Claudio Thum and Marcel Thum University of Munich. July 1999

Transcription

1 REPEATED INTERACTION AND THE PUBLIC PROVISION OF PRIVATE GOODS by Claudio Thum and Marcel Thum University of Munich July 1999 Abstract The public provision of private goods can be used as a self-selection device to identify income groups. This allows cost efficient redistribution even if the government cannot observe the individuals' incomes. This paper examines how redistribution through public provision of private goods extends to the case of repeated interaction between government and transfer recipients. By implementing the self-selection device, the government gains information about the households which facilitates redistributive transactions in the future. This, in turn, may trigger strategic behavior of households and weaken the self-selection mechanism. JEL Classification: H42, H2 Correspondence Address Claudio Thum Department of Economics University of Munich Schackstrasse Munich, Germany Phone: + 49 (89) Fax: + 49 (89) claudio.thum@ces.vwl.uni-muenchen.de Marcel Thum Department of Economics University of Munich Schackstrasse Munich, Germany Phone: + 49 (89) Fax: + 49 (89) mthum@ces.vwl.uni-muenchen.de

2 1 Introduction Conventional economic wisdom teaches that superior for redistributive purposes monetary transfers are to in-kind transfers as monetary transfers do not distort consumption decisions. This traditional view of in-kind transfers was challenged by Nichols and Zeckhauser (1982) and Guesnerie and Roberts (1984) who showed that, by deviating from a full information first best scenario, in-kind transfers may dominate monetary transfers. Based on this result Blackorby and Donaldson (1988) and Besley and Coate (1991) argued that public provision of private goods can be used to separate income groups if the government has no information about the individuals' incomes. Further publications confirmed this result in an optimal taxation framework, 1 e.g. Blomquist and Christiansen (1995a, 1995b) and Munro (1991, 1992), and in political economy approaches, e.g. Bergstrom and Blomquist (1996) and Blomquist and Christiansen (1999). The basic idea of this literature is that publicly provided goods can be used as a device to select income groups. If individuals with higher incomes prefer a higher quality (or a higher quantity) of a good such as education, child-care or public housing, the government can redistribute from high income to low income individuals by providing this good publicly. 2 The public provision at a relatively low quality allows the low income people to consume the good for free. Individuals with higher incomes will prefer to consume a higher quality of this good in the private sector. Even if the publicly provided good is financed by a lump-sum tax, there is a redistribution from rich to poor because of the self-selection of the income groups. All individuals finance the publicly provided good (via the tax) but this good is solely consumed by lower income groups. The crucial assumption of this literature is that the government cannot observe the individuals' incomes. However, in repeated interactions between government and individuals, the government knows who consumed the publicly provided good in the past. This information allows the government to pay monetary transfers to the lower income groups in the following periods. Once the income groups are identified, monetary transfers are better than in-kind transfers for a budget minimizing government. What at first sight seems to be an additional advantage of in-kind transfers in a multi-period setting, may prove to be fatal for 1 For a survey of the literature, see Balestrino (1995). 2 These selection models allow either for a variation of the quality given a fixed quantity or for a choice of the quantity given a fixed quality. The two approaches are used equally in this literature. 1

3 the self-selection device once individuals adapt to this mechanism. The prospect of monetary transfers in future attracts higher income groups for the publicly provided good in the first period and decreases the chances of redistribution at a low budgetary cost. 3 When the standard approach is extended to a multi-period setting the following questions arise. Can the government still redistribute efficiently towards low income households through the public provision of private goods? What kind of transfer policies are credible? To what extent will the results of a static model hold in a dynamic setting? This paper shows that the dynamic information gains increase the government s incentive to use the public provision of private goods as an incentive device. If the government wants to fully exploit the revelation mechanism, it will initially give in-kind transfers in order to gain information about the households. Later, the government can switch to the cheaper cash transfers because, with the information about the individuals types, it can now target the monetary transfers to the needy. The government, however, faces two obstacles in implementing such a cost minimizing policy. One obstacle is the individuals incentive to mimic low income households by accepting (per se unfavorable) in-kind transfers. They may do so because they anticipate that the government will switch to cash transfers later. The other obstacle is the government s credibility. To avoid the first problem, the government may want to promise inkind transfers not only in the first period but forever. This, however, is not a time consistent policy. Once the government has the information on household types, it has an incentive to switch to cash transfers. Without commitment opportunities, the government will lose the ability to select households via the public provision of private goods. With commitment, the government has to implement the more costly policy of in-kind transfers for each period in which transfers are made. For the latter case, we show that the government can always improve by randomizing between cash and in-kind transfers. The organization of the paper is the following. In the next section, we develop a simple static model to show the potential cost efficiency of publicly provided private goods through self-selection. The third section discusses how the self-selection mechanism extends to a two period model where the government has the power to credibly commit to its future policies. In Section 4, we show that it can be optimal for the government to randomize between cash and in-kind transfers. Section 5 discusses the consequences if the government lacks the ability to commit to future transfer policies. The last section summarizes the results of this paper. 3 This effect is known as ratchet effect in the industrial organization literature, see e.g. Laffont and Tirole (1993). 2

