Parliamentarism or Presidentialism? 1

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1 Parliamentarism or Presidentialism? 1 Peter Buisseret Princeton University JOB MARKET PAPER Abstract In parliamentary and presidential systems, the voter delegates policy proposal and veto responsibilities to executive and legislative agents. Under parliamentarism, she directly appointments only the legislative agent; under presidentialism she enjoys the ability to directly appoint both agents. Why she should wish to forfeit the additional degree of expost control associated with presidential government? I develop a model in which politicians abilities are private information, and in which actions taken by one agent provide information to the voter about both agents types. A system in which the electoral fate of these agents is institutionally fused reduces the incentives of the legislative agent to build reputation through the specious rejection of executive proposals. This can improve the voter s inference about the realized types of politicians, her decision about whether to retain or replace either agent, and her welfare, relative to a system in which the survival of the legislative agent is institutionally separated from that of the executive. 1 For invaluable support and advice throughout the project, I thank Adam Meirowitz, John Londregan, Matias Iaryczower, Kris Ramsay and Leonard Wantchekon. I also thank Scott Ashworth, Brandice Canes- Wrone, Massimo Morelli, Gabriel Negretto and Ken Shotts, in addition to participants at MPSA and EPSA 01 meetings. In addition to a number of graduate colleagues, Benjamin Brooks and Elizabeth Petcu offered many helpful and patient discussions. The usual disclaimer applies.

2 1. Introduction What are the consequences of parliamentarism and presidentialism for political accountability and the quality of legislative output? Can one system more reliably empower the voter to make accurate retrospective judgements about the qualities of her elected representatives? Under each system of government, the voter delegates competing responsibilities to multiple elected agents. One agent, often an executive body, serves as a proposer, tasked with designing and submitting policy initiatives; the other, typically a legislative body, is a veto player, whose role is to scrutinize these initiatives and either pass or reject them. A fundamental distinction in the organization of this delegation across systems lies in whether the voter s decision to retain or replace each agent is institutionally separated, or fused. Under presidentialism, the legislature and the executive are independently appointed. Under parliamentarism, the voter directly controls only the appointment of the legislature, and therefore forfeits a degree of ex-post control in the selection and retention of these respective agents. Why should she wish to tie her hands in this way? To address this puzzle, I conceive of the legislature as an information intermediary which stands between the executive and the voter, in two distinct senses. First, since the executive submits initiatives of variable quality and appropriateness for a given policy context, the legislature must assume responsibility for scrutinizing and vetoing some policy proposals before they can actually be implemented. That is, the improved information that the legislature may have about a policy allows it to protect the voter from bad policies. Second, by vetoing bills, it controls the information available to the voter about the executive. This is because the voter does not get to see whether the policy initiative would have been successful (since it was vetoed), and so her ex-post evaluation of the executive after observing a veto will depend on whether she believes the legislature correctly identified a bad policy initiative. These forces are somewhat at odds with one another: though it is valuable for the voter to be inoculated against bad policies, it is also useful for her to see the outcome of these policies in order to draw more potent inferences about the kinds of politicians in office, so The reader will note that in some settings, these roles are reversed, and there is nothing in the conceptual framework or in the formal analysis that relies on thinking of the executive as a proposer. 1

3 that in turn her decision to replace or retain them is maximally informed. This tension is exacerbated by the fact that the legislature is staffed by re-election oriented agents with an independent motive to convince the voter of their discerning abilities, and since discerning legislatures should sometimes reject policies, this generates incentives for spurious legislative obstruction. As such, I argue that a constitutional commitment on the part of the voter not to separate the retention of the executive and legislature may induce the latter to act as a more efficient intermediary than would be the case when this commitment is absent. By providing an original theoretical framework with which to pose and resolve fundamental questions about the limits of accountability and delegation under parliamentary and presidential government, this paper builds on seminal work by Strom (003) and Muller et al. (006) and Lupia (003). I show that the voter is able to form more accurate retrospective inferences about the ability of the executive under a parliamentary than under a presidential system (informativeness) but that under presidentialism, she is more likely to successfully remove bad executives from office (accountability). The mechanism that generates superior information for the voter under parliamentarism is the unwillingness of the legislature to intervene in the executive s program, since any improved reputation she obtains in the process comes at the expense of the voter s assessment of the executive. When the voter s decision to retain the legislature and the executive are institutionally inseparable, the legislature may prefer to take its chances on implementing the executive s program even though it strongly doubts that it will succeed. Since the voter therefore observes more policy outcomes when bills are implemented, she gets powerful information about the executive. But she is also exposed to a greater risk of bad policy outcomes as a result. Thus, I show that whilst presidentialism maximizes the probability that a good policy initiative is rejected by the legislature (Type I error), parliamentarism maximizes the probability that a bad policy initiative is passed (Type II error). Finally, I compare voter welfare under each system and elaborate the conditions under which the voter should favor either parliamentary or presidential government. The paper is organized as follows: after reviewing related literature, I present the model and preliminary results. I begin the main analysis with a benchmark setting in which there is no private information. In this case, I show that presidentialism is always strictly pre-

