus have an expected net control cost function and an expected damage cost function. We will assume that these functions as well as the EMEP matrix that relates the emissions from one country to deposition in all other countries, are known by all countries. The net control cost functions, the EMEP matrix and the damage functions define a

non-cooperative game, in which the strategy for a country consists of choosing an emission level and the payoff is equal to minus the sum of the net control cost and the For a summary of different hypotheses explaining the death of forests, see Hinrichson (1986).

235

damage cost (except for an uninteresting constant). This game is quite similar to the ones analysed for common property resources, except that those games generally deal with a symmetric situation while this acid rains game deals with a highly asymmetric case. The reason this 'acid rain game' is asymmetric is that the matrix A is non-symmetric because of the prevalent wind directions. Emissions in some countries are more harmful than in others simply because of their locations. In section 2, different non-cooperative solutions to this game are defied and analysed and compared with the full cooperative solution (is. the solution that would emerge if all countries would cooperate and maximize their joint payoff, assuming that utility is transferable). In the following sections different cooperative equilibrium concepts are defied, discussed and illustrated by simulations. 2 NON-COOPERATIVE EQUILIBRIA AND THE FULL COOPERATIVE SOLUTION

The purpose of the simulations to be presented in the next section is to get a feeling for the gains from cooperation the European countries could expect. Ideally, one would therefore be interested in the core and related equilibrium concepts of the acid rain game. In section 6 these concepts are defined and discussed in more detail. In this section the interest is focused on the "full cooperative solution". This was defined in the previous section as simply that vector E of emission levels that minimizes the expected total cost,

i.e.

C (Ci(Ei) i

subject to Q

-I-Di(Qi)) =

AE.

This solution concept implicitly requires transferable utility, i.e. that gains in one country can be transferred to other countries in order to achieve another distribution of gains and losses. As both cost and damage functions are measured in monetary units we thus assume that utility is linear in income and transferable between countries (which incidentally requires that the current exchange rates are equilibrium rates). The reason the solution is defined as the minimum of expected cost (expected instead of simply cost) is that in general both damage- and control costs are uncertain. However, we shall in the sequel disregard this kind of uncertainty. Thus, the full cooperative solution could as well be defied without the expectation operator5 There is another kind

The expectation operator has been included because in some companion papers the role of uncertainty is the focus of analysis.

236

of uncertainty which we must look into, however. This has to do with the information one country may have about costs and damage in other countries. In general, the control costs and environmental damage in one particular country is known only to that country (under the present assumptions). The lack of information is, in fact, so great that total emissions of sulfur in one country are unknown to other countries and the total deposition of sulfur in one country can only be estimated with the aid of the EMEP-model given the assumpti-

ons about the pattern of emissions. In this report, this aspect wiU be neglected. Instead, in a subsequent paper, this aspect will be the main problem to be discussed.

The full cooperative solution is a special case of the ”Pareto-efficient’’ outcome. A vector (E,Q) ={El, Q,

..., En, Q,, ..., Q,}

is said to be Pareto efficient if there does not

exist another feasible vector (E, Q ) such that the total cost (control- and damage cost) for each country at these alternative emission and deposition levels is less than or equal to the total cost at the (E, Q) level. If the feasible set is convex (which it is with our assumptions on the control- and damage cost functions and the linearity of the transport models), then all Pareto-efficient outcomes can be characterized as vectors (E, Q) that minimize

C “i{Ci(Ei>

+ Di(Qi>l

1

for a certain selection of al,...,an,with a’i > 0, i = 1, ..., n. If (E, Q’) is any allocation of emissions and depositions that is feasible (i.e. Q’ =

AE?),then P(E, Q’) denotes the set of feasible allocations of emissions and depositions that Pareto dominates (E, Q’), i.e.

+ D;(Q;),

P(E‘, Q*) = {(E, Q); c ~ ( E ~+ ) D~(Q5 ~ )c;(E;)

Q=AE)

A subset of the Pareto efficient allocations is thus a subset of the boundary of P(E ,

Q’). Note that for a given (E’, a’), the full cooperative solution need not be a member of P(E,

a’).If

that is not the case when (E’, Q’) is the initial situation, then the full

cooperative solution will not be obtained unless there are sidepayments among the countries. We can define (at least) two different non-cooperative equilibrium concepts.

*

*

*

*

i) Dominant equilibrium (Ek, Qk), Qk = A Ek, k = 1,...n is a dominant equilibrium if for all E, Q such that Q

=

AE it is true that for all k = 1,..a

Ck(Ei) -I-Dk(Q;) < Ck(Ek> + Dk(Qk) * Thus, a dominant equilibrium is characterized by a set of strategies Ek such that

237

irrespective of what other countries do, it would not be beneficial for country k to change its strategy. It is very easy to see that in general no dominant equilibrium will exist and we will give a proof in connection with the discussion of Nash equilibrium. However, under one special condition which is the basis for the simulations discussed later, a dominant equilibrium will exist. This condition is that the expected damage function is linear so that the marginal damage is constant. If that is the case the cost minimization emission in a country is determined by the condition that marginal abatement cost equals the marginal damage times the proportion of the emission that will be deposited in the own country. As the marginal damage is independent of the emissions in other countries, it follows that the cost minimizing emission is independent of the emissions in other countries and thus constitutes a dominant strategy.

ii) Nash equilibrium. A Nash equilibrium is defined as a pair (E*, Q*) such that

+ Dk(Qi) 5 Ck(EL) + Dk(Qk), k = 1,...n

Ck(Ei)

where Q’ is defined by Q =AE? ?

