Top PDF A Strategic market game approach for the private provision of public goods

Abstract. Bergstrom, Blume and Varian (1986) provides an elegant game- theoretic model of an economy with one private good and one public good. Strategies of players consist of voluntary contributions of the private good to public good production. Without relying on …rst order conditions, the authors demonstrate existence of Nash equilibrium and an extension of Warr’s neutral- ity result – any redistribution of endowment that left the set of contributors unchanged would induce a new equilibrium with the same total public good pro- vision. The assumption of one-private good greatly facilities the results. We provide analogues of the Bergstrom, Blume and Varian results in a model allow- ing multiple private and public goods. In addition, we relate the strategic market game equilibrium to the private provision of equilibrium of Villanaci and Zengi- nobuz (2005), which provides a counter-part to the Walrasian equilibrium for a public goods economy. Our techniques follow those of Dubey and Geanakoplos (2003), which itself grows out of the seminal work of Shapley and Shubik (1977). Our approach also incorporates, into the strategic market game literature, eco- nomies with production, not previously treated and, as a by-product, establishes a new existence of private-provision equilibrium.

3 In recent years several different price-influencing schemes have been proposed as a tool for international climate policy. Barrett (1990), Rübbelke (2006), Boadway, Song and Tremblay (2007, 2011) and Fujita (2011) suggested applyingmatching schemes in order to address the inefficiency in global climate protection.By matching, which is an approach that was first proposed by Guttman (1978, 1987), governments negotiate about so-called matching rates, i.e. rates at which they - conditionally on other countries’ contributions - provide additional climate protection efforts. In this way, governments mutually subsidize climate policy. As Buchholz, Cornes and Rübbelke (2011) demonstrate, these matching schemes are equivalent to so-called tax-subsidy schemes, which have been proposed, e.g. by Andreoni and Bergstrom (1996) as well as Falkinger (1996). In particular, Falkinger, Hackl and Pruckner (1996) suggest applying these schemes to induce an efficient private provision of public goods in the sphere of international climate protection. Due to the subsidization within matching or tax-subsidy schemes, the effective price or marginal cost of climate protection is reduced so that it becomes more attractive for governments to contribute to the public good ‘global climate protection/stabilisation’.

The questions designed to measure altruistic attitudes followed the same format. Re- spondents were asked to indicate on a …ve-point scale the extent to which they agree or disagree with a series of statements that probed di¤erent aspects of the Schwartz (1970, 1977) model for the activation of altruistic behavior. While questions of this type are com- monly used in experimental economics to explain private provision of public goods, they are less commonly used in the …eld where such data are more di¢ cult to obtain. 13 This, however, was not a limitation for this study given the household mail survey. The scale that we use is based on a subset of the items used by Clark, Kotchen, and Moore (2003). The speci…c items are listed in the Appendix Table, along with the statistics to test for internal consistency. Based on these results, it is reasonable to combine the responses to form another summated scale that measures a general altruistic attitude.

Regarding other types of public goods, there have been surprisingly few studies that use microdata to analyze privately provided public goods in a …eld setting. 2 This paper reports on two case studies— one for a pure public good and one for an impure public good. After developing and comparing the theoretical models (Section 2), we further describe the empirical settings and data collection (Section 3). Three results of the econometric analysis (Section 4) contribute to the literature on private provision of public goods. First, we …nd that, while several household characteristics in‡uence the decision of whether to contribute to a public good, only household income in‡uences the size of a contribution. This result supports Smith, Kehoe, and Cremer’s (1995) …nding that di¤erent factors in‡uence the extensive and intensive margins of charitable giving. Second, household income in‡uences participation in a green-electricity program that provides a pure public good, but not one that provides an impure public good. This empirical …nding, as we will show, is consistent

Corollary 3. (Bergstrom, Blume, and Varian [6]) Suppose the public good is pure, that is, the network is complete, and assume both public and private goods are normal goods. Then relatively small transfers among contributors are neutral. Corollary 3 establishes the standard neutrality result of Warr [38] and Bergstrom, Blume, and Varian [6] by following an alternative approach based on analysis of the private provision of public goods on networks. More generally, the light shed by Theorem 3 on the neutrality of income redistribution in networks is insightful. In interpretation, although one might not expect the neutrality result from the usual pure public good setting to extend to other settings with local interaction patterns accounted for, it is still important to point out that the neutrality result has some serious limitations as it fails in all networks where the set of contributors is not neighborhood homogenous.

