Likelihood Ratio test for Equation Systems

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Description

Testing linear hypothesis on the coefficients of a system of equations by a Likelihood Ratio test.

Usage

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   ## S3 method for class 'systemfit'
lrtest( object, ... )

Arguments

object

a fitted model object of class systemfit.

...

further fitted model objects of class systemfit.

Details

lrtest.systemfit consecutively compares the fitted model object object with the models passed in ....

The LR-statistic for sytems of equations is

LR = T \cdot ≤ft( log ≤ft| \hat{ \hat{ Σ } }_r \right| - log ≤ft| \hat{ \hat{ Σ } }_u \right| \right)

where T is the number of observations per equation, and \hat{\hat{Σ}}_r and \hat{\hat{Σ}}_u are the residual covariance matrices calculated by formula "0" (see systemfit) of the restricted and unrestricted estimation, respectively. Asymptotically, LR has a χ^2 distribution with j degrees of freedom under the null hypothesis (Green, 2003, p. 349).

Value

An object of class anova, which contains the log-likelihood value, degrees of freedom, the difference in degrees of freedom, likelihood ratio Chi-squared statistic and corresponding p value. See documentation of lrtest in package "lmtest".

Author(s)

Arne Henningsen arne.henningsen@googlemail.com

References

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

See Also

systemfit, lrtest (package "lmtest"), linearHypothesis.systemfit

Examples

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

## unconstrained SUR estimation
fitsur <- systemfit( system, "SUR", 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( system, "SUR", data = Kmenta, restrict.matrix = R1 )

## perform LR-test
lrTest1 <- lrtest( 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( system, "SUR", data = Kmenta, restrict.matrix = R2 )

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

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