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 = 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, TX = 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 (α_0).
TX logical. Method to impose homogeneity and symmetry restrictions: either via R.restr (default) or via TX (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

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 begin{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'). end{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')

    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.
    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).
    lnp log of the price index used for estimation.
    hom logical. Was the homogeneity condition imposed?
    sym logical. Was the symmetry condition imposed?
    estMethod estimation method (see systemfit).
    rcovformula formula used to calculate the estimated residual covariance matrix (see systemfit).
    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.

    Author(s)

    Arne Henningsen ahenningsen@agric-econ.uni-kiel.de

    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, 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 )
    

    [Package micEcon version 0.3-8 Index]