Title: A simple robust procedure in instrumental variables regression
Authors: Xiyu Jiao - University of Oxford (United Kingdom) [presenting]
Abstract: Due to the frequent concern that outliers may invalidate the empirical findings, in practical applications of instrumental variables regression the common practice is to first run ordinary two stage least squares and remove observations with residuals beyond a chosen cut-off value that classifies outliers. 2SLS is subsequently re-calculated with non-outlying observations, and this procedure can be iterated until robust results are obtained. We analyze this simple robust algorithm asymptotically, then provide consistent estimation and valid inferential procedures for practical implementation given the cut-off value. Moreover, we provide asymptotic theory for setting the cut-off, which is chosen to control the gauge (proportion of outliers wrongly discovered). Asymptotics are derived under the null hypothesis that there is no contamination in the cross-sectional i.i.d. data. The established weak convergence result, involving empirical processes and fixed points, provides a starting point for statistical tests that formalize robustness checks on the difference between ordinary and robust 2SLS.