Finite-sample corrected inference for two-step GMM in time series

This paper develops a finite-sample corrected inference for the efficient generalized method of moments (GMM) in time series. To capture higher-order uncertainty embodied estimating series GMM weight matrix, we extend variance formula Windmeijer (2005) to heteroskedasticity autocorrelated robust (HAR) inference. Using fixed-smoothing asymptotics, show that our test statistics lead standard asymptotic t or F critical values and suffer from less over-rejection null hypothesis than existing procedures on finite-samples, including continuously updating GMM. Not only does correct bias arising plugged-in long-run estimation, but it is also not exposed potential side effect Windmeijer’s formula, which can introduce an additional source after correction.