21 October 2015

ENGEL’S LAW, DIET DIVERSITY AND THE QUALITY OF FOOD CONSUMPTION*

by

Kenneth W Clements and

Jiawei Si

Business School The University of Western Australia

Abstract

Increasing income brings about a decline in the relative importance of food

consumption, a wider spread of spending patterns and a demand for higher-quality goods.

Using an index-number approach, this paper analyses these three closely related tendencies.

Stripping out the impact of prices from the dispersion of food expenditures gives a volume-

based measure of diet diversity that is relevant for nutrition. Using unpublished ICP data for

28 items of food in more than 100 countries, we find that the income elasticity of diet

diversity ranges from 0.2 (for the poorest) to 0.5 (for the richest countries). The quality of the

food consumption basket, measured by an income elasticity-consumption covariance,

increases with income, but the elasticity is small. Approximately three-quarters of spending

on higher quality food is on account of larger volumes, with the remainder going into prices.

As the prices of luxuries relative to necessities tend to be higher in richer countries, the

structure of prices has a progressive impact on the global distribution of real incomes.

* We thank Aiden Depiazzi and Haiyan Liu for excellent research assistance and comments. For providing us with unpublished data, we thank the World Bank. The research was financed in part by the ARC and BHP Billiton.

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1. INTRODUCTION

In 1857, Engel (pp. 28-29) stated “the poorer a family, the greater the proportion of its

total expenditure that must be devoted to the provision of food,” and then extended this to

whole countries by arguing the richer a country, the smaller the food share (Stigler, 1954).

This is now known as “Engel’s law”, a law that enjoys such elevated status due to empirical

support that is near overwhelming. To describe it as immutable would be an overstatement,

but still the widespread applicability of Engel’s law gives it an almost unique status in

economics and something worthy of further examination.1

Chai and Moneta (2010) provide a useful retrospective on Engel’s work which was

written during the aftermath of the Industrial Revolution amid Malthusian concerns with too

rapid population growth. They succinctly describe the great importance of Engel’s research in

the context of that environment:

Engel argued that, even if there are no natural constraints on population growth, it was possible to avoid catastrophe if the economy’s productive capacity could be balanced with growing demand. This balancing is possible if the composition of goods and services supplied adapts to the evolving demand patterns of the population. For this reason, it was fundamental to Engel to investigate how the pattern of demand changes as household income changes. The finding that an increase in household income leads to a less than proportional increase in household food expenditures allayed fears that food demand grows at the same (geometrical) rate as the population. This finding enabled Engel to claim that population growth does not necessarily lead to a decline in welfare. (Chai and Moneta, 2010, p. 227)

Some insight into Engel’s law is given by the case of linear demands. When prices are

constant (as they might be at least approximately in a cross section of consumers), food

expenditure, e, depends on income, M: e e M . Denote the marginal propensity to spend

on food by θ e M, and the income elasticity by η log e log M θ w, where

w e M is the share of income devoted to food. It is usual to refer to θ and w as the

marginal and budget shares. When income grows, the change in the budget share is

dw θ w dM M η 1 w dM M , so that w falls with income growth when the

marginal share is less than the budget share or, equivalently, when the income elasticity is

less than unity, that is, when food is a necessity. Thus, a less-than-unity income elasticity is

just another way of expressing the law. In the simplest possible case of proportionality,

e βM, β 0, Engel’s law is not satisfied as the income elasticity is unity, and the budget

1 The classic reference for the validity of Engel’s law is Houthakker (1957). See also Chai and Moneta (2010), Chakrabarty and Hildenbrand (2009), Gao (2012), Houthakker (1987) and Ogaki (1992).

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share is constant and equal to β. It is only when some part of food expenditure is independent

of income that the elasticity is less than unity:

(1.1) β

e α βM, α,β 0, η , 0 η 1.α M β

Theα-part of food expenditure might be interpreted as the cost of “subsistence” consumption

needed to sustain life, perhaps something like the $1.25-per-day poverty line of the World

Bank. This would seem to be a natural way of thinking about the workings of Engel’s law.

The coefficient β in equation (1.1) is the marginal share.

Although simple, the linear Engel curve (1.1) is used in applied work to analyse the

allocation of income to the n commodities in the budget. Income is now interpreted as total

consumption, ni 1 iM Σ e , where ie is expenditure on good i, and there is a system of Engel

curves of the form (1.1),

(1.2) n n

i i i i ii 1 i 1

e α β M, i 1, , n, α 0, β 1.

The cross-equation restrictions on the parameters follow from the budget constraint

ni 1 iM Σ e . Suppose we define n positive parameters, 1 nγ , , γ and reparameterise the

intercepts in equation (1.2) as ni j 1 ij i jα Σ δ β γ , where ijδ is the Kronecker delta

ijδ 1 if i j, 0 otherwise . Then, (1.2) becomes Stone’s (1954) linear expenditure system

(LES):

(1.3) n n

i i i j ij 1 i 1

e γ β M γ , i 1, ,n, β 1.

The new intercept iγ is interpreted as the subsistence cost of good i and iβ is the

corresponding marginal share. According to (1.3), the consumer first spends nj 1 jΣ γ to satisfy

subsistence requirements and then a fraction iβ of the remaining income, nj 1 jM Σ γ , is

allocated to good i.

The income elasticity is the ratio of the marginal to the corresponding budget share.

The linear expenditure system (1.3) implies that elasticity takes the form:

(1.4) i

i nni i j 1 ji i j 1 j

β 1η ,

γ β 1 Σ γγ β M Σ γ M

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where i iγ γ M is the fraction of income accounted for by the subsistence cost of good i.

Thus, if good i is food, for its income elasticity to be less than unity, we require

ni j 1 j iγ Σ γ β ,

or, equivalently,

(1.5) iin

j 1 j

γβ .

Σ γ

In words, when the share of food in the total cost of subsistence exceeds its marginal share,

the income elasticity implied by the linear expenditure system is less than unity. This

attractively simple result again emphasises the importance of the independent-of-income

element of consumption for Engel’s law.

Something more can be said of food income elasticity in the context of (1.3). When

income increases by dM 0, it follows from (1.4) that the change in the income elasticity is

(1.6) i i

ni i i j 1 j

dη β M dM1 .

η Mγ β M Σ γ

Thus, the elasticity increases when the term in square brackets is positive, which occurs when

condition (1.5) is satisfied, that is, when good i is a necessity. This can be seen even more

clearly if we use equation (1.4) to express (1.6) as i i idη η 1 η dM M , which is

positive when iη 1. This means that in LES, the income elasticity of food increases with

income, so that food is less of a necessity, or more of a luxury, for the rich. This violates

economic intuition. This problem stems from the assumed constancy of the marginal shares

in LES, which is a weakness also shared by the Rotterdam model (Barten, 1964, Theil, 1965).

Working’s (1943) model provides a simple solution to the problem. Here the budget

share is a linear function of the logarithm of income:

(1.7) i i iw α β log M,

where the i and i are parameters satisfying n ni 1 i i 1 iΣ α 1, Σ β 0. The income part of the

almost ideal demand system (Deaton and Muellbauer, 1980) is (1.7). The implied marginal

share is i i iw , which is not constant. The income elasticity is i i i1 w , so good i

is a necessity if i 0. The differential of this elasticity is

i i i i i id 1 d w w , or, as i i id w w 1 dM M ,

2

ii

i i

1d dM.

M

4

Now, the income elasticity always falls as income grows (as long as i 0 ): The food

income elasticity for the rich is now lower than that for the poor, which solves the problem.2

In a series of studies, Seale, Theil and others mostly from Florida used Working’s

model to analyse cross-country consumption patterns with the data from the International

Comparisons Project.3 After allowing for differences in prices, Theil et al. (1989), for

example, estimate the food i in (1.7) to be in the vicinity of 0.15 , a value in broad

agreement with estimates from a number of other studies.4 To interpret this value, suppose

one country has income 0M and another’s is 02M , so it is twice as rich and the logarithmic

difference is 0 0log M log 2M M log2 0.69. Model (1.7) for i = food then implies

that the difference in the food share is i iw log M 0.15 0.69 0.10. In words, a

doubling of income leads to a fall in the food budget share by 10 percentage points, a result

Theil et al. (1989) refer to as “the strong version of Engel’s law”. Engel’s law in its

conventional form states that the food share declines as income rises, while the strong version

is a specific numerical statement of the nature of the decline in the share.5 The logical

extension of the strong version is to use the food share itself as an inverse measure of living

standards; see Clements and Chen (2010) and the references therein. The advantage is the

ready availability of this share and because it is unit free and dimensionless, immediate

comparisons of can be made across countries and time without tricky exchange-rate or

inflation adjustments.6

2 Working’s model is the income term of the almost ideal demand (AID) model of Deaton and Muellbauer (1980). In reporting Angus Deaton’s Nobel Prize, The Economist (2015) describes the advantages of the response to an income increase in AID: “... in earlier models, demand was assumed to increase in lock-step with income, regardless of how rich the person was. The new approach allowed for different responses according to the level of income, so that a 1 percent pay boost might raise porridge demand by 2 percent for a pauper, but only 0.1 percent for a prince.” Part of this colourful example is correct – the income elasticity of porridge falls as income rises, from 2 for the pauper to 0.1 for the prince. But this means porridge transforms itself from a luxury into a necessity, something ruled out by AID as is clear from the expression for the income elasticity

i i1 β w , with

iβ constant and

i0 w 1.

3 Clements and Theil (1979), Theil and Suhm (1981), Theil (1987), Theil et al. (1989) and Seale and Regmi (2006). Related research includes Meade et al. (2014), Muhammad et al. (2011), Regmi and. Seale (2010), Seale et al. (1991), Seale et al. (2003), Seale and Regmi (2009), Seale and Solano (2012) and Theil (1996). 4 See Chen (1999), Chung and Lopez (1988) and Yuen (1999). It should be noted, however, that there is some

other evidence indicating that Working’s food i

is closer to -0.10 (Izan and Clements, 1979, Clements and

Chen, 2010), in which case a doubling of income leads to a fall in the budget share of about 7 percentage points (rather than 10 points). 5 The strong version of Engel’s law also has implications for the price elasticity of demand for food. If the Slutsky price elasticity (which hold constant real income) is approximately constant, then under preference independence a doubling of income leads to the Cournot price elasticity (money income constant) falling in absolute value by about 0.10. For details, see Clements and Chen (1996). 6 Engel (1857) himself suggested the food share as a measure of living standards.

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Another related example of the use of Engel’s law is in the measurement of inflation.

The most frequently quoted measure of inflation in many countries is the consumer price

index. This is usually a Laspeyers’ index, which uses base-period budget shares as weights.

The fixed weights cause “true” inflation to be underestimated due to substitution and quality

biases. One approach to adjust for the bias is to examine the Engel curve for food – a plot of

the food share against real income over time. A share lying below the regression line is

interpreted as an underestimation of real income stemming from an over estimate of the price

level. If in the context of model (1.7) for i = food, the residual is iε̂ 0, then income is

understated and the price level overstated by i iˆ100 exp ε β 1 percent, where iβ 0 is

the income slope. Thus, if, for example, the budget share is understated by one-half of a

percentage point, then with iβ 0.15, there is an overstatement of the price level of about 3

percent. This approach to the CPI bias was initiated by Hamilton (2001).

