Re: [Gretl-users] R:VAR parameters

On Wed, 14 Dec 2011, Sven Schreiber wrote: > No, non-linear restrictions are not available for system estimators > (yet), AFAIK. > > Of course there are workarounds, for example specifying an equivalent > GMM block, where I think it is possible now to test nonlinear > restrictions. But this is admittedly not the most friendly way. Sven's idea is a good one, and in fact it's not too difficult to implement. Since this is quite a nice showcase for gretl's GMM I've appended a complete (albeit trivial) example script below. The first GMM invocation is just to show that the unrestricted VAR can be replicated by this method. In the restricted variant, the "trick" is to set the length of the parameter vector to the number of free parameters, and to calculate the coefficients so as to impose the required restriction. The nice thing is that if you estimate the restricted model with the --two-step option the automatic J-test tests the overidentifying restriction. One further point: restricted GMM may fail to converge if the restriction is too "violent" (too far distant from the unrestricted estimates). For example, you can set the "c" parameter below to 1 and see what happens. In a very informal sense this might be taken as "reject the null"! <hansl> open data9-7 -q var 2 UNEMP PRIME list X = const UNEMP(-1 to -2) PRIME(-1 to -2) series u1 = $uhat[,1] series u2 = $uhat[,2] matrix B1 = $coeff[,1] matrix B2 = $coeff[,2] # unrestricted one-step GMM (should replicate the VAR) gmm u1 = UNEMP - lincomb(X, B1) u2 = PRIME - lincomb(X, B2) orthog u1 ; X orthog u2 ; X params B1 B2 end gmm # look at the unrestricted product of two terms eval B1[5]*B2[5] # impose nonlinear restriction: B1[5]*B2[5]=c matrix theta = B1 | B2[1:4] scalar c = 0.05 gmm B1 = theta[1:5] B2 = theta[6:9] | {c / theta[5]} u1 = UNEMP - lincomb(X, B1) u2 = PRIME - lincomb(X, B2) orthog u1 ; X orthog u2 ; X params theta end gmm --two-step </hansl> Allin Cottrell _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users