On Wed, 3 May 2006, Marta Regulez wrote: That's good to hear. I'm copying the gretl-users mailing list on my reply to your questions below, since these questions may come up for others too. I am going by the presentation of the Anderson-Rubin test as given in Davidson and MacKinnon, "Econometric Theory and Methods" (ETM) chapter 12. They write the LR test statistic as T log(lambda) [in their notation, n log \hat{\kappa}], and state that it is asympotically distributed as chi-square with degrees of freedom equal to the number of overidentifying restrictions. T(lambda - 1) is a reasonable approximation to T log(lambda) for lambda close to 1. This is the cross-equation variance-covariance matrix, with correlation coefficients in parentheses. For example, the (2,1) entry, 3.8790, gives the covariance of the residuals from equations 1 and 2. The (1,2) entry, 0.748, gives the correlation coefficient for the residuals from equations 1 and 2. This is the minimized value of the 3sls criterion function (that is, the analog to the sum of squared residuals in OLS estimation). I think it's sometimes called Hansen's J statistic. For the specific calculation, please see pages 525 and 532 of ETM. Systems estimation in gretl needs to be better documented. But the gretl code is closely based on the presentation in chapter 12 of Davidson and MacKinnon's ETM, so that is the best place to look for clarification at present. Allin Cottrell