vpSl%86 POLICY RESEARCH WORKING PAPER 1869 Risk Reduction and Public Government spending on risk reduction could improve Spending welfare in developing economies, either by Sbantayanan Devaralan alleviating a risk-market faflure or by reducing uricertainry in Jeffrey S. Hammer otherwise distorted markets The World Bank Development Research Group Public Economics January 1998 I POLICY RESEARCH WORKING PAPER 1869 Summary findings As governments grow richer, the share of their GDP They argue that there is a case for incorporating risk devoted to public spending rises. Public spending in the reduction into government spending, if doing so meets United States was 7.5 percent of GDP in 1913. It is 33 standard welfare-economics criteria for government percent today. Although industrial countries spend twice intervention in the economy. Through examples- as much as developing countries, government spending government-provided health insurance and crop on goods and services is the same in both groups of insurance, price stabilization schemes, transfer programs countries. The difference is almost entirely due to for income support, public investments, publicly transfer payments, which are about 22 percent of GDP in provided health care, and government credit guarantees the industrial world. - they show where government spending on risk Most of these transfer payments - pensions, health reduction could improve welfare, either by alleviating a insurance, unemployment insurance, guaranteed loans - failure in risk markets or by reducing uncertainty in are aimed at mitigating risk in the private sector. otherwise distorted markets. They illustrate calculations Devarajan and Hammer explore how the framework for of the risk-reduction benefits of public spending and cite evaluating government spending on goods and services cases where their neglect could lead to serious can be extended to incorporate the government's various underestimates. risk-reducing activities. This paper - a product of Public Economics, Development Research Group - is part of a larger effort in the group to improve the allocation of public expenditures in developing countries. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact CynthiaBernardo, room MC2-501, telephone 202-473- 1148, fax 202-522-1154, Internet address cbernardo@worldbank.org. January 1998. (33 pages) The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of tbe series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Produced bv the Policv Research Dissemination Center Risk Reduction and Public Spending Shantayanan Devarajan Jeffrey S. Hammer * An earlier version of this paper was presented at the World Congress of the International Institute of Public Finance, August 1997, Kyoto, Japan.. We are grateful to Vito Tanzi for helpful comments. i i I One of the more common facts in public finance is that, as countries grow richer, the share of their GDP devoted to public expenditures rises. Public spending in the U.S., for example, was 7.5 percent of GDP in 1913 and is 33 percent today. Present-day developed country governments spend about twice as much as developing countries. Yet, government spending on goods and services is the same in developed and developing countries; the difference is almost entirely du^ to transfer payments, which are about 22 percent of GDP in the industrialized world (Tanzi and Schuknecht [1997]). Most of these transfer payments-unemployment insurance, pensions, health insurance, guaranteed loans-have the characteristic that they are aimed at mitigating risk in the private economy. In this paper, we explore how the existing framework for evaluating government spending on goods and services, welfare economics (Samuelson [1954], Musgrave [1959]), can be extended to incorporate the government's various risk-reducing activities. Since governments do not typically classify their expenditures by their risk- altering characteristics, our approach will be more conceptual than empirical. We illustrate our points with some simple examples and models designed to capture the risk- reducing properties of various public expenditures. Our conclusion is that, when viewed from a risk-reducing perspective, the benefits and costs of certain public expenditures can be quite different, indicating directions of change in the composition of public spending that are welfare-enhancing. In section I of the paper, after speculating on why, as countries grow richer, governments spend more on these risk-mitigating transfer programs, we spell out our analytical framework. In section II, we apply the framework to a series of common 2 programs associated, directly or indirectly, with the reduction of risk, including crop insurance, medical care, income support, flood control and education loans. Section III offers some concluding remarks. I. Analytical Framework The framework for evaluating public expenditures aimed at reducing risk begins with the metric for valuing the reduction of risk to the individual, which is the familiar von Neumann-Morgenstem framework. The value of reducing risk (or, alternatively, the demand for risk-reducing activity) is due to the assumption that individuals have declining marginal utility of income, or, are risk-averse. As a result, people will generally prefer a certain outcome to a risky one with the same expected value. A job at $20,000 per year is better than taking a 50% chance on getting one at $40,000 with a 50% chance of no income at all. How much that is worth depends on how much greater the difference in utility is between $20,000 and zero than the difference between $20,000 and $40,000. There is an amount of money that one is willing to pay to assure an income of $20,000 (minus that payment) as opposed to taking the risk. This is called the risk premium and the amnount of income left over after paying the premium is called the certainty equivalent income to the risky situation. Fornally, this can be expressed as U(W-V) = EU(W + Ze.) where U(-) is the utility function of income (strictly speaking, wealth) denoted W, V is the maximum amount