Hausman (1983) has suggested that the simultaneous equation model is perhaps the most remarkable development in econometrics. In this chapter we shall be concerned with the problem of testing the specification of such models.

YB + Z Γ = U

where Y is the n by m matrix of endogenous variables, Z is the n by k matrix of predetermined variables, U is the n by m matrix of stochastic disturbances, B is the m by m matrix of structural coefficients of endogenous variables and Γ is the k by m matrix of structural coefficients of predetermined variables.

The special case in which B is a diagonal matrix and (1.1) represents a system of seemingly unrelated regression equations (SURE) will not be given separate consideration. The corresponding simplifications of tests derived for the general case are straightforward. The tests discussed below do not, however, include a check of the assumption that the disturbances of the system are contemporaneously uncorrelated. This assumption may be of interest in the context of SURE models, and Breusch and Pagan (1980, p. 247) derive an appropriate LM statistic.