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C.I Public Goods and Welfare Economics: Incentive Mechanisms, Finance and Governance

C.I.1 Introduction

An important part of the institute's research programme concerns the conceptual framework for the normative analysis of public-goods provision when decision makers cannot be presumed to have the information needed to properly assess the amount of resources that should be devoted to such goods, in particular, when decision makers cannot be presumed to know the values that the different decision makers attach to the different public goods.
In the past few years, research in this area has been somewhat crowded out by research on financial stability and regulation. Therefore there has not been much progress in this area. However, this area remains on our agenda, and we plan to devote more resources to it again in the future. The following summary should be read as a statement of what is distinctive about our approach, with explanations of where we stand and what topics are on our agenda.
Our approach has three distinct features:
Whereas most of the literature considers the problem of public-good provision with private information in the context of small-economy models, in which each participant has the power to affect aggregate outcomes, we consider large economies, in which any one individual is too insignificant to affect the level of public-good provision aggregate outcome. Whereas small-economy models are useful to think about condominium owners deciding how much to spend on gardening services, it is not so useful for thinking about how a country with millions of inhabitants should decide on the level of resources devoted to the judiciary.
We look at public-goods provision and taxation in an integrated manner. The problem of how to pay for public goods is intimately related to the problem of what is an appropriate system of taxes and prices for public services.
We also want to integrate the supply side into the analysis. Many questions of funding for public goods are intimately related to questions of incentives and governance in production and provision of these goods.
Although the focus of our work is normative, in the tradition of Pigou and Samuelson, the incentive and governance considerations that we introduce lend themselves naturally to political-economy considerations. We consider these as well, but still consider the normative focus to be important because it provides a measuring rod by which to assess the strengths and weaknesses of decision procedures that are actually used.
By now, normative economics has learnt that it must take account of information and incentive problems. The theory of mechanism design provides a basis for doing so, focussing on what measure of efficiency can be achieved when these problems are taken into account. This is the very type of question that we are asking about the provision and financing of public goods in large economies.
The importance of the question is readily seen if one goes back to the typical economist's critique that political decision making gives rise to inefficient outcomes because it fails to take account of preference intensities. A majority of people who care just slightly about an issue can impose its will on a minority who care intensely about it. If the disparity between the two groups is sufficiently large, the result is inefficient in the sense that everybody would be better off if the minority was able to "bribe" the majority to vote differently.
In this critique of collective decision making by voting, no account is taken of possible information asymmetries. One result of our research shows that, once these information asymmetries are taken into account, it may not even be possible to rely on anything else than a voting mechanism.
Our research and research interests in this area can be roughly divided into three broad topics:
Development of a conceptual and formal framework that is suitable for dealing with issues that concern the revelation, communication and use of private information in a large economy.
Development of an overarching conceptual and formal framework that can be used to integrate the theory of public-goods provision with the rest of normative economics, in particular, the theories of public-sector pricing and of taxation.
Development of a conceptual and formal framework that is suitable to address issues concerning incentives and governance on the supply side of public-good provision and can also be used to integrate the analysis of such issues with the more conventional analyses of demand and funding.
The following Sections C.I.2 – C.I.4 of this report will take up each of these topics in turn.

C.I.2 The Mechanism Design Approach to Public-Good Provision

C.I.2.1 Public Goods versus Private Goods: What is the Difference?

To fix semantics, we define a public good to be one that exhibits nonrivalry in the sense that one person's "consumption" of this good does not preclude another person from "consuming" it as well. When several people "consume" the public good, there may be external effects, e.g. negative externalities from crowding or positive externalities from mutual entertainment, but there is not the kind of rivalry in consumption that one has with private goods where one person's eating a piece of bread precludes another person's eating it as well.
We focus on nonrivalry as the key characteristic because this property is at the core of the allocation problem of public-good provision. Because of nonrivalry, it is efficient for people to get together and to coordinate activities so as to exploit the benefits from doing things jointly. Other characteristics, such as nonexcludability, affect the set of procedures that a community can use to implement a scheme for public-good provision and finance, but such considerations seem secondary to the main issue that nonrivalry is the reason why public-good provision is a collective, rather than individual concern.
The mechanism design approach to public-goods provision asks how a community of n people can decide how much of a public good should be provided and how this should be paid for. If each person's tastes were publicly known, it would be easy to implement an efficient level of public-good provision. If tastes are private information, the question is whether and how "the system" can obtain the information that is needed for this purpose. Because this information must come from the individuals who hold it, the question is whether and how these individuals can be given incentives to properly reveal this information to "the system".
The bottom line of the literature is that it is always possible to provide individuals with the incentive to reveal their preferences in such a way that an efficient level of public-good provision can be implemented. For this purpose, financial contributions must be calibrated to individuals' expressions of preferences for the public good in such a way that there are neither incentives to overstate preferences for the public good in the hope that this raises the likelihood of provision at the expense of others nor incentives to understate preferences for the public good in the hope that this reduces one's payment obligations without too much of an effect on the likelihood of provision. The mechanism design literature shows that one can always find payment schemes which satisfy this condition.1
However, there may be a conflict between incentive compatibility, feasibility, i.e., the ability to raise sufficient funds for provision of the public good, and voluntariness of participation. In some instances, it is impossible to have a public good provided efficiently on the basis of voluntary contracting. Some coercion may be needed. The original idea of Lindahl (1919) that the notion of a public good may provide the basis for a contractarian theory of the state is then moot. Samuelson's (1954) conjecture that private, spontaneous arrangements are inappropriate for efficient public good provision is vindicated.
Samuelson (1954) stressed the difference between public and private goods. However, the mechanism design literature is not so clear on the matter. Indeed, if we consider an economy with n participants with independent private values,2 we get the same kinds of impossibility theorems for private and for public goods: On the basis of voluntary participation and in the absence of a third party providing a subsidy to "the system", it is impossible to have a decision rule that induces an efficient allocation under all circumstances, unless the information that is available ex ante is sufficient to determine what the allocation should be.3 If coercion is allowed, there is no problem in achieving efficiency for either kind of good.
To find a difference between public and private goods, one must look at the behaviour of such systems as the number of participants becomes large. For private goods, a larger number of participants means that there is more competition. This reduces the scope for dissembling, i.e., acting as if one cared less for a good than one actually does, in order to get a better price. With competition from others, attempts to dissemble are likely to be punished by someone else getting the good in question. Hence, there are approximation theorems showing that, for private goods, there are incentive mechanisms that induce approximately efficient allocations, even with a requirement of voluntary participation, if the number of participants is large.4
For public goods, there is no such competition effect. An increase in the number of participants has two different effects. On the one hand, there are more people to share the costs. On the other hand, the probability that an individual's expression of preferences affects the aggregate decision is smaller; this reduces the scope for getting a person to contribute financially, e.g., by having an increase in financial contribution commensurate to the increase in the probability that the public good will be provided. The second effect dominates if individual valuations are mutually independent and if the cost of providing the public good is commensurate to the number of participants, e.g., if the public good is a legal system whose costs are proportional, or even more than proportional, to the number of parties who may give rise to legal disputes. In this case, the expected level of public-good provision under any incentive mechanism that relies on voluntary participation must be close to zero.5
Samuelson's view about public goods versus private goods, the latter being efficiently provided by a market system, the former not being efficiently provided at all by a "spontaneous decentralized" solution, thus seem to find its proper place in a setting with many participants where, on the one hand, the forces of competition eliminate incentive and information problems in the allocation of private goods, and, on the other hand, incentive and information problems in the articulation of preferences for a public good make it impossible to get the public good financed.
However, in the transition from a finite economy to a large economy, the question of what is the proper amount of resources to be devoted to public-goods provision is lost, at least in the independent private values framework that has been used by this literature. In this framework, a version of the law of large numbers implies that cross-section distributions of public-goods valuations are commonly known. Given this information, the efficient amount of public-goods provision, first-best, second-best, or fifty-sixth-best, is also known. The only information problem that remains is the assignment problem of who has a high valuation and who has a low valuation for the public good. This assignment problem matters for the distribution of financing contributions but not for the decision on how much of the public good to provide.

