Blame-game politics in a coalition government

Journal of Public Economics 91 (2007) 77 – 96 www.elsevier.com/locate/econbase

Blame-game politics in a coalition government Arnaud Dellis ⁎ University of Hawaii-Manoa, Department of Economics, 2424 Maile Way, Honolulu, HI 96822, USA Received 15 October 2004; received in revised form 31 July 2006; accepted 22 August 2006 Available online 13 October 2006

Abstract Delays in the adoption of reforms is an important question in political economics. This paper explores this issue in the context of a representative democracy where the government is a coalition and citizens observe neither the decision-making process, nor politicians' preferences for a reform. We show that a coalition member who favors a reform may nonetheless choose to veto its adoption (thus delaying it until after the next election) and let his coalition partners share the blame for the non-adoption. We refer to this strategy as blame-game politics. We then identify three reasons for a politician to play the blame-game. One is to make an issue salient in the next election. A second reason is to avoid a split in his electorate, which is accomplished by hiding his stance on an issue. A third reason is to enhance ‘bargaining power’ during the formation of the next government. © 2006 Elsevier B.V. All rights reserved. JEL classification: D7; D82; H0 Keywords: Reputation; Delayed adoption of reforms; Coalition government

1. Introduction Delays in the adoption of reforms is an important question in political economics. This question is of particular relevance when the government is a coalition. For example, Roubini and Sachs (1989) and Grilli et al. (1991) show that coalition governments tend to be associated with large budget deficits, and they interpret this finding as an indication that coalition governments have difficulty passing reforms quickly. Conventional wisdom and scholarly works have offered two explanations for those delays. Under the first explanation, delays arise because coalition partners have different interests and different constituencies. Thus, it is necessary for coalition partners to reach a consensus, and obviously reaching a consensus takes time, which explains the delays in the adoption of reforms. ⁎ Tel.: +1 808 956 7653; fax: +1 808 956 4347. E-mail address: [email protected]. 0047-2727/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jpubeco.2006.08.006

78

A. Dellis / Journal of Public Economics 91 (2007) 77–96

Under the second explanation, delays arise because of a fear that the government may break soon (for evidence on the instability of coalition government, see Laver and Schofield, 1998). Neither coalition member is thus willing to grant a favor to a coalition partner, passing a reform that hurts him but benefits his coalition partner, in exchange for future reciprocity.1 Interestingly, those two explanations start with the assumption that coalition partners differ in their policy preferences. An open question in the literature is why some reforms all coalition partners consider desirable are implemented only after long delays.2 The present paper seeks to address this question. Our explanation for the delays is based upon two observations. The first observation is that it is commonplace for a politician to blame other politicians for the non-adoption of a reform.3 The second observation concerns two rules under which coalition governments usually operate.4 The first is the unanimity rule, which requires that all coalition members agree in order for a decision to be made, thus effectively giving each coalition partner a veto power. The second rule is known as collective responsibility or government solidarity. Under this rule, each coalition member is responsible for the decisions made by the government, and while in office, a cabinet member is not allowed to publicly voice opposition to the government's decisions. Together these two rules imply that if any one coalition member vetoes the adoption of a reform, the citizens will know that someone has made use of his veto power, but not who.5 We consider a coalition government that must decide on whether to adopt a reform. Citizens do not observe the decision-making process and are uncertain about the politicians' preferences for the reform. We then show that a pro-reform member of a stable coalition government may choose to veto the adoption of the reform, thus effectively delaying it until after the next election. Citizens then observe that the reform was not adopted, but do not have knowledge of who is responsible for the veto. All coalition partners thus share the blame for the non-adoption, which in turn prevents each member from acquiring a better reputation as a supporter of the reform. We then identify three reasons why a coalition member may play the blame-game. One motivation is to keep the issue salient for the next election. A second reason for a member to play this 1

To see this, imagine you are in a coalition government, and suppose that you want a tax cut while your coalition partner wants a reform of the Social Security system. Also, let's assume that you are not very keen about your coalition partner's Social Security reform, while your coalition partner dislikes your tax cut. Now, suppose that on the day when the Social Security reform is debated your coalition partner comes and offers you the following deal: if you let your partner's Social Security reform pass in exchange your partner will let your tax cut be debated and passed. You will probably be reluctant to accept such a deal if you anticipate the government may break soon. Indeed, you would then run the risk of having pass a reform you dislike without getting the one you like. 2 The following two examples provide possible cases in point. Between 1997 and 2002 the French government was divided between Prime Minister Jospin (Socialist) and President Chirac (Conservative), both being responsible for the policy of the government. By the end of their term in office, homeland security reforms had not yet been adopted despite the fact that a vast majority of the population wanted those reforms and both Jospin and Chirac seemed to agree on their desirability. Also, in 1999 a new coalition government formed in Belgium. At that time one of the most salient issues was a reform of the judicial system. A quasi-unanimity in the population and all the coalition partners agreed on its desirability. Yet, at the end of the coalition's term in office four years later the reform had not yet been adopted. 3 This had been the case in the two examples discussed above. Indeed, during the 2002 French presidential election campaign Chirac blamed Jospin for the non-adoption of homeland security reforms. And in May 2003, just before the general election, the two major parties in the Belgian coalition government were blaming each other for not having reformed the judicial system. 4 For a cross-country study of coalition governments, see Laver and Shepsle (1994) or Muller and Strom (2000). 5 This is nicely illustrated by Gisela Stuart (MEP) who said about the Council of the European Union: “Right now, if my prime minister goes to Brussels and makes decisions behind closed doors, I as a parliamentarian cannot hold him to account because I only know the outcome, I don't know the process … It's the same with the ministers. They can tell me anything” (New York Times, 16 June 2003).

A. Dellis / Journal of Public Economics 91 (2007) 77–96

79

game is to hide his stance on an issue in order to prevent a split in his electorate. A third motivation is to improve ‘bargaining power’ during the formation of the next coalition government. The model predicts that we can expect a coalition member to veto the adoption of a reform and play the blame-game if he is sufficiently office-motivated and if: (1) he has a strong reputational advantage on the reform issue; (2) a coalition partner has a strong advantage on another issue; (3) his electorate represents a majority of the community but is divided on the reform issue; or (4) the next government is expected to be a coalition government and all but one party share the same preferences on the reform issue. The remainder of the paper is organized as follows. Section 2 briefly reviews some related literature. Section 3 outlines the model, and Section 4 studies blame-game equilibria. Section 5 concludes. All proofs are in the appendix. 2. Related literature This paper is related to the political economy literature on delayed adoption of reforms. Following Drazen (2000), the models are classified into three categories. The first strand, often associated with Olson (1982), considers policy decisions made by a powerful group with a vested interest in keeping the status quo. The second strand is based on the public-good nature of the reform. In their seminal contribution, Alesina and Drazen (1991) consider a war-of-attrition model where each group waits for the other one to concede and accept a larger share of the costs associated with the reform. Their argument hinges on asymmetric information as to how costly the reform is for each group as well as the need for unanimity to pass the reform. Consensus and uncertainty are also key in our analysis but, in contrast to Alesina and Drazen's model, the reform is costless for the governing parties. The third strand is based on the uncertainty about individual benefits. Laban and Sturzenegger (1994) use a dynamic version of Fernandez and Rodrik's (1991) model to show that the adoption of a socially beneficial reform can be delayed by rational voters, even though economic conditions are deteriorating over time. This status quo bias relies on ex-ante uncertainty about who will gain and who will lose from the adoption of the reform. This contrasts with the present model (1) where individuals know with certainty whether or not they will gain from the reform and (2) where there is no deterioration of the status quo over time. A common feature to those three strands is a conflict of interests, i.e., some policy makers consider the adoption of the reform undesirable. This contrasts with the present paper which explains the existence of delays in the adoption of reforms even when all policy makers consider the reforms to be desirable. At a more general level, the current analysis is also related to the literature on reputational and career concerns initiated by Fama (1980) and formalized by Holmstrom (1999). The basic idea is that if an agent's competence is not completely known, the principal can use past outcomes in order to draw some inferences about the agent's ability and then forecast future performances. The agent, being concerned about his future career and anticipating that his current decisions may signal his competence, then takes reputation-enhancing actions. A number of other papers have subsequently looked at situations where reputational and career concerns lead to inefficient actions. One strand of this literature considers situations where an agent adopts an inefficient action in order to preserve or build-up a reputation.6 The present analysis departs from those models in that the inefficiency comes instead from politicians trying to prevent the build-up of better reputations. Another strand of this literature has focused on situations where an 6

See Rogoff and Sibert (1988), Rogoff (1990), Coate and Morris (1995), Holmstrom and Ricart I Costa (1986), Prendergast and Stole (1996), Morris (2001) and Scharfstein and Stein (1990).

