a vector of strings containing the names of the prices.
shareNames
a vector of strings containing the names of the expenditure
shares.
totExpName
a string containing the variable name of total expenditure.
data
a data frame containing all required variables.
method
character string specifying the method to estimate the AIDS:
either 'LA' or 'IL' (see deatils).
priceIndex
character string specifying the price index
for the 'Linear Approximation':
either 'S', 'SL', 'P', 'L', 'Ls', or 'T' (see details).
pxBase
The base to calculate the LA-AIDS price indices
(see aidsPx).
hom
logical. Should the homogeneity condition be imposed?
sym
logical. Should the symmetry condition be imposed?
shifterNames
an optional vector of strings containing the names of
the demand shifters.
instNames
a vector of strings containing the names of instrumental
variables.
estMethod
estimation method (e.g. 'SUR' or '3SLS',
see systemfit).
ILmaxiter
maximum number of iterations of the
'Iterated Linear Least Squares Estimation'.
ILtol
tolerance level of the 'Iterated Linear Least Squares
Estimation'.
alpha0
the intercept of the translog price index (α_0).
restrict.regMat
logical. Method to impose homogeneity and symmetry restrictions:
either via restrict.matrix (default) or via restrict.regMat
(see systemfit).
x
An object of class aidsEst.
...
additional arguments of aidsEst are passed to
systemfit;
additional arguments of print.aidsEst are currently ignored.
Details
Argument method can specify two different estimation methods:
The 'Linear Approximate AIDS' (LA) and the 'Iterative Linear Least Squares
Estimator' (IL) proposed by Blundell and Robin (1999).
Argument priceIndex can specify six different price indices
for the LA-AIDS:
Stone price index ('S'),
Stone price index with lagged shares ('SL'),
loglinear analogue to the Paasche price index ('P'),
loglinear analogue of the Laspeyres price index ('L'),
simplified loglinear analogue of the Laspeyres price index ('Ls'), and
Tornqvist price index ('T').
The 'Iterative Linear Least Squares Estimator' (IL) needs starting
values for the (translog) price index.
Starting values are taken from an initial estimation
of the 'Linear Approximate AIDS' (LA) with the price index
specified by argument priceIndex.
Value
a list of class aidsEst containing following objects:
coef
a list containing the vectors/matrix of the estimated
coefficients (alpha, beta, and gamma).
r2
R^2-values of all share equations.
r2q
R^2-values of the estimated quantities.
wFitted
fitted expenditure shares.
wResid
residuals of the expenditure shares.
qObs
observed quantities / quantitiy indices.
qFitted
fitted quantities / quantitiy indices.
qResid
residuals of the estimated quantities.
est
estimation result, i.e. the object returned
by systemfit.
iter
iterations of SUR/3SLS estimation(s).
If the AIDS is estimated by the 'Iterated Linear Least Squares
Estimator' (ILLE):
a vector containing the SUR/3SLS iterations at each iteration.
ILiter
number of iterations of the 'Iterated Linear Least Squares
Estimation'.
method
the method used to estimate the aids (see details).
priceIndex
the name of the price index (see details).
lnp
log of the price index used for estimation.
pMeans
means of the prices.
wMeans
means of the expenditure shares.
xtMean
mean of total expenditure.
call
the call of aidsEst.
priceNames
names of the prices.
shareNames
names of the expenditure shares.
totExpName
name of the variable for total expenditure.
basePrices
the base prices of the Paasche, Laspeyres,
or Tornqvist price index.
baseShares
the base shares of the Laspeyres, simplified Laspeyres,
or Tornqvist price index.
Author(s)
Arne Henningsen
References
Deaton, A.S. and J. Muellbauer (1980)
An Almost Ideal Demand System.
American Economic Review, 70, p. 312-326.
Blundell, R. and J.M. Robin (1999)
Estimationin Large and Disaggregated Demand Systems:
An Estimator for Conditionally Linear Systems.
Journal of Applied Econometrics, 14, p. 209-232.
See Also
summary.aidsEst, aidsElas,
aidsCalc.
Examples
# Using data published in Blanciforti, Green & King (1986)
data( Blanciforti86 )
# Data on food consumption are available only for the first 32 years
Blanciforti86 <- Blanciforti86[ 1:32, ]
## Repeating the demand analysis of Blanciforti, Green & King (1986)
## Note: Blanciforti, Green & King (1986) use scaled data,
## which leads to slightly different results
estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
data = Blanciforti86, priceIndex = "SL", maxiter = 100 )
print( estResult )
elas( estResult )
## Estimations with a demand shifter: linear trend
priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )
Blanciforti86$trend <- c( 0:( nrow( Blanciforti86 ) - 1 ) )
estResult <- aidsEst( priceNames, shareNames, "xFood",
data = Blanciforti86, shifterNames = "trend" )
print( estResult )
# Estimations with two demand shifters: linear + quadratic trend
Blanciforti86$trend2 <- c( 0:( nrow( Blanciforti86 ) - 1 ) )^2
estResult <- aidsEst( priceNames, shareNames, "xFood",
data = Blanciforti86, shifterNames = c( "trend", "trend2" ) )
print( estResult )