WORKING PAPERS Col·lecció “DOCUMENTS DE TREBALL DEL DEPARTAMENT D’ECONOMIA” “A Political Agency Model of Coattail Voting” Galina Zudenkova Document de treball nº -21- 2010 DEPARTAMENT D’ECONOMIA Facultat de Ciències Econòmiques i Empresarials Edita: Departament d’Economia http://www.fcee.urv.es/departaments/economia/public_html/index.html Universitat Rovira i Virgili Facultat de Ciències Econòmiques i Empresarials Avgda. de la Universitat, 1 432004 Reus Tel. +34 977 759 811 Fax +34 977 300 661 Dirigir comentaris al Departament d’Economia. Dipòsit Legal: T – 2017 - 2010 ISSN 1988 - 0812 DEPARTAMENT D’ECONOMIA Facultat de Ciències Econòmiques i Empresarials A Political Agency Model of Coattail Voting Galina Zudenkovaa,b,y a b Department of Economics, Universitat Rovira i Virgili Department of Economics, Universidad Carlos III de Madrid December 15, 2010 Abstract In this paper, I provide a formal justi…cation for a well-established coattail e¤ect, when a popular candidate at one branch of government attracts votes to candidates from the same political party for other branches of government. A political agency framework with moral hazard is applied to analyze coattails in simultaneous presidential and congressional elections. I show that coattail voting is a natural outcome of the optimal reelection scheme adopted by a representative voter to motivate politicians’e¤orts in a retrospective voting environment. I assume that an o¢ ce-motivated politician (executive or congressman) prefers her counterpart to be a¢ liated with the same political party. This correlation of incentives leads the voter to adopt a joint performance evaluation rule, which is conditioned on the politicians belonging to the same party or di¤erent parties. The two-sided coattail e¤ects then arise. On the one hand, the executive’ sucs cess/failure props up/drags down her partisan ally in congressional election, which implies presidential coattails. On the other hand, the executive’ reelection itself is a¤ected by s the congressman’ performance, which results in reverse coattails. s JEL classi…cation: D72, D86. Keywords: Coattail voting; Presidential coattails; Reverse coattails; Simultaneous elections; Political Agency; Retrospective voting. The author is grateful to Luis Corchón, Raquel Fernández, M.A. de Frutos, Ignacio Ortuño, two anonymous referees and Kai Konrad, the editor, for helpful comments, suggestions and encouragement. The author also thanks Nikolay Archak, David Austen-Smith, Carmen Beviá, Anna Bogomolnaia, Antonio Cabrales, Micael Castanheira, Jacques Crémer, Mikhail Drugov, François Maniquet, Diego Moreno, Rebecca Morton, António Osório-Costa, Nicola Persico, Maria Petrova, James Snyder and seminar and conference participants at several institutions for useful comments and suggestions. The FPI Grant BES-2005-10017 and project ECO2008-02738 of the Spanish Ministry of Science and Innovation are gratefully acknowledged. The usual disclaimer applies. y Department of Economics, Facultat CCEE, Universitat Rovira i Virgili, Av. de la Universitat 1, Reus 43204, Spain. E-mail address: galina.zudenkova@gmail.com. 1. Introduction The coattail e¤ect is de…ned as the tendency of a popular candidate at one level of government to attract votes to candidates from the same political party for other levels of government. The presidential coattails, when the congressional voting decision is a¤ected by the executive’ performance, have been a topic of frequent study in the empirical literature (see Miller s 1955, Press 1958, Kaplowitz 1971, Calvert and Ferejohn 1983, Campbell 1986, Campbell and Sumners 1990, Flemming 1995, Cohen et al. 2000, Mattei and Glasgow 2005, Gélineau and Remmer 2006, Golder 2006, among many others). Other studies have reported evidence of reverse coattails, when popular lower-tier candidates prop up their parties’ candidates for higher levels of government (see Ames 1994, Samuels 2000a, Samuels 2000b).1 While a number of studies have identi…ed and measured coattails, "there remains a great deal of uncertainty concerning the causal mechanism responsible for these e¤ects."2 Mondak and McCurley (1994) suggest that the coattails arise mainly due to "voters’ reliance on a speci…c cognitive e¢ ciency mechanism" and test this claim empirically at the individual voter level.3 There is however no formal model of coattail voting, to the best of my knowledge. In this paper, I explain coattail e¤ects within a retrospective voting model (i.e., a political agency model with moral hazard). In my framework, coattail voting arises as an outcome of the optimal implicit reward scheme voters use to induce politicians’e¤orts. I consider a representative voter that has to elect an executive and congressman in simultaneous elections. The politicians want to be reelected, and are held accountable for their performance at the moment of election. The politicians therefore have incentives to satisfy the voter’ wishes. In addition, I assume that the politicians are loyal to their respective s political parties: the executive prefers her partisan ally to win in congressional election, and vice versa.4 Hence, the incentives of the executive and congressman are correlated. The 1 The cited works provide evidence of reverse coattails in Brazil. Broockman (2009) however found no evidence of reverse coattails in congressional district-level data from the US presidential elections between 1952 and 2004. 2 See Hogan (2005), p. 587. 3 See Mondak and McCurley (1994), p. 151. 4 Fox and Van Weelden (2010) and Brollo and Nannicini (2010) introduce similar assumptions about the partisan preferences of the legislature and the executive, respectively. In particular, in Fox and Van Weelden’ s career concerns setup the legislature ("overseer") can care about the executive’ reputation. For example, s a partisan overseer may seek to damage the reputation of an executive from the other party while seeking to protect the reputation of an executive from his own party. In turn, Brollo and Nannicini (2010) assume that an executive wants to maximize "the political capital represented by aligned mayors," by increasing the likelihood that a municipality is run by a mayor aligned with the central government. 