aidsEst: 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 = NULL,
      instNames = NULL, shifterNames = NULL,
      method = "LA:L", hom = TRUE, sym = TRUE, pxBase,
      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 the data.

instNames

a vector of strings containing the names of instrumental variables.

shifterNames

an optional vector of strings containing the names of the demand shifters.

method

the method to estimate the AIDS (see details).

hom

logical. Should the homogeneity condition be imposed?

sym

logical. Should the symmetry condition be imposed?

pxBase

The base to calculate the LA-AIDS price indices (see aidsPx).

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 ($\alpha_0$).

restrict.regMat

logical. Method to impose homogeneity and symmetry restrictions: either via restrict.matrix (default) or via restrict.regMat (see systemfit).

An object of class aidsEst.

...

additional arguments of aidsEst are passed to systemfit; additional arguments of print.aidsEst are currently ignored.

Details

At the moment two basic estimation methods are available: The 'Linear Approximate AIDS' (LA) and the 'Iterative Linear Least Squares Estimator' (IL) proposed by Blundell and Robin (1999). The LA-AIDS can be estimated with itemize Stone price index ('LA:S'), Stone price index with lagged shares ('LA:SL'), loglinear analogue to the Paasche price index ('LA:P'), loglinear analogue of the Laspeyres price index ('LA:L'), and Tornqvist price index ('LA:T'). itemize

The 'Iterative Linear Least Squares Estimator' (IL) needs starting values for the (translog) price index. The price index used to calculate the initial price index can be specified in the same way as for the LA-AIDS (e.g. 'IL:L')

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).} px{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.} call{the call of aidsEst.} priceNames{names of the prices.} shareNames{names of the expenditure shares.} totExpName{name of the variable for total expenditure.}

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.

[object Object]

# 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, method = "LA: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 )

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