Heteroskedasticity-consistent instrument-free inference in linear regressions with endogenous regressors

The kinkyreg command (Kripfganz and Kiviet, 2021) implements instrument-free estimation and inference procedures for linear regression models with endogenous regressors. By exploiting nonorthogonality conditions under a range of suppositions on the degree of endogeneity, the ordinary least-squares estimator can be modified to obtain asymptotically valid inference. This avoids appealing too hard to validate external instrumental variables and enables a sensitivity analysis. We propose a refinement of this instrument-free approach to realize robustness regarding both endogeneity and unknown heteroskedasticity under symmetrically distributed disturbances, which can be done with a suitable modification of the moment conditions. Although the resulting estimator is more complex because of nonlinearity in the moment conditions, asymptotic inference is straightforward using standard results for method-of-moments estimators.