Sargan Test

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A Sargan Test is a statistical hypothesis test for assessing the validity of over-identifying restrictions in statistical inference of time series.



References

2016

  • (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Sargan–Hansen_test Retrieved:2016-12-17.
    • The Sargan–Hansen test or Sargan's [math]\displaystyle{ J }[/math] test is a statistical test used for testing over-identifying restrictions in a statistical model. It was proposed by John Denis Sargan in 1958, and several variants were derived by him in 1975. Lars Peter Hansen re-worked through the derivations and showed that it can be extended to general non-linear GMM in a time series context. The Sargan test is based on the assumption that model parameters are identified via a priori restrictions on the coefficients, and tests the validity of over-identifying restrictions. The test statistic can be computed from residuals from instrumental variables regression by constructing a quadratic form based on the cross-product of the residuals and exogenous variables. Under the null hypothesis that the over-identifying restrictions are valid, the statistic is asymptotically distributed as a chi-square variable with [math]\displaystyle{ (m - k) }[/math] degrees of freedom (where [math]\displaystyle{ m }[/math] is the number of instruments and [math]\displaystyle{ k }[/math] is the number of endogenous variables). This version of the Sargan statistic was developed for models estimated using instrumental variables from ordinary time series or cross-sectional data. When longitudinal ("panel data") data are available, it is possible to extend such statistics for testing exogeneity hypotheses for subsets of explanatory variables. Testing of over-identifying assumptions is less important in longitudinal applications because realizations of time varying explanatory variables in different time periods are potential instruments, i.e., over-identifying restrictions are automatically built into models estimated using longitudinal data.

1982

1958