systemfit (version 0.8-0)

lrtest.systemfit: Likelihood Ratio test for Equation Systems

Description

Likelihood Ratio test for linear parameter restrictions in equation system.

Usage

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

Arguments

resultc

an object of type systemfit that contains the results of the restricted estimation.

resultu

an object of type systemfit that contains the results of the unconstrained estimation.

x

an object of class ftest.systemfit.

digits

number of digits to print.

...

currently not used.

Value

• lrtest.systemfit returns a list of class lrtest.systemfit that includes following objects:
• statistic
  the empirical likelihood ratio statistic.
• p.value
  the p-value of the $\chi^2$-test.
• nRestr
  number of restrictions ($j$, degrees of freedom).

Details

The LR-statistic for sytems of equations is $$LR = T \cdot \left( log \left| \hat{ \hat{ \Sigma } }_r \right| - log \left| \hat{ \hat{ \Sigma } }_u \right| \right)$$ where $T$ is the number of observations per equation, and $\hat{\hat{\Sigma}}_r$ and $\hat{\hat{\Sigma}}_u$ are the residual covariance matrices calculated by formula "0" (see systemfit) of the restricted and unrestricted estimation, respectively. Asymptotically, $LR$ has a $\chi^2$ distribution with $j$ degrees of freedom under the null hypothesis (Green, 2003, p. 349).

References

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

See Also

systemfit, ftest.systemfit, waldtest.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 impose \eqn{beta_2 = \beta_6}
R1 <- matrix( 0, nrow = 1, ncol = 7 )
R1[ 1, 2 ] <- 1
R1[ 1, 6 ] <- -1

## constrained SUR estimation
fitsur1 <- systemfit( "SUR", system, data = Kmenta, R.restr = R1 )

## perform LR-test
lrTest1 <- lrtest.systemfit( fitsur1, fitsur )
print( lrTest1 )   # rejected

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

## constrained SUR estimation
fitsur2 <- systemfit( "SUR", system, data = Kmenta, R.restr = R2 )

## perform LR-test
lrTest2 <- lrtest.systemfit( fitsur2, fitsur )
print( lrTest2 )   # accepted