Reconciling Theory and Estimation: Testing Theories of Lawmaking Using Ideal Point Estimates ∗ Joshua D. Clinton Department of Politics Princeton University Princeton, NJ 08544-1012
[email protected] Version 1.1: Under Active Revision December 1, 2005
Abstract Theories of lawmaking generate equilibrium predictions about the set of acceptable policy outcomes. Tests of theoretical predictions often use independently estimated ideal points based on roll call votes to estimate what appear to be theoretically relevant quantities. This paper demonstrates that such measures are invalid because of the endogeneity of the roll call record; predictions regarding equilibrium outcomes necessarily yield predictions about the agenda used to enact the outcomes. I demonstrate how divorcing the statistical model from the theoretical model results in the misleading use of ideal point estimates and the potential for incorrect inferences. Using the 103rd Congress and the predictions from prominent gatekeeping and veto theories, I illustrate how to integrate theoretical predictions within the statistical model used to estimate ideal points and reconcile the problematic disconnect between theory and estimation. In demonstrating how to account for the endogeneity of roll calls when theory-testing, I highlight the considerable complexity that results from testing predictions from models assuming perfect spatial voting using probabilistic voting model estimates and I argue that the properties of commonly used measures are not well-understood.
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The author would like to thank Keith Krehbiel, David Lewis, Nolan McCarty, Adam Meirowitz, Keith Poole and Eric Schickler for helpful comments.
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The ability to generate theories of lawmaking has not been matched by the ability to conclusively evaluate theoretical predictions. One difficulty in achieving scientific consensus is the absence of theoretically consistent measures and disagreement about the evidence for and against theories of interest. The lack of consensus is extremely consequential because the accumulation of knowledge and scientific progress depends on the ability to identify measures whose relationship to theories of lawmaking is clear and uncontested (Kramer (1986)). Estimates derived from roll call behavior are prominently used to test theories of lawmaking. Ideal point estimates (hereafter ideal points) such as NOMINATE (Poole and Rosenthal 1997) appear to offer the ability to achieve such diverse and critically important tasks as: measuring the width of pivot gridlock intervals (e.g., Coleman 1999; Epstein and O’Halloran 1999; Chiou and Rothenberg 2003), party-cartel gridlock intervals (e.g., Cox and McCubbins 2005), presidential veto intervals (McCarty and Poole 1995), party heterogeneity (e.g., Binder 1999; 2003, and Schickler 2000) and the extremity of congressional committees (e.g., Kiewiet and McCubbins 1991; Cox and McCubbins 1993; Londregan and Snyder 1994). As the partial but impressive list suggests, many prominent tests of lawmaking rely on roll call estimates to measure theoretically implied concepts. A fundamental problem in using roll calls to test theories of lawmaking is that roll calls – and therefore measures derived from roll calls – are not exogenous to the theories they are used to test.1 Almost every existing use of recorded roll calls to test lawmaking theories fails to account for the fact that in generating predictions about Congressional policymaking, the theories necessarily generate predictions about member behavior on roll calls enacting the predicted policies. Scholars have long-recognized the endogeneity of the observed roll call record (e.g., Snyder 1992; 1992b, Shepsle and Weingast 1994), but only recently have attempts been made to reconcile theoretical predictions and statistical models. For example, Groseclose and Snyder (2000) and McCarty, Poole and Rosenthal (2001) provide an application to the question of party influence, Londregan (2000; 2000b) provides an application to proposal behavior, and Clinton and Meirowitz (2003; 2004) provide an application to strategic voting.2 In this paper I expand the reconciliation of theory and estimation and demonstrate that the theories of lawmaking most frequently subjected to tests using ideal points actually yield predictions 1
This critique is independent of the difficulty of interpreting roll calls across changing institutional environments (e.g., Smith and Roberts 2003) or determining precisely what an ideal point estimate represents (e.g., Krehbiel 2000). 2 Krehbiel, Meirowitz and Woon (2004) provide a partial resolution to the issue in testing competing theories of lawmaking.
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directly in terms of the estimated ideal points. The theories speak directly to the type of agenda that we ought to observe and consequently the pattern of ideal points we should recover. To illustrate the necessity of employing theoretically informed tests when using ideal points, I show how the theoretical predictions of formal models of gatekeeping with majority-party gatekeepers (Cox and McCubbins 1993; 2005) or committee gatekeepers (Shepsle 1979; Shepsle and Weingast 1987) and models with veto players such as the president (e.g., McCarty and Poole 1995) or pivotal politics (Krehbiel 1998) yield very simple tests for determining the validity of the theory once the connections between the statistical model used to analyze roll call behavior and theory are realized. I show that the ability to calculate a gridlock interval using ideal points constitutes evidence either that the theoretical prediction is false or else that ideal points are generated using roll calls or methods outside the scope of the theory and therefore irrelevant for theory-testing. Addressing the endogeneity problem and deriving testable predictions directly in terms of the observed roll call record highlights a second problem: the underlying voting models for the theory and estimation differ. In implementing a test that accounts for the endogeneity of roll calls I demonstrate that testing predictions from a perfect voting model using estimates from a probabilistic voting model introduces considerable complexity. To illustrate the claims of the paper I assess the support for prominent theories of lawmaking in the 103rd Congress. Despite this focus, the arguments are relevant to any such theory applied to any parliament, court or deliberative body that implements outcomes via recorded votes. The paper proceeds as follows. Section 1 briefly discusses the differences between preferences as used in formal models and ideal points from roll call analysis and section 2 reviews the statistical model of voting behavior. Section 3 outlines two prominent theoretical models that ideal points are frequently used to test and derives testable predictions for each in terms of estimated ideal points. Section 4 argues that existing uses of ideal points to test these theories are inadequate, implements the tests derived in Section 3 using the 103rd Congress and discusses unresolved issues.