It is not widely appreciated that Engel’s law has broader implications for the structure

of all consumption expenditure. First, with food occupying a larger part of the poor’s budget,

this tendency to specialise means that their budgets are less diversified than those of more

affluent consumers. Relatedly, within the food budget, cheaper, more starchy foods (such as

rice, potatoes and bread) are likely to be predominant for the poor, leading to less nutritious,

less diversified diets. There has been some fairly recent research on the diversity of

consumption patterns and its relation to income by, e. g., Chai and Moneta (2012), Drescher

et al. (2008), Falkinger and Zweimüller (1996), Jackson (1984), Shonkwiler et al. (1987),

Theil and Finke (1983) and Thiele and Weiss (2003); for a survey, see Chai et al. (2015).

A second implication of Engel’s law is the quality of consumption. With food a

necessity, all other goods as a group must be a luxury. Thus, if we identify luxurious goods

with quality, the relative importance of luxuries can be used as a measure of the quality of the

overall budget. The declining food share that accompanies income growth means that the

quality of consumption rises. This approach to quality measurement, due to Theil (1975/76)

and extended by Clements and Gao (2012), involves a covariance between the income

elasticities and consumption of the n goods in the budget, such that when consumption moves

in the direction of luxuries, away from necessities, the quality of the budget is said to

improve. That high quality goods tend to be intensively consumed by the rich is an

uncontroversial statement. The converse is that low quality goods are intensively consumed

by the poor. As food is the good consumed intensively by the poor, there is a natural link

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between Engel’s law and the measurement of quality. In other words, quality and luxury are

inextricably bound up.7

This paper deals with the three related themes of Engel’s law, the diversity of food

consumption patterns and their quality. Sections 2 and 3 introduce the data to be used --

unpublished disaggregated data on consumption of 28 food items in more than 100 countries

from the International Comparison Program. Those sections also contain an examination of

the implications of Engel’s law for the individual food items: Some items are less responsive

to changes in income than food as a whole, so when income rises, their budget shares fall

relative to that of food as a whole; for other items of food, the opposite occurs. Using a

statistical approach to consumption economics that contains elements of index-number theory

(Theil, 1967), we show in Sections 4 and 5 how diversity of the consumption budget can be

split naturally into components due to differences in prices and volumes. This distinction is

key for food, since it is the diversity of volumes that makes for a more varied, more

nutritional diet. This is different to some other measures of diet diversity that simply use the

diversity of expenditure shares without stripping out the effects of prices. Sections 6 and 7

analyse the quality of food consumption with the covariance approach. This includes

measures of the quality of spending, the “volume” of quality and its price. Better quality

comes with higher prices, as expected, but about three-quarters of spending on higher quality

food is on account of a larger volume, with the remainder going into prices. Higher incomes

bring higher quality, but the elasticity is small -- consumers aspire to better quality food, but

this can only be achieved with substantially higher incomes. Concluding comments are given

in Section 8.

2. THE STRUCTURE OF FOOD BUDGETS

Engel’s law says that food absorbs a decreasing part of the budget as affluence rises.

But by exactly how much does the food share fall and, relatedly, how does the composition of 7 There are two conventional approaches to measuring quality. The first is the hedonic approach, according to which prices paid are regressed on the important physical characterises of the goods to obtain their shadow prices; constant-quality prices are then obtained by stripping out the effects of the enhanced characteristics of the goods (Griliches, 1961). The second approach involves using prices themselves as a measure of quality. On the understanding that prices are approximately constant in a cross section of consumers, the income elasticity

of food is usually measured by the elasticity of expenditure, η log e log M , where e p q. But when

prices paid vary with the income of consumers, η becomes the sum of (i) a quantity elasticity log q log M ;

and (ii) a quality elasticity log p log M (on account of the rich purchasing higher-priced items, which is

taken to represent higher quality). Houthakker (1987) describes the distinction between the two components as “agriculture produces quantity, while food processing and trade produce quality”. The second approach is due to Prais and Houthakker (1955) and Theil (1953). For related research, see Bils and Klenow (2001), Cox, and Wohlgenant (1986), Cramer (1973), Deaton (1988), Gale and Hang (2007), Hicks and Johnson (1968) and Yu and Abler (2009).

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the food spending change as we move from poor to rich consumers? This section deals with

these issues by studying the underlying components of Engel’s law.

Table 2.1 lists 128 countries in terms of decreasing 2005 income per capita (which we

measure by real total consumption per capita).8 The richest is Luxembourg, while Liberia is

the poorest. Countries are grouped into income quartiles and, roughly speaking, these

correspond to the rich, middle income, poor and very poor, respectively. The average income

of countries in the first quartile is $22,557, $10,434 in the second, $4,034 in the third and

$1,115 in the bottom. Thus, on average, the rich are about 20 times as affluent as the poorest.

The bottom of the table gives the corresponding food budget shares, the proportions of total

consumption devoted to food. In the rich countries, food absorbs just a bit more than 10

percent of the budget, while this is well over 40 percent in the very poor. Figure 2.1 plots the

food shares against the logarithm of income and as can be seen, there is a strong tendency for

the share to fall with increasing affluence, in agreement with Engel’s law. The regression line

is of the Working (1943) form (1.7), w log M with 0 . The coefficient is

interpreted as the change in the share corresponding to a one-percent increase in income.

Thus, if we move from a poor country to a richer one with twice the income, the food share

falls by w log 2, as before, or about 7.5 percentage points when the slope coefficient,

×100, 11 .9

If the food share falls with increasing income, which food items do most of the

adjusting? Some will fall at the about same rate as total food, while others will change faster

or slower; conceivably, the shares of some items of food may even increase with higher

income. To investigate this issue, we consider for the 128 countries the 28 food items listed in

column 1 of Table 2.2. Let i ip q be expenditure on good i i 1, , n goods , so that

i i iw p q M is the budget share of i, where ni 1 i iM Σ p q is total consumption. If the n goods

are ordered so that the food items are the first 28, then 28i 1 iW w is the (total) food share.

Averaging over all countries, it can be seen from column 6 of Table 2.2 that the important

items in the food budget are rice, other cereals and bread, which absorb 2.1, 2.2 and 1.4

percent of the budget, respectively. Then come beef and veal (accounting for 1.6 percent) and

fruit and vegetables (1.4 and 2.1 percent). Columns 2-5 contain the budget shares for each

8 The data to be used are derived from unpublished disaggregated data from the 2005 International Comparison Program (World Bank, unpublished), supplied to us by the World Bank. Hereafter, we use the abbreviation “ICP” to refer to this source. For details of the data, see Appendix A1. 9 A scatter plot shows that our measure of income is roughly proportional to GDP per capita.

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income quartile and as is to be expected, for many items there is considerable disparity across

the income distribution. Taking rice as an example, consumers in the first quartile (the

richest) spend only 0.2 percent of their income (that is, total consumption) on this item, while

that proportion increases by a factor of more than 20 to be 5.6 percent for the fourth quartile

(the poorest).

To make a systematic comparison of the differences in the shares, consider the food

share in country groups G and H, to be denoted by G HW and W . The differences

G HW W for G, H 1, ,4 income quartiles form a 4 4 comparison matrix that is skew

symmetric, the upper triangle of which is given in Table 2.3. This shows that for the

poorest/richest comparison, the food share falls by 34 percentage points as income rises. This

overall fall is made up of the corresponding changes in the shares of the 28 food items.

Column 2 of Table 2.4 gives these changes for the same poorest/richest comparison: The

large falls are for rice (whose budget share falls by 5 percentage points), cereals (5 points),

beef (2 points), vegetables and potatoes (3 points each). As beef would be considered to be

consumed more intensively by the more affluent, the fall in its share as income rises is

surprising. But the other falls are reasonable as they refer to staples (rice and cereals) and

vegetables that are heavily consumed by the poor because of their cheap nutritional value.

These falls account for almost one-half of the overall fall in the food share of 34 points (the

last element of the column). The other items account for the remaining half of the overall fall.

However, there are two positive elements at the bottom of the column: The share of cheese

and confectionary both rise with income, which is understandable as these might reasonably

considered to be luxuries, consumed more heavily by the more wealthy. The other columns of

the table refer to the results for the other four pairs of country groups. These results are

broadly similar to the poorest/richest comparison, but are less dramatic as the income

differences are less substantial.

3. THE CASE OF STAPLES

On the basis of the budget shares, rice and cereals standout, especially for poorer

countries. At the other end of the income distribution, bread and other bakery products are

important for the richer countries. Because of the special nature of these products, which can

be termed “staples”, we shall consider them in some more detail. As pasta products would

seem to be closely related, it is reasonable to also include these in the staples group. Thus, the

staples group comprises the first five items of Table 2.2.

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Consider expenditure on the thi staple, expressed as a fraction of total spending on all

5 staples, 5i i j 1 j jp q Σ p q , which is the conditional budget share of i. These conditional shares

are given in Table 3.1 for each income quartile. The contrast between spending on rice and

bread can be summarised as follows:

Income quartile

Commodity First Second Third Fourth All

Rice 9 15 26 39 22

Bread 37 40 28 13 29

The shaded elements reveal that bread consumption dominates rice in the higher-income

countries (the first and second quartiles), but things are reversed for the less affluent

countries. For the first quartile, the shares for rice and bread are 9 and 37 percent,

respectively, while these become 39 and 13 percent for the fourth; these are not the exact

mirror image of each other, but close to it. Table 3.1 also reveals large changes across the

income distribution in the budget share for other cereals (the share is 11 and 40 percent for

the top and bottom quartiles, respectively), as well as that for other bakery products (32 vs 4

percent).

These large disparities mean that it is worthwhile to consider further the degree of

specialisation in staples consumption. As expenditures on goods within a country are

measured in terms of the country’s currency, they can be added over goods. Thus, we can

aggregate the five staples into three by simply adding expenditures of the relevant

components or, what amounts to the same thing, adding the (conditional) budget shares. This

yields three budget shares with a unit sum that can be represented as a point in an equilateral

triangle. Panel A of Figure 3.1 contains such a triangle with the budget share vectors for each

of the 128 countries. Here, the three goods are rice, cereals and other, where other is the sum

of the three more basic goods (i) bread, (ii) other bakery products and (iii) pasta. As can be

seen, 70 of the 128 countries are located in the sub-triangle at the top with base the dotted

horizontal line which corresponds to the budget share of the good “other” being 50 percent.

Accordingly, in these 70 countries the good “other” accounts for at least one-half of staples

expenditure: As these countries devote very little of their staples expenditure to cereals and

rice, and most to other, it could be said they are “specialised” in the consumption of this

good. Similarly, 13 percent of countries are cereal specialists (the sub-triangle at the bottom

left) and 14 percent rice specialists (bottom right). The remaining 18 percent of countries

have a more even distribution of expenditure and since no single good accounts for more than

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50 percent, they could be described as being more “diversified” (generalists?). As 100 - 18 =

82 percent of countries specialise in one or other of the three goods, the conclusion is that the

staples consumption has a distinct tendency to be specialised. The other two panels of the

figure confirm that this conclusion continues to hold when the staples basket is aggregated

differently.

