Dynamic Voluntary Provision of Public Goods and Optimal Steady-State Subsidies

This paper examines a differential game model of voluntary provision of a public good in which private agents' contributions accumulate over time and derives subsidy rules that achieve the socially efficient steady state. It is shown that the optimal subsidy rule is a simple one when agents use the open‐loop strategy, while under Markovian strategies it intricately depends on the parameters of the economy.     

Optimal Nonlinear Redistributive Taxation and Public Good Provision in an Economy with Veblen Effects

This paper deals with the consequences of the assumption of negatively interdependent preferences for the shape of the optimal nonlinear income tax and the efficient level of public good provision in a setting where the agents' market ability is private information. The analysis points out that the terms added in the tax formulas due to the presence of Veblen effects might justify a reduction in the optimal marginal tax rates faced by the different individuals. Also, the desirability of negative marginal tax rates cannot be ruled out. With respect to the issue of the optimal level of public good provision, I derive a modified Samuelson rule and highlight the fact that the Veblen‐based part of the formula might require to distort downwards the efficient level of public good provision.     

FISCAL STRUCTURAL REFORM AND ECONOMIC ACTIVITY: PUBLIC SPENDING AND PRIVATE EFFORT*

This paper explores governments' and private agents' incentives to implement or postpone fiscal structural reform attempts. Both fiscal consolidation and fiscal reorganization often create spillover effects and thereby induce free‐riding problems. It is thus important to cope with the free‐riding behaviour of interest groups. It is often argued that in order to attain successful outcomes, a good macroeconomic situation is needed, since we expect positive income effects. In this paper, we first explain the dynamic aspects of insufficient fiscal consolidation due to free‐riding problems in the framework of private provision of public goods. Then, using a static model between central and local governments, we examine the sign of income effects for reform attempts to pursue fiscal reorganization. It is shown that good economic circumstances do not necessarily enhance reform of reorganizing fiscal expenditures, although it could enhance fiscal reconstruction.     

Can a raise in your wage make you worse off? A public goods perspective

We show that a seemingly paradoxical result is possible—an increase in one's wage can reduce one's welfare. Such outcome can occur in an economy populated by agents who value a private good bought using labor income and a public good produced by voluntary time contributions. A raise in the wage (in general, opportunity cost of time) makes each agent substitute away from contributing to the public good, failing to internalize the negative externality imposed on others. The result is a decrease in public good provision. Under quite general conditions, the implied cumulative negative effect on agents' welfare can more than offset the positive effect of the wage raise from increased private good consumption and lead to an equilibrium in which all agents are worse off. Our result is particularly relevant for developing economy settings as it holds for relatively low initial wage levels. We discuss the applicability of our findings to a number of important problems in development, such as market integration, cooperation in common pool resource conservation and social capital.     

On the evolution of conditional cooperation

A long series of laboratory and field experiments, as well as conventional empirical studies, has established that (1) individuals voluntarily provide themselves with public goods at levels exceeding those predicted by the Nash voluntary contributions mechanism, and (2) agents reciprocate increases in the contributions of their counterparts in such settings (conditional cooperation). This paper presents a simple model of the evolution of preferences for conditional cooperation in the presence of a public good, which explains these two empirical findings without employing reputational or group selection arguments. In this model, individuals inherit preferences to match other agents' contributions to the provision of a public good, at some specified “matching rate.” Agents whose preferences induce them to be relatively successful – in material terms – increase in number, from one generation to the next. Under complete information and with randomly matched groups of N agents who have quasilinear preferences over the public good and a private good, the unique evolutionarily stable matching rate is 1, leading to Pareto optimal voluntary provision of the public good, regardless of group size N. The evolutionarily stable matching rate can be viewed as an endogenous social norm.     

PRIVATE PROVISION OF PUBLIC GOODS AND INFORMATION DIFFUSION IN SOCIAL GROUPS

I describe a dynamic model of costly information sharing where private information affecting collective‐value actions is transmitted by social proximity. Individuals make voluntary contributions toward the provision of a pure public good, and information transmission about quality of provision is a necessary condition for collective provision to take place in a stationary equilibrium. I show that unlike in the case of private goods, better informed individuals face positive incentives to incur a cost to share information with their neighbors and that these incentives are stronger and provision of the pure public good greater the smaller are individuals' social neighborhoods.     

Bergstrom,Blume, and Varian: Voluntary contributions and neutrality

Bergstrom, Blume, and Varian provided a neutrality result for the private provision of public goods that has inspired a considerable literature. The result has significant implications for income redistribution and broader policy interventions. This paper reviews the basic result and its applications, and discusses extensions to general private provision economies.     

