linearmodels.iv.results.IVResults.sargan¶
- property IVResults.sargan : InvalidTestStatistic | WaldTestStatistic¶
Sargan test of overidentifying restrictions
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.
\[v = n_{instr} - n_{exog}\]