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

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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 afford only 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 r in 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 I.The model II.The political equilibria: 1.The Proportional System (PS); 2.The Majoritarian Systems: single district (SDS), multiple districts (SMS) III. Comparing electoral systems IV. Empirical implications

I.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. 5

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.

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,s 1,…,s n } The government faces 3 feasibility constraints: Non negative transfers: s i > 0. An upper bound on debt (no Ponzi schemes): 7

8 I.3 A model of electoral politics Electoral competition is modelled a' la Lindbeck and Weibull [1987] as in Persson and Tabellini [1999]. Candidates L, R run 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 linkage between electoral cycles.

I.3.1 Voters Voter ls utility for policy p={r,g,x,s 1,…,s n } 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 L iff: κ j is an ideological preference for party R in district j σ l is idiosyncratic to voter l 9

Both σ j, κ l 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. 10

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.

I.3.2 Vote shares The votes received by L in district j given p L and p R 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. 12

13 I.3.3 Candidates Candidates maximize:, where R is a constant and I i τ 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 short p(b;A,h)).

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

15 Given v, L chooses 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)(A) (B)(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:

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. 18 Expected benefit Expected cost of reducing future pork tranfers.

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

20 Given v, L chooses 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 v i satisfies (B) given p for any i. (A)(A) (B)(B)

21 Lets assume that there are only 3 districts, L, M and R and 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 districts 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 d0. The candidates problem must solve: depends on b,A only through: In a symmetric equilibrium: ΔW j =0 for any b,A,

26 IV.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 a ω * such that for ω< ω * Eg and Er in the invariant distributions are, respectively, higher and lower in a MMS than in a PS. t r

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. Two conceptual 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 majoritarian rules. 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.

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