Semiparametrically Modified OLS and IV Estimators for Linear Cointegrating Models

This paper proposes a semiparametrically modified OLS (SM-OLS) estimator and a semiparametrically modified IV (SM-IV) estimator via kernel method for linear cointegrating models when cointegrating equilibrium errors respond instantaneously to changes of the first-differenced integrated regressor in the linear cointegrating models. Both the proposed estimators are shown to have a mixed normal limiting distribution with zero mean and possibly smaller asymptotic variance than Phillips and Hansen’s (1991) fully modified OLS (FM-OLS) estimator and Marmol et al.’s (2002) fully modified instrumental variable (FM-IV) estimator when the first-differenced integrated regressor affects the cointegrating equilibrium errors in nonlinear way. Finite sample Monte Carlo simulations and an empirical application are given to illustrate the performance and usefulness of our proposed estimators.