4 2 Self-selection and Minimum Income Guarantee The public provision of private goods allows the government to target its redistribution policy efficiently to low income households even if no information about the individuals' incomes is available. This result from the literature is presented in a simple one period model in order to create a reference case for the intertemporal model in the following sections. To keep the set up as simple as possible, we will focus on a redistributive policy that guarantees a minimum income to poor households. Consider a government that wants to support those (and only those) who are unable to reach the minimum living standards on their own. The abilities of these people in terms of human capital endowment may be too low to earn the necessary amount in the labor market. Then the government would like to make up for the difference between what these people can earn on their own and what is needed for a minimum living standard. Such a policy of minimum income guarantees, however, is hindered by the existence of households with somewhat higher abilities. Even though these households may still be at the lower end of the economy wide income distribution, they already can earn more than the minimum living standard in the labor market and, therefore, should not receive any government support. The government, however, cannot distinguish between the two types of households. Households can hide part of their earnings on the income tax returns, or they can make some of their income in the shadow economy. So from the government s viewpoint, those who are really needy and those who are somewhat better off are practically indistinguishable. To facilitate the formal analysis we restrict our model to two types of individuals: high and low ability. 4 The ability levels are associated with two different income levels Y { Y, Y } where Y is the low income and Y is the high income (for the low and high ability individuals, respectively). 5 Even though the government cannot observe the individuals' income, it knows that a fraction of households belongs to the low income group. All individuals have the same (homothetic) utility function U U ( S, Z ) = with positive marginal utilities ( U > 0 and U > 0 ) where S and Z are the quantities of two private goods. Z S Quantities are normalized in such a way that both prices are equal to 1. S denotes the good 4 The two income groups considered here are close to the minimum living standard in the economy. There are of course many other households with earnings far above the minimum income level. As the government can observe large deviations from the minimum income levels, e.g. via the (imperfect) tax returns, these households can never apply for government support. In fact, these households will pay the taxes to finance the system of social assistance. For simplicity, we will not explicitly model the revenue side of the government budget. 5 The perfect correlation of ability and income insures that there is no income mobility across the two groups. For households at the lower end of the income schedule, this assumption is not too unrealistic. 3

5 that can be provided by the government and Z represents a bundle of all other goods in the economy. The government tries to minimize the budget for a given distribution target. To specify this distribution target, we assume that each individual in the population is guaranteed a minimum utility level U. This utility level can be interpreted as the maximized utility of an (hypothetical) individual with income Y. U = max U S, Z ( S, Z ) s. t. Y = S + Z Therefore, the guaranteed minimum utility level is the indirect utility U V ( Y ) individual with income Y. Throughout the paper we will assume (1) = of an Y < Y < Y, i.e. to meet the distribution target the government has to make transfers to the low ability group but not to the high ability group. With full information, the government would give a monetary transfer of Y Y to the low ability households to minimize the budgetary burden of its policy. Without full information, the government chooses between two instruments: (1) monetary transfers (policy M) or (2) public provision of a private good (policy P). Once the government has made its choice, each individual decides whether to apply for the transfer. Before deriving the optimal policy, we briefly discuss the two instruments. The monetary transfer per capita is just the difference between the low income Y and the guaranteed income level Y. Since the government cannot observe the individuals' incomes, all individuals apply for and get the monetary transfers. Let the number of households be normalized to unity. Then, the budget M B of the monetary transfer is given by B M = Y Y. (2) The second instrument is the public provision of a private good. The government provides a fixed quantity of the good S free to all individuals who apply for the transfer. The necessary quantity S is implicitly given by the utility target U and the utility of the individual with the lowest income Y, i.e. U ( S Y ) U, = (3) Households accepting the transfer can neither resell the publicly provided good nor buy additional units of this good. 6 Hence, the entire private income Y is spent on good Z. An 6 A good example is public housing. A transfer recipient can certainly not increase the size of the publicly provided flat. Also subletting is hardly possible. Relaxing the restriction on resale and additional purchases would bring in-kind transfers closer to cash transfers. Therefore a government that wants to use the self-selection property of in-kind transfers will always choose those goods where reselling and topping up is hardly possible. The role of topping up is discussed e.g. in Blomquist and Christiansen (1995b). 4

