| Title: | Demand Analysis with the Almost Ideal Demand System (AIDS) |
|---|---|
| Description: | Functions and tools for analysing consumer demand with the Almost Ideal Demand System (AIDS) suggested by Deaton and Muellbauer (1980). |
| Authors: | Arne Henningsen |
| Maintainer: | Arne Henningsen <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.6-20 |
| Built: | 2024-11-14 06:46:56 UTC |
| Source: | CRAN |
Search for the intercept of the translog price index
() that gives the best fit to the
Almost Ideal Demand System (see Michalek and Keyzer, 1992)
aidsBestA0( priceNames, shareNames, totExpName, a0min = -50, a0max = 50, stoprange = 3, stopiter = 10, verbose = FALSE, ... )aidsBestA0( priceNames, shareNames, totExpName, a0min = -50, a0max = 50, stoprange = 3, stopiter = 10, verbose = FALSE, ... )
priceNames |
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. |
a0min |
lower limit of the range for searching for |
a0max |
upper limit of the range for searching for |
stoprange |
stop searching when the search interval is smaller than
or equal to |
stopiter |
maximal number of iterations. |
verbose |
print each determinant of the residual covariance matrix immediately after its calculation. |
... |
arguments passed to |
The demand system is estimated using the Iterative Linear Least Squares Estimator (ILLE) suggested by Blundell and Robin (1999). This iterative procedure is equivalent to the method proposed by Michalek and Keyzer (1992). However, the latter do not correct the coefficient covariance matrix.
The fit of the model is measured in terms of the likelihood value. Since the determinant of the residual covariance matrix is monotonically decreasing with the likelihood value, we search for the smallest determinant of the residual covariance matrix.
Since each call of aidsEst generally takes a long time,
the search algorithm is constructed to minimize the
calls of the function aidsEst.
a list containing following objects:
alpha0 |
|
allValues |
all |
iter |
number of iterations. |
Arne Henningsen
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.
Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.
Michalek, J. and M. A. Keyzer (1992) Estimation of a two-stage LES-AIDS consumer demand system for eight EC countries. European Review of Agricultural Economics, 19 (2), p. 137-163.
data( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] bestA0 <- aidsBestA0( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, useMatrix = FALSE ) # may take some time (argument 'useMatrix = FALSE' decreases # the computation time only if the model and data set are small) print( bestA0$alpha0 ) plot( bestA0$allValues ) # this should be convexdata( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] bestA0 <- aidsBestA0( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, useMatrix = FALSE ) # may take some time (argument 'useMatrix = FALSE' decreases # the computation time only if the model and data set are small) print( bestA0$alpha0 ) plot( bestA0$allValues ) # this should be convex
Given prices, total expenditure and coefficients this function calculates the demanded quantities and expenditure shares based on the Almost Ideal Demand System.
aidsCalc( priceNames, totExpName, coef, data, priceIndex = "TL", basePrices = NULL, baseShares = NULL, shifterNames = NULL ) ## S3 method for class 'aidsEst' predict( object, newdata = NULL, observedShares = FALSE, ... )aidsCalc( priceNames, totExpName, coef, data, priceIndex = "TL", basePrices = NULL, baseShares = NULL, shifterNames = NULL ) ## S3 method for class 'aidsEst' predict( object, newdata = NULL, observedShares = FALSE, ... )
priceNames |
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. |
priceIndex |
a character string specifying the price index
(see |
basePrices |
a vector specifying the base prices for the Paasche, Laspeyres, and Tornqvist price index. |
baseShares |
a vector specifying the base expenditure shares for the Laspeyres, simplified Laspeyres, and Tornqvist index. |
shifterNames |
a vector of strings containing the names of the demand shifters. |
object |
an object of class |
newdata |
an optional data frame which should contain the variables for the prediction. If omitted, the data frame used for the estimation is used also for the prediction. |
observedShares |
logical. Using observed shares? (see details). |
... |
currently not used. |
The predict method for objects of class aidsEst
extracts all relevant elements from an object returned by aidsEst
and passes them as arguments to aidsCalc.
The optional argument observedShares determines
whether fitted (default) or observed expenditure shares are
used in the price index of the LA-AIDS.
aidsCalc and
the predict method for objects of class aidsEst
return a list with following elements:
shares |
a data frame containing the calculated expenditure shares. |
quantities |
a data frame containing the calculated quantites. |
Arne Henningsen
Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.
