Analytical formulae for accurately sized t-tests in the single instrument case

Narayana Kocherlakota

Economics Letters, 2020, vol. 189, issue C

Abstract: I construct novel analytical expressions for asymptotically valid right-tailed and left-tailed t-tests in the single instrument-single regressor case. The underlying disturbances are allowed to be non-Gaussian and (in a simple extension of the baseline case) heteroskedastic. The critical values for the tests are constructed under the (testable) assumption that the expectation of the F-statistic in the first-stage regression is greater than a lower bound (1+μLB2). The asymptotic sizes of the implied one-tailed (two-tailed) tests are within 2Φ(−μLB)(4Φ(−μLB)) of their nominal values, where Φ is the cdf of a standard normal random variable. The resulting degree of control over asymptotic test sizes is considerably superior to that provided by the standard Stock–Yogo (2005) approach.

Keywords: Instrumental variables; t-test; Heteroskedasticity-consistent (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:189:y:2020:i:c:s0165176520300641

DOI: 10.1016/j.econlet.2020.109053

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