aidsEst {micEcon}R Documentation

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 (α_0).
restrict.regMat logical. Method to impose homogeneity and symmetry restrictions: either via restrict.matrix (default) or via restrict.regMat (see systemfit).
x An object of class aidsEst.
... additional arguments of aidsEst are passed to systemfit; additional arguments of print.aidsEst are currently ignored.

Details

Argument method can specify two different estimation methods: The 'Linear Approximate AIDS' (LA) and the 'Iterative Linear Least Squares Estimator' (IL) proposed by Blundell and Robin (1999).
Argument priceIndex can specify six different price indices for the LA-AIDS:

The 'Iterative Linear Least Squares Estimator' (IL) needs starting values for the (translog) price index. Starting values are taken from an initial estimation of the 'Linear Approximate AIDS' (LA) with the price index specified by argument priceIndex.

Value

a list of class aidsEst containing following objects:

coef a list containing the vectors/matrix of the estimated coefficients (alpha, beta, and gamma).
r2 R^2-values of all share equations.
r2q R^2-values of the estimated quantities.
wFitted fitted expenditure shares.
wResid residuals of the expenditure shares.
qObs observed quantities / quantitiy indices.
qFitted fitted quantities / quantitiy indices.
qResid residuals of the estimated quantities.
est estimation result, i.e. the object returned by systemfit.
iter iterations of SUR/3SLS estimation(s). If the AIDS is estimated by the 'Iterated Linear Least Squares Estimator' (ILLE): a vector containing the SUR/3SLS iterations at each iteration.
ILiter number of iterations of the 'Iterated Linear Least Squares Estimation'.
method the method used to estimate the aids (see details).
priceIndex the name of the price index (see details).
lnp log of the price index used for estimation.
pMeans means of the prices.
wMeans means of the expenditure shares.
xtMean mean of total expenditure.
call the call of aidsEst.
priceNames names of the prices.
shareNames names of the expenditure shares.
totExpName name of the variable for total expenditure.
basePrices the base prices of the Paasche, Laspeyres, or Tornqvist price index.
baseShares the base shares of the Laspeyres, simplified Laspeyres, or Tornqvist price index.

Author(s)

Arne Henningsen

References

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

Blundell, R. and J.M. Robin (1999) Estimationin Large and Disaggregated Demand Systems: An Estimator for Conditionally Linear Systems. Journal of Applied Econometrics, 14, p. 209-232.

See Also

summary.aidsEst, aidsElas, aidsCalc.

Examples

   # Using data published in Blanciforti, Green & King (1986)
   data( Blanciforti86 )
   # Data on food consumption are available only for the first 32 years
   Blanciforti86 <- Blanciforti86[ 1:32, ]

   ## Repeating the demand analysis of Blanciforti, Green & King (1986)
   ## Note: Blanciforti, Green & King (1986) use scaled data,
   ##       which leads to slightly different results
   estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
      c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
      data = Blanciforti86, priceIndex = "SL", maxiter = 100 )
   print( estResult )
   elas( estResult )

   ## Estimations with a demand shifter: linear trend
   priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
   shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )
   Blanciforti86$trend <- c( 0:( nrow( Blanciforti86 ) - 1 ) )
   estResult <- aidsEst( priceNames, shareNames, "xFood",
      data = Blanciforti86, shifterNames = "trend" )
   print( estResult )

   # Estimations with two demand shifters: linear + quadratic trend
   Blanciforti86$trend2 <- c( 0:( nrow( Blanciforti86 ) - 1 ) )^2
   estResult <- aidsEst( priceNames, shareNames, "xFood",
      data = Blanciforti86, shifterNames = c( "trend", "trend2" ) )
   print( estResult )

[Package micEcon version 0.5-14 Index]