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Uniform Inference after Pretesting for Exogeneity

Firmin Doko Tchatoka () and Wenjie Wang ()

No 2020-05, School of Economics Working Papers from University of Adelaide, School of Economics

Abstract: Pretesting for exogeneity has become a routine in many empirical applications involving instrumental variables (IVs) to decide whether the ordinary least squares (OLS) or the two-stage least squares (2SLS) method is appropriate. Guggenberger (2010) shows that the second-stage t-test– based on the outcome of a Durbin-Wu-Hausman type pretest for exogeneity in the first-stage– has extreme size distortion with asymptotic size equal to 1 when the standard asymptotic critical values are used. In this paper, we first show that the standard residual bootstrap procedures (with either independent or dependent draws of disturbances) are not viable solutions to such extreme size-distortion problem. Then, we propose a novel hybrid bootstrap approach, which combines the residual-based bootstrap along with an adjusted Bonferroni size-correction method. We establish uniform validity of this hybrid bootstrap in the sense that it yields a two-stage test with correct asymptotic size. Monte Carlo simulations confirm ourtheoretical findings. In particular, our proposed hybrid method achieves remarkable power gains over the 2SLS-based t-test, especially when IVs are not very strong.

Keywords: DWH Pretest; Instrumental Variable; Asymptotic Size; Bootstrap; Bonferroni-based Size-correction; Uniform Inference. (search for similar items in EconPapers)
JEL-codes: C12 C13 C26 (search for similar items in EconPapers)
Date: 2020-03
New Economics Papers: this item is included in nep-ore
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