4 ferred to parliamentarism. Then, I consider the more realistic setting of private information about politicians abilities and characterize the equilibria under each system. I subsequently compare the properties of these equilibria in order to rank each system with respect to the normative criteria elaborated, above.. Related Literature This paper contributes to a nascent literature concerning delegation and accountability in parliamentary and presidential democracies, and in particular the seminal contribution of Strom (003) and subsequent work by Muller et al. (006). Like these scholars, I conceive of these systems as alternative delegation regimes, whose fundamental distinction lies in the indirect appointment of the executive under parliamentarism as contrasted with her direct and separate appointment under presidentialism. Yet my approach builds on their contributions in a number of important ways. First, I provide a formal theoretic framework to pose and resolve crucial normative questions and rank systems in respect of their relative performance on each dimension. Second, I provide a corrective to a problematic substantial orientation in the conception of accountability that prevails in this literature. Prior authors conceive of accountability as a process of control, rather than as a type of outcome, in the typology of Lupia (003). Under the former conception, an agent is accountable to her principal if she is subject to direct electoral control, regardless of how this electoral control is exercised and whether it actually delivers the results that the voter would like. In this vein, Shugart and Carey (199) argue that in respect of accountability, presidentialism is clearly superior to parliamentarism, since voters vote directly for an executive that cannot be removed by shifting coalitions in the legislative assembly (Shugart and Carey, 199, 44). But it is at least as important to understand the consequences of this electoral control for the voter s ability to secure good policy outcomes, since it is outcomes that ultimately matter. A voter can only make appropriate decisions to retain or replace politicians if her beliefs about them after observing their actions in office are accurate (Anderson (007)). An insight of my formal argument is that the subsequent degree of ex-post electoral control that is available to the voter will condition the incentives of players at an earlier stage to reveal more or less relevant information through their actions about each others abilities. This 3

5 connects to a broader literature which considers the tendency of different political systems to generate clarity of responsibility in the perceptions of the voter (Powell Jr and Whitten (1993) and Lewis-Beck (1990)). This literature focuses on the ability of voters to attribute economic outcomes to the actions of political actors, and, broadly speaking, suggests that in systems in which executive and legislative control is vested in a single agent, such as a political party, the ability of the voter to make such attributions is maximized. This paper extends these ideas by evaluating whether institutions that strategically reveal greater information about politicians to the voter should be desired for their own sake, and if not, how the prospective benefits to the voter from more transparent institutions should be weighed against potential opportunity costs in other dimensions of institutional design. For example, consider Westminster-style parliamentarism, in which the empirical success rate of executive-sponsored legislation is virtually one hundred percent. In this case, the voter is able to obtain very good information about the type of executive in the sense that she observes the payoff consequences of every bill. If the result is a sequence of bad bills, however, is the cost of learning too high? Would the voter prefer to have a more active legislator who occasionally censored the voter s observation of the policy outcome if this provided her with less potent information about the executive, but inoculated her against bad policy initiatives? The analytical framework I construct provides answers to these questions. The model also relates to formal-theoretic treatments of the veto under presidential and parliamentary systems. 3 One notable work in this vein is Huber (1996), which considers the consequences of the prime ministerial right to attach a motion of confidence to a policy initiative. Huber shows that this institutional procedure may endow the prime minister with significant agenda-setting powers, since it effectively permits her to make the final take-or-leave offer to the legislature. My model provides a complementary explanation for the agenda-setting powers enjoyed by prime ministers. It locates the imperative for the veto player to acquiesce to the executive s policies in the fact that a veto carries a reputational consequence for both the veto player and the proposer. A veto may be a potent means for 3 Many such models study the role of vetoes in Baron-Ferejohn bargaining settings, in which the (distributive) policy context is quite different from the one considered in this paper; recent work includes Diermeier and Vlaicu (011) and Nunnari (011). 4

