Matching is a conceptually straightforward method to make groups of units comparable on observed characteristics. The method is, however, limited to settings where the study design is simple and the sample is moderately sized. We illustrate these limitations by asking what the causal effects would have been if a large-scale voter mobilization experiment that took place in Michigan for the 2006 election were scaled up to the full population of registered voters. Matching could help us answer this question, but no existing matching method can accommodate the six treatment arms and the 6,762,701 observations involved in the study. To offer a solution for this and similar empirical problems, we introduce a generalization of the full matching method that can be used with any number of treatment conditions and complex compositional constraints. The associated algorithm produces near-optimal matchings; the worst-case maximum within-group dissimilarity is guaranteed to be no more than four times greater than the optimal solution, and simulation results indicate that it comes considerably closer to the optimal solution on average. The algorithm’s ability to balance the treatment groups does not sacrifice speed, and it uses little memory, terminating in linearithmic time using linear space. This enables investigators to construct well-performing matchings within minutes even in complex studies with samples of several million units.

Political districts may be drawn to favor one group or political party over another, or gerrymandered. A number of measurements have been suggested as ways to detect and prevent such behavior. These measures give concrete axes along which districts and districting plans can be compared. However, measurement values are affected by both noise and the compounding effects of seemingly innocuous implementation decisions. Such issues will arise for any measure. As a case study demonstrating the effect, we show that commonly used measures of geometric compactness for district boundaries are affected by several factors irrelevant to fairness or compliance with civil rights law. We further show that an adversary could manipulate measurements to affect the assessment of a given plan. This instability complicates using these measurements as legislative or judicial standards to counteract unfair redistricting practices. This paper accompanies the release of packages in C++, Python, and R that correctly, efficiently, and reproducibly calculate a variety of compactness scores.

In text, images, merged surveys, voter files, and elsewhere, data sets are often missing important covariates, either because they are latent features of observations (such as sentiment in text) or because they are not collected (such as race in voter files). One promising approach for coping with this missing data is to find the true values of the missing covariates for a subset of the observations and then train a machine learning algorithm to predict the values of those covariates for the rest. However, plugging in these predictions without regard for prediction error renders regression analyses biased, inconsistent, and overconfident. We characterize the severity of the problem posed by prediction error, describe a procedure to avoid these inconsistencies under comparatively general assumptions, and demonstrate the performance of our estimators through simulations and a study of hostile political dialogue on the Internet. We provide software implementing our approach.

Various theories in political science point to temporal heterogeneity in relationships of interest. Yet, empirical research typically ignores such heterogeneity or employs fairly crude measures to evaluate it. Advances in models for change point detection offer opportunities to study temporal heterogeneity more carefully. We customize a recent such method for political science purposes, for instance so that it accommodates panel data, and provide an accompanying R-package. We evaluate the methodology, and how it behaves when different assumptions about the number and abrupt nature of change points are violated, by using simulated data. Importantly, the methodology allows us to evaluate changes to different quantities of interest (for various estimators). It also allows us to provide comprehensive estimates concerning uncertainty in the timing and size of changes. We illustrate the utility of this flexible change point methodology on two types of regression models (Probit and OLS) in two empirical applications. We first re-investigate the proposition by Albertus (2017) that labor-dependent agriculture had a more pronounced negative effect on democratic survival before the “third wave of democratization.” Next, we utilize data extending from the French revolution to the present, from V-Dem, to examine the time-variant nature of the income–democracy relationship.

Regression discontinuity (RD) designs are increasingly common in political science. They have many advantages, including a known and observable treatment assignment mechanism. The literature has emphasized the need for “falsification tests” and ways to assess the validity of the design. When implementing RD designs, researchers typically rely on two falsification tests, based on empirically testable implications of the identifying assumptions, to argue the design is credible. These tests, one for continuity in the regression function for a pretreatment covariate, and one for continuity in the density of the forcing variable, use a null of no difference in the parameter of interest at the discontinuity. Common practice can, incorrectly, conflate a failure to reject evidence of a flawed design with evidence that the design is credible. The well-known equivalence testing approach addresses these problems, but how to implement equivalence tests in the RD framework is not straightforward. This paper develops two equivalence tests tailored for RD designs that allow researchers to provide statistical evidence that the design is credible. Simulation studies show the superior performance of equivalence-based tests over tests-of-difference, as used in current practice. The tests are applied to the close elections RD data presented in Eggers et al. (2015b).

