Over the last 15 years a large amount of scholarship in legislative politics has used NOMINATE or other similar methods to construct measures of legislators' ideological locations. These measures are then used in subsequent analyses. Recent work in political methodology has focused on the pitfalls of using such estimates as variables in subsequent analysis without explicitly accounting for their uncertainty and possible bias (Herron and Shotts 2003, Political Analysis 11:44–64). This presents a problem for those employing NOMINATE scores because estimates of their unconditional sampling uncertainty or bias have until now been unavailable. In this paper, we present a method of forming unconditional standard error estimates and bias estimates for NOMINATE scores using the parametric bootstrap. Standard errors are estimated for the 90th U.S. Senate in two dimensions. Standard errors of first—dimension placements are in the 0.03 to 0.08 range. The results are compared with those obtained using the Markov chain Monte Carlo estimator of Clinton et al. (2002, Stanford University Working Paper). We also show how the bootstrap can be used to construct standard errors and confidence intervals for auxiliary quantities of interest such as ranks and the location of the median senator.

Welcome to the special issue of Political Analysis dedicated to Bayesian methods. We hope that you enjoy the varied and interesting contributions herein featuring Bayesian statistical methods. For many people in empirical political science, Bayesian statistics seems like a weird offshoot of probability that surfaces occasionally in journals and books but does not occupy a particularly central role. This perception appears to be changing. In fact, it appears to be changing quite rapidly. The purpose of this issue is to support and accelerate this momentum by further demonstrating the full flexibility and power of Bayesian methodology.

How do political actors learn about their environment when the “data” provided by political processes are characterized by rare events and highly discontinuous variation? In such learning environments, what can theory predict about how learning actors will take costly actions that are difficult to reverse (e.g., eliminating programs, approving a risky new product, revising a security policy, firing or recalling an appointed or elected official)? We develop a formal model for this problem and apply it to the termination of bureaucratic agencies. The conventional wisdom that “the older a bureau is, the less likely it is to die” (Downs 1967, Inside Bureaucracy) persists but has never been properly tested. This paper offers a learning-based stochastic optimization model of agency termination that offers two counterintuitive predictions. First, politicians terminate agencies only after learning about them, so the hazard of agencies should be nonmonotonic, contradicting Downs's prediction. Second, if terminating agencies is costly, agencies are least likely to be terminated when politicians are fiscally constrained or when the deficit is high. We assess the model by developing a battery of tests for the shape of the hazard function and estimate these and other duration models using data on U.S. federal government agencies created between 1946 and 1997. Results show that the hazard rate of agency termination is strongly nonmonotonic and that agencies are less likely to be terminated under high deficits and divided government. For the first 50 years of the agency duration distribution, the modal termination hazard occurs at five years after agencies are enabled. Methodologically, our approach ties the functional form of a hazard model tightly to theory and presents an applied “agenda” for testing the shape of an empirical hazard function. With extensions, our model and empirical framework are applicable to a range of political phenomena.

In pursuing their goals, members of the U.S. Supreme Court are affected by their institutional setting. How has that institutional environment changed over time and what have been the political consequences of those changes? Despite considerable analysis of the institutional dynamics of legislatures and executives, political scientists have been slow to bring time series techniques to the study of the Supreme Court, and as a result much less is known about its evolutionary path. Measuring a variety of organizational characteristics, I construct an index of the institutionalization of the Supreme Court from 1790 to 1996. This indicator suggests that the integration of the Court into the system of federal policy making has better enabled the justices to satisfy their objectives. To demonstrate this empirically, I test a series of error correction models of judicial influence, each of which confirms that the nature of the Supreme Court's character has had considerable implications for the scope of the justices' legal and political impact. These results underscore the need for judicial scholars to examine the Court's policy making in longitudinal perspective.

We study the properties of a three-step approach to estimating the parameters of a latent structure model for categorical data and propose a simple correction for a common source of bias. Such models have a measurement part (essentially the latent class model) and a structural (causal) part (essentially a system of logit equations). In the three-step approach, a stand-alone measurement model is first defined and its parameters are estimated. Individual predicted scores on the latent variables are then computed from the parameter estimates of the measurement model and the individual observed scoring patterns on the indicators. Finally, these predicted scores are used in the causal part and treated as observed variables. We show that such a naive use of predicted latent scores cannot be recommended since it leads to a systematic underestimation of the strength of the association among the variables in the structural part of the models. However, a simple correction procedure can eliminate this systematic bias. This approach is illustrated on simulated and real data. A method that uses multiple imputation to account for the fact that the predicted latent variables are random variables can produce standard errors for the parameters in the structural part of the model.