6 generating a favorable posterior assessment in the eyes of the voter about the discerning qualities of the veto player. However, in a system where electoral fates are fused, this may constitute a pyrrhic achievement if it simultaneously leads to a sufficiently unfavorable assessment of the executive that the voter prefers to remove both players, rather than retain them. The informational content of a veto is also explored in Groseclose and McCarty (001), who consider a model in which the policy preferences of the veto player (in this setting, the President) are unknown to the voter. The president wishes to convince the electorate that she is moderate, but the proposer (Congress) wishes to portray her policy preferences as extreme relative to those of the median. Therefore, the proper may choose bills with the intention of fomenting a veto, if such a veto conveys an unfavorable image of the veto player to the electorate. My model is distinguished from this contribution in a number of ways. First, the players types are vertically, rather than horizontally distinguished, since in my model types represent differing abilities to discern an underlying policy-relevant state. Second, both of the players in my model seek to build their own favorable assessment in the eyes of the voter: each has solely her own re-election imperative, and any concern for the reputation of the other arises only in equilibrium. My formal argument connects with a number of models of signaling in legislative politics that feature a single, privately informed party - most notably Canes-Wrone, Herron & Shotts (001). The authors focus on a single re-election oriented executive who must select one of two policies under aggregate uncertainty as to which of two possible states has been realized. My model introduces a strategic, re-election oriented legislative agent, who chooses whether or not to pass bills submitted by the executive. Since the voter learns the state if and only if the bill is passed, the legislator renders the probability with which the state is revealed an endogenous quantity. What drives the behavior of the executive under either presidential or parliamentary government, then, is the variation in the strategic effect of the legislator s propensity to reject bills under each system. Another closely related paper in this line of literature is Fox and Van Weelden (010).The authors consider a model of the President and a partisan Congress in the US. The former may choose between a status quo and a revision policy, and the policy is subject to the possible veto of the Congress. The authors show that partisanship, defined as a situation in 5

7 which Congress has a primitive, exogenous preference over the posterior reputation of the executive, can overcome the deleterious tendency of the Congress to veto executive proposals excessively, in order to build its own reputation with the electorate. The present model differs from that of Fox and Van Weelden (010) in a number of important ways. First, the authors do not attempt to compare presidential and parliamentary systems. Second, the authors assume that the value of a player s reputation is a smooth and strictly increasing function of her posterior assessment. In the multi-agent setting, however, this implicitly assumes a rather particular and stark form for the voter s trade-off between high and low types of each politician. If the objective of each politician is to be re-elected, her objective function certainly must depend on the voter s posterior belief about both herself and that of the other politician. In the present paper, however, the politicians objectives are endogenous to the relative value placed by the voter on each politician s type, which is itself endogenous to the institutional setting and resultant flexibility given to the voter in separating or fusing her ability to replace each of the executive and legislator. So, when the voter can only jointly retain or jointly replace both politicians, the value she places, and thus the legislator places, on believing that the legislator is a high type if this is jointly delivered with the executive being a low type will be quite different from a system in which each politician may be separately retained or replaced. Finally, the authors focus on equilibria in which the executive always submits the bill which conforms to her belief, and as such do not study the effect of the legislator s behavior on the policy submission of the executive. In my model, specious rejection of executive proposals can generate an additional distortion in the executive s policy submission in a presidential system, which leads her to submit bills that she believes would be less likely to succeed, conditional on being implemented. That they are relatively unlikely to succeed makes them more likely to be submitted only by competent types, which makes them more likely to be passed by the legislature and thus the low type executive may submit these policies sometimes in order to at least have a chance of seeing a policy be implemented. 6

8 3. Model I consider a two-period game with three players: an executive (e), a decisive legislator (m) and a voter (v). There are two possible states of the world, X and Y, each of which is associated with an optimal policy, x or y, respectively. The players in the model are distinguished by their private information about which of the states has been realized. The voter knows only that each state is equally likely (that is, Pr(X) = 1 ).4 An executive is either a high type, or a low type, denoted e H and e L, respectively. A high type executive knows which of the two states has been realized, whereas a low type has no information beyond the prior belief. In the same way, the legislator may also be a high or low type, denoted m H and m L, respectively, with the same information structure. Thus, a high type executive and a high type legislator knows which of the two policies x and y should be implemented. I assume that neither the legislator nor the executive know the other s type, and the voter does not know the realized type of either politician. 5 However, each politician is believed to be a high type with probability α (0, 1). After nature has drawn the state and each player s type, the strategic interaction in this model takes place in the context of a simple legislative process: (1) The executive selects a policy to submit to the legislator, either x or y. This submission is observed by all agents, including the voter. () The legislator may either pass or veto the bill: (a) if the legislator passes the bill, the state is observed by all agents, and the game proceeds to step (3). (b) if the legislator vetoes the bill, the state remains unobserved by the agents who are initially uninformed beyond the prior, and the game proceeds to step (3). (3) the voter updates her beliefs about both agents and chooses whether to replace either one or both actors according to the constitutional setting (see below); 4 In the Appendix, I study a more general setting in which Pr(X) = θ > 1, and all equilibria studied here are robust to θ within a neighborhood of 1. 5 The results are unchanged if we assume that each politician knows the other s realized type. 7