6 implicit differentiation of (3), using U V ( Y ) level Y requires an increase in the publicly provided quantity S : There is one (and only one) income target level =, shows that an increase in the target income ds 0. (4) dy + Y where public provision and monetary transfers generate equal budgetary costs per low ability recipient. For all other income targets, the policy of public provision is more expensive per capita since the consumption decision of the low ability household is distorted. There is either too little or too much of the publicly provided good in that group s consumption basket. To avoid the (uninteresting) distinction between these two cases in the further analysis, we assume that the distribution target is + sufficiently high, i.e. Y Y. Here - compared to households ideal consumption bundle - the government has to provide an excess amount of the private good to meet the utility target. 7 Whether the high ability group applies for the transfer will depend on the quantity of the in-kind transfers. A high ability individual compares the utility from accepting the in-kind transfers with the utility from consuming all goods in the private sector. She is indifferent between these two alternatives if the amount of the publicly provided good is equal to S *. ( S Y ) V ( Y ) U *, =. (5) Therefore, S* is the maximum amount of goods that can be publicly provided without inducing the high income group to apply for the transfer. Let Y* denote the income target level that corresponds to an in-kind transfer of S*. The two cases that can be distinguished according to this income target level Y*, are the following: (1) The guaranteed income is below this critical income target ( Y Y * ). High income individuals purchase the good in the private sector and only the low income group consumes the publicly provided good. The budget times the amount of the publicly provided good. 8 P B is given by the fraction of the low income groups B P = S (6) (2) In the second case ( Y > Y * ), all individuals consume the publicly provided good. Therefore, the budgetary costs P B 1 are B P 1 = S. (7) 7 For tractability, we also assume that the amount the publicly provided quantity is strictly convex in Y. This condition is fulfilled e.g. for Cobb-Douglas utility functions. 5

7 Having characterized both policies, we can now compare the budgets for public provision and for monetary transfers to obtain the optimal policies. When the income groups can be separated by public provision ( Y Y * ), there is a threshold P M Y below which the public provision is cheaper. 9 B P > = B < M > S = Y Y < > Y = Y < P M for Y Y * (8) For income targets above Y*, the self-selection mechanism of in-kind transfers becomes ineffective. Therefore, monetary transfers are always cheaper. B > B We can summarize (8) and (9) by the threshold P M 1 for * P M Y Y > Y (9) B P > = B < M > Y = Y < P M = min P M { Y, Y *} (10) with B P B = B for Y < Y * Y > * P P 1 for Y (11) Figure 1 shows this comparison of the two budgets. At the distribution target + Y, the two types of transfer policies create the same costs per capita. As the public provision has the benefit of attracting only the low ability types, this policy is cheaper than monetary transfers. There are two effects from increasing the distribution target. First, the public provision of goods distorts the consumption and is therefore more expensive in per capita terms than monetary transfers. Second, public provision allows the groups to be separated until the distribution target Y* is reached. If the first effect is smaller than the advantage of targeted transfers, the public provision is the cost efficient policy. This is the case to the left of P M Y where both policies require the same budget. Above this critical income monetary transfers are optimal The index indicates that there is a separation of the income groups. Correspondingly, the index 1 means that there is no separation. 9 It is assumed throughout the paper that such an interior solution exists. Otherwise the government s decision problem becomes trivial. P M 10 In the following, we will make the requirement Y < Y * as in Figure 1 which is always fulfilled if the low ability group is sufficiently small (low ). Extending the analysis to the alternative case is straightforward. 6