C.I.2.2 Do Correlations Make Incentive Problems Disappear?

If one wants to avoid the conclusion that the proper amount of resources to be devoted to public-goods provision is known a priori because the cross-section distribution of valuations for the public good is pinned down by the law of large numbers, one must assume that the public-goods valuations of different people are correlated so that the law of large numbers does not apply. However, for models with correlated valuations, the impossibility theorems mentioned above are no longer valid. Indeed, for models with private goods, Crémer and McLean (1988) and McAfee and Reny (1992) have shown that one can use the correlations in order to prevent people from obtaining "information rents", i.e., benefits that they must be given if they are to be induced to properly reveal their information. For public goods, Johnson, Pratt, and Zeckhauser (1990) and d'Aspremont, Crémer, and Gérard-Varet (2004) show that, generically, incentive schemes that use correlations to harshly penalize deviations when communications from different people are too much in disagreement, can be used to implement first-best outcomes – with voluntary participation and without a third party providing a subsidy, at least in expected-value terms. The incentive schemes that these analyses involve are not very convincing. They look more like artefacts of the mathematics than anything that might be used in reality. But then the question is what precisely is deemed to be implausible about them.
One answer to this question has been proposed by Neeman (2004) and Heifetz and Neeman (2006). In their view, the results of Crémer and McLean (1988), as well as the other literature, rest on an implicit assumption, which they deem to be unpalatable, namely, that agents' preferences for a good can be inferred from their beliefs about the rest of the world. Crémer and McLean (1988) do not actually specify people's beliefs. They assume that people's preference parameters are the only source of information asymmetry and heterogeneity. Beliefs about the rest of the world are implicitly defined as conditional expectations given their own characteristics and given the overall structure of correlations of characteristics across agents. Generically, preference parameters can be inferred from these beliefs. Moreover, because differences in beliefs induce differences in attitudes towards bets, i.e., state-contingent payment schemes, these differences in attitudes towards bets can be used to extract all rents. According to Heifetz and Neeman (2006), the logic of the Crémer-McLean argument breaks down if people have sources of information other than their preference parameters. In this case, it is quite possible for a given belief about the rest of the world to be compatible with two distinct values of preferences, say a value of zero and a value of ten for the good in question. Because the person with a value of ten for the good in question has the same beliefs as the person with a value of zero, it is then not possible to make the person with a value of ten reveal his high valuation and at the same time surrender the benefit that he obtains if he is actually given the enjoyment of the good; after all, this person could always act as if his value was zero. Neeman (2004) uses a version of this argument in order to prove a version of the Mailath-Postlewaite (1990) theorem on the impossibility of public-good provision in a large economy with voluntary participation, this one with correlated values and under an assumption that, uniformly across economies with varying numbers of participants, there always is a probability that a person holding a certain set of beliefs might assign zero value to the public good. Heifetz and Neeman (2006) argue that, in the set of relevant incomplete information models, the "Beliefs Determine Preferences" (BDP) property of Crémer and McLean is in fact negligible.
Gizatulina and Hellwig (2010, 2014 a, 2014 b) cast some doubt an these claims. In Gizatulina and Hellwig (2010) we showed that the uniformity of violation of BDP in Neeman (2004) is incompatible with the notion of Palfrey and Srivastava (1986) and McLean and Postlewaite (2002) that agents are informationally small. In Gizatulina and Hellwig (2010), each person has private information about his preferences, but other people have noisy signals about these preferences so, if there are many such people and they can be induced to reveal their signals, an average of the signals provides fairly precise information, which can be used to induce truthful preference revelation at practically no cost. If the number of participants is large, an approximately efficient allocation rule can be implemented although participation is voluntary, the cost of the public good provision is proportional to the number of participants, and the BDP property is violated.
Gizatulina and Hellwig (2014 a) observe that Heifetz and Neeman (2006) do not actually study the BDP property as a property of belief functions but as a property of priors from which the belief functions are derived as conditional distributions. Moreover, they make no use of the fact that belief functions are conditional distributions. The same is true of Chen and Xiong (2011, 2012), who consider the genericity of the BDP property and of full surplus extraction in the context of the universal type space. In the universal type space, it does not actually make any sense to talk about properties of belief functions; belief functions in the universal type space are trivially given as projections from universal types to belief hierarchies (or to the measures on other agents' type spaces that are induced by the belief hierarchies). The question of how beliefs are generated, what information they reflect, and whether the information can be inferred from the beliefs cannot be addressed as a question about belief functions. At best it can be treated as a question about belief-closed subsets of the universal type space and about priors on such sets.
Instead of working with the universal type space, Gizatulina and Hellwig (2014 a) work with abstract type spaces à la Harsanyi. Under the assumption that each agent's types are finite-dimensional vectors and that belief mappings are continuous regular conditional probability distributions, they show that, for each agent, the set of belief functions exhibiting the BDP property is a generic subset of the set of all belief functions in the sense that it contains a countable intersection of open and dense sets of functions. The space of all (continuous) belief functions is given the topology of uniform convergence. The result follows from an extension of the classical embedding theorem for continuous functions. The reason is that beliefs are probability measures and thus infinite-dimensional objects. Gizatulina and Hellwig (2014 a) also show that their genericity result for the BDP property can be extended to tuples of belief functions that are compatible with common priors.
In a new paper, Gizatulina and Hellwig (2013) show that in a framework with abstract type spaces, under certain conditions, not only the BDP property but also the McAfee-Reny condition for full surplus extraction (FSE) are generic. Type spaces are compact metric spaces, beliefs are assumed to have continuous densities with respect to some fixed measure on the range, belief functions are assumed to map the type spaces continuously into beliefs with density functions, where the topology on the range is the topology of uniform convergence of density functions, the space of belief functions itself has the uniform topology. The result rests on the insight that the McAfee-Reny condition can be interpreted as a strengthening of the BDP condition, namely, if one knows an agent's beliefs, then one also knows that the agent himself knows his type, i.e., his beliefs cannot come from a non-degenerate mixture of types, and one can infer the type from the beliefs. Given this insight, an adaptation of the proof of the classical embedding theorem yields the desired result.
This work raises the question how our analysis of genericity of BDP or FSE belief functions in an abstract type space setting relates to the analysis of strategic behaviour in a universal type space setting, in particular, the discussion about the appropriate specification of topologies to reflect desired continuity properties of strategic behaviour. For example, the analysis of genericity of BDP and FSE belief functions in Chen and Xiong (2011, 2012) works with the product topology on the universal type space and with the denseness of finite models in that topology, but it is well known that the product topology on the universal type space gives rise to failures of continuity. The reason is that the product topology assigns ever smaller weight to ever higher-order beliefs whereas, e.g. in Rubinstein's e-mail game, such higher-order beliefs retain their importance regardless of how high the order might be. Given these questions, we are currently studying the strategic implications of our chosen topology on abstract type spaces. For the version of the model we use in our FSE paper, we find that the topology we use has the desired strategic continuity properties; by a corollary to this result, the natural mapping from abstract type spaces to (a subset) of the universal type is continuous if the universal type space is given the strategic topology of Dekel et al. (2006). Rubinstein's e-mail game does not cause problems because in any abstract-type-space representation of that game, belief functions will not be given as continuous maps from types to continuous density functions (with respect to some measure). A paper with this result is in preparation.
Gizatulina and Hellwig (2014 b) extend the analysis to families of models as studied by Heifetz and Neeman (2006). Heifetz and Neeman introduced the notion of a family of models to represent the mechanism designer's uncertainty as to what the right model might be. They showed that, if a given collection of such models is what they call "closed under finite unions", then any convex combination of common priors for a set of models will be a common prior for the union of these models. Moreover, the convex combination exhibits the BDP property if and only if the priors for the base models all exhibit the BDP property. If just one prior for one of the base models fails to exhibit the BDP property, then, within the set of common priors for the union of the models, failure of the BDP property is geometrically and measure theoretically generic. However, Gizatulina and Hellwig (2014 b) use the results of Gizatulina and Hellwig (2013, 2014 a) to show that unions of models with common priors of which one or more fail to exhibit the BDP of the FSE property are topologically meagre, i.e., the set of families within which the Heifetz-Neeman results are applicable is itself a negligible set.
Perhaps as importantly, Gizatulina and Hellwig (2014 b) show that the notion of model uncertainty in Heifetz and Neeman (2006) can be formally analysed by mapping the "unions of models" into a single larger model in which all dimensions of the relevant uncertainty are captured by uncertainty about the participants' types. Once this is seen, the problem of how the mechanism designer should deal with model uncertainty itself becomes a problem of mechanism design. In dealing with this problem, the mechanism designer can make use of the fact that, among the participants, it is common knowledge which of the original (sub-)model environments they are in. A "shoot-the-liars" reporting game may then provide him with the means of extracting this information without cost, after which he can stipulate the implementation of whatever mechanism is optimal for the original (sub-)model. Even in a Heifetz-Neeman world, the dichotomy between models with the BDP property, or with full surplus extraction, and models without the BDP property, or without full surplus extraction would then be replaced by a smooth transition between the two: If the mechanism designer assigns a small positive probability to models that do not permit full surplus extraction, then, in expected-value terms he will extract all but a small amount of the overall surplus.
The work discussed in the preceding paragraphs should not be interpreted as saying that we regard Crémer-McLean type mechanisms as plausible, or that we consider the mechanisms of Johnson, Pratt, and Zeckhauser (1990) and d'Aspremont, Crémer, and Gérard-Varet (2004) as an appropriate basis for tackling social choice problems involving public goods. The problem is to understand precisely why these approaches should be considered unsatisfactory. Gizatulina and Hellwig (2010, 2013, 2014 a, 2014 b) should be interpreted as saying that the reliance of Crémer-McLean type mechanisms on the BDP property is less problematic than has been suggested and that an effective criticism of such mechanisms must dig deeper.