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Preferences and Ideal Points
Most formal theories of Congressional action assume members possess single-peaked (typically Euclidean) preferences (e.g., Enelow and Hinich (1984)). These preferences may be explicitly defined over policy outcomes or they may include both outcome and position-taking considerations;
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they may reflect purely personal preferences or they may represent re-election constituency preferences. The important point is that preferences in the context of formal models are primitives independent of actions. Because members’ preferences are unobserved, scholars are forced to try to measure preferences using observed actions. Roll call votes are one of the most common (and longest used) measures in Congressional scholarship; Rice proposed using roll calls in political science as early as 1925 and examining subsequent scholarship reveals their prominent and ubiquitous use (see, for example, Poole’s (2005) recent treatise). The suggestive possibility roll calls offer is the ability to measure members’ preferences. A known complication is that the mapping from preferences to observed behavior is imperfect; considerations such as strategic voting or agenda control may distort the mapping. Because roll calls are a function of member preferences expressed through potentially strategic votes on a potentially strategic agenda, it is unclear whether roll call voting behavior accurately reflects members’ policy preferences. It is well-known that the impact of possible strategic voting on such measures can arguably be limited by restricting the analysis to the set of final passage votes; legislators have an undominated voting strategy to vote sincerely – and presumably based on policy preferences – on final passage so long as they cannot credibly commit to log rolls. A more consequential, but less recognized, fact is that ideal points are based on roll calls that are endogenous to theories of lawmaking. In generating predictions about equilibrium policy outcomes, theories also predict which roll calls should be observed to enact those outcomes. Theories typically tested with ideal points actually yield testable implications directly in terms of the recovered ideal points. Because theories of lawmaking necessarily generate predictions about the roll call agenda, analyzing member voting behavior independent from a theory of lawmaking and using such estimates in a second-stage analysis to proxy for member preferences may lead to erroneous substantive conclusions. An important caveat is that these concerns are inconsequential for some uses of ideal points. Most notably, if behavior on roll call votes is of interest rather than the latent preference structuring a member’s roll call behavior – as is the case for testing theories about voting behavior (e.g., Snyder and Ting (2003) and the literature on shirking (see, for example, Rothenberg and Sanders (2000) for a recent contribution) then neither concern is problematic. Ideal points are arguably exactly
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the right measure to test accounts of member position-taking because the measure of interest is observed voting behavior (Mayhew 1974; Arnold 1990).
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A Statistical Voting Model
Analyzing roll call voting behavior and testing theoretical predictions requires a statistical model for describing member voting behavior. Typically, such models presume that members vote for the policy-outcome or position closest to their most-preferred policy (position) with error. To explicate the link between the theoretical and statistical models it is useful to consider the statistical model in some depth. For exposition, I use the model of Clinton, Jackman and Rivers (2004).3 Associated with each roll call vote t (t = 1...T ) is a pair of locations in the policy space – one associated with a successful roll call vote (θy(t) ), and one associated with an unsuccessful roll call vote (θn(t) ). Given that the theories suppose a unidimensional policy space, I restrict attention to a unidimensional statistical model. Assume that the utility for representative i (i = 1...L) with ideal point xi is given by: Ui (θt ) = −||xi − θy(t) ||2 + ηit Ui (ψt ) = −||xi − θn(t) ||2 + νit
(1)
where ηit and νit represent the stochastic portion of the utility function and || • || represents the Euclidean norm. The latent utility differential for representative i in roll call t is therefore: ∗ = U (θ yit i y(t) ) − Ui (θn(t) )
= −||xi − θy(t) ||2 + ηit − (−||xi − θn(t) ||2 + νit ) = −||xi − θy(t) ||2 + ||xi − θn(t) ||2 + ²it
(2)
2 2 = 2x(θy(t) − θn(t) ) − θy(t) + θn(t) + ²it
where ²it = (ηit − νit ). 3
Although the details slightly differ from other statistical models of roll call behavior (see, for example, Heckman and Snyder (1997), Poole and Rosenthal (1997) and Poole (2000)), the fundamental conclusion of the paper is not sensitive to the particulars of the statistical model employed.
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Assuming ²it is iid N (0, σt2 ), and letting Φ()˙ denote the standard normal CDF yields: ∗ = 1|x , θ ∗ Pit (yit i y(t) , θy(t) ) = Pr(yit > 0) ³ ³ ´´ 2 2 = Φ σt−1 2x(θy(t) − θn(t) ) − θy(t) + θn(t) .
