The Economics of Social Protection

The Economics of Social Protection

The Economics of Social Protection Lars Söderström Professor Emeritus of Economics, Lund University, Sweden

Edward Elgar Cheltenham, UK • Northampton, MA, USA

© Lars Söderström, 2008 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 or photocopying, recording, or otherwise without the prior permission of the publisher. Published by Edward Elgar Publishing Limited The Lypiatts 15 Lansdown Road Cheltenham Glos GL50 2JA UK Edward Elgar Publishing, Inc. William Pratt House 9 Dewey Court Northampton Massachusetts 01060 USA A catalogue record for this book is available from the British Library Library of Congress Control Number: 2008929274

ISBN 978 1 84720 239 0 Printed and bound in Great Britain by MPG Books Ltd, Bodmin, Cornwall

Contents List of figures and tables Preface Acknowledgements 1 2 3 4 5 6 7 8

vii ix xi

Introduction Inequality Social justice Pensions: basic model Pensions: extended model Liquidity constraints Income security Benefits in kind

1 15 41 61 84 105 125 147 164 173

References Index

v

Figures and tables FIGURES 2.1 2.2 2.3 5.1 6.1

The Lorenz curve Earnings (EE), income (YY) and consumption (CC) over the life cycle Optimal consumption path for r
 and r Situation for two risk categories, I and II, buying insurance Consumption and savings over the life cycle: three cases

21 25 30 96 110

TABLES 2.1 3.1 3.2 3.3 3.4 4.1 4.2 4.3 5.1 5.2 6.1 6.2 6.3 6.4

Equivalence scales for Greek families with one child Tentative classification of inequality according to Foley, Roemer and Rawls Marginal cost of public funds for a marginal tax increase in the kth income bracket Income dispersion annually and life-long Contribution to the dispersion of income by various components of the public budget Cases considered in the portfolio model Optimum conditions in the portfolio model when R1 Real capital holdings, earnings and savings by individuals of different ages Implications of second order conditions for utility maximization Changes in endogenous variables when exogenous variables change The propensity to consume out of wealth: hypothetical values Aggregate household saving as a percentage of total household income Aggregate savings ratio and the PAYG pension scheme The impact of wage and income change on completed fertility vii

17 50 54 56 57 71 71 74 85 86 108 112 113 118

viii

6.5 7.1 7.2 8.1 8.2a 8.2b 8.3 8.4

Figures and tables

Private returns from schooling for men and women, 1997–2000 Pay-offs to the insured and the insurer in the two-person non-zero sum game Employment ratio, sickness absence, unemployment and temporary contracts Co-insurance and health care consumption Demand, out-of-pocket costs and tax rates with different caps and subsidies Out-of-pocket cost, risk premium and total cost with different caps and subsidies Aggregate effects of introducing co-insurance in the financing of health care Consumption of health care in different income groups when subsidies vary

121 128 137 153 156 158 161 162

Preface On and off, I have been analysing various aspects of the welfare state for almost forty years. It started with an invitation to participate in a government inquiry on remaining poverty in the Swedish welfare state. Who was poor, and why? My task was to find suitable measures of an individual’s or family’s income and wealth, and to collect relevant statistical data. Some of this work can still be traced in tables on the distribution of income presented by Statistics Sweden. I then returned to the university to teach public finance and social insurance, and to form a seminar group to discuss various aspects of the economics of human capital, in particular health economics. Particularly exciting for me in the 1970s was participating in the workshop run by Gary Becker while I was a visiting scholar at the University of Chicago. Back in Lund, I became engaged in a campaign to change the Swedish tax system. Inspired by Knut Wicksell and Erik Lindahl, we formed a group in Lund to argue in favour of the view that taxes should be seen in relation to the kind of expenditures they were supposed to finance. Instead of discussing whether taxes, in general, should be direct or indirect, progressive or flat, and so on, we tried to find out the best way to finance health care, public pensions, income security, and so on. Much of this book is based on the discussions we had at that time. It is fair to say, I believe, that this is a book on social protection for the middle classes. It is not about social assistance and ‘welfare’ directed toward the poorest members of society, and it is not about the kind of protection needed by the wealthiest. Instead, it is a book about ways and means to secure a decent living standard for an average citizen in case of a lack of working ability and/or unemployment. Providing such protection is, in my view, a fundamental aspect of civilization. It is fascinating to see how this was done in ancient cultures, and how it is done around the world today. The rather desperate search for institutions for social protection after the collapse of communism in Eastern Europe is illustrative, and we are now witnessing how (truly) developing countries are trying to establish a society where people may feel economically safe. The purpose of this book is to present an overview of the kind of advice economics can offer on the design of institutions for social protection. The reader I have in mind has passed the introductory courses in economics, and now seeks an orientation of main issues rather than a comprehensive ix

x

Preface

account of the research frontier on the welfare state and its alternatives. For those interested in the latter there are ‘handbooks’ and surveys intended for specialists in the field. My experience is that this kind of book, supplemented with a selection of (downloadable) papers of particular interest, fits well into a course at the intermediate level. However, I hope that there will be something of interest for the layman as well. To my knowledge there are presently no close substitutes for this book. I am grateful to all, colleagues, students and administrative staff alike, who, over the years, have helped me formulate the views expressed in this book. In particular, I am indebted to Andreas Berg, Margareta Ekbladh and Eric Rehn for information and comments, to Jaya Reddy for improving my language, and to Anna Hedborg for asking me to present a survey of what economic research has to say about income security, thereby giving me the necessary push to get started with the manuscript for this book. I am also grateful to the Department of Economics at the National University of Singapore for inviting me to stay there last winter to work on the manuscript. Lars Söderström Lund, 2008

Acknowledgements Permission from American Economic Association, Centre for Business and Policy Studies (SNS), European Institute of Education and Social Policy, and Trentham Books Ltd, to quote from my earlier publications is gratefully acknowledged.

xi

For Margareta

1.

Introduction

Periods of reduced or non-existent working capability (childhood, old age, illness) are experienced by all. Moreover, situations have to be faced when capabilities cannot be used to their fullest (lack of demand, unemployment); or when the return from work is unexpectedly low (for example, because of crop failure); or when consumption needs are exceptionally large, for example in connection with a fire or an illness. Solving these kinds of problems is one of society’s major functions, perhaps the most fundamental function. Under normal conditions, where life actually requires a great deal of labour, these problems must be solved through cooperation. The solution is to create pools enabling several persons to share the fruits of each other’s labour. How these pools are organized is of fundamental importance for the character of a society and its possibilities for development. We refer to arrangements serving this purpose by the term social protection. An extreme case is the pure socialist model where all earnings are placed in a common ‘pot’ and shared according to need. Another case, no less extreme, is the pure market model where all resources are allocated through different financial arrangements (banks, insurance companies, and so on) to the extent that individuals decide through mutual agreements. Between these extremes are models with differing degrees of cooperation. One of the most important organizations for the pooling of resources is the family. Arrangements for social protection may be studied from a long-term or a short-term perspective. From a short-term point of view (which dominates in the general debate) it is natural to emphasize people’s differences and view the pooling of resources as a means to change the distribution of income in society. It seems, then, that the aged, sick and unemployed receive benefits at the expense of people who are young, healthy and employed. From a long-term point of view, however, things look different. Nobody may count on being healthy, employed, and so on, for an entire lifetime. In the long run the pooling of resources is clearly a mutual concern, where the objective is not mainly to redistribute incomes among individuals but to render more effective the use of each individual’s earnings in society. The idea, then, is that one should have access to consumption possibilities when they are most needed.

1

2

The economics of social protection

AGENTS OF SOCIAL PROTECTION The Family A resource pool may be arranged as a common household for individuals belonging to several generations. Members of the household do not have to be related to each other, but family ties certainly contribute to strengthening the household. This is the family model where transfers take the form of gifts. Children and the aged are supported by the middle-aged who voluntarily refrain from consuming all incomes themselves. This does not mean that these persons are motivated by altruistic reasons. As mentioned above, everyone may expect to become dependent on the support of others. By being generous today, the middle-aged may hope to meet generosity from others tomorrow. This probability increases if children are brought up to regard giving as a duty. The importance of transfers within families and other groups has been eloquently stated by Oded Stark (1995). For a biological family it would seem natural to use transfers in kind. For example, children and the aged may be given shelter, food, clothes and other necessities to the extent deemed suitable. For a family living in a monetary economy, an alternative would be that transfers are given in cash, either as a lump sum or as a voucher for certain consumption. Different types of transfers can be mixed. For a child one can supplement food, housing and other benefits in kind with special accounts for the purchase of items such as clothing, as well as a lump sum to be used freely. In this way the receiver is given discretion over the content as well as the timing of at least some consumption. Whether this is a positive or a negative feature of supporting grants will now be left as an open question. Benefit Societies, Insurance Companies and Banks Other private associations for mutual assistance are common among occupational groups or neighbours. The usual arrangement is to form a benefit society (sometimes called a friendly society) such as a sickness or an unemployment benefit society. Members of the society commit themselves, subject to certain regulations, to contribute towards the formation of a common fund from which they are entitled, subject to certain conditions, to receive benefits either in cash or in kind, for example medical care that is partly or wholly paid for by the benefit society. Benefit societies typically supplement the family as a source of security. The distinction that is made here between benefit societies and normal insurance companies is simply that the latter are more clearly commercial in their operations. They sell security and are not normally confined to a

Introduction

3

particular occupational category or neighbourhood. Otherwise, insurance companies operate in the same way as benefit societies. The insured pay a premium that entitles them to receive benefits, subject to certain conditions, from a common fund. It should be noted that benefit societies and insurance companies provide only the basic framework for private security arrangements in society. Access to good banking facilities and so on, and the willingness of other individuals to take part in charitable work provide additional sources of security. Are family members able to obtain a better standard of living for themselves through the market system? To clarify this alternative, let us imagine an economy without any private real capital. Real assets are limited to stores of foodstuff, and so on, for immediate consumption. It is easiest to imagine this example as an economy where all real capital is owned by the state, but one may also think of an economy with practically no real capital at all, for example a nomadic society where people survive by hunting, fishing, picking fruits, and so on. A conceivable possibility in this case is that transfers take the form of loans. One borrows during childhood, saves by paying back the loan and by issuing new loans to younger persons during middle age, and dissaves (has loans paid back) during old age. A typical situation in such a model would be that middle-aged people give loans to children. As children grow up and earn an income, they can repay the loans and thereby provide the older generation with a ‘pension’. It is worth noting that borrowing conditions may be rather poor. Take as an example the case where children are cared for by their parents and therefore do not demand any loans for themselves. The only possibility of obtaining a ‘pension’ is then that older workers give loans to younger workers. Of course, there is no guarantee that the latter have an immediate interest in consuming more than they earn. They may have enough earnings to cover their own consumption as well as the consumption of their children. For older workers the situation may clearly become very stressful. At the same time as they need to give loans in order to secure support for their own old age, presumptive borrowers are far from willing to get into debt. The outcome might be that older workers have to pay younger workers to accept a loan, which would imply a negative rate of interest. Giving loans to younger generations is not necessarily an individual’s only form of savings. If there are other possibilities, for example to buy gold, the situation might be less problematic. Gold may be bought by both younger and older workers, and then sold in old age. Should the distribution of income be unequal in favour of younger workers, then older workers might also be sellers of gold. In this case an individual may buy a large amount of

4

The economics of social protection

gold as a young worker, sell some as an old worker and the rest during old age. There is no guarantee, however, that gold holdings will be profitable, since the price of gold must be increasing over time for this to be the case. With a given stock of gold, this will not be the case unless the economy itself is growing. In the opposite case there will probably be an excess supply of gold and, therefore, a gradual downward pressure on the price of gold. A falling price of gold is equivalent to a negative rate of interest. The State There are, roughly speaking, three ways in which the government might supplement and improve private security arrangements in society. First, government authorities may make an effort to promote conditions of general stability. Policies to reduce cyclical fluctuations and to facilitate structural adaptations in the economy would come under this heading. At a more fundamental level, government policies seeking to improve law and order within the country or to reduce the risk of foreign aggression or natural disasters are also an essential part of the stabilization policy. It goes without saying that a failure of either of these types of preventative measures might have very serious consequences for individual security. Consequently, government policies in this field are of major importance. Second, the government may encourage the growth of private security arrangements. The promotion of stable family conditions and the establishment of associations or companies providing insurance services would be appropriate measures under this heading. An incentive might be provided in the form of a subsidy that might be used to influence the pattern of security arrangements. An early example of this type of social security is the German legislation implemented in the 1880s on the initiative of Otto von Bismarck. With regard to benefit societies, the subsidy may be conditional on the degree of access to membership, meaning that the society cannot be confined to members of a particular labour union, political party, or religious group. As previously indicated, people have a special interest in obtaining ‘child loans’ in one form or another. In the market model, children are potentially the most important group of borrowers. In the family-only model, no loans exist but it is not difficult to imagine a mixed model where parents take loans for the purpose of supporting children. Such loans, more or less subsidized by the state, would be an alternative to the kind of child allowances (or tax deductions) used in many countries. Note how the burden of bringing up children changes in these cases. In the pure family model without any external support, or when parents are borrowers, parents carry the entire cost of their children. To the extent that bequests are reduced,

Introduction

5

however, certain parts of the cost will be passed on to the children themselves. When children are supported out of public funds, the cost is borne by the population at large. In the case of formal child loans the responsibility for repayments rests with each child. Depending on which model is used, an individual is faced with three quite different prospects: (1) to pay the cost of one’s own children, no matter how many, (2) to pay a higher tax in order to finance subsidies to children in general, and (3) to pay back one’s own child loan. In the two latter cases the expense is independent of the number of one’s own children. Third, the government may itself administer different types of social security schemes, such as on a normal insurance basis by means of premiums, funds and benefits. However, the government is able to offer a wide range of other opportunities. For instance, the insurance may be arranged as a general, tax-financed, basic income guarantee. As in the case of private social security schemes, a public system may take the form of both cash payments and benefits in kind such as medical care and labour market training. The two latter categories of government measures – the provision of incentives to private schemes and the government’s own insurance schemes – come under the common designation of social policy. Far-reaching ambitions in this area of policy, particularly when these aspirations are expressed in terms of government administered insurance schemes are characteristic of the welfare state. The principal idea of the welfare state is to guarantee that all citizens can satisfy basic needs. It is typical of the welfare state that (1) entitlements to benefits like child care, schooling, health care and nursing homes are given by virtue of citizenship, refugee status and the like and not merit based; (2) benefits are produced by public agencies, provided in kind and distributed according to egalitarian ideals; and (3) benefits/subsidies are financed by progressive taxation. Compared with the traditional family model, the welfare state has a clear advantage and a just as clear disadvantage. The advantage is that everyone is included. For example, individuals are not required to have children of their own to get provisions for old age. Furthermore, there is no risk that defectors might cause a setback in the standard of living for those remaining in a family. Defection may also happen in a welfare state – as in the case of emigration – but the effect from a social security point of view is likely to be small. (This is not to say that the brain drain, which is a result of people moving out of a country, would lack economic meaning.) A disadvantage of the welfare state is that it generates disincentives of various kinds. Since benefits are more or less independent of each individual’s own efforts, these benefits tend to be forgotten in one’s decisions on the scope and direction of work, savings, and so on. Hence, people behave

6

The economics of social protection

as if their jobs and savings are worth less than they actually are. This will most likely lessen people’s interest in economic virtues, and be harmful to the economy at large. Another disadvantage with the welfare state lies in the fact that benefits are provided uniformly, for example the same amount of schooling and the same elderly care for all. Differentiation with respect to individual needs and interests would make it possible to reach a higher level of utility with the same amount of resources. Such differentiation is easier to obtain in the family. Since people in a family live near each other it should be quite easy to take individual differences in tastes and interests into account. We have so far been referring to an extreme welfare state. In reality, the state’s involvement in social security has a less extreme design, one of the reasons being to keep costs down. One modification is that certain benefits are given as a voucher or in cash. This allows beneficiaries to influence the content of the benefit, especially when the state does not have a monopoly in producing child care, housing and so on. Another deviation from the extreme welfare state is that certain benefits are paid according to merit, making them appear as a wage component. For example, old age pensions might be differentiated, at least partly, according to earnings earlier in life. Through such modifications the welfare state takes on a somewhat different character. Eventually, the role of the state might be reduced to administrating transfers based on the principle of quid pro quo. As in the market model, this means that each person directly pays for his or her own welfare.

THE CORE OF SOCIAL POLICY There is no simple answer to the question of what the state should do in the area of social policy. But we may try to find out what a social policy serving the interest of all citizens would look like. For the sake of argument we assume that this must be implemented with unanimity among those concerned. For obvious reasons it would be difficult to assemble unanimous support for public policies in a world where private solutions do exist and are effective. There would then be nothing to gain from collective actions. Hence, market failures are a prerequisite for such actions. We now limit the discussion to market failures with respect to private provision against risks of income losses and excessive expenditures. The provisions under discussion include some kind of insurance scheme organized by friendly societies, other cooperatives or insurance companies. Each individual (or family) would then pay an amount that covers his or her expected benefit from the insurance (actuarial fees) plus a contribution towards the costs of

Introduction

7

administration as well and, in the case of commercial insurance, an additional amount that reflects the organization’s planned profit. The question of interest here is the extent to which these schemes require state involvement to provide a satisfactory level of social protection. This question will now be examined with respect to the following problems: (1) exclusion and free riding; (2) adverse selection; (3) moral hazard; and (4) collective risks. Exclusion and Free Riding In a system where insurance premiums are charged on an actuarial basis, different categories of risk will pay different premiums. For certain individuals, this system may be prohibitively expensive. For example, for an individual in need of kidney dialysis the actuarial premium for health insurance including dialysis could exceed the individual’s annual income. As a result, this individual would be forced to rely on charity. There are two ways in which charity may be administered. The traditional method is to offer free medical care to those in need. This arrangement may, for example, be organized by a religious group. The other method is to allow the individual to receive regular insurance on particularly favourable terms. This would mean that other individuals covered by the same insurance scheme would have to be willing to pay premiums that are higher than would be justified on purely actuarial grounds. Both of these methods give rise to free riding. In the first case, individuals are given an incentive to evade responsibility for the costs of insurance provision by assuming that they will still be able to receive the benefits they require. A suspicion that people will play this game might make potential donors less enthusiastic about charity. In the second case, free riding could mean that individuals may avoid cooperatives or insurance companies subsidizing premiums for certain individuals. In either case the outcome will be unfavourable for those who are in real need of charity. Adverse Selection The problem of exclusion arises because it is possible to identify those individuals who have substantial expectations regarding insurance benefits. The problem confronting dialysis patients would have been less difficult if their situation had remained unknown to the insurer. However, a different problem then arises, namely that of adverse selection. This problem is caused by the fact that the insurer’s information regarding the policy-holders’ anticipated benefits (risks) diverges from that actually held by the policy-holders themselves (asymmetric information). Adverse selection also arises where

8

The economics of social protection

there is a lack of adequate differentiation of premiums. As a result, premiums diverge from the policy-holders’ expected benefit from the insurance. In essence, adverse selection means that an insurer is unable to allocate people into different risk categories (for example, with respect to longevity) and therefore offers everyone the same premium, corresponding to an average risk. This is considered unfavourable by low-risk policy-holders who become increasingly reluctant to take out insurance cover. As a result, the average risk among those insured, and therefore the average insurance premium, may gradually increase until only those with the highest risk find it worthwhile buying the insurance. As a result of adverse selection, individuals belonging to low- or medium-risk categories cannot be offered the insurance policies that would meet their requirements. An insurer introducing a low-risk alternative onto the market would soon be subject to losses unless he or she could find some way to prevent high-risk categories from purchasing this alternative. The low-risk alternative must therefore contain certain provisos that make it unattractive for high-risk categories, for example a maximum limit on the level of protection. From the standpoint of social policy, the problem with adverse selection is that low-risk individuals are confronted by a situation where they either have no insurance at all or are required to pay a premium that is appropriate only for high-risk individuals. A tax-financed subsidy might be viewed as a more satisfactory alternative. Moral Hazard The imposition of a maximum limit on the level of protection may be motivated by reasons other than adverse selection. One such reason might be a desire to limit the administrative costs of the insurance. The non-payment of sickness benefits for one or several days following the start of a period of illness is an example. As a consequence, there will be fewer claims for insurance benefits. Another motive for less than 100 per cent insurance cover is the problem of moral hazard, which is a particularly severe problem in, for example, unemployment insurance. The fact that work involves a degree of sacrifice means that an unemployment insurance that does not contain an element of co-insurance will provide strong incentives to be unemployed. Such a tendency will be held back when benefits are lower than the loss of income, because of an initial period of non-payment of benefits, limitations in the duration of the payment of benefits, or a less than 100 per cent ratio between the daily benefit and the income loss. An optimal arrangement would depend on the circumstances. We return to these issues in Chapter 7.

Introduction

9

Collective Risks A further reason for restricting the insurance cover available to individuals on the insurance market is that certain risks affect a large number of individuals at the same time. The inclusion of such collective risks in insurance contracts may endanger the financial viability of friendly societies and private insurance companies, as well as call into question the overall economic security of policy-holders. Even today, a common influenza epidemic may give rise to considerable financial problems for a local sickness benefit pool. However, the problem of collective risks is less severe when insurers take the opportunity to buy reinsurance, whereby insurers all over the world may compel themselves to compensate for (a small part of) the damage caused by, for example, infectious diseases, earthquakes or heavy storms wherever they occur. Most cases of collective risks may be covered by reinsurance arrangements but, of course, there are also some collective risks of a global character that may not be included in reinsurance contracts, such as the discovery (in the future) of an inexpensive medicine that effectively prevents heart attacks. If such a medicine came into use, everyone’s life expectancy would increase and insurers all over the world would be faced with a dramatic increase in justified health insurance claims and pension benefits. The normal method of avoiding the problem of collective risks is to exclude them from individual insurance contracts. However, it is difficult to see how this could be carried out in the above example. In this and similar cases, the only apparent option available for the insurer would be to charge a higher premium that allows him or her to set up a buffer fund serving as a precautionary measure for the future. The problem is that some insurers might be tempted to run their business without such a fund, and try to increase their market share by offering insurance policies without the extra charge. This would tend to raise questions about the financial viability of the insurance system. The above arguments point towards government intervention on the market, either by a law stating that a premium surcharge must be levied or by an offer to act as ‘insurer of last resort’. When necessary, this would permit the government to use tax revenues to meet obligations laid down in private insurance contracts.

IMPLICATIONS FOR SOCIAL POLICY Given this picture of the problems confronting private insurance arrangements, what role would be decided unanimously for the government? We

10

The economics of social protection

shall return to this question many times in later chapters. For now it will suffice to give a few hints. 1.

2.

Of the various methods available for smoothing out fluctuations in expenditures over an individual’s life cycle, bank loans would appear to be quite non-controversial. Government obligations are then limited to the provision of the requisite guarantees for such loans. A further step in this direction would be to force adult citizens to have a savings account in proportion to annual earnings or at least covering basic expenditures for a certain period of time, for example three months. Singapore, just to give one example, illustrates how such an arrangement may be implemented. Bank loans do not serve the purpose of pooling risks and are therefore not sufficient as a social policy device; they must be supplemented by arrangements providing basic insurance cover. Let us assume that there is a legal requirement to have a certain level of insurance cover. This would force individuals who are tempted to become free riders to take on the responsibility for their own insurance provision, at the same time as they support those who are unable to pay an actuarial premium for themselves. Still, for the latter category, which may include many old individuals, any premium might be too high. In this case some supplementary form of assistance must be made available, either as a voucher to the individuals concerned, entitling them to buy the insurance they need, or as a subsidy to those insurance policies being offered under particularly favourable conditions. These measures are available in the case of competing private insurance schemes. Another possibility is to introduce a social insurance scheme financed by taxes instead of premiums. At first sight it may seem paradoxical that unanimous agreement may be reached on a compulsory basic cover, as potential free riders, at the very least, should be opposed to this idea. However, it should be borne in mind that individuals find themselves here in the situation known as the ‘prisoner’s dilemma’; each individual has an opportunity to establish a private advantage by means of free riding, but only on the condition that an overwhelming majority of individuals refrain from free riding. If this condition did not hold, everyone would suffer. An awareness of this risk tends to make the idea of compulsory basic cover more acceptable. For the sake of argument, let us assume that the basic cover relates to (1) essential medical expenditures; (2) a basic minimum standard of living after retirement or in the event of a permanent loss of income; and (3) sickness or unemployment benefits to compensate for temporary losses of income.

Introduction

3.

4.

11

In principle the basic insurance cover would be financed by means of premiums representing its actuarial value. However, the size of these premiums presents a practical problem because of fluctuations in people’s ability to pay. Some individuals will never be able to pay an actuarial premium, and many would have occasional difficulties in doing so as a result of illness, unemployment, parental obligations to pay for school fees, and so on. Hence, to be acceptable to everyone, it is essential for a payments model to take ability to pay into account. A possible solution would be a model with the following characteristics. Each individual is assigned an account. A certain fraction of the individual’s income, for example 40 per cent of income from employment, is paid into this account annually. These payments appear on the credit side of the account. Each year, the account is also debited by an amount corresponding to the individual’s annual premiums for basic insurance cover and possibly also other insurance benefits. The idea is that payments credited to the account will balance, in due time, debited premiums. Any remaining surplus at the time of retirement may be used by the individual as a pension fund. In the opposite case with a deficit, the debt will have to be either totally or partially written off. The resultant loss may be shared by the insurer via a fund that is financed jointly by policy-holders, or by the government acting as insurer of last resort. As we will see, in relatively advanced welfare states, like Sweden, most taxes are used to finance benefits of a social policy nature for the tax-payer’s own benefit. In Sweden, transfers between individuals account for less than 20 per cent of all transfers. Hence, a payments model of the kind under discussion might cover over 80 per cent of social expenditures. Of the remaining transfers, only a fraction would refer to the basic insurance cover and therefore constitute a possible debt that might be written off. Note that this kind of account is different from a so-called forced savings account, where the amounts credited are used directly to pay for social policy benefits, such as sickness benefits. The important difference is that savings accounts lack the insurance element, and therefore will run out for individuals with relatively large needs, for example because of bad health. In the payments model described above, ‘savings’ are transformed into premiums for insurance, securing benefits according to need in line with what is stipulated for the insurance policy in question. The problems of exclusion from the market for insurance, adverse selection and collective risks provide a justification for the use of tax revenues to finance social insurance grants and subsidies. Together

12

5.

6.

The economics of social protection

with government loan guarantees these grants and subsidies may easily fit into the above payment model. In the case of a debt that has to be written off, a grant could conveniently be awarded in conjunction with the final adjustment of the individual’s account. In this way decisions on grants may be delayed until one has obtained a good overall view of the ability of the individual to pay for his or her own social benefits. For the sake of argument, we may assume that individual policyholders make the following payments for their basic insurance cover: (1) a fixed basic premium with regard to health insurance and old age pension, (2) a variable premium related to the impact of a loss of income from employment, and (3) a variable risk surcharge related to gender, choice of occupation, and so on. Long-run changes in average life expectancy, medical costs, and so on may be reflected via a differentiation of premiums among different cohorts. The variable risk surcharge permits a differentiation of premiums to reflect the anticipated level of benefits for each individual. In addition to this differentiation of premiums being considered to be fair per se, it also produces certain efficiency gains since the private costs of individual choices of action now provide a better reflection of the social costs of such actions. The existence of special charges for, say, motor cycling or working in a slaughterhouse, provides individuals with an incentive to avoid these ‘dangerous’ activities – or to take proper precautions. Hence the function of risk surcharges is to cover the insurance benefits that are directly related to occupational accidents and illness and also to the unemployment that affects particular occupations. In practice, however, risk surcharges are not fully applied, which means that certain individuals receive subsidized insurance cover, at the same time as others pay relatively more. It is implicitly understood that individuals do not need to restrict their insurance cover to the basic cover alone. The latter does not represent any kind of norm for the level of protection that may be considered desirable. It should be seen as a social obligation rather than as a social right. This also implies that social policy does not have to restrict its operations to questions of compulsory basic cover. Subsidies and other measures justified on the grounds of, for instance, adverse selection may also be assumed to apply to parts of the voluntary insurance cover.

In later chapters we have an opportunity to discuss how social protection devices might be improved with respect to efficiency, and thereby also adapted to better serve certain notions of social justice. But we must be wary of the economist’s habit of using the mere existence of market failures

Introduction

13

as an argument in favour of government intervention. As stressed by Herman B. Leonard and Richard J. Zeckhauser (1983) and others, market failures should be seen as a necessary, but not sufficient, argument for government intervention. There is another side of the coin, which they call nonmarket failures. Leonard and Zeckhauser note three sources of non-market failures: (1) public provision often escapes the useful discipline of the private market in balancing the budget of the provider; (2) some features of the information and incentive structure that make it difficult to provide private insurance perfectly are inherent in the nature of the insurance itself, and so apply to public provision as well; (3) state involvement in the provision of social protection sets in motion dynamic political processes that substantially change the focus of the original programme. They refer to this evolutionary pattern as the ‘political sociology’ of public efforts to provide social protection (p. 150). One component of the political sociology is that participants gradually come to view their risk-reduction benefits as entitlements and eventually as rights, and ultimately become dependent on the programme. Income support programmes for farmers may be used as an example. These programmes typically include subsidies, whose value tends to be capitalized in farm prices. The first generation of farmers can reap a capital gain when they sell the farm, but those who start farming would make a capital loss, and even be ruined, the day a programme is cancelled. Hence, these farmers use political influence for the preservation, and possibly even enlargement, of the programme. For similar reasons health care workers and other professional groups are eager to preserve public provisions in their respective fields. Another component of the political sociology is a result of the fact that the tenure of political officials is relatively short. Thus, programmes having current benefits but deferred costs may be particularly attractive. From this point of view, obfuscation of costs is not seen as a too serious problem in the management of public provisions, and indirect financing by taxes and loans is preferred to direct financing by user charges. As a consequence, these parts of the social protection system will be managed without the useful information one can get from market prices, such as insurance premiums that reflect differences in risk. * * * In the following discussion we start with issues of inequality. Some statistical aspects of the distribution of income and the anatomy of inequalities in wealth, income and consumption are presented in Chapter 2. We then go on, in Chapter 3, to discuss how inequality is viewed from the point of view of social justice. We look at some visionary notions of social justice as well

14

The economics of social protection

as popular views on the subject. Swedish data are used to illuminate the kind of redistribution one can expect to find in an advanced welfare state. In the rest of the book we focus on efficiency issues. We start, in Chapters 4 and 5, with a discussion of various aspects of pension schemes. The purpose of these chapters is to build a theoretical basis for the discussion of the virtues of alternative pension schemes. Then, in Chapter 6, we turn to issues of social protection for non-pensioners, starting with the fact that especially younger individuals are faced with liquidity constraints that might have a negative effect on human capital investments, in children as well as schooling. We look at some of the measures used to ease the situation for parents and students. Chapter 7 addresses the problem of income insecurity for working adults because of unemployment and illness. Permanent as well as temporary income losses will be discussed. In Chapter 8, finally, we look at an important benefit in kind, namely health care. This is done with a focus on the financing aspects, but a few words will also be said about the remuneration of care producers.

2.

Inequality

Market economies give rise to a great variety of economic positions with differences in wealth, income and consumption. Such differences are commonly called ‘inequality’. This chapter attempts to bring some of the controversies surrounding inequality into perspective by emphasizing three aspects. First, inequality reflects differences in choice as well as in opportunities. It is rarely the case that an individual has to have a particular wealth, income or consumption. Second, choices and opportunities are interrelated over an individual’s life cycle. Present opportunities are to some extent the result of choices made earlier in life, and choices today shape opportunities in the future. Third, there is an element of chance. The wealth, income or consumption an individual is observed to have may be different from what he or she was planning to have. Three sets of choices are crucial in determining an individual’s economic position. Over and over again the individual must decide what the portfolio of assets should look like, how time should be divided between different uses and what to consume. The first two choices determine the individual’s (expected) income from capital and labour, respectively. Consumption choices are not only important for the individual’s immediate well being, but also have an effect on the individual’s wealth and future productivity. All of these choices play an important role in shaping his or her economic position over the life cycle.

STATISTICAL ASPECTS Inequality in income, wealth and consumption has received much attention during the last century. Here, we limit our discussion to income inequality, which has been studied by statisticians as well as economists and sociologists. Equivalence Scales In order to compare incomes in households of a different size and composition, one needs to work out how the standard of living varies with demographic factors. The answer is a so-called equivalence scale, which 15

16

The economics of social protection

may be based on norms saying what individuals ought to have in terms of consumer goods, or may be based on empirical observations of the demand for consumer goods in various circumstances. In the latter case an equivalence scale is constructed in the following way. Let x be a vector of consumer goods, z a vector of demographic characteristics, and y a measure of total expenditures (or income). Then, (1) define the expenditure function as M(u, p, z)
y, where p is a vector of consumer prices, and (2) select a particular demographic structure z0 for reference. The expenditure function measures the minimum expenditure for a consumer to reach a particular level of utility at a particular set of prices. The consumer may be a family with children. An equivalence scale is then defined as the ratio M(u0, p0, z)/M(u0, p0, z). This ratio measures the minimum cost for a particular level of utility, u
u0, at a particular set of prices, p
p0, for a household with demographic characteristics z compared to the reference household (with z
z0). The reference household may, for example, be a single adult person. Equivalence scales are typically based on the assumption that the expenditure function for a particular type of household, zh, may be written as a product of a scalar determined by the demographic factor, (zh), and the reference household’s level of expenditures, M(u, p, z0), for a certain level of utility, that is M(u, p, zh)
(zh) M(u, p, z0). The scalar (zh) is interpreted as the number of ‘consumer units’ in the household in question (in relation to the reference household). There are many equivalence scales used in the literature. An early example is Ernst Engel’s observation that (1) richer households use a lower share of their expenditures for food than poorer households, and (2) smaller households have a lower average propensity to consume food than larger households when they are at the same level of total expenditures. These observations suggest that the share of food expenditure in total expenditure may be considered as an inverse indicator of the standard of living. Two households with the same share for food may accordingly be assumed to enjoy the same living standard irrespective of differences in size, composition and total expenditures. Engel’s approach may be applied to any category of goods, but in some cases this approach does not seem appropriate. Take consumption of wine as an example. Since wine is not much consumed by children, we cannot reasonably argue that families with children should have a relatively large share of this type of consumption in their budget. The truth is rather the opposite. In view of this observation, Erwin Rothbarth (1943) suggested an equivalence scale based on a subset of goods that are exclusively or predominantly consumed by adults (‘adult goods’). Instead of the multiplicative form of the Engel cost function, the Rothbarth model assumes an

Inequality

17

Table 2.1

Equivalence scales for Greek families with one child

Child’s age

Engel

Rothbarth

0–5 years 6–13 years 0–13 years

1.299 1.352 1.334

1.098–1.084 1.141–1.119 1.126–1.107

Source: Panos Tsakloglou (1991).

additive cost function M(u, pA, pC, zC)
A(u, pA, pC)  C(u, pC, zC), where pA and pC are the price vectors for adult goods and other goods, respectively, and zC is a vector of demographic characteristics of children only. The cost function has been split into one part A(.) referring to consumption for adults, whether they have children or not, and one part C(.) exclusively referring to the cost of children. The Rothbarth equivalence scale for households with children is measured by the ratio Eh
[A(.)  C(.)]/A(.). Panos Tsakloglou (1991) used both the Engel and Rothbarth models to estimate equivalence scales for families with children in Greece. For the Engel model he used expenditures on food, while expenditures on meals out, alcohol, tobacco, adult clothing and footwear and entertainment were used to represent the consumption of adult goods in the Rothbarth model. His results for families with one child are shown in Table 2.1. The two values in the Rothbarth scale refer to families with low and high incomes, respectively, while the values shown for the Engel scale refer to families with an intermediate (median) level of income. Two adults are ascribed the value 1 in both scales. Note that the Rothbarth scale is much lower than the Engel scale. That the two scales are so different should warn us to be very cautious in comparisons of the well being of households with different demographic characteristics and income. In Great Britain, the McClements scale is used as an equivalence scale for relatively poor households. According to this scale, household members should have the following weights: first adult (head) 0.61, spouse of the head 0.39, third adult 0.46, subsequent adults 0.36, child aged 0–1 year 0.09, child aged 2–4 years 0.18, child aged 5–7 years 0.21, and so on (Peter J. Lambert, 2001). By adding such weights we get the number of consumer units in any particular household. Then, as a final step, we may calculate the household’s income per consumption unit and compare this measure for different households. The idea is, of course, that households are worse off the lower their income per consumption unit. For international comparisons, Anthony Atkinson has suggested a strikingly simple scale, the so-called square root rule. In this case incomes are deflated with

18

The economics of social protection

the square root of the number of household members (Anthony Atkinson et al., 1995). In this type of equivalence scale the idea is to compare the utility that may be reached by different households. An alternative, avoiding interpersonal utility comparisons, would be to compare different situations for the same individual. For example, one could study what expenditures a person would need to reach a particular level of utility when either living alone or living with a spouse. In the latter case there will be some goods consumed by each spouse alone (‘private’ goods) and some goods consumed jointly (‘collective’ goods). This is the approach used in so-called collective household models where two or more individuals have their own preferences and try to maximize a sort of ‘social welfare function’. This is a promising approach, but so far no attempts have been made to calculate the cost of children in such a model (Arthur Lewbel, 2002). Statistical Theories An early attempt to describe the distribution of income in statistical terms was made by Vilfredo Pareto (1897), who gathered information about the income distribution in many countries at different points in history. He noticed that there were similarities between the distributions, and he claimed that all distributions could be described by the same frequency function. The latter has since been called the Pareto distribution. If f(x) is the number of incomes equal to x (currency units) or larger, this distribution may be written f(x)
A x,

(2.1)

where A and  are parameters. Pareto found that the ‘Pareto parameter’  had a value in the region of 1.5. In his view this regularity could not be coincidental, but was an expression of some universal principle governing the distribution of income. Pareto’s discovery – called Pareto’s law – inspired economists and statisticians to look for the principle of income distribution. They soon discovered that the Pareto law was far from universal. First, Pareto’s own data already showed that the value of  varied a great deal; except for the German city Augsburg in 1526, where it was just 1.13,  varied between 1.24 and 1.89. In later data, values of  above 2.0 have been found. Second, the data on the distribution of income in various countries in earlier days were far from comprehensive. In fact, most data were collected for administrative purposes and covered only the top of the distribution. It is nowadays understood that the Pareto distribution, at best, gives a good

Inequality

19

description of the highest quintile of incomes. An interesting hypothesis in line with this observation is that the Pareto distribution may describe the outcome of wage settings for better paid white-collar workers. Herbert A. Simon (1957) and Harold F. Lydall (1968), among others, have used this idea for the purpose of finding out how earnings are determined in hierarchical organizations. For the remaining 80 per cent of the distribution of income, many attempts have been made to fit a normal distribution or a log-normal distribution. A normal distribution seems appropriate when the distribution of income is assumed to reflect some personal characteristic of income earners, such as intelligence, which is known to be normally distributed. A log-normal distribution, on the other hand, might be appropriate when the distribution of income is seen as the result of a stochastic process. A famous example of the latter is Robert Gibrat’s claim that the law of proportionate effects (see the next section) will imply a log-normal distribution that, under certain conditions, fits observed data well (Gibrat, 1931). There is much evidence, however, to refute the claim that the law of proportionate effect is the sole determinant of inequality in earnings. There are many alternatives to Gibrat’s hypothesis though, and nowadays there are several statistical theories dominating the literature on income differences. This line of research is very controversial anyway. For example, in a survey of the literature, Gian S. Sahota complains that stochastic theories of the distribution of incomes are impossible to refute by the usual Popperian principle of tenacity, and he places attempts to keep this theory alive in the category ‘Lakatosian degenerate research programs’ (Sahota, 1978, p. 9). This is certainly going a bit too far. Many statistical theories may in fact be refuted with scientific criteria. The famous theory suggested by R.S.G. Rutherford (1955) is an example. He assumed, first, that there is a flow of new entrants into the labour market, and that the distribution of earnings within this group is log-normal; and, second, that each individual’s earnings evolve stochastically with an error term that is normally distributed; and, finally, that individuals gradually leave the labour market with an exit probability that is independent of earnings. Rutherford showed that processes of this kind generate a Gram-Charlier type A distribution of income. The problem is not that this theory cannot be refuted by facts, but that it does not explain how the distribution of income is determined. What is the role of inheritance, parents, schools, labour unions, employers, globalization, politicians and other factors in the processes determining an individual’s income? A theory that does not explain how the world might be changed for the purpose of advancing some interesting aspect of the world, is certainly a rather poor theory.

