Regression-Based Causal Analysis from the Potential Outcomes Perspective

Abstract

Most empirical economic research is conducted with the goal of providing scientific evidence that will be informative in assessing causal relationships of interest based on relevant counterfactuals. The implementation of regression methods in this context is ubiquitous. With this as motivation, we detail a comprehensive regression-based potential outcomes framework for causal modeling, estimation and inference. This framework facilitates rigorous specification of the effect parameter of interest and makes clear the sense in which it is causally interpretable, when appropriately defined in a potential outcomes setting. It also serves to crystallize the conditions under which the effect parameter and the underlying regression parameters are identified. The consistent sample analog estimator of the effect parameter is discussed. Juxtaposing this framework with a stylized version of a commonly implemented and routinely applied modeling and estimation protocol reveals how the latter is deficient in recognizing, and fully accounting for, conditions required for identification of the relevant effect parameter and the causal interpretability of estimation results. In the context of an example, we demonstrate the conceptual advantages of this general potential outcomes framework for regression modeling by showing how it resolves fundamental shortcomings in the conventional approach to characterizing and remedying omitted variable bias.