Finitely Repeated Voluntary Provision of a Public Good

This paper theoretically explores the voluntary provision of a public good when either one of the following holds: (i) agents’ utility is the sum of their monetary earnings and a nonmaterial component, or (ii) agents’ exhibit satisficing behavior. We show that a small degree of either nonmaterial payoffs or satisficing behavior can generate large contributions in a finitely repeated game, even if the incentive to free‐ride on others’ contributions calls for negligible public good provision in the static game. The equilibrium is characterized by a sharp decline in contributions toward the end of the game. Several comparative results regarding group size and technology are consistent with laboratory data obtained in experimental studies. The model also predicts the restart effect observed in previous experiments.     

Resource Utilization and Economies of Size in Secondary Schools

This paper identifies the determinants of costs per pupil in English secondary schools. A distinction is made between the short run and the long run in order to estimate the separate effects on costs per pupil of short‐run variations in school output and school size. A school’s capacity utilization rate is used to indicate short‐run deviations in output from pupil capacity, and pupil capacity is used as an indicator of school size to capture scale effects on costs per pupil. The statistical analysis uses both published and unpublished data for secondary schools in England. Two separate analyses are undertaken, one for grant‐maintained schools alone and the other for all schools. A separate analysis is undertaken for grant‐maintained schools since cost data are available only for schools in this sector. Staff hours per pupil is used as a proxy for costs per pupil for schools as a whole. The main finding is that costs per pupil and staff hours per pupil are both highly significantly negatively related to both school size and the capacity utilization rate of schools. A range of other variables are also estimated to have a significant effect on costs per pupil in secondary schools. The main finding is that there is scope for reducing the costs of schooling in the secondary schools sector in England.     

Entry into the Schooling Market: How is the Behaviour of Private Suppliers Influenced by Public Sector Decisions?

This research examines the location choice of private schools entering the California schooling market in 1979–80. We find that entrants are more likely to locate in public school districts with lower levels of per–pupil expenditure and higher fractions of public school students who reside in low–income households. In addition, we provide evidence of differences in the responsiveness of different types of private schools to the underlying conditions. Also, in comparing our results to those of previous research, we find that the determinants of the location choices of entrants appear to be the same as the determinants of the location pattern of incumbent private schools.     

Weak Moral Motivation Leads to the Decline of Voluntary Contributions

We develop a model that accounts for the decay of the average contribution observed in experiments on voluntary contributions to a public good. The novel idea is that people's moral motivation is “weak.” Their judgment about the right contribution depends on observed contributions by group members and on an intrinsic “moral ideal.” We show that the assumption of weakly morally motivated agents leads to the decline of the average contribution over time. The model is compatible with persistence of overcontributions, variability of contributions (across and within individuals), the “restart effect” and the observation that the decay in contributions is slower in longer games. Furthermore, it offers a rationale for conditional cooperation.     

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

In this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.     

Funding Public Goods with Lotteries: Experimental Evidence

Why do individuals participate in charitable gambling activities? We conduct a laboratory investigation of a model that predicts risk-neutral expected utility maximizers will participate in lotteries when they recognize that lotteries are being used to finance public goods. As predicted by the model, we find that public goods provision is higher when financed by lottery proceeds than when financed by voluntary contributions. We also find support for other comparative static predictions of the model. In particular we find that ticket purchases vary with the size of the fixed prize and with the return from the public good: lotteries with large prizes are more effective, and ticket purchases drop dramatically when the public good is not valued by subjects.     

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.     

