Bayesian analysis of programmatic competition and state delegation effects in the Mexican Congress

Transcription

1 Bayesian analysis of programmatic competition and state delegation effects in the Mexican Congress Guillermo Rosas Amanda Driscoll Abstract We use tools of Bayesian inference to address debates regarding the nature of programmatic competition in a young democracy. First, we resort to scaling methods to probe whether the attitudes, beliefs, opinions, and values of representatives to Mexicos lower chamber can be sufficiently captured by a single political dimension, rather than the two cross-cutting Left-Right and regime dimensions that putatively patterned Mexican politics during the 1990s. Second, we look into roll-call votes in Mexico s Lower Chamber for evidence that the voting behavior of PRI legislators is strongly patterned by their state origin. In both cases, appealing to Bayesian inferential methods provides us with a more nuanced, complete, and theoretically appealing analysis than is possible with more limited methods. Prepared for the Conference on Bayesian Methods in the Social Sciences, ITAM-CIDE, Mexico City, November 6 7, We thank Mariana Medina for help in collecting and analyzing part of our data. 1

2 1 Introduction Over the past decade, the use of Bayesian inference methods has gained a growing number of adherents in the social sciences. Practitioners of applied Bayesian analysis are attracted to this inferential framework for various reasons, including the philosophical appeal of an approach that uses data to update a priori expectations in a systematic fashion and the flexibility that MCMC simulation affords to tackle otherwise intractable problems. Detractors often underscore the notion that subjectivity plagues Bayesian analysis, insinuating instead that frequentist inference is somehow capable of uncovering Objective Truth. For many researchers interested in applied work, such debates often seem byzantine; though these researchers perceive the usefulness of Bayesian inference, the main obstacle they see is the rather steep learning curve that is required to use these methods proficiently. Lacking overbearing evidence that Bayesian models allow better inferences, the resolve to adopt a Bayesian framework of analysis wavers in the face of these obstacles. In this paper, we use tools of Bayesian inference to address debates regarding the nature of programmatic competition in a young democracy. In Section 2, we resort to scaling methods to probe whether the attitudes, beliefs, opinions, and values of representatives to Mexico s lower chamber can be sufficiently captured by a single political dimension, rather than the two cross-cutting Left-Right and regime dimensions that putatively patterned Mexican politics during the 1990s (Domínguez and McCann 1996, Magaloni 2006). We consider the programmatic organization of four successive Mexican congresses based on survey questionnaires to gauge whether the ideological positions that underlie legislators responses still lead to recognizable party clusters. In Section 3, we use item-response theory models to explore the possibility that state/party delegations in Congress are now voting in clearly recognizable ways that are distinct from the national party s position. Since the PRI lost the presidency in 2000, this party in particular has lost control of access to resources for patronage that had been useful in guaranting legislator subservience to the national party. We speculate that loss of these resources now means that governors hold sway over the political careers of state representatives to the Mexican Congress. Before presenting our models, it is convenient to start with a brief overview of changes in the Mexican party system over the recent past. As is obvious to even casual observers, Mexican politics changed immensely over the past two decades. A series of unfortunate events a contested presidential election in 1988, a devastating economic crisis in 1995, a string of political murders, and the rise of armed insurgency affected dynamics of party competition, as opposition parties on the Left (PRD) and Right (PAN) maneuvered throughout the 1990s to capture larger seat shares in Congress and, eventually, the Mexican presidency. The PRI s loss of control over executive power in 2000 was a momentous event, as it suggested even to skeptic commentators that the political elite had finally embraced the possibility of untrammeled electoral competition. Beyond this obvious consequence, the loss of PRI control over the presidency may have had an impact in patterns of programmatic competition in Mexico, which is to say in the ways in which parties are internally organized, the clarity of programmatic 2