9 (4) Steps (1) and () are repeated with the state being independently drawn from the same distribution, after which all payoffs are collected and the game ends. Though stylized, this process contains a number of important features. First, the legislator is able to control how much the voter learns about the policy initiative. The substantive interpretation of this assumption is that if a policy is implemented, a reasonable approximation is to suppose that the voter will see whether or not it succeeded, and so will be able to learn whether it was ultimately the appropriate policy. Significantly, if the policy is vetoed, she will be able to make inferences only based on the strategies of the players, since the policy is not implemented and so its consequences cannot be immediately observed. There are six possible outcomes that the voter can observe after step (): for each of the two policies that might be submitted by the executive, she may either see the policy be implemented and that it matches the state or does not match the state, or she may see only that it is vetoed. The role of the voter is summarized in step (3): she must draw an inference about the type of each politician from whichever of these outcomes she observes, and choose a retention strategy from a constitutionally determined set of possible actions. To that end, let A v ={(1 e, 1 m ), (0 e, 0 m ), (1 e, 0 m ), (0 e, 1 m )} (1) denote the set of possible actions from which the voter might choose, where 1 i for i {e, m} denotes a decision to retain politician i, whereas 0 i denotes a decision to replace the politician. So, (1 e, 1 m ) is the action in which she retains both politicians, whereas (1 e, 0 m ) denotes an action in which she retains the executive, but replaces the legislator. If either politician is replaced, a new politician accedes to the corresponding office, with the same probability of being a high type, α. In order to focus attention on the comparative institutional effects of the degree of separation of origin under parliamentary and presidential government, I model the distinction between each system solely in the following assumption: Assumption 1. (Separation of Origin) Under presidentialism, the voter may select any action in A v. Under parliamentarism, the voter may only select from one of the first two actions in A v. 8

10 So, under presidentialism, the voter can retain or replace each politician, independent of the other. Of course, she may also choose to jointly replace or jointly retain each politician. Under parliamentarism, her ability to replace the executive is indirect: she may only jointly replace or jointly retain both politicians. Thus, an important initial observation is that the voter can select any strategy under presidential government that she can choose under parliamentary government, but the reverse is not true. The per-period payoffs of the players are as follows: in each round in which the state is X and the policy x is passed, or in which the state is Y and the policy y is passed, the voter receives a payoff of 1. If either bill is rejected by the legislator, the voter receives a payoff of 0. Finally, if the state is X and the policy y is passed, or if the state is Y and the policy x is passed, the voter receives a payoff of 1. Politicians are entirely office-motivated, and receive a payoff of 1 if and only if they are retained. 6,7 To avoid knife-edge multiplicity, I make some additional assumptions about how players behave when indifferent between two actions in a pure strategy equilibrium. 8 Since I present the main results of the model informally throughout the main body of the paper, I relegate notation that is used in proofs to the Appendix. The solution concept for this model is perfect bayesian equilibrium; a formal definition is in Appendix A. Since this game possesses many perfect bayesian equilibria, I restrict attention to a class of 6 Note that I do not give politicians direct preferences over the retention of the other politician. This is because I want to focus on institutional effects, and because giving politicians these direct preferences would only strengthen my results. 7 The choice of wholly office-motivated politicians is designed to simplify some of the algebraic manipulations in the proofs. In the second period, I select the strategy profile which corresponds to the strategies played by agents who care about policy outcomes (which always dominate in the second period since there is no re-election motive). If one wished to introduce an explicit policy motivation i.e. concern for the voter s welfare in the first period behavior, one could do so and simply preface all of the results in the paper with the qualification that the policy motivation cannot be too large, relative to the office motivation. 8 I assume that if either legislator type is retained or replaced with probability 1 regardless of her choice of action, or with probability 0 regardless of her action, she passes a bill. In addition, if a bill is passed which fails to match the state, and the voter is indifferent between an action in which the legislator is retained and one in which she is replaced, under a strategy profile in which both legislator types play pure strategies, I assume that her indifference is resolved in favor of replacement. 9