School Finance Induced Migration and Stratification Patterns: The Impact of Private School Vouchers

This paper introduces a general equilibrium model of public school finance that includes: (i) multiple school districts that finance local public schools via property taxes set by majority vote; (ii) multiple neighborhoods within school districts where each neighborhood is characterized by a quality level of housing; (iii) local public schools that are obligated to admit all interested students who reside within the school district; (iv) private schools that function as clubs of parents who share the cost of the private school equally and who can choose to exclude others; (v) an educational production process that depends on both per pupil spending and average peer quality within the school; and (vi) individual peer quality levels that are correlated with the socioeconomic status of households. Since it allows for various degrees of imperfect stratification of residents across communities, the model is well suited for investigating empirically relevant migration forces induced by school finance reform proposals. The abstract model itself, however, is too complex to yield many analytic results. A computational counterpart to the model isnb therefore developed, calibrated to data, and utilized for policy experiments. In particular, the impact of vouchers in the context of different types of prevoucher educational finance systems is investigated, and it is found that migration patterns in general would cause vouchers to benefit public schools in poor communities while hurting public schools in wealthy communities.     

Public goods provision,inequality and taxes

The impact of redistributive policies on voluntary contributions is still not well understood. While a higher level of redistributive taxation decreases the price of voluntary giving, it also changes the income distribution by decreasing income inequality. This paper provides a controlled laboratory experiment to investigate the net impact of the tax rate on public goods provision. The experimental findings show that while the participants decrease their voluntary contributions as the pre-tax income distribution becomes more equal, they increase their contributions with taxation. These findings have important implications for government policies regarding privately provided public goods.     

Contribution to a public good under subjective uncertainty

This paper examines how voluntary contributions to a public good are affected by the contributors' heterogeneity in beliefs about the uncertain impact of their contributions. It assumes that contributors have Savagian preferences that are represented by a two‐state‐dependent expected utility function and different beliefs about the benefit that will result from the sum of their contributions. We establish general comparative statics results regarding the effect of specific changes in the distribution of beliefs on the (unique) Nash equilibrium provision of the public good, under certain conditions imposed on the preferences. We specifically show that the equilibrium public good provision is increasing with respect to both first‐ and second‐order stochastic dominance changes in the distribution of beliefs. Hence, increasing the contributors' optimism about the uncertain benefit of their contributions increases aggregate public good provision, as does any homogenization of these beliefs around their mean.     

Commitment and matching contributions to public goods

We study multi-stage processes of non-cooperative voluntary provision of public goods. In the first stage, one or more players announce contributions that may be conditional on the subsequent contributions of others. In later stages, players choose their own contributions and fulfill any commitments made in the first stage. Equilibrium contributions are characterized under different assumptions about the commitment ability of players, the number of public goods and whether players commit to matching rates or to discrete quantities. We focus on contribution mechanisms that can emerge and be sustainable without a central authority, and that may be particularly relevant for international public goods. Efficient levels of public goods can be achieved under some circumstances, while in others commitment is ineffective.     

‘Expressive’ obligations in public good games: Crowding-in and crowding-out effects

We study individual contributions in a repeated linear public good experiment in which, in each period, subjects are required to contribute a minimum amount and face a certain probability of being audited. Audited subjects who contribute less than the required amount are convicted to pay the difference between the obligation and the voluntary contribution. We investigate the ‘expressive’ force of the obligations. While at early stages subjects contribute the minimum level, with repetition contributions decline below the required amount. We observe that expressive obligations exert a rather robust crowding-out effect on voluntary contributions as compared to a linear public good game. Crowding-out is stronger when payments collected through the auditing procedure are distributed to subjects rather than when they are a deadweight loss.     

A Case for Bundling Public Goods Contributions

We extend the model of voluntary contributions to multiple public goods by allowing for bundling of the public goods. Specifically, we study the case where agents contribute into a common pool which is then allocated toward the financing of two pure public goods. We explore the welfare implications of allowing for such bundling vis‐à‐vis a separate contributions scheme. We show that for high income inequality or for identical preferences among agents bundling leads to higher joint welfare. Interestingly, a welfare improvement can in some cases occur despite a decrease in total contributions. On the contrary, when agents are heterogenous, for low income inequality bundling can lead to lower total contributions and may decrease welfare compared to a separate contribution scheme. Our findings have implications for the design of charitable institutions and international aid agencies.     

