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).