Good afternoon,
The Seemingly Unrelated Regressions estimator of Stata sureg is unable to do three things that I need:
1. It cannot calculate robust variance of the estimates.
2. It cannot accept initial covariance of errors matrix from which the iteration to start
3. It cannot accept covariance of errors matrix, and do a one step estimator.
There are some equivalences between the Maximum Likelihood, and the Seemingly Unrelated GLS estimator. If I am not wrong, for a given covariance of errors matrix, the Maximum Likelihood and the GLS estimator are the same. Also if one iterates the GLS estimator to convergence, one obtains the Maximum Likelihood.
This suggests that I might be able to achieve what I want through sem. I already learned that
sureg (y z1 z2) (x z3 z4), isure
gives the same result as
sem (y<- z1 z2) (x<- z3 z4), cov(e.y*e.x)
Therefore getting robust standard errors is easy,
sem (y<- z1 z2) (x<- z3 z4), cov(e.y*e.x) vce(robust)
gives me seemingly unrelated regression with robust variance.
My question is how do I achieve goals 2. and 3. above:
2. How can I tell sem that I want "onestep" estimator where I supply by hand the matrix of covariances of the errors? In other words, how can I give sem a matrix of variances and covariances of the errors, and tell sem it to optimise/find the solution only with respect to the slopes/intercepts in the linear equations?
3. How can I tell sem to start the iterations from a given covariance matrix of errors, and to iterate until convergence?
The Seemingly Unrelated Regressions estimator of Stata sureg is unable to do three things that I need:
1. It cannot calculate robust variance of the estimates.
2. It cannot accept initial covariance of errors matrix from which the iteration to start
3. It cannot accept covariance of errors matrix, and do a one step estimator.
There are some equivalences between the Maximum Likelihood, and the Seemingly Unrelated GLS estimator. If I am not wrong, for a given covariance of errors matrix, the Maximum Likelihood and the GLS estimator are the same. Also if one iterates the GLS estimator to convergence, one obtains the Maximum Likelihood.
This suggests that I might be able to achieve what I want through sem. I already learned that
sureg (y z1 z2) (x z3 z4), isure
gives the same result as
sem (y<- z1 z2) (x<- z3 z4), cov(e.y*e.x)
Therefore getting robust standard errors is easy,
sem (y<- z1 z2) (x<- z3 z4), cov(e.y*e.x) vce(robust)
gives me seemingly unrelated regression with robust variance.
My question is how do I achieve goals 2. and 3. above:
2. How can I tell sem that I want "onestep" estimator where I supply by hand the matrix of covariances of the errors? In other words, how can I give sem a matrix of variances and covariances of the errors, and tell sem it to optimise/find the solution only with respect to the slopes/intercepts in the linear equations?
3. How can I tell sem to start the iterations from a given covariance matrix of errors, and to iterate until convergence?
