A Note on R2 in the Instrumental Variables Model

The properties of two goodness-of-fit measures are analyzed for the instrumental variables model. One measure is based on the two-step approach to IV estimation and is equal to the coefficient of determination in the second stage equation. This measure therefore measures the fit of a transformation of the original model. The other measure is the one proposed by Barten (1987) for the linear model without a constant term. In comparison with the other R2-measure, Barten's measure has as an advantage that it measures the fit of the original model. As a disadvantage, the measure does not have a relation with the chi-squared statistic, testing whether all slope coefficients are equal to zero.