[Gretl-devel] VECM restrictions and scaling

[Allin Cottrell]

A few more thoughts.

On Sun, 16 Sep 2007, Sven Schreiber wrote:

> Next, with some overidentifying restrictions on beta (both 
> exclusion and more general restrictions, partly also applied to 
> the restricted exogenous variable, and apart from 
> normalization), gretl's results are not so good (I also append 
> pcgive's results for comparison):
> 
> <gretl>
> Rank of Jacobian = 34, number of free parameters = 34
> Model is fully identified
> Based on Jacobian, df = 2
> Switching algorithm: 29552 iterations ...

When the switching algorithm takes thousands of iterations, it's a 
pretty safe bet that the results will not be good.  I haven't 
seen that happen lately (since adding the scale-removal code), 
but clearly you've got a case here that is not handled correctly 
in gretl.

> So I tried out something more modest: removing the restricted 
> exogenous variable and imposing some just-identifying but 
> somewhat unusual restrictions...

> <gretl>
> Rank of Jacobian = 32, number of free parameters = 32
> Model is fully identified
> Based on Jacobian, df = 0
> Switching algorithm: 2319 iterations
>  -(T/2)log|Omega| = 1855.6699, lldiff = 3.99838e-011
> 
> Unrestricted loglikelihood (lu) = 910.76493
> Restricted loglikelihood (lr) = 910.65685
> </gretl>

I suppose we need a check: if df = 0, and yet the "restricted" 
likelihood is less than the unrestricted, then clearly something 
has gone awry.  Again, I haven't seen a result of this sort, but 
then I haven't yet tried a wide range of test cases.

Allin.