Estimation bias in the Ornstein-Uhlenbeck process with flow data

This article derives an analytical expression to approximate the bias of the conditional maximum likelihood estimator in a univariate continuous-time autoregressive model when the variable of interest is a flow. The analytical bias expression is then used to compute a bias-corrected estimator, which is compared to other bias reduction methods that have been employed in the literature, these being the bootstrap, jackknife, and indirect inference. A Monte Carlo experiment shows that all approaches deliver substantial bias reductions. We also explore the robustness of the results to model misspecifications and provide an empirical application to U.S. personal consumption expenditures on energy goods and services. Empirical findings indicate that estimation bias could lead us to erroneous conclusions due to the distortions it can cause in statistical inference.