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st: st : endogeneous variables with nlsur and reg3


From   Valerie Orozco <Valerie.Orozco@toulouse.inra.fr>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: st : endogeneous variables with nlsur and reg3
Date   Wed, 9 Apr 2008 15:54:08 +0200

Hello,

I 'm estimating a system of equations with nlsur. I have some variables that are endogeneous and I would like to instrument them. I don't know if it is possible or not, thanks to nlsur or by hand...
If I can add one equation (the instrumentation one) to the nlsur command, it would be easy.
Another idea I had, was to estimate in two steps (first the instrumentation equation, then taking the predicted value and put it in the general equation...but I will probably have a problem with the standard errors.)
Like I know how to deal with endogeneity with reg3 (with  linear equations), I made some comparisons between reg3 and nlsur...

/*****************************************************/
/*1st comparison : without any endogeneous variable*/
/*****************************************************/
nlsur (w1 = {c1} + {b01}*X1 + {b11} * lnp1 + {b21} * lnp2 )
reg3(w1  X1 lnp1 lnp2 )
--> nlsur and reg3 give same results

/*****************************************************/
/*2nd comparison : one variable is endogeneous (suppose it is lnp1)*/
/*****************************************************/
reg3(w1  X1 lnp1 lnp2),endog(lnp1) exog(Z1 Z2)
nlsur (w1 = {c1} + {b1}*X1 + {bp1} * lnp1 + {bp2} * lnp2 ) ///
      (lnp1 = {c2} + {z1}*Z1 +{z2}*Z2 +{x1}*X1 + {l2}*lnp2 )

--> not the same coefficients, nor the standard errors

/*****************************************************/
/*3rd comparison : */
/*****************************************************/
reg3(w1  X1 lnp1 lnp2), endog(lnp1) exog(Z1 Z2)

quietly reg lnp1 Z1 Z2 X1 lnp2
predict lnp1hat, xb
reg3 (w1 X1 lnp1hat lnp2)   or nlsur (w1 = {c1} + {b1}*X1 + {bp1} * lnp1hat + {bp2} * lnp2 )
 --> same coefficients, problem with the standard errors


So, is someone able to help me to apply the best method to instrument endogeneous variables with nlsur?
If I use 2 steps, how can I recover the true standard errors?

Thank you very much.

Valérie

-------------------------------
Valérie OROZCO
Toulouse School of Economics (INRA-GREMAQ)
21, allée de Brienne
F-31000 Toulouse, France

MF 426
+33 5 61 12 85 91
-------------------------------

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