October 2016 THE INCOME AND PRICE SENSITIVITY OF DIETS GLOBALLY by Haiyan Liu* UWA Business School The University of Western Australia Abstract This paper analyses detailed consumption patterns of food items in a large number of countries with a three-stage budgeting approach. Under the assumption of separable preferences, the first stage separates total consumption into food and non-food; the second splits food into the major food groups; and the third stage allocates consumption to the elementary goods within each food group. The model is implemented for the second two stages with 25 food items divided into 6 groups: staples, meats, dairy, fruit and vegetables, sweet things and other food. For each group, there is a system of conditional demand equations (with one equation for each elementary good), which depend on expenditure and prices within the group. The six systems are estimated with unpublished International Comparison Program data for more than 100 countries. These estimates are then combined with estimates of the group demand equations, which depend on total food consumption and prices indexes of the six groups, to give the overall income and price responses, conditional upon total food. * This research is supported by an Australian Postgraduate Award at UWA. I would like to thank Professor Ken Clements and Associate Professor Yihui Lan for excellent supervision. My thanks also go to the World Bank who provided the data and Grace Taylor who gave the helpful comments. All errors and omissions are mine.
Transcript
October 2016
THE INCOME AND PRICE SENSITIVITY
OF DIETS GLOBALLY
by
Haiyan Liu*
UWA Business School
The University of Western Australia
Abstract
This paper analyses detailed consumption patterns of food items in a large number of
countries with a three-stage budgeting approach. Under the assumption of separable
preferences, the first stage separates total consumption into food and non-food; the second
splits food into the major food groups; and the third stage allocates consumption to the
elementary goods within each food group. The model is implemented for the second two
stages with 25 food items divided into 6 groups: staples, meats, dairy, fruit and vegetables,
sweet things and other food. For each group, there is a system of conditional demand
equations (with one equation for each elementary good), which depend on expenditure and
prices within the group. The six systems are estimated with unpublished International
Comparison Program data for more than 100 countries. These estimates are then combined
with estimates of the group demand equations, which depend on total food consumption and
prices indexes of the six groups, to give the overall income and price responses, conditional
upon total food.
* This research is supported by an Australian Postgraduate Award at UWA. I would like to
thank Professor Ken Clements and Associate Professor Yihui Lan for excellent supervision.
My thanks also go to the World Bank who provided the data and Grace Taylor who gave the
helpful comments. All errors and omissions are mine.
2. THE DATA ......................................................................................................................................... 2
3. SPECIALISATION AND DIVERSIFICATION IN CONSUMPTION ............................................ 4
4. DEMAND EQUATIONS IN CHANGES AND LEVELS ................................................................. 6
5. DEMAND WITHIN FOOD GROUPS ............................................................................................... 9
5.1 The Estimates ................................................................................................................................ 9
Table 5.2 Homogeneity and Symmetry Tests .................................................................................... 26
Table 5.3 Homogeneity- and Symmetry-Restricted Estimates .......................................................... 27
Table 5.4 Normality Tests of Residuals ............................................................................................. 28
Table 5.5 Own-Price and Income Elasticities of Demand within Groups ......................................... 29
Table 6.1 Estimates of Group Demand Equations for Food .............................................................. 30
Table 6.2 Elasticities of Demand for Food Groups............................................................................ 31
Table 6.3 Comparison of Income Elasticities .................................................................................... 31
Table 7.1 Own-Price and Income Elasticities of Unconditional Demand .......................................... 32
LIST OF FIGURES
Figure 1.1 A Three-Stage Budgeting System ..................................................................................... 33
Figure 3.1 Quantity-Price Scatter Plots for Food Items ...................................................................... 34
Figure 6.1 Quantity-Prices Plots for Food Groups.............................................................................. 36
Figure 7.1 Stylised Matrix of Price Elasticities, Direct and Indirect Effects Combined .................... 37
Figure 7.2 Own-Price Elasticities: Unconditional versus Conditional................................................ 39
Figure 7.3 Average Unconditional Price Elasticities .......................................................................... 40
ii
PREFACE
Thesis title: Cross-Country Food Consumption Patterns: Theory and Measurement
Supervisors: Professor Ken Clements, Economics Discipline, UWA
Associate Professor Yihui Lan, Accounting and Finance Discipline, UWA
Food consumption is necessary to sustain life and a primary indicator of consumers’
wellbeing. Due to the heterogeneity of consumers, huge disparities exist in food consumption
across countries. Taking the US and the African country of Guinea as an example, where
GDP of the former is roughly 40 times that of the latter, the food share increases from less
than 10 percent to over one half. This is in agreement with Engel’s law, arguably one of the
most important and convincing laws of economics. However, there are still substantial
international differences in the consumption of more detailed food items -- just think of how
rice and bread consumption, for example, differs across countries. Are these differences due
to custom, culture and climate, or economic factors such as incomes and prices? My thesis
analyses this issue with considerable commodity disaggregation of food.
I use unpublished data from the International Comparison Program that cover the
consumption of 25 items of food in 140 countries. These data contain substantial differences
in incomes and prices across countries, which is both an attraction and challenge. I employ a
three-stage budgeting system that deals with the allocation of consumption expenditure
between (i) food and non-food, (ii) the major food groups and (iii) the food items within each
group. This is a tractable approach to obtaining the 25×25 matrix of own- and cross-price
elasticities.
I estimate a “levels version” of a differential demand model for each of the six groups
in a form of a conditional demand system; and then one additional system at the group level.
This leads to the direct and indirect effects on consumption of changes in incomes and prices,
which are combined to give the total effects. The results show that in most cases, the total
income effect is close to the indirect effect from group demand, while the total price effect is
dominated by the direct effect from conditional demand.
The thesis will take the following structure:
Chapter I: Introduction
Chapter II: The International Demand for Alcohol
Chapter III: The Demand for 25 Food Items
Chapter IV: Multi-Stage Consumption Theory with Application to Food
Chapter V: Conclusions
This paper contains material on the conditional demand for detailed food items from Chapter
III; and part of Chapter IV on the demand for groups of goods.
1. INTRODUCTION
Food consumption is necessary to sustain life and a primary indicator of consumers’
wellbeing. One of the most robust and famous empirical regularities in economics is Engel’s
(1857) law, whereby poor countries spend a larger fraction of their income on food than do
the rich. But at the same time, due to differences in climate, culture, incomes and prices, there
are large disparities in food consumption across countries, especially when we consider
detailed food items. For example, the consumption of pork and alcohol is prohibited in
Islamic countries; geographically, Europeans prefer bread, while rice is common to most
Asians; and Australians eat pies, while Americans consume hamburgers. Additionally, in rich
countries, consumers are concerned about the nutritional and health aspects of their diets,
while poor countries can face food shortages and nutritional inadequacies. This paper shows
that considerable progress can be made in analysing the diversity of food consumption
patterns internationally with relatively simple models, in which incomes and prices determine
consumer demand.
The modern literature on international consumption patterns starts with the analysis of
the allocation of income to broad groups such as food, housing, clothing, etc. This is denoted
by “stage 0” in Figure 1.1, where, for simplicity, the non-food items are grouped together.
Perhaps the most prominent early example of this style of research is Houthakker (1957),
who estimates Engel curves for about 30 countries with cross-sectional survey data and
provides compelling evidence in favour of Engel’s law. In the 1970s, Lluch and Powell
(1975) and Lluch et al. (1977) made a substantial advance by estimating versions of the linear
expenditure system for a number of countries. Then came a series of studies that used
international data to estimate demand systems that applied to groups of countries. This work
continued to use broad commodity groups and includes Clements and Theil (1979), Theil et
al. (1981), Theil (1987), Theil et al. (1989), S. Selvanathan (1993), Theil (1996), Chen
(1999), E. A. Selvanathan and S. Selvanathan (2003) and Gao (2012).1
Another subsequent strand of this cross-country research splits total food into food
groups (meat, dairy, etc.) as in stage 1 of Figure 1.1. Seale et al. (2003) use the International
Comparison Program (ICP) data to estimate a system of demand equations for seven food
groups. Thereafter, Seale and Regmi (2006, 2009 and 2010), and Meade et al. (2014)
examined some ICP data issues and used more recent ICP data to obtain the income and price
sensitivity of demand for the major food groups.
