Errors-in-Variables Models with Many Proxies

This paper introduces a novel method to estimate linear models when explanatory variables are observed with error and many proxies are available. The empirical Euclidean likelihood principle is used to combine the information that comes from the various mismeasured variables. We show that the proposed estimator is consistent and asymptotically normal. In a Monte Carlo study we show that our method is able to efficiently use the information in the available proxies, both in terms of precision of the estimator and in terms of statistical power. An application to the effect of police on crime suggests that measurement errors in the police variable induce substantial attenuation bias. Our approach, on the other hand, yields large estimates in absolute value with high precision, in accordance with the results put forward by the recent literature