Social scientific theories frequently posit that multiple causal mechanisms may produce the same outcome. Unfortunately, it is not always possible to observe which mechanism was responsible. For example, IMF scholars conjecture that nations enter IMF agreements both out of economic need and for discretionary domestic political reasons. Typically, though, all we observe is the fact of agreement, not its cause. Partial observability probit models (Poirier 1980, Journal of Econometrics 12:209–217; Braumoeller 2003, Political Analysis 11:209–233) provide one method for the statistical analysis of such phenomena. Unfortunately, they are often plagued by identification and labeling difficulties. Sometimes, however, qualitative studies of particular cases enlighten us about causes when quantitative studies cannot. We propose exploiting this information to lend additional structure to the partial observability approach. Monte Carlo simulation reveals that by anchoring “discernible” causes for a handful of cases about which we possess qualitative information, we obtain greater efficiency. More important, our method proves reliable at recovering unbiased parameter estimates when the partial observability model fails. The paper concludes with an analysis of the determinants of IMF agreements.

Many situations exist in which a latent construct has both ordinal and continuous indicators. This presents a problem for the applied researcher because standard measurement models are not designed to accommodate mixed ordinal and continuous data. I address this problem by formulating a measurement model that is appropriate for such mixed multivariate responses. This model unifies standard normal theory factor analysis and item response theory models for ordinal data. I detail a Markov chain Monte Carlo algorithm for model fitting. I apply the model to cross-national data on political-economic risk and find that the model works well. Software for fitting this model is publicly available in the MCMCpack (Martin and Quinn 2004, “MCMCpack 0.4–8”) R package.

Borrowing an approach from the literature on the economics of discrimination, we estimate the impact of nonvoters on the outcome of presidential elections from 1952–2000 using data from the National Election Study (NES). Our estimates indicate that nonvoters are, on average, slightly more likely to support the Democratic Party. Of the 13 presidential elections between 1952 and 2000 we find no change in the eventual outcome of the election with two possible exceptions: 1980 and 2000. Thus our results are not all that dissimilar from other research on participation. Higher turnout in the form of compulsory voting would not radically change the partisan distribution of the vote. When elections are sufficiently close, however, a two percentage point increase may suffice to affect the outcome. Limitations of the NES data we use suggest that our estimates underestimate the impact of nonparticipation. We also compare our method with other econometric techniques. Finally, using our findings we speculate as to why the Democratic Party fails to undertake widespread “get out the vote” or registration drives.

This article argues that a key step in King's iterative approach to R × C ecological inference problems—the aggregation of groups into broad conglomerate categories—can introduce problems of aggregation bias and multimodality into data, inducing model violations. As a result, iterative EI estimates can be considerably biased, even when the original data conform to the assumptions of the model. I demonstrate this problem intuitively and through simulations, show the conditions under which it is likely to arise, and illustrate it with the example of Coloured voting during the 1994 elections in South Africa. I then propose an easy fix to the problem, demonstrating the usefulness of the fix both through simulations and in the specific South African context.

We present a simulation technique for sorting out the size, shape, and location of the uncovered set to estimate the set of enactable outcomes in “real-world” social choice situations, such as the contemporary Congress. The uncovered set is a well-known but underexploited solution concept in the literature on spatial voting games and collective choice mechanisms. We explain this solution concept in nontechnical terms, submit some theoretical observations to improve our theoretical grasp of it, and provide a simulation technique that makes it possible to estimate this set and thus enable a series of tests of its empirical relevance.

Political relationships often vary over time, but standard models ignore temporal variation in regression relationships. We describe a Bayesian model that treats the change point in a time series as a parameter to be estimated. In this model, inference for the regression coefficients reflects prior uncertainty about the location of the change point. Inferences about regression coefficients, unconditional on the change-point location, can be obtained by simulation methods. The model is illustrated in an analysis of real wage growth in 18 OECD countries from 1965–1992.

We fit a multilevel logistic regression model for the mean of a binary response variable conditional on poststratification cells. This approach combines the modeling approach often used in small-area estimation with the population information used in poststratification (see Gelman and Little 1997, Survey Methodology 23:127–135). To validate the method, we apply it to U.S. preelection polls for 1988 and 1992, poststratified by state, region, and the usual demographic variables. We evaluate the model by comparing it to state-level election outcomes. The multilevel model outperforms more commonly used models in political science. We envision the most important usage of this method to be not forecasting elections but estimating public opinion on a variety of issues at the state level.

The dominant methodology for short-term forecasting of electoral outcomes uses trial-heat polls, where respondents report their current electoral preferences (not their election-day predictions). Election markets, where self-selected participants trade shares of candidates at prices predictive of election-day results, provide an alternative method that often produces more accurate forecasts. Consequently, increasing attention is being paid to this methodology. However, it is poorly understood and lacks theoretical justification. Surprisingly, the rationale for forecasting using trial-heat polls has not been completely developed either. We develop the justification for using both election markets and public opinion polls to forecast electoral outcomes, giving conditions under which each method performs ideally. For the ideal case, we prove (under the reasonable assumption that market participants are aware of the poll results) that the mean square prediction error for the market forecast is smaller than that of any forecast based on one or more polls. The case in which the assumptions supporting each method fail is also considered. It is often reasonable to expect that the best case results hold approximately, in which case the market forecast should also beat any poll-based forecast. We also compare the bias and variance of market and poll-based forecasts; our results suggest the utility of using the series of market prices to study the course of campaigns.

