On Fri, 24 Aug 2007, Franck Nadaud wrote:
I am currently working on AIDS models to be estimated as sytems.
So I use the command :
with restrictions inside. However those restrictions imply a
singular covariance matrix. In other pacakges (SAS for example)
estimation is done by deleting one equation, and the missing
coefficient is recovered by the restrictions.
I would like to know how GRETL handles such cases, and more
specifically whith which methods.
Gretl first estimates the unrestricted system, then estimates the
restricted system. The method for the second step is to form
augmented versions of the X and y matrices using R, R' and q, as
in the representation of the restriction as Rb = q. Depending on
whether an F-test or a likelihood ratio test is appropriate, we
either save the original coefficient vector and covariance matrix
(F-test) or the original log-likelihood.
The procedure is found in plugin/sysest.c in the gretl source: the
main driver is the function system_estimate(). See William
Greene, Econometric Analysis, 4e, section 7.3, "The Restricted
Least Squares Estimator". Note 7 on page 281 deals with the
question of possible singularity of X'X, which doesn't matter so
long as the restriction-augmented matrix is of full rank.
I would like to know if it is possible in system estimation to
recover all the coefficients and standards errors, because i
have to compute the AIDS elasticities.
Right now, it's not. But I should add that. The question is, how
should one define the matrix of coefficients for an arbitrary set
of equations? Two possibilities occur to me:
(a) Create a matrix with a column for each equation, and a number
of rows equal to the maximum number of coefficients in any
equation. For each column (equation) enter the coefficients in
the order they're printed, starting from the top, and pad out the
rest of the column with zeros if required.
(b) More complicated: create an n x g zero matrix, where n is the
total number of distinct variables appearing on the right hand
side of *any* equation and g is the number of equations. Fill in
the appropriate values.
I'm inclined towards (a) but I'd welcome comments. Just to
clarify, consider this example:
equation I_GE 0 F_GE C_GE
equation I_WE 0 F_WE C_WE
estimate Grunfeld method=sur
Under method (a) the coefficient matrix would be 3 x 2, with no
zero entries, while under method (b) it would be 5 x 2, with two
blocks of zeros, since the variables on the right-hand sides of
the two equations differ.