Proxy-quality thresholds: Theory and applications

We consider alternative models of a regression containing a proxy for an unobserved regressor. For each model at most two pieces of prior information are necessary to determine the sign of any regressor coefficient: the sign of the partial correlation between the proxy and the unobserved regressor, and a lower bound on the partial or simple correlation between the proxy and the unobserved regressor. We apply our technique to investment and leverage regressions that contain a proxy for the incentive to invest. In both cases proxy quality must be high for the coefficient of interest to be non-zero.