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" ) ## LA-AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, priceIndex = "S" ) # using observed shares in the Stone index lnp <- aidsPx( "S", priceNames, Blanciforti86, shareNames ) fitted <- aidsCalc( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86, priceIndex = lnp ) fitted$shares # equal to estResult$wFitted fitted$quant # equal to estResult$qFitted # now the same with the predict method fitted2 <- predict( estResult, observedShares = TRUE ) all.equal( fitted, fitted2 ) # using fitted shares in the Stone index fitted <- aidsCalc( priceNames, "xFood", coef = estResult$coef, data = Blanciforti86, priceIndex = "S" ) # now the same with the predict method fitted2 <- predict( estResult ) all.equal( fitted, fitted2 ) ## AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) fitted <- aidsCalc( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) fitted$shares # equal to estResult$wFitted fitted$quant # equal to estResult$qFitted fitted2 <- predict( estResult ) all.equal( fitted, fitted2 )data( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" ) shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" ) ## LA-AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, priceIndex = "S" ) # using observed shares in the Stone index lnp <- aidsPx( "S", priceNames, Blanciforti86, shareNames ) fitted <- aidsCalc( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86, priceIndex = lnp ) fitted$shares # equal to estResult$wFitted fitted$quant # equal to estResult$qFitted # now the same with the predict method fitted2 <- predict( estResult, observedShares = TRUE ) all.equal( fitted, fitted2 ) # using fitted shares in the Stone index fitted <- aidsCalc( priceNames, "xFood", coef = estResult$coef, data = Blanciforti86, priceIndex = "S" ) # now the same with the predict method fitted2 <- predict( estResult ) all.equal( fitted, fitted2 ) ## AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) fitted <- aidsCalc( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) fitted$shares # equal to estResult$wFitted fitted$quant # equal to estResult$qFitted fitted2 <- predict( estResult ) all.equal( fitted, fitted2 )
Check whether the expenditure function of the AIDS is concave in prices.
aidsConcav( priceNames, totExpName, coef, data, shareNames = NULL ) ## S3 method for class 'aidsConcav' print( x, header = TRUE, ... )aidsConcav( priceNames, totExpName, coef, data, shareNames = NULL ) ## S3 method for class 'aidsConcav' print( x, header = TRUE, ... )
priceNames |
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 |
header |
logical. Print a header? |
... |
currently unused. |
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.
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 ). |
Arne Henningsen
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.
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 )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 )
Check whether the specification of the AIDS is consistent with microeconomic demand theory (i.e. utility maximisation).
aidsConsist( priceNames, totExpName, coef, data, priceIndex = "TL", basePrices = NULL, baseShares = NULL, shareNames = NULL ) ## S3 method for class 'aidsConsist' print( x, ... ) ## S3 method for class 'aidsEst' checkConsist( object, observedShares = FALSE, ... )aidsConsist( priceNames, totExpName, coef, data, priceIndex = "TL", basePrices = NULL, baseShares = NULL, shareNames = NULL ) ## S3 method for class 'aidsConsist' print( x, ... ) ## S3 method for class 'aidsEst' checkConsist( object, observedShares = FALSE, ... )
priceNames |
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. |
priceIndex |
a character string specifying the price index
(see |
basePrices |
a vector specifying the base prices for the
Paasche, Laspeyres, and Tornqvist price index
(passed to |
baseShares |
a vector specifying the base expenditure shares for the
Laspeyres, simplified Laspeyres, and Tornqvist index
(passed to |
shareNames |
a vector of strings containing the names of the expenditure
shares (passed to |
x |
an object of class |
object |
an object of class |
observedShares |
logical. Using observed shares? (see details). |
... |
currently not used. |
The checkConsist method for objects of class aidsEst
extracts all relevant elements from an object returned by aidsEst
and passes them as arguments to aidsConsist.
The optional argument observedShares determines
whether fitted (default) or observed expenditure shares are
used in the price index of the LA-AIDS to check monotonicity
and in the calculation of the subsitution matrix to check concavity.
aidsConsist and the checkConsist method
return a list of class aidsConsist
that contains following elements:
addingUp |
logical. Is the addinp-up condition fulfilled? |
homogeneity |
logical. Is the homogeneity condition fulfilled? |
symmetry |
logical. Is the symmetry condition fulfilled? |
mono |
an object returned by |
concav |
an object returned by |
Arne Henningsen
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.
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" ) estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) aidsConsist( priceNames, "xFood", data = Blanciforti86, coef = estResult$coef ) # the same can be obtained in an easier way checkConsist( estResult )data( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" ) shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" ) estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) aidsConsist( priceNames, "xFood", data = Blanciforti86, coef = estResult$coef ) # the same can be obtained in an easier way checkConsist( estResult )
These functions calculate and print the demand elasticities of an AIDS model.
