Fully Modified GLS Estimation for Seemingly Unrelated Cointegrating Polynomial Regressions
提出一种新的可行广义最小二乘估计量，结合多维误差逆自协方差矩阵和二阶偏差校正，用于似不相关协整多项式回归，并构建了多元KPSS型协整检验，蒙特卡洛模拟显示有限样本性能良好。
ABSTRACT A new feasible generalized least squares estimator is proposed. Our estimator incorporates (1) the inverse autocovariance matrix of multidimensional errors, and (2) second‐order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second‐order bias corrections are convenient byproducts of our approach and lead to conventional asymptotic inference. Based on the proposed fully modified (FM) estimator, a multivariate KPSS‐type test for the null of cointegration is constructed. We subsequently undertake a comprehensive Monte Carlo study to compare the performance of the FM estimators and the related tests. The proposed estimator and the implied test statistics for linear hypotheses and cointegration show good performance in finite samples. We illustrate our methods by estimating long‐run fiscal reaction functions for Austria, Germany, Norway, Portugal, and Switzerland.