80

A. Dellis / Journal of Public Economics 91 (2007) 77–96

incumbent manipulates a state variable in an inefficient way so as to make his fellow politicians less attractive to the voters, and thus increase his own probability of reelection.7 While strategic manipulation is also key in this study, current policy decisions have an impact on citizens' voting behavior not only because they can constrain future governments, but also because they provide some information about parties' policy preferences. Finally, the present analysis is also related to Holmstrom (1982) who studies moral hazard in teams. As in this paper, he shows that in a multiagent setting, people can cover up improper actions behind the uncertainty as to who is at fault. However, he also argues that group penalties are sufficient to discipline agents, a result that does not hold here since the threat of group penalties is not credible. This analysis is also related to the literature on sabotage. Lazear (1989) considers a situation where a manager observes each worker's output and rewards them based upon their relative performance. Lazear shows that such rank-order tournaments discourage cooperation among workers and can lead to sabotage: workers taking actions that adversely affect others' output. Relative performance–i.e., parties' reputations–is also key in this study. However, the present analysis differs in at least two important ways. First, citizens observe only the ‘aggregate outcome’ of the coalition, not the ‘output’ of each party. Second, vetoing the adoption of the reform affects the output of all coalition members, while only the output of the worker who is the victim of sabotage is affected. Finally, the Groseclose and McCarty (2001) model has some features in common with our analysis. In their paper, a one-member Congress submits a bill to a president who can either sign or veto it. The electorate is uninformed about the president's policy preferences but can learn about them from the veto decision. They show that when the government is divided, the Congress may propose a bill it knows will be vetoed in order to damage the reputation of the president by making him appear more extremist.8 3. The model 3.1. Overview We consider a two-period model where in each period t ∈ {1, 2} a government must decide on a reform. Let rt denote the status of the reform in period t, with rt = 1 if the reform is in place and rt = 0 otherwise.9 The community consists of a (odd) finite number of citizens N, indexed by n = 1,…, N. Each citizen is characterized by a preference for the reform and an ideology.10 With respect to the reform, there are two preference types: pro-reform (P) and anti-reform (A). A citizen of reform type j ∈ {P, 7

See Aghion and Bolton (1990), Milesi-Ferretti and Spolaore (1994) and Besley and Coate (1998). There are, however, several ways in which their analysis differs from ours. First, they seek to explain the use of the presidential veto while we seek to explain delays in the adoption of reforms when the government is a coalition. Second, they assume the Congress and the president have heterogenous preferences on a reform, while we allow homogenous preferences among the coalition partners. Finally, they assume citizens observe both the bill the Congress submits and the president's veto decision. They then conclude that the decision-making process should sometimes be kept secret. The present model shows this may not be true since it allows politicians to cover up inefficient actions. 9 We consider a discrete reform that can be either implemented or rejected. But the same argument would apply to a continuous variable, like for example a fiscal stabilization program. Indeed, a party may agree only on a too moderate program and then blame its coalition partners for not having been able to pass a better one. 10 In an earlier version of this paper (Dellis, 2004) the government was making a decision on two policies, and citizens were differing in terms of their preferences for the two policies. This specification yielded similar results. I thank an anonymous referee for having suggested replacing the second policy with ideology, which greatly simplifies the analysis since ideology is not a choice variable for the government. 8

A. Dellis / Journal of Public Economics 91 (2007) 77–96

81

A} obtains a net benefit βj when the reform is in effect, with βP N 0 N βA. With respect to ideology, citizens are of three types: leftist (L), centrist (C) and rightist (R). A citizen of ideology i derives a utility αi N 0 if that ideology is represented in the government. We shall interpret αi as the utility obtained from ideology-related policies that only the citizens of ideology i care about, and which are therefore implemented only if someone with that ideology is in office. Let un (rt, Gt) be the utility a citizen n obtains in period t when the reform status is rt and the government Gt, where un (rt, Gt) = (βj rt +αi) if his ideology is represented in government Gt and un (rt, Gt) =βj rt otherwise. Let Nji (≥ 1) denote the number of reform type j citizens with ideology i. In addition, let Nj ≡ (NjL + NjC + NjR) denote the number of citizens with reform type j and Ni ≡ (Npi + NAi) the number of citizens with ideology i. We assume throughout that a majority of citizens are proreform, i.e., NP N NA. Implementing the reform is thus the majoritarian outcome. Candidates are put forward by three parties which are treated as unitary actors.11 Each party i ∈ {L, C, R} represents an ideology and has a reform-preference type ji ∈ {P, A}. Each party's reform type is chosen independently by Nature. Politicians are both policy- and office-motivated. Let mg denote the ego-rent a politician obtains if in a government G, with g ≡ #G the number of parties in government G. We assume mg N mg + 1 N 0, i.e., the ego-rent decreases with the number of parties in government. The utility that a reform type j party i obtains in period t is given by ui (rt, Gt) = (βj rt + αi + mg) if party i is in government Gt and ui(rt, Gt) = βj rt otherwise. Future utility is discounted by a factor δ ∈ (0, 1). We make the following assumption on the preference parameters. Assumption 1. βP ≤ δ(m1 − m2).|| This assumption implies that a pro-reform politician is sufficiently office-motivated such that the present value of being in a single-party government tomorrow instead of a two-party coalition government exceeds the utility of getting the reform passed and implemented today. While politicians observe each other's preferences for the reform, citizens do not. However, the latter have beliefs about the likelihood that a politician is pro-reform.12 For each party i let θi ∈ (0, 1) denote its initial reputation, i.e., citizens' beliefs that party i is pro-reform. In addition, let Θ ≡ (θL, θC, θR ) denote the profile of parties' initial reputations. We assume that all citizens share the same prior beliefs and that those beliefs are common knowledge. In addition to the uncertainty about parties' preferences for the reform, citizens are uncertain about the reform decision of each coalition member. That is, in each period t, citizens observe the reform outcome rt but not the individual decision of each coalition member. 3.2. Political equilibrium The timing of the game is as follows. First, parties L and C are in office. They must decide whether or not to adopt the reform. The reform is passed only if both parties agree. Second, citizens observe the reform outcome and update their beliefs about each party's reform type. Each citizen 11 Considering parties as unitary actors is motivated by the observation that they are traditionally well-disciplined in parliamentary democracies (for a discussion, see Laver and Shepsle [1994] or Laver and Schofield [1998]). Throughout the analysis we shall therefore speak equally of parties and politicians. 12 For example, citizens may observe roll-call votes on related issues. Citizens' beliefs can also be related to the proportion of pro- and anti-reform citizens. This would follow a citizen–candidate approach where each party selects its candidate among the citizens who share its ideology. Citizens' beliefs would then reflect the probability that party i picks a candidate who is pro-reform. The results are consistent with this interpretation.

82

A. Dellis / Journal of Public Economics 91 (2007) 77–96

then decides as to which party to vote for in the election. The election is held under proportional representation and a party's share of seats in parliament corresponds to its vote share in the election. Third, parties bargain over the formation of a government. Finally, the newly-formed government assumes office and chooses the second-period reform outcome r2. The first-period reform outcome r1 is now the status quo and unanimity among the governing parties is again necessary if the status of the reform is to change. We now describe each of these stages in greater detail. 3.2.1. Second-period reform choice Let G2 denote the second-period government. It must choose the reform outcome r2. To capture the unanimity requirement, we assume that each governing party proposes a reform outcome. If all propose the same outcome, then it is implemented. Otherwise, the first-period reform outcome r1 remains in place. Formally, let ηi ∈ {0,1} be the second-period reform decision of party i, and η ≡ (ηi )i∈G2 the profile of reform decisions. We then have r2 (η) = ηi if ηi = ηh for all parties i and h in government G2, and r2(η)=r1 otherwise. We are now ready to define a second-period reform choice equilibrium. Definition 1. Given a government G2 , a reform strategy profile η* is a second-period reform choice equilibrium if, and only if, for all non-empty group S of parties in G2 and profile of reform strategies ηS for the member(s) of group S, there exists a party i in group S with ui (r2(η*), G2)≥ui(r2(ηs,η*−S) ,G2).|| Thus, a profile of second-period reform decisions is an equilibrium if there are not one or several parties in the government, all of which can be strictly better off by jointly deviating. In other words, the second-period reform choice equilibrium must be strong.13 Since the second period is the last one, neither party has an incentive to support a reform outcome different from the one it prefers. As a result, if the second-period government is a singleparty government, then the reform will be in place in period 2 only if the governing party is proreform. However, if the second-period government is a coalition, all the governing parties must agree in order for the reform status to be changed. It follows that if the reform was not implemented in period 1, then it is adopted in period 2 only if all coalition members are proreform. Likewise, if the reform was implemented in period 1, then it is repealed in period 2 only if all coalition members are anti-reform. These results are summarized in Lemma 1. Lemma 1. Suppose the second-period government G2 is a single-party government. Then r2 =1 if the governing party is pro-reform and r2 =0 otherwise. Suppose instead that the second-period government G2 is a coalition. If r1 =0, then r2 =1 when all coalition members are pro-reform and r2 =0 otherwise. Instead, if r1 =1, then r2 =0 when all coalition members are anti-reform and r2 = 1 otherwise.|| 3.2.2. Government formation There are several ways to model the government formation process. We adopt here the fixed-order selection procedure–due to Austen-Smith and Banks (1988)–where the government formateur is 13

This refinement of Nash Equilibrium–due to Aumann (1959)–imposes stability against deviations by every nonempty subset of the set of players. The rationale for imposing this refinement is because Nash Equilibrium is too weak. To see this, suppose the reform is not adopted during the first period and the second-period government is a coalition. In this context, there exists a Nash equilibrium where all the coalition members veto the adoption of the reform, even if they all want the reform to be implemented. This is because neither party is pivotal given that the others are vetoing the adoption of the reform, and thus neither party has an incentive to deviate. However, this equilibrium requires a coordination failure, which is not realistic in the context of a coalition government. Imposing the strong Nash refinement eliminates those equilibria.

