Public Expenditures and Risk Reduction

Governments in developing countries spend money on goods and services that have an impact on people’s exposure to risk. This paper presents a simple approach to valuing such expenditures from the perspective of risk reduction. There are two types of expenditures: public provision of insurance, such as for health care or crop yields; and policies aimed at other objectives that change peoples’ risk profile, such as transfer programs, tax and subsidy policies, and infrastructure investments. Several examples of each type show that incorpo223 Shantayanan Devarajan ([email protected]) is Chief Economist for the Human Development Network of the World Bank. Jeffrey Hammer ([email protected]) is a Lead Economist in the Development Economics Research Group of the World Bank. Earlier versions of this paper were presented at the World Congress of the International Institute of Public Finance, Kyoto, and the World Bank’s Economists’ Forum. We are grateful to Trina Haque, Kathy Lindert, Vito Tanzi, and Karla Hoff, for helpful comments. The findings, interpretation, and conclusions are the authors’ own and should not be attributed to the World Bank, its Executive Board of Directors, or any of its member countries. World Bank Economists’ Forum Vol. 2 (2002), pp. 223–246. 224 Shantayanan Devarajan and Jeffrey S. Hammer rating the risk-reducing perspective significantly alters the value of public expenditures, which indicates that these considerations should be included in standard public expenditure analysis. That public spending rises with a country’s per capita income is well known. In the United States, for example, public spending was 7.5 percent of gross domestic product (GDP) in 1913 and is 33 percent today. Governments in present-day developed countries spend about twice as much as developing countries. Less well known is that government spending on goods and services is the same in developed and developing countries; the difference is almost entirely the result of transfer payments, which are about 22 percent of GDP in the industrial world (Tanzi and Schuknecht 1997). Many of these transfer payments— unemployment insurance, pensions, health insurance, and 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. Because 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. We show that adopting a risk-reducing perspective has implications for the costs and benefits of certain public expenditures and taxes that are different from the standard analysis, which indicates directions of change in the composition of public spending that are welfare-enhancing. In the first section of the paper, Analytical Framework, we present an approach to evaluating the welfare consequences of policies that influence the size and distribution of risks that people face. We also show how the approach can provide insight into the positive question of why governments of developed countries spend more on riskrelated expenditures than governments of developing countries. In the next section, Applying the Framework, we apply the framework to the normative question of evaluating the benefits and costs of common programs associated, directly or indirectly, with the reduction of risk, including crop insurance, medical care, income support, flood control, education, and loans. The last section offers some concluding remarks. PUBLIC EXPENDITURES AND RISK REDUCTION 225 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-Morgenstern framework. Risk aversion is modeled in this framework by a utility of income function that rises at a decreasing rate. 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 percent chance on getting one at $40,000 with a 50 percent 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 amount of income left over after paying the premium is called the certainty equivalent income to the risky situation. Formally, this can be expressed as U(W – V) = EU(W + ∑ei) where U(⋅) is the utility function of income (strictly speaking, wealth) denoted W, and 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 ∑ei is the sum of all risky components of wealth, each normalized to have zero mean. This expression says that there is a value V that makes the individual indifferent between the situation with a certain 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. Even if we can “explain” the higher government expenditure in developed countries by showing the value of reducing risks (box 1), it does not follow that all those expenditures are justified. Public expenditures in general are justified only when market failures or distributional concerns exist, and this is true for risk-reducing public expenditures, too. After briefly sketching out the foundations of this approach to the analysis of public expenditures, 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. 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 wel226 Shantayanan Devarajan and Jeffrey S. Hammer BOX 1: WHY DO RICH COUNTRIES SPEND MORE ON REDUCING RISK THAN POOR COUNTRIES? At first glance, the fact that public spending on risk reduction rises with income seems counterintuitive, because a common assumption is that people’s aversion to risk declines with income, such that the risk premium (and therefore the benefits from government spending to reduce risk) would be higher in poorer countries. The 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 spending. If, however, the losses are more than proportional to income, 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 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 may be an explanation for the difference. Risk-reducing expenditures and income 0 5 10 15 20 0 1,000 2,000 3,000 4,000 5,000 6,000 FIGURE 1. RISK PREMIUM AS A SHARE OF INCOME — ILLUSTRATIVE PARAMETERS Premium (in percent of income) PUBLIC EXPENDITURES AND RISK REDUCTION 227 fare economics. If the conditions of the first welfare theorem were to hold, there would be no need for a government, because the unfettered market would reach a Pareto-efficient allocation. If there is a concern for equity, 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 might not have an incentive