one would pay to have a certain income relative to the variable one. The expectations operator E takes the average of utility when wealth is risky and Yei is the 3 sum of all risky components of wealth. This expression says that there is a value V which makes the individual indifferent between the certainty equivalent income W-V and the situation in which that person faces all risks. The risky component is written as a sum of potentially many different "shocks" to income in which only their sum-their net impact on income-is of ultimate concern to the individual. We can use this framework to speculate on why public spending on risk-reduction increases with incomes. At first glance, this seems counter-intuitive, since a common assumption is that people's aversion to a given amount of risk declines with income, so that the risk premium (and therefore the benefits from government spending to reduce risk) would be higher in poorer countries'. T'he countervailing effect is that the magnitude of the shocks to income is much greater in rich countries. Many of the risks that public programs mitigate are related to income. If someone earning $100,000 loses a job, the absolute value of the loss is considerably greater than if the initial income was $20,000. Can this feature explain the large variation in public spending on risk-reduction across countries and over time? With constant relative risk aversion, if losses are strictly proportional to income, then so will be the premium, in which case this feature alone cannot explain the variation in public spending2. If, however, the losses are more than proportional to income, then the premium (as a percentage of income) rises quite dramatically with income (Figure 1). If, for example, the level of income that one is left with after a typical shock to income rises 'A more common assumption is that people have declining absolute risk aversion but constant relative risk aversion. 2 model is one where the individual with income YO has a probability p of having his income drop to Y, (and probability (l-p) of keeping it at YO). If a is the degree of relative risk aversion (so that the utility 4 with income, but only with an elasticity of 0.8, we observe that the risk premium rises from zero to nearly 18 percent of income at levels of around $6,000. That this gap of 18 percent also happens to be close to the difference in public spending on transfers between developed and developing countries suggests that such reasoning is a plausible explanation for the difference. That income after losses rises less-than-proportionately with income is plausible, but context-specific. Losses could be more than proportionate to income if financial losses are related to wealth, which rises faster than income. As argued by Pritchett [1997], average incomes in poor countries are simply too close to actual subsistence that drops from these levels cannot be very large and still be sustainable. Losses could also be less than proportional. When disaster strikes, people in rich countries have more to lose, but not proportionately so, since there may be other mechanisms to cushion the blow. To take one example, an earthquake in California will do significantly more damage (in terms of the value of the capital stock lost) than a comparable one in Armenia. Yet, the difference is not proportional to the relative income of the two places because California can afford to build more earthquake-resistant structures. function is U(Y) = Y"'/(l-a)), then the risk premium is given by V = - [pY,'u + (I-p)YO 1]"('') . If Y,= fY0, then V/Yo is a constant 5 Figure 1: Risk premium as a share of income - illustrative parameters 20 15 10 5 0 1000 2000 3000 4000 5000 6000 A second possibility might be that, as countries develop, traditional ties that provided informal insurance through families and communities tend to loosen, increasing demand for insurance services from more formal markets or from the government if insurance markets don't grow to accommodate this demand. However, the causality could just as easily run the other way: the development of formal insurance markets or government programs may be the reason that family structures loosen in the first place. This evaluation of risk-reducing expenditures in terms of displacement of alternative mechanisms is discussed in more detail below. Just because we can "explain" the higher government expenditure in developed countries in terms of risk-reduction does not mean all of those expenditures are justified. The reason is that public expenditures in general are justified only when there are market failures or distributional concerns, and this is true for risk-reducing public expenditures too. After briefly sketching out the foundations of this approach to public-expenditure analysis, we turn therefore to an examination of potential failures in risk markets, and proceed to explore the implications for public policy in some special cases. 6 The framework for evaluating government spending on goods and services is based on the rationale for public intervention in the economy which, in turn, is derived from the fundamental theorems of welfare economics. If the conditions of the first welfare theorem were to hold, there would be no need for a government, since the unfettered market would reach a Pareto-efficient allocation. If there is a concern for equity, then the second welfare theorem shows how, with a suitable redistribution of initial endowments, the desired Pareto-efficient allocation can be achieved by the private market. Hence, the rationale for public intervention must be associated with one or more of the conditions of the welfare theorems not being met. The most common ones are the existence of externalities, public goods, noncompetitive markets, and various elements of imperfect information (often collectively referred to as "market failure") on the one hand, and the inability to redistribute endowments to achieve equity objectives on the other. This simple point alone can be a powerful tool in scrutinizing public expenditures. The largest item in the