aidsElas( coef, prices = NULL, shares = NULL, totExp = NULL, method = "AIDS", priceIndex = "TL", basePrices = NULL, baseShares = NULL, quantNames = NULL, priceNames = NULL, shifterValues = NULL, coefCov = NULL, df = NULL ) ## S3 method for class 'aidsEst' elas( object, method = NULL, observedShares = FALSE, ... ) ## S3 method for class 'aidsElas' print( x, ... )aidsElas( coef, prices = NULL, shares = NULL, totExp = NULL, method = "AIDS", priceIndex = "TL", basePrices = NULL, baseShares = NULL, quantNames = NULL, priceNames = NULL, shifterValues = NULL, coefCov = NULL, df = NULL ) ## S3 method for class 'aidsEst' elas( object, method = NULL, observedShares = FALSE, ... ) ## S3 method for class 'aidsElas' print( x, ... )
coef |
a list containing the coefficients alpha, beta and gamma. |
prices |
a vector of the prices at which the elasticities should be calculated. |
shares |
a vector of the shares at which the elasticities should be calculated. |
totExp |
total expenditure at which the elasticities should be calculated. |
method |
the elasticity formula to be used (see details). |
priceIndex |
the price index (see details). |
basePrices |
a vector specifying the base prices for the Paasche, Laspeyres, and Tornqvist price index. |
baseShares |
a vector specifying the base expenditure shares for the Laspeyres, simplified Laspeyres, and Tornqvist index. |
quantNames |
an optional vector of strings containing the names of the quantities to label elasticities. |
priceNames |
an optional vector of strings containing the names of the prices to label elasticities. |
shifterValues |
a vector of values of the shifter variables, at which the elasticities should be calculated. |
coefCov |
variance covariance matrix of the coefficients (optional). |
df |
degrees of freedom to calculate P-values of the elasticities (optional). |
object |
an object of class |
observedShares |
logical. Using observed shares for calculating the demand elasticities? |
x |
an object of class |
... |
additional arguments of |
Argument priceIndex has two effects:
first it determines the price index that is used
for calculating (fitted) expenditure shares,
if argument shares is not provided (see aidsCalc);
second it determines which version of the formulas for calculating
demand elasticities of the LA-AIDS are used,
because formulas B1/LA, B2, and Go/Ch
have different versions depending on the price index.
elas.aidsEst is a wrapper function to aidsElas
that extracts the
estimated coefficients (coef),
mean expenditure shares (wMeans),
mean prices (pMeans),
names of the prices (priceNames),
estimated coefficient variance covariance matrix (coef$allcov), and
degrees of freedom (est$df)
from the object of class aidsEst
and passes them to aidsElas.
If argument method in elas.aidsEst is not specified,
the default value depends on the estimation method.
If the demand system was estimated by the linear approximation (LA),
the default method is 'Ch'.
If the demand system was estimated by the iterative linear least squares
estimator (ILLE),
the default method is 'AIDS'.
At the moment the elasticity formulas of the orginal AIDS (AIDS),
the formula of Goddard (1983) or Chalfant (1987) (Go or Ch),
the formula of Eales and Unnevehr (1988) (EU),
the formula of Green and Alston (1990) or the first of Buse (1994)
(GA or B1) and
the second formula of Buse (1994) (B2)
are implemented.
The variance covariance matrices of the elasticities are calculated using the formula of Klein (1953, p. 258) (also known as the delta method). At the moment this is implemented only for the elasticity formulas of the orginal AIDS.
a list of class aidsElas containing following elements:
method |
the elasticity formula used to calculate these elasticities. |
priceIndex |
the price index used (see details). |
df |
degrees of freedom to calculate P-values of the elasticities
(only if argument |
exp |
vector of expenditure elasticities. |
hicks |
matrix of Hicksian (compensated) price elasticities. |
marshall |
matrix of Marshallian (uncompensated) price elasticities. |
allVcov |
variance covariance matrix of all elasticities. |
expVcov |
variance covariance matrix of the expenditure elasticities. |
hicksVcov |
variance covariance matrix of the Hicksian (compensated) price elasticities. |
marshallVcov |
variance covariance matrix of the Marshallian (uncompensated) price elasticities. |
expStEr |
standard errors of the expenditure elasticities. |
hicksStEr |
standard errors of the Hicksian (compensated) price elasticities. |
marshallStEr |
standard errors of the Marshallian (uncompensated) price elasticities. |
expTval |
t-values of the expenditure elasticities. |
hicksTval |
t-values of the Hicksian (compensated) price elasticities. |
marshallTval |
t-values of the Marshallian (uncompensated) price elasticities. |
expPval |
P-values of the expenditure elasticities. |
hicksPval |
P-values of the Hicksian (compensated) price elasticities. |
marshallPval |
P-values of the Marshallian (uncompensated) price elasticities. |
Arne Henningsen
Chalfant, J.A. (1987) A Globally Flexible, Almost Ideal Demand System. Journal of Business and Economic Statistics, 5, p. 233-242.
Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.
Eales J.S. and L.J. Unnevehr (1988) Demand for beef and chicken products: separability and structural change. American Journal of Agricultural Economics, 70, p. 521-532.