8 Figure 1: Budgetary Costs in the One Period Model 3 A Two Period Model with Commitment This section addresses the question of whether the public provision of private goods can be used for a policy of minimum income guarantees if the government and the individuals interact repeatedly. To analyze this problem we replicate the structure of the static model in a two period setting. For each period the government announces the type of transfer and the individuals decide whether to apply for transfers. The two period setting is nevertheless more than a mere replication of the static model. The government receives additional information because it can observe who consumed the publicly provided good in the first period. The second period transfer can then be based on this information. Hence, learning is the first new feature in the two period model. The second new feature is strategic behavior on households' side. Knowing that the government will exploit any information, even high ability households have an additional incentive to mimic low ability types. To isolate the effects from repeated interaction, we will first assume that the government can initially commit to the transfer types in both periods. (In Section 5 we will discuss the alternative case where no commitment is feasible for the government.) 7

9 For simplicity, the utility function is just the sum of the instantaneous utility functions. There is no discounting and the income is constant and exogenously given for both periods. Again, as in the one period model the good can neither be resold nor topped up. In addition, we make the requirement that the government meets the redistributive income targets in each period. 11 Since the government can choose between public provision and monetary transfers in each period, there are four possible combinations of policies: (1) monetary transfers in both periods (MM), (2) monetary transfers in the first period and public provision in the second period (MP), (3) public provision in the first period and monetary transfers in the second period (PM), (4) public provision in both periods (PP). To derive the cost minimizing policy, we first calculate the budget for each of the four scenarios and then compare the outcomes. Policy MM: monetary transfers in both periods Since the government cannot observe the individuals' income and does not gain any information, the budget of this policy model. MM B is twice as high as the budget B MM ( Y Y ) M B of the static = 2 (12) Policy MP: monetary transfers and public provision As all individuals choose monetary transfers in the first period, the government remains uninformed. Minimizing the budget, the government chooses the lowest public provision level S which guarantees the distribution target. Depending on whether the self-selection mechanism works in the second period, the budgetary costs B MP ( Y Y ) ( Y Y ) MP B amount to MP B = + S for Y Y * = MP B1 = + S for Y > Y * This formulation implicitly assumes that individuals cannot be punished if they consume the monetary transfers in the first period but do not for apply for the in-kind transfers in the second period. (13) 11 In particular, the government is not allowed to make a first period transfer large enough to meet the distribution target in both periods. If such a policy were feasible, we would be back to the static approach. Moral hazard on the consumers side could prevent such an upfront transfer. If the consumers receive all transfers in the first period, they could consume the entire transfer in the first period and poor again in the second period - sue the government for additional transfers. 8

10 Policy PM: public provision and monetary transfers Announcing monetary transfers for the second period will have an impact on the participation in the transfer program of the first period. In contrast to the static model, high income individuals will not only compare their instantaneous utilities with and without participation, they will also take into account the fact that the government receives some information from the first period transfers. Only those who have participated in the first period will be eligible for the monetary transfers in the second period. In the static model, the high income group applied for in-kind transfers only if the guaranteed income level exceeded Y*. In the two period setting, the high income group will accept the publicly provided goods with even lower income levels because of the additional benefit of future cash transfers. Let Y** denote the guaranteed income level where the high income individuals are just indifferent whether to apply for the (per se unfavorable) publicly provided goods in order to receive cash transfers later or whether to stay entirely out of government transfer programs. Because of the additional future benefit from participating in the first period, we get Y** < Y*. The budget of this policy PM depends on the self-selection of groups: B PM B = B = S + ( Y Y ) ( Y Y ) für Y < Y ** Y > ** PM PM 1 = S + für Y Below the selection income Y**, only the low ability group consumes the publicly provided good in the first period. In both periods, transfers can be targeted to the low ability group which is only a share of the total population. The budgetary cost (14) PM B is the sum of the expenditures for public provision and the monetary transfers. For higher distribution targets ( Y > Y * *), both household types consume the publicly provided good in the first period and, PM therefore, receive cash transfers in the second period ( B 1 ). Policy PP: public provision in both periods With policy PP, transfers are given via publicly provided goods in both periods. The budgetary costs are simply twice as high as in the static model and depend on whether the self-selection of the low ability types works: B PP PP B = S + S für Y < Y * = (15) PP B1 = S + S für Y > Y * 9