(3)
Conditional on x and the T -length vectors of proposal locations θy(t) and θn(t) , assuming that representatives vote independently with respect to both indexes yields the probability of observing the L × T matrix of roll call votes Y : ³ ´´Yit ³ 2 2 T Φ σ −1 2x(θ − θ ) − θ + θ L(x, θ) = ΠL Π y(t) n(t) t i=i t=1 y(t) n(t) µ ³ ³ ´´1−Yit ¶ −1 2 2 × 1 − Φ σt 2x(θy(t) − θn(t) ) − θy(t) + θn(t)
(4)
where the only observable portion of the likelihood function is Y . To draw a similarity to item response models and facilitate estimation, it is possible to derive an expression for the item discrimination parameter as βt = 2σt−1 (θy(t) − θn(t) ) and the item difficulty parameter as αt = 2 2 ).4 This yields the likelihood of: σt−1 (−θy(t) + θn(t)
T Yit L(x, θ) = ΠL × (1 − Φ(βt x + αt )1−Yit ). i=i Πt=1 Φ(βt x + αt )
(5)
A choice of priors and a set of identifying restrictions completes the specification in the Bayesian context (see Clinton, Jackman and Rivers (2004) for details). The cutpoint associated with each vote is the ideal point at which the probability of voting “yea” is the same as voting “nay” (i.e., the position of an indifferent member on vote t). In terms of the model, this implies Φ(βt x + αt ) = .5, or βt x + αt = 0. Solving for x yields: −αt /βt . A Bayesian model enables the computation of any statistic of the posterior and yields an immediate assessment of the precision of each estimate. This offers two benefits. First, ideal point standard errors are estimated directly and it is straightforward to determine whether ideal point differences are non-zero.5 Second, an estimate and standard error for any quantity of theoretical interest such as the chamber median ideal point or the majority party median ideal point can be computed while accounting for any uncertainty about the identity of each. 4
An alternative factorization yields the expression employed by Bafumi et. al. (2005). But see work by Lewis and Poole (2004) which provide a means of generating bootstrapped standard error estimates for ideal points estimates generated using NOMINATE. 5
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Having outlined the basic statistical model used to analyze roll call behavior, I now demonstrate how the predictions of formal theories of lawmaking regarding the impact of gatekeepers and vetoplayers can be integrated, and therefore tested, within this statistical model.
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Selected Theories of Lawmaking
A debate of some ferocity in the Congressional scholarship concerns the nature of lawmaking. A prevalent argument (see, for example Rohde (1991), Aldrich (1995), Cox and McCubbins (1993; 2005)) is that the majority party leadership (in the House) exercises tremendous influence through its ability to control the agenda. Although the details vary, Cox and McCubbins (1993; 2005) provide one of the most complete articulations. The argument is that members have correlated electoral fates by virtue of their party affiliation and that these correlated fates offer the possibility of collective electoral gain (or loss). To solve the resulting collective action problem, party members endow a party leader with the ability to punish members who act contrary to party interests through committee assignments and other institutional prerogatives. The party leader is willing to undertake costly monitoring and organizational activities because of the rents resulting from agenda control; in return for solving the collective action problem the party leadership can determine the agenda. The competing claim is that the gains from collective action are insufficient to motivate party members to maintain cohesion (see, for example Mayhew 1974). In combination with the fact that Congressional institutions themselves are adopted by majority rule and therefore endogenous (Krehbiel’s (1992) Majoritarian Postulate) - the result is a more individualistic environment. Policymaking depends on the preferences of individual members and institutional features such as the possibility of a filibuster in the Senate and a presidential veto (Krehbiel 1998; Brady and Volden 1998). To make the comparison between the theoretical predictions and the analysis of roll call behavior explicit, I consider simple versions of the two accounts. Although the results are not novel (see, for example, Krehbiel, Meirowitz and Woon (2004)), it is useful to present the results to illuminate their connection with roll calls and ideal point estimation.
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3.1
Theoretical Predictions: Gate-Keeping Theories
Assume a unidimensional policy space X. Members have single-peaked preferences in X that are defined in terms of spatial proximity and member i’s most preferred outcome/position is xi ∈ X. Consider two players, a gatekeeper g with ideal point xg and the pivot required for passage – the median member in the case of a majority voting rule – m with ideal point xm . For simplicity, suppose xm < xg . The theoretical result is well-known and it has been widely adopted in the Congressional scholarship to model both committee (see, for example, Shepsle 1979; Denzau and Mackay 1983; Shepsle and Weingast 1987; Snyder 1992a; Crombez, Groseclose and Krehbiel 2005) and majority party (see, for example, Cox and McCubbins (1993; 2005), Aldrich (1995)) agenda control. The play of the game is as follows: • Nature draws a status quo policy q ∈ X that is perfectly observed by all. • Gatekeeper g decides to allow or disallow action on q. If action is allowed, play continues. If action is disallowed, status quo policy q is realized. • If gatekeeper g allows action, the chamber median m makes chooses the proposal p ∈ X to enact into law. The Nash Equilibria to this game consists of a set of decisions by the gatekeeper and a set of proposals by the chamber median. The latter is trivial – under majority rule the chamber median is decisive and proposes her ideal point p = xm in every instance. The set of equilibrium actions by the gatekeeper is likewise trivial. Since any status quo for which action is allowed results in the policy p = xm , the gatekeeper only permits actions for which xm is closer to xg than q. Consequently, if xm < xg , inaction should be observed for any realization of q ∈ [xm , 2xg − xm ]. The gatekeeper allows action on all other realizations. Figure 1A denotes the set of unique equilibrium policy outcomes p∗ for each realization of the status quo.6 [Insert Figure 1 About Here] Given an equilibrium prediction p∗ and a status quo q, the cutpoint for the enacting vote – defined as the point at which a member is indifferent to the two outcomes – is |p∗ + q|/2.7 The set of equilibrium cutpoints for this game is given in Figure 1B. Cutpoints are undefined in the region of [xm , 2xg − xm ] because gatekeeping prevents votes being taken on these status quos. 6 7
Figure 1 and 2 summarize the results presented in Krehbiel, Meirowitz and Woon (2004). Assuming both p∗ and q are greater than (or less than) 0.
