Sensitivity analysis for inference in 2SLS/GMM estimation with possibly flawed instruments

Credible inference requires attention to the possible fragility of the results (p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} values for key hypothesis tests) to flaws in the model assumptions, notably accounting for the validity of the instruments used. Past sensitivity analysis has mainly consisted of experimentation with alternative model specifications and with tests of over-identifying restrictions which actually presuppose instrument validity. We provide a feasible sensitivity analysis of two-stage least-squares and GMM estimation, quantifying the fragility/robustness of inference with respect to possible flaws in the exogeneity assumptions made, and also indicating which of these assumptions are most crucial. The method is illustrated via application to a well-known study of the education–earnings relationship.