3 stances they take vis-à-vis the electorate, and the ability of party leaders to impose discipline in congressional votes. Despite its weak powers on paper, the Mexican presidency had historically been a strong executive, a feat made possible through the exercise of meta-constitutional powers (Carpizo McGregor 1977). As Weldon (1997) argues, the strong Mexican presidency depended on fulfillment of three conditions that the PRI was able to deliver from 1936 onwards: (1) unified government, (2) party discipline, and (3) presidential leadership over the party. Combined with the constitutional prohibition of immediate reelection for Congress, Mexico s hyperpresidentialist regime determined the political careers of representatives. Indeed, the Mexican Congress traditionally embodied party-centered incentives that motivated representatives to toe the party line. As a consequence, Mexico boasted very healthy rates of party unity. The arrangement that provided for a strong presidency unraveled in the late 1990s. Once unified government was lost the PRI lost majority control of the lower chamber in 1997 the president s ability to control political careers was severely curtailed. These developments had a deleterious impact on party discipline and in the ideological profiles that parties adopt as they engage in programmatic competition. These are the two aspects of party competition that we consider in our exploration of the usefulness of Bayesian methods. 2 Changes in the programmatic structure of Mexican politics A common claim in the study of party politics is that democracies work well only under conditions of responsible party government (APSA 1950, Schattschneider 1942). These conditions obtain when there exists policy divergence among political parties, policy stability on the part of political parties, and policy voting on the part of the electorate (Adams 2001). A legislative party system with a programmatic structure is one that facilitates the first two conditions. Programmatic structure increases the quality of legislative representation of social preferences and advances accountability to constituents. For this reason, it is important to understand the levels and characteristics of programmatic structure in Latin America generally, and in Mexico in particular. Because political parties in the region are not always sufficiently ideological (Coppedge 1998) and ideologically specialized (Cavarozzi 1995), they are often deemed imperfect instruments of representation and accountability. Rosas (2005) and Kitschelt, Hawkins, Luna, Rosas and Zechmeister (forthcoming) explore the programmatic structure of Latin American legislative party systems based on data from the Salamanca surveys. Based on responses to a variety of survey questions, these sources conclude that the attitudes, beliefs, and opinions of Mexican legislators evinced a relatively structured legislative party system during the latter part of the 1990s, at least when compared to other Latin American systems. In this section, we explore whether the relatively high degree of programmatic structuration among Mexico s major legislative parties survived executive alternation in 2000 and what have been in effect nine years of divided government. To do so, we seek to infer the ideological positions of the major parties based on four waves of Salamanca surveys corresponding to the LVI, LVII, LVIII, and LIX Legislatures 3

4 ( , , , and ). Our main purpose is to document changes in the programmatic organization of the Mexican Congress throughout the period We purport to shed some light on the following questions: Do legislative parties take distinct and recognizable ideological positions? Have these positions changed? Has change followed from diminished salience of old, divisive issues? Has it followed from increased variation in the ideal positions of legislators? If so, what are the sources of this variation? What are the ideological dimensions over which parties remain coherent, what are the ideological dimensions over which parties show increasing internal dissent? Regarding our empirical analysis, one advantage of analyzing surveys rather than roll call votes is that legislators are presumably not constrained by mechanisms of party discipline when volunteering answers. An informed analysis of their responses can therefore throw light into degrees of within-party ideological coherence among legislators, independent of Congressional mechanisms of party discipline. Furthermore, Kitschelt et al. (forthcoming) confirms that, at least for Mexico and some other countries in the region, inferences about the ideological positions of political parties based on survey data provide good indicators of the programmatic stances that parties relay to voters. However, even when the variables used as input to infer ideological party positions are appropriate, the tools of the trade to process this information factor (FA) and discriminant analysis (DA) leave ample room for improvement. We use Bayesian hierarchical models to understand the degree to which legislators ideological positions cluster within parties, and compare our inferences with those obtained from FA and DA. In fact, we build our more sophisticated hierarchical models in an effort to avoid the restrictive assumptions of such models. 2.1 A statistical model of ideological party positions Factor and discriminant analyses can be seen as latent trait techniques that summarize information from a variety of manifest indicators into a handful of constructed variables. The latent trait interpretation of these models considers manifest indicators (i.e., input variables like legislators issue stances) to be imperfect measures of an unobserved theoretical construct (legislator s ideology) that is generally the object of interest. In the case of legislative party systems, scholars tap into survey responses or observed roll-call votes to infer legislators positions on an ideological space of low dimensionality. Legislators ideal points in this space can then be analyzed or used as primordial data in other applications. Though these latent trait techniques are useful for preliminary analyses, they rely on restrictive assumptions that do not always conform either with data characteristics or with theoretical knowledge about legislative party systems. First, FA and DA assume that manifest indicators are continuous, unbounded, and normally distributed (Dunson 2003, Quinn 2004). Second, canonical FA and DA models assume that latent traits are orthogonal, i.e., they construct latent dimensions that are forced to be uncorrelated (Jolliffe 1986, Thurstone 1947). Third, FA and DA models are not invariant under rotation, which means that they can yield an infinite number of solutions. In typical applications, it is common to choose a single rotation, often 4