to adopt it. Today, the marketfailure 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 and inflicts a cost to downstream users of that stream. Although the competitive equilibrium in this case will not be Pareto optimal, the solution is typically to levy a pollution tax on the factory, rather than to initiate a 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. Because governments have limited resources, we need to have a sense of the quantitative benefits and costs of these different expenditure programs to allocate public resources rationally. The quantitative assessment is made up of two components: (a) the difference between social and private benefits (in the price dimension), and (b) 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 228 Shantayanan Devarajan and Jeffrey S. Hammer and numerate population, beyond the benefit increasing the wage the individual receives from education.2 Yet education is a private good, so the benefit of public provision of education (assuming that provision is the best instrument), then, is only the external effect of the additional educational attainment over and above what the private sector would have achieved in the absence of public intervention. Because 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 private sector. If the government was providing education, but the private sector could still provide more (with perfectly elastic supply), the public education would completely crowd out private education, which would make the net benefit of this public program zero (Devarajan, Squire, and Suthiwart-Narueput 1997; Hammer 1997). Although quantitative analyses of the benefits of public expenditure programs (in the welfare-theoretical sense developed here) are hard to come by, some suggestive evidence exists. Hammer, Nabi, and Cercone (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, which left 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 and Lockheed (1995). Finally, the theory of the second best is often invoked in justifying and evaluating public expenditures. If there is a distortion in the economy, 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 a failure in the 2. Some claim education to be a “public good” on these grounds, but this does not accord with standard definitions. A public good is nonexcludable, meaning that you cannot charge for it even in principle, because nonpayers cannot be excluded from benefiting. A public good is also nonrivalrous, meaning that one person’s use of the good does not reduce the amount available for others. Although underutilized classrooms may fall into this category, usually teachers’ time and classroom seats are limited. PUBLIC EXPENDITURES AND RISK REDUCTION 229 credit market prevents young people from obtaining student loans, 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 be more difficult or costly than this “second-best” approach. As to the first, the mere fact that government policies change conditions in related markets is not in itself a justification. Such effects could be in 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; for example, 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 markets are incomplete, even pecuniary externalities with competitive markets could have effects on efficiency (Greenwald and Stiglitz 1986, de Meza and Gould 1992). Of course, when serious market failures are associated with these affected activities, the activities need to be taken into account. For example, a project, such as a road that 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 they 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 that would have to be valued. This example also illustrates the second condition. Appropriate pollution control policies applied directly to the steel industry would obviate the need for the road project to worry about steel production. Only when such policies are unavailable—for example, 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 the existence of a public expenditure program to mitigate risk. Many markets associated with the bearing of risk, however, are characterized by market failures. In some cases, the markets may simply not exist. In others, private agents will supply a suboptimal 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. 230 Shantayanan Devarajan and Jeffrey S. Hammer Applying the Framework Several important failures in risk and risk-related markets can be discussed with reference to the framework outlined in the previous section. The most common one in the literature is the frequent absence of insurance markets. The simple model of individual decisionmaking 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, and gaining consumer surplus from the difference. Many reasons explain 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 1976). 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. At this price, however, assuming no quantity constraints, 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 riskier population than they expected. If the company raises its premium, even more people leave the market, and eventually the market dries up. Rothschild and Stiglitz (1976) show that, for a market to exist, insurance companies will have to offer price-quantity packages, thereby limiting the amount of insurance at a given price that an individual can buy. This kind of quantity rationing, however, as they show, can be Pareto inefficient. 