11 Optimal Policies This completes our list of feasible policies. In the next step we search for the cost efficient policies. This task is facilitated considerably when we first eliminate the policies that are obviously inefficient. First, whenever the self-selection mechanism fails, the public provision of goods is inferior. In-kind transfers are more costly but create no benefits in these cases. Hence, with an optimizing government, the budgetary costs MP B 1, PM B 1 and PP B 1 will never arise. Second, a policy that first gives monetary transfers and then switches to in kind transfers (MP) can also never be optimal. For this policy, there is no additional effect from repeated interaction. Therefore, either cash transfers or in kind transfers in both periods will be chosen. If cash transfers are cheaper for a single period, it will be better to choose policy MM instead of MP. Conversely, if in-kind transfers generate the lower cost, this type of transfer should be used for both periods; hence, policy PP dominates MP. We are left with the following three policy alternatives: MM B ( Y Y ) MM = 2 PP B PP = 2 S for Y Y * B PM = S + Y Y for Y Y * * PM ( ) Through pairwise comparisons, we will determine the optimal policy as a function of the minimum income target Y. To facilitate the evaluation of the outcomes, we use the illustration in Figure 2. On the horizontal axis, the minimum income target Y is denoted which is in the range Y [ Y ; Y ] +. The vertical axis measures the critical income level Y ** above which the self selection mechanism breaks down for policy PM. Recall that this is the strategy that in principle could make the best use of the mechanism: the relevant information is generated in the first period and can be used in the second period to reduce the budgetary cost of social policy. Depending on how strongly the high ability types react to the future availability of cash transfers, Y ** can be anywhere between + Y and Y *. A low value for Y ** indicates that the high ability types accept a distortion in their consumption bundle today even for a relatively low cash transfer tomorrow. 10

12 Figure 2: Optimal Policies with Commitment A comparison of policies MM and PP reveals that the latter creates lower budgetary costs if S Y Y. This is of course the same condition as in the one period framework because we simply replicate the one period game. For transfer targets below P M Y, public provision dominates cash transfers in the second period; above this threshold the reverse relationship holds. Now we turn to the second pair of policies: MM vs. PM. The comparison of the budgetary costs B > = < yields a new threshold Y > = < > 2 (16) < PM MM P M ( ) ( Y Y ) Y = Y Y PM MM B S > PM MM. Below this threshold, it pays the government to implement policy PM ; for higher income targets, MM is the policy with the lower costs. The reason is the same as in the static model. Policy PM allows the income groups to be identified, but requires a costly distortion of consumption. Since this distortion only occurs in the first period - thus paving the way for targeted income transfers to low income households in the second period -, the threshold Y PM MM lies above the threshold in the static model 2, the new threshold is illustrated by the vertical line at Y PM MM P M Y. In Figure Finally, we have to compare PP and PM. The budgetary costs with policy PM are clearly lower as the public provision in the first period generates the relevant information for targeted 11.

13 transfers in the second period. With the alternative policy, the costly self selection mechanism is also used for the second period transfers even though the information is already available. Hence, in general, policy PM dominates PP. However, the former is applicable only in a subset of cases, namely if Y Y * *. For higher income targets, implementing the selfselection mechanism only in the first period will fail because high ability households apply for the publicly provided goods to qualify for future cash transfers. In Figure 2, PM can only be a dominant policy above the 45 degree line. Summarizing the pairwise comparisons, we find that all three types of policies can be cost efficient. If the transfer level is low (low Y ) and the high ability households are not easily willing to consume a distorted consumption bundle to qualify for future cash transfers (high Y**), the government can fully exploit the self selection mechanism. It first gives inkind transfers and uses the information later on to give targeted cash transfers (policy PM). If the transfer level is low (low Y ) but the high ability households are easily willing to mimic the low ability types (low Y**), the government has to rely on the permanent use of costly in kind transfers. Otherwise it will lose the beneficial effects of self selection (policy PP). Finally, if the income targets become sufficiently large, the self selection mechanism becomes too large and the government has to abandon any public provision of private goods (policy MM). A First Evaluation of Repeated Interaction How does repeated interaction between government and potential transfer recipients affect the use of in-kind transfers? To evaluate the results we now compare the static model [cf. Figure 1] with the outcome in the two period game [Figure 2]. Let us start with the case where the self-selection constraint Y** lies above the critical level of in-kind transfers in the static model ( P M Y ) and we get Proposition 1: If self-selection is still operative at the critical level of in-kind transfers in the P M static model ( Y ** > Y ), then, with repeated interaction, the government has both an incentive and an opportunity to increase its use of in-kind transfers. For guaranteed income P M PM MM Y Y, min Y **, Y in-kind transfers are more expensive levels in the range of [ { }] than cash transfers. The higher costs in the first period are, however, more than offset by the lower targeted cash transfers in period 2. 12