NIZAR ALLOUCH Queen Mary, University of London, School of Economics and Finance, Mile End Rd, London, E1 4NS, UK February 2012 Abstract. This paper analyzes the private provision of public goods where consumers interact within a fixed network structure and may benefit only from their direct neighbors’ provisions. We present a proof for existence and uniqueness of a Nash equilibrium with general best-reply functions. Our uniqueness result simultaneously extends similar results in Bergstrom, Blume, and Varian (1986) on the private provision of public goods to networks and Bramoull´ e, Kranton, and D’Amours (2011) on games of strategic substitutes to nonlinear best-reply functions. In addition, we investigate the neutrality result of Warr (1983) and Bergstrom, Blume, and Varian (1986) whereby consumers are able to offset income redistributions and tax-financed government contributions. To this effect, we establish that the neutrality result has a limited scope of application beyond regular networks.

Note that the intervention studied will coexist along with private provision of public goods. The cases we cover include using taxes only on the households contributing strictly positive amounts towards the public good, which is the case where the existing standard neutrality results on the amount of public good produced apply with full force. Thus, even when private fi nancing of public goods is taken as a given institutional assumption, we show that there exists a standard type of intervention involving government provision of public good via lump-sum taxation that Pareto improves upon the equilibrium outcome. Therefore, a general non-neutrality result (in terms of utilities) holds, and this is the case even when all households are strict contributors to the public good. This result has no direct or indirect counterpart in the one private good, one public good with linear production technology framework, since there interventions that involve only the contributing households are neutralized in equilibrium.

Private contributions to public goods are important phenomena for many reasons. In the U.S. annual reported donations to charity amount to approximately 2% of its GDP. In Kenya, the voluntary cooperation of members of the community is essential for the provision of social infrastructure (Wilson 1992). Bergstrom, Blume and Varian (1986) developed a model to study the private provision of public goods which applies to the examples given above as well as to many other less obvious instances. Campaign funds for political parties or interest groups also fall under the scope of this model. In addition, much of the activity that takes place within the family unit can be explained as the out- come of voluntary contributions, see Becker (1981), and Konrad and Lommerud (1995). Kemp (1984), and Boadway, Pestieau and Wildasin (1989) have used this model to study multilateral foreign aid issues. The provision of national defense in alliances can also be studied within this model —see, e.g., Bruce (1990). More recently, Hoel (1991) and Chichilinsky and Heal (1994) have used variants of this model to tackle global environ- mental issues. See Bergstrom, Blume and Varian (1986) —and references therein— for further discussion on the relevance of this model.

In this paper we examine the commonly used policy approach to subsi- dize the private provision of public goods by granting agents deductions with respect to their income or corporate tax burden. We especially take into ac- count that most income tax schemes are progressive and that deductibility is limited. The problems that arise from these specific properties of the con- sidered tax-refund schemes are pointed out first. We then turn towards the effects which such a tax-refund scheme has with respect to the provision of the public good on the one hand and individual as well as aggregate wel- fare on the other hand. We show that the effects of this commonly practised method of supporting private public good provision depend crucially on the specific properties of the progressive tax scheme and the preference structure of agents. While Pareto-improvements and even Pareto-efficiency can result from the implementation of such a scheme, it is also conceivable that at least some agents perceive a utility reduction. Due to the dependency of welfare effects on the tariff structure, income tax reforms as they are planned in many countries might not only induce a reduction in private public good provision, but might also alter the induced welfare effects.

1 Introduction The standard framework for the analysis of private provision of public goods is the Nash-Cournot model in which agents choose their contributions si- multaneously and independently. An important assumption of these models is that each contributor is a single individual or else a private organization which behaves as a single player in provision games. In reality, most volun- tary public goods are contributed by a variety of groups consisting of het- erogenous agents, such as private companies, NPO’s, groups of volunteers, families and so on, in the society rather than individuals. Torsvik (1994) recognizes the importance of this observation, and shows how a representa- tive democracy may induce each group to act strategically in the election of representatives who subsequently decide the contribution to a public good when several groups voluntarily contribute towards the public good. In this paper we particularly focus on the contributing behavior of the family to public goods. Each family comprises several heterogeneous agents character- ized by different preferences as well as different income sources - for example, a given family may consist of a husband, a wife, children, a grandmother, and so on. Families make significant voluntary contributions to public goods in the real world. Furthermore, members of a given family strategically interact with each other, not only through voluntary contributions to household pub- lic goods, but also through voluntary income transfers. Thus their collective contribution decisions to contribute to public goods may be quite different from that of a single agent. Our main task is to clarify the implications for income redistribution policy between different families rather than be- tween members of a given family (see, e.g., Konrad and Lommerud, 1995); in particular, given the complicated collective decisions within a family, we examine whether Warr’s neutrality theorem holds or not.

