systemfit (version 0.8-5)

waldtest.systemfit: 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.

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).

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).

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