14 Now we turn to the alternative case. Here, high income households react strongly to the potential benefits of future cash transfers. At the critical level of in-kind transfers government can no longer distinguish between high and low income households. P M Y Proposition 2: If self-selection is not operative at the critical level of in-kind transfers in the P M static model ( Y ** < Y ),the government only gains from repeated interaction if Y < Y * *. For all other cases, the government has the same costs per period as with a single interaction. Either the government selects low income individuals via the public provision of public goods; then it has to give these in-kind transfers in each period. Or the government relies on cash transfers without any selection effect. This section has shown that repeated interaction per se is never to the disadvantage of the government, though, in some cases, the government may be forced not to exploit the informational gains., the 4 Mixing between Transfer Types The analysis so far has assumed that the government redistributes either through in-kind transfers or through monetary transfers. With the feasibility of commitment, however, there is an additional policy option. The government can announce that it will mix the two transfer types with a certain probability in the second period. The randomization of transfer types might be an alternative to policy PP to partly avoid the high expenditures for public provision of goods in the second period, and simultaneously to prevent the high income group from applying for the transfers. 12 To see this, assume that the government can initially commit to giving monetary transfers with probability γ and to publicly providing goods with probability ( γ) 1 in the second period. For γ = 1, this policy is equivalent to policy PM; for γ = 0, it is equivalent to policy PP. Therefore, by changing the mixing probability γ, the government can shift the threshold for self selection between the two previous selection incomes Y* and Y**. We denote this critical level for the minimum income, below which only the low income group applies for transfers, by Y***. Suppose that this threshold where the incentive 12 The randomization of policies is not available in the static model since the individuals with high incomes cannot be forced to consume the publicly provided good. In contrast, repeated interaction allows a cost to be imposed on high ability households that try to mimic low ability types. In order to qualify for the potential monetary transfers in the second period, the high ability households have to consume the publicly provided good, which is badly suited to their preferences, in the first period. 13

15 constraint becomes binding is a continuous (decreasing) function of the mixing probability γ. The budgetary cost of this mixing policy amounts to B Mix ( Y Y ) ( Y Y ) Mix B = S + (1 γ) S + γ für Y Y *** Mix B1 = S + (1 γ) S + γ für Y > Y *** = Implementing this policy without any selection effect ( Y > Y ** * ) is obviously inferior; pure cash transfers would be cheaper in this case. Let γ*** denote the maximum probability with which the government can make cash transfers without attracting the high ability individuals, i.e. for each Y the probability γ*** makes the incentive constraint binding. To see whether the mixing strategy can dominate any of the pure transfer types, we will now compare the budgetary costs. First, the mixing strategy can never be cheaper than policy PM whenever the latter policy is feasible. Policy PM makes the most efficient use of the selfselection mechanism as it generates all the relevant information in the first period and relies on the cheaper monetary costs in the second period. Giving in-kind transfers with a positive probability in the second period would only generate additional costs. Second, the mixing strategy will dominate the pure in-kind transfers PP. The costs of policy PP amount to B PP Mix = 2 S. A comparison with the budgetary cost of the mixed strategy B reveals that the latter is cheaper if Y Y < S holds. As the per capita costs of monetary transfers are always below the per capita cost of in-kind transfers, this condition is always fulfilled. As the incentive constraint is continuous in expected future transfers, the government can always choose a strictly positive probability for cash transfers (γ*** > 0) and, therefore, save on its expenditure by replacing policy PP by a mixed strategy. Proposition 3: If the government can commit to future transfer mechanisms, a policy that randomizes between transfer types is always cheaper than permanent transfers via publicly provided goods (policy PP). Third, whether the mixing strategy is also cheaper than pure cash transfers depends on the minimum income level Y and the sensitivity of the incentive constraint. A comparison of the budgetary costs of the mixing strategy with the policy of pure cash transfers yields (17) B Mix > = B < MM > S ( 2 γ) = ( 2 γ) ( Y Y ) (18) < 14

