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

2022/08/02 by Licheng Liu, Ye Wang, Yiqing Xu · 357 citations
Economics, Econometrics and Finance · Mathematics · Psychology · #Advanced Causal Inference Techniques #Artificial intelligence #Causal inference #Computer science #Counterfactual conditional #Counterfactual thinking #Econometrics #Economic Policies and Impacts #Estimator #Inference #Mathematics #Psychology #Series (stratigraphy) #Spatial and Panel Data Analysis #Statistics #Time series

paper · doi:10.1111/ajps.12723

published in American Journal of Political Science 68(1), 160-176 (Wiley)

openalex publication_date 2022/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

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 two‐way 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.

Citations

• Semiparametric Difference-in-Differences Estimators
• Inference and missing data
• A Practitioner’s Guide to Cluster-Robust Inference
• Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects

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