A. Dellis / Journal of Public Economics 91 (2007) 77–96

83

selected in a pre-specified order; that is, the party with the largest vote share goes first, then the one with the second largest vote share, and so on. In the event of a tie between several parties, each is selected first with an equal probability.14 The formateur proposes a government that holds a majority. Each of the proposed parties then decides whether to accept the offer or not. If they all accept, the government forms and assumes office. Otherwise, the party with the next largest vote share is selected as the formateur. The process continues until either an offer is accepted, or all three parties have successively made an offer that was rejected. In the latter case, a caretaker government assumes office, keeps the first-period reform status unchanged, and neither party obtains an ego-rent. In this framework, a formateur is never willing to propose a government that includes more parties than necessary to hold a majority. This is because the greater the number of parties, the lower is the ego-rent and the more difficult it is to change the reform status. In addition, a formateur always proposes a government that he is a member of. As a result, if one party gets a majority of votes in the election, it forms a government on its own. Otherwise, a two-party coalition government assumes office. In this case, which parties will join the government depends on the first-period reform outcome and the reform types of the different parties. More specifically, if exactly two parties are pro-reform and the reform was not adopted in period 1, then those two parties will form a coalition government. This is because it is the only coalition government that will implement the reform in period 2 (by Lemma 1). Likewise if exactly two parties are antireform and the reform was implemented in period 1, then those two parties will again form a coalition government. In any other case, the second-period reform outcome is independent of who is in the coalition. Each party is then indifferent between forming a government with any of the other two parties. The first party to be appointed as the formateur then proposes each of the other two parties with an equal probability, and the party who is proposed accepts. These results are summarized in Lemma 2. Lemma 2. If one party receives a majority of votes in the election, then it forms a government on its own. Otherwise, a two-party coalition government forms. If the reform was (not, resp.) adopted in period 1 and exactly two parties are anti-reform (pro-reform, resp.), then those parties form the coalition government. Otherwise, the coalition government consists of the party which is first appointed as the formateur and one of the other two parties, each with an equal probability.|| 3.2.3. Election Citizens make their voting decisions strategically, anticipating which government will assume office in period 2 and what the reform outcome will be. However, citizens do not observe parties' reform types, and therefore cannot predict the reform outcome each party will want to implement and who will assume office if a coalition government has to be formed. However, from observing the first-period reform outcome r1 and parties' initial reputations Θ, they can form beliefs about each party's reform type. Formally, let μi(Θ, r1 ) denote a citizen's posterior belief that party i is pro-reform, and μ(Θ, r1 ) the profile of beliefs.15 They are derived using Bayes' rule whenever possible. We assume all citizens share the same beliefs. 14

The other selection procedure commonly used in the literature is the probabilistic one—due to Baron and Ferejohn (1989). Under this procedure each party is appointed as the formateur with a probability proportional to its vote share. For an application of this procedure see, for example, Baron and Diermeier (2001). There is a debate on which of those two procedures is empirically relevant. While Austen-Smith and Banks (1988) claim that the fixed-order selection procedure is a widespread convention, Diermeier and Merlo (2004) find little empirical support for this procedure while the probabilistic one fits the data well. It is worth noting that, qualitatively, our results do not depend on which of those two selection procedures we use. 15 In order to simplify notation we shall omit the argument Θ whenever it is possible to do so without causing confusion.

84

A. Dellis / Journal of Public Economics 91 (2007) 77–96

Let γn(r1) be citizen n's voting strategy when the first-period reform outcome is r1. The profile of voting strategies is denoted by γ (r1 ). In addition, let Eun (γ(r1)) be citizen n's expected second-period utility. We can now define a voting equilibrium as follows: Definition 2. Given the first-period reform outcome r1, a profile of voting strategies γ (r1) is a voting equilibrium if, and only if, for all non-empty group of citizen(s) S and profile of voting strategies γ˜ S for the member(s) of group S, there exists a citizen n in group S for whom Eun(γ(r1)) ≥ Eun(γ˜ S (r1), γ−S (r1)).|| Thus, a strategy profile is a voting equilibrium if there does not exist a group of citizens who can all be strictly better off by jointly deviating. In other words, the voting equilibrium must be strong.16 3.2.4. First-period reform choice Parties L and C are in office, and must decide on whether or not to implement the reform. The decision-making process is similar to the second-period scenario. 3.2.5. Political equilibrium A political equilibrium consists of: (i) first-period reform choice strategies for parties L and C, (ii) a voting strategy for each citizen, (iii) government formation strategies for each party, (iv) secondperiod reform choice strategies for each party, and (v) voters' beliefs concerning the reform type of each party. These must satisfy the following requirements. First, strategies for parties L and C must be optimal given other parties' strategies and citizens' strategies and beliefs. Second, strategies for party R must be optimal given other parties' strategies. Third, citizens' posterior beliefs are derived from incumbents' strategies through Bayes' rule where possible. Finally, a citizen's strategy must be optimal given his beliefs and parties' strategies. Throughout the analysis, we shall focus on equilibria in pure strategies where, in addition to being strong, the voting equilibrium is iteratively weakly undominated. Focusing on equilibria in pure strategies is done to simplify the analysis. Imposing the iterative weak undominance refinement is made to ensure that in most of our results, the voting equilibrium is unique. 4. Blame-game political equilibria A blame-game political equilibrium is a political equilibrium where a pro-reform incumbent vetoes the adoption of the reform and lets his coalition partners share the blame for it. In the present framework, this occurs only in period 1. Indeed, neither politician is willing to play the blame-game in period 2 since it is the last period of the game. Each of the following subsections identifies a different motivation for party L to play the blame-game (equilibria where party C plays the blame-game can be derived likewise). 4.1. Salience of an issue in an election The first motivation applies when an incumbent is willing to play the blame-game in order to make the reform issue salient in the election. This may occur for two different reasons. The first 16

The rationale for imposing this refinement at the voting stage is twofold. First, as we noted in the case of the secondperiod reform choice, Nash is too weak an equilibrium concept. Second, it shows that even if voters were able to coalesce, equilibria exist where the blame-game is played.

A. Dellis / Journal of Public Economics 91 (2007) 77–96

85

applies when party L has a high initial reputation compared to the other parties' and seeks to cash in on this reputational advantage. More specifically, L N −1 Proposition 1. Suppose that ðNPL þ NPC Þz N þ1 2 and N V 2 . Under Assumption 1, there exists a political equilibrium where party L always vetoes the adoption of the reform in the first period, if its initial reputation θL is high enough.||

