Testing Covariance Restrictions in Systems of Simultaneous Equations with Vector Autoregressive Errors

Abstract

This paper considers inference procedures in a system of linear simultaneous equations with errors generated by a vector autoregressive process in situations where the null hypotheses involve the elements of the dispersion matrix of the errors. The problem is approached through the reduced form of the system and the first-order conditions for a maximum of the likelihood function are presented in an explicit form. This analysis in turn affords the development of the expressions for the asymptotic variance-covariance matrix of the estimated dispersion matrix, as well as the asymptotic covariance between these elements and the structural form parameter estimates under minimal assumptions on the actual distribution function of the errors. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.