linearmodels.iv.results.IVGMMResults.j_stat

property IVGMMResults.j_stat: Union[InvalidTestStatistic, WaldTestStatistic]

J-test of overidentifying restrictions

Returns
WaldTestStatistic

J statistic test of overidentifying restrictions

Notes

The J statistic tests whether the moment conditions are sufficiently close to zero to indicate that the model is not overidentified. The statistic is defined as

\[n \bar{g}'W^{-1}\bar{g} \sim \chi^2_q\]

where \(\bar{g} = n^{-1}\sum \hat{\epsilon}_i z_i\) where \(z_i\) includes both the exogenous variables and instruments and \(\hat{\epsilon}_i\) are the model residuals. \(W\) is a consistent estimator of the variance of \(\sqrt{n}\bar{g}\). The degree of freedom is \(q = n_{instr} - n_{endog}\).

Return type

Union[InvalidTestStatistic, WaldTestStatistic]