Interpreting Circuit Court Voting Patterns: A Social Interactions Framework

Transcription

1 Interpreting Circuit Court Voting Patterns: A Social Interactions Framework Joshua B. Fischman* Northwestern University School of Law JLEO, V31 N4 808 Many empirical studies have found that circuit judges votes are significantly influenced by their panel colleagues. Although this influence is typically measured in terms of colleagues characteristics, this article argues that it is better understood as an effect of colleagues votes. Applying the latter interpretation, this article reanalyzes 11 prior studies of panel voting, as well as three novel data sets, and reveals the impact of colleagues votes to be strikingly uniform. In almost every type of case, each colleague s vote increases the likelihood that a judge will vote in the same direction by roughly 40 percentage points. This result is consistent with a strong norm of consensus and can account for nearly all of the perceived impact of colleagues party, gender, and race. This finding raises questions about strategic and deliberative models of panel voting and helps clarify measurement issues regarding the relationship between judicial characteristics and voting behavior (JEL C31, K40). 1. Introduction Empirical studies on decision making in federal circuit courts have repeatedly demonstrated that judges votes are significantly influenced by their panel colleagues. In diverse areas of case law, these studies have shown that judges are more likely to vote in a conservative direction when *Associate Professor, Northwestern University School of Law, Chicago, IL, joshua.fischman@law.northwestern.edu. I thank the following people for generously sharing their data: Christina Boyd, Lee Epstein, and Andrew Martin; Adam Cox and Tom Miles; David Law; Nicholas Linder and John Niles; Tom Miles and Cass Sunstein; Jennifer Peresie; Richard Revesz; Greg Sisk, Michael Heise, and Andrew Morriss; Cass Sunstein, David Schkade, Lisa Ellman, and Andres Sawicki. I thank Deborah Beim, Michael Gilbert, Jim Greiner, Rich Hynes, Tonja Jacobi, Jonathan Kastellec, Lewis Kornhauser, David Law, Jonathan Masur, Tom Miles, Greg Mitchell, John Pepper, Kevin Quinn, Greg Sisk, Max Schanzenbach, Matthew Stephenson, Sean Sullivan, Chad Westerland, three anonymous referees, and audiences at the American Law and Economics Association Annual Meeting, the Conference on Empirical Legal Studies, the Political Economy and Public Law Conference, Georgetown University Law Center, Northwestern University, and the University of Virginia School of Law and Department of Economics for helpful comments. Renee Birenbaum, Will Carlson, Christopher Clapp, Jonathan Potts, and Joy Williamson provided outstanding research assistance. The Journal of Law, Economics, and Organization, Vol. 31, No. 4 doi: /jleo/ews042 Advance Access published January 22, 2013 ß The Author Published by Oxford University Press on behalf of Yale University. All rights reserved. For Permissions, please journals.permissions@oup.com

2 Interpreting Circuit Court Voting Patterns 809 empaneled with Republican colleagues than with Democratic colleagues. Some studies have also shown that judges votes are similarly affected by their colleagues race, gender, or prior work experience. These empirical phenomena, which are often referred to as panel effects, have generated a growing literature that seeks to identify how judges influence their colleagues decisions. Some scholars have emphasized deliberative accounts, whereby judges may change their votes as a result of persuasion by their colleagues (Revesz 1997; Edwards 2003). Posner (2008: 32 34), however, argues that judges do not engage in much collective deliberation, and attributes panel effects to dissent aversion. 1 Cross and Tiller (1998) provide a strategic explanation, suggesting that panel effects may be the result of judicial whistleblowing. According to this theory, the threat that a dissenting judge could blow the whistle would deter a majority decision that is contrary to precedent. Finally, Sunstein et al. (2006: 71 78) provide a group polarization thesis, in which deliberation has a pathological effect when judges are like-minded and causes them to take extreme positions. Formal models have been constructed to explain each of the above theories. 2 According to these theoretical accounts, judges are influenced exclusively or primarily by their colleagues votes. Yet, most empirical studies of panel voting report whether judges are affected by their colleagues characteristics. The distinction between the impact of colleagues votes and characteristics is not merely semantic; it has long been central in econometric studies of social interactions. Although these effects are difficult to isolate empirically, they provide different interpretations of the causal channels of collegial influence. For this reason, it is essential for studies of panel voting to clarify whether judges are assumed to be influenced by their colleagues votes or characteristics, and to use empirical methodologies that are appropriate for the hypothesized effects. To illuminate the difference between these two approaches, I compare two empirical models of panel voting one that models influence using colleagues characteristics, the other using colleagues votes and reexamine data from 11 prior studies of panel voting and three novel data sets. Consistent with prior studies, when judges are assumed to be influenced by their colleagues characteristics, the results vary across different areas of case law. When judges are assumed to be influenced by colleagues 1. Various scholars use different terms to describe the same phenomenon, such as Revesz s (1997) dissent hypothesis and the concept of collegial concurrence discussed in Sunstein et al. (2006). Earlier work in judicial politics described a norm of consensus (Goldman 1968; Atkins and Green 1976; Howard 1981; Songer 1982), which is also equivalent but arguably suggests a more dominant effect. 2. See Spitzer and Talley (forthcoming) for a model of panel deliberation, Fischman (2008, 2011) for structural models of consensus voting, Kastellec (2007) for a model of whistleblowing, and Glaeser and Sunstein (2009) for a model of group polarization.

