Bounding Omitted Variable Bias Using Auxiliary Data

Abstract

This paper proposes a new estimator that bounds omitted variable bias using proxies for omitted variables with an asymptotically valid bootstrap procedure. The estimator is useful in many applications because it uses proxies that do not need to appear in the same dataset as the outcome variable. Many surveys include rich proxy variables for a diverse set of unobservable characteristics including abilities, beliefs, and preferences; such surveys can be used as auxiliary datasets in computing my estimator. I provide Monte Carlo simulation results that compare my estimator to the alternative estimator proposed by Pacini (2017) and to the Altonji et al. (2005) - Oster (2019) bound estimator. I show from a simulation that my estimator is robust when proxy variables are contaminated with a large amount of measurement error. I illustrate the application of my estimator in the context of a Mincerian wage regression. Last, I provide open-source software to implement the estimator and to compute the confidence interval.

Keywords: Omitted Variable Bias, Two Sample Least Squares, Data Combination, Data Fusion, Auxiliary Data, Proxy Variable

JEL Classification: C01, C80, J01