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3.2
Theoretical Predictions: Veto Theories
Models of gatekeeping are typically talked about in conjunction – more precisely, opposition to majoritarian theories. Such theories posit that restrictions to lawmaking occur not because proposals are kept off the agenda, but rather because any successful policy must circumvent a series of veto players (e.g., the president (e.g., McCarty and Poole (1995) and Cameron (2000) or the president and the filibuster pivot Krehbiel (1998)). For exposition, suppose the chamber median m has an ideal policy outcome denoted by xm and that there are two veto players denoted l and r with most preferred policies xl ∈ X and xr ∈ X such that xl < xm < xr . With the same assumptions as above, typical play in a veto game is as follows:8 • Nature draws a status quo policy q ∈ X that is perfectly observed by all. • Chamber median m decides whether to make a proposal p ∈ X. If so, she reports p, if not, the game ends and q is realized. • Veto player l decides whether to veto p. If so the game ends and q is realized. If not, play proceeds. • Veto player r decides whether to veto p. If so the game ends and q is realized. If not p is realized. The equilibrium prediction from such a game is a unique mapping from the set of status quo realization q to a set of policy outcomes. Figure 2 presents the equilibrium outcomes and the equilibrium cutpoints. [Insert Figure 2 About Here] For status quo realizations in the interval defined by the minimum and maximum of the veto players’ policy preferences [xl , xr ] – the gridlock interval – policy change is impossible.
3.3
Implications for Roll Call Estimates
As roll calls are the mechanism by which policy change occurs, the theoretical predictions regarding equilibrium outcomes – and therefore proposals – have direct consequences for observed roll call behavior and therefore for ideal points estimated from roll call behavior. Following Krehbiel, Meirowitz and Woon (2004), Table 1 recounts the equilibrium policy prediction for each possible realization of the status quo q and the implied cutpoint for each theory. 8
Krehbiel’s (1998) pivotal politics version of this game adds the possibility of overriding the decision of one of the veto-players with a super-majority vote.
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Status Quo Location (q) q < xm q ∈ [xm , 2xg − xm ] q > 2xg − xm q < 2xl − xm
Proposal Attempted yes no yes yes
Eqm. Outcome
Eqm. Cutpoint
xm q xm xm
¢ ¡ q + xm2−q None ¡ ¢ m q − ¡ q−x 2 ¢ xm −q 2 ´ ³q +
q ∈ [2xl − xm , xl ]
yes
2xl − q
q ∈ (xl , xr )
no
q
q ∈ [xr , 2xr − xm ]
yes
2xr − q
q > 2xr − q
yes
xm
(2xl −q)−q 2
q+ ³ q+
= xl
None ´
q−(2xr −q) = ¡2q−xm ¢ q− 2
xr
Table 1: Theoretical Predictions: Gatekeeping (top) and Veto (bottom) Models. Cutpoints describe the ability to distinguish between member preferences using roll calls under perfect spatial voting. Because cutpoints denote the location of a member indifferent between the status quo q and the equilibrium proposal p∗ , if two members’ preferences are separated by a cutpoint then the members should vote against one another on that vote. As Table 1 makes clear, predictions about equilibrium proposals also predict which cutpoints should be observed and therefore which members should vote together. In other words, because ideal points are a function of member induced preferences and the observed agenda, the predictions about equilibrium outcomes from gatekeeping and veto theories have implications about the pattern of estimated ideal points.9 For example, gatekeeping theories predict that we should never observe a cutpoint in the interior of [xm , xg ] that results in policy change. Consequently, g and m should never be observed voting differently on votes implementing policy change because g would never allow an issue that divides them on the agenda. Because no cutpoint that divides the two are ever observed in equilibrium, this is equivalent to the prediction that the ideal points of the gatekeeper and chamber median are indistinguishable. The width of the gatekeeper interval calculated using ideal points generated according to an agenda in which the theory is true and under perfect spatial voting is therefore zero. A non-zero difference results if roll calls exist that distinguish the ideal points; under perfect spatial voting this is possible only if the members vote differently from one another – an impossibility if the theory is true. 9
As Krehbiel, Meirowitz and Woon (2004) argue (and Table 1 shows), the theories generate predictions about the location of successful final passage cutpoints. I focus on the pattern of ideal points because in order to test whether the cutpoints lie in theoretically impossible locations of the policy space requires the ability to estimate member preferences in the space. However, estimating member ideal points on the correct subset of votes (using a perfect voting model) is equivalent to testing the theory.
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Denoting the (perfect spatial voting) ideal point on the observed roll call agenda as xˆ yields the prediction that: Gatekeeping Theory: x ˆg = x ˆm . Testing gatekeeping theories therefore requires identifying the set of successful final passage votes and determining whether the ideal points of the gatekeeper and chamber median estimated using those votes are distinguishable. To illustrate the test for gatekeeping models, I use the predictions of the party cartel model (Cox and McCubbins 1993; 2005) which supposes gatekeeping by the majority party caucus. The relevant test involves estimating ideal points using all successful final passage roll calls and determining whether the ideal points of the chamber median and majority party median are statistically indistinguishable. An analogous argument yields the prediction for veto theories. Veto Theory: x ˆl = x ˆm = x ˆr . Testing the predictions of a veto model, of which Krehbiel’s (1998) pivotal politics is perhaps the most widely analyzed, requires estimating ideal points on the set of successful final passage votes and determining whether it is possible to distinguish between the ideal points of the set of members whose policy preferences are in the interior of the gridlock interval.10 Because status quos in the gridlock interval cannot be changed, veto players should never vote against one another on successful enactments; under perfect voting veto players’ ideal points should be indistinguishable. A complication results from the apparent need to compute gridlock intervals using members from different chambers and branches (see Bailey (2005)). Calculating the gridlock interval appears to require directly comparing Senate, House and Presidential preferences to one another which entails assuming either that members voting in both chambers have identical induced preferences (as Poole’s (1998) Common Space scores assume), or else that legislation considered in both chambers have identical status quos. It is possible to circumvent these complications by examining whether it is possible to distinguish between members assuredly in the interior of the gridlock interval. To test whether the veto players’ ideal points are indistinguishable I determine the largest set of legislators centered around the chamber median whose ideal points are indistinguishable and 10 The theory makes slightly different predictions for budget-related legislation since these have statutory debate limits that preclude filibusters.
