On the feasibility of unpopular policies under re-election concerns.

• Author: Chiu, Y. Stephen

1. Introduction

   A common concern about political decision making is that re-election motives lead incumbent politicians to select policies that, although popular among the electorate, are inferior to available, less popular alternatives. This concern, reflected in the notions such as demagogy and mob rule, implies that politicians may be penalized for choosing policies that they believe to be the best, but ironically are rewarded for choosing popular policies that they do not necessarily believe to be the best. In this paper, I study this common concern through a series of models. (1)

   For the main model that I will study, politicians differ only in utility from holding office. The main result is that strong re-election motives on the part of the incumbent politicians in general do not render efficient and unpopular policies infeasible. In fact I will show that, under very general conditions, voters' voting decisions do not depend on whether the incumbents have chosen popular policy options, nor are incumbents' policy decisions responsive to policy popularity. We may call this result the irrelevance or neutrality of policy popularity. Note that voters only have limited information, and there is a possibility that the unpopular policy may be superior to its alternatives. Voters would take their policy opinions as tentative and be willing to revise them upon the arrival of new information. Then an incumbent's re-election chances will not deteriorate simply because of her choice of unpopular policies. Foreseeing this, incumbents with even strong re-election motives will not find it beneficial to choose popular but inefficient polices. (2)

   To convey the above ideas, I will examine an infinite horizon political agency model, along the line pioneered by Barro (1973). There are two important ingredients in this model. First, politicians are of two types: strong and weak. Both types of politicians are concerned about both social welfare and the utility gained from holding office, whereas the strong type puts a smaller weight on the latter. Each politician's type is the politician's private information. If the politicians were homogeneous, the choice between different incumbents would be inconsequential. If their heterogeneity were public information, voters would not need the politicians' past records to infer their preferred future policies. In either case, the question of policy manipulation would no longer exist. (In section 6, I will introduce a third type of politicians.)

   The second ingredient is a proper modelling of "a policy that could be unpopular but potentially superior." A policy is popular when more voters think that the policy will yield a welfare greater than those of its alternatives. Such a policy's "popularity" reflects its ex ante efficiency as perceived by the electorate. The incumbent politician, nevertheless, observes an additional imperfect-information signal about the likely efficacy of the policy. (3) Therefore, a popular policy might be interim inefficient, whereas an unpopular policy might be interim efficient.

   One crucial assumption for the policy popularity irrelevance result is that the only difference among politicians is their utility derived from holding office. This suggests that for policy popularity to be relevant, other sorts of heterogeneity among politicians are needed. Suppose, for instance, that the public believes with some probability that the incumbent is ignorant in the sense that she knows about different policy options even less than the public does. Then a choice of an unpopular policy might signal the incumbent's ignorance; an incumbent who is informed but with a strong re-election motive might then reject the unpopular policy even if it is interim efficient.

   The rest of the paper is organized as follows. Section 2 introduces the model. Section 3 prepares preliminaries for later sections. Section 4 establishes the efficient perfect Bayesian equilibrium under the assumption that voters vote for the candidate who has a greater probability of being strong. It also discusses the issue of equilibrium uniqueness. Section 5 argues that the basic efficiency result holds in several extensions of the basic model. Section 6 discusses an extension in which there are three types of politicians. This section qualifies my basic efficiency result. Section 7 contains some concluding remarks.

2. Model

   I use a political agency approach pioneered by Barro (1973) and Ferejohn (1986) and later developed by Austen-Smith and Banks (1989), Banks and Sundaran (1993), and Coate and Morris (1995). In particular, the model presented here closely resembles that of Coate and Morris in the way that informational characteristics about the policy are modeled. I use an infinite horizon model: In each period, the incumbent politician must decide whether to implement a policy or to maintain the status quo. The policy's outcome is uncertain and voters have only limited information about the policy's efficacy. At the end of the period, upon the revelation of the policy outcome, an election between the incumbent and a challenger is held. The winner will become the next period's office holder and will face a policy decision and an election as did the immediate predecessor.

