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st: Cross-equation restrictions using -ml- command

From   "Randall Charles Juras" <>
Subject   st: Cross-equation restrictions using -ml- command
Date   Mon, 13 Oct 2008 11:32:02 -0400

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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