20

The economics of social protection

Another statistical approach is to collect as much information as possible on individuals who are placed in various parts of the distribution of income. One may then do regressions with respect to the income earners’ age, gender, race, family situation, education, industry, region, and other aspects of their socioeconomic status. Such studies are illuminating, and may generate many interesting hypotheses about the distribution of income, but they cannot explain how the distribution of income is actually being determined. They have this flaw in common with the type of theories suggested by Pareto, Gibrat, Rutherford and others. An explanation must tell us how things happen and how parents, schools, labour unions, politicians and so on may change the outcome, in the short run as well as in the long run. An attempt in this direction (in microeconomics) was made by Gary S. Becker and Nigel Tomes (1979). They used the human capital approach, assuming that an individual’s earnings are proportional to the amount of human capital he or she has accumulated, which in turn is assumed to be determined by the family into which the individual was born. Parents are assumed to derive utility not only from their own consumption, but from the number of children and their ‘quality’ as well. Hence, parents use family resources to improve their children’s human capital and earnings capacity. The better off a family the more human capital investments parents will give their children. These children will then do relatively well later in life and in due time give their own children relatively large human capital investments; and so on generation after generation. By adding stochastic elements, for example an ‘endowment lottery’, Becker and Tomes are able to include negative as well as positive intergenerational mobility into this process. Some families become wealthier at the same time as other families become poorer. Measures of Inequality Statistical theory may also be used to illuminate a particular aspect of the distribution itself. Measures of the size of income inequality are particularly interesting and there are many such measures suggested in the literature. Here, we confine ourselves to only a few of them. The Lorenz curve is the most common way to illuminate income inequality. This curve plots the cumulative share of the population on the horizontal axis against the cumulative share of total income on the vertical axis, as shown in Figure 2.1. Individuals are ordered by the size of their income. If all individuals have the same income, the Lorenz curve coincides with the 45˚-line. The more unequally incomes are distributed in the population, the larger is the area between the Lorenz curve and the 45˚-line (A) compared to the area below the Lorenz curve (B). This property is used for a simple

21

Inequality

Cumulative % of total income

100

A B 45° 0

100 Cumulative % of population

Figure 2.1

The Lorenz curve

measure of inequality. The ratio between the areas A and AB is called the Gini coefficient N

 (N  1  n)yn 1 Gini
A (A  B)
2A
1  2B
N  N  1  2  yn n
1

N

(2.2)

n
1

where N denotes the number of individuals and yn is the nth individual’s income, ordered such that yn yn1. This coefficient takes values between 0 and 1. As an alternative to the Gini coefficient, Anthony B. Atkinson (1970) has suggested the measure Atkinson
1 


  i

y1 i y

1 1

(2.3)

where  is a parameter expressing aversion towards inequality. For 
0, there is no aversion to inequality and Atkinson’s measure does not change when income is transferred from an individual with high income to an individual with low income. Only the average income matters. The value 
, on the other hand, indicates a very strong aversion to inequality. In this case Atkinson’s measure focuses on the situation for individuals with an extremely low level of income. Then, only transfers to or from this group have an influence on Atkinson.

22

The economics of social protection

In many situations we are interested in a decomposable measure of inequality. We might, for example, be interested in measuring income dispersion between educational groups at the same time as we want to measure income dispersion within these groups, or between states/countries at the same time as we want to measure income dispersion within states or countries. A measure with this property was suggested by Henri Theil (1967). When there are K groups, denoted Gk, with income shares Mk, k
1, 2, . . ., K, this measure may be written Theil


K



k
1

M MklogN N k  k

Mk MiklogNkMik m

K

k
1

m

(2.4)

i Gk

where N is the total number of individuals, of which Nk belong to the kth group. Income shares at the individual level, yi/Y, are denoted mi. The first term on the right hand side measures income inequality between groups, and the expression within parentheses measures income inequality within the respective group. In the aggregation of these latter measures the respective group’s share of total income is used as weights. Theil’s measure is related to the measure of ‘entropy’ in the theory of information and is therefore often called Theil’s entropy measure. In addition to being decomposable, it has two important properties: it is not dependent on the income scale, for example whether incomes are measured in pounds or dollars, and it is sensitive to every change in the distribution of income. Among other things, Theil’s measure allows us to identify socioeconomic groups that are homogeneous with respect to income. We may, for example, calculate how large the dispersion between groups is compared to total dispersion. This could be done for different socioeconomic groups and for various categories of individuals, for example those working full time. Such calculations may be made for any concept of income. What is the relevance of calculating income inequality? Do we really mean that a lower value of the measures Gini, Atkinson or Theil always implies more social justice? Few would argue that every income inequality is socially unjust and that eliminating all kinds of inequality should be a major objective for social policy. It is generally understood, instead, that some income inequality is necessary to achieve a socially just distribution of income (or wealth, or consumption). We shall have a look at some alternative notions of social justice in Chapter 3. *

*

*

In the rest of this chapter, we take a closer look at the nature of inequality in income, wealth and consumption one may expect to find in a market economy. Our point of departure is a simple case where all assets, all

23

Inequality

occupations and all consumption goods are homogeneous, and – moreover – all individuals are identical except for age. Under these conditions, the next section illuminates inequality with respect to age, economic growth, random variations and private cooperation. Inequality related to differences in savings and portfolio choice is discussed in the following section. Among other things, this section focuses on the important distinction one may make between compensating and non-compensating inequality. Inequality related to earnings is discussed in the section after that, focusing on differences in the supply of working effort, differences in the earnings rate in various occupations and differences in human capital investments.

INEQUALITY AMONG IDENTICAL INDIVIDUALS Consider an economy where all assets, all occupations, and all consumption goods are homogeneous and, moreover, all individuals have the same preferences and the same inheritance of material as well as non-material wealth (assets and personal skills, ‘human capital’). As we shall see, quite substantial inequality may evolve even in such a uniform case. The Budget Equation It is convenient to start this discussion by looking at an individual’s budget equation. Let v be an individual’s vintage age (
the individual’s actual birth date plus the length of his or her childhood). After that date the individual is a potential member of the labour force until retirement or death. For an individual of a certain vintage the current budget equation at time t is It Et Gt
Ct St

(2.5)

The left hand side summarizes the individual’s income from capital (investments), labour (earnings) and beneficial transfers (gifts, government benefits). Incomes are counted as received by the individual, that is net of direct taxes but including income-related grants. The right hand side summarizes the individual’s outlays on consumption goods (including indirect taxes) and savings. Income from capital It may be expressed, we assume, as the product rtAt, where At denotes asset holdings at the beginning of the time period in question, say a day, and rt denotes the rate of return obtained on these assets during the day. Changes in asset prices, negative as well as positive, are included in the rate of return. It is assumed that rt does not vary with

24

The economics of social protection

the size of At. Since assets are assumed to be homogeneous, all assets have the same expected rate of return. Likewise, we assume that the individual’s income from labour or earnings Et may be expressed by the product wtht, where ht denotes hours spent in various occupations, and wt denotes the (hourly) wage rates in these occupations. Since occupations are homogeneous, all occupations have the same expected wage rate. It is assumed that wt does not vary with the size of ht. Working overtime may be seen as a different occupation. The individual may, in addition, get income in the form of transfers Gt, which may be negative as well as positive; private as well as public. A child allowance and an old age pension unrelated to earnings earlier in life are examples at hand. Pensions related to former earnings are counted as a part of the labour income. Transfers, like incomes from capital and labour, are counted as received by the individual. Incomes are consumed or saved. Hence, the individual’s choice of consumption outlays will, ceteris paribus, determine savings and, accordingly, how assets change over time St
At  1  At

(2.6)

With this notion of savings, expenditures on investments in the preservation and development of one’s working capability are seen as private consumption. Hence, consumption may be more or less ‘productive’. Johnson’s Example Now we turn to the matter of inequality. A first observation is that inequality in income and wealth at a certain point in time cannot be ruled out even in a society where all individuals follow exactly the same path of earnings and consumption through life. This is true even in a stationary economy without any random events. An example suggested by Harry G. Johnson (1973) will be used to illustrate this point: Envisage a pure market economy in which all individuals are being brought up at a commercially run orphanage, then enter the labour force at the same age, work the same amount at a standard earnings rate, retire at the same age, and finally die at the same age. Moreover, these individuals consume exactly the same amount all days as long as they live. Since this is a market economy in its purest form, each child is debited by the orphanage with the costs of its upkeep. Then, in the course of working life, these debts are paid back at the same time as savings are accumulated for consumption outlays after retirement. In these circumstances there will be no inequality among individuals of the same vintage, but in a cross-section of the population one would nevertheless observe inequality in earnings and wealth.

25

Inequality

E

E Y

C

C Y

0

Y

20

40

60

80

Age/time

Figure 2.2 Earnings (EE), income (YY) and consumption (CC) over the life cycle Assume, as shown in Figure 2.2, that everyone enters the labour force at the age of 20, retires at the age of 60, and dies at the age of 80. With a static population and a zero rate of interest, half of the population gets all the available income. Moreover, half of the population has negative wealth. At the lower end of the wealth distribution are individuals at the age of 20. They have debts corresponding to ten years of earnings. At the upper end are individuals at the age of 60 with positive assets of the same size. Clearly, this is a society with large inequality at any particular moment of time. With a positive rate of interest the picture becomes somewhat more complex. In this case, people have a negative income during childhood, a gradually increasing income during their working life, and then a smaller and gradually decreasing income after retirement. Compared with the situation with a zero rate of interest, total debt at the age of 20 will be larger and accumulated savings at the age of 60 will be smaller. There are no transfers in this hypothetical economy. Personal debts and savings cover consumption expenditures in years without earnings. Transfers make a drastic change in the picture, for example when consumption during childhood is financed by a transfer from the parents rather than by the child itself. As an illustration, assume that each individual, at the age of 20, becomes the parent of one child and then cares for this child during its entire childhood. In this case there is a daily transfer equal to the child’s consumption, G
C. At the same time as the parent has his or her non-capital income reduced by the amount of the transfer, to E  C, the child will have its income increased by the same amount, from zero to C. A financial arrangement of this kind clearly tends to reduce the inequality of both income and wealth. In our example above, everyone will now have a zero net wealth until the age of 40.

26

The economics of social protection

A similar arrangement may be used with respect to consumption expenditures after retirement. In this case the child provides consumption opportunities for the parent after retirement, which starts as the child reaches the age of 40 and goes on until the parent dies and the child reaches retirement age. During this period both parent and child will have the net income C. An alternative way to provide consumption opportunities after retirement would be for each individual to open a savings account and accumulate a sufficient amount of wealth before retirement. With such an arrangement we would see income as well as wealth inequality. Random Variation Let us now consider a couple of situations where earnings are determined by a stochastic process. A simple example is when realized labour earnings Et vary randomly around a constant value (‘random walk’). Compared with our previous case, there is no change in the total amount one earns in the course of a working life. The only difference is that individuals now earn more on some days, and less on others. A constant level of consumption is still possible, at least approximately. On a daily basis, variations in savings may be used to match variations in earnings. In the long run, nobody will be worse off than anybody else. Yet, inequality recorded for a limited period of time will be larger in this new situation. A somewhat different situation evolves with a stochastic process working cumulatively. A well-known example, which we referred to in the previous section, is the model formulated by Robert Gibrat (1931). This model is called ‘the law of proportionate effect’ and may be written Et
Ev * Qv * Qv1 * . . . * Qt1

(2.7)

where Ev is the initial level of earnings (at vintage age) and Qj, j
1,2, . . ., t  1, are independent random variables assuming values around 1. With respect to models of the Gibrat type we would like to make two comments: (1) The law of proportionate effect (or some similar stochastic mechanism) applies to all individuals in exactly the same way. Ex ante, individuals who are fortunate under this ‘law’ cannot be separated from those who are unfortunate. In this sense there is a perfect equality of opportunity. In the end, however, there might nevertheless be quite substantial differences between fortunate and unfortunate individuals. For example, some individuals may experience long-term (or frequent shortterm spells of) unemployment or illness; (2) One must exercise caution not to conclude unconditionally that stochastic factors must make some individuals end up in great wealth at the same time as others end up in

Inequality

27

poverty. Rational individuals should take actions to prevent such an outcome of the stochastic process by joining cooperatives for the purpose of pooling earnings and capital incomes. Economic Growth The discussion above was confined to a stationary economy in which average earnings per day were assumed to remain at the same level over time. Our analysis will now be extended to include economic growth. Let Et be the average level of earnings at time t. Except for random variations, this is the level of earnings common to all individuals participating in the labour force at time t. When the average level of earnings grows at a constant rate g we have Et
E0(1g)t, where E0 is the average level of earnings some time back in history. In particular, Et is the starting level of earnings for individuals joining the labour force at time t. What will this situation look like in a cross-section of the population? Despite the fact that the distribution of earnings for each cohort of individuals will look exactly as it does in the stationary economy, it will no longer be true that all individuals are equally well off. Because of the growth in earnings younger individuals are better off than older individuals. Even when the rate of growth is moderate, say 2 per cent annually, the younger generation may expect to earn more than twice as much as their grandparents over the life cycle. Hence, they may be able to afford more consumption, both immediately and later on. It might still be the case that all individuals have the same level of consumption on a particular day. Such a situation would evolve if random variations in earnings were of a non-cumulative type and everyone increased his or her level of consumption day by day at the same rate as the growth of aggregate earnings, that is if Ct
C0(1g)t, where C0 is the common level of consumption some time back in history. However, this is hardly a reasonable way to use one’s resources. An alternative is for the younger generation to take immediate advantage of their more favourable earnings prospects and consume more than the older generation from the very first day of life. For example, if everyone prefers to have the same level of consumption every day for as long as he or she lives, each vintage group would start out by consuming (1g) times more than their immediate predecessors, given that the credit market permits such behaviour. If so, in a crosssection of the population we would observe how an equal distribution of earnings per day is transformed into a very unequal distribution of consumption. Note that this outcome may require that people are able to run into debt before they retire. If this is not possible for one reason or another, people

28

The economics of social protection

will have to enter the retirement period better off than they really wish. They would then have to consume too little before retirement, and too much after. We address this problem in Chapter 6.

CAPITAL INCOME INEQUALITY Inequality among identical individuals is a result of differences in age and stochastic factors. We now turn to non-stochastic inequality among individuals of the same age. This is the case of non-identical individuals. Stochastic factors aside, there are just two basic differences between individuals of the same age: they may have different preferences and a different initial position, that is different endowments of wealth and personal ability at the time they reach vintage age. These endowments are denoted Av and v, respectively. Differences in earnings are discussed in the next section. First we look at differences in capital income. There are three reasons why somebody has a larger income from capital than somebody else of the same age: he or she may have larger wealth; a larger expected rate of return on asset holdings; or simply be luckier. These differences are discussed in turn. Differences in Wealth Why do two individuals of the same age have a different amount of wealth at a particular time t? In discussing this issue we disregard random variations and assume that all assets are homogeneous and have a constant rate of return. It is straightforward, under these assumptions, to calculate how an individual’s wealth grows over time. From the budget equation (2.5) and the notion of savings applied in the previous section, it follows that At
Av(1r)tv


t

 Evi  Gvi  Cvi] (1 r)ti

(2.8)

i
v

where Av denotes the initial endowment of wealth and (1r)t  i is the capitalization factor from i to t. According to equation (2.8) there are four factors determining the amount of wealth owned by an individual at time t: ● ● ● ●

initial endowment of wealth, Av; flow of non-capital income Ei Gi, v  i  t; flow of consumption outlays Ci, v  i  t; the rate of interest r (assumed to be constant).

Inequality

29

Except (perhaps) for the rate of interest, these factors vary among individuals. For the moment we assume that an individual’s initial endowment of wealth and the (expected) flow of non-capital incomes are given exogenously. This assumption leaves only the flow of consumption outlays to be determined by the individual. To illustrate this point, we assume that the budget constraint for an individual planning for T periods (days) is T

T

t
1

t
1

Ct(1  r)1t  AT(1  r)1T
 (Et  Gt)(1  r)1t  A1

(2.9)

We assume that the planning period starts at t
1. The first term on the left hand side is the present value of consumption outlays during the planning period, and the second term is the present value of what remains of the individual’s resources at time T (‘terminal wealth’). When the planning period covers the entire remaining lifetime, AT is the estate left to inheritors, assumed to be non-negative. The rate of interest r is assumed to be constant. The right hand side of equation (2.9) is the individual’s total resources during the planning period, consisting of the present value of expected noncapital income and initial wealth. What the individual actually does with these resources is a matter of choice. Among other things, this choice will depend on the individual’s rate of time discount, , and his or her preference for terminal wealth versus consumption at time T, denoted (T). To illustrate the role played by and (T), we assume that the individual’s preferences for consumption and terminal wealth may be represented by an additively separable and iso-elastic utility function; and, furthermore, that this function has unit elasticity. In this case there is a simple solution to the individual’s maximizing problem (denoted *): 1.

2.

The starting level of consumption C*1 is proportional to total resources as shown by the right hand side of equation (2.9), the factor of proportionality being dependent on the parameters (T) and , and the length of the time period considered. The consumption path grows exponentially at the rate (r  ), that is, C*t
C*1 (r  ) t, 1  t  T

3.

(2.10)

The present value of terminal wealth is proportional to the amount of consumption at time T, the factor of proportionality being (T).

What does the optimal consumption path look like when the subjective rate of time discount is high (higher than r) and low (lower than r)? In the first case the individual starts out with a relatively high level of consumption

30

The economics of social protection

ct r>ρ

r<ρ V

Figure 2.3

Age/time

T

Optimal consumption path for r and r

and, accordingly, a relatively low level of savings, as shown in Figure 2.3. After some time, the level of consumption will in this case become lower, and the level of savings correspondingly higher than in the second case. Thus, in the short run, a high level of savings is consistent with a relatively high as well as a relatively low rate of time discount. In the long run, on the other hand, these two cases are quite distinct. When the rate of time discount is low, accumulated savings will be larger, ceteris paribus, than when it is high. According to the conditions stated, the optimal level of terminal wealth varies inversely with . Suppose that there is an increase in the individual’s initial endowment of wealth. It is readily seen in the condition (2.9) that a change in A1 does not have any effect on the shape of the optimal consumption path. It is only the level of the path that changes. The optimal level of terminal wealth changes as well. A part of the increase in inherited wealth should be saved for future use (or for one’s inheritors). An increase in the individual’s non-material wealth has an analogous effect. A decrease in the individual’s relative preference for terminal wealth should have a similar effect on the level of consumption, but with the disadvantage of a smaller terminal wealth. Savings are affected inversely. An increase in consumption will, ceteris paribus, decrease savings. Note that the level of savings does not only depend on the size of the individual’s non-material wealth, but also on how non-capital incomes are spread out during the period in question. Savings are larger and the accumulation of wealth faster the earlier in life non-capital incomes are realized. In conclusion, at time t an individual will be observed to have a relatively large accumulated stock of wealth At for one or more of the following reasons: He or she has a strong preference for terminal wealth (bequests), a low rate of time discounting, a large initial endowment of wealth, a large

Inequality

31

non-material wealth, or an early flow of non-capital income. To the extent that these factors differ between individuals they will give rise to inequality in the distribution of wealth. At any particular point in time some individuals of a certain age are relatively rich and others relatively poor. Note that individuals who are relatively rich at one time may be relatively poor at another time. For example, an individual with an early flow of noncapital incomes and a low rate of time discount may start out with a relatively high level of savings, although he or she might have relatively small resources and in the end will be seen to have a relatively small stock of accumulated wealth. Differences in the Expected Rate of Return We now relax the assumption that all assets are homogeneous and include inequality generated by the fact that different individuals select different assets in their portfolio. An individual’s portfolio may consist of company stocks, bonds, bank accounts, pension plans, gold, objects of art, real estate, fine furniture, and so on. In selecting a portfolio the individual should take into account the fact that assets differ with respect to pecuniary and nonpecuniary returns, convertibility into cash, risk, and so on. To the extent that differences in risk and other such factors are relevant to investors, they will be reflected in the expected rate of return demanded from the investments under consideration. Investments that are risky or otherwise less attractive must, as a rule, have a comparatively high expected rate of return in order to attract investors. Differences in the expected rate of return that compensate for high risk and other such factors are said to be compensating. They are related to intrinsic properties of the investments themselves. There are also two categories of non-compensating differences in the expected rate of return related to differences among the investors. The first category consists of monopoly rents; that is extraordinary profits in cases where one investor (or a group of investors) has an exclusive right to exploit certain investment opportunities. The monopoly rent is the difference between the expected rate of return that is actually being achieved and the expected rate of return that would prevail under competitive conditions. The second category consists of entrepreneurial rents. An example is when one investor (or a group of investors) is better informed about investment opportunities than others, a so-called ‘insider’, who gains entrepreneurial rents by acting on confidential information. Normally, however, there is nothing unethical about entrepreneurial rents. Those who make innovations in the form of new products or better ways of producing or marketing old products, for example, get their remuneration as an entrepreneurial rent. In many cases these rents are of a temporary nature.

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The economics of social protection

Extraordinary profits attract competitors and are gradually dissipated in the process of competition. This is an essential feature of a well functioning market economy. What are the effects of these differences on savings? To begin with, suppose that the capital market is perfectly competitive, implying that everyone has the same information. All differences in the expected returns are then compensating. A comparatively low rate of return indicates either a high non-pecuniary return (‘consumption’) or a low risk exposure (‘safety’). These differences may be interpreted as the price paid for consumption and safety. In equilibrium, these prices are the same all over the market and, consequently, equal for all investors. Compared to a truly safe portfolio without any consumption value, and with the expected rate of return equal to rsafe at time t, observed portfolios will, approximately, have t the expected rate of return rt
rsafe  t  t t

(2.11)

where t denotes non-pecuniary returns, and t denotes the premium received for risk exposure (the risk premium). Selecting t is a choice between present and future consumption. This choice may be analysed in the same way as differences in savings were analysed in our earlier discussion. For example, individuals with relatively large initial resources might be expected to choose a relatively large t. By selecting a portfolio with a comparatively high non-pecuniary return they get a smaller capital income and less to consume in the future. Of course, this does not mean that they are worse off. The choice of  will depend on the individual’s attitude towards risk. With a high risk aversion one chooses a portfolio with relatively low risk and, therefore, a comparatively low expected rate of return. To what extent this choice also depends on the individual’s accumulated wealth, his or her rate of time discount, and the like, is a much discussed issue, first raised by Edmund Phelps (1962). With respect to our present discussion we may set this debate aside and just note that all values of  available to rich individuals are equally available to poor individuals, at least in a perfect capital market. One does not have to be rich to avoid risks. Monopoly rents and entrepreneurial rents are a result of ‘imperfections’ in the capital market. They may be seen as a discounted price of t and/or  offered to certain individuals in certain investments. As a rule, monopoly rents and entrepreneurial rents are temporary phenomena. It is extremely hard to keep advantages of this kind in a free capital market, where everything happens quickly and every success is easily imitated. In the presence of governmental regulations, however, there might be quite a few

Inequality

33

rents of this kind, some of them long lasting. Credit constraints are a particular category of imperfections in the capital market. Because of such constraints, poor individuals, especially, have to look for more expensive credit outside the regular credit market. Differences in Luck We have now indicated how inequality in the stock of wealth is determined, and also pointed out a number of reasons why there is inequality in individuals’ expected rate of return from wealth holdings. One point remains to be made before we end this section on capital income inequality: people cannot be sure that expected rates of return will be realized. Some investments turn out better than expected, and others worse. Investments in lottery tickets are an obvious example. As it happens, some investors are luckier than others.

INEQUALITY IN EARNINGS There are also three reasons why some have a larger income from labour than others: they may supply more hours of work; work in an occupation with a higher expected rate of earnings; or be luckier in their remuneration from work. These factors are discussed in this section. Differences in Working Effort Let us start with the question of why two individuals of the same age supply a different amount of work during a certain (short) period of time. In discussing this question we disregard random variations and assume that all occupations are homogeneous with a constant rate of earnings that is the same for all individuals. These assumptions will be relaxed later on. Under the assumptions stated, an individual’s supply of work may be analysed in the same way as his or her savings behaviour was analysed in the preceding section. We only have to add leisure as a desired use of the individual’s total resources. Leisure is labour income forgone. At time t the individual has potential earnings equal to Et, of which the proportion ht is realized. The remaining part (1  ht)Et is labour income forgone because of leisure. To get some leisure the individual has to give up consumption or terminal wealth. With a utility function of the type assumed in the preceding analysis, the optimal level of leisure is proportional to the optimal level of consumption at the same time. The factor of proportionality is /wt, where

34

The economics of social protection

 denotes the individual’s preference for leisure versus consumption and wt denotes his or her real wage rate at time t. As in the earlier analysis, consumer prices are set equal to 1. What the optimal path of leisure looks like depends on how the earnings rate develops over time. With a constant earnings rate, and therefore a constant price of consumption in terms of labour, the optimal path of leisure is parallel to the optimal path of consumption as illustrated by the condition (2.10). This path is exponentially increasing (decreasing) when the rate of interest r is larger (smaller) than the subjective rate of time discount . Changes in the earnings rate over time change the optimal path of leisure. One should work relatively more, as a rule, when the real wage is relatively high. Hence, if the real wage decreases over time, which would be natural for many middle-aged individuals, one should try to postpone leisure. This analysis has identified a number of reasons why individuals of the same age enjoy a different amount of leisure on a particular day. It is rational to have more leisure if one has: ● ● ● ●

high preference for leisure low preference for terminal wealth temporarily low rate of earnings large inherited wealth.

Differences in the subjective rate of time discount are also important but, as we have seen, these differences have an ambiguous effect. A comparatively high generates a relatively high level of consumption and leisure in the early part of the planning period, and a relatively low level thereafter. Differences in the Expected Earnings Rate Our discussion is now extended to heterogeneous work tasks. As before, we focus on compensating inequality generated by differences in occupations and preferences, as well as non-compensating inequality in the form of, for example, monopoly rents. An occupation is defined as a set of work tasks. Occupations differ with respect to locality, time schedule, amount of strength and skills required by the worker, responsibility, working hazards, and so on. A great number of such aspects are taken into account when individuals make their occupational choice. It is reasonable to assume that different jobs cannot be equally attractive unless differences in working hazards, and so on, are balanced by differences in earnings rates. Our discussion of these differences will proceed in steps. We assume, for the sake of simplicity, that there are just a few types of occupations and, furthermore, that an individual cannot have more than one job at a time.

Inequality

35

Consider an individual at time t who may choose to work in one of J occupations. Compared to the alternative of being idle, working in the jth occupation at time t is acceptable if this occupation has an (expected) earnings rate of at least w0jt, which is the individual’s reservation wage for this particular occupation. We assume that w0jt is independent of the amount of hours the individual is planning to work. The reservation wage is relatively low for occupations he or she likes. Other individuals may have different tastes. To begin with, assume that all individuals are identical with respect to ability, wealth and preferences. Provided that everyone has the same information, all individuals will have the same set of reservation wages. This will also be the set of equilibrium wages (possibly) observed in the labour market. It follows that all prevailing differences in earnings rates are entirely compensating in this case. In other words, all occupations are in this case equally attractive to all individuals. Under competitive conditions that are less than perfect, there could be non-compensating differences in earnings rates as well. As an example, think of a butcher who finds a way to reduce working hazards in his line of work, and does not tell anybody about it. He will earn an entrepreneurial rent for some time. There is a drop in his reservation wage since he knows that the job has become less dangerous, but he still gets the normal earnings rate for butchers based on the old reservation wage, since nobody else knows about his innovation. After some time other butchers will find out about the innovation and so will the rest of the labour force. More individuals will then be attracted to the job of butcher, and there will be a tendency for the earnings of butchers to fall. This tendency gives an incentive for those already working as butchers to turn their occupation into a ‘closed shop’. If they succeed, the entrepreneurial rent will be preserved as a monopoly rent. This kind of ‘rent seeking’ is claimed to be an important rationale for labour unions and similar organizations among the self-employed (Mancur Olson, 1982). Differences in preferences among individuals tend to reduce inequality in earnings rates. Because of different preferences there will be a different reservation wage for each occupation. In the competition for jobs the individual with the lowest reservation wage will always win. Note that we are talking about equally able individuals. Differences in working capability are considered below. An individual who does not care much about working hazards will be willing to assume the risks involved for a relatively small compensation. Consequently, because of competition, compensating differences in earnings rates will be kept within narrow limits in this case. When preferences differ it is no longer necessarily true that a single structure of earnings rates may make all occupations equally attractive to all

36

The economics of social protection

individuals. However, we may still say that an equilibrium structure of earnings rates is compensating in a limited sense: a small decrease in an occupation’s earnings rate would make this occupation less attractive than some other occupation for at least one individual. Note that we are assuming a one-job situation. If it was possible for workers to hold more than one job at a time in different occupations, the equilibrium structure of earnings rates would still be compensating in the general sense. This is the kind of situation prevailing in the capital market where all individuals are free to hold all sorts of assets at the same time. Differences in the preference for leisure or terminal wealth may be important in this context. For example, there could be a relevant trade-off between leisure and working hardships. The same amount of earnings may be obtained by a few hours of work in a more demanding occupation or by many hours of work in a less demanding occupation. Individuals with a strong preference for leisure would probably choose the more demanding job. However, a reasonable alternative might be to choose an occupation offering relatively more ‘on-the-job leisure’, for example as many coffeebreaks as one likes. In the preceding analysis we saw that rich individuals consume more and work less than poor individuals. As a corollary, based on simple intuition, it might be argued that rich individuals choose less demanding occupations. Differences in Personal Ability We now turn to the case of heterogeneous human capital. People are assumed to differ in the composition of personal ability and, accordingly, in the ability to perform certain tasks, implying that a particular individual may have relatively high productivity in some occupations, but not necessarily in other occupations. An extreme case is when each individual has zero productivity in all occupations but one, and, moreover, all occupations are strictly complementary as factors of production. This is the much discussed case of noncompeting groups, a concept that was introduced in the 1800s by John E. Cairne, emphasizing various barriers to labour mobility. All individuals belonging to one of the groups must have the same type of job. Hence, an individual just has to decide how many hours he or she is going to work in this particular type of job. This is exactly the kind of situation considered above. As we have seen, the supply of labour will differ among individuals because of differences in wealth and preferences. What about differences in earnings rates between groups? For all we know they may be purely incidental. As an illustration, assume that there are just two categories of workers, A and B, each working in the

Inequality

37

production of a particular consumption good, i
1, 2. Earnings rates (at a particular time) are in this case determined by the famous formula wi
pi MPi , i
1, 2

(2.12)

where the price of the ith good is denoted pi and MPi is the marginal productivity of workers engaged in the production of this good. When each group of workers has a given and constant (marginal) productivity, it must be true that earnings rates are proportional to product prices. Hence, as soon as these prices are determined, so are the earnings rates. The crux of the matter is that product prices may be undetermined. This point was stressed by John R. Hicks (1963) in his comment on the marginal productivity theory of wages. Suppose that the economy rests in some sort of equilibrium, and that the B-group increases the price p2 in order to get a higher earnings rate. This will cause a redistribution of real income from the A-group to the B-group. The B-group will consequently demand more goods, at the same time as the A-group demands less. If the two groups have the same marginal propensity to consume, and consume the two goods in the same proportion, nothing further will happen. Besides, in these circumstances the new pair of prices is compatible with a sort of equilibrium. This is true for all pairs of prices. Accordingly, all pairs of earnings rates are in this case feasible from a theoretical point of view. In practice, most individuals are able to work in more than one occupation. Increasing the earnings rate in one occupation will therefore attract competitors from other occupations. This will be a check on the size of differences in earnings rates that may evolve. Under perfectly competitive conditions, all differences in earnings rates between occupations will actually be compensating, as in the previous analysis. The only new aspect is that these compensations will differ between individuals because of unequal ability. If wjt is the compensating earnings rate for an unskilled worker in the jth occupation at time t, a skilled worker will now have the earnings rate twjt, where t is a scalar measuring the latter’s relative superiority in productivity (or skill) at time t. This structure of earnings rates is easily realized when wages are set as piece rates. Do more able individuals supply more or fewer working hours, and do they choose more or less demanding work tasks? There is no straight theoretical answer to these questions. Differences in the level of personal skills do not have clear-cut implications for the supply of labour. A more able individual earns more per hour in at least some occupations. Increases in the level of human capital have a substitution effect as well as an income (or rather wealth) effect on the individual’s supply of labour. Either of these effects may dominate. At the same time as one may be able to afford more

38

The economics of social protection

leisure and a less demanding job, one has to pay more (in the form of income forgone) by making this choice. Empirically, however, there is evidence that schooling has a positive effect on working effort (see Chapter 6). Excess Supply and Private Rationing So far in this discussion the labour market has been viewed solely as a matching mechanism by which individuals are assigned jobs of various kinds. Given that wages are flexible with respect to personal ability, perfect competition will generate an equilibrium in the sense that (1) everyone gets a job, (2) each individual prefers the job he or she has to all other jobs existing at the same time, and (3) it is impossible for employers to increase their profits by altering the structure of earnings or substituting existing jobs for non-existent (but feasible) jobs. This seems to be a very idealistic view of the labour market. In reality, the matching mechanism does not bring about equilibrium of this kind. Instead, we witness a more or less permanent excess supply of labour and lots of disappointments when individuals are denied jobs they apply for. How do we account for this? One reason might be that individuals applying for a particular job in fact have the same reservation wage for this type of job. In this case there will be no applicants at all when the wage offered is lower than the reservation wage, but a large number of applicants when the wage offered is at least as high as the reservation wage, forcing the employer to select from many of those interested in the job. Another reason might be that some applicants in fact have a lower reservation wage, and consequently would apply for the job even if the wage offered was lowered, but that the employer is forced not to hire workers at a lower wage. There might, for example, be an agreement with the labour union to keep the wage above a certain level. A related motive is that the employer wants to have a ‘fair’ structure of wages. Richard Thaler (1989) argued that this motive applies to unskilled or otherwise normally low-paid workers in an industry with a large proportion of workers earning relatively well. Whatever the reason, the result of setting the wage rate above its equilibrium level will be that workers end up unemployed rather than (reasonably) well paid. We return to this issue in Chapter 7. A third reason might be that the employer makes a profit by offering a higher wage than necessary. There are at least two motives for being generous. One is that the employer wants to be selective in the hiring of workers, which is worthwhile whenever workers differ in working capability (expected productivity) and the employer wants to make sure of getting the right individual for the job. Another motive, suggested by Carl Shapiro and Joseph E. Stiglitz (1984), is that the employer pays for loyalty. By paying a bonus wage at the same time as workers are threatened with dismissal for

Inequality

39

not working satisfactorily, those hired are given an incentive to act in the employer’s best interest. The same incentive may be obtained in a hierarchical structure of occupations where workers are gradually promoted to a higher rank. As long as promoted workers earn a bonus wage and promotions are based on past performance, workers will have an incentive to work in the best interest of the employer. This latter type of incentive is common in the public sector. In all of these cases there will be non-compensating differences in earnings rates. Note that these differences are of a different category to monopoly rents and entrepreneurial rents, and also that they are confined to the labour market. For lack of a better term, we call them hiring-and-firing rents. Within this category we may distinguish between selection rents, incentive rents, and so on. Differences in Human Capital Investments Our last topic in this section concerns investments in personal ability. Schooling is an obvious case. How do we account for the fact that individuals do not follow the same human capital investment programme? There are at least three possible answers to this question. First, there might be financial market imperfections preventing some individuals from taking advantage of investment opportunities. It might, for example, be the case that one needs wealthy parents in order to be able to pay for investments in schooling. This inequality is stressed by Gary S. Becker (1967, 1975). Second, there might be essential differences in inherited personal ability. For example, suppose that more able individuals learn more per hour of schooling. Although they have a larger opportunity cost for the investment, more able individuals will get a larger profit from a given investment and should, accordingly, invest comparatively more than other individuals. If so, we may say that the return in respect of schooling to some extent is attributable to superior ability. Third, when human capital investments have little or no value outside the working place, the profitability of these investments will differ among individuals because of differences in the supply of labour. As seen in the previous analysis, a number of factors cause such differences. The point to be made here is that individuals who plan to supply a low amount of labour should make a comparatively small amount of human capital investment. We return to this point in Chapter 6. Differences in Luck We have indicated what causes inequality in the stock of human capital, and also pointed out a number of reasons why there is inequality in

40

The economics of social protection

individuals’ expected rate of earnings from their human capital. One point remains to be made before we leave inequality in earnings. People cannot be sure of getting the earnings they expect. Some workers are lucky and earn more, while others are unlucky and earn less. An obvious example is when two farmers work equally hard during the year but face quite different weather at the time of harvesting.

3.

Social justice

The preceding analysis showed the nature of inequality in a market economy. We identified a number of factors explaining why people receive different amounts of income (or wealth, or consumption) during a particular period of time. Our presentation of these factors began with the case of identical individuals living in a world of homogeneous assets and jobs. In this case inequality was a result of random events and differences in age, but its size was modified by the rate of economic growth and private transfers. Next, we considered the case of non-identical individuals of the same age living in a world of homogeneous assets and jobs, with inequality generated by differences in initial position, preferences and random events. Initial positions are characterized by inherited ability and inherited material wealth. Finally, we relaxed the assumption of homogeneous assets and jobs and considered inequality related to differences in portfolios and occupations chosen by different individuals. Here, we made a distinction between compensating and non-compensating differences in the expected rate of return from various assets and in the expected rate of earnings in various jobs. With respect to non-compensating differences we divided rents into monopoly rents, entrepreneurial rents and hiring-and-firing rents. We shall now take a look at the relationship between inequality and social justice. There are many notions of social justice in the literature, but we only cover a few of them here. We start with the notion proposed by Duncan K. Foley, Hal R. Varian and others according to which the meaning of social justice is an envy-free outcome of economic activities. A related, but different, view on social justice is that only inequality outside the control of the individuals should count. This was proposed by John E. Roemer, among others, and is called equality of opportunity. Finally, we look at the notion proposed by John Rawls, Friedrich A. Hayek, Robert Nozick and others stating that social justice is a characteristic of the procedure by which an outcome is generated rather than characteristics of the outcome itself. All of these notions of social justice imply that some inequality is either irrelevant or necessary for the achievement of social justice. From these rather visionary concepts of social justice we move on to the notions of justice used by ordinary people. The survey of these by James Konow and his attempt to formulate an empirically based notion of social justice are described in the second section. In the third section we discuss 41

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The economics of social protection

distributional policy and illustrate how this policy works. Finally, in the fourth section we take a closer look at the approach to social justice suggested by Knut Wicksell.

