COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 929

"Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests
in Partially Identified Structural Equations"

Peter C.B. Phillips and In Choi

October 1989

General formula for the finite sample and asymptotic distributions of the instrumental variable estimators and the Wald statistics in a simultaneous equation model are derived. It is assumed that the coefficient vectors of both endogenous and exogenous variables are only partially identified, even though the order condition for identification is satisfied. This work extends previous results in Phillips (1989) where the coefficient vector of the exogenous variables is partially identified and that of the endogenous variables is totally unidentified. The effect of partial identification on the finite sample and asymptotic distributions of the estimators and the Wald statistics is analyzed by isolating identifiable parts of the coefficient vectors using a rotation of the coordinate system developed in Phillips (1989).  The pdf's of the estimators and the Wald statistics are illustrated using simulation and compared with their respective asymptotic distributions.

JEL Classification: 211

Keywords: Instrumental variable estimator, Wald statistics, finite sample theory, simultaneous equation model