Klein L.R. (1953) A Textbook of Econometrics. Row, Petersen and Co., New York.
data( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86 ) wMeans <- colMeans( Blanciforti86[ , c( "wFood1", "wFood2", "wFood3", "wFood4" ) ] ) aidsElas( estResult$coef, shares = wMeans, method = "Ch", priceIndex = "S" ) ## Repeating the evaluation of different elasticity formulas of ## Green & Alston (1990) priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" ) shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" ) # AIDS estimation and elasticities estResultA <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86[ -1, ], method = "IL", maxiter = 100 ) diag( elas( estResultA, method = "AIDS" )$marshall ) summary( elas( estResultA, method = "AIDS" ) ) # LA-AIDS estimation estResultLA <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, priceIndex = "SL", maxiter = 100 ) # LA-AIDS + formula of AIDS diag( elas( estResultLA, method = "AIDS" )$marshall ) # LA-AIDS + formula of Eales + Unnevehr diag( elas( estResultLA, method = "EU" )$marshall ) # LA-AIDS + formula of Goddard or Chalfant: diag( elas( estResultLA, method = "Go" )$marshall ) diag( elas( estResultLA, method = "Ch" )$marshall ) # LA-AIDS + formula of Green + Alston (= 1st of Buse): diag( elas( estResultLA, method = "GA" )$marshall )data( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86 ) wMeans <- colMeans( Blanciforti86[ , c( "wFood1", "wFood2", "wFood3", "wFood4" ) ] ) aidsElas( estResult$coef, shares = wMeans, method = "Ch", priceIndex = "S" ) ## Repeating the evaluation of different elasticity formulas of ## Green & Alston (1990) priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" ) shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" ) # AIDS estimation and elasticities estResultA <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86[ -1, ], method = "IL", maxiter = 100 ) diag( elas( estResultA, method = "AIDS" )$marshall ) summary( elas( estResultA, method = "AIDS" ) ) # LA-AIDS estimation estResultLA <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, priceIndex = "SL", maxiter = 100 ) # LA-AIDS + formula of AIDS diag( elas( estResultLA, method = "AIDS" )$marshall ) # LA-AIDS + formula of Eales + Unnevehr diag( elas( estResultLA, method = "EU" )$marshall ) # LA-AIDS + formula of Goddard or Chalfant: diag( elas( estResultLA, method = "Go" )$marshall ) diag( elas( estResultLA, method = "Ch" )$marshall ) # LA-AIDS + formula of Green + Alston (= 1st of Buse): diag( elas( estResultLA, method = "GA" )$marshall )
aidsEst does an econometric estimation
of the Almost Ideal Demand System (AIDS)
aidsEst( priceNames, shareNames, totExpName, data, method = "LA", priceIndex = "Ls", pxBase = 1, hom = TRUE, sym = TRUE, shifterNames = NULL, instNames = NULL, estMethod = ifelse( is.null( instNames ), "SUR", "3SLS" ), ILmaxiter = 50, ILtol = 1e-5, alpha0 = 0, restrict.regMat = FALSE, ... ) ## S3 method for class 'aidsEst' print( x, ... )aidsEst( priceNames, shareNames, totExpName, data, method = "LA", priceIndex = "Ls", pxBase = 1, hom = TRUE, sym = TRUE, shifterNames = NULL, instNames = NULL, estMethod = ifelse( is.null( instNames ), "SUR", "3SLS" ), ILmaxiter = 50, ILtol = 1e-5, alpha0 = 0, restrict.regMat = FALSE, ... ) ## S3 method for class 'aidsEst' print( x, ... )
priceNames |
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 |
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 |
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 ( |
restrict.regMat |
logical. Method to impose homogeneity and symmetry restrictions:
either via restrict.matrix (default) or via restrict.regMat
(see |
x |
An object of class |
... |
additional arguments of |
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.
a list of class aidsEst containing following objects:
coef |
a list containing the vectors/matrix of the estimated coefficients (alpha, beta, and gamma). |
r2 |
|
r2q |
|
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 |
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. |
sMeans |
means of shifter variables (only if shifter variables are used). |
call |
the call of |
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. |
Arne Henningsen
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.
summary.aidsEst, aidsElas,
aidsCalc.
# 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 )# 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 )
aidsMono checks whether the expenditure function
of an estimated Almost Ideal Demand System (AIDS)
is monotonic increasing in prices,
which implies that all demanded quantities and expenditure shares
are non-negative.
aidsMono( priceNames, totExpName, coef, data, priceIndex = "TL", basePrices = NULL, baseShares = NULL ) ## S3 method for class 'aidsMono' print( x, header = TRUE, ... )aidsMono( priceNames, totExpName, coef, data, priceIndex = "TL", basePrices = NULL, baseShares = NULL ) ## S3 method for class 'aidsMono' print( x, header = TRUE, ... )
priceNames |
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. |
priceIndex |
a character string specifying the price index
(see |
basePrices |
a vector specifying the base prices for the Paasche, Laspeyres, and Tornqvist price index. |
baseShares |
a vector specifying the base expenditure shares for the Laspeyres, simplified Laspeyres, and Tornqvist index. |
x |
an object of class |
header |
logical. Print a header? |
... |
currently unused. |
Internally, aidsMono passes its arguments to aidsCalc
and then checks for each observation, wether all expenditure shares
are non-negative.