1 For additional research on international consumption patterns within a system-wide framework, see
Goldberger and Gamaletsos (1970), Parks and Barten (1973), Pollak and Wales (1987), S. Selvanathan (1991),
Clements and S. Selvanathan (1994), Rimmer and Powell (1996), Cranfield et al. (2000, 2002) and Reimer and
Hertel (2010).
2
Two recent meta-studies of food demand should also be noted here. Green et al
(2013) summarise more than 3,000 food price elasticities from 162 countries and report what
they call “synthesized” elasticity estimates for food groups across the income distribution.
These are fitted values from a meta-regression equation. In a second meta-analysis,
Andreyeva et al. (2010) review food price elasticities for the US and, in the main, the results
are consistent with those of Green et al. (2013).
This paper examines the demand of the elementary food goods described by stage 2 of
Figure 1.1. These demands are embedded in a broad model that includes the demand for food
groups, stage 1 of Figure1. As there seems to be no prior research with this level of
commodity detail, this paper expands the analysis of cross-country consumption patterns.
The paper is structured as follows. Section 2 introduces the data to be used: This
comprises disaggregated data on prices of and expenditures on 25 food items from 146
countries. Section 3 analyses specialisation and diversification in consumption patterns in
different countries by examining expenditure shares. Section 4 sets out the basic approach to
demand analysis, a multivariate system of demand equations, which is followed in Section 5
by an application to each of the six food groups. When demand equations for individual items
are aggregated over goods within a group (such as those within the staples group comprising
rice, cereals, bread, and bakery and pasta), we obtain a demand equation for the group as a
whole (the demand for staples). When preferences are separable in groups of goods, the
group demand equations have an appealing tractable form. This material is contained in
Section 6, where the demand for six food groups is analysed. Section 7 combines the within-
group demands and the group demands to give the direct and indirect determinants of the
demand for each item. Finally, Section 8 summarises the results and gives some implications.
2. THE DATA
We use unpublished data from the International Comparison Program (ICP) provided
by the World Bank. Population and GDP in 146 countries are listed in Table 2.1. This table
reveals that China, country number 102, has the largest population with more than 1,300
million people, followed by India (country 104) with 1,100 million. Sao Tome (105) is the
smallest with a population of only 150,000. GDP and total consumption per capita are also
given in the table; these variables are expressed in US dollars using PPP exchange rates.
Countries are ordered in terms of decreasing consumption per capita, which is given as the
third last figure for each country; the second last figure is normalised consumption with the
value for the US set equal to 100. Thus, on the basis of consumption per capita, the US is the
richest country, while the Democratic Republic of the Congo is the poorest with consumption
3
about 1 percent that of the US; more precisely, its consumption is 0.51 percent of that in the
US. Consumption is used to rank countries here on the basis that it is often a better indicator
of long-term affluence than GDP.
In poor countries, an especially important component of overall consumption is food.
As indicated in the last value for each country in Table 2.1. food can account for more than
one-half of overall consumption for the very poor, while this falls to less than 10 percent in
the richest countries. As mentioned previously, this tendency for the food share to fall as
income rises is enshrined in what is known as Engel’s (1857) law. It is helpful to divide the
146 countries into income quartiles, where income is taken to be consumption per capita. The
countries in each quartile are indicated by the grid lines in Table 2.1. The average food share
in the first quartile (the rich countries) is 12 percent and the corresponding value of per capita
consumption is $18,400 per annum, as indicated by the last two entries of column 2 of Table
2.2. This share rises to 47 percent in the fourth quartile (the poor countries), where
consumption is $834.
Next, we disaggregate food into its components in a two-stage manner. First, food is
divided into the six commodity groups listed in the top six panels of Table 2.2 – staples, meat
and seafood, dairy, and so on. Consider the first panel, which refers to the staples group. The
row labelled “Group” gives the shares in total food expenditure accounted for by staples;
these are the averages over countries in each quartile, as well as that for all countries. As can
be seen, there is a strong tendency for this share to rise as income falls – from 16 percent for
the rich countries to 33 percent in the poor. The share for dairy (panel 3) moves in the
opposite direction and falls by almost one-half in moving from the rich to the poor. There is a
similar, but less dramatic, fall in the share for sweet things (panel 5).
The second stage of food disaggregation is within each group. From panel 1 of Table
2.2, the staples group is made up of four products: rice, other cereals, bread, bakery and pasta.
The within-group allocation of expenditure can be measured by the conditional budget
shares, the proportions of the total spent on each member of the group. In all four cases, there
are large swings in these shares across income quartiles, with rice, for example rising
spectacularly from 9 percent for the rich to 39 percent for the poor. In contrast, the share of
bread falls from 38 to 14 percent for the same income change. The other elements of Table
2.2 give the conditional shares for the other food products.2
2 Three other aspects of the data need to be noted. (i) In its original form, the ICP data distinguishes bakery and
pasta as separate goods. As consumption of these two goods is trivial in a number of countries, especially those
in Africa, they are combined into one (“bakery and pasta”). (ii) For the same reason, pork and lamb are
combined into a single good. (iii) Butter is excluded from the analysis. In preliminary results not reported here,
residuals from the butter demand equation appeared to be highly non-normal with a Jarque-Bera statistic of
4
This disaggregation scheme means that food expenditures are characterised by three
sets of shares. (i) The share of food in total consumption. As mentioned before, the average
of this for poor countries is 47.4 percent (from the second last element of column 5 of Table
2). (ii) The share of food expenditure devoted to a certain food group, which is 32.5 percent
for staples for the poor (fifth element of column 5). Accordingly, for these countries, the
share of staples in total consumption is 0.474 0.325 15.4 percent. (iii) The within-group
share. For rice in the poor countries, this is 38.6 percent, meaning that this product accounts
for 0.386 0.474 0.325 5.95 percent of total consumption. As their income is $834, rice
expenditure in these countries averages 0.0595 834 $50 per capita per annum.
3. SPECIALISATION AND DIVERSIFICATION IN CONSUMPTION
This section first introduces a simple way, based on the shares, to identify goods that
are most important in each country’s consumption of food. We then introduce some index
numbers to give a preliminary analysis of the data in the form of quantity-price scatter plots.
Let ip be the price of good i and iq be the corresponding quantity demanded for
i 1,...,n. Thus, i ip q is expenditure on good i, n
i 1 i iM Σ p q is total expenditure (to be referred
to as income) and i i iw p q M is the thi budget share. Suppose good j has the largest share,
that is, j 1 nw max w ,...,w . As i0 w 1 , in the extreme case, a country with jw close to
1 could be classified as “specialised” in that commodity. This is a clear-cut case. But what if
jw is just above the average of 1 n? It would not seem appropriate to declare that country to
be intensive in good j. Some minimum value of budget share needs to be specified, which
shall be called the “cut-off” value, denoted by w. Accordingly, a country is declared to be
intensive in good j only if its share is (i) the maximum in the group; and (ii) larger than the
cut-off w. In the case where no good exceeds the cut-off, consumption can be described as
“diversified”.
Panel 1 of Table 3.1 illustrates the workings of this procedure for the staples group.3
In column 2, the cut-off value of the budget share w is set at 30 percent and in this case, 33
around 90 (the 5-percent critical value is 5.51). Although it is not possible to be definitive on the matter, this
raises substantial doubts regarding the quality of the butter data. While the fundamental reason for the lack of
quality of the data for this commodity in particular is uncertain, it seems desirable to drop butter from further
consideration. Thus, the food budget is now interpreted as excluding this good. 3 There are originally 146 countries in total; but as some countries consume small amounts of some food items,
they are eliminated from further consideration in what follows. For the staples group, there are 17 countries
where consumption of at least one of the items is small, 4 for meat and seafood, 27 for dairy, 14 for fruit and
vegetables, 17 for sweet things and 3 for other food. These countries are omitted subsequently from the analysis.
The number of remaining countries in each group is denoted in Table 3.1 by gC . The criterion for “small” for
5
countries are classified as intensive consumers of rice, 25 intensive in other cereals, 43 in
bread and so on. In columns 3-6, the cut-off value is increased successively to 50 percent. As
w increases, as expected, more countries are classified as being diversified (indicated by the
row label “none” in the table).
