Hausman Test
hausman.systemfit returns the Hausman statistic for a specification test.
hausman.systemfit( results2sls, results3sls )
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.
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 |
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. |
Jeff D. Hamann jeff.hamann@forestinformatics.com,
Arne Henningsen arne.henningsen@googlemail.com
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
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 )
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