If argument priceIndex specifies a price index of the LA-AIDS,
'fitted' values are used for current and lagged expenditure shares
in these price indices
(see aidsCalc).
However, if argument priceIndex is a numeric vector
containing the log values of a price index
(e.g.\ the price index used in the estimation),
this price index is used for the calculations.
aidsMono returns a list of class aidsMono
that contains following elements:
monotony |
a logical vector indicating whether the monotony condition is fulfilled at each observation. |
nValidObs |
number of (valid) observation at which monotonicity could be checked. |
nMonoObs |
number of observation at which the monotonicity codition is fulfilled. |
monoPercent |
percent of observations where the monotony condition is fulfilled. |
priceIndex |
a chacter string indicating the price index
specified by argument |
Arne Henningsen
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.
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" ) ## AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) aidsMono( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) ## LA-AIDS with Tornqvist price index estResultLaT <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, priceIndex = "T" ) # with fitted expenditure shares in the price index aidsMono( priceNames, "xFood", coef = coef( estResultLaT ), data = Blanciforti86, priceIndex = "T", basePrices = estResultLaT$basePrices, baseShares = estResultLaT$baseShares ) # with observed expenditure shares in the price index aidsMono( priceNames, "xFood", coef = coef( estResultLaT ), data = Blanciforti86, priceIndex = estResultLaT$lnp )data( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" ) shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" ) ## AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) aidsMono( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) ## LA-AIDS with Tornqvist price index estResultLaT <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, priceIndex = "T" ) # with fitted expenditure shares in the price index aidsMono( priceNames, "xFood", coef = coef( estResultLaT ), data = Blanciforti86, priceIndex = "T", basePrices = estResultLaT$basePrices, baseShares = estResultLaT$baseShares ) # with observed expenditure shares in the price index aidsMono( priceNames, "xFood", coef = coef( estResultLaT ), data = Blanciforti86, priceIndex = estResultLaT$lnp )
Calculate log price indices for the AIDS and LA-AIDS.
aidsPx( priceIndex, priceNames, data, shareNames = NULL, base = 1, coef = NULL, shifterNames = NULL )aidsPx( priceIndex, priceNames, data, shareNames = NULL, base = 1, coef = NULL, shifterNames = NULL )
priceIndex |
the price index to be used (see details). |
priceNames |
a vector of strings containing the names of the prices. |
data |
a data frame containing the required variables. |
shareNames |
a vector of strings containing the names of the expenditure shares. |
base |
the base to calculate the indices (see details). |
coef |
a list containing the coefficients alpha0, alpha, beta, and gamma (only needed for the translog price index). |
shifterNames |
an optional vector of strings containing the names of the demand shifters that modify the alphas of the Translog price index. |
Currently 7 different price indices are implemented:
translog price index ('TL'),
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 argument base can be either
a single number: the row number of the base prices and quantities,
a vector indicating several observations: The means of these observations are used as base prices and quantities, or
a logical vector with the same length as the data: The
means of the observations indicated as 'TRUE' are used as base prices
and quantities.
a list with elements prices and/or shares
that are numeric vectors specifying the values of the base prices
and/or base expenditure shares.
A vector containing the log price index.
If argument priceIndex is "P", "Ls", or "T",
the returned vector has the attribute(s)
basePrices and/or baseShares
that are numeric vectors of the base prices and/or base expenditure shares
for calculating the price indices.
Arne Henningsen
Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.
Moschini, G. (1995) Units of Measurement and the Stone Index in Demand System Estimation. American Journal of Agricultural Economics, 77, p. 63-68.
data( Blanciforti86 ) # Stone price index aidsPx( "S", c( "pFood1", "pFood2", "pFood3", "pFood4" ), Blanciforti86, c( "wFood1", "wFood2", "wFood3", "wFood4" ) ) # (log-linear analogue of the) Paasche price index aidsPx( "P", c( "pFood1", "pFood2", "pFood3", "pFood4" ), Blanciforti86, c( "wFood1", "wFood2", "wFood3", "wFood4" ), base = row.names(Blanciforti86) == "1970" ) # Tornqvist price index aidsPx( "T", c( "pFood1", "pFood2", "pFood3", "pFood4" ), Blanciforti86, c( "wFood1", "wFood2", "wFood3", "wFood4" ), base = list( prices = rep( 100, 4 ), shares = rep( 0.25, 4 ) ) )data( Blanciforti86 ) # Stone price index aidsPx( "S", c( "pFood1", "pFood2", "pFood3", "pFood4" ), Blanciforti86, c( "wFood1", "wFood2", "wFood3", "wFood4" ) ) # (log-linear analogue of the) Paasche price index aidsPx( "P", c( "pFood1", "pFood2", "pFood3", "pFood4" ), Blanciforti86, c( "wFood1", "wFood2", "wFood3", "wFood4" ), base = row.names(Blanciforti86) == "1970" ) # Tornqvist price index aidsPx( "T", c( "pFood1", "pFood2", "pFood3", "pFood4" ), Blanciforti86, c( "wFood1", "wFood2", "wFood3", "wFood4" ), base = list( prices = rep( 100, 4 ), shares = rep( 0.25, 4 ) ) )
These functions calculate the utility level given prices and total expenditure using the indirect utility function of the Almost Ideal Demand System and the partial derivatives of this indirect utility function with repect to prices and total expenditure.