3 810 The Journal of Law, Economics, & Organization, V31 N4 votes, however, the results are strikingly uniform. In almost every data set, each colleague s vote increases a judge s probability of voting in the same direction by roughly 40 percentage points. This result holds even in several types of cases in which Sunstein et al. (2006) did not find panel effects, and remains true whether judges voting propensities are explained using party, gender, race, or other characteristics. Thus, much of the variation in panel effects observed in prior studies may be due to the manner in which they are estimated. Interpreting panel effects as the influence of colleagues votes also reveals these effects to be much stronger than had been perceived in the prior literature. The estimated impact of colleagues votes on a judge s vote is 80% as large as one would find on courts that mandate unanimity, such as in many civil law countries. Thus, nearly all findings in these prior studies can be explained by a strong norm of consensus in circuit courts. This explanation should hardly be surprising; the existence of this norm was documented decades ago by scholars of judicial politics (Goldman 1968; Atkins and Green 1976; Howard 1981: ; Songer 1982). The article proceeds as follows. Section 2 discusses the econometric literature on social interactions and how it applies to the study of circuit court voting. Section 3 describes the data, which cover diverse areas of law, such as administrative law, sex discrimination, asylum law, criminal appeals, capital punishment, religious freedom, and abortion. Section 4 presents the results from both empirical frameworks. Section 5 discusses the implications of the results for theories of panel voting, arguing that the results raise questions about deliberative and strategic theories that predict variation in panel effects in different types of cases. Section 6 applies the social interactions framework to explain why the estimated effects of judicial characteristics vary depending on whether they are measured at the panel level, at the individual level, or using variation within panels. Section 7 concludes. Due to the large number of regressions conducted for this article, the results for individual data sets are reported in Supplementary material. 2. Empirical Framework 2.1 Econometrics of Social Interactions A rapidly growing literature in empirical economics studies how individuals behavior is affected by their neighbors or peers, for example, in levels of educational achievement (e.g., Sacerdote 2001; Hanushek et al. 2003), choice of housing location (e.g., Ioannides and Zabel 2008), investment decisions (e.g., Duflo and Saez 2002, 2003), unemployment (e.g., Topa 2001), receipt of public assistance (e.g., Bertrand et al. 2000), propensity to engage in criminal activity (e.g., Ludwig and Kling 2007), and substance abuse (e.g., Gaviria and Raphael 2001). Although this literature has developed important insights regarding econometric techniques for

4 Interpreting Circuit Court Voting Patterns 811 studying these social interactions, these insights have not been absorbed in the study of judicial voting behavior. 3 Manski s (1993) distinction between three types of social effects is central to the empirical study of social interactions. Endogenous effects occur when an individual s behavior is influenced by the behavior of the group. Contextual effects occur when an individual s behavior is influenced by the characteristics of the group members. Correlated effects are present when individuals with correlated characteristics self-select into groups or individuals within a group are subject to common unobserved influences. Figure 1 provides a causal diagram depicting endogenous and contextual effects in the context of circuit court panels. Nearly every study of panel voting assumes a direct effect between a judge s characteristics and that judge s votes. 4 There are also contextual effects if a judge s vote is directly influenced by her colleagues characteristics, irrespective of their votes. Endogenous effects are present if each judge s vote influences the other judges votes. The distinction between these effects depends upon whether the colleagues characteristics have a direct impact on the judge s vote or whether the colleagues characteristics predict their votes, which in turn influence the judge s vote. To illustrate the distinction between contextual and endogenous effects, suppose that a hypothetical judge is empaneled with female colleagues in a sex discrimination case. In conference, both of these colleagues have stated their intention to affirm the dismissal of the plaintiff s suit. In this scenario, how should one expect these colleagues to influence the vote of our hypothetical judge? Under a theory of contextual effects that the gender of panel colleagues has a direct causal effect on a judge s decision the judge would be more likely to vote to reinstate the suit. Under a theory of endogenous effects, however, the colleagues intended votes would make the judge more likely to vote to affirm. The contextual effects explanation in the above example may sound implausible; it is hard to imagine that a judge s ideology or personal characteristics would affect her colleagues votes irrespective of the position that the judge herself took in the case. A more useful question is whether judges influence each other solely through endogenous effects or through a combination of endogenous and contextual effects. Many explanations of panel effects are formulated purely in terms of endogenous effects. According to the dissent aversion theory, a judge s willingness to vote in a particular direction is affected by the other judges votes. Judges votes may be correlated with their colleagues characteristics, but only insofar as these characteristics predict the colleagues votes. Similarly, whistleblowing is a theory of endogenous effects, since the 3. One exception is a working paper by Cameron and Cummings (2003). 4. This effect should not be interpreted as the effect of directly manipulating the judge s characteristics, but rather as the effect of replacing a judge with another judge who has different characteristics (Greiner and Rubin 2011).