2 voter cares about the politicians’ performances, which are observable but not contractible. The voter evaluates the incumbents’performance and votes accordingly. More precisely, the voter employs implicit evaluation rules when deciding whether to reward (reelect) politicians. Obviously, the voter can in‡ uence the politicians’behavior through the choice of evaluation rules. I restrict the space of possible evaluation rules to linear functions of performance. I show that given the correlation between the two politicians’incentives, the voter is better o¤ adopting a joint performance evaluation rule (conditioned on the incumbents belonging to the same party or di¤erent parties) rather than an individual politician performance evaluation rule. In particular, the voter evaluates the performance of the executive and congressman from the same party as a team. If the executive and congressman belong to di¤erent parties, then the voter compares their performances to create a competitive environment. This combination of coattail voting rules implies that improved performance increases a politician’ own s reelection probability, while increasing/decreasing the reelection probability of her partisan ally/rival in the other o¢ ce. Politicians therefore have extra incentives to perform better, for the sake of their party as well as for themselves. In equilibrium, the reelection outcomes of incumbents from the same party are therefore positively correlated: the voter tends to reward/punish one incumbent for the good/poor performance of the other incumbent. The two-sided coattail e¤ects therefore arise. On the one hand, the executive’ performance a¤ects the congressman’ reelection that gives rise to s s presidential coattails. On the other hand, the executive’ reelection itself depends on the s congressman’ performance that results in reverse coattail e¤ect. s The equilibrium reelection outcomes of incumbents from di¤erent parties are negatively correlated: the voter is more likely to punish one incumbent the better the performance of the other incumbent. In particular, the executive’ good performance drags down the incums bent congressman’ reelection chances and therefore props up the executive’ partisan ally in s s congressional election, which implies presidential coattails. In turn, the congressman’ sucs cess relegates the executive’ reelection and thus promotes for presidential o¢ ce a candidate s partisanly aligned with the congressman. As a result, the reverse coattails arise. These results rest on the assumption of politicians’partisan alignment; that is, I assumed that an executive/congressman prefers their partisan ally to win in the other election. The coattail voting rules then serve as an extra tool to discipline the politicians. If I relax the assumption of partisan alignment, this e¤ect vanishes and the voter no longer evaluates incumbents jointly. Instead the voter uses a cut-o¤ rule that each incumbent is reappointed only when her individual performance exceeds a critical threshold. There is no coattail e¤ect then. 3 I turn now to the fundamental question of why political process is modeled as political agency. In addition to a sound theoretical framework, this approach has received considerable empirical support (see, for example, Peltzman 1992 and Besley and Case 1995a, 1995b, 2003). Besley (2006) provides an excellent introduction to political agency models and "emphasizes the empirical potential of these models in explaining real world policy choices."5 In a recent article in the New York Times, Glaeser points out that the "president ... is both our leader and our employee. We (the voters) chose him, our taxes pay his salary, and we can …re him in four years."6 The political agency approach may therefore be appropriate to model political interactions between politicians and voters. Even so, elected politicians can only be o¤ered implicit incentive schemes; public policies are di¢ cult to reward with explicit contracts. The retrospective voting model I use goes back to Barro (1973). Ferejohn (1986) extended the model and studied subgame-perfect equilibria rather than Nash equilibria. Persson et al. (1997) use a retrospective voting approach to study rent extraction. In Austen-Smith and Banks (1989) voters adopt retrospective voting strategies that are conditioned on the di¤erence between the incumbent’ performance and her initial policy platform. Banks and s Sundaram (1993, 1996) analyze retrospective voting settings with both moral hazard and adverse selection, and with term limits respectively. The results of this paper are also related to the literature on horizontal and vertical intergovernmental competition. Most analyses of horizontal competition are based on the assumption of interjurisdictional mobility of consumers, à la Tiebout (1956). In a similar vein, the literature on yardstick competition between jurisdictions started with the seminal work of Salmon (1987), to be followed by Besley and Case (1995a), Bordignon et al. (2004), SandZantman (2004), Belle‡ amme and Hindriks (2005), Besley and Smart (2007) and others. The main assumption of this literature is that under decentralization, voters use a comparative performance evaluation between di¤erent local governments to create yardstick competition. The vertical competition literature, on the other hand, assumes that "senior and junior governments provide similar or comparable services, and that o¢ ce-holders in the government which is judged by citizens to be the more e¢ cient supplier will increase their probability of getting the vote of these citizens"7 (see Breton 1996, Breton and Fraschini 2003, Breton and Salmon 2001, Volden 2005 and Volden 2007). I follow these authors in assuming that voters compare the performance of local and regional governments, and are likely to reward the 5 6 Besley (2006), p. 3. Edward L. Glaeser "Lower (and More Realistic) Presidential Expectations," January 20, 2009. Available online at http://economix.blogs.nytimes.com/2009/01/20/lower-and-more-realistic-presidential-expectations/ (accessed December 1, 2010). 