# lrtest.systemfit: Likelihood Ratio test for Equation Systems In systemfit: Estimating Systems of Simultaneous Equations

 lrtest.systemfit R Documentation

## Likelihood Ratio test for Equation Systems

### Description

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

### Usage

   ## 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 \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).

### 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".

### References

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

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

### Examples

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


systemfit documentation built on March 31, 2023, 9:26 p.m.