5 812 The Journal of Law, Economics, & Organization, V31 N4 Figure 1. Contextual And Endogenous Effects In Panel Voting. majority is influenced by the minority judge s willingness to dissent. Knowing the minority judge s intended vote is sufficient; the minority judge s characteristics do not add any additional predictive value. Deliberative accounts, however, could involve both endogenous and contextual effects. If liberal judges work harder to uncover information that supports the liberal position, and conservative judges act similarly, then the judges characteristics would also influence their colleagues votes (Spitzer and Talley, forthcoming). Peresie (2005: 1783) offers an explanation that male judges defer to female judges because [they] view them as more credible and persuasive in gender-coded cases, suggesting that both the female judges actions (their willingness to support a plaintiff) and their characteristics (gender) jointly affect their male colleagues votes. Alternatively, contextual effects might operate in the opposite direction; a conservative judge s argument supporting a liberal outcome, for example, may seem more credible than a liberal judge s argument supporting the same position. In theory, correlated effects should not be present in circuit court voting, due to the random assignment of judges to panels. 5 However, correlated effects may arise in subtle ways, for instance, if the announcement of the panel composition leads some parties to settle. This effect is likely to be small, however, since most circuits do not announce panel composition until shortly before oral argument (Revesz 2000; Jordan 2007). Some studies may also introduce correlated effects by selecting cases on the basis of endogenous characteristics, such as whether an 5. It is worth noting that assignment is only random within a particular circuit and time period. Boyd et al. (2010) argue against relying on random assignment but are unspecific as to the reasons, citing only the difficulty of inter-circuit comparisons and the fact that senior judges might remove themselves from the pool for certain broad classes of cases. The key inquiry is whether there would be a correlation between the characteristics of a case and the characteristics of the judges assigned to it.

6 Interpreting Circuit Court Voting Patterns 813 opinion was published 6 or whether it cited a particular precedent. 7 The analysis in this article ignores correlated effects, under the assumption that deviations from random assignment are minor. 2.2 Empirical Specifications for Contextual and Endogenous Effects The interpretation of regressions involving social interactions will vary depending on whether these interactions are characterized as endogenous, contextual, or correlated effects. Unfortunately, these effects are difficult to distinguish empirically and are typically identified only by assumption. Manski (1993) demonstrates that in linear regression models, endogenous and contextual effects cannot be separately identified, but correlated effects may be distinguished from the other social effects under certain conditions. In nonlinear models, it may be theoretically possible to separately identify endogenous and contextual effects by exploiting the nonlinearities in the regression model. This is difficult in practice, however, because it requires a priori knowledge of the correct functional form (Manski 2000). 8 When social interactions are assumed to be exclusively due to contextual effects, estimation is straightforward because the causation operates in a single direction. Estimation is more complicated when endogenous effects are present, however, since they involve two-way causation. As depicted in Figure 1, endogenous effects result in a self-reinforcing feedback loop among all the judges of the panel. A model of endogenous effects results in a system of simultaneous equations, which can be estimated using instrumental variables or by estimating the reduced form of the system of equations. In this subsection, I provide empirical specifications for several empirical models of social interactions. The first model assumes purely contextual effects, as in most prior empirical studies of voting behavior in circuit courts. The remaining models assume purely endogenous effects, which is consistent with most theoretical accounts of panel voting Contextual Effects. The contextual effects model assumes that each judge is directly influenced by the characteristics of her panel colleagues. Consider a panel consisting of judges i, j, and k who are deciding case t. Let v it be a dichotomous variable that denotes the vote of judge i in case t, where v it ¼ 1 could represent the liberal outcome and v it ¼ 0 the 6. Wald (1999) and Law (2005) discuss how publication may be endogenous. Berdejo (forthcoming) provides empirical evidence that panel composition affects the decision whether to publish an opinion. 7. For example, Miles and Sunstein (2006) examine circuit court cases that apply Chevron U.S.A., Inc. v. Natural Resources Defense Council, 467 U.S. 837 (1984). But Eskridge and Baer (2008) show that many cases that involve deference to agency interpretations do not cite Chevron explicitly. 8. Brock and Durlauf (2007) propose a semi-parametric estimator that can separately identify endogenous and contextual effects, but their estimator requires greater variation in the regressors than is available in the circuit court voting data analyzed in this article.

