Questions of causation are important issues in empirical research on political behavior. Most of the discussion of the econometric problems associated with multiequation models with reciprocal causation has focused on models with continuous dependent variables (e.g., Markus and Converse 1979; Page and Jones 1979). Yet, many models of political behavior involve discrete or dichotomous dependent variables; this paper describes two techniques which can consistently estimate reciprocal relationships between dichotomous and continuous dependent variables. The first, two-stage probit least squares (2SPLS), is very similar to two-stage instrumental variable techniques. The second, two-stage conditional maximum likelihood (2SCML), may overcome problems associated with 2SPLS, but has not been used in the political science literature. We demonstrate the potential pitfalls of ignoring the problems of reciprocal causation in nonrecursive choice models and examine the properties of both techniques using Monte Carlo simulations: we find that 2SPLS slightly outperforms 2SCML in terms of bias but that 2SCML produces more accurate standard errors. However, the 2SCML model offers an explicit statistical test for endogeneity. The results from our simulations, and the statistical test for exogeneity, lead us to advocate the use of 2SCML for estimation of this class of causal models. We then apply both of these techniques to an empirical example focusing on the relationship between voter preferences in a presidential election and the voter's uncertainty about the policy positions taken by the candidates. This example demonstrates the importance of these techniques for political science research.

Equivalent separate-subsample (two-step) and pooled-sample (one-step) strategies exist for any multilevel-modeling task, but their relative practicality and efficacy depend on dataset dimensions and properties and researchers' goals. Separate-subsample strategies have difficulties incorporating cross-subsample information, often crucial in time-series cross-section or panel contexts (subsamples small and/or cross-subsample information great) but less relevant in pools of independently random surveys (subsamples large; cross-sample information small). Separate-subsample estimation also complicates retrieval of macro-level-effect estimates, although they remain obtainable and may not be substantively central. Pooled-sample estimation, conversely, struggles with stochastic specifications that differ across levels (e.g., stochastic linear interactions in binary dependent-variable models). Moreover, pooled-sample estimation that models coefficient variation in a theoretically reduced manner rather than allowing each subsample coefficient vector to differ arbitrarily can suffer misspecification ills insofar as this reduced specification is lacking. Often, though, these ills are limited to inefficiencies and standard-error inaccuracies that familiar efficient (e.g., feasible generalized least squares) or consistent-standard-error estimation strategies can satisfactorily redress.

Over the past eight decades, millions of people have been surveyed on their political opinions. Until recently, however, polls rarely included enough questions in a given domain to apply scaling techniques such as IRT models at the individual level, preventing scholars from taking full advantage of historical survey data. To address this problem, we develop a Bayesian group-level IRT approach that models latent traits at the level of demographic and/or geographic groups rather than individuals. We use a hierarchical model to borrow strength cross-sectionally and dynamic linear models to do so across time. The group-level estimates can be weighted to generate estimates for geographic units. This framework opens up vast new areas of research on historical public opinion, especially at the subnational level. We illustrate this potential by estimating the average policy liberalism of citizens in each U.S. state in each year between 1972 and 2012.

In this paper, we argue that claims of necessity and sufficiency involve a type of asymmetric causal claim that is useful in many social scientific contexts. Contrary to some qualitative researchers, we maintain that there is nothing about such asymmetries that should lead scholars to depart from standard social science practice. We take as given that deterministic and monocausal tests are inappropriate in the social world and demonstrate that standard multiplicative interaction models are up to the task of handling asymmetric causal claims in a multivariate, probabilistic manner. We illustrate our argument with examples from the empirical literature linking electoral institutions and party system size.

Using a scale of child rearing preferences, scholars find that African Americans are far more authoritarian than Whites. We argue that this racial gap in authoritarianism is largely a measurement artifact. The child rearing scale now used to measure authoritarianism is cross-racially invalid because it draws heavily on a metaphor about hierarchy. Akin to someone who favors enforcing conformity in a child, the authoritarian is thought to be inclined toward enforcing conformity in social subordinates. In both cases, one's perspective is drawn from a position of relative power. We believe this metaphor is effective among members of a majority racial group because individual dominance at home meshes with group dominance in society. For members of a racial minority, we believe this metaphor breaks down. Using multi-group confirmatory factor analysis, we establish that Blacks and Whites construe the child rearing items differently. Consequently, authoritarianism correlates highly with the things it should for Whites, but rarely so for Blacks. Using an illegal immigration experiment, we then show divergent patterns of intolerance based on the same child rearing scale. Our results highlight measurement's role in producing large racial gaps in authoritarianism, while illuminating the racial boundaries of the child rearing scale.

