st: Cross-equation restrictions using -ml- command

["Randall Charles Juras" <rjuras@msu.edu>]

Hi, 

I am trying to estimate a structurally-based likelihood function using 
Stata’s –ml- command.  I am having trouble imposing a necessary 
cross-equation restriction. 

I assume that the data-generating process involves three latent variable 
equations, one of which is a function of the other two: 

y1* = Xb1 + e1
y2* = Xb2 + e2
y3* = y1* - y2* 

so that y1 ... y3 = 0,1.  I also assume that the errors e1 and e2 follow a 
bivariate normal distribution, with mean zero and std. error sigma.  For 
each observation in the data, I observe either y1 and y2, or y1 and y3 (but 
never all three).  A sample of the relevant ml code might look like: 

program my_lf
	args lnf x1 x2 x3 rho
	quietly replace `lnf’ = ln(binormal( `x1’, `x2’, `rho’)) if ($ML_y1 
== 1 & $ML_y2 == 1)
	quietly replace `lnf’ = ln(binormal( `x1’, `x3’, `rho’)) if ($ML_y1 
== 1 & $ML_y3 == 1)
	(etc.) 

Setting any other issues aside, I obviously need to tell Stata that x3 is 
related to x1 and x2 – and at the same time I need to input $ML_yn for all 
3 equations (so I can’t input x1 and x2, and generate x3 as a function of 
those two).  Any suggestions on how I can do that? 

Thanks for your consideration. 

Randy Juras 


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