Package 'micEconAids'

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: 2024-10-15 06:45:00 UTC
Source: CRAN

Help Index


Find 'best' Value for alpha 0 in the AIDS

Description

Search for the intercept of the translog price index (α0\alpha_0) that gives the best fit to the Almost Ideal Demand System (see Michalek and Keyzer, 1992)

Usage

aidsBestA0( priceNames, shareNames, totExpName,
      a0min = -50, a0max = 50, stoprange = 3, stopiter = 10,
      verbose = FALSE, ... )

Arguments

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 α0\alpha_0.

a0max

upper limit of the range for searching for α0\alpha_0.

stoprange

stop searching when the search interval is smaller than or equal to stoprange.

stopiter

maximal number of iterations.

verbose

print each determinant of the residual covariance matrix immediately after its calculation.

...

arguments passed to aidsEst.

Details

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.

Value

a list containing following objects:

alpha0

α0\alpha_0 that gives the best fit.

allValues

all α0\alpha_0 values that have been tested and the determinants of the corresponding residual covariance matrices.

iter

number of iterations.

Author(s)

Arne Henningsen

References

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.

See Also

aidsEst

Examples

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 convex

Shares and Quantities of the Almost Ideal Demand System

Description

Given prices, total expenditure and coefficients this function calculates the demanded quantities and expenditure shares based on the Almost Ideal Demand System.

Usage

aidsCalc( priceNames, totExpName, coef, data, priceIndex = "TL",
   basePrices = NULL, baseShares = NULL, shifterNames = NULL )

## S3 method for class 'aidsEst'
predict( object, newdata = NULL,
   observedShares = FALSE, ... )

Arguments

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 aidsPx) or a numeric vector providing the log values of the price index.

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 aidsEst.

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.

Details

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.

Value

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.

Author(s)

Arne Henningsen

References

Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.

See Also

aidsEst, aidsPx

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" )

   ## 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 )

Concavity of the AIDS

Description

Check whether the expenditure function of the AIDS is concave in prices.

Usage

aidsConcav( priceNames, totExpName, coef, data, shareNames = NULL )

## S3 method for class 'aidsConcav'
print( x, header = TRUE, ... )

Arguments

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 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 )

Check Consistency of the AIDS

Description

Check whether the specification of the AIDS is consistent with microeconomic demand theory (i.e. utility maximisation).

Usage

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, ... )

Arguments

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 aidsPx) or a numeric vector providing the log values of the price index (passed to aidsMono.

basePrices

a vector specifying the base prices for the Paasche, Laspeyres, and Tornqvist price index (passed to aidsMono.

baseShares

a vector specifying the base expenditure shares for the Laspeyres, simplified Laspeyres, and Tornqvist index (passed to aidsMono.

shareNames

a vector of strings containing the names of the expenditure shares (passed to aidsConcav.

x

an object of class aidsConsist.

object

an object of class aidsEst.

observedShares

logical. Using observed shares? (see details).

...

currently not used.

Details

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.

Value

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 aidsMono.

concav

an object returned by aidsMono (only if the symmetry condition is fulfilled and the translog price index is used, i.e. argument priceIndex is "TL".

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

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" )

   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 )

Elasticities of the AIDS model

Description

These functions calculate and print the demand elasticities of an AIDS model.

Usage

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, ... )

Arguments

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 aidsEst.

observedShares

logical. Using observed shares for calculating the demand elasticities?

x

an object of class aidsElas.

...

additional arguments of elas.aidsEst are passed to aidsEla; additional arguments of print.aidsElas are currently ignored.

Details

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.

Value

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 df is provided).

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.

Author(s)

Arne Henningsen

References

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.

See Also

aidsEst

Examples

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 )

Estimating the Almost Ideal Demand System (AIDS)

Description

aidsEst does an econometric estimation of the Almost Ideal Demand System (AIDS)

Usage

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, ... )

Arguments

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 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 (α0\alpha_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

R2R^2-values of all share equations.

r2q

R2R^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.

sMeans

means of shifter variables (only if shifter variables are used).

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 )

Monotonicity of the AIDS

Description

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.

Usage

aidsMono( priceNames, totExpName, coef, data,
   priceIndex = "TL", basePrices = NULL, baseShares = NULL )

## S3 method for class 'aidsMono'
print( x, header = TRUE, ... )

Arguments

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 aidsPx) or a numeric vector providing the log values of the price index.