aidsUtility( priceNames, totExpName, coef, data ) aidsUtilityDeriv( priceNames, totExpName, coef, data, rel = FALSE )aidsUtility( priceNames, totExpName, coef, data ) aidsUtilityDeriv( priceNames, totExpName, coef, data, rel = FALSE )
priceNames |
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 in elements alpha0 (scalar), alpha (vector), beta (vector), gamma (matrix), and possibly beta0 (scalar, if not given, it is assumed to be 1). |
data |
a data frame containing the data. |
rel |
logical. If |
aidsUtility returns a numeric vector
that contains the utility levels;
aidsUtilityDeriv returns a data.frame
that contains the partial derivatives
of the indirect utility function
with repect to prices and total expenditure.
Arne Henningsen
Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.
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 (non-linear) AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) # calculate the utility levels of each year utility <- aidsUtility( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) utilityDeriv <- aidsUtilityDeriv( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) utilityEla <- aidsUtilityDeriv( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86, rel = TRUE )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 (non-linear) AIDS estResult <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, method = "IL" ) # calculate the utility levels of each year utility <- aidsUtility( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) utilityDeriv <- aidsUtilityDeriv( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86 ) utilityEla <- aidsUtilityDeriv( priceNames, "xFood", coef = coef( estResult ), data = Blanciforti86, rel = TRUE )
The Blanciforti86 data frame contains annual U.S. consumption data
from 1947 to 1978 or 1981.
These data include eleven aggregate commodity groups:
(1) food, (2) alcohol plus tobacco, (3) clothing, (4) housing,
(5) utilities, (6) transportation, (7) medical care, (8) durable goods,
(9) other nondurable goods, (10) other services, and
(11) other miscellaneous goods;
four food groups:
(1) meats, (2) fruits and vegetables, (3) cereal and bakery products, and
(4) miscellaneous foods;
and four meat groups:
(1) beef and veal, (2) pork, (3) fish, and (4) poultry.
For each of these groups the consumption expenditures, price indices,
and expenditure shares are available.
This data frame contains the following variables / columns:
The year.
Expenditure on the aggregate commodity group X (in Millions of US-Dollars).
Total expenditure on all eleven aggregate commodity groups (in Millions of US-Dollars).
Deflated expenditure on the aggregate commodity group X (in Million of 1972 US-Dollars).
Total deflated expenditure on all eleven aggregate commodity groups (in Million of 1972 US-Dollars).
Price index for the aggregate commodity group X (1972 = 100).
Expenditure share of the aggregate commodity group X.
Per capita expenditure for food group X (in US-Dollars).
Total per capita expenditure for all four food groups (in US-Dollars).
Deflated per capita expenditure for food group X (in 1972 US-Dollars).
Total deflated per capita expenditure for all four food groups (in 1972 US-Dollars).
Price index for food group X (1972 = 100).
Expenditure share of food group X.
Expenditure on food published by the US Department of Commerce (USDOC) (in Millions of US-Dollars).
Expenditure on food published by the US Department of Agriculture (USDA) (in Millions of US-Dollars).
Expenditure on food (new estimates) (in Millions of US-Dollars).
Per capita expenditure for meat group X (in US-Dollars).
Total per capita expenditure for all four meat groups (in US-Dollars).
Price index for meat group X (1972 = 100).
Per capita consumption of meat group X (in pounds).
Price index for the meat group (1972 = 100).
Price index for the meat group (new estimate) (1972 = 100).
Population as presented in Table 5.A.3 (in Millions).
Population as presented in Table 5.A.12 (in Millions).
data(Blanciforti86)data(Blanciforti86)
Blanciforti, Laura. A., Richard D. Green and Gordon A. King (1986) U.S. Consumer Behavior Over the Postwar Period: An Almost Ideal Demand System Analysis. Giannini Foundation Monograph Number 40, August 1986.
These methods return and print the coefficients from an Almost Ideal Demand System.
