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