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

See all articles by Licheng Liu

Licheng Liu

Massachusetts Institute of Technology (MIT) - Department of Political Science

Ye Wang

New York University

Yiqing Xu

Stanford University

Date Written: June 21, 2020

Abstract

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

Suggested Citation

Liu, Licheng and Wang, Ye and Xu, Yiqing, A Practical Guide to Counterfactual Estimators for Causal Inference with Time-Series Cross-Sectional Data (June 21, 2020). Available at SSRN: https://ssrn.com/abstract=3555463 or http://dx.doi.org/10.2139/ssrn.3555463

Licheng Liu

Massachusetts Institute of Technology (MIT) - Department of Political Science ( email )

77 Massachusetts Avenue
Cambridge, MA 02139
United States

Ye Wang

New York University ( email )

Bobst Library, E-resource Acquisitions
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New York, NY 10003-711
United States
6083384999 (Phone)
19104 (Fax)

Yiqing Xu (Contact Author)

Stanford University ( email )

Stanford, CA 94305
United States

HOME PAGE: http://yiqingxu.org

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