Sargan–Hansen test
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,[1] and several variants were derived by him in 1975.[2] 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.[3]
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.[4]:132–33 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).
See also
References
- ↑ Sargan, J. D. (1958). "The Estimation of Economic Relationships Using Instrumental Variables". Econometrica 26 (3): 393–415. doi:10.2307/1907619.
- ↑ Sargan, J. D. (1988). "Testing for misspecification after estimating using instrumental variables". Contributions to Econometrics. New York: Cambridge University Press. ISBN 0-521-32570-6.
- ↑ Hansen, Lars Peter (1982). "Large Sample Properties of Generalized Method of Moments Estimators". Econometrica 50 (4): 1029–1054. doi:10.2307/1912775.
- ↑ Sargan, J. D. (1988). Lectures on Advanced Econometric Theory. Oxford: Basil Blackwell. ISBN 0-631-14956-2.
Further reading
- Davidson, Russell; McKinnon, James G. (1993). Estimation and Inference in Econometrics. New York: Oxford University Press. pp. 616–620. ISBN 0-19-506011-3. https://books.google.com/books?id=Ot6DByCF6osC&pg=PA616.
- Verbeek, Marno (2004). A Guide to Modern Econometrics (2nd ed.). New York: John Wiley & Sons. pp. 142–158. ISBN 0-470-85773-0. https://books.google.com/books?id=VplRX78ZQgsC&pg=PA142.
- Kitamura, Yuichi (2006). "Specification Tests with Instrumental Variable and Rank Deficiency". in Corbae, Dean. Econometric Theory and Practice: Frontiers of Analysis and Applied Research. New York: Cambridge University Press. pp. 59–124. ISBN 0-521-80723-9. https://books.google.com/books?id=mXitlEaAy8AC&pg=PA59.
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