What value should be used for the cut-off? There are two considerations that guide
this choice. First, it would seem reasonable for the cut-off to be no larger than 50 percent:
When one good absorbs one-half of total expenditure, it is larger than the consumption of all
others combined; this seems sufficient for a country to be classified as intensive in that good.
Second, even when the cut-off is less than 50 percent, if the cut-off is set too high, too many
countries would be classified as diversified; a too low value leads to too few diversified
countries. A balance needs to be struck such that roughly the same number of countries are
classified as intensive in each good and diversified. Thus, we choose w to minimise the
“classification imbalance” as measured by the standard deviation (SD) of the number of
countries in each category. For the staples group (panel 1 of Table 3.1), the minimum-SD
criterion leads to a 40 percent cut-off value, where the SD = 6 (countries). The other panels in
this table apply the procedure to the other five groups, with the results corresponding to the
minimum SD for each group given in a box. For all groups except sweet things, the minimum
SD seems to be an interior minimum; for sweet things, the minimum corresponds to w 50
percent, which is the upper limit discussed above.
As discussed above, the budget share iw is the proportion of total income devoted to
good i; thus, it reflects the economic importance of goods in the basket. Summary measures
of prices and quantities are their budget-share weighted averages, which in logarithmic form
are
(3.1) n
i i
i 1
log P w log p ,
n
i i
i 1
log Q w log q .
The price (quantity) index is the logarithm of the weighted geometric mean of the prices
(quantities). As the prices ip are expressed in term of local currency units, they are not
comparable across countries. However, the quantity units iq are US dollars, making them
comparable across countries. When the price is deflated by the index, we obtain the relative
price i ilog p log P log p P , which is comparable. Thus, we define:
staples is considerably larger than that for other groups as consumption of items in these groups tends to be
smaller. For details, see Liu (forthcoming).
6
(3.2) ii
plog log p log P,
P
i
i
qlog log q log Q
Q
,
which are both unit free concepts.
To apply the above concepts to food data, we consider each food group by itself.
Thus, for the staples group, for example, the consumer’s budget is understood to refer to the n
= 4 food items listed in column 1 of panel 1 of Table 2.2, that is, (i) rice, (ii) other cereals,
(iii) bread and (iv) bakery and pasta. The share iw is now interpreted as the share of
expenditure on the group that is devoted to the thi member. The means of these shares are
contained in panel 1 of Table 2.2, discussed previously. Panel 1 of Figure 3.1 contains scatter
plots of relative quantities against relative prices for staples. For rice, the slope of the
regression line is -2.2, indicating that a 1-percent price increase results in 2.2 percent decline
in consumption. As an estimate of the price elasticity of demand, this would seem to be on
the high side. The other slopes are -0.8 (for cereals), -0.1 (bread), and -1.0 (bakery and pasta).
When the four members of staples are pooled, the slope is -1.0, as shown in the plot on the far
right of panel 1 of Figure 3.1.
4. DEMAND EQUATIONS IN CHANGES AND LEVELS
The discussion thus far has analysed food consumption by examining the budget
shares and the relationship between prices and quantities. This has been intentionally
preliminary in nature, designed to provide an overall “feel” for the data and some initial
evidence on the price-sensitivity of consumption. In what follows, a more formal approach is
adopted with a system of demand equations for each of the six groups of goods.
We start by defining the Divisia (1925) price and volume indexes as:
(4.1) n
i i
i 1
d log P w d(log p ),
n
i i
i 1
d log Q w d(log q ).
These can be considered as differential versions of the indexes in levels given in equation
(3.1). To interpret them more precisely, take the differential of the identity n
i 1 i iM p q to
give n
i 1 i i i idM p dq q dp , or using d logx dx x, x>0,
d log M d log P d logQ , where d log P and d logQ is defined in (4.1). The price
index is a budget-share weighted average of the n price changes and, thus, measures the
change in the cost of living. The quantity (or volume) index d logQ d log M d log P ,
is the change in money income deflated by the cost-of-living index, or the change in the
consumer’s real income.
7
The Marshallian demand equation for good i takes the form i i 1 nq q M, p ,...,p , or
(4.2) n
i i ij j
j 1
d logq d log M d log p
,
where i ilogq log M is the ith income elasticity and ij i jlogq log p is
the th
i, j uncompensated price elasticity. The Slutsky decomposition is ij ij i jw ,
where ij is the compensated elasticity. Using this in (4.2), we have
n n
i i j 1 j j j 1 ij jd logq d(log M) w d(log p ) d(log p ) , or, using (4.1),
n
i i ij j
j 1
d logq d logQ d log p
.
As real income is now on the right, this is a Slutsky demand equation. Multiplying both sides
of the above equation by iw gives the ith equation of the differential approach to demand
analysis (Theil, 1980):
(4.3) n
i i i ij j
j 1
w d logq d logQ d log p .
The variable on the left-hand side of equation (4.3), i iw d logq , is the contribution of
good i to the volume index d logQ of equation (4.1). It can easily be shown that this
variable is also interpreted as the quantity component of the change in the budget share of
good i. According to equation (4.3), i iw d logq is explained by the change in real income
d logQ and the n price changes jd logp , j 1,...,n. The coefficient attached to income,
i , is the marginal share of good i. This coefficient is defined i ip q M and answers the
question, if income rise by $1, how much of this is spent on good i? As the $1-increase in
income is taken to be spent in its entirety, n
i 1 i 1.
The price term in (4.3) is n
i 1 ij jd logp . This is a weighted sum of the price changes
where the weight attached to the thj price is ij . This is known as the (i, j)th Slutsky
coefficient and is defined as ij i j i jutility constant
p p M q p . The “utility constant”
subscript indicates that this coefficient removes the income effect of the price change and
refers only to the substitution effect of a change in price of good j on the demand for good i.
As there are n commodities in the budget, there are n demand equations, each of the form
(4.3). The 2n Slutsky coefficients in this system of n equations satisfy the homogeneity and
symmetry constraints,
8
(4.4) n
ij
j 1
0, i 1, ,n,
ij ji , i, j 1, ,n.
Dividing both sides of (4.3) by iw , we obtain i iw as the income elasticity of demand for
good i, while ij iw is the (compensated) elasticity of demand for i with respect to the price
of j. A notable characteristic of the system (4.3) for i 1, ,n is that while it is not linked to
any specific form of the utility function, it is based on utility-maximisation. As the model is
consistent with a wide range of utility functions, this represents an appealing robustness
property.
In a time-series application, the changes in the variables in equation (4.3) are taken to
refer to successive differences from one period to the next, and the marginal shares and
Slutsky coefficients are taken to be constants. This is the basis for the Rotterdam model of
Barten (1964) and Theil (1965); for a recent review, see Clements and Gao (2015). A feature
of this model is that homogeneity and symmetry involve linear restrictions of constant
coefficients as indicated by (4.4). This greatly facilitates testing and estimation. However,
this approach is not applicable to cross-country data as there is no natural ordering of
countries. Instead we employ a “levels version” of model (4.3) by simply removing the “d’s”
from the (logarithms of the) quantities and prices (Barten, 1989), to give
(4.5) n
i i i ij j
j 1
w logq logQ log p .
Here, n
i 1 i ilogQ w logq is the volume index in levels, as in equation (3.1). The
coefficients have the exact same interpretation as before and are still subject to the
homogeneity and symmetry constraints (4.4).
When the marginal share i is treated as a constant, the Engel curve is linear, which is
not particularly attractive. Instead, we take the marginal share to exceed the corresponding
budget share by a constant i , so that i i iw . 4 As n n
i 1 i i 1 iw 1, it follows that
n
i 1 i 0. Substituting i iw for i in equation (4.5) and rearranging, we have
(4.6) n
i i i ij j
j 1
w logq logQ logQ log p .
It can be easily shown that i i1 w is the income elasticity of the demand for good i.
4 This specification is due to Working (1943) and Leser (1963).
9
5. DEMAND WITHIN FOOD GROUPS
As mentioned in Section 1, Figure 1.1 sets out a three-stage budgeting system in
which the separation into recursive stages is based on the assumption of preferences being
block independent in the food groups, or strongly separable. This section examines the
demand for the elementary food items in stage 2 of the figure, that is, for items within each
group. Stage 1 -- the demand for groups of goods -- will be considered in the next section.
