A Practical Guide to Counterfactual Estimators for Causal Inference with Time-Series Cross-Sectional Data

American Journal of Political Science, 2024, with Licheng Liu and Yiqing Xu

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Why this paper matters

This paper provides a practical framework for causal inference with time-series cross-sectional (TSCS) data that addresses well-known problems with the standard two-way fixed effects (TWFE) model. TWFE is popular because it controls for unit and time fixed effects, but it relies on assumptions such as strict exogeneity, constant treatment effects, and no carryover effects, which are often unrealistic and can generate biased or even sign-flipped estimates when treatment timing is staggered and effects are heterogeneous. To avoid these problems, we propose a counterfactual estimation framework that treats treated observations as having missing counterfactual outcomes. Under this approach, researchers estimate the average treatment effect on the treated (ATT) by imputing the missing counterfactuals using statistical models fitted exclusively on untreated observations.

What the approach contributes

Within this framework, we develop and compare three concrete estimators: the fixed effects counterfactual (FEct) estimator, the interactive fixed effects counterfactual (IFEct) estimator, and the matrix completion (MC) estimator, all of which leverage low-rank structure of time-varying unobserved confounders to capture their influences. These estimators impose uniform weights on treated observations, flexibly incorporate covariates, and produce reliable ATT estimates under heterogeneous effects. We also introduce improved dynamic treatment effect plots and a suite of diagnostic tests—including placebo, pre-trend, and carryover-effect tests, each available in both difference-in-means and equivalence forms—to assess identifying assumptions and guide model choice. Two political-economy applications demonstrate how researchers can implement these estimators and diagnostics in practice. The accompanying R/Stata package fect is publicly available for download.