micEcon (version 0.1-3)

aidsEst: 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" ),
      maxiterMk = 50, tolMk = 1e-5, alpha0 = 0, ... )

Arguments

pNames

a vector of strings containing the names of prices.

wNames

a vector of strings containing the names of expenditure shares.

xtName

a name of the total expenditure variable.

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

should the homogeneity condition be imposed?

sym

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", see systemfit).

maxiterMk

maximum number of iterations of the Michalek and Keyzer estimation

tolMk

tolerance level of the Michalek and Keyzer iteration

alpha0

the intercept of the translog price index ($\alpha_0$)

...

argunents passed to systemfit

Value

• a list of class aidsEst containing following objects:
• coef
  a list containing the vectors/matrix of the estimated coefficients (alpha = $\alpha_i$, beta = $\beta_i$, gamma = $\gamma_{ij}$.
• ela
  a list containing the elasticities (see aidsEla).
• r2
  $R^2$-values of all budget share equations.
• r2q
  $R^2$-values of the estimated quantities.
• wFitted
  fitted budget shares.
• wResid
  residuals of the budget shares.
• qObs
  observed quantities / quantitiy indices.
• qFitted
  fitted quantities / quantitiy indices.
• qResid
  residuals of the estimated quantities.
• iter
  iterations of SUR/3SLS estimation a vector containing the iterations of each iteration of the Michalek and Keyzer estimation.
• iterMk
  iterations of the Michalek and Keyzer estimation.
• method
  the method used to estimate the aids (see details).
• lnp
  log of the price index used for estimation.
• hom
  was the homogeneity condition imposed?
• sym
  was the symmetry condition imposed?
• estMethod
  estimation method (see systemfit).
• rcovformula
  formula used to calculate the estimated residual covariance matrix (see systemfit).

Details

At the moment two basic estimation methods are available: The 'Linear Approximate AIDS' (LA) and the iterative estimation method of Michalek and Keyzer (MK). The LA-AIDS can be estimated with * 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').

The iterative estimation method of Michalek and Keyzer needs starting values for the (translog) price index. Which price index is used to calculate the initial price index can be specified in the same way as for the LA-AIDS (e.g. 'MK:L')

References

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

aidsEla, aidsCalc.

Examples

## Repeating the demand analysis of Blanciforti, Green & King (1986)
   data( Blanciforti86 )
   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)
   data( Blanciforti86 )
   pNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
   wNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )

   # AIDS
   estResultA <- aidsEst( pNames, wNames, "xFood",
    data = Blanciforti86[ 2:nrow( Blanciforti86 ), ], maxiter = 1,
      elaFormula = "AIDS", rcovformula=1, tol=1e-7,
   method = "MK: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 ) )