*

1=1, ..., n, 1#k El = El Thus a Nash equilibrium is characterized by the condition that if all other countries are emitting their Nash equilibrium quantities, then it is optimal for the remaining country to do that too. The Nash equilibrium concept has a very solid base in economic theory and the intuitive reasons behind the concept should be clear6 It is based on the idea that the countries

are rational. That means that they, if they have the necessary information, can calculate the optimal behavior of all other countries (including the other’s optimal response to the amount emitted in the own country) and therefore the own optimal response. This rationality is based on one crucial assumption, however, namely that each country has complete information on the others’ emissions, control costs, depositions and damage costs. As was noted above, such is not the case and the Nash equilibrium concept (at least as it has been defined here) cannot be rigorously defended. However, in spite of this we will for the rest of this section disregard this criticism and continue as if the game under consideration is a game with complete certainty.

See.Binmore and Dasgupta (1986).

238

In order to be able to prove the existence of a Nash equilibrium we will make the following assumptions: a) The control cost-and damage functions are twice continuously differentiable;

b) D;(Qk)

(here and in the sequel the symbol ' attached to a function denotes the

derivative) goes to infity with Qk (that is, we are looking at the other extreme compared with the assumption of constant marginal damage made above); f

C)

c k goes to Zero with Ek;

d) all elements a E of matrix A are different from zero for all countries k. The best reply of country k given that the other countries emit El, 1=1,

...,n, 1 # k,

is

given by the function &E) defined as the emission that minimizes the total cost in country k given the emissions in the other countries. It is easily seen that for each k = l , ..q,nthere exist Ek such that there exists an E

,

0

within the cube defined by the origin and Ek, k = 1,...,n in n + 1 space, such that Ck(Ek)

+

Dk(AE?) is less than the corresponding costs for points outside the cube. Thus we can restrict ourselves to this compact set when searching for a Nash equilibrium. But then the feasibility sets of all.players are compact and the payoff functions are continuous and there exists a Nash equilibrium. It is easily seen that under the assumptions made, the best reply functions are implicitly defined by dCi/dEi

+ % dDi/dQi

=

0, i = 1,2, ...,n.

The Jacobian of this system of equations is given by

C';(E1)

+ a l l D"(Ql)

...allalnD"(Q1)

...

I

... C J E ~ ) + & D " ( Q ~ )

ann anl D"(Q,)

where the symbol " denotes the second derivative.

The sum of the off-diagonal elements in row i is equal to

C

D'(Q;)

jzi and the diagonal element is c;(E~)

+~DII(Q~)

The Jacobian has therefore a dominant diagonal if

239

C;"

+ a;;D" (% - C

a-) > 0. j+i

Scrutiny of the EMEP model reveals that the term within paranthesis is positive for most European countries. In the cases where this term within paranthesis is less than zero, it has a rather small magnitude (in the order of .I). Multiplied with % the second term will be small and it seems reasonable to assume that the Jacobian has a dominant diagonal. This means, however, that the Nash equilibrium is unique according to well-known theorems.7 Thus, it seems reasonable to assume that there exists a unique Nash equilibrium in the European acid rain game as it has been formulated in this section. What are the differences between the full cooperative solution and the Nash solution? This question is interesting from the following points of view. A natural hypothesis would be that the present situation can be characterized as a Nash equilibrium. A comparison between the Nash equilibrium and the full cooperative solution would then indicate first the gains from cooperation but second, and more importantly, the allocation of the necessary reductions of sulfur oxide emissions among different countries. However, the assumption that the present situation can be characterized as a Nash equilibrium may appear to be far removed from reality. In fact, there are a number of international agreements on reductions of sulfur emissions in Europe and it is questionable whether these agreements can be interpreted as part of a Nash equilibrium. However, so far no transnational payments have been involved in these agreements, which could be interpreted by saying that the present situation must belong to the set P(En,Qn) of allocations that dominate the Nash equilibrium (En,Qn). If it can be shown that the full cooperative solution does not belong to the set P(En,Qn), then one can conclude that some kind of side payments are called for when the full cooperative solution between the European countries is looked for.

3 SIMULATION RESULTS In order to enable numerical simulations of the Nash equilibrium, the set of allocations that dominates that equilibrium and the full cooperative solution, the following strategy has been followed: a) Control cost functions were guesstimated on the basis of some plots produced by the Acid Rains Project at IIASA, Laxenburg.8 These cost functions were taken to be quadratic See for example James Friedman (1986), Chapter 5.3, Theorem 2.6. Amann, M., and G. Kornai (1987).

240

(with the exception of German Democratic Republic), The IIASA cost functions have the drawback that they do not include fuel substitution or switch to fuels with lower sulfur content and that they assume exogenous given energy demands. In particular, the cost functions are estimated on the basis of the expected energy demands for the year 2000. In spite of this, the functions have been applied in this paper to the energy consumption pattern 1984. Moreover, based on the information from U S A , maximum amounts of pollution control have been assumed for the different countries. This grossly overstates the cost of control of sulphur emissions. b) The damage cost functions were assumed to be linear, so that the marginal damage cost is constant, independent of the amount of deposition. If the initial situation is a Nash equilibrium then the absolute value of the marginal damage cost times the appropriate diagonal element in the EMEP matrix must be equal to the marginal control cost i.e. -dC;/dE;

=

a;idDi/dQc

By using this necessary condition for a Nash equilibrium, the damage cost function can be calibrated such that the marginal damage cost is equal to the marginal control cost divided by a;i. In particular, this means that the damage cost function represents the evaluation of the damage that the respective governments make today. It thus corresponds to what is usually called revealed preferences. It is, however, important to understand that this does not necessarily mean that the damage cost function estimated by conventional methods would be equal to the assumed damage cost function. The approach taken here is simply to assume that the damage evaluation revealed by actual policy decisions is used for the simulations. In the discussion on acid rains in Europe, it is often claimed that some countries are

using too low estimates of the damage. Therefore, in some simulations it has been assumed that the marginal damages in GDR and Czeckoslovakia are 50 percent higher than what the corresponding control cost would generate, and for Poland, the damage cost has been assumed to be 100 percent higher. However, these adjustments turned out to be of minor importance, and these simulations are not reproduced in this paper. It is obvious that changed information will change the perceived damage and therefore the chosen strategy also. Our numerical illustrations therefore only represent the current perception of damage. As the following will show, this does not really matter so long as the perceptions change uniformly over countries. c) This calibration thus yields a damage cost function for each country that can *be used to calculate the set of Pareto efficient outcomes, the full cooperative solution and

