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Powerful t-tests in the presence of nonclassical measurement error

Author

Listed:
  • Dongwoo Kim

    (Institute for Fiscal Studies and Simon Fraser University)

  • Daniel Wilhelm

    (Institute for Fiscal Studies and University College London)

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.

Suggested Citation

  • Dongwoo Kim & Daniel Wilhelm, 2021. "Powerful t-tests in the presence of nonclassical measurement error," CeMMAP working papers CWP18/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:18/21
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    References listed on IDEAS

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