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

Licheng Liu, Ye Wang+1 more|arXiv (Cornell University)|Jul 2, 2021

Economic Policies and Impacts63 citations

TL;DR

The paper presents a counterfactual imputation framework for TSCS data and introduces three estimators (FEct, IFEct, MC) plus diagnostic tools and an open-source package (fect) to improve causal inference over traditional TWFE.

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.

Motivation & Objective

• Introduce a simple counterfactual imputation framework for TSCS data with dichotomous treatments.
• Develop and compare three estimators (fixed effects counterfactual, interactive fixed effects counterfactual, matrix completion).
• Provide diagnostics and visualizations to assess identifying assumptions and model validity.
• Offer an open-source implementation (fect) in R and Stata to facilitate usage.

Proposed method

• Define potential outcomes and a counterfactual Y_it(0) for treated observations.
• Estimate ATT by imputing counterfactual outcomes for treated units and averaging treatment effects.
• Describe FEct, IFEct, and MC estimators as different regularization approaches to recover untreated outcomes.
• Propose dynamic treatment effects plots based on counterfactuals to assess heterogeneity and carryover/pretrends.
• Introduce diagnostic tests: placebo test, test for no pretrend, and test for no carryover effects; include equivalence testing for limited power.

Experimental results

Research questions

• RQ1 How can counterfactual imputation improve causal estimates in TSCS data with time-varying confounders and treatment reversal?
• RQ2 What are the properties and when should FEct, IFEct, or MC be used for ATT estimation?
• RQ3 How can researchers diagnose the validity of identifying assumptions using dynamic treatment effects and diagnostic tests?
• RQ4 What is the role of the fect software in implementing these estimators and diagnostics across TSCS applications.

Key findings

• Counterfactual estimators (FEct, IFEct, MC) provide more reliable causal estimates than conventional TWFE when treatment effects are heterogeneous or unobserved time-varying confounders exist.
• FEct acts as a weighting estimator that avoids negative weights and aligns with convex combinations of individual treatment effects.
• IFEct and MC relax strict exogeneity via factor-augmented and low-rank decompositions to account for time-varying confounders.
• A set of diagnostic tools, including dynamic treatment effect plots and placebo/no-pretrend/no-carryover tests, helps assess identifying assumptions.
• An open-source package, fect, implements these estimators in R and Stata to facilitate application.