5 one selected by canned procedures, that the analyst considers interpretable, but this makes for an unprincipled and often arbitrary approach (Heaton and Solo 2004). Frequentist techniques necessitate these restrictive assumptions in order to properly identify FA and DA models, yet these assumptions are seldom innocuous. Finally, DA is most useful to predict the (presumably unknown) party membership of legislators based on observed responses to survey questions. In many applications, however, we are not interested in predicting party membership of legislators based on their issue stances; indeed, the analyst knows the party membership of legislators more often than not. Rather than predicting partisanship, we would like to incorporate information about party membership to recover a complete picture about the distribution of parties and legislators in the ideological space. We propose a latent model of ideology in Mexico s Congress that addresses some of these shortcomings. We start by building from distributional assumptions about manifest indicators Y iq that appropriately account for the type of data contained in the Salamanca surveys. 1 Most survey items are coded as ordinal indicators with four or five possible responses, which suggests the use of ordinal logit links. Thus, for each manifest score Y iq (i indices individuals, q indices survey questions), we estimate parameters θ iqk = p iq p iqk, where θ iqk is the probability that legislator i will choose category k or lower in response to question q (Quinn 2004). We model these cumulative probabilities θ iqk as a logistic function of an underlying score Yiq and question-specific cutpoints γ cq : 2 ( ) θiqk log = Yiq γ cq (1) 1 θ iqk Theoretically, we know that the Mexican political system during the period of transition to democracy was strongly patterned by two divides, namely, the traditional economic-distributive Left-Right dimension and a regime dimension separating supporters of the incumbent PRI and opposition voters (Domínguez and McCann 1996, Greene 2008, Magaloni 2006). Other analyses have also uncovered the existence of a religious-secular dimension that partially overlaps the economic Left-Right dimension (Rosas 2005). Based on this knowledge, we make the underlying scores Yiq for our q survey questions a linear function of legislator-specific latent scores on two dimensions (φ i1 and φ i2 ) and indicator-specific factor loadings λ q, as in Equation 2: Y iq = λ q1 φ i1 + λ q2 φ i2 (2) Note that Equation 2 poses a deterministic relation between latent scores (or ideal points) and Y iq; the stochastic component is captured in the relation between 1 Many indicators have a small number of missing values. In a Bayesian framework, these missing values are treated as parameters to be estimated. The updating algorithm used to obtain Bayesian estimates performs multiple imputation, as it were, of these parameters through data augmentation, so no pre-analysis imputation is necessary (Tanner and Wong 1987). 2 To achieve model identification, the first and last cutpoints are assumed to be ± ; the second cutpoint is fixed at 0, and the rest of the cutpoints are parameters to be estimated. Thus, if a survey question has four ordered categories, we estimate two parameters: one for the cutpoint between responses 2 and 3, and one for the cutpoint between responses 3 and 4 (the cutpoint between responses 1 and 2 is fixed at 0). 5

6 Y iq and Yiq (Equation 1). We are interested in making inferences about loadings λ and especially ideal points φ using as input legislators responses to survey items. We have selected twelve survey items from the Salamanca surveys to use as manifest variables of underlying ideological stances. 3 These items correspond to legislators opinions on economic, regime, and morality issues (the latter tap into a religious/secular divide). By focusing on the same twelve indicators over the entire observation period, we implicitly assume that there were no radical changes over the set of issues that were salient in Mexican politics, and that these twelve indicators accurately describe the political landscape of the time. As can be seen in Table 1, economic issues are preponderant in this set. Because of the substantive importance of the Left-Right economic distributive divide in Mexico, we rely on economic issues to identify the first ideological dimension. We do so by constraining the loadings λ corresponding to these issues to be positive on the first dimension and 0 on the second one. These constraints make the first dimension invariant under rotation. To fully identify the model, we constrain the loadings for democracy and branch conflict on the first dimension to be 0. 4 Thus, rather than atheoretically endorsing a factor rotation selected by a canned procedure in statistical software, we identify our model based on extant knowledge about Mexican politics. To finalize the description of our model, note that latent scores φ are not scaleinvariant, which means that resulting ideal points can be multiplied by any constant value without affecting model fit. In factor analysis it is customary to constrain the distribution of factor scores to have unit variance to solve this problem, centering the distribution at zero with the extreme values fixed at -1 and 1. Rather than relying on this artificial construct, we instead rely on our background knowledge of the case at hand to deal with scale invariance. Because we are interested in arriving at inferences about the ideological positions of legislative parties, we conceive of legislators ideal points as draws from normal distributions centered around their party s ideal position. For example, we stipulate that the ideal positions of PAN legislators (φ ip AN ) have mean µ P AN and variance σ 2 P AN, and estimate both of these parameters from data itself. Thus, we stipulate the following prior distributions for parties p 1, 2, 3 and dimensions k 1, 2: φ ipk N (µ pk, σ 2 pk) (3) µ pk N (0, 10) (4) It is important to clarify the role that parameters µ pk and σpk 2 play in the model. By estimating different party-specific mean location parameters µ pk we are admitting that parties may take distinct positions on the two-dimensional ideological space. By implication, the ideal positions of legislators that belong to the same party may also cluster in distinct regions of the ideological space (Equation 3). That party positions 3 Because we are focusing on a smaller set of issues, our results are not readily comparable with those in Rosas (2005) or Kitschelt et al. (forthcoming), which explore a larger ste of questions. We focus on a smaller set to increase comparability across the four waves of the Salamanca surveys. See the Appendix for question wording. 4 Loadings λ corresponding to divorce and abortion are left unconstrained. 6