7 Breton and Salmon (2001), p. 139. 4 more e¢ cient politicians with reelection. There is, however, an important di¤erence between my research and the papers just cited. In the intergovernmental competition literature, the comparative performance evaluation result is driven by either correlated shocks or interjurisdictional spillover. In my model, the joint performance evaluation arises from the fact that the politicians’ incentives are correlated: each one cares not only about her own reelection prospects, but also about the success of other politicians a¢ liated with the same political party. The remainder of the paper is organized as follows. Section 2 lays out a model. Section 3 proceeds with the formal analysis. Finally, Section 4 concludes. 2. Model Consider a representative voter that has to elect executive E and congressman C in simultaneous elections. Politicians running for both o¢ ces belong to one of the two political parties. I assume that there is exactly one candidate from each party– the incumbent and an opponent– each election. The opponents are identical to the incumbents in all respects in except party label. There is no ideological heterogeneity in politicians’ preferences.8 The participation constraints of the politicians are always satis…ed. unobservable e¤ort ai . The set of e¤orts available to each politician is taken to be a nondegenerate interval [0; a] with an independent and unobservable noise "i : pi = ai + "i ; with "i 8 While in o¢ ce, each politician i 2 fE; Cg has to implement a policy determined by her R. I assume that the performance of politician i, pi , is observed N 0; 2 .9,10,11 Since there is no ideological component it is convenient to consider a single representative voter in this framework. 9 I have an extended version of the model, available upon request, where the two noise terms "E and "C are correlated and follow a bivariate normal distribution. I want to concentrate however on the case where the voter introduces joint performance evaluation due to the correlation between politicians’incentives rather than the correlation between shocks. The latter topic has been widely studied in the context of team evaluation in contract theory (for an overview, see Bolton and Dewatripont 2005) and in the literature on yardstick competition (see the references on yardstick competition in the Introduction). 10 One can assume that policy outcomes are determined by e¤ort and ability (rather than by e¤ort and noise). The results are qualitatively the same if politicians choose e¤orts before knowing their abilities. Otherwise, one has to solve an asymmetric information model. I leave this extension for future research. 11 Alternatively, the voter might not be able to distinguish between the politicians’ performances, and 5 The reward of politician i is denoted by convex cost function a2 12 i 2 . i (ai ). E¤ort is costly, and I assume the standard The executive and congressman independently choose e¤ort levels ai to maximize their utility, which is given by i (ai ) a2 i : 2 The function i (ai ) will be explicitly de…ned in subsection 2.1. The voter cares about the politicians’performances according to a linear utility function pE + pC : I assume that the voter applies retrospective reappointment rules to reelect the incumbents, i.e., she bases the reappointment decision on the politicians’performances pE and pC . Denote by executive E and congressman C are members of the same party, and where E and C are a¢ liated with di¤erent parties. This is a sequential political agency game between politicians (the executive and congressman) and a representative voter. The timing of events is as follows. First, the incumbents are drawn randomly, and state reappointment rules to be used in the coming elections. Third, the politicians exert e¤orts aE and aC . Finally, nature chooses noises "E and "C , and the politicians’performances pE and pC are observed. Both elections take place simultaneously and the voter applies the selected reappointment rules to reward or punish the incumbents.13 In the following subsection I describe the politicians’preferences. I will then turn to the voter’ problem and de…ne an equilibrium concept. s 2.1. Politicians The politicians’ preferences are as follows. First, executive E and congressman C want to be reelected. Moreover, E wants to improve her party’ representation in legislature. If C s and E belong to the same party, then E prefers C to be reelected. Otherwise, E wants a therefore observes just their aggregate performance p = aE + aC + ". In that case the politicians would face a free-riding problem, as each of them contributes a costly e¤ort to an aggregate output. I leave the analysis of that alternative framework for future research. 12 I have an extended version of the model, available upon request, where the cost of policy implementation for the executive and congressman from the same party is di¤erent than for the politicians from rival parties (e.g., because of synergy). The results of this extended model are qualitatively the same. 13 This model can be extended to several periods. I want to concentrate however on voter’ motives for s coattail voting rather than on dynamic political agency. A static model su¢ ces this task. 2 fS; Dg the state variable. Then = S corresponds to the case where = D to the case 2 fS; Dg is realized. Second, the voter commits to the 6 new congressman (from her own party) to be elected for the next term. Likewise, C wants to improve his party’ chances to win the presidential election. Thus, C wants E to be reelected s if they are members of the same party, and wants the opponent to be appointed if E is from the rival party. The value of holding o¢ ce is normalized to 1. The values, which E and C associate to their parties’winning the other elections, are denoted by politician i has the following reward function 8 < Pri (ai ; aj ) + : Pri (ai ; aj ) + E and C respectively. Furthermore, denote by Pri ( ) the probability of winning election i 2 fE; Cg. Therefore, i both politicians’e¤orts: : [0; a]2 ! R that depends continuously on (ai ; aj ) if =S = D; i (ai ; aj ; )= i Prj i (1 Prj (ai ; aj )) if where i; j 2 fE; Cg and j 6= i. The preferences stated above re‡ the politicians’allegiance ect to their respective parties; individual politicians care about their party’ overall representation s in executive and legislative branches of government, not just their own reelection prospects.14 Still, the reasonable assumption here is that a politician values her own o¢ ce more than her party’ representation in the other o¢ ce; i.e., 0 s i 1.15 I call i the degree of politician i’ loyalty to her party (or the strength of her partisan s 2.2. Representative Voter alignment).16 The politicians’performances pE and pC (but not their composition between e¤ort and noise) are observed but are not contractible. Public policies are di¢ cult to reward with explicit contracts. It is more natural to use implicit incentive contracting in this situation. The voter observes politicians’ performances pE and pC , and in the elections rewards incumbents according to their performances; i.e., the voter reappoints incumbents who have shown "good" results. In case an incumbent is thrown out of o¢ ce, an opponent from the rival party is elected. 14 Alternatively, the stated preferences could arise because the executive and congressman have to interact while in o¢ ce. Each prefers working with a member of her own party rather than a rival. 15 In other words, politician i does not mind reducing her reelection chances by 1% in exchange for increasing her ally’ election probability by 1i % 1%. s 16 I have an extended version of the model, available upon request, where the strength of partisan alignment i might vary across states. If there is some preference for incumbents over unknown candidates, then S i S i D i . (This case re‡ ects the idea that an executive/congressman might prefer an incumbent ally to an unknown ally for the other o¢ ce.) If politicians prefer newcomers, then qualitatively the same. < D i . (In this case an executive/congressman would like a new ally (a newcomer) to be elected for the other o¢ ce.) The results of this extended model are 7 Obviously the voter can in‡ uence the politicians’behavior through the choice of evaluation rules. Intuitively, since politicians care about each others’reelection chances, the reward rules should allow for joint performance evaluation. Under joint performance evaluation the voter conditions politician i’ reelection on her own performance pi (giving her an incentive to s perform well since she wants to be reelected) and on the performance pj of politician j (giving an incentive to politician j since he cares about i’ reelection chances). s I restrict the functional space of performance evaluation rules to linear joint evaluation rules ( E; E ; bE ) and ( 2 R, j C ; bC ). E and C are the slopes of the executive’ and congressman’ s s performance evaluation rules respectively, while bE and bC are the corresponding intercepts; C ; bE ; bC reelected for o¢ ce i is E Cj 1.17 Under rules ( i ; bi ), i 2 fE; Cg, the probability of being P ri (ai ; aj ) = P (fpi (ai ) + i pj (aj ) bi g) with i; j 2 fE; Cg and j 6= i. Figure 1 depicts the possible outcomes for E and C under rules ( pC + not. Note that under linear rules ( bE "C + aE C "E E aC , E ; bE ) E ; bE ) and ( C ; bC ) in the two-dimensional space of observed performances pE and 1, so that line pE + E pC pC . Note that I require j C pE = bC . Otherwise, as one can see from Figure 1, an executive and congressman E Cj = bE is steeper than line with poor performance would be reelected while politicians with better performance would and ( C ; bC ), E 1+ 2 2 E C "E is reelected when "E + 2 C 2 E "C where "E + aC E "C N 0; . In turn, C is reelected when . I say that the = 0, positively correlated when C bC C aE , where "C + E N 0; 1 + C two reelection events are independent when E = 0 and E > 0 and C > 0, and negatively correlated when < 0 and < 0. Throughout the rest of the paper, I use F to denote the normal distribution function and f for the corresponding density. 2.3. Equilibrium Concept I search for a subgame perfect equilibrium by analyzing the game backwards. First, I solve for the politicians’e¤orts aE and aC under rules ( I examine the voter’ choice of evaluation rules s what follows I introduce two de…nitions. 17 E ; bE ) and ( C ; bC ) in each state . Second, for each state . In E ; bE and C ; bC The linear evaluation rules allow for a closed-form solution in this framework. I leave the analysis of general evaluation rules for future research. 8 Given linear performance evaluation rules ( strategies is a pro…le of e¤orts aE ; aC ai ; aj ; ai 2 2 E ; bE ) and ( C ; bC ), the equilibrium in e¤ort such that ai ; aj ; a2 i for each ai 2 [0; a] ; 2 E ; bE ; E ; bE ; C ; bC i i where i; j 2 fE; Cg, i 6= j. I de…ne an equilibrium in rule strategies as the tuple E ; bE ; C ; bC such that ( E ; bE ; C ; bC ) ; aE +aC E ; bE ; C ; bC = E ;bE ; C ;bC max aE ( C ; bC )+aC j E Cj 1 where aE ( ) ; aC ( ) is an equilibrium in e¤ort strategies. 