Reducing Model Misspecification and Bias in the Estimation of Interactions

Abstract Analyzing variation in treatment effects across subsets of the population is an important way for social scientists to evaluate theoretical arguments. A common strategy in assessing such treatment effect heterogeneity is to include a multiplicative interaction term between the treatment and a hypothesized effect modifier in a regression model. Unfortunately, this approach can result in biased inferences due to unmodeled interactions between the effect modifier and other covariates, and including these interactions can lead to unstable estimates due to overfitting. In this paper, we explore the usefulness of machine learning algorithms for stabilizing these estimates and show how many off-the-shelf adaptive methods lead to two forms of bias: direct and indirect regularization bias. To overcome these issues, we use a post-double selection approach that utilizes several lasso estimators to select the interactions to include in the final model. We extend this approach to estimate uncertainty for both interaction and marginal effects. Simulation evidence shows that this approach has better performance than competing methods, even when the number of covariates is large. We show in two empirical examples that the choice of method leads to dramatically different conclusions about effect heterogeneity.