Private investment with social benefits under uncertainty: The dark side of public financing

We develop a game‐theoretic model of private–public contribution to a long‐term project with sequential actions and moral hazard. A private agent is one who is in charge of both the financial contribution and the management effort, these two actions entailing private costs and uncertain ex‐post private and social benefits. A public agent is one who decides the amount of public funding to this quasi‐public good, knowing that the size and the probability of attaining a surplus ex post depend on the private agent's effort. We consider four public‐funding scenarios: benefit‐sharing versus cost‐sharing crossed with ex‐ante versus ex‐interim government intervention. We test our theoretical predictions by means of an experiment that confirms the main result of the model: Cost‐sharing public intervention is more effective than benefit‐sharing in boosting private financial contribution to the project. Furthermore, when public intervention comes after private contribution ( ex‐interim government intervention), both public‐funding scenarios have a negative impact on the private management effort. In our model, the latter result is explained by the private agent's high degree of risk aversion. These results have policy implications for strategic investments with long‐term social consequences. In deciding the optimal timing and method of the contribution, governments should also consider the indirect effects on agents’ long‐term management efforts.     

Social Insurance and Redistribution with Moral Hazard and Adverse Selection*

Rochet (1991) showed that with distortionary income taxes, social insurance is a desirable redistributive device when risk and ability are negatively correlated. This finding is re‐examined when ex post moral hazard and adverse selection are included, and under different informational assumptions. Individuals can take actions influencing the size of the loss in the event of accident (or ill health). Social insurance can be supplemented by private insurance, but private insurance markets are affected by both adverse selection and moral hazard. We study how equity and efficiency considerations should be traded off in choosing the optimal coverage of social insurance when those features are introduced. The case for social insurance is strongest when the government is well informed about household productivity.     

A utilitarian approach to the provision and pricing of excludable public goods

This paper studies utilitarian welfare maximization in a large economy with an excludable public good where individual preferences are private information. If inequality aversion is large, optimal allocations involve the use of admission fees and exclusion to redistribute resources from people who benefit a lot from the public good to people who benefit little. If inequality aversion is close to zero, optimal admission fees are zero. Because of inequality aversion, information rents of people who benefit a lot from the public good receive less weight, so optimal provision levels for the public good are below first-best levels.     

Employee cost-sharing and the welfare effects of flexible spending accounts

Flexible Spending Accounts (FSAs) subsidize out-of-pocket health expenses not covered by employer-provided health insurance, making health care cheaper ex post, but also reducing the incentive to insure. We use a cross section of firm-level data to show that FSAs are indeed associated with reduced insurance coverage, and to evaluate the welfare consequences of this shift. Correcting for selection effects we find that FSAs are associated with insurance contracts that have coinsurance rates about 7 percentage points higher, relative to a sample average coinsurance rate of 17%. Meanwhile, coinsurance rates net of the subsidy are approximately unchanged, providing evidence that FSAs are only welfare neutral if we ignore distributional considerations and the deadweight loss of the taxes necessary to finance the subsidy. These results also suggest that FSAs may explain a significant fraction of the shift in health care costs to employees that has occurred in recent years.     

Speculative Attacks with Multiple Sources of Public Information*

We propose a speculative attack model in which agents receive multiple public signals. Diverse pieces of public information can be taken into account differently by different players and are likely to lead to different appreciations ex post. This process defines players' expected private values of a successful attack. The main result shows that equilibrium uniqueness depends on two conditions: (i) signals are sufficiently dispersed and (ii) private beliefs about signals' relative precision differ sufficiently. We derive some implications for information dissemination policy. Transparency in this context is multidimensional: it concerns the publicity of announcements, the number of signals disclosed and their precision.     

Unemployment Insurance under Moral Hazard and Limited Commitment: Public versus Private Provision

This paper analyzes a model of private unemployment insurance under limited commitment and a model of public unemployment insurance subject to moral hazard in an economy with a continuum of agents and an infinite time horizon. The dynamic and steady‐state properties of the optimum private unemployment insurance scheme are established. The interaction between public and private unemployment insurance schemes is examined. Examples are constructed to show that for some parameter values increased public insurance can reduce welfare by crowding out private insurance more than one‐to‐one and that for other parameter values a mix of both public and private insurance can be welfare maximizing.     

