Re: st: Re:

 From "Paolo Caruso" To , Subject Re: st: Re: Date Thu, 23 Mar 2006 21:56:00 +0000

```I have used the usual ivreg however, I am not sure about the validity of doing so as it is including these interaction terms in the first stage which are in fact the exactly value of the instrumented variable simply multiplied by a dummy variable. Therefore, because the interaction terms are based on the variable I am instrumenting I believed that I would have to estimate the two stages separately not including the interaction terms.

If you believe that I should simply use ivreg then I shall.

Thank you all for your time.

Regards,

Paolo

>>> arnehole@gmail.com 03/23/06 18:44 PM >>>
I agree that the -ivreg- approach is the best one.

(The omission of s in the first stage regression was an oversight).

Cheers,
Arne

On 23/03/06, Austin Nichols <austinnichols@gmail.com> wrote:
> The code Arne supplies is an example of how to get the answer
> requested by Paolo, but that answer is still incorrect.  Just run that
> code (including the variable s in both first and second stages, since
> I think its omission was an oversight) to get:
>
> . qui use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta, clear
> . qui regress iq med kww s expr tenure rns smsa
> . qui predict double iq_hat
> . gen double intact = iq_hat*expr
> . qui regress lw iq_hat intact s expr tenure rns smsa
> . replace iq_hat = iq
> . qui replace intact = iq*expr
> . predict double res, residual
> . gen double res2 = res^2
> . qui sum res2
> . scalar iv_mse = r(mean)*r(N)/e(df_r)
> . matrix b = e(b)
> . matrix V = e(V)*(iv_mse/e(rmse)^2)
> . ereturn post b V
> . ereturn display
> ------------------------------------------------------------------------------
>              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>       iq_hat |   .0151927   .0061657     2.46   0.014     .0031081    .0272772
>       intact |  -.0005875   .0008488    -0.69   0.489    -.0022512    .0010762
>            s |   .0595681   .0188307     3.16   0.002     .0226605    .0964757
>         expr |   .1018824   .0848968     1.20   0.230    -.0645121     .268277
>       tenure |   .0295226   .0085698     3.44   0.001     .0127262     .046319
>          rns |  -.0440594   .0349568    -1.26   0.208    -.1125736    .0244547
>         smsa |   .1269817   .0301617     4.21   0.000     .0678657    .1860976
>        _cons |   3.104997   .4183089     7.42   0.000     2.285127    3.924868
> ------------------------------------------------------------------------------
>
> and then compare to the IV estimate:
> . ivreg lw s expr tenure rns smsa (iq inta=kww med)
> ------------------------------------------------------------------------------
>           lw |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           iq |   .1019604   .7498967     0.14   0.892    -1.370186    1.574107
>       intact |   -.031272   .2663122    -0.12   0.907     -.554078    .4915341
>            s |  -.0457328   .9088715    -0.05   0.960    -1.829968    1.738502
>         expr |    3.17964   26.70891     0.12   0.905    -49.25347    55.61275
>       tenure |   .0273913   .0324433     0.84   0.399    -.0362991    .0910818
>          rns |  -.0274002   .1739247    -0.16   0.875    -.3688374     .314037
>         smsa |  -.0344371   1.379771    -0.02   0.980    -2.743109    2.674235
>        _cons |  -4.338579     64.363    -0.07   0.946    -130.6916    122.0145
> ------------------------------------------------------------------------------
>
> Note particularly the SEs and p-values on the two endog vars.
>
> I believe this impulse to "plug in" y2hat in various incorrect ways
> comes from conceiving of the IV estimator as a two-step estimator,
> which it is not.  The better two-step estimator analogy uses the
> control function approach, IMHO, since folks are less likely to apply
> it incorrectly in a nonlinear second stage, or to square or interact
> y2hat.
>
> Arne, do you concur?
>
> On 3/23/06, Arne Risa Hole <arnehole@gmail.com> wrote:
> > I suppose an alternative approach would be to do something like this:
> >
> > use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta, clear
> > qui regress iq med kww expr tenure rns smsa
> > predict double iq_hat
> > gen double intact = iq_hat*expr
> > qui regress lw iq_hat intact s expr tenure rns smsa
> > replace iq_hat = iq
> > replace intact = iq*expr
> > predict double res, residual
> > gen double res2 = res^2
> > qui sum res2
> > scalar iv_mse = r(mean)*r(N)/e(df_r)
> > matrix b = e(b)
> > matrix V = e(V)*(iv_mse/e(rmse)^2)
> > ereturn post b V
> > ereturn display
> >
> > i.e. get the forecast y2hat (iq_hat in the example) from the
> > first-stage regression and interact this with the exogenous RHS var x1
> > (expr in the example). Then you replace the interaction with y2*x1
> > before calculating the residuals/MSE.
> >
> > Austin's suggestion is probably the better one though, but this seems
> > to me to be ok.
> >
> > Cheers
> > Arne
> >
> > On 23/03/06, Austin Nichols <austinnichols@gmail.com> wrote:
> > > If your endog RHS var y2 is interacted with an exog RHS var x1, then
> > > you have a "new" endog RHS var y2x1, and you may need additional
> > > excluded instruments.  Use -ivreg- as suggested.
>
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