Applications of Semiparametric
Modeling Methods
ECON 721
Economies of Scale, Household Size and the
Demand for Food
• Deaton and Paxon (JPE, 1998)
• Question – do scale economies make larger household
better off at the same level of per capita resources?
• Larger households have more to spend on private
goods, because of savings on public goods. There will
be an income and a substitution effect in the opposite
direction, but expenditure on private good (food) should
increase if income effect dominates.
• Examine whether larger households spend less per
capita on food consumption
• Find that empirical evidence is contrary to theoretical
predictions – expenditure per capita on food falls with
size of household
• Examine data from the United States,
Britain, France, Taiwan, Thailand,
Pakistan and South Africa and find similar
results
Nonparametric approach
• Examine per capita expenditure on food
for household types with constant PCE,
i.e. test inequality for different household
types i and j:
• Equation (8) is equivalent to the following,
where wf is the budget share of food:
• Nonparametrically regress the food share
on log PCE (x/n) using Fan’s (1992) LLR
• Use quartic kernel function, bootstrap
standard errors
• Figure 2 – Thailand
• Food share declines with PCE
• At a constant PCE, food share declines
with household size (unexpected result)
• Because there is some crossing of the
lines, compute weighted averages. Need
to use constant weights, because different
households have different distributions of
PCE:
Comparing two types of households with
constant weighting:
• France is exception – food share there
does not fall with household size
• Need to also account for differences
across households in other factors that
may affect food expenditures and are
correlated with household size.
Semiparametric model
• Fourth term describes the household
composition in terms of age and sex
• v includes fraction of adults who work (workers
may eat more at restaurants and have different
caloric requirements), whether household
received food stamps or public housing.
• Find a decline in the coefficient on
household size as move from richer to
poorer countries
Some plausible explanations for
results:
• Direct economies of scale in food consumption
(larger households buy in bulk)
• Economies of scale in food preparation
• Larger households waste less.
• Collective models – households with different
compositions have different tastes for food.
Household Gasoline Demand in the
United States
• Schmalensee and Stoker (Econometrica,
1999)
• In 1991, average household spent $1,161
for motor vehicle fuel, which accounted for
about one third of US petroleum
consumption.
Questions of interest
• Do high income households display same
income elasticity as other households?
• Study data from the Residential
Transportion Energy Consumption Survey
(RTECS)
• Estimate Engel demand curves
• Compute local average estimates of the
gasoline regression surface and present
them graphically.
• LDRVRS = Log drivers
• LY = log income, LAGE = log age (both
continuous)
• Leads to partially linear model:
• Use Robison (1988) estimator, trimming
out 5% of the sample with the lowest
density.
• Table I – coefficient estimates
• Figure 1: Plots of G(x)
• Based on figures, choose a piecewise
linear function, permitting different
elasticities above and below $12,000 and
above and below age 50:
• Find that increase in the number of
licensed drivers can account in large part
for the increase in the demand for gasoline
over the last decades, and is more
important than income in explaining the
changing demand.
• Find big difference between OLS and
average derivative estimates
• Seemingly bimodal demand is result of
different grades of gasoline.
• Could not take this into account because
of some data limitations.