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

["Brian P. Poi" <bpoi@stata.com>]

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