241

other solution concepts such as the core. However, if the true damage cost function is convex instead of linear, which seems probable, then this calibration will yield an underestimate of the true damage cost function. In particular, one may end up with overestimates of the gains from cooperation, as the benefits from reductions in sulphur deposition will be overstated. It is therefore very important to bear this bias in mind when the following results are interpreted. Moreover, although this assumption of constant marginal damage enables explicit calculations, it also removes one important and interesting connection between the European countries. With constant marginal damage, the best strategy choice in one country is independent of what other countries do, and the Nash equilibrium turns out to be a dominant equilibrium. d) The way the game is set up implies that the utility can be measured in monetary terms and that the cost (damage- and control cost) figures have the same meaning for all

countries involved. This requires that the exchange rate is an equilibrium one and that the cost of capital (freely transferable across national borders) is the same in all countries.

We know for sure that this assumption is not correct, partly because some of the European countries experience different economic systems than others.

e) All simulations have been carried out with GAMS - General Algebraic Modelling System, a software developed at the World Bank.9 The data in the matrix of transport coefficients and the initial emissions (1984) and the assumed maximal emission reductions are taken from Lehmhaus, Saltbones and Eliasson (1986). 4 FULL COOPERATIVE SOLUTION WITH SIDEPAYMENTS (Fcs)

We will start by looking at the "full cooperative solution" when sidepayments between

the different countries are possible. This means that the net benefits for some countries may turn out to be negative but these countries can be compensated by cash payments if the total European benefits are positive. The results are given in Table 1. The calculations show that the total emissions in Europe would be reduced by about

40 percent in the full cooperative solution compared with the present situation (emissions 1984), that almost all countries would gain from the full cooperative solution and that a

few countries - UK, Italy and Spain - would loose from participating in the cooperation.

GAMS was developed at the World Bank by David Kendrick and Alexander Meeraus. It is now marketed by The Scientific Press, 507 Seaport Court, Redwood City, CA 94062, USA.

242

(The losses that Finland and Luxemburg would experience are neghgible). Spain’s loss is

also almost negligible, while Italy would experience a moderate loss and the UK a substantial loss. Obviously, the UK would have no incentives to participate in organized cooperation to reduce the sulfur emissions in line with the full cooperation. These results do not depend crucially on the assumed control cost functions. If we have assumed too high a value for the marginal control cost for a particular country, this TABLE 1 Net benefits from the full cooperative solution. Emission control 1000 ton SO2

ALB AUS BEL BUL CZE DEN

mN

FRA GDR FRG GRE HUN IRE ITA NET NOR POL POR ROM SPA SWE SWI TUR USSR UK YUG

TOT

Percentage reduction

Benefits mill.

D Mark

6 10 299 107 1494 465

83 14 4 23 62 2 81 79

22 324 191 28 152 119 -2 879 11 328 52 5 71 -84 565 272 599 10 420 -29 606 192 0 1510 -336 346

9011

39

6248

10 31 112 179 1219 130 25 104 1040 1183 303 635 27 634 105 3 560 15 83 231

42 21 36 36 75 86 14 10 80 86 86 77 38 33 62 6 27 19

243

would to a certain extent be compensated by too high a value for the marginal damage cost, because of the way we calibrate the damage cost function. In fact, sensitivity analysis yields the expected result that it is the EMEP matrix that is crucial as long as we are willing to make the assumption that the damage cost function is linear. A few things should be noted about the figures in this table (some of which also apply

to later tables). First, a few countries are required to abate their emissions of sulphur up to the maximum amount. In this group are the UK, Czeckoslovakia, East and West Germany and a few others. In view of the rather arbitrary upper limits on emission reductions that have been imposed on the solutions, it can be concluded that these countries would have to reduce their emissions further given a more realistic cost of abatement function, Furthermore, it should be observed that the total emission reduction required is about forty percent, which is more than the thirty percent agreed upon in the "30-~lub".~~ One should also note that the abatement requirements vary very much among the countries. In general, the Scandinavian countries are required to abate less than the central European countries. One reason for this is that abatement in the Scandinavian countries has already driven up the marginal control cost so that it would be cheaper from an European perspective to reduce the emissions elsewhere. But, perhaps a more important factor is that Scandinavia is downstream or "downwind" in the EMEP model relative the rest of Europe. Moreover, the Mediterranian countries are at average, not required to do as much abatement as the countries in Central Europe. This is so because the damage in Africa and Middle East from their emissions is not included in the analysis. Finally, a few countries will end up with net losses. It would not be rational for any country to sign a binding agreement by which they would expect losses. Therefore, we can conclude that even if binding agreements between countries on emission reductions could be made, we should not expect a full cooperative solution to result, unless the strategy space for each country is expanded to include sidepayments. Without sidepayments, we would not expect the UK, Italy and Spain to agree on an emission control plan that would result in non-negligible losses.

lo The "30-club" is a group of European and North American countries that have agreed to reduce their emissions by at least 30 percent.