7 814 The Journal of Law, Economics, & Organization, V31 N4 conservative outcome. Let p it be a scalar or vector representing characteristics of judge i in case t, such as the judge s party, gender, or race. Finally, let x t be a vector containing a constant term as well as characteristics of case t, such as the year, circuit, direction of the lower court opinion, or the type of claim that is presented on appeal. As long as cases are randomly assigned to panels, it is not necessary to include any case characteristics aside from time and circuit dummy variables, although additional characteristics may improve the efficiency of the estimation. Equation (1) provides a standard linear model of contextual effects, which employs a specification similar to most prior studies of panel voting behavior. 9 The first term in each equation captures the impact of each judge s own characteristics on the judge s own vote. The second term captures the impact of the panel colleagues characteristics. For example, when p it indicates whether judge i is a Democrat, the terms inside parentheses represent the number of Democratic panel colleagues. The third term captures the influence of case characteristics on each judge s vote. v it ¼ b own p it +b other p jt +p kt +bcase x t +" it v jt ¼ b own p jt +b other ðp it +p kt Þ+b case x t +" jt ð1þ v kt ¼ b own p kt +b other p it +p jt +bcase x t +" kt Model (1) can be estimated using ordinary least squares regression, treating each equation as a separate observation. However, the error terms " it will generally not be independent, so standard errors must be clustered by case and judge Endogenous Effects with a Single Judicial Characteristic. Equation (2) provides a model of endogenous effects. It looks similar to equation (1), except that the votes of each judge s panel colleagues are on the right-hand side of each equation, instead of their characteristics. v it ¼ own p it + other v jt +v kt +case x t +" it v jt ¼ own p jt + other ðv it +v kt Þ+ case x t +" jt ð2þ v kt ¼ own p kt + other v it +v jt +case x t +" kt Note that the votes of the three judges are endogenous, since they appear on both the left- and the right-hand side in the system of equations. 10 For this reason, this model cannot be estimated consistently by 9. Many empirical studies of panel voting use logit or probit models, which are specifically suited to dichotomous dependent variables. Comparison of endogenous and contextual effects is straightforward in a linear model but is far more difficult in a nonlinear model. For a comparison between the linear model used here and nonlinear models used in other studies, see Section 2.6 below. 10. Equation (2) could alternatively be formulated in terms of judges expectations about their colleagues votes, so that v it ¼ own p it + other Ev jt +v kt +case x t +" it. As long as the judges

8 Interpreting Circuit Court Voting Patterns 815 ordinary least squares regression. Instead, equation (2) may be estimated using instrumental variables regression, where the colleagues characteristics are used as instruments for the colleagues votes. 11 This approach assumes that the impact of colleagues is purely an endogenous effect, since the instruments are invalid in the presence of contextual effects. Thus, in this model, judges can only be influenced by their colleagues through their votes; their characteristics cannot have a direct impact. Because equation (2) uses a linear functional form, it models colleagues votes as having a constant effect. Of course, the marginal impact of one colleague voting in the liberal direction may be different from the marginal impact of a second colleague voting in the liberal direction. In addition, the magnitude of these effects may vary across cases. When the impact of colleagues votes is heterogeneous, the estimate from an instrumental variables regression can be interpreted as an average causal response (Angrist and Imbens 1995), which represents a weighted average taken over the subset of cases in which the instrument creates variation in the colleagues votes. When there is only a single judicial characteristic used to explain voting behavior, the model is just-identified, so instrumental variables regression will be equivalent to indirect least squares (Greene 2000: 684). Solving the system of simultaneous equations yields the following reduced form: 12 v it ¼ own p it + other p jt +p kt +case x t + ~" it v jt ¼ own p jt + other ðp it +p kt Þ+ case x t + ~" jt ð3þ v kt ¼ own p kt + other p it +p jt +case x t + ~" kt Note that the reduced form in equation (3) is equivalent to the contextual effects regression in equation (1). In fact, estimating equation (3) by ordinary least squares will yield exactly the same estimates of own, other, case as estimating equation (1) will yield of b own, b other, b case. 13 But these estimates have different interpretations in the two models. In the contextual effects regression, the coefficients are directly causal, representing the impact of panel colleagues characteristics and case characteristics on a judge s vote. In the endogenous effects model, the coefficients in equation (3) are not causal parameters. In order to estimate the have rational expectations, this equation will have the same reduced form. I use the formulation in equation (2) on the assumption that there will typically be little uncertainty about colleagues final votes. 11. Because equation (2) assumes that each colleague s vote has an equal impact, it is irrelevant whether each colleague s characteristics are used as instruments for that colleague s vote, or the sums of colleague characteristics are used as an instruments for the sum of the colleagues votes. 12. See Heckman and Macurdy (1985) for a comprehensive discussion of the properties of the linear probability model in the context of simultaneous equations. 13. Note that in the reduced form, ~" it, ~" jt, ~" kt will be linear combinations of " it, " jt, " kt.