This specialisation-in-consumption characteristic of countries is perused further in

Table 3.2. Column 2 refers to the 35 countries where spending on rice is the largest among

the five members of the staples group (“rice eaters”). The next three columns refer to

countries for which the other staples dominate. As can be seen, the “other” group is the

richest with a per capita income more than three times that of rice eaters, the poorest group.

But it is to be emphasised there is considerable (huge?) diversity within groups of countries,

especially the rice eaters: The standard deviation of rice eaters’ income exceeds 100 percent

of mean income. There is also an interesting difference regarding spending on all staples:

From the last row of the table, rice and cereal eaters spend about one-quarter of their food

budget on staples, while in the remaining countries this share is about 9 points lower at 16

percent. In large part, this reflects the lower incomes of the rice and cereal eaters, as is

confirmed by Table 3.3 which cross classifies countries by income and the dominant staple.

This shows that among rice and cereal eaters, there is a preponderance of lower income

countries, while richer countries are over represented in the bread eaters and other groups.

The hypothesis that the dominant staple is independent of income is firmly rejected, as

indicated by the large 2χ value.

4. SPECIALISATION AND DIVERSIFICATION OF THE MENU

Table 2.2 showed that the budget share of food in the poorest countries is, on average,

more than 40 percent, while this falls to a little above 10 percent for the richest. Thus, in this

sense, the budgets of the poor tend to be specialised in food, while the rich consume a more

diversified baskets of goods. The same rule also applies within the staples budget. Looking

again at Table 3.1, there is a tendency for the cross-commodity dispersion of the conditional

shares for staples to increase as income falls. Here, the standard deviation (SD) for the rich is

16 percent, while this increases to 22 for the poor; as a lower SD implies more equal shares,

this means more diversity of consumption. The emphasis that nutritionists place on the role of

a balanced, or diversified, diet for good health is one reason for interest in the diversity of

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consumption.10 A related reason is that greater diversity is usually thought to be a good thing

in and of itself, which possibly reflects a basic concavity of the utility function. Diversity

usually goes with enhanced opportunities for choice as encapsulated in aphorisms such as

“variety is the spice of life”, “don’t put all your eggs in one basket” and “a change is as good

as a holiday”.11 In this section we explore the measurement of diversity of the food budget,

how this varies internationally and its relationship with income differences.

Suppose there are n goods in the consumption basket with prices 1 np , , p and

quantities demanded 1 nq , ,q . Thus, as before, i ip q is expenditure on good i and

i i iw p q M is its share in total expenditure ni 1 i iM Σ p q , or the thi budget share; for

brevity, we shall continue to refer to M as “income”. An obvious measure of central tendency

of the n prices is the budget-share weighted average, which in logarithmic form is

(4.1) n

i ii 1

log P w log p .

This index is the logarithm of the weighted geometric mean of the prices, the weights being

the budget shares which serve to reflect the relative economic importance of each good to the

consumer. To interpret this index further, consider a discrete random variable X that can take

n possible values 1 nlog p , , log p , and suppose prices are drawn at random from this

distribution. If each dollar of expenditure has an equal chance of being selected, the

probability of drawing ilog p is iw . Accordingly, the expected value of X is

ni 1 i iE X w log p , which is index (4.1). Thus, the index log P can be interpreted as the

expected value of the distribution of prices, which is an appealing way of summarising the

distribution of prices (Theil, 1967, pp. 136–137).12 Prices are measured in terms of domestic

currency units, euros in Italy and pounds in the UK, for example, which are obviously not

comparable. The same applies to the price index (4.1). But as currency units drop out in the

relative price of good i, i ilog p P log p log P, this is comparable across countries.

A summary measure of quantities, similar to the price index (4.1), is

(4.2) n

i ii 1

log Q w log q .

10 The Healthy Eating Index of the US Department of Agriculture, e., g., advocates the inclusion of a variety of food types in the diet (Guenther et al., 2013). For a review of measures of diet diversity that appear in the nutritional and economics literature, see Doan (2013). 11 Conceivably, we could add to this list “diversity is our strength”, “two heads are better than one” and “the wisdom of crowds”. 12 Deaton and Muellbauer (1980) refer to expression (4.1) as Stone’s (1954) index.

12

As this is a budget-share weighted average of the n quantities, it can be viewed as a

logarithmic volume index or a measure of real income. To be able to average across

commodities in this manner requires that their units be comparable, which is the case with the

ICP data as they are all expressed in terms of US dollars. Finally, a similar weighted

logarithmic mean of the n budget shares 1 nw , , w is

(4.3) n

i ii 1

log W w log w .

This is the negative entropy of the distribution of the shares.13 The above indexes can be

considered as weighted first-order moments of the n prices and quantities. The corresponding

second-order moments are:

(4.4)

n n2 2

p i 1 q i ii 1 i 1

2n

w i ii 1

w log p log P , w logq logQ ,

w log w log W .

These are measures of dispersion of prices, quantities and budget shares around their

weighted means. There is also the weighted price-quantity covariance and the associated

correlation

(4.5) n

pqpq i i i

i 1 p q

w log p log P logq logQ , ,

As the consumer tends to move away from those goods with higher prices towards those with

lower prices, we expect the covariance and correlation to usually be negative. The measures

in (4.4) and (4.5) are all pure numbers and thus unit free. The logarithmic deviation of the

share from its weighted mean can be expressed as

i i ilog w log W log p log P logq logQ . Squaring, weighting by iw and then

summing over i = 1,..., n, gives

(4.6) w p q pq2 .

13 As budget shares are nonnegative and have a unit sum, as mentioned above they can be interpreted as probabilities of drawing at random each of the n goods. One way of measuring information is by some function that increases with the reciprocal of the probability of an event 1 . Thus, the occurrence of a low-probability

event is more informative than one that is more likely. For example, we learn more from being informed that it rained in January in Perth, than it being dry and hot, as it usually is. The logarithmic function is usually employed because of its convenient additive property for independent events, so the measure of information is log log1 . If there are n possibilities with probabilities 1 n, , , the expected information contained in

this distribution is then ni 1 1 iH log , 0 H log n. This H is the entropy of the distribution (Shannon,

1948, Thiel, 1967).

13

In words, the variance of the budget shares is made up of the sum of the variance of the

prices, the variance of the quantities and twice the price-quantity covariance.

To apply the above concepts to the food basket, iw is interpreted as the proportion of

food expenditure devoted to the t hi type of food (the conditional budget share), iq is the

corresponding per capita volume and n is the number of food items. The averages over the

128 ICP countries of these conditional shares for n = 28 food items are contained in Table

4.1. The volume index (4.2) for food by income quartile is contained in column 2 of Table

4.2. Thus, for example, the log difference in the volume of food consumption per capita

between the second and first quartiles is 4.07 - 4.46 = -0.39, or 0.39100 e 1 32

percent. There is a much bigger drop in going from the third to the fourth quartile, where the

log difference is 2.74 - 3.59 = -0.85, or almost 60 percent.14 The budget-share variance of

(4.4) is an inverse measure of diet diversity as a more specialised diet has a larger variance of

the budget shares and is thus less diverse. As can be seen from column 3 of Table 4.2, this

variance rises noticeably as income falls, which confirms the greater diversity of the diets of

the rich and the lower diversity of those of the poor. For the first quartile, the standard

deviation (SD) 2w 51.05 10 71 percent, while this is about 98 percent for the

fourth quartile.

As shown by equation (4.6), the budget-share variance comprises price, quantity and

covariance terms. As nutrition is associated with the quantities consumed, the quantity

variance q is the relevant measure as it strips out the influence of prices. Columns 4 and 5

of Table 4.2 reveal that quantities contribute a relatively large part of the budget-share

variance and prices a small part. On average, quantities are more than five times more

variable than prices on the basis of the variances, or more than twice as large if the SDs are

used. One other feature of the results of this table should be noted. The SD of budget shares

lies between the other two, p and q . From equation (4.6), w q when

p pq2 , or, using pq p q , where is the correlation, when p q 2 .

Similarly, w p when p q 1 2 . These two inequalities are simultaneously

satisfied when 0.5 ρ 1. When we aggregate over diverse countries, some satisfying the

basic inequalities, some not, the sharpness of the bounds on the correlation is lost, but still the

14 For a further discussion of the food volume index, see Appendix A2.

14

analysis can be used as an informal guide. From the last entry of column 7 of Table 4.2, the

average value of the price-quantity correlation is slightly less than -1 2 , so that the above

condition is satisfied in an average sense (but this is not the case for the first quartile where

the correlation is -0.28). A final point on the indexes is that in more than two-thirds of the

128 countries the correlation is negative (Figure 4.1), so there is a distinct tendency of food

consumption to move away from the more expensive items, towards the cheaper ones.

To provide some more detail of the income sensitivity of the variances, Figure 4.2

plots the three variances against income. The coefficient of the log of income in panel A is

-28.88. This means that a 10-percent increase in income leads to an almost 3-percentage-

point fall in the quantity variance q. The income elasticity takes the form q28.88 ,

which using the values of q from column 5 of Table 4.2, ranges from about

-0.5 for the first income quartile to -0.2 for the fourth quartile. Thus, we see again that diet

diversity increases with income, but the elasticity is not particularly high. The other two

panels of Figure 4.2 reveal that the budget share and price variances also both fall with

income; and that a 10-percent increase in income leads to a fall in the budget share variance

of 1.7 percentage points, while the price variance falls by 0.6 points.

5. THE COMPONENTS OF DIVERSITY

What more can be said about the nature of diversity of the food consumption? Do

particular items behave in a ways that are especially important in driving overall diversity?

Dividing goods into broader groups means that the dispersion of the budget as a whole can be

partitioned into a within-group component and a between-group component. It might be

expected that if goods within each group are sufficiently similar, the majority of the

dispersion is confined to the between-group component. But in view of the huge differences

in incomes, this might not be the case because of the large differences in budget shares across

countries. Other issues arising include, Are prices more different than quantities within each

group and in their within- and between-group patterns? What of the price-quantity covariance

at the group level? This section investigates these matters.

Suppose the n goods are combined into G < n groups, to be denoted by 1 G, , ,S S

such that each good belongs to one group only. Define the share of income spent on group g

and the share of group expenditure devoted to giS as

i S i i i i i

g i i gi S i i i gg

g

g

p q p q wW w , w , i .

M p q W

S

S

15

The indexes of prices, volumes and budget shares for group g are

g i i g i i g i ii S i S i Sg g g

log P w log p , logQ w logq , log W w log w .

These indexes are the group counterparts of the indexes for the n goods, equations (4.1)-(4.3),

and satisfy G G Gg 1 g g g 1 g g g 1 g gW log P log P, W logQ logQ and W log W log W,       so they

are consistent in aggregation.15 The variance of the n budget shares can be decomposed into

between- and within-group components:

(5.1) n G G2 2 2

i i g g g i i gi 1 g 1 g 1 i g

w log w log W W log W log W W w log w log W .

