Re: constraints in xtgls and xtpcse [was: st: QUESTION]

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

At 05:33 PM 4/29/2008, Samira Bakhshi wrote:
> I am so thankful for your reply.
> Actually, I have a system of panel data equations with 45 constraints.
> So imposing these constraints in way you have described would be
> difficult. Is not there any other way that Stata accpets the option ,
> const () after xtgls?
>
> Thanks,
> Samira
I've never tried it with xtgls, but you might check out Jeroen 
Weesie's -linest- command (which he maintains on his own site; use 
-findit-).  From the help file:

linest performs linear constrained estimation based on the results of an
unconstrained estimation command (e.g., regress, qreg, logit, stcox,
heckman, mvreg, ...). linest displays the table with the two-stage
constrained estimates and their confidence intervals, and a Wald test for
the hypothesis that the parameters satisfy the constraints...
The two-stage constrained estimator is asymptotically equivalent to the
one-stage constrained estimator (Gourieroux and Montfort 1995: Ch 10). This
result is based, however, on additional linearization. Thus, if a one-stage
constrained estimator is available (e.g., cnsreg, mlogit, reg3), I expect
this estimator and the associated inference procedures to be better behaved
in small samples.

In other words, it is nice when an estimation command directly 
supports constraints, but when it doesn't linest is often a decent 
alternative.  A simple example:

. sysuse auto
(1978 Automobile Data)

. constraint 1 weight = length

. logit foreign  weight length, nolog

Logistic regression                               Number of obs   =         74
                                                  LR chi2(2)      =      31.99
                                                  Prob > chi2     =     0.0000
Log likelihood = -29.040272                       Pseudo R2       =     0.3551

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0028419   .0016763    -1.70   0.090    -.0061273    .0004436
      length |   .0089197   .0542959     0.16   0.870    -.0974983    .1153376
       _cons |   5.366227    5.77534     0.93   0.353    -5.953232    16.68568
------------------------------------------------------------------------------

. linest, c(1)

Two-step constrained logit
                                           Dim unrestricted model   =        3
                                           Dim restricted model     =        2
                                           # restrictions           =        1
                                           Wald X2 for restrictions =   0.0443
                                           Prob > 
chi2(1)           =   0.8332 ( 1)  weight - length = 0
------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0025117   .0005925    -4.24   0.000     -.003673   -.0013504
      length |  -.0025117   .0005925    -4.24   0.000     -.003673   -.0013504
       _cons |   6.530763   1.662454     3.93   0.000     3.272413    9.789113
------------------------------------------------------------------------------

Constrained estimation results are not stored.
Post-estimation commands use the unconstrained model!




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Richard Williams, Notre Dame Dept of Sociology
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