Re: [Gretl-users] non-linear Wald-Test
On Thu, 6 Aug 2009, artur tarassow wrote:
is there any possibility to test a restriction of the kind
b[4]/b[2]=b[3]/b[2] using the wald-test?
If I read the manual correctly it does not seem to be implemented. Or
does there exist an alternative to test this kind of restriction?
Assuming you mean, b[4]/b[2] = b[3]/b[5] (or at least
something that does not reduce to b[4] = b[3]) ... no, you can't
do it with the standard Wald test.
One approach is to estimate (a) the unrestricted model and (b) the
non-linear model that results when the restriction is applied.
If the unrestricted model, was, say
u: y = b1 + b2x2 + b3x3 + b4x4 + b5x5 + e
then applying b4/b2 = b3/b5 gives the restricted model
r: y = b1 + b2x2 + b3x3 + (b2b3/b5)x4 + b5x5 + e
If the original model was estimated via OLS, the restricted one
could be estimated via NLS. Then construct an F-test based on the
difference between the restricted and unrestricted sums of squared
residuals.
An alternative is to apply an ML estimator (or maybe *LS is
already ML?) and use the restricted and unrestricted
log-likelihoods to form a Likelihood Ratio test: 2 * (llu - llr)
is asymptotically distributed as chi-square(1) in this example.
Allin Cottrell