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assess the plausibility that this set includes the veto players. Given that many of the veto players of interest in the pivotal politics model involve particular quantiles of the chamber (e.g., the 41st (60th) most liberal Senator needed to invoke cloture and stop a conservative (liberal) filibuster, or the 1/3rd (2/3rd) most liberal House member needed to override a Republican (Democratic) President), this determination is informative with respect to theoretical predictions. Testing these predictions using a probabilistic voting model like that of section 2 appears straightforward: identify the set of successful final passage votes, estimate member ideal points using the statistical model and examine whether the estimated difference between the chamber median and majority party median is non-zero (party cartel) and the percentage of members whose estimated ideal points are indistinguishable from the chamber median (pivot theory). A problem in testing these predictions is the noise that results from using estimates derived from a probabilistic voting model to test predictions generated under perfect spatial voting.11 Under perfect voting, theoretically consistent data would provide no ability to distinguish between the estimates of the chamber median and majority party median (for example). Unfortunately, this statement is not true for probabilistic voting models such as W-NOMINATE (Poole and Rosenthal 1997), D-NOMINATE (Poole and Rosenthal 1997), DW-NOMINATE (McCarty, Poole and Rosenthal 1997), Quadratic-Normal (Poole 2001), Heckman and Snyder (1997) and Bayesian models (Jackman 2001; Martin and Quinn 2002; Clinton Jackman and Rivers 2004). In other words, for the type of ideal point estimates that are almost universally used to test theories, the difference in the underlying voting models may prove problematic. The problems introduced by employing different voting models at the theoretical and empirical stage is a subject I return to in section 4.2. Having demonstrated that the theories of most interest to contemporary scholars have testable implications in terms of ideal points estimated on the set of relevant roll calls (under the assumption of perfect spatial voting), I now consider the inadequacy of existing tests that ignore this fact and the implementation of the tests I propose as a solution. 11 Rosenthal and Voeten (2004) propose Poole’s Optimal Classification (2000) for instances in which perfect spatial voting occurs. Even if Optimal Classification proves better than probabilistic voting models in such instances because it relaxes the iid assumption to allow unspecified voting errors, further investigation is required to derive testable predictions (e.g., because only rank orderings are identified in one dimension, the party cartel model predicts that a majority of the majority party has the same rank ordering – the chamber median, the majority party median and all intermediate members should vote identically) and examine the ability of Poole’s OC to measure theoretical quantities. I focus on probabilistic voting models because existing scholarship uses these models almost exclusively in theory-testing.
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4
Empirical Tests of Theoretical Predictions
To test the theoretical predictions of section 2, scholars frequently use estimates from statistical models of roll call behavior. A prevalent application is to use the ideal points xˆ from a probabilistic model such as NOMINATE to calculate the partisan (i.e., |2xˆg −xˆm |) and non-partisan (i.e., |xˆl −xˆr |) gridlock intervals for use as independent variables in a subsequent analysis. Despite widespread use, at least two severe problems result from treating ideal points as exogenous.12 First, to the extent that ideal-point based measures are used in a regression analysis (e.g., predicting the incidence of legislation as a function of the width of a theoretically implied gridlock interval), the fact that the theory being tested has implications for both the dependent variable and the measures of the gridlock interval means that such an analysis is plagued by endogeneity concerns. Because the tested theory has direct implications for the types of roll calls that should be observed, roll call based measures are not exogenous. Although the resulting inconsistency of regression estimates from endogenous regressors would appear to be sufficiently severe, the problem is actually worse. A second, deeper point is that the entire endeavor of calculating gatekeeping intervals for use in a regression analysis is misguided. As section 3 makes clear, because the theory being tested yields predictions about the distribution of recovered ideal points directly, the existence of a nonzero interval indicates: the theory is false, the theory is true but the votes used to generate ideal points are irrelevant to the theory, or the theory is true, the correct votes are used and that the probabilistic voting model used to estimate ideal points introduces sufficient error into the test. It is therefore unclear what controlling for the width of a gridlock interval accomplishes (for example) as the width of the gridlock interval should be zero if the correct votes and estimator are used and the theory is true. Finding a non-zero interval using the set of final passage votes is either: 1)the only evidence required to test a theory or 2) evidence that the votes and method are insufficient to test the theory.
4.1
Integrating Theory and Method: 103rd Congress
Given the problematic existing usage of ideal points to test theories, I demonstrate how the theoretical predictions can be tested directly using the observed roll call record. Testing the model 12
As previously noted, a separate, but equally important, question concerns the ability of estimates from probabilistic voting models to measure quantities from perfect voting models.
