aidsMono function

Monotonicity of the AIDS

aidsMono checks whether the expenditure function of an estimated Almost Ideal Demand System (AIDS) is monotonic increasing in prices, which implies that all demanded quantities and expenditure shares are non-negative.

aidsMono( priceNames, totExpName, coef, data,
   priceIndex = "TL", basePrices = NULL, baseShares = NULL )

## S3 method for class 'aidsMono'
print( x, header = TRUE, ... )

Arguments

• priceNames: a vector of strings containing the names of the prices.
• totExpName: a string containing the variable name of total expenditure.
• coef: a list containing the coefficients alpha, beta, gamma, and (only for the translog price index) alpha0.
• data: a data frame containing the data.
• priceIndex: a character string specifying the price index (see aidsPx) or a numeric vector providing the log values of the price index.
• basePrices: a vector specifying the base prices for the Paasche, Laspeyres, and Tornqvist price index.
• baseShares: a vector specifying the base expenditure shares for the Laspeyres, simplified Laspeyres, and Tornqvist index.
• x: an object of class aidsMono.
• header: logical. Print a header?
• ...: currently unused.

Details

Internally, aidsMono passes its arguments to aidsCalc

and then checks for each observation, wether all expenditure shares are non-negative.

If argument priceIndex specifies a price index of the LA-AIDS, 'fitted' values are used for current and lagged expenditure shares in these price indices (see aidsCalc). However, if argument priceIndex is a numeric vector containing the log values of a price index (e.g.\ the price index used in the estimation), this price index is used for the calculations.

Returns

aidsMono returns a list of class aidsMono

that contains following elements: - monotony: a logical vector indicating whether the monotony condition is fulfilled at each observation.

• nValidObs: number of (valid) observation at which monotonicity could be checked.

• nMonoObs: number of observation at which the monotonicity codition is fulfilled.

• monoPercent: percent of observations where the monotony condition is fulfilled.

• priceIndex: a chacter string indicating the price index specified by argument priceIndex

  ("numeric" if the price index is specified numerically).

References

Deaton, A.S. and J. Muellbauer (1980a) An Almost Ideal Demand System. American Economic Review, 70, p. 312-326.

Deaton, A.S. and J. Muellbauer (1980b) Economics and Consumer Behavior, Cambridge University Press, Cambridge.

Author(s)

Arne Henningsen

See Also

aidsEst, aidsCalc

Examples

data( Blanciforti86 )
   # Data on food consumption are available only for the first 32 years
   Blanciforti86 <- Blanciforti86[ 1:32, ]

   priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
   shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )

   ## AIDS
   estResult <- aidsEst( priceNames, shareNames, "xFood",
      data = Blanciforti86, method = "IL" )
   aidsMono( priceNames, "xFood", coef = coef( estResult ),
      data = Blanciforti86 )

   ## LA-AIDS with Tornqvist price index
   estResultLaT <- aidsEst( priceNames, shareNames, "xFood",
      data = Blanciforti86, priceIndex = "T" )
   # with fitted expenditure shares in the price index
   aidsMono( priceNames, "xFood", coef = coef( estResultLaT ),
      data = Blanciforti86, priceIndex = "T",
      basePrices = estResultLaT$basePrices,
      baseShares = estResultLaT$baseShares )
   # with observed expenditure shares in the price index
   aidsMono( priceNames, "xFood", coef = coef( estResultLaT ),
      data = Blanciforti86, priceIndex = estResultLaT$lnp )