aidsBestA0 function

Find 'best' Value for alpha 0 in the AIDS

Search for the intercept of the translog price index ($\alpha_0$) that gives the best fit to the Almost Ideal Demand System (see Michalek and Keyzer, 1992)

aidsBestA0( priceNames, shareNames, totExpName,
      a0min = -50, a0max = 50, stoprange = 3, stopiter = 10,
      verbose = FALSE, ... )

Arguments

• 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.
• a0min: lower limit of the range for searching for $\alpha_0$.
• a0max: upper limit of the range for searching for $\alpha_0$.
• stoprange: stop searching when the search interval is smaller than or equal to stoprange.
• stopiter: maximal number of iterations.
• verbose: print each determinant of the residual covariance matrix immediately after its calculation.
• ...: arguments passed to aidsEst.

Details

The demand system is estimated using the Iterative Linear Least Squares Estimator (ILLE) suggested by Blundell and Robin (1999). This iterative procedure is equivalent to the method proposed by Michalek and Keyzer (1992). However, the latter do not correct the coefficient covariance matrix.

The fit of the model is measured in terms of the likelihood value. Since the determinant of the residual covariance matrix is monotonically decreasing with the likelihood value, we search for the smallest determinant of the residual covariance matrix.

Since each call of aidsEst generally takes a long time, the search algorithm is constructed to minimize the calls of the function aidsEst.

Returns

a list containing following objects: - alpha0: $\alpha_0$ that gives the best fit.

• allValues: all $\alpha_0$ values that have been tested and the determinants of the corresponding residual covariance matrices.

• iter: number of iterations.

References

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.

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

Michalek, J. and M. A. Keyzer (1992) Estimation of a two-stage LES-AIDS consumer demand system for eight EC countries. European Review of Agricultural Economics, 19 (2), p. 137-163.

Author(s)

Arne Henningsen

See Also

aidsEst

Examples

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

   bestA0 <- aidsBestA0( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
      c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
      data = Blanciforti86, useMatrix = FALSE )
   # may take some time (argument 'useMatrix = FALSE' decreases
   # the computation time only if the model and data set are small)
   print( bestA0$alpha0 )
   plot( bestA0$allValues ) # this should be convex