11 equilibria in which the high type executive submits the bill matching the state, and the high type legislator passes a bill which matches the state. This rules out pathological equilibria in which, for example, the high type executive demonstrates her competence by submitting only bills which do not match the state, or the high type legislator demonstrates her competence by passing bills which fail to match the state. It does not guarantee, however, that the low type executive will submit the bill which corresponds to her belief about the state, nor does it ensure that the low type legislator will pass a bill that she believes to be relatively likely to match the state, nor that the high type legislator will veto bills which fail to match the state. I also impose conditions on beliefs formed about players from the observation of events which do not occur with positive probability under a given strategy profile. Recall that the voter s belief after observing the first period outcome is a probability distribution over four possible politician-type pair realizations: (e H, m H ), (e H, m L ), (e L, m H ) or (e L, m L ). I impose the following restrictions on the voter s beliefs for events which take place off the equilibrium path, for a given strategy profile: (a) If a bill is vetoed, off the path, her beliefs place probability 0 on the realization (e H, m H ), and her belief about the legislator s type is strictly more favorable than the prior. (b) If a bill is passed which fails to match the state, off the path, her beliefs place probability 1 on the union of (e L, m L ) and (e L, m H ). The first part of (a) states that the voter cannot believe that she faces two high type politicians after a bill is vetoed: she may believe that one is a high type and the other a low type, or that both are low types, however. The interpretation of this requirement therefore is that if both politicians were high types who knew the state, and high type executives and high type legislators submit and pass the correct policy, respectively, we should not observe vetoes. Part (b) states that if a bill passes and fails to match the state, we cannot have a high type executive. 9 Finally, where a strategy profile can be supported as an equilibrium 9 Note that the specification of these off-path beliefs is not redundant, given our assumption about the strategy of the high type executive and the assumption that the high type legislator always passes bills which match the state. 10

12 only when Pr(X) = 1, and cannot be supported when the prior is imbalanced in favor of the state X by some arbitrarily small amount, I eliminate it. All references to an equilibrium refer to beliefs and strategies satisfying these requirements, which are formally stated in Appendix A Second Period Strategies To begin, we must specify the strategies of each politician in the second period of the game, since this behavior will generate the voter s incentives to retain or replace politicians in the first period, depending on her beliefs about their type. Since there is no re-election motive in the second period, I select the strategy profile which maximizes the expected payoff of the voter beginning in that period. Since this strategy profile does not depend on the history of the game, or any of the players beliefs about the other s realized type, I make no reference to the history of play, or beliefs. Lemma 1. Under each system of government, in the second period, the following strategy profile maximizes the expected payoff of the voter: (i) the high type executive submits the bill matching the state; (ii) the low type executive submits x; (iii) the high type legislator passes a bill if and only if it matches the state; and, (iv) the low type legislator passes all bills. 10 This approach to focusing on a particular class of equilibria in which a subset of player types choose a particular strategy is also adopted in Fox and Stephenson (011). The reader may wonder why I do not make reference to one of the standard refinements for this class of games, e.g. D. In short, this game structure possesses some non-standard properties such that standard belief-based refinements are not defined for this environment. Extending a given belief-based refinement is a notationally intensive and unedifying exercise, not least because it is possible to fix a strategy profile in which we can go three steps off the equilibrium path. 11

13 Under the strategy profile, since the low type legislator has no information beyond the prior, conditional on the strategy of the high type executive, and for any belief she holds about the executive s realized type, if she receives the policy x or the policy y, she believes that it matches the state with probability greater than 1. So, she will pass all initiatives. The high type legislator passes a bill if and only if it matches her signal. For the rest of the equilibrium characterization under each system, I focus on behavior in the first period. 5. Benchmark: Complete Information In order to motivate the trade-offs in the case of incomplete information, I begin by examining the best equilibrium for the voter in the stark case in which the voter has complete information about the type of executive and legislator in office. This benchmark yields a strong conclusion: there are no trade-offs between systems in this setting, and presidentialism is unambiguously preferred to parliamentarism by the voter. Proposition 1. If the voter has complete information about players types, she receives a strictly higher expected payoff from presidentialism than parliamentarism. With complete information, presidential democracy is superior to parliamentary democracy because it offers the voter a richer set of replacement strategies than is available to her under parliamentary democracy. In particular, any strategy that the voter may choose under parliamentary democracy is also available to her under presidential democracy. This expanded set of feasible actions is most useful to the voter when the executive is known to be a low type and the legislator is known to be a high type, in which case the voter would prefer to replace the former and retain the latter. Under presidential democracy, this strategy is available to her, whereas it is it not available to her under parliamentary democracy. If the probability of drawing a high type executive is sufficiently large and in the first round the voter knows that the executive is a low type, it is worth taking the risk of jointly replacing the politicians under parliamentary democracy, since obtaining a high type executive is sufficient for obtaining an expected payoff of one in the next period. If the probability of drawing a high type executive is sufficiently low, however, it is better to 1

