Efficient estimation of varying coefficient seemly unrelated regression model

In this paper, we propose a class of varying coefficient seemingly unrelated regression models, in which the errors are correlated across the equations. By applying the series approximation and taking the contemporaneous correlations into account, we propose an efficient generalized least squares series estimation for the unknown coefficient functions. The consistency and asymptotic normality of the resulting estimators are established. In comparison with the ordinary least squares ones, the proposed estimators are more efficient with smaller asymptotical variances. Some simulation studies and a real application are presented to demonstrate the finite sample performance of the proposed methods. In addition, based on a B-spline approximation, we deduce the asymptotic bias and variance of the proposed estimators.