Practical Implementation of a CLI

There are a number of problems in practically estimating a CLI from demand system estimation. Firstly it is difficult to include the consumption of non-market goods, such as government provided services, in the utility function, since such data is often not available. Thus the CLI estimated must be considered a sub index of the true CLI that ignores substitution between market and non-market goods. Secondly, the commodity groups used in the demand system estimation limit the degree of substitution that a CLI can record. Since the number of parameters to estimate in a full demand system rises with the square of the number of commodity groups less one, it is difficult to allow for any detailed disaggregation. More product substitution is likely to occur within goods of a similar nature, such as between different types of food than between broad commodity groups such as food and recreation. Thus the estimation of a CLI from broad commodity groups, as in this study, will only pick up the smaller broad level product substitution effects. Finer level substitution between goods within broad commodity groups has not been totally ignored, since the ABS and SC attempt to account for it in their price indices of broad commodities. Thirdly, demographic effects on the CLI are also limited by what can be successfully recovered through demand system estimation. Finally, in practice the construction of

producing their CPI and thus may be prone to lower level substitution bias contained within these price indices.

In this study a PS-QAIDS is estimated for Australian and Canadian households with nine broad expenditure commodities of food, accommodation, household power, clothing and footwear, transport, health, recreation, alcohol and tobacco and miscellaneous, using regional price indices. The model allows for differing price effects on households that vary with respect to their adult equivalent expenditure and household demographics. It has implicitly been assumed that within each broad commodity group, spending behaviour is the same for households with given total expenditure and household demographics. More details on the specification of the demand system and cost of living index are contained in Chapter 6 after a discussion of the data used in the study in Chapter 5.

4.3 Summary of Key Points

The following ‘dot points’ summarise the issues discovered in this chapter in accounting for variations in household size and composition and prices across households. This and the previous chapter conclude the review of past theoretical and empirical approaches to measuring inequality and accounting for differences in household size and composition and prices. Chapter 5, which follows, presents a discussion of the datasets used in this study, their problems and their basic statistics and a brief discussion on the demand system estimation.

Unit of Analysis

• Comprehensive surveys of nations are normally available at a household level

• If all units of the population are considered then the household as the unit of analysis generally results in lower inequality than if smaller family units are considered.

Equivalence Scales

• Equivalence scales are used to deflate household expenditure, for variations in household size and composition to facilitate welfare comparison across different households.

• They are normally defined as the ratio of total expenditure of a household to the reference household when the two households have the same standard of living or utility.

• If household size and composition are the object of control of households then unconditional equivalence scales provide a framework for justifiable welfare comparisons.

• However such unconditional scales require that they be independent of base (IB) utility.

Australian and Canadian Equivalence Scales

• Past evidence suggests that the cost of different demographic structures in different across countries and should be constructed independently.

• Past Australian equivalence scales are reasonably constant across past studies for the same model. However the estimates vary across the different techniques and models.

• Past studies suggest that there are significant differences in the cost of children of different ages.

• Past Canadian evidence suggests that there are economies of scale in caring for children.

Fixed Bundle Price Indices

• Fixed bundle price indices do not consider consumer preferences or substitution between goods.

Consumer Price Indices (CPI)

• CPI are effectively floating bundle price indices in that the weights used to construct the price indices are updated periodically to reflect changes in the average household spending behaviour.

• Criticism has been mounted at the CPI in the ignoring substitution effects and other measurement errors it overstates inflation. Efforts have been made to some of these issues by the relevant statistical authorities.

Cost of Living Indices

• Cost of living indices are specified as the ratio of the households cost functions in two price regimes and provide a theoretical and practical framework for considering substitution, demographic and utility effects of price changes.

Dependence of the CLI on Base Utility

• CLI depend on the base utility level at which the household cost function is evaluated.

• In order to be independent of the base level of utility preferences must be homothetic to the origin and the implied demand functions are

proportional in expenditure.

• Thus CLI should be specified separately for groups with different preferences

Demographics, Equivalence Scales and the CLI

• The demographic CLI is the product of the non-demographic CLI and the ratio of the equivalence scale in the two price regimes.

Practical Implementation of a CLI

• The amount of substitution between goods that can be captured in a CLI is limited by the growth in the parameters required to estimate at a demand system at a detailed commodity level.