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