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 aidsMono.

header

logical. Print a header?

...

currently unused.

Details

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.

Value

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 priceIndex ("numeric" if the price index is specified numerically).

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, aidsCalc

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" )

   ## 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 )

Price Index for the AIDS

Description

Calculate log price indices for the AIDS and LA-AIDS.

Usage

aidsPx( priceIndex, priceNames, data, shareNames = NULL, base = 1, coef = NULL,
      shifterNames = NULL )

Arguments

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.

Details

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.

Value

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.

Author(s)

Arne Henningsen

References

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.

See Also

aidsEst

Examples

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 ) ) )

Indirect Utility Function of the Almost Ideal Demand System

Description

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.

Usage

aidsUtility( priceNames, totExpName, coef, data )

aidsUtilityDeriv( priceNames, totExpName, coef, data, rel = FALSE )

Arguments

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 TRUE the returned partial derivatives are given in relative terms (like elasticities), i.e.\ they indicate the percentage change in the utility level when a price or total expenditure is increased by 1%.

Value

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.

Author(s)

Arne Henningsen

References

Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.

See Also

aidsEst, aidsCalc

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 (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 )

U.S. consumption data

Description

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:

year

The year.

xAggX

Expenditure on the aggregate commodity group X (in Millions of US-Dollars).

xAgg

Total expenditure on all eleven aggregate commodity groups (in Millions of US-Dollars).

xcAggX

Deflated expenditure on the aggregate commodity group X (in Million of 1972 US-Dollars).

xcAgg

Total deflated expenditure on all eleven aggregate commodity groups (in Million of 1972 US-Dollars).

pAggX

Price index for the aggregate commodity group X (1972 = 100).

wAggX

Expenditure share of the aggregate commodity group X.

xFoodX

Per capita expenditure for food group X (in US-Dollars).

xFood

Total per capita expenditure for all four food groups (in US-Dollars).

xcFoodX

Deflated per capita expenditure for food group X (in 1972 US-Dollars).

xcFood

Total deflated per capita expenditure for all four food groups (in 1972 US-Dollars).

pFoodX

Price index for food group X (1972 = 100).

wFoodX

Expenditure share of food group X.

xFoodUsdoc

Expenditure on food published by the US Department of Commerce (USDOC) (in Millions of US-Dollars).

xFoodUsda

Expenditure on food published by the US Department of Agriculture (USDA) (in Millions of US-Dollars).

xFoodNew

Expenditure on food (new estimates) (in Millions of US-Dollars).

xMeatX

Per capita expenditure for meat group X (in US-Dollars).

xMeat

Total per capita expenditure for all four meat groups (in US-Dollars).

pMeatX

Price index for meat group X (1972 = 100).

cMeatX

Per capita consumption of meat group X (in pounds).

pMeat

Price index for the meat group (1972 = 100).

pMeatNew

Price index for the meat group (new estimate) (1972 = 100).

population3

Population as presented in Table 5.A.3 (in Millions).

population12

Population as presented in Table 5.A.12 (in Millions).

Usage

data(Blanciforti86)

Source

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.


Coefficients of an Almost Ideal Demand System

Description

These methods return and print the coefficients from an Almost Ideal Demand System.

Usage

## S3 method for class 'aidsEst'
coef( object, ... )

   ## S3 method for class 'coef.aidsEst'
print( x, ... )

Arguments

object

an object of class aidsEst.

x

an object of class coef.aidsEst.

...

further arguments for methods

Value

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).

Author(s)

Arne Henningsen

See Also

aidsEst


Covariance matrix of an Almost Ideal Demand System

Description

These method returns the covariance matrix of the coefficients from an Almost Ideal Demand System (AIDS).

Usage

## S3 method for class 'aidsEst'
df.residual( object, ... )

Arguments

object

an object of class aidsEst.

...

currently not used.

Value

The df.residual method for objects of class aidsEst returns a symmetric matrix: the covariance matrix of the coefficients.

Author(s)

Arne Henningsen

See Also

aidsEst, coef.aidsEst


Fitted values of an Almost Ideal Demand System

Description

This method extracts the fitted demanded quantities and expenditure shares from an estimated Almost Ideal Demand System.