5.1 The Estimates
Suppose the n food items are separated into G n groups, denoted by 1 GS ,...,S , with
each item belonging to one group only. Let gn be the number of items in gS . Then, under
block independence, the demand for good gi S takes the form
(5.1) g
g g g
i i g i g ij j
j S
w logq logQ logQ log p
, gi 1,...,n .
Here the additional “g” super/subscript indicates a conditional, or “within group”, concept.
Thus, g
g
i i i i S i iw p q p q is the share of group expenditure devoted to good i;
g
g
g i S i ilogQ w logq is the group volume index; and g
i and g
ij are the conditional income
and Slutsky coefficients that are to be estimated.5 Clearly, equation (5.1) has the same form
as (4.6), but now all variables are confined to the group g.S
Consider the staples group comprising rice, other cereals, bread, bakery and pasta.
Then, (5.1) with gn 4 is the conditional demand system for the four members of this group.
Preliminary results show that the residuals display a distinct pattern related to the intensity of
consumption in different countries, as defined in Section 3: For countries that are intensive
consumers of good i, the residuals from that equation tend to be positive, while the values for
other countries tend to be negative. Such a tendency casts doubt on the assumption that the
disturbances are independent across countries. To deal with this problem, we add intercepts
for each country group to (5.1). The gC countries for group g are split into four groups
according to their intensity of consumption; there is an additional group for those countries
having “diversified” consumption. Denote these country groups by g g
1 5, ,C C and define the
indicator functions as g
k kI (c )C , k 1,...,5, which take the value 1 when country g
kc C , 0
otherwise. Then, the demand for good gi S in country c, with an error term added, is
5 Previously in Section 3, we used iw to denote the share of expenditure on a group devoted to good i. For
clarity, now we use the symbol g
iw to denote this share.
10
(5.2) 5 4
g
ic gc gc ij jc
k 1 j 1
g g g g g
ic ik k k i ic(c )w (log q log Q ) log Q log pI
C .
Here, g
ik is an intercept in equation i for countries intensive in good k, gi,k S . The term g
ic
is a zero-mean disturbance with g g
ic jd gE( ) 0, i, j , c d. S The vector of 4 disturbances
g g
1c 4c[ , , ] is taken to have a constant covariance matrix.
Panel 1 of Table 5.1 contains the estimates for the staples. The intercepts for the
diversified group of countries have been omitted on the basis that they were all insignificant;
this is indicated by the blanks in column 7, the column that is labelled “None”. Consider the
intercepts for four items as a 4×4 matrix: The diagonal elements are positive and the off-
diagonals are negative, which is consistent with the pattern observed in the preliminary
residuals. The income coefficients g
i for the four items are close to 0 and mostly
insignificant. Regarding the 4×4 Slusky matrix g
ij[ ] , the own-price coefficients are
significant and negative; and the cross-price coefficients are positive and mostly significant,
implying the goods are pairwise substitutes. The results for the other five groups in Table 5.1
exhibit similar qualitative patterns as do staples.
5.2 Testing
As discussed in Section 4, the Slutsky coefficients satisfy the homogeneity and
symmetry constraints. The conditional coefficients g
ij are also subject to similar restrictions
and this subsection tests these restrictions. The methodology is mostly from Chen (1999,
Chap. 7) and Theil (1987, pp. 103-107).
The null hypothesis of homogeneity of the demand for good i takes the form
gn g
j 1 ij 0 . This can be tested for each item by itself using a t statistic. Column 14 in Table
5.1 contains the value of gn g
j 1 ij for gi 1,..,n and the standard errors are given in
parentheses. The corresponding absolute t-values are given in column 2 of Table 5.2. Among
the 25 values, 19 are less than the 5-percent critical value. The bulk of the evidence is not
inconsistent with the homogeneity postulate. Homogeneity can also be tested jointly for all
goods within each group and the test statistics are given in column 2 of Table 5.2 in boldface.
The values are significant for three out of the six groups – dairy, sweet things and other food.
Each of these three contain a member with a significant t-value, so the results are consistent
in this sense. But the fundamental reason for the lack of homogeneity remains a puzzle,
11
especially since the absence of money illusion would seem to be a mild requirement of
consumer behaviour.6
The null hypothesis of symmetry takes the form g
g gij ji ., i, j 1,....,n As this is a
cross-equation constraint, it can only be tested for all goods jointly. Column 4 of Table 5.2
gives the symmetry test statistics; as five out of the six statistics are insignificant, there seems
to be little evidence against symmetry. Imposing the homogeneity and symmetry constraints
on (5.2), we obtain the constrained SUR estimates in Table 5.3. A comparison with the
unrestricted counterparts in Table 5.1 shows that the point estimates do not change
appreciably, while there are minor reductions in many of the standard errors.
Next, we test the normality of the residuals from the constrained equations. Write the
g gC n matrix of residuals for group g as gε . Column 2 in Table 5.4 gives the Jarque-Bera
statistics for gε for g 1,...,6. Among 25 values, 22 are less than the critical value,
suggesting that the bulk of the evidence supports normality. To test multivariate normality,
we orthogonalise the residuals. Let g
be the estimated covariance matrix of gε , written as
2DΛ D , where D is the orthogonal matrix of the characteristic vectors and 2
Λ is a diagonal
matrix of the roots of .g
The transformed residuals 1
gε DΛ D are then uncorrelated with
mean 0 and standard deviation 1. Column 3 of Table 5.4 gives the Jarque-Bera test statistics
for the normality of the transformed residuals. In most cases, normality cannot be rejected.
5.3 The Elasticities
The implied (compensated) own-price elasticity by equation (5.2) is g g
ij iw , while
the income elasticity is g g
i i1 w . 7 Based on the Table 5.3 estimates, these elasticities are
contained in Table 5.5. Within staples, the absolute price elasticity for rice decreases
dramatically in moving from the rich to poor countries; the same elasticity for other cereals
also decreases with income, but less spectacularly than rice. In contrast, the price elasticity
6 Homogeneity testing has an interesting history. In a widely cited survey of research up to the mid 1970s,
Barten (1977, p. 27) reports that homogeneity is frequently rejected. One response to this troubling result was
for researchers at The University of Chicago to show that there was a major problem with the econometric tests:
The tests have a large-sample justification, but were applied to small samples, causing misleading inferences as
the tests are biased against the null (that is, the tests have an over-rejection problem). See Laitinen (1978) and
Theil (1987, pp. 104-106). In our application, the samples consist of more than 100 countries, which is not
small. Thus, the conventional tests should perform satisfactorily. This is confirmed with further results not
reported here: When Laitinen’s (1978) finite-sample correction is applied there is little or no change in the test
results. For more on the history of homogeneity testing, see Keuzenkamp and Barten (1995). 7 Strictly speaking, this “income elasticity” is the elasticity of consumption of good i with respect to the volume
index of the group to which the good belongs, gexp log Q . As it is less clumsy, we shall refer to it as the
“income” elasticity. This type of nomenclature is also used subsequently.
12
for bread and bakery and pasta increases when income declines. In part at least, this reflects
the fact that rice and other cereals are the dominant staple in poor countries, while bread, and
bakery and pasta play that role in rich countries. The price elasticities for all countries in
column 10 are harmonic means of the four quartile elasticities. These are less than 1 in all
cases. The income elasticities of the four items of staples are all close to 1, reflecting the
small values of the income coefficients g
i .
Panels 2 to 6 of Table 5.5 contain the elasticities for goods in the other five groups.
Within meat and seafood, the absolute price elasticities are quite stable across quartiles; the
exception to this rule is other meat, whose elasticity increases substantially in moving from
rich to poor countries. For dairy, the price elasticity for cheese increases as income falls,
while the reverse is true for eggs. The other two items have fairly stable elasticities across the
income distribution. In the other three groups, the goods whose price elasticities increase with
income include fresh fruit, chocolate and mineral water; while the goods with the opposite
pattern are fresh potatoes, sugar and other edible oil. The price elasticities of remaining goods
in these three groups are stable across quartiles. The income elasticities are close to 1 in all
cases, except fresh fruit in poor countries, where it is a luxury.
