linearmodels.iv.results.IVResults.sargan

property IVResults.sargan: InvalidTestStatistic | WaldTestStatistic[source]

Sargan test of overidentifying restrictions

Returns:
WaldTestStatistic

Object containing test statistic, p-value, distribution and null

Notes

Requires more instruments than endogenous variables

Tests the ratio of re-projected IV regression residual variance to variance of the IV residuals.

\[n(1-\hat{\epsilon}^{\prime}M_{Z}\hat{\epsilon}/ \hat{\epsilon}^{\prime}\hat{\epsilon})\sim\chi_{v}^{2}\]

where \(M_{z}\) is the annihilator matrix where z is the set of instruments and \(\hat{\epsilon}\) are the residuals from the IV estimator. The degree of freedom is the difference between the number of instruments and the number of endogenous regressors.

\[v = n_{instr} - n_{exog}\]