Usage

## S3 method for class 'aidsEst'
fitted( object, ... )

Arguments

object

an object of class aidsEst.

...

currently unused.

Value

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.

Author(s)

Arne Henningsen

See Also

aidsEst

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, ]

   estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
      c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
      data = Blanciforti86 )
   fitted( estResult )

Log-Likelihood value of an object of class aidsEst

Description

This method extracts the log-likelihood value of a fitted Almost Ideal Demand System (AIDS)

Usage

## S3 method for class 'aidsEst'
logLik( object, ... )

Arguments

object

an object of class aidsEst.

...

currently ignored.

Value

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).

Author(s)

Arne Henningsen

See Also

aidsEst.

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)
   estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
      c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
      data = Blanciforti86, priceIndex = "SL" )
   logLik( estResult )

Likelihood Ratio test for Almost Ideal Demand Systems

Description

Testing hypothesis in Almost Ideal Demand Systems by a Likelihood Ratio test.

Usage

## S3 method for class 'aidsEst'
lrtest( object, ... )

Arguments

object

a fitted model object of class aidsEst.

...

further fitted model objects of class aidsEst.

Details

lrtest.aidsEst consecutively compares the fitted model object object with the models passed in ....

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".

Author(s)

Arne Henningsen

See Also

aidsEst, lrtest (package "lmtest"), logLik.aidsEst

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, ]

   # 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 )

Summarizing the Elasticities of an Almost Ideal Demand System

Description

These functions summarize and print the estimated elasticities of an Almost Ideal Demand System (AIDS).

Usage

## S3 method for class 'aidsElas'
summary( object, ... )

## S3 method for class 'summary.aidsElas'
print( x, ... )

Arguments

object

an object of class aidsElas.

x

an object of class summary.aidsElas.

...

currently ignored.

Value

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).

Author(s)

Arne Henningsen

See Also

aidsElas, aidsEst.

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)
   estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
      c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
      data = Blanciforti86, method = "IL" )
   summary( elas( estResult ) )

Summarizing the Estimation of an Almost Ideal Demand System

Description

summary.aidsEst summarizes the estimation results of an Almost Ideal Demand System (AIDS).

Usage

## S3 method for class 'aidsEst'
summary( object, ... )

## S3 method for class 'summary.aidsEst'
print( x, ... )

Arguments

object

an object of class aidsEst.

x

an object of class summary.aidsEst.

...

currently ignored.

Value

summary.aidsEst returns a list of class summary.aidsEst that is currently identical to the provided object (except for its class).

Author(s)

Arne Henningsen

See Also

aidsEst, aidsElas.

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)
   estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
      c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
      data = Blanciforti86, priceIndex = "SL" )
   print( summary( estResult ) )

U.S. Meat Consumption Data

Description

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.

Usage

data(USMeatConsump)

Format

This data frame contains the following columns:

year

Year.

qtr

Quarter of the year.

t

Time trend.

pop

Population [million].

cpi

Consumer price index.

total_exp

Total per capita expenditure.

meat_exp

Per capita expenditure on meat.

beef_q

Per capita consumption of beef [pound].

pork_q

Per capita consumption of pork[pound].

chick_q

Per capita consumption of chicken [pound].

turkey_q

Per capita consumption of turkey [pound].

beef_p

Retail price of beef [cents / pound].

pork_p

Retail price of pork [cents / pound].

chick_p

Retail price of chicken [cents / pound].

turkey_p

Retail price of turkey [cents / pound].

beef_w

Expenditure share of beef (in meat).

pork_w

Expenditure share of pork (in meat).

chick_w

Expenditure share of chicken (in meat).

turkey_w

Expenditure share of turkey (in meat).

Source

SAS, SAS/ETS Examples: Estimating an Almost Ideal Demand System Model, https://support.sas.com/rnd/app/ets/examples/aids/index.htm.

Examples

## 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 )

Covariance matrix of an Almost Ideal Demand System

Description

These method returns the covariance matrix of the coefficients from an Almost Ideal Demand System (AIDS).

Usage

## S3 method for class 'aidsEst'
vcov( object, ... )

Arguments

object

an object of class aidsEst.

...

currently not used.

Value

The vcov method for objects of class aidsEst returns a symmetric matrix: the covariance matrix of the coefficients.

Author(s)

Arne Henningsen

See Also

aidsEst, coef.aidsEst