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" ),
      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 ($\alpha_0$).

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 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).} 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.}

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.

aidsEla, 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) 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 ) )

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