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On bootstrap validity for specification tests with weak instruments

Doko Tchatoka, Firmin (2013): On bootstrap validity for specification tests with weak instruments.

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This paper investigates the asymptotic validity of the bootstrap for Durbin-Wu-Hausman (DWH) specification tests when instrumental variables (IVs) may be arbitrary weak. It is shown that under strong identification, the bootstrap offers a better approximation than the usual asymptotic chi-square distributions. However, the bootstrap provides only a first-order approximation when instruments are weak. This indicates clearly that unlike the Wald-statistic based on a k-class type estimator (Moreira et al., 2009), the bootstrap is valid even for the Wald-type of DWH statistics in the presence of weak instruments.

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