Bias-robust causal inference for panel data

Abstract

We develop a bias-robust causal inference method for observational panel data settings. Such methods typically impute untreated outcomes, so counterfactual error passes straight into the estimated treatment effect while conventional standard errors ignore it. We adapt bias-aware minimax methods, developed for estimating regression coefficients in factor-model panels, to a causal target: the average effect on the treated, which has to be imputed and may vary across units and periods. The estimator corrects the imputed counterfactual with weighted untreated residuals and reports intervals with an explicit allowance for the error that remains. In simulations the proposed method holds nominal coverage where alternatives such as the generalized synthetic control have almost none, especially when the factor rank is underfitted, at the cost of wider intervals. By applying the developed methodology to real data the estimated effect remains significant for counterfactual errors nearly twice the size that the design's placebos typically exhibit.