16 Hence, the government saves on its expenditures by mixing between transfer types 13 if 2 S ( Y Y ) γ >. (19) S ( Y Y ) Besides the budgetary aspect, we also have to consider whether the incentive constraint is fulfilled. Hence, a policy that replaces pure cash transfers (PP) by mixing between transfer types can only be optimal if there is a γ that fulfills the inequality 2 S ( Y Y ) < γ γ ***. (20) S ( Y Y ) Whether there is such a value or not will depend on the precise nature of the individuals utility functions. If feasible, the mix of policies can improve the outcome until the selfselection constraint becomes binding. This advantage of a randomization strategy in public transfers might explain why we often see both in-kind and cash transfers in real world transfer systems. Overall, the previous two sections have shown that, with the feasibility of commitment, the government gains from repeated interaction in its social policy: Proposition 4: Exploiting information in a dynamic context can never be to the disadvantage of the government if it can commit to its future transfer policies. 5 No Commitment So far we have pointed out how repeated interaction between government and transfer recipients affects the use of publicly provided goods as an instrument for a targeted minimum income guarantee. There we assumed that the government can credibly commit to its future transfer policy. How is the effectiveness of in-kind transfers as a self-selection device affected if the government cannot commit to its future policy? Once the government has gained the relevant information, it always has an incentive to switch to pure cash transfers. And the government often has the flexibility to give way to its ex post opportunism by changing the law or enacting new procedural rules. This section shows that, due to the credibility problems, repeated interaction between government and potential transfer recipients limits the feasibility of in-kind transfers as a selection device and makes the government worse off. 13 Note that S ( Y Y ) > 0 in the relevant range. 15

17 It will not be necessary to repeat all calculations for the no-commitment case. A simple thought experiment will show that it is sufficient to focus on those income targets where policy PP is optimal in the commitment case [cf. Figure 2]. 14 In the other cases (policies PM and MM), the government s optimal policy will not change whether a commitment strategy is feasible or not. First, if policy PM can be implemented, it efficiently exploits the relevant information. In the first period, the government succeeds in separating the two household types through in-kind transfers. In the second period, the information gained from the selfselection is used when the government limits its monetary transfers to the low ability households. If the government is not able to commit ex ante to its second period policy, this will have no effect on the outcome. Given the perfect information on the households types, the best policy in period 2 is indeed to give monetary transfers. Hence, this policy is always time consistent. Second, for policy MM to be time consistent, the government must not have an incentive to switch to in-kind transfers in the second period. Such an incentive would exist P M for all income targets Y Y. However, as policy MM is only implemented for income targets above this critical value [cf. Figure 2], the government once again does not face a credibility problem. Finally, we can focus on the credibility of the remaining policy PP. This policy of in-kind transfers cannot be credible in situations of repeated interaction. The reason is simply that the government once it has acquired the relevant information in period 1 no longer has an incentive to use in-kind transfers in the second period as cash transfers would always be cheaper. However, there is a way for the government to do both, i.e., to use in-kind transfers in both periods and avoid the time consistency trap. The government has to induce the high income group to choose the publicly provided good in the first period. This can be achieved by publicly providing a sufficiently large amount S* ( S* S ) where the high ability group is at least indifferent between consuming and opting out. Then the government is unable to distinguish high and low ability types at the beginning of the second period. In the second period, the government can then choose the minimal quantity S to guarantee the distribution target. As in the one period model, only low income individuals choose this publicly provided quantity. A necessary condition for the credibility of this policy is of course that the public provision in the second period is cheaper than monetary transfers. Let us denote this policy which is characterized by excessive in-kind transfers by P P. The budget P P B ' is given by the 14 A more detailed derivation of credible policies without commitment is available from the authors upon request. In what follows, we will focus again on pure strategies and neglect the possibility of mixing between transfer types. 16

