Structural Breaks in Seemingly Unrelated Regression Models

This paper develops an efficient Stein-like shrinkage estimator for estimating slope parameters under structural breaks in seemingly unrelated regression models, which is then used for forecasting. The proposed method is a weighted average of two estimators: a restricted estimator that estimates the parameters under the restriction of no break in the coefficients, and an unrestricted estimator that considers break points and estimates the parameters using the observations within each regime. It is established that the asymptotic risk of the Stein-like shrinkage estimator is smaller than that of the unrestricted estimator, which is the method typically used to estimate the slope coefficients under structural breaks. Furthermore, this paper proposes an averaging minimal mean squared error estimator in which the averaging weight is derived by minimizing its asymptotic risk. The superiority of the two proposed estimators over the unrestricted estimator in terms of the mean squared forecast errors are also derived. Further, analytical comparison between the asymptotic risks of the proposed estimators is provided. Insights from the theoretical analysis are demonstrated in Monte Carlo simulations, and through an empirical example of forecasting output growth rates of G7 countries.