aidsEst: Estimating the Almost Ideal Demand System (AIDS)
In micEconAids: Demand Analysis with the Almost Ideal Demand System (AIDS)

Description Usage Arguments Details Value Author(s) References See Also Examples

aidsEst does an econometric estimation of the Almost Ideal Demand System (AIDS)

aidsEst( priceNames, shareNames, totExpName, data,
      method = "LA", priceIndex = "Ls", pxBase = 1,
      hom = TRUE, sym = TRUE,
      shifterNames = NULL, instNames = NULL,
      estMethod = ifelse( is.null( instNames ), "SUR", "3SLS" ),
      ILmaxiter = 50, ILtol = 1e-5, alpha0 = 0, restrict.regMat = FALSE, ... )

## S3 method for class 'aidsEst'
print( x, ... )

`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 all required variables.
`method`	character string specifying the method to estimate the AIDS: either 'LA' or 'IL' (see deatils).
`priceIndex`	character string specifying the price index for the 'Linear Approximation': either 'S', 'SL', 'P', 'L', 'Ls', or 'T' (see details).
`pxBase`	The base to calculate the LA-AIDS price indices (see `aidsPx`).
`hom`	logical. Should the homogeneity condition be imposed?
`sym`	logical. Should the symmetry condition be imposed?
`shifterNames`	an optional vector of strings containing the names of the demand shifters.
`instNames`	a vector of strings containing the names of instrumental variables.
`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).
`restrict.regMat`	logical. Method to impose homogeneity and symmetry restrictions: either via restrict.matrix (default) or via restrict.regMat (see `systemfit`).
`x`	An object of class `aidsEst`.
`...`	additional arguments of `aidsEst` are passed to `systemfit`; additional arguments of `print.aidsEst` are currently ignored.

Argument method can specify two different estimation methods: The 'Linear Approximate AIDS' (LA) and the 'Iterative Linear Least Squares Estimator' (IL) proposed by Blundell and Robin (1999).
Argument priceIndex can specify six different price indices for the LA-AIDS:

Stone price index ('S'),
Stone price index with lagged shares ('SL'),
loglinear analogue to the Paasche price index ('P'),
loglinear analogue of the Laspeyres price index ('L'),
simplified loglinear analogue of the Laspeyres price index ('Ls'), and
Tornqvist price index ('T').

The 'Iterative Linear Least Squares Estimator' (IL) needs starting values for the (translog) price index. Starting values are taken from an initial estimation of the 'Linear Approximate AIDS' (LA) with the price index specified by argument priceIndex.

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).
`priceIndex`	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.
`xtMean`	mean of total expenditure.
`call`	the call of `aidsEst`.
`priceNames`	names of the prices.
`shareNames`	names of the expenditure shares.
`totExpName`	name of the variable for total expenditure.
`basePrices`	the base prices of the Paasche, Laspeyres, or Tornqvist price index.
`baseShares`	the base shares of the Laspeyres, simplified Laspeyres, or Tornqvist price index.

Arne Henningsen

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.

   # 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, priceIndex = "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 )

Loading required package: lmtest
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

Loading required package: micEcon

If you have questions, suggestions, or comments regarding one of the 'micEcon' packages, please use a forum or 'tracker' at micEcon's R-Forge site:
https://r-forge.r-project.org/projects/micecon/

Demand analysis with the Almost Ideal Demand System (AIDS)
Estimation Method: Linear Approximation (LA) with lagged Stone Index (SL)
Coefficients:
alpha
    wFood1     wFood2     wFood3     wFood4 
-0.2545522  0.1104474  0.2593077  0.8847972 
beta
     wFood1      wFood2      wFood3      wFood4 
 0.32868512  0.05562033 -0.07367372 -0.31063173 
gamma
            pFood1       pFood2        pFood3        pFood4
wFood1  0.11076015 -0.138877911 -0.0111913071  0.0393090730
wFood2 -0.13887791  0.159838976 -0.0054339530 -0.0155271120
wFood3 -0.01119131 -0.005433953  0.0157126674  0.0009125927
wFood4  0.03930907 -0.015527112  0.0009125927 -0.0246945536

Demand Elasticities (formulas of Goddard / Chalfant for Stone price index)
Expenditure Elasticities
 q_wFood1  q_wFood2  q_wFood3  q_wFood4 
2.0493874 1.2734653 0.4479842 0.1123031 

Marshallian (uncompensated) Price Elasticities
              pFood1      pFood2      pFood3     pFood4
q_wFood1 -0.97506309 -0.65682890 -0.17578474 -0.2417107
q_wFood2 -0.76846684 -0.26974917 -0.06321432 -0.1720350
q_wFood3  0.08904707  0.07155991 -0.80859582  0.2000047
q_wFood4  0.39037517  0.13617734  0.12108267 -0.7599383

Hicksian (compensated) Price Elasticities
             pFood1      pFood2      pFood3     pFood4
q_wFood1 -0.3331618 -0.24000233  0.09773276  0.4754314
q_wFood2 -0.3695969 -0.01073803  0.10674625  0.2735887
q_wFood3  0.2293630  0.16267578 -0.74880648  0.3567677
q_wFood4  0.4255503  0.15901876  0.13607098 -0.7206401

Demand analysis with the Almost Ideal Demand System (AIDS)
Estimation Method: Linear Approximation (LA) with simplified Laspeyres Index (Ls)
Coefficients:
alpha
    wFood1     wFood2     wFood3     wFood4 
0.28073055 0.43866687 0.20163828 0.07896429 
beta
       wFood1        wFood2        wFood3        wFood4 
-0.0007791322 -0.1473429310 -0.0381697454  0.1862918086 
gamma
           pFood1       pFood2       pFood3      pFood4
wFood1  0.1493078 -0.113296453 -0.019590398 -0.01642090
wFood2 -0.1132965  0.169089960 -0.009388282 -0.04640522
wFood3 -0.0195904 -0.009388282  0.018445085  0.01053360
wFood4 -0.0164209 -0.046405224  0.010533596  0.05229253
delta
               trend
wFood1  0.0018731550
wFood2  0.0011744250
wFood3 -0.0002280388
wFood4 -0.0028195412

Demand analysis with the Almost Ideal Demand System (AIDS)
Estimation Method: Linear Approximation (LA) with simplified Laspeyres Index (Ls)
Coefficients:
alpha
   wFood1    wFood2    wFood3    wFood4 
0.3207103 0.3433149 0.1931900 0.1427848 
beta
     wFood1      wFood2      wFood3      wFood4 
-0.02082632 -0.09951136 -0.02998234  0.15032002 
gamma
            pFood1       pFood2      pFood3       pFood4
wFood1  0.13429216 -0.080439220 -0.02637782 -0.027475119
wFood2 -0.08043922  0.102444103 -0.02101332 -0.000991559
wFood3 -0.02637782 -0.021013324  0.05850485 -0.011113704
wFood4 -0.02747512 -0.000991559 -0.01111370  0.039580382
delta
              trend        trend2
wFood1  0.001032483  2.603329e-05
wFood2  0.003262571 -6.388237e-05
wFood3 -0.001252129  2.865015e-05
wFood4 -0.003042926  9.198927e-06