a vector of strings containing the names of the prices.
totExpName
a string containing the variable name of total expenditure.
coef
a list containing the coefficients alpha, beta, gamma,
and (only for the translog price index) alpha0.
data
a data frame containing the data.
shareNames
a vector of strings containing the names of the expenditure
shares.
x
an object of class aidsConcav.
header
logical. Print a header?
...
currently unused.
Details
If argument shareNames is specified,
observed shares are used for the calculation of the 'C' matrices
to check for concavity;
if argument shareNames is NULL (e.g., not specified),
fitted shares are used for the calculation of the 'C' matrices.
Please note that checking concavity of the expenditure function requires
that the expenditure function of the model exists.
Therefore, the concavity condition can be checked,
only if the symmetry condition is fulfilled and
the translog price index is used.
Value
aidsConcav returns a list of class aidsConcav
that contains following elements:
concavity
a logical vector indicating whether the concavity
condition is fulfilled at each observation.
nValidObs
number of (valid) observation at which concavity
could be checked.
nConcavObs
number of observation at which the concavity codition
is fulfilled.
concavPercent
percent of observations where the concavity condition is
fulfilled.
cMatrices
a list of the 'C' matrices for each observation to check
for concavity (see Deaton and Muellbauer, 1980b, p.76 ).
Author(s)
Arne Henningsen
References
Deaton, A.S. and J. Muellbauer (1980a)
An Almost Ideal Demand System.
American Economic Review, 70, p. 312-326.
Deaton, A.S. and J. Muellbauer (1980b)
Economics and Consumer Behavior,
Cambridge University Press, Cambridge.
See Also
aidsEst, aidsElas
Examples
data( Blanciforti86 )
# Data on food consumption are available only for the first 32 years
Blanciforti86 <- Blanciforti86[ 1:32, ]
priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )
# estimate the AIDS
estResult <- aidsEst( priceNames, shareNames, "xFood",
data = Blanciforti86, method = "IL" )
# check concavity with fitted shares
aidsConcav( priceNames, "xFood", coef = estResult$coef,
data = Blanciforti86 )
# check concavity with observed shares
aidsConcav( priceNames, "xFood", coef = estResult$coef,
data = Blanciforti86, shareNames = shareNames )