aidsUtility function

Indirect Utility Function of the Almost Ideal Demand System

These functions calculate the utility level given prices and total expenditure using the indirect utility function of the Almost Ideal Demand System and the partial derivatives of this indirect utility function with repect to prices and total expenditure.

aidsUtility( priceNames, totExpName, coef, data )

aidsUtilityDeriv( priceNames, totExpName, coef, data, rel = FALSE )

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 in elements alpha0 (scalar), alpha (vector), beta (vector), gamma (matrix), and possibly beta0 (scalar, if not given, it is assumed to be 1).
• data: a data frame containing the data.
• rel: logical. If TRUE the returned partial derivatives are given in relative terms (like elasticities), i.e.\ they indicate the percentage change in the utility level when a price or total expenditure is increased by 1%.

Returns

aidsUtility returns a numeric vector that contains the utility levels; aidsUtilityDeriv returns a data.frame that contains the partial derivatives of the indirect utility function with repect to prices and total expenditure.

References

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

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" )

   ## estimate the (non-linear) AIDS
   estResult <- aidsEst( priceNames, shareNames, "xFood",
      data = Blanciforti86, method = "IL" )

   # calculate the utility levels of each year
   utility <- aidsUtility( priceNames, "xFood", coef = coef( estResult ),
      data = Blanciforti86 )

   utilityDeriv <- aidsUtilityDeriv( priceNames, "xFood",
      coef = coef( estResult ), data = Blanciforti86 )

   utilityEla <- aidsUtilityDeriv( priceNames, "xFood",
      coef = coef( estResult ), data = Blanciforti86, rel = TRUE )