A joint test of unconfoundedness and common trends

TL;DR

This paper develops a joint overidentification test for unconfoundedness and common trends assumptions in panel data, enabling researchers to validate causal inference methods like propensity score matching and DiD.

Contribution

It introduces a doubly robust joint test combining machine learning with overidentification testing for two key causal assumptions in panel data analysis.

Findings

The test can reject the null hypothesis in empirical applications.

Simulation studies show the test's finite sample properties are promising.

Applied to real datasets, the test identified violations of assumptions in some cases.

Abstract

This paper introduces an overidentification test of two alternative assumptions to identify the average treatment effect on the treated in a two-period panel data setting: unconfoundedness and common trends. Under the unconfoundedness assumption, treatment assignment and post-treatment outcomes are independent, conditional on control variables and pre-treatment outcomes, which motivates including pre-treatment outcomes in the set of controls. Conversely, under the common trends assumption, the trend and the treatment assignment are independent, conditional on control variables. This motivates employing a Difference-in-Differences (DiD) approach by comparing the differences between pre- and post-treatment outcomes of the treatment and control group. Given the non-nested nature of these assumptions and their often ambiguous plausibility in empirical settings, we propose a joint test using a doubly robust statistic that can be combined with machine learning to control for observed confounders in a data-driven manner. We discuss various causal models that imply the satisfaction of either common trends, unconfoundedness, or both assumptions jointly, and we investigate the finite sample properties of our test through a simulation study. Additionally, we apply the proposed method to five empirical examples using publicly available datasets and find the test to reject the null hypothesis in two cases.