An experimental dynamic public goods game with carryover

We examine voluntary contributions in a two-stage public good experiment with ‘carryover.’ In two treatments, each subject's second-stage endowment is determined by the return from the public good in the first-stage. We manipulate payoffs across treatments such that, relative to our no-carryover baseline, earnings from either Nash Equilibrium (constant NE) play or Pareto Optimal (constant PO) play are held constant. The remaining two treatments maintain a constant endowment in each stage, but vary the marginal per capita return (MPCR high or MCPR low) to contributions in the second-stage. Our results indicate that carryover increases first-stage contributions. Our implementation of carryover enables us to examine the effects of changing endowments and a wide range of MPCR's. Consistent with the literature, we find that MPCR and endowment effects are important determinants of subject contributions to the group account. While stage 1 contributions tend to increase in the presence of carryover, efficiency levels across both stages fall relative to the baseline. Efficiency levels fall because the maximum earnings possible increase with carryover (due to higher endowments or MPCR levels in stage 2).     

The benefits of voluntary leadership in experimental public goods games

We study the effects of voluntary leadership in experimental public goods games when each group member can volunteer to contribute before the other members. We find that voluntary leadership increases contributions significantly, compared to a treatment where leadership is enforced exogenously.     

Economic growth and stability with public pay-as-you-go pensions and private intra-family old-age insurance

This paper compares the steady-state and dynamic outcomes of two historical alternatives as a means of old-age insurance, namely, voluntary intra-family transfers from young to old members versus pay-as-you-go public pensions, in a general equilibrium overlapping generations model with children as a desirable good. We show that the shift from a private system of old-age support to public pensions increases the gross domestic product (GDP) per worker. Moreover, although in both cases the steady-state stock of capital, under myopic expectations, may be (globally) unstable depending on the size of the inter-generational transfer, we show that the existence of public pensions rather than private intra-family gifts considerably reduces the possibility of cyclical instability.     

Public Good Contributions Between Communities

The four fundamental determinants of voluntary contributions to public goods are taste, community size, wealth, and wealth distribution. This paper argues that for policy purposes it is important to discriminate between the four hypotheses. To do this, it is necessary to consider the comparative static effects of the above determinants not only on total contribution, but also on per capita contribution and the participation rate. Furthermore, just as members of a smaller community would contribute more than their identical counterparts in a larger community, we show that members of a community that has more poor members would also contribute more than their identical counterparts in a community that has more rich members.     

A SAVINGS SUBSIDISATION SYSTEM IN A MODEL OF ENDOGENOUS FERTILITY AND ENDOGENOUS GROWTH: AN EXTENSION OF WIGGER (1999)

Population ageing is now an established demographic characteristic of many economies. Economists working in the endogenous growth theory tradition have sought to model the relationship between public pensions, financed on a 'Pay-As-You-Go' basis, and the growth in per capita incomes. The resultant intergenerational wealth redistribution from young to older people seems to decrease private savings, diminish capital accumulation, and lower the growth of per capita incomes. The underlying transmission mechanism appears to be a crowding out effect in private capital markets contingent upon the introduction of public pension systems. A growing literature exists on the interrelationships between public pension schemes, fertility rates and endogenous growth. Following Wigger's (1999) pioneering overlapping generations endogenous growth model, we extend this model to examine the effects of a savings subsidisation system on the rate of per capita income growth, fertility and voluntary intrafamily wealth transfers, where parents view children both as an insurance good and a consumption good. Moreover, children care about the consumption levels of their parents. An increase in contributions to a savings subsidised public pension scheme will crowd out private intergenerational transfers from the young to the old and thereby negate the usefulness of children as an insurance good.     

Income Heterogeneity in the Voluntary Provision of Dynamic Public Goods

This paper explores the effect of income inequality on the voluntary contributions to a dynamic public good. We find that income heterogeneity has a significant impact both on contributions and welfare. The results show that the often observed decay of cooperation does not carry over to the asymmetric environment considered in this study. Our results also suggest that subjects in each income class make different contribution amounts in an absolute sense and give the same percentage of their income. Moreover, we find that contributions of individuals with the same endowment are sensitive to how heterogeneous the environment is.