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

Description

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

Usage

 `1` ``` 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 [email protected],
Arne Henningsen [email protected]

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

`systemfit`

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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 ) ```

Example output

```Loading required package: Matrix

Attaching package: 'zoo'

The following objects are masked from 'package:base':

as.Date, as.Date.numeric

Please cite the 'systemfit' package as:
Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/.

If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site:
https://r-forge.r-project.org/projects/systemfit/

Hausman specification test for consistency of the 3SLS estimation

data:  Kmenta
Hausman = 2.5357, df = 7, p-value = 0.9244
```

systemfit documentation built on May 29, 2017, 9:50 p.m.