How to write a joint maximum likelihood estimation?

[Bing Zhang]

Dear statalist:
I want to write a joint maximum likelihood estimation(JMLE) for wage and unemployment rate,but I don't know how to do it .I have found a similar paper,but it didn't provide original code and math equations.The paper is:Wage employment, earnings and returns to schooling for men and women in Turkey(Economics of Education Review Volume 13, Issue 4, 1994, Pages 305-320）
And my equations are:

could you tell me how to do it,I'm looking forward to your help,Thanks!
Zhang Bing
Southwestern University of Finance and Economics

[FernandoRios]

Hi Bing
Everything depends on what are your assumptions regarding the correlations of the errors across models. The simplest assumption is that the errors are conditionally independent, in which case the joint log likelihood is just the sum of the individual Loglikelihood of both models.
Look into this paper i wrote that provides some examples on this regard: https://papers.ssrn.com/sol3/papers....act_id=2970659
You can also check (if you have access to) to the final version on Stata journal. SJ 18 (1)
If you want to download the examples provided there look into the following "net describe st0520"
Hope that helps
Fernando

[Joseph Coveney]

In addition to Fernando's recommendation, you could look into something like this:

gsem ///
    (wage <- c.age##c.age##c.age c.eduyear, family(gaussian) link(log)) ///
    (unemployed <- c.age##c.age##c.age c.eduyear, family(binomial) link(logit))
display in smcl as text e(ll)

suest is another approach you could consider.

[Bing Zhang]

Hi Bing
Everything depends on what are your assumptions regarding the correlations of the errors across models. The simplest assumption is that the errors are conditionally independent, in which case the joint log likelihood is just the sum of the individual Loglikelihood of both models.
Look into this paper i wrote that provides some examples on this regard: https://papers.ssrn.com/sol3/papers....act_id=2970659
You can also check (if you have access to) to the final version on Stata journal. SJ 18 (1)
If you want to download the examples provided there look into the following "net describe st0520"
Hope that helps
Fernando

Thank you!I am going to try it

[Bing Zhang]

In addition to Fernando's recommendation, you could look into something like this:

gsem ///
(wage <- c.age##c.age##c.age c.eduyear, family(gaussian) link(log)) ///
(unemployed <- c.age##c.age##c.age c.eduyear, family(binomial) link(logit))
display in smcl as text e(ll)

suest is another approach you could consider.

thank you !