NOTIONS OF SOCIAL JUSTICE The three notions of social justice proposed by Foley, Roemer and Rawls are all ‘egalitarian’ in spirit, but they represent different approaches to the subject matter. According to Foley, social justice is a property of the distribution itself, while Rawls claims that social justice is a property of the processes by which the distribution is brought about, and Roemer suggests that the perspective of social justice should be limited to differences in opportunity. Envy-free Allocations Foley’s notion of social justice is based on the principle of fair division, according to which the entity to be divided should be split in such a way that everyone prefers the piece he or she gets to the pieces others get. After a fair division, nobody has anything to gain from being in somebody else’s shoes. An allocation of goods (and ‘bads’) with this property is said to be envy-free (Duncan K. Foley, 1967). The terminology is a little bewildering since ‘fair’ or ‘envy-free’ allocations are sometimes also called ‘equitable’ allocations. Sometimes ‘fair’ refers to allocations that are both ‘envy-free’ and Paretoefficient. For an overview of the literature, see William J. Baumol (1986). This idea of social justice may easily be applied in situations where the entity to be divided is given exogenously, like manna from heaven. In such a case we may be sure that a fair distribution exists. For example, if the entity to be divided consists of apples and oranges it would be fair to give everyone an equal share of each. But this is not the only solution. If people have different preferences for apples and oranges it would also be fair to let some have relatively more apples and others relatively more oranges. Inequality is not ruled out; what matters is that everyone is at least as happy with the share he or she gets as they would be with what others get. In the case of manna from heaven, there is a straightforward device to make sure that the allocation of goods is both fair and efficient. We could simply assign an identical endowment of apples and oranges to each individual, and then let them trade these goods among themselves under conditions of perfect competition. Trade will go on until the allocation is efficient in the Pareto sense. The same result would be obtained in an economy involving production, provided that everyone starts out with identical personal abilities, all live

Social justice

43

during the same period of time, and there are no random events. Everyone would then be able to earn the same income and have the same consumption as anybody else. Because of different preferences, individuals might choose to work and consume differently, but these differences should not give rise to envy among reasonable individuals. Of course, it cannot be taken for granted that people are reasonable in the sense that everyone takes full responsibility for his or her own behaviour. Suppose, as an example, that the individuals we are talking about live for two time periods and have the same preferences except that some have a high and others a low subjective rate of time discount. Because of this difference some individuals will consume more and save less during the first period, and consequently have less to consume during the second period. If these individuals are reasonable they will accept the situation as fair, but we cannot be sure. Suppose that they, anyhow, start to envy their more thrifty fellows during the second period. Clearly, in this case it would not be possible to obtain a fair allocation unless everyone had been forced to consume and save exactly the same amount in the first period, but then the allocation would hardly be efficient. This is admittedly a very simple case. To be of more practical use, Foley’s notion of social justice must apply in situations where individuals differ in inherited ability, are born and die at different points in time, and where there are unforeseen events having an impact on the distribution. But reasonably fair (and even more so, both fair and efficient) allocations are hard to find in these more complex cases. To illustrate this point we use the distinction between wealth-fair allocations and income-fair allocations suggested by Hal R. Varian (1974). Income-fair allocations are also known as full-income-fair allocations. In the case of wealth-fairness, an equal endowment of material wealth is assigned to each individual, but no compensation is made for differences in personal ability. Varian characterizes the resulting allocation in the following way: It only allows you to complain about another agent’s consumption if you are willing to match his contribution to the social product. . . . Thus I may ‘envy’ a doctor who only works one day a week doing brain surgery and yet has substantial consumption; but unless I am willing to put in enough labor time to match his production of services – for example, 6 years of medical school required – my complaint against him cannot count as legitimate in the sense of equity. (Varian, 1974, p. 73)

Since individuals may differ with respect to personal ability, social justice in the sense of wealth-fairness is compatible with inequality in both income and consumption opportunities. This proves, it seems, that

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The economics of social protection

wealth-fairness does not capture the true meaning of Foley’s notion of social justice. There is an interesting similarity between wealth-fair allocations and the popular norm that personal incomes should be distributed ‘according to labour’. The latter would point to a wealth-fair allocation when each individual’s ‘labour’ correctly measured his or her efforts in the production processes or contribution to the social product. Both meanings of ‘labour’ may be used. In this context, note that Karl Marx and his followers view distribution ‘according to labour’ as a temporary principle during the socialistic transition from capitalism to communism. By ‘labour’ they seem to mean effort rather than contribution to the social product, which is essentially what is said in Marx’s criticism of the so-called Gotha programme (Marx, 1875). According to him, work should ideally be a social virtue without any material remuneration at all. When such a stage is reached, that is when true communism has been established, consumption opportunities should be distributed ‘according to need’ and not ‘according to labour’. Income-fairness, on the other hand, means that inequality in the distribution of personal ability should be fully compensated. If there are N individuals, this compensation might be carried out by giving each person a coupon worth 1/Nth of all other persons’ potential earnings, in addition to 1/Nth of initial endowments of material wealth in society. Such a scheme would give everyone the same potential income and, given that all individuals work full time, consumption bundles of the same value. When people choose to have more or less leisure there will be differences in realized earnings as well as consumption bundles. One’s net ‘earnings’ will then be the difference between the lump sum everyone gets and the amount one chooses to spend on leisure. There are two snags with this scheme. First, complete equality will not be achieved. Since individuals differ in working capability, and these differences are reflected in earnings rates, leisure will be available on more favourable terms to less able persons than to more able persons. The more able a person, the higher the earnings rate and the more he or she must sacrifice in terms of income (and consumption goods) for an extra hour of leisure. Hence, if all individuals choose to have the same amount of leisure, the less able persons might at the same time be able to afford more consumption goods. Second, from a practical point of view it is imperative that the differences in personal ability counted in this compensation scheme are truly exogenous (inherited). If income-fairness is defined in such a way that everyone gets 1/Nth of the (potential) return from human capital investments undertaken by others in society, it would hardly be surprising if such investments disappeared altogether. The tax rate on human capital investments would be nearly 100 per cent. With less human capital, probably everyone in society would be worse off. In order to avoid this implication,

Social justice

45

income-fairness should be defined in such a way that differences in personal ability are compensated for only to the extent that they are truly exogenous (inherited). This is the point of departure for the notion of social justice proposed by John E. Roemer, as discussed below. What is meant by truly inherited differences in personal ability? Earlier in our analysis, it was stipulated that individuals reach the initial position (‘vintage age’) when they are ready to join the labour force, for example at the age of 20. With respect to the problem at hand it might be better to say that the initial position is at the time of birth. If so, since most inequality in personal ability is created through schooling and personal experiences, there would only be a small portion of inequality in personal ability left to compensate for; and income-fairness would not be much different from wealth-fairness. The fact that individuals are born and die at different points in time adds to the complexity of achieving an income-fair allocation. Somehow it must be taken into account that people born at different points in time experience more or less economic growth, are more or less exposed to the risk of becoming unemployed, pay more or less for defending the country against foreign aggression, and so on. In addition, we must find a way to deal with the fact that unforeseen/random events have something to do with the outcome. Would it be enough if everyone had the same income opportunity ex ante, or does Foley’s notion of social justice require that those who gain from unforeseen/random events fully compensate those who lose? Clearly, there is a long way to go before we have an operational definition of social justice in the sense Foley has suggested. Equality of Opportunity Differences in the way people consume, work and invest reveal different preferences and/or different opportunities. Differences in opportunities occur for a number of reasons. Some individuals lack personal skills because of, among other things, a bad inheritance or a neglected childhood; some are victims of discrimination; and some are simply ignorant of the options at hand. From a normative point of view, inequality generated by such factors might seem to be more serious than inequality merely reflecting differences in preferences. The notion of social justice suggested by John E. Roemer in the 1960s and elaborated in Roemer (1998) is based on the distinction between choice and opportunity. He argues that inequality only matters to the extent that differences in income and so on reflect differences in opportunity. That people choose to study more or less or save more or less, or work more or less, is not a social injustice according to Roemer, as long as they are able

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The economics of social protection

to choose the same amount of studies, savings, work, and so on. Only differences in opportunity count as social injustices. The proposal by Roemer and others, for example Ronald Dworkin (1977), is that social policy should focus on ways and means to eliminate differences in opportunity, or at least to compensate for such differences. In one way or another, equality of opportunity must be established. Roemer does not claim that equality of opportunity can be fully implemented. There are situations where it would be absurd to fully compensate for differences in natural ability, caring by parents, and so on. But there are also many situations, he argues, when it is important to establish equality of opportunity. Roemer’s favourite example is education. There is much evidence that individuals are born with a different ability to study and take advantage of schooling. Since we cannot change basic differences in learning ability, the question is how to compensate for these differences. One possibility is to vary the amount of resources for schooling so that the outcome of schooling becomes the same (similar) for everyone concerned. For example, individuals with a low IQ should be placed in schools with excellent teaching facilities. Another possibility would be to compensate for a lack of personal ability with extra material wealth. For example, one could calculate expected differences in earnings because of differences in IQ and give individuals a personal account of wealth varying inversely with the level of IQ. Accounts with a positive amount for individuals with a relatively low IQ could be financed by letting individuals with a relatively high IQ start life with a negative account. Whether such compensations would be absurd or not is up to the reader to decide. Among inherited factors are age (date of birth), gender, race, and so on. Roemer suggests that such factors are neutralized by so-called affirmative action. With respect to Varian’s notion of income-equality we have pointed out that equality of opportunity should be defined in terms of the initial position at birth, and that inequality in inherited wealth and ability might be relatively small compared with differences in acquired wealth and ability. In an application of Roemer’s notion of social justice we would also have to consider how individuals should be compensated for differences in circumstances such as economic growth and luck. Such factors should be included among opportunities. If they are, a socially just policy must include various compensations for differences in these factors among individuals, but it is hard to see how this may be done. A Fair Procedure John Rawls claims that he has found a way to avoid the problems one is bound to encounter on the route suggested by Foley, Roemer and others.

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47

According to Rawls, social justice is not a matter of what the distribution of income (or wealth, or consumption) actually looks like. The important thing, in his view, is not whether inequality is small or large, but how it is brought about. A similar view was expressed by Friedrich Hayek (1976). The suggestion is that we look at the rules by which society is organized rather than at particular outcomes of these rules: the principles of justice do not select specific distributions of desired things as just, given the wants of particular persons. This task is abandoned as mistaken in principle, and it is, in any case, not capable of a definite answer. Rather, the principles of justice define the constraints which institutions and joint activities must satisfy if persons engaging in them are to have no complaints against them. If these constraints are satisfied, the resulting distribution, whatever it is, may be accepted as just (or at least not unjust). (Rawls, 1963, p. 102)

Rawls does not mean that any set of rules constitutes a just society. There must be a way by which just rules may be distinguished from unjust rules. The question is how? To say that just rules are such that people ‘have no complaints against them’ does not settle the issue. How may we be sure that people will refrain from making unreasonable complaints? If such complaints should be ignored, where do we draw the line between reasonable and unreasonable complaints? And are we not back in the kind of evaluation Rawls wanted to avoid in the first place? A situation may easily be envisaged where people make complaints about the rules by which society is organized precisely because they do not like particular outcomes generated under these rules. Is there a way out? Rawls’s solution to this problem is that we should imagine ourselves in a situation where we have to evaluate the rules under consideration without knowing who we are and in what position in society we are likely to turn up, ‘behind a veil of ignorance’ (Rawls, 1972). In such a situation, he argues, each of us would have to contemplate the common good and try to work out what would be best for everyone in society. The rules agreed on in such a situation would be the ones constituting a just society. Behind the veil of ignorance, Rawls claims, we would unanimously agree on rules satisfying the following two basic principles (quoted from Rawls, 1993, p. 291): ●

●

A. Principle of liberty: Each person has the same indefeasible claim to a fully adequate scheme of equal basic liberties, which scheme is compatible with the same scheme of liberties for all. B. Principle of difference: Social and economic inequality are to satisfy two conditions: first, they are to be attached to offices and positions open to all under conditions of fair equality of

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The economics of social protection

opportunity; and second, they are to be to the greatest benefit of the least-advantaged members of society. The second condition is the so-called maxmin principle, stating that inequality in income (or wealth, or consumption) is permissible, provided that it directly or indirectly benefits the least advantaged individuals in society. For example, private returns from schooling and other forms of human capital investments are permissible to the extent that they promote economic growth and the level of living attained by the poorest members of society. Rawls strongly objects to the view that all sorts of inequality should be avoided at any cost. If inequality attached to offices and positions is needed to enhance the least advantaged individuals’ welfare, the difference principle states that such offices and positions should be accessible with a fair equality of opportunity. For example, if it is desirable that taxi drivers have a licence, such licences should be issued under free (or rather, perfect) competition. It is obvious that the difference principle rules out monopoly rents. Whether this principle also rules out the entrepreneurial rents and hiring-and-firing rents mentioned in Chapter 2 depends on the effect of these rents on the situation of the least well-off individuals. The same would be true for differences generated by chance. It should be pointed out that Rawls places the principle of liberty and the principle of difference in lexicographic order. In his view, nobody should be forced to give up basic liberties for the sake of enhancing anybody else’s welfare, not even if this individual is the least fortunate in society. It is a different matter that concern for others may lead us to voluntarily give up some freedom. Rawls does not object to curtailments of personal liberties, but he insists that decisions to give them up should be agreed on unanimously. It is interesting to see how well Knut Wicksell’s notion of just taxation fits into Rawls’s scheme (or, rather, how well Rawls’s scheme fits into Wicksell’s notion of justice). Wicksell did not oppose taxation as such, but he argued that it would seem to be ‘a blatant injustice if someone should be forced to contribute toward the costs of some activity which does not further his interests or may even be diametrically opposed to them’ (Wicksell, 1896, quoted in Musgrave and Peacock, 1958, p. 89). According to Wicksell, justice requires all decisions concerning taxes to be agreed on unanimously (when possible). Furthermore, also like Rawls, Wicksell held the view that justice in this sense only applies in situations where all the conditions of social justice are met: ‘one cannot take a just part out of an unjust whole’. He was particularly concerned with monopoly rents and inherited differences in wealth. (Wicksell, 1896, was written in German, but a translation into English of one of the most important parts was included

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in the anthology edited by Richard A. Musgrave and Alan T. Peacock, 1958.) Many would probably agree that the principles suggested by Rawls are reasonable, but there are some notable exceptions. For example, in his review of A Theory of Justice, Herbert L.A. Hart (1973) criticized Rawls for not stating clearly where the two principles come from and for not explaining how they may be used in everyday legislation. Rawls accepted this criticism and wrote a number of papers on the subject, summarized in Political Liberalism (1993). Another example is Robert Nozick (1974). From a libertarian point of view he argues that Rawls, by placing his individuals behind a veil of ignorance, completely misses the point of having a procedural notion of social justice. The reason is, he says, that individuals behind the veil of ignorance have nothing else to care about than what the distribution actually looks like. According to Nozick, a procedural notion of social justice must take history into account. Entitlements should be recognized whenever they have been acquired, be it through work, trade or gifts over hundreds of years. From this point of view, Nozick does not see any virtue in Rawls’s difference principle. Anyway, we have no reason to believe that rules based on these principles and the distributions generated in accordance with them will be generally accepted. As soon as the veil of ignorance is lifted, and people get to know who they are and in what position they are likely to turn up, their views on society are likely to change. People might then start making complaints about rules that do not favour their particular interests. This is one of the points made by Hart that Rawls finds difficult to avoid. It is a dilemma for which moral philosophy seems to be unable to offer a remedy. Summary Table 3.1 is an attempt to summarize what the three discussed notions of social justice might imply vis-à-vis the different kinds of inequality pointed out in Chapter 2. ‘Yes’ means that the inequality is acceptable or even necessary, and ‘No’ means that it is not. It is clear that Roemer objects to inherited differences in opportunity and argues that those who are unfortunate should be fully compensated. An interesting question is whether such compensations would be acceptable under Rawls’s difference principle. The problem is that compensations for differences in inherited IQ and so on might have a negative effect on parents’ wish to provide good opportunities for their off-spring. If so, this might harm the situation of the least well off individuals, both directly and indirectly. This is an example of possible conflicts between different

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The economics of social protection

Table 3.1 Tentative classification of inequality according to Foley, Roemer and Rawls Foley

Roemer

Rawls

Yes Yes ? No

Yes Yes ? No

Yes Yes Yes Yes*

No No

Yes* Yes*

Yes

Yes*

Yes

Yes

No

No

?

Yes*

?

Yes*

Yes

Yes*

Identical individuals Age Random events, ex ante Random events, ex post Growth

Non-identical individuals of the same age Inherited differences in wealth and/or ability No Acquired differences in wealth and/or ability No because of different opportunities Acquired differences in wealth and/or ability Yes because of different preferences Compensating differences in the return on Yes assets and/or ability Non-compensating differences in the return on No assets and/or ability: monopoly rents Non-compensating differences in the return on ? assets and/or ability: entrepreneurial rents Non-compensating differences in the return on ? assets and/or ability: hiring-and-firing rents Random differences in the return on assets ? and/or ability

Note: * Provided that the inequality directly or indirectly benefits the least advantaged individual.

notions of social justice. The reader is welcome to question the content of the table.

POPULAR VIEWS ON SOCIAL JUSTICE None of the notions mentioned above have unconditional popular support. Experiments and questionnaires show that ordinary people have a rather complex view on social justice, which should not come as a surprise to economists. Unlike philosophers and sociologists and to some extent psychologists, economists have always been rather sceptical about the idea of social justice. A different view, expressed by James Konow (2003), is that economists should take an active interest in the issue of social justice. According to him, people do care about social justice and are influenced by some

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51

notion(s) of it in their daily life. For this reason, he argues, we should try to find out what these notions really are and let them be a vivid part of our theory of human behaviour. As a first step, Konow reviewed a vast literature on empirical research in the area, in economics as well as other disciplines. His conclusion was that an integrated theory of social justice should include three major elements – equality, efficiency and equity – with variable importance depending on circumstances (context). Regarding equality, the empirical findings surveyed by Konow contradict the ideas that social justice requires all individuals to have equal original positions (inheritance), equal opportunities or equal right to the results of economic activities. Neither is there any support for Rawls’s idea of maximizing the position of the least well off individual. Instead, it seems that most people prefer a policy that maximizes social welfare, given that basic needs are secured for everyone. To what extent differences in need should be taken into account is unclear. Regarding efficiency, Konow mentions findings indicating that individuals have a utilitarian view in the sense that they prefer an organization that maximizes the surplus of joint activities. He also finds some support for the Pareto criterion as a notion of justice, but he cannot find strong support for Foley’s idea that just distributions are envy-free. Regarding equity, finally, Konow does not find empirical support for Nozick’s view that social justice is determined by the processes by which people have acquired and transferred wealth throughout history. It seems that most people mistrust historical transfers and perhaps also original acquisitions. Anyway, many think that desert is an important component of social justice. Desert (in the sense of getting one’s ‘just deserts’) incorporates the efforts and choices that affect an individual’s contribution to the social product, but it disregards birth, luck and choices that do not affect productivity. In the empirical studies referred to by Konow, desert is directly related to an individual’s responsibility for his or her contribution to the outcome. These latter findings support an idea by Elliott Jaques (1956), according to which wages should be set in proportion to the amount of responsibility carried in the respective positions in the production process. Jaques, whose task was to find a wage structure that white-collar workers in a large company could consider fair, found that the amount of responsibility may be measured by a position’s ‘maximum time span of discretion’, which is determined by the value of possible damages that may be done and the length of time that elapses before the employee may be relieved of responsibility by reporting to somebody placed higher in the hierarchy of positions. As mentioned, Konow’s empirical findings indicate that the role played by these elements of justice depends on the context. The term local justice

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The economics of social protection

is used to emphasize the relative nature of social justice. Anyway, many of those who do this kind of research also point out some universal (global) elements of justice, such as need, desert and free exchange (Michael Walzer, 1983); efficacy, need and disadvantage (H. Payton Young, 1994); desert, need and efficiency (Norman Frohlich and Joe A. Oppenheimer, 1992); efficiency, need and exogenous opportunity (Jon Elster, 1992); and equality, equity/merit, efficiency and need (John T. Scott et al., 2001). In Jon Elster’s view on social justice the elements mentioned are ordered lexicographically: (1) maximize total welfare, (2) deviate from (1) if necessary to ensure a minimum level of welfare, (3) deviate from (2) if people fall below the minimum level because of their own choices, and (4) deviate from (3) if the failed choices are a result of conditions beyond their control (Konow, 2003, p. 1229). Of the basic elements of justice mentioned, it seems that equity has highest priority. Konow finds evidence that the term ‘fair’ is used with both a narrow and a broad meaning. In the narrow sense fairness refers to equity, and in the broader sense it refers to ‘good’, in which case it also includes need and efficiency. He is careful to point out that equity guides distributive preferences, but does not monopolize them. Although people care about equity, the allocations they prefer for themselves and consider right are also influenced by concerns for efficiency and need (p. 1235). It seems, then, that people value equity but prefer to live in a society that sacrifices some equity in order to provide for a higher minimum and mean income.

POLITICS Governments have the powers necessary to reshape the distribution of income (or wealth, or consumption) in society and thereby realize any notion of social justice politicians might have, provided that this notion is practicable. But a government cannot be expected to use its powers for the purpose of achieving a common good like social justice. The simple truth, as political science teaches us, is that rulers have competitors and must compete to stay in power. In return for their support for one (potential) ruler rather than another, various factions of society demand special favours. Policies in the general interest buy less support than policies that appeal to special interests. For these reasons, as for example Niccolò Machiavelli clearly recognized, politics may be described as an interaction of supportseeking politicians and rent-seeking special interests (see Edmund Phelps, 1985). Special interests may be served in a number of ways, notably in the form of public offices (or employment), subsidies and protective regulations, often camouflaged as a common interest (Dan Usher, 1981).

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Where rulers look for support will depend on circumstances. During medieval times, when Machiavelli made his observations, the scene was dominated by aristocratic families. Granting them favours was then the easiest if not the only way to acquire and keep the powers of government. Later on, after the industrial revolution, new groups entered the scene and made (potential) rulers less dependent on the aristocracy. However, politicians continued to be very much in the hands of those from whom they sought support. For example, Karl Marx claimed that the capitalists of his day had become the real rulers of society; politicians were just acting on their behalf. According to some Marxists this is still the case (James O’Connor, 1973). Nowadays the situation is seemingly more complex. In a democracy, where all are counted equally, politicians cannot hope to gain (and keep) the powers of government unless they appeal to many special interests at the same time. As argued by Gordon Tullock (1983) and others, this situation invites very diverse policies and great varieties of favours are spread among members of society. Kenneth Boulding and Martin Pfaff (1972) refer to this phenomenon as a grants economy, in which they include much more than transfer payments and subsidies proper, for example tax expenditures and regulatory measures of various kinds, like foreign trade quotas. In their view, most government policies fall into the category of grants. A consequence of the political process is that the policies used will tend to be rather inefficient from a strictly redistributive point of view. Although politicians become much involved in the allocation and distribution of work, savings and consumption in society, the redistributive effects they achieve will often seem to be of a highly circular nature. Over the life cycle most individuals will find, by and large, that they themselves have to pay for the benefits they get from government. This point is illustrated below. This is not to say that no real redistribution is going on in modern democracies. What it means is that the net effect of all the redistributive measures actually in use – leaving the rhetoric aside – may be expected to be on a relatively modest scale and, moreover, not systematically favouring any particular notion of social justice. It does not follow that redistributive policies are harmless. The measures used in granting favours to special interests, and the taxes it takes to finance them, are costly because they interfere with the conditions of an efficient allocation of resources in society. People will be less productive, on average, in their savings and working efforts. In addition there might be damage to the political system itself. When incomes (or assets, or consumption goods) are assigned to people by majority votes rather than earned through market processes, and the majority tends to use its powers to gain favours at the

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The economics of social protection

Table 3.2 Marginal cost of public funds for a marginal tax increase in the kth income bracket Country

Denmark France Germany Italy UK

Bracket/decile where the marginal tax is increased 1

2

3

4

5

6

7

8

9

10

1.34 1.29 1.26 1.13 1.10

1.51 1.59 1.37 1.19 1.13

1.92 1.71 1.51 1.46 1.17

4.50 1.89 1.98 1.80 1.24

4.10 2.01 4.13 2.48 1.26

9.91 2.12 3.97 2.62 1.31

L 2.34 59.07 3.27 1.34

L 2.14 37.30 4.65 1.51

L 2.36 L 4.77 1.52

L 14.69 14.94 L 2.68

Note: L
the tax rate is above the Laffer curve maximum, meaning that tax revenues decrease as the tax rate increases. Source: H. Jacobsen Kleven and C. Thustrup Kreiner (2006, p. 1969).

expense of minorities, the political climate will indeed be harsh; some may even lose faith in the system. The cost of transfers, positive as well as negative, is measured by the social marginal cost of public funds (SMCF) defined as SMCF
 (1/)(dSU/d)/(dPB/d),

(3.1)

where  denotes the average social marginal utility of income, and  is some component of the tax-transfer system, such as a tax on earnings, or an unemployment benefit, having an effect on social utility (SU) and the public budget (PB). Note that the measure (3.1) refers to a marginal change in public revenues and/or public expenditures. Table 3.2 illustrates the cost of income taxation with respect to labour supply effects, both in terms of participation rates and working hours. The marginal cost of public funds shows what the general public must sacrifice to pay one unit of tax. This sacrifice is different for different taxes (or grants) and for different categories of taxpayers. The table shows how the cost varies with the size of the taxpayer’s income. Because of the progressive nature of the income tax, tax rate increases are more costly in higher income brackets. An ‘L’ in the table indicates an infinitive cost, meaning that increases of the tax rate reduce the tax base, for example earnings, by so much that tax revenues actually decrease when the tax rate is raised. Table 3.2 also shows that the social marginal cost of public funds through income tax varies a great deal among countries, with the United Kingdom at the bottom and Denmark at the top. To some extent these differences reflect the level of taxation, but how the tax is designed is also

Social justice

55

important, for example to what extent the tax schedule is progressive. A particularly interesting aspect of the design is how labour force participation is affected. H. Jacobsen Kleven and C. Thustrup Kreiner show that taxes (and grants) giving people an incentive to abstain from (regular) work altogether, for example by applying for early retirement, are quite costly. An Illustration To illustrate how a grants economy works, at least partly, we shall use figures for Sweden. In connection with the 2003 Long Term Plan by the Swedish Ministry of Finance, Thomas Pettersson and Tomas Pettersson (2003) used simulations to estimate how the public budget was related to the budgets of individual households, both annually and life-long. Households were classified according to their income per capita and to correct for differences in household size Pettersson and Pettersson used the following equivalence scale consumer units
(A0.7*a)0.7,

(3.2)

where A is the number of adults and a is the number of children in the household. All individuals in a household, children as well as adults, were assumed to have the same income (
gross household income divided by the number of consumer units). Two measures of inequality were used: the Gini coefficient as defined above (denoted G) and the ratio between the eighth and second deciles (denoted D). The following four concepts of income were used: ● ● ● ●

Factor income
Taxable income from labour and capital Disposable income
Factor incomecash benefits – direct taxes Private consumption and savings
Disposable income – indirect taxes Total income
Private consumption and savingspublic consumption of private goods.

Cash benefits include pensions, child allowances and other transfers received. Direct taxes include income taxes, wealth taxes, and other direct taxes. For these calculations Pettersson and Pettersson made use of detailed data for single individuals and (formal) households. The equivalence scale (3.2) was used to make transfers and taxes comparable between households. Since both disposable incomes and savings were known, it was straightforward to calculate the size of each household’s consumption. The amount of indirect taxes paid was assumed to be proportional to the

56

Table 3.3

The economics of social protection

Income dispersion annually and life-long

Factor income Disposable income Private consumption and savings Total income

Annually

Life-long

Difference

G

D

G

D

%

0.490 0.217 0.224 0.189

15.6 1.90 1.95 1.75

0.196 0.102 0.104 0.086

1.73 1.35 1.36 1.28

60 53 54 55

Note: G
Gini coefficient, D
Decile quotient. Source: Thomas Pettersson and Tomas Pettersson (2003).

amount of private consumption. Finally, each household’s share of public consumption was calculated as the value of schooling, health care, and so on. For health care and other ‘insurance goods’ this value was calculated as the premium one would have to pay for a hypothetical insurance covering the same amount of benefits in kind (or subsidies). Life-time incomes were calculated from observations of annual incomes from 1982 to 2001 and were measured as the average income per year during the period in question. The simulations incorporated demographic and other changes. Table 3.3 shows the two dispersion measures for different concepts of income. The dispersion was 50 to 60 per cent higher for annual incomes than for life-long incomes. We may also see that total incomes were much more evenly distributed than factor incomes. The dispersion of annual incomes was reduced by about 60 per cent when direct taxes and transfers as well as indirect taxes and public consumption were taken into account. The corresponding figure for life-long incomes was about 55 per cent. Table 3.4 shows the effect of particular components in the transactions between the public budget and individual households. Three measures were used. K is the concentration index measuring how a component is distributed compared to the distribution of total incomes. A negative value for grants received by households indicates that the component is more evenly distributed than total income. For taxes and other outlays the sign is the opposite. The measure W is simply each component’s weight in total incomes, and the measure GC is the component’s contribution to the value of the Gini coefficient for total incomes. These contributions may be aggregated. The table shows, among other things, that income taxes alone reduced the overall inequality in total annual incomes by almost a third (from 0.2675 to 0.1821). The corresponding figure for life-long total incomes was somewhat higher (from 0.1302 to 0.0842). National pensions as well as negotiated pensions contributed to increased income inequality, both annually and over the

57

Social justice

Table 3.4 Contribution to the dispersion of income by various components of the public budget Annual income K Factor incomes Negotiated pensions Old age pensions Disability pensions Spouse/child pensions Labour market support Sickness benefits Parental allowances Child allowances Housing allowances Housing supplement for pensioners Maintenance support received Study grants and loans received Social assistance Health care Child care Elderly care Secondary schooling Labour market programmes Adult education (local gov’ment) Prescribed medicine Primary schooling Adult education (other) Tertiary schooling Income taxes Other direct taxes Study loans repaid Indirect taxes Total income

W

Life-long income GC

K

W

GC

0.2924 0.2343 0.0601 0.2309 0.3307

0.8750 0.2559 0.1306 0.0398 0.0093 0.3271 0.1622 0.0097 0.1060 0.0387 0.0089 0.3190 0.0013 0.0004 0.0044

0.8517 0.1112 0.0442 0.0145 0.1767 0.0187 0.0415 0.0132 0.0006 0.0000

0.0337

0.0283 0.0010 0.0234

0.0275 0.0006

0.0711 0.4806 0.0960 0.5072 0.2025

0.0325 0.0121 0.0202 0.0032 0.0080

0.0023 0.0526 0.0058 0.0239 0.0019 0.0407 0.0016 0.2264 0.0016 0.3166

0.0344 0.0018 0.0113 0.0003 0.0188 0.0008 0.0032 0.0007 0.0097 0.0031

0.1622

0.0060 0.0010 0.1226

0.0058 0.0007

0.1217

0.0105

0.0104

0.6378 0.1076 0.1282 0.5763 0.1364 0.0261

0.0048 0.0031 0.2907 0.0640 0.0069 0.0459 0.0212 0.0027 0.0315 0.0526 0.0303 0.1985 0.0110 0.0015 0.0025 0.0073 0.0002 0.0503

0.0047 0.0014 0.0683 0.0031 0.0200 0.0006 0.0564 0.0112 0.0104 0.0000 0.0071 0.0004

0.3954

0.0003 0.0001 0.1341

0.0003

0.0652 0.0263 0.0156

0.0109 0.0345 0.0004

0.0117 0.0003 0.0327 0.0011 0.0005 0.0000

0.1397 0.2575 0.3461 0.1830 0.1178

0.0051 0.3316 0.0283 0.0097 0.0804 1.000

0.0013

0.0317

0.0007 0.0279 0.0009 0.0323 0.0000 0.0038 0.0007 0.0854 0.0098 0.0018 0.0095 0.1821

Source: Thomas Pettersson and Tomas Pettersson (2003).

0.0669 0.1368 0.1454 0.0727 0.0596

0.0051 0.3361 0.0230 0.0104 0.0834 1.000

0.0003

0.0000

0.0003 0.0460 0.0034 0.0008 0.0050 0.0842

58

The economics of social protection

life cycle. The concentration index was particularly large for negotiated pensions. Alongside factor incomes, elderly care was the single most ‘regressive’ component in the public budget, contributing 17 per cent of the total dispersion in annual incomes and 13 per cent of the total inequality in life-long incomes. Disability pensions had an opposite effect. To study the redistribution among socioeconomic groups, Pettersson and Pettersson calculated the net balance for each group on the assumption that each cohort fully paid for its own benefits. Since benefits were given exogenously, this balance was achieved by varying the amount of taxes paid by the cohort. Pettersson and Pettersson applied different assumptions about the taxes in use, but for us it is sufficient to look at the situation when the taxes needed consisted of all payroll taxes and a sufficient amount of additional direct and indirect taxes. In this case, Pettersson and Pettersson found that most taxes were returned to the taxpayer. On average, no less than 45 per cent of taxes paid were used to finance grants that come back to the taxpayer the same year. Another 38 per cent of taxes paid were returned within the taxpayer’s life cycle, and only 18 per cent were used for interpersonal redistribution. The latter figure is relatively low. For example, interpersonal redistribution accounts for 48 to 62 per cent of taxes paid in Australia, 45 per cent in Ireland, and 29 to 38 per cent in Great Britain. A major reason for the low Swedish figure is that Sweden has adopted the ‘universal’ welfare state model, where the public sector manages many transfers and consumption goods that are handled privately in other countries. Means-tested benefits take a relatively small share of the Swedish budget for social policy. In the simulations conducted by Pettersson and Pettersson, given a zero net balance, an average Swede was expected to pay SEK 6.8 million in taxes during a lifetime. In return, he or she was expected to get back 3.8 million in cash benefits and 2.9 million in public consumption of private goods (benefits in kind). The balance between payments and receipts was expected to be better for women ( 941 thousand) than for men (963 thousand). About one quarter of the difference between men and women was a result of the fact that women live longer and therefore benefit more from the pension system (237 compared to 244 thousand for men). Those belonging to the highest income quintile were expected to pay 3.3 million more than they get back, while those in the lowest income quintile were expected to receive 2.5 million more than they pay. Hence, in spite of the low figure for interpersonal redistribution mentioned above, there was a substantial amount of redistribution going on in the Swedish economy. The net balance for individuals with tertiary education was 434 thousand, compared with  129 thousand for individuals with at most secondary education and 824 thousand for individuals with just primary

Social justice

59

education. Is this redistribution sufficient to satisfy Roemer’s proposal that inherited differences in educational ability should be compensated for? Does it improve the position of the least advantaged in the Rawlsian scheme? Or is it compatible with an envy-free allocation? It is obviously not easy to see a clear connection between these notions of social justice and a practical distribution policy. Compared with many other studies of redistribution through the public budget, the Pettersson and Pettersson approach has an advantage in the way public consumption of private goods is handled. It is certainly better to ascribe a positive option value to everyone concerned than to let the full value of benefits in kind, like health care, be credited to actual users in a particular year. The latter method is bound to generate larger income inequality, especially on an annual basis.

THE WICKSELL APPROACH As we have noted, Wicksell claimed that it would be ‘a blatant injustice if someone should be forced to contribute toward the costs of some activity which does not further his interests or may even be diametrically opposed to them’. The solution he suggested is to have a system where political decisions, to the extent possible, are taken unanimously. This would guarantee that everyone concerned would (expect to) benefit from the decisions in the sense that one’s marginal utility from all components of the public budget would be at least as large as one’s contribution to the budget. The mathematics of this device was later elaborated by Erik Lindahl (1919). In modern welfare economics, Wicksell’s idea has been known as the Pareto principle, according to which departures from present conditions are not acceptable unless at least one person gains thereby, and nobody loses. A common criticism of this principle is that it favours status quo and prevailing privileges. This is a relevant objection when present conditions include various obvious injustices, and the principle is used without exceptions. But this was not what Wicksell had in mind. He emphasized that the principle of unanimity should only be applied in situations where there is equality. It is not quite clear what kind of equality Wicksell was referring to, but he expressed concern about the wealth distribution in particular, and a fair guess is that he meant something similar to Roemer’s equality of opportunity. One of his proposals was that estates should be confiscated and distributed equally among young individuals, preferably as an investment in their future. Anyhow, it seems worthwhile to think through Wicksell’s proposal and try to work out what kind of social policy his view on social justice implies.

60

The economics of social protection

To make things simple, let us assume that equality of opportunity prevails and, therefore, that unanimity is sufficient for an acceptable policy improvement in the Wicksell sense. What kind of social policy would then be chosen? We take a closer look at this issue in later chapters, but we have touched on the subject already in Chapter 1. What we then called the core of social policy is certainly close to the ideal Wicksell’s norm implies, provided that there are ways and means to avoid non-market failures. There is now not much to add to the discussion in Chapter 1, other than to point out that the kind of social policy discussed there might be seen as socially just.

4.

Pensions: basic model

In Chapter 1 we mentioned three principal devices for resource pooling: the family, the market and the state. How these devices work with respect to the problem of providing consumption opportunities during old age is discussed in this chapter. We focus, in particular, on the ways and means by which the state may improve the solutions provided by private arrangements. A simple model is used to clarify the basic mechanisms of old age protection. We assume that there are just four phases of life – childhood, lower middle-age, upper middle-age, and old age – each covering some 20 years. We now disregard problems related to uncertainty and assume that everyone lives through all phases of life. We assume, moreover, that earnings are given exogenously. These assumptions are relaxed in later chapters.

THE ATOMISTIC MARKET To keep the analysis simple we now disregard childhood and assume that an individual’s life cycle consists of just three periods. Since everyone is assumed to live exactly three periods, population growth is determined by the increase in new entrants at the age of 20. Let this growth rate in period t be denoted gt. As before, Ni,t, i
1, 2, 3, denotes the number of individuals of age i during period t. From now on we set N1,t
1. By assumption, individuals work during the two first periods of the life cycle – as lower middle-aged with earnings Y1 and upper middle-aged with earnings Y2. Exogenous Rate of Interest For the moment we assume that consumption goods may be transferred between periods; forwards by savings and backwards by borrowing, in both directions with the rate of interest r. Leaving capital incomes aside, the present value of an individual’s earnings determines how much he or she may consume. The budget constraint in this case is C1 RtC2 RtRt1C3 Y1 RtY2 61

(4.1)

62

The economics of social protection

where Ci, i
1, 2, 3, denotes consumption during period i and Rt
(1  rt)1 is the discount factor when the rate of interest in period t is rt. The budget constraint shows the individual’s consumption possibilities. We assume that these are used to maximize a utility function u(C1, C2, C3) with conventional properties, that is u/Ci 0 and 2u/Ci2 0, i
1, 2, 3. For a maximum it is necessary that the budget constraint is fully exhausted and that (u/C2)/Rt(u/C1)
(u/C3)/RtRt1(u/C1)

(4.2)

These conditions, showing what the marginal rate of substitution between consumption in period 2 and period 1 and between consumption in period 3 and period 1 should be, determine the optimal consumption path Ci*, i
1, 2, 3, as well as optimal savings Si*
Yi  Ci*, i
1, 2, 3. Since the individual has not been ascribed any motive to leave bequests, the present value of savings during his or her entire life is zero, that is Si* RtSi* RtRt1Si*
0

(4.3)

When the optimization problem has a unique solution, it may be expressed as demand functions Ci*
C(Y1, Y2, Rt, Rt1)

i
1, 2, 3

(4.4)

These functions have the following properties Ci*/Yj

0

i
1, 2, 3; j
1, 2

(4.5a)

Ci*/Rt


0

i
1, 2, 3

(4.5b)

Ci*/Rt1

 0


i
1, 2

(4.5c)

C3*/Rt1 0

(4.5d)

The effect of additional earnings is that the desired level of consumption rises in all periods. Concerning the effect of a change in the interest rate, we may only say that a lowering of the interest rate in the third period decreases the desired consumption level at that time. (Note that the discount factor R varies inversely with the rate of interest r.) Changes in the interest rate may otherwise result in either increases or decreases in the desired consumption level.

