aidsConcav function

Concavity of the AIDS

Check whether the expenditure function of the AIDS is concave in prices.

aidsConcav( priceNames, totExpName, coef, data, shareNames = NULL )

## S3 method for class 'aidsConcav'
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.
• shareNames: a vector of strings containing the names of the expenditure shares.
• x: an object of class aidsConcav.
• header: logical. Print a header?
• ...: currently unused.

Details

If argument shareNames is specified, observed shares are used for the calculation of the 'C' matrices to check for concavity; if argument shareNames is NULL (e.g., not specified), fitted shares are used for the calculation of the 'C' matrices.

Please note that checking concavity of the expenditure function requires that the expenditure function of the model exists. Therefore, the concavity condition can be checked, only if the symmetry condition is fulfilled and the translog price index is used.

Returns

aidsConcav returns a list of class aidsConcav

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

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

• nConcavObs: number of observation at which the concavity codition is fulfilled.

• concavPercent: percent of observations where the concavity condition is fulfilled.

• cMatrices: a list of the 'C' matrices for each observation to check for concavity (see Deaton and Muellbauer, 1980b, p.76 ).

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, aidsElas

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

   # check concavity with fitted shares
   aidsConcav( priceNames, "xFood", coef = estResult$coef,
      data = Blanciforti86 )

   # check concavity with observed shares
   aidsConcav( priceNames, "xFood", coef = estResult$coef,
      data = Blanciforti86, shareNames = shareNames )