On “Imputation of Counterfactual Outcomes when the Errors are Predictable”: Discussions on Misspecification and Suggestions of Sensitivity Analyses

Abstract

Gonçalves and Ng propose an interesting and simple way to improve counterfactual imputation methods when errors are predictable. For unconditional analyses, this approach yields smaller mean-squared error and tighter prediction intervals in large samples, even if the dependence of the errors is misspecified. For conditional analyses, this approach corrects the bias of standard methods, and provides valid asymptotic inference, if the dependence of the errors is correctly specified. In this comment, we first discuss how the assumptions imposed on the errors depend on the model and estimator adopted. This enables researchers to assess the validity of the assumptions imposed on the structure of the errors, and the relevant information set for conditional analyses. We then propose a simple sensitivity analysis in order to quantify the amount of misspecification on the dependence structure of the errors required for the conclusions of conditional analyses to be changed.