Reducing Model Misspecification and Bias in the Estimation of Interactions


(with Michael Olson)

Studying variation in treatment effects across subsets of the population is an important way that scholars in the social sciences evaluate theoretical arguments. A common strategy to assess such treatment effect heterogeneity is to include a multiplicative interaction term between the treatment and a hypothesized effect modifier in a regression model. In this paper, we show that this approach results in biased inferences that are highly sensitive to modeling choices about how the effect modifier interacts with other covariates. Researchers can avoid bias by including additional interactions between the effect modifier and the covariates, but, as we show, this can lead to unstable estimates due to overfitting. We propose an alternative strategy that uses machine learning techniques to greatly reduce the bias in estimating interactions while guarding against large increases in uncertainty. Simulation evidence shows that our approach outperforms traditional methods for estimating interactions, and in two empirical examples, the choice of method leads to dramatically different conclusions about effect heterogeneity.