7 Table 1: Summary statistics for Salamanca indicators LVI Legislature LVI Legislature LVI Legislature LVI Legislature Indicator Mean SD NA Mean SD NA Mean SD NA Mean SD NA Economic issues Regbasic Regempleo Reglife Regprice Regunemp Regime issues Stabdem Stateconf Threatjud Threatlabor Threatsop Morality issues Divorce Abortion

8 may vary does not mean that they will necessarily do so; to admit the possibility of ideological convergence of party positions, we chose a prior distribution on parameters µ pk that is not extremely informative (Equation 4). If it were to turn out that the data did not support our assumption that parties matter in a general sense, then no grouping of opinions or actions by party would be apparent in our results. Additionally, this specification also avoids the FA identifying assumption of orthogonal dimensions. This follows from the fact that party means can potentially take on any alignment in the two-dimensional ideological space. Finally, note that Equation 3 also allows the possibility that legislators will cluster around their party s position with varying spread. For example, it might well be that PRD legislators differ markedly on their ideal positions on the Left-Right dimension even if they share similar positions along the second axis of competition. By estimating a different spread parameter per party and dimension we allow a priori the very reasonable possibility that within-party ideal points are clustered more or less tightly around party means. Contrast this with the common and contrived DA identification assumption that sets within-party variance equal to 1 on all issue-dimensions Comparison of factor, discriminant, and Bayesian analyses As mentioned before, applied researchers may remain unconvinced about the usefulness of Bayesian statistics without an unequivocal answer to the following questions: Does all of this matter? Does Bayesian modeling lead to different, presumably better, inferences? We make two points as we build our case for the usefulness of Bayesian methods. First, we make inferences about the items that pattern programmatic competition between 1994 and Second, we consider changes in the programmatic structure of the legislative party system during this same period Interpreting loadings Table 2 displays factor loadings (columns labeled FA), discriminant coefficients (DA), and parameters λ of our Bayesian model (Bayes) for each of two latent dimensions in each of the four legislatures covered by the Salamanca surveys. As is common in applied analysis, we present point estimates of factor loadings and discriminant functions; for our Bayesian analysis, we are able to present interval estimates, in this case the 95% credible interval of the posterior distribution of λ. 6 Scholars resort to FA to discover the issues over which legislators stances differ the most, regardless of their party membership. Instead, DA uncovers issues over which maximal betweenparty variation exists. In Table 2, FA scores larger than 0.4 would be considered 5 Even then, parameters σpk 2 must be restricted in order to achieve scale invariance. To do so, we express σpk 2 = 1/τ pk (i.e., we work with precision, rather than variance, parameters) and stipulate the prior distribution τ pk Gamma(0.1, 0.1). This prior distribution means that we expect σpk 2 to equal 1. 6 For example, the interval estimate for regbasic in the first dimension during the LVI Legislature is We interpret this credible interval as suggesting that loading λ falls in this range with very high probability (0.95). Credible intervals that straddle 0 would not be considered relevant. 8

9 to proxy for relevant issues, whereas a cutoff point of about 0.3 would perhaps be more appropriate for DA coefficients. These cutoff points are arbitrary, but are the best that one can do to decide on the importance of different issues in the absence of interval estimates for factor loadings and discriminant coefficients. Our FA and DA results are indicative of some of the classic pitfalls one encounters when performing this type of analysis. First, consider the covariate jobs along the first dimension. This issue varies substantially across the waves, going from 0.19 to 0.49 to 0.15 to 0.19 throughout the four legislatures, changing in size and direction along the way. Moreover, it would seem that this issue has larger discriminating capacity along the second dimension especially for the last legislature (the discriminant coefficient is 0.35). Second, consider the importance of economic issues (basic, jobs, house, price, and dole) in FA and DA. For our inferred factors, we would consider that legislators really are divided in their stances on economic issues, as suggested by very high factor loadings on the first dimension in every legislature. 7 Instead, discriminant coefficients for these very same issues are all over the map, making a clear cut joint interpretation of these results nearly intractable. In the LVI legislature, only the coefficient on basic approaches our stated cutoff, so it would be difficult to conclude that parties took recognizable positions on an economic-distributive divide. In the other legislatures, discriminant coefficients suggest that economic issues are important in dividing parties, but these issues are scattered on the two different dimensions. In the LVII legislature, for example, jobs has a high coefficient in the first dimension, dole has a high coefficient in the second dimension, and price has high coefficients on both dimensions. In light of these somewhat disparate results, we emphasize a second advantage of our model over inferences obtained from combined inspection of FA and DA results: The ability to choose a rotation that makes theoretical sense means that we do not tend to see huge changes from one wave to the next in the discriminating capacity of some issues. Given the way in which we have chosen to identify our Bayesian model, we ensure that all economic issues will load together on a single dimension and with the same positive sign, a restriction which is theoretically motivated and therefore justified. Further, we are still able to check if this restriction makes sense by figuring whether reported credible intervals bump against the restriction at 0. Figure 1 displays graphically the 95% credible intervals on loadings λ. Consider the upper panel, which shows loadings along the first dimension for all four legislatures. Consistent with stipulated constraints, the distribution of λ parameters corresponding to the five economic issues are positive and centered away from 0. Were these intervals essentially piled against the vertical dotted line at 0, we would conclude that our loading restriction was not supported by data Interpreting party and legislators ideal points Both FA and DA yield latent scores factors and discriminant functions that scholars interpret as political dimensions. Kitschelt et al. (forthcoming) makes a useful 7 The one exception is the low factor loading (0.05) for jobs in the LIX legislature. 9