6. FOOD GROUPS
The previous section considered the allocation of group expenditure to the elementary
goods within each of the six groups. We now move from the elementary goods in stage 2 of
Figure 1.1 to the demand for groups in stage 1.
6.1 Preliminaries and Data
Define the share of total food spent on group g and the share of group expenditure
devoted to giS , the conditional budget share of Section 5:
i S i i g i i i
g i i gni Si 1 i i i i i g
g
gg
p q p q wW w , w , i .
p q p q W
S
S
The summary measures of prices and volumes for group g are:
g g
g i i g i i
i S i Sg g
log P w log p , logQ w logq .
These measures aggregate consistently as the price and volume indexes for total food are:
G G
g g g g
g 1 g 1
log P W log P , logQ W logQ .
13
The relative price and quantity of group g are g glog P P log P log P and
g glog Q Q logQ logQ .
Applying the above concepts to the six food groups, Figure 6.1 contains scatter plots
of relative quantity against relative price. For staples, the slope of the regression line is -
0.97, implying that a 1-percent price increase leads to a 1-percent decline in consumption.
The slopes range across groups from -0.4 for meat and seafood to -2.2 for sweet things. These
values can be interpreted as preliminary measures of the price elasticities; a more formal
approach is applied next.
6.2 Demand Equations
To obtain the demand for group gS as a whole, we aggregate equation (4.3) over
gi S . Under the separability, we have (see, e. g., Clements, 1987)
(6.1) g
g g g g
PW log Q log Q log
P
.
The left-hand side of this equation is simply an “uppercase” version of that of equation (4.3).
The first term on the right of equation (6.1), g logQ , is just the sum of i logQ in (4.3),
that is, gg i S ilogQ logQ , where
gg i S i is the marginal share of group g. The
new form of the relative price on the right of (6.1) is
g g
g G g
g g i S i i g 1 g j S j jlog P P log P log P logp logp , where g
i i g is the
conditional marginal share of good gi .S As the indexes are marginal-share weighted, this is
the Frisch (1932) relative price of the group g. The coefficient controls the overall degree
of substitutability: As the Frisch own-price elasticity (which holds constant the marginal
utility of income) is gg g gW and as G
g 1 g 1, we have G
g 1 g ggW , which shows
that is a weighted average of the price elasticities. We shall thus refer to as the “food
flexibility”. In summary, equation (6.1) shows that the demand for gS depends on real
income logQ (strictly, the total volume of food) and the relative price of the group
glog P P .
The relative price on the right of equation (6.1) involves the Frisch index of the price
of group g, g
g
i S i ilogp , which uses the conditional marginal shares g
i as weights. As
these shares cannot be directly observed, we use the previous estimates. That is, as in
14
equation (5.1), we set g g g
i i iw , in which g
iw is the observed conditional budget share
and g
i is now the conditional income coefficient as estimated in Table 5.3.
As the assumption of constant group marginal shares is not attractive, we express g
as gc gW B , where gcW is the group share in country c and gB is a constant. This is
analogous to what we did with the conditional demand equations of the previous section.
Thus, the variable on the left of equation (6.1) is reformulated as gc gc cW logQ logQ , while
the income term on the right becomes g cB logQ . The relative price term requires a somewhat
different treatment, as gcW already appears on the left of the equation; to have it also on the
right would lead to problems of endogeneity. Accordingly, we replace gcW in the relative
price term with its average for the relevant income quartile, 4 d d
d 1 d gI (c )WQ , where d
gW is
the average share for countries within the dth quartile and the indicator function, d
dI (c )Q ,
equals to 1 when country c is in the dth quartile, 0 otherwise. Thus, the group marginal share
in the relative price term takes the form 4 d d
g d 1 d g gI (c )W BQ . It is also desirable to
let the food flexibility vary in a similar manner, so we assume 4 d d
d 1 dI (c )Q , where
d is the flexibility for countries in quartile d.
With the above adjustments, equation (6.1), with an intercept gA and an error term
gcE added, becomes
(6.2) 6
gc gc c g g c g gc k 1 k kc gcW logQ logQ A B logQ log P log P E ,
where 4 d d
d 1 dI (c )Q and 4 d d
g d 1 d g gI (c )W BQ . The error term gcE has a zero
mean, with gc hdE E E 0, g, h=1, ,6, c d. The vector of 6 disturbances 1c 6c[E , ,E ] is
assumed to have a constant covariance matrix. Table 6.1 contains the SUR estimates of this
equation for g 1,...,6 . Panel I allows to vary across quartiles as discussed above.
Looking at column 3, the estimated value of gB is significantly negative for staples, implying
a necessity (within food), while it is significantly positive for meat and seafood, making it a
luxury group. As can be seen from column 4, the - estimate changes markedly across the
income distribution, from -0.6 for the first quartile to roughly double that value for the other
three quartiles.
15
Panel II in Table 6.1 treats as a constant. The point estimates of gA and
gB do not
change substantially from those of Panel I. The “pooled” estimate of is -1.18. To test the
hypothesis d
oH : for d 1,2,3,4 , we make the additional assumption that the error
vector follows a multivariate normal distribution. This yields the log-likelihood values under
the null and alternative of 862.68 and 873.52, respectively. The test statistic is then
2 862.68 873.52 21.68 , greater than the critical value 2
0.95 3 7.82 . Thus, the
hypothesis is rejected and we conclude the income flexibility varies with income.
Based on the estimates in Table 6.1, the implied elasticities are tabulated in Table 6.2.
Across all quartiles, the staples group has the lowest income elasticity of about 0.6. Then,
comes dairy with an income elasticity of about 0.8. Meat and seafood have the highest
elasticity of about 1.2. The other three groups have unitary income elasticities. The absolute
price elasticities for all groups increase from about 0.5 in the 1st quartile to around, or little
over, 1 in the other quartiles, indicating that the food groups in the poor countries are more
elastic than in the rich. In any given quartile, staples have the lowest price elasticity, while
sweet things has the highest.
We return to the food flexibility . This parameter is closely related to Frisch’s
(1959) income flexibility, which we denote by t . This
t is the reciprocal of the income
elasticity of the marginal utility of income; that is, t 1( log logM) 0 , where is
the marginal utility of income and M is income. The two parameters are related according to
t F , where F is the income elasticity of demand for food as a whole. Column 6 of
Table 6.3 gives the values of t implied by the estimates of of Table 6.1. Comparing the
implied t values with Frisch’s in column 4, they are reasonably close for the 1st quartile, but
not in the other quartiles. The reasons for this are unclear at present.
7. COMBINING THE DIRECT AND INDIRECT EFFECTS
The demand for good gi S expresses consumption as a function of the volume of gS
as a whole and the prices of goods that are members of this group. Let gq and gp be vectors
of quantities and prices in gS . The vector form, we have g g g g(Q , )q q p , where gQ is the
volume of group g. The group demand equations are a function of the volume of total food
(Q) and the price indexes of the six groups 1 6(P ,....,P ) : g g 1 6Q Q (Q, P ,....,P ) , g 1,...,6 . The
price index gP is a function of the price within the group, so we write g g gP P ( )p . These two
16
systems give the direct and indirect effects of income and price changes. By substitution,
these effects can be combined to give the total effect
(7.1) g g g 1 1 6 6 g gQ (Q,P ( ),...,P ( ), Q,q q p p p f p ,
where p is a vector of the 25 items of food. Let 1 6 1 25[ ,..., ] [q ,...,q ]q q q , so that (7.1) for
g 1,...,6 , can be expressed as (Q, )q q p with log( ) (log )q p A .
The 25 25 matrix A has its th(i, j) element i j(logq ) (log p ) , the elasticity of
demand for i with respect to the price of j. As this holds constant the volume of total food Q,
this is a compensated elasticity of a type of “unconditional” form. 8 The row sums of A are
zero due to homogeneity. Slutsky symmetry takes the form
i i j j j iw (logq ) (logp ) w (logq ) (logp ) . Let w be a diagonal matrix with 1 25w ,..., w
on the main diagonal. Then, symmetry implies that the product wA is symmetric:
wA wA . Figure 7.1 is a stylised representation of the matrix A . The light shaded blocks
on the main diagonal represent the own- and cross-price elasticities for goods within each
group, while the darker shaded elements are the own-price elasticities. These blocks contain
both the within-group direct and indirect effects. The off-diagonal blocks are non-zero and
contain cross-price elasticities for goods from different groups and, thus, only contain the
indirect effects. In what follows, we present values for some elements of matrix A on the
basis of the estimates of the conditional and group demands.