S

The between-group component -- the first term on the right-hand side -- is a weighted

variance of the (logarithmic) group shares. The second term is the within-group component,

which is a weighted average of the group variances 2

i i i ggw log w log W , g 1, ,G. S  

In both cases, the weights are the group budget shares 1 GW , ,W , which are positive

fractions with a unit sum. The price and quantity variances of (4.4) can also be decomposed

in an analogous manner.

We apply the decomposition (5.1) to the n = 28 food items that are divided into the G

= 6 groups of column 1 of Table 5.1.16 Columns 2-5 contain, for each quartile, two sets of

budget shares, those for the group (the emboldened figures) and the conditional shares (not

emboldened).17 Consider first the six group shares. Column 6 refers to all countries and this

shows that with a budget share of 26 percent, meat and seafood account for the largest part of

the budget, on average. Then follows staples with a budget share of 21 percent, and fruit and

vegetables are a close third (20 percent). As before, there is considerable diversity of the

budget shares across the income distribution. As discussed in Section 3, this diversity is

particularly large for the staples group, where the share rises from 16 percent for the first

quartile to almost 30 percent for the fourth. The conditional budget shares describe the

allocation within each group. Thus, from column 6 again, on average for all countries,

15 Note that glog W is not the same as glog W where ig i g

W w . S 16 The broad guiding principles of the classification scheme are that (i) groups contain items that could reasonably be considered to be “similar” in the eyes (mouths?) of consumers; and (ii) the number of items in each group be fairly similar. 17 The information in Table 5.1 can be derived from Table 2.2: The group budget shares are the sums of the component shares of Table 2.2, while the conditional shares are normalised versions of the original (unconditional) shares of Table 2.2. Although Table 5.1 contains the same basic information, it is nonetheless instructive to present the data in this format. Note also that the conditional shares for staples in Table 5.1 are the same as those of Table 3.1.

16

spending on staples is made up of 22 percent for rice, 25 percent for other cereals, 29 percent

bread and so on.

Table 5.2 applies decomposition (5.1). Consider the last row of panel A, which refers

to the budget-share variances for all countries. The variances for the first five food groups

(given in columns 5 to 9) are roughly the same at around 0.4-0.5, but the variance for the last

group, other food, is somewhat lower at 0.32 (column 10). The weighted average of these six

variances is 0.44, which is the within-group component of column 4 of this row. As the total

variance is 0.67 (column 2), the share in the total of the within-group part is 0.44/0.67, or

about two-thirds, so the within-group component dominates. Panel A of Figure 5.1 is a

visualisation of this decomposition by income quartile. As can be seen, the within component

is always more than one-half and less than 80 percent, not too far away from two-thirds. The

other panels of this figure summarise the decompositions for prices, quantities and the price-

quantity covariance.18 In the majority of the 20 cases, the within-group component of the total

variance dominates; and across the world income distribution, the rule of two-thirds does not

lead us too far astray.

As noted above, from the perspective of the nutritional value of the budget, the

diversity in food volumes is the important concept. The decompositions of the variance of the

quantities, given in panel C of Table 5.2, show that in all cases, the staples group has the

largest, or second largest, dispersion among the six groups. This again underscores the special

role of staples in cross-country consumption patterns. The quantity variance for other food is

the lowest in three of the four quartiles and second lowest in the remaining quartile. The

between-group component of the quantity variance is an inverse measure of diet diversity

among the food groups – the spread of food consumption across staples, meats, diary, fruit,

etc. Arguably, this is the important measure of the nutritional value of the diet as it measures

diversity of consumption at the broad level. Column 3 of panel C reveals huge differences in

this measure across the income distribution. For this variance, the ratio for the richest to the

poorest consumers is 13.80 68.09 1 5, so that diets of the rich are about 5 times more

diverse than the poor’s. Contrast this with the total variance (column 2), for which the

diversity ratio is 160.78 143.63 2.4,

or about half as much as the between-group measure.

The conclusion is clear: Ignoring the between-within distinction for the broader food groups,

and just focusing on the total variance, masks a substantial part of the inequality of diet

diversity.

18 Appendix A3 contains the detailed results for the covariance.

17

Figure 5.2 is similar to Figure 4.2 and contains scatter plots of the second moments of

staples against income. This shows that the dispersion of staples quantities, prices and budget

shares all fall as income rises, as before for total food; but now the effect is somewhat

smaller. This might seem surprising in view of the large cross-country differences in the

expenditure patterns for staples, but the variances under consideration here measure the

degree of cross-commodity dispersion within each country, not across countries. Table 5.3

summarises in another way the within-group dispersion measures. Columns 2 and 3 show that

in a clear majority of cases, prices and quantities are negatively correlated. Sweet things are

the exception to this rule, especially in the richer countries – is this prima facie evidence that

higher incomes come with a near-addiction to sweet-tasting foods? Quantities are more

variable than prices in almost all cases (column 4), while, from column 5, the dispersion of

budget shares mostly lies between those of quantities and prices (the only substantial

exception is sweet things again). This result is consistent with the price-quantity correlation,

averaged over all items, being slightly less than -1/2, as discussed in the previous section.

6. CONSUMING QUALITY

As emphasised previously, the fall in the food budget share as income rises is

dramatic, from 44 percent in the poorest countries to 11 percent in the rich (Table 2.2). Thus,

as affluence rises, spending moves away from the dominant necessity of life to goods with a

less-of-a-necessity status. In a fundamental sense, the “quality” of the consumption basket in

the rich countries is noticeably higher. This notion of quality can be applied to all goods, not

just food: As spending moves away from necessities towards luxuries, the quality of

consumption can be said to improve. Here, quality is based on the revealed preference of the

consumer, not on any outside judgments as to what constitutes quality. This measure of

quality is different to the usual hedonic approach, which deals with the physical

characteristics of good (Griliches, 1961). The hedonic quality of a computer, for example, is

based on its memory, speed, etc., not on intangibles like its “feel”.19 That many people buy

expensive Apple computers (especially prestige-conscious Gen Ys) points to the importance

of such intangibles in a broader view of quality. The luxury/necessity quality framework, due

to Theil (1975/76) and extended by Clements and Gao (2012), leads to indexes of quality of

the consumption basket and its price.20

19 See, for example, Berndt and Rappaport (2001). 20 In what follows, we present a levels-formulation of the approach of Clements and Gao (2012). To aid interpretation, we also introduce an index of the quality of spending, which is a covariance between the income elasticities and expenditure. This approach to quality avoids the problem of hedonic analysis that there are only

18

The quality of the consumption basket is based on its composition in terms of luxuries

and necessities. We defined in equation (4.2) a volume measure of consumption as a budget-

share weighted average of the quantities consumed of the n goods as ni 1 i ilog Q Σ w log q .

Here, i i iw p q M is the budget share of good i, the proportion of total spending (M,

“income” for short) devoted the good. The relative importance of the volume of consumption

good i can be measured by its logarithmic deviation from average,

i ilog q Q logq logQ, which satisfies ni 1 i iΣ w log q Q 0. If the good is a luxury, so

that its income elasticity iη 1 , it contributes positively to the quality of the basket when its

consumption is above average, that is, when ilog q log Q 0. Alternatively, were good i a

necessity, its above-average consumption detracts from quality. Thus, the general proposition

is that intensive (limited) consumption of a luxury (necessity) enhances quality, while limited

(intensive) consumption of a luxury (necessity) detracts from quality. This measure of quality

involves the sign of the product i iη 1 log q log Q . To apply this to all n goods

simultaneously, we take a budget-share weighted average of these products:

(6.1) n

η,q i i ii 1

y w η 1 logq logQ .

This can be considered as an index of the quality of consumption. It is a weighted covariance

between the n income elasticities, 1 nη , η , and consumption, 1 nlogq , , logq . The use of

budget shares recognises that some goods are more important than others to the consumer and

serves to make η,qy a representative index.

To interpret index (6.1) further, define i i iθ p q M as the marginal share of good

i, which answers the question, if income increases by $1, what fraction is spent on the good?

As the additional $1 is completely spent, the n marginal shares have a unit sum. The

relationship between iθ and i is that the income elasticity is the ratio of the marginal share

to the corresponding budget share, i i i iη θ w log q log M . As ni 1 iΣ θ 1,

ni 1 i iΣ w η 1, so the term iη 1 in (6.1) is the deviation of the income elasticity from its

a limited number of commodities that possess easily-identified physical characteristics -- many services (such as education and medicine) have little or no physicality. Another problem is that if the baseline “constant-quality” good of hedonics is no longer available to consumers, the meaning of a decline in the price of a now-non-existent good is unclear. For a further discussion, see Clements and Gao (2012).

19

weighted mean. As only one variable needs to be deviated from its mean in a covariance, and

using i i iw η θ , index (6.1) can be expressed as

n n n n

η,q i i i i i i i i i ii 1 i 1 i 1 i 1

y w η 1 logq θ w logq θ logq w logq .

The term to the right of the third equals sign is the difference between two weighted averages

of the quantities. The first is marginally weighted, while the second is weighted by the budget

shares and equal to logQ. As these are both logarithmic averages, so is their difference,

which establishes that the quantity index η,qy is logarithmic. In terms of levels,

i iθ wn nη,q i 1 i i 1 iexp y Π q Π q . Thus, if, for example, for some country η,qy 0.05, then the

marginally weighted index is approximately 5 percent larger than its budget-share

counterpart. If in some other country η,qy 0.02, it can then be said that the quality of the

consumption basket in the first country is 7 percentage points above that in the second.

If consumption is log-linear in income, as measured by the index exp log Q ,

i i ilog q α η log Q, then η,q ηy V logQ A, where 2nη i 1 i iV Σ w η 1 is a weighted

variance of the income elasticities and ni 1 i i iA Σ w η 1 α . This shows the income

sensitivity of quality is the variance ηV . 21 Thus, when all income elasticities are unity, budget

shares remain unchanged with income growth, the variance is zero and quality is constant; in

all other cases, ηV 0 and quality increases with income. The more dispersion there is

among the elasticities, the greater is the income sensitivity of quality.

The quality of spending (price times quantity) can also be measured by a weighted

covariance between the income elasticities and expenditure on the n goods,

1 1 n nlog p q , , log p q :

(6.2) n n

η,pq i i i i j j ji 1 j 1

y w η 1 log p q w log p q .

This index satisfies η,pq η,q η,py y y , where

(6.3) n

η,p i i ii 1

y w η 1 log p log P

21 When

η ,qy is used to measure quality, the income elasticity of quality is

η η,qV y , so that η

V is the

percentage-point change in η ,q

y following a one-percent change in income (a type of semi-elasticity, in inverse

form). Alternative, if we were to choose η ,qexp y to measure quality, then

ηV is its income elasticity.

20

is a weighted covariance between the income elasticities and the n prices, with

ni 1 i ilog P Σ w log p , a cost-of-living index. Thus, η,py acts as a deflator that transforms the

quality of spending, η,pqy , a nominal concept, into the quality of consumption, η,qy , a real

concept. This means that η,py can be interpreted as an index of the price of quality.