18 expenditures for the amount S* to the total population and the minimal amount S to the low income individuals. B P ' P = S * + S What are the alternative policies in the relevant range [ Y Y P M (21) and Y Y * * ]? We already know that PM is not a credible policy as there would incentive to switch to monetary transfers in period 2. For the same reason, we can exclude policy MM. In the second period, the government would prefer in-kind transfers over cash transfers. That leaves us with only one alternative to policy P P, namely policy MP. The cash transfers in the first period reveal no information about the individuals types. Therefore, the government still has an incentive P M in period 2 to use in-kind transfers as a self-selection device. (Recall that for Y Y targeted in-kind transfers are cheaper than cash transfers to both groups.) The budget for policy MP amounts to B MP ( Y Y ) + S =. (22) Comparing the budgets in (21) and (22) reveals that policy MP causes lower budgetary costs than P P because cash transfers are cheaper than in-kind transfers in per capita terms. Hence, if the government loses the ability to commit to future transfer types, policy PP is replaced by policy MP. Figure 3 summarizes the outcome in the no commitment case. Figure 3: Optimal Policies without Commitment 17

19 The credibility problem forces the government to abolish the cost efficient policy PM. Without commitment, the government can no longer separate the two groups in the first period and generate the relevant information for the second period. The high ability types would anticipate that government can use the information to give targeted cash transfers. Then each high ability type has an incentive to mimic low ability types and the intended policy breaks down. In a dynamic setting, the per se beneficial effect of self-selection works against the government s own interest. The best time consistent policy that the government can adopt is MP. And this policy is more than twice as expensive as the cost of the static P setting ( 2 ). B Proposition 5: If self-selection is not operative at the critical level of in-kind transfers in the P M static model ( Y ** < Y ), then, with repeated interaction, the government loses its power to select low income individuals via the public provision of private goods for income targets P M Y Y **, Y. The dynamic setting works against the government s interests. The average [ ] costs per period are higher than in the static setting. Strategic Non-Information The Value of Data Protection Even if a government cannot directly commit to certain transfer types, there is still another useful policy option which is available to many state institutions. A government can commit to not using any information gained by repeated interaction. 15 Evidence for this type of commitment might be found in data protection authorities which supervise state offices in particular. Often, such data protection regulations force state institutions to delete personal data regularly and prohibit forwarding of information among agencies or jurisdictions. If these authorities are sufficiently independent and data protection is an element of the constitution, the credibility problem vanishes. By implementing data protection, the government becomes unable to use information in an intertemporal context and, therefore, can always imitate the static setting. In the scenario of the previous section, such a strategy can improve the outcome whenever policy MP is the equilibrium. Instead of making costly cash transfers to both types, strategic non-information via data protection allows the targeted in-kind transfers to be used in both periods. Hence, even without direct commitment to future transfer types, the government can fully imitate the commitment case if credible data protection is feasible. 15 For a model of strategic non-information in a principal agent environment, see e.g. Kessler (1998). 18

20 6 Conclusion The public provision of private goods as a self-selection device is well established in the literature. In a dynamic setting, it becomes even more attractive for the government to receive information on potential transfer recipients. The dynamic nature, however, also makes it more difficult to use in-kind transfers as a selection device. The first problem arises from the individuals incentive to mimic low income types even in times of in-kind transfers because they hope to receive monetary transfers in the future. The second hurdle for an efficient implementation of in-kind transfers is the government s credibility problem. Once the government has gained the relevant information on the individuals types, it always has an incentive to switch back to cash transfers. In summary, we can highlight three results of our approach. First, despite the problem of mimicking, the government cannot lose (and sometimes gains) from repeated interaction if it can commit to the type of future transfers. Second, mixing between cash and in-kind transfers a strategy often observed in real world programs of social assistance can be a rational budget-minimizing strategy from the government s point of view. Third, if the government cannot commit to future transfer types, the government may lose from repeated interaction; the average budgetary costs per period rise above the costs in a one shot game 7 References Balestrino, Alessandro (1995): "Public Provision of Private Goods and User Charges", Recherches Economiques de Louvain 61, Bergstrom, Ted and Sören Blomquist (1996): "The Political Economy of Subsidized Day Care", European Journal of Political Economy 12, Besley, Timothy and Stephen Coate (1991): "Public Provision of Private Goods and the Redistribution of Income", American Economic Review 81, Blackorby, Charles and David Donaldson (1988): "Cash versus Kind, Self-selection, and Efficient Transfers", American Economic Review 78, Blomquist, Sören and Vidar Christiansen (1995a): "Public Provision of Private Goods as a Redistributive Device in an Optimum Income Tax Model", Scandinavian Journal of Economics 97, Blomquist, Sören und Vidar Christiansen (1999): "The Political Economy of Publicly Provided Private Goods", Journal of Public Economics 73,

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