10 Table 2: Comparison of factor loadings, discriminant coefficients, and Bayesian coefficients LVI Legislature LVII Legislature LVIII Legislature LIX Legislature FA DA Bayes FA DA Bayes FA DA Bayes FA DA Bayes Indicator (95% CI) (95% CI) (95% CI) (95% CI) First dimension basic jobs house price dole democracy conflict justice labor branch divorce abortion Second dimension basic jobs house price dole democracy conflict justice labor branch divorce abortion

11 Figure 1: Posterior distribution of Bayesian loadings on two dimensions (80% credible intervals) LVI Leg. LVII Leg. LVIII Leg. LIX Leg. abortion abortion abortion abortion divorce divorce divorce divorce sop sop sop sop labor labor labor labor justice justice justice justice conflict conflict conflict conflict democ democ democ democ dole dole dole dole price price price price life life life life jobs jobs jobs jobs basic basic basic basic LVI Leg. LVII Leg. LVIII Leg. LIX Leg. abortion abortion abortion abortion divorce divorce divorce divorce sop sop sop sop labor labor labor labor justice justice justice justice conflict conflict conflict conflict democ democ democ democ dole dole dole dole price price price price life life life life jobs jobs jobs jobs basic basic basic basic

12 theoretical distinction between the two, employing factor scores as indicators of ideological dimensions and discriminant function scores indicators of partisan dimensions. This is an extremely beneficial theoretical distinction: In principle, we would like to know both the issues over which legislator stances differ the most (ideological dimensions), regardless of party membership, and the issues over which party stances differ the most (partisan dimensions). In general, we would not expect all ideological dimensions to translate into partisan dimensions. Instead, some ideological dimensions may continue to divide legislators over issues that were politically salient in the past but are now muted; some other ideological dimensions may relate to issues on which parties have not taken clear and distinct stances. Though the theoretical distinction among ideological and partisan dimensions is compelling, the use of FA and DA as tools to uncover their substantive contents is not entirely satisfying. Part of the problem stems from the assumption of equal within-party variance that is needed to identify DA models. Because the spread of legislators issue stances around party means is assumed constant and equal across parties, DA might paradoxically place more weight on issues over which betweenparty variance is not maximal. Consider for example two indicators, y 1 and y 2, over which parties take mirror-image positions: On y 1, parties take positions at 1 and 1, and on y 2 they take positions at 2 and 2. Assume as well that the stances of legislators on these issues are normally distributed about their party means with unit variance. Under these circumstances, DA will unveil y 2 to have a higher loading on the underlying discriminant function, just as one would expect. If the variance of legislators stances around y 2 were to increase, DA would start placing more weight on y 1 as the main substantive component of the discriminant function. The importance of y 1 in defining the substance of the underlying partisan dimension increases very rapidly with even relatively small increases in variance around y 2, though the distance between mean party positions continues to be much larger along y 2 (four units) than along y 1 (two units). For this reason alone, we observe so much variation in the set of issues that FA and DA uncover as making up the substantive structure of ideological and partisan dimensions. Consider again programmatic structure in the LVII Legislature, particularly the first dimension. According to FA loadings, the five economic indicators are crucial components of a left-right economic-distributive divide. DA coefficients confirm that two of these indicators jobs and price partly explain between-party variation along the first dimension, but the size of the coefficient on abortion would indicate that the main partisan dimension in this legislature had an overwhelming morality component. Furthermore, when we turn to the second dimension, two economic issues price again and dole have coefficients that are higher than the cutoff point (though they have opposite signs), but the main divisive issue concerns positions on democracy. The disparity between the sets of indicators that are important in FA and DA does not sit well with the theoretical distinction between ideological and partisan dimensions. In the theoretical account, partisan dimensions are meant to be a subset of ideological dimensions. Instead, from comparison of FA and DA results, we find either (1) indicators with high DA coefficients and high FA loadings, or (2) indicators 12

