Powerful t-tests in the presence of nonclassical measurement error

Dongwoo Kim and Daniel Wilhelm

No CWP18/21, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper proposes a powerful alternative to the t-test in linear regressions when a regressor is mismeasured. We assume there is a second contaminated measurement of the regressor of interest. We allow the two measurement errors to be nonclassical in the sense that they may both be correlated with the true regressor, they may be correlated with each other, and we do not require any location normalizations on the measurement errors. We propose a new maximal t-statistic that is formed from the regression of the outcome onto a maximally weighted linear combination of the two measurements. Critical values of the test are easily computed via a multiplier bootstrap. In simulations, we show that this new test can be signi?cantly more powerful than t-statistics based on OLS or IV estimates. Finally, we apply the proposed test to the studies of returns to education based on twins data from the US and the UK. With our maximal t-test, we are able to discover statistically signi?cant returns to education when standard t-tests do not.

Date: 2021-04-09
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Related works:
Journal Article: Powerful t-tests in the presence of nonclassical measurement error (2024)
Working Paper: Powerful t-tests in the presence of nonclassical measurement error (2023)
Working Paper: Powerful t-tests in the presence of nonclassical measurement error (2023)
Working Paper: Powerful t-Tests in the presence of nonclassical measurement error (2017)
Working Paper: Powerful t-Tests in the presence of nonclassical measurement error (2017)
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