The intuition underlying this result is as follows. Suppose that the leftists do not represent a majority of the community while together the pro-reform leftists and centrists do. In addition, suppose that party L always vetoes the adoption of the reform in period 1. To see that this strategy is indeed a best response for party L, let us first assume that it deviates and that, consequently, the reform is adopted in period 1. Moreover, suppose the profile of posterior beliefs is μ (1)= (1, 1, θR), where the first entry (second and third, resp.) is the citizens' posterior belief that party L (C and R, resp.) is pro-reform.17 Citizens then anticipate that if party L or party C receives a majority of votes, it will form a government on its own and keep the reform in place (given Lemmas 1 and 2). At the same time, citizens anticipate there is a probability (1−θR) that party R is anti-reform, and thus that the reform will be repealed if this party gets a majority of votes. Finally, if neither party gets a majority of votes in the election, then a two-party coalition government will form. Since citizens believe that at least two parties are pro-reform, those citizens anticipate that the reform will not be repealed under a coalition government (given Lemma 1). It follows that no one among the pro-reform leftists and centrists is willing to vote for party R since they anticipate the reform may be repealed only if that party gets a majority of votes. Moreover, since the pro-reform leftists and centrists represent a majority of the electorate, party R never receives a majority of votes in the election. Citizens then anticipate that none of the governments that may assume office in period 2 will repeal the reform. Ideology-related issues are then salient in the election and each citizen votes for his own party. Either the centrists constitute a majority of the community, in which case party C gets a majority of votes in the election and forms a government on its own, or neither ideology constitutes a majority of the community, in which case neither party gets a majority of votes in the election and a coalition government assumes office in period 2. Note that at best, party L will join a coalition government in period 2. Suppose now that party L vetoes the adoption of the reform in period 1. Since this occurs with probability one along the equilibrium path, the non-adoption of the reform does not signal anything to the citizens. Citizens' posterior beliefs about parties' reform types thus coincide with their priors. The pro-reform leftists and centrists then vote for party L if its initial reputation is high enough compared to other parties.18 Party L then gets a majority of votes in the election and forms a government on its own. Thus, vetoing the adoption of the reform in period 1 is a best response for an anti-reform party L. This is also the case for a pro-reform party L since, under Assumption 1, it is better off vetoing the adoption of the reform in period 1 and forming a government on its own in period 2, rather than getting the reform implemented in period 1 and joining a coalition government in period 2. 17 Given that the reform is never adopted along the equilibrium path, those beliefs are out-of-equilibrium ones. It is worth mentioning that they correspond to the posterior beliefs that would be derived using Bayes' rule if there had been no electoral concerns, and thus that the pro-reform incumbents had supported the adoption of the reform while the anti-reform ones had vetoed it. Hence, those beliefs would correspond to a situation where, upon observing the reform implemented in period 1, citizens believe that party L chose not to play the blame-game, and thus that both incumbents are pro-reform since both need to agree to pass the reform. Note also that those beliefs are not the only ones supporting this political equilibrium. 18 The Proof of Proposition 1 shows that this happens if party L's initial reputation θ¯ L exceeds a critical value θ¯ . The latter depends positively on other parties' initial reputations as well as on (αC / βP), a pro-reform centrist's relative utility from the ideology-related policies. This is very intuitive. For the pro-reform centrists to vote for party L instead of party C it must be that they care enough about the reform and that they perceive party L as the most likely to be pro-reform.

86

A. Dellis / Journal of Public Economics 91 (2007) 77–96

Playing the blame-game is, therefore, a way to make the reform issue salient in the next election. Indeed, if the reform is passed in period 1, then ideology-related issues are salient and citizens vote for their party. Instead, if the reform is not adopted in period 1, the reform issue is salient and the pro-reform citizens vote for party L. Hence, by playing the blame-game–thus effectively delaying the adoption of the reform until after the election–a pro-reform party L can make the reform issue salient in the election and cash in on its reputational advantage.19 Proposition 1 leaves two open questions. First, it does not rule out the existence of a political equilibrium where neither party plays the blame-game. Second, one may wonder how restrictive the condition on party L's initial reputation is. The following example sheds some light on these two questions. Example 1. Consider a community with 101 citizens where 24 (30 and 4, resp.) are pro-reform leftists (centrists and rightists, resp.) and 6 (25 and 12, resp.) are anti-reform leftists (centrists and rightists, resp.). Normalize βP to 1, and assume δ = 9/10. Let αC = 1/4, and suppose m2 = 1 and m1 = 5/ 2. Finally, assume the profile of initial reputations is Θ = (4/5, 1/2, 1/4), where the first entry (second and third, resp.) is the citizens' initial belief that party L (C and R, resp.) is pro-reform. Let us first check that there exists a political equilibrium where party L vetoes the adoption of the reform in period 1. Posterior beliefs are μ(1)= (1, 1, 1/4) if the reform is adopted in period 1 and μ (0) = (4/5, 1/2, 1/4) otherwise. When the reform is not implemented in period 1, citizens then anticipate that the reform will be adopted in period 2 with a probability 4/5 (1/2 and 1/4, resp.) if party L (C and R, resp.) gets a majority of votes and forms a government on its own. If neither party gets a majority of votes and a coalition government must be formed, they anticipate that the reform will be adopted with a probability 21/40, the probability that at least two parties are pro-reform. As a result, party L obtaining a majority of votes is the outcome that the pro-reform leftists prefer. The same holds true for the proreform centrists since 4/5 N (21/40 +αC)= 31/40, where the left-hand side is their expected secondperiod utility if party L forms a government on its own and the right-hand side is their expected secondperiod utility if a coalition government that includes party C assumes office. Hence, voting for party L is an equilibrium strategy for all the pro-reform leftists and centrists, and thus party L is able to form a government on its own. Instead, when the reform is implemented in period 1, citizens anticipate it may be repealed in period 2 only if party R gets a majority of votes in the election. As discussed above, all citizens casting their ballot for the party representing their ideology is then a voting equilibrium. Party C thus gets 55 votes and forms a government on its own. Thus, a pro-reform party L would be willing to play the blame-game since it would receive a total utility of [α L + m2 + δ ( βP + α L + m1)], which is larger than ( βP + α L + m2 + δβP), which is the maximum it can get when the reform is passed in period 1. Let us now check that there does not exist a political equilibrium where neither party plays the blame-game. To do so, suppose on the contrary that pro-reform incumbents support the adoption of the reform and anti-reform incumbents veto it. Using Bayes' rule, we then get μ (1) = (1, 1, 1/4) as the posterior beliefs when the reform is adopted in period 1, and μ (0) = (2/3, 1/6, 1/4) otherwise. Since μ (1) is the same as above, party C gets a majority of votes when the reform is implemented. Moreover, it is easy to see that given μ (0), party L gets a majority of votes when the adoption of the reform is vetoed. With the election outcomes the same as above, a pro-reform party L will want to deviate and play the blame-game. Hence, this cannot be a political equilibrium. 19 This provides a possible explanation for the strategy followed by Chirac during the 2002 presidential election campaign in France, where he blamed Jospin for the non-adoption of homeland security reforms. Chirac had a better reputation as a supporter of a tight security policy than Jospin. He may have then strategically chosen to delay the adoption of those reforms knowing that Jospin was weaker on that issue, and thus could be defeated if it became salient in the presidential election.

A. Dellis / Journal of Public Economics 91 (2007) 77–96

87

Finally, it is worth noting that a political equilibrium does not exist where a party plays the blame-game for one of the other motives described in the paper. □ The second reason for a pro-reform party L to play the blame-game applies when party C has an advantage on ideology-related issues, which occurs when the centrists represent a majority of the community. To see this, note that ideology-related issues are salient in the election if the reform is adopted in period 1 (the argument is similar to the one in Proposition 1). Citizens then vote for the party representing their ideology. Party C then gets a majority of votes in the election and forms a government on its own in period 2. In contrast, the reform issue is salient in the election if the reform is not adopted in period 1. A majority of citizens then prefer that a coalition government assumes office in period 2 if neither party has a strong reputational advantage and the probability that two or all parties are pro-reform is larger than the probability that party C is pro-reform. The latter condition implies that if the pro-reform centrists care enough about the reform, they will then prefer that party C forms a coalition instead of a single-party government since it is then more likely that the reform will be implemented. Party L's prospects of staying in office are thus better when the reform is not adopted in period 1 than when it is. Consequently, a pro-reform party L that is sufficiently office-motivated is willing to play the blame-game. Thus, as in Proposition 1, party L plays the blame-game in order to influence which issue is salient in the election. However, in contrast to Proposition 1, the objective is no longer to make the reform issue salient per se, but instead to prevent the ideology-related issues from becoming salient.20 The following example illustrates this result (a formal statement and proof are available from the author). Example 2. Consider the community described in example 1, and suppose that βA = − 5/4 and αi = 1/2 for all ideology i. Also let m2 = 7/4 and assume the initial reputations are Θ = (4/5, 1/ 2, 1/2). Suppose party L always vetoes the adoption of the reform in period 1. Posterior beliefs are μ(0) = (4/5, 1/2, 1/2) and μ (1) = (1, 1, 1/2). If party L deviates and the reform is implemented in period 1, then party C obtains a majority of votes in the election and forms a government on its own (the argument is the same as in example 1). If instead, the reform is not implemented in period 1, citizens anticipate that the reform will be adopted in period 2 with a probability 4/5 (1/2 and 1/2, resp.) if party L (C and R, resp.) gets a majority of votes and with a probability 13/20 if neither party gets the majority. Now let the voting strategies be as follows: all the leftists and rightists vote for their party, all the anti-reform centrists vote for party C, and 25 of the pro-reform centrists vote for party C while the remaining 5 vote for party R. Hence, party L (C and R, resp.) gets 30 (50 and 21, resp.) votes. A coalition government thus assumes office in period 2, with party C the first to be appointed as the formateur. Citizens then anticipate that party L (C and R, resp.) will be in the second-period government with a probability 27/40 (4/5 and 21/40, resp.).21 20 One implication is that, contrary to Proposition 1, a pro-reform party L may choose to play the blame-game even when it has the lowest initial reputation among the three parties. For example, suppose a left-wing party is perceived as the least likely to support an immigration reform. It may choose to block the reform and let its right-wing coalition partner share the blame for the non-adoption. Its objective would be to weaken the electoral position of its coalition partner by inducing some of the latter's supporters to switch their vote to an extreme right-wing party that is perceived as more likely to support such a reform. 21 To see this, consider party L. Given their beliefs citizens anticipate that with probability 2/5 party L and exactly one other party are pro-reform. In that case, those two parties form the coalition government (by Lemma 2). Also, citizens believe that with probability 11/20 the number of pro-reform parties is different from two. In that case, party C proposes party L with probability 1/2, and party L accepts. In all other cases, party L is not in the government. Hence, citizens anticipate that party L will be in the second-period government with a probability [2/5 + (11/20) (1/2)] = 27/40. The same argument applies for parties C and R.