   Voters

   There is a continuum of infinitely living citizens among whom is a median voter, whose interest coincides with social welfare. As will subsequently become clear, the median voter's preferences dictate the election outcome. (4) Among the citizens is also an incumbent. All agents in the model are risk neutral. In each period t, the current period social welfare, [w.sub.t], is defined as the sum of the income of citizens. Normalizing the measure of citizens to one and assuming all agents discount future payoffs with the common discount factor [delta], the discounted social welfare (the same as the median voter's discounted payoff) measured at period t is thus [[sigma].sup.[infinity].sub.t'=t] [[delta].sup.t'-t][w.sub.t'].

   Policy Choices

   In each period t, an observable choice between the status quo and an alternative policy, which can differ from period to period, is required for the incumbent politician. The status quo payoff is deterministic and equals zero, whereas the alternative policy payoff, which is revealed immediately before the election, is stochastic and takes the value of either [W.sub.tG] (for a good outcome) or [W.sub.tB] (for a bad outcome), where [W.sub.tG] > 0 > [W.sub.tB]. At the beginning of period t, nature chooses between a high-yield state and a low-yield state with probabilities [[PHI].sub.t] and 1 - [[PHI].sub.t], respectively. In case of the high-yield (low-yield) state, nature chooses between the good outcome and bad outcome with probabilities [[theta].sub.tH] and 1 - [[theta].sub.tH] (probabilities [[theta].sub.tL] and 1 - [[theta].sub.tL], where [[theta].sub.tH] > [[theta].sub.tL]), respectively. Although these probabilities and the values of [W.sub.tg] and [W.sub.tB] are commonly known, the realized state is know n only to the incumbent. Because of this, voters are never certain whether the incumbent has chosen efficiently. Define [W.sub.tH] [equivalent to] [[theta].sub.tH][W.sub.tG] + (1 - [[theta].sub.tH])[W.sub.tB] and [W.sub.tL] [equivalent to] [[theta].sub.tL][W.sub.tG] + (1 - [[theta].sub.tL])[W.sub.tB] as the expected payoff from the policy given the state is high yield and low yield, respectively. To be economically interesting. I assume that [W.sub.tH] > 0 and [W.sub.tL] < 0 for all t.

   DEFINITION 2.1. The policy at time t is popular if [[PHI].sub.t] [greater than or equal to] [[PHI].sub.t] where [[PHI].sub.t] is defined by [[PHI].sub.t][W.sub.tH] + (1 - [[PHI].sub.t])[W.sub.tL] = 0. In other words, the policy is popular if and only if it is ex ante efficient. The policy is unpopular if it is not popular. In addition, the policy is interim efficient if the economic state is high yield.

   Therefore, a policy can be popular but interim inefficient, and can be unpopular but interim efficient.

   Politicians

   Each politician can be either strong or weak, and the type is the politician's private information. The current period utility of a type i politician at period t is [w.sub.t] if she is not in office, and [w.sub.t] + [k.sub.i] if she is in office, i = S. W. In the above stipulation, [w.sub.t] is the social welfare of period t and [k.sub.i] is the politician's utility derived from holding office where 0 [less than or equal to] [k.sub.s] < [k.sub.w]. Therefore, the objective of a politician of type i, i S, W, at time t is to maximize the expected value of [summation over ([infinity]/t'=t)] [[delta].sup.t'-t][[p.sub.t'][k.sub.i] + [w.sub.t'] where [p.sub.t'] is the (endogenously determined) probability of being in office at time t'. The preferences of each type of politician are commonly known. Denote by [[lambda].sub.t] the prior probability that the incumbent in period t is strong. The parameter [[lambda].sub.1] is chosen by nature, whereas the determination of [[lambda].sub.t], t = 2, 3, ... will be explained later.

   Election

   At the end of each period t, an election takes place in which the incumbent is matched with a random challenger whose probability of being strong is drawn from a cumulative function [M.sub.t]([[micro].sub.t]). Each voter chooses either the incumbent or the challenger. The one who receives more votes will be the incumbent in the next period. Since there are two candidates only, the single peakedness condition of preferences (defined over the two candidates) trivially holds. Therefore, the median voter's preferences will dictate the election outcome. I assume that the median voter will use the voting strategy that the politician with a greater probability of being strong is selected. (5) This voting strategy is natural since the median voter's preferences coincide with that of social welfare, and a strong politician cares relatively more about social welfare than a weak...