On the Robustness of Coefficient Estimates to the Inclusion of Proxy Variables

Abstract This paper considers the use of multiple proxy measures for an unobserved variable and contrasts the approach taken in the measurement error literature to that of the model specification literature. We find that including all available proxy variables in the regression minimizes the bias on coefficients of correctly measured variables in the regression. We derive a set of bounds for all parameters in the model, and compare these results to extreme bounds analysis. Monte Carlo simulations demonstrate the performance of our bounds relative to extreme bounds. We conclude with an empirical example from the cross-country growth literature in which human capital is measured through three proxy variables: literacy rates, and enrollment in primary and secondary school, and show that our approach yields results that contrast sharply with extreme bounds analysis.