As before, the indexes (6.2) and (6.3) are logarithmic measures. If, for example, for

two countries c and d, c dη,p η,py y , then the relative prices of luxuries are, on average, higher

than those of necessities in c in comparison to d. As the rich spend relatively more on

luxuries, in this case, the structure of prices in country c has a progressive impact on the

distribution of real income as compared to the price structure in d. Conversely, when

c dη,p η,py y , prices are regressive in c relative to d.22

As with diversity, it is useful to decompose the quality indexes by dividing the n

goods into G n groups, 1 G,..., .S S Given real total spending on group g, the income

elasticity of demand for good giS is i i gη η η , where i iη log q log M is the

conventional income elasticity of i and gg i i iη Σ w η S is income elasticity of the group gS as

a whole. Here, i i gw w W is the share of group expenditure devoted to i, where iw is the

budget share of i, and ig i gW w S is the group budget share, as before. In other words, iη

and iw are the within-group, or conditional, income elasticity and budget share of good

gi .S As in the previous section, define the volume index for group g as

g

gi i ilogQ Σ w logq . S The quality index (6.1) can expressed as

(6.4) gn G G

i ii i g g g g i i g

i 1 g 1 g 1 i g

q Q qw 1 log W 1 log W w 1 log .

Q Q Q

S

The first term on the right is a group-budget-share weighted-average of the terms

g gg g1 log Q Q 1 logQ logQ , g 1, ,G. This is the group-wise version of

(6.1) and is the between-group component of the quality index. The term in square brackets

on the right of equation (6.4) is gi g i i iw 1 log q Q , S which is the quality index within

group g. Thus, the entire last term on the right, G gg gg 1 i g i i iW w 1 log q Q ,

S is a

weighted average of the quality indexes of the G groups. The weights here are 22 For other approaches to measuring the impact of relative prices on income distribution, see Broda and Romalis (2009), Muellbauer (1974), Nicholas et al. (2010) and Pendakur (2002).

21

g g gW M M, where g i g i iM p q S is expenditure on group g and G ng 1 g i 1 i iM M p q is

total expenditure. These are group marginal shares which have a unit sum. Accordingly, the

last term on the right of (6.4) is the within-group component of quality. Similar

decompositions also apply to spending and prices.23

7. THE QUALITY OF THE FOOD BASKET

We apply the quality index (6.1) to food with iw interpreted as the proportion of food

expenditure devoted to the t hi food item and i as this good’s income elasticity within

food.24 Table 7.1 gives these values for the 28 items of food.

If cη,qy is the value of quality index (6.1) for food in country c, then c d

,q ,qy y , for

c d, c,d 1,...,128, are the pairwise differences. Panel A of Figure 7.1 summarises the

results in the form of a histogram of these differences. The standard deviation (SD) of about

15 percentage points indicates a reasonable amount of diversity in food quality around the

world. In approximately 17 percent of cases the absolute differences exceed 20 percentage

points, while 9 percent exceed 25 points. For some pairs of rich and poor countries, the

difference in quality is as much as 50 percentage points. This large quality gap applies to

pairs of countries having large income differences, such as such as Luxembourg, the US and

Norway, on the one hand, and Guinea-Bissau, Niger and Liberia, on the other. More will be

said subsequently about the role of income in driving quality.

When compared to the quality of consumption, there is substantially less dispersion in

the differences in its price: As can be seen from panel B of Figure 7.1, the SD of the price

differences is about 6 percentage points. For the comparisons involving the rich and poor

example countries of the previous paragraph, the difference in the price of quality is of the

order of 20 points (while the quality difference was about 50 points). As discussed in Section

4, the variance of quantities is more than five times that of prices. In large part, this accounts

for the lower dispersion of the price of quality in panel B of Figure 7.1. The sum of the

variances of the quality of consumption and prices 100 is 14.73 5.75 250.03,

which is less than the variance of the quality of spending 100 of 17.60 309.76,

from panel C of Figure 7.1. As the sum of the quality of consumption and its price is the 23 For the derivation of equation (6.4), see Appendix A7. 24 That is, this share and the elasticity are now conditional. This is an application to the food part of the within-group component of the total quality of consumption, the food part of the term in square brackets on the right of

equation (6.4), g

i g i i iw 1 log q Q S for g food.S However, in order not to overburden the notation, we

simply reinterpret equation (6.1) as referring to the quality of the food basket. This interpretation will be clear from the context.

22

quality of spending, the implication is that the quality of consumption and its price are

positively correlated -- quality enhancement comes at a higher price, at least on average.

Using var x+y var x var y 2ρ var x var y , where ρ is the correlation

coefficient, the implied correlation is 309.76 250.03 2 14.73 5. . 5.75 0 3 Thus, the

extent of the correlation between the quality of consumption and its price is moderately

positive.

To investigate the relationship between income and quality, Figure 7.2 gives

distributions of the cross-country differences of quality with countries classified by income

quartile. The first row refers to the differences between countries in the first quartile and

others in the first, second, third and fourth quartiles, successively. There is a tendency for the

centre-of-gravity of the distributions to move to the right as we move across the row from left

to right. This means that, on average, the quality differences increase as rich countries (those

in the first quartile) are compared to countries that are successively poorer and poorer. The

other three rows of the figure are interpreted similarly. In short, the quality of food

consumption is lower for poorer consumers, as is to be expected. One other aspect of Figure

7.2 is worth noting: As the dispersion within the fourth quartile is substantially less than that

in the other three, if you are poor, the quality of your consumption is not only lower than that

of the more affluent, it is also quite similar to that of most of your immediate neighbours

(who are also poor).

Next, consider quality in two countries c and c+x. If countries are ranked in terms of

decreasing income, c is richer than c+x for x 1. As the country c+x is x places below c in

the ranking, x can be used as a measure of the “economic distance” between them, with

distance increasing the larger the income gap. For all pairs of countries x places apart, the

quality differences are c c x,q ,qy y ,c 1, ,127.

Figure 7.3 plots, for each distance between

countries, the relative frequency of positive quality differences. This measures the probability

that quality in a country exceeds that in a poorer country x steps below it. There is a clear

pattern of an increasing probability, so that, on average, the quality difference between

countries is larger the greater the economic distance between them. For example, consider

countries that are 50 steps apart, such as Serbia and India. For such countries, the chance that

the quality of the richer country’s diet exceeds that of the poorer one is about 80 percent.

A final indicator of the degree to which income influences the quality of consumption

is panel A of Figure 7.4, which plots the differences between countries in the index against

the corresponding differences in income and as is clear, quality increases with income, on

23

average. The coefficient of log income in the regression is 4.76, which is a semi-elasticity and

highly significant. Thus, when we move from one country to another that is ten-percent

richer, according to the regression, quality of the food basket is about one-half of a

percentage point higher in the richer one. While this income sensitivity might be considered

low, it can also be interpreted as simply saying that it is not easy to increase the quality of the

food basket.25 The two other panels of the figure are similar plots for the indexes of prices

and spending. It follows from the identity (in logarithmic terms) spending = consumption +

prices, that the coefficient in the spending equation is the sum of those in the consumption

and price equations. Accordingly, the semi-elasticity of spending of 6.43 (the coefficient of

the log of income in panel C) is made up of 4.76 6.43 75 percent consumption and 25

percent prices, so the bulk of additional spending on quality flows into a larger volume.

As discussed in the previous section, the price of quality is a summary measure of the

prices of luxuries relative to those of necessities. Thus, as the rich are intensive consumers of

luxuries, when the price of quality in one country exceeds that in another, the structure of

prices has a progressive impact on the distribution of real income in the first country as

compared to that in the second. Panel B of Figure 7.4 shows that the majority of these

differences are positive, so that, on average, the structure of food prices in richer countries,

relative to that in the poorer ones, has a progressive impact on the distribution of income. In

other words, when the rich consume food of more luxurious kinds, the prices they pay are

higher, as compared to the prices of necessities. Moreover, as the regression coefficient of the

income difference is positive and highly significant, these price differences are amplified as

the income gap rises.

As diversity and quality both increase with income, the two elements are themselves

positively related. This is made explicit in the bivariate histogram of Figure 7.5. While the

dependence is visually clear, surprisingly, the relationship is not especially strong. The

correlation across the whole income distribution is only -0.53 and there is a tendency for this

to be smaller for the poorer countries (Table 7.2).

To gain further insight into the drivers of food quality, we divide the 28 food items

into the same 6 groups as before and use equation (6.4) to decompose total quality. Table 7.3

contains the necessary ingredients and Table 7.4 contains the results. The picture differs from

that for diet diversity where the between-group component clearly dominated. For the quality

25 As a qualification, note the group of observations that form a “break away cloud” located midway above the mother cloud. These observations mostly involve three low-income countries -- Lesotho, Vietnam and Philippines -- and could point to issues with the measurement of their incomes.

24

of consumption (panel A of Table 7.4), the opposite signs of the between- and within-group

components for the first two quartiles make interpretation somewhat more difficult, but it

seems fair to say that the role of the between component is now substantially reduced. Still,

the between component in the poorer countries is relatively more important than it is in the

richer ones. Panels B and C of Table 7.4 contain analogous decompositions for the price of

and spending on food quality. For prices the within component dominates (although there is

an opposite-sign issue for the fourth quartile). Among the six groups, staples and meats and

seafood tend to have the largest contribution to the within component of the price of quality.

Figure 7.6 considers the effect of income on the contribution of each of the six groups to the

within component of the quality of consumption. As can be seen, in two cases only is income

significant – higher income decreases the contribution of staples share and increases that of

meats and seafood. This result is understandable as the budget share of staples declines

sharply as income rises, while the opposite happens for meats and seafood (see Table 7.3).

8. CONCLUDING COMMENTS

It is well known that as consumers become richer, the share of spending devoted to

food falls. This tendency is so powerful and pervasive that it has been elevated to the status of

one of the few “laws” in economics, and christened Engel’s law, after Engel (1857). Less

well known is the strong link between Engel’s law, the variety of foods in the diet and their

quality. A varied diet brings nutritional advantages and for most, diet diversity is valued in

and of itself, if not an essential part of their life. As an extreme example, think of a “banquet

fit for a king (or queen)”. Diversity of the diet is thus a desirable attribute that could be

described as a “normal good”. While the food share falls with higher incomes, there is a

tendency for spending to be spread more evenly over foodstuffs reflecting a more diverse

diet.

This paper has used an approach based on index-number theory to analyse the

interrelationships between Engel’s law, the diversity of food consumption and its quality. To

study these matters, we used data from more than 100 countries, where the substantial

differences in per capita incomes leads to sharp, almost extreme, differences in consumption

patterns. Highlights of the results include:

Diet diversity increases with income with an elasticity between 0.2 (for the poorest

countries) and 0.5 (for the richest). Arguably, the spread of the food budget across

broad groups brings much of the nutritional value of a diversified diet. When the 28

items are divided into 6 groups (staples, meat and seafood, dairy, fruit and vegetables,

25

sweet things and other food), it is found that the between-group component of

diversity for the poor countries is much lower than that for the rich: On the basis of

the broad groups, diets of the rich are about five times more diverse than the poor’s. If

the important between-within distinction is ignored, measured inequality in diet

diversity is substantially understated (by as much as 50 percent).

Using a covariance between income elasticities and consumption to measure the

quality of food consumption, there is a reasonable amount of diversity around the

world. For example, in almost one-fifth of cases, the quality difference exceeds 20

percentage points, while 9 percent exceed 25 points.

