A Practical Guide to Counterfactual Estimators for Causal Inference with Time-Series Cross-Sectional Data
50 Pages Posted: 10 Apr 2020 Last revised: 26 Oct 2020
Date Written: June 21, 2020
This paper introduces a unified framework of counterfactual estimation for time-series cross-sectional data, which estimates the average treatment effect on the treated by directly imputing treated counterfactuals. Its special cases include several newly developed methods, such as the fixed effects counterfactual estimator, interactive fixed effects counterfactual estimator, and matrix completion estimator. These estimators provide more reliable causal estimates than conventional two-way fixed effects models when the treatment effects are heterogeneous or unobserved time-varying confounders exist. Under this framework, we propose two sets of diagnostic tests, tests for (no) pre-trend and placebo tests, accompanied by visualization tools, to help researchers gauge the validity of the no-time-varying-confounder assumption. We illustrate these methods with two political economy examples and develop an open-source package, fect, in both R and Stata to facilitate implementation.
Keywords: counterfactual methods, two-way fixed effects, parallel trends, interactive fixed effects, matrix completion, equivalence test, placebo test, time-series cross-sectional data, panel data
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