88

A. Dellis / Journal of Public Economics 91 (2007) 77–96

From this, it is easy to check that the above strategies constitute a voting equilibrium and that party L is willing to veto the adoption of the reform in period 1. Note that, as in example 1, there is no political equilibrium wherein neither party plays the blame-game, nor a political equilibrium wherein a party plays the blame-game for one of the other motives described in the paper. □ 4.2. Divided electorate The second motivation applies when an incumbent seeks to hide his preferences for the reform in order to avoid a split in his electorate. This arises when his electorate constitutes a majority of the community, but is divided on the reform issue. More specifically, N −1 N þ1 Proposition 2. Suppose ðNPL þ NPC ÞV and N L z . Under Assumption 1, there exists a 2 2 political equilibrium where party L always vetoes the adoption of the reform in the first period, if its initial reputation θL is similar enough to other parties' and aL zð1−hR ÞjbA j.22|| The intuition underlying this result is as follows. Suppose that the leftists constitute a majority of the community, but that neither the pro-reform nor the anti-reform leftists do. Moreover, suppose that party L always vetoes the adoption of the reform in period 1. To see that this strategy is indeed a best response for party L, let us first assume party L deviates and that, consequently, the reform is adopted in period 1. In addition, suppose the profile of posterior beliefs is as in Proposition 1, i.e., μ (1) = (1, 1, θR). Citizens then believe that both incumbents are pro-reform, and thus that neither will repeal the reform in period 2. At the same time, citizens anticipate with probability (1 − θR) that party R is anti-reform, and thus will repeal the reform in period 2 if it forms a government on its own. This may then induce some anti-reform leftists to cast their ballot for party R, which may then prevent party L from obtaining a majority of votes in the election. Let us now assume party L vetoes the adoption of the reform in period 1. Since this happens with probability one along the equilibrium path, the non-adoption of the reform does not signal anything to the citizens and posterior beliefs coincide with the priors. Since party L's initial reputation is similar enough to other parties, the leftists cannot be better off casting their vote for party C or party R. Thus, party L gets a majority of votes (since the leftists constitute a majority of the community) and forms a government on its own. Hence, vetoing the adoption of the reform in period 1 is a best response for an anti-reform party L. Furthermore, under Assumption 1, the same holds true for a pro-reform party L. Playing the blame-game is therefore a way for a pro-reform incumbent to hide his preferences for the reform and avoid a split in his electorate. Indeed, the adoption of the reform in period 1 reveals that both incumbents are pro-reform. This may yield a split in the incumbents' electorates, with some of their anti-reform supporters voting for the opposition party. Instead, the nonadoption of the reform does not signal anything about the incumbents' preferences for the reform and thus prevents such a split if the initial reputations are not too different from one another. 4.3. Issue salience in the government formation The third motivation applies when an incumbent is willing to play the blame-game in order to influence whether or not the reform issue is salient at the government formation stage. This arises αL ≥ (1 − θR) ∣βA∣ is a technical assumption. It guarantees the existence of a voting equilibrium following the adoption of the reform in period 1. 22

A. Dellis / Journal of Public Economics 91 (2007) 77–96

89

when a coalition government must be formed and not all parties share the same preferences for the reform. More specifically, Proposition 3. Suppose that the leftists are not the largest group in the community and that neither ideology represents a majority. Moreover, suppose that prior beliefs are such that, following the non-adoption of the reform in period 1, parties' reputations μi(0) are similar enough. Then, there exists a political equilibrium where party vetoes
L  the adoption of the reform aL þm2 in period 1, if at least one party is anti-reform and jbA jzd 2 zbp .23|| The intuition underlying this result is as follows. Since the reform is adopted in period 1 only if all three parties are pro-reform, citizens' posterior beliefs are μ (1) = (1, 1, 1) and ideology-related issues are salient in the election. The same is true if the reform is vetoed in period 1 and parties' posterior reputations μi (0) are similar enough. In both cases, citizens are willing to vote for the party representing their ideology. Since neither ideology represents a majority, neither party gets a majority of votes and the second-period government is a coalition. Moreover, since the leftists are not the largest group in the community, party L is not the first one to be appointed as the formateur. Whether a party's stance on the reform matters in government formation depends on who has veto power in period 2, and this depends on whether the reform is in place or not. More specifically, a pro-reform politician has veto power when the reform is in place (since he can veto its repeal) and an anti-reform politician has veto power when the reform is not in place (since he can veto its adoption). A pro-reform party L is disadvantaged at the government formation stage if the party is the only one that has veto power. This occurs when parties C and R are anti-reform and the reform is implemented in period 1. Indeed, in this case, neither party C nor party R is willing to form a government with party L since they both (correctly) anticipate that party L will veto a repeal of the reform. Hence, they prefer forming the government together. In contrast, if the reform is not adopted in period 1, party L does not have veto power in period 2. As a result, its stance on the reform does not matter during the government formation and the formateur proposes party L with probability 1/2. In other words, the reform issue is salient at the government formation stage only if the reform is implemented in period 1. Hence, by playing the blame-game, party L improves its prospects of being in the government. A pro-reform party L is then willing to play
second-period  aL þm2 such a game since bP Vd 2 , i.e., the discounted value of being in the second-period government with probability 1/2 exceeds the utility loss of not getting the reform passed and implemented in period 1. In contrast, a pro-reform party L has an advantage at the government formation stage if exactly one other party has veto power. This occurs when the reform is not implemented in period 1 and either party C or party R is anti-reform. To see this, suppose parties L and C are pro-reform and party R is anti-reform. Neither party L nor party C is then willing to form a government with party R since they both (correctly) anticipate party R will veto the adoption of the reform. Hence, parties L and C form the government together. In contrast, if the reform is adopted in period 1, party R does not have veto power in period 2. In that case, its stance on the reform does not matter during the government formation and the formateur thus proposes party L with probability 1/2. In other words, the reform issue is salient at the government formation stage only when the reform is not adopted in period 1. Hence, by playing the blame-game, party L increases the probability it will
L  2 guarantees that an anti-reform party L does not play the symmetric game, i.e., The assumption that jbA jzd a þm 2 adopts the reform when at least one party is pro-reform. 23

90

A. Dellis / Journal of Public Economics 91 (2007) 77–96

be in the second-period government from 1/2 to 1. For the same reason as above, it is then willing to play such a game. 5. Conclusion Most of the models that attempt to explain delays in the adoption of reforms do so in the context of a single-party government. In this paper, we propose a model where the government is a coalition. The model takes into account two features of coalition governments–namely, that decisions must be unanimous and that cabinet members are collectively responsible for the decisions made—that create a rationale for delaying the adoption of reforms. In particular, the model shows that this can happen even in the context of a stable coalition government where all members are pro-reform, the citizens are rational and a majority of the electorate wants the reform to be passed. While our focus was on the delayed adoption of reforms, the model can also explain failures in the adoption of reforms, i.e., the reform is never implemented. However, it is worth noting that this happens only if one incumbent is anti-reform. To see this, suppose both incumbents are pro-reform. In Propositions 1 and 2, party L gets a majority of votes in the election and forms a government on its own. In example 2 and Proposition 3, neither party receives a majority of votes and a pro-reform coalition government assumes office. In all cases, the reform is implemented in period 2. The model can also generate reversal in the implementation of a reform, i.e., the reform is adopted in period 1 and repealed in period 2. This occurs when an anti-reform incumbent supports the adoption of the reform because of career concerns.24 It is worth noting, however, that such early-implementation strategies are not symmetric to blame-game strategies. Indeed, while earlyimplementation requires the consent of all coalition partners, the blame-game strategy does not. Early-implementation is thus more difficult to achieve than blame-game. While this model analyzes the case of a coalition government, its logic can be applied to other political systems where the government is divided. The French cohabitation between 1986 and 1988, where the executive branch was divided between a socialist president and a conservative cabinet, is a good illustration. During the 1988 French presidential election campaign, incumbent President Mitterand and Prime Minister Chirac (the two major candidates in that election) blamed each other for having blocked the adoption of some reforms. The 1997–2002 cohabitation between President Chirac (Conservative) and Prime Minister Jospin (Socialist) is another good example. As previously mentioned, during the 2002 presidential election campaign, Chirac who was running against Jospin blamed him for a lax attitude towards homeland security, thus exploiting his better reputation as a supporter of a stringent security policy. The model can also be applied to more general situations where several agents, having some private information, choose an action while the principal observes only the aggregate outcome. Consider first the example of a negotiation between a trade union and the management of a firm. An agreement satisfying both sides may be rejected by one of them in order to spoil the reputation of the other and obtain public support. The argument also applies to sports teams. Consider a football team that has just appointed a new coach the players dislike. The players may then decide to play badly and blame this new coach for the team's poor results, hoping that the coach will be laid off. Finally, 24

