Hello all, I've been spending time on this topic lately. The current target is for gretl to support: (a) General restrictions on VECM beta: not necessarily homogeneous, and possibly differing across the cointegrating relations (where the cointegrating rank > 1). But excluding cross-equation restrictions. (b) Homogeneous restrictions on VECM alpha, possibly differing across the equations. (c) Combinations of the above. We're getting close. We've implemented both a limited-memory BFGS optimizer and the Boswijk-Doornik switching algorithm. On current evidence the latter seems preferable. But there are still some weird things to sort out. Perhaps I can illustrate with a gretl script (which should work with current CVS or the current Windows snapshot). Take Johansen's Danish data. <script> open denmark vecm 2 1 LRM LRY IBO IDE --rc --seasonals restrict b1 + b2 = 0 end restrict --full # The "--full" flag results in the creation of a new VECM # system subject to the restriction in question. # Now test a second restriction "within" the first: restrict b3 + b4 = 0 end restrict --verbose # Re-estimate the basic system vecm 2 1 LRM LRY IBO IDE --rc --seasonals # Maintain the previous beta restrictions, and add # a restriction on alpha. restrict b1 + b2 = 0 b3 + b4 = 0 a[3] = 0 a[4] = 0 end restrict --verbose # Fine, except for two things: # (1) It would be nice to have the results normalized # (2) It would be nice to have standard errors for beta # To achieve these things we try adding a normalization # saying that the first beta term = 1 restrict b1 = 1 b1 + b2 = 0 b3 + b4 = 0 a[3] = 0 a[4] = 0 end restrict --verbose # Ah, but now the results are bad. We fail to get close to # the true ML solution. If we go back to the previous result # and manually normalize to beta[1] = 1, we get the following # initialization: matrix B0 = { 1, -1, 5.8, -5.8, -6.2 }' matrix A0 = { -0.14, 0.13, 0, 0 }' matrix U = B0 | A0 set initvals U restrict b1 = 1 b1 + b2 = 0 b3 + b4 = 0 a[3] = 0 a[4] = 0 end restrict --full </script> The final "restrict" command produces nice results. But what has gone wrong in the previous case? Clearly the automatic initial values computed by gretl were bad. But can anyone test this against other software and see if the competition gets it right? That would be very helpful. One other thing: I'm not forgetting Sven's suggestion that we support adding "restricted" exogenous variables. This is feasible, it's just that there are many places in the code where it's assumed that (a) there's at most one additional restricted term in the cointegration relation(s), and (b) that it's either a constant or a trend. That should be fixable with some work, but right now I'm focused on the beta and alpha tests. Allin.