9 816 The Journal of Law, Economics, & Organization, V31 N4 coefficients from the structural model (2), it is necessary to solve for own, other, case in terms of own, other, case : ð own ¼ own+2 other Þð own other Þ ð own + other Þ other other ¼ ð4þ ð own + other Þ case ¼ own other case own + other Note that even though equations (1) and (3) are functionally equivalent, the meaning and significance of the social effects depends upon how they are measured. In some of the data sets examined in this article, the estimate of b other in equation (1) is statistically insignificant but the estimate of other in equation (4) is highly significant. The significance of judge and case characteristics may similarly depend on the model assumptions Endogenous Effects with Multiple Judicial Characteristics. To estimate endogenous effects using multiple judicial characteristics (such as party and gender), let p it in equation (2) be a vector. In the endogenous effects model, these characteristics affect colleagues votes only through the judge s own vote. As in the single-characteristic model, the sum of the colleagues characteristics (the components of p jt +p kt ) can be used as instruments for the sum of the colleagues votes (v jt +v kt ). When multiple instruments are available, equation (2) can be estimated separately for each instrument or using multiple instruments. If this model is correctly specified that is, if judges are only affected by colleagues votes and the effect is linear then the estimated effects should be similar regardless of which instruments are used. If some colleagues characteristics have a direct effect on judges votes, however, then these characteristics will be a invalid instruments, and the regressions may yield divergent estimates. Even if the endogenous effects assumption is correct, estimation of equation (2) can yield varying estimates if the effect of colleagues votes is heterogeneous. This is because the estimated effect is an average causal response, taken over those cases in which the instrument causes variation in the colleagues votes. If colleagues characteristics affect their votes in different groups of cases, different instruments may yield different estimates of the average causal response. The hypothesis that the estimated average effect of colleagues votes does not vary by instrument can be tested using a test of overidentifying restrictions. A rejection of the test would support the inference that either contextual effects are present or the effect of colleagues votes is heterogeneous. Of course, failing to reject such a test does not prove that the endogenous effects model is correctly specified.

10 Interpreting Circuit Court Voting Patterns Interpreting Estimates of Endogenous Effects To interpret the results from the endogenous effects regression, consider a spectrum of norms governing the announcement of judgments in multimember courts. On one end is a court of autonomous judges who are never influenced by their colleagues. Courts that announce judgments seriatim, such as the British Law Lords before the 1980s (Ginsburg 1990), most English courts before the 18th Century, or the early years of the US Supreme Court (Henderson 2007), might approximate such a court. The mere practice of issuing seriatim opinions, however, does not guarantee autonomous voting. 14 It is not clear if there exists any court in which voting is truly autonomous. 15 At the other extreme, consider a court operating under strict consensus, as is the standard practice in the European Court of Justice, the French Cour de Cassation (Alder 2000; Law 2009), and most courts in Austria, Belgium, Italy, and the Netherlands (Laffranque 2003). In such a court, it may seem peculiar to even refer to a judge s participation in a unanimous judgment as a vote. If one did so, however, one would obviously find that judges votes were strongly influenced by their panel colleagues. Moreover, the influence of colleagues would necessarily be an endogenous effect, since each judge s vote, when not pivotal, would be determined by the votes of the judge s colleagues. If judges are autonomous, it must hold that other ¼ 0 in the endogenous effects model, since each judge s decision would be unaffected by the colleagues votes. The votes of judges on such a court may still be highly correlated if there are many easy cases, but their votes would not be correlated with the characteristics of their panel colleagues. In a court with three judges operating under strict consensus, an endogenous effects regression will always yield an estimate of other that is exactly 0.5. If all votes are unanimous, then the sum of colleagues votes ðv jt +v kt Þ will always perfectly predict a judge s own vote v it, resulting in a coefficient of Thus, the range from 0 to 0.5 for the coefficient other 14. White (2006) describes some practices of the early Supreme Court that are not consistent with strictly independent decision making. Chief Justice Jay, for example, would follow his opinion with a brief paragraph announcing the Court s disposition. Such a paragraph could not be composed without foreknowledge of the other Justices positions. The notion that seriatim opinions do not guarantee independent judgments is also illustrated by a short-lived Louisiana law that required members of the state supreme court to issue opinions seriatim. Most of these seriatim opinions consisted of the statement I concur in the opinion for the reasons adduced (Sanders 1963). 15. Judges in some kinds of tournaments or sporting events, such as boxing or figure skating, are not permitted to communicate, and might therefore behave in a more purely autonomous manner. However, it would strain terminology to characterize a group of such judges as a court. Moreover, even in the absence of deliberation, judges may still be influenced by their colleagues. Zitzewitz (2006) finds evidence that Olympic figure skating judges strategically compensate for the nationalistic biases of their colleagues. 16. This holds even though ðv jt +v kt Þ is an endogenous variable and other is estimated using instrumental variables regression. This result follows from the discussion of instrumental