Optimal pricing and capacity choice for a public service under risk of interruption

We develop rules for pricing and capacity choice for an interruptible service that recognize the interdependence between consumers’ perceptions of system reliability and their market behavior. Consumers post ex ante demands, based on their expectations on aggregate demand. Posted demands are met if ex post supply capacity is sufficient. However, if supply is inadequate all ex ante demands are proportionally interrupted. Consumers’ expectations of aggregate demand are assumed to be rational. Under reasonable values for the consumer’s degrees of relative risk aversion and prudence, demand is decreasing in supply reliability. We derive operational expressions for the optimal pricing rule and the capacity expansion rule. We show that the optimal price under uncertainty consists of the optimal price under certainty plus a markup that positively depends on the degrees of relative risk aversion, relative prudence and system reliability. We also show that any reliability enhancing investment—though lowering the operating surplus of the public utility—is socially desirable as long as it covers the cost of investment.     

Optimal Universal and Categorical Benefit Provision with Classification Errors and Imperfect Enforcement

We determine the optimal combination of a universal benefit and categorical benefit when individuals differ in their ability to work and, if able to work, their productivity. The categorical benefit is conditioned ex ante on applicants being unable to work and ex post on recipients not working. The awards test makes Type I/II errors. If the ex post condition is (i) not enforced, the optimal categorical benefit is positive only if the awards test has discriminatory power, while maximum welfare falls with both error propensities; but if (ii) fully enforced, the optimal categorical benefit is positive always and maximum welfare can increase with the Type II error propensity.     

Willingness‐to‐pay for parallel private health insurance: evidence from a laboratory experiment

Abstract Debate over the effects of public versus private health care finance persists in both academic and policy circles. This paper presents the results of a revealed preference laboratory experiment that tests how characteristics of the public health system affect a subject's willingness‐to‐pay (WTP) for parallel private health insurance. Consistent with the theoretical predictions of Cuff et al. (2010), subjects’ average WTP is lower and the size of the private insurance sector smaller when the public system allocates health care based on need rather than randomly and when the probability of receiving health care from the public system is high.     

Income Disparity, Inequity Aversion and the Design of the Healthcare System

An ex post social welfare function is used to evaluate alternative healthcare systems. If a society is averse to inequality and there is some income disparity, social welfare under private healthcare insurance is sometimes higher and sometimes lower than social welfare under public healthcare. However, a third system—public healthcare with the option to purchase supplemental healthcare insurance—is always socially preferred to private healthcare insurance. Moreover, it is either socially preferred to public healthcare or equivalent to it.     

Discrepancies between ex ante and ex post efficiency under identical subjective probabilities

Summary. Starr (1973) showed that, if people have different subjective probabilities, ex ante and ex post efficiency conflict. Conversely, under the simple preferences that he considered, the discrepancy between ex ante and ex post efficiency disappears when subjective probabilities are identical. Here I consider identical subjective probabilities, but more general preferences. First, risk attraction is admitted. Second, I dispense with the double requirement (dubbed IZU) of additive separability and state-independence of the utility of zero-date consumption, an unrealistic requirement when modeling the investment in durable goods. I find that, under IZU, and as long as ex post preferences satisfy the natural assumption of quasiconcavity (and satisfy some technical qualifications), an ex ante efficient allocation is indeed ex post efficient, but the converse is not necessarily true under risk attraction. If, on the other hand, IZU is violated, then one can have ex ante efficient allocations that are not ex post efficient, and vice-versa, even under risk aversion. Received: June 25, 1999; revised version: March 2001     

FINANCIAL SAFETY NETS

We study the optimal design of financial safety nets under limited private credit, asking whether and when it is optimal to restrict ex ante the set of investors that can receive public liquidity support. When the government lacks commitment, we show that the optimally designed safety net covers only a subset of investors. Compared to an economy where all investors are protected, this results in more liquid portfolios, better social insurance, and higher welfare. Our results can rationalize the prevalence of limited safety nets as well as the coexistence of traditional and shadow banks.     

Information and crowding externalities

Summary. We analyze a model in which agents have to make a binary choice under incomplete information about the state of the world, but also care about coordination with other agents who have the same problem. In some of these situations, the larger the share choosing the same alternative, the better off are agents. In others, if too many people choose the same alternative, agents could be worse off, due to crowding externalities. Agents receive public and private information about the state of the world. We determine whether agents rely more on private or public information, and whether or not their choice behavior is socially efficient. We characterize existence conditions for equilibria in which either all available information, or only the public information is used for decisions, compare the two equilibria in terms of welfare, and analyze the effects of better information. Surprisingly, increasing signal accuracy may be welfare decreasing.Received: 24 March 2004, Revised: 19 November 2004, JEL Classification Numbers: D82. Correspondence to: C. Robert ClarkWe would like to thank Ig Horstmann, Gilbert Laporte, Andrew Leach, Matthias Messner, Bernard Sinclair-Desgagné, Howard Thomas, Nicholas Yannelis, and two anonymous referees for helpful comments. The first author wishes to acknowledge the Strategic Research Grant he received from HEC Montreal for this project.     