Endogenous timing and income inequality in the voluntary provision of public goods: Theory and experiment

This study theoretically and experimentally investigates the effects of income inequality on donors' decisions regarding timing choices and contributions to public goods when contribution timing is endogenously chosen by contributors. To this end, we use the conventional voluntary provision models of Warr (1983) and Bergstrom, Blume and Varian (1986), with Cobb–Douglas preferences augmented with a two-stage game of Hamilton and Slutsky (1990). The following results were obtained and experimentally confirmed. First, when the distribution of income is extremely unequal, donors are indifferent between the simultaneous and sequential moves in the contribution game. Second, as income inequality is decreased, the simultaneous-move contribution game is likely to emerge because every donor prefers to act as a leader. Nevertheless, a higher-income donor may also prefer to act as a follower without specific social preferences and uncertainty regarding the quality of public goods. Third, most theoretical predictions regarding timing decisions are supported in our laboratory experiment, provided that the participants had enough time to learn the consequences of their timing choices.     

Public Versus Private Provision of Public Goods

It is well known that public goods are underprovided in a static setting with voluntary contributions. Public provision—in a median voter framework with proportional taxation—generally exceeds private provision. This paper compares private and public provision of public goods in a dynamic setting. In a dynamic setting, voluntary donations can result in efficient provision. Also, majority‐rule solutions exist even when taxes are not proportional to income. At low discount factors, public provision tends to exceed private provision. As patience increases, however, private provision may exceed public provision. This occurs because many outcomes with a low level of public good provision—and potentially large targeted transfer payments to particular individuals—become sustainable under public provision. Under private provision, however, large targeted transfers are unsustainable. To finance the public good, private provision tends to result in benefit taxation, and public provision tends to result in progressive taxation.     

Budget Balancedness and Optimal Income Taxation

We make two contributions to the theory of optimal income taxation. First, assuming conditions sufficient for existence of a Pareto optimal income tax and public goods mechanism, we show that if agents' preferences satisfy an extended notion of single crossing called capacity constrained single crossing, then there exists a Pareto optimal income tax and public goods mechanism that is budget balancing. Second, we show that, even without capacity constrained single crossing, existence of a budget balancing Pareto optimal income tax and public goods mechanism is guaranteed if the set of agent types contains no atoms.     

Uncertainty and the Voluntary Provision of a Pure Public Good in a Two‐Moment Decision Model

In this paper, we explore the potential benefits of uncertainty that may arise in a two‐moment model of the voluntary provision of a pure public good. We find that an increase in a given contributor i’s risk associated with the aggregate contribution level of the other contributors (i.e., an increase in social uncertainty) induces that contributor to increase his own contribution level if and only if the uncertainty's incremental effect on the expected value of his net marginal utility is negative. Contributor i’s welfare likewise increases when a closely related condition is met, namely that the uncertainty's marginal effect on his expected marginal utility value of the public good exceeds its countervailing effect on the numeraire. Further, the corresponding aggregate contribution to the public good increases in the presence of free‐riding if and only if the incremental effect of contributor i’s contribution on the aggregate expected value of all other contributors’ net marginal utilities is small‐enough positive. We derive similar conditions for the case of private uncertainty, where the increase in contributor i’s risk is associated with his own marginal valuation of the public good. A simple example illustrates these conceptual results. Numerical analysis demonstrates that an increase in private uncertainty can have a nonmonotonic impact on contributor i’s welfare.     

Woodsy the optimal owl: Environmental campaigns, norms, and implications for public goods policy

Norms regarding private provision of a public good (e.g. cutting down on energy use, not littering) can affect the marginal gains from contributing to a public good and therefore people's decisions about contributing to the public good. A model is proposed in which norms of private contributions to a public good can be influenced by public policy, and these norms affect people's self-image, which derives from a comparison of one's own contribution with the norm contribution. In this context, we examine the conditions under which private contributions to a public good are efficient, and the conditions under which policy affecting these norms improves social welfare. We find that (1) a benevolent social planner who fails to account for private provision norms will underprovide the public good, and (2) public policy that attempts to raise the norm contribution of private provision can increase social welfare if the effect of raising the norm does not have an extreme negative effect - either extremely small or extremely large - on peoples' self-image.     