11 818 The Journal of Law, Economics, & Organization, V31 N4 represents a spectrum from a court of autonomous judges to a strictly consensual court. 2.4 Estimation Details All contextual effects models are estimated using ordinary least squares. For endogenous effects models, I use the limited information maximum likelihood (LIML) estimator to minimize potential bias due to weak instruments. 17 The tests of overidentifying restrictions are implemented using the Anderson-Rubin test. Many empirical studies of panel voting treat each judge s vote in each case as an independent observation, thus assuming that the error terms " it are uncorrelated. 18 This assumption, however, is almost always violated, 19 and can lead studies to overstate the significance of their results. 20 Therefore, unless otherwise indicated, all standard errors computed in this article are clustered at both the case level and the judge level, using the variance variables regression found in Greene (2000: 683). In regressions with a single judicial characteristic, this result can be seen more easily by observing that each judge s characteristics will make an equal contribution to the panel disposition, and hence to each judge s vote. Thus, it must hold in the reduced form equation (3) that own ¼ other. By equation (4), it follows that other ¼ In regressions with a single judicial characteristic, LIML and two-stage least squares provide identical estimates (Greene 2000: 684). With multiple instruments, the results were similar using either estimator. 18. One exception is Revesz (1997), which accounts for correlation of error terms by judge, although not by case. Revesz used a two-step approach, following Ashenfelter et al. (1995), which estimates fixed effects for each judge and then regresses those fixed effects on the party variable. This has a similar effect as the clustering approach employed here, but the Revesz approach assigns equal weight to each judge whereas clustering assigns equal weight to each vote. 19. The error terms may be correlated for several reasons. First, any unobserved characteristic of a case that has a common effect on all three judges may induce correlation in the error terms. Second, the interdependence of the judges votes in the reduced form of the endogenous effects model will induce additional correlation in the error terms. This is most easily seen in a court that always decided cases unanimously, where it would clearly be inappropriate to treat each judge s vote as an independent observation. Finally, the error terms associated with a particular judge s votes may be correlated across cases. For example, if judge i is a liberal Republican, then judge i s votes will generally be more liberal than predicted by a regression model that relies on the party variable, and hence many of the error terms " it associated with judge i will be positive. 20. This is particularly important in studies of single circuits, where each judge is observed many times but the number of judges observed is small, as well as studies of the effect of judges gender, since there are relatively few female judges. Imagine, for example, a study of the impact of judge gender using data from the First Circuit. Such a study might collect data on hundreds of votes by female judges, but they would clearly not be independent observations, since there was only one active female judge on the First Circuit prior to Treating each vote by Judge Sandra Lynch as representing an independent draw from a hypothetical pool of female judges would clearly overstate the significance of any finding on judge gender. While no existing study makes such an extreme error, failure to cluster by judge nevertheless overstates the significance of the findings. The data from Peresie (2005) include 280 votes by female judges and the data from Boyd et al. (2010) include 170 votes by female judges, but in both studies, roughly half of these votes can be attributed to 10 judges.

12 Interpreting Circuit Court Voting Patterns 819 estimator of Cameron et al. (2011). 21 However, for computational reasons, the tests of overidentifying restrictions are unclustered. 2.5 Judicial Characteristics The judicial characteristics analyzed here vary among the data sets, depending on the information collected in prior applications and the relevance of the characteristics to the types of cases being examined. I give a brief overview below Party of Appointing President. Each judge is classified on the basis of whether he or she was appointed by a Democratic or Republican President. While admittedly a simplistic measure of judicial ideology, this variable has been demonstrated to robustly correlate with judicial voting behavior across a wide variety of issue areas (Pinello 1999). Its use has become sufficiently standard that it was already coded and analyzed in all prior studies of panel effects examined in this article. For each of the data sets, I report the effect of the party variable, which is uniformly significant Gender. Several recent studies have examined whether there are systematic differences between male and female judges, both in their own voting behavior and whether they influence panel colleagues (Peresie 2005; Boyd et al. 2010). Some of these studies have found significant differences between the sexes, primarily in cases involving sex discrimination (Boyd et al. 2010). In data sets where gender was already coded, I perform separate regressions using a variable indicating whether the judge is female Previous Work Experience. Some studies have examined whether judges behavior can be predicted by their prior work experience. In the examination of sentencing cases, I include a previously coded variable denoting whether a judge had prior experience as a prosecutor Voting Rates in Other Cases. In the data sets in which there are a large number of observed votes per judge, I construct a simple measure based on a judge s voting rate in the entire data set. In order to avoid 21. Note that even clustering on both case and judge is imperfect. This would still not account for correlation between a judge s vote and the votes of his panel colleagues in other cases, or the correlations among his panel colleagues in different cases. 22. I do not report results using Judicial Common Space scores (Giles et al. 2001; Epstein et al. 2007), since this measure is highly correlated with party of appointment but less intuitive to interpret. The correlation between common space scores and party of appointment is 0.86 in the Boyd et al. (2010) sex discrimination data, 0.88 in the Peresie (2005) sex discrimination data, 0.86 in the Law (2003) asylum data, and 0.84 in the Sisk et al. (2004) free exercise data. In all of these data sets, the regression results using common space scores were virtually identical to the results using party of appointment.

