# linearmodels.system.results.GMMSystemResults.j_stat¶

property GMMSystemResults.j_stat: 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 $$\bar{g}$$ is the average of the moment conditional and $$W$$ is a consistent estimator of the variance of $$\sqrt{n}\bar{g}$$. The degree of freedom is $$q = n_{instr} - n_{endog}$$.

Return type:

WaldTestStatistic