244

5 PARETO DOMINANT OUTCOMES Assume that sidepayments are not feasible. What would be a "good" outcome if the countries would cooperate? One such outcome would be an agreement on emission reductions that would minimize the total European damage- and emission costs but that would leave no country worse off. That outcome (the Pareto dominating outcome - Pdo) is given in Table 2. TABLE 2 Net benefits when no country is made worse off (Pdo). Emission control 1000 ton SO2

ALB AUS BEL BUL CZE DEN FIN FRA GDR FRG GRE HUN IRE ITA NET NOR POL POR ROM SPA SWE SWI

TUR USSR UK W G TOT

11 33 123 181 1219 130 24 119 1026 1183 303 635 57 508 119 3 571 26 83 116 6 10 299

Percentage reduction

Benefits mill. D Mark

465

42 22 40 36 75 86 14 12 79 86 86 77 82 27 70 6 28 32 83 7 3 24 62 7 40 79

225 565 2 416 0 549 173 0 1437 0 329

8440

37

5892

444 747

22 314 96 27 148 119 8 696 0 242 52 2 6 0

464

245

The total benefits are reduced by about 6 percent compared to the full cooperative solution with sidepayments if sidepayments are not allowed. The total emission control in Europe would also be about 6 percent smaller in the Pdo than in the full cooperative solution. The main difference between the two solutions is the level of emission control in the U.K. In the Pdo the U.K. is required to abate 40 percent of the initial emissions while in the full cooperative solution it is required to abate 81 percent. However, when side payments are not feasible, it is not certain that the countries would agree on minimizing the total European damage- and control costs. The main reason for choosing the minimization of the total damage- and control cost is that this would yield a maximal surplus which could be distributed among the countries in some way and thereby secure

TABLE 3 Maximum potential gains from individual minimization; million D mark. Countries

USSR

ALB AUS BEL BUL CZE DEN FIN

17 115 253 131 24 477 57 20 10

Poland

Germany

16 246

17 97

17 76

17 39

11 209 122

232 129

96

62

130

687 6 330 56 11 7 49 434 131 190

629 224 57 19

407 57 10

300 890 57 2 1

335

477 222 864

146

440 2

452 6

388

423

176 1737

608 135 1492

146

176 1276

125 1360

386

345

349

316

477 224 455

SWE SWI USSR UK YUG

UK

3

FRA GDR FXG GRE HUN IRE ITA NET NOR POL POR ROM SPA

Sweden

96 368

246

for each country a maximum payoff. With no sidepayments, the interests of the countries are much more in conflict with each other. In order to analyse this issue, the following simulations were carried out. The optimal allocation of emission control was calculated when the objective was to minimize the total damage and control cost in the USSR, Sweden, the U.K, Poland and the two Germanies combined, respectively. Each of these calculations then shows the m h u m potential gain each of these countries could expect from participating in the cooperation. The reason The Federal Republic of Germany and the German Democratic Republic are combined is simply that they are very similar with respect to the atmospheric transport model. The results are given in Table 3. Table 3 is quite revealing. It is quite clear that Sweden should have a very strong interest in reducing the total emissions. When the Swedish net benefits are maximized, she gains only 11 per cent compared with the Pdo and only 0.3 percent compared with the full cooperative solution. The important role the UK is playing is also clear. If the British benefits are maximized, the net benefits in many countries would drop to zero. It is also clear from the table that Czeckoslovakia would gain quite a lot, irrespective of which country is maximizing. If the Germans would be successful and more or less dictate the emission control strategy, Poland would suffer because it would then be forced to reduce its emissions to such an extent that its own net benefits would fall to zero. Anyhow, the table shows that the countries have quite disparate wishes in negotiations on voluntary restrictions of emissions. 6 COALITION FORMATION

Instead of either paying some countries for reducing their emissions (with side payments) or in some other way making concessions (for example by making extra big emission control efforts) in order to achieve an agreement involving all European countries, some countries could try to form coalitions to find out whether they could do better than on their own. In theory, this should be analysed with the aid of cooperative game theory, but as has already been pointed out, the sheer number of countries makes it almost impossible to calculate the characteristic function and the equilibrium concepts that are based on it. However, a few analytical results can be derived. Assume that the vector E of national emissions is a candidate for ?n agreement. That vector is blocked by a coalition M of countries if there exist emission levels Ei for the countries in the coalition such that no country in the coalition is worse off and at least one is better off, irrespective of what the other countries do. A vector E is said to belong to the core if it cannot be

247

blocked."

An allocation of emissions among countries that is in the core has thus-a

certain stability. No coalition can do better for itself than it can with a vector in the core, because the countries outside the coalition can "revenge" by making certain changes in their emissions. However, this concept is not terribly interesting because all Pareto efficient allocations will belong to the core. The reason is that a coalition trying to block a vector in the core can be met by big increases of emissions from the countries outside the coalition. Only if the coalition consists of countries that do not import any sulfur from other European countries, would it be able to block a Pareto efficient allocation. The only such coalition would consist of Iceland alone, a not very interesting case. Moreover, the only way countries outside a coalition M can prevent M from blocking is by increasing emissions and thereby increasing their own damage cost. This threat is therefore hardly credible. A more interesting equilibrium concept is the strong equilibrium."

This concept is

based on a more restricted assumption of what countries outside the coalition will do. In particular, a coalition can upset a vector E if there exists E;, for all i in the coalition, such that none of the countries in the coalition is worse off with E;, given that the countries outside the coalition will not find it to their advantage to change their behaviour (is. their emissions). In terms of the model in this section, this means that a coalition could gain by playing the noncooperative game against the coalition of all other countries. It is shown in the Appendix that if the EMEP matrix were symmetric, the set of emission allocations that are strong equilibria would be empty if the number of countries is sufficiently large. However, it is possible to extend that argument to an asymmetric EMEP matrix as long as all countries are damaged by acid rain and they also contribute to the rains. Thus, in the European acid rain game, one should therefore not expect to find strong equilibria. Any Pareto efficient allocation of emissions can therefore be upset by a coalition that can do better on its own compared with a complete European agreement. However, in spite of this rather negative result, quantitative studies of the economic l1 This concept and the following one - the strong equilibrium - is defined and discussed in most textbooks on game theory. For a lucid discussion see Luce and Raiffa (1964). The concept of strong equilibrium is discussed in Dasgupta and Heal (1981), Chapter 2.

l2See Dasgupta, Heal, op.cit.