Anti-insurance: Analysing the Health Insurance System in Australia

This paper develops a model to analyse the Australian health insurance system when individuals differ in their health risk and this risk is private information. In Australia private insurance both duplicates and supplements public insurance. We show that, absent any other interventions, this results in implicit transfers of wealth from those most at risk of adverse health to those least at risk. At the social level, these transfers represent a mean preserving spread of income, creating social risk and lowering welfare – what we call anti-insurance. The recently introduced rebate on private health insurance can improve welfare by alleviating anti-insurance.     

Can a Mixed Health Care System be Desirable on Equity Grounds?*

Should health care provision be public, private, or both? We consider this question in a setting where people differ in their earnings capacity and face some illness risk. We assume that illness reduces an individual's time endowment when waiting for treatment. Treatment can be obtained in a competitive private sector (through private insurance) or in the National Health Service (NHS) where it is provided free of charge but after some (endogenous) waiting time. The equilibrium in the health care sector consists of a waiting time in the NHS such that no patient wants to switch health care provider. This equilibrium is governed by two public policies: the income tax system and the size of the NHS. We find that: (i) a mixed system with a small NHS is never desirable; (ii) actuarially fair sickness insurance is never desirable either; (iii) a mixed system with a sufficiently large NHS may improve on a pure public system if the dispersion of earnings capacities is large enough; and (iv) the welfare gains from such a mixed system are not likely to be significant.     

Partial privatization in mixed duopoly with price and quality competition

We analyze price and quality competition in a mixed duopoly in which a profit-maximizing private firm competes against a state-owned public firm. We first show that the welfare-maximizing public firm provides a lower quality product than the private firm when they are equally efficient. In order to maximize social welfare, government manipulates the objective of the public firm that is given by a convex combination of profits and social welfare. It is demonstrated that an optimal incentive of the public firm is welfare maximization under the absence of quality competition, but it is neither welfare maximization nor profit maximization under the presence of quality competition. The result supports a completely mixed objective between welfare and profit maximizations or partial privatization of the public firm.      

International Integration, Risk and the Welfare State

How does international integration affect the welfare state? Does it call for a leaner or an expanded welfare state? International integration may affect the distortions caused by welfare state activities but also the risks motivating social insurance mechanisms. This paper addresses these potentially counteracting effects in a fully specified intertemporal two–country stochastic endowment model, focusing on the implications when product market integration reduces trade frictions across national product markets. It is shown that lower trade frictions may increase the marginal costs of public funds, which gives an argument for reducing (steady–state) public consumption. However, tighter integration of product markets unambiguously leads to more variability in private consumption, and this gives a case for expanding the social insurance provided via state–contingent public sector activities (automatic stabilizers). JEL classification: E30; F10; H11     

Risk aversion and incentive compatibility with ex post information asymmetry

Summary. The paper extends Diamond's (1984) analysis of financial contracting with information asymmetry ex post and endogenous “bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literature, in which debt contracts are optimal for risk averse as well as risk neutral borrowers. Received: December 7, 1998; revised version: June 9, 1999     

Do Consumers Purchase Too Much Health Insurance? The Role of Market Power in Health‐Care Markets

Several authors have suggested that consumers purchase too much health insurance in private markets. We readdress this issue within a model that combines excess health‐care demand due to health insurance with market power due to monopolistic production of health‐care services. We evaluate the market equilibrium in terms of consumer welfare and social welfare. The consumer welfare criterion suggests that in the market equilibrium consumers in fact purchase too much health insurance coverage. The social welfare criterion, in contrast, suggests that because profits of the health‐care industry are properly accounted for, consumers should purchase more insurance coverage than they choose to do in the market equilibrium.     

The public management of risk: Separating ex ante and ex post monitors

When a firm undertakes risky activities, the conflict between social and private incentives to implement safety care requires public intervention which can take the form of both monetary incentives and also ex ante or ex post monitoring, i.e., before or after an accident occurs. We delineate the optimal scope of monitoring depending on whether public monitors are benevolent or corruptible. We show that separating the ex ante and the ex post monitors increases the likelihood of ex post investigation, helps prevent capture and improves welfare.