2.4. Intuition Before proceeding with the formal analysis, I provide some intuitive considerations. The incumbents care about reelection chances of each other, which provides the voter with an additional tool to discipline them. The voter uses then joint performance evaluation to increase the politicians’accountability. Intuitively, the voter rewards an incumbent from one branch of government not only for her own performance but also for the performance of the incumbent from the other branch of government. That joint evaluation gives extra incentives for the latter incumbent to perform better since he cares about the reelection prospects of the former incumbent. Such an evaluation strategy of the voter leads to coattail e¤ects. Intuitively, the executive wants a congressman from the same party to be elected. An executive thus will perform better if her own performance increases the reelection chances of the allied incumbent congressman, while decreases those of the rival incumbent congressman. The voter uses this correlation of incentives and rewards (reelects) the incumbent congressman for the good executive’ s performance if the politicians are members of the same party. She however punishes the incumbent congressman for the good executive’ performance if the politicians are a¢ liated s with di¤erent parties. In this case, an opponent candidate (exactly from the same party as the executive) is elected in congressional election. Note that the presidential coattails arise here. The good performance of the incumbent executive leads not only to her own reelection but also to the election of a congressman from the same party, who "rides on the executive’ s coattails". If the incumbent executive shows poor performance in o¢ ce her reelection chances decrease, likewise the election chances of a congressman from the same party. In this case there is a negative presidential coattail e¤ect. 9 The same intuition (in reverse) works to show the emergence of reverse coattail e¤ect. Since the congressman wants his partisan ally to be elected for presidential o¢ ce, he has extra incentives to exert higher e¤ort if the reelection chances of the allied executive increase, while those of the rival executive decrease, with his performance. The voter knows this and is more likely to reelect the incumbent executive a¢ liated with the same party as the congressman, if the congressman performs well. If the incumbents belong to di¤erent parties, then the voter tends to punish the incumbent executive for the good congressman’ performance, which s leads to the election of a challenger (a¢ liated with the same party as the congressman) for presidential o¢ ce. The executive thus may bene…t or su¤er from a reverse coattail e¤ect because her reelection is a¤ected by the congressman’ performance. The good congressman’ s s performance props up, while the poor drags down, a candidate from the same political party for presidential o¢ ce. Note that the coattail e¤ects arise because of the correlation of politicians’ incentives such that each politician prefers her partisan ally to win the other election. Relaxing this assumption results in no coattail e¤ect prediction. Indeed, if politicians just care about their own reelection the voter will reward them only for their own performance. So no coattail voting arises. 3. Analysis In this section I analyze the game backwards to …nd a subgame perfect equilibrium. First, I characterize an equilibrium in e¤ort strategies, and then an equilibrium in rule strategies. 3.1. Equilibrium in E¤ort Strategies Let the voter use evaluation rules ( i ; bi ), i; j 2 fE; Cg. Under these rules the politician i’ s i (ai ; aj ; utility is ) 8 < P (fpi (ai ) + : P (fpi (ai ) + a2 i = 2 j pi (ai ) i pj i pj (aj ) (aj ) bi g) + bi g) + iP i pj (aj ) + P bj bj a2 i 2 a2 i 2 if if =S = D: 1 pj (aj ) + j pi (ai ) Politician i chooses e¤ort ai before observing realization of the noise, and takes the voter’ s expectations as given. The proposition below establishes the existence of an equilibrium in e¤ort strategies. Continuity properties of the politicians’ best response functions and Brouwer’ Fixed Point Theorem are used to provide the result. Proofs of this and other s propositions are given in the Appendix. 10 Proposition 1. Under linear performance evaluation rules ( 1, there exists an equilibrium in e¤ort strategies aE ; aC ditions are satis…ed: 8 > f0 ai < "i + i "j bi > : 0 f"i + i "j E ; bE ) and ( C ; bC ) if the following second-order con- with j E Cj i aj i aj 2 0 i j f"j + j "i bj bj aj aj j ai j ai 1 < 0 if 1 < 0 if =S (3.1) = D; bi ai + 2 i j f"j + j "i where i; j 2 fE; Cg, i 6= j. This equilibrium is de…ned implicitly by 8 > f" + " bi a aj ai = 0 if < i i j i aj + i j f"j + j "i bj j ai i > : f"i + i "j =S = D: bi ai i aj i j f"j + j "i bj aj j ai ai = 0 if Figure 2 depicts the politicians’ best response functions in states S and D for three scenarios: independent reelection outcomes with correlated reelection outcomes with reelection outcomes with E E E C = 0 and C = 0 (black), positively > 0 and C > 0 (red), and negatively correlated < 0 and < 0 (blue), while bE and bC are …xed. Note that for independent reelection outcomes (black) the best responses are ‡ in both states at (since each politician’ reelection depends only on her own e¤ort). For positively correlated s reelection outcomes (red) the best responses shift upwards if the politicians are members of the same party ( = S) and downwards if the politicians are a¢ liated with di¤erent parties ( = D). Intuitively, under positively correlated reelections a politician has extra incentive to exert e¤ort if if = S (to increase her partisan ally’ reelection chances) and less incentive s = D (to avoid helping her partisan rival get reelected). Finally, for negatively correlated reelection outcomes (blue) the best responses shift downwards if the politicians belong to the same party ( = S) and upwards if the politicians are a¢ liated to rival parties ( = D). In this scenario a politician does not want to damage her partisan ally’ reelection prospects, so s exerts a lower e¤ort if = S. However, if = D she has extra incentive to work harder and reduce her partisan rival’ reelection chances. s Note that under positively correlated reelection outcomes there is a free-riding e¤ect between partisan allies ( = S). Intuitively, politician i might prefer to exert a lower e¤ort (and reduce e¤ort cost) if her partisan ally j is performing well enough to improve her reelection prospects. In fact, she "rides on the other incumbent’ coattails". s 3.2. Equilibrium in Rule Strategies Turn now to the voter’ choice of evaluation rules ( s with respect to E, E ; bE ) and ( C ; bC ). Maximizing aE + aC E ; bE ; C ; bC bE , C and bC yields an equilibrium in rule strategies . I summarize the results in the following proposition. 