248

TABLE 4 Net benefits with coalition formation. Coalition members

ALB AUS BEL BUL CZE DEN

FRA GDR FRG GRE HUN IRE NET NOR POL POR ROM SWE SWI TUR USSR W G TOT

Emission control 1000 ton SO2

9 29 106 127 1219 124 91 1040 1183 303 635 11 99 3 560 5 83 5 8 299 465 9011

Percentage reduction

Benefits mill.

D Mark

37

20 35 34 75 82 9 80 86 86 77 15 58 6 27 6 83 3

19 62

22 277 50 33 125 127 466 -47 78 51 -9 -1 400 175 544 0 398 478 95

79

1377 253

391)

6002

Non-coalition members FiN ITA SPA UK

TOT EUROPE 1) average for all countries

5 148 5 87 246

40

249

incentives for various coalitions may yield further insights. In this section, one particular coalition will be studied, namely the coalition of all countries that are not making a negative net benefit in the full cooperative solution. Thus, we will look at the coalition consisting of all countries except Finland, Italy, Spain and the UK. These countries, not in the coalition, are assumed to maximize their net benefits. As the marginal damage cost does not depend on the emissions in other countries, it follows that they will carry out their Nash-strategies, i.e. they will stick to their initial emissions, whatever the coalition decides to do. The result is shown in Table 4. The total net benefits accruing to the coalition is less than what the coalition could have obtained by having cooperation with all countries and compensating those countries that would have experienced negative net benefits. The net benefit to the coalition would in that case have been 6248 million D-Mark after sidepayments of the order of 451 million D-Mark had been made. Moreover, the emission control in Europe would be significantly lower with the non-coalition countries outside an agreement. However, Table 4 shows that both Italy and the UK have strong incentives to stay out

of any agreement. By staying outside and sticking to the Nash-strategies, both countries can gain significantly. This is probably what can be seen today on the scene of international negotiations on emission control, at least for the role played by the UK. Thus, although this analysis is far from complete, in that it does not study the coalition formation systematically, it gives some insights into the possibility of international bargaining. 7 SUMMARY

In this paper, an attempt has been made to accomplish two objectives: to create an analytical framework for problems of international cooperation on transboundary pollution and to present a first round of estimates of the incentives different European countries may have to participate in such cooperation on controlling sulphur emissions. The framework chosen has been the theory of cooperative games. The formulation of the conflicts between different European countries as variable sum game has certain advantages. First of all, it points out and identifies the strategic aspects of the behaviour of the different countries at the negotiating table. It also identifies the kind of gains that a cooperative outcome would imply. Finally it gives a means of quantifying the net benefits to the countries from participating in European cooperation. More specifically, the present situation was assumed to represent a Nash non-cooperative equilibrium, in which each

250

country optimizes its own net benefit, taking the strategies and payoffs of the other countries into account. By assuming that the damage cost function is linear in the deposition of sulphur and by using some crude estimates of the cost of controlling sulphur emissions it is possible to calibrate the damage cost function with the help of the EMEP atmospheric transport model in such a way that the present situation represents a Nash equilibrium in the corresponding model of the game. Having thus calibrated the damage cost function, calculations of the gains for the different countries from different cooperative solutions can easily be made. The common conclusion from almost all simulations was that there is a need for international transfers in order to motivate all countries to participate. Thus some countries should be bribed to reduce their emissions. Only if the cooperative agreement is such that not all possibilities of mutual gain are exploited it will be unnecessary to make such transfers. However, even the full cooperative solution in which the countries agree to reduce their emissions in such a way as to minimize the total European damage- and control cost is not stable for coalition

formation. It was shown that the set of strong equilibria, is. agreements on reductions such that no coalition of countries could do better on their own, given that the other countries minimi7.e their costs, is problably empty. Thus, it may very well be so that for every possible agreement, there exists a coalition that could upset that agreement. The reason the conclusion is rather vague is due to the fact that it was shown for a symmetric game of managing a common property resource that if the number of players is great enough, there is no strong equilibrium. However, we have no indication on the precise meaning of "great enough". Moreover, the European acid rain game is highly asymmetric. Nevertheless, as long as countries are mainly concerned with their own welfare, it seems that international transfers are necessary to support European wide agreements on emission reductions. In this paper, these transfers have been assumed to be cash payments. However, other kinds of transfer of wealth or command over resources are possible.

251

APPENDIX Assume there is a common property resource which is exploited by n agents. Let the benefit to agent i from exploiting the resource be B1(3,Xy), where 9 is the amount of j exploitation on part of agent i. B’ is assumed to be increasing in its first argument and decreasing in its second argument. In terms of the acid rain game, B’ could be interpreted as the negative of the damage and control cost in country i, C

3 emission in country i and

5 the deposition of sulphur in country i (thus the EMEP matrix would simply consist of

“ones”in all cells). Let us assume that the benefit functions are the same for all agents. That makes the game completely symmetrical and each equilibrium concept will give the same value of

3

for all agents. The Nash equilibrium is defined as p defined by

+Bz(P,S)

Bl(p,S)

=

0

where B1 and B2 are the partial derivatives with respect to the first and second argument resp. h

The Pareto efficient equilibrium x is defined from h

A

h

h

+ IIB~(X, W

B ~ ( x, w ,)

)

=

0.

where subscripts denote derivatives. We will show that for n great enough, there does not exist a strong equilibrium. Let M be a coalition of agents that tries to upset x‘. Let M have m members and let the complementary coalition have s = n - m members. Assume that the members of M chooses % in such a way that B(x,, % + sxs> = mxmB(x, mx

+ sxJ.