C.I.2.3 Robustness and Large Economy Models

The ability to exploit correlations between valuations requires precise information not just about the joint distribution of the different participants' public-good valuations, but also about the different participants' beliefs about the other agents' valuations, the other agents' beliefs about the other agents' valuations, etc. It seems implausible that a mechanism designer should have this information. Ledyard (1979) and Bergemann and Morris (2005) have proposed a robustness requirement that would eliminate the dependence of an incentive scheme on this kind of information. According to Bergemann and Morris, a social choice function, e.g. in the public-good provision problem a function mapping cross-section distributions of valuations into public-good provision levels and payment schemes, is robustly implementable if, for each specification of "type spaces", in particular, for each specification of beliefs that agents hold about each other, one can find an incentive mechanism that implements the outcome function in question.
In public-good provision problems with quasi-linear preferences, robust implementability is, in fact, equivalent to ex post implementability and to implementability in dominant strategies. This eliminates all social choice functions whose implementation would involve an exploitation of correlations and agents' beliefs about correlations. In particular, social choice functions with first-best outcomes are not robustly implementable. The mechanisms for first-best implementation in Johnson et al. or d'Aspremont et al. make essential use of information about beliefs, beliefs about beliefs, etc.
Given these findings, Bierbrauer and Hellwig (forthcoming) argue that the robustness criterion of Ledyard (1979) and Bergemann and Morris (2005) provides the proper setting for understanding the essence of the difference between public and private goods. All the findings from the independent-private-values case carry over to robust implementation with correlated values. In particular, (i) for private goods, approximately efficient implementation is possible with voluntary participation if the number of participants is large, and (ii) for public goods with provision costs commensurate to the number of participants, hardly any provision at all is possible with voluntary participation if the number of participants is large. These results hold regardless of what is being assumed about correlation structures. In particular, they leave room for an analysis of large economies in which the question of how much of the public good should be provided is not moot.
However, the analysis of such large economies "in the limit" when each participant is insignificant give rise to some technical and conceptual questions. First, if one thinks about uncertainty in the large economy as involving a mixture of individual and aggregate shocks, there is a need for developing the appropriate mathematical framework for this purpose. The issue is how to formalize the notion of a continuum of conditionally independent random variables in such a way that cross-section distributions are well defined. Second, since most concepts of game theory and mechanism design have been developed for models with finitely many participants, the question is how to adapt these concepts with a continuum of participants.
Hellwig (2011) develops a formulation of incomplete-information models for a continuum of agents who only care about the cross-section distribution of characteristics in the economy and gives conditions for the existence and uniqueness of common priors in such models. The conditions given are a straightforward adaptation of a simple condition for finite-player models that is developed in Hellwig (2013). Following a referee's questions about the mathematical foundations for dealing with a continuum of conditionally independent random variables, this paper is currently being revised. With arguments and techniques from Sun (2006) and Hammond and Sun (2008), the formulation of Hellwig (2011) is now derived from more fundamental assumptions, most importantly essential pairwise exchangeability of the assignment of (random) types to agents, which is a strong form of anonymity. By a version of De Finetti's theorem, this assumption implies that agents' types are conditionally independent and identically distributed and that, in symmetric games, agents care only about the cross-section distribution of types.
The formulation of a large-economy model in Hellwig (2011) is an abstract version of the model used in Bierbrauer and Hellwig (2011/2013) to study mechanism design for public-good provision. In such models, the existence of a common prior is useful as a basis for welfare analysis in the presence of incomplete information.

