Dynamic Electoral Competition and Constitutional Design

1. Dynamic Electoral Competition and Constitutional Design Marco Battaglini Princeton University, CEPR and NBER

2. Introduction • Consider the comparison between proportional vs. majoritarian electoral systems. • A robust finding: PS lead to higher g and lower r than MS. • In a static model, this comparison is done ceteris paribus: same underlying parameters, etc. • In a dynamic model, some of these values are endogenous. • Debt affects the performance of the voting rule; but the voting rule affects debt.

3. If in the steady state we have more public debt in a PS than in a MS, then even if politicians desire to have a larger g, they may be able to affordonly a lower g. • The main result of this paper is that this is indeed the case: • PS tend to be more dynamically inefficient, and so accumulate more debt; • This may lead to a lower g and higher rin the steady state, despite the fact that a lower fraction of citizens is “represented.” • This phenomenon may reverse the received wisdom on welfare comparisons.

4. Plan for the talk • The model • The political equilibria: • TheProportional System(PS); • The MajoritarianSystems: single district (SDS), multiple districts(SMS) • Comparing electoral systems • Empirical implications

5. The model • I.1 The economy • A continuum of infinitely-lived citizens live in n identical districts. The size of the population in each district is one. • There are three goods - a public good g, private consumption z, and labor l. • Each citizen's per period utility function is: • We assume A evolves according to a Markov process.

6. Linear technology: z=wl and g=z/p. • The discount factor is δ. • There are markets for labor, the public good, and one period, risk free bonds. • In a competitive equilibrium: • price of the public good is p, • the wage rate is w, • and the interest rate is ρ=1/δ-1.

7. I.2 Politics and policies • Public decisions are chosen in national elections. • A policy choice is described by an n+3-tuple: • {r,g,x,s1,…,sn} • The government faces 3 feasibility constraints: • Non negative transfers: si> 0. • An upper bound on debt (no Ponzi schemes):

8. I.3 A model of electoral politics • Electoral competition is modelleda' laLindbeck and Weibull[1987] as in Persson and Tabellini [1999]. • Candidates L, Rrun for office, simultaneously and noncooperatively committing to • Voters vote for the preferred party and the electoral rule determines the winning party. • A key difference: election is embedded in a dynamic game. Debt creates a strategic linkagebetween electoral cycles.

9. I.3.1 Voters • Voter l’s utility for policy p={r,g,x,s1,…,sn}in a state A is: • where v(x; A’)is the expected continuation value function. • Voters care about the policy and about an intrinsic quality of • the candidate. Voter l in district j will vote for Liff: • κjis an ideological preference for party Rin district j • σl is idiosyncratic to voter l

10. Both σj, κl are independent random variable that are realized at the beginning of the period: • Districts, therefore, differ in their expected ideology and in ideological dispersion. • The shocks are not observed by the candidates; • The distribution of the shocks is known by the candidates.

11. These differences, moreover, may change over time. • is a r.v. with density φ(h;A). • We assume districts are symmetric with respect to the distribution of ideological components.

12. I.3.2 Vote shares • The votes received by L in district j given pL and pR are: • The votes received by R will be one minus the above. • We consider two alternative voting systems: • Proportional: a candidate is elected with a probability equal to the share of votes he/she receives; • Majoritarian: A candidate is elected if he wins a majority in a majority of electoral districts.

13. I.3.3 Candidates • Candidates maximize: , where R is a constant and Iiτ is 1 if the candidate is in office, zero otherwise. Candidates are not myopic. • I.3.4 Equilibrium • For all the electoral systems we consider, we focus on symmetric Markov equilibria(SME) in WSU strategies. • A SME can be described by a collection of proposal functions r(b;A,h), b(b;A,h), g(b;A,h), s(b;A,h)and a value function v(b;A,h) (in shortp(b;A,h)).

14. II.1 The proportional system • In a proportional system candidate L maximizes the expected share of votes: • Given v, Lchooses a platform to solve: • Note that: .

15. Given v, Lchooses a platform to solve: • On the other hand, given r,g,x, the value function is: • Definition.A political equilibrium in a proportional system (PS) is a collection of policies p and a value function v such that p solves (A) given v; and v satisfies (B) given p. (A) (B)

16. Proposition.In a proportional voting rule system, a well-behaved symmetric political equilibrium exists. An equilibrium is well-behaved if v is continuous and weakly concave in b for any A.

17. When is a political equilibrium Pareto efficient? • Let us define the MCPF as: • i.e. the marginal increase in income that compensates for a marginal increase in tax revenues. • Dynamic efficiency requires:

18. In a PS we have a “similar” condition: • The equilibrium is dynamically efficient only if, , therefore, generically it is dynamically inefficient. • Proposition.In a PS, policies can not be rationalized by any set of Pareto weights. The MCPF is a submartingale. Expected benefit Expected cost of reducing future pork tranfers.

19. III.1 The majoritarian system: The MMS case • Given platforms pL, pR, L wins in district j with probability: • In this case the probability that L wins the election is:

20. Given v, Lchooses a platform to solve: • On the other hand, given p, the value function is: • Definition.A political equilibrium in a MMS is a collection of policies p and a value function v such that p solves (A) given v; and vi satisfies (B) given p for any i. (A) (B)

21. Let’s assume that there are only 3 districts, L, M and Rand that, with and . • h is uniform and i.i.d. over • As σ↑ the probability that L wins (looses) the R (L) district converge to 0. So both candidate will focus on district M. • Proposition.There is a σ*such that for σ>σ*, a unique well-behaved MME exists. Policies are chosen to maximize M district’s utility: • The MCPF is a martingale.

22. With respect to a PS, there are two differences. • For any b,A, PS induces a higher g. Compare the objective functions in a MMS and PS: • This point was first made in Persson and Tabellini [1999] • A PS, however, is more dynamically inefficient.

23. Proposition.For σ>σ*, a political equilibrium in a MMS converges to a steady state in which g, r are: In a PS, g converges to a stationary distribution, non degenerate with support in:

24. Lets go back to the general case. • In general a MMS may not be Pareto efficient • Let • We have:

25. Proposition. A MMS is Pareto efficient whenever the candidates use the fully symmetric strategies. In general, the inefficiency → to zero as d→0. • The candidate’s problem must solve: • depends on b,A only through: • In a symmetric equilibrium: ΔWj=0 for any b,A,

26. Comparing electoral Systems • If we fix a state A,b and a v, we have a static model: • In this case, PS induces higher g, lower r, higher utilitarian welfare:

27. Consider now the dynamic case with endogenous b. • Proposition 9.There is aω*such that for ω< ω*Eg and Er in the invariant distributions are, respectively, higher and lower in a MMS than in a PS. r t

28. V. Empirical Implications • Our work may contribute an understanding why: • Empirical evidence on electoral rules is mixed; • positive correlation between budget deficits and MMS. • Twoconceptual limitations on the two most common empirical approaches: • Panel datasets: even if the economies are at the steady state, ignoring the dynamic nature of the data process may generate biased findings; • Country studies: cannot fully explain the differences across sovereign countries where public debt may diverge substantially in the long term.

29. VI. Conclusion • We have characterize dynamic model of elections under proportional and majoritarianrules. • We have shown: • PS tend to accumulate more debt than MS • Though politicians may desire higher g under PS, they can afford less g, even in the steady state. • Previous static models focused on what politician desire. • Contrary to static models, policies in dynamic electoral models are not Pareto optimal in any sense.