In a similar way, the complementary coalition will choose % in such a way that B(a,

+ sxs)

=

mxzB(x,”m + =I.

If n is sufficiently greater than m, xs will be close to x’ and it follows that A

B(%,%

+ sxs) 2 B(x

h

,mx

A

+sx)

N

h

B(x , mx

h

+ sx

A

) = B(x

h

,w

).

Thus if the number of agents is sufficiently large, it is possible to find a coalition that would upset the Pareto efficient solution. REFERENCES

Amann M. and G . Kornai, 1987. Cost Functions for Controlling SO2 emissions in Europe. Working Paper May 1987, WP-87-065, IIASA, A-2361 Laxenburg, Austria.

252

Air pollution across national boundaries, 1972. The impact on the environment of sulfur in air and precipitation. Sweden's case study for the United Nations Conference on the human environment, Stockholm. Binmore K. and P. Dasgupta, eds, 1986. Economic Organkations as Games, Basil Blackwell Ltd. Dasgupta P. and G.Heal, 1981. Economic Theory and Exhaustible Resources, Cambridge.Eliasson A. and J. Saltbones, 1983. Modelling of long-range transport of sulphur over Europe: a two-year model run and some model experiments. Atmos. Environ. 17 14571473. Friedman J., 1986. Game Theory with Application to Economics, New York. Hinrichson D.,1986. Multiple Pollutants and forest Decline, AMBIO, Vol. XV,No 5. Lehmhaus J., J. Saltbones, and A. Eliasson, 1986. A modified Sulphur Budget for Europe 1980, EMEP/MSC-W Report 1/86, Norwegian Meteorological Institute, Oslo. Luce D., H.Raiffa, 1964, Games and Decisions, New York 1964. The Norwegian Meteorological Institute, 1987. Sulphur Budgets for Europe for 1979, 1980, 1981,1982,1983,1984 and 1985. EMEPNSC-W Not 4/87.

253

INDEX abatement costs 232 Abelson, J. 188 acid depositions 69 acid rain 231 adding up restriction 129 age distribution of forest 55 air poilution 105,123 air quality 131 altruistic motives for existence values 39 Amam, M. 239 Arrow, K.J. 162 Arrow-Debreu 54 asbestos 139 asessed valuation 22,25 assessor’s valuation 19 averting behaviour method 109 model 110 extended model 115 Barro, R.J. 163. Bartik, T. 111,114,142 Baumol, W.J. 1,59 Beld, C.A. van den 188 Bell, C. 163 benefit estimation 219 bequest motive 39

Berck-Johansson-LofgrenmodeI55 Berger, M.C. 108,109,111,114,116 Bhagia, G.S. 107 Bhagwati, J.N. 162 bias of contingent valuation method 9,26,108 bid curve 136 bidding games 90 bidding scheme 75, 96 bids 27 binary logit estimates 150 Binmore, K. 233,237 Bishop, R. 33,38,39,43 Blinder, A.S. 144 Blitzer, C. 163 Boadway, R.W. 162,167,177 Bockstael, N. 114,115 Bohm, P. 175 Bowes, M. 50 Bowes-Krutilla model 55

Boyle, K.J. 38, 39 Bradford, D.F. 124,130 Brautigam, R. 220 Brewer, D. 220,228 Brookshire, D. 15-18,29,37,109 brown trout populations 101 budget constraint 18 budget share equation 130 Burt, 0.220,228 Cameron, T.A. 134 Carson, R.T. 37,84 Chernobyl74 Chestnut, L. 106,109,116, 117,120 choke price 22 Christainsen, G. 191 Christensen, L.R. 126-129 cIassical unemployment 168,191 climatic change 2,11 coalition formation 246 collective preferences 11 combustion technology 232 commodity specification bias 71 common property resource 2 compensating surplus 26 compensating variation 41,45, 72, 107 ex ante 41,45 compensating wage differentials 139, 141 compensation 28 compensation function 125 complex policies 219 conflicting services of forests 49 consistency test 43 constant budget bias 72,78,90 consumer surplus 34 expected measure 42 Marshallian 34 Hicksian 34 contingent markets 71 contingent valuation method 4,9, 15, 22,26,69,70, 123, 131 and payment cards 74 and health 108 control cost function 232 Cooper, B.S. 106 Cory, D.C.47 cost and benefits of regulations 139 cost benefit analysis 10, 187

254

macroeconomic 187 social 187 and disequilibrium 10 cost benefit rules and general equilibrium 167 and disequilibrium 167 cost function of forestry 59 cost of illness method 106 cost of job-search 143 Courant, P. 114 Crocker, T. 16,77, 119 Cropper, M.L. 117, 119 Cuddington, J. T. 163, 167, 169, 173, 182 Cummings, R. 28,72,108,123 Curington, W.P. 141 cutting patterns of forests 65 cutting rules in forestry 59 d’Arge, R.C. 4, 15,26,33,72 damage function estimates 107 damage functions 108 Dasgupta, P.S. 162,190,175,233,237, 247 De, V. 109,134 delphi-technique 77 demand system partial 125 full 125 Desvousges, W.H. 15,116 Devarajan, S. 163 Dickie, M. 7,105,109, 115,117 Diewert, W.E. 162 Dillingham, A.E. 140 diminishing marginal utility 30 direct market values methods 4 discount rate 27, 162 discounted and undiscounted profits in forestry 65 disequilibrium cost benefit rules 161 distortion of relative prices 3 Dixon, J. 188 Dorsey, S. 140 dose-response functions 78, 108 Dreze, J.H. 163 Dreze, J.P. 163 dry deposition 233 Duncan, G.J. 140 Dupuit, J. 161, 219 Durden, G. 26