C.I.2.4 Coalition Proofness

Even if one is not concerned about problems of power abuse, one may be less than convinced by the proposition that, in the absence of participation constraints, it is always possible to implement first-best allocations. Following Bierbrauer (2009a), Bierbrauer and Hellwig (2011/2013) consider the implications of imposing an additional requirement of coalition proofness.
The additional requirement is motivated by the observation that robust implementation of first-best allocation rules may have to rely on people giving information that they would be unwilling to give if they appreciated the way it is being used. In a large economy, where no one individual has a significant impact on the level of public-good provision, individual incentive compatibility conditions are trivially met if payments are insensitive to people's communications about their preferences. One can thus use a scheme with equal cost sharing to find out the aggregate valuation for a public good and to implement a first-best provision rule; this kind of implementation is actually robust in the sense of Bergemann and Morris (2005).
However, this kind of implementation is abusing the notion that, if a person's communication about his or her preferences does not make a difference to either the level of public-goods provision or the payment that the person has to make, then the person is indifferent between all messages and therefore may as well communicate the truth. If there was just the slightest chance that a person's communication would make a difference, at least some people would strictly prefer not to communicate the truth.
To see why this might happen, observe that first-best implementation relies on information concerning the intensities of people's preferences. If there is a large number of people whose benefits from the public good are just barely less than their share of the cost, first-best implementation may require that the public good be provided because the large benefits that the public good provides to a few other people are more than enough to outweigh this small shortfall. If, instead, the people who oppose the public good have no benefit at all from it, first-best implementation may require that the public good should not be provided because the shortfall of their benefits relative to their costs is not compensated by the net benefits that are available to others. In this constellation, the overall outcome depends on the information that can only be obtained from people who don't want the public good to be provided at all, namely whether their opposition is mild or strong. Truthtelling is individually incentive compatible because nobody believes the information that he provides to make a difference. However, truthtelling is not coalition-proof: If someone was to organize a coalition of opponents so as to coordinate on a manipulation of the information they provide, the overall incentive mechanism would no longer be able to implement first-best outcomes.
Bierbrauer and Hellwig (2011/13) provide an abstract formulation of the requirement of coalition proofness and its implications for robust implementability in the public-good provision problem. Following Laffont and Martimort (1997, 2000), in addition to robust incentive compatibility, they require that the incentive mechanism for public-good provision be immune to the introduction of a "manipulation mechanism" whereby a coalition organizer collects information from coalition members and uses this information to distort the information that is provided to the overall mechanism. The introduction of a manipulation mechanism is itself modelled as a mechanism design problem with its own set of incentive and participation constraints. Coalition proofness fails if there exist a manipulation mechanism and a set of agents such that, if all agents in this set subscribe to the manipulation mechanism, and all other agents do not, then all agents in the set are strictly better off than they would be without the manipulation mechanism.
For the simplest version of the public-good provision problem, with a non-excludable public good coming as a single, indivisible unit that costs k, Bierbrauer and Hellwig (2011/13) show that robust implementability and coalition proofness jointly imply that (i) people's payments must be the same in all states in which the public good is provided and the same in all states in which the public good is not provided, and that (ii) the decision to provide the public good must be a non-decreasing function of the number of participants for whom the benefits of the public good exceeds the difference between provision-state payments and non-provision-state payments. Information about the intensities of likes and dislikes cannot be used because reports about this information are subject to manipulation by the coalitions concerned. Whereas conditions (i) and (ii) are only shown to be necessary for robust implementability and coalition proofness, they are in fact necessary and sufficient if the requirement of coalition proofness is weakened to the effect that immunity is only required against manipulations by coalitions that are themselves immune to manipulations by further subcoalitions.
Bierbrauer and Hellwig (2011/13) also show that robustly implementable and (weakly) coalition-proof social choice functions can in fact be implemented by voting mechanisms, i.e., by mechanisms where people are simply asked to vote for or against provision of the public good, and the outcome is made to depend on the number of "yes" votes. The standard economist's criticism that voting abstracts from intensities of likes and dislikes and therefore leads to inefficient outcomes is therefore moot, at least if one allows for the formation of coalitions that distort information about the intensities of likes and dislikes.
In the course of several revisions of this paper, we have also shown that the given results for large-economy models can in fact be obtained as limits of the corresponding results for finite-economy models as the number of participants goes out of bounds. In finite-economy models as well as large-economy models, robustly implementable and coalition-proof mechanisms must be voting mechanisms. The new version of the paper also shows that the analysis is not limited to binary choices, i.e., choices involving the provision or non-provision of the public good. For an example with multiple provision levels, the paper shows that implementable and coalition-proof mechanisms must again be voting mechanisms. We conjecture, but have not yet been able to prove, that, depending on the provision cost function, there may be voting paradoxes. Specifically, we expect such paradoxes to arise if the provision cost function involves increasing returns to scale (decreasing marginal costs).
Robustness in the transition from finite economies to large economies distinguishes the coalition proofness approach of Bierbrauer and Hellwig (2011/2013) from the informative voting approach of Bierbrauer and Sahm (2006/2010), which also tries to articulate our unease about first-best implementation in large economies. In the informative voting approach, people's choices are required to satisfy the additional condition that they should still be considered optimal if there was even the slightest chance of their affecting aggregate outcomes. This condition, which corresponds to the assumption of informative voting in political economy, eliminates the possibility that people choose what they choose because they believe that their choices matter anyway. As a result, they vote their preferences even though they do not expect their votes to have an effect on aggregate outcomes. In a large economy, this imposes additional constraints on mechanism design. These constraints typically preclude first-best implementation, for reasons that are roughly the same as for coalition proofness. However, in contrast to coalition proofness, informative voting restrictions do not have any bite in large finite economies. For example, Groves-Clarke mechanisms can satisfy informative voting restrictions (with strict preference for chosen actions) in all finite specifications but, as one takes limits, in the transition to a large economy, strict preference becomes indifference, and, in the limit, informative voting restrictions are violated.

