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"Note that the covariance of the coefficients between equations is not estimated
under
this option and that cross-equation tests should not be performed after
estimation with
ols.  For cross-equation testing, use sureg or 3sls (the default)."

Another possible way is pool the data, estimate a single fully interacted model
and test whether or not the coefficient of the interaction term is equal to
zero. However, this does impose the assumption of homoskedasticity across the
model.

Hope this helps,
Scott


----- Original Message ----- 
From: "Richard Williams" <Richard.A.Williams.5@nd.edu>
To: <statalist@hsphsun2.harvard.edu>
Sent: Thursday, March 04, 2004 12:53 PM
Subject: Re: st: constrained least squares, multiple equations


> At 11:39 PM 3/3/2004 -0600, olena-stavrunova@uiowa.edu wrote:
> >Dear Statalist,
> >I have the model: Y1=X1*b1, Y2=X2*b1. I want to estimate these two equations
> >by least squares subject to constraint that b1=b2 , that is I want to
> >estimate
> >the equation:          [Y1 =  [X1 *b
> >                         Y2]    X2]
> >Please, let me know how to do this in Stata.
> >Thank you!
> >Olena
>
> I just tried the following, and it SEEMED to work ok.  Nonetheless, it
> would be nice if someone confirmed that this was the way to go. (Are you
> sure you want to use OLS, as opposed to reg3's default, which is 3 stage
> least squares?  Read the help for -reg3-)
>
> . reg3 (income educ) (jobexp black), ols
>
> Multivariate regression
> ----------------------------------------------------------------------
> Equation          Obs  Parms        RMSE    "R-sq"     F-Stat        P
> ----------------------------------------------------------------------
> income            500      1    5.243321    0.6593     963.54   0.0000
> jobexp            500      1    4.931661    0.0526      27.66   0.0000
> ----------------------------------------------------------------------
>
> ------------------------------------------------------------------------------
>               |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
> -------------+----------------------------------------------------------------
> income       |
>          educ |   1.830332   .0589651    31.04   0.000     1.714622
1.946042
>         _cons |   3.702833   .8106362     4.57   0.000     2.112082
5.293584
> -------------+----------------------------------------------------------------
> jobexp       |
>         black |       -2.9   .5513765    -5.26
0.000    -3.981993   -1.818007
>         _cons |       14.1   .2465831    57.18   0.000     13.61612
14.58388
> ------------------------------------------------------------------------------
>
> . test educ = black, coef
>
>   ( 1)  [income]educ - [jobexp]black = 0
>
>         F(  1,   996) =   72.77
>              Prob > F =    0.0000
>
>
> Constrained coefficients
>
> ------------------------------------------------------------------------------
>               |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
> -------------+----------------------------------------------------------------
> income       |
>          educ |   1.776845   .0586308    30.31   0.000     1.661931
1.891759
>         _cons |    4.40672   .8064257     5.46   0.000     2.826154
5.987285
> -------------+----------------------------------------------------------------
> jobexp       |
>         black |   1.776845   .0586308    30.31   0.000     1.661931
1.891759
>         _cons |   13.16463   .2208621    59.61   0.000     12.73175
13.59751
> ------------------------------------------------------------------------------
>

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