Title: GMM for regression models with exogenous regressors and non-spherical disturbances
Authors: Taku Yamamoto - Hitotsubashi University (Japan) [presenting]
Hiroaki Chigira - Tohoku University (Japan)
Abstract: GMM (generalized method of moments) is applied to regression models with the endogeniety probrem where regressors are correlated with disturbances. When there is no endogeniety, GMM is usually not recommended in econometrics textbooks, since GMM reduces to OLS (ordinary least squares) when the original regressors themselves are used as its instrumental variables. The purpose is to present the effectiveness of GMM for linear regression models of exogenous regressors with non-spherical disturbances, that is, the disturbances are heteroscadastic and/or serially correlated. It appears to be an overlooked feature of GMM. We in particular demonstrate that GMM with the suitable extra instrumental variables in addition to the original regressors can improve efficiency of the estimator when disturbances are non-spherical. For the model with heteroscadastic disturbances, we propose the extra instrumental variables which are modifications of those proposed for PGLS (partial generalized least squares) by Amemiya. For the model with autocorrelated disturbances, we propose lagged regressors as the extra instrumental variables. The analytical results for some illustrative models and the suitably designed Monte Carlo experiments exhibit that GMM with these extra instrumental variables gives more efficient estimates than OLS.