The “price” of quality (a covariance between income elasticities and prices) exhibits

less dispersion across countries than quality itself (a volume concept, mentioned in

the previous bullet). Better quality food comes with higher prices, as expected.

Nevertheless, about three-quarters of spending on higher quality food is because of

larger volumes, with the remainder going into prices. The price of quality also

measures the price of luxuries relative to necessities. As the rich are intensive

consumers of luxuries, if the price of quality is higher in one country than another,

then the distributional impact of prices is progressive in the first country. As we find

that quality costs more in the richer countries, the structure of prices is progressive in

its impact on the global distribution of real incomes.

Higher incomes bring higher quality food, but the elasticity is small, so that enhanced

food quality can only be achieved with substantially higher incomes.

26

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29

Table 2.1 Income and Food Consumption in 128 countries in 2005

Income quartile First Second Third Fourth

(1) (2) (3) (4)

Con

stit

uent

Cou

ntri

es

1. Luxembourg 33. Czech Republic 65. Malaysia 97. China 2. United States 34. Hungary 66. Venezuela 98. Pakistan 3. Iceland 35. Bahrain 67. Albania 99. Yemen, Rep. 4. Norway 36. Lithuania 68. Jordan 100. India 5. United Kingdom 37. Korea, Rep. 69. Moldova 101. Cambodia 6. Sweden 38. Estonia 70. Tunisia 102. Sudan 7. Canada 39. Poland 71. Ecuador 103. Congo, Rep. 8. Switzerland 40. Slovak 72. Peru 104. Cameroon 9. Austria 41. Latvia 73. Egypt 105. Kenya 10. France 42. Macao, China 74. Botswana 106. São Tomé & P. 11. Australia 43. Croatia 75. Georgia 107. Zambia 12. Denmark 44. Mexico 76. Gabon 108. Senegal 13. Belgium 45. Belarus 77. Bolivia 109. Nigeria 14. Japan 46. Russia 78. Fiji 110. Uganda 15. Germany 47. Kazakhstan 79. Armenia 111. Côte d'Ivoire 16. Ireland 48. Mauritius 80. Syria 112. Gambia, The 17. Finland 49. Bulgaria 81. Namibia 113. Mauritania 18. Hong Kong 50. Serbia 82. Swaziland 114. Benin 19. Taiwan, China 51. Romania 83. Azerbaijan 115. Nepal 20. Italy 52. Saudi Arabia 84. Paraguay 116. Ghana 21. Qatar 53. Oman 85. E. Guinea 117. Madagascar 22. Spain 54. Iran 86. Kyrgyz 118. Sierra Leone 23. Greece 55. Argentina 87. Tajikistan 119. Burkina Faso 24. New Zealand 56. Chile 88. Sri Lanka 120. Guinea 25. Israel 57. Macedonia 89. Cape Verde 121. Rwanda 26. Kuwait 58. Ukraine 90. Philippines 122. Malawi 27. Malta 59. Bos. and Herz. 91. Mongolia 123. C. African Rep 28. Cyprus 60. Uruguay 92. Iraq 124. Mozambique 29. Singapore 61. South Africa 93. Indonesia 125. Tanzania 30. Portugal 62. Montenegro 94. Morocco 126. Guinea-Bissau 31. Brunei 63. Turkey 95. Lesotho 127. Niger 32. Slovenia 64. Brazil 96. Vietnam 128. Liberia

Mean Income ($ pc) 22,557 10,434 4,034 1,115 Food share (%) 10.79 21.38 34.69 44.47

Notes: 1. Countries are ranked in terms of per capita income and are divided into 4 equal quartiles. 2. Income is defined as total consumption per capita at PPP prices. More precisely, income is total

consumption expenditure, defined as the sum of expenditure by households (ICP categories 110XXX) and individual government (130XXX) on 106 food and non-food items, deflated by the cost of living. In logarithmic form, this is log Q log M log P, where M is total consumption expenditure, and

106

i 1 i ilog P Σ w log p

is a cost-of-living index, with

iw the budget share of good i and

ip its PPP price.

3. The food share is the proportion of total consumption expenditure devote to food, expressed as a percentage. Food is defined as the sum of all food items and non-alcoholic beverages (items in the 1101XX categories).

30

Table 2.2 Budget Shares, 28 Foods Items

Commodity Income quartile

First Second Third Fourth All (1) (2) (3) (4) (5) (6)

1. Rice 0.18 0.51 2.04 5.56 2.07 2. Other cereals and flour 0.19 0.58 2.58 5.27 2.15 3. Bread 0.60 1.44 2.13 1.46 1.41 4. Other bakery products 0.55 0.69 0.48 0.61 0.58 5. Pasta products 0.19 0.29 0.47 0.42 0.34 6. Beef and veal 0.43 1.14 2.22 2.46 1.56 7. Pork, Lamb, mutton and goat 0.57 1.34 1.55 1.55 1.25 8. Poultry 0.47 1.06 1.78 1.14 1.11 9. Other meats and preparations 0.80 1.73 0.98 0.91 1.10 10. Fresh or frozen fish and seafood 0.56 0.60 1.72 2.09 1.24 11. Preserved fish and seafood 0.28 0.27 0.42 1.35 0.58 12. Fresh milk 0.33 0.86 1.07 1.54 0.95 13. Preserved milk and milk products 0.42 0.93 1.13 0.93 0.85 14. Cheese 0.45 0.71 0.66 0.11 0.48 15. Eggs and egg-based products 0.13 0.48 0.80 0.47 0.47 16. Butter and margarine 0.12 0.35 0.55 0.65 0.42 17. Fresh or chilled fruit 0.74 1.41 1.85 1.72 1.43 18. Frozen, preserved or processed fruits 0.18 0.20 0.37 0.41 0.29 19. Fresh or chilled vegetables 0.64 1.54 3.17 3.23 2.14 20. Fresh or chilled potatoes 0.15 0.50 1.34 3.35 1.33 21. Frozen or preserved vegetables 0.28 0.51 0.49 0.89 0.54 22. Sugar 0.07 0.44 0.98 1.82 0.83 23. Jams, marmalades and honey 0.07 0.21 0.16 0.12 0.14 24. Confectionery, chocolate and ice cream 0.63 0.69 0.65 0.28 0.56 25. Other edible oils and fats 0.18 0.53 1.40 1.92 1.01 26. Food products n.e.c. 0.56 0.76 1.71 2.42 1.36 27. Coffee, tea and cocoa 0.27 0.54 0.83 0.85 0.62 28. Mineral waters, soft drinks, fruit and veg juices 0.77 1.09 1.17 0.94 0.99 All food 10.79 21.38 34.69 44.47 27.83 Note: The figures are the proportions of total consumption expenditure devoted to each commodity, averaged over countries. All entries are 100.

31

Table 2.3 Food Budget Share Differences

Country Group Richer Poorer

Quartile 1 Quartile 2 Quartile 3

Poorer Quartile 4 -33.68 -23.90 -9.77

Quartile 3 -23.09 -13.32

Richer Quartile 2 -10.59

Note: The 128 countries are ranked by income and divided into 4 groups of 32 countries each. The elements of this table refer to the change in the food budget share in moving from a poorer country group (identified by the row label) to a richer one (the column label). For example, the budget share falls by 33.68 percentage points in moving from the fourth to the first income quartile, that is, from the poorest to the richest group. All entries are

100.

32

Table 2.4 Budget Share Differences for 28 Food Items GHiw 100

Food item Country pair G, H

1, 4 1, 3 1, 2 2, 4 2, 3 3, 4 (1) (2) (3) (4) (5) (6) (7)

Rice -5.38

-1.86

-0.33

-5.05

-1.53

-3.52

Other cereals & flour -5.08 -2.39 -0.39 -4.69 -1.99 -2.69 Fresh/chilled potatoes -3.20 -1.19 -0.35 -2.85 -0.84 -2.01 Fresh/chilled vegetables -2.59 -2.53 -0.90 -1.69 -1.63 -0.06 Beef & veal -2.03 -1.80 -0.72 -1.31 -1.08 -0.24 Food products n.e.c. -1.86 -1.15 -0.20 -1.66 -0.95 -0.71 Sugar -1.74 -0.91 -0.37 -1.37 -0.54 -0.83 Other edible oils & fats -1.74 -1.22 -0.35 -1.39 -0.87 -0.52 Fresh/frozen fish & seafood -1.54 -1.16 -0.04 -1.50 -1.12 -0.38 Fresh milk -1.21 -0.74 -0.53 -0.68 -0.21 -0.47 Preserved fish & seafood -1.07 -0.13 0.02 -1.09 -0.15 -0.94 Fresh/chilled fruit -0.98 -1.11 -0.67 -0.31 -0.44 0.13 Pork, Lamb, mutton & goat -0.97 -0.98 -0.76 -0.21 -0.21 0.00 Bread -0.87 -1.53 -0.84 -0.02 -0.69 0.67 Poultry -0.67 -1.31 -0.59 -0.08 -0.72 0.64 Frozen/preserved vegetables -0.62 -0.21 -0.23 -0.39 0.02 -0.40 Coffee, tea & cocoa -0.58 -0.56 -0.26 -0.32 -0.29 -0.02 Butter & margarine -0.53 -0.43 -0.23 -0.31 -0.21 -0.10 Preserved milk & milk prod. -0.51 -0.71 -0.50 0.00 -0.20 0.20 Eggs & egg-based prod. -0.34 -0.67 -0.35 0.01 -0.32 0.33 Frozen/preser./process. fruits -0.23 -0.19 -0.02 -0.22 -0.17 -0.04 Pasta products -0.23 -0.28 -0.10 -0.13 -0.18 0.06 Min. wat., sft drks, juices -0.17 -0.40 -0.32 0.15 -0.08 0.23 Other meats & preparations -0.11 -0.18 -0.94 0.83 0.76 0.07 Other bakery products -0.06 0.07 -0.14 0.08 0.21 -0.13 Jams, marmalades and honey -0.05 -0.09 -0.13 0.09 0.05 0.04 Cheese 0.34 -0.21 -0.27 0.60 0.05 0.55 Confect., choc. & ice cream 0.35 -0.02 -0.07 0.42 0.05 0.37 All food -33.68 -23.90 -10.59 -23.09 -13.32 -9.77 Note: The country groups G, H = 1, 2, 3, 4 are the income quartiles (G = 1 for the richest, H = 4 poorest). For example, the country pair 1, 4 (column 2) refers to the move from the poorest group to the richest whereby the share of all food falls by 33.68 percentage points (last entry of the column); the other entries of the column disaggregate this total change into the 28 food items.

33

Table 3.1 Staples Conditional Budget Shares

Food item Income quartile

First Second Third Fourth All

(1) (2) (3) (4) (5) (6)

Rice 9.12 14.76 25.51 38.96 22.09

Other cereals and flour 11.36 16.35 32.25 39.92 24.97

Bread 36.89 39.73 27.85 13.49 29.49

Other bakery products 32.39 21.00 7.61 4.48 16.37

Pasta products 10.24 8.17 6.78 3.14 7.08

SD 15.70 15.89 18.13 22.24 17.99

Note: The conditional budget shares are shares in expenditure on staples (the sum of the five items), averaged over countries. All entries are 100.

