| ftest.systemfit {systemfit} | R Documentation |
F-test for linear parameter restrictions in equation systems.
ftest.systemfit( object, R.restr,
q.restr = rep( 0, nrow( R.restr ) ) )
## S3 method for class 'ftest.systemfit':
print( x, digits = 4, ... )
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 ftest.systemfit. |
digits |
number of digits to print. |
... |
currently not used. |
The F-statistic for sytems of equations is
F = frac{ ( R hat{b} - q )' ( R ( X' ( hat{Σ} otimes I )^{-1} X )^{-1} R' )^{-1} ( R hat{b} - q ) / j }{ hat{e}' ( Σ otimes I )^{-1} hat{e} / ( M cdot T - K ) }
where j is the number of restrictions, M is the number of equations, T is the number of observations per equation, K is the total number of estimated coefficients, and Σ is the residual covariance matrix used in the estimation. Under the null hypothesis, F has an F-distribution with j and M cdot T - K degrees of freedom (Theil, 1971, p. 314).
ftest.systemfit returns a list of class ftest.systemfit
that includes following objects:
statistic |
the empirical F statistic. |
p.value |
the p-value of the F-test. |
nRestr |
number of restrictions (j, degrees of freedom of the numerator). |
dfSys |
degrees of freedom of the equation system (M cdot T - K, degrees of freedom of the denominator). |
Arne Henningsen ahenningsen@agric-econ.uni-kiel.de
Theil, Henri (1971). Principles of Econometrics, John Wiley & Sons, New York.
systemfit, waldtest.systemfit,
lrtest.systemfit
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 F-test
fTest1 <- ftest.systemfit( fitsur, R1 )
print( fTest1 ) # 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 F-test
fTest2 <- ftest.systemfit( fitsur, R2 )
print( fTest2 ) # accepted