# st: ML estimation of equation system with random regressors

 From "David GIVENS" To Subject st: ML estimation of equation system with random regressors Date Thu, 22 Mar 2007 12:19:34 -0400

```This is my first posting to Statalist. Please excuse errors of
SETUP:
I am trying to estimate the following system of equations model by
maximum likelihood (ML):
y_jk = a_k + b_k*(g_j + e_jk)       j = 1, ..., J; k = 1,...,K
where,
g_j ~ N(0,1), iid
e_jk ~ N(0, s_k), iid
E(g_j * e_jk) = 0
E(e_jk*e_j'k')=0, if j not equal j' OR k not equal k'
W (K x K) = VC(b_k*(g_j + e_jk)) = bb' + diag{b_k^2*s_k^2}
- K equations, 3K parameters - an alpha, beta and sigma for each
equation
- J observations per equation
- Observations within the k-th equation are independent
- j-th observations across equations are correlated (they have the
same random component, g_j).
- the model is identified for K >= 3
- I have the likelihood function written down - it meets STATA's
"lf" restriction
- no non-stochastic regressors (aside from column of ones)!
- use seemingly unrelated regression (SUR) model?

QUESTION:
Is SUR the paradigm to use for this model, given that I want to go
ML?
-If so, is there a way to explicitly define the elements of
STATA's "sigma" matrix in the likelihood equation so it equals W
(defined above)?
-If not, is there another, more general technique of ML
estimation for systems of equations I can use?
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```