C.I.3 Public-Goods Provision, Public-Sector Pricing and Taxation

C.I.3.1 Public-Goods Finance under Participation Constraints

Textbook treatments of public economics are usually split into treatments of mechanism design and public-goods provision, public-sector pricing under a government budget constraint, and redistributive taxation. Relations between these three locks are rarely discussed. Our work over the past few years has attempted to overcome this separation and to provide an integrated framework for public economics within which relations of the different parts to each other can be discussed and potential conflicts and contradictions assessed. As a step in this direction, Hellwig (2004/2009, 2007a) has shown that the traditional three-way split between the theory of mechanism design and public-goods provision, the Ramsey-Boiteux theory of public-sector pricing under a government budget constraint, and the theory of redistributive taxation should be replaced by a two-way split between models with and models without participation constraints.
Specifically, Hellwig (2004/2009) shows that it may be desirable to use income taxes for public-goods finance. In a model with endogenous production and with productivity levels differing across people, income taxation provides a way of extracting some of the surplus from production though, as in Mirrlees (1971), the extraction is limited by incentive constraints because individual productivity levels are private information. Under the additional assumption that people are free to retrade private goods and unbundled public-goods admission tickets, the paper shows that it is always desirable to use nonlinear income taxes as well as public-goods admission tickets as a source of funds for financing public goods. This confirms the Atkinson-Stiglitz (1976) critique of the Ramsey-Boiteux approach for not paying sufficient attention to the role of direct taxation as a source of government funds. However, contrary to the claims of Atkinson and Stiglitz, positive admission fees for excludable public goods as well as non-uniform indirect taxes are desirable, in addition to income taxation, if participation constraints are imposed. Optimal public sector prices and indirect taxes and optimal income tax schedules must satisfy a version of the Ramsey-Boiteux inverse-elasticities rule and a version of the Mirrlees formula for the optimal marginal income tax.
Bierbrauer (2009c, 2011a) criticizes Hellwig's dichotomy between models with and models without participation constraints on the grounds that, if participation constraints are to be taken seriously, they must be derived rather than imposed. For a model of the provision of a single excludable public good, he shows that this can actually be done if the provision is delegated to a profit-maximizing entrepreneur. If the entrepreneur's cost is his own private information, the imposition of participation constraints, i.e., giving each agent a veto right may be the only viable way of limiting the monopoly profits that the entrepreneur might otherwise extract.
Within a Ramsey-Boiteux setting, Aigner and Bierbrauer (2014) study the problem of how to tax financial services, a question that has been prominent in recent policy debate. They use a model of "boring banking", in which the bank uses some inputs to provide services for depositors and some other inputs to screen loan customers, to study optimal taxation in a general-equilibrium setting. Under the assumptions of perfect competition and constant returns to scale, they find that a variety of "different" modes of taxation that have been considered in the policy debate are in fact equivalent. The differences that have been stressed in the policy debate have in fact been due to differences in revenue raised by the government and in utility obtained by the private participants. Once these differences are corrected for, different modes of taxation that end up having the same effects on margins between final outputs and final inputs are shown to be equivalent. Matters are different if there are rents, from monopoly power or from decreasing returns to scale. In this case, the different tax modes that have been proposed may differ with respect to their impact on rents but the logic of Ramsey, Boiteux, Diamond, and Mirrlees, which demands that these rents should be taxed away, still dominate the analysis.

C.I.3.2 Public Goods Provision, Income Taxation, and Redistribution Without Participation Constraints

If no participation constraints are imposed, public-good provision can in principle be financed by nondistortionary, lump sum taxation. The Atkinson-Stiglitz (1976) critique of the Ramsey-Boiteux approach to public-sector pricing and indirect taxation is therefore applicable. There remains the question of what can be said about distributive concerns and, in particular, the relation between public-good provision and utilitarian redistribution à la Mirrlees (1971). If differences in earning abilities were the only source of heterogeneity and, hence, the only source of distributive concerns, the Atkinson-Stiglitz theorem would imply that, even with distributive concerns, it is undesirable to charge public-sector prices in excess of marginal costs or to levy distortionary indirect taxes unless, due to complementarities in consumption, these measures help to reduce distortions in redistributive income taxation. As discussed in Hellwig (2004/2009, 2005, 2010 a), however, one must also take account of differences in public-goods preferences as a source of heterogeneity and of distributive concerns. For a single excludable public good, Hellwig (2005) has shown that such distributive concerns can make it desirable to charge access prices above marginal costs in order to facilitate redistribution from people who gain a lot of utility from the enjoyment of the public good to people who do not draw such benefits from it. Hellwig (2010 a) shows that, in this setting, simple pricing mechanisms may actually be dominated by mechanisms with nondegenerate admission lotteries, with higher prices charged for admission lotteries with higher admission probabilities. Hellwig (2010 a) also provides a sufficient condition for randomization to be undesirable; remarkably, this condition is the same that ensures undesirability of randomization in the literature on price discrimination by a multi-product monopolist.
Whereas Hellwig (2005, 2010 a) deals with the case of a single excludable public good, without any concern for the production side of the economy, Hellwig (2004/2009) allows for multiple public goods and endogenous production, with heterogeneity in productivities (earning abilities) as well as public-goods preferences. In this model, each source of heterogeneity gives rise to distributive concerns of its own. If the different sources of heterogeneity are independent, each one of them calls for distortions in pricing or taxation as a basis for redistribution, in admission fees for excludable public goods as well as income taxes. If the different sources of heterogeneity are positively affiliated, the distributive concerns are even stronger. The resulting formulae for optimal public-sector prices and income taxes can be interpreted as a combination of a Ramsey-Boiteux weighted inverse-elasticities and the Mirrlees rule for the optimal marginal income tax. Because of the multiple sources of heterogeneity and distributive concerns, the Atkinson-Stiglitz theorem does not apply.
As an offshoot from this work, Hellwig (2007 b, c) had also taken a new look at the standard model of optimal utilitarian income taxation. Hellwig (2007 b) provided the most general formulation to date of the Mirrlees-Seade characterization of the optimal income tax schedule, with a unified proof for finite and for continuum models that relates the mathematics to the economics and shows what exactly is the role of each assumption that is imposed. Hellwig (2007 c) had shown that randomization in income taxation is undesirable if preferences exhibit a property of nondecreasing risk aversion/inequality aversion; examples in the literature, in which randomization is desirable, are thereby put into perspective.
Bierbrauer (2011b) uses the result in Hellwig (2007c) to refute the criticism that Piketty (1993) has raised against the Mirrleesian approach, namely, that taxes levied on one agent are independent of the other agents' productivity levels. Bierbrauer shows that Piketty's analysis rests an implicit assumption that different agents' productivity levels are negatively correlated.
Bierbrauer and Boyer (2010, 2013) place the analysis of Mirrleesian income taxation in a setting of political competition. To avoid running into voting paradoxes, they assume that there are only two productivity levels and consider the implications of competition for votes when politicians differ in ability, i.e., the costs of running the government, and any redistribution scheme must be incentive compatible. Assuming that the low-productivity group is larger, they find a tradeoff between distributive concerns and efficiency concerns for the politicians. Outcomes depend on parameter constellations. The leading case is shown to be one where the optimal Mirrleesian income tax for a Rawlsian welfare function is implemented.
Aigner (2014) studies the interaction of distributive and allocative concerns in the context of environmental taxation, which might have adverse distributive effects-The problem is considered in a standard Mirrleesian framework of optimal income taxation with two productivity groups, augmented by a second consumption good, which induces a negative environmental externality. The analysis of optimal taxation is done once in a setting with first-best income taxation and once in a setting with second-best income taxation à la Mirrlees. After identification of a term in the formalism that can be taken to stand for the "greenness" of the Pigouvian tax on the good with the negative externality (which is an issue because, in a general-equilibrium setting, there is no natural numéraire), the paper shows that, somewhat surprisingly, an increase in the welfare weight of the less productive group makes the "greenness" term go up if a first-best allocation is to be implemented and to go down if a second-best interior allocation is to be implemented. The reasons have little to do with the political considerations that originally motivated the analysis and a lot with the effects of the welfare weight of the low-productivity group on the shadow price of the resource constraint: In a first-best allocation, only high-productivity people work; if their welfare weight goes down, the shadow price of the resource constraint goes down because it is less problematic to have these people work extra. In a second-best interior allocation, in contrast, the shadow price of the resource constraint goes up because with more redistribution, deadweight losses from having to satisfy incentive constraints are higher.
Whereas Hellwig (2004/2009, 2005, 2010 a) had studied models of large economies with cross-section distributions of taste and productivity parameters satisfying a law of large numbers (and therefore being common knowledge). In contrast, Bierbrauer (2009 a, 2014) studies the interdependence of public-good provision and income taxation when there is aggregate uncertainty about public-good preferences, i.e., there is a genuine problem of finding out what level of public-good provision is desirable. These papers show that, if a robustness condition is imposed, the standard procedure of having separate analyses of public-good provision and income taxation, effectively neglecting the information problems in public-good provision, can be vindicated, at least if preferences are additively separable between consumption and leisure. In this case, the arguments given in Section C.I.2.3 imply that, in a large economy, it is always possible to induce truthtelling about public-good preferences by having payments be independent of reported preferences; moreover, implementation is independent of people's beliefs about each other, i.e., robust. Given the financing needs that arise from efficient public-goods provision, there remains the Mirrlees problem of determining an optimal income tax schedule with a view to these financing needs and redistribution.

