aidsEst {micEcon}R Documentation

Estimation of the Almost Ideal Demand System (AIDS)

Description

aidsEst does a full demand analysis with the Almost Ideal Demand System (AIDS): econometric estimation, calculation of elasticities, ...

Usage

 aidsEst( pNames, wNames, xtName, data = NULL,
      ivNames = NULL, qNames = wNames,
      method = "LA:L", hom = TRUE, sym = TRUE,
      elaFormula = "Ch", pxBase,
      estMethod = ifelse( is.null( ivNames ), "SUR", "3SLS" ),
      maxiterIL = 50, tolIL = 1e-5, alpha0 = 0, TX = FALSE, ... )

Arguments

pNames a vector of strings containing the names of the prices.
wNames a vector of strings containing the names of the expenditure shares.
xtName a string containing the variable name of total expenditure.
data a data frame containing the data.
ivNames a vector of strings containing the names of instrumental variables.
qNames an optional vector of strings containing the names of the quantities (just to label elasticities).
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?
elaFormula the elasticity formula (see aidsEla).
pxBase The base to calculate the LA-AIDS price indices (see aidsPx).
estMethod estimation method (e.g. 'SUR' or '3SLS', see systemfit).
maxiterIL maximum number of iterations of the 'Iterated Linear Least Squares Estimation'.
tolIL 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).
... arguments passed to systemfit.

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).
    ela a list containing the elasticities (see aidsEla).
    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.
    iterIL 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.

    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

    aidsEla, 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)
       estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
          c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
          data = Blanciforti86, method = "LA:SL", elaFormula = "Ch",
          maxiter = 1, rcovformula = 1, tol = 1e-7 )
       print( estResult )
    
       ## Repeating the evaluation of different elasticity formulas of
       ## Green & Alston (1990)
       pNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
       wNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )
    
       # AIDS
       estResultA <- aidsEst( pNames, wNames, "xFood",
          data = Blanciforti86[ -1, ], maxiter = 1,
          elaFormula = "AIDS", rcovformula=1, tol=1e-7,
          method = "IL:L" )
       print( diag( estResultA$ela$marshall ) )
    
       # LA-AIDS + formula of AIDS
       estResultL1 <- aidsEst( pNames, wNames, "xFood",
          data = Blanciforti86, maxiter = 1, elaFormula = "AIDS",
          rcovformula=1, tol=1e-7, method = "LA:SL" )
       print( diag( estResultL1$ela$marshall ) )
    
       # LA-AIDS + formula of Eales + Unnevehr
       estResultL2 <- aidsEst( pNames, wNames, "xFood",
          data = Blanciforti86, maxiter = 1, elaFormula = "EU",
          rcovformula=1, tol=1e-7, method = "LA:SL" )
       print( diag( estResultL2$ela$marshall ) )
    
       # LA-AIDS + formula of Chalfant:
       estResultL3 <- aidsEst( pNames, wNames, "xFood",
          data = Blanciforti86, maxiter = 1, elaFormula = "Ch",
          rcovformula=1, tol=1e-7, method = "LA:SL" )
       print( diag( estResultL3$ela$marshall ) )
    

    [Package micEcon version 0.2-4 Index]