A Robust Instrumental-Variables Estimator

The classical instrumental-variables estimator is extremely sensitive to the presence of outliers in the sample. This is a concern because outliers can strongly distort the estimated effect of a given regressor on the dependent variable. Although outlier diagnostics exist, they frequently fail to detect atypical observations because they are themselves based on nonrobust (to outliers) estimators. Furthermore, they do not take into account the combined influence of outliers in the first and second stages of the instrumental-variables estimator. In this article, we present a robust instrumental-variables estimator, initially proposed by Cohen Freue, Ortiz-Molina, and Zamar (2011, Working paper: http://www.stat.ubc.ca/~ruben/website/cv/cohen-zamar.pdf), that we have programmed in Stata and made available via the robivreg command. We have improved on their estimator in two different ways. First, we use a weighting scheme that makes our estimator more efficient and allows the computations of the usual identification and overidentifying restrictions tests. Second, we implement a generalized Hausman test for the presence of outliers.