Re: [Gretl-devel] VECM restrictions and scaling

Hi, thanks very much for the new snapshots with T-c and restricted exogenous variables. This makes it possible to compare directly to PcGive's results and thus testing is quite easy. I've done some testing with a real-world case; it's a 6-dim Vecm with a restricted step dummy in the equilibrium (cointegration) relations. The unrestricted estimates (cointegration rank r=4) are exactly identical, including the standard errors. The only difference is that gretl prints "Determinante der Kovarianzmatrix = 1.614282e-015" (determinant of the covariance matrix), whereas pcgive reports "-T/2log|Omega| 1873.29374". Now I guess these numbers are not supposed to mean the same thing, but nevertheless a result of 1e-15 strikes me as strange. Maybe it's actually the last improvement of the convergence algorithm or something like that? --------------------------- 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 -(T/2)log|Omega| = 1873.9556, lldiff = 3.99749e-011 Unrestricted loglikelihood (lu) = 932.72411 Restricted loglikelihood (lr) = 928.94253 2 * (lu - lr) = 7.56317 P(Chi-Square(2) > 7.56317 = 0.0227865 </gretl> <pcgive> log-likelihood 932.00515 -T/2log|Omega| 1877.01821 no. of observations 111 no. of parameters 100 rank of long-run matrix 4 no. long-run restrictions 2 beta is identified LR test of restrictions: Chi^2(2) = 1.4379 [0.4873] Switching (scaled linear) using analytical derivatives (eps1=0.0001; eps2=0.005): Weak convergence </pcgive> Adding some restrictions on alpha, I sometimes manage to hit gretl's bound of 50000 iterations :-) -------------------- So I tried out something more modest: removing the restricted exogenous variable and imposing some just-identifying but somewhat unusual restrictions. Then PcGive reports: <pcgive> log-likelihood 910.764932 -T/2log|Omega| 1855.778 no. of observations 111 no. of parameters 98 rank of long-run matrix 4 no. long-run restrictions 0 beta is identified No restrictions imposed Switching (scaled linear) using analytical derivatives (eps1=0.0001; eps2=0.005): Strong convergence </pcgive> But gretl's output is: <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> So gretl seems to have some problems with "rotations" of the cointegration space, which in theory (and confirmed by pcgive) leave the likelihood unaffected. Let me know if some other details or setups would help you. I'll also try to think about what other approaches could help. Cheers, sven