Bias-corrected estimation in potentially mildly explosive autoregressive models

This paper provides a comprehensive Monte Carlo comparison of different finite-sample bias-correction methods for autoregressive processes. We consider classic situations where the process is either stationary or exhibits a unit root. Importantly, the case of mildly explosive behaviour is studied as well. We compare the empirical performance of an indirect inference estimator (Phillips, Wu, and Yu, 2011), a jackknife approach (Chambers, 2013), the approximately median-unbiased estimator by Roy and Fuller (2001) and the bootstrap- aided estimator by Kim (2003). Our findings suggest that the indirect inference approach o ers a valuable alternative to other existing techniques. Its performance (measured by its bias and root mean squared error) is balanced and highly competitive across many different settings. A clear advantage is its applicability for mildly explosive processes. In an empirical application to a long annual US Debt/GDP series we consider rolling window estimation of autoregressive models. We find substantial evidence for time-varying persistence and periods of explosiveness during the Civil War and World War II. During the recent years, the series is nearly explosive again. Further applications to commodity and interest rate series are considered as well.