OLS and IV estimation of regression models including endogenous interaction terms

We analyze a class of linear regression models including interactions of endogenous regressors and exogenous covariates. We show that, under typical conditions regarding higher-order dependencies between endogenous and exogenous regressors, the OLS estimator of the coefficient of the interaction term is consistent and asymptotically normally distributed. Although not a necessary condition, we demonstrate that multivariate symmetrically distributed data are sufficient for OLS consistency. In general, we propose a Wald test to test for the validity of these higher-order moments. Applying heteroskedasticity-consistent covariance matrix estimators, we then show that standard inference based on OLS is valid for the coefficient of the interaction term. Furthermore, we analyze several IV estimators, and conclude that an implementation exploiting instruments interacted with the exogenous part of the interaction term is to be preferred. Using our theoretical results we con.rm recent empirical findings on the nonlinear causal relation between financial development and economic growth.