Powerful t-tests in the presence of nonclassical measurement error
提出一种新的t统计量，用于线性回归系数为零的原假设检验，当解释变量存在非经典测量误差时，该检验比基于OLS或IV的t检验更有效，并在英国双胞胎教育回报数据中发现了显著结果。
This article proposes a powerful alternative to the t-test of the null hypothesis that a coefficient in a linear regression is equal to zero when a regressor is mismeasured. We assume there are two contaminated measurements 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. The critical values of the test are easily computed via a multiplier bootstrap. In simulations, we show that this new test can be significantly more powerful than t-statistics based on OLS or IV estimates. Finally, we apply the proposed test to a study of returns to education based on twin data from the UK. With our maximal t-test, we can discover statistically significant returns to education when standard t-tests do not.