Bayesian Equilibrium in a Public Good Economy

This paper studies the provision of a public good via voluntary contributions in an economy with uncertainty and differential information. Consumers differ in their private information regarding their future endowment as well as in their preferences. Each consumer selects her consumption ex ante, i.e., before knowing the state of nature. Contributions to the provision of the public good are determined ex post, i.e., when the state of nature is realized. Assuming that some normality conditions hold, a Bayesian equilibrium exists. Further, equilibrium is unique, regardless of the number of consumers, when either (1) the information partitions of consumers can be ranked from the finest to the coarsest, or (2) there are only two types of consumers.     

How widespread are nonlinear crowding out effects? The response of private transfers to income in four developing countries

This article investigates the relationship between household income and private transfers received in developing countries. If private transfers are unresponsive to household income, there is less likelihood of expansions in public social security crowding out private transfers. Most literature finds that private transfers are unresponsive, but this may be because responses have been obscured by the methods that ignore nonlinearities. Threshold regression techniques find such nonlinearity in the Philippines and scope for serious crowding out, with 30–80% of private transfers potentially displaced for low-income households (Cox et al., 2004). To see if these nonlinear effects occur more widely, semiparametric and threshold regression methods are used to model private transfers in four developing countries – China, Indonesia, Papua New Guinea and Vietnam. The results reported in this article suggest that nonlinear crowding out effects are not important features of transfer behaviour in these countries. The transfer derivatives under a variety of assumptions only range between 0 and ?0.08.     

Collective Choice and Voluntary Provision of Public Goods*

Some public goods are provided entirely with private contributions, others with a mixture of public and private funding, and still others are entirely publicly funded. In order to study this variation, a model of dual provision is developed that endogenizes public and private funding. Households vote over an income tax that finances public supply of the good and on whether to permit private contributions. While permitting private contributions may lead to a reduction in total provision, a majority always favors permitting private contributions. Results are developed for small and large economies, and the relevance of nonexcludability and noncongestion are investigated.     

Information Advantage in a Public Good Economy with Multiplicative Structure of Utilities

This paper extends results on information advantage in Cournot oligopoly to a public good economy with uncertainty and private information where the state‐dependent utilities have a multiplicative structure. We show that in a Bayesian–Nash equilibrium where consumers’ contributions are positive in all states of nature, a consumer with superior information is rewarded with a higher ex ante expected utility. Our counter example shows that in the case where one consumer does not contribute, information disadvantage might emerge. Thus, the interiority assumption is essential to obtain our results.     

Long‐term care policy with lazy rotten kids

This paper studies the determination of informal long‐term care (LTC) provided by children in a scenario which is somewhere in between perfect altruism and selfish exchanges. Parents are altruistic but children are purely selfish, and neither side can make credible commitments. The model is based on Becker's “rotten kid” specification except that it explicitly accounts for the sequence of decisions. In Becker's world, with a single good efficiency is achieved. We show that when family aid is introduced the outcome is likely to be inefficient. Still, the rotten kid mechanism is at work and ensures that a positive level of LTC is provided as long as the bequest motive is operative. We identify the inefficiencies by comparing the laissez‐faire (subgame perfect) equilibrium to the first‐best allocation. We first assume that families are identical ex ante and then consider the case where dynasties differ in wealth. We study how the provision of LTC can be improved by public policies. Interestingly, crowding out of private aid by public LTC is not a problem in this setting. With an operative bequest motive, public LTC will have no impact on private aid. More amazingly still, when the bequest motive is (initially) not operative, public insurance may even enhance the provision of informal aid.     

Keynesian Multipliers, Direct Crowding Out, and the Optimal Provision of Public Goods

This paper studies Keynesian multipliers in a macroeconomic model with monopolistic competition. We allow public and private consumption goods to be perfect substitutes in private utility. This enables us to study the effect of direct crowding out on the size of national income, profit and employment multipliers for a given rise in real public spending. A positive real national income multiplier is obtained if consumers value public consumption less than private consumption. In addition, we determine the effective marginal cost of public funds and the optimal provision of public goods, both in the short run and in the long run.     

Social Norms and Private Provision of Public Goods

The formation of social norms for voluntary contributions to a public good is analyzed in a game in which people have preferences for private consumption, a public good, and social approval. Each person chooses to be one of the two types: a contributor or a non‐contributor. Thereafter, each person meets people who can observe his type. A non‐contributor feels disapproval, whereas a contributor feels approval if he believes that a contributor observes his type. The game has two asymptotically stable states: one in which everybody is a contributor, and one in which nobody is a contributor. Governmental subsidization of the public good can move the society to the former state, whereas a governmental contribution to the public good can move the society to the latter. Indeed, this crowding in or crowding out prevails even after policy reversal.