Although methodologists have provided us ample notice of both the problem of nonproportional hazards (NPHs) and the means of correcting for them, less attention has been paid to the postestimation interpretation. The suggested inclusion of time interactions in our models is more than a statistical fix: These corrections alter the substantive meaning and interpretation of results. Framing the issue as a specific case of multiplicative-interaction modeling, I provide detailed discussion of the problem of NPHs and present several appropriate means of interpreting both the substantive impact and the significance of variables whose effects may change over time.

This article investigates inconsistency and invalid statistical inference that often characterize dynamic panel analysis in international political economy. These econometric concerns are tied to Nickell bias and cross-sectional dependence. First, we discuss how to avoid Nickell bias in dynamic panels. Second, we put forward factor-augmented dynamic panel regression as a means for addressing cross-sectional dependence. As a specific application, we use our methods for an analysis of the impact of terrorism on economic growth. Different terrorism variables are shown to have no influence on economic growth for five regional samples when Nickell bias and cross-dependence are taken into account. Our finding about terrorism and growth is contrary to the extant literature.

A ranking exists in electoral systems research of different electoral formulas—the mathematical functions governing the conversion of votes into legislative seats—in terms of both proportionality of seats and votes and favorability to the largest party. I reexamine this issue with new methods and new evidence, attempting to cross-validate previous rankings using a larger and more controlled data set and more precise parametric methods than have been applied previously. The results by and large confirm previous knowledge but also illuminate several important new facets obscured in previous investigations. For example, at common ranges of district magnitude (from 5 to 15 seats), it is shown that electoral formula may matter at least as much as district magnitude in shaping proportionality.

While traditionally considered for non-stationary and cointegrated data, DeBoef and Keele suggest applying a General Error Correction Model (GECM) to stationary data with or without cointegration. The GECM has since become extremely popular in political science but practitioners have confused essential points. For one, the model is treated as perfectly flexible when, in fact, the opposite is true. Time series of various orders of integration–stationary, non-stationary, explosive, near- and fractionally integrated–should not be analyzed together but researchers consistently make this mistake. That is, without equation balance the model is misspecified and hypothesis tests and long-run-multipliers are unreliable. Another problem is that the error correction term's sampling distribution moves dramatically depending upon the order of integration, sample size, number of covariates, and the boundedness of Yt. This means that practitioners are likely to overstate evidence of error correction, especially when using a traditional t-test. We evaluate common GECM practices with six types of data, 746 simulations, and five paper replications.

DW-NOMINATE scores for the U.S. Congress are widely used measures of legislators' ideological locations over time. These scores have been used in a large number of studies in political science and closely related fields. In this paper, we extend the work of Lewis and Poole (2004) on the parametric bootstrap to DW-NOMINATE and obtain standard errors for the legislator ideal points. These standard errors are in the range of 1%–4% of the range of DW-NOMINATE coordinates.

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.

This letter deals with a very simple question: if we have grouped data with a binary-dependent variable and want to include fixed effects in the specification, can we meaningfully compare results using a linear model to those estimated with a logit? The reason to doubt such a comparison is that the linear specification appears to keep all observations, whereas the logit drops the groups where the dependent variable is either all zeros or all ones. This letter demonstrates that a linear specification averages the estimates for all the homogeneous outcome groups (which, by definition, all have slope coefficients of zero) with the slope coefficients for the groups with a mix of zeros and ones. The correct comparison of the linear to logit form is to only look at groups with some variation in the dependent variable. Researchers using the linear specification are urged to report results for all groups and for the subset of groups where the dependent variable varies. The interpretation of the difference between these two results depends upon assumptions which cannot be empirically assessed.

Self-reported measures of media exposure are plagued with error and questions about validity. Since they are essential to studying media effects, a substantial literature has explored the shortcomings of these measures, tested proxies, and proposed refinements. But lacking an objective baseline, such investigations can only make relative comparisons. By focusing specifically on recent Internet activity stored by Web browsers, this article's methodology captures individuals' actual consumption of political media. Using experiments embedded within an online survey, I test three different measures of media exposure and compare them to the actual exposure. I find that open-ended survey prompts reduce overreporting and generate an accurate picture of the overall audience for online news. I also show that they predict news recall at least as well as general knowledge. Together, these results demonstrate that some ways of asking questions about media use are better than others. I conclude with a discussion of survey-based exposure measures for online political information and the applicability of this article's direct method of exposure measurement for future studies.

Researchers studying discrimination and bias frequently conduct experiments that use racially distinctive names to signal race. The ability of these experiments to speak to racial discrimination depends on the excludability assumption that subjects’ responses to these names are driven by their reaction to the individual’s putative race and not some other factor. We use results from an audit study with a large number of aliases and data from detailed public records to empirically test the excludability assumption undergirding the use of racially distinctive names. The detailed public records allow us to measure the signals about socioeconomic status and political resources that each name used in the study possibly could send. We then reanalyze the audit study to see whether these signals predict legislators’ likelihood of responding. We find no evidence that politicians respond to this other information, thus providing empirical support for the excludability assumption.