Indian government's agriculture budget, for example, is a fertilizer subsidy. Forty years ago, the subsidy was justified on the grounds that it was a new technology so unknown and inherently risky that individual farmers may not have an incentive to adopt it. Today, the market-failure rationale for the subsidy has all but disappeared (Pradhan and Pillai-Essex [1994]). The existence of a market failure only indicates a rationale for government intervention; it does not necessarily imply a need for public expenditure. The textbook case of an externality is the polluting factory, which emits toxic chemicals into a stream, inflicting a cost to downstream users of that stream. While the competitive equilibrium in 7 this case will not be Pareto optimal, the solution is typically to levy a pollution tax on the factory, rather than some public expenditure program. Finally, for cases where there is some market failure, and where public expenditure is the most appropriate instrument, there remains the issue of how important the market failure is. Since governments have, limited resources, we need to have a sense of the quantitative benefits and costs of these different expenditure programs in order to allocate public resources rationally. The quantitative assessment is made up of two components: the difference between social and private benefits (in the price dimension), and the net addition of service (in the quantity dimension). In evaluating these benefits and costs, we need to keep in mind that most cases of market failure are ones where a private market exists, but does not provide the socially optimal level of output For example, many believe that education carries with it a positive externality, insofar as society attaches a value to having a literate and numerate population, beyond the benefit increasing his wage that the individual receives from education3. Yet, education is mainly a private good, since it benefits the individual by increasing his wages. The benefit of public provision of education (assuming provision is the best instrument), then, is the increment in the external effect of the additional educational attainment over and above what the private sector would have achieved in the absence of public intervention. Since education, and many other public services, are nontraded goods, the calculation of net benefits should take into account the extent to which public provision crowds out the Some claim education to be a "public good" on these grounds, but this does not accord with standard definitions. A public good is non-excludable, meaning you cannot charge for it even in principle, since non-payers cannot be excluded from benefitting. A public good is also non-rivalrous meaning that one person's use of the good does not reduce the amount available for others. While underutilized classrooms may fall into this category, usually teacher's time and classroom seats are limited. 8 private sector. If the government was providing education but the private sector could still provide more (with perfectly elastic supply), then the public education would completely crowd out private education, making the net benefit of this public program zero (Devarajan et al. [19971, Hammer [1997]), While quantitative analyses of the benefits of public-expenditure programs (in the welfare-theoretic sense developed here) are hard to come by, there is some evidence that is suggestive. Hammer et a. [1995] evaluate the impact on infant mortality of the Malaysian government's expenditures on public medical personnel and immunization. They find that government spending on doctors at the margin has no significant effect on infant mortality whereas spending on services such as immunization which have clear external effects is highly significant. Spending on public medical personnel was simply crowding out private medical personnel, leaving the net effect not significantly different from zero. Similar results for health care have been found by Alderman and Lavy [1996]; for income transfers by Cox and Jimenez [1995], and for secondary education by Jimenez, Lockheed and associates [1996]. Finally, the theory of the second-best is often invoked in justifying and evaluating public expenditures. If there is a distortion in the economy, then government intervention, and possibly government expenditure, in some other (undistorted) market may be warranted because it can affect welfare in the distorted market. For example, if there is a failure in the credit market that prevents young people from obtaining student loans, then public support to education may be justified. Note however that two conditions have to be met. First, the market in which intervention is being considered must be linked to a truly distorted market. Second, removing the original distortion must 9 be more difficult or costly than this "secon4-best" approach. As to the first, the mere fact that government policies change conditions in related markets is not per se a justification. Such effects could be of the form of a "pecuniary externality" where the impact of a policy is solely through the workings of competitive markets. There may be distributional consequences as, say, universal primary education supported by government could well raise the wages of teachers (or all people who are potential teachers) but if the supply of such factors is competitive, the existence of such effects poses no difficulties or particular issues for policy analysis. If, however, there are serious market failures associated with these affected activities, then there is a need for taking these into account. For example, a project such as a road which indirectly increases steel output would not have to take into account the changes in steel or of the coal or labor used in its production if these were all competitive markets. If, however, steel production caused pollution, the value of the reduction of pollution would be a further cost of the project which would have to be valued. This example also illustrates the second condition. Appropriate pollution control policies directdy applied to