Coalition governments and distributive programs: a simple model

Abstract

Casual empiricism reveals that a government's program implementation policy frequently fails to maximize the representative citizen's welfare. Inthis paper, I construct a model that incorporates political economy considerations and examine the equilibrium policy distortions that a coalition government begets. I show that coalition governments are fiscally profligate when program benefits are divisible and excessively conservative when these benefits are indivisible. In other words, program characteristics (divisible or indivisible) affect even the qualitative nature of coalition-related policy distortions.

Keywords:

• distributive program
• coalition government
• inefficiency

Acknowledgement

The author thanks Satish Jain for his advice, encouragement and comments. Of course, the usual disclaimer applies.

Notes

1. This presumption has generated a steady flow of empirical papers (see, for example, Perotti and Kontopoulos 2002) which have, with mixed results, tested for evidence of the fiscal profligacy of coalition governments.

2. The ‘encompassing interests’ terminology is due to Olson (1991) and McGuire and Olson (1996).

3. The underspending effect is in line with observations in Boix's (1997) empirical study of the privatization experiences of various countries. In contrast to single-party governments, coalition governments are posited to generate gridlock effects: ‘parties within the coalition are prone to veto each other's projects whenever the resulting policies are believed to result in significant costs for their corresponding constituencies.’

4. The availability of fresh resources, s, plays an important role in my model. To see this, let fresh resources be assumed away. Consider the indivisible program . Notice that this program cannot be implemented in equilibrium in period two of the public investment stage. Why? Were the program to be implemented, one coalition partner (say, r _i ) would receive no program-specific benefits in period two while it would have to incur the cost of . But, r _i would then refuse to have the program undertaken. In other words, absent s, no indivisible program gets undertaken in period two. But guaranteed inaction in period two, it can be shown, leads also to inaction in period one. Now introduce s. Suppose agreement (a ¹, g) recommends that the program be implemented in period two and that the period-two benefits be assigned to r _j . If r _i honors the agreement, the period-two payoff it receives is . Hence, if s is large enough, r _i will be willing to comply with (a ¹, g).

5. Recall that U _k (g(s)) is 0 if g(s) = N and U _k (g(s)) is if g(s) ≠ N.

6. The agreement (a ¹, g) is not required to be the agreement corresponding to the equilibrium proposal that r _i and r _j agree upon during the government formation stage of the game. It is only after examining what happens in the case of any feasible agreement (a ¹, g) can one construct the equilibrium agreement and proposal.

7. Observe that has two components: the period-two resources received by r _k (that is, ) and the program-specific payoff for r _k in period two (that is, U _k (g(s)).

8. Of course, it is possible that Br (a ¹, g|ij) =  or .

9. Observe that an inessential but simplifying assumption has been invoked to obtain the expression for in equation (2): the payoffs received in period two of the public investment stage are not discounted.

10. Observe that since k ∉  {i, j}, the aggregate payoff for r _k is based on its program-specific benefits in the two periods of the public investment stage; r _k has no access to the period-two resources, s.

11. The ordered triple selected is one out of the six permutations of {1, 2, 3}. Thereishowever no requirement that each permutation be selected with probability .

12. See Austen-Smith and Banks (1988) and Diermeier and Merlo (2000) for formal analyses of alternative processes of government formation.

13. Notice that the government formation process is a well-specified game. There are three players. If at a certain node, r _i is the formateur, r _i 's strategy must specify the choice of a coalition partner and an element from Λ(B, d) for every (B, d) ∊ P. On the other hand, if at a certain node, r _i is the recipient of a proposal, its options are either to accept the proposal or to reject the proposal. To complete the description, I need to assign region-specific payoffs to the terminal nodes of the government formation game. If the game ends with no government formed, the payoff for region k is 0. Suppose, instead, that the game ends with r _i and r _j forming a government with a certain proposal in place. Let π(B, d) denote the probability with which program (B, d) ∊ P comes up for review in the public investment stage. Let h(B, d) ∊ Λ(B, d) be the agreement corresponding to program (B, d). The expected payoff for region k conditional on (B, d) being considered in the public investment stage is V _k (h(B, d)| ij). Thus, the expected payoff for region k at the terminal node is .

14. Corresponding to (B, d) ∊ P, let Λ₁(B, d) denote the set of agreements (a ¹, g) such that (a ¹, g) ∊ Λ(B, d) and V ₁(a ¹, g |13) ≥ 0. Then, the agreement offered by r ₃ is any element of Λ₁(B, d) that maximizes V ₃(a ¹, g |13). It is easy to show that such an element exists.

15. The proofs of Propositions 2–5 are given in the Appendix.

16. Note that the two-party government gets all of the aggregate benefits generated by the program but incurs only two-thirds of the program cost.

17. Note that ‘’ is a shorthand for the following statement: let be the set on which ; then has measure 0.

18. Notice that Proposition 3 does not indicate what happens when B is less than . It is easy to show that when the program is very inefficient (B less than ), the program is not implemented in either of the two periods of the public investment stage. In the intermediate case (B between ), the equilibrium outcome depends in a complicated way on the distribution of S.

19. Note that ‘’ is a shorthand for the following statement: let be the set on which ; then has measure 0.

20. To obtain this upper bound on r ₁'s payoff, set s to its maximum possible value, .

21. A complete characterization of the equilibrium agreement when is less than is available upon request.