63

Pensions: basic model

Example An example may be used to illustrate this optimization. Assume that an individual has the utility function u
logC1  logC2 2 logC3

(4.6)

where 
(1 ) 1 is a subjective factor of discount and is the rate of subjective discount. (Note that each period corresponds to 20 calendar years. Hence, an annual rate of subjective discount of 2 per cent implies a subjective factor of discount equal to 0.67.) In the special case Y1
Y, Y2
1 and Rt
Rt1
R consumption will be optimized when C1*
(YR)/(12)

(4.7a)

C2*
C1* /R

(4.7b)

C3*
C1* 2/R2

(4.7c)

This follows directly from equation (4.2) and the budget constraint, given that this constraint is fully binding. In this example it is clearly the case that income increases raise the desired level of consumption and that the effect of a change in the interest rate may be either positive or negative. With  (12) we have:

C1* C2* C3*

Ci*/Y

Ci*/R

1/0 /R0 2/R20

1/0  Y/R20 – 2(2YR)/R30

The signs ascribed to the derivatives presume non-negative values for , Y and R. In terms of utility, the outcome is u*
 [log(YR)  log](22)(log  logR)

(4.8)

The indirect utility function u(Y, R) describes how this outcome (attainable utility) varies with Y and R. For this function we have u/Y
/(YR)0

 u/R
/(YR)  (22)/R
0

(4.9a) (4.9b)

Increases in income allow the attainable utility to rise, while a lowering of the rate of interest (increases in R) may cause the attainable utility to either rise or fall.

64

The economics of social protection

A fall in the interest rate will cause the attainable utility to increase if the following conditions are met: 1, and RY(12)/(1  2). In the special case
0.49 and consequently 
0.67 (which implies an annual rate of subjective discount of 0.02), this condition is only met if R2.31Y. If the distribution of earnings is not too unequal, implying that Y  1, this condition may only be met when R1 and consequently r 0. For the conditions (4.9) to be met with a positive rate of interest, the distribution of earnings over the life cycle must be quite skewed. Hence, we may say that a lowering of the rate of interest – under the conditions specified – is unlikely to have a positive effect on the attainable utility. Endogenous Rate of Interest Thus far, the market rate of interest has been assumed to be set exogenously. As a second step in the analysis we let the market rate of interest be dependent on the situation in the market for savings and credits. Unless otherwise stated, this market is assumed to be characterized by perfect competition. A feature of this market is that individuals act by themselves; there are no collective actions and no organized cooperation. To emphasize this feature of the market we use the term ‘atomistic’. In 1958, Paul A. Samuelson showed that the equilibrium rate of interest in this type of financial market may be negative and even strongly so. A crucial condition for this result is that individuals are unable to keep their savings in the form of real property. All that is produced in the economy is immediately consumed (‘nothing will keep at all’, p. 468). As a consequence, individuals cannot take any of their own earnings into old age. If they do get a pension, it must be paid from younger persons’ earnings. In an atomistic market this may only happen if the young are in debt to the old. Hence, pensions are created in two steps. In the first step the upper middle-aged give loans to the lower middle-aged. In the second step, when everyone has become one period older, loans are repaid (with interest). It should be mentioned, in passing, that this system cannot function when there are only two homogeneous categories of individuals – workers with earnings Y and pensioners with earnings 0. No atomistic market solution for the transfer problem exists in this situation. The old have nothing to give and they are not capable of repaying what they may get from the young. Thus the market condition of mutually beneficial agreements cannot be fulfilled in this case. Let us now look more closely at the case with three generations. Equilibrium in the financial market requires total savings to be equal to zero. If all individuals are alike (apart from age) and the relative number of individuals in each age group is 1, Nt and Nt1 the equilibrium condition is

Pensions: basic model

(Y1  C1*)Zt(Y2  C2*)  ZtZt1C3*
0

65

(4.10)

where Zi
(1ni)1, i
t, t1. The equilibrium condition simply states that, in any period, total consumption must be equal to total earnings. When the population grows exponentially at the rate n, (4.10) simplifies to (Y1  C1*)Z (Y2  C2*)  Z 2C3*
0

(4.10)

Unless otherwise stated, n is assumed to be non-negative. By combining (4.10) and the solution to the individual’s optimization problem (4.4), we may obtain the rate of interest which clears the financial market. As an illustration we use the example mentioned earlier. Recall that we have set Y1
Y and Y2
1. After substituting (4.7) into equation (4.10), we obtain the following third degree equation to determine R R3  (Y2YZZ2)R2 (ZYZ22)R Z22Y
0 (4.11) It is straightforward to see that R
Z is one of the roots of equation (4.11). Hence, (4.11) may be written (R  Z) [R2  (YYZ) R  Z2Y]
0

(4.11)

from which we may identify the two remaining roots as R
1/2 {(YYZ)  2 (Y   Y  Z) 2  4Z2Y } (4.12) One of these roots is negative and implies r– 100 per cent. This root has no economic meaning. Samuelson used the same example in his analysis but limited his discussion to the case Y
Z

1. In this case, the roots are Ra
1 and Rb
(3  √13)/2
3.303. He showed that only Rb has the necessary characteristics for a stable equilibrium. The corresponding value for r
1/R  1 is  0.7. Hence, the market rate of interest compatible with a stable equilibrium in the circumstances specified is  70 per cent per period (corresponding to about  2.7 per cent annually). For obvious reasons, the equilibrium rate of interest becomes higher (and even positive) for lower values of , Z or Y. In the case Y
1 and Z

0.67, for example, the annual equilibrium rate of interest is just around  1.5 per cent. A positive rate of interest requires a skewed distribution of earnings. For example, when Y
0 (which is an extreme case) and as before Z

0.67, the annual equilibrium rate of interest increases to 4.4 per cent.

66

The economics of social protection

A positive rate of interest reflects a positive demand for loans among the lower middle-aged. In this case loans provide necessary consumption opportunities for the lower middle-aged as well as pensioners. A large portion of young people in society and a high rate of subjective discount imply a relatively high rate of interest for loans.

SOCIAL OPTIMUM As mentioned earlier, Samuelson did not use his model just to demonstrate the possibility of a negative equilibrium interest rate. He also used the situation he described as an argument for seeking non-atomistic solutions to the problem of optimizing consumption over the life cycle. To illustrate the atomistic market’s insufficiency, Samuelson compared this with the maximization of a social welfare function of the individualistic type subject to a budget constraint common for all individuals concerned. He assumed that all individuals are treated equally and that total consumption is limited by the sum of all working people’s earnings. When everyone is given the same weight in the social welfare function, this is the same as the case in which any given individual’s utility is maximized subject to the average of all individuals’ consumption possibilities. Let us focus on a representative individual and, as before, assume that the population grows exponentially. The representative individual’s utility function u(C1, C2, C3) is to be maximized subject to the budget constraint (1n)2C1 (1n)C2 C3
(1n)2Y1 (1 n)Y2

(4.13)

With Z
(1 n)1, the optimality condition may be written (u/C2)/Z(u/C1)
(u/C3)/Z2(u/C1)

(4.14)

This is the condition for a social optimum. It coincides with the condition (4.2) for an atomistic market equilibrium when Rt
Rt1
Z, and thus rt
rt 1
n. Samuelson called the rate of interest that brings these two optima to coincide, the biological rate of interest. This rate is defined for the case in which the population grows exponentially. In a static situation without population growth, Z
1, the biological rate of interest is zero. As shown in our earlier example, the biological rate of interest is a possible equilibrium rate of interest. The problem, as Samuelson made clear, is that this rate does not have the necessary stability characteristics. We have therefore no reason to believe that equilibrium with the biological rate of interest will be established spontaneously or, if it happens to be established,

Pensions: basic model

67

that it will last. Any disturbance, for example a temporary change in the rate of population growth, would start a movement towards the stable equilibrium rate of interest, which in our example is the positive root of (4.12). This result raises the question of how individuals may secure a socially optimal solution to the transfer problem. Measures to this end may be private as well as public. In the latter case, we limit ourselves to looking for solutions of general interest in the sense proposed by Wicksell; that is, that they may be implemented through voluntary cooperation. The most obvious solution seems to be that the individuals concerned decide to establish an asset for saving that has lasting value. One candidate, mentioned by Samuelson, is money. In a situation with a constant supply of money, consumer prices will vary inversely with regard to the production volume, which means that the value of money will grow at the same rate as the volume of production. If the latter increases at the same rate as the population (that is n) the value of money will also increase at that rate. This in turn implies that money holdings will yield a real return corresponding to the biological rate of interest, which is the socially optimal rate in Samuelson’s model. As an alternative, let us suppose that bonds are introduced with a real rate of return equal to the biological rate of interest. This would also turn the atomistic market solution into a social optimum. An advantage of this solution, compared with the constant supply of money solution, is that bonds are not directly used to pay for consumption. They are only used for the purpose of transfers and may be allowed to change without any direct concern for the effect on consumption prices. All one has to worry about is that individuals should be able to cash bonds at the promised real rate of return whenever they like. One important consequence of the introduction of money or bonds is that upper middle-aged individuals may secure pension needs without giving loans to the lower middle-aged. There is no longer any need for them to give these loans. However, there might still be a need for them to obtain such loans. In a situation where the lower middle-aged earn less than their optimal consumption profile requires, YC1*, they may make good use of a loan. Hence, to secure a social optimum some supplementary device is called for by which lower middle-aged individuals may get the loans they need to realize the optimal consumption profile. One period later these loans are paid back with interest, (1r) (C1* – Y). Social optimum requires that the rate of interest on such loans is set equal to the biological rate of interest. In case upper middle-aged individuals are reluctant to give loans spontaneously, although the return is as good as the return on money or bonds, it might be necessary to make these loans mandatory, for example by having a portion of the revenues from the sale of bonds converted to

68

The economics of social protection

loans. Since it is hard to see how a corresponding arrangement may be made in the constant money supply solution, we may conclude that bonds are a more useful instrument for achieving a social optimum. Would the introduction of bonds benefit everyone concerned? Lower middle-aged workers, in our example, plan to save as follows S1
Y  (YZ)/(12) S2
1  (YZ)/Z(12) S3
 2(YZ)/Z2(12)

(4.15a) (4.15b) (4.15c)

Expected utility from this plan cannot, by definition, be larger than is attained in the social optimum. With these savings, lower middle-aged workers are at least as well off as with the market solution, and are probably considerably better off. The introduction of bonds may therefore be expected to have unreserved support from this group. The first generation of upper middle-aged workers is a slightly different case, since they cannot completely adapt themselves to the new situation. First of all, they must fulfil obligations according to earlier loan agreements, which makes their demand for bonds smaller and reduces their gain from the introduction of bonds. However, with nr they get a higher return on what they save in addition to repaying loans. For the oldest individuals, the introduction of bonds has no immediate effect. Their consumption possibilities, which they receive from loan repayments by upper middle-aged workers, remain unchanged. Presumably, the oldest generation has therefore no reason to oppose a proposal to introduce these bonds. To sum up: as long as the rate of interest in the atomistic market solution is less than or equal to the biological rate of interest (r  n), some individuals gain and nobody loses from the introduction of bonds. At the time of the introduction, especially, lower middle-aged workers receive a – possibly substantial – windfall gain. Once the bond system has been installed, it will generate no further capital gains. There is a risk, however, of a corresponding capital loss in the future should the system be discontinued for some reason. That would particularly affect those who have reached old age at the time and who need to be able to exchange bonds for consumption possibilities. But not much is needed for the system to continue working. As long as the stability conditions are met, the system is able to keep going under its own steam. In case of a disturbance, the ‘biological’ equilibrium condition may be restored through suitable open market operations. Social insurance, meaning that the elderly are given a grant, , which is financed by taxes on current earnings, 1Y1 2Y2, is an alternative solution to the transfer problem pointed out by Samuelson. It should not be

Pensions: basic model

69

difficult to mobilize the political support necessary for the introduction of such a scheme. In our example, the optimal level of the tax/grant is given by (4.15). The sum that individuals pay in taxes would otherwise have been used to buy bonds. The grant replaces the amount they would have received from the sale of the bonds. Given that earnings grow at the same rate as the population, tax revenues and therefore grants should also grow at the same rate. Hence, the biological rate of interest would be the rate of return on taxes paid. To ensure that nobody loses because of the introduction of social insurance, the grant entitlement could, at least initially, be made conditional on tax payments. In this way only the lower middle-aged are completely covered by social insurance from the start, while the upper middle-aged are partially covered and the elderly are left aside. What the upper middle-aged pay to the elderly might in this case be deducted from their tax duty. It would seem that social insurance as a system is more reliable than the system with bonds. Minor variations in external conditions cannot bring about capital losses in this case. If taxes do not rise enough at some time, one may increase the tax rate and/or reduce the grant to pensioners. Alternatively the system could be supplemented with a buffer fund for such occasions. Hence, one does not have to worry too much about the economic sustainability of the pension scheme.

PORTFOLIO CHOICE Money, bonds and taxes/grants are not necessarily alternative instruments for securing a social optimum. We now briefly look at a model where these assets are used side by side, allowing individuals to choose among them. This situation has been analysed by Leigh Tesfatsion (1984) in an extended Samuelson model in which individuals are not identical and the price level may vary. For our present purpose a simpler version with identical individuals will do. An individual who lives in periods t, t1 and t2 has gross earnings Y1,t during the first period. After tax, net earnings are (1  1,t)Y1,t. Earnings not consumed may be saved as part of the individual’s cash holdings, M1,t, or used to buy bonds, B1,t. The latter are assumed to have a nominal value of 1 and to mature in two periods. With a purchase price of t, the return on a bond is (1 – t)/t and the implicit rate of return is determined by the equation rt
√1 t – 1. In these circumstances an individual’s budget equation during the first period may be written C1,t tB1,t M1,t
(1 – t)Y1,t

(4.16a)

70

The economics of social protection

It is taken for granted that cash as well as bond holdings are non-negative. Following Tesfatsion, we assume that the government has a monopoly in trading bonds and that each bond may be bought only once. Since bonds must be held for two periods, this means that the upper middle-aged are excluded from the market for bonds. For the two remaining periods the individual’s budget constraint is C2,t1 (M2,t1 – M1,t)
(1 – t1)Y2,t1

(4.16b)

C3,t2
(1rt)2tB1,t t2 M2,t1

(4.16c)

where t2 is the pension received from social insurance. This pension, together with the proceeds from the sale of bonds and the individual’s remaining cash holdings, provides consumption opportunities during old age. In the previous discussion we used only one budget constraint for the entire life cycle. If the interest rate on bonds is used as the discount factor, the overall constraint in the present case may be written C1,t RtC2,t1 Rt2C3,t2 (1 – t)Y1,t – tB1,t – M1,t Rt(1 – t1)Y2,t1 – Rt(M2,t1 – M1,t)Rt2(1rt)2tB1,t Rt2t2 Rt2M2,t1
(1 – t)Y1,t Rt(1 – t1)Y2,t1 Rt2t2 (Rt – 1)(M1,t RtM2,t1) (4.17) The effect of compressing the budget constraint in this way is that bonds become invisible in the equation. They figure only in the background as an equalizing factor between the first and third period. However, cash holdings are still expressed in the equation because they are costly or profitable when Rt 1 and consequently rt 0. The opportunity cost of cash is the return one could get from bonds, t  1. If cash had no worth in itself (because M is not an argument in the utility function) it would seem as if the individual should avoid having cash at all. This is all very well, but a non-negative value for either M1 or M2 is called for whenever C2*  (1  )Y2. A surplus or deficit between earnings and consumption in the second period cannot be eliminated by changes in the stock of bonds. That is why cash holdings must be used as a balance. Now, to consider situations with R 1 we look at the cases shown in Table 4.1. Only the first of these cases does not require cash holdings. The reason is that net income during the second period precisely corresponds to the desired consumption level during that period. In this situation the

71

Pensions: basic model

Table 4.1

Cases considered in the portfolio model Case

(1  )Y1  C1* (1  )Y2  C2* B1* M1* M2* Note:

†

1

2

3

4

(5)†

0
0 0
0
0

0 0 0
0 0

0 0 0 0
0


0 0 0
0 0

0 0 0
0 0

Note that case 5 may not exist when R  1.

budget constraint (4.16) is equivalent to (4.17) and for this reason the optimum conditions are (u/C2)/(u/C1)
(u/C3)/(u/C2)
R (u/C3)/(u/C1)
R2

(4.18a) (4.18b)

In all other cases cash is kept at some time, which implies that the marginal rate of substitution of consumption in the two periods must be equal to one. It is easy to convince oneself that the conditions for (second-best) efficiency in the different cases are as shown in Table 4.2. The marginal rate of substitution between consumption in the first period and in the third period is correct throughout. This is because purchasing power may be transferred between these periods with a constant present value. Only in case 1 are the two other rates of substitution correct. The social optimum conditions are not dependent on how transfers are actually carried out. The statements derived above hold even when individuals have different sorts of holdings in their portfolios. It is still true that the market solution is not socially optimal. To secure a social optimum in line with (4.18), the government must make sure that Table 4.2

Optimum conditions in the portfolio model when R1

(U/C2)/(U/C1)
(U/C3)/(U/C1)
(U/C3)/(U/C2)


1

2

R R2 R

R2 R2 1

3

4

(5)

1 R2 R2

R2

R2 R2 1

Note: Departures from the optimal solution (4.18) are marked in bold.

R2 1

72

The economics of social protection

individuals avoid cash holdings at the same time as the interest rate on bonds is made equal to the biological rate of interest. With a positive rate of population growth, n  0, this may most easily be accomplished by allowing individuals to trade bonds with a one period maturity. Alternatively, it is possible to have two-year bonds and raise taxes to the point where (1 – 2)Y2 – C2*
0. In both instances one may reach the point where M1*
M2*
0. Of course, the government is free to decide what the rate of interest on bonds should be. When the rate of population growth, and therefore the biological rate of interest, is negative, n  0, the problem is somewhat different. In a situation without inflation, cash holdings will then be more attractive than bonds. In such a situation social insurance is not a satisfactory arrangement either. It will not be sufficient to set taxes and grants so that wage earners’ net earnings exactly fit the socially optimal consumption level. The problem is that wage earners no longer need to be content with living from hand to mouth and accepting a negative rate of return from taxes paid. Since there is money in the economy, they may choose to postpone some consumption without any cost. To prevent cash holdings in this situation the government would have to hold down the rate of return on such holdings, perhaps by increasing the money supply to generate inflation. It would be sufficient for the rate of inflation to be high enough to make even bonds with a negative rate of interest more attractive than cash.

MARKET SOLUTION WITH REAL CAPITAL Our discussion is extended now to include savings with a lasting value in the form of real capital goods. To begin with, we assume that investments in such goods are the only form of savings. The main question now, as before, is whether an efficient solution to the transfer problem requires some form of cooperative arrangement. We approach this question from the point of view of a neo-classical production model, an approach first used in relation to social protection by Samuelson (1975) in a model with two generations: workers and pensioners. Here we retain the three-generation model, which makes the analysis somewhat more complicated but gives us an opportunity to see the role played by age-related differences in earnings. In the neo-classical production model, income is generated by production processes described by the production function Qt
f(Kt, Lt)

(4.19)

Pensions: basic model

73

with the usual characteristics, f0, f 0, and so on. Qt is the value added produced in period t. The factors of production, capital K and labour L, are assumed to be remunerated so that rt
f(Kt, Lt)0 wtLt
f(Kt, Lt)  rtKt

(4.20a) (4.20b)

where rt is the rate of interest and wt is the wage rate prevailing during period t in the capital and labour markets, respectively. This formulation refers to the situation in labour-managed companies (workers’ cooperatives). Such associations demand real capital, we assume, as long as the (value of) capital’s marginal product is at least as large as the rate of interest. Up to this point more capital contributes to a larger wage sum. The residual remaining after capital owners have been paid is distributed among workers. In an alternative scenario, which we shall leave aside, production is organized by capital owners hiring workers as long as the (value of) marginal product of labour, we assume, is at least as large as the wage rate, f/Lt wt. In this case capital owners get the residual, rtKt
f(Kt, Lt)  wtLt. With a linearly homogeneous production function these scenarios give identical outcomes for the distribution of income. We still assume that the labour supply is exogenously given. Lit is the amount of labour supplied by an individual of age i during period t. The total supply of labour is Lt
N1,tL1,t N2,tL2,t
L1,t ZL2,t during this period. Later on we broaden the analysis to allow for a variable supply of labour, but for now, individual optimization is restricted to the choice of a consumption plan and the corresponding savings plan. Earnings obtained through the described labour supply are, as before, denoted Y1 and Y2. We have Yi,t
wiLi,t, i
1, 2. Furthermore, we keep the earlier definition of savings as non-consumed earnings, Si,t
Yi,t  Ci,t, i
1, 2, 3. Savings now take the form of real capital accumulation (shares). We assume that savings occur on the last day of each period and that the transformation into real capital occurs on the first day of the following period. Capital owners are not paid a dividend. Instead, the return according to (4.20) is added to the stock of capital and not realized until shares are sold. Our earlier assumptions and this dating rule imply the relations among the main variables as shown in Table 4.3. The amounts listed in this table refer to single (otherwise identical) individuals of different age. Hence, Ki,t denotes the amount of capital (shares) owned by an individual of age i at the beginning of period t. Total capital in a particular period is the sum of all individual shares in that period, for example

74

The economics of social protection

Table 4.3 Real capital holdings, earnings and savings by individuals of different ages t2 K1,t  2
0 Y1,t  2 S1,t  2

t1

t

K2,t  1
(1  rt  1) S1,t  2 Y2,t  1 S2,t  1

K3,t
(1 rt) [S2,t  1  (1 rt  1) S1,t  2] Y3,t
0 S3,t
 K3,t

K1,t  1
0

K2,t
(1 rt) S1,t  1

Y1,t  1 S1,t  1

Y2,t S2,t

K3,t 1
(1rt1) [S2,t (1rt) S1,t  1] Y3,t 1
0 S3,t 1
 K3,t 1

K1,t
0 Y1,t S1,t

K2,t 1
(1 rt1) S1,t Y2,t 1 S2,t 1

t 1

K1,t 1
0 Y1,t 1 S1,t 1

Kt
Z1,tK1,t Z2,tK2,t Z3,tK3,t
ZK2,t Z2K3,t
Z(1rt)S1,t–1 Z2(1rt)[S2,t–1 (1 rt– 1)S1,t–2]

(4.21)

With a constant rate of interest this expression simplifies to Kt
Z(1r)[S1,t– 1 Z S2,t–1 Z(1r)S1,t– 2]

(4.21)

The amount of capital available for production in period t is a result of savings in the two preceding periods. Note that part of this capital is owned by pensioners who no longer take an active part in the production process. Since, by assumption, people do not leave any bequests, it follows that C3,t
(1rt)[S2,t–1 (1rt–1)S1,t–2]

(4.22)

A pensioner in period t has saved S1,t–2 as lower middle-aged and S2,t–1 as upper middle-aged. With the return on capital included, at the time of retirement he or she may consume C3,t according to (4.22). Pensioners sell shares to pay for consumption during old age. According to our dating rule this is done on the last day of life. Z2 individuals sell their shares on the same day of period t. The total amount of capital for sale is everything that is not owned by upper middle-aged individuals, Kt  Z(1  rt) S1,t–1. This amount might be the entire stock of capital available at the beginning

Pensions: basic model

75

of the period. Even such a seemingly odd situation will be optimal when lower middle-aged workers have earnings that exactly cover their immediate consumption. S1* would then be zero and savings for old age postponed until upper middle-age. Should the lower middle-aged earn even less we would have to consider negative savings (loans) for this category. In this model, there is no logic demanding that total savings should be zero. Since real capital may be maintained from period to period, total savings in a particular period may be positive or negative. Instead, the overall budget constraint is that aggregate consumption and net investments, Kt 1  Kt, must be equal to the volume of production. The overall budget constraint is C1,t ZC2,t Z 2C3,tKt  1
Qt Kt

(4.23)

Bearing in mind that Qt  rtKt
Y1,t ZY2,t the budget constraint may be written Kt  1  (1rt)Kt
S1,t ZS2,t Z 2S3,t

(4.23)

That is, total investments should be equal to total net savings plus the return on capital. As far as an individual’s optimization is concerned, we can use most of the earlier results. Just replace Yit, i
1, 2 in the first section with wtLit, i
1, 2, but note that the rate of interest must be positive according to (4.20a). This distinguishes the present model from the earlier model. Note also that the rate of interest may fluctuate over time, and that for every change in the equilibrium rate of interest there is a corresponding change in the equilibrium wage rate. Steady State For more precise conclusions the model must be made more specific. One specification that has received much attention in the literature is the steady state path, in which case the analysis is restricted to equilibrium solutions capable of repeating themselves infinitively, meaning that Sit
Si, and so on for all t. Such solutions are characterized by constant (relative) prices, rt/wt
r/w for all t, and so on, and therefore include, among other things, a constant capital intensity, Kt/Lt
K/L for all t, meaning that real capital grows at the same rate as labour. This is sometimes called the ‘golden rule of accumulation’. With exponential population growth at the rate n it must then be the case that Kt1
(1n) Kt. In view of (4.231) this condition may be written

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The economics of social protection

(n  r)Kt
S1,t ZS2,t Z 2S3,t

(4.24)

This is easily satisfied in the case of a linearly homogeneous production function. With constant capital intensity, both the production volume and the wage sum would then expand at the rate n and earnings per capita would remain constant over time. As shown in the first section, the optimum consumption profile would also be constant and for this reason it must be the case that S1,t*
S1* and S2,t*
S2*. This ensures that condition (4.24) is met.

SOCIALLY OPTIMAL CAPITAL STOCK We now turn to social optimization. When we looked at this issue in the section before last the task was quite simple. It was merely to pick a representative individual and find out how his or her earnings could be used most advantageously. Now we are faced with a complication, namely that individual earnings are interdependent over time. What earnings an individual may count on depends on other individuals’ behaviour. This interdependence must be taken into account in social optimization. Samuelson and others who have confronted this problem have limited their discussion to situations where individuals have equal opportunities in the sense that nobody should be any worse off than anyone else. Since, by assumption, all have the same preferences this means that all must have the same consumption profile over the life cycle, irrespective of when they were born, Ci,t
Ci, i
1, 2, 3. To achieve this result the production capacity per capita must be held constant over time. For the moment, we have no reason to question this interpretation of what a social optimum means, but it should be said that it is rather special. We restrict our analysis to the case of a linearly homogeneous production function. The budget constraint for social optimization in this case is C1 ZC2 Z 2C3
Q  nK

(4.25)

Consumption should be limited to the volume of production minus the capital formation that is necessary to maintain a constant capital intensity and thereby the present level of production per capita. Necessary conditions for the maximization of a representative individual’s utility subject to the budget constraint (4.25) are still given by (4.13). In the special case of (4.5) the socially optimal consumption profile is C1*
(Q  nK)/

(4.26a)

Pensions: basic model

77

C2*
C1*/Z

(4.26b)

C3*
C1*2/Z2

(4.26c)

To make the socially optimal consumption profile compatible with the consumption profile that individuals select spontaneously, it is (not surprisingly) necessary for the market rate of interest to be equal to the biological rate of interest n. In condition (4.24) we see that total net savings (out of earnings) should be zero in this case. This is essentially the same situation as we analysed in the second section, and the same problem has to be taken care of: it cannot be taken for granted that the market rate of interest adjusts itself to this level spontaneously. Some form of intervention might be needed. Before we proceed it should be emphasized that the budget constraint (4.25) and its corresponding optimum conditions are derived under the assumption of a linearly homogeneous production function. That is why total savings/investments should be exactly nK. In other circumstances the amount of savings needed could be both larger and smaller than nK. In any case, the policy problem is to ensure a certain level for both the rate of interest and the total amount of savings. With decreasing returns to scale, for example, it would be necessary to invest relatively more each period. Social Insurance To examine possibilities of implementing the socially optimal solution, we introduce the government and assume that it has the power not only to tax and give grants, but also to accumulate wealth. To begin with, we assume that all government holdings are in the form of real capital (shares), denoted KG. National wealth, K, now consists of one part owned by the government and the other part owned by individuals, hence Kt
KGt (K1,t ZK2,t Z2K3,t)
KGt Z(1rt)S1,t–1 Z2(1rt)[(1rt–1)S1,t – 2 S2,t–1]

(4.27)

Among the possible ways of securing a social optimum, social insurance is considered first. This case, which was discussed by Samuelson (1975), has dominated the debate ever since. Note that social insurance serves two functions in the present model. In addition to the basic function of financing pension grants it has the function of securing a sufficient accumulation of real capital. Let t be the grant received under the social insurance scheme in period t. There are Z 2 such grants, financed, we assume, by taxes on current earnings and proceeds from the government’s wealth. In period t we have

78

The economics of social protection

Z2t 1tY1,t Z2tY2,t1 rtKGt

(4.28)

Unlike individuals, the government may hold its capital forever. Government’s total capital holdings change over time according to KGt1
(1rt)KGt t(Y1,t ZY2,t)  Z 2t

(4.29)

Government holdings per capita are constant when KGt1
(1n)KGt. Hence, along such a steady-state path the government’s budget constraint is Z 2
1Y1 Z2Y2 (r  n)KG

(4.30)

Given (4.30), an individual’s steady-state budget constraint is C1 RC2 R2C3
(1  1)Y1 R(1  2)Y2 R2
(1  1)Y1 R(1  2)Y2 [1Y1 Z2Y2 (r  n)KG]R2/Z2 (4.31) With this budget constraint the representative individual optimizes his or her life cycle consumption by saving S1* and S2* during the two first phases of the life cycle and then, as a pensioner, consumes C3*
(1 r)2S1* (1r)S2* . So far, our analysis does not give a clear indication of what the optimal social insurance scheme looks like. It merely points to a class of schemes with the required characteristics, a class in which all levels of government investments, KG 0, are included. We shall take a closer look at the extreme cases: the pure pay-as-you-go (PAYG) scheme without any government funds whatsoever (KG
0), and the fully funded capital reserve (CR) scheme where government funds are large enough to cover all benefit payments. As before, we limit our discussion to production processes characterized by linearly homogeneous technology and steady-state equilibrium paths. PAYG scheme In a pure PAYG scheme pensions are financed entirely by taxes on current earnings. In this case the representative individual’s steady-state budget constraint (4.31) becomes C1 RC2 R2C3
(1  ) (Y1 RY2)(Y1 ZY2) R2/Z 2

(4.31)

When the market rate of interest is equal to the biological rate of interest, r
n, (4.31) simply says that total consumption should be equal to total earnings in the same period. In other words, total savings (out of earnings)

Pensions: basic model

79

should be zero. The return on capital, rK, is itself sufficient, when reinvested, to maintain constant capital intensity. These observations seem to suggest that it would be fairly straightforward to implement an optimal social insurance scheme of the PAYG type. This is also the general impression one gets from the literature based on models with just two generations, workers and pensioners. However, there is one difficulty. Even if taxation were confined to upper middle-aged individuals there would be no guarantee that lower middle-aged individuals would earn enough to finance the optimal amount of consumption, C1*. Private loans might be a solution, but it cannot be taken for granted that the upper middle-aged will not charge too much for such loans. The ideal, in our model, would be a rate of interest on loans at the same level as the real rate of interest, r, which is the rate of interest used to find the optimal consumption profile. If the upper middle-aged are inclined to charge more than r for loans, government loans are an alternative. Such loans could be given with a guarantee that the rate of interest will be the same as the real rate of interest. For the financing of such loans the government would have to raise the tax on earnings. The optimal amount of loans for lower middle-aged workers, denoted V1*, is V1*
C1*  (1  1)Y1

(4.32)

as long as the right hand side is positive. Otherwise, V1*is zero. There is a possibility that upper middle-aged individuals will not be able to pay for an optimal amount of consumption out of current earnings (after tax), and therefore will accept a loan. Still, in this case there is an alternative, which is to allow the upper middle-aged to sell shares bought earlier in life. By selling the amount V2 as upper middle-aged, they will consume (1 r)V2 less as pensioners. Hence, a pure PAYG pension scheme may be an insufficient device for implementing a social optimum. As long as earnings for the lower middleaged are relatively low, and private loans tend to be expensive, the PAYG scheme must be supplemented with government funds for consumption loans. We return to this issue in the discussion on liquidity constraints in Chapter 6. CR scheme The capital (or premium) reserve model (CR model) is an alternative way to implement (4.29). The basic idea in this model is that each generation should pay for its own pensions. Fees paid when individuals work, 1Y1 and 2Y2, are set aside into so-called capital (or premium) reserves, which are then invested and earn a return on the capital market. In this case we get the capital reserve (1 r)1Y1 2Y2 and the pension benefit

80

The economics of social protection

CR
(1r)[(1r)1Y1 2Y2]

(4.33)

This is the pension received in the CR scheme. In the PAYG scheme the pension is instead PAYG
(1n)[(1n)1Y1 2Y2]

(4.34)

The difference between these schemes in terms of the absolute pension received is  CR   PAYG
(1r) [(1r)1Y1 2Y2)  (1n)[(1n)1Y1 2Y2]

(4.35)

This difference may be positive as well as negative, depending on the size of the rate of interest and the rate of population growth. Along the socially optimal path, where the biological rate of interest prevails, the two pension schemes give the same result. Then it does not matter whether pensions are financed with taxes or fees (premiums). On the other hand, when R Z the two schemes are different and may result in different consumption patterns and wealth for individuals. Unless the earnings profile is constant over time, this comparison does not tell us what the rates of return of the two schemes really are. With productivity growth the PAYG scheme becomes more attractive. Let g denote the rate of productivity growth, and assume that this growth rate applies to all earnings. With a constant tax rate, those retiring in period t will then receive (1 n)(1 g) for every dollar they paid as upper middle-aged and (1 n)2(1g)2 for every dollar they paid as lower middle-aged. Hence, the rate of return on taxes paid is (1 n)(1g) – 1, which may be compared to the rate of return on payments in the CR scheme, hence the real rate of interest, r. Whether the PAYG scheme or the CR scheme yields the higher rate of return – in the present circumstances – depends on the sign of the expression  (1n)(1g)  (1r)
0

(4.36)

This relationship is sometimes called Aaron’s condition (Henry Aaron, 1966). A modified version of this condition is discussed in Chapter 5. Private Cooperatives In a society made up of many independent cooperatives, the corresponding private solution (for example, ‘social insurance’ within the family circle)

Pensions: basic model

81

does not necessarily lead to a similar situation for society at large. A further condition in this case is that the same norm for social optimization must be accepted by all cooperatives. Samuelson’s norm – that all individuals at all times should have the same amount of consumption – is not perhaps generally accepted. Rather, many people’s aspiration seems to be that we, whenever possible, should give our children better consumption possibilities than we ourselves received. This means that we wish to move toward a capital growth rate that is above the biological interest rate. This may be done if the level of savings is relatively high or if the number of children is low. Now, imagine an economy made up of many cooperatives (families, tribes, and so on) running their own companies and having different views about the rate at which their wealth should grow. What happens in this case? If the cooperatives act in isolation, capital intensity and the marginal product of capital will vary among companies. Companies belonging to thrifty cooperatives will have relatively high capital intensity and a correspondingly low marginal product of capital. From a national point of view resources will be used inefficiently. However, cooperation among cooperatives would improve the situation. By means of investments in each others’ companies cooperatives may reach a higher level of production. For companies introduced at the stock market there would be a tendency for differences in capital intensity and in real capital’s marginal product to disappear over time. Note that the outcome may be different from the one obtained in a situation with a centralized social insurance system following Samuelson’s norm that everyone should have the same consumption opportunity whenever he or she lives. In the case of a decentralized system, individuals do not necessarily have the same consumption. In thrifty cooperatives, individuals save relatively more and gradually increase their share of the real capital in the economy. This generates wealth differences (inequality) and possibly also too much aggregate capital accumulation in the economy – compared with the golden rule of accumulation. The latter consequence might be avoided if some cooperatives consume more than they earn, for example by selling real capital or by borrowing from their thrifty neighbours, but that would make the wealth inequality even larger. A Small Open Economy Our analysis has thus far been confined to a closed economy with an endogenously determined rate of interest. We now change the perspective to a small open economy with an exogenously given return on capital. Let r 0t be this rate of interest and let K 0t be the corresponding total amount of real capital invested in the country according to (4.20), that is f/K 0t
r 0t.

82

The economics of social protection

Because the labour supply is assumed to be given exogenously, the production volume and total earnings will also be given exogenously in this case, Y 0t
Q0t – r0t K 0t. The corresponding optimal level of domestic savings and domestically owned real capital is KDt1
S1,t* Z[(1r 0t)S1,t–1* S2,t*] 
K 0t 

(4.37)

This amount may be larger or smaller than the total amount of capital employed in the country, K 0t  1. The difference is covered by capital export or capital import. Let us have a closer look at the situation when the (world market) real interest rate is held constant. A linearly homogeneous production function then implies a constant capital intensity, which means that the stock of capital employed in the country grows at the same rate as the population, n. As a result, average earnings will also be constant and Samuelson’s norm will be followed; no one will have greater consumption possibilities than anyone else. This situation arises without any policy measures whatsoever. Furthermore, no demands are made on the domestically owned real capital’s growth to maintain this situation. If real capital grows at the rate x, there is no reason why x cannot be either greater or smaller than n. Differences are balanced by capital export or import. Will this situation be socially optimal? In the case n r0 the condition for a social optimum could be secured by giving citizens an opportunity to buy bonds with a rate of return equal to the biological rate of interest. To the extent that this opportunity is used there will be correspondingly smaller real capital investments and a correspondingly higher real rate of return. The only difficulty in this case is to prevent citizens from buying similar bonds in other countries. If such bonds yield an even higher return, individual optimization will be attained with the wrong discount factor. Whether foreigners should be allowed to buy bonds is an open question. In the short run such purchases lead to capital gains, which enhance consumption opportunities, but in the long run there might be difficulties securing the promised rate of return. In the opposite situation when r0 is greater than n, individuals cannot be induced to buy bonds without further incentives. A complementary measure might then be to impose a tax on the returns from domestic real capital holdings. If such a tax is used, then it is possible to reach an optimum when n0 as well. Measures like these might also be successful in an economy with many cooperatives acting independently. These observations suggest that there is no need for social insurance in a small open economy. The straightforward solution to the social optimiza-

Pensions: basic model

83

tion problem is to issue bonds with a guaranteed rate of return, with or without a supplementary tax on returns from real capital investments. This conclusion is based on two important assumptions: that earnings are exogenous and that there is no uncertainty concerning an individual’s life expectancy. Both of these assumptions are relaxed in the next chapter.

5.

Pensions: extended model

All the assumptions made in Chapter 4 about the situation for lower middleaged individuals are retained in the following analysis. However, our assumption of a fixed retirement age is now relaxed. In the present model the last two phases of the life cycle are collapsed into one, and the share of these periods to be used for retirement/leisure () and work (1  ) is left for each individual to decide. L2 is now the potential rather than the actual labour supply from individuals in the group of upper middle-aged and old. The actual labour supply from this group is (1  )L2. Whether individuals work full time or part time until retirement is not important for the analysis, but to simplify the discussion we assume that they work full time. To begin with, we assume that all individuals have the same life expectancy and are offered the same pension scheme. We later extend the analysis to situations where individuals have a different life expectancy and are offered a choice of different pension schemes.

INDIVIDUAL OPTIMIZATION Apart from the changes mentioned above, the model from the previous chapter is retained. With variable retirement age, the budget constraint for an individual living during the periods t and t1 is C1,t Rt C2,t  1 Rt (wt1 L2,t1)2,t1 Y1,t Rt Y2,t1

(5.1)

Here, Y2,t 1 represents the individual’s potential labour income during the second period. The right hand side in (5.1) is what Gary S. Becker (1965) called the individual’s ‘full income’, that is the income he or she would have earned by working full time. This income is used for consumption (C2) and retirement/leisure (L2). The price of retirement/leisure is the wage the individual otherwise would have earned. Since retirement is now subject to choice, retirement activities must be included as an argument in the utility function, which is now written u
u(C1, C2, 2) 84

(5.2)

Pensions: extended model

Table 5.1

85

Implications of second order conditions for utility maximization

dwt 1, dL1,t dwt 1, dL2,t1 dRt

dC1,t*

dC2,t 1*

d2,t 1*

0 0 0

0 0 ?

