Bias-corrected estimation for speculative bubbles in stock prices

Abstract

We provide a comparison of different finite-sample bias-correction methods for possibly explosive autoregressive processes. We compare the empirical performance of the downward-biased standard OLS estimator with an OLS and a Cauchy estimator, both based on recursive demeaning, as well as a second-differencing estimator. 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 levels of persistence. In terms of bias-correction, the jackknife works best for stationary and unit root processes, but with a typically large variance. For the explosive case, the indirect inference method is recommended. As an empirical illustration, we reconsider the “dot-com bubble” in the NASDAQ index and explore the usefulness of the indirect inference estimator in terms of testing, date stamping and calculations on overvaluation.