Despite the desire to focus on the interconnected nature of politics and economics at the global scale, most empirical studies in the field of international relations assume not only that the major actors are sovereign, but also that their relationships are portrayed in data that are modeled as independent phenomena. In contrast, this article illustrates the use of linear and bilinear random—effects models to represent statistical dependencies that often characterize dyadic data such as international relations. In particular, we show how to estimate models for dyadic data that simultaneously take into account: (a) regressor variables, (b) correlation of actions having the same actor, (c) correlation of actions having the same target, (d) correlation of actions between a pair of actors (i.e., reciprocity of actions), and (e) third-order dependencies, such as transitivity, clustering, and balance. We apply this new approach to the political relations among a wide range of political actors in Central Asia over the period 1989–1999, illustrating the presence and strength of second- and third-order statistical dependencies in these data.

An important property of any party system is the set of choices it presents to the electorate. In this paper we analyze the distribution of parties relative to voters in the multidimensional issue space and introduce two measures of the dispersion of the parties in the issue space relative to the voters, which we call measures of the compactness of the parties in the issue space. We show how compactness is easily computed using standard survey items found on national election surveys. Because we study the spacing of the parties relative to the distribution of the voters, we produce metric-free measures of compactness of the party system. The measures can be used to compare party systems across issues, over time within countries, and across countries. Comparing the compactness of party systems across countries allows us to determine the relative amount of issue choice afforded voters in different polities. We examine the compactness of the issue space and test the impact it has on voter choice in four countries: the United States, the Netherlands, Canada, and Great Britain. We demonstrate that the more compact the distribution of the parties in the issue space on any given issue, the less voters weight that issue in their vote decision. Thus we provide evidence supporting theories suggesting that the greater the choice offered by the parties in an election, the more likely it is that issue voting will play a major role in that election.

This paper presents a method for using dimensional reduction in the analysis of political content. We draw inspiration from latent semantic analysis (LSA) theory, which posits that factor analysis can successfully model human language. We suggest that the factor analysis of word frequencies generated from any political text—for example, open-ended survey responses—provides adequate content analysis categories and can substitute for more commonly practiced techniques. The method proceeds in three steps: data preparation, exploratory factor analyses, and hypothesis testing. This method may produce other benefits by allowing the data to speak more clearly in the development of coding dictionaries while avoiding the problems of inferential circularity common in other data-driven approaches. We demonstrate the method using responses collected in the execution of an experimental design dealing with the topic of partial-birth abortion and assess the demonstration by presenting a human coding of the same material.

This paper replicates the findings that appeared in the article “Severing the Electoral Connection: Shirking in the Contemporary Congress,” published in the American Journal of Political Science (44:316–325), in which Lawrence Rothenberg and Mitchell Sanders incorporated a new research design and, contrary to all previous studies, found evidence of ideological shirking in the U.S. House of Representatives. We investigate the robustness of their results by reestimating their model with Congress-specific fixed effects and find that their results no longer hold.

In political science and related disciplines in the social and behavioral sciences, there exists an unfortunate de facto divide between qualitative and quantitative empirical research. Sometimes this divide is purely a function of training and disciplinary socialization, but often it reflects a valid dispute over the philosophical foundations of inquiry. I argue here that the Bayesian approach to quantitative empirical modeling is an amenable starting point for building a rapprochement between qualitative and quantitative research, and I introduce as an example a straightforward model that allows for the Bayesian estimation of the difference between means of very small samples with unknown and possibly unequal variances. I then extend this approach to consider nonnormal variates, informative priors, and a multivariate test of the difference of means useful for the researcher who is interested in determining whether two small samples are different on several dimensions simultaneously.

Existing research on electoral politics and financial markets predicts that when investors expect left parties—Democrats (US), Labor (UK)—to win elections, market volatility increases. In addition, current econometric research on stock market volatility suggests that Markov-switching models provide more accurate volatility forecasts and fit stock price volatility data better than linear or nonlinear GARCH (generalized autoregressive conditional heteroskedasticity) models. Contrary to the existing literature, we argue here that when traders anticipate that the Democratic candidate will win the presidential election, stock market volatility decreases. Using two data sets from the 2000 U.S. presidential election, we test our claim by estimating several GARCH, exponential GARCH (EGARCH), fractionally integrated exponential GARCH (FIEGARCH), and Markov-switching models. We also conduct extensive forecasting tests—including RMSE and MAE statistics as well as realized volatility regressions—to evaluate these competing statistical models. Results from forecasting tests show, in contrast to prevailing claims, that GARCH and EGARCH models provide substantially more accurate forecasts than the Markov-switching models. Estimates from all the statistical models support our key prediction that stock market volatility decreases when traders anticipate a Democratic victory.