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 would be better off if they did. Perhaps the most graphic example is that of arson—when people burn 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 PUBLIC EXPENDITURES AND RISK REDUCTION 231 market imposes costs on people of the full amount of V, although 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 government 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. In exchange for absorbing more risk, they are paid some of the risk premium, V, that the risk-averse individuals gain in the bargain. Government may be in the position to bear this risk itself better than some individuals. The government would then do the pooling. It is not clear, however, how publicly provided insurance gets around the problem of moral hazard. Mandatory, publicly provided insurance can get around the problem of adverse selection. Alternatively, the government may choose to regulate insurance markets to correct some of the existing failures. In all these cases, the main thrust of the policy would be to shift risks, and the value of doing so would be 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, a premium is to be paid to any one asset ei if it can reduce the variation of the sum of all returns—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 intrafamily transfers with either explicit or implicit repayment arrangements; that is, 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 that reduce the risk that one would borrow against. 232 Shantayanan Devarajan and Jeffrey S. Hammer In sum, the valuation of mitigating risk needs to be in comparison to the net exposure ∑ei after diversification or other protective activities are undertaken. Savings on any real costs associated with the protection, however, would be another benefit from 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, caused by 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. Other costs associated with protection include delayed schooling of children (Alderman and Paxson 1992), inefficient (in terms of expected income) crop mixes (Morduch 1994), mobilityreducing insurance arrangements (Bannerjee and Newman 1993), and nepotism in labor markets (Hoff and Sen 2001). 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 because 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 is equal, unless markets are working so well as to allow the equalization of marginal risk across people. If such markets did exist, however, 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 to 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: (a) public provision of insurance and (b) other public expenditures that alter the risk profile facing individuals. Government Provision of Insurance Government policies can affect various different components that go into the calculation of the risk premium. Sometimes governments PUBLIC EXPENDITURES AND RISK REDUCTION 233 attempt to provide insurance directly when the market does not. Two common areas where this occurs are in health and crop insurance. Health Insurance. Although 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 Organisation for Economic Co-operation and Development (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 United States 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 1985). 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 on the benefits of insurance per se. By ignoring risk-reducing aspects, many discussions of health 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 because of 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 example, 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 treatment, the value of public coverage of that condition is no longer related to the medical value of the treatment because 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 234 Shantayanan Devarajan and Jeffrey S. Hammer insurance will be: V = Y – U–1(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. 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 if it had 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 buying it if the following equality holds: pU(H1,Y – pC) + (1 – p)U(H0,Y – pC) = pU(H2,Y) + (1 – p)U(H0,Y) (1) where H0 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 a person is insured and getting treatment that improves his or her 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 the person gets ill. All this is contingent on U(H1,Y – C) < U(H2,Y) because we have assumed that this treatment would not have been purchased out of pocket. The value of providing insurance in this case is the difference between the leftand right-hand sides of the above inequality. Figure 2 shows the above relations graphed in the space of cost of treatment and health benefits of treatment. For the case of treatments that would be purchased out of pocket, curve OA is drawn with a health status of H1 when illness occurs because it is assumed that treatment will be taken. The line segment DE is the combination of H1 and C that solves equation (1). The vertical line at C = B is the level of treatment costs such that the administrative costs of insurance exceed the value of the insurance itself. The figure is thus divided (by solid lines) into four areas. In area I, treatment would be paid for out of pocket, but people would prefer to insure against it. In area II, people would pay for treatment out of pocket, but would not bother to buy insurance because such treatments are too cheap to cover the administrative costs of insurance (aspirin for headaches is a good example).3 In area III, people would neither buy the treatment out of PUBLIC EXPENDITURES AND RISK REDUCTION 235 pocket nor demand actuarially fair insurance for it. In area IV, people would not buy the treatment out of pocket, but would pay for insurance for it. This represents a catastrophic loss for direct purchase, but is rare enough to have a sufficiently low expected cost to be worth the insurance value. For comparison, the ray OC has been superimposed on the graph. These points share a common “cost-effectiveness ratio,” or a constant health benefit per dollar spent on a medical treatment. This has been proposed as a criterion for public intervention in health care (Jamison and others 1993) and as a criterion for inclusion in an insurance package, public or private (Gold and others 1996). As illustrated here, treatments sharing a common cost-effectiveness ratio fall into all four areas. Thus, cost-effectiveness ratios provide no information whatsoever concerning the value of provision when insurance markets are absent—the market failure that justifies public coverage of the private benefits of health care.4 Further, within areas I and IV, where insurance 3. The actuarially fair costs of insurance should, strictly speaking, have included the administrative costs, A, and be equal to Y – pC – A. 4. The external benefits would be evaluated separately. II I