Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis

Graham Elliott (), Ulrich K. Müller and Mark Watson

Econometrica, 2015, vol. 83, 771-811

Abstract: This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.

Date: 2015
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