The coefficient of determination and simultaneous equation systems

In this paper we show that the Carter-Nagar (1977) R²'s for single structural equations and systems are in fact R² for the reduced form where the partially restricted reduced form estimation method is employed. We also show that the results of McElroy (1977) may be used to derive the Carter-Nagar system measure. If the reduced form equations are estimated by Kakwani's (1975) k-class reduced form estimator a new R² may be defined which is shown to be asymptotically equivalent to the Carter-Nagar measure.