Heteroskedasticity–Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation

In this note we show that the heteroskedasticity-autocorrelation (HAC) robust tests recently proposed by Kiefer, Vogelsang, and Bunzel (2000) are exactly equivalent to using Bartlett kernel HACstandard errors without truncation. This result suggests that valid tests (asymptotically pivotal) can be constructed using kernel based estimators with band- width equal to sample size. For clarity, we focus on the simple linear regression model yt = x t + utt = 1 2 T , whereand xt are k × 1 vectors, ut is autocorrelated and possibly conditionally heteroskedastic, and Eu txt = 0. This last condition rules out lagged dependent variables but can be dropped by doing the analysis in the context of instrumental variable estimation. See Vogelsang (2000). The focus is testing linear hypotheses about . We consider the ordinary least squares (OLS) estimator, ˆ = T t=1 xtxt −1 T t=1 xtyt. Define vt = xtut. Using standard calculations we can write the normalized estimator as √ T ˆ − = T −1 T t=1 xtx t −1