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

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  • Kocherlakota, Narayana R.

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.

Suggested Citation

  • Kocherlakota, Narayana R., 2020. "Analytical formulae for accurately sized t-tests in the single instrument case," Economics Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:ecolet:v:189:y:2020:i:c:s0165176520300641
    DOI: 10.1016/j.econlet.2020.109053
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    References listed on IDEAS

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    1. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, September.
    2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    3. Woglom, Geoffrey, 2001. "More Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 69(5), pages 1381-1389, September.
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