hausman.systemfit: Hausman Test

In systemfit: Estimating Systems of Simultaneous Equations

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 [e-mail],
Arne Henningsen [e-mail]

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.