13 with high DA coefficients but irrelevant FA loadings. The second type of indicators are problematic in that they correspond to issues that discriminate among parties but not among legislators, which as suggested above may be a consequence of DA assumptions rather than lack of differentiation in party positions. The first type of indicators are less problematic, but even here we detect a basic lack of correspondence between the substantive contents of ideological and partisan dimensions. This variation may at times be the consequence of cumbersome but necessary identifying assumptions of DA. Our Bayesian hierarchical model, in contrast, captures the importance of economic and regime issues in determining dissent among legislators, which is the distinguishing characteristic of factor analysis, while at the same time preserving the intuition that legislators ideological stances tend to cluster around more or less distinct party means, which is a distinguishing feature of discriminant analysis. This property is best seen in Figure 2, where we plot legislators stances along two dimensions for members of the LVI legislature. For the LVI legislature, both FA and DA reveal a more or less distinct cluster of PAN legislators on the right of the first political dimension. From results in Table 2, this dimension comprises mostly economic issues. DA analysis results add to this depiction a more clear-cut separation between PRI and PRD legislators on the left of the first political dimension. When we consider the DA discriminant coefficients in Table 2, it appears that democracy, dole, and price make up the substance of this second dimension. Because of the size of the coefficient for democracy ( 0.89), it is tempting to interpret this dimension as the regime divide that separated Mexican political actors during the 1990s. Note however that this interpretation leaves some other questions unsolved: What should we make of the relatively high coefficient of democracy along the first dimension ( 0.47)? Why is it that none of the economic variables have coefficients higher than the cutoff point when they proved to be the main components of an economic distributive ideological dimension (and, as a matter of fact, they carry relevant discriminant coefficients in the other legislatures)? We believe our model provides a more accurate representation of ideological and partisan divides in Mexico s legislature. First, because of the restrictions that we placed on loadings λ, the first dimension is mostly informed by legislators stances on economic issues, as can be seen in columns 3 and 4 of Table 2. A couple of the regime variables (justice and conflict) have positive loadings on both dimensions, but because of our chosen constraints the full contribution of democracy is captured in the second dimension. 8 Because of the constraints that we chose to use in order to identify the model, it is more appropriate to refer to this second dimension as a regime partisan dimension separating the opposition PRD and PAN from the incumbent PRI. Finally, we note that our morality issues (abortion and divorce) fit poorly in our two dimensional model for the first legislative session we consider. These issues tend to low positively in one dimension and negative in the other dimension in the first, third, and fourth legislature. This suggests that we could eventually expand the model to 8 Incidentally, the constraint on branch conflict returns an interval estimate that lies on the positive orthant, but is so close to 0 as to remain inconsequential. 13

14 Figure 2: Ideological positions of legislators based on factor, discriminant, and Bayesian analysis of Legislature LVI. Factor analysis Discriminant analysis Bayesian hierarchical model First dimension Second dimension PAN PRD PRI First dimension Second dimension PAN PRD PRI Regime divide Economic Left Right X X X PAN PRD PRI 14

15 consider three underlying latent traits, an extension we leave for future work. To understand the changing programmatic structure of Mexico s legislative party system, we now consider the ideal points of the three parties under consideration. These ideal points correspond to parameters µ pk in Equation 4. For the case of the LVI legislature, we have marked with an X the mean of the posterior distribution of these party location parameters in the rightmost plot of Figure 2. These point estimates do not convey information about uncertainty in our inferences. To avoid this pitfall, we portray in Figure 3 credible contours for party means for each of the four Legislatures. These contours reflect the regions of the ideological space where party means are located with high probability. For example, the mean PAN position lies with probability 0.25 within the region delimited by the innermost blue circle in the northwest plot of Figure 3. Thus, the contours reflect uncertainty about our inferences after using data to update our prior beliefs. The picture that we obtain about legislative programmatic structure for the LVI Legislature confirms the basic outline in Rosas (2005) and Kitschelt et al. (forthcoming). The regime dimension which has been posited by several authors is clearly present in the LVI Legislature, with the PAN clearly differentiating itself from the other parties on both the economic and regime dimensions (Domínguez and McCann 1996, Greene 2008, Magaloni 2006). For the LVII legislature, after the PRI lost its 50% majority in Congress, we see the collapse of the two ideological dimensions into a single partisan dimension on which we can place the PAN to the right of the PRI with high probability and the PRI to the right of the PRD. By 2003, the ideological distance between PRI and PRD seems slightly diminished, though the left-right order of party means is still preserved. By this point, our results from the FA, DA and Bayesian analyses suggest that this second dimension became more strongly associated with issues of morality, rather than disputes over the appropriateness of democracy. As expected, the more socially conservative PAN scores higher than the other two, favoring more restriction on issues such as divorce and abortion. The radical departure from this pattern of programmatic structure occurs in the LVIII Legislature, where our model suggests convergence in party positions. The posterior distributions of the PAN and PRD parameters are practically indistinguishable from each other. Part of the explanation for this effect lies in the PRD s seeming incapacity to nominate candidates with a minimum degree of ideological coherence. We base this claim on inspection of parameters σpk 2 (Equation 3), which as suggested before capture the spread of legislators positions around their party s ideal points. 9 As seen in Table 3, the dispersion parameters that correspond to PRD legislators are systematically larger than those for the PRI and PAN. In the third legislature, we estimate the variance parameters of PRD legislators around their party s mean to be 0.51 and However, PRD legislator positions showed higher dispersion during the LVII 9 The conditional posterior distribution of party s p mean along dimension k is µ pk σpk 2 N (ȳ k, σpk 2 /n), where ȳ is the mean position of party p s legislators on dimension k and n is the number of legislators. Consequently, the posterior distribution of µ pk (the contours in Figure 3) tend to increase with σpk 2. 15

