Many areas of political science focus on causal questions. Evidence from statistical analyses is often used to make the case for causal relationships. While statistical analyses can help establish causal relationships, it can also provide strong evidence of causality where none exists. In this essay, I provide an overview of the statistics of causal inference. Instead of focusing on specific statistical methods, such as matching, I focus more on the assumptions needed to give statistical estimates a causal interpretation. Such assumptions are often referred to as identification assumptions, and these assumptions are critical to any statistical analysis about causal effects. I outline a wide range of identification assumptions and highlight the design-based approach to causal inference. I conclude with an overview of statistical methods that are frequently used for causal inference.

The accuracy of U.S. Social Security Administration (SSA) demographic and financial forecasts is crucial for the solvency of its Trust Funds, other government programs, industry decision-making, and the evidence base of many scholarly articles. Because SSA makes public insufficient replication information and uses antiquated statistical forecasting methods, no external group has ever been able to produce fully independent forecasts or evaluations of policy proposals to change the system. Yet, no systematic evaluation of SSA forecasts has ever been published by SSA or anyone else—until a companion paper to this one. We show that SSA's forecasting errors were approximately unbiased until about 2000, but then began to grow quickly, with increasingly overconfident uncertainty intervals. Moreover, the errors are largely in the same direction, making the Trust Funds look healthier than they are. We extend and then explain these findings with evidence from a large number of interviews with participants at every level of the forecasting and policy processes. We show that SSA's forecasting procedures meet all the conditions the modern social-psychology and statistical literatures demonstrate make bias likely. When those conditions mixed with potent new political forces trying to change Social Security, SSA's actuaries hunkered down, trying hard to insulate their forecasts from strong political pressures. Unfortunately, this led the actuaries into not incorporating the fact that retirees began living longer lives and drawing benefits longer than predicted. We show that fewer than 10% of their scorings of major policy proposals were statistically different from random noise as estimated from their policy forecasting error. We also show that the solution to this problem involves SSA or Congress implementing in government two of the central projects of political science over the last quarter century: (1) transparency in data and methods and (2) replacing with formal statistical models large numbers of ad hoc qualitative decisions too complex for unaided humans to make optimally.

In this article, I use joint scaling methods and similar items from three large-scale surveys to place voters, parties, and politicians from different Latin American countries on a common ideological space. The findings reveal that ideology is a significant determinant of vote choice in Latin America. They also suggest that the success of leftist leaders at the polls reflects the views of the voters sustaining their victories. The location of parties and leaders reveals that three distinctive clusters exist: one located at the left of the political spectrum, another at the center, and a third on the right. The results also indicate that legislators in Brazil, Mexico, and Peru tend to be more “leftists” than their voters. The ideological drift, however, is not significant enough to substantiate the view that a disconnect between voters and politicians lies behind the success of leftist presidents in these countries. These findings highlight the importance of using a common-space scale to compare disparate populations and call into question a number of recent studies by scholars of Latin American politics who fail to adequately address this important issue.

Spatial theories of lawmaking predict that legislative productivity is increasing in the number of status quo policies that lie outside the gridlock interval, but because locations of status quo policies are difficult to measure, previous empirical tests of gridlock theories rely on an auxiliary assumption that the distribution of status quo points is fixed and uniform. This assumption is at odds with the theories being tested, as it ignores the history dependence of lawmaking. We provide an alternative method for testing competing theories by estimating structural models that explicitly account for temporal dependence in a theoretically consistent way. Our analysis suggests that legislative productivity depends both on parties and supermajority pivots, and we find patterns of productivity consistent with a weaker, contingent form of party influence than found in previous work. Parties appear to exert agenda power only on highly salient legislation rather than strongly influencing outcomes through voting pressure and party unity.

Duration data are often subject to various forms of censoring that require adaptations of the likelihood function to properly capture the data generating process, but existing spatial duration models do not yet account for these potential issues. Here, we develop a method to estimate spatial-lag duration models when the outcome suffers from right censoring, the most common form of censoring. We adapt Wei and Tanner's (1991) imputation algorithm for censored (non-spatial) regression data to models of spatially interdependent durations. The algorithm treats the unobserved duration outcomes as censored data and iterates between multiple imputation of the incomplete, that is, right censored, values and estimation of the spatial duration model using these imputed values. We explore the performance of an estimator for log-normal durations in the face of varying degrees of right censoring via Monte Carlo and provide empirical examples of its estimation by analyzing spatial dependence in states' entry dates into World War I.