13 820 The Journal of Law, Economics, & Organization, V31 N4 circularity, I exclude the votes from each case when calculating a judge s voting rate for that particular case. When a judge has fewer than 20 votes in the data set, I use the average voting rate for judges appointed by presidents of the same party. A judge s voting behavior in comparable cases is a good predictor of a judge s vote in a particular case, and in most instances, this measure is superior to party and gender in terms of explanatory power. It should be interpreted merely as a proxy for ideology; it does not have any direct causal interpretation. Nevertheless, when available, this variable provides more precise estimates of the influence of panel colleagues as well as the impact of panel composition on case outcomes Indicator Variables for Individual Judges. When there are many observations per judge, it is also possible to use a vector of binary variables indicating the presence of a particular judge. For example, a Posner indicator would equal one if the judge was Richard Posner and zero otherwise. Variables indicating the presence of particular judges as colleagues serve as instruments for the colleagues votes. Judges who appear in the data fewer than 20 times are assigned to groups Democrat-other and Republican-other, which have separate indicator variables. 2.6 Comparison with Other Empirical Methods The use of linear probability models to examine panel voting is unusual in the literature on circuit court voting behavior. Linear models have two important advantages in this context. First, the contextual effects model in equation (1) is equivalent to the reduced form of the endogenous effects model in equation (3), which facilitates easy estimation of the endogenous effects model and comparison between the two approaches. Second, an estimate from the endogenous effects model in equation (2) can be interpreted as an average causal response, even if the linear functional form is misspecified. The primary disadvantages of linear probability models are that they may generate fitted probabilities outside the unit interval and that the linearity restriction may be unrealistic. Both shortcomings are ameliorated, however, when the regressors are discrete or bounded (Wooldridge 2002: 456), as is the case in all of the regressions reported here. In addition, linear probability models have been shown to perform reasonably well for estimating average marginal effects rather than predicting probabilities (Angrist 2001). I ran a comparable probit regression for each contextual effects regression in this article, and the marginal effects were nearly identical in every instance. Most prior studies of panel voting that report regression results use logit or probit models (e.g., Revesz 1997; Farhang and Wawro 2004; Peresie 2005; Boyd et al. 2010) and use colleagues characteristics as regressors. Since these models are not equivalent to the reduced form of an endogenous effects model, they are misspecified if endogenous effects are present.

14 Interpreting Circuit Court Voting Patterns 821 Boyd et al. (2010) use the potential outcomes framework of Neyman (1923) and Rubin (1974) to estimate the causal effect of panel colleagues gender on judicial voting. This approach matches female judges with comparable male counterparts, and examines how these matched judges influence panel colleagues voting. One advantage to this matching approach is that it controls for aggregate differences between male and female circuit judges. However, it is only appropriate under the assumption of contextual effects; the assumptions of the Neyman-Rubin model are violated if endogenous effects are present (Heckman and Vytlacil 2007). 23 Furthermore, if the judges observed votes are equilibrium outcomes determined through endogenous panel interactions, then it would be inappropriate to selectively remove votes within a case. The consensus voting model in Fischman (2011), on the other hand, assumes purely endogenous effects. This approach assumes that judges incur a cost of dissent when disagreeing with panel colleagues, but does not consider the impact of judges characteristics. The consensus voting model has several advantages over the current framework, particularly that it has more appealing structural foundations and it is superior for predicting voting probabilities. However, it requires a much larger number of observations per judge, and cannot be used to compare the assumptions of contextual versus endogenous effects. The simplicity of the linear model used here and the ease in implementation and interpretation may recommend it as a useful tool for exploratory analysis or when data are limited. Note that the linear endogenous effects model in equation (2) assumes that the endogenous effects are symmetric: each judge s vote exerts the same effect on each of the judge s colleagues, and vice versa. Thus, the linear framework used here cannot test competing theories of minority versus majority acquiescence. By contrast, the consensus voting model in Fischman (2011) assumes that panel effects are the result of suppressed dissents, while the more general model in Fischman (2008) separately estimates a majority and minority panel effect. 3. Data This article examines 11 data sets taken or modified from previous studies of panel voting, in addition to three newly constructed data sets. I included many of the most prominent studies of panel voting and several of the most notable examples in which authors did not find significant panel effects. A summary of the data sets is provided in Table Formally, the stable-unit treatment value assumption (Rubin 1980) in theneyman- Rubin model requires that each judge s vote be unaffected by the treatment assigned to other judges. If two judges on the same panel are assigned to the treatment group in this setting, by having a female panel colleague then each judge s treatment would affect the other s vote when endogenous effects are present.

15 822 The Journal of Law, Economics, & Organization, V31 N4 All data sets include the party-of-appointing-president variable for each judge. Any additional judicial characteristics examined are indicated in the text. When data sets span multiple circuits, the regressions include circuit dummy variables. All regressions include year dummies as well, unless otherwise indicated. 3.1 Judicial Review of Agency Decisions I reexamine the data from two prior studies involving judicial review of administrative agencies: the Revesz (1997) study of environmental cases and the Miles and Sunstein (2006) study of cases involving Chevron deference. The Revesz study examined 154 cases 24 in the D.C. Circuit from 1971 to 1995 challenging decisions by the Environmental Protection Agency. Revesz (1999) reported that the data include unpublished opinions. The second study, Miles and Sunstein (2006), involved challenges to decisions by the Environmental Protection Agency and the National Labor Relations Board in which courts applied Chevron deference to agency interpretations of law. This data set includes 252 cases from all circuits during the years , and includes only published opinions. In the Miles and Sunstein data, a decision is coded as liberal if it affirms the agency decision against an industry group challenge, or if it vacates or remands the agency decision in a challenge by a public interest group. The Revesz data codes cases in the same manner, except that it codes claims separately in cases involving cross-challenges. Thus, if a panel affirms an agency decision that is subject to both an interest group and a public interest challenge, the case would be coded as one liberal decision and one conservative decision. All regressions for both data sets include a variable specifying the ideological direction of the agency decision. 3.2 Sex Discrimination I reexamine the data from two studies of sex discrimination cases: Boyd et al. (2010) and Peresie (2005). The Boyd et al. data, which is modified from the sex discrimination data used in Sunstein et al. (2006), 25 include 415 cases from 1995 to 2003, but only includes published opinions. The Peresie data include 554 cases from 1999 to 2001, including unpublished opinions. The Boyd et al. data include sex discrimination cases but not sexual harassment cases; the Peresie data include both. I code judges for party and gender in both data sets, as in the original studies. Both studies reported that common space scores and gender were significant predictors of voting, but gender was only significant in the Boyd et 24. The original data set included 159 cases. I excluded five cases that were decided by a quorum of two judges. 25. I do not reexamine the full sex discrimination data set from Sunstein et al. (2006), which did not report results by judge gender. Kim (2009) also examined a subset of this data and Farhang and Wawro (2004) reported panel effects in a different set of sex discrimination cases.