16 Figure 3: Mexican Congress party locations based on survey questions, Credible contours correspond to 0.25, 0.50, and 0.75 probability mass. LVI Legislature ( ) LVII Legislature ( ) Regime divide 25 Regime divide PAN PRD PRI PAN PRD PRI Economic Left Right Economic Left Right LVIII Legislature ( ) LIX Legislature ( ) Regime divide Regime divide PAN PRD PRI PAN PRD PRI Economic Left Right Economic Left Right 16

17 Table 3: Spread of legislators positions around their party s ideal points (ˆσ 2 ) Leg. LVI Leg. LVII Leg. LVIII Leg. LIX Party PAN PRI PRD Legislature, so ideological incoherence within the PRD does not suffice to explain the collapse of programmatic structure of all parties in the LVIII Legislature. To complement this explanation, we should consider the collapsing distance among party means. In short, ideological incoherence within the PRD, along with a seeming confluence of positions among all parties, led to a legislative party system lacking programmatic structure. As mentioned before, when the distribution of politicians stances around their party s mean ideological position is not narrow, parties are not sufficiently ideological, and voters are uncertain about the policy stances their vote buys. When the distance among party positions is minimal, voters might not find any political platform to be desirable, and even if they do, they will face large information costs in understanding what party labels mean in terms of policy stances. Further investigation into this issue is warranted, but a precursory consideration of the political environment points to a variety of potential explanations for this apparent ideological collapse. The PRI, having lost the presidency and their majority in the legislature was wrought with coalitional splits between Madrazo and Gordillo factions and substantial infighting about the future direction of the party. Meanwhile the PAN, faced with the challenging realities of governing and a diminishing base of support for their president and his economic promises was similarly challenged in coherently presenting a unified front for the midterm elections. We might explain this collapse on the part of the backbencher respondents in our survey to be a calculated and strategic response of these politicans, essentially a convergence to the median voter in the face of uncertain futures and feuding leadership. The positions of PRD representatives along the first ideological dimension seem to have become less consistent starting in the LVIII legislature. We can see that in the widening spread around their party s estimated ideal point (last row of Table 3. Before moving on to the next section, let us take stock of the advantages of this Bayesian hierarchical model specification over a combined analysis based on FA and DA. First, the Bayesian model is principled in that it requires theoretically-informed assumptions, rather than contrived identification assumptions such as orthogonality or maximization of factor loadings. Second, the Bayesian model can be easily extended to incorporate information about legislators party membership, which can then be used to estimate party positions in ideological space. Third, our approach allows imputation of missing values as a by-product of the estimation process. Fourth, 17

18 the flexibility added in a hierarchical setup allows us to derive estimates of spread along different parties and dimensions, along with information on cutpoints for ordered variables. Admittedly, an appropriately-specified hierarchical model of the sort we have described could in principle be estimated through maximum likelihood. However, ML techniques are not able to recover appropriate measures of uncertainty about high-level parameters (party-specific means and dispersion, in our case). Moreover, Bayesian estimation of the model does not rely on asymptotic justifications requiring a very large number of data points. Though the Salamanca surveys for Mexico include a large number of legislators, ML inference in other legislatures is not possible due to the small-n problem. 3 Can state elites sway their Congressional delegations? In the next paragraphs we consider some of the recent political changes that should have diminished PRI voting discipline and perhaps increased the clout of local (i.e., state) politicians in affecting politicians careers. Changes in party nominations and campaign financing have slowly nibbled away at the advantages that the national leadership of the PRI, centered around the office of the President, once held in controlling the fate of PRI politicians. As is well known, this advantage stemmed in part from the nonconsecutive reelection clause for Congress representatives that was established in Paired with changes in nomination processes, which had been mostly in hands of local elites, the nonconsecutive reelection clause led to the establishment of a disciplined legislative party that would support the Executive s agenda (Nacif 1997, 122). Consider the case of PRI nominations to Congress. Traditionally, the sectoral organizations of the PRI, along with the Executive, were in charge of nominating candidates for Congress (Langston 1998, 468). Within this system, candidate loyalties were first and foremost to the sectoral leader, whose support was necessary in order to obtain an appointment. As the system became more competitive and it also became obvious that not all sectors were electorally successful, the responsibility for nominating candidates was devolved to the territorial, rather than the sectoral, organizations of the PRI. As early as 1991, for example, state branches of the party started placing more local (as opposed to sectoral) politicians in Congress, and the unions lost six percent of their nominations (Langston 1998, 487). By 2003, the PRI relied on two methods for selecting candidates for SMD districts: district-level primaries and district-level delegate conventions (Wuhs 2006, 43). As? argues in his review essay of Ugalde s The Mexican Congress, the loosening of national-level control over nomination in the PRI may lead to interesting dynamics down the road. In particular, It is thus conceivable that in the future, PRI legislators will approximate the position of the Argentine legislators in the nature of their party loyalty (greater loyalty to the state part and less loyalty to the national party). This process is likely to be catalyzed by the fact that for the first 18

