Politically sustainable targeted transfers

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We show that a transfer received by a minority of the population may be sustained by majority voting, however small the minority targeted may be, when the attribution of the transfer is seen as stochastic by voters. We build a simple model wherein voters differ in income and vote over a proportional tax whose proceeds are distributed lump-sum, and each voter has a probability of receiving the transfer that depends on his income. In progressive steps, we present intuitively appealing sufficient conditions on this probability function for the social program to be supported by majority voting. We also develop intuitive conditions for the emergence of the “paradox of redistribution”, whereby more focused targeting reduces the size of the transfer program chosen by the majority. We finally apply our framework to the French social housing program and obtain that our model is consistent with a majority of French voters supporting a positive size for that program.

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  1. 1.

    Cardak et al. (2013) study a similar model wherein agents vote, first, over the size of the program and then over the extent of means-testing. They find that the majority chosen means-testing level is determined by the median income voter, so that minority targeting cannot be an equilibrium.

  2. 2.

    So, unlike Moene and Wallerstein (2001), we assume uncertainty as to the attribution of the benefit rather than as to future pre-tax income.

  3. 3.

    Or, to borrow Gelbach and Pritchett (2002)’s title: “Is more for the poor less for the poor?”.

  4. 4.

    Marx et al. (2013) contend that this paradox “no longer holds as a robust empirical generalisation” when more countries and more recent data are introduced.

  5. 5.

    Introducing endogenous labor supply so that incomes also would be endogenous would not affect qualitatively our results. See footnote 10.

  6. 6.

    We model a monetary transfer rather than the public provision of a private good for simplicity, but the reasoning developed in this paper applies to the latter case as well. Note that what matters is that the attribution process is seen as random by the citizens.

  7. 7.

    We follow the canonical model of Meltzer and Richard (1981) by assuming a lump sum transfer. This model can be generalized to more complex transfer schemes, but the canonical model allows us to make our point in the most transparent way.

  8. 8.

    We simplify notation by not reporting the arguments of p unless a risk of confusion exists.

  9. 9.

    Moreover, \(t^{V}\) corresponds to the median most-preferred value of t. As we are going to show, there is no need to determine the identity of the decisive voter (which requires additional assumptions, especially on the utility function) before Sect. 2.2.

  10. 10.

    Observe from the Proof of Proposition 2 that even the average income voter favors a positive value of t (because he has a larger-than-average probability of receiving the transfer), so that the lowest income individual who most prefers \(t=0\) has a higher-than-average income. Also, the introduction of distortionary taxation, for instance in the form of endogenous labor supply, would not change the statement of Proposition 2, provided that the distortions when t tends towards zero are not too large.

  11. 11.

    Karagyozova and Siegelman (2012) survey the empirical literature on relative risk aversion. They report very large ranges for empirically plausible individual values of the coefficient of relative risk aversion: from [0.35, 1] for Hansen and Singleton (1983) to [0.029, 680] for Halek and Eisenhauer (2001). Holt and Laury (2002) estimate that two thirds of respondents in their study have coefficient values between 0.15 and 0.93. Chetty (2006) finds that “using 33 sets of estimates of wage and income elasticities, the mean implied value of [the coefficient of relative risk aversion] is 0.71, with a range of 0.15 to 1.78 in the additive utility case”. Gandelman and Hernandez-Murillo (2014) study risk aversion at the country level and reject the null hypothesis that the coefficient of relative risk aversion equals one for only two of the 23 developed countries studied, and 10 of the 52 developing countries studied.

  12. 12.

    Except that we assume income to be distributed over [0.5,1.5] rather than [0,1].

  13. 13.

    In 2011, 5.192 million out of the 28.2 million (main) residences in France consisted of social housing. That figure represents 44% of the rental market, and slightly less than 20% of the total housing market for main residences. According to Trannoy and Wasmer (2013), social housing represents the equivalent of a transfer (the gap between market and actual rent) varying from 500€ to 1,500€ per household per year.

  14. 14.

    A recent report sponsored by the office of the Prime Minister (France Stratégie 2014) mentions (on p. 48) the “clarification of the conditions under which social housing is attributed” as one of the main challenges facing housing policies in France within the next 10 years.

  15. 15.

    This estimate represents to a slight over-representation of social housing in the sample compared to the overall French situation.

  16. 16.

    We thus make the underlying assumption that the assignment is based in large part on income, which seems correct according to the report mentioned in footnote 14. We also assume that the probability of benefitting from social housing can be inferred from the social housing composition at the time of voting—i.e., that the attribution procedure used at the time of voting is not too different from the one used in the past, as reflected by the current mix of people occupying social housing. The income measure we use is total household income in 2006 (including labor income, capital income and social transfers) per unit of consumption, i.e., using the OECD equivalence scale to correct for the household size. Also, we know the incomes and residency status of households in 2006, but not when first entering social housing. Selecting in the database the households occupants who have moved recently to social housing results in a subsample that is too small to be exploited.

  17. 17.

    Testing this prediction would allow us to distinguish our explanation for political support of social housing from other possible explanations, but we are unaware of any data allowing us to do so. Also, comparing the majority voting equilibrium with the actual size of the social housing system would require, among other challenging steps, estimating the utility functions of the voters as well as the size (tax cost) of the current social housing system.

  18. 18.

    Self-interest does not always do a good job in explaining the voting behavior of citizens, as shown, for instance, by Parlevliet (2017) in the context of pension policies. Other characteristics such as identity (see Ansolabehere and Puy 2016) likewise may explain voting behavior, including choices amongst redistributive policies, as shown by Lindqvist and Östling (2013).

  19. 19.

    See, for instance, Bischoff and Siemers (2013) on “why democracies choose mediocre policies”, and Candel-Sánchez and Perote-Peña (2013) on how political competition results in the creation of distortive policies, generating rents for politicians that are then used for vote-buying purposes.


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Correspondence to Philippe De Donder.

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De Donder, P., Peluso, E. Politically sustainable targeted transfers. Public Choice 174, 301–313 (2018). https://doi.org/10.1007/s11127-018-0500-1

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  • Paradox of redistribution
  • A program for the poor is a poor program
  • Majority voting
  • Social housing in France

JEL Classification

  • D72
  • H53
  • I38