William E. Taylor

A generalized specification test

Abstract In a non-linear parametric setting, a class of specification tests developed by Hausman (1978) is extended to accomodate a singular covariance matrix. An application to limited information tests for the exogeneity of instrumental variables is presented.

Identification in linear simultaneous equations models with covariance restrictions : an instrumental variables interpretation

Necessary and sufficient conditions for identification with linear coefficient and covari- ance restrictions are developed in a limited information context. For the limited informa- tion case, covariance restrictions aid identification if and only if they imply that a set of endogenous variables is predetermined in the equation of interest (generalizing the idea of recursiveness). Under full information, covariance restrictions imply that residuals from other equations are predetermined in a particular equation and, under certain conditions, can aid in identification. Sufficient conditions for identification are obtained for the hierarchical system in which the identification of a particular equation does not depend upon the identifiability of higher-numbered equations. In the general case, the FIML first order conditions show that if the system of equations is identifiable as a whole, covariance restrictions cause residuals to behave as instruments. In both limited and full information settings, the link between identification and estimation is worked out: restrictions useful for identification yield instruments required for estimation.

Efficient Estimation and Identification of Simultaneous Equation Models with Covariance Restrictions

The authors consider estimation of simultaneous equations models with covariance restrictions. They consider FIML estimation and extend J. A. Hausmans instrumental variables interpretation of the FIML estim ator to the covariance restrictions case. A slight variation on the i nstrumental variables theme yields a simple, efficient alternative to FIML. The authors augment the original equation system by equations implied by the covariance restrictions, linearized around an initial consistent estimator, and perform three-stage least squares to obtain an asymptotically efficient estimator. They also present a simple me thod of obtaining an initial consistent estimator when the covariance restrictions are needed for identification. Finally, they consider i dentification from the standpoint of the moment restrictions implied by instrument-residual orthogonality and covariance restrictions. Copyright 1987 by The Econometric Society.

Panel data and unobservable individual effects

Abstract An important purpose in pooling time-series and cross-section data is to control for individual-specific unobservable effects which may be correlated with other explanatory variables, e.g. latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions. Using instrumental variables and the time-invariant characteristics of the latent variable, we derive: 1. (1) a test for the presence of this effect and for the over-identifying restriction we use; 2. (2) necessary and sufficient conditions for identification of all the parameters in the model; and 3. (3) the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within-groups estimator. We calculate efficient estimates of a wage equation from the Michigan income dynamics data which indicate substantial differences from within-groups and Balestra-Nerlove estimates — particularly a significantly higher estimate of the returns to schooling.