[Gretl-users] Re: Questions in Simultaneous Equations Systems
On Wed, 3 May 2006, Marta Regulez wrote:
I am teaching now a new course in Simultaneous Equations Models,
and the new features that are in Gretl is being very usefu for
my teaching and for the students.
That's good to hear. I'm copying the gretl-users mailing list on
my reply to your questions below, since these questions may come
up for others too.
I have used the klein.inp script to estimate "Klein Model
I" and
I have the following questions (I couldn´t find some hint in the
guide):
1) Once you estimate by LIML, the program shows the Smallest
eigenvalue "lambda" and the overidentification LR test that I
thought was the Anderson-Rubin test
T(lambda - 1)
For example for the Consumption Equation it is obtained
Smallest eigenvalue = 1,49875
Contraste de sobreidentificación LR:
Chi-cuadrado(4) = 8,4972 con valor p 0,0749722
But if you calculate T(lambda - 1)= 21( 1,49875 - 1) = 10, 47375
that is not the value given for the LR test.
I am going by the presentation of the Anderson-Rubin test as given
in Davidson and MacKinnon, "Econometric Theory and Methods" (ETM)
chapter 12. They write the LR test statistic as
T log(lambda)
[in their notation, n log \hat{\kappa}], and state that it is
asympotically distributed as chi-square with degrees of freedom
equal to the number of overidentifying restrictions. T(lambda -
1) is a reasonable approximation to T log(lambda) for lambda close
to 1.
2) In the output obtained with ols, tsls, 3sls, fiml, and liml,
What are the following items?
Matriz de covarianzas cruzada residual
(correlaciones por encima de la diagonal principal)
2,1041 (0,748) (0,247)
3,8790 12,771 (0,804)
0,48169 3,8575 1,8011
logaritmo del determinante = 0,366633
This is the cross-equation variance-covariance matrix, with
correlation coefficients in parentheses. For example, the (2,1)
entry, 3.8790, gives the covariance of the residuals from
equations 1 and 2. The (1,2) entry, 0.748, gives the correlation
coefficient for the residuals from equations 1 and 2.
3) Finally, the overidentification test given with 3sls for the
whole system, refered as Hansen-Sargan overidentification test,
how is it calculated?
This is the minimized value of the 3sls criterion function (that
is, the analog to the sum of squared residuals in OLS estimation).
I think it's sometimes called Hansen's J statistic. For the
specific calculation, please see pages 525 and 532 of ETM.
Systems estimation in gretl needs to be better documented. But
the gretl code is closely based on the presentation in chapter 12
of Davidson and MacKinnon's ETM, so that is the best place to look
for clarification at present.
Allin Cottrell