14 retain both politicians, since at the very least the high type legislator serves as an effective antidote to an ineffective executive and redrawing both politicians may result in two low types. Regardless of which case obtains, however, the expected utility of the voter is strictly greatest under presidential government. Therefore, if the provision of more finely grained replacement strategies to the voter has no effect on the incentives of each politician in the first period, their sole effect is to benefit the voter through her ability to maximize her expected payoff in the second period through her replacement strategy. But if these more finely grained strategies induce strategic behavior by re-election oriented agents when their abilities are privately known, a tension may arise between better ex-post electoral control and the behavior of politicians in the first round. I now explore this possibility in a strategic environment with incomplete information. 6. Incomplete Information 6.1. Parliamentary Government: Incomplete Information To provide intuition for the strategic incentives under parliamentary government, let us ask whether an equilibrium can be sustained in which both legislator types pass every bill with probability 1, for any beliefs they may hold about the probability with which it matches the state. Under such a strategy profile, a veto does not occur with positive probability. Suppose that, upon observing a veto, the voter believes with probability 1 that the legislator is a high type who knows that the bill does not match the state, and that the bill must therefore have been sent by a low type executive. Suppose, moreover, that the probability of drawing a high type politician in the second period, α, is large (the precise threshold will be clarified, shortly), so that upon redrawing both politician types, the voter is relatively likely to obtain a high type executive, which is sufficient for her to receive an expected payoff of 1 in the second period. Then, even if she believes that the legislator is a high type with probability 1, her assessment of the executive may be sufficiently unfavorable for her to prefer joint retention to joint removal. The expected payoff to retaining a low type executive and a high type legislator is Pr(X) = 1, since in the second period the low type executive s policy submission matches the state with probability 1 and the high type 13

15 legislator vetoes the bill if and only if the bill fails to match the state. Therefore, the voter prefers to remove both politicians given that she believes with probability one that she faces a low type executive and a high type legislator if: or 1 α + 1 (1 α)α () α Thus, as long as the probability of drawing a high type politician is greater than this threshold, the voter removes both politicians after a veto, even though the veto yields the legislator the highest possible reputation. In fact, for α 3 5, I establish that in any equilibrium, no veto occurs on the equilibrium path. When the probability of drawing a high type politician is relatively low, on the other hand, it is still possible to support this equilibrium through the appropriate specification of beliefs off the equilibrium path. I summarize this observation in the following proposition. A rigorous statement of this and all propositions, including a specification of off-path beliefs, is contained in the Appendix. Proposition. Under parliamentarism, for α [0, 1], an equilibrium exists in which: (i) Each legislator type passes all bills with probability 1. (ii) The high type executive submits the policy matching the state, and the low type executive submits the policy x with probability 1. (iii) If a bill is passed which does not match the state, or after a veto, the voter removes both politicians with probability 1. (iv) If a bill is passed which matches the state, the voter retains both politicians with probability 1. When α > 3 5, points (i) through (iii) are true in every equilibrium. Suppose, instead, that α 3 5, so that the probability of drawing a high type politician in the second period is relatively small. Now a high type legislator is a substitute for a low 14

16 type executive, when the voter s only option is joint retention or joint removal. For that reason, so long as the voter believes that the legislator is sufficiently likely to be a high type after a bill is vetoed, the high type legislator is prepared to reject a bill that does not match the state, since the information that the executive is a low type no longer leads the voter to prefer joint removal. In turn, however, this creates an incentive for the low type legislator to pool with the high type, speciously rejecting bills which she believes to match the state. This partially obviates the ability of the voter to learn about either politician: she is less able to infer that the legislator is a high type after observing a veto, and for the same reason cannot be sure that a veto evidences unfavorable information about the executive. Later, we will see that the magnitude of this effect is relatively small compared to the equilibrium under presidentialism. Proposition 3. Under parliamentarism, for α 3 5, there exists an equilibrium in which: (i) The high type legislator vetoes bills which do not match the state, and passes bills that do match the state. (ii) The low type legislator vetoes the bill x with positive probability and passes the bill y with probability 1. (iii) The high type executive submits the policy matching the state, and the low type executive submits the policy x with probability 1. (iv) The voter retains both politicians with probability 1 after a bill is passed which matches the state and removes both politicians after a bill is passed which fails to match the state. After the bill x is vetoed, both politicians are retained with positive probability, and after the bill y is removed, both politicians are removed with probability 1. In addition to this equilibrium and the equilibrium characterized in Proposition, there also exist two additional equilibria. In one of these, the low type executive randomizes over her policy submission, and this equilibrium is fully characterized in the Appendix. In the remaining equilibrium, the strategies of the players resemble those characterized in Proposition 3, but the low type executive submits y with probability 1, and the low type 15

