Estimating PIGLOG Demands Using Representative versus Average Expenditure

Economists often use aggregate time series data to estimate consumer demand functions. Some of the popular applied demand systems have a PIGLOG form. In the most general PIGLOG cases the “average” demand for a good is a function of the representative consumer expenditure not the average consumer expenditure. We would need detailed information on each period’s expenditure distribution to calculate the representative expenditure. This information is generally unavailable, so average expenditures are invariably used. Since we are estimating these demand systems using the wrong expenditure terms, our estimates may be wrong. There are special cases where the average expenditure is a perfect proxy for the representative expenditure. We do an indirect test of this case by estimating a demand system using quarterly U.S. data on three categories of consumer expenditure. To the usual price and expenditure effects we added variables that may be associated with shifts in the distribution of expenditure.