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.