11 Proposition 2. There exists an equilibrium in rule strategies 8 > < > : j ; ai E ; bE ; C ; bC given by + j aj j aj if if =S (3.2) = D; i ; bi = j ; ai where i; j 2 fE; Cg, i 6= j. The politicians’equilibrium e¤orts ai in each state are equal to 0 1 2 1 1 @ A: q +q i (3.3) ai = p 2 2 2 1+ 1+ j i It is important to mention that the second-order conditions (3.1) hold for E ; bE ; C ; bC . The equilibrium in e¤ort strategies in Subsection 3.1 is therefore well de…ned. The voter is rational, so she realizes that the only alternative to reelecting incumbents is voting for opponents from rival parties. The politicians’performances are additively separable in e¤ort and noise, and all politicians behave in the same way irrespective of the noise. If elected, opponent i will exert equilibrium e¤ort ai , which maximizes her expected utility. Thus, the voter compares the incumbents’performances with their opponents’expected performances and votes accordingly. That is why in equilibrium bi = ai + i aj : j According to Proposition 2, if politician j is loyal to his political party (i.e., to o¢ ce i under this rule is equal to 8 n > P pi (ai ) + < P ri (ai ; aj ; ) = n > : P pi (ai ) voter adopts a coattail voting rule to reelect politician i. The probability of being reelected o o 6= 0), the j pj (aj ) j pj ai + ai j aj j aj if if =S = D: (aj ) Intuitively, the incentives of an executive and congressman are correlated, because they care about the overall representation of their party at both branches of government. The voter therefore rewards politicians jointly rather than separately. If the politicians belong to the same political party ( performance of politician j ( = S), then the voter uses a coattail voting rule under which the reelection of politician i is positively correlated with the i > 0). As a result, the voter evaluates the performance of the politicians from the same party as a team and tends to reward the incumbents from a well-performing party while punish the incumbents from a badly-performing party. However, if the politicians belong to di¤erent parties ( 12 = D), the voter uses a coattail voting rule under which the reelection of politician i is negatively correlated with the performance of politician j ( i < 0). As a result, the voter compares the performance of one politician to that of the other, creating a competitive environment between the parties. In this scenario the voter tends to reward the incumbent from the better-performing party, while punishing the incumbent from the worse-performing party. In sum, due to the correlation between the executive’ and congressman’ incentives such that they care about their party chances s of holding o¢ ce, the voter is better o¤ adopting party performance evaluation rather than individual performance evaluation. This leads to two-sided coattail e¤ects. On the one hand, the executive’ good pers formance props up, while the poor drags down, the congressman candidate from the same party. The presidential coattails arise then. On the other hand, the executive’ own reelecs tion depends on the congressman’ performance, which gives rise to a reverse coattail e¤ect. s Indeed, the successful performance of the congressman advances the election of his partisan for presidential o¢ ce, while the congressman’ failures cut it down. s Note that the intensity of coattail e¤ects depends on the strength of politicians’partisan alignment. The more loyal the executive is to her political party (the higher (positively if = S or negatively if E is), the more correlated the optimal reward scheme for the congressman is with the executive’ performance s = D). The more intense therefore the presidential coattail e¤ect. Analogically, the greater the partisan alignment of the congressman (the higher C is), the more correlated the executive’ reelection is with the congressman’ performance. s s If the politicians care equally about their own reelection chances and their party’ election s So the stronger the reverse coattail e¤ect. chances, then the best reward scheme are perfectly correlated: the incumbents from the same party are always reelected or dismissed together; as for the incumbents from di¤erent parties, reelection of one implies dismissal of the other. The less loyal the politicians are to their political parties, the less correlated their incentives. As a result, the voter adopts the less correlated reelection rules in equilibrium, and the coattail e¤ects lessen. If politician j is not at all loyal to his political party ( j = 0), then the optimal rule to reappoint politician i is a simple cut-o¤ rule: she is reappointed only if her observed performance exceeds a critical threshold given by the equilibrium e¤ort for this o¢ ce. That is, the probability of being reelected to o¢ ce i depends only on the performance in this o¢ ce: P ri (ai ) = P (fpi (ai ) ai g) : 13 Intuitively, when politicians care only about their own reelection prospects, the voter is better o¤ rewarding politician’ individual performance rather than the party’ performance. So s s coattail e¤ects vanish. Indeed, if an executive cares only about her own reelection ( coattail e¤ect disappears. In turn, the performance of a non-partisan congressman ( incumbent congressman cares only about his own reelection prospects. How do the equilibrium e¤orts ai in (3.3) depend on parameters’ values? First, larger variance of noise 2 E = 0) = 0) then her performance does not a¤ect the congressman’ reelection chances, and a presidential s C has no impact on the executive’ reelection. So a reverse coattail e¤ect does not arise if the s decreases the politicians’ e¤orts. Intuitively, more randomness in the is strength- observed performances pE and pC makes the reelection probabilities less sensitive to e¤ort, reducing the politicians’incentives. Second, if politician i’ partisan alignment s i ened, the equilibrium e¤ort of politician i, ai increases while that of politician j, aj decreases. Intuitively, the more politician i cares about her ally’ appointment to o¢ ce j, the more ins centives she has to perform better. However, this weakens politician j’ incentives to exert s e¤ort, because his reelection becomes less sensitive to his own e¤ort. Note that the partisan executive and congressman exert the same equilibrium e¤ort as the politicians from di¤erent parties. The reason is that the politicians’preferences are symmetric across the states. The voter adopts therefore symmetric strategies, and the politicians exert the same equilibrium e¤ort regardless of the state. 