17 executive vetoes with positive probability when she receives y, and passes x with probability 1. Nonetheless, I emphasize that there always exists an equilibrium on this interval in which the low type executive submits the bill which corresponds to her belief about the optimal policy, since it is a property of parliamentarism that I will show is never true under presidentialism. In the equilibrium characterized in the Proposition, the high type legislator is making use of her private information by rejecting bills which she knows do not match the underlying state, but this provides the low type legislator with an incentive to mimic such behavior by vetoing bills. Nonetheless, she recognizes that vetoes convey unfavorable information to the voter about the executive, and so she must veto with sufficiently low probability that, conditional on observing the veto, the adverse inference on the part of the voter about the executive is compensated by a sufficiently favorable inference about the legislator s type. This ensures, in equilibrium, that the probability with which the low type vetoes a bill is relatively small (in fact, depending on the probability that the executive is a high type - α - it ranges from zero to one quarter). The incentive compatibility of the low type executive s efficient policy submission is in spite of the fact that the policy x is sometimes rejected by the legislator. But this propensity to veto and, with positive probability, suffer removal after a veto, is mitigated by the fact that the legislator may prevent the executive s removal by rejecting the bill x when the state is Y, since she is retained with positive probability even if the bill is vetoed. This ensures that the low type executive s strategy can be supported, even though both legislator types interpose themselves between her and the voter, and the low type legislator s strategy is driven by her attempt to pool with the high type legislator. To summarize the case of parliamentary government: when the probability of drawing a high type politician is sufficiently large, there is a unique equilibrium in which all policies are vetoed with probability zero. The high type legislator fails in her role as an information intermediary with respect to protecting the voter from bad policies. In that sense, the outcome is as it would be if there were no legislator at all. Nonetheless, the lack of engagement on the part of the high type legislator conveys two benefits. First, it provides the low type legislator with no incentive to mimic the high type by rejecting bills that she believes to match the state. Second, the lack of parliamentary scrutiny nonetheless provides 16

18 the low type executive with the incentive to serve the voter s interest, since her probability of re-election is strictly increasing in the voter s first period payoff and thus her probability of matching the bill to the state. When the probability of drawing a high type politician is sufficiently low, each legislator type is willing to engage with the executive more forcefully (though, in the case of a low type, undesirably), however there is always an equilibrium in which, despite the increased legislative obstruction, both executive types submit the policy that they believe is most likely to match the state. 6.. Presidential Government: Incomplete Information In order to explore the properties of equilibria under presidential government, we begin by considering the difference, from the perspective of the legislator, between the two systems. Under parliamentarism, she is retained if and only if the executive is retained. Under presidentialism, however, there are two ways that she can be retained: either both politicians can be retained, or the executive can be replaced and the legislator retained. Thus, in an equilibrium in which a veto occurs with positive probability, the legislator requires that, from the perspective of the voter, the best expected payoff from taking either of these actions weakly exceeds the best expected payoff to the voter from replacing either both politicians, or just the legislator. With this in mind, a useful starting question is whether we can sustain under presidential government an equilibrium in which neither legislator type rejects a bill with positive probability. The reason that such an equilibrium exists under parliamentarism is that each politician can only be replaced or removed, jointly. Under presidentialism, by contrast, the voter can choose to retain or replace each agent, separately. Under a strategy profile in which no bill is vetoed, suppose that the voter were to observe that a bill is rejected. Then, even if she believes that the legislator is a high type, and that the executive is a low type, since the legislator can now be retained independently of the executive, the former no longer has any qualms about inducing such a belief on the part of the voter. For this reason, we will see that in the unique equilibrium under presidentialism, the high type legislator always vetoes bills which do not match the state. What, in turn, does this imply for the low type legislator? She now has a powerful 17

19 incentive to veto bills, speciously, in order to pool with the high type legislator. The frequency with which she vetoes such bills is determined by a condition that the voter should be indifferent between taking an action in which the legislator is retained, and one in which she is removed. In turn, this requirement implies that when the voter observes a veto, her posterior belief that the legislator is a high type must be equal to the prior. This contrasts with the milder pooling incentive of the legislator under parliamentary government, who in equilibrium must compensate for the deterioration in the executive s reputation after a veto by rejecting bills with sufficiently low frequency to convince the voter that she is very likely to be a high type legislator, conditional on her having vetoed a bill. Under presidentialism, the legislator does not internalize the reputation of the executive as a result of her veto, and this leads her to veto with higher probability than in the equilibrium of Proposition 3. Proposition 4. In the unique equilibrium under presidential government: (i) The high type executive submits the policy that matches the state. (ii) The low type executive randomizes uniformly over the submission of policies x and y. (iii) With probability 1, the high type legislator passes a bill which matches the state and rejects a bill which does not match the state. (iv) The low type legislator rejects both policies with positive probability that strictly exceeds the corresponding probability of all the equilibria under parliamentarism. (v) The executive is removed with probability 1 after either policy is rejected, and whenever a policy is passed which fails to match the state; if a policy is passed which matches the state, she is retained with probability 1. (vi) The legislator is retained with positive probability after either bill is rejected and removed with probability 1 whenever a bill is passed which fails to match the state; if a bill is passed which matches the state, she is retained with probability 1. (vii) The voter s posterior belief about the legislator after either policy is rejected is equal to the prior. 18

