Re: st: constrained least squares, multiple equations

[Richard Williams <Richard.A.Williams.5@nd.edu>]

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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