The Estimated Costs of Children in Australian Families in 2005-06 

This appendix provides some further details about the methodology used in this study. The study involved the estimation using OLS and the 1998-99 Household Expenditure Survey data of two key equations – to predict the total consumption of a family and the second to predict household living standards.

Equation (1) had the following form:

C = f (fY, fY2, Age_i…Age_n)     (1)

Where

C = household consumption expenditure

fY = total household weekly income

fY2 = the square of total household weekly income

Age_i = number of persons of age i in household

For the second equation (2) a functional form specified by Betson (1990) was used.

LNPF = g (LEFS, LEFS2, LNF, CKA_i…CKA_n)     (2)

Where

LNPF = the logit of the proportion of household consumption expenditure spent on the selected basic goods

LEFS = the log of per capita consumption

LEFS2 = LEFS squared

LNF = the log of family size

CKA_i = number of persons of age i in household divided by family size

This form is derived from a class of equations which are referred in the literature as Working - Leser (WL) equations (Working, 1943; Leser, 1963). These have the general form of:

w = l (lnC, f, d)     (3)

Where

w = the expenditure share of a particular item (e.g. food)

lnC = the log of total expenditure

f = household size

d = vector of selected demographic variables (eg. number and ages of children, number of adults, etc.)

Equations of this form have been widely used in estimating expenditure-based equivalence scales (see, for example, Carlucci and Zelli 1998; Tran Nam and Whiteford 1990). This form was preferred to that used by Espenshade (1984) as investigation indicated that this form both provided a better fit for data and was better able to differentiate the costs of children of different ages.

Having estimated both equations, the total cost of a child was calculated as follows:

1. Assuming values for husband’s income (hY), spouse’s income (if present) (sY) and Age_i…Age_n, estimate the value of C₁ using equation (1) for a couple family with one child.
2. By substituting this estimated value of C₁ for the couple with one child into equation (2), calculate the predicted value of LNPF.
3. Assuming the same value of LNPF (that is, the same standard of living), substitute this value into equation (2) for a couple without a child and solve for C₂.
4. The difference between the two estimated costs (i.e. C₁ - C₂) is the estimated cost of a child at income level hY + sY.