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| The SYSLIN Procedure |
In the instrumental variables methods (2SLS, LIML, K-class, MELO), first-stage predicted values are substituted for the endogenous regressors. As a result, the regression sum of squares (RSS) and the error sum of squares (ESS) do not sum to the total corrected sum of squares for the dependent variable (TSS). The "Analysis of Variance" table printed for the second-stage results serves to display these sums of squares and the mean squares used for the F-test, but this table is not a variance decomposition in the usual analysis of variance sense.
The F-test shown in the instrumental variables case is a valid test of the no-regression hypothesis that the true coefficients of all regressors are 0. However, because of the first-stage projection of the regression mean square, this is a Wald-type test statistic, which is asymptotically F but not exactly F-distributed in finite samples. Thus, for small samples the F-test is only approximate when instrumental variables are used.
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