Bias-corrected estimation in mildly explosive autoregressions

This paper provides a comprehensive Monte Carlo comparison of different finite-sample biascorrection methods for autoregressive processes. We consider situations where the process is either mildly explosive or has a unit root. The case of highly persistent stationary is also studied. We compare the empirical performance of the plain OLS estimator with an OLS and a Cauchy estimator based on recursive demeaning, as well as an estimator based on second differencing. In addition, we consider three different approaches for bias-correction for the OLS estimator: (i) bootstrap, (ii) jackknife and (iii) indirect inference. The estimators are evaluated in terms of bias and root mean squared errors (RMSE) in a variety of practically relevant settings. Our findings suggest that the indirect inference method clearly performs best in terms of RMSE for all considered orders of integration. If bias-correction abilities are solely considered, the jackknife works best for stationary and unit root processes. For the explosive case, the bootstrap and the indirect inference can be recommended. As an empirical application, we study Asian stock market overvaluation during bubbles and emphasize the importance of bias-correction for explosive series.