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requires identifying the relevant set of roll calls, imposing the required identification constraints, estimating the statistical voting model and computing posterior differences. I put aside the potential complication arising from differences in the underlying voting models (which is not unique to the tests I propose) until section 4.2 Once the set of theoretically relevant roll calls have been identified, testing the predictions involves estimating two statistical ideal point models – one that is unconstrained and one that imposes the theoretically implied constraints – and testing whether the constraints are valid (Clinton and Meirowitz 2003). This appears to be difficult for the testing the predictions of section 3 because the identity of the legislators whose ideal points should be constrained are unknown.13 An alternative, but statistically equivalent approach involves estimating an unconstrained model and testing whether the relevant recovered ideal points are statistically distinguishable. To illustrate the integration of estimation and theory-testing, as well as the resulting problems, I consider the 103rd House and Senate (1993-1995). Although irrelevant for the tests I conduct, since the Democrats controlled both chambers of Congress, there is some reason to suspect that the two agendas might share a similar focus.14 The results should be interpreted as illustrating the need for integrating theory and data in testing theories of lawmaking using roll call behavior. The point of the analysis is not to engage in the ongoing “pivots-vs-party” debate, but rather to suggest that at least some of the debate is being waged on the wrong terrain. Table 2 summarizes the roll call record. Chamber & Source House (Rohde 2004) House (KMW 2004) Senate (KMW 2004)
Total Roll Calls 1094 (1010) 1094 (1010) 724 (671)
Final Passage 263 (225) 102 (100) 60 (58)
Successful Final Passage 207 (207) 100 60
Table 2: Roll Calls Used for 103rd Congress: Number in parentheses is the number of nonunanimous votes on which estimates are based. Total Roll Calls lists the total number of roll calls and the number for which less that 99 % of 13
The inability to determine the identify of the relevant members (i.e., g, m, l and r) is why ideal points are often used to test the theory. Although it might appear possible to use a computationally simpler method such as counting the number of times that the relevant actors vote differently, without external information as to which members we should compare this calculation is uninformative. Not only do ideal points account for differences in voting behavior by construction, but, in so doing they also provide an ability to identify the identity of the theoretically critical members using information in the observed voting patterns. 14 But see accounts such as that by Johnson and Broder (1996) which clearly indicate friction between the different branches.
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participating Democrats and Republicans vote together.15 For identifying the set of Final Passage votes in the House I use the determinations of both Rohde (2004) and Krehbiel, Meirowitz and Woon (2004) (hereafter KMW) as there appears to be ambiguity and disagreement over what constitutes a final passage vote.16 For the Senate, only KMW identify final passage votes. For Successful Final Passage votes I determine whether the vote passes accounting for super-majoritarian rules where required (e.g., votes considered under Suspension of the Rules) when using Rohde’s code and whether KMW indicates that the motion carried using KMW’s scheme. Treating successful final passage votes as indicating successful policy change is appropriate so long as members believed that the legislation they passed was likely to become law. The differences in the determinations reported in Table 2 are troubling from a measurement standpoint, but from a theory-testing perspective the differences represent a robustness check. To the extent that substantive conclusions are robust to different interpretations of how observed roll calls relate to the production of policy outcomes, our confidence in the conclusion is enhanced. Given the simplicity of the test, the analysis is straightforward. For each set of successful final passage votes described in Table 2, I estimate members’ ideal points using the statistical model of section 2 while imposing the identification restriction that Rep. Nancy Pelosi’s (D,CA) and Sen. Edward Kennedy’s (D,MA) ideal points are -1 and Rep. Newt Gingrich’s (R-GA) and Sen. Jesse Helms’s (R,NC) ideal points are 1.17 Using the resulting ideal point estimates I test the party gatekeeping model by calculating whether the posterior estimates for the chamber median and 15
This is a more relaxed standard than some applications (for example, Poole and Rosenthal (1997) omit votes with more than 97.5 % agreement), but it does not pose any statistical problems (see Clinton, Jackman and Rivers 2004). It might initially appear that excluding the set of unanimous votes – which are uninformative for estimating ideal points because of the lack of variation in voting – is problematic for theory-testing because so doing excludes votes consistent with the predictions of both theories. This is not the case for several reasons. First, to the extent that the set of unanimous votes is small relative to the set of non-unanimous votes (as is the case for the 103rd Congress), the fact that ideal points are distinguishable is still problematic. Second, just as such votes are uninformative for ideal point estimation, so too are they uninformative for distinguishing between theoretical predictions; unanimity is consistent both theories. 16 Using Rohde’s (2004) classification of House roll calls for the 83rd through 106th Congresses, I use roll calls classified as (the number of such roll calls is listed in parentheses): Final Passage/Adoption of a Bill (100), Final Passage/Adoption of a Conference Report (38), Final PAssage/Adoption of a Resolution (9), Final Passage/Adoption of a Joint Resolution (5), Passage/Adoption of a Bill under Suspension of the Rules (66), Passage/Adoption of a Joint Resolution under Suspension of the Rules (0), Final Passage/Adoption of a Concurrent Resolution (3), Passage/Adoption of a Concurrent Resolution under Suspension of the Rules (1), or Passage/Adoption of a Resolution under Suspension of the Rules (3). For KMW I used the determination as described in Krehbiel, Meirowitz and Woon (2004). 17 Because Gingrich’s voting behavior is relatively moderate in the 103rd House, the recovered set of ideal points is not bounded between [−1, 1] as in some estimators (e.g., W-NOMINATE (Poole and Rosenthal 1997)). The existence of more extreme members than Gingrich is inconsequential; identification only requires two fixed, distinct points (Rivers 2003), not that the fixed points bound the recovered space. As the recovered space is defined relative to the constrained legislators, choosing different members to constrain would rescale the space but not change the substantive results.
