This paper proposes a new approach to testing in the generalized method of moments (GMM) framework. The new tests are constructed using heteroskedasticity autocorrelation (HAC) robust standard errors computed using nonparametric spectral density estimators without truncation. While such standard errors are not consistent, a new asymptotic theory shows that they lead to valid tests nonetheless. In an over-identified linear instrumental variables model, simulations suggest that the new tests and the associated limiting distribution theory provide a more accurate first order asymptotic null approximation than both standard nonparametric HAC robust tests and VAR based parametric HAC robust tests. Finite sample power of the new tests is shown to be comparable to standard tests.
Vogelsang, T.J. (2003), "TESTING IN GMM MODELS WITHOUT TRUNCATION", Fomby, T.B. and Carter Hill, R. (Ed.) Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later (Advances in Econometrics, Vol. 17), Emerald Group Publishing Limited, Bingley, pp. 199-233. https://doi.org/10.1016/S0731-9053(03)17010-7
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