0 ? ?

with the usual characteristics, in particular u/2 0 and 2u/22 0. The necessary conditions for a maximization of (5.2) subject to the budget constraint (5.1) are (u/C2,t  1)/(u/C1,t)
Rt (u/2,t  1)/(u/C1,t)Rt wt1 L2,t1 (u/2,t  1)/(u/C2,t  1)wt1 L2,t1

(5.3a) (5.3b) (5.3c)

As before, it is assumed that the budget constraint is binding (no ‘unused’ resources). The inequality signs in conditions (5.3b) and (5.3c) indicate that there might be a regulation of the size of  preventing the individual from retiring as early as he or she wants. But we shall disregard this possibility, simply by assuming that (5.3b) and (5.3c) hold with equality. In other words,  may take any value in the interval [0,1]. The solution to the maximization problem may be expressed by the following demand functions, showing how an individual’s choice depends on the independent variables C1,t*
C1(wt, wt1, L1,t, L2,t1, Rt) C2,t1*
C2(wt, wt1, L1,t, L2,t1, Rt) 2,t1*
2(wt, wt1, L1,t, L2,t1, Rt)

(5.4a) (5.4b) (5.4c)

On the basis of the second order conditions for utility maximization (which are not shown here) the statements shown in Table 5.1 may be made. Question marks indicate cases where the income effect and substitution effect have opposite signs. An Example To illustrate the individual’s optimization, let us have a closer look at the utility function u
logC1 logC2 !log2

(5.5)

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The economics of social protection

Table 5.2 Changes in endogenous variables in our example when exogenous variables change

dwt, dL1,t dwt 1, dL2,t1 dRt

dC1,t*

dC2,t 1*

d2,t 1*

0 0 0

0 0 0

0 0 0

where ! is a positive parameter. The implication of a value of ! equal to 0 is that the individual does not value leisure/retirement as such, while a value of ! equal to 1 implies that leisure/retirement is valued as much as consumption in the second period. One unit of leisure/retirement has then the same weight in the utility function as one unit of consumption. With " (1!), the demand functions may be written C1,t*
(Y1,t RtY2,t1)/" C2,t  1*
C1,t* /Rt 2,t  1*
C1,t* !/Rtwt1Lt1

(5.6a) (5.6b) (5.6c)

By combining (5.6a) and (5.6c) we get the individual’s labour supply in the second period L2,t  1(1  2,t  1*)
L2,t  1 ["  !Y1,t/RtY2,t1]"

(5.7)

It is clear that the supply of labour varies negatively with earnings (the wage rate) in the first period and positively with the wage rate and the discount factor in the second period. It is also apparent that the effect of a change in the subjective discount factor (d0) on the labour supply depends on whether Y1,t is greater or less than RtY2,t  1. The individual’s reactions to changes in the observed variables when the utility function is given by (5.5) may be summarized as shown in Table 5.2. As far as the effect on the age of retirement is concerned, the substitution effect of wage earnings in the second period and the discount factor are stronger than the income effect. This same relation also holds for the effect of the discount factor on consumption during the second period. Note that this result refers to the special case under discussion. When the labour supply is determined by (5.7), realized earnings during the second period are

Pensions: extended model

Y2,t  1*
[("  !)RtY2,t1  !Y1,t]"Rt
Y2,t  1 – (Y1,t RtY2,t1)!/"Rt

87

(5.8)

The second term in the expression to the right is the monetary value of retirement. This may also be calculated by multiplying 2,t1* in (5.6c) with wt1L2,t1. With the definition of savings used in Chapter 4, we obtain S1,t*
Y1,t – C1,t*
[(" – 1)Y1,t – RtY2,t1]/"

(5.9a)

S2,t 1*
Y2,t  1 – C2,t  1*
Y2,t  1 – (" – 1)Y1,t – RtY2,t  1]/"Rt

(5.9b)

It is clear that S2,t 1*
– S1,t*/Rt and, consequently, that the present value of total net savings is equal to zero. Depending on how income is distributed, savings during the first period may be either positive or negative. S1,t*
0 occurs when Y2,t1
Y1,t("  1)/Rt. In this case, consumption during retirement is financed completely by savings from the second period, that is C2,t1*
Y2,t1/("  1), of which a share, perhaps 2,t  1*, is taken out after retirement.

MARKET EQUILIBRIUM As before, we assume that the population grows exponentially at the rate n. To achieve equilibrium, it is no longer sufficient to balance the investment–savings gap as in Chapter 4, that is Kt  1  (1rt)Kt
S1,t ZS2,t

(5.10)

It is now also required that the labour market must clear LDt
L1,t N(12,t)L2,t

(5.11)

where LDt is the demand for labour. The values of S1,t, S2,t and 2,t in (5.10) and (5.11) should be consistent with the individual’s optimization so that his or her budget constraints (5.1) and optimum conditions (5.3) are fulfilled. Still, this is not sufficient. In addition, the conditions for dividing the production result (4.20) must be met. For the economy to be in steady-state equilibrium, all of these conditions must be met for all values of t. The difference between this and the

88

The economics of social protection

situation we discussed in Chapter 4 is that both factor prices, rt and wt, are now determined simultaneously. The relation they exhibit is called the factor price frontier and may be written: wt
#(rt)

(5.12)

When the production function is linearly homogeneous, the slope of the factor price frontier is dwt/drt
 Kt/Lt 0. Without specifying the conditions further, we cannot determine the longrun equilibrium solution more precisely. The factor price ratio w/r may be rising, constant or falling. A rising factor price ratio over time implies a gradually rising capital intensity in the production, but it is not obvious whether this is because the capital stock increases more rapidly than the population, Kt  1 (1n)K, or because the number of hours worked gradually decreases due to earlier retirements, L2,t1 (1 n)L2,t. Either of these situations or a combination of them is possible. The example discussed earlier may also be used to illustrate the market solution, assuming that the interest rate and the wage rate are constant over time. Total labour supply is Lt
L1,t ZL2,t(1  2,t)
L1,t ZL2,t [("  !)  !Y1,t  1/RY2,t]/"
L1("  !Z/R)/"ZL2("  !)/" (5.13) and total consumption is Ct
C1,t ZC2,t
(Y1,t RY2,t  1)/"Z(Y1,t  1 RY2,t)/R"
w(1 Z/R)(L1 RL2)/" (5.14) Hence, investments may be written Kt  1  Kt
Qt  Ct
wLt rKt  Ct
wL1(" – !Z)/R  1  Z /RZwL2 (" – !RZ)/"rKt
rKt w(1 – Z/R)[("  1)L1  RL2]/" (5.15) Recall that the production function is linearly homogeneous and that L1,t
L1 and L2,t
L2. In this case, constant factor prices imply constant capital intensity. Hence, total investments must be equal to nK. According to (5.15), this is possible if either r
n

(5.16a)

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Pensions: extended model

or, provided that L2 L1("  1)/R, K
Zw[("  1)L1  RL2]/"

(5.16b)

In the first case K may have any non-negative value. In the second case K must have a certain value that depends on many things, including the relationship between L1 and L2. Note that L2 L1("  1)/R implies a negative value for K. This is not possible in a closed economy. As before, we use the notation Z
(1n)1. The purpose of this discussion is to demonstrate the possibility of a balanced equilibrium path. Such a development is possible under the assumptions made if either (5.16a) or (5.16b) holds.

SOCIAL OPTIMUM The social optimization problem, as defined in Chapter 4, is to find a path that maximizes a randomly chosen individual’s utility over time, independently of when this individual lives. Hence, circumstances should be stable as far as income per capita, and so on, are concerned, implying that the selected individual’s consumption possibilities should be C1 ZC2 Q  nK

(5.17)

In the case of a linearly homogeneous production function the budget constraint is C1 ZC2
Lf/LK(f/K  n) C1 ZC2
[L1 ZL2(1  2)]f/LK(f/K  n)

(5.18)

With this budget constraint the individual’s utility is maximized when (u/C2)/(u/C1)
Z (u/2)/(u/C1)ZL2f/L (u/2)/(u/C2)L2f/L

(5.19a) (5.19b) (5.19c)

These conditions will be met by the market equilibrium solution when rt
r
f/K
n wt
w
f/L

(5.20a) (5.20b)

When factor prices are set in this way an individual’s realized life income, Y1,t RtY2,t 1*, will be equal to Q  nK.

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The economics of social protection

Prices determined by (5.20) correspond to a possible equilibrium solution of the same type as the one described earlier. We do not know what the capital intensity is; only that it should be constant over time. It is not certain that this equilibrium will be reached spontaneously and some policy measures might be needed to ensure that the socially optimal path is followed. The sort of measures that may be used have been described before, so it should now suffice to emphasize that condition (5.20b) puts a constraint on how condition (5.20a) may be met. For example, if taxes and/or subsidies enter the picture, they must be designed in such a way that they do not distort the relationship between the wage rate and the marginal product of labour. Taxes and subsidies that depend on income must therefore be avoided. Of course, this observation is nothing new in the field of public finance. A first best optimum may only be obtained when taxes have no substitution effects, except in those cases where the substitution effect serves a special purpose, for example to neutralize an external effect. In a small open economy it is relatively easy to secure a social optimum. Real capital will then flow into (out of) the country as long as capital’s marginal product is larger (smaller) than the global rate of interest, r0. In this way, a certain capital intensity will be established. Apart from the adjustment period when some taxes or subsidies might be useful, a constant wage rate is sufficient to ensure that this criterion is met. The difference between this and the socially optimal path in a closed economy is that the total labour income is f(K0,L0)  rK0 instead of what is achieved with the biological rate of interest, f(Kn,Ln)  nKn. As in the case without a variable labour supply, the socially optimum conditions may be met by encouraging people to hold an optimal amount of savings in the form of bonds with the biological rate of interest as the rate of return. This is easily achieved when n is larger than r0. In the opposite case, people need an incentive to choose bonds instead of real capital, for example a tax on wealth in the form of real capital. This tax can easily be reserved for the country’s own citizens. Social Insurance In this model, a socially optimal pension scheme must not cause a discrepancy between labour’s marginal product and the net wage rate. This condition applies during the period in which people may choose between work and retirement. Given that working hours during the first period are given exogenously, it is not difficult to impose a tax on earnings in the first period for the purpose of financing a pension benefit. Let the part of the total pension that is financed by young workers be denoted 1t1. In a PAYG model we have 1 t  1
(1n)t  1

wt 1 L1,t1

(5.21a)

Pensions: extended model

91

while in a CR model we have 1 t  1
(1r)t

wt L1,t

(5.21b)

During the second period, to ensure the condition (5.20), a tax on earnings may only be used to increase the individual’s own pension. If 2t  1 is the pension earned during the second period, there is no distortion when 2 t1
t  1

wt1 L2,t1(1  2,t1)

(5.22)

By adding both components, the total pension is t1
1t1  2t1. A special case occurs when 2t  1
0. The condition (5.22) is met automatically by a capital (premium) reserve pension scheme, but it is not necessarily met by a PAYG scheme. It is not always recognized that the conditions stated above are a requirement for a socially optimal pension system. For example, it is sometimes the case that the pension is financed by a proportional tax on all earnings and then paid out as a fixed sum, bt  1, every month of retirement. This means that an individual who is entitled to the pension, but continues to work, gets a net wage, (1  t1)wt1  bt  1, which is lower than the value of his or her marginal product, f/L. Should the individual, as a consequence, be discouraged from working and choose to retire early, there might be a substantial loss to society. When the tax is raised the net wage decreases and approaches zero. The kind of pension scheme just described is a so-called defined-benefit (DB) type, in which the pension benefit is defined independently of actual contributions (payments). The only condition might be that one has to be a citizen for a certain number of years. For the purpose of financing a DB scheme the government may use any tax, but it is customary to use a special proportional tax on earnings, earmarked for the pension scheme, with the tax rate set so that contributions balance anticipated expenditures. The budget equation for a PAYG pension scheme in this case takes the form P
LY

(5.23)

Here we use P to denote the number of pensioners,  an average pension, L the number of employed persons, Y average earnings, and  the tax rate. The budget equation may also be written 
(P/L)(/Y)

(5.23)

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where we clearly see that the tax rate is equal to the product of the dependency ratio (P/L) and the replacement ratio (/Y). If, for example, there are six pensioners for every ten employed persons, P/L
0.6, and the pension makes up 70 per cent of an average salary, /Y
0.7, then the necessary tax rate is equal to 42 per cent, 
0.42. Alternatively, a PAYG scheme may be of the so-called defined-contribution (DC) type. Such schemes are based on fixed contributions, for example a proportional tax on earnings with a fixed tax rate, and benefits adapted to the amount of revenues collected. In this case the budget equation may be written 
LY/P

(5.23)

With the tax rate given, the pension benefit will be positively related to the sum of earnings (LY) and negatively related to the number of pensioners (P). In either case, certain provisions are needed to secure condition (5.22). The following example is illustrative. There is a typical retirement age, for example 2,t1
0.5. On the assumption that people actually retire at this age, equation (5.22) may be used to calculate 2t1 and, accordingly, t1. The individual’s pension (per month) multiplied by the remaining life expectancy at the normal retirement age, properly discounted, defines his or her typical ‘pension wealth’. If an individual wishes to retire earlier or later, the pension he or she receives per month should be adjusted accordingly. By retiring earlier (later) the individual should get a lower (higher) monthly pension during the entire retirement period. If 20 and b0 are the typical retirement age and the corresponding monthly pension, respectively, and the individual chooses 2*, the correct adjustment, assuming that the discount factor is equal to 1, is made when bt1*
20b0/2* t1wt1L2(20  2*)D/2*

(5.24)

The first term on the right hand side is the individual’s typical pension wealth divided by the number of months he or she is expected to receive a pension benefit. The second term on the right hand side is the amount of pension capital the individual gains by retiring later, or loses by retiring earlier, than the typical retirement age. D is a demographic factor reflecting how the surviving probability changes with age. Sweden may be used to illustrate how these rules might be applied. Here, the monthly pension benefit for the rest of one’s life is reduced by 0.5 per cent per month of early retirement (advanced withdrawals) and increased by 0.7 per cent per month of postponed retirement (deferred withdrawals). Hence, by retiring one year earlier or later an individual’s annual pension

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benefit for the rest of his or her lifetime decreases by 6 per cent or increases by 8.4 per cent respectively. The difference in the per centage rate reflects how the risk of death increases with age. In principle, it is possible for individuals to have advanced withdrawals of pension benefits at the same time as they continue working and earn new pension rights. This could be arranged in an actuarially correct manner. Other Exit Routes Ordinary retirement with or without advanced or deferred withdrawals of pension benefits is not the only exit route from the labour market. An alternative might be to claim compensation for unemployment or work incapacity owing to sickness, disability or injury. Unemployment benefits, sickness benefits and disability pensions make up a substantial share of incomes for individuals with less than five years left to the typical retirement age. In addition there might be various forms of part-time work offered by employers, or some insurance arrangement. The latter is typically private, but there are examples of public schemes for partial retirement. In Sweden, for example, individuals in the age group 61–65, who choose to reduce their working hours by up to 50 per cent, get 60 per cent compensation (‘part-time pension’) for the drop in earnings (within a certain limit). Thus, someone reducing his or her working hours by 50 per cent will get 80 per cent of previous earnings, 50 per cent from the employer and 30 per cent from the social insurance authority; see Agneta Kruse and Lars Söderström (1989). There are also private pension schemes. In addition to traditional individual schemes organized by insurance companies, there are negotiated schemes organized on the labour market. These are sometimes designed with the purpose of neutralizing incentives laid down in the national schemes, for example by eliminating the cap on pension benefits. This makes the negotiated schemes particularly valuable for well-paid wage earners who may receive pension benefits many times the maximum amount in the national scheme. In this context it is important to note that benefits in the negotiated schemes are usually calculated on the basis of earnings just a few years before retirement. An example may clarify the last point. Let us look at the situation in Sweden for an individual employed by the central government with earnings equal to 20 basic units (
SEK 918 000 EUR 100 000 per year). Benefits from the national scheme are maximized to 60 per cent of 7.5 basic units (
SEK 205 200 per year), corresponding to a benefit ratio of just 22 per cent. From the negotiated scheme the individual gets 60 per cent of income in excess of 7.5 basic units, that is another SEK 344 400 per year.

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The total pension, disregarding individual pensions, will in this case be 12 basic units (
SEK 549 600), corresponding to a benefit ratio of about 60 per cent. Note that benefits are subject to income taxation. The level of the negotiated pension benefit is determined by average earnings five years before retirement. Hence, even if one has worked full time and contributed to the pension scheme earlier in life, there is a significant reduction of the pension benefit if one reduces working hours during the years immediately before retirement. For example, the individual mentioned above would lose SEK 172 200 per year in benefits from the negotiated schemes should he or she decide to work 50 per cent part time from the age of 60. This is certainly a strong incentive for not reducing working hours before retirement. Those who want to work fewer hours should instead apply for a partial pension. Immediate earnings will be reduced, but pensions will be calculated as if the individual is working full time. Note that an application for a partial pension must be approved by the employer and that some employers in fact are reluctant to give their approval. A typical requirement is that the employee should be healthy and capable of working full time. Many, if not all, of these alternative exit routes violate the condition (5.22). This is also true for a part-time pension of the Swedish type. For an overview of exit routes from the labour market in 12 countries and a discussion of their effects, see Jonathan Gruber and David A. Wise (2007). They find that three features of the pension system have an important effect on labour force participation. The first is the age at which benefits become available (‘the eligibility age’). This age ranges from about 53 for some groups in Italy to 62 in the United States. The second feature is the pattern of benefit accrual after the age of first eligibility. In many countries life-time pensions actually decline for those who postpone retirement. This is a clear violation of the condition (5.22). The third feature mentioned by Gruber and Wise is that disability insurance and special unemployment programmes sometimes provide early retirement benefits. The effect is quite large. For example, at age 64, the range of men collecting disability benefit was 7 per cent in Spain and 37 per cent in Sweden.

DIFFERENCES IN LIFE EXPECTANCY Pension benefits could be distributed as a lump sum on retirement. The pensioners would then be free to put the sum in a bank account or any other asset and use what they have received to pay for consumption during old age. Provided that there is some uncertainty regarding life expectancy, a better alternative for individuals with risk aversion would be to buy an

Pensions: extended model

95

annuity that lasts as long as the individual lives. Unless stated otherwise, we assume that pension benefits always take this form. As long as everyone has the same life expectancy (at the typical age of retirement) it is straightforward to make the appropriate corrections for advanced and deferred withdrawals of pension benefits. Such corrections could be based on the average life expectancy. However, this kind of correction is somewhat problematic when the life expectancy differs between individuals – and individuals know (or are able to make a qualified guess) whether they have a relatively long or relatively short life expectancy. When all are given the same schedule for corrections, individuals with a relatively short life expectancy will subsidize individuals with a relatively long life expectancy. To simplify the discussion we assume that there are just two categories of individuals, group I with long life expectancy and group II with short life expectancy. If it is common knowledge which group a particular individual belongs to, a simple solution would be to design two different schemes, one for each category, and make sure that retiring individuals are assigned to the appropriate scheme. For obvious reasons a scheme designed for people with a relatively short life expectancy would be more favourable in terms of annual pensions than a scheme designed for people with a relatively long life expectancy. For example, if the life expectancy at the typical retirement age is 30 years for individuals in group I and just 10 years for individuals in group II, the total amount of pension benefits would be identical if the annual benefit was three times higher in the scheme designed for group II than in the scheme designed for group I. The situation becomes more complicated when life expectancy is private knowledge in the sense that only the individual (or possibly the doctor) knows to which group he or she belongs. How could individuals belonging to group I then be prevented from pretending that they have a short life expectancy in order to obtain the scheme meant for group II? The device proposed by A. Michael Spence (1978) to handle this problem is simply to make the latter scheme so much less advantageous in terms of cover that the temptation for individuals in group I to choose it disappears. Individuals in group II will be in a worse situation, but they have no better choice than to stay in the scheme designed for individuals with a long life expectancy. Should they change to the scheme designed for individuals with a relatively short life expectancy, they would find themselves in an even worse situation. Figure 5.1 shows the situation for two risk categories, I and II, buying insurance. x is the level of protection and premiums are assumed to be set equal to the expected cost of the insurance cover, pI
cIx and pII
cIIx, respectively, where cI and cII are the expected costs per unit of coverage for

96

The economics of social protection Premium value

a

cx

V(x)
p

b

cx

1

A

1

B

B0

A0

x0

Figure 5.1

x1

Level of protection

Situation for two risk categories, I and II, buying insurance

the respective category. The question is how individuals belonging to the high-risk category may be prevented from buying the inexpensive alternative. Spence’s suggestion is that people buying the expensive policy should be allowed to choose the level of protection they prefer. With the preferences shown by the indifference curve in Figure 5.1, the optimal insurance for those paying the high premium is AI with the level of protection x1. To prevent them from switching to the inexpensive insurance policy, Spence suggests that there should be a ceiling on the level of protection in the latter policy equal to x0. In this case there is nothing to gain from a switch. It will now be left as an open question as to whether these policies, AI and 0 A , could constitute an equilibrium outcome. It might, for example, be profitable for a competing insurer to offer a more attractive combination of policies by using a cross-subsidy where individuals in the low-risk category pay a premium in excess of their expected cost, pII cIIx, and individuals in the high-risk category at the same time pay a premium lower than their expected cost, pI cIx. B0 and BI could be such a combination. Since B0 is better than A0 and B1 is better than A1, this outcome might be preferred by all parties. But there are many such solutions of which, perhaps, none have

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97

the characteristics of a stable equilibrium. The literature dealing with equilibrium conditions on insurance markets distinguishes among several concepts of equilibrium. A basic distinction is between a separating equilibrium, illustrated in Figure 5.1, and a pooling equilibrium where all individuals are offered the same insurance policy. Anyway, equilibrium implies that profit possibilities are exhausted; insurers have nothing to gain by trying to offer any other kind of insurance scheme (Michael Rothschild and Joseph E. Stiglitz, 1996). Equity aspects of systems with more than one pension scheme have been analysed by András Simonovits (2006). Considering optimal design, he found that second-best contracts are separating. In a pooled system, the shorter-lived retire too early with too low benefit. It is possible, Simonovits claims, to design a structure of separating contracts in such a way that both shorter-lived and longer-lived are better off, even if the former are subsidizing the latter.

PENSION REFORM Most national pension schemes introduced in the 20th century were PAYG schemes of the defined-benefit (DB) type. Some, like the Swedish ‘Bismarckian’ scheme of 1914 and the American New Deal scheme of 1935, started as CR schemes, but were later converted to PAYG schemes. The problem with CR is that it takes some 40 years to accumulate the funds necessary to reach a mature stage. In the meantime, some ad hoc arrangements are needed to support those retiring without the necessary amount of savings. This is typically done with a basic pension at the subsistence level, financed from the general public budget. Of course, such a pension is of the PAYG type. Because of inflation, and other problems, the Swedish CR scheme did not turn out well during the 1920s and 1930s, and it was decided that the national pension scheme should be converted to a basic pension for all (from the age of 67). The situation in the United States was of a slightly different nature, as explained by Kriss Sjoblom (1985). A major problem was that many veterans from World War II were unable to save the amount necessary to get a decent pension, and therefore relied on the government to provide at least a basic pension guarantee. As in Sweden, the response was to convert the entire national scheme to a basic pension for everyone (‘social security’). This is the so-called Beveridge model, which was introduced in the United Kingdom about the same time. Not all PAYG DB schemes are confined to a basic tax-financed pension. In many countries there are also supplementary pensions of the PAYG DB type. The latter are typically earnings-related, although often in a rather crude way.

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The economics of social protection

In recent years, there has been increasing dissatisfaction with PAYG DB type of schemes. One criticism is that they become excessively expensive as the population grows older. Another criticism is that they include disincentives to work and save, and therefore are harmful to economic growth. A third criticism is that supplementary schemes tend to favour the middle class and therefore are at variance with generally accepted notions of social justice. The Ageing Problem Pictures of the population structure used to take the form of a pyramid, but no longer. The situation in Japan is illustrative. Between 1950 and 2005 the Japanese population increased from 83 to 128 million, mainly because of increased life expectancy, and the population ‘pyramid’ became more like a lemon, with the largest cohorts around the age of 60. The proportion over 65 has increased from 5 per cent just after World War II to 20 per cent at present. According to a forecast by the Japanese National Institute of Population and Social Security Research, the Japanese population will decrease to 95 million by 2050, in spite of increasing life expectancy, and the largest cohorts will be around the age of 75–80. By then, the elderly will make up 40 per cent of the population. Since all cohorts below the age of 50 are expected to be smaller than their immediate predecessor, the population ‘pyramid’ takes the form of the blade of a knife standing on its point (with the very top of the point cut off ). According to the forecast, there will be two elderly for every three adults of working age. In many communities, especially in rural areas, the elderly will be in the majority. A low fertility rate in combination with increasing life expectancy is not a situation unique to Japan. As far as the original population is concerned we find a similar picture in most OECD countries. In many European countries, for example, the lowest number of children per woman (completed fertility) is reported for women born around the year 1900 (Tuija MeisaariPolsa and Lars Söderström, 1995). The more dramatic effects of low fertility in Japan can be explained by the fact that Japan has relatively few immigrants. In countries where immigration is larger the ageing effect of low fertility is less drastic. That immigration will be sufficient to prevent a declining and older population in other OECD countries is conceivable, but definitely not certain. Many countries may follow Japan’s fate and have to face the challenges of a declining and ageing population. China is possibly among these countries, as a result of the ‘one-child policy’. There are many measures a country may use to accommodate an ageing population. One is to encourage people to postpone retirement and work longer. A natural first step is then to stop penalizing those who work after

Pensions: extended model

99

the ‘ordinary’ retirement age. It is not reasonable that people should lose pension wealth by working an extra year or two. Ideally, the conditions for retirement should be neutral in accordance with (5.24). Note that neutrality is incompatible with mandatory retirement at a certain age. Such legislation is questionable also in a situation without an ageing population, and it has been criticized by for example Nicholas Barr and Peter A. Diamond (2006). Another measure should be to prevent productivity increases from spilling over in increased pensions for those already retired. To this end pensions should be indexed to the consumer price index (CPI) instead of a wage index, but only as long as the CPI is the lower index. Occasionally, when prices increase faster than wages, pensions should follow the wage index instead. It is a nice thought that pensioners should enjoy a higher standard of living as a result of ongoing productivity increases, but this may turn out to be excessively costly in a situation with an ageing (and even declining) population. Of course, a third kind of measure would be to invite more immigrants and to encourage the middle-aged to have more children. Among measures to promote child rearing, subsidized child care seems to be relatively effective. In an earlier contribution to the discussion of the ageing problem David M. Cutler et al. (1990) did careful calculations on the United States showing that the decline in living standards caused by an increased dependency ratio would be fully reversed by a 0.15 per cent a year increase in productivity growth. If we include the effect of postponed retirement, this estimate indicates that measures counterbalancing the effects of ageing might be successful, as far as the average standard of living is concerned. The most serious problem may instead be to provide elderly care and health care in regional areas where the elderly make up a large share of the population. Tax Wedges We have already mentioned one tax wedge that should be eliminated, namely the lack of neutrality in the condition for postponed or early retirement. This may be done within a PAYG DB scheme, simply by changing how the benefit is defined. An example is given by (5.24). However, the basic problem with PAYG DB schemes cannot be eliminated in this way. The problem is that people contribute to the system during their entire working lives with little or no immediate return in the form of (extra) pension benefits. This is obvious in a system with just a basic pension for all, like social security in the United States. But the situation is not fundamentally different in systems including supplementary pensions for those who earn

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The economics of social protection

higher incomes. They have a situation similar to those with low earnings since most national systems have a ceiling for the level of pension an individual can get. When the ceiling is reached there are no more benefits to gain by extra work efforts. Hence, only individuals in the middle of the earnings distribution may gain pension entitlements by working (and contributing) more, but not even for this group is there, as a rule, a one-to-one correspondence between extra efforts and entitlements. Typically only certain years qualify for entitlements, such as an individual’s best years in terms of earnings, or his or her last year(s) before retirement. It is hard to say to what extent work efforts are discouraged by a pension system of the PAYG DB type, but it is well known that the excess burden of taxation tends to be quite large (see Table 3.2) and that tax wedges therefore should be avoided. The obvious solution, as demonstrated in the previous section, is to change the pension system from the defined-benefit (DB) model to the defined-contribution (DC) model. In the latter model, workers have an account to which entitlements to pension benefits are credited as they are earned. In the simplest case an individual’s pension wealth increases year by year proportionally to his or her earnings. The idea is that payments to the pension system should be thought of as insurance premiums instead of taxes, and that this will encourage workers to make extra efforts. Anyway, the remuneration from work then includes pension entitlements in addition to the immediate income. Notional Defined-contribution Pension Scheme A switch to the DC type scheme does not require a fully funded system. Individual accounts do not have to be real in the sense of a bank account. An alternative is the notional defined-contribution (PAYG DC) scheme, where a ‘virtual’ account is assigned to each individual, i
1, 2, . . . . This account is credited with a fixed percentage () of the individual’s earnings, Yi, year by year. During a particular period (1, T) the amount of ‘notional wealth’, $iT, accumulated on the account is $i,T


I

  Yi,t Tt,

(5.25)

t
1

where Tt is an index expressing a stipulated internal rate of return (IRR). The latter is set to preserve the financial balance of the entire PAYG DC scheme; that is, to make sure that the present value of overall system liabilities equals the present value of total system assets. System liabilities at any time are the sum of commitments to all living participants, workers as well as pensioners, and total system assets consist of the stream of future contributions for all workers plus funded reserves. Ole Settergren and

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101

Boguslaw D. Mikula (2006) showed that the internal rate of return in the PAYG DC scheme may be written IRR
gn%

(5.26)

where, as before, g denotes the rate of productivity growth, n denotes the rate of population growth (or rather the rate of growth of the labour force), and % denotes an adjustment factor. The main reason for the latter is that the time between contributions paid and benefits received (the ‘turnover duration’) may change. The meaning of a positive value on % is that the present value of assets increases relative to the present value of liabilities. Of course, % is zero in a steady state situation. At the time of retirement the amount accumulated on the account is converted to explicit pension entitlements with the idea that the individual’s ‘notional wealth’ should match the present value of his or her expected pension benefits. For simplicity, we assume that the life expectancy used in this conversion, at the time of the individual’s retirement, is the average life expectancy for all men and women of the same age, LEk. Thus, the individual’s annual pension is determined so that j,t
$j,t  1/G(LEk, IRR)

(5.27)

where G is an annuity factor expressing for how long time benefits will be received. This factor is a function of the life expectancy for cohort k at time v, and the internal rate of return. For a closer look at this model, see Edward Palmer (2006). It should be pointed out that the entire national pension scheme cannot be transformed into a PAYG DC scheme. First of all, there is a need for a basic pension guarantee for those who are unable to accumulate a sufficient amount of ‘notional wealth’. The basic pension must, for obvious reasons, be of the PAYG DB type. Moreover, the PAYG DC scheme needs to be supported by some sort of buffer fund to solve temporary macroeconomic problems and to even out differences between cohorts. Among countries having introduced (or starting to introduce) the PAYG DC model – the NDC model as it has come to be called – are Italy, Latvia, Poland and Sweden. For a discussion of the experiences in these countries, see Robert Holzmann and Edward Palmer (2006). Fully Funded Pension Scheme The advantage of a PAYG DC scheme compared with the PAYG DB scheme is that the tax wedges disappear, except in the basic pension guarantee. But

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The economics of social protection

some of the criticism remains, for example that the PAYG model is detrimental to private savings. This criticism is based on the assumption that the alternative to a public PAYG scheme is private savings in the form of bank accounts, insurance policies, real capital, and so on. Empirical research by Martin Feldstein (1998) and others supports the view that the fall in private savings is quite large, about 60 per cent. However, the universality of this observation may be debated. As we have noted elsewhere, the alternative to a mandatory public pension scheme may be a family arrangement where children are raised to take care of their parents. If this is the alternative, the effect on private savings might be relatively mild. However, in the debate on pensions a possible detrimental effect on private savings causes much concern, and there are many proposals to convert the national pension system into a fully funded (CR) model. Chile is the most famous example of such a conversion. In a survey of the literature on pension reform, Assar Lindbeck and Mats Persson (2003) distinguish three steps in a thorough pension reform. The first step is to make pensions mandatory. This is achieved by the introduction of a PAYG DB model. The second step is to make the system more actuarial for the purpose of eliminating tax wedges, and possibly also for the purpose of promoting social justice. This is the step from PAYG DB to PAYG DC with the help of notional accounts as described above. Lindbeck and Persson argue that this step increases efficiency on the labour market and enhances financial stability of the pension system. The third step is from the PAYG DC model to the CR model. This is achieved by replacing notional accounts with real accounts. The main argument for this step is that real accounts give higher returns than notional accounts; that is, the market rate of interest, r, is larger than the internal rate of return, IRR, as defined in equation (5.26). Most of the literature on the gains from pension reform is based on Aaron’s condition according to (4.36). As we have seen, with a positive value for %, Aaron’s condition does not give full credit to the PAYG DC model. This was also pointed out by Miriam Steurer (2003) in an attempt to give an exact formulation of the Aaron condition for alternative specifications of the PAYG model. Using US data covering the period 1933 to 2001, she showed that the results of the comparisons are highly sensitive to different specifications and assumptions concerning, for example, participation rates. The PAYG model turns out relatively better the higher the growth in population, productivity and/or participation. After comparisons with the actual interest rate, Steurer found that the PAYG DB model had a higher rate of return than the CR model most of the time, but the CR model improved its position during later years. As expected, the PAYG DC model turned out even better, also during the end of the period studied.

Pensions: extended model

103

Comparisons of pension models based on historical data are illuminating, but have limited value in pointing out the best pension system for the future. So far, there are good reasons to believe that PAYG DB schemes should be replaced by a PAYG DC scheme whenever possible, but there is no strong evidence to support a further step to the CR model. According to the literature, such a step might or might not be a Pareto improvement. However, given the gloomy demographic development awaiting Japan and possibly other countries, it would be very surprising if a comparison of the two models today did not select the CR model as the best choice. According to the forecast mentioned earlier the Japanese population is expected to decrease by some 3 per cent annually. Hence, the IRR as defined in (5.26) is likely to become negative, and therefore probably smaller than the market rate of interest. In such circumstances, it seems wise to consider a switch to the CR model. Given that we want to make a switch to the CR model, the question is how? Should the termination of the old system be immediate, or should it be gradual during a period of, say, 20 years? Should it just be announced today that there will be a termination 20 years from now? With a relatively slow reform, people have more time to adapt to the new conditions. However, it seems that a slow reform has less political support than a quick reform (see Juan Carlos Conesa and Dirk Kruger, 1999). Among those arguing for a quick reform is James M. Buchanan Jr (1981). His suggestion is that the process should start with an investigation of implicit contracts with the state, resulting in statements showing each individual’s net entitlement/claim on the state. This investigation may be limited to the national pension system. To the extent that the system is underfinanced, many statements may be negative. The next step, suggested by Buchanan, is to substitute each individual’s net entitlement/claim with government bonds of the same value. These bonds should be indexed to the CPI and have an infinite horizon. The implicit government debt will in this way be replaced by an explicit government debt, to be paid off in due time. In the meantime, bonds may be used to establish individual accounts in the CR scheme, and to finance private pension insurance policies. Of course, there will still be need for a basic pension guarantee of the PAYG DB type. Political Feasibility and Risks As previously noted, it has happened before that a national pension system based on the CR model was transformed to a simple PAYG DB system. Do we have reason to believe that future pension reforms in the opposite direction are sustainable? From the survey of the public choice literature on pension reform by Vincenzo Galasso and Paola Profeta (2002) we may

104

The economics of social protection

conclude that economic theory does not provide any generally accepted answer to this question. There are many more or less contradictory theories of the subject and, of course, very little empirical evidence for or against particular theories. Before ending this discussion, one further aspect of the CR model should be mentioned, namely that funds accumulated on individual accounts will be enormous. This is illustrated by Singapore, where the Central Provident Fund (CPF) has been accumulating wealth since 1955 and now manages a substantial amount of the country’s national wealth. Mukul G. Asher (2004) pointed out that the CPF has a very strong position in the Singaporean economy, but still does not provide a satisfactory rate of return on individual CR accounts. From the start, savers were guaranteed a rate of return of 2.5 per cent, and this is what they get in spite of the fact that estimates by the International Monetary Fund (IMF) indicate that the returns on investments by the CPF abroad are several times higher. Asher did not provide an explanation for this gap. Partly on account of the Singaporean records, there are a number of pertinent questions one may raise in connection with the CR model, such as: By whom and how should all this capital be managed? Should CR funds be allowed to become the dominant owner of private companies? If not, should they be allowed to invest abroad? Should agents in charge of the CR funds be free to take any risk they like, or should they be carefully monitored by the government or some other political body? How may corruption be prevented, for example CR agents investing in projects initiated by relatives or friends, or CR funds being used to support political campaigns? For the moment we do not have any good answers to these questions, but it is worth pointing out that explicit CR funds involve risks that are avoided in a system with notional pension wealth.

6.

Liquidity constraints

The assumption that individuals have access to a perfect capital market in the sense that they may borrow (or save) as much as they want at the prevailing rate of interest is now relaxed. Instead, we assume that credits for household expenditures are rationed. Without the possibility of borrowing as much as they want, individuals will have difficulties optimizing investments and consumption over the life cycle. Some investments – even greatly profitable ones – will be cancelled or at least postponed because of a lack of financing, and the consumption path will not be as smooth as utility maximization prescribes. For obvious reasons, lower middle-aged individuals in particular are hurt by credit rationing. A life cycle model including liquidity constraints is described in the first section. We then go on to look at some measures that are used to compensate especially the lower middle-aged for a lack of credit possibilities. Some aspects of family policy are discussed in the second section, and educational finance is taken up in the third section.

MANDATORY PENSIONS AND LIQUIDITY CONSTRAINTS In this section we use simulations to illustrate the role played by mandatory pensions and liquidity constraints in a life cycle model. We are interested in how aggregate saving, among other things, is influenced by the size of mandatory pensions and liquidity constraints. An essential feature of the model presented below is that individuals are uncertain of the time of their death. This has two important implications. First, one’s life expectancy will change over time. Those who grow older expect to live a longer life. This, in turn, will make them inclined to revise consumption plans downward, that is, to save more at each successive age than they originally, say, at the age of 20, planned to do. Without too much loss of generality we may assume that each individual makes a new plan for economic activities every year and that these plans are made on the assumption that death will occur exactly #t, t
1,. . ., T, years in the future. Hence, the expected age at death for an individual of age t is t#t and T is the maximum life span (at t
1). Second, even though we assume that there 105

106

The economics of social protection

are no planned bequests, uncertainty about the time of death means that there will be unplanned bequests. Individuals will die unexpectedly and their net worth will then somehow be transferred to surviving individuals. These transfers of wealth may be regarded as capital gains for the beneficiaries. If so, they will mostly be saved, at least in the short run, and thus show up in the figure for aggregate saving. We assume that all individuals belonging to a certain cohort are alike and have the same earnings. They start to work at age 20 (t
1) and retire at age 65 (t
46). Earnings (net of tax) are exogenously given, yt, t
1, . . ., 45. Out of these a certain fraction, , is paid each year to a pension scheme, from which the individuals may expect to receive a fixed pension, t
 per year after retirement for as long as they live, according to the condition 1  #1

45

t
46

t
1



 (1  r)1  t
yt(1  r)1  t,

(6.1)

where r is the real rate of interest, assumed to be constant. Moreover, we assume that the earnings profile is increasing over the entire working life, and that there is no secular growth in earnings (stationary conditions, that is, g
0). Individual behaviour is assumed to be governed by successive maximization of the utility functions ut


t#t

, i  (1  )ti 1 1 &c1&

t
1, . . ., T,

(6.2)

i
t

with respect to the budget constraints t#t

45

i
t

i
t

ci(1  r)ti  kt  (1  ) yi(1  r)ti 

t#t

 (1  r)ti

(6.3)

t
1, . . ., T

j
46

and the liquidity constraints kt  kt,

t
1, . . ., T

where:
subjective rate of discount  &
elasticity of marginal utility with respect to consumption

(6.4)

107

Liquidity constraints

ci
(real) consumption at age it r
(real) rate of interest kt
(real) net worth at age t kt
the smallest amount of net worth required at age t. The right hand side of (6.3) is the individual’s total real wealth at age t, which we denote Wt. In this case the optimal consumption path over the life cycle will be c*t
min(qtWt, (1  )yt  t  (1  r)kt  kt1 ) t
1, . . ., T

(6.5)

where qt




tLt i
t

1r 1



1 (it) &

t
1, . . ., T

(6.6)

(1  r) ti

is the propensity to consume (out of wealth) at age t. We can see how qt varies over the life cycle in Table 6.1. Because of this variation, the aggregate propensity to consume will vary with demographic changes. Ceteris paribus, an aging population will have an increasing propensity to consume. Note in (6.5) that either yt or t is zero. The role played by the parameter kt in (6.5) is explained below. The corresponding solution for savings and net worth over the life cycle is st
(1  )yt  t  rkt  bt  ct

t
1, . . ., T

(6.7)

and kt


t1

st(1  r)ti1

t
1, . . .,T

(6.8)

i
1

respectively, where bt is inherited net worth at age t. How bt is determined will be clear in a moment. Note that premiums paid to the pension scheme are excluded from private savings. In the budget constraint, such premiums are balanced by expected pension benefits, as shown by (6.3). It is assumed that k1
0. It should be pointed out that Wt and kt refer to the situation at the beginning of the year and that all transactions are assumed to take place at the end of the year in question. Inherited net worth received in one year is assumed to be unexpected and of no importance to the plans made in that same year.

