In addition to using QR methodology to allow for individual heterogeneity, we
also make use of the fact that decisions about consumption of individual commodities are
not made in isolation from decisions about consumption of other commodities. The
individual’s preference structure will be reflected in their consumption decisions about all
of the commodities in the consumption basket, not just consumption of the commodity
whose demand function is being estimated. In standard textbook discussions of
consumption theory, this is reflected in the fact that the demand function for a single
commodity is written as a function of the prices of the entire set of consumption
commodities. In empirical applications, we tend to simplify by replacing the vector of
prices of other commodities by a single price index, with the CPI or some other shareweighted
price index. There is, however a body of empirical work (Pollack and Wales,
1992) which uses information on the entire vector of an individual’s purchases (or at least
a significant subset, invoking multi-stage budgeting arguments) to determine the form of
her consumption preferences. In the expenditure share literature, Seemingly Unrelated
Regression techniques are used to estimate an interrelated system of equations where the
share of the consumer’s expenditure which is allocated to each good is estimated as a
function of the prices all of the commodities in the budget set. System estimation
methods have been applied to addictive commodities such as alcohol and tobacco, and
Pollack and Wales discuss variants of the demand system approach which allow for habit
formation, although not for the forward looking element of the RA model.
The basic structure, then, is a Becker-Murphy RA model augmented with
variables characterizing the individuals’ health status, their educational attainment, their
family circumstances, their age, whether they face workplace restrictions on smoking,
whether anyone in their household smokes in the house, their income, their education
level and their choices with regard to purchases of fruits and vegetables.