Throughout the analysis we have only considered political equilibria where an anti-reform incumbent always vetoes the adoption of the reform. This is because situations where elections serve as a disciplining device have already been studied extensively. See, for example, Barro (1973), Ferejohn (1986) or Austen-Smith and Banks (1989) for agency style models of political competition.

A. Dellis / Journal of Public Economics 91 (2007) 77–96

91

consider a firm that has just hired a new manager. In this case, some of the incumbent managers, fearing that the new manager will get the promotion they were expecting, may sabotage several projects and put the blame on that new manager. What these examples all have in common is the principal's inability to determine who is responsible for the current bad results. Finally, this model also shows that having a small party advocating a specific issue (the Green party, for instance) does not necessarily help their cause. Indeed, those parties often have a small electorate and therefore have no hope of controlling a majority of seats in parliament. In addition, citizens perceive those parties as the most likely to support the issue they champion. Thus, example 2 suggests that if their office-motivation is strong enough, those small parties may have an incentive to block reforms they favor in order to prevent other parties from holding a majority. Moreover, Proposition 3 indicates that they may also want to keep the issue they champion salient, thus preserving during the government formation the advantage they derive from their policy stance. In fact, this argument holds even if they are not in the government. Indeed, some of the major governing parties may use the policy concerns of those small parties as a ‘battlefield’ during the election campaign (as Chirac may have done with homeland security, an issue championed by Le Pen's National Front party). Acknowledgement I thank Steve Coate for his invaluable support and comments. I thank Antonio Merlo and an anonymous referee who made important suggestions that considerably improved the paper. Helpful comments were also provided by Georges Casamatta, Mandar Oak, Ted O'Donoghue, Christoph Vanberg, Stanley Winer, and various conference and seminar participants. Appendix We first introduce a few definitions and notations that will be useful to prove the results.25 We can distinguish three ways in which a group of voters can be pivotal in the election, i.e., can change the electoral outcome: (1) they can be majority-pivotal for a party, i.e., they can give that party the majority of votes; (2) they can be coalition-pivotal against a party, i.e., they can take the majority away from some party without giving it to another one; or (3) they can be formateurpivotal, i.e., they can affect the order in which parties are selected as the formateur, in the event neither party receives a majority of votes. Suppose neither party receives a majority of votes and a coalition government has to be formed. We need to derive citizens' beliefs about which parties will join the second-period government and whether the reform will be in place in period 2 or not. Suppose r1 = 0—the case where r1 = 1 is symmetric. Let I ≡ {L, C, R} denote the set of parties. Define P ≡ {i ∈ I: ji = P} the set of pro-reform parties and A ≡ {i ∈ I:ji = A} the set of anti-reform parties. Given their posterior beliefs μi that party i is pro-reform citizens anticipate that #Pz2–and thus r2 = 1–with a probability θˆ ≡ {μCμR + μL[μC(1 − μR ) + (1 − μC)μR]}.Let θˆ ≡ (θ˜ − μLμCμR) be citizens' posterior beliefs that #P ¼ 2. Also let pi ≡ Pr (i ∈ G2|G¯2) be the probability that party i is in government G2 when the first party to be appointed as the formateur proposes each of the other two parties with an equal probability and each accepts, i.e., G2 ∈ G¯2 = {{i, h},{h, k}} with party h the first to be appointed as the formateur. It follows from Lemma 2 that citizens' posterior beliefs that party i 25

For the sake of brevity some of the details are omitted here. They are available from the author or can be found at http://www2.hawaii.edu/∼adellis/blame.pdf.

92

A. Dellis / Journal of Public Economics 91 (2007) 77–96

will be in G2 are given by θ˜ i ≡ [(1 − θ˜ ) pi + θ˜ − (1 − μi)μhμk], with h ≠ i ≠ k. Note that θ˜ is independent of the order in which parties are selected as the formateur, but not θ˜ i; the latter i depends on it through pi. Let N denote the set of citizens and N j the set of citizens with ideology L C R i and reform type j. Finally, let J uð j ; j ; j Þ denote the profile of parties' reform types. We are now ready to prove the results. Proof of Proposition 1. Let the strategy profiles and beliefs be as follows: 1 rLP ðJ L Þ ¼ riA ðJ i Þ ¼ 0 (for i = L, C) and rCP ðJ C Þ ¼ 1 for all J h afP; Ag2 , where rhj ðJ h Þaf0; 1g is the first-period reform decision of a reform type j party h when the profile of other parties' reform types is J h ; 2 Posterior beliefs are μ (0) = Θ and μ (1) = (1, 1, θR ); 3 γn(1) = i(n) for all citizen n–where i(n) is the party that represents citizen n's ideology–, while γn(0) = L for all naN P and γn(0) = i (n) for all naN A -where N j ufnaN : jn ¼ jg is the set of reform type j citizens; and 4 Let the government formation and second-period reform strategies be as in Lemmas 1 and 2. n n foo C P Define humax h R ; ab þ max hC ; h and assume θ¯L N θ˜ . That γ is a voting equilibrium is P proved via the following two claims. N þ1 and N L V N2−1. Let r1 = 1 and μ (1) = (1, 1, θR). Then Claim 1.1. Suppose ðNPL þ NPC Þz 2 γ(1) is a voting equilibrium. || Proof of Claim 1.1. To prove the result it is sufficient to show that for any non-empty group of citizens S and any profile of voting strategies γ˜ S for the member(s) of group S there exists a citizen n ∈ S for whom Eun (γ˜ S, γ−S) ≤ Eun(γ). Note that given μ (1) = (1, 1, θR) citizens believe r2 = 1 with probability θR if party R gets a majority of votes and with probability 1 otherwise (by N þ1 L C Lemmas 1 and 2). Note also that N R V N−1 2 — since ðNP þ NP Þz 2 . n C C N þ1 Suppose N z 2 . Since γ (1) = i(n) for all citizen n, we have kC ðgÞz N þ1 2 , where π (.) denotes party C's vote total. This, together with Lemma 2, implies G2 = {C}. And given their beliefs citizens expect a second-period utility Eun(γ) = (βj + αC) if i (n) = C and (βj) otherwise. Now, take a non-empty group of citizens S and profile of voting strategies γ˜ S arbitrarily. There f n ˜ n are three cases to consider. First, kC ð gs ; g−s Þz N þ1 2 , in which case Eu (γS, γ−S) = Eu (γ) for all R f Nþ1 citizen n. Second k ð gs ; g−s Þz 2 , in which case there must exist a citizen ℓ in S, L C L C n ℓ ∈ (N P N P )—the latter since ðN P þ N Þz Nþ1 2 and γ (1) = i(n) for all citizen n. But for this f citizen ℓ we have Euℓ(γ˜ S, γ−S) =θRβP b Euℓ(γ)-since θR b 1. Third, kh ð gs ; g−s ÞV N2−1 for h =C, R, n in which case there must exist a centrist citizen ℓ in S—since γ (1) = i (n) for all citizen n. But then Euℓ(γ˜ S, γ−S) ≤ Euℓ(γ). To see this, note that citizens anticipate r2 = 1 with probability 1. Hence, Euℓ(γ˜ S, γ−S) ≤ (βj +αc) =Euℓ(γ) for any citizen S aN C . Since those three cases exhaust all possibilities we have shown that there exists a citizen n in S for whom Eun(γ˜ S, γ−S) ≤ Eun(γ). Hence, we are done since we took S and γ˜ S arbitrarily. N −1 for all ideology i. We then have ki ðgÞV N2−1 for all party i and #G2 = 2. Given Suppose N i V 2 the posterior beliefs μ (1), a citizen n expects a second-period utility Eun(γ) = (βj + θ˜ i(n)αi(n)). Now, take arbitrarily a non-empty group of citizen(s) S and a profile of voting strategies γ˜ S for the member(s) of group S. There are four cases to consider. First, S is majority-pivotal for party f n i ∈ {L, C}—i.e., ki ð gs ; g−s Þz N þ1 2 W.l.o.g. take i = L. Since γ (1) = i(n) for all citizen n and i N −1 N V 2 there must then exist a citizen ℓ in S whose ideology i (ℓ) ≠ L. But for that citizen ℓ we