The functions g ( )q and gQ ( ) take the form of equations (5.1) and (6.1):
(7.2) g
g g g
i i i g ij j
j S
w logq logQ log p
, gi S ; g
g g g g
PW log Q log Q log
P
,
where g
i i gw w W is the conditional budget share for i and gg i S iW w is the group share;
g
g
g i S i ilog Q w log q and n
i 1 i ilogQ w logq are the volume indexes for group g and
total food, respectively; g
g
g i S i ilog P log p and
G
g 1 g glog P log P are the Frisch price
indexes for group g and total food, respectively. The conditional and group equations can be
combined to eliminate glogQ in two steps. First, multiply both sides of conditional equation
by gW to give g
g g
i i i g g j S g ij jw logq W logQ W log p . Second, substitute the right-hand
side of the group equation for g gW logQ :
8 The term “unconditional” here, strictly speaking, is conditioned on total food expenditure. As this paper
focuses on the demand within food, the term unconditional is used for the sake of simplicity.
Indirect
effects Direct effects
17
(7.3) g
ngg g g
i i i g i g g ij j i ij j
j S j 1
Pw logq logQ log W log p logQ log p
P
.
Here, g
i i g and the unconditional Slutsky coefficient is
g h
ij g ij gh i j gh hW , g hi , jS S , g, h 1,...,G,
where gh is the Kronecker delta, which takes the value 1 when g h , 0 otherwise.
From (7.3), the implied unconditional income elasticity is
g g g
i i i g i g i gw w W , where g g g
i i iw is the conditional elasticity and
g g gW is the group elasticity. The unconditional price elasticity is
(7.4) g
ij ij g h h
gh g i j j gh h hg
i i
w Ww w
.
The first term, g g
gh ij iw , is the direct effect on the demand for good i of a change in the
price of j, gi, j S . This term is zero when i and j belong to different groups. The second
term, g h h
g i j j gh h hw ( W ) , operates as the indirect effect of the price change on group
expenditure. Equation (7.4) leads to the following conclusions:
When goods i and j are from the same group. The indirect effect is
g h h g g g
g i j j gh h h g i j g g iw W 1 W w . As 0 and the shares are all
positive fractions, the whole term is negative. This establishes that (i) for i j , the
unconditional own-price elasticity is more negative than the conditional counterpart;
and (ii) for i j , gi, j S , the unconditional elasticity is also more negative than the
conditional version, implying that the goods are either less of a substitute for each
other or more of a complement.
When i and j are from different groups. The unconditional elasticity only contains the
indirect effect, g h h g h
g i j j h h g i j h jw W w . As this is positive, in this case
goods are always substitutes. To illustrate the possible size of this term, suppose the
three income elasticities are all unitary and, on the basis of Table 6.1, suppose the
food flexibility 1.2 . Further, if good j absorbs an average share of total food
expenditure on the 25 items, then jw 1 25 . In this case, the indirect effect is
g h
g i j h jw 0.05 , which is clearly small.
18
The unconditional income and own-price elasticities are contained in Table 7.1. In
most cases, the income elasticity, g
i g , is dominated by the group elasticity g , as the
conditional elasticity g
i is close to unitary. Thus, within a given group, the elasticities of the
goods are fairly close to one another. The income elasticities are also quite similar across
income quartiles, except for fresh potatoes where the elasticity increases from 0.6 in rich
countries to 0.9 in poor ones. The price elasticities are the elements on the main diagonal of
the matrix .A As mentioned before, the unconditional own-price elasticity is the total effect
of the price change, made up of the direct and indirect effects, effects that are both negative.
Consequently, the total effects of Table 7.1 are more negative than the direct effects (the
conditional elasticities) of Table 5.5.
Figure 7.2 contains scatter plots of the two price elasticities, the unconditional and
conditional version. Take, as an example, the plot for staples in the fourth income quartile,
the one on the far right of the first row of the figure. This plots the four unconditional own-
price elasticities on the vertical axis against the conditional counterparts on the horizontal.
Each of the four points lies below the 45-degree line, reflecting that the unconditional
elasticities are more negative. But the points are not too far from the line, as indicated by the
average difference of -0.22, the figure given in the box in the plot. As this represents
something like an average of 20-percent difference, this might be described as a nontrivial,
but not huge difference. However, there is a noticeable pattern of the differences as we move
across the income distribution. For all groups of goods, the difference is considerably smaller
for the richest countries (those in the first quartile) and in relative terms, larger in all other
countries (the second, third and fourth quartiles). This is due primarily to differences in the
food flexibility , the estimate of which for the rich is about one-half that of the other
countries (Table 6.1).
Figure 7.3 adds to Figure 7.1 averages of the unconditional price elasticities. The
average of the own-price elasticities for each group (represented by the dark-shaded elements
on the main diagonal) is somewhat less than unity (in absolute value) in all cases except for
dairy, where it is unity. For the cross-price elasticities within a group, to avoid double
counting, we average over the entries in the upper triangle of the corresponding block on the
main diagonal. Except for sweet things, these cross-price elasticities within the group are of
modest size as the indirect effect tends to offset the direct effect. On average, the items in
staples, dairy and fruit and vegetables are substitutes for one another, while goods in the other
three groups are complements. For the cross-price elasticities between goods from different
19
groups, the averages are in the off-diagonal blocks. As foreshadowed above, these values are
small.
8. CONCLUDING COMMENTS
Food consumption has been studied extensively in the form of food as a whole and
broad food groups such as meat, dairy, etc. However, there is much less prior research on the
demand for detailed food items within the broad groups. This paper expands the analysis of
food demand by examining the consumption of 25 food items in large number of countries,
using a three-stage budgeting approach. The paper includes preliminary data analysis; tests of
the predictions from microeconomic theory that demand is homogeneous of degree zero and
that the substitution effects are symmetric; the estimation of six systems of conditional
demand equations and an additional system of group demands; and an investigation of the
nature and numerical values of the income and price elasticities. This research has presented
a tractable approach to the estimation of large matrices of price elasticities needed in CGE
models. Such matrices can be used to analyse the full impacts of policies that tax/subsidise
the consumption of certain items of food.
There are still some unresolved puzzles, however. First, the conditional income
elasticities are unity in many cases. This may come as a bit of a surprise and it is not easy to
provide a plausible explanation. (Here, “income” refers to real total expenditure of the group
as a whole.) Second, the homogeneity hypothesis is rejected in three out of six groups. Taken
at face value, this says (some?) consumers are subject to money illusion. The reason for this
unappealing result is unclear, but this problem has been encountered in previous research.
Third, for some parts of the income distribution, the implied value of income flexibility,
which controls the overall degree of substitutability among the items, seems to differ from
prior studies.
20
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Consumption: A Systematic Review of Research on the Price Elasticity of Demand for
Food.” American Journal of Public Health 100: 216-22.
Barten, A. P. (1964). “Consumer Demand Functions Under Conditions of Almost Additive
Preferences.” Econometrica 32: 1–38.
Barten, A. P. (1977). “The Systems of Consumer Demand Functions Approach: A Review.”
Econometrica 45: 23-50.
Barten, A. P. (1989). “Toward a Levels Version of the Rotterdam and Related Demand Systems.” In
B. Cornet and H. Tulkens (eds) Contributions to Operations Research and Economics: The
Twentieth Anniversary of CORE. Cambridge, Mass. : MIT Press. Pp. 441-65.
Chen, D. L. (1999). World Consumption Economics. Singapore: World Scientific Publishing.
Clements, K. W. (1987) “The Demand for Groups of Goods and Conditional Demand.” In H. Theil
and K. W. Clements (eds) Applied Demand Analysis: Results from System-Wide
Approaches. Ballinger, Cambridge, Massachusetts. Pp. 163–184.
Clements, K. W., and D. L. Chen (2010). “Affluence and Food: A Simple Way to Infer Incomes.”
American Journal of Agricultural Economics 92: 909-26.
