COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1082 Fully Modified IV, GIVE and GMM Estimation Yuichi Kitamura and Peter C. B. Phillips September 1994 This paper develops a general theory of instrumental variables (IV) estimation that
allows for both I(1) and I(0) regressors and instruments. The estimation techniques
involve an extension of the fully modified (FM) regression procedure that was introduced
in earlier work by Phillips-Hansen (1990). FM versions of the generalized instrumental
variable estimation (GIVE) method and the generalized method of moments (GMM) estimator
are developed. In models with both stationary and nonstationary components, the FM-GIVE
and FM-GMM techniques provide efficiency gains over FM-IV in the estimation of the
stationary components of a model that has both stationary and nonstationary regressors.
The paper exploits a result of Phillips (1991a) that we can apply FM techniques in models
with cointegrated regressors and even in stationary regression models without losing the
method's good asymptotic properties. The present paper shows how to take advantage jointly
of the good asymptotic properties of FM estimators with respect to the nonstationary
elements of a model and the good asymptotic properties of the GIVE and GMM estimators with
respect to the stationary components. The theory applies even when there is no prior
knowledge of the number of unit roots in the system or the dimension or the location of
the cointegration space. An FM extension of the Sargan (1958) test for the validity of the
instruments is proposed. See CFP 955 |
