# Sargan–Hansen test

Sargan test
The Sargan–Hansen test or Sargan's J test is a statistical test used for testing over-identifying restrictions in a statistical model.wikipedia
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### Instrumental variables estimation

instrumental variableinstrumental variablestwo-stage least squares
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.
The most common test of these overidentifying restrictions, called the Sargan–Hansen test, is based on the observation that the residuals should be uncorrelated with the set of exogenous variables if the instruments are truly exogenous.

### Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
The Sargan–Hansen test or Sargan's J test is a statistical test used for testing over-identifying restrictions in a statistical model.

### Statistical model

modelprobabilistic modelstatistical modeling
The Sargan–Hansen test or Sargan's J test is a statistical test used for testing over-identifying restrictions in a statistical model.

### Denis Sargan

John Denis SarganJohn D. SarganSargan
It was proposed by John Denis Sargan in 1958, and several variants were derived by him in 1975.

### Lars Peter Hansen

Lars P. HansenHansenLars Hansen
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.

### Generalized method of moments

GMM
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.

### Time series

time series analysistime-seriestime-series analysis
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.

### Errors and residuals

residualserror termresidual
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.

### Chi-squared distribution

chi-squaredchi-square distributionchi square distribution
Under the null hypothesis that the over-identifying restrictions are valid, the statistic is asymptotically distributed as a chi-square variable with (m - k) degrees of freedom (where m is the number of instruments and k is the number of endogenous variables).

### Panel data

longitudinal datapanel(panel)
When longitudinal ("panel data") data are available, it is possible to extend such statistics for testing exogeneity hypotheses for subsets of explanatory variables.

### Durbin–Wu–Hausman test

Hausman specification testHausman testThe Hausman test, ''or'' Hausman specification test
* Durbin–Wu–Hausman test

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