What follows is a longish controversy (two critiques, a reply and two rejoinders) over the quality of the estimates and associated SEs provided by Plümper and Troeger's (2007) “fixed-effect vector decomposition” (FEVD) procedure; Plümper and Troeger (PT) will refer to that article and not any persons. My role is to lay out some issues that separate the authors rather than to adjudicate between them. As with many controversies, a bit of heat is generated along with some light. Readers care a bit less than the authors about what was said when, but they do care a lot about what appropriate method to use when a panel data model has both unit-specific intercepts and variables that are invariant over a unit. Thus, I also take it upon myself to discuss some things that I gleaned from this controversy; this discussion has a bit less heat than what follows, but of course readers should judge the evidence for themselves.

The proliferation of elections in even those states that are arguably anything but democratic has given rise to a focused interest on developing methods for detecting fraud in the official statistics of a state's election returns. Among these efforts are those that employ Benford's Law, with the most common application being an attempt to proclaim some election or another fraud free or replete with fraud. This essay, however, argues that, despite its apparent utility in looking at other phenomena, Benford's Law is problematical at best as a forensic tool when applied to elections. Looking at simulations designed to model both fair and fraudulent contests as well as data drawn from elections we know, on the basis of other investigations, were either permeated by fraud or unlikely to have experienced any measurable malfeasance, we find that conformity with and deviations from Benford's Law follow no pattern. It is not simply that the Law occasionally judges a fraudulent election fair or a fair election fraudulent. Its “success rate” either way is essentially equivalent to a toss of a coin, thereby rendering it problematical at best as a forensic tool and wholly misleading at worst.

Although a growing number of political scientists are conducting randomized experiments, many of them only report the average treatment effects and do not systematically explore the variation in treatment effects across subpopulations. This is unfortunate from a scientific point of view because heterogeneous treatment effects can provide additional substantive insights. This current state of affairs is also problematic from a policy makers' perspective since such studies do not identify subgroups for which treatments are effective. In this paper, we propose a formal two-step framework that first identifies heterogeneous treatment effects from a randomized experiment and then uses this information to derive an optimal policy about which treatment should be given to whom. Our proposed method avoids the risk of false discoveries that are likely in post hoc subgroup analysis routinely conducted in the discipline. We discuss our methodology in the context of get-out-the-vote randomized field experiments and show how the proposed two-step framework can be applied in real-world settings.

Political scientists have long been interested in citizens' support level for such actors as ethnic minorities, militant groups, and authoritarian regimes. Attempts to use direct questioning in surveys, however, have largely yielded unreliable measures of these attitudes as they are contaminated by social desirability bias and high nonresponse rates. In this paper, we develop a statistical methodology to analyze endorsement experiments, which recently have been proposed as a possible solution to this measurement problem. The commonly used statistical methods are problematic because they cannot properly combine responses across multiple policy questions, the design feature of a typical endorsement experiment. We overcome this limitation by using item response theory to estimate support levels on the same scale as the ideal points of respondents. We also show how to extend our model to incorporate a hierarchical structure of data in order to uncover spatial variation of support while recouping the loss of statistical efficiency due to indirect questioning. We illustrate the proposed methodology by applying it to measure political support for Islamist militant groups in Pakistan. Simulation studies suggest that the proposed Bayesian model yields estimates with reasonable levels of bias and statistical power. Finally, we offer several practical suggestions for improving the design and analysis of endorsement experiments.

Ordinal variables—categorical variables with a defined order to the categories, but without equal spacing between them—are frequently used in social science applications. Although a good deal of research exists on the proper modeling of ordinal response variables, there is not a clear directive as to how to model ordinal treatment variables. The usual approaches found in the literature for using ordinal treatment variables are either to use fully unconstrained, though additive, ordinal group indicators or to use a numeric predictor constrained to be continuous. Generalized additive models are a useful exception to these assumptions. In contrast to the generalized additive modeling approach, we propose the use of a Bayesian shrinkage estimator to model ordinal treatment variables. The estimator we discuss in this paper allows the model to contain both individual group—level indicators and a continuous predictor. In contrast to traditionally used shrinkage models that pull the data toward a common mean, we use a linear model as the basis. Thus, each individual effect can be arbitrary, but the model “shrinks” the estimates toward a linear ordinal framework according to the data. We demonstrate the estimator on two political science examples: the impact of voter identification requirements on turnout and the impact of the frequency of religious service attendance on the liberality of abortion attitudes.