108

Lars Söderström (1982, p. 592).

.043 .046 .050 .058 .073 .103

Source:

.029 .033 .038 .046 .062 .093

.010 .014 .019 .027 .044 .075

.092 .093 .094 .098 .109 .134


.07


.01

r
.04
.04

r
.02
.02

.018 .022 .027 .036 .053 .083

r
.00
.00

&
.50, r
.04

Any &

.023 .027 .032 .041 .057 .088


.01 .067 .068 .071 .077 .090 .118

.020 .024 .030 .038 .055 .086


.07 r
.00
.01

&
1.00, any r

The propensity to consume out of wealth: hypothetical values

25 35 45 55 65 75

Age

Table 6.1

.039 .042 .047 .054 .070 .100

r
.00
.07 .026 .030 .035 .043 .060 .090

r
.02
.01

.036 .039 .044 .052 .066 .098

.047 .050 .053 .061 .076 .105

.033 .036 .041 .049 .065 .095

.055 .057 .060 .067 .082 .110

r
.02 r
.02 r
.04 r
.04
.04
.07
.01
.07

&
2.00

Liquidity constraints

109

Specifications for the Numerical Analysis As mentioned, we assume stationary conditions. All individuals, regardless of date of birth, are assumed to receive earnings according to the profile yt
y(1  e't )

t
1, . . ., 45

(6.9)

with y
10 000 (currency units), 
0.6 and '
0.1. With some approximation, assuming the net income tax to be proportional, this is a typical earnings profile for (Swedish) men. To illustrate the role of mandatory pensions we consider three pension levels: 0
0, 2
2000 and 6
6000 (currency units). The highest level corresponds to 60 per cent of earnings just before retirement and may be regarded as fairly high. The corresponding tax rates are 0
0, 2
0.045, and 6
0.135 when the rate of interest is 2 per cent, compared with 0
0, 2
0.024, and 6
0.072 when the rate of interest is 4 per cent. Three cases for the distribution of bequests are considered. In the first, denoted B0, all bequests are confiscated by the state. Nevertheless, in this case as well, the total amount of bequests is included in the figure for aggregate saving. This amount is given by the sum B


T

Vt1dtkt

(6.10)

t
1

where Vt – 1 is the number of people surviving at age t – 1, and dt is the proportion dying at age t. Note that B only covers unplanned bequests. In the second case, denoted B1, all bequests are assumed to be evenly distributed to individuals of a certain age, t
t1. Hence, bt
B/Vt for t
t1 and bt
0 for tt1. In the third case, denoted BC, the beneficiaries are assumed to belong to the same cohort as the deceased, that is bt
dt(1  dt)– 1kt, t
1, . . ., T. Inherited net worth will occasionally be negative in this case. These assumptions are admittedly crude, but they cover a wide range of possibilities and will suffice for illustrative purposes. The parameters kt, t
1, . . ., T will also be dealt with in a rather crude way. We assume that kt
(t  1)at, t
1, . . ., T

(6.11)

and that at
0 for t  t2. Three cases are considered. In the first case, denoted I, at, t
1, . . ., T, is assumed to be negative and large, indicating an almost perfect capital market. In the second case, denoted II, at is equal to zero from the start, implying that nobody can become a net debtor.

110

The economics of social protection

Consumption Saving (dollar)

8000

II4 I4 II2

6000

4000

2000

0

70 30

40

50

80

90

60

Age

2000

Note: &
2.00, B
B0, p
p6,
0.04, I4
no credit constraints and r
0.04, II4
net debtor positions not allowed and r
0.04, II2
net debtor positions not allowed and r
0.02. Source: Lars Söderström (1982, p. 594).

Figure 6.1

Consumption and savings over the life cycle: three cases

Finally, in the third case, denoted III, at
200 (currency units), t
1, . . ., t2, implying a fairly strong element of forced saving. In this case one may think of down-payments and instalments related to the purchase of durable goods that are kept by the individuals until the age t2 (see the discussion on housing investments by Roland Artle and Pravin Varaiya, 1978). Simulations have been run for fixed values of the parameters t1, t2 and T, namely t1
35, t2
55, and T
83, and for various values on the parameters r, and &. The demographic parameters, Vt, t
1, . . ., T have been identified from actual figures for (Swedish) women.

Liquidity constraints

111

To illustrate how the model works, three cases are shown in Figure 6.1. These cases differ with respect to the liquidity constraints and the rate of interest, and may therefore be said to show the (long-run) effect of various strategies for credit market policy. In this illustration, it is assumed that bequests are confiscated (B0), that pensions are relatively high (6), that the subjective rate of discount is 0.04, and that the elasticity of marginal utility with respect to consumption is  2.00. The latter value has been suggested by Ragnar Frisch (1964). In the case I4, individuals are allowed to borrow as much as they want. As a result net savings are negative early in life. In the particular case depicted in Figure 6.1 net savings are negative until the age of 35. With credit constraints, younger individuals cannot consume more than they earn. As long as consumption equals earnings, there are no net savings. If, in addition, the rate of interest is kept low (2 instead of 4 per cent), net savings are postponed even further. In Figure 6.1, net savings in the case II2 are postponed until the age of 50, and then quickly consumed. At the age of 85 individuals are back in a situation where the consumption path follows the path for current income. This is far from an optimal use of lifetime earnings. Aggregate Savings Under the simplifying assumptions made above, aggregate savings in a particular year will be given by the sum S


T

Vtst

(6.12)

t
1

where st, t
1, . . ., T is given by the model for individual savings and Vt, t
1, . . ., T is the size of each cohort in the year in question (here assumed to be constant over time). Note that B according to (6.10) is added in the case B0. For our present purpose it is sufficient to look at the saving ratio S/R, where R


T

Vt{(1  )yt  t  rkt}

(6.13)

t
1

is the aggregate household income during the year in question. Simulated values for the aggregate saving ratio are reported in Table 6.2. Negative values do appear when the subjective rate of discount is larger than the real rate of interest, but these cases are clearly exceptions. In spite of the assumptions made to keep the saving ratio down – no planned bequests, positively sloped earnings profile, mandatory pensions, and so

112

The economics of social protection

Table 6.2 Aggregate household saving as a percentage of total household income 0

Pension Bequests

2

B0

B1

BC

B0

I, r
0.04 II, r
0.04 II, r
0.02 III, r
0.02 III, r
0.04

29.4 30.0 24.4 24.5 19.7

25.0 20.3 15.7 15.8 12.0

28.0 28.1 21.7 21.7 16.6

24.9 25.1 18.3 18.5 12.7

I, r
0.04 II, r
0.04 II, r
0.02 III, r
0.02 III, r
0.00

18.7 19.9 16.2 16.5 13.8

12.0 12.6 9.9 10.2 8.2

18.0 18.9 14.5 14.8 11.6

13.2 14.8 10.6 11.0 7.7

I, r
0.04 II, r
0.04 II, r
0.02 III, r
0.02 III, r
0.00

10.2 14.1 11.9 12.3 10.5

6.5 9.0 7.4 7.6 6.4

10.1 13.4 10.6 11.0 8.8

3.9 9.1 6.4 7.0 4.7

B1
0.01 16.1 16.2 11.5 11.6 7.7
0.04 8.7 9.7 6.7 7.0 4.8
.07 2.5 6.0 4.2 4.4 2.9

6 BC

B0

B1

BC

24.0 24.2 16.8 17.0 11.1

15.4 15.8 7.2 7.5 2.9

10.5 10.8 4.7 4.9 1.6

15.7 16.1 7.0 7.3 2.3

13.1 14.5 9.7 10.1 6.7

2.4 5.5 1.0 2.6 1.2

1.9 3.8 0.7 1.5 1.1

2.7 5.7 0.8 2.0 1.5

4.2 8.9 5.9 6.3 3.7

neg. 0.1 0.0 1.1 1.9

neg. 0.1 0.0 0.1 0.1

neg. 0.1 0.0 1.3 1.2

Note: Simulated values, &
2.00. Source: Lars Söderström (1982, p. 595).

on – it turns out that the model generates a saving ratio well above actual figures in many cases. The table shows that there is an effect on aggregate savings from the distribution of bequests. The savings ratio is lower in the case B1 than in the cases B0 and BC. The reason is simply that beneficiaries receive their inheritance at a younger age in this case. Anyway, even unplanned bequests seem to make up a substantial share of total savings. The effect of pension schemes on aggregate savings has been discussed for half a century. Critics of the PAYG model have claimed that public pensions will have a strong negative effect on private savings, thereby increasing the real rate of interest (except, perhaps, in a small open economy), which tends to hold back real capital investments, real wages and GDP per capita. In defence of the PAYG model it has been argued that lower private savings will induce people to postpone retirement, which will have an oppo-

113

Liquidity constraints

Table 6.3

Aggregate savings ratio and the PAYG pension scheme Level of mandatory pension


0.01
0.02
0.07

I4 II2 I4 II2 I4 II2

0

2

6

25.0 15.7 12.0 9.9 6.5 7.4

16.1 (36%) 11.5 (27%) 8.7 (28%) 6.7 (32%) 2.5 (62%) 4.2 (43%)

10.5 (58%) 4.7 (59%) 1.9 (84%) 0.7 (93%) neg. 0.0 (100%)

Note: Bequests distributed according to B1. Differences in parentheses. Percentages. Source: Table 6.2.

site effect on earnings and GDP per capita. To what extent this effect is sufficient to change the gloomy picture painted by the critics is, of course, a question for empirical research. In the simulations reported in Table 6.2 we can only show the primary effect of the pension scheme. Secondary effects regarding real capital investments, the wage rate, retirement and so on are not included in the simulations. The results reported in Table 6.2 are repeated in Table 6.3 for the case B1. Here, we clearly see the negative effect of the pension scheme on private savings. In the cases reported the aggregate saving ratio decreases by 27 to 62 per cent when the pension benefit is just 20 per cent of earnings immediately before retirement and by 58 to over 100 per cent when the pension benefit is 60 per cent of earnings immediately before retirement. Moreover we see that the aggregate savings ratio is smaller with than without credit constraints for a relatively low subjective rate of discount, but larger for a relatively high subjective discount. Note that this is not the full picture. To calculate the total net effect of the pension system we must not only include secondary effects, as mentioned above, but also be prepared to modify the starting point. The alternative to a pension system of the PAYG type is not necessarily private savings in an atomistic market. As we have emphasized many times in earlier chapters, there is more than one alternative to the welfare state. A plausible alternative would be the extended family. In this case, the middleaged take care of elderly relatives whether the latter are parents or not. Expenditures for this purpose are not counted as private savings and therefore aggregate savings will be relatively low in this alternative as well. Consequently, the effect on private savings of introducing a public pension scheme would then be less dramatic.

114

The economics of social protection

Welfare Loss Figure 6.1 illustrates how credit constraints disturb the consumption path and prevent individuals from taking full advantage of earnings. The corresponding welfare loss may be calculated by comparing an individual’s consumption plan when he or she is facing liquidity constraints with the plan that is optimal without these constraints. The result may be expressed as a negative effect on initial wealth (W1


 (1  )1t
c1t  1 t1

c

&

(ct  (1  r) 1(k

(6.14)

where (c1/ct)&, t
1, . . ., T is the marginal utility of consumption according to the initial plan without liquidity constrains, (ct is the difference in planned consumption when the individual has either full or restricted access to credits, t
1, . . .,   1, and (k is the corresponding difference in the individual’s net worth. Net worth is discounted with the rate of interest prevailing in the unconstrained case. Note that these comparisons are made on the basis of initial plans at the age of 20, not the paths followed when plans are successively revised. A comparison of cases I4 and II2 indicates that it would take a 5 per cent increase in initial wealth to compensate for the disadvantage caused by the credit market policy II2 with credit constraints and a low rate of interest compared to the policy I4 without credit constraints, but with a higher rate of interest. This is a primary effect. The indirect effect, via a change in aggregate savings, has to be added. As we have seen in Table 6.2 this effect too might be negative. Unless the subjective rate of discount is relatively high, liquidity constraints will decrease aggregate savings and therefore generate the same kind of effects as a mandatory pension scheme of the PAYG type.

FAMILY POLICY Liquidity constraints force individuals to postpone some of their lifetime consumption. This is true for all individuals, whether they are single or cohabiting, with or without children. In the simulations just discussed we have seen that liquidity constraints may have the same effect on lifetime utility as a reduction of an individual’s total wealth by 5 per cent. This corresponds to about two years of full-time work. For obvious reasons, liquidity constraints hurt the lower middle-aged more than the upper middle-aged. How they react to this situation is a matter of public concern in many countries. In particular, there is a fear that the lower middle-aged

115

Liquidity constraints

will cut down on investments in human capital, both by refraining from having children and by abstaining from education. In order to mitigate such behavioural responses, governments use measures to promote child rearing and school attendance. Here, we first take a look at family policy. Demand for Children The most important objective for family policy is to compensate parents for the costs of having children. The 1949 UN survey of family policies in various countries noted that this objective relied on two categories of measures: first, measures that express a recognition of the differential needs of the large and the small family, or of the family and persons without dependents to support; and second, measures related to the subsistence needs of the family in the normal circumstances of life (including the needs directly associated with marriage) and in periods of normal family earnings, employment and economic activity. (United Nations, 1952)

The statistical aspect of this issue is expressed by the various equivalence scales in use (see the first section of chapter 2). Implications for family policy are studied in the theory of demand for children. Contemporary economic theory on the demand for children dates from the work of Harvey Leibenstein (1957) and Gary S. Becker (1960). Becker, in particular, has made a number of contributions in this field. He views households as producers; they use time and various market goods as inputs to produce commodities. Almost anything could qualify as a commodity, given that it carries utility. Examples are dinner parties, holiday trips and stamp collections. Children are also viewed as a commodity. Becker’s model assumes that children, like other commodities, are demanded for the purpose of bringing utility to the household. More precisely, parents are assumed to maximize a household utility function u
(n)%(x); , %0

, %0,

(6.15)

relative to the household’s budget constraint pnnpxx  y

(6.16)

where (n) is the utility derived from children and %(x) is the utility derived from other commodities. It is assumed that utility is increasing at a decreasing rate in both the quantity of children (n) and the quantity of other commodities (x). Moreover, pn and px are the unit prices of n and x, respectively,

116

The economics of social protection

and y is the household’s income during the period studied. Note that the prices pn and px depend on the production technology used by the household as well as prices of various inputs (market goods and labour). Clearly, pn is the cost of raising one more child, a cost that depends on the price of food, clothing, housing, and so on, as well as the value of the time spent on child nursing or care by the parents. To make sure that children are a normal good, it is postulated that dn/dy0 dn/dpn 0

(6.17a) (6.17b)

Thus, the demand for children is assumed to increase with income and to decrease with the cost of raising children. Note that the assumptions (6.17a) and (6.17b) do not give a clear implication regarding the effect of economic growth on the demand for children. Economic growth not only raises incomes, which has a positive effect on the demand for children, but also increases the value of time and thereby the cost of raising children, which has a negative effect. It is a task for empirical research to find out if one or the other of these effects is dominant. Studies from several countries indicate that the negative effect of increasing time values dominates the positive effect of larger incomes (Becker, 1991). This is the simplest version of Becker’s model. A straightforward extension is to assume that parents care about the quality of their children as well as their number. A first step is to modify the utility function so that u
(n, m)%(x)

(6.15)

where m denotes the quality of children (measured by the amount of education and so on per child) and the  function is assumed to be weakly concave in both n and m. A second step is to modify the budget constraint so that pnnpmnmpxx  y

(6.16)

where pm is the cost of raising the (average) quality of children. The marginal cost of children may be divided into two parts. The first part, pn pmm, is the cost of child bearing and child rearing with a given quality of children, while the second part, pmn, is the cost of increasing the quality per child. These modifications are reasonable, but they make things complicated. There are no simple assumptions like (6.17a) and (6.17b) to be made for the extended Becker model. We can no longer be sure that the demand for children rises with income. The reason is that an (anticipated) income rise is likely to make parents want higher child quality, which raises the cost of

Liquidity constraints

117

having children and, therefore, has a negative effect on the number of children demanded. Of course, this effect will be reinforced when the income rises in a way that increases pn, typically a wage increase. Hence, on purely theoretical grounds, we are unable to tell how fertility is influenced by policy measures of various sorts. Empirical Findings Careful empirical analysis, such as the work by James J. Heckman and James R. Walker on Swedish fertility data (Heckman and Walker, 1990, 1991), is needed to make up for ambiguities in the theoretical model. They found, first, that economic variables of the kind included in the Becker model in fact have statistical significance. Models without such explanatory variables, what they call ‘demographic models’, do not fit the data as well. Second, they found that male and female wages influence fertility in different ways. The influence exercised by the male wage is clearly positive while that of the female wage is negative. An illustration is given in Table 6.4, which reports the results of simulations using data for the cohort born in 1936–40. Panel A shows how the distribution of women, according to the number of births at the age of 40 (almost completed fertility), changes with changes in the male and female wage. Panel B shows the average number of children at age 40 and the implied elasticity of wage changes. Finally, Panel C shows how wage changes influence time spells between conceptions. Statistically, Swedish women in this cohort had their first conception at the age of 23. A 12.2 per cent increase in the male wage lowered this age by 3 months, while an equally large change in the female wage postponed the first conception by 5 months. Later conceptions were affected less. The results in Table 6.4 refer to a particular cohort. Heckman and Walker showed that there are some differences among cohorts. The effect of increasing wages, both male and female, was lower for later cohorts, indicating a structural change resulting from either policy changes (incentives) or taste changes, or both. They note that the intercohort patterns of estimated coefficients provided indirect evidence in support of policy effects. A plausible hypothesis is that women in later cohorts were less dependent on the male’s income in initiating the fertility process and, furthermore, that the growth in work-related child-care benefits made the measured female wage an increasingly less accurate proxy of the price of time devoted to child bearing and child rearing. Note that changes in the intercohort pattern refer to the first conception. The data used by Heckman and Walker did not allow them to study how wage effects on the second and third conception changed for later cohorts.

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Table 6.4

The impact of wage and income change on completed fertility Base

Rise in male wagea

Rise in female wagea

Panel A Percent childlessb Percent with 1 childb Percent with 2 childrenb Percent with 3 childrenb Number of childrenc Implied elasticity To first conceptiond To second conception To third conception

10.9 15.4 44.4 29.3

0.40 1.10 1.70 3.20

Panel B 1.92 0.05 – 0.21 Panel C, mean time (months) 120 3 38 2 44 2

1.5 2.8 3.4 7.7 0.13 0.55 5 3 1

Notes: Swedish women born 1936–40. a by 12.2 percent; b at the age of 40; c predicted for the age of 40; d from the age of 13. Source:

James J. Heckman and James R. Walker (1991).

Family Policy Measures Given these empirical results, we can use the Becker model to classify different family policy measures with respect to fertility effects. The model identifies three strategic prices in the demand for children, two of which relate to the cost of raising children at the subsistence level. We call them the price of caring and the price of feeding. They refer to the time cost of being with the child and the price of food and other goods consumed by the child, respectively. In addition there is the price of child quality, which is the price parents pay for schooling and other human capital investments. With these prices in mind, we can classify family policy measures into three broad categories. T measures The first category consists of measures that (primarily) have an effect on the price of caring. This category includes labour market regulations, community child care and cash benefits when one stays at home to give birth to or take care of a child. A common denominator of these measures is that

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they lower the time cost of child bearing and child rearing. Increasing female labour market participation and increasing female wages are balancing factors. C measures The second category consists of measures that (primarily) have an effect on the price of child consumption. Among these measures are child allowances, housing allowances, free school lunches and similar benefits. They stimulate the demand for children by lowering the price of providing food and shelter for the child. Q measures The third category consists of measures that primarily have an effect on lowering the price of schooling and other human capital investments. Such measures are also expected to have a positive effect on the demand for children. Y measures Note that T, C and Q measures refer to price effects in the Becker model. In addition, there are income effects. Therefore, a fourth category of measures should be added, which includes, among other things, income taxes to pay for the kinds of benefits we have mentioned. Such measures tend to lower the demand for children by depressing the family income. But note that income tax increases, for example, have an ambiguous effect on the demand for children. This tax lowers a family’s disposable income at the same time as it lowers the price of caring. Among Y measures we may also count mandatory contributions to the pension system. The effects of such contributions are illustrated in Table 6.2. To what extent these measures actually give younger individuals a better budget situation is hard to say. Many families with children pay more in taxes than they receive in cash benefits. The effects in Sweden of some family policy measures on the distribution of income were reported in Table 3.4.

STUDENT LOANS Since we are talking about liquidity constraints, a straightforward alternative or supplement to the various measures mentioned above would be to offer families with children some sort of loan. So far, such loans are typically tied to studies at the graduate and postgraduate level (tertiary education), but other categories of students could be included as well.

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Return from Education Human capital investments may be profitable. The basic idea is simple. By giving up some income now, an individual may increase his or her ability to earn income in the future. An obvious case is schooling, during which the individual does not work at all. The cost to the individual is the income forgone plus tuition fees, and so on. Let  be the proportion of time used for human capital investments. The corresponding income forgone at time t is (t)w(t) (t), where (t) is a scalar measuring the individual’s productivity. For simplicity, all occupations are assumed to have the same basic earnings rate, w(t). Variations in earnings rates because of differences in working hazards, and so on, could be taken into account, but including them here would add unnecessary complexity to the analysis. Human capital investments in the form of ‘on-the-jobtraining’ may be analysed in an analogous manner. For example, (t) may in this case be interpreted as a factor indicating how much of the ordinary wage an individual has to give up as an apprentice. As a result of the human capital investment the individual’s (potential) earnings later in life will typically be larger. The increment in (potential) earnings at time v is w(v)( (v), and the present value at time t of the benefits achieved by the investment may be written (t,T)


T

w(v)((v)h(v)(1  )tv,

v
t, . . ., T

(6.18)

v
t

where h(v) is the amount of time used for work and , as before, is the subjective rate of discount. For simplicity we assume that each period consists of 1 unit of time. Hence, h(v) is also the proportion of available time used for work. It has been assumed that the individual’s human capital does not have any value outside the work place. Therefore, the present value of the investment will depend on how the individual plans to divide his or her time between work and leisure. A different situation would emerge if one’s human capital was equally useful in leisure activities. The return from human capital investments would then be independent of the division of time, that is (t,T)


T

w(v)((v)(1  )tv,

v
t, . . ., T

(6.18)

v
t

From an analytical point of view this is a simpler case, since decisions governing human capital investments may be analysed independently of deci-

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Table 6.5

Private returns from schooling for men and women, 1997–2000

Country

Canada Denmark France Germany Italy Netherlands Sweden United Kingdom United States

Secondary school

Higher education

Men

Women

Men

Women

13.6 11.3 14.8 10.8 11.2 7.9 6.4 15.1 16.4

12.7 10.5 19.2 6.9 – 8.4 0 – 11.8

8.1 13.9 12.2 9.0 6.5 12.0 11.4 17.3 14.9

9.4 10.1 11.7 8.3 – 12.3 10.8 15.2 14.7

Source: OECD (2002).

sions governing working efforts (and consumption). Both (6.18) and (6.18) are used in the literature. When there are no further costs for schooling, such as tuition fees, the profit from a human capital investment, evaluated at the time it is made, t, may be written )(t,T)
(t,T)  (t)w(t)(t)

(6.19)

Investments at other points in time are evaluated in the same way, and together they constitute an investment programme. When there are tuition fees, these costs will reduce the private return of the investment. In a calculation of the social return, tuition fees and similar ‘financial’ costs will be substituted by the real costs of teaching and so on, such as wages and rents. What does the (privately) optimal human capital investment programme look like? Clearly, individual preferences play a minor role. When (6.18) holds, the role of individual preferences is limited to the subjective rate of discount. In order to minimize incomes forgone and to maximize benefits, given that the subjective rate of discount is positive, investments in human capital should be made as early as possible. As a rule, schooling has a nice return. In a survey of the literature on the returns from schooling, David Card (1999) reports that the effect on earnings is around 14 per cent for men and 16 per cent for women per year of schooling. Although annual earnings depend on hours worked per week and weeks worked per year, and these variables are positively correlated to years of schooling, the main effect of schooling is on hourly earnings (10 per cent per year of schooling for men and 11 per cent for women).

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This is the general picture. Table 6.5 illustrates how the private return from schooling varies among countries and levels of schooling, and between men and women. There is obviously a different pattern from country to country. In addition, there is variation over time. It seems that there is a negative trend for the return from schooling (Anders Björklund and Christian Kjellström, 2002). Even if schooling, on average, can be very profitable, individuals must be aware that there is a considerable risk in the return from schooling. One cannot be sure what the labour market will look like in the future. Wars, depressions, industrial relocations, and other ‘macro risks’ will dramatically change one’s opportunities, and thereby change the return from schooling. In addition, there are a number of ‘micro risks’ preventing particular individuals from taking advantage of actual opportunities. A health problem is just one example of such a risk. To the extent that potential students are risk averse, these risks will lower the demand for schooling. In addition, in view of these risks, banks and other creditors are reluctant to provide loans for human capital investments without additional collateral, which will worsen the negative effect on demand. As a result, the amount of schooling (in an atomistic market economy) will probably be suboptimal, leaving many profitable investments unexploited. Tuition Fees and Student Loans The solution offered by the welfare state to the problems mentioned above is free tuition in publicly run colleges and universities and, in addition, subsidized student loans with the debt written off if an individual is unable to repay the loan before retirement. This solution is controversial and certainly not optimal. For example, Nicholas Barr (2004) argues that such a system does not only suffer from the malady of central planning and lack of resources, but is also unfair, supporting the rich at the expense of the poor. Barr’s ideal is a system where schools compete for students by offering a diversity of courses of high quality, and where students from all strata of society are able to enrol. This ideal is best realized, he argues, when teaching institutions are financed through tuition fees that each institution is free to set as it likes. In principle, fees should cover all teaching costs, but subsidies are motivated in cases where there is evidence of external benefits, for example when a particular course is considered to be of essential national interest. Note that this condition refers to external benefits at the margin. There is no doubt that a country is better off with some higher education than with no higher education at all. But it does not follow that there is a substantial external benefit from increasing enrolment from, say, 100 000

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students to 100 001 students. Hence, careful investigations are needed before we can use external benefits as an argument for subsidizing higher education. Furthermore, in order to pay for tuition and ‘realistic’ living costs, the state should make sure that students receive a reasonable amount in loans, with built-in insurance for the purpose of limiting the consequences of the risks mentioned above. The solution, Barr argues, is for all students to be able to borrow a full amount (independent of the student’s own income or parents’ income) and for repayments to be made in proportion to realized earnings (in excess of the subsistence income) later in life. In special cases there should be a possibility of writing off the remaining debt. In order to broaden enrolment, Barr also suggests that students from ‘poor backgrounds’ should be given a special grant and annual bursaries to help them pay for their tuition. In Barr’s model higher education is free at the point of use, but its costs still enter the students’ life-time budget constraint. Unlike the welfare state, this model solves the liquidity constraint without disturbing the conditions for optimal human capital investments, at least not much. Ordinary students will be faced with prices showing the real costs of tuition (less recognized external benefits) and be allowed to make their choice of school and particular courses (programme) on the basis of these prices. Of course, the major cost will in many cases still be the income forgone as shown by equation (6.19). Given that Barr’s model would realize a socially optimal amount of higher education, we may say that a model with free tuition, as in the welfare state, will be suboptimal. Since students cannot see the real costs of tuition in this model, they cannot make a rational choice between courses, and they tend to take too many courses. In addition, because of a lack of funds, the providers of education will not be able to increase the teaching quality as much as students are prepared to pay for; both the diversity of courses and the amount of teaching per course will suffer. In many cases even small fees will make a big difference, and still not count much compared with the student’s income forgone while the course lasts. Secondary education may be organized in a similar way. Subsidies To the extent that higher education produces external benefits at the margin, we have an argument in favour of subsidizing education. Another argument that has been used in the discussion of educational finance is that human capital investments should have the same tax treatment as investments in real capital, meaning that only net returns should be taxed. If

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gross returns are taxed as income, investment costs should be deducted from taxable income. This is hardly a good argument. Much household expenditure may be seen as costs for the purpose of generating earnings. Food expenditure is an example. To deduct all such expenditure from taxable income would severely limit the role of income taxation. It is hard to see why the costs of an education should be an exception. Anyway, one may pose the question of how higher education should be subsidized, given that a subsidy is warranted. There are various ways to administer a subsidy, such as free tuition, a relatively low interest rate on student loans, scholarships/grants for all students or particular groups of students, and the possibility of deducting instalments of student loans from taxable income. A peculiarity of the latter device is that the subsidy will be restricted to individuals who stay in the country and pay income tax after graduation. Life-long Learning The total amount of time used for education by students at the tertiary level is certainly very large, but in many countries it is not as large as the amount of time used for training by those who have already joined the labour force. Training of the latter kind might be less intense, but it goes on for many years and covers a larger group. There is hardly any occupation that can do without periodic training. It is used by lawyers, doctors, nurses, teachers, engineers, consultants, public servants, social workers, artists, construction workers, and many others. Training is used for the purpose of staying on a particular career track, and for changing from one track to another. As a rule, the first kind of training is paid for, or at least subsidized, by the employer while the second type is normally paid for by the individual himself or herself. Individuals may use current earnings and their own savings for the financing of life-long learning not paid for by the employer. Training will then be part of private consumption. Since periodic training will be an activity for the middle-aged, there is a source of finance not available at the secondary and tertiary level, namely one’s own pension account. Provided that the pension system is of the CR type, at least partly, each individual has an account that might be used for the purpose of education one or several times during middle-age. As long as this opportunity is restricted to training with an expected positive net impact on lifetime earnings, the expected effect on the individual’s future pension benefits will not be negative. But, of course, the actual effect might be negative, depending on the risks involved. As in the case of student loans the individual may be compensated for this risk by having his or her pension account credited with a suitable amount.

7.

Income security

We now take a closer look at the risk of losing one’s income before retirement, either temporarily or permanently, the most common reasons being illness and unemployment. We begin with some general comments on income insurance and then turn to unemployment insurance, sickness insurance, and disability insurance.

INSURANCE: THEORETICAL BACKGROUND Income security is a classical topic in the economics of insurance. Modern utility theory started with Daniel Bernoulli’s claim, in 1738, that an individual’s utility from income, u(Y), is increasing but at a decreasing rate, u(Y) 0, u(Y)0. He used this postulate to explain the demand for insurance in a model where individuals were supposed to maximize expected utility, Eu(Y). This approach was advanced in 1944 when John von Neumann and Oscar Morgenstern developed a method to measure utility as a function of income/wealth. This was done in the following way: 1. 2. 3.

4. 5.

Define a relevant interval for income/wealth. Assign particular values to the endpoints of the interval, for example u(Y min)
0 and u(Y max)
50. In order to evaluate an intermediate point, say Y
Y*, ask the individual whether he or she prefers this income with certainty to a lottery with the outcome Ymax with probability *, and the outcome Ymin with probability (1  *). Let * vary and find out at which value of the probability, **, the individual is indifferent between the lottery and the certain income Y*. The expected utility theorem implies that u(Y *)
**u(Y max)(1  **)u(Y min)

As an example, assume that ** is 0.70. Then, in our example, it follows that u(Y*)
35. In this way the entire von Neumann–Morgenstern utility function may be derived. Further steps were taken in 1948, when Milton Friedman and Leonard Savage introduced the standard gamble specification of the insurance 125

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problem – a demand for certainty – and, in 1964 and 1965, when first John W. Pratt and then Kenneth J. Arrow showed how the curvature of the utility function might be used to measure relative risk aversion +
 Y (u/u)

(7.1)

In the standard gamble specification, individuals have a choice between buying and not buying insurance offered at an actuarially fair price, , equal to the expected benefit. Without insurance the individual has an expected utility E(u)0
*u(Y  m)(1  *)u(Y)

(7.2)

where m is some ‘loss’, which occurs with probability *. With insurance that fully compensates for the loss, the expected utility is E(u)1
*u(Y    mm)(1  *)u(Y  )
u(Y  )

(7.3)

Since the individual has a choice between being uninsured with an uncertain income and insured with a certain income, one may say that the demand for insurance is a demand for certainty. The difference between E(u)1 and E(u)0 measures the gain in expected utility from full insurance. This difference is larger the more curved the utility function. The gain from insurance may be expressed in money terms. The largest amount an individual is willing to pay in excess of the actuarially fair premium () is his or her risk premium. Pratt and Arrow showed that the risk premium depends not only on the degree of risk aversion, but also on the statistical variance of the income distribution underlying the insurance problem; that is, the loss distribution. They found that the risk premium is equal to 0.5+,2, where + is the individual’s relative risk aversion as defined by (7.1) and ,2, is the variance of the income loss m when the individual is uninsured. Moral Hazard The term ‘moral hazard’ used to refer to dishonest behaviour among insurance customers. A distinction was made between moral hazard ex ante, when the customers did not take all the precautions they had promised, and moral hazard ex post, when they did not try to limit the damage as much as expected. A typical example of moral hazard ex ante is a shipping company that buys insurance for the value of a certain ship (and its cargo) that has to pass through difficult waters, and then employs a captain known

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127

to have a drinking problem, thereby exposing the ship to a larger risk than was understood in the insurance contract. Should the same company be reluctant to act promptly to save as much as possible of the ship and its cargo in case of distress, this would be an example of moral hazard ex post. Nowadays, economists tend to use the term moral hazard to refer to (almost) all behavioural effects of insurance, even unintentional. For example, on the existence of moral hazard Kenneth J. Arrow (1970, pp. 243–4) notes: Suppose an individual were to purchase insurance which would guarantee that his annual income would equal his expected yearly lifetime income. Suppose that the estimate of this were based on projections of the average annual income of men in a class similar to that of this individual. Such a projection, however, presumes a certain level of motivation. If this individual has the insurance, his motivation to earn might be substantially lower. His expected income with the policy would be lower than his expected income without it.

In this sense, moral hazard is just a matter of rational behaviour, which the insurer should take into account in designing the policy, realizing that ‘the probability distributions are functions of individual actions’, as pointed out by Elhanan Helpman and Jean-Jaques Laffont (1975). The real issue from an economic point of view is not whether behavioural effects are immoral or not, but how insurance policies might be designed to enhance social welfare, given all behavioural effects. There is clearly need for a compromise between full insurance and no insurance at all. In Arrow’s words: If a complete absence of risk-shifting is bad because it inhibits the undertaking of risky enterprises and if total risk-shifting is bad because it reduces the incentives for their success, then it is reasonable to suggest that partial risk-shifting might be best. (Arrow, 1970, p. 143)

The usual term for partial risk-shifting is co-insurance, meaning that the compensation for damage is less than full. These comments do not mean that cheating may be ruled out. As a matter of fact, insurance fraud seems to be quite common. An example, in the area of income security, is when somebody claims unemployment or sickness benefit at the same time as he or she is working in the black economy. The difficulty of revealing this type of fraud is one reason why private insurance companies are reluctant to offer generous insurance policies in this area. Karl Borch (1990) suggested that the relationship between the insurance company and each of its customers should be viewed as a

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Table 7.1 Pay-offs to the insured and the insurer in the two-person nonzero sum game Insurer

Insured

Keep Break

Trust

Check

K  (P  A), P  K K0  P, P  K0

K  (PA), P  (K B) K0  (PQ), P  K0  (B  Q)

Source: Karl Borch (1990, p. 348).

two-person non-zero sum game. The issue in Borch’s analysis is what precautionary measures the insured agrees to take, and what punishment he or she should receive in the case where the insurer discovers neglect on the part of the insured to take these measures. Let P0 and K0 be the insurance premium and expected claim without an agreement of precautionary measures by the insured. Should the insured agree to take such measures (at the cost A), the premium will be lowered to P  P0. The corresponding advantage to the insurer is that the expected claim is reduced to K  K0. The insurer’s cost of checking that the agreement is followed is B, and Q is a penalty the insured must pay if he or she is observed cheating. In this game the insured chooses between keeping the agreement and breaking it, and the insurer chooses between trusting the insured to keep the agreement and checking that this is the case. Net pay-offs are shown in Table 7.1. For the penalty to be of interest, it must be larger than the gain to the insured from undiscovered cheating Q AK0  K

(7.4)

The penalty must cover both the cost of preventive measures and the enlargement of claims. At the same time, for checking to be worth while the penalty must be larger than the cost of checking QB. Table 7.1 shows net pay-offs from pure strategies, but a mixed strategy is perhaps more interesting to consider. In this case the insured cheats with a certain probability, %, and the insurer checks his or her behaviour with a certain probability, . Borch showed that the pair of strategies corresponding to %*
B/Q and *
[AK0 – K]/Q is the only equilibrium point in the game. The lowest acceptable premium, disregarding administrative costs, will then be P
K(K0  K) B/Q

(7.5)

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129

In addition to the expected claim, the lowest premium acceptable to the insurer must cover the expected cost related to moral hazard. This cost is proportional to the cost of checking, B, and the gain to be obtained from precautionary measures by the insured, K0 – K, and inversely proportional to the penalty, Q, indicating that cheating becomes less frequent as the penalty increases. When the premium is determined by equation (7.5) the net pay-off to the insurer is zero. The corresponding net payment by the insured is A(K0 – K) B/Q

(7.6)

Hence, the insured will have to pay not only the full cost of precautionary measures, A, even if he or she does not always carry them out, but also the insurer’s cost of checking that these measures are carried out. The latter term is inversely related to the penalty, which shows that a severe penalty may be to the advantage of the insured. Borch compares a severe penalty with a ‘strong oath’ that increases the credibility of a promise not to break an agreement.

UNEMPLOYMENT INSURANCE Unemployment is a situation where individuals are out of work and actively searching for a job. Some individuals are unemployed before they get their first job, some are unemployed because they left a job voluntarily and some are unemployed because they are no longer required in their previous job. It is often the case that unemployment insurance only applies to the latter situation. Hence, eligibility for unemployment benefits typically requires that the individual used to have a job that he or she did not leave voluntarily. Moreover, it is required that the individual is actively searching for a new job and is prepared to accept any reasonable job offer. It goes without saying that these conditions are rather vague and may be given different interpretations. Since it is up to the insurer, in a given situation, to decide whether they are fulfilled or not, it is only natural that workers sometimes feel that benefits are received at the mercy of the insurer, and that they are eager to find an insurer they trust. This is certainly an important reason why many unemployment pools are organized with strong influence for representatives of the workers, such as pools run by labour unions. The Baily Model To see how unemployment insurance works, consider the following model, introduced by Martin N. Baily (1978). All individuals are alike. Adult life

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before retirement consists of two periods, when those working (full time) earn Y1 and Y2. To facilitate the notation, the length of each period is set equal to 1. Everyone works the entire first period, but in the second period the proportion (1  &) of workers become unemployed. Let (1  ) be the proportion of the second period used by an unemployed individual to search for a new job. In doing so he or she has a certain cost per unit of time, c, depending on how intense the search is, and a lowest acceptable wage (reservation wage), w0, indicating the motivation with which the search is conducted. It is reasonable to assume that searching will take more time the lower the cost of searching and the higher the reservation wage. Hence, with respect to the proportion of the second period used for work we may assume that -/-c 0 and -/-w0 0

(7.7)

Let b be the unemployment benefit per unit of time. Assuming that this benefit is financed by a proportional ‘tax’ on earnings with the tax rate , the budget constraint for the unemployment insurance may be written [Y1 &Y2 (1  &)w0]
(1  &)(1  )b

(7.8)

In the special case Y1
Y2
Y, we get b


(1  &)Y  (1  &)w0   (1  &)(1  )

(7.9)

Given this insurance scheme, the individual’s net income during the second period in case of unemployment is Y
(1  )(b  c)  w0 (1  )

(7.10)

and his or her expected utility, given that utility is a function of consumption, is E(u)
u[Y(1  )  S] &u[Y(1  )  S]  (1  &)u[Y  S] (7.11) where S denotes savings during the first period. (It is often assumed that S
0, and that individuals always live from hand to mouth.)