This paper investigates in a simple, Downsian model of electoral com- petition how the private provision of public goods interacts with the insti- tutions of democracy and taxation. We assume that a public good, such as non-excludable innovation, is produced by the private sector, but that the income derived from the good is taxed at a (positive or negative) rate determined by a democratically elected political leader. The paper stud- ies how democracy, taxation and economic inequality a¤ect the production of the public good. In particular, two seemingly divergent …ndings from the literature are brought together: on the one hand, Mancur Olson (1965) and others have argued that higher inequality increases the supply of public goods, because only the most well-endowed agents in an economy have the incentives to contribute to the production of these goods. Redistribution in favour of these agents strengthens their incentives to produce. On the other hand, Meltzer and Richard (1981), building on Romer (1975), argued that in a democracy, higher inequality leads to lower economic activity, because a poorer median voter, relative to the mean, prefers a higher tax rate, which diminishes incentives for production. 2 The present paper shows that when democracy and taxation are introduced in a public goods dependant econ- omy, the “Olson-” and “Meltzer-Richard” e¤ects tend to cancel out. The net e¤ect of economic inequality on production might be either positive or negative.

We consider a sequential game in which one player produces a public good and the other player can influence this decision by making an unconditional transfer. An efficient allocation requires the Lindahl property: the sum of the two (implicit) individual prices has to be equal to the resource cost of the public good. Under mild conditions this requires a personal price for the providing player that lies below half of the resource cost. These results can, for example, justify high marginal taxes on wages of secondary earners.

According to Ben-Ner (2002), in the U.S. nonprofit organizations may benefit from the recent tendency of some large for-profit financial institutions to rapidly turn into important fund-raising channels. 4 Nonprofits may rely, in principle, on multiple, distinct sources of funding: beside individual donations, further significant channels are income from the sale of goods and/or services, user fees and (direct and indirect) public subsidies. In the U.S., where nonprofit revenues make up about 10% of the GNP, it is increas- ingly harder to precisely define the boundaries between for-profit and nonprofit sectors (Arrow 1998) and the essence of such phenomenon is well captured by Weisbrod (1998), as he notices that nowadays “Many nonprofits face increasing financial pressure because the gap between their resources and what they see as social “need” is growing. (. . . ) “Need” is difficult to define and measure, but if nonprofits search for new revenues, they have few choices: to increase private donations and/or to increase income from the sale of goods or services — that is, “commercial” activity”. The problem is that if nonprofits choose to mainly rely on user fees, i.e. on revenues from the sale of goods or services on the market, they run the risk to lose their specific identity and not to differentiate themselves anymore from for-profit firms, by ending up mimicking their sta- tus of private goods sellers and profit-oriented organizations. Commenting on this phenomenon, which seems to be characteristic of the current phase of rapid growth of the nonprofit sector in the U.S., Weisbrod (1998) points out that such trend risks to induce people to perceive nonprofit organizations as ‘for-profits in disguise’. Therefore, as to the issue of how to balance nonprofits’ pursuit 3 Segal and Weisbrod (1998) show, through an empirical study on tax-return data regarding

Finally, there is one last feature that makes collective action possible: it is the creation of a specific entrepreneurial space for the class counsel, who undertakes to identify an unmet demand for justice and, acting self-interestedly, restores access to legal action for the victims. The class counsel is generally driven by the purely utilitarian motives of a "bounty hunter", who offers a service in exchange for recompense. It is thus a behaviour consistent with the paradigm of methodological individualism, and which is sometimes regarded with suspicion by those who consider private interests unsuitable for representing the collective interest. Such misgivings have, moreover, helped give support to regulation over individual civil action on the grounds that, as Justice Robert Young suggests (2001, p. 3) “in the judiciary, the process, though public in name, is private in essence” 5 . Yet this mechanism, endorsed by economic theory starting from the paradigm of the invisible hand, also underpins the economic analysis of law, given that many institutions, beginning with property rights, are designed to promote the collective interest through individual initiative (Ramello, 2011). Hence, the reluctance to pursue collective welfare through private interest is not only theoretically unfounded (and in fact contradicts decades of scientific investigation), but also assumes the peculiar and unproven hypothesis that it is possible to select for particular roles–such as regulators or public prosecutors– special human beings entirely unmoved by individual utility, and who are on the contrary able to exclusively promote the collective interest without any eye to their private benefit. The reality appears to be greatly different 6 .

