The 1995/1996 Household Income, Expenditure - (PDF, 101 mb ...

11.15
involves the difficulty in defining the extent of investment (saving) inherent
in many "consumed" goods. For example, in some sense the purchase of
schoolbooks is consumption, but it is partly investment as well, as indirect
learning will eventually (it is hoped!) generate income. Housing purchases are
another example: it is difficult to separate the investment aspects of the
purchase of a house from its consumption (use and depreciation) aspects. So
the estimation of savings rates often hinges on categorization of goods as
either consumption or savings goods, when in truth many commodities retain
continuous properties of both.
A better relationship, therefore, focusses on the residuals of the
consumption function. With consumption on the left hand side, and
expenditure on the right hand side, parameter estimates for the regions
appear in Table II.13. Here 92.0568 piasters of every Egyptian pound of
expenditures is consumed. The unexplained variation in consumption (less
than 3%) goes to transfers and premiums. To refine this equation for a better
savings estimate one would subtract from the left hand side those goods (or
components of goods) which clearly are investments. Heteroskedasticity
appears to be a feature of the model; the residuals vary with the magnitude
of the total expenditures, the means turning positive somewhere above 6000
£E, and the variances growing ever larger:
Evidence of Heteroskedasticity in the Crude Consumption/Expenditure Function
Expenditure Group Number of Std Dev of the
Observations Residuals
o - 1500 £E 304 51.761
1501 - 2000 £E 393 63.614
2001 - 2500 £E 478 80.361
2501 - 3500 £E 1563 87.289
3501 - 4500 £E 2059 139.390
4501 - 6000 £E 3361 133.156
6001 - 8000 £E 3041 237.981
8001 + £E 3606 1500.35
The F Statistic computed for the Goldfeld-Quandt test produces a value of
204.19 with {14805 - 4935 - 2 (9)}/2 degrees of freedom for both the numerator
and the denominator, indicating easy rejection of the null of homoskedasticity.
Although the least squares model still produces unbiased coefficients, the
model is not efficient in the sense that it will have a higher variance than a
maximum likelihood estimator, regardless of the sample size.
ILL Back to the Engel Relationship
This chapter concludes by returning to the Engel relationship, to place
some empirical bounds around the expenditure level/food share relationship.
It will be extended to group expenditures below using Pearson correlation