# 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