Following David Lee's pioneering work, numerous scholars have applied the regression discontinuity (RD) design to popular elections. Contrary to the assumptions of RD, however, we show that bare winners and bare losers in U.S. House elections (1942–2008) differ markedly on pretreatment covariates. Bare winners possess large ex ante financial, experience, and incumbency advantages over their opponents and are usually the candidates predicted to win by Congressional Quarterly's pre-election ratings. Covariate imbalance actually worsens in the closest House elections. National partisan tides help explain these patterns. Previous works have missed this imbalance because they rely excessively on model-based extrapolation. We present evidence suggesting that sorting in close House elections is due mainly to activities on or before Election Day rather than postelection recounts or other manipulation. The sorting is so strong that it is impossible to achieve covariate balance between matched treated and control observations, making covariate adjustment a dubious enterprise. Although RD is problematic for postwar House elections, this example does highlight the design's advantages over alternatives: RD's assumptions are clear and weaker than model-based alternatives, and their implications are empirically testable.

This paper analyzes the properties of the fixed-effects vector decomposition estimator, an emerging and popular technique for estimating time-invariant variables in panel data models with group effects. This estimator was initially motivated on heuristic grounds, and advocated on the strength of favorable Monte Carlo results, but with no formal analysis. We show that the three-stage procedure of this decomposition is equivalent to a standard instrumental variables approach, for a specific set of instruments. The instrumental variables representation facilitates the present formal analysis that finds: (1) The estimator reproduces exactly classical fixed-effects estimates for time-varying variables. (2) The standard errors recommended for this estimator are too small for both time-varying and time-invariant variables. (3) The estimator is inconsistent when the time-invariant variables are endogenous. (4) The reported sampling properties in the original Monte Carlo evidence do not account for presence of a group effect. (5) The decomposition estimator has higher risk than existing shrinkage approaches, unless the endogeneity problem is known to be small or no relevant instruments exist.

“Benford's Law and the Detection of Election Fraud” raises doubts about whether a test based on the mean of the second significant digit of vote counts equals 4.187 is useful as a test for the occurrence of election fraud. The paper mistakenly associates such a test with Benford's Law, considers a simulation exercise that has no apparent relevance for any actual election, applies the test to inappropriate levels of aggregation, and ignores existing analysis of recent elections in Russia. If tests based on the second significant digit of precinct-level vote counts are diagnostic of election fraud, the tests need to use expectations that take into account the features of ordinary elections, such as strategic actions. Whether the tests are useful for detecting fraud remains an open question, but approaching this question requires an approach more nuanced and tied to careful analysis of real election data than one sees in the discussed paper.

Plümper and Troeger (2007) propose a three-step procedure for the estimation of a fixed effects (FE) model that, it is claimed, “provides the most reliable estimates under a wide variety of specifications common to real world data.” Their fixed effects vector decomposition (FEVD) estimator is startlingly simple, involving three simple steps, each requiring nothing more than ordinary least squares (OLS). Large gains in efficiency are claimed for cases of time-invariant and slowly time-varying regressors. A subsequent literature has compared the estimator to other estimators of FE models, including the estimator of Hausman and Taylor (1981) also (apparently) with impressive gains in efficiency. The article also claims to provide an efficient estimator for parameters on time-invariant variables (TIVs) in the FE model. None of the claims are correct. The FEVD estimator simply reproduces (identically) the linear FE (dummy variable) estimator then substitutes an inappropriate covariance matrix for the correct one. The consistency result follows from the fact that OLS in the FE model is consistent. The “efficiency” gains are illusory. The claim that the estimator provides an estimator for the coefficients on TIVs in an FE model is also incorrect. That part of the parameter vector remains unidentified. The “estimator” relies upon a strong assumption that turns the FE model into a type of random effects model.

Our goal in this paper is to provide a formal explanation for how within-unit causal process information (i.e., data on posttreatment variables and partial information on posttreatment counterfactuals) can help to inform causal inferences relating to total effects—the overall effect of an explanatory variable on an outcome variable. The basic idea is that, in many applications, researchers may be able to make more plausible causal assumptions conditional on the value of a posttreatment variable than they would be able to do unconditionally. As data become available on a posttreatment variable, these conditional causal assumptions become active and information about the effect of interest is gained. This approach is most beneficial in situations where it is implausible to assume that treatment assignment is conditionally ignorable. We illustrate the approach with an example of estimating the effect of election day registration on turnout.

Markov chain Monte Carlo (MCMC) methods have facilitated an explosion of interest in Bayesian methods. MCMC is an incredibly useful and important tool but can face difficulties when used to estimate complex posteriors or models applied to large data sets. In this paper, we show how a recently developed tool in computer science for fitting Bayesian models, variational approximations, can be used to facilitate the application of Bayesian models to political science data. Variational approximations are often much faster than MCMC for fully Bayesian inference and in some instances facilitate the estimation of models that would be otherwise impossible to estimate. As a deterministic posterior approximation method, variational approximations are guaranteed to converge and convergence is easily assessed. But variational approximations do have some limitations, which we detail below. Therefore, variational approximations are best suited to problems when fully Bayesian inference would otherwise be impossible. Through a series of examples, we demonstrate how variational approximations are useful for a variety of political science research. This includes models to describe legislative voting blocs and statistical models for political texts. The code that implements the models in this paper is available in the supplementary material.