earnings in manufacturing 148 Eckstein, 0. 162 economic r e g h e 196 EMEP model 233 employment 162 endangered species 38 Engel elasticity 87 environmental attributes 55 environmental policy 139 environmental regulation 139 environmental value of trees 51 EPA 139,155 Epple, D. 142 equivalent compensation 72 equivalent variation 107 ethylene oxide 139 exchange rate 164 existence value 38,43,73 expenditure function 125,136 expressed values 120 externalities 1,140 externality in consumption 49,51 fatal injury risk award 152, 154 Feenburg, D. 28 Feldstein, M.S. 194 first best optimum and forestry 67 fish and acidification 69 Fisher, A. 84,105 Fisher, I. 52 Fisherian separation theorem 52 Foley, D. 49 Forest and rangeland renewable resource planning act 50 forestry 49 and cutting technology 40 forestry ban 40 FORPLAN 50 Fourgeaud, C. 163,182 free riders 71 Freeman, A.M. 4,17,26,123, 188, 198 Friedman, J. 142, 239 Friedman-Savage diagram 45 Friedman-Savage theory 10 full cooperative solution 235,241 with sidepayments 241 functions of the environment 2 future generations 11

255

Gallaway, L.E. 143 Gallup 46,74 game theory and environment 10,231 GAMS 241 Gegax, D. 140 general equilibrium approach 56 Gerking, S. 7, 105,111, 117, 119, 140 goals of economic policy 3 Golan, L. 7,123 government and cost benefit analysis 165 Graham, D.A. 47 Green, A. 109 Greenly, D.A. 37,73, 84 Gregory, R. 72 Crossman, H.I. 163 Guesnerie, R. 182 Hammond, P. 182 Hanemann, M. 125,134 Harberger, A.C. 162,167,177 Harford, J.D. 110 Harrington, W. 108,111, 114 Hartman, R. 49,55, 59 Hartunian, N. 106 Havemann, R.H. 190,191 Heal, G. 247 Heal, M. 175 health and safety 139 health benefits 105 health technology 116 Heberlein, T.A. 39,43 hedonic 15 hedonic equations 24, 153 hedonic equilibrium conditions 143 hedonic price 28 hedonic price equation 19 hedonic pricing method 4,71, 123 hedonic wage equations 139,140 Herzog, H. 7,143,144 Herzog, Jr., H.W. 139 Hicks-Kaldor compensation test 219 Hicksian compensated demand function 125 Hildebrandt, G.G. 124 Hinrichson, D. 233 history of economic thought 1 Hite, M. 50 Hoehn, J. 8,219,226

HoMund, B. 140 Hori, H. 115 Hotelling, H. 1, 162 Hotelling’s rule 175 housing prices 127 Hufschmidt, M. 188,190 human capital 143,144 hypothetical bias 71 IIASA 240 illness cost prevalence based 106 incidence based 106 illness symptoms 128 imperfect information 142 implied value of life 154 imputed bids 27 incentives 2 indirect utility 166 indirect utility function 38,47, 51 cardinal 38 industry switching 143,144 determinants of 151 inflation 27,191 repressed 191 information bias 71 input-outputmodel 201 instrument bias 71 interindustry mobility 139,143, 150 international dimension of environment 10 intertemporal equilibrium 55 intertemporal multi-sectoral model 161 investment function 172 isocostline and health 113 isoquant and health 113 Jaksch, J. 107,110 James, M.D. 134 Jansen, E. 88 Jensen’s inequality 41,43 job-related risk 139 Johansson, P.O. 5,6,7,37, 42,43, 49,50,55,60, 161,163, 164,167, 173,175,177,190,191 joint production 115 Just, R. 26,124,126,177 Kahenman, D. 132 Kaldoriau compensation criterion 165

256

Kapp,K.W. 1 Kendrick, D. 241 keynesian inflation 211 keynesian inflationary disequilibrium 197 keynesian macroeconomics 163 keynesian unemployment 161,168, 170,174,190,208 Kim, M. 7, 123 Klaassen, G. 192,200,202 Knetsch, J. 5, 28, 72 Kornai, G. 239 Kosters, M. 149 Krutilla, J. 33,50, 162, 190 Kuhn-Tucker condition 17,56 Kurz, M. 162 Kuyvenhoven, A. 190 Kydland, F.E. 182 Lagrange multipliers 57 Lal, D. 190 Lave, L. 119,220 learning process and contingent valuation 76 Lesourne, J. 162,167,190 liming of freshwaters 70,74 Lindhal equilibrium 54 Little, I.M.D. 162, 190 Loehman, E.T. 109,134 Lofgren, K.G. 6,7,49,55,60, 161, 164,177,191 Luce, D. 247 lump sum 125 lumpsum transfer 54, 165 Maass, A. 162 macroeconomic benefits 198 macroeconomic cost benefit analysis 187 macroeconomic effects 163 Maler, K.G. 4, 6, 9, 49, 50, 54, 124, 188,231 Malinvaud, E. 63 Maneschi, A. 163 Manser, M.E. 129 m;saufacturing employment 146 Marchand, M. 164,168,173,182 Marglin, S. 162, 190 market failure 152 market for securities 196

market price 139,152 of risk reduction 152 of safety 139 market valuation 15 Martin, A.140,142,149 Matzow, D.91 maximim sustainable yields of forests 64 Mayo, S.K. 142 McConnel, R.114,115 McKean, R.N. 162 McKenzie, G. 26,125 Meade, J.E. 162 medical services 128 medication expenditure 128 Meeraus, A. 241 Mennes, L.B.M. 190 microeconomics 163 Middelhoek, A.J. 188 Milleron, J.C. 49,54 Mills, E. 28 Mincer, J. 143,144 Mincer’s model of schooling 142 Mirrlees, J.A. 162, 190 Mishan, E.J. 190 Mitchell, R.C. 37, 72,84 Mitra, T. 64 model of wage determination 144 money metric utility 125 money supply 195 money values of a forest 49 morbidity and air pollution 105, 123 Morey, E.R. 125,220 mortality and air pollution 105,123 Mullahy, J. 107 Mullen, J.K. 91 multipart policy 222 Munitz, F.P.69 Musgrave, R.A.162,194 Nash equilibrium 237 natural resources, 1,175 non-renewable 175 Navrud, S. 6,69, 108 Neary, J.P. 164,169 Nentjes, A. 8, 187, 200, 202 neoclassical equilibrium 206 neoclassical unemployment 207 nitrogenoxides 231 Noll, R.220