Table 3.2 Who Eats What Staples?

Characteristic Type of country

Rice eaters

Cereal eaters

Bread eaters

Other

(1) (2) (3) (4) (5)

Income ($ p. c.) 5,663 2,666 12,831 20,112

SD of income (% of income) 111.27 83.96 62.68 31.45

Number of countries 35 29 47 17

Budget shares (%)

Rice 53.90 16.38 7.82 5.76

Cereals 17.23 56.16 15.55 13.75

Bread 14.84 15.89 49.08 28.70

Other bakery products 8.05 6.56 19.80 40.74

Pasta products 5.98 5.00 7.74 11.05

Staples 24.79 25.71 16.44 16.47 Note: A country is a rice eater if its expenditure on rice is the largest within the staples group; and the same applies for the other country types. The budget shares for rice, cereals, bread, other bakery and pasta are conditional, that is, the budget shares within staples. The “staples share” is the budget share within food.

34

Table 3.3 Income and Staples Consumption

(Number of countries)

Income quartile Type of country

Rice eater Cereals eater Bread eater Other Total

(1) (2) (3) (4) (5) (6)

First 4 0 14 14 32

Second 7 1 21 3 32

Third 8 13 11 0 32

Fourth 16 15 1 0 32

Total 35 29 47 17 128

0H : Type of country independent of income, 2 = 83.31 [<0.001]

Notes: This table cross classifies the 128 countries according to income (quartiles) and the dominant staple consumed (type of country), as defined in the notes to Table 3.2. The figure in square brackets is the p-value.

35

Table 4.1 Conditional Budget Shares of 28 Food Items

Food item Income quartile

First Second Third Forth (1) (2) (3) (4) (5)

1. Rice 1.34 2.62 5.84 11.97 2. Other cereals and flour 1.82 2.67 7.47 11.84 3. Bread 5.70 6.51 5.60 3.34 4. Other bakery products 5.17 3.35 1.45 1.29 5. Pasta products 1.66 1.40 1.37 0.91 6. Beef and veal 4.08 5.20 6.20 5.52 7. Pork, Lamb, mutton and goat 5.01 6.19 4.60 3.44 8. Poultry 4.13 4.93 5.38 2.59 9. Other meats and preparations 8.13 7.93 2.98 2.07 10. Fresh or frozen fish and seafood 4.62 2.93 5.19 4.76 11. Preserved fish and seafood 2.62 1.26 1.27 3.05 12. Fresh milk 3.21 3.98 3.08 3.44 13. Preserved milk and milk products 3.74 4.41 3.40 2.09 14. Cheese 4.21 3.27 1.81 0.22 15. Eggs and egg-based products 1.17 2.14 2.16 1.25 16. Butter and margarine 1.22 1.61 1.37 1.42 17. Fresh or chilled fruit 6.44 6.62 5.28 4.04 18. Frozen, preserved or processed fruits 1.62 0.91 1.01 0.94 19. Fresh or chilled vegetables 5.68 7.08 8.98 7.38 20. Fresh or chilled potatoes 1.39 2.16 3.75 7.39 21. Frozen or preserved vegetables 2.65 2.47 1.36 1.96 22. Sugar 0.65 2.03 2.85 4.57 23. Jams, marmalades and honey 0.68 0.99 0.43 0.28 24. Confectionery, chocolate and ice cream 6.25 3.33 1.86 0.67 25. Other edible oils and fats 1.47 2.38 3.89 4.37 26. Food products n.e.c. 5.42 3.78 5.30 5.23 27. Coffee, tea and cocoa 2.52 2.57 2.30 1.78 28. Min. water, soft drink, fruit & veg juice 7.40 5.27 3.81 2.19 Total 100 100 100 100 Note: The conditional budget share of food item i is the proportion of total food expenditure

devoted to food. These shares are averaged over countries and are ×100.

36

Table 4.2 Food Moments

Income quartile

Volume index log Q

Variances 100

Price-quantity 100

Budget shares

w

Prices

p

Quantities

q

Covariance

pq Correlation

(1) (2) (3) (4) (5) (6) (7)

1 4.46 51.05 8.26 60.78 -8.99 -28.27

2 4.07 50.89 14.10 78.51 -20.86 -60.18

3 3.59 69.86 21.25 115.02 -33.20 -65.85

4 2.74 96.50 27.53 143.63 -37.33 -57.26

All 3.72 67.20 17.86 99.79 -25.22 -53.08

37

Table 5.1 Group and Conditional Budget Shares

Group/Commodity Income quartile

First Second Third Fourth All (1) (2) (3) (4) (5) (6)

1. STAPLES 15.69 16.54 21.73 29.35 20.83 Rice 9.12 14.76 25.51 38.96 22.09 Other cereals and flour 11.36 16.35 32.25 39.92 24.97 Bread 36.89 39.73 27.85 13.49 29.49 Other bakery products 32.39 21.00 7.61 4.48 16.37 Pasta products 10.24 8.17 6.78 3.14 7.08 2. MEAT AND SEAFOOD 28.58 28.43 25.62 21.43 26.02 Beef and veal 14.89 19.13 25.13 27.07 21.55 Pork, Lamb, mutton and goat 17.08 21.41 16.99 16.23 17.93 Poultry 14.74 17.45 21.46 12.87 16.63 Other meats and preparations 29.26 27.33 11.48 8.41 19.12 Fresh or frozen fish and seafood 15.06 10.35 19.80 21.49 16.67 Preserved fish and seafood 8.97 4.33 5.13 13.92 8.09 3. DAIRY 13.54 15.43 11.83 8.42 12.30 Fresh milk 23.75 25.86 25.45 36.16 27.80 Preserved milk and milk products 29.58 28.88 31.75 25.91 29.03 Cheese 28.47 20.75 12.69 2.81 16.18 Eggs and egg-based products 9.64 14.32 19.54 16.43 14.98 Butter and margarine 8.56 10.19 10.58 18.69 12.01 4. FRUIT AND VEGETABLES 17.78 19.25 20.38 21.71 19.78 Fresh or chilled fruit 35.70 34.21 26.63 17.71 28.56 Frozen, preserved or processed fruits 8.89 4.58 4.49 4.61 5.64 Fresh or chilled vegetables 31.83 36.59 44.08 37.23 37.43 Fresh or chilled potatoes 8.27 11.93 18.15 30.13 17.12 Frozen or preserved vegetables 15.31 12.70 6.65 10.33 11.25 5. SWEET THINGS 7.59 6.35 5.14 5.52 6.15 Sugar 9.95 30.57 58.01 75.72 43.56 Jams, marmalades and honey 9.79 16.14 9.21 6.91 10.51 Confectionery, chocolate and ice cream 80.25 53.29 32.78 17.38 45.93 6. OTHER FOOD 16.81 14.00 15.30 13.57 14.92 Other edible oils and fats 10.06 18.35 27.97 34.06 22.61 Food products n.e.c. 29.10 26.13 30.37 34.35 29.99 Coffee, tea and cocoa 15.97 19.10 16.79 13.49 16.34 Mineral waters, soft drinks, fruit and vegetable juices 44.87 36.42 24.88 18.10 31.06 Note: Emboldened figures are group budget shares, averaged over countries. Non-emboldened figures are conditional budget shares, averaged over countries. All entries are

100.

38

Table 5.2 Decomposition of Food Diversity

Income quartile

Total variance

Components

Group variances

Between group

Within group

Staples Meats and Seafood

Dairy Fruits and vegetables

Sweet things

Other food

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

A. Budget shares

1 51.05 10.74 40.32 44.23 42.01 34.93 35.51 63.51 34.47

2 50.89 12.60 38.29 47.96 46.62 23.39 39.36 30.38 25.89

3 69.86 23.63 46.23 57.08 48.57 42.71 44.58 37.86 28.51

4 96.50 44.64 51.85 66.44 43.61 57.57 45.95 45.83 37.65

All 67.20 23.00 44.20 54.00 45.23 39.69 41.40 44.24 31.61

B. Prices

1 8.26 2.94 5.32 5.46 8.93 4.35 3.42 1.65 1.93

2 14.10 5.01 9.09 16.64 10.44 4.46 11.53 3.38 2.75

3 21.25 8.16 13.09 23.72 16.29 5.62 10.25 9.13 3.59

4 27.53 11.65 15.88 20.78 30.29 5.23 9.71 3.39 4.18

All 17.86 6.97 10.89 16.74 16.55 4.92 8.77 4.41 3.12

C. Quantities

1 60.78 13.80 46.98 52.50 48.89 45.82 45.58 53.26 34.21

2 78.51 22.37 56.14 92.68 60.89 29.06 65.20 29.50 33.02

3 115.02 42.80 72.22 93.42 85.38 48.33 77.66 46.60 34.32

4 143.63 68.09 75.53 81.80 93.83 68.61 71.57 46.30 45.67

All 99.79 36.95 62.84 80.32 72.43 47.97 65.15 43.84 36.83

Notes:

1. Column 2 of panel A: This contains the weighted logarithmic variance of the food 28 budget shares,

w

228i 1 i iw log w log W , where iw is the proportion of food expenditure devoted to item i and

28i 1 i ilog W w log w . The elements of this column are averages over countries.

2. Columns 3 and 4 of panel A: Dividing food into six groups and using equation (5.1), the total variance of the budget shares can be decomposed into between- and within-group components:

(T5.2.1) g

6 62

w g g g i i gg 1 g 1 i

pe

Total Between grou Within groupvarianc

W log W log W W w log w log W .

S

Here, gg i iW w S is the budget share of group g; gS is the set of goods in group g;

i giw w / W is the

share of group expenditure devoted to gi S ; gg i i iilog W logw w ; S and G

g 1 g g .log W W log W

Columns 3 and 4, respectively, contain the above between- and within-group components, averaged over countries.

3. Columns 5-10 of panel A: These columns contain each of the six within-group variances of equation

(T5.2.1), g

2

i i i g g 1, , 6,w log w log W , S averaged over countries.