16 Interpreting Circuit Court Voting Patterns 823 Table 1. Summary of Data Sets Case type Source Years Circuits Number of cases Percent liberal votes Percent unanimous Unpublished opinions excluded Definition of liberal outcome Comments Review of EPA Revesz (1997) D.C No Affirming EPA against industry challenge or reversing EPA against public interest challenge EPA and NLRB cases applying Chevron Miles and Sunstein (2006) All Yes Affirming agency against industry challenge or reversing agency against public interest challenge Votes coded by claim, rather than by case (543 total votes) Sex discrimination Boyd et al. (2010) All Yes Some relief for plaintiff Includes sex discrimination but not sexual harassment Sex discrimination Peresie (2005) All No Some relief for plaintiff Includes sex discrimination and sexual harassment Criminal appeals Sunstein et al. (2006) Death penalty Sunstein et al. (2006) Third, Fourth, D.C Yes Some relief for defendant Removed 2002 due to coding inconsistencies All Yes Some relief for defendant Death penalty Original Fourth No Some relief for defendant Abortion Sunstein All Yes No support for pro-life side et al. (2006) Abortion rights Original All Yes Substantial relief for pro-choice side Abortion protest Original All Yes Substantial relief for pro-choice side Asylum Law (2005) Ninth No Some relief for asylum petitioner Federal sentencing Linder and Ninth No Some relief for defendant Removed prosecution appeals Niles (2008) (4% of cases) Free Exercise Clause Sisk et al. (2004) All Yes In favor of free exercise claim Removed district court, en Voting Rights Act Cox and Miles (2008) banc, and establishment clause cases from original data set All Yes Finding Section 2 violation Removed district court cases

17 824 The Journal of Law, Economics, & Organization, V31 N4 al. study when the authors employed semi-parametric matching. In both data sets, outcomes are coded as liberal if they provide some relief for the plaintiff in a discrimination case. The Boyd et al. data also include a variable for the direction of the lower court decision. 3.3 Criminal Appeals In the comprehensive study of circuit court voting behavior by Sunstein et al. (2006), the analysis of criminal appeals was the only instance of a large data set in which the authors did not find significant differences between Democratic and Republican appointees or significant panel effects. I demonstrate that this result was largely due to flaws in the data. The original data included 1388 cases from the Third, Fourth, and D.C. Circuits from 1995 to 2004, which were collected from three web pages that maintained lists of decisions for the corresponding circuits. Cases were coded as liberal if they provided some relief to the criminal defendant. The original data identified cases using the last name of the defendant, but did not include judge identifiers, cases citations, or dates. Using the defendant s name, the year and circuit of decision, and the appointing presidents for the judges on the panel, I was able to identify all but one of the cases. 26 I dropped seven cases that did not meet the criteria for inclusion, 27 leaving a total of 1381 cases, and corrected some miscodings of the judges appointing presidents. Because the same judges appear numerous times in the data, I use party of appointment, judges voting rates in other cases, and indicator variables for each judge to predict their voting behavior. In the Sunstein et al. data, the Third Circuit heard four times as many cases in 2002 as in any other year, but the success rate for defendants in 2002 was only 9%, as compared to 32% 46% for the other years. This anomaly was due to the fact that the Third Circuit data included unpublished opinions in 2002, but only published opinions in the other years. In the Fourth Circuit, however, all cases from 2002 are missing. 28 Due to these inconsistencies in the Sunstein et al. data, I exclude the year 2002 when analyzing the criminal appeals. 26. Some defendants with common or misspelled last names were difficult to match, and it is possible in some instances that I identified a different case than the one coded in the original data set. Cases that were difficult to identify were matched to cases with similar or identical names, the same number of Democratic and Republican judges on the panel, and decided on a date that would be consistent with the chronological ordering in the original data. 27. Of the excluded cases, three were civil forfeiture cases, one was decided by a quorum of two judges, one was an en banc opinion, one was a duplicate of another case that was already coded, and one was an opinion that was vacated and withdrawn from the Federal Reporter. 28. Details of the discrepancies in the criminal appeals data are provided in the Supplementary material, Supplementary Table S10.