the steel industry would obviate the need for the road project to worry about steel production. Only when such policies are unavailable (for technical or political reasons) is this interconnectedness important (Sen [1972]). As the discussion on evaluating public expenditures makes clear, the fact that governments affect the risk profile (and hence welfare) of private agents is not sufficient justification for there to be a public expenditure program to mitigate risk. But many markets associated with the bearing of risk are characterized by market failures. In some cases, the markets may simply not exist. In others, private agents will supply a sub- 10 optimal level of risk-reduction. Consequently, there is a role for government, both in attempting to correct these market failures directly, and-where that may not be feasible-in addressing risk-market failures through intervention in other markets. IL Applying the Framework Several important failures in risk and risk-related markets can be discussed with reference to the framework outlined in section I. The most common one in the literature is the frequent absence of insurance markets. The simple model of individual decision- making under risk specified above implies that there will be a demand for insurance-a willingness to pay the quantity V above and beyond the actual expected cost of assuring wealth W. A firm that can pool all risks and ensure a payment to all customers to make their income W-V can collect V as profit. Competition should drive this profit down to the actual cost of providing the insurance itself, so that people will end up paying this cost which is less than V, gaining consumer surplus from the difference. However, there are numerous reasons why such a market will fail to emerge or will supply insurance in far less than optimal amounts. They fall under the general categories of adverse selection and moral hazard (Rothschild and Stiglitz [1974]). Adverse selection occurs when there is asymmetric information between buyers and sellers of insurance. For example, an individual may know if he is a bad health risk, but an insurance company may not be able to detect this. Consequently, insurance companies offer health insurance reflecting the average risk of the population. But at this price, only those with a higher-than-average risk will purchase insurance. As a result, the lower- than-average risk population leaves the market, saddling the insurance company with a 11 riskier population than they expected. If the company raises its premium, even more people leave the market, and eventually the market dries up. Moral hazard is a situation where an individual, having purchased insurance, may have an incentive to undertake suboptimal levels of risk-reducing activity. For instance, purchasers of theft insurance may not lock their doors, even though society will be better off if they did. Perhaps the most graphic example is that of arson-when people bum down their own houses to collect on fire insurance. The existence of moral hazard and adverse selection can prevent the insurance market from appearing at all. The complete absence of the market imposes costs on people of the full amount of V. But this fact alone does not justify government intervention-let alone government expenditure-in risk markets. The first question to ask is whether, by intervening, the govenment can do better. That someone, such as an insurance company, has the ability to pool or otherwise bear the risks that, at least, some individuals would prefer not to is a basic insight into the value that government can bring to the market. Efficient markets will result in those who either do not care as much (are less risk averse) or who have such risk-reducing options as diversification opportunities available to them actually having more risk shifted onto them from the more risk-averse, less protected consumers, picking up some, fraction of V along the way. Government may be in the position to bear this risk itself better than some individuals. Then the government does the pooling. However, it is not clear how publicly-provided insurance gets around the problems of adverse selection and moral hazard. Alternatively, the government may choose to regulate insurance markets, to 12 correct some of the existing failures. In either case, the main thrust of the policy will be to shift risks and the value of doing so is V per affected person. Explicit insurance is not the only way that people deal with exposure to risk. In many circumstances, people have opportunities to reduce their own exposure through diversification of various sorts. The classic example forms the basis of the contemporary theory of finance. The value of any security is not simply its expected return but is related to the degree to which it is correlated with the rest of the market and therefore serves to reduce the risk of holding portfolios. In our notation, there is a premium to be paid to any one asset e, if it can reduce the variation of the sum of all retuns-the investor's net variance. People have other means to help deal with risk. In traditional societies, the extended family provides an insurance policy of sorts. Hard times may result in intra- family transfers with either explicit or implicit repayment arrangements, i.e., they may be gifts or loans. The credit market itself may serve as an insurance mechanism if people use it to borrow or draw down savings in bad years and pay back or build up savings in good. However, as will be seen shortly, credit markets themselves are often faulty for reasons similar to insurance markets, especially for consumption loans. The degree to which they are faulty will determine the value of policies which reduce the risk that one would borrow against. In sum, the valuation of mitigating risk needs to be in comparison to the net exposure Yei after diversification or other protective activities are undertaken. Savings on any real costs associated with the protection, however, would be another benefit from 13 the program. For example, agricultural households are sometimes