C.I.3.3 Enforcement and Compliance

Issues of enforcement have been central to the work of Christian Traxler while he was at the institute. Even before coming to the institute, he had initiated a large-scale project investigating enforcement and compliance with respect to the payment of fees for radio and television in Austria. Results of this project are presented in Traxler and Winter (2012), Rincke and Traxler (2011), and Fellner, Sausgruber and Traxler (2013).
Traxler and Winter (2012) report on the results of a survey that was conducted concerning compliance with respect to the obligation to pay fees for radio and television in Austria. Econometric analysis of the evidence from the survey suggests that compliance behaviour is very much influenced by people's beliefs on the frequency of compliance by others. This finding cannot be explained by sanctions varying with the frequency of compliance; actual sanctions are independent of this frequency and depend mainly on the severity of the delinquency.
Fellner, Sausgruber, and Traxler (2013) report on a field experiment involving mailings to suspected evaders of television fees in Austria. Some mailings just reminded people of their obligation to pay these fees, some were accompanied by a threat of legal sanctions, some by an appeal to moral norms, and some by information about the compliance behaviour of others. Relative to a control group, there was a strong effect of these mailings on all people receiving such mailings. Mailings threatening legal sanctions had a strong additional effect, mailings appealing to moral norms or containing information about the behaviour of others did not have such an additional effect. For the addressees of the mailings, the findings confirm the economic model of delinquent behaviour as a result of a consideration of costs and benefits, with little regard for moral or social norms. However, the addressees consist of a selected group of the population, namely people who were known to live at a given address and had not previously registered to pay their television fees. Attitudes and behaviours of people in this select group are probably not typical for the population at large, of which more than 90 % are in compliance anyway. However, when thinking about enforcement policies, the attitudes and behaviours of the potential delinquents may be the thing to focus on, even if these attitudes and behaviours cannot be generalized to the population at large.
Rincke and Traxler (2011) study the effects of enforcement activities on compliance behaviours. Econometrically, the problem is to avoid spurious correlations and simultaneity bias, due to the fact that enforcement officers' choices of where to go and look for potential evaders are endogenous, perhaps driven by information on where suspected evasion rates are high or by the consideration that it is more comfortable to do this job in a densely settled area, e.g., a city, than in a distant mountain valley. To deal with the identification problem, Rincke and Traxler make use of a natural experiment that was provided by extraordinary snow fall in the winter of 2005/2006. The snow fall had a differential impact on enforcement officers' costs of getting to different parts of the country, e.g., more severe effects in remote mountain valleys or in places at higher altitudes. Using such weather-related variables as instruments, Rincke and Traxler find that compliance behaviour is positively affected by enforcement activities, not just directly, because offenders are caught, but also indirectly, because, presumably through word of mouth, information about such activities spreads in the local community and people who have failed to comply so far begin to have second thoughts. To be more precise: Rincke and Traxler find that, following enforcement activities in a given area, registration for television fees in that are goes up, i.e., some non-compliers begin to register even though they have not been directly affected by the enforcement as such.