In this paper, we introduce an innovative method to diagnose electoral fraud using vote counts. Specifically, we use synthetic data to develop and train a fraud detection prototype. We employ a naive Bayes classifier as our learning algorithm and rely on digital analysis to identify the features that are most informative about class distinctions. To evaluate the detection capability of the classifier, we use authentic data drawn from a novel data set of district-level vote counts in the province of Buenos Aires (Argentina) between 1931 and 1941, a period with a checkered history of fraud. Our results corroborate the validity of our approach: The elections considered to be irregular (legitimate) by most historical accounts are unambiguously classified as fraudulent (clean) by the learner. More generally, our findings demonstrate the feasibility of generating and using synthetic data for training and testing an electoral fraud detection system.

The study of Latino public opinion has renewed interest in the relationship between language and survey response. However, extant research generally relies on statistical methods that cannot distinguish between two related yet distinct types of language effects in Latino surveys: (1) differences in attitude and (2) differences in measures of attitude. The former reflects varied levels of a latent attitude between English and Spanish interviewees. The latter—formally known as Differential Item Functioning (DIF)—refers to linguistic differences in the interpretation of survey items, which lead Latino respondents to misreport their level of attitude. This paper proposes Multiple Indicators Multiple Causes models to decouple these two types of language effects. Using this modeling framework, I examine language differences in measures of subjective and factual political attitudes from the Latino National Survey (2006). I find that the language of interview systematically colors Latinos' interpretation of survey items, even after controlling for measurement error and individual differences in the latent variable being assessed. I then show through an applied analysis how ignoring language DIF can yield misleading inferences about hypothesized relationships between variables. Together, these findings highlight a need for greater theoretical work on the psychological origins of language effects in multilingual political surveys.

Many studies in economics and political science include the concept of ethnic diversity as a key independent variable in empirical studies. To date, however, only single-dimensional measures of ethnic diversity, such as ethnic fractionalization, have been available. In this paper, I define and measure three multidimensional characteristics of social structure—cross-cuttingness, cross-fractionalization, and subgroup fractionalization—and present a new cross-national data set comprised of indices along combinations of five cleavages: race, language, religion, region, and income. After addressing important definitional and measurement issues, I discuss the data and show how their inclusion in economic growth regressions reopens the theoretical debate regarding the influence of ethnic diversity, indicating the potential for these new indices to shed light on the role of ethnic diversity (and social structure more generally) with regards to a number of phenomena of concern to political scientists. The data set is publicly available from the Inter-University Consortium for Political and Social Research data archives and the Institute for Quantitative Social Science Dataverse Network.

This article reinforces our 2007 Political Analysis publication in demonstrating that the fixed-effects vector decomposition (FEVD) procedure outperforms any other estimator in estimating models that suffer from the simultaneous presence of time-varying variables correlated with unobserved unit effects and time-invariant variables. We compare the finite-sample properties of FEVD not only to the Hausman-Taylor estimator but also to the pretest estimator and the shrinkage estimator suggested by Breusch, Ward, Nguyen and Kompas (BWNK), and Greene in this symposium. Moreover, we correct the discussion of Greene and BWNK of FEVD's asymptotic and finite-sample properties.

The similarity of states' foreign policy positions is a standard variable in the dyadic analysis of international relations. Recent studies routinely rely on Signorino and Ritter's (1999, Tau-b or not tau-b: Measuring the similarity of foreign policy positions. International Studies Quarterly 43:115–44) S to assess the similarity of foreign policy ties. However, S neglects two fundamental characteristics of the international state system: foreign policy ties are relatively rare and individual states differ in their innate propensity to form such ties. I propose two chance-corrected agreement indices, Scott's (1955, Reliability of content analysis: The case of nominal scale coding. The Public Opinion Quarterly 19:321–5) π and Cohen's (1960, A coefficient of agreement for nominal scales. Educational and Psychological Measurement 20:37–46) κ, as viable alternatives. Both indices adjust the dyadic similarity score for a large number of common absent ties. Cohen's κ also takes into account differences in individual dyad members' total number of ties. The resulting similarity scores have stronger face validity than S. A comparison of their empirical distributions and a replication of Gartzke's (2007, The capitalist peace. American Journal of Political Science 51:166–91) study of the ‘Capitalist Peace’ indicate that the different types of measures are not substitutable.