noted to have more livestock or other, relatively liquid, productive assets than would be justified by considerations of profitability alone. The increase in farm profits from shedding such unprofitable activities, due to having to handle less risk or having more efficient means of handling those risks, would be a benefit of an insurance program for say, crops or health or even unemployment. The actual calculation of certainty equivalent incomes, or, the risk premium that could be obtained from people, requires specifying an explicit functional form for utility. This introduces a highly subjective element into the calculation as this is not a directly observable function. Further, there is no reason to believe it is common across people, nor even that the degree of risk aversion on the margin are equal, unless markets are working so well as to allow the equalization of marginal risk across people. But if such markets did exist, there would be no particular justification of government intervention at all. The most careful calculation would try to approximate the willingness-to-pay for a particular degree of risk-reduction for different types of people and add up across types (differing by income, risk aversion and degree of wealth at risk). Finally, in addition to providing insurance, governments use a variety of other instruments to address problems of risk. For instance, governments may attempt mitigate the risk of price fluctuations facing farmers by agreeing to buy farm output at a fixed price, even when the world price is varying. In what follows, therefore, we examine two forms of public expenditures associated with risk-reduction: public provision of insurance, and other public expenditures that alter the risk profile facing individuals. 14 A. Government provision of insurance Government policies can affect various different components that go into the calculation of the risk premium. Sometimes govermments attempt to provide insurance directly when the market does not. Two common areas where this occurs is in health and crop insurance. Health insurance. While direct provision of services is more common in the developing world, many countries have instituted explicit health insurance as a means to help people deal with the financial consequences of medical care. The issue of health insurance is a complicated one to be sure-witness the recent debates in the United States and most other OECD countries. Here we only want to highlight the issue of valuation of the benefits of health insurance. From the perspective of correcting market failures, the benefit that the public can obtain over and above the laissez-faire equilibrium can be substantial. As mentioned, insurance markets for medical services are likely to be seriously distorted. In the early part of this century, the insurance industry in the U.S. considered medical care an uninsurable service because of the severe problems of adverse selection in voluntary markets and in the potential for abuse in terms of moral hazard (Arrow, 1966). In the developing world, this situation still holds with very little private insurance existing even where medical care itself is largely private (Lewis and Chollet, 1997). To a large extent, evaluations of health insurance have focused on the benefits of medical services rather than the benefits of the service that the programs actually provide: insurance per se. By ignoring risk-reducing aspects, many discussions of health 15 insurance and the relative merits of services to be covered by public schemes have been seriously flawed. The benefits of publicly provided health insurance should be the willingness to pay for insurance services that are not available due to the market failure reasons stated above. As a result, the value of public coverage depends at least as much on the probability of illness and the size of the expenses avoided by the policy as on the medical benefits of the treatments covered. For example4, if there is no insurance, what happens when a person falls ill with a condition that is treatable? The person could either choose to take the treatment or decide that it is too expensive and suffer with the condition. If he chooses to take the treatmnent, then the value of public coverage of that condition is no longer related to the medical value of the treatment since the person is treated with or without public support. The value that public policy brings to this case is purely financial and is the willingness to pay, ex ante, for insurance against that disease condition. If the standard (constant relative risk aversion) utility function is used to analyze this situation, the value of insurance will be: V= Y-U-'(pU(Y-C)+ (1-p)U(Y)) where Y is income, p is the probability of illness and C is the cost of the treatment. Note that health effects of the treatment do not appear in the valuation. This value must be higher than the administrative cost associated with processing the insurance. Otherwise there is no gain to be had from insuring the service at all and it would be better to have people pay out of pocket when they need it. ' This example is taken from Hammer and Pritchett (1997). 16 If the person would not purchase the treatment out of pocket because it was too expensive, we might still ask if the person would have purchased actuarially fair insurance for the treatment had it been available. The answer to this question is no longer independent of the health benefits that the treatment provides. A person would be indifferent between buying insurance and not if the following equality holds: pU(H1, Y- pC) + (l-p)U(HO, Y-pC) = pU(H2, Y) + (l-p)U(HO,Y) where Ho is health status when not sick at all, H1 is health status after treatment when sick and H2 is health status when sick and left untreated. The left hand side is expected utility if you are insured and getting treatment that improves your health status from H2 to H1 and the right hand side is the expected utility of refusing to insure and taking the risk of suffering with health status H2 if you get ill. All of this is contingent on U(H,, Y-C)