waldtest.systemfit {systemfit}R Documentation

Wald-test for Equation Systems

Description

Wald-test for linear parameter restrictions in equation systems.

Usage

   waldtest.systemfit( object, R.restr,
      q.restr = rep( 0, nrow( R.restr ) ) )

   ## S3 method for class 'waldtest.systemfit':
   print( x, digits = 4, ... )

Arguments

object an object of type systemfit.
R.restr j x k matrix to impose linear restrictions on the parameters by R.restr * b = q.restr (j = number of restrictions, k = number of all parameters, b = vector of all parameters).
q.restr an optional vector with j elements to impose linear restrictions (see R.restr); default is a vector that contains only zeros.
x an object of class waldtest.systemfit.
digits number of digits to print.
... currently not used.

Details

The Wald-statistic for sytems of equations is

W = ( R hat{b} - q )' ( R widehat{Cov} [ hat{b} ] R' )^{-1} ( R hat{b} - q )

Asymptotically, W has a chi^2 distribution with j degrees of freedom under the null hypothesis (Greene, 2003, p. 347).

Value

waldtest.systemfit returns a list of class waldtest.systemfit that includes following objects:

statistic the empirical Wald statistic.
p.value the p-value of the Wald-test.
nRestr number of restrictions (j, degrees of freedom).

Author(s)

Arne Henningsen ahenningsen@agric-econ.uni-kiel.de

References

Greene, W. H. (2003) Econometric Analysis, Fifth Edition, Prentice Hall.

See Also

systemfit, ftest.systemfit, lrtest.systemfit

Examples

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

## unconstrained SUR estimation
fitsur <- systemfit( "SUR", system, data=Kmenta )

# create restriction matrix to test whether \eqn{beta_2 = \beta_6}
R1 <- matrix( 0, nrow = 1, ncol = 7 )
R1[ 1, 2 ] <- 1
R1[ 1, 6 ] <- -1

## perform Wald-test
waldTest1 <- waldtest.systemfit( fitsur, R1 )
print( waldTest1 )   # rejected

# create restriction matrix to test whether \eqn{beta_2 = - \beta_6}
R2 <- matrix( 0, nrow = 1, ncol = 7 )
R2[ 1, 2 ] <- 1
R2[ 1, 6 ] <- 1

## perform Wald-test
waldTest2 <- waldtest.systemfit( fitsur, R2 )
print( waldTest2 )   # accepted
[Package systemfit version 0.8-0 Index]