Estimating Causal Effects With Matching Methods in the Presence and Absence of Bias Cancellation

This article explores the implications of bias cancellation on the estimate of average treatment effects using ordinary least squares (OLS) and Rubin-style matching methods. Bias cancellation (offsetting biases at high and low propensities for treatment in estimates of treatment effects that are uncorrected for nonrandom selection) has been observed when job training is the treatment variable and earnings is the outcome variable. Contrary to published assertions in the literature, bias cancellation is not explainable in terms of the standard selection model, which assumes a symmetric distribution for the errors in the structural and assignment equations. A substantive rationale for bias cancellation is offered, which conceptualizes bias cancellation as the result of a mixture process based on two distinct individual-level decision-making models. While the general properties are unknown, the existence of bias cancellation appears to reduce the average bias in both OLS and matching methods relative to the symmetric distribution case.