# hausman.systemfit: Hausman Test In systemfit: Estimating Systems of Simultaneous Equations

 hausman.systemfit R Documentation

## Hausman Test

### Description

`hausman.systemfit` returns the Hausman statistic for a specification test.

### Usage

``````   hausman.systemfit( results2sls, results3sls )
``````

### Arguments

 ` results2sls ` result of a 2SLS (limited information) estimation returned by `systemfit`. ` results3sls ` result of a 3SLS (full information) estimation returned by `systemfit`.

### Details

The null hypotheses of the test is that all exogenous variables are uncorrelated with all disturbance terms. Under this hypothesis both the 2SLS and the 3SLS estimator are consistent but only the 3SLS estimator is (asymptotically) efficient. Under the alternative hypothesis the 2SLS estimator is consistent but the 3SLS estimator is inconsistent.

The Hausman test statistic is

`m = ( b_2 - b_3 )' ( V_2 - V_3 ) ( b_2 - b_3 ) `

where \$b_2\$ and \$V_2\$ are the estimated coefficients and their variance covariance matrix of a 2SLS estimation and \$b_3\$ and \$V_3\$ are the estimated coefficients and their variance covariance matrix of a 3SLS estimation.

### Value

`hausman.systemfit` returns a list of the class `htest` that contains following elements:

 `q` vector of the differences between the estimated coefficients. `qVar` variance covariance matrix of `q` (difference between the variance covariance matrices of the estimated coefficients). `statistic` the Hausman test statistic. `parameter` degrees of freedom. `p.value` P-value of the test. `method` character string describing this test. `data.name` name of the data.frame used for estimation.

### Author(s)

Jeff D. Hamann jeff.hamann@forestinformatics.com,
Arne Henningsen arne.henningsen@googlemail.com

### References

Greene, W. H. (1993) Econometric Analysis, Fifth Edition, Macmillan.

Hausman, J. A. (1978) Specification Tests in Econometrics. Econometrica. 46:1251-1271.

Kmenta, J. (1997) Elements of Econometrics, Second Edition, University of Michigan Publishing

### See Also

`systemfit`

### Examples

``````data( "Kmenta" )
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice + trend
inst <- ~ income + farmPrice + trend
system <- list( demand = eqDemand, supply = eqSupply )

## perform the estimations
fit2sls <- systemfit( system, "2SLS", inst = inst, data = Kmenta )
fit3sls <- systemfit( system, "3SLS", inst = inst, data = Kmenta )

## perform the Hausman test
h <- hausman.systemfit( fit2sls, fit3sls )
print( h )
``````

systemfit documentation built on March 31, 2023, 9:26 p.m.