Sargan–Hansen test

The Sargan–Hansen test or Sargan's ${\displaystyle J}$ test is a statistical test used for testing 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 ${\displaystyle (m-k)}$ degrees of freedom (where ${\displaystyle m}$ is the number of instruments and ${\displaystyle k}$ is the number of endogenous variables).

See also[]

• Durbin–Wu–Hausman test

References[]

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.
• Verbeek, Marno (2004). A Guide to Modern Econometrics (2nd ed.). New York: John Wiley & Sons. pp. 142–158. ISBN 0-470-85773-0.
• Kitamura, Yuichi (2006). "Specification Tests with Instrumental Variable and Rank Deficiency". In Corbae, Dean; et al. (eds.). Econometric Theory and Practice: Frontiers of Analysis and Applied Research. New York: Cambridge University Press. pp. 59–124. ISBN 0-521-80723-9.

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