## S3 method for class 'aidsEst' coef( object, ... ) ## S3 method for class 'coef.aidsEst' print( x, ... )## S3 method for class 'aidsEst' coef( object, ... ) ## S3 method for class 'coef.aidsEst' print( x, ... )
object |
an object of class |
x |
an object of class |
... |
further arguments for methods |
The coef method returns an object of class coef.aidsEst
containing following objects:
alpha0 |
a scalar, coefficient alpha0 (only for the AIDS with translog price index). |
alpha |
a vector of the alpha coefficients. |
beta |
a vector of the beta coefficients. |
gamma |
a matrix of the gamma coefficients. |
delta |
a matrix of the delta coefficients (only if the model was estimated with demand shifters). |
Arne Henningsen
These method returns the covariance matrix of the coefficients from an Almost Ideal Demand System (AIDS).
## S3 method for class 'aidsEst' df.residual( object, ... )## S3 method for class 'aidsEst' df.residual( object, ... )
object |
an object of class |
... |
currently not used. |
The df.residual method for objects of class aidsEst
returns a symmetric matrix: the covariance matrix of the coefficients.
Arne Henningsen
This method extracts the fitted demanded quantities and expenditure shares from an estimated Almost Ideal Demand System.
## S3 method for class 'aidsEst' fitted( object, ... )## S3 method for class 'aidsEst' fitted( object, ... )
object |
an object of class |
... |
currently unused. |
The fitted method returns a list
containing following objects:
shares |
a data frame for the fitted expenditure shares. |
quant |
a data frame for the fitted demanded quantities. |
Arne Henningsen
# 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, ] estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86 ) fitted( estResult )# 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, ] estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86 ) fitted( estResult )
This method extracts the log-likelihood value of a fitted Almost Ideal Demand System (AIDS)
## S3 method for class 'aidsEst' logLik( object, ... )## S3 method for class 'aidsEst' logLik( object, ... )
object |
an object of class |
... |
currently ignored. |
A numeric scalar (the log-likelihood value) with 2 attributes:
nobs (total number of observations in all equations) and
df (number of free parameters, i.e. coefficients
+ elements of the residual covariance matrix).
Arne Henningsen
# 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) estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, priceIndex = "SL" ) logLik( estResult )# 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) estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, priceIndex = "SL" ) logLik( estResult )
Testing hypothesis in Almost Ideal Demand Systems by a Likelihood Ratio test.
## S3 method for class 'aidsEst' lrtest( object, ... )## S3 method for class 'aidsEst' lrtest( object, ... )
object |
a fitted model object of class |
... |
further fitted model objects of class |
lrtest.aidsEst consecutively compares
the fitted model object object
with the models passed in ....
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".
Arne Henningsen
aidsEst, lrtest
(package "lmtest"),
logLik.aidsEst
# 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, ] # names of prices and expenditure shares priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" ) shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" ) # estimation with symmetry and homogeneity imposed estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86 ) # estimation with only homogeneity imposed estResultHom <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, sym = FALSE ) # unrestricted estimation estResultUnr <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, sym = FALSE, hom = FALSE ) # LR tests lrtest( estResult, estResultHom, estResultUnr, estResult ) ## Estimation with a demand shifter: linear trend Blanciforti86$trend <- c( 0:( nrow( Blanciforti86 ) - 1 ) ) estResultTrend <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, shifterNames = "trend" ) # LR tests lrtest( estResult, estResultTrend )# Using data published in Blanciforti, Green & King (1986) data( Blanciforti86 ) # Data on food consumption are available only for the first 32 years Blanciforti86 <- Blanciforti86[ 1:32, ] # names of prices and expenditure shares priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" ) shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" ) # estimation with symmetry and homogeneity imposed estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86 ) # estimation with only homogeneity imposed estResultHom <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, sym = FALSE ) # unrestricted estimation estResultUnr <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, sym = FALSE, hom = FALSE ) # LR tests lrtest( estResult, estResultHom, estResultUnr, estResult ) ## Estimation with a demand shifter: linear trend Blanciforti86$trend <- c( 0:( nrow( Blanciforti86 ) - 1 ) ) estResultTrend <- aidsEst( priceNames, shareNames, "xFood", data = Blanciforti86, shifterNames = "trend" ) # LR tests lrtest( estResult, estResultTrend )
These functions summarize and print the estimated elasticities of an Almost Ideal Demand System (AIDS).
## S3 method for class 'aidsElas' summary( object, ... ) ## S3 method for class 'summary.aidsElas' print( x, ... )## S3 method for class 'aidsElas' summary( object, ... ) ## S3 method for class 'summary.aidsElas' print( x, ... )
object |
an object of class |
x |
an object of class |
... |
currently ignored. |
summary.aidsEst returns a list of class summary.aidsElas.