C.I.4 Governance, Finance, and Efficiency in Public-Goods Production 8

C.I.4.1 The Research Problem

Most of normative public economic theory, including the work on which we have reported in Sections C.I.2 and C.I.3 does not pay any attention to the supply side of the economy, in particular to the production of public goods. The focus is exclusively on the demand side and on the implications of nonrivalry for preference revelations and finance under conditions of incomplete information. The nature and properties of the public goods are taken as given; the production side is represented by an exogenously given cost function.
The significance of this lacuna is obvious if one considers the financing of production. According to Atkinson and Stiglitz (1976), the government budget constraint is just what the term says, a constraint, whose impact should be minimized. Therefore any need for funds to finance production should be covered from direct taxes, preferably lump sum taxes. According to Hellwig (2004/2009), the scope for direct taxation may be limited by participation constraints, and therefore one may need entry fees as well as direct taxes to finance production. Even so, a subsidization of public-goods provision from direct taxation is desirable, as is some cross-subsidization between the different public goods. There is no notion that any one public good or any one subset of public goods ought to be self-supporting. Any notion that the production sector should be divided up into separate units, with a proviso that each unit finance itself, is rejected because this would entail replacing the single, integrated budget constraint for the entire production sector by a multiplicity of separate constraints for the different subunits. This would further restrict the set of admissible allocations and would presumably reduce welfare.
However, this line of argument neglects information and incentive problems on the production side of the economy. The notion that welfare is increased by having an integrated production sector with a single, consolidated budget constraint stems from the Pigouvian tradition of welfare economics, in which the planner has complete information about preferences and technologies. The modern theory of normative public economics has done away with the complete-information assumption, but it has done so in a piecemeal fashion, with mechanism design models of the demand for public goods and screening models for the supply, without integrating the two.
Taking account of information and incentive problems in production, one expects subsidization and cross-subsidization schemes to have negative effects on producers' efforts. If a producer knows that any deficit is going to be covered by funds from another source, he may be less concerned about cost efficiency or about tailoring his product to the needs of his customers. The same holds for a producer who knows that any surplus he earns is going to be siphoned off for use in some other part of the system. This should lead to a more critical view of subsidization and cross-subsidization schemes in the financing of production.
However, the insights concerning the benefits of such schemes that have been developed in normative public economics so far do not automatically become obsolete. The mere fact that incentive effects in production matter does not by itself invalidate the arguments underlying the inverse-elasticities rule, e.g., arguments in favour of cross-subsidizing local public transport from profits in electricity distribution. What we need is a framework for comparing such benefits of cross-subsidization with the costs of negative incentive effects. As yet, we do not have a conceptual framework for assessing the trade-offs that are involved.
The problem has been around for a long time. Remarkably, though, hardly any work has been done on it. Laffont and Tirole (1993, Ch. 15) provide an example in which it is better to have average cost pricing, i.e. to have the activity in question finance itself, rather than marginal-cost pricing with a public subsidy covering fixed costs. In the example, the firm has private information about the level of fixed costs, i.e. about the size of the subsidy it can claim under marginal-cost pricing. The supervisory authority has this information as well, but this authority is captured and tends to go along with the firm's demands unless it is under pressure from consumers. Average-cost pricing is a device to make consumers be interested in and to exert pressure with respect to the level of fixed costs that the supervisory authority certifies.
However, this model cannot be regarded as a basis for the development of a more general normative analysis. The analysis and its conclusion are highly dependent on the details of the specification of information and of political interdependence. A general conceptual framework for studying the tradeoffs between negative incentive effects and positive Ramsey-Boiteux effects of subsidization and cross-subsidization schemes has not yet been developed.
Bierbrauer (2011) also obtains the conclusion that the imposition of a self-financing requirement may be desirable if a regulated firm with private information about costs produces and sells access to an excludable public good. The key assumption is that the relation between the policy maker and the regulated firm is incomplete, i.e., not fully contingent on all possible configurations of technologies and public goods preferences. While access to public funds certainly is in the firm's interest and, moreover, is conducive to achieving undistorted first-best outcomes, as opposed to distorted second-best outcomes, the consumers may prefer the imposition of a self-financing requirement for the firm because this limits the fraction of the surplus that the firm can extract and therefore leads to a higher level of consumer surplus. This analysis, however, involves a single excludable public good and as such is not suitable for studying cross-subsidization.

C.I.4.2 Ingredients of the Analysis: An Overview

It seems appropriate to start by looking at the problem in terms of standard incentive theory. Any one activity requires the effort of a manager as an input, this effort is unobservable, and must be called forth by appropriate incentives. Providing the activity with a separate budget, which is taken out of the general public budget, provides a basis for using profit as a basis for rewarding managerial effort. The incentive effects of subsidization and cross-subsidization schemes will then be similar to the incentive effects of a profit tax or subsidy, which are well known from the literature on moral hazard in insurance and in finance. The problem would be to compare the efficiency losses associated with these incentive effects to the efficiency gains from the allocative effects considered in Ramsey-Boiteux theory.
However, there are a few difficulties that must be dealt with. Most importantly, the notion that every activity should self-finance is unrealistic. For some activities, self-financing seems impossible, for others, it is undesirable. An example where self-financing is impossible is provided by the railway system in Germany; most experts believe that this system is unable to finance the costs of the railway track network. An example where self-financing is undesirable is provided by the judicial system. Even though the services that the judicial system provides are, in principle, excludable, overriding social and political concerns in a democratic society militate against the use of user fees as a basis for financing this system.
Even in the private sector, private parties' limited ability to pay and limited liability cause problems for incentive provision based on profits. The impossibility of making the manager or entrepreneur participate in large losses tends to weaken incentives for effort and to induce excessive risk taking. The treatment of insolvency therefore figures among the central issues in the theory of financial contracting. Going beyond the discussion of incentive effects ex ante, this theory also focuses on the implications of insolvency for governance, e.g. the specification of intervention and control rights of the different claimants to the firm's assets. A major issue concerns the credibility – and the incentive effects – of contractual arrangements ex ante when these arrangements are subject to renegotiation, or to breach, ex post.
Credibility is likely to be even more difficult to establish when the activities in question serve the public interest. For a company or a person producing a purely private good, especially when in competition with others, insolvency poses a serious threat. New money is unlikely to be forthcoming unless the financiers can expect to recover the opportunity costs of their funds. For a company of person producing a public service, the prospect of insolvency is less threatening, especially if there are no other companies or persons producing the same service. The public at large has some interest in having the provision of the service continued, and the politicians in charge do not want to be blamed for its being discontinued. This makes it likely that, even if, ex ante, a self-financing requirement was imposed, in the event of insolvency ex post, the public purse would be used to provide continued finance.
The research problem of studying tradeoffs between incentive effects and allocative (Ramsey-Boiteux) effects of subsidization and cross-subsidization in public production must therefore be widened so as to encompass the problem of how to establish the credibility of arrangements that are intended to limit the scope for subsidization and cross-subsidization of individual activities. The scope for subsidization and cross-subsidization in public production must not be regarded as a policy parameter, but must be treated as a consequence of institutions and contracts that govern subsidization procedures and that provide for greater or lesser credibility of budget constraints.
In pursuing these questions, we want to draw on the large literature on soft versus hard budget constraints, as well as the literature on cross-subsidization in private corporations. Combining ideas from financial contracting and governance theory, these literatures investigate how the "hardness" of a budget constraint affects behaviours in different settings with different specifications of information asymmetries, moral hazard, and control rights assignments. Cross-subsidizations arising from soft budget constraints are sometimes treated as desirable and sometimes as the unavoidable consequences of a lack of arrangements that would make ex ante commitments credible. Some indications of the different possibilities are given in the analyses that Schmidt und Schnitzer (1993) and Schmidt (1996) provided of the effects of hardening budget constraints by privatization. For private corporations, Inderst and Müller (2003) and Inderst and Laux (2006) have indicated some incentive and governance implications of intra-firm cross-subsidization through internal capital markets. The task will be to adapt and extend the insights from this research so as to provide a basis for the more general welfare theoretic analysis of incentives, governance, and allocative (Ramsey-Boiteux) effects that we are interested in.