The welfare property of the subgame-perfect Nash equilibria is related to the result of Kukushkin (1992). Using an abstract one-shot game, he characterizes a condition for utility functions under which there is a Nash equilibrium with Pareto efficiency. The Leontief utility functions satisfy his condition. However, he does not clarify the equilibrium behavior (contribution and participation) of agents because his model is abstract and does not examine a concrete model of a public good economy. Unlike the findings of Kukushkin (1992), our result shows the behavior of each agent. For example, Proposition 1 shows that the participation decision of the agent depends solely on his/her initial endowment of the private good; Proposition 5, together with Proposition 4, shows that the partial participation of agents, not necessarily that of all agents, achieves the i-Pareto- efficient allocation at the equilibrium of the voluntary participation game. In Saijo and Yamato’s (1999, 2010) model, the i-Pareto-efficient allocation is achieved only if all agents participate.

informed is therefore θ E [ G t − i ′ ] ≡ Φ; when i ′ is informed, the corresponding level is θ ( E [ G − t i ′ ] + ρµ ) ≡ Φ = Φ + θρµ > Φ. So, if the cost, c, of sending an in- formative signal to her neighbours is not too high relative to the expected gain θρµ ≡ Ψ, i may choose to voluntarily incur that cost. We interpret this behaviour as fundraising. Note that in an analogous setting where private information about supplier quality concerns private consumption, individuals would never incur a private cost to inform their neighbours about their own consumption experience. It is only in the case of contributions to collective consumption that the actions of uninformed individuals are of concern to better informed individuals, inducing them to actively share their information with others. 7

To complete the computation of equilibrium we must also address the possibility that demand and cost differences combine with small num- bers of Žrms to produce equilibria in which one version is not sold in equilibrium. Equilibria in which only the nl-version (l-version) is sold arise when r (i) is relatively small (large) and c r is relatively large (small). Under these conditions, monopolizing the sale of the l-version may lead to lower proŽts than competing and earning Cournot proŽts from selling the nl-version of the private good (or vice versa). Note that since Cournot proŽts from selling a version of the private good are decreasing (and converge to zero) in the number of Žrms, equilibria in which only one version is sold also require a limit on the number of active Žrms. If the number of Žrms in the industry and the parameter conditions are such that monopoly proŽts from selling one version exceed Cournot proŽts if all Žrms sell the other version, then, ignoring integer problems, equilibrium is found by setting the proŽts from selling the two versions equal (recalling that N 5 N l 1 N n ), and so N* l and N* n satisfy

more nuanced insight of this performance. W M L indicates that winners from the previous months by far outperform recent losers in all time periods: The momentum strategy generates monthly returns exceeding 1% in all periods. The returns of the SM B and HM L strategy, 0.41% and 0.55% respectively, are both explained by their strong performance in the first sub-period. In the second sub-period, these strategies were barely profitable. These observations are in line with the theoretical reasoning of SM B and HM L. The second sub- period largely covers an economic recession. During these harsh times, small and value firms are said to perform worse. Small firms exhibit problems in raising capital, and value firms find themselves unable to substantially lower any running capital costs, something growth firms are apt to do. Unlike value firms, growth firms can postpone investment expenditures as they are more flexible. Table 5.1 reports the Carhart four-factor model regression results for the full time period and the two sub-periods. Within a given estimation window, the factor loadings are assumed to be fix even though they might change as portfolio composition, risk perceptions, and demanded risk premia are likely to vary through time. In this sense, the sub-periods serve as a rough first robustness check in terms of temporal dependence. Below, we implement a more sophisticated approach to this issue. In order to control for possible distortions in the covariance of the estimates due to heteroskedasticity or autocorrelation in the disturbance term, only robust heteroskedasticity- and autocorrelation-consistent z-statistics according to Newey and West (1987) are reported. In line with common practice (Greene, 2002), the error structure is assumed to be possibly autocorrelated up to three lags. 6

Theorems 5 and 6 also pose a number of strong testable hypotheses that could be investigated by experimental economists who could, for example, impose identical payoff functions, or coul[r]

To model private provision in a dynamic setting, I consider an infinitely repeated version of the static voluntary contributions game. To model public provision, I apply Bernheim and Slavov’s (2009) notion of a dynamic Condorcet winner (DCW), which extends the Condorcet winner concept to dynamic settings. A DCW prescribes a policy for every possible history in such a way that for any history, the prescribed policy choice is majority preferred to any other policy given the implications of the current choice for future outcomes. In contrast to the static setting, a one-parameter tax system is not required to ensure the existence of DCWs. Indeed, DCWs exist with a completely unrestricted tax system, in which each individual pays a different positive or negative tax rate. Lifting the one-parameter restriction on the tax system allows income redistribution to be chosen jointly with the level of the public good. 1 While the DCW concept is intuitively appealing because of its similarity to the static Condorcet concept, applying it in practice can be analytically difficult, even for very simple problems (see, e.g., Bernheim and Slavov 2004, Bernheim and Slavov 2009, Slavov 2006). Thus, an additional contribution of this paper is to demonstrate how DCWs can be found computationally, allowing one to apply it to more complex problems.