On Bias in the Estimation of Structural Break Points

Based on the Girsanov theorem, this paper obtains the exact finite sample distribution of the maximum likelihood estimator of structural break points in a continuous time model. The exact finite sample theory suggests that, in empirically realistic situations, there is a strong finite sample bias in the estimator of structural break points. This property is shared by least squares estimator of both the absolute structural break point and the fractional structural break point in discrete time models. A simulation-based method based on the indirect estimation approach is proposed to reduce the bias both in continuous time and discrete time models. Monte Carlo studies show that the indirect estimation method achieves substantial bias reductions. However, since the binding function has a slope less than one, the variance of the indirect estimator is larger than that of the original estimator.