14
majority party median are indistinguishable and I test the pivotal politics model by determining the percentage of the chamber whose ideal points are indistinguishable from the chamber median. Figure 3 presents the results graphically.18 [Insert Figure 3 About Here] For the 103rd House, the results are immediately evident and discouraging for both theories. The predictions of section 3 imply that we should be unable to distinguish between the chamber and majority party median ideal points if the party cartel model is true and a supermajority of member ideal points should be indistinguishable from the chamber median if the pivot model is true. There is no doubt that the estimated chamber median and the estimated majority party median are disjoint; the illuminated 95 % regions of highest posterior density do not overlap regardless of the coding scheme. Although the width of the confidence interval for the chamber and party median ideal point increases as the number of votes used decreases, it is never the case that the party and chamber median cannot be statistically distinguished. From this we can conclude that the observed roll call record for each subset contains enough information to distinguish between the chamber median and the majority party median.19 The results for the pivot theory are no more encouraging. Instead of attempting to map behavior from different chambers and institutions into the same space, I calculate the percentage of the chamber which cannot be distinguished from the chamber median (i.e., whose posterior difference excludes zero). Figure 3 is suggestive of the result as the distribution of ideal points is far from contained in the 95 % region of highest posterior density for the chamber median. Using successful final passage votes according to Rohde, only 14 % (60) of the chamber is indistinguishable from the chamber median using a 90 % threshold – a quantity that is far less than the supermajority suggested by the theory. Using the set of roll calls identified by KMW, the percentage rises slightly to 27 % (116 members). As Figure 3 indicates, the Senate results are only slightly more encouraging for the two theories. For the party cartel model, the overlap between the 95 % confidence intervals for the chamber and 18
In each case, I generate 5,000,000 samples thinning by 2,000 using IDEAL 0.5 (Jackman 2004). No evidence of non-convergence presents itself. 19 Specifically, the average posterior difference (and standard deviation) between the chamber and majority party median is .43 (.03) for Rohde’s final passage votes in the House, .43 (.03) for Rohde’s successful final passage votes in the House, .50 (.04) for KMW’s final passage votes in the House.
15
majority party median is .006 – the upper 97.5 % quantile for the majority party median is -.292 and the lower 2.5 % quantile for the chamber median is -.298. Nonetheless, the average posterior difference (and standard deviation) between the chamber and majority party median is .37 (.07).20 Using final passage votes to test the predictions of the pivot theory results in more encouraging results; 43 % of the chamber (43 members) are estimated to be indistinguishable from the chamber median at a 90 % confidence level. Although not intended as a definitive resolution to the question of whether lawmaking is shaped by party institutions – such a resolution would require replicating the above analysis across longer periods of congressional history, reconciling discrepancies in what constitutes “final passage” and perhaps restricting the analysis to further subsets of the roll call record (e.g., classifying votes according to the issues they raise or by the “importance” of the legislation being considered) to test for robustness – the suggestive results are that neither performs particularly well. For every subset of votes I consider in the House, the chamber median and party median can be distinguished. The pivot theory predictions perform only slightly better. Although support is more forthcoming in the Senate, where 43 % of the estimated ideal points on final passage are indistinguishable from the chamber median, in the House, only 14 % (Rohde) or 27 % (KMW) of member ideal points on final passage votes are indistinguishable from the chamber median.
4.2
Perfect Versus Probabilistic Voting
Section currently under revision.
4.3
Problems of Theory or Problems of Estimation and Data?
A second, but related, objection is the possibility that the detected differences between the chamber and majority party medians’ ideal points (and between the chamber median’s and members’ ideal points) do not constitute evidence contradicting the theoretical predictions, but rather evidence that the empirical model is insufficient. One problem could be that because the statistical estimation model allows for errors, it is possible that the observed difference between the chamber median and the gatekeeper is the result of a higher dimensional space being projected into a lower dimension representation with error. This is certainly possible, as a statistical model that allows 20
The difference is non-zero because whereas the difference calculation accounts for the two estimates’ covariance, the confidence interval calculations assume the quantities are independent.
16
for probabilistic voting recovers a much smaller dimensional space than one which assumes perfect spatial voting. There are two responses to this plausible objection. First, if it is the case that the recovered dimensions are insufficient for explaining the votes and that the observed difference is due to incorrectly projecting a multi-dimensional space into a single dimension, it cannot follow that existing uses of ideal point estimates are appropriate. If the objection to the above test is the possibility that the observed differences are due to incorrectly estimating the relevant policy space, then it follows that all similar uses of ideal points to understand lawmaking (i.e., all published findings making use of gridlock intervals and measures of party polarization and party heterogeneity) are also invalid. This objection is not inconsistent with the conclusion of the paper – if ideal points are to be used to test theories they should be used in a manner that is theoretically consistent. However, if it is the case that using them in a theoretically consistent manner is difficult because we do not know the dimensions of policy preferences underlying the recovered roll call record, this does not invalidate the paper’s arguments. Instead, it provides (yet another) reason for caution in using ideal points to test theories of lawmaking; scholars need to ensure that the statistical models are properly restricted to relevant set of votes when conducting the test presented above. This may include using only behavior on “important” legislation or votes within certain issue areas. In light of this possibility, one “solution” would be to abandon the use of ideal points and test theories using implications about the roll call record. For example, because the party cartel model predicts that the chamber median and majority party median should never vote differently on final passage votes, we can examine the roll call record for such instances (using Rohde’s classification yields 206 (out of 207) instances of this behavior).21 Testing the pivot theory similarly reduces to examining whether have enacting coalitions on successful final passage votes are larger than 66 % of the participating chamber (which 72 % (150) are for the same set of votes). Moving away from roll call based estimates avoids the problems introduced by using estimates based on the wrong dimension or the wrong voting model, but the cost of doing so is high. The tests become so crude and incorporate so little of the theoretical explanation so as to be almost uninformative with respect to the suggested causal mechanism.22 Is it surprising that a majority of 21 22
A majority of the minority party votes “yea” on final passage in 53 % (107/207) of the instances. Absent an ability to identify the identify of the members in each coalition, it also becomes difficult to distinguish
17
the Democratic party in the 103rd House voted together on successful final passage votes? Although this does not refute the possibility that the reason is because of Democratic agenda control, this fact says nothing about the causal mechanism and is consistent with several interpretations. Likewise, is the fact that 72 % of votes have super-majority enacting coalitions strong or weak evidence for a self-described simple theory based on veto pivots? These reactions are not intended to dismiss the importance of these investigations and results, but rather to suggest that testing theories using measures only weakly related to postulated causal mechanisms results in weak conclusions and subsequent debates about the interpretation of the results (see, for example, Krehbiel 2000). In contrast, tests that utilize theoretically implied concepts are more powerful for evaluating claims concerning the causal mechanism. In the event that our ability to measure theoretically implied covariates introduces error as a consequence of making measurement assumptions that cruder tests avoid, both examinations are useful. If so, the arguments and conclusions of this paper are important and informative.