It is very difficult to know how international social linkages affect domestic ideological polarization because we can never observe polarization occurring both with and without international connections. To estimate this missing counterfactual, we employ a new statistical method based on Bayesian item-response theory that permits us to disaggregate polarization after the Arab Uprisings into domestic and transnational components. We collected a dataset of Twitter accounts in Egypt and Tunisia during the critical year of 2013, when the Egyptian military overthrew the Islamist President Mohamed Morsi. We find that the coup increased retweets among Egyptian ideological allies by 50% each day following the coup and decreased cross-ideological retweets by 25%. Tunisian Twitter communities also showed stronger intragroup retweeting although at lower levels than in Egypt. Counter-intuitively, our model shows that the additional polarization in Tunisia after the coup appears to have dampened further polarization among Islamists in Egypt.

Citizens’ beliefs about uncertain events are fundamental variables in many areas of political science. While beliefs are often conceptualized in the form of distributions, obtaining reliable measures in terms of full probability densities is a difficult task. In this letter, we ask if there is an effective way of eliciting beliefs as distributions in the context of online surveys. Relying on experimental evidence, we evaluate the performance of five different elicitation methods designed to capture citizens’ uncertain expectations. Our results suggest that an elicitation method originally proposed by Manski (2009) performs well. It measures average citizens’ subjective belief distributions reliably and is easily implemented in the context of regular (online) surveys. We expect that a wider use of this method will lead to considerable improvements in the study of citizens’ expectations and beliefs.

This letter reports the results of a study that combined a unique natural experiment and a local randomization regression discontinuity approach to estimate the effect of polls on turnout intention. We found that the release of a poll increases turnout intention by 5%. This effect is robust to a number of falsification tests of predetermined covariates, placebo outcomes, and changes in the time window selected to estimate the effect. The letter discusses the advantages of the local randomization approach over the standard continuity-based design to study important cases in political science where the running variable is discrete; a method that may expand the range of empirical topics that can be analyzed using regression discontinuity methods.

Debate on the use of lagged dependent variables has a long history in political science. The latest contribution to this discussion is Wilkins (2018, Political Science Research and Methods, 6, 393–411), which advocates the use of an ADL(2,1) model when there is serial dependence in the outcome and disturbance. While this specification does offer some insurance against serially correlated disturbances, this is never the best (linear unbiased estimator) approach and should not be pursued as a general strategy. First, this strategy is only appropriate when the data-generating process (DGP) actually implies a more parsimonious model. Second, when this is not the DGP—e.g., lags of the predictors have independent effects—this strategy mischaracterizes the dynamic process. We clarify this issue and detail a Wald test that can be used to evaluate the appropriateness of the Wilkins approach. In general, we argue that researchers need to always: (i) ensure models are dynamically complete and (ii) test whether more restrictive models are appropriate.

Binary outcome models are frequently used in the social sciences and economics. However, such models are difficult to estimate with interdependent data structures, including spatial, temporal, and spatio-temporal autocorrelation because jointly determined error terms in the reduced-form specification are generally analytically intractable. To deal with this problem, simulation-based approaches have been proposed. However, these approaches (i) are computationally intensive and impractical for sizable datasets commonly used in contemporary research, and (ii) rarely address temporal interdependence. As a way forward, we demonstrate how to reduce the computational burden significantly by (i) introducing analytically-tractable pseudo maximum likelihood estimators for latent binary choice models that exhibit interdependence across space and time and by (ii) proposing an implementation strategy that increases computational efficiency considerably. Monte Carlo experiments show that our estimators recover the parameter values as good as commonly used estimation alternatives and require only a fraction of the computational cost.