"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" <[email protected]>
To: <[email protected]>
Sent: Thursday, March 04, 2004 12:53 PM
Subject: Re: st: constrained least squares, multiple equations
> At 11:39 PM 3/3/2004 -0600, [email protected] 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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