Reference

Daniel Wilhelm (University College London), Powerful t-tests in the presence of nonclassical measurement error, Econometrics and Empirical Economics Seminar, TSE, September 13, 2016, 15:30–17:00, room MS 001.

Abstract

This paper proposes a powerful alternative to the t-test in linear regressions when the regressor of interest is not observed. We assume there are two contaminated measurements of the regressor of interest. The two corresponding measurement errors may each possess arbitrary correlation with the regressor of interest as well as between each other, and we do not require any location normalizations on the measurement errors. We propose a new t-statistic that is formed from the regression of the outcome onto an optimally weighted linear combination of the two measurements. In simulations, we show that this new test can be considerably more powerful than t-statistics based on OLS or IV estimates. (with Dongwoo Kim).