Why Does the Engel Method Work? Food Demand, Economies of Size and Household Survey Methods
| DOI | http://doi.org/10.1111/1468-0084.00023 |
| Author | John Gibson |
| Published date | 01 September 2002 |
| Date | 01 September 2002 |
Why Does the Engel Method Work? Food
Demand, Economies of Size and Household
Survey Methods
John Gibson*
Department of Economics, University of Waikato, Private Bag 3105, Hamilton,
New Zealand. E-mail: jkgibson@waikato.ac.nz
I. Introduction
Economists are increasingly aware of the effect that assumptions about
economies of household size have on poverty and inequality comparisons
(Coulter, Cowell and Jenkins, 1992). For example, whether people in Indian
households headed by women are more likely to be poor than are those in
male-headed households depends on the adjustment made for size economies
(Dreze and Srinivasan, 1997). In the transition economies, the rising relative
cost of housing has made size economies more important, shifting the
incidence of poverty toward small households and affecting conclusions about
whether public interventions should be aimed at children or at the elderly
(Lanjouw, Milanovic and Paternostro, 1998).
But despite their importance, there is no generally accepted method of
measuring household size economies. The Engel method is popular because it
is simple, using food budget shares to indicate the welfare of different sized
households (Lancaster, Ray and Valuezuela, 1999).
1
But this method is silent
on how larger households actually achieve economies and it also lacks
theoretical justification. For example, Deaton (1997) constructs two separate
*I am grateful to Ron Bewley, Angus Deaton, Les Oxley,Peter Phillips, Scott Rozelle, Christopher
Scott, Jeffrey Williams, Fred Zimmerman and an anonymous referee for helpful advice. Data for this
research are part of a World Bank poverty assessment for Papua New Guinea, for which financial
support from the governments of Australia (TF-032753), Japan (TF-029460), and New Zealand (TF-
033936) is gratefully acknowledged. All views in this paper are those of the author and should not be
attributed to the World Bank.
1
Anand and Harris (1994) review the empirical performance of various welfare indicators and
conclude that the food share has little merit as an overall welfare indicator.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 64, 4 (2002) 0305-9049
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cost functions that a household of size nfaces to reach utility level uat prices
p,c(u, p, n). The size elasticities, @ln c=@ ln n, of these cost functions differ
but the same food Engel curve is derived from both of them, indicating a lack
of identification. The Engel method also appears contradictory; if there are
size economies, a larger household with the same per capita expenditures as a
smaller household is better-off, and so should have a lower food share. But a
decline in the food share with constant per capita expenditures can occur only
if there is a decline in food spending per person, which is not what is expected
when welfare increases, especially in poor countries (Deaton and Paxson,
1998).
In addition to these theoretical problems, this paper reports evidence on the
empirical fragility of Engel estimates of household size economies. The results
use a survey where a sample of households had each adult report daily
purchases in diaries, while a matched sample had a single respondent give a
verbal recall of the household’s expenditure for the past fortnight.
2
Both of
these methods are widely used by household expenditure surveys in
developed and developing countries. Regression results from the matched
samples, when compared with the results from Monte Carlo experiments,
suggest that recalled food expenditures have measurement errors correlated
with household size. These correlated errors cause a negative bias in the
coefficient on household size in regression models of food budget shares and,
consequently, cause Engel estimates of size economies to be overstated. This
error is shown to affect the cross-sectional pattern of poverty in the sampled
population.
Given these problems with the Engel method, it would be helpful to have
another simple method of estimating household size economies. A promising
approach is based on the effect of public goods within the household (Deaton,
1997). The intuition is that increases in household size (holding outlay per
head constant) allow the resources released by the wider sharing of public
goods (e.g., heat and light) to be spent on both public and private goods. The
effective price of public goods is lower in larger households, so substitution
effects are away from private goods. Hence, there is a positive income effect
and a negative substitution effect on the demand for private goods. But for
private goods like food, the income effect should prevail because the absolute
value of the own-price elasticity is likely to be lower than the income
elasticity, and food demand should rise, especially in poor countries. A
measure of size economies could be calculated from the notional reduction in
outlay needed to prevent the rise in per head spending on food.
2
The respondent was usually the senior female, especially for food expenditures. However, for
certain items like alcohol and tobacco, the senior male usually provided the information. The
principle of asking the respondent best informed to answer questions regarding each type of con-
sumption is widely used by recall surveys.
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