New Distribution Theory for the Estimation of Structural Break Point in Mean

Based on the Girsanov theorem, this paper rst obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and tri-modal, indicating that the estimator is seriously biased. These two properties are also found in the nite sample distribution of the least squares estimator of structural break point in the discrete time model. The paper then builds a continuous time approximation to the discrete time model and develops an in- ll asymptotic theory for the least squares estimator. The obtained in- ll asymptotic distribution is asymmetric and tri-modal and delivers good approximations to the nite sample distribution. In order to reduce the bias in the estimation of both the continuous time model and the discrete time model, a simulation-based method based on the indirect estima- tion approach is proposed. 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.