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

“A Practical Guide to Counterfactual Estimators for Causal Inference with Time‐Series Cross‐Sectional Data” (2022), by Licheng Liu et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Licheng Liu, Ye Wang, Yiqing Xu
- Published: August 2, 2022
- Field: Mathematics
- DOI: https://doi.org/10.1111/ajps.12723
- Free PDF: https://arxiv.org/pdf/2107.00856

## 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.

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