In many social science applications, researchers use the difference-in-differences (DID) estimator to establish causal relationships, exploiting cross-sectional variation in a baseline factor and temporal variation in exposure to an event that presumably may affect all units. This approach, which we term factorial DID (FDID), differs from canonical DID in that it lacks a clean control group unexposed to the event after the event occurs. In this paper, we clarify FDID as a research design in terms of its data structure, feasible estimands, and identifying assumptions that allow the DID estimator to recover these estimands. We frame FDID as a factorial design with two factors: the baseline factor, denoted by G, and the exposure level to the event, denoted by Z, and define the effect modification and causal interaction as the associative and causal effects of G on the effect of Z, respectively. We show that under the canonical no anticipation and parallel trends assumptions, the DID estimator identifies only the effect modification of G in FDID, and propose an additional factorial parallel trends assumption to identify the causal interaction. Moreover, we show that the canonical DID research design can be reframed as a special case of the FDID research design with an additional exclusion restriction assumption, thereby reconciling the two approaches. We extend this framework to allow conditionally valid parallel trends assumptions and multiple time periods, and clarify assumptions required to justify regression analysis under FDID. We illustrate these findings with empirical examples from economics and political science, and provide recommendations for improving practice and interpretation under FDID.

In 1986, Robert LaLonde published an article that compared nonexperimental estimates to experimental benchmarks (LaLonde 1986). He concluded that the nonexperimental methods at the time could not systematically replicate experimental benchmarks, casting doubt on the credibility of these methods. Following LaLonde’s critical assessment, there have been significant methodological advances and practical changes, including (i) an emphasis on estimators based on unconfoundedness, (ii) a focus on the importance of overlap in covariate distributions, (iii) the introduction of propensity score-based methods leading to doubly robust estimators, (iv) a greater emphasis on validation exercises to bolster research credibility, and (v) methods for estimating and exploiting treatment effect heterogeneity. To demonstrate the practical lessons from these advances, we reexamine the LaLonde data and the Imbens-Rubin-Sacerdote lottery data. We show that modern methods, when applied in contexts with significant covariate overlap, yield robust estimates for the adjusted differences between the treatment and control groups. However, this does not mean that these estimates are valid. To assess their credibility, validation exercises (such as placebo tests) are essential, whereas goodness of fit tests alone are inadequate. Our findings highlight the importance of closely examining the assignment process, carefully inspecting overlap, and conducting validation exercises when analyzing causal effects with nonexperimental data.

Why do authoritarian regimes charge political opponents with non-political crimes when they can levy charges directly related to opponents’ political activism? We argue that doing so disguises political repression and undermines the moral authority of opponents, minimizing backlash and mobilization. To test this argument, we conduct a survey experiment, which shows that disguised repression decreases perceptions of dissidents’ morality, decreases people’s willingness to engage in dissent on behalf of the dissident, and increases support for repression of the dissident. We then assess the external validity of the argument by analyzing millions of Chinese social media posts made before and after a large crackdown of vocal government critics in China in 2013. We find that individuals with larger online followings are more likely to be charged with non-political crimes, and those charged with non-political crimes are less likely to receive public sympathy and support.

Two-way fixed effects (TWFE) models are widely used for causal panel analysis in political science. However, recent methodological advancements cast doubt on the validity of the TWFE estimator in the presence of heterogeneous treatment effects (HTE) and violations of the parallel trends assumption (PTA). In response, researchers have proposed a variety of novel estimators and testing procedures. Our study aims to gauge the effects of these issues on empirical political science research and evaluate the practical performance of these new proposals. We undertake a review, replication, and reanalysis of 38 papers recently published in the American Political Science Review, American Journal of Political Science, and Journal of Politics that use observational panel data with binary treatments. Through both visual and statistical tests, we discover that the use of HTE-robust estimators, while potentially impacting precision, generally does not alter the substantive conclusions originally drawn from TWFE estimates. However, violations of the PTA and lack of sufficient statistical power persist as the primary challenges to credible inference. In light of these findings, we put forth recommendations to assist empirical researchers to improve practices.

This chapter surveys new development in causal inference using time-series cross-sectional (TSCS) data. I start by clarifying two identification regimes for TSCS analysis: one under the strict exogeneity assumption and one under the sequential ignorability assumption. I then review three most commonly used methods by political scientists, the difference-in-differences approach, two-way fixed effects models, and the synthetic control method. For each method, I examine its assumptions, explain its pros and cons, and discuss its extensions. I then introduce several new methods under strict exogeneity or sequential ignorability, including the factor-augmented approach, panel matching, and marginal structural models. I conclude by pointing to several directions for future research.

Instrumental variable (IV) strategies are widely used in political science to establish causal relationships, but the identifying assumptions required by an IV design are demanding, and assessing their validity remains challenging. In this paper, we replicate 67 articles published in three top political science journals from 2010-2022 and identify several concerning patterns. First, researchers often overestimate the strength of their instruments due to non-i.i.d. error structures such as clustering. Second, the commonly used t-test for two-stage-least-squares (2SLS) estimates frequently underestimates uncertainties, resulting in uncontrolled Type-I errors in many studies. Third, in most replicated studies, 2SLS estimates are significantly larger than ordinary-least-squares estimates, with their ratio negatively correlated with instrument strength in studies with non-experimentally generated instruments, suggesting potential violations of unconfoundedness or the exclusion restriction. We provide a checklist and software to help researchers avoid these pitfalls and improve their practice.