Clements, K. W., and G. Gao (2015). “The Rotterdam Demand Model Half a Century On.” Economic
Modelling 49: 91–103.
Clements, K. W., and S. Selvanathan (1994). “Understanding Consumption Patterns." Empirical
Economics 19: 69-110.
Clements, K. W., and H. Theil (1979). “A Cross-Country Analysis of Consumption Patterns.” Report
7924 of the Center for Mathematical Studies in Business and Economics, The University of
Chicago. Subsequently published in H. Theil Studies in Global Econometrics. Dordrecht:
Kluwer Academic Publishers, 1996, pp. 95-108.
Cranfield, J. A. L., P. V. Preckel, J. S. Eales, and T. W. Hertel (2000). “On the Estimation of An
73. Albania 3.14 8,066 4,179 14 25 146. Congo, D. R. 59.52 380 152 1 62
Source: ICP (2008). This source contains the expenditures ic ic(p q ) and prices
ic(p ) for i 1,...,129 categories in c 1,...,146 countries. GDP
is the sum of the volumes ic(q ) of the 129 categories, from rice (item number 1101111) to the balance of exports and imports (180000),
while consumption is the sum of volumes of the first 105 categories, from rice (1101111) to other services (111270). The food share is the
percentage of total consumption expenditure devoted to food (item 1101111 to 110122). The grid lines indicate income quartiles.
23
Table 1.2 Budget Shares and Total Consumption
Commodity Income Quartiles All
countries 1st 2nd 3rd 4th
(1) (2) (3) (4) (5) (6)
1. Staples
Rice 8.92 15.46 32.92 38.64 24.03
Other cereals 11.27 18.01 32.48 40.96 25.73
Bread 37.96 39.70 21.52 13.66 28.19
Bakery and pasta 41.85 26.84 13.07 6.75 22.05
Group 15.92 17.49 22.71 32.51 22.20
2. Meat and Seafood
Beef and veal 14.35 21.11 25.15 26.48 21.80
Pork and lamb 18.00 19.34 18.71 15.27 17.82
Poultry 14.72 19.08 18.78 14.23 16.70
Other meat 30.93 23.26 8.98 8.00 17.76
Fish and seafood 22.01 17.21 28.38 36.02 25.91
Group 28.41 28.48 25.02 20.81 25.67
3. Dairy
Fresh milk 26.90 25.46 33.40 39.76 31.40
Preserved milk 31.39 33.34 33.64 35.74 33.54
Cheese 31.38 24.30 10.84 3.10 17.36
Eggs 10.32 16.90 22.12 21.40 17.71
Group 13.01 13.61 10.33 7.06 10.99
4. Fruit and Vegetables
Fresh fruit 35.93 32.62 27.60 14.11 27.51
Frozen fruit 8.67 5.18 3.69 4.11 5.40
Fresh vegetabels 31.53 37.46 45.38 39.38 38.44
Fresh potatoes 8.62 13.07 17.12 31.32 17.60
Frozen vegetables 15.25 11.67 6.22 11.08 11.06
Group 18.09 20.65 20.45 21.71 20.24
5. Sweet Things
Sugar 10.63 35.58 62.26 77.61 46.66
Jam 10.61 15.58 9.42 6.40 10.51
Chocolate and ice cream 78.76 48.83 28.32 15.99 42.83
Group 7.67 6.09 5.20 4.86 5.95
6. Other Food
Other edible oil 9.65 21.81 27.59 32.75 23.01
Food products 29.94 24.04 32.19 35.23 30.34
Coffee, tea 16.11 18.43 17.10 12.06 15.91
Mineral water 44.30 35.73 23.13 19.96 30.74
Group 16.90 13.68 16.28 13.04 14.95
7. Consumption Aggregates
Food share 11.70 25.84 37.83 47.36 30.76
Total consumption ($ p.c.) 18,380 7,018 2,631 834 7,171
Notes:
1. This table contains three forms of budget shares:
(i) For a given group, the share of expenditure for each member of the group. Thus, for
example, on average, the countries in the first income quartile devote 8.9 percent of staples
expenditure to rice. This is known as the conditional budget share and these have a unit sum
over members of the group.
(ii) Each group’s share of total food expenditure. Thus, for the first income quartile, staples
absorb 15.9 percent of food expenditure. This is known as the group budget share and these
have a unit sum over groups.
(iii) The food shares (given in the second last row of the table) are the proportions of total
consumption expenditure devoted to food. Thus, food absorbs 11.7 percent of total
consumption in the first quartile.
2. The shares here refer to averages over the 146 countries of Table 2.1. with appropriate
reinterpretations for the quartile averages. The countries in each quartile are indicated by the
grid lines of Table 2.1.
3. All entries (except total consumption) are × 100.
24
Table 2.1 Classification of Countries by Intensity of Consumption (Number of Countries)
Intensive in
Minimum value of budget share
(Cut-off w )
30% 35% 40% 45% 50%
(1) (2) (3) (4) (5) (6)
1. Staples (Cg=129 countries)
Rice 33 30 28 20 17
Other cereals 25 23 20 18 14
Bread 43 42 37 32 21
Bakery and pasta 28 28 24 20 12
None 0 6 20 39 65
Standard deviation 14 12 6 8 20
2. Meat and Seafood (Cg=142)
Beef and veal 33 28 21 12 6
Pork and lamb 18 16 11 4 1
Poultry 7 5 3 2 2
Other meat 30 25 20 16 8
Fish and seafood 44 43 31 20 15
None 10 25 56 88 110
Standard deviation 13 12 17 29 39
3. Dairy (Cg=119)
Fresh milk 38 31 27 22 15
Preserved milk 45 40 31 25 15
Cheese 28 26 14 7 3
Eggs 4 4 3 3 1
None 4 18 44 62 85
Standard deviation 17 12 14 21 31
4. Fruit and Vegetables (Cg=132)
Fresh fruit 38 34 22 12 3
Frozen fruit 0 0 0 0 0
Fresh vegetables 70 64 47 35 20
Fresh potatoes 15 13 9 9 8
Frozen vegetables 3 1 0 0 0
None 6 20 54 76 101
Standard deviation 25 22.1 21.5 27 36
5. Sweet Things (Cg=129)
Sugar 57 57 55 55 52
Jam 4 4 4 3 2
Chocolate and ice cream 68 68 66 63 61
None 0 0 4 8 14
Standard deviation 31 31 29 27 25
6. Other Food (Cg=143)
Other edible oil 29 27 21 13 8
Food products 48 44 36 30 17
Coffee, tea 7 6 6 3 3
Mineral water 56 52 45 32 22
None 3 14 35 65 93
Standard deviation 21 17 14 21 33
Notes:
1. The elements of this table are the number of countries classified as intensive in the
consumption of the good indicated in the row label when (i) expenditure on the good is the
largest within the group; and (ii) the good has a budget share exceeding the cut-off value
indicated in the column (w ). Thus, the first entry of column 2, for example, indicates that 33
of the 129 countries in the staples group are rice intensive; in these countries, (i) rice has the
largest budget share; and (ii) the rice share exceeds 30 percent. 2. The boxes indicate the cut-offs where the standard deviation of the number of countries in each
category is minimised.
25
Table 5.1 Unrestricted Demand Equations
g g
ic gc
n 1 ng g g g g g
ic gc ik k k i ij jc ick 1 j 1w (log q log Q ) log QI c log p
C ,
gi 1,..., n goods in group g, gc 1,...,C countries for g
Commodity Intercepts for countries that are intensive in
k g,k 1,...,n 1, C are the country groups based on Table 3.1. That is, the gC countries are split into
gn intensive
groups and one “diversified” group. However, if initially the coefficient g
ik is insignificant, the corresponding indicator function is removed, as indicated by a dash. 2. The number of countries in group g here
g( )C is somewhat less than that for Table 3.1 g( )C due to the exclusion of outlying countries.
3. For fruit and vegetables, the intercepts for (i) frozen fruit and (ii) frozen vegetables are omitted as there are no countries intensive in these commodities.