257

nominal wages 144 non-cooperative equilibria 235 non-market asset prices 15 non-respondents 28 non-use values and contingent valuation 85 nonconvexities 54 nonrespondent bias 72 nonuser value 33,73 normalized prices 124 O’Connor, C.J. 142 OECD 191 Ohlsson, H. 175 Okoboji 15 once and for all payment 40 opportunity cost of capital 162 of labour 162 OSHA 139,155 Ostro, B. 107 Overrein, L.N. G9 Panzar, J.C. 59 Pareto dominant outcomes 244 Pareto optimality 49 Pareto optimum 53 Pearce, D. 125, 188, 190 perceived air quality changes 132 perceived pollution level 128 perfect and imperfect labour markets 142 Peskin,H.M. 2 Pigou, A.C. 1,187 planning horizon 63 Pollak, R.A. 115 polluter pays principle 76,92 pooled regression 25 Porter, R.C. 114 Portney, P.R. 107,108,111,114 Prescott, E.C. 182 present value function 164 present value maximization 50 preservation of species 38 price-hyperplane 54 probability of programmes 40 property rights 3 protest bids and contingent valuation 76 protest zero-bids 83

Psacharopoulos, G..140, 142,149 pseudoequilibrium prices 63 public finance theory 163 public goods 37,123 valuation of 37, 123 and risk 37 questionnaire 49,69 example of 96 techniques 49 Raiffa, H. 247 Rand&, A. 8,71,125,219 rational expectations 181 realtor’s best estimate and hedonic estimate 32 realtors and real estate agents 22 recreational values 49 referendum 134 regression and WTP 85 regression estimates 31 of WTP 86 regressions coefficients 24 regulations 2 rent gradient 18 residential market 19 revealed values 120 Rice, D.P. 106 risk aversion 41 risk of fatal injury 144 risk valuation 141 risk-aversion 44 and women 44,46 and male respondents 46 Roberts, K.W.S. 163, 169, 182 robustness of CVh4 134 Rosen, S. 18,141,149 Rosseland, B.O. 69 rotation period 49,50 Rothbarth, E. 169 Rowe, R. 109,116 Roy’s identity 128 Saliba, B.C. 47 SAS SYSNLIN procedure 129 Schlottmann, A. 7,139,143,144 Schulze, W.D. 15, 19,37,73, 109, 119,

140 Seip, H.M. 69 Seller, C. 15 Seskin, E. 107

258

Sevaldrud, I.H. 69 shadow price 3,49,54,188 Shechter, M. 7,123,128 Shogren, J. 4, 15,26,72 significance levels 132 Sinden, J. 28,72 site valuation 15 Smith, A. 139 Smith, R.S. 116,141,153, Smith, V.K. 43 social cost benefit analysis 187 society’s welfare function 166 Somers, G.G. 175 specification uncertainty 119 Srinivasan, T.N.162 Stanley, L. 111,117 Starret, D. 55,167 starting point bias 71, 109 statistical WTP functions 85 steady stae and forestry 66 Stiglitz, J.E. 164, 167 Stoevener, H. 107 Stoll, J.R. 125 Strand, J. 73,77,84,89,90 Strang, W.J. 55,69 strategic bias 71 strategic incentives 29 Sugden, R. 190 sulfuroxide 231 sulphur emissions 69 sustainable economic development 1 technical spin-off 200 techniques to reveal preferences 70 Thaler, R. 149 Thompson, C.S. 88 Tiebout, C.M. 143 timber prices 49 timber supply 49 Tinbergen, J. 162 translog function 126 travel cost method 71,91 travel cost models 22 Tsuneki, A. 167 Turnovsky, S.J. 48 Tversky, A. 132 uncertainty and contingent valuation 37 UNIDO 190

use value 33,38,43,73 utility curve 18 utility function direct 124 indirect 124 utility maximization 17 valuation direct 123 indirect 123 of benefits 29 of health and life 4 of life 139 of the environment 2 value of life 105,140,153 of safety 105 value additivity theorem 50 values revealed 120 expressed 120 Varian, H.R. 125,128,165,177 Vaughan, W. 26 vehicle bias 71, 109 Violette, D.M. 91, 106, 117, 120 vktual price 172 Viscusi, W.K. 142,153 Wachter, M. 115 wage bargaining 149 wage determination 147 wage rate 197 wage-risk trade-off 140, 141, 152 wagelearnings equations 155 Waldmann, S. 139 Walrasian model 189 Walsh, R.G. 73 Wan, Jr, H.Y. 64 water quality 15 water quality ladder 26 Watson, W. 110 Weinberg, D.H. 142 Weisbrod, €4.177 welfare 39 welfare change 130 and air quality 123 welfare economics 34,187 welfare measures 124 well-defined market 33 wet deposition 233

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Wijzga, R.E. Williams, A. 190 Willig, R.D. 27, 34, 59 willingness to accept 20,28 willingness to pay 3,20, 28,30,37, 40,44,53,63,72,82,112 and health 112 and air pollution 131 and risk 143

and risk reduction 140,152,153 for improvement of fish populations 80 versus willingness to accept 28 Wood, W.D. 175 Woodbury, S.A. 128 World Bank 241 Zeidner, M. 128 Zuidema, T. 194

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