20 These facts contrast notably with parliamentary government. First, a high type legislator always responds to her information, since she now reaps the reward of a positive probability of re-election. This probability would be one, were it not for the indirect incentive that this provides the low type legislator to pool with the high type, by speciously vetoing bills. The consequence of this pooling incentive is to mitigate entirely any informational benefit to the voter from the observation of a veto, with respect to the legislator s type. To see why it must be the case that the voter cannot learn anything about the legislator s type from the observation of a veto, suppose that she subsequently believes that the legislator is a high type with a probability strictly greater than the prior. In that case, she strictly prefers to retain the legislator, regardless of her retention or replacement of the executive. But then, the low type legislator would veto all bills, which is not consistent with the voter s belief. Not only does this worsen the inferential ability of the voter with respect to the legislator s realized type after observing a veto: it also provides commensurately less information about the executive, since the veto is comparatively likely to have come from a low type legislator, rather than reflecting that the executive submitted a bill which fails to match the state. In addition, the relatively greater frequency of vetoes censors observations of whether the bill matched the state, further obscuring the voter s inference about the executive s type, as well as that of the legislator. To see why there exists no equilibrium in which the policy x is submitted by the low type with probability 1, let us try to construct such an equilibrium. In that case, the executive is removed with probability 1 after the bill is vetoed. To make the policy y as unattractive as possible to the low type executive, let us suppose that if she submits y and it is passed and subsequently fails to match the state, then the voter believes that she is a low type with probability 1 and removes her. Then, since the low type executive is removed with probability 1 after either a veto or x is passed but the state is revealed to be Y, the low type executive weakly prefers to submit the policy x if and only if the following inequality holds: 1 (Probability x is passed state is X) 1 (3) where the quantity in brackets is strictly less than 1 because the low type legislator vetoes with positive probability and thus such an equilibrium cannot exist. Note that the difference 19

21 between this case and that of parliamentarism when the probability of drawing a high type is low (α 3 5 ) is that, unlike parliamentarism, under presidentialism the executive is retained with zero probability after the bill x is vetoed and this is why an equilibrium in which the low type executive plays a pure strategy can be sustained under parliamentarism but not presidentialism. Thus, the effect of the low type legislator s pooling is to drive a strategic wedge between the low type executive s belief about the policy environment, and her best response. It is important to note that what drives this wedge is not the fact that the bill x is vetoed, per se. If only the high type legislator were to veto the bill x when the state were Y, there would be no distortion in the low type executive s policy submission. Rather, this wedge exists because the frequency with which the bill x is vetoed by the low type legislator is driven by the latter s attempt to pool with the high type, rather than purely being driven by her belief that the state is X. This tendency renders y a plausible strategic substitute for the low type executive, even if her information about the state is that x is strictly more likely to be the better policy. 11 Earlier, I mentioned that there exists one equilibrium under parliamentary government when α, the probability of drawing a high type politician, is sufficiently low, in which the low type executive also randomizes uniformly over policies x and y. In this equilibrium, the low type legislator vetoes each of these policies with the same probability, which is strictly lower than in the corresponding unique equilibrium under presidential government. 1 Moreover, under parliamentarism, both the executive and legislator are retained with positive probability after the veto of either policy, in this equilibrium, whereas under presidentialism, the executive is removed with probability 1 after a veto. This is in spite of the fact that the voter s inference about the executive s type after a veto is strictly less favorable in the parliamentary setting than it is in the presidential case. 11 Here, I am using the result in the Appendix in which this equilibrium property holds for a prior belief about X strictly greater than 1. 1 Under presidentialism, the probability with which the low type legislator passes each of bills x and y is 1+α 1+α α, whereas under parliamentarism, it is (1 α), in an equilibrium in which σ(e L) = 1. The latter quantity strictly exceeds the former for any α 3 5, which is the interval on which the parliamentary equilibria exist. 0