5
Conclusion
Proper tests of theoretical predictions require that measures used to test the predictions are generated using models that, at the very least, are not inconsistent with the theory being tested. This point has important implications for theory-testing using roll call data because the theories being tested typically have implications for the roll calls that should be observed. If the goal is to test theories of lawmaking using roll calls, it is important to account for the fact that the theories have implications for the set of observable actions and that those actions cannot be considered to be exogenous to the theoretical account. Treating ideal points as if they are independent of the theories being tested is improper and potentially misleading. Because the agenda of legislative institutions are typically endogenous, I show how that – for the properly restricted set of votes – theoretical predictions for common models of lawmaking are properly assessed using estimated ideal points directly. Contrary to current interpretations, the common practice of using ideal points to calculate a gridlock interval for use in a regression equation between the theories. Most notably, although the pivot theory precludes an enacting coalition smaller than a supermajority, observing a super-majority coalition does not invalidate the predictions of the party theory – evidence supportive of the pivot theory is also supportive of the party gatekeeping theory. The only way to reject the party theory is to observe an enacting majority that does not contain a majority of the majority party.
18
is shown to actually indicate that: 1) the theory is false (if the interval is non-zero), 2) the theory is true but the votes used to generate ideal points are irrelevant to the theory, or 3) the theory is true, the correct votes are used and that the probabilistic voting model used to estimate ideal points introduces sufficient error into the test so as to recover a non-zero interval. Any conclusion is informative for theory-testing and scientific progress. I illustrate the importance of accounting for the fact that theories of lawmaking have direct implications for the voting patterns (and consequently ideal points) that we should observe by conducting a test of the party-cartel model and pivot model using the 103rd Congress. The suggestive substantive conclusion is that neither performs particularly well (although the slippage introduced as a consequence of employing a probabilistic statistical model makes definitive inference difficult). Addressing the endogeneity of roll calls is an important and necessary advance, but it does not resolve the difficulties of using roll call based measures to test theories of lawmaking. In examining the ability of roll call based estimates to measure theoretically implied quantities in a world in which the theory is true, I find considerable slippage. In other words, solving the endogeneity problem highlights the need for further investigation into the consequences of testing predictions from perfect voting models using estimates from probabilistic voting models. Scholars interested in using ideal point estimates to test theories of lawmaking need to address both concerns. Although I suggest a solution to the former, further work is required to address the latter. The arguments of this paper are intended to be constructive and illuminate what is required for future scientific progress by demonstrating the pitfalls of current practices. Although attempts at reconciling theory and data to incorporate substantive information and theoretical implications are increasingly being made, most scholarship separates the tasks of theorizing, measurement and estimation. Documenting and reconciling the differences that emerge from translating theoretical predictions into statistical tests using observable is critically important for interpreting the significance of existing and future investigations. Assessing the support for theoretical predictions using measures that are questionably (and differentially) related to theoretically implied concepts results in noisy, if not uninformative, tests. Achieving consensus on measures is difficult in political science because theoretically relevant quantities are almost never observed and the data that is observed (and collected) is often faintly related to theoretical concepts. Similar to Poole’s (2005) caution that “anyone can construct a
19
spatial map...but the maps are worthless unless the user understands both the spatial theory that the computer program embodies and the politics of the legislature that produced the roll calls” (p. 209), the arguments of this paper demonstrate that not only is recognizing and accounting for the connections between the roll calls and theories of lawmaking absolutely essential for the proper use of ideal points to test theories of lawmaking, but also that work investigating these connections remains.
20
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Smith, Steven S. and Jason M. Roberts. 2003. “Procedural Contexts, Party Strategy and Conditional Party Voting in the U.S. House of Representatives, 1971-2000.” American Journal of Political Science 47(2):305–17. Snyder, James M. Jr. 1992. “Committee Power, Structural-Induced Equilibria, and Roll Call Votes.” American Journal of Political Science 36(1):1–30. Snyder, James M. Jr. 1992b. “Gatekeeping or Not, Sample Selection in the Roll Call Agenda Matters.” American Journal of Political Science 36(1):36–39. Snyder, James M. Jr. and Michael M. Ting. 2003. “Roll Calls, Party Labels and Elections.” Political Analysis 11(4):419–33.
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2xg– xm xg
Equilibrium Outcome
1A
xm Status Quo Realization (q)
1B 2xg – xm xg
xg 2xg – xm
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xm
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xm
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Figure 1: Equilibrium Predictions from Gatekeeping Model.
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2xr – xm xr xm
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2A
xl 2xl – xm
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2B 2xr – xm xr xm
xl
xm
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Equilibrium Cutpoint
2xl – xm)
xl 2xl – xm Status Quo Realization (q)
2xl – xm
xl
xm
xr 2xr – xm
Figure 2: Equilibrium Predictions from Veto Model.
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House Final Passage Votes (Rohde)
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Figure 3: Theoretically Implied Estimates for the 103rd Congress: The figure graphs the density of Democratic (blue) and Republican (red) ideal points and the 95 % quantiles for the chamber (m) and majority party (g) medians. 27