4. All values ×100; standard errors are in parenthesis.
26
Table 3.2 Homogeneity and Symmetry Tests
Group/Item
Homogeneity Symmetry
Test statistic
Critical value 2
0.95 g(n 1)
0.975 g gt (C 2n 1)
Test statistic Critical value
2
0.95 g g((n 1)(n 2) 2)
(1) (2) (3)
(4) (5)
1. Staples 3.49 7.81 1.62 7.81
Rice 1.09
Other cereals 0.94
Bread 0.48
Bakery and pasta 1.30
2. Meat and Seafood 2.27 9.49 21.40 12.59
Beef and veal 0.76
Pork and lamb 0.28
Poultry 0.54
Other meat 0.20
Fish and seafood 1.60
3. Dairy 9.68 7.81 1.79 7.81
Fresh milk 0.58
Preserved milk 2.40
Cheese 2.69
Eggs 1.45
4. Fruit and Vegetables 7.13 9.49 9.56 12.59
Fresh fruit 2.29
Frozen fruit 1.15
Fresh vegetables 0.11
Fresh potatoes 1.74
Frozen vegetables 0.67
5. Sweet Things 7.71 5.99 1.25 3.84
Sugar 0.67
Jam 2.80
Chocolate and ice cream 1.13
6. Other Food 12.49 7.81 0.14 7.81
Other edible oil 2.00
Food products 0.95
Coffee, tea 3.20
Mineral water 1.21
Notes: The boldface entries of column 2 are the test statistics for the joint homogeneity of the
gn items in group g. The
non-boldface entries are the test statistics for each good. The same convention applies to the critical values of columns 3 to
5.
1.96
1.96
1.96
1.96
1.96
1.96
27
Table 5.3 Homogeneity- and Symmetry-Restricted Estimates
g g
ic gc
n 1 ng g g g g g
ic gc ik k k i ij jc ick 1 j 1w (log q log Q ) log QI c log p
C ,
gi 1,..., n goods in group g, gc 1,...,C countries for g
Commodity Intercepts for countries that are intensive in
Mineral water 0.98 -0.67 0.98 -0.97 0.98 -1.03 1.00 -1.25 0.98 -0.94
Note: The unconditional income elasticity is defined as g g g
i i i g i g i gw w W . The conditional own-price elasticity is
defined as g g g 2 g
ii i ii i g i i g gw w ( ) w (1 W ) .
33
Figure 1.1 A Three-Stage Budgeting System
Not considered here
This study
Food Non-Food
Group 1
Group 2
Group G
Income
…… …… ……
Stage 0
Stage 1
Stage 2
……
……
34
Figure 3.1 Quantity-Price Scatter Plots for Food Items
1. STAPLES (Cg=129 countries)
Rice
Other Cereals
Bread
Bakery and pasta
Total
2. MEATS AND SEAFOOD (Cg=142) Beef
Pork and lamb
Poultry
Other meat
Fish and seafood
Total
3. DAIRY (Cg=119) Fresh milk
Preserved milk
Cheese
Eggs
Total
(Continued on next page)
-3
-2
-1
0
1
-1 0 1
Country
Quartile mean
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
Relative price
Relative quantity
Slope coefficient
-2.17
-0.79 -0.11
-2.46 -3.10 -2.17 -1.73
-0.73 -1.15 -1.70 -3.15 -2.50
-1.04 -1.02
-1.63
-2.09
35
Figure 3.1 Quantity-Price Scatter Plots for Food Items (Continued)
4. FRUIT AND VEGETABLES (Cg=132) Fresh fruit
Frozen fruit
Fresh vegetabels
Fresh potato
Frozen vegetables
Total
5. SWEET THINGS (Cg=129) Sugar
Jam
Chocolate and ice cream
Total
6. OTHER FOOD (Cg=143) Other edible oil
Food products
Coffee, tea and Cocoa
Mineral waters
Total
Notes:
1. Each scatter refers to good i which is a member of food group g, written giS , g 1,...,6 . There are gn goods in gS and the scatter refers to the gC countries. The variable on the vertical axis is the relative consumption of good i,
i glogq logQ , where g
g
g i S i ilogQ w logq is the volume index of gS and g
iw is the expenditure share of giS ; the horizontal axis refers to the corresponding relative price, i glog p log P , where g
g
g i S i ilogP w logp is the price
index of gS . The solid line is the regression line and the estimated slope is given in the text box.
2. To enhance visualisation, observations are omitted if (a) relative consumption lies outside the range (-3,1) or (b) the relative price lies outside (-1,1). In most cases, the number of omitted observations is less than 10 percent of the total.
The exceptions are other meat (22 percent of observations omitted), frozen fruit (29 percent) and frozen vegetables (24 percent); in these cases, there are more instances of relative consumption being below -3. These observations are
included in the regressions.
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-3
-2
-1
0
1
-1 0 1
-0.18 -1.91
-0.77 -0.62
-1.32 -0.35 -1.42
-3.01 -1.83 -1.28
-0.52 -2.96
-0.03
-2.69
-1.28
36
Figure 6.1 Quantity-Prices Plots for Food Groups
Notes:
1. Each scatter refers to one food group and contains 106 per circles, one for each country, and four diamonds for the income quartiles. The variable on the vertical axis is the
relative consumption of group g, glogQ logQ , where glog Q is group volume index defined in the notes to Figure 1.1; 6
i 1 g glogQ W logQ is the volume index of total
food and gW is the expenditure share of group g. The horizontal axis refers to the corresponding relative price, glog P log P , where glog P is group price index defined in
Figure 1.1; and 6
g 1 g glogP W logP is the index of price of all food. The solid line is the regression line and the estimated slope is given in the text box.
2. To enhance visualisation, observations are omitted if (a) relative consumption lies outside the range (-2, 1.5) or (b) the relative price lies outside (-1, 1). In most cases, the number of omitted observations is less than 5 percent of the total. The exception is sweet things where 13 percent of observations have been omitted. These observations are
included in the regressions.
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-1 -0.5 0 0.5 1
1. Staples
Country
Quartile mean
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-1 0 1
2. Meat and seafood
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-1 -0.5 0 0.5 1
3. Dairy
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-1 0 1
4. Fruit and vegetables
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-1 0 1
5. Sweet things
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-1 0 1
6. Other food
Slope coeff
-0.97
-1.80 -2.23
-1.40
-1.50 -0.36
Relative
Price
Relative
Quantity
37
Figure 7.1 Stylised Matrix of Price Elasticities, Direct and Indirect Effects Combined
Note: This 25×25 matrix illustrates the structure of price elasticities for the 25 food items. The light shaded blocks on the diagonal represent the price
elasticities for goods within each group. Within these blocks, the darker shaded elements are the own-price elasticities. The off-diagonal blocks contain non-
zero elements, which are the cross-price elasticities between goods from different groups.
Figure 7.2 Own-Price Elasticities: Unconditional versus Conditional
Group 1st Quartile 2nd Quartile 3rd Quartile 4th Quartile
Staples
Meat and
Seafood
Dairy
Fruit and
Vegetables
Sweet things
Other food
All
Note: The variable on the vertical axis is the unconditional own-price elasticity that contains the direct and indirect effects of the price change;
the horizontal axis is the conditional elasticity, made up of just the direct effect. The average difference between the unconditional and
conditional elasticities is given in the box in each plot. As the negative indirect effect makes the unconditional elasticity more negative than
the conditional version, these average differences are always negative and the observations (indicated by the circles) all lie below the 45-
degree line (the straight line in each plot).
-0.09 -0.18 -0.22 -0.21
-0.12 -0.23 -0.29 -0.27
-0.20 -0.41 -0.53 -0.48
-0.13 -0.14 -0.29 -0.28
-0.10 -0.19 -0.26 -0.22
-0.12 -0.22 -0.26 -0.26
-0.11 -0.20 -0.24 -0.23
39
Figure 7.3 Average Unconditional Price Elasticities
Note: This 25×25 matrix has the same structure as that of Figure 7.1. In addition, the matrix contains the averages over countries and goods of certain
classes of prices elasticities. Take, for example, the first main diagonal block, which refers to the within-group price elasticities of the items that belong to.
The average of the own-price elasticities is -0.88, while the average of the cross-price elasticities in the upper triangle of the block is 0.06. The adjacent
block immediately to the left refers to the effects on the consumption of staples of changes in the prices of meat and seafood. The average cross-price
elasticity here is 0.06 also. The other entries are interpreted similarly.