3.3. Equilibrium Election Probabilities In this subsection I calculate the equilibrium probabilities of election of partisanly aligned candidates and election of candidates a¢ liates with di¤erent parties. Denote by P probability that the candidates from the same party are elected in state , and by P following result. Proposition 3. The equilibrium probability of election of the partisanly aligned candidates is given by P S S D the the probability that the candidates from di¤erent parties are elected in state . I establish the = 1 1 + (arctan 2 E + arctan C) , 2 fS; Dg . The equilibrium probability of election of the candidates a¢ liated with di¤erent parties is given by P D = 1 2 1 (arctan E + arctan C) , 2 fS; Dg , where arctan ( ) is the arctangent function. 14 Note that independently of the incumbents’ party labels, the election of partisan candidates is more likely than that of candidates a¢ liated with di¤erent political parties. Indeed, the probability of election of candidates from di¤erent parties is never greater than 1 : 2 P D 1 2 0; 2 . Intuitively, if the politicians belong to the same party ( = S), the voter adopts a coattail voting rule under which the incumbents’reelection outcomes are positively corre- lated: the good performance of one incumbent tends to prop up (while the poor performance drags down) her incumbent partisan ally in the other election. As a result, the incumbents are more likely to be reelected together or dismissed together than they are to receive opposite rewards. Thus, the partisanly aligned candidates are more likely to be elected at both branches of government. If the incumbents are members of di¤erent parties ( = D), then the voter uses a coattail voting rule under which their reelection outcomes are negatively correlated: the good performance of one incumbent increases (while the poor performance decreases) the opponent’ chances to win in the other election. Thus, it is more likely that s one incumbent will be dismissed while the other is reelected, and again the partisanly aligned candidates are more likely to be elected at both branches of government. To con…rm this intuition, in Figure 3 I depict the politicians’reelection outcomes under equilibrium rules and C E in the two-dimensional space of performances pE and pC . The density function of is increasing in the joint distribution of pE and pC is symmetric around (aE ; aC ). The probability of election of politicians from the same party, P and C. S E This probability takes its maximal value of 1 when 1 2 E = C = 1, and its minimal value of when E = C = 0. Intuitively, the more aligned politicians are to their parties, = S or negatively if = D) the optimal performance the more correlated (positively if evaluation rules. The election of partisanly aligned candidates is more probable in both states, as explained above, so stronger party alignment just increases the probability of this outcome. Note furthermore that this probability does not vary across the states due to the symmetry of the politicians’preferences (which in turn implies the symmetry of performance evaluation rules the voter adopts in equilibrium). 3.4. Discussion The results above show that coattail voting is in fact a tool that the voter uses to discipline partisan politicians. The model generates both presidential and reverse coattails. Since the executive wants her party to be presented in the legislature, in order to give her extra incentives the voter adopts a coattail voting rule such that the executive’ good performance s promotes the election of her partisan ally in congressional election. As a result, the presiden- 15 tial coattails arise. In turn, the congressman’ partisan preferences lead to reverse coattail s e¤ect. The voter rewards or punishes the executive for the congressman’ performance in s order to incentify the latter who wants to increase his party chances to win presidential o¢ ce. I must stress that in the model coattail e¤ects arise only if politicians are aligned with their political parties (in the sense that they want their party to win at both branches of government). So it is important to reason the assumption on partisan preferences of politicians at di¤erent levels of government. The literature on allocation of intergovernmental transfers provides support to this assumption. According to Cox and McCubbins (1986), the incumbents may use intergovernmental transfers to increase their reelection probability by allocating the funds to the districts with their supporters. The alignment between the two levels of government thus increases the amount of transfers because the central government favors its partisan allies and penalizes its partisan rivals. The recent empirical literature provides evidence in favor of this hypothesis (Arulampalam et al. 2009 (India), Brollo and Nannicini 2010 (Brazil), Larcinese et al. 2006 (the United States), Rozevitch and Weiss 1993 (Israel), Solé-Ollé and Sorribas-Navarro 2008 (Spain), Veiga and Pinho 2007 (Portugal)). Then the assumption on the partisan preferences of politicians is more than reasonable. On the one hand, lower-tier politicians prefer their partisan ally to take presidential o¢ ce in hope to receive more generous transfers. On the other hand, the executive allocates more funds to the districts governed by her partisan allies exactly because she wants lower-tier politicians to be aligned with the central government. And she wants it "either because local politicians are important opinion leaders and they may turn to be useful allies in the next presidential campaign, or because they may engage in rent-seeking activities for the President."18 4. Conclusion This paper studies coattail e¤ects in simultaneous presidential and congressional elections. In a political agency model with moral hazard, coattail voting is an additional tool that voters use to motivate the politicians’e¤orts. I assume that the politicians’ incentives are correlated, as an executive/congressman prefers her counterpart (the congressman/executive) to be a¢ liated with the same political party. A representative voter is therefore better o¤ adopting a joint performance evaluation rule rather than an individual performance evaluation rule when deciding whether to reward the incumbents. Under a joint rule, I have shown that the reelection outcomes of politicians 18 See Brollo and Nannicini (2010), p. 6. 