It is identical to the provided object (except for its class),
but it contains following additional element:
table |
a matrix with 4 columns: all elasticities, their standard errors (if available), their t-values (if available), and their P-values (if available). |
Arne Henningsen
# 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) estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, method = "IL" ) summary( elas( estResult ) )# 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) estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, method = "IL" ) summary( elas( estResult ) )
summary.aidsEst summarizes the estimation results
of an Almost Ideal Demand System (AIDS).
## S3 method for class 'aidsEst' summary( object, ... ) ## S3 method for class 'summary.aidsEst' print( x, ... )## S3 method for class 'aidsEst' summary( object, ... ) ## S3 method for class 'summary.aidsEst' print( x, ... )
object |
an object of class |
x |
an object of class |
... |
currently ignored. |
summary.aidsEst returns a list of class summary.aidsEst
that is currently identical to the provided object
(except for its class).
Arne Henningsen
# 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) estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, priceIndex = "SL" ) print( summary( estResult ) )# 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) estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ), c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood", data = Blanciforti86, priceIndex = "SL" ) print( summary( estResult ) )
The USMeatConsump data set contains quarterly retail prices
and consumption quantities for four meat product categories:
beef, pork, chicken, and turkey.
The data period ranges from the first quarter of 1975
to the third quarter of 1999.
Hence, there are 99 observations.
data(USMeatConsump)data(USMeatConsump)
This data frame contains the following columns:
Year.
Quarter of the year.
Time trend.
Population [million].
Consumer price index.
Total per capita expenditure.
Per capita expenditure on meat.
Per capita consumption of beef [pound].
Per capita consumption of pork[pound].
Per capita consumption of chicken [pound].
Per capita consumption of turkey [pound].
Retail price of beef [cents / pound].
Retail price of pork [cents / pound].
Retail price of chicken [cents / pound].
Retail price of turkey [cents / pound].
Expenditure share of beef (in meat).
Expenditure share of pork (in meat).
Expenditure share of chicken (in meat).
Expenditure share of turkey (in meat).
SAS, SAS/ETS Examples: Estimating an Almost Ideal Demand System Model, https://support.sas.com/rnd/app/ets/examples/aids/index.htm.
## replicating the LA-AIDS estimation of the SAS example # loading data set data( USMeatConsump ) # adding shifter variables for modeling seasonal effects USMeatConsump$co1 <- cos( 1 / 2 * 3.14159 * USMeatConsump$t ) USMeatConsump$si1 <- sin( 1 / 2 * 3.14159 * USMeatConsump$t ) # Scaling prices by their means USMeatConsump$beef_pm <- USMeatConsump$beef_p / mean( USMeatConsump$beef_p ) USMeatConsump$pork_pm <- USMeatConsump$pork_p / mean( USMeatConsump$pork_p ) USMeatConsump$chick_pm <- USMeatConsump$chick_p / mean( USMeatConsump$chick_p ) USMeatConsump$turkey_pm <- USMeatConsump$turkey_p / mean( USMeatConsump$turkey_p ) # Estimation of the model meatModel <- aidsEst( c( "beef_pm", "pork_pm", "chick_pm", "turkey_pm" ), c( "beef_w", "pork_w", "chick_w", "turkey_w" ), "meat_exp", shifterNames = c( "co1", "si1", "t" ), priceIndex ="S", data = USMeatConsump, maxiter=1000 ) summary( meatModel )## replicating the LA-AIDS estimation of the SAS example # loading data set data( USMeatConsump ) # adding shifter variables for modeling seasonal effects USMeatConsump$co1 <- cos( 1 / 2 * 3.14159 * USMeatConsump$t ) USMeatConsump$si1 <- sin( 1 / 2 * 3.14159 * USMeatConsump$t ) # Scaling prices by their means USMeatConsump$beef_pm <- USMeatConsump$beef_p / mean( USMeatConsump$beef_p ) USMeatConsump$pork_pm <- USMeatConsump$pork_p / mean( USMeatConsump$pork_p ) USMeatConsump$chick_pm <- USMeatConsump$chick_p / mean( USMeatConsump$chick_p ) USMeatConsump$turkey_pm <- USMeatConsump$turkey_p / mean( USMeatConsump$turkey_p ) # Estimation of the model meatModel <- aidsEst( c( "beef_pm", "pork_pm", "chick_pm", "turkey_pm" ), c( "beef_w", "pork_w", "chick_w", "turkey_w" ), "meat_exp", shifterNames = c( "co1", "si1", "t" ), priceIndex ="S", data = USMeatConsump, maxiter=1000 ) summary( meatModel )
These method returns the covariance matrix of the coefficients from an Almost Ideal Demand System (AIDS).
## S3 method for class 'aidsEst' vcov( object, ... )## S3 method for class 'aidsEst' vcov( object, ... )
object |
an object of class |
... |
currently not used. |
The vcov method for objects of class aidsEst
returns a symmetric matrix: the covariance matrix of the coefficients.
Arne Henningsen