A. Dellis / Journal of Public Economics 91 (2007) 77–96

93

have Euℓ(γ˜ S, γ−S) = βj ≤ Euℓ(γ). Second, S is majority-pivotal for party R. Then the same argument as when N i z Nþ1 2 applies. Third, S is formateur-pivotal for some party i. Again, take i = L. Since γn (1) = i (n) for all citizen n there must then exist a citizen ℓ in S whose ideology i (ℓ) ≠ L—say i(ℓ) = C. Now, for Eu ℓ(γ˜ S, γ−S) N Eu ℓ(γ) it must then be that S is formateurpivotal for party C as well. And by the same argument as above there must then exist a citizen k in S whose ideology i (k) = R. But since S cannot be formateur-pivotal for all three parties, we then have Euk(γ˜ S, γ−S) ≤ Euk(γ). Fourth, S is neither majority- nor formateur-pivotal for any party, in which case Eun(γ˜ S, γ−S) = Eun (γ) for all citizen n. Hence, we are done since those four cases exhaust all possibilities and we took S and γ˜ S arbitrarily. □ L ¯ Claim 1.2. Suppose ðNPL þ NPC Þz N þ1 2 and θ Nθ . Let r1 = 0 and μ (0) = Θ. Then γ (0) is a voting equilibrium.|| n Proof of Claim 1.2. Since ðNPL þ NPC Þz N þ2 2 and γ (0) =L for all n ∈ ðN P [ N P Þ, any group S L C with ðS \ ðN P [ N P ÞÞ ¼ K is not pivotal, and thus Eun (γ˜ S, γ−S) =Eun(γ) for any citizen n and any L C γ˜ S. Hence, we only need consider group S with ðS \ ðN P [ N P ÞÞpK. Pick any such group S and L C citizen n in ðN P [ N P Þ. Now, this citizen expects a second-period utility Eun(γ) = (θLβP +αL) if L C n ∈ N P and (θLβP) if n ∈ N P . At the same time, we have for any profile of voting strategies γ˜ S for the member(s) of group S n o 8 L L < max hC bP ; h R bP ; f hb þ a if naN P P f n o Eun ð gS ; g−S ÞV ; C : max hC b þ aC ; h R b ; f if naN CP P P hbP þ a

L

C

where the first (second, resp.) term within the brackets is citizen n's expected second-period utility if party C (R, resp.) gets a majority of votes and forms a government on its own, and the third term the maximum expected second-period utility if a coalition government has to be formed. But θL N θ¯ implies Eun (γ˜ S, γ−S) b Eun (γ). Hence the result. □ It remains to prove that σ (.) is an equilibrium profile of first-period reform choice strategies. To do so, we have to show that for any non-empty S ⊆ {L, C} and σ˜ S there exists i ∈ S such that U i(σ˜ S, σ−S) ≤ U i(σ), where U i (.) denote party i's expected total utility. Note that we only have to consider S and σ˜ S which are such that r1 (σ˜ S, σ−S) = 1 since otherwise r1(σ˜ S, σ−S) = r1(σ) and U i (σ˜ S, σ−S) = U i(σ) for all party i. Let us first consider the case where party L is pro-reform. Take S with L ∈S. Note that U L(σ) = L α +m2 +δ(βP +αL +m1) —party L receives a majority of votes, forms a government on its own and adopts the reform in period 2. Instead, U L(σ˜ S, σ−S) = ( βP +αL +m2 +δβP) if N C z Nþ1 2 and party C is pro-reform, or (βP +αL +m2) if party C is anti-reform—party C receives a majority of votes and forms a government on its own. Similarly, U L(σ˜ S, σ−S) ≤ (1 +δ) ( βP +α L +m2) if N i V N−1 2 for all ideology i (the maximum is reached when, for example, all three parties are pro-reform and N L N N h, for h =C, R). Hence, U L(σ˜ S, σ−S) ≤U L(σ) (given Assumption 1). Let us now consider the case where party L is anti-reform. Take S with L ∈ S. That U L(σ˜ S, σ−S) ≤ U L(σ) follows from βA b 0 and G2 = {L} if r1 = 0. It only remains to consider S = {C}. But rLj ðJ L Þ ¼ 0. for all j ∈ {P,A} and J L afP; Ag2 implies that r1(σ˜ S, σ−S) = r1(σ) for all σ˜ S. Hence the result. □ Proof of Proposition 2. Let the strategy profiles and beliefs be as follows: (1) rLP ðJ L Þ ¼ riA ðJ i Þ ¼ 0 (for i = L, C ) and rCP ðJ C Þ ¼ 1 for all J h afP; Ag2 ; (2) Posterior beliefs are μ (0) = Θ and μ (1) = (1, 1, θR);

94

A. Dellis / Journal of Public Economics 91 (2007) 77–96

(3) γn (0) = i (n) for all 8 > :R

citizen n, and L

L

for all naN P and a fraction k of N A ; C R for all naðN [ N P Þ; R L for all naN A and a fraction ð1−kÞ of N A ;

where λ ∈ (0,1) is such that ðNPL þ k NAL Þ ¼ N2−1. Note that this is possible since i L C N −1 N L z N þ1 2 ; ðNP þ NP ÞV 2 and N j ≥ 1 for all i, j; and (4) Let the government formation and second-period    reform strategies be as inLemmas 1 and 2. f

fL

f

P

fL

Define P hu maxfhC ; hR ; hg− ð1−bh Þa and hu minfhC ; hR ; hg þ ð1−jbh jÞa . Assume θL ∈ P A ¯ (θ, θ ). ¯ To prove that γ(0) is a voting equilibrium we proceed as in the Proof of Claim 1.2. That γ(1) is a voting equilibrium is proved in the following claim. N −1 N þ1 and N L z . Let r1 = 1 and μ (1) = (1, 1, θR). Then γ Claim 2.1. Suppose ðNPL þ NPC ÞV 2 2 (1) is a voting equilibrium if αL ≥ (1 − θR)|βA|.|| L

L

Proof of Claim 2.1. Given the posterior beliefs μ(1) and the profile of voting strategies γ (1) citizens anticipate G2 = {L, C} or {L,R}, each with probability 1/2, r2= 1. Thus, a citizen n's
and iðnÞ expected second-period utility is Eun(γ) = (βj + αL) if i(n) = L and bj þ a 2 otherwise. Now, take arbitrarily a group of citizen(s) S and a profile of voting strategies γ˜ S for the member(s) of group S. We have to show that there exists a citizen n in S for whom Eun(γ˜ S, γ−S) ≤ Eun(γ). L First, note that Eun(γ˜ S, γ−S) ≤ (βP + αL) for any citizen n ∈ N P , and thus Eun(γ˜ S, γ−S) ≤ Eun(γ). L We can thus restrict our attention to groups S such that ðS \ N P Þ ¼ K, Second, if S is majoritypivotal for party L, then a citizen n's expected second-period utility is Eun(γ˜ S, γ−S) = (βj + αL) if i(n) = L and (βj) otherwise. Thus, Eun(γ˜ S, γ−S) ≤ Eun (γ) all citizen n. Suppose S is majority- or formateur-pivotal for party C. Since γn(1) = C for all citizen C R L R n ∈ ðN [ N P Þ, there must then exist a citizen ℓ in S, with ℓ ∈ ðN [ N A Þ. We have already L shown that Euℓ(γ˜ S, γ−S) ≤ Euℓ (γ) if citizen ℓ ∈ N P . And it is easy to see that the same holds L R true if citizen ℓ ∈ ðN A [ N A Þ. Suppose S is majority-pivotal for party R. First note that for any n ∈ ðS \ N LA Þ we have Eun(γ˜ S, γ−S) = θRβA ≤ Eun(γ)—the latter since αL ≥ (1 − θR)|βA|. Hence, there must be a citizen C n ∈ ðS \ N P Þ. But Eun(γ˜ S, γ−S) = θRβP b Eun(γ), the inequality since θR b 1. Suppose S is formateur-pivotal for party R. Note that Eun(γ˜ S, γ−S) b Eun(γ) for any citizen L L n ∈ N A . Hence, we can focus only on groups S such that ðS \ N A Þ ¼ K. And since we already L f consider only group S such that ðS \ N P Þ ¼ K, the only possibility left is kR ð gS ; g−S Þ ¼ f f C kL ð gS ; g−S Þ ¼ N−1 2 and k ð gS ; g−S Þ ¼ 1. And for this to be true it must be that there exist a citizen n in S, with i (n) = C. But Eun(γ˜ S, γ−S) = Eun(γ). And since no other S is pivotal, we are done. □ The proof of σ (.) an equilibrium profile of first-period reform strategies is similar to the one in Proposition 1 where N i V N2−1 for all party i. □ Proof of Proposition 3. Let the strategy profiles and beliefs be as follows: (1) rLP ðJ L Þ ¼ 1 if J L ¼ ðP; PÞ and 0 otherwise, rCP ðJ C Þ ¼ 1 for all J C afP; Ag2 and riA ðJ i Þ ¼ 0 (for i = L, C) for all J i afP; Ag2 ; hi − ∏ hh (2) Posterior beliefs are μi (1) = 1 and li ð0Þ ¼ 1− haI ðfor i ¼ L; C; RÞ; ∏ hh haI