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131

The individual chooses c, w0 and S to maximize E(u). A maximum is reached when marginal revenues – from a more intense search and a lower reservation wage – are equal to the respective marginal cost. For obvious reasons, unemployment insurance of the type we are discussing increases the returns from being unemployed and therefore tends to decrease the individual’s search intensity and increase his or her reservation wage, thereby increasing unemployment duration. To balance this effect the pool of unemployment benefits and the ‘tax’ financing them must be larger. This is a cost shared by all workers, which should be taken into account in designing the insurance. As stressed by Arrow in the previous quotation, the solution is not to cancel the unemployment insurance altogether, but to find a reasonable level of co-insurance. In Baily’s own version of the model, the optimal level of unemployment benefit is determined by just three parameters (1) the proportional drop in consumption resulting from unemployment, (2) the degree of relative risk aversion of workers (evaluated at the level of consumption when unemployed), and (3) the elasticity of the duration of unemployment with respect to balanced budget increases in unemployment insurance benefits and taxes. This has been much debated, the argument being that his model is too simple and that his result, therefore, is unrealistic and of limited practical use. It has been suggested that human capital accumulation effects, liquidity constraints, and leisure benefits of unemployment must be taken into account. However, Raj Chetty (2006) showed that Baily’s result is more generally valid than these critics seem to believe. In fact, he found that Baily’s result may be obtained under fairly general conditions. In the model used by Chetty there is only one period, which a representative individual enters with consumption opportunities Ce and Cu depending on whether he or she is employed or unemployed. In the case of unemployment, the individual will search for a job for some time determined by his or her utility maximization. The duration of unemployment/search depends on, among other things, the search cost, the leisure value of unemployment and the benefits of additional search via improved job matches. The (socially) optimal insurance benefit according to Chetty is implicitly defined by * + (C C (b )  ,b

(7.12a)

1 (C * * + (C C (b )[1  2 C (b )]  ,b

(7.12b)

or

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where (C
Ce  Cu
relative consumption drop when unemployed C Ce u(Ce ) C
degree of relative risk aversion +
 u(Ce ) e 
 ,b


u(Ce ) C
degree of relative prudence u(Ce ) e

log(1  )
elasticity of unemployment duration with respect to logb benefits

(7.12a) applies when the third-order terms of u(C) are small. This is the case considered by Baily. (7.12b) applies otherwise, provided that the fourth and higher order terms of u(C) are small. Chetty’s main point is that the four parameters listed above are sufficient, as a rule, to characterize an optimal unemployment insurance scheme, and possibly also other social insurance schemes. However, it is not easy to see how his result may be used in practice. Some of these parameters are hard to calculate empirically. The latter aspect was stressed by Robert Shimer and Iván Werning (2007) in their search for a simpler way to design the optimal insurance scheme. They claimed to have found an extremely simple device, namely that the optimal scheme maximizes the representative individual’s after-tax reservation wage. This wage is the take-home pay required to make a worker indifferent between working and remaining unemployed. Hence, according to Shimer and Werning the unemployment benefit, b, should be raised as long as it raises the after-tax reservation wage, w0(1  ). This criterion may be decomposed into two effects. On the one hand, a higher benefit reduces the cost of remaining unemployed and therefore raises the pre-tax reservation wage, which is an indication of higher welfare. On the other hand, a higher benefit requires a higher employment tax, which is detrimental to the individual’s welfare. It is characteristic of an optimal scheme that these effects balance. This is a clear-cut view, conceptually, but it is not easy to say what the optimal level of coverage should be in practice. Empirical studies of reservation wages are scarce and, moreover, point in various directions. Alternative Schemes In the above models the unemployment benefit is assumed to be a flat rate, b, from the first day of unemployment and for as long as the individ-

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ual is actively searching for a job. An alternative, also mentioned by Baily, is that the benefit has two parts, a lump sum severance payment, b0, and a stochastic daily (or weekly) benefit, (1 –
)b1, depending on the duration of unemployment. The latter may still be assumed to depend on c and w0, as shown in (7.7), but now with an added random element, reflecting the fact that individuals cannot be certain of getting a job they would accept. When the outcome is uncertain, an individual with risk aversion searches less. It is customary that the severance payment, b0, is proportional to the length of employment, for example one week’s (or one month’s) pay per year of employment. This kind of lump sum is attractive from a social policy point of view. It has an income effect, allowing the individual to be selective in his or her search, but at the same time it does not have a substitution effect subsidizing a prolonged search. Hence, both (C/C and the elasticity ,b are relatively small, implying a relatively large unemployment benefit. But, as pointed out by Baily, the severance payment should not make up the entire unemployment benefit. An optimal scheme must also have a component compensating the individual for ‘bad luck’ in the search for a job. From this perspective it seems hard to justify a model where a relatively generous unemployment benefit, perhaps 80 per cent of the previous wage, is offered with a waiting period of a week or two. This frequently used scheme implies a negative severance payment. Given that people become unemployed for reasons they cannot control, a better alternative seems to be a combination of a generous severance payment and a relatively low daily benefit, possibly for a limited time, for example 300 days. However, a low and even negative severance payment may be warranted when people do influence their risk of becoming unemployed, for example by working less well than expected. A negative severance payment will then be a kind of penalty. Hence, the best model seems to be a scheme where the daily benefit is relatively low and the severance payment varies, and even becomes negative, depending on circumstances. As a compromise the severance payment might have two components: a negative amount in the form of a waiting period and a variable positive amount proportional to the length of employment. Such schemes may be operated at the company level and incorporated in the employment contract. The insurer’s role in such a scheme may be carried out by a large company itself, while smaller companies may have to find a solution involving a third party, for example an insurance company. In the case of unemployment insurance schemes administrated by the state, labour unions, or, perhaps even better, by private and/or public employment agencies, an analogous situation might be obtained if (1) employers are responsible for the severance pay and (2) the daily benefit is financed by

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premiums in proportion to the amount of costs each company generates (experience rating). The main task for the external insurer would then be to certify that those receiving the daily benefit are actively searching for a job and are prepared to accept any reasonable job offer. This is a task for which individual employers do not have a particular advantage. In practice, we see few examples of private unemployment schemes including both a severance payment and a daily benefit. Such schemes are rare even in the United States where public provisions for the unemployed are meagre; they are scant in the manufacturing sector, and hardly exist at all in the non-manufacturing sector. Andrew J. Oswald (1986) mentions several reasons why this is the case. First, there is a lack of interest from potential insurers to enter this kind of business because of, among other things, difficulties in predicting unemployment risks and controlling the amount of moral hazard. Second, there is a limited demand for this type of insurance, mainly because lay-offs are made in order of inverse seniority (last-in-first-out). One consequence of this rule is that senior workers (‘insiders’) consider the risk of unemployment to be small and feel that they can do without the insurance. Another consequence is that young or otherwise loosely connected workers (‘outsiders’) face a high risk of unemployment and therefore might be unable to afford an actuarially priced insurance policy. If so, they are referred to means-tested social assistance and similar provisions. On the basis of data from the United Kingdom, Michael Beenstock and Valerie Brasse (1986) argued that competitive pricing of private unemployment insurance would imply premiums that vary with age and marital status rather than income. Rigid Wages The preceding discussion was based on the assumption that wages are flexible in accordance with equilibrium conditions on the labour market, and that all workers are able to find a job, sooner or later. In practice, there are various wage rigidities preventing the market from reaching equilibrium. Some of these rigidities are a result of wage regulations, preventing wages from becoming ‘too low’. This kind of regulation is common in negotiated collective agreements, but in some countries there are also legislated minimum wages. An obvious consequence of a minimum wage regulation is that low productivity workers become less attractive on the labour market. Some may even become permanently unemployed. This effect might, in principle, be avoided with a wage subsidy neutralizing the regulation and allowing employers to make a profit from hiring low productivity workers as well. But such a device would not be easy to implement. For obvious reasons, the

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subsidy must vary inversely with individual productivity. The problem, though, is that productivity differences are hard to measure. Since it would be useless to subsidize all wages to the same extent, we must consider alternative ways to compensate those who are hurt by the minimum wage regulation. Various alternatives are discussed in the literature, such as subsidized vocational training programmes, public works, and some kind of pension. A pension differs from a life-long unemployment benefit in that the beneficiary does not have to search for a job. All of these alternatives are relatively expensive. The main motivation for minimum wage regulations is to avoid so-called ‘working poor’; people who are poor in spite of the fact that they work. There are, of course, alternative ways to accomplish this result, such as (1) a basic income guarantee or negative income tax, providing the same amount of income to everyone, whether they work or not; or (2) income tax credits. The first type of programme turns out to be excessively expensive. The second type is more reasonable. Examples are the earned income tax credit (EITC) in the United States and the working families tax credit (WFTC) in the United Kingdom. The idea of these programmes is to supplement the income of poor families up to a targeted level, which depends on the number of children, and so on. For a discussion of these programmes from the perspective of optimal taxation, see for example Bernard Salanié (2003). Some Empirical Observations Various aspects of unemployment insurance schemes have been studied empirically for many years. Peter Fredriksson and Bertil Holmlund (2006) provide a survey of these studies. They mention, among other things, observations concerning the effect of the replacement rate (i.e. the fraction of earnings replaced by unemployment benefits), the effect of a time limit on benefit receipts and the effect of various ways of monitoring search activities. The latter category includes workfare, meaning that recipients are required to participate in some kind of work. For a theoretical model including all these measures, see Peter Fredriksson and Bertil Holmlund (2006). A 1 per cent higher replacement rate seems to prolong the duration of unemployment by about 0.5 per cent in the United States; see for example Alan B. Kreuger and Bruce D. Meyer (2002). Studies for Europe give diverse results; see for example Jaap H. Abbring et al. (2005). A time limit on benefit receipts, or a gradually decreasing replacement rate, has a positive effect on search activities (Fredriksson and Holmlund, 2003). This effect seems to be stronger in Europe than in the United States.

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It is typical for the United States that unemployment benefit schemes are financed at the company level with experience rated premiums; that is, premiums differentiated with respect to how much the insurance was used in the past. Such premiums have an effect on the distribution of employment between more and less risk prone companies/industries. They also have an effect on the number of temporary lay-offs (Patricia M. Anderson and Bruce D. Meyer, 1997, 2000). As one might expect, these effects depend on the extent to which premiums are shifted onto the remuneration of workers. It seems that premiums reflecting industry risks are shifted to a larger extent than premiums reflecting risk differences at the company level. Hence, this financing method should encourage companies to be careful with lay-offs.

SICKNESS INSURANCE Sickness may cause income losses as well as health care costs. We are now interested in the former type of damage. Health care costs will be discussed in Chapter 8. For the moment we focus on shorter episodes of illness for which the loss of income may be compensated by sick pay provided directly by the employer or sickness benefit provided by, for example, a mandatory social insurance scheme. These compensations may be combined, the sick pay typically covering the first weeks or months of an episode of illness and the sickness benefit the rest. The amount of sickness absence varies from country to country. Some examples for European welfare states are shown in Table 7.2. On the one hand, the Netherlands and Sweden show an average sickness absence of over 4.5 per cent of the work force (including temporarily sick workers as well as individuals searching for a job). On the other hand, Denmark and Germany show less than 2 per cent. The United Kingdom and France take an intermediate position. The table also shows the proportion of individuals in the age group 20 to 64 participating in the work force (the participation ratio), the proportion of the work force unemployed, and the proportion of the work force hired on a temporary employment contract. Note that there is a negative correlation between sickness absence and unemployment, and that some unemployed individuals may be classified as sick. By combining columns two and three in the table we get the proportion of the work force not working. This proportion varies from about 16 per cent in Germany and the United Kingdom, to over 20 per cent in France and the Netherlands. With this measure, Denmark and Sweden take an in-between position. It is reasonable to assume that these differences are a

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Table 7.2 Employment ratio, sickness absence, unemployment and temporary contracts

Denmark France Germany Netherlands Sweden United Kingdom

Participation rate

Sickness absence

Unemployment

Temporary contract

68.4 55.5 59.7 55.7 74.8 64.2

1.9 2.8 1.8 4.6 5.0 2.4

7.4 10.7 7.3 6.8 5.4 8.2

8.3 8.6 6.7 9.3 9.4 5.7

Note: Average for the period 1987–2000. Individuals 20–64 years of age. Percentages. Source: Sisko Bergendorff and Hanna Larheden (2002).

result of differences in the design of the insurance schemes, but there might also be other factors reflecting cultural and socioeconomical differences between countries. Like unemployment insurance, sickness insurance covers a period the length of which depends on the insured individuals themselves. How soon they are prepared to go back to work depends on how well they recover from sickness, which is partly dependent on their own behaviour, and at what health status they consider themselves fit for work; that is, their ‘reservation health’. For a quicker recovery an individual may have to consult a doctor, take medicine, or do certain exercises. Such activities are costly in the same sense as search for a new job is costly. Reservation health serves the same role for the duration of an episode of illness as the reservation wage does for the duration of unemployment. Hence, sickness insurance and unemployment insurance have much in common. Note, however, that sickness insurance is about a temporary inability to perform a particular job and that hardly any job requires perfect health. But there is a major difference between sickness and unemployment. As a rule, it is up to the individual to say whether he or she is unable to work at all or just part time. There are, of course, situations when an individual for obvious reasons is too sick to work, but in many situations his or her present capability is a matter of judgement. This is true even when the individual’s own judgement must be supported by a doctor’s certificate. Hence, it seems irrelevant to assume, as in the Baily model, that the amount of sickness is governed by an exogenous stochastic process. Individuals always have some health problems which they, at the margin (!), may either ignore or use as an excuse for not going to work.

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Given this perspective, we must avoid seeing sickness insurance as insurance against the consequences of poor health. An individual’s health status is only one factor influencing the decision to stay home from work in a particular situation. This decision is also influenced by factors characterizing the individual’s workplace, such as the work load, and/or his or her leisure opportunities, for example time to enjoy some entertainment or to take care of grandchildren. Some of these factors change over time, thereby changing the probability that a particular individual will decide to claim sick pay or sickness benefit. Anyhow, we may assume that this probability is positively correlated to the replacement rate in the insurance scheme, mutatis mutandis. What does the alternative model look like? With reference to Tim Barmby et al. (1994), Assar Lindbeck and Mats Persson (2006) suggested an answer to this question. They proposed a model where an individual’s utility is a function of consumption (C), working time (h), and leisure time (1 – h). More precisely, they assume that the utility function is additively separable in these arguments, so that u(C, h)
u(C)Ah B(1  h)

(7.13)

where A and B are stochastic preference variables, assuming negative as well as positive values depending on the individual’s perceived health status and factors characterizing the individual’s workplace and leisure opportunities. To simplify the analysis, Lindbeck and Persson assume that the individual’s choice (on a particular day) is whether to work full time (h
1) or not to work at all (h
0). They, furthermore, assume that the individual consumes C1
w(1  ) when working and C0
w when ‘sick’, where w is the wage per day,  is the ‘tax’ rate used to finance the insurance, and  is the replacement rate in the insurance. The utility functions then become u1
u(C1)A
u(C1)&

(7.14a)

u0
u(C0)B
u(C0)

(7.14b)

where &
A – B, and the parameter B has been subtracted in both functions. Of course, the individual chooses to work when u1 u0, and to stay home when u1 u0. Depending on circumstances, either of these cases will occur. Lindbeck and Persson define the probability of being absent from work and find, using comparative statics, that this probability decreases the more pleasant work is relative to leisure, &, and increases with the replacement rate, , and the ‘tax’ rate, . The latter result is because a higher tax rate lowers the net wage and makes the working option relatively less attractive. Hence, one may question the sustainability of this kind of insurance scheme.

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An Optimal Scheme It should be stressed that the Lindbeck and Persson model is designed to highlight sickness absence at the margin; that is, among individuals with a real choice between working and staying at home. We must not forget that there are, at the same time, individuals too sick to have this choice, definitely unable to work and therefore entirely dependent on the insurance benefit. This group must not be forgotten in discussions of the optimal design of the sickness insurance scheme. Hence, we may not, as before, pick a ‘representative’ individual and look for the optimal scheme by maximizing this individual’s expected utility. This approach does not make sense in this case. Instead, we must try to find a compromise between the interests of individuals in different categories. Here, we are content to just point out that the discussion of this compromise should focus on the designer’s choice between the two major devices to bring down the amount of sickness absence: a lower replacement rate and more intense monitoring of the utilization. There are several ways to lower the replacement rate. One way is to give no compensation at all for a number of days at the beginning of each sickness absence period. Such a waiting period may be anything from one day to several weeks. Individuals with frequent spells of sickness, in particular, will be hurt by this device. Another way to lower the replacement rate is to cut off compensation after a certain period of time. Those who are considered seriously ill may then be given a pension or other permanent benefit, while others are moved to a more suitable job. Finally, the level of the replacement rate may be lowered by a reduction in the amount of sick pay or sickness benefit per day. Since many welfare states have a replacement rate of 90 per cent or more, a lowering of the replacement rate to 80 per cent would (at least) double the co-insurance rate in the sickness insurance scheme. One way to intensify monitoring of the insurance utilization is to require a doctor’s certificate regarding the individual’s ability to work and health status. Such certificates should be issued by somebody familiar with the individual’s working conditions, such as a company doctor. Another way is to require active rehabilitation of those claiming compensation from sickness insurance. Rehabilitation does not have to be confined to health care. Training the individual for a new job might in some cases be a better way. Finding a suitable new job is a task that requires participation from the employer as well as the company doctor. A typical example would be a nurse who is unable to lift heavy objects. Instead of trying to get this nurse back to a job involving lifting patients, and so on, he or she might be trained to distribute medicine to patients or to work in the hospital’s reception.

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Empirical research in this area indicates that the devices mentioned have a substantial effect on the amount of sickness absence, see for example Rigmar Osterkamp and Oliver Röhn (2007). However, we should bear in mind that there are also other factors explaining differences in sickness absence, for example employment protection legislation, as argued by Bernd Frick and Miguel Á. Malo (2008). Among the many studies made of single factors, a social experiment in Sweden should be mentioned (Patrick Hesselius et al., 2005). Normally, those claiming sickness benefit had to present a doctor’s certificate within 7 days, but in the experiment some individuals were allowed to wait up to 14 days. No effect on the incidence of sickness was observed, but the length of the episode turned out to be longer for the ‘fortunate’ group. (Since then, Sweden has introduced an initial period with compensation in the form of sick pay instead of sickness benefit.) On the basis of a study of sickness absence in a number of OECD countries, David Rae (2005) concludes that a policy to reduce sickness absence should try to develop a culture of ‘mutual obligations’ in which the sick person, the employer and the social insurance office each have clear responsibilities. For the social insurance office it is essential to improve the assessment process, for example with occasional random checks; for employers it is essential to have clear financial responsibilities, for example by having a sickness pay (instead of sickness benefit) during the first 2–3 months of an absence spell; for the sick person by increasing the focus on active measures, for example by having the receipt of a benefit depend on participation in employment, vocational rehabilitation and other integration measures. Rae argues that benefit rates should be generous and only reduced as a last resort. Workers’ Compensation The damage caused by accidents at the workplace is, as a rule, compensated for as part of the employment contract, under the heading of workers’ compensation. However, in this discussion of work injuries we start from the assumption that the employee takes out a separate insurance policy (, b), where b is the compensation in case of injury and  is the actuarially fair premium. To simplify the discussion we furthermore assume that there is just one kind of injury with probability *, with the effect that the utility function changes from u(x) to v(x), where x denotes the worker’s net income. We assume that there is no effect on the worker’s gross earnings, Y. The worker’s expected utility from work is E(u)
(1  *)u(Y – )*v(Y b  )

(7.15)

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Note that 
*b, and that b  
(1  *)b. Hence, a necessary condition for the expected utility to be maximized (with respect to b) is that the marginal utility of income should be the same whether damage occurs or not. This condition may be written u(Y  *b)
v(Y(1  *)b)

(7.16)

It is worth pointing out, as stressed by Peter Diamond (1977), that the premium  is different from the worker’s willingness to pay for a completely safe job, unless the damage is entirely financial. In the latter case we have v(x)
u(x) for all x. When the damage is non-financial as well, the worker’s willingness to pay for a safe job is typically larger than the premium . In the case of a non-financial risk we have v(x)u(x) for all x. When there are administrative costs, the premium will not be actuarially fair in the above sense, but will be larger than the expected compensation. Utility maximization will then require that the worker chooses an insurance policy with less than full compensation for the possible damage. With purely financial damage it will still be the case that v(x)
u(x) for all x, but to maximize utility the worker should choose an insurance policy implying a higher marginal utility of income with than without the damage. In his seminal paper on health insurance, Kenneth J. Arrow (1963) showed that the best way to cover an administrative cost (in the form of a fixedpercentage loading above the actuarial value) is to include a deductible in the compensation formula, meaning that the insurance provides full compensation for damages above a certain level. We now turn to a situation where the insurance is provided by the employer as part of the employment contract. To illuminate this case we assume, like Diamond, that a worker has a choice between a perfectly safe job with the wage ws and risky job with the wage w and the risk of injury *. In the event of an injury the employer provides the compensation b. Workers are indifferent between these jobs when the expected utility from both jobs is equal. If workers have the same utility function and maximize expected utility, if accidents result in a complete loss of wages and if the disutility of labour does not differ between jobs, indifference between these jobs requires that (1  *)U(w)*v(b)
u(ws)

(7.17)

By total differentiation we get dw
 *v(b) db (1  *)u(w)

(7.18)

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A negative correlation between the equilibrium wage and the compensation in case of an accident is intuitively clear. It is readily understood that the lowest cost to the employer will be achieved when he or she offers an insurance that is optimal from the worker’s point of view. We are then back in the previously discussed case. It is straightforward to extend this analysis to situations with a risk depending on the amount of preventive efforts exercised by the worker and/or the employer. The social cost of work hazards is the sum of these efforts and the injury cost. The latter may be born by either the worker as an insurance premium or, in the case of workers’ compensation, by the employer. Depending on which one is liable, either the worker or the employer will have the stronger incentive to exercise preventive efforts. However, the worker’s incentive is only effective when the insurance premium is lowered in proportion to the amount of preventive efforts he or she exercises. There is an analogous condition in the case of workers’ compensation, which is automatically fulfilled as long as the employer is responsible for compensating the worker for the full injury cost. In situations with inflexible insurance premiums, it seems that workers’ compensation should be the preferred alternative. The effect should be similar to that of experience-rated premiums in unemployment insurance provided by employers.

DISABILITY PENSIONS The compensation for a permanent loss of working capability before retirement takes the form of a disability pension, as distinct from the old age pension. One definition of disability is the following: ‘the inability to engage in any substantial gainful activity by reason of any medically determinable physical or mental impairment which can be expected to result in death or which has lasted or can be expected to last, for a continuous period of no less than 12 months’. This definition is used in the US social security programme and similar formulations are used in other countries. Disability may originate at birth, or even earlier, or be caused by accidents or illness later in life. Not least, traffic accidents cause a large number of cases. The Tagging Process The value of a disability pension may be very large. In many cases the pension provides (at least) a basic income over 10–20 years, and even longer. It is therefore not surprising that many apply for a pension even though they are not really qualified. As we have noted before, it is very

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difficult to measure an individual’s working ability. Some really disabled individuals are denied a pension (error of Type I) at the same time as individuals who in fact are able to work are granted a pension (error of Type II). In a famous study of the screening system in the US, Richard T. Smith and Abraham M. Lilienfield (1971) found that about 40 per cent of all applicants were classified in the wrong category – Type I and Type II errors had about the same weight. In a later study, Hugo Benítez-Silva et al. (2004) confirmed that about 20 per cent were wrongly granted a pension, but in their study no less than 60 per cent were denied a pension in spite of being disabled. Hence, the process of being awarded a disability pension is far from precise. Donald O. Parsons (1996) suggested a theoretical model by which this kind of situation might be analysed. He divided applicants into six categories depending on whether they are able to work (A) or disabled (D), whether they are ‘tagged’ for a pension (T) or not (NT), and whether they work (W) or not (NW). The indented categories are (A, NT, W) and (D, T, NW), that is able, non-tagged and working, and disabled, tagged and nonworking, respectively. In Parsons’s analysis there are also three erroneous classifications: (D, NT, NW) is a typical Type I error while (A, T, W) and (A, T, NW) are examples of Type II errors. In addition, there is the category (A, NT, NW) which is classified correctly, but with an unwanted outcome – NW instead of W. Parsons assumes that truly disabled individuals never work. Parsons takes the poor tagging process for granted and investigates how the outcome might be improved anyway. There are two problems to be solved. First, capable individuals should be encouraged to seek employment whether they are tagged for a pension or not. The solution, according to Parsons, is to let them keep at least a part of the pension at the same time as they work. The idea is that those working should earn so much more than those not working that all able individuals choose to work. The category (A, T, NW) would then become smaller and possibly vanish. However, it is difficult to say what the effect would be. For example, the so-called work premium offered in the US social security system does not seem to have much effect on returning to work, see for example John C. Hennessey and L. Scott Muller (1994). One reason for this poor result, pointed out by Sophie Mitra (2006), is that disability beneficiaries in fact have a relatively high reservation wage. Anyhow, even a small effect would be welcomed. It was estimated that expenditures for disability pensions in the United States would decrease by US$3 billion if the number of beneficiaries returning to work increased by 1 per cent (Jo Anne Barnhart, 2003). Second, able individuals must be made reluctant to apply for a disability pension. Parsons suggested that an application fee might prove efficient. Such

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a fee will not affect the application behaviour of the disabled, since they have no choice but to apply for a pension, but able individuals do have a choice, and should respond to the fee with fewer applications. A system where the fee is paid back in the case of a positive answer might be considered. Insurance Premiums There are various ways by which the risks of disability in society might be reduced. One measure with great potential is to finance the costs of disability – both the loss of income and the costs of rehabilitation – with insurance premiums that are differentiated according to the risks involved. Of course, this formula may only be used successfully in situations where the risks are known and those responsible may be identified. Events where these conditions are often met include work accidents and traffic accidents. When disability is related to work injuries, the compensation may be included in the employment contract and financed by the employer as a worker’s compensation. Actions to lower the risk will then contribute to the company’s profit and affect competition and economic development within as well as between industries. Research by Terry Thomason (2003) and others shows that differentiated insurance premiums stimulate investments in safety and reduce the amount of injuries. However, risk differentiation cannot be applied universally. One problem is that risks are hard to identify in small companies. Another problem is that workers move between companies, making it difficult to decide from which company a particular injury originates. A way out of this dilemma might be to restrict the application of differentiated premiums to injuries caused by accidents, and treat work-related diseases as health problems in general. Compensations for traffic injuries (from accidents) may also be financed by differentiated premiums for traffic insurance. Such premiums should ideally cover health care costs and compensation for pain and suffering as well losses of income, in addition to the costs for material damages. Premiums could vary with respect to characteristics of the driver as well as to the vehicle, region, and so on. This would have an effect on the distribution of welfare as well as the number of traffic accidents, and most certainly reduce the number of injuries and deaths. However, it is hard to say how large these effects would be. Many injuries cannot be classified as work injuries or traffic injures. Hence, there is need for a more general disability pension. Should this insurance cover health care costs as well as income losses? Should it be more or less generous than the disability pension one can get from the employer or the traffic insurance policy? Should it be financed out of general taxation or from a separate disability insurance scheme? In the

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latter case, how should premiums be differentiated? When the insurance only covers income losses, and individuals are equally likely to experience an income loss, we may conjecture that the willingness to pay for the insurance is approximately proportional to an individual’s earnings. This financing model would be relatively simple and also satisfy Knut Wicksell’s notion of social justice. With respect to the last comment, it should be pointed out that some individuals are born disabled and that compensation for congenital disability cannot be financed by premiums in proportion to earnings. A separate insurance policy offered to parents for babies not yet conceived would most likely be limited to a basic coverage for everyone insured. It would therefore be difficult to argue for differentiated premiums.

A ROLE FOR PRIVATE INSURERS? At first glance, the family seems well suited to handle temporary losses of income. As long as the amounts are small – seen from the perspective of the entire life cycle – the family needs no large buffer to deal with the problem. Should the family purse occasionally need to be strengthened, there are possibilities of taking a loan. Providing such loans might be a task for government bodies, as a form of social assistance. If people are reluctant to collect the buffers needed, some form of mandatory savings might be considered. For example, families may be required to have a savings account covering, say, three months earnings. This account may then be used by those who are classified as unemployed and/or unable to work as a complement to the basic unemployment or sickness benefit. A problem with this type of arrangement is that the account will dry out for families hit by income losses relatively often. The purpose of an insurance scheme is to prevent such outcomes, the idea being that individuals contribute according to expected losses and are compensated according to actual losses. To realize this idea families must form a cooperative or turn to an insurance company. Historically, cooperatives in the form of friendly societies have been the dominant solution. Typical members of such societies are people working in a certain workplace, belonging to a particular union or living in a certain area. As we have noted before, friendly societies function in a similar way to ordinary insurance; members deposit part of their earnings into a common pool when they work, and receive compensation from the pool when they become ill or are unemployed. The compensation for illness may include health care. Because members of a society know each other relatively well, it is rather easy to prevent abuse of the system, but friendly societies cannot escape the

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problem entirely; for example, unemployed members may take an undue length of time to find a new job. This increases the amount of legitimate loss of income. Friendly societies had a hard time in the 1920s and 1930s. Resources of both health insurance funds and unemployment funds were greatly strained. For unemployment funds, the 1930s mass unemployment was a clear reminder of the collective nature of the unemployment risk. For health insurance funds it was more a question of technical developments increasing medical costs. Various public measures may be used to ease these kinds of problems. In the welfare state the natural solution is to make unemployment insurance as well as sickness insurance part of the social insurance system. An alternative is to grant a subsidy to friendly societies in proportion to the total amount of compensation paid out, possibly on the condition that the society asks a moderate premium and is open to everyone, such as people who are not members of a union, or living in a different neighbourhood.

8.

Benefits in kind

Economists have a long tradition of arguing for cash benefits instead of benefits in kind. Still, benefits in kind constitute a large part of the public budget for social protection. Child care, health care and elderly care are important examples. Benefits in kind include vouchers – that is, rights to purchase a particular good, such as child care – giving the recipient the choice of producer from whom the good should be bought. What economists refer to when advocating cash benefits is benefits in kind like food stamps, subsidized housing, school lunches and other typically private goods. The argument is that the same amount of money would be better used if recipients were given a choice to consume what they like best. For example, a particular family getting £100 worth of food stamps might prefer to use this amount for, say, better housing. Since a cash benefit of the same amount has a higher (or equally large) value to the family, food stamps are seen as a wasteful/inefficient way to support families. This argument may be found in most textbooks on public finance and social policy. The economists’ view is criticized for assuming that the purpose of benefits in kind is to enhance the general well being of the recipients, when the purpose in fact may be to satisfy some aspect of social justice. As we have seen in Chapter 3, equality of opportunity may require, for example, disadvantaged children to have relatively more teaching resources. If this is the case, cash benefits are not a perfect substitute for free education. Another criticism of the view that cash benefits are better (or at least not worse) than benefits in kind is that the recipients may be unable to use them efficiently. This could be the case even if recipients are able to act in an economically rational way. The problem, in this case, is that benefits are sometimes given to the head of a household who may not know for certain what the best interests of the household members really are. For the same reason as we are sceptical about the idea of a social welfare function expressing the preferences of ordinary citizens, we should be sceptical about the idea of a ‘household welfare function’ expressing the preferences of household members. Thomas W. Ross (1991) was one of the first to make this point. A third criticism of the traditional view refers to the fact that many needs are uncertain, which is an important aspect of benefits like education, elderly care and health care. It is hard to predict how much extra teaching a disadvantaged child needs, what kind of elderly care an old person with 147

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multiple dysfunctions needs, and how much health care an individual with a certain diagnosis needs. We cannot, accordingly, calculate what the cash benefit must be to compensate for the expected costs. In this case, statistical evidence is not sufficient. The average cost for dealing with a particular problem is a poor guide when dealing with individual cases. That a particular surgical procedure, say, is effective in most cases is not to say that it will be successful for a particular individual in a particular situation. We must be prepared to give extra resources to individuals with larger needs than implied by statistical evidence. The extra cost is offset by the fact that some individuals will need relatively fewer resources. These gains are easier to capture in the public purse with benefits in kind than with cash benefits. This chapter takes a closer look at health care, which represents the category ‘insurance goods’ mentioned in the previous paragraph. As it is impossible to cover all aspects of health care provision in a single chapter, the discussion focuses on funding issues, in particular the role of co-insurance.

HEALTH CARE INSURANCE In 1963, Kenneth Arrow argued in favour of government intervention to expand health (care) insurance. His argument was based on a model where risk-averse individuals maximize expected utility and are charged actuarially fair premiums for health care insurance. Arrow concluded that a programme like Medicare – subsidized care for elderly citizens – would enhance social welfare. Such a programme was introduced in the United States two years later, but not everyone agreed that it was a good idea. For example, Mark V. Pauly (1968) claimed that government subsidies would induce excessive consumption because of moral hazard. People would demand more health care than they were willing to pay for if prices were set according to marginal costs. Pauly argued that the welfare loss from ‘over-consumption’ could be substantial. Rationing might be a solution to the problem of holding back consumption, but the favourite device among health economists is some kind of co-insurance. To see how this works, consider the following model. Let m be an individual’s cost for health care, and let B(m) be the co-insurance formula; that is, the share of the cost paid directly by the individual. One possibility is a so-called indemnity policy where the insurance covers all costs up to a certain limit (per period), m*, and the patient pays for all costs in excess of this amount B(m)
m  m*,

for mm*

(8.1a)

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149

An alternative is a so-called service benefit policy where the patient pays for all costs up to a ‘stop loss’ (per period), m**, and the insurance covers all costs in excess of this amount B(m)
m,

for mm**

(8.1b)

where m** is the deductible advocated by Arrow and mentioned at the beginning of Chapter 7. The most common assumption in the literature is that the patient pays a fixed share, , of all health costs: B(m)
m,

for all m

(8.1c)

These schemes may be combined. For example, in a combination of (8.1b) and (8.1c) the patient pays a part of the costs up to a certain maximum per year. The cap on out-of-pocket costs in (8.1b) may be designed in many ways. Some of the options at hand are the following. First, the cap may refer to out-of-pocket costs for a family or for each individual separately. In either case children may be counted separately or together with one or both of their parents. The risk for a family is lower, ceteris paribus, when family members are insured separately than when they are insured jointly. Second, the cap could be set at a uniform level for all, or at a variable level depending on some characteristic of the insured person, like age, gender, or ability to pay (income). For obvious reasons, a uniform cap would have to be at a rather low level. If out-of-pocket costs are to be felt by wealthy persons as well, one should choose a cap that increases with income. A further option in this case is to make the cap progressive (or regressive) relative to income. Third, one may have a common cap for all health care expenditures or separate caps for doctors’ visits, hospital care, pharmaceuticals, dental care, and so on. It would also be possible to exclude certain types of health care altogether. There are also several models of subsidization. In the simplest case all (approved) health care is subsidized to the same degree. However, some differentiation may be preferred on grounds of efficiency as well as equity. Finding the best structure of subsidy rates is a matter of policy design, as studied in the literature on optimal taxation (or optimal public pricing). From this literature we know that the optimal structure of indirect taxes is sensitive to changes in the tax system as a whole, for example whether there is an (optimal) income tax or not. Accordingly, one should expect the optimal structure of subsidy rates to depend on the design of the cap on individual health expenditures.

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Optimal Co-insurance What does the optimal co-insurance look like? To shed some light on this issue, let us take a look at the situation for a single individual and assume that his or her health is given by the function H
H(, m())

(8.2)

where  is a measure of the individual’s health status without/before health care and m() is the amount of health care consumed by the individual. Let us, furthermore, assume that the individual’s utility function has two arguments: health, H, and consumption other than health care, x
Y  m; that is, u
u(H, x)

(8.3)

Assuming that this utility function has the usual characteristics, utility will be maximized when, for any given value of , the marginal utility of increased health care is equal to the marginal cost; that is, Hmuh
B(m)ux

(8.4)

The left hand side represents the gain in utility from spending another dollar on health care, and the right hand side is the utility cost to the individual from spending that dollar. Hm, uh and ux are partial derivatives and B(m) is the marginal increase in the amount paid directly by the individual as m increases; ux is the marginal utility loss from reducing other consumption. When health care is offered free of charge, the right hand side is zero and the individual demands health care as long as it has a positive health effect. Let m# be the solution to equation (8.4). There is such a solution for every value of . Taking into account that individuals differ with respect to , the insurer’s problem is to find a co-insurance formula maximizing expected utility, given that the insurance premiums must cover expected costs. The optimal co-insurance rate makes an ideal trade-off between minimizing deadweight losses and reducing risk. The optimal level of co-insurance depends on the elasticity of income and risk aversion; see the Chetty formula in Chapter 7. An explicit analytical solution to this problem is hard to find, but simulations can give us a rough idea of the solution. On the basis of such simulations, David M. Cutler and Richard J. Zeckhauser (2000) found that co-insurance should cover at least 25 per cent of health care costs. We return to the results of simulations in the next section.

Benefits in kind

151

Private Insurance and Public Choice Given a public health insurance plan, private insurance may be introduced by excluding certain services from the stop-loss benefit. Candidates for disqualification are glasses, certain drugs, dental care, certain cosmetic care, and so on. An alternative would be to raise the stop-loss level, for example from 2 to 5 per cent of taxable income, and let private insurers provide balancing insurance. Private insurance would also be encouraged if certain categories of individuals were excluded from the insurance, for example gainfully employed workers who can get insurance in their employment contracts. We now turn to a model where the social insurance coverage of health care, and thereby the scope for private insurance, is decided in the political process by majority voting rather than by maximizing a social welfare function. The income tax rate to finance health care is 
(1  B)m Y

(8.5)

where the terms with bars refer to the average level for the entire population. For simplicity, the price of health care has been set to 1. Given this tax rate, the tax price for health care for an individual with income Yi, i
1, 2, . . ., is TPi
[(1  B)mi Y]Yi

(8.6)

Depending on the individual’s income, the tax price is larger or smaller than a corresponding insurance premium for private insurance. It is straightforward to see that an actuarially fair insurance premium i
(1  B)mi

i
1, 2, . . .

