kinkyreg: Instrument-free inference for linear regression models with endogenous regressors

In models with endogenous regressors, a standard regression approach is to exploit just- or over-identifying orthogonality conditions by using instrumental variables. In just-identified models, the identifying orthogonality assumptions cannot be tested without the imposition of other non-testable assumptions. While formal testing of over-identifying restrictions is possible, its interpretation still hinges on the validity of an initial set of untestable just-identifying orthogonality conditions. We present the kinkyreg Stata program for kinky least squares (KLS) inference that adopts an alternative approach to identification. By exploiting non-orthogonality conditions in the form of bounds on the admissible degree of endogeneity, feasible test procedures can be constructed that do not require instrumental variables. The KLS confidence bands can be more informative than confidence intervals obtained from instrumental variable estimation, in particular when the instruments are weak. Moreover, the approach facilitates a sensitivity analysis for the standard instrumental variable inference. In particular, it allows assessment of the validity of previously untestable just-identification exclusion restrictions. Further KLS-based tests include heteroskedasticity, function form, and serial correlation tests.