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

63 Pages Posted: 10 Apr 2020 Last revised: 4 Mar 2022

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: March 2, 2022

Abstract

This paper introduces a simple framework of counterfactual estimation for causal inference with time-series cross-sectional data, in which we estimate the average treatment effect on the treated by directly imputing counterfactual outcomes for treated observations. We discuss several novel estimators under this framework, including the fixed effects counterfactual estimator, interactive fixed effects counterfactual estimator, and matrix completion estimator. They provide more reliable causal estimates than conventional twoway fixed effects models when treatment effects are heterogeneous or unobserved time-varying confounders exist. Moreover, we propose a new dynamic treatment effects plot, along with several diagnostic tests, to help researchers gauge the validity of the identifying assumptions. 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 (March 2, 2022). 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
20 Cooper Square 3rd Floor
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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