(8.7)

is higher than the tax price for individuals with mi  (m Y) Yi, i
1, 2, . . . . These individuals are subsidized by tax-financed health care. If, furthermore, it is assumed that individuals have constant relative risk aversion, in the Arrow–Pratt sense, we know that the optimal co-insurance rate increases with income; see Johanna Jacob and Douglas Lundin (2005), who also showed that the optimal co-insurance rate decreases with income when individuals have increasing relative risk aversion. When the political process favours the median voter, and this individual has an income below the average, it seems unavoidable that the political process will result in relatively little co-insurance. Nevertheless, for any chosen level of out-of-pocket costs, it would typically be low-income

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people who demand complementary private insurance. By doing so, they consume more and impose an externality onto tax payers. To find out in which regime total health expenses would be largest, Jacob and Lundin compared a purely private model and a model where public provision might be supplemented with private insurance and found that both income effects and price effects work in the direction of increased consumption in the latter case, given that the income elasticity is less than 1. Taxes redistribute income to low-income groups, who presumably demand relatively more health care, and the combination of public provision and supplementary provision lowers the co-insurance rate for everyone. The Nyman Criticism John Nyman (2003) claimed that the conventional theory of health insurance is utterly wrong. In his view, Pauly (1968) made a fundamental mistake when he assumed that demand increases generated by insurance are a waste of resources. According to Nyman, the purpose of insurance is to transfer income from situations when people are well to situations when they are ill and by doing so enhance their possibilities of getting more health care. From his point of view increasing consumption is the raison d’être of insurance. If over consumption occurs, Nyman considers this to be a minor problem. In rebuttals by Åke G. Blomquist (2001) and others on earlier papers by Nyman on the same subject, it is claimed that Nyman confuses marginal and intra-marginal effects. It is certainly the case, as argued by Nyman, that most individuals cannot afford to pay for advanced/urgent health care, like organ transplants, unless they are insured. But the discussion of moral hazard is not primarily concerned with this kind of care; instead it is concerned with demand for the least urgent care, what we usually mean by marginal care. In the next section we take a closer look at the empirical picture. We refer to the Health Insurance Experiment (HIE), conducted by the Rand Corporation in the 1970s. The picture provided by this study is admittedly becoming rather old, but the fact is that there are no other studies in this area coming even close to the rigour and richness of the HIE, which is still the largest controlled experiment ever carried out in the social sciences.

THE RAND HEALTH INSURANCE EXPERIMENT (HIE) The objective of the HIE was to compare 14 models of co-insurance for the financing of health care. Out-of-pocket costs varied from 0 per cent to

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Table 8.1

Co-insurance and health care consumption

Co-insurance

Ambulatory care

Hospital care

Total consumption

100 76 60 69

100 87 82 96

100 82 72 84

Free 25 95 95/0 Note: Free care
100.

Source: Willard G. Manning et al. (1987).

95 per cent of the actual cost, but within the limit of a stop-loss. Hence, as suggested by Arrow (1963), there was a cap on the annual health expenditure. Some 6000 participants in the experiment, who were spread out over various parts of the United States, were randomly assigned a particular co-insurance scheme. Health effects were of particular interest. Observations of health status and the consumption of health care were made for the years 1974–77 with a follow-up concerning health effects after five years. Participating individuals belonged to the active age group, and none were on welfare. The effects on outpatient services (ambulatory care), inpatient services (hospital care), and total consumption are reported in Table 8.1. Here, ‘free’ refers to a situation where all health care is offered free of charge. In the 95 plan both ambulatory care and hospital care are offered with a 95 per cent co-insurance rate, while in the 95/0 plan ambulatory care is offered with a 95 per cent co-insurance rate at the same time as hospital care is offered free of charge. The table shows that the demand for health care is sensitive to the out-of-pocket cost. Compared with charges covering 95 per cent of the costs, free care increases total consumption by 39 per cent, from 72 to 100. For ambulatory care the increase is 67 per cent. Note that charges for ambulatory care have a negative effect on the consumption of hospital care. It seems, therefore, that ambulatory care and hospital care are complementary goods rather than substitutes. The effects reported in Table 8.1 are pure demand effects. Since the number of people participating in the experiment was small wherever they were, there was hardly any income effect for doctors, and therefore hardly any incentive for them to generate compensating increases in consumption. An objection to co-insurance is that people try to avoid visits to the doctor and as a result risk more severe health problems. In other words, people exhibit penny-wise and pound-foolish behaviour. HIE does not give support to this view. On the contrary, in spite of a rather large decrease in health care consumption, there were few signs of a worsening health status

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among participants. In fact, it was only possible to measure three significant health effects, namely concerning (1) corrected vision, (2) oral health status, and (3) hypertension. With co-insurance, people did not change glasses, or check their dental status and/or blood pressure as often. As pointed out by Emmet B. Keeler (1992), these findings suggest that the additional care consumed in the free health care plan has little value besides relief of temporary anxiety and symptoms. He also mentioned the seemingly paradoxical effect that free care led to more self-reported diseases and worry, especially among the initially well and rich.

A CASE FOR CO-INSURANCE? It is tempting to speculate on what the results reported in Table 8.1 imply for countries with tax-financed health care. Let us consider a switch to an alternative where health care is financed by user charges, but with a stoploss. To underline the equity aspect, the stop-loss is set proportional to the patient’s annual taxable income, implying that high-income groups pay considerably more than low-income groups. Expenditures above the cap are financed by a proportional income tax. The role played by out-of-pocket costs will naturally depend on the context. For example, it certainly makes a difference whether patients pay directly to individual producers as a fee for service or to some fund from which doctors and hospital staff are then paid a more or less fixed salary. Out-of-pocket costs paid as a fee for service give producers an incentive to prescribe more care (‘supplier-induced demand’). Such effects may be avoided when payments are made to a separate fund. This distinction is not always observed. Out-of-pocket costs are frequently judged on the presumption that they take the form of an ‘extra billing’ by doctors. For a critical assessment of patient charges of this type, see Robert G. Evans (2002). The following discussion is confined to a model without ‘extra billing’ by doctors. For simplicity, we assume that there is only one insurer, the government, and that the health care personnel are remunerated by fixed salaries. In the role of insurer the government provides subsidies as well as compensations for out-of-pocket costs in excess of the stop-loss limit. To show that a case might be made for co-insurance it suffices to look at a rather simple scheme of co-insurance with the following features: ●

There is a uniform rate of subsidization for all (approved) health care expenditures, granted to all individuals. This rate is denoted s. Hence, consumer prices cover 100(1  s) per cent of prices asked by producers.

Benefits in kind ●

●

155

Each individual is granted a cap on the total amount of out-of-pocket costs he or she has to pay for approved health care within a 12-month period. This cap is set equal to 100v per cent of the individual’s annual taxable income (earnings, pensions, and various capital incomes). Expenditures for subsidies and compensations for out-of-pocket costs above the ceiling are financed by a proportional income tax.

Note that this scheme has been selected as an illustration, by virtue of its simplicity, and that later it will be assumed to apply to the entire population. The co-insurance schemes studied by the Rand Corporation were more complex. Under certain conditions a transition from ‘free’ care (that is, s
1 and/or v
0) to a system of patient charges according to this scheme will be an advantage to everyone concerned. If so, the reform will qualify as a Pareto improvement and will be potentially socially just according to Wicksell’s norm. This possibility is now illuminated. To keep the analysis simple, we assume that taxable incomes do not vary as a result of changes in the way health care is financed. To the extent that the earnings of doctors and other groups in the health care sector change, some kind of compensation may be needed to secure general agreement on the reform. Free care is characterized by a certain amount of health care consumption, denoted X 0, a certain amount of taxable income, denoted Y0, and a corresponding tax rate, denoted 0, equal to 100X 0/Y 0 per cent. As an illustration we assume that 0 is equal to 16 per cent. (Assuming that taxable incomes cover some 50 to 60 per cent of GDP, 16 per cent tax is sufficient to finance health care corresponding to 8–10 per cent of GDP.) The tax rate needed to finance health care will be lower after the transition to co-insurance, one reason being that the demand for health care will decrease. The new level of consumption is denoted (1  %)X, with an obvious interpretation. Another reason is that a fraction, denoted , of this consumption is paid for by the patients as out-of-pocket costs. The tax rate needed to finance health care after the switch to co-insurance, denoted , is equal to (1  )(1  %)X/Y. In addition to this tax, individuals are charged for outof-pocket costs varying with the size of each individual’s consumption, but never exceeding 100v per cent of taxable income. Total outlays for health care may in this case never exceed 100(v) per cent of an individual’s taxable income. As long as (v) is less than 0, all consumers gain, at least financially, from the transition to co-insurance. Is it reasonable to assume that the demand for health care will decrease enough to meet the condition just stated? Results from the Rand HIE shown in panels A, B, and C of Table 8.2a provide a tentative answer to this question.

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The economics of social protection

Table 8.2a Demand, out-of-pocket costs and tax rates with different caps and subsidies 5

10

A. Demand for health care (relative to taxable income) 0 16.0 13.5 13.0 12.2 50 13.9 13.3 12.8 75 14.0 13.5 13.2

11.6 12.4 13.1

9.8 11.2 12.1

B. Implied out-of-pocket costs relative to total consumption 0 0 5.3 9.9 17.2 50 5.1 9.0 14.3 75 4.6 7.4 10.6

30.2 22.6 15.5

46.8 31.1 19.5

C. Implied tax rates relative to taxable income 0 16.0 12.8 11.7 50 13.2 12.1 75 13.3 12.5

8.1 9.6 11.1

5.4 7.7 9.7

s\v

0

0.5

1

2

10.1 11.0 11.8

Note: Subsidy rates relative to producer prices. Results reported by Keeler and Rolph are based on observations with the cap on out-of-pocket costs expressed in absolute terms. These amounts have been translated into percentages of the taxable income per capita. Source: Own calculations based on Emmet B. Keeler and John Rolph (1988).

Panel A shows how the level of demand for health care varied with different subsidization rates and caps on out-of-pocket costs. It is evident from these results that co-insurance has a strong negative effect on the demand for health care. This is seen most clearly in the case of unsubsidized care where there was a 15 per cent decrease in demand even at a very low cap (v
0.5 per cent). Raising the cap decreased demand to less than 60 per cent of its ‘free’ care level. But there was hardly any effect from raising the cap above 10 per cent, since few individuals had expenditures for health care above this level. Emmet Keeler and John Rolph (1988) estimated that 10 per cent of people in the studied group had out-of-pocket costs in excess of the cap in this case. Panel A also shows that there might be quite substantial positive demand effects from increasing the subsidy, especially when the cap is relatively high. It is interesting to note, however, that the sign of these effects would be reversed if, simultaneously, the cap on out-of-pocket costs was raised to the same extent. For example, per capita consumption will decrease from 13.0 to 12.8 if subsidies are increased from 0 to 50 per cent, and at the same time the cap on out-of-pocket costs is raised from 0.5 to 1 per cent; and from 11.6 to 11.2 when the cap is raised from 5 to 10 per cent. Panel B shows

Benefits in kind

157

the share for out-of-pocket costs relative to total consumption. Finally, panel C shows the tax rates implied by the results shown in panels A and B, given that free care requires a 16 per cent income tax. Recall that the sum of v and  has to be less than t0 (
0.16). It is easily seen in panel C when this is the case. Such cases are marked in bold. Just to illustrate these results, suppose that we would like to minimize the costs incurred for those individuals who are worse off in terms of health care needs. These costs are v . Panel C clearly shows that these individuals do not benefit from subsidies. Raising the rate of subsidization would only mean that they have to pay a higher tax. Lowering the cap on out-ofpocket costs would of course have a beneficial effect per se, but this effect is more or less offset by the accompanying tax increase. Thus there is a trade-off between cap cuts and tax increases. As shown by Panel C, the sum v is minimized when v is around 2 per cent. Given these results, cap cuts below this level are not beneficial to those individuals who are worse off in terms of health care consumption. Pareto Improvement Ex Ante? It is fair to say that our analysis so far has had a conservative bias. The norm that has been employed states that a Pareto improvement cannot occur unless everyone is sure to gain from the transition. This is an extremely cautious position. Most individuals would certainly be in favour of the transition even if a loss could not be ruled out, provided that there is a fair chance of a welfare gain. A less conservative view would be that the transition is a Pareto improvement if, hereby, everyone gains in terms of expected utility. This notion of a Pareto improvement is employed next. We proceed from the same basic assumptions as in the preceding analysis. The only difference is that we focus on the expected amount of out-of-pocket costs, denoted q, rather than the ceiling set for them. This is a major difference, however, since q is a random variable and we must take into account the fact that individuals normally have risk aversion. Gains in consumption opportunities of other goods must be large enough to compensate for an increased risk exposure. The condition for a Pareto improvement may now be written 0  E(q) 

(8.8)

where  is the representative individual’s risk premium. A transition to coinsurance will not be a Pareto improvement unless the representative individual thereby gains enough from the tax cut to compensate for the

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The economics of social protection

Table 8.2b Out-of-pocket cost, risk premium and total cost with different caps and subsidies 1

2

5

10

D. Out-of-pocket costs (q) 0 0 0.7 50 0.7 75 0.6

1.3 1.2 1.0

2.1 1.8 1.4

3.5 2.8 2.0

4.6 3.5 2.4

E. Risk premium () 0 0 50 75

– – –

0.1 0.1 0.1

0.5 0.5 0.4

1.3 1.1 0.8

13.0 13.3 13.5

12.3 12.9 13.3

12.1 12.9 13.5

11.1 12.3 12.9

s\v

0

0.5

– – –

F. Expected total private costs 0 16.0 13.5 50 13.9 75 13.9

Note: Expected total private costs include out-of-pocket costs (panel D), risk premiums (panel E), and taxes (panel C in Table 8.2a). Source: See Table 8.2a.

expected out-of-pocket costs for health care and the disutility of increased risk exposure. Some results from the Rand HIE of relevance in this context are included in Table 8.2b. Panel D shows the amount of out-of-pocket costs the representative individual was expected to pay with different combinations of s and v. These amounts are here expressed as a percentage of the taxable income per capita. (By assumption, out-of-pocket costs as a percentage of income should never exceed the cap. However, this is possible here, since the results reported by Keeler and Rolph were obtained from a model using an absolute cap.) The risk premiums shown in panel E are measured in accordance with suggestions made by M. Susan Marquis and Martin R. Holmer (1996) on the basis of interviews with families participating in the Rand study. Both prospect theory and traditional expected utility theory were used to analyse the data generated by the interviews. The table shows that the risk premium is rather low, not exceeding 1.5 per cent of taxable income, as long as the cap on out-of-pocket costs is less than 10 per cent. However, the risk premium rises considerably when the cap is removed altogether. Finally, on the assumption that health care expenditures in the case of ‘free’ care are 16 per cent of taxable incomes, panel F summarizes the representative individual’s ex ante costs for health care after a transition to

Benefits in kind

159

co-insurance. It is evident that his or her expected costs may be much lower in the case of co-insurance. In fact, all the combinations shown with v0.5 are compatible with a Pareto improvement. These results are fairly robust. For example, the (s, v) combinations shown in the table would be compatible with a Pareto improvement even if the Arrow–Pratt measure of risk aversion was doubled. But these combinations are not equivalent. The co-insurance scheme preferred by the representative individual is without subsidies (s
0) and with a rather high cap on out-of-pocket costs (v
0.10). A transition to this particular scheme would lower the individual’s expected costs for health care by more than 30 per cent, from 16.0 to 11.1 per cent of taxable income. Total health care costs would in this case be divided in the following way (relative to taxable income): income tax 5.2, out-of-pocket costs 4.6, and risk premium 1.3 percentage points. Once again, note that this analysis has been carried out for a ‘representative’ single individual. Individuals differing in relevant aspects, for example in health status, would certainly prefer different co-insurance schemes. It seems fair to conclude, however, that all preferred schemes would be without subsidies. This is an argument about subsidies in the basic financial structure. A subsidy as a device to handle external economies is a different matter. Note also that the gains reported in Table 8.2 do not include the effect of lower excess burden as far as taxation is concerned. As we have seen in Table 3.2, the excess burden could be very large. Neither has the cost lowering effect of more intense competition among producers in the health care sector been accounted for. This effect was first mentioned by Martin Feldstein (1971), and it has been suggested that the size of this effect might be as large as 20 per cent. Equity Considerations Most people would probably be satisfied to know that a transition to coinsurance is a Pareto improvement. However, there are (at least) two reasons why this transition might be objectionable on equity grounds. First, there is no guarantee that everyone will actually be better off in terms of access to health care. People gain from the transition to co-insurance in the form of enhanced consumption opportunities resulting from a lower tax rate. It cannot be taken for granted that enough of these increments of income will be set aside to cover out-of-pocket expenses in case of illness. This is, as we know, a common argument for benefits in kind. Given that nobody should be denied essential health care because he or she cannot pay the bill, the discussed co-insurance scheme would not be equitable unless it included some provision for those who were unable or unwilling to set aside

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The economics of social protection

the amount needed. This point was emphasized by Leonardo C. Gasparini and Santiago Pinto (2006), suggesting that all citizens should have an account with the insurer covering 100v per cent of taxable income. Of course, those not earning enough to have a taxable income will not need to have such an account. For this category there will be ‘free’ care also after a transition to co-insurance. Second, gains from the transition to co-insurance are spread out in a manner that may upset some people’s notion of social justice. As a matter of fact, there will be more in the form of other consumption than of health care for everyone, but most for those who do not need any health care at all. Individuals in this category will only pay the tax shown in panel C of Table 8.2a, while those in need of health care have to pay additional charges of as much as v per cent of taxable income. This ‘inequality’ is present even if we take into account the fact that nobody can be certain of belonging to the first category. To compensate those gaining least from the transition, the co-insurance scheme might be combined with an income support programme favouring especially those expected to need relatively more health care. Social security supplements are worth considering in this context. Since health expenditures have a tendency to increase with age, people in the oldest age group are likely to benefit relatively little from a transition to co-insurance, a fact that J.-Mattias von der Schulenburg (1987) used as an argument for co-insurance, in view of the problems faced by an ageing population. From his point of view, co-insurance is a method of reducing the amount of transfers going to the older generation. Increased social security supplements would moderate this effect. Aggregate Effects Table 8.3 shows some aggregate effects of the hypothetical reform under discussion. We look particularly at the case (s
0, v
0.10). The effects reported in the table have been calculated in accordance with the simulations used in Table 8.2. The decline in the total consumption of health care is 27.5 per cent. Because of the skewed distribution, 70 per cent of this consumption is above the cap and is therefore reimbursed from the public purse. The rest is paid directly by the patients themselves. In spite of the fact that taxes are used to a large extent in the co-insurance model as well, the total amount of taxes needed declines by nearly 50 per cent. Total savings from the reform under discussion correspond to about 4 per cent of GDP. Savings consist of two parts: fewer resources needed in the health care sector, and less excess burden of taxation because of lower

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Benefits in kind

Table 8.3 Aggregate effects of introducing co-insurance in the financing of health care

Consumption User fees Taxes Excess burden (25%) Savings

Before

Change

After

100 0 100

27.5 22.3 49.8 12.5 40.0

72.5 22.3 50.2

Note: Simulated values. Free care consumption
100. Source: Own calculations based on Emmet B. Keeler and John Rolph (1988).

taxes. In this calculation we have assumed that the excess burden of taxation is 25 per cent of the tax revenue, which is a relatively low figure compared with the measures of SMCF reported in Table 3.2. The role of subsidies is shown in Table 8.4, where the equity aspect is illustrated on the basis of original Rand data. The table shows how the consumption of health care changed with increasing subsidies in three income groups, representing one third of the population each. The subsidy was measured as a percentage of prices asked by producers. As shown, people with higher income reacted more to changes in consumer prices (prices asked by producers less the subsidy). A reasonable hypothesis explaining this phenomenon is that (1) the demand for health care is positively related to both needs and income; (2) low-income groups have larger needs, but at any particular level of need they demand less (and probably more urgent) health care than high-income groups; (3) with coinsurance, the least urgent consumption decreases most. The first two tendencies may balance out and give the impression that the demand for health care is (practically) independent of income. A Lasting Improvement? It is an open question whether a transition to co-insurance will be a lasting improvement. The reform would have no effect if people were to buy complementary insurance covering expected out-of-pocket costs. This would bring back ‘free’ care, though financed in a different way. Because of risk aversion, individuals would be willing to pay more than an actuarial premium for additional insurance. The so-called MediGap in the United States, covering out-of-pocket costs in the Medicare system, is an example of a complementary insurance scheme. The problem with such schemes is

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The economics of social protection

Table 8.4 Consumption of health care in different income groups when subsidies vary Subsidy rate 5 50 75 100

Low income

Medium income

High income

581 610 680 788

494 550 588 736

527 590 623 809

Source: Willard G. Manning et al. (1987).

that those insured demand substantially more health care, as we have seen in Table 8.2a. It follows that more people are billed out-of-pocket costs above the ceiling, and that expenditures for the social insurance system rise. The tax used to finance health care accordingly has to be raised, and it is no longer possible to guarantee that the transition to co-insurance will benefit everyone concerned. Theoretically, a tax on complementary insurance would be a remedy for this problem. The tax should, in principle, cover all extra expenditures incurred on the social insurance system. An example may be illustrative. Suppose that a co-insurance scheme with s
0 and v
0.05 has been selected, and that everyone has an additional insurance policy, denoted , offering full coverage for out-of-pocket costs. In Panels D and E in Table 8.2b we can see that the representative individual is prepared to use 3.5 0.5
4 per cent of his or her taxable income to buy . As shown in Panel A in Table 8.2a, expenditures for health care will then increase from 11.6 to 16.0 per cent of an average taxable income. Since most of this increase in demand will be financed out of social insurance funds, it seems reasonable that the tax on  should be 3 to 4 per cent of the average taxable income. Given the risk premiums shown in Panel E, this is well above the amount of ‘loading’ the representative individual is prepared to pay. Hence, a tax incorporating the external effect on the health care financing system caused by complementary insurance may be sufficient to spoil the market for this type of insurance. However, the idea that complementary insurance may be specifically taxed in this way is possibly based on a false premise, namely that the government is free to use such a tax. A government having ratified the ILO Convention on Collective Bargaining and the Right to Organise has promised not to interfere with (reasonable) agreements in wage negotiations. When workers (and their employers) really want to have a complementary health insurance plan included in the employment contract, there is probably not

Benefits in kind

163

much the government can do to stop it. Of course, not everyone will get this kind of workers’ compensation. Non-unionized and unemployed workers, the self-employed and pensioners are excluded, and would probably not escape out-of-pocket costs. Their reaction to out-of-pocket costs would have some effect on the demand for health care, but it is hard to say how large this effect would be. It is too early, anyway, to say that we actually have a case for coinsurance. The data used in the preceding analysis are first class and certainly the best to be found on the issues raised, but we cannot claim more for the conclusions than that they are promising. There are several reasons why findings in the Rand HIE may be misleading. First, these findings were obtained in an experimental situation. It is not unreasonable to assume that a different pattern of consumption would emerge if co-insurance was introduced for real. Among other things, producers of health care might then be tempted to prescribe more expensive treatments than they did in the Rand experiment. Second, findings in the Rand study refer to selected adults of working age and their children. We do not know whether results obtained for this group apply also to senior citizens, welfare recipients and other excluded categories. Third, the study was conducted in the United States. It is hard to tell whether the same results would be obtained elsewhere. The fact that health care consumption per capita is much higher in the United States than anywhere else suggests that the demand elasticity measured in the Rand study probably exaggerates the response one would get elsewhere.

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Index Benítez-Silva, Hugo 143 bequests 28–31, 50, 112 Bernoulli, Daniel 125 Beveridge model (UK) 97 biological rate of interest PAYG (pay-as-you-go) schemes 78–9 portfolio choice 72 social optimum 66–9, 77, 80, 90 Bismarck, Otto von 4, 97 Blomquist, Åke G. 152 bonds 67–72 Borch, Karl 127–8 Boulding, Kenneth 53 Brasse, Valerie 134 Buchanan, James M., Jr 103 Buchinsky, Moshe 143 budget equation 23–4

Aaron’s condition 80, 102 Abbring, Jaap H. 135 abilities, personal 36–8, 39 ability to pay 11 accidents at work 140–42 administrative costs 8, 141 adult goods 16–17, 57 adverse selection 7–8, 11–12 age agei`ng population 98–9 and inequality 23–6 pension eligibility 94 variable retirement age 84–7 annuities 94–7 application fee 143–4 Arrow, Kenneth J. 126, 127, 131, 141, 148, 153 Asher, Mukul G. 104 Atkinson, Anthony B. 17–18, 21 atomistic market 61–9 Australia 58 Baily, Martin N. 129–32, 133 Baily model 129–32 bank loans 10 banks 2–3, 10 Barmby, Tim 138 Barr, Nicholas 99, 122–3 Baumol, William J. 42 Becker, Gary S. 20, 39, 84, 115–16, 119 Beenstock, Michael 134 benefit societies (friendly societies) 2–3, 145–6 benefits accrual 94 benefits in kind distributional policy 58 family support 2 health care insurance 148–52, 154–63 Rand Corporation, Health Insurance Experiment (HIE) 152–4 state support 5 versus cash benefits 147–8

Cairne, John E. 36 capital 72–6, 90 capital income 28–33 capital reserve (CR) schemes fully funded schemes 101–3 model 79–80 risks 103–4 social insurance 91 and training 124 capital stock 76–83 Card, David 121 cash distributional policy 58 family support 2 portfolio choice 69–72 state support 5, 6 versus benefits in kind 147–8 Central Provident Fund (CPF) 104 charity 7 cheating 127–9 Chetty, Raj 131, 150 children child care 57, 147

173

174

Index

family policy 115–19 social protection 4–5 Chile 102 China 98 choices 15 co-insurance health care consumption 154–63 model 148–9 optimal 150 public choice 151–2 Rand Corporation, Health Insurance Experiment (HIE) 152–4 risk-shifting 127 collective household models 18 collective risks 9, 11–12 compensating inequalities 31–3, 34–6 compensation health care insurance 154–63 workers’ 140–42 complementary insurance 161–3 compulsory insurance 10 consumption atomistic market 61–6 health care insurance 153–4, 154–63 and liquidity constraints 105–11 social optimum 66–9, 76–83 cooperatives 80–81, 145–6 costs 8, 141 credit rationing education 119–24 family policy 114–19 and pensions 105–14 welfare loss 114 cross-subsidies 96–7 Cutler, David M. 150 defined-benefit (DB) pension schemes 91–2, 97–8, 99–100, 101–3 defined-contribution (DC) pension schemes 92, 100–103 Denmark 54, 136, 137 desert (‘just deserts’) 51 Diamond, Peter A. 99, 141 difference principle 47–9 disability pensions 57, 58, 93, 94, 142–5 distributional policy 52–9 Dworkin, Ronald 46

earned income tax credit (EITC) 135 earnings 20, 33–40, 120–22; see also income; wages economic growth 27–8, 46 education income dispersion of public budget 57 and inequality 39 and liquidity constraints 119–24 returns from 120–24 and social justice 58–9 uncertain needs 147–8 efficiency 51–2 effort 33–4 elderly care 57, 58, 147 Elster, Jon 52 empirical studies family policy 117–18 health care insurance 152–4, 155–6, 158, 161, 163 social justice 55–9 unemployment insurance 135–6 Engel, Ernst 16 entrepreneurial rents 31, 32–3, 35, 48 envy-free outcomes 41, 42–5 equal opportunities 76 equality 51–2, 59 equality of opportunity (social justice) 41, 45–6 equitable allocation (envy-free outcomes) 41, 42–5 equity (fairness) 51–2, 159–60 Evans, Robert G. 154 exclusion 7, 11–12 exports 82 extended family 113 factor price frontier 88 fair allocation (envy-free outcomes) 41, 42–5 fairness 46–50, 52, 159–60 family as agents of social protection 2, 4–5 extended family 113 income security 145–6 policy 114–19 transfers 25–6 versus welfare state 5–6 farmers 13 Feldstein, Martin 102, 159

Index fertility 98, 115–19 Foley, Duncan K. 41, 42–5, 50, 51 food 16 food stamps 147 France 54, 136, 137 fraud 127–9 Fredriksson, Peter 135 free riding 7, 10 Frick, Bernd 140 Friedman, Milton 125–6 friendly societies (benefit societies) 2–3, 145–6 Frisch, Ragnar 111 full-income-fair allocations 43, 44, 46 fully funded pension schemes 101–3 Galasso, Vincenzo 103–4 Gasparini, Leonardo C. 160 Germany 4, 54, 136, 137 Gibrat, Robert 19, 26 Gini coefficient 21, 55 golden rule of accumulation 75–6 government as agents of social protection 4–6 distributional policy 52–9 social policy role 9–13 social policy structure 6–9 taxation of complementary insurance 162–3 wealth accumulation 77–8 grants 11–12, 72, 77–8 grants economy 53, 55–9 Great Britain 17, 58; see also United Kingdom (UK) Greece 17 growth 27–8, 46 Gruber, Jonathan 94 Hart, Herbert L.A. 49 Hayek, Friedrich A. von 41, 47 health care 57, 147, 160–61 health care insurance aggregate consumption 160–61 co-insurance 154–63 complementary insurance 161–3 empirical study 152–4 equity in 159–60 model of 148–52 private insurance 146, 151–2, 161–3 Health Insurance Experiment (HIE)

175

(Rand Corporation) 152–4, 155–6, 158, 161, 163 Heckman, James J. 117 Helpman, Elhanan 127 Hennessey, John C. 143 Hicks, John R. 37 hiring-and-firing rents 39, 48 Holmer, Martin R. 158 Holmlund, Bertil 135 Holzman, Robert 101 housing 57, 147 human capital 20, 36–8, 39, 120–22 identical individuals 23–8, 50 immigration 98 imports 82 income 90, 135, 161, 162; see also earnings; wages income inequality capital income 28–33 distribution of income 18–20 earnings 33–40 equivalence scales 15–18 identical individuals 23–8, 50 non-identical individuals 28–40, 50 public policy effects 56–8 size of 20–22 income security disability pensions 142–5 insurance theory 125–9 private insurance 145–6 sickness insurance 136–42, 146 unemployment insurance 129–36, 146 income support 13, 160 income tax 54–5, 56, 57, 119 income-fair allocations 43, 44, 46 indemnity policy 148 indexation of pensions 99 individuals choices 15 identical, inequality between 23–8, 50 non-identical, inequality between 28–40, 50 retirement optimum 84–7 welfare loss 114 inequality capital income 28–33 distribution of income 18–20

176

Index

earnings 33–40 equivalence scales 15–18 identical individuals 23–8 non-identical individuals 28–40, 50 public policy effects 56–8 size of income 20–22 inherited wealth 28–31, 50, 112 initial wealth 28–31, 50, 112 insurance accounts 11 compulsory 10 disability pensions 142–5 health care insurance 148–52, 154–63 life expectancy 94–7 moral hazard 126–9 private insurance 133–4, 145–6, 151–2, 161–3 Rand Corporation, Health Insurance Experiment (HIE) 152–4, 155–6, 158, 161, 163 sickness insurance 136–42, 146 social insurance 68–9, 77–83, 90–93, 146 and social policy 6–9 theoretical background 125–9 unemployment insurance 129–36, 146 insurance companies 2–3 insurance goods 148 Ireland 58 Italy 54, 101

retirement age 84–7 supply 38–9, 54–5 and taxes 90 wage rigidity 134–5 withdrawal from work 93–4 Laffont, Jean-Jaques 127 Latvia 101 law of proportionate effect 19, 26 Leiberstein, Harvey 115 leisure 33–4, 36 Leonard, Herman B. 13 liberty principle 47–9 life expectancy 94–7, 98–9, 105–6 lifecycle model 105–14 life-long learning 124 Lilienfield, Abraham M. 143 Lindahl, Erik 59 Lindbeck, Assar 102, 138, 139 liquidity constraints education 119–24 family policy 114–19 and pensions 105–14 welfare loss 114 loans 10, 67–8, 79 local justice 51–2 Lorenz curve 20–21 loyalty 38–9 luck 33, 39–40, 46, 133 lump sum unemployment benefits 133 Lundin, Douglas 151, 152 Lydall, Harold F. 19

Jacob, Johanna 151, 152 Japan 98, 103 Jaques, Elliott 51 Johnson, Harry G. 24–6 just taxation 48–9

Machiavelli, Niccolò 52–3 Malo, Miguel Á. 140 mandatory pensions 105–14, 119 marginal productivity theory of wages 37 market system 3–4, 6–9, 12–13 Marquis, M. Susan 158 Marx, Karl 44, 53 maxmin principle 48 Medicare 148, 161 MediGap 161 merit 6 Meyer, Bruce D. 135 Mikula, Boguslaw D. 101 minimum wage 134–5 Mitra, Sophie 143 money 67

Keeler, Emmet B. 154, 156 Kleven, H. Jacobsen 55 Konow, James 41, 50–52 Kreuger, Alan B. 135 labour contribution of 44 earnings inequality 33–40 income dispersion of public budget 57 mobility 36–8

Index monopoly rents 31, 32–3, 35, 48 moral hazard 8, 126–9, 148, 152 Morgenstern, Oscar 125 mortality 94–7, 98–9, 105–6 Muller, L. Scott 143 neo-classical production model 72–6 Netherlands 136, 137 Neumann, John von 125 New Deal (US) 97 non-compensating inequalities 31–3, 34–6 non-competing groups 36 non-identical individuals 28–40, 50 non-market failures 13 notional defined-contribution (DC) pension schemes 100–101 Nozick, Robert 41, 49, 51 Nyman, John 152 open economy 81–3, 90 Osterkamp, Rigmar 140 Oswald, Andrew J. 134 Palmer, Edward 101 Pareto, Vilfredo 18 Pareto distribution 18–19, 51 Pareto improvement in health care insurance 157–9 Pareto principle 59 Parsons, Donald O. 143 Pauly, Mark V. 148, 152 PAYG (pay-as-you-go) schemes defined-benefit (DB) pension schemes 91–2, 97–8, 99–100, 101–3 defined-contribution (DC) pension schemes 92, 100, 101–3 notional defined-contribution (DC) pension schemes 100–101 and savings 112–13 social insurance 90–91 social optimum 78–9, 80 pensions ageing population, effect of 98–9 alternatives 113 atomistic market 61–6 defined-benefit (DB) pension schemes 91–2, 97–8, 99–100, 101–3

177

defined-contribution (DC) pension schemes 92, 100–103 and family policy 119 fully funded schemes 101–3 income dispersion of public budget 57 indexation of 99 individual optimum 84–7 and inequality 56–8 life expectancy 94–7 and liquidity constraints 105–14 market equilibrium 87–9 market system 3 notional defined-contribution (DC) pension schemes 100–101 portfolio choice 69–72 real capital 72–6 reform 97–8, 101 social optimum 66–9, 76–83, 89–94 and tax 68–9, 90–93, 99–100 and training 124 and unemployment benefits 135 Persson, Mats 102, 138, 139 Pettersson, Thomas 55–9 Pettersson, Tomas 55–9 Pfaff, Martin 53 Phelps, Edmund 32 Pinto, Santiago 160 Poland 101 political influence 52–3, 103–4, 151–2 political sociology 13 portfolio choice 69–72 Pratt, John W. 126 premium reserve model (capital reserve model) 79–80 ‘prisoner’s dilemma’ 10 private cooperatives 80–81 private insurance friendly societies (benefit societies) 2–3, 145–6 health care insurance 146, 151–2, 161–3 incentives 4 unemployment insurance 133–4 private pension schemes 93–4 production model 72–6 Profeta, Paola 103–4 promotion 39 public funds 54, 57

178

Index

Rae, David 140 Rand Corporation, Health Insurance Experiment (HIE) 152–4, 155–6, 158, 161, 163 random variation 26–7 rate of earnings 34–6 rate of interest atomistic market 61–6 biological rate of interest 66–9, 72, 77, 78–9, 80, 90 endogenous 64–6 exogenous 61–4, 81–3 portfolio choice 69–72 social insurance 77–83 social optimum 66–9 rate of return 31–3 rationing 38–9; see also credit rationing Rawls, John 41, 46–50, 51, 59 real capital 72–6, 90 reinsurance 9 relative risk aversion 126 rent seeking 35 reservation wage 35, 38 retirement 84–7, 93, 98–9 risk adverse selection 7–8 aversion 126 of capital reserve (CR) schemes 103–4 collective risks 9, 11–12 disability pensions premiums 144–5 insurance 125–9 premium 126 surcharge 12 workers’ compensation 142 Roemer, John E. 41, 45–6, 49–50, 59 Röhn, Oliver 140 Rolph, John 156 Ross, Thomas W. 147 Rothbarth, Erwin 16–17 Ruser, John 143 Rutherford, R.S.G. 19 Sahota, Gian S. 19 Salanié, Bernard 135 Samuelson, Paul A. 64–7, 69, 72, 77, 81 Savage, Leonard 125–6 savings aggregate savings 111–13 atomistic market 61–6

compulsory 11 lifecycle model 110–11 and pensions 102 portfolio choice 69–72 real capital 72–6 social optimum 66–9, 76–83 school lunches 147 schooling income dispersion of public budget 57 and inequality 39 and liquidity constraints 119–24 returns from 120–24 and social justice 58–9 uncertain needs 147–8 Schulenburg, J.-Mattias von der 160 security, see income security selectiveness 38 service benefit policy 148 Sessions, John 138 Settergren, Ole 100–101 severance payments 133 Shapiro, Carl 38–9 shares 73–4, 79; see also real capital Shimer, Robert 132 sick pay 136 sickness benefits 2, 57, 93, 136 sickness insurance 136–42, 146 Simon, Herbert A. 19 Simonovits, András 97 Singapore 10, 104 Sjoblom, Kriss 97 small open economy 81–3, 90 Smith, Richard T. 143 social insurance 68–9, 77–83, 90–93, 146 social justice definitions of 41 distributional policy 52–9 popular opinion 50–52 theories of 42–50 Wicksell’s approach 59–60 social marginal cost of public funds 54–5 social optimum 66–9, 76–83, 89–94 social policy core of 6–9 definition 5 government role 9–13 lump sum unemployment benefits 133

Index social protection 1, 2–6 social security supplements 160 Söderström, Lars 93, 98, 108, 110, 112 special interests 52–3 Spence, A. Michael 95, 96 square root rule 17–18 stability 4 standard gamble 125–6 Stark, Obed 2 state as agents of social protection 4–6 distributional policy 52–9 social policy role 9–13 structure of social policy 6–9 taxation of complementary insurance 162–3 wealth accumulation 77–8 steady state 75–6 Steurer, Miriam 102 Stiglitz, Joseph E. 38–9 student loans 57, 119–24 subsidies to counteract exclusion 11–12 education 123–4 health care insurance 148–9, 154–63 housing 147 pensions 90 and private insurance 4 wages 134–5 Sweden family policy 117, 119 grants economy 55–9 partial retirement 93 PAYG (pay-as-you-go) schemes 97 pension reform 101 private pension schemes 93–4 sickness insurance 136, 137, 140 social insurance 92–3 welfare state 11 tagging 142–4 tax complementary insurance 162–3 government wealth accumulation 77–8 health care insurance 151–2, 154–63 just taxation 48–9 and labour 90

179

PAYG (pay-as-you-go) schemes 78–9 and pensions 68–9, 90–93, 99–100 portfolio choice 72 terminal wealth 28–31, 36 Tesfatsion, Leigh 69–72 Thaler, Richard 38 Theil, Henri 22 Theil’s (entropy) measure 22 Thomason, Terry 144 Thustrup Kreiner, C. 55 Tomes, Nigel 20 trade 42 trade unions 38 traffic accidents 144 training 124 transfers 25–6 Treble, John 138 Tsakloglou, Panos 17 tuition fees 122–3 Tullock, Gordon 53 unemployment 8, 38–9 unemployment insurance 2, 93, 94, 129–36, 146 United Kingdom (UK) 54, 97, 135, 136, 137; see also Great Britain United States (US) disability pensions 142, 143 health care insurance 148, 153, 161, 163 pensions 97 unemployment insurance 134, 135, 136 utility from income 125–9 van den Berg, Gerhard J. 135 van Ours, Jan C. 135 Varian, Hal R. 41, 43–4, 46 veil of ignorance 47 vouchers 147 wages 37, 134–5 Walker, James R. 117 wealth accumulation 77–83 differences 28–33 inherited 28–31, 50, 112 wealth-fair allocations 43–4 welfare loss 114 welfare state 5–6, 11

180 Werning, Iván 132 Wicksell, Knut 48–9, 59–60 Wise, David A. 94 work accidents 140–42, 144 disincentives 99–100 effort 33–4

Index workers’ compensation 140–42 workfare 135 working families tax credit (WFTC) 135 working poor 135 Zeckhauser, Richard J. 13, 150