19 Table 4: Descriptive Statistics LVII Legislature ( ) LIX Legislature ( ) Party Seat share AWU score Seat share AWU score PRI PRD PAN PT PVEM Other 1.0 time in modern Mexican history, the PRI does not control the presidency for the current term ( ). All else equal, local level nomination processes undermine national party elites, but these may retain a measure of control if they have power over campaign financing. Mexican parties receive public funds for campaigning, and national party leaders are in principle charged with disbursing money to their state chapters as they see fit. Though we lack this data specifically for the PRI, in 2003 more than a third of public funding to the national parties was transferred to local branches, and overall 47% percent of those transfers were used to fund campaigns (Poiré 2005, 11-12). We also lack studies about fund transfers to the states before 2003, but it is clear that, at least before the electoral reform of 1996, campaign funds were mainly spent by a national committee in national level campaigns. In our view, when deputies obtain significant portions of their campaign funds from the local party organization, local bosses recover some measure of control over representatives to the national Congress. With changes in nomination and campaign spending practices, the PRI s loss of a Congressional majority in 1997 in effect represented the end of the conditions identified by Weldon (1997) as conducive to a powerful presidency (see Section 1). Needless to say, the loss of the presidency itself spelled doom to the possibility that the PRI would at least sustain a disciplined voting bloc in Congress. As the political system democratized and the PRI lost the Presidency, the central leadership of the party lost power to the local elites of the states, especially to those where the PRI is still in power. Being in good terms with the President was no longer a surefire way of obtaining a seat in Congress or any other political plum job. It is then a bit surprising that PRI voting discipline has not entirely broken down. Consider Table 4, which shows seat shares and average weighted unity scores for the three major parties in Legislatures LVII and LIX (we use roll-call votes from these legislatures to assess the existence of state effects in legislators behavior). We follow advice in Morgenstern (2004, 45) to build party unity Rice scores that downplay unanimous votes and therefore over-estimate degrees of discipline among legislative 19

20 parties (see also Carey 2003, 2). 10 Table 4 reveals the PRD and PAN as the leastand most-disciplined parties, respectively, in both Legislatures (this is consistent with our findings based on survey questions in Section 2). What is slightly surprising is that the PRI receives a higher unity score in a Legislature following the loss of the Presidency than in the one we use for our baseline results. In the next section, we inspect a Bayesian hierarchical model to estimate PRI state delegation effects. We compare inferences about ideal points based on this model to inferences one could make based on non-bayesian W-Nominate scores. 3.1 Data and Methods We build and estimate a Bayesian hierarchical model to explore the voting patterns of PRI state delegations. Mexico has a mixed electoral system in which 300 representatives are elected in as many single-member districts (SMD) and 200 representatives are elected in five multi-member districts (MMD) of equal size. In consequence, rollcall votes by Mexico s Congress representatives provide data that are nested within parties and, for different subsets of representatives, within five MMD and within 32 states. The model we propose can be extended to estimate party effects and MMD effects. In this paper, however, we consider a much simpler model in which we estimate PRI state delegation effects exclusively. We estimate our models based on voting records of PRI, PAN, and PRD legislators; for PRI legislators, we assign a state of origin variable that is either the state in which the legislator s district is located (for SMD members) or the state of origin of MMD legislators. We start from the item-response theory (IRT) model of Clinton, Jackman and Rivers (2004), which is commonly used to infer ideal points from roll-call votes. In this model, Pr(y ij = 1) the probability that legislator i will vote in favor of proposal j is a function of legislator- and item-specific parameters. For the purpose of statistical estimation, this probability can be parameterized as in Equation 5: Pr(y ij = 1) = Φ(β j x i + α j ) (5) We are especially interested in parameters x i, which correspond to ideal points of legislators. We believe that the PRI s loss of the presidency represents a change in the incentive structure that patterns politicians behavior. During the period of PRI control of the presidency, the various factors alluded to in Section 1 contributed to extremely high party discipline. Once the presidency was lost, control over career paths of PRI politicians presumably went to PRI state governors. Especially for Congressional representatives elected in SMDs, we speculate that this effect should be 10 Average weighted unity scores are defined as: AW U i = n j=1 R i,j w j n j=1 w j where n is the number of votes over which the average is taken, w is a vote-specific weight defined as 1 #Ayes #Nays #V otes, and R i,j is the Rice score of party i on vote j (excluding abstentions and missing values). 20