In most multidimensional spatial models, the systematic component of agent utility functions is specified as additive separable. We argue that this assumption is too restrictive, at least in the context of spatial voting in mass elections. Here, assuming separability would stipulate that voters do not care about how policy platforms combine positions on multiple policy dimensions. We present a statistical implementation of Davis, Hinich, and Ordeshook's (1970) Weighted Euclidean Distance model that allows for the estimation of the direction and magnitude of non-separability from vote choice data. We demonstrate in a Monte-Carlo experiment that conventional separable model specifications yield biased and/or unreliable estimates of the effect of policy distances on vote choice probabilities in the presence of non-separable preferences. In three empirical applications, we find voter preferences on economic and socio-cultural issues to be non-separable. If non-separability is unaccounted for, researchers run the risk of missing crucial parts of the story. The implications of our findings carry over to other fields of research: checking for non-separability is an essential part of robustness testing in empirical applications of multidimensional spatial models.

The strategic nature of political interactions has long captured the attention of political scientists. A traditional statistical approach to modeling strategic interactions involves multi-stage estimation, which improves parameter estimates associated with one stage by using the information from other stages. The application of such multi-stage approaches, however, imposes rather strict demands on data availability: data on the dependent variable must be available for each strategic actor at each stage of the interaction. Limited or no data make such approaches difficult or impossible to implement. Political science data, however, especially in the fields of international relations and comparative politics, are not always structured in a manner that is conducive to these approaches. For example, we observe and have plentiful data on the onset of civil wars, but not the preceding stages, in which opposition groups decide to rebel or governments decide to repress them. In this article, I derive an estimator that probabilistically estimates unobserved actor choices related to earlier stages of strategic interactions. I demonstrate the advantages of the estimator over traditional and split-population binary estimators both using Monte Carlo simulations and a substantive example of the strategic rebel–government interaction associated with civil wars.

Over the past several years, there has been growing use of the draft lottery instrument to study political attitudes and behaviors (see, e.g., Bergan 2009; Erikson and Stoker 2011; Henderson 2012; Davenport 2015). Draft lotteries, held in the United States from 1969 to 1972, provide a potentially powerful design; in theory, they should provide true randomization for the “treatment” of military service or behavioral reactions to the threat of such service. However, the first draft lottery conducted in 1969 was not conducted in a random manner, giving those citizens born in the fourth quarter of the year disproportionately higher chances of being drafted. In this note, we describe the randomization failure and discuss how this failure could in theory compromise the use of draft lottery numbers as an instrumental variable. We then use American National Election Studies data to provide support for the conclusion that individuals most affected by the randomization failure (those born in the fourth quarter of the year) largely do not look statistically distinct from those born at other times of the year. With some caveats, researchers should be able to treat the 1969 draft numbers as if they were assigned at random. We also discuss broader lessons to draw from this example, both for scholars interested in using the draft lottery as an instrumental variable, and for researchers leveraging other instruments with randomization failures. Specifically, we suggest that scholars should pay particular attention to the sources of randomization failure, sample attrition, treatment and dependent variable selection, and possible failure of the exclusion restriction, and we outline ways in which these problems may apply to the draft lottery instrument and other natural experiments.

This text reports the results of an evaluation of the performance of multilevel regression modeling and poststratication (MRP) in reconstructing state-level estimates from federal-level data. The evaluation makes use of Eurobarometer data and relies on the fact that Eurobarometer provides representative survey data for each European Union state to further explore the performance of MRP. I repeatedly draw subsets of the entire Eurobarometer sample, then I compute adjusted country means using MRP with census data, and I compare the resulting estimates to the true country means from the full sample. I do that for ten survey items from various Eurobarometer waves. The results show that MRP is generally successful in producing estimates that are highly correlated with the true values (mean of 0.90). But the approach is less capable of reconstructing the relative rankings of the country means and hitting the range of plausible values of the individual state means. I also show that the great part of the adjustment comes from the modeling of the state means and not from poststratification, and that population-weighted samples perform no worse than samples in which countries have equal shares of the pool of respondents.

Courts of last resort in the American states offer researchers considerable leverage to develop and test theories about how institutions influence judicial behavior. One measure critical to this research agenda is the individual judges' preferences, or ideal points, in policy space. Two main strategies for recovering this measure exist in the literature: Brace, Langer, and Hall's (2000, Measuring preferences of state supreme court judges, Journal of Politics 62(2):387–413) Party-Adjusted Judge Ideology and Bonica and Woodruff's (2014, A common-space measure of state supreme court ideology, Journal of Law, Economics, & Organization, doi: 10.1093/jleo/ewu016) judicial CFscores. Here, we introduce a third measurement strategy that combines CFscores with item response (IRT) estimates of judicial voting behavior in all fifty-two state courts of last resort from 1995 to 2010. We show that leveraging two distinct sources of information (votes and CFscores) yields a superior estimation strategy. Specifically, we highlight several key advantages of the combined measure: (1) it is estimated dynamically, allowing for the possibility that judges' ideological leanings change over time and (2) it maps judges into a common space. In a comparison against existing measurement strategies, we find that our measure offers superior performance in predicting judges' votes. We conclude that it is a valuable tool for advancing the study of judicial politics.