Implementing Valid Two-Step Identification-Robust Confidence Sets for Linear Instrumental-Variables Models

Abstract

In this article, we consider inference in the linear instrumental-variables models with one or more endogenous variables and potentially weak instruments. I developed a command, twostepweakiv, to implement the two-step identification-robust confidence sets proposed by Andrews (2018, Review of Economics and Statistics 100: 337–348) based on Wald tests and linear combination tests (Andrews, 2016, Econometrica 84: 2155–2182). Unlike popular procedures based on first-stage F statistics (Stock and Yogo, 2005, Testing for weak instruments in linear IV regression, in Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg), the two-step identification-robust confidence sets control coverage distortion without assuming the data are homoskedastic. I demonstrate the use of twostepweakiv with an example of analyzing the effect of wages on married female labor supply. For inference on subsets of parameters, twostepweakiv also implements the refined projection method (Chaudhuri and Zivot, 2011, Journal of Econometrics 164: 239–251). I illustrate that this method is more powerful than the conventional projection method using Monte Carlo simulations.