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Re: st: RE : nlsur, function evaluator program not the same resultsthan interactive version


From   "Brian P. Poi" <bpoi@stata.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: RE : nlsur, function evaluator program not the same resultsthan interactive version
Date   Mon, 4 Aug 2008 12:13:33 -0500 (CDT)

On Mon, 4 Aug 2008, Valerie Orozco wrote:

Hi,

I’m trying to estimate a system of equations with “nlsur” because I have some non–linearity in my system (In my example below, there is no nonlinearity because my problem is not on that, and to simplify the example, I write a very simple system). What I am trying to do is to instrument an endogeneous variable (suppose it is the variable lnp1). My system looks:

w1 = a1 + x1 * X1 + b11 * lnp1 + b12 * lnp2 + b13 * lnp3 +b14 * lnp4
w2 = a2 + x2 * X1 + b21 * lnp1 + b22 * lnp2 + b23 * lnp3 +b24 * lnp4
w3 = a3 + x3 * X1 + b31 * lnp1 + b32 * lnp2 + b33 * lnp3 +b34 * lnp4
lnp1 = c +x4 * X1 + l2 * lnp2 + l3 * lnp3 + l4 * lnp4 + z1 *Z1 +z2 *Z2
/*instrumentation equation*/

With “nlsur”, I can use two methods : interactive or write an evaluator program. I just would like to know :

1) Why these 2 methods don’t give the same results (especially concerning the standard errors) (look my example below)

In general, whether you use the interactive or programmed version of -nlsur- should not matter -- you should get identical results.

If Valerie sends to me (bpoi@stata.com) her do-file and dataset, I'd be happy to figure out why her results do not match.



2) Which method is correct (if one of the 2 is correct) to specify an equation to instrument endogeneous variable
I do not think it is possible to include endogenous regressors in -nlsur-. Your fourth equation, for lnp1, is just another equation as far as -nlsur- is concerned, and it won't address the potential correlation between lnp1 and the error terms in the first three equations (which is what I presume you are trying to address). In general, you cannot implement the nonlinear 2SLS estimator in two steps; that only works for the linear version.

Notice that your equations are in fact linear. I suspect that you will also want to include cross-equation restrictions on the parameters. Then one solution might be to use -reg3-. However, I also suspect that there is a fourth good, whose parameters you'll want to recover after estimation. Iterating the 3SLS estimator does not produce the maximum likelihood estimator, so your results will not be invariant to which one of the four goods' equations you drop.

-- Brian Poi
-- bpoi@stata.com




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