16 from the same party should be positively correlated while the reelection outcomes of politicians from di¤erent parties are negatively correlated. The two-sided coattail e¤ects therefore result. On the one hand, the presidential coattails arise, as the executive’ success/failure s props up/drags down a candidate from the same party in congressional election. On the other hand, the executive’ reelection itself depends on the congressman’ performance, which ims s plies the reverse coattails. I have focused on single task policies. However, in reality public policies pursue many goals. So it is of interest to study coattail voting under a more realistic assumption of multiple-task policy where the problem of e¤ort allocation among tasks can create policy trade-o¤s. One can also add an adverse selection problem by assuming that the politician’ s performance is determined by e¤ort and her privately known ability. I leave these tasks for future research. Appendix A. Proof of Proposition 1 Under linear performance evaluation rules ( i ; bi ) the probability of being reelected for o¢ ce i is P ri (ai ; aj ) = P (f"i + i "j bi ai i aj g) =1 F"i + i "j (bi 2 ai i aj ) ; where noises "i and "j (i; j 2 fE; Cg, i 6= j) are independent normally distributed random variables, so by the convolution formula "i + is 8 > 1 < are i (ai ; aj ; i "j N 0; 1 + 2 i . Politician i’ utility s ) a2 i = 2 j "i F"i + F"i + i "j (bi (bi ai ai i aj ) i aj ) + + i 1 F"j + j "i bj aj aj j ai j ai a2 i 2 a2 i 2 if if j ; bj =S = D: as given, The …rst-order conditions with respect to actual e¤ort ai , taking ( i ; bi ) and 8 < f"i + : f"i + (bi (bi ai ai i aj ) i aj ) > : 1 i "j i F"j + bj i "j i "j + i j f"j + i j f"j + j "i j "i bj bj aj aj j ai j ai ai = 0 if ai = 0 if =S = D: The second-order conditions are 8 0 < f"i + "j (bi ai i aj ) i : 0 f"i + 2 0 i j f"j + 2 i j f"j + j "i j "i bj bj aj aj j ai j ai 1 < 0 if 1 < 0 if =S (A.1) = D: (bi i "j ai i aj ) + 17 De…ne the best response functions by Ri : [0; a] ! [0; a] such that Ri (aj ) = arg max ai 2[0;a] i (ai ; aj ; ) a2 i : 2 Then the best response functions are determined implicitly by the …rst-order conditions 8 > f" + " bi R (aj ) aj Ri (aj ) = 0 if < i i j i aj + i j f"j + j "i bj j Ri (aj ) i Since Ri > : f"i + i "j =S = D: bi Ri (aj ) ) a2 i 2 i aj i j f"j + j "i bj aj j Ri (aj ) Ri (aj ) = 0 if i (ai ; aj ; is continuous, Ri (aj ) is continuous. Therefore, a composite function Rj (ai ) = Ri Rj (ai ) ) is a continuous function s from [0; a] into itself, where [0; a] is a nonempty, compact, convex set. Then by Brouwer’ Fixed Point Theorem, Ri ai = Ri Rj ai . So there exists a pro…le Rj has a …xed point; that is, there exists ai 2 [0; a] such that aE ; aC such that aE = RE aC and is such that i Rj : [0; a] ! [0; a] (de…ned as Ri aC = RC aE . This implies that aE ; aC i ai ; aj ; ai 2 = max 2 ai 2[0;a] ai ; aj ; a2 i 2 where i; j 2 fE; Cg, i 6= j. Thus, aE ; aC is an equilibrium in e¤ort strategies if it satis…es the second-order conditions (A.1), which completes the proof. B. Proof of Proposition 2 The voter chooses ( 8 > (1 + < > : (1 E ; bE ) and ( C ; bC ) to maximize aE + aC = C E ) f"E + C E ) f"E + E "C bE bE aE aE E aC E aC + (1 + + (1 E C ) f"C + E C ) f"C + C "E bC bC aC aC C aE C aE if if =S = D: E "C C "E The implicit function theorem can be used to show that bE = aE + bC maximize aE + aC in state = aC + E aC ; C aE = S, and maximize aE + aC in state 1+ C p 1+ 1 = D if 1 j i 0, i; j 2 fE; Cg, i 6= j. This yields 8 > > > < aE + aC = > > > : p1 2 p1 2 E 2 E E 2 E p + 1+ p +1 1+ E C 2 C if if =S = D: p C 1+ 1+ E C 2 C 18 Maximizing aE + aC with respect to evaluation rules i E and j j C yields the slopes of equilibrium performance if if =S = D; D j i = 8 < : where i; j 2 fE; Cg, i 6= j. Note that in state = D the condition 1 0 is satis…ed. where ai = ai Therefore the intercepts of equilibrium performance evaluation rules are given by 8 < ai + j aj if =S bi = : ai = D; j aj if E ; bE ; C ; bC is the politicians’ equilibrium e¤orts, which do not depend on the current state . The rest of the proof is straightforward. C. Proof of Proposition 3 The reelection of incumbent i is determined by random variable "i + i "j "E + E "C N 0; 1 + 2 i 2 , i; j 2 fE; Cg, i 6= j. The density function of bivariate normal distribution of random variables and "C + C "E , denoted by f"E + q 1 ( E "C ;"C + C "E (x; y), is (x f"E + In state E "C ;"C + C "E (x; y) = 2 2 exp 1)2 E C ( y E )2 + (y x 2 2 ( E C 1)2 2 C) ) : = S, partisanly aligned candidates are elected either when both incumbents are reappointed or when none of them is reappointed (so, opponents from rival parties are elected). Denote by pi = ai + "i the performance of politician i in equilibrium. The equilibrium election probabilities in state PSS = P (fpE + P (fpE + P (f"E + P (f"E + C pC C pC C "C C "C = S are given by C aC g C aC g aE + < aE + \ fpC + \ fpC + E "E E "E E pE E pE aC + < aC + E aE g) + E aE g) = 0g \ f"C + < 0g \ f"C + 0g) + < 0g) = Z0 Z0 f"E + C "C ;"C + E "E +1+1 Z Z f"E + 0 0 1 2 C "C ;"C + E "E (x; y) dxdy + C) ; (x; y) dxdy = + 1 1 1 (arctan 1 2 E 1 + arctan (arctan E PSD = 1 PSS = + arctan 19 C) : In state state = D, candidates from di¤erent parties are elected when both incumbents are reappointed or when none of them is reappointed. 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