Sensitivity Analysis of OLS Multiple Regression Inference with Respect to Possible Linear Endogeneity in the Explanatory Variables

This work describes a versatile sensitivity analysis of OLS hypothesis test rejection p-values with respect to possible endogeneity in the explanatory variables of the usual k-variate linear multiple regression model which practitioners can readily deploy in their research. This sensitivity analysis is based on a derivation of the asymptotic distribution of the OLS parameter estimator, but extended in a particularly straightforward way to the case where some or all of the explanatory variables are endogenous to a specified degree — that is, where the population covariances of the explanatory variables with the model errors are given. In exchange for restricting attention to possible endogeneity which is solely linear in nature, no additional model assumptions must be made, beyond the usual ones for a model with stochastic regressors. In addition, we also use simulation methods to quantify the uncertainty in the sensitivity analysis results introduced by replacing the population variance-covariance matrix by its sample estimate. The usefulness of the analysis — as a `screen' for potential endogeneity issues — is illustrated with an example from the empirical growth literature.