CQLIM Procedure

Multivariate models are similar to bivariate models. The generic form of the multivariate limited dependent variable model is

where m is the number of models to be estimated. The vector has a multivariate normal distribution with mean 0 and variance-covariance matrix . As with bivariate models, calculating the likelihood can involve computing multivariate normal integrations. This is done using Monte Carlo integration. (See Genz 1992; Hajivassiliou and McFadden 1998.)

When the number of equations, N, increases in a system, the number of parameters increases at the rate of because of the correlation matrix. When the number of parameters is large, sometimes the optimization converges but some of the standard deviations are missing. This usually means that the model is overparameterized. The default method for computing the covariance is to use the inverse Hessian matrix. The Hessian is computed by finite differences, and in overparameterized cases, the inverse cannot be computed. It is recommended that you reduce the number of parameters in such cases. Sometimes it might also help to use the outer product covariance matrix (the COVEST=OP option in the PROC CQLIM statement).