On Robust Inference in Time Series Regression

Least squares regression with heteroskedasticity and autocorrelation consistent (HAC) standard errors has proved very useful in cross section environments. However, several major difficulties, which are generally overlooked, must be confronted when transferring the HAC estimation technology to time series environments. First, in plausible time-series environments involving failure of strong exogeneity, OLS parameter estimates can be inconsistent, so that HAC inference fails even asymptotically. Second, most economic time series have strong autocorrelation, which renders HAC regression parameter estimates highly inefficient. Third, strong autocorrelation similarly renders HAC conditional predictions highly inefficient. Finally, The structure of popular HAC estimators is ill-suited for capturing the autoregressive autocorrelation typically present in economic time series, which produces large size distortions and reduced power in HACbased hypothesis testing, in all but the largest samples. We show that all four problems are largely avoided by the use of a simple dynamic regression procedure, which is easily implemented. We demonstrate the advantages of dynamic regression with detailed simulations covering a range of practical issues.