In political science research these days, the R 2 is out of fashion. A chorus of our best methodologists sounds notes of caution, at varying degrees of pitch. Berry and Feldman (1985, 15) remark in their popular regression monograph: “A researcher should be careful to recognize the limitations of R 2 as a measure of goodness of fit.” In their more general statistics text, Hanushek and Jackson (1977, 59) claim that “one must be extremely cautious in interpreting the R 2 value for an estimation and particularly in comparing R 2 values for models that have been estimated with different data sets.” Perhaps the most pointed attack comes from Achen (1982, 61), who argues that the R 2 “measures nothing of serious importance.” His contention is that it should be abandoned, and the standard error of the regression (SEE) substituted as a goodness-of-fit measure. Developing these lines of inquiry further, King (1986) provides the latest set of criticisms. Accordingly, “In most practical political science situations, it makes little sense to use [the R 2]” (King 1986, 669). And, concerning the “proportion of variance explained” definition more particularly, “it is not clear how this interpretation adds meaning to political analyses.” (King 1986, 678).

Researchers in comparative research are increasingly relying on individual level data to test theories involving unobservable constructs like attitudes and preferences. Estimation is carried out using large-scale cross-national survey data providing responses from individuals living in widely varying contexts. This strategy rests on the assumption of equivalence, that is, no systematic distortion in response behavior of individuals from different countries exists. However, this assumption is frequently violated with rather grave consequences for comparability and interpretation. I present a multilevel mixture ordinal item response model with item bias effects that is able to establish equivalence. It corrects for systematic measurement error induced by unobserved country heterogeneity, and it allows for the simultaneous estimation of structural parameters of interest.

In a recent article in the American Political Science Review, Laver, Benoit, and Garry (2003, “Extracting policy positions from political texts using words as data,” 97:311—331) propose a new method for conducting content analysis. Their Wordscores approach, by automating text-coding procedures, represents an advance in content analysis that will potentially have a large long-term impact on research across the discipline. To allow substantive interpretation, the scores produced by the Wordscores procedure require transformation. In this note, we address several shortcomings in the transformation procedure introduced in the original program. We demonstrate that the original transformation distorts the metric on which content scores are placed—hindering the ability of scholars to make meaningful comparisons across texts—and that it is very sensitive to the texts that are scored—opening up the possibility that researchers may generate, inadvertently or not, results that depend on the texts they choose to include in their analyses. We propose a transformation procedure that solves these problems.

The large majority of inferences drawn in empirical political research follow from model-based associations (e.g., regression). Here, we articulate the benefits of predictive modeling as a complement to this approach. Predictive models aim to specify a probabilistic model that provides a good fit to testing data that were not used to estimate the model’s parameters. Our goals are threefold. First, we review the central benefits of this under-utilized approach from a perspective uncommon in the existing literature: we focus on how predictive modeling can be used to complement and augment standard associational analyses. Second, we advance the state of the literature by laying out a simple set of benchmark predictive criteria. Third, we illustrate our approach through a detailed application to the prediction of interstate conflict.

Regression discontinuity (RD) designs enable researchers to estimate causal effects using observational data. These causal effects are identified at the point of discontinuity that distinguishes those observations that do or do not receive the treatment. One challenge in applying RD in practice is that data may be sparse in the immediate vicinity of the discontinuity. Expanding the analysis to observations outside this immediate vicinity may improve the statistical precision with which treatment effects are estimated, but including more distant observations also increases the risk of bias. Model specification is another source of uncertainty; as the bandwidth around the cutoff point expands, linear approximations may break down, requiring more flexible functional forms. Using data from a large randomized experiment conducted by Gerber, Green, and Larimer (2008), this study attempts to recover an experimental benchmark using RD and assesses the uncertainty introduced by various aspects of model and bandwidth selection. More generally, we demonstrate how experimental benchmarks can be used to gauge and improve the reliability of RD analyses.

Selection bias is an important but often neglected problem in comparative research. While comparative case studies pay some attention to this problem, this is less the case in broader cross-national studies, where this problem may appear through the way the data used are generated. The article discusses three examples: studies of the success of newly formed political parties, research on protest events, and recent work on ethnic conflict. In all cases the data at hand are likely to be afflicted by selection bias. Failing to take into consideration this problem leads to serious biases in the estimation of simple relationships. Empirical examples illustrate a possible solution (a variation of a Tobit model) to the problems in these cases. The article also discusses results of Monte Carlo simulations, illustrating under what conditions the proposed estimation procedures lead to improved results.