C.I.4.3 Some Research Questions

Along the lines suggested above, the first task would be to study the tradeoff between incentive effects and allocative effects of cross-subsidization mechanisms in a model of incentive contracting. The question is how the consideration of allocative effects changes optimal incentive schemes, in particular, how the effects of different degrees of hardness of budget constraints on output prices are to be taken into account.
In a second step, the analysis should take in the problem of making budget constraints credible. This must be treated as a problem of institutional design. The problem is likely to be most difficult for those activities where hard budget constraints are in principle problematic because (i) the community is dependent on these activities and (ii) these activities cannot or should not be self-financing in the market. Of particular interest will be quasi-market arrangements under which subsidies are not paid to producers directly, but subsidies are paid to users who can then use them to pay for the goods or services in question. Examples would be voucher schemes for subsidizing education or, in the case of Germany, the subsidies which the Länder use to pay in order to maintain railway traffic on certain lines, relying on competition among railway transportation companies to keep the costs down.
In this context, it will be necessary to extend the theory of hard versus soft budget constraints and of privatization. Apart from taking account of the impact that alternative arrangements have on output prices, it will be also important to consider the difficulties of contracting on matters of public interest. "Incomplete-contracts" theory gives many arguments for why the specification and subsequent enforcement of contractual obligations give rise to incentive problems of their own. These arguments apply to obligations concerning the public interest at least as much as to obligations concerning the delivery of goods of services to another private party. The theory would therefore suggest that control rights are needed as a substitute for effective contractual rules. But then, something like the privatization of a production activity involves a tradeoff between the hardening of budget constraints and the loss of control that are thereby induced. We should develop a framework for studying the determinants of this tradeoff.
An example of these issues was provided by the discussion about the privatization of Deutsche Bahn AG a few years ago. There seems to be a consensus that the network of railway tracks is not viable on its own, but needs a public subsidy of some 3 billion euro per year. Political discussion of privatization had focussed on whether the company should be privatized as a whole, including the network of railway tracks, or whether the privatization should be limited to the transportation companies, which, in principle, should be economically viable on their own, without direct public subsidies. Underlying this question is the conflict between different concerns about control rights assignments in a world in which contracts are incomplete. Deutsche Bahn AG prefers to retain the integrated structure of railway track and transportation in one company, in combination with a contract determining the Federal Government's yearly subsidies, as well as the track investments that are to be made. The alternative solution of having the railway track continue to be run by a public company, with contracts governing relations between the public railway track company and the privatized transportation company is rejected because the incompleteness of contracting is seen as an impediment to efficiency in relations between the public railway track company and the privatized transportation company. However, the very reasons for being sceptical about a reliance on contracts in relations between the railway track company and the transportation company are also reasons for being sceptical about a reliance on contracts between the Federal Government as a financier and the integrated railway company as a manager of the railway tracks.
Underlying this conflict is the theoretically interesting question how one might balance conflicting concerns about control rights assignments when the vertical chain of relations involves more than two parties (here, the Federal Government, the railway track company, and the railway transportation company), and an overall vertical integration of all three parties is ruled out. What factors determine which control rights assignment is to be preferred? To what extent is it possible to use contractual arrangements in order to implement flexible control rights assignments that provide for a compromise between the two alternatives mentioned above? As a matter of pure contract theory, these questions are of interest and shall be pursued in their own right. In addition, it will be of interest to investigate how the treatment of conflicting control rights concerns affects the tradeoff between the incentive effects of hardening budget constraints and the disadvantages from control loss by privatization.
Apart from contractual arrangements, the analysis must also take account of the possibility of using sector-specific regulation in order to govern conduct so as to take account of the public interest even after privatization. In practice, sector-specific regulation is used to enforce the provision of network access to other companies so that they can compete in downstream markets. Sector-specific regulation is also used to implement universal-service regulations by which an industry is obliged to provide a certain minimum of services at uniform and low prices to everybody. However, the insights of contract theory concerning the limits of "complete contracting" for incentive provision apply to such regulation as well; the assignment of intervention rights to the regulator himself raises new questions about incentives and accountability.
In the wake of the financial crisis, plans for the privatization of Deutsch Bahn have been shelved, at least for a while. However, the conceptual questions raised have appeared anew in the context of the electricity industry and the plans for replacing nuclear energy by renewable energy, in particular wind energy. Whereas in the past, investment in long-distance electricity transmission grids played a minor role, relative to the costs of generation, the switch from a steady to a volatile source of electricity generation, with much larger distances between places of generation and places of use, has put grid investments, and funding needs for such investments, squarely on the agenda for economic policy. For earlier research on this kind of issue, see Höffler and Kranz (2011 a, 2011 b), Höffler and Wambach (2013).
The research projected in this subsection is closely related to a research project, "Corporate Control, Corporate Finance, and Efficiency", which is funded by the Deutsche Forschungsgemeinschaft as part of the Sonderforschungsbereich/TR 15, Governance and the Efficiency of Economic Systems.

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1 This is shown by Clarke (1971) and Groves (1973) for implementation in dominant strategies and by d'Aspremont and Gérard-Varet (1979) for Bayes-Nash implementation.

2 Independent private values: If one person is known to have a high preference for the good in question, this contains no information about any other person's preference for this good. Preferences of different people are stochastically independent.

3 For private goods, see Myerson and Satterthwaite (1983), for public goods, Güth and Hellwig (1986), Mailath and Postlewaite (1990).

4 Wilson (1985).

5 See Mailath and Postlewaite (1990), Hellwig (2003).

6 Minor extensions of this theorem are given in Hellwig (2009, 2010 b).

7 See, e.g., Boadway and Keen (1993).

8 This part of the report is not much changed since 2009. As mentioned in the introduction to this chapter, the financial crisis has diverted our attention away from the issues raised here, but we continue to believe that the problems raised are important and promising and hope to return to them soon.

9 Fang and Norman (2005) argue that, in addition, the cross-subsidization scheme should encompass all private goods.

10 For the latter, see Baron and Myerson (1982), Laffont and Tirole (1993).

11 This insight is at least as old as the Ramsey-Boiteux theory itself. Indeed, Boiteux (1956) considered a single public enterprise subject to a stand-alone budget constraint precisely because he was aware of the incentive implications of a requirement of cost recovery for this enterprise, without any prospect for cross-subsidization from other parts of the public sector.

12 E.g. Holmström (1982), Jensen and Meckling (1976).

13 Jensen and Meckling (1976), Stiglitz and Weiss (1981), Hellwig (2009).

14 Gale and Hellwig (1985), Aghion and Bolton (1992), Hart and Moore (1990, 1998)

15 For a survey, see Kornai, Maskin, Roland (2003).

16 For a survey, see Hellwig, Laux, Müller (2002).

17 This problem concerns not just budget constraints for providers of public goods but also budget constraints for local and regional governments in a federal state or for national governments in a currency union. For a discussion in the context of the European Monetary Union, see Franz et al. (2010), Hellwig (2011c).

18 Hellwig (2006).