Evaluating the impact of misclassification when estimating heterogeneous causal effects
There is increasing attention given to assessing treatment effect heterogeneity arising from individuals belonging to different underlying classes in the population. Inference proceeds by separating the individuals into distinct classes, then estimating the causal effects within each class. In practice, the individual class memberships are rarely known with certainty, and often have to be estimated. Ignoring the uncertainty in the assumed class memberships precludes the possibility of misclassification, which can potentially lead to biased results and incorrect conclusions. In this paper, we propose a strategy for conducting sensitivity analyses to possible misclassification when estimating heterogeneous treatment effects for different classes. We exploit each individual's (typically nonzero) estimated probabilities of belonging to any given class to evaluate the impact of changing the assumed class memberships - one individual at a time - on the resultant class-specific effect estimates. Because the estimated probabilities are themselves subject to sampling variability, we propose Monte Carlo bounds that explicitly reflect the uncertainty in the individual class memberships via perturbations using a parametric bootstrap. We illustrate our proposed strategy using publicly available data from a field experiment with almost 11,000 voters to investigate whether the effect of voter mobilization on turnout varies across different voter classes. We demonstrate via simulation studies that the perturbed class membership probabilities may be used to construct confidence intervals that perform better empirically at attaining the nominal coverage rate, than existing methods that hold the estimated class memberships fixed.