A. Dellis / Journal of Public Economics 91 (2007) 77–96

95

(3) γn (1) = γn (0) = i (n) for all citizen n; and (4) Let the government formation and second-period reform strategies be as in Lemmas 1 and 2. fh  fh    f minh pi h ah f minh pi h ah Pi i For each party i let l u h− and l u h þ . Assume μi (0) ∈ (μ i, μ¯ i) jbA j bP P ¯ for all party i. That γ (1) is a voting equilibrium is obvious given μ (1) = (1, 1, 1). And to prove that γ (0) is a voting equilibrium we proceed as in the proof of Claim 2.1. It remains to prove that σ (.) is an equilibrium profile of first-period reform strategies. Before doing so, note that γn (1) = γn (0) for all citizen n implies that πi (γ (1)) = πi (γ (0)) for all party i. Let us first consider the case where the profile of parties' reform types is J ¼ ðP; P; PÞ. Take a non-empty S ⊆ {L, C} and σ˜ S arbitrarily. Note that πi (γ (1)) = πi (γ (0)) (for i = L, C, R) and r2 = 1 independent of r1 (the latter since #P ¼ 3) imply that G2 ∈ G¯2 independent of r1. Now, either r1(σ˜ S, σ−S) = 1 and Ui (σ˜ S, σ−S) = U i (σ) for all party i. Or, r1(σ˜ S, σ−S) = 0 and U i (σ˜ S, σ−S) b U i (σ) for all party i. Hence the result. Let us now consider J pðP; P; PÞ. We can restrict our attention to S and σ˜ S such that r1(σ˜ S, σ−S) L = 1 since otherwise Ui(σ˜ S, σ−S) = Ui (σ) for all party i. Take S with L ∈ S, and suppose
L  j = P. a þm2 L L L There are two cases to consider. First, if J ¼ ðA; AÞ, then U ðrÞ ¼ a þ m2 þ d 2 while

UL(σ˜ S, σ−S) = (βP
+ αL + m2).  Otherwise, UL(α) = αL + m2 + δ(βP + αL + m2) and
U L ðf rs ; r−s Þ ¼ L L L a þm2 aL þm2 L ˜ bP þ a þ m2 þ d bP þ 2 . In both cases U (σS, σ−S) ≤ U (σ) since bP Vd 2 .

Suppose instead that j L = A. That U L (σ˜ S, σ−S) ≤ U L (σ) is obvious if J L ¼ ðA; AÞ, so we are left with only two cases to consider. First, if
script J superscript L = (P,P), then U L(σ) = (αL + m
2 + δβA)  L L 2 2 rs ; r−s Þ ¼ bA þ aL þ m2 þ d bA þ a þm while U L ðf . Otherwise, U L ðrÞ ¼ a L þ m2 þ d a þm 2 2 and U L (σ˜ S, σ−S) = β A + α L + m2 + δ(α L + m2). In both cases U L (σ˜ S, σ−S) ≤ U L (σ) since
L  2 jbA jzd a þm . 2 We are thus left only with S = {C}. But rLj ðJ L Þ ¼ 0 for all J pðP; P; PÞ implies that r1 (σ˜ S, σ−S) = r1 (σ) for all σ˜ S. Hence the result.

□

References Aghion, Ph., Bolton, P., 1990. Government domestic debt and the risk of default: a political–economic model of the strategic role of debt. In: Dornbusch, R., Draghi, M. (Eds.), Public Debt Management: Theory and History. Cambridge University Press, Cambridge, pp. 315–345. Alesina, A., Drazen, A., 1991. Why are stabilizations delayed? American Economic Review 81, 1170–1188. Aumann, R., 1959. Acceptable points in general n-person games. Contributions to the Theory of Games, vol. IV. Princeton University Press, Princeton, pp. 287–324. Austen-Smith, D., Banks, J., 1988. Elections, coalitions, and legislative outcomes. American Political Science Review 82, 405–422. Austen-Smith, D., Banks, J., 1989. Electoral accountability and incumbency. In: Ordeshook, P. (Ed.), Models of Strategic Choice in Politics. University of Michigan Press, Ann Arbor, pp. 121–148. Baron, D., Diermeier, D., 2001. Elections, governments, and parliaments in proportional representation systems. Quarterly Journal of Economics 16, 933–967. Baron, D., Ferejohn, J., 1989. Bargaining in legislatures. American Political Science Review 83, 1181–1206. Barro, R., 1973. The control of politicians: an economic model. Public Choice 14, 19–42. Besley, T., Coate, S., 1998. Sources of inefficiency in a representative democracy: a dynamic analysis. American Economic Review 88, 139–156. Coate, S., Morris, S., 1995. On the form of transfers to special interests. Journal of Political Economy 103, 1210–1235. Dellis, A., 2004. Blame-Game Politics in a Coalition Government. Mimeo.

96

A. Dellis / Journal of Public Economics 91 (2007) 77–96

Diermeier, D., Merlo, A., 2004. An empirical investigation of coalitional bargaining procedures. Journal of Public Economics 88, 783–797. Drazen, A., 2000. Political Economy in Macroeconomics. Princeton University Press, Princeton. Fama, E., 1980. Agency problems and the theory of the firm. Journal of Political Economy 88, 288–307. Ferejohn, J., 1986. Incumbent performance and electoral control. Public Choice 50, 5–25. Fernandez, R., Rodrik, D., 1991. Resistance to reform: status quo bias in the presence of individual-specific uncertainty. American Economic Review 81, 1146–1155. Grilli, V., Masciandaro, D., Tabellini, G., 1991. Political and monetary institutions and public financial policies in the industrial countries. Economic Policy 13, 341–392. Groseclose, T., McCarty, N., 2001. The politics of blame: bargaining before an audience. American Journal of Political Science 45, 100–119. Holmstrom, B., 1982. Moral hazard in teams. The Bell Journal of Economics 13, 324–340. Holmstrom, B., 1999. Managerial incentive problems: a dynamic perspective. Review of Economic Studies 66, 169–182. Holmstrom, B., Ricart I Costa, J., 1986. Managerial incentives and capital management. Quarterly Journal of Economics 101, 835–860. Laban, R., Sturzenegger, F., 1994. Distributional conflict, financial adaptations and delayed stabilizations. Economics and Politics 6, 257–276. Laver, M., Schofield, N., 1998. Multiparty Government. The Politics of Coalition in Europe. University of Michigan Press, Ann Arbor. Laver, M., Shepsle, K. (Eds.), 1994. Cabinet Ministers and Parliamentary Government. Cambridge University Press, Cambridge. Lazear, E., 1989. Pay equality and industrial politics. Journal of Political Economy 97, 561–580. Milesi-Ferretti, G.M., Spolaore, E., 1994. How cynical can an incumbent be? Strategic policy in a model of government spending. Journal of Public Economics 55, 121–140. Morris, S., 2001. Political correctness. Journal of Political Economy 109, 231–265. Muller, W., Strom, K. (Eds.), 2000. Coalition Governments in Western Europe. Oxford University Press, Oxford. Olson, M., 1982. The Rise and Decline of Nations. Yale University Press, New Haven. Prendergast, C., Stole, L., 1996. Impetuous youngsters and jaded old-timers: acquiring a reputation for learning. Journal of Political Economy 104, 1105–1134. Rogoff, K., 1990. Equilibrium political budget cycles. American Economic Review 80, 21–36. Rogoff, K., Sibert, A., 1988. Elections and macroeconomic policy cycles. Review of Economic Studies 55, 1–16. Roubini, N., Sachs, J., 1989. Political and economic determinants of budget deficits in the industrial democracies. European Economic Review 33, 903–938. Scharfstein, D., Stein, J., 1990. Herd behavior and investment. American Economic Review 80, 465–479.