4. Panels B and C: These panels are defined analogously to panel A. 5. All entries are ×100.

39

Table 5.3 Summary of Dispersion of Food Budget

Food group

Price-quantity correlation

pq

q p

Π

Π Π

Dispersion inequality

Quantities and prices negatively

related

Quantities more variable than

prices

Budget share variance bracketed by quantity and price variances

pqΠ 0

q pΠ Π

q w pΠ Π Π

(1) (2) (3) (4) (5)

A. First quartile 1. Staples -0.29 71 97 58 2. Meats and Seafood -0.15 58 100 52 3. Dairy -0.49 87 100 81 4. Fruits and Vegetables -0.35 81 100 81 5. Sweet things 0.49 13 100 13 6. Other food -0.06 45 100 42 All food -0.28 74 100 52

B. Second quartile 1. Staples -0.76 97 100 88 2. Meats and Seafood -0.35 69 97 59 3. Dairy -0.37 84 100 66 4. Fruits and Vegetables -0.68 100 100 100 5. Sweet things 0.07 44 94 44 6. Other food -0.48 81 97 66 All food -0.60 100 100 97

C. Third quartile 1. Staples -0.57 81 97 59 2. Meats and Seafood -0.69 100 97 84 3. Dairy -0.35 88 97 72 4. Fruits and Vegetables -0.78 97 100 91 5. Sweet things -0.06 53 100 41 6. Other food -0.28 75 100 66 All food -0.66 97 100 91

D. Fourth quartile 1. Staples -0.33 69 100 56 2. Meats and Seafood -0.76 100 91 63 3. Dairy -0.26 63 97 50 4. Fruits and Vegetables -0.70 94 97 81 5. Sweet things 0.01 53 94 44 6. Other food -0.37 75 100 75 All food -0.57 97 100 78

E. All countries 1. Staples -0.49 80 98 65 2. Meats and Seafood -0.49 82 96 65 3. Dairy -0.37 80 98 67 4. Fruits and Vegetables -0.63 93 99 88 5. Sweet things 0.13 41 97 35 6. Other food -0.30 69 99 62 All food -0.53 92 100 80 Note: The entries in columns 3-5 are percentages of the 127 countries satisfying the inequalities (the US is excluded as it is the base country).

40

Table 7.1 Conditional Budget Shares and Income Elasticities of Food

Food item

Income quartile

First

Second

Third

Fourth

Budget share

Income elasticity

Budget share

Income elasticity

Budget share

Income elasticity

Budget share

Income elasticity

(1) (2) (3) (4) (5) (6) (7) (8) (9)

1. Rice 1.34 0.16 2.62 0.14 5.84 0.34 11.97 0.92

2. Other cereals and flour 1.82 0.16 2.67 0.14 7.47 0.39 11.84 0.83

3. Bread 5.70 0.81 6.51 0.72 5.60 0.70 3.34 0.64

4. Other bakery products 5.17 1.63 3.35 1.44 1.45 1.41 1.29 1.28

5. Pasta products 1.66 0.88 1.40 1.01 1.37 1.15 0.91 1.01

6. Beef and veal 4.08 0.16 5.20 0.87 6.20 1.12 5.52 1.04

7. Pork, Lamb, mutton and goat 5.01 1.25 6.19 1.30 4.60 1.28 3.44 1.17

8. Poultry 4.13 1.01 4.93 1.20 5.38 1.26 2.59 1.08

9. Other meats and preparations 8.13 1.88 7.93 1.54 2.98 1.58 2.07 1.45

10. Fresh or frozen fish and seafood 4.62 0.66 2.93 0.65 5.19 1.14 4.76 1.08

11. Preserved fish and seafood 2.62 0.16 1.26 0.14 1.27 0.29 3.05 0.96

12. Fresh milk 3.21 0.02 3.98 0.90 3.08 0.98 3.44 1.01

13. Preserved milk and milk products 3.74 1.16 4.41 1.25 3.40 1.25 2.09 1.11

14. Cheese 4.21 2.08 3.27 1.69 1.81 1.67 0.22 2.71

15. Eggs and egg-based products 1.17 0.97 2.14 1.28 2.16 1.31 1.25 1.13

16. Butter and margarine 1.22 0.06 1.61 0.95 1.37 1.11 1.42 1.05

17. Fresh or chilled fruit 6.44 1.44 6.62 1.35 5.28 1.34 4.04 1.21

18. Frozen, preserved or processed fruits 1.62 0.98 0.91 0.92 1.01 1.14 0.94 1.06

19. Fresh or chilled vegetables 5.68 0.16 7.08 0.83 8.98 1.12 7.38 1.02

20. Fresh or chilled potatoes 1.39 0.16 2.16 0.14 3.75 0.50 7.39 0.95

21. Frozen or preserved vegetables 2.65 0.63 2.47 0.95 1.36 0.92 1.96 1.03

22. Sugar 0.65 0.16 2.03 0.14 2.85 0.64 4.57 0.90

23. Jams, marmalades and honey 0.68 1.44 0.99 1.38 0.43 1.33 0.28 1.19

24. Confectionery, chocolate and ice cream 6.25 1.94 3.33 1.69 1.86 1.67 0.67 1.83

25. Other edible oils and fats 1.47 0.16 2.38 0.14 3.89 0.87 4.37 0.92

26. Food products n.e.c. 5.42 0.16 3.78 0.31 5.30 0.91 5.23 0.96

27. Coffee, tea and cocoa 2.52 0.75 2.57 1.05 2.30 1.15 1.78 1.06

28. Min. water, soft drink, fruit & veg juice 7.40 1.57 5.27 1.40 3.81 1.37 2.19 1.24

Note: For food item i, the conditional budget share of is the proportion of total food expenditure devoted to i. These shares are averaged over countries and are ×100. The conditional income elasticity is conditional on total food expenditure and is defined as i g , where

i ilog q log M is the conventional income elasticity and g i g i iw S is the income elasticity of demand for the food group g ,S

with iw the conditional budget share. The elasticities are averaged over countries. For the source of the elasticities, see Appendix A4.

41

Table 7.2 Quality, Dispersion and Income Correlations

Quality Dispersion Income A. Quartile 1

Quality - -0.49 0.37 Dispersion - -0.40 Income -

B. Quartile 2 Quality - -0.07 0.33 Dispersion - -0.34 Income -

C. Quartile 3 Quality - -0.32 0.46 Dispersion - -0.54 Income -

D. Quartile 4 Quality - -0.16 0.22 Dispersion - -0.25 Income -

E. All Quality - -0.53 0.64 Dispersion - -0.67 Income -

42

Table 7.3 Budget Shares and Income Elasticities of Food Groups and Food Items

Food Income quartile

First

Second

Third

Fourth

Group

Conditional

Group

Conditional

Group

Conditional

Group

Conditional

Group/Item Budget share

Incomeelast.

Budget share

Incomeelast.

Budget share

Incomeelast.

Budget share

Incomeelast.

Budget share

Incomeelast.

Budget share

Incomeelast.

Budget share

Incomeelast.

Budget share

Incomeelast.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) 1. Staples 15.69 0.94 16.54 0.71 21.73 0.59 29.35 0.86 1.1 Rice 9.12 0.17 14.76 0.22 25.51 0.59 38.96 1.07 1.2 Other cereals and flour 11.36 0.17 16.35 0.22 32.25 0.69 39.92 0.96 1.3 Bread 36.89 0.87 39.73 1.08 27.85 1.22 13.49 0.74 1.4 Other bakery products 32.39 1.76 21.00 2.17 7.61 2.45 4.48 1.48 1.5 Pasta products     10.24 0.95     8.17 1.51     6.78 1.99     3.14 1.17 2. Meats and Seafood 28.58 1.04 28.43 1.14 25.62 1.19 21.43 1.10 2.1 Beef and veal 14.89 0.16 19.13 0.76 25.13 0.94 27.07 0.95 2.2 Pork, Lamb, mutton and goat 17.08 1.23 21.41 1.14 16.99 1.08 16.23 1.06 2.3 Poultry 14.74 0.99 17.45 1.06 21.46 1.06 12.87 0.98 2.4 Other meats and preparations 29.26 1.84 27.33 1.36 11.48 1.33 8.41 1.32 2.5. Fresh or frozen fish and seafood     15.06 0.65     10.35 0.57     19.80 0.96     21.49 0.98 2.6 Preserved fish and seafood 8.97 0.16     4.33 0.13     5.13 0.24     13.92 0.88 3. Dairy 13.54 1.04 15.43 1.22 11.83 1.23 8.42 1.11 3.1 Fresh milk     23.75 0.02     25.86 0.74     25.45 0.80     36.16 0.91 3.2 Preserved milk and milk products     29.58 1.16     28.88 1.02     31.75 1.02     25.91 1.00 3.3 Cheese     28.47 2.08     20.75 1.38     12.69 1.36     2.81 2.45 3.4 Eggs and egg-based products     9.64 0.97     14.32 1.05     19.54 1.07     16.43 1.03 3.5 Butter and margarine     8.56 0.06     10.19 0.78     10.58 0.90     18.69 0.95 4. Fruits and Vegetables 17.78 0.76 19.25 0.95 20.38 1.05 21.71 1.03 4.1 Fresh or chilled fruit     35.70 1.91     34.21 1.44     26.63 1.28     17.71 1.17 4.2 Frozen, preserved or processed fruits     8.89 1.30     4.58 0.98     4.49 1.09     4.61 1.02 4.3 Fresh or chilled vegetables     31.83 0.22     36.59 0.88     44.08 1.07     37.23 0.98 4.4 Fresh or chilled potatoes     8.27 0.22     11.93 0.15     18.15 0.48     30.13 0.92 4.5 Frozen or preserved vegetables     15.31 0.84     12.70 1.02     6.65 0.88     10.33 1.00 5. Sweet things 7.59 1.71 6.35 1.17 5.14 1.03 5.52 1.08 5.1 Sugar     9.95 0.10     30.57 0.13     58.01 0.63     75.72 0.84 5.2 Jams, marmalades and honey     9.79 0.85     16.14 1.22     9.21 1.32     6.91 1.12 5.3 Confectionery, chocolate and ice cream     80.25 1.14     53.29 1.49     32.78 1.66     17.38 1.72 6. Other food 16.81 0.88 14.00 0.81 15.30 1.05 13.57 1.01 6.1 Other edible oils and fats     10.06 0.19     18.35 0.18     27.97 0.83     34.06 0.91 6.2 Food products n.e.c.     29.10 0.19     26.13 0.39     30.37 0.87     34.35 0.95 6.3 Coffee, tea and cocoa     15.97 0.88     19.10 1.34     16.79 1.10     13.49 1.05 6.4 Min. water, soft drink, fruit & veg juice     44.87 1.83     36.42 1.80     24.88 1.30     18.10 1.23

Note: The budget share of group g ( g 1,...,6 ) is gg i i i

W p q M , S

where g

S is the set of food items belonging to subgroup g , i ip q expenditure on i and M = total food expenditure. The conditional income elasticity of

item i within gS is i i g , where i ilogq log M is the conventional unconditional income elasticity and gg i i iw S is the income elasticity of demand for the group as a whole, with

gi i i i i iw p q p q S

the conditional budget share of item i within g .S The budget shares are averages over countries. For the source of the income elasticities i , see Appendix A4.

43

Table 7.4 Components of Food Quality

Income quartile

Total quality

Components

Within-group

Between group

Within group

Staples Meats and

seafood Dairy

Fruits and vegetables

Sweet things

Other food

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

A. Consumption

1 10.22 -1.37 11.58 0.98 3.15 1.82 1.62 2.23 1.79

2 2.62 -0.72 3.34 -0.36 1.76 -0.51 1.23 0.31 0.90

3 -6.96 -3.78 -3.18 -2.58 0.23 -0.49 0.94 -0.86 -0.42

4 -6.35 -2.60 -3.75 -0.85 -0.59 -0.74 -0.42 -0.62 -0.53

B. Prices

1 5.25 2.03 3.22 0.82 1.65 0.35 -0.19 0.14 0.44

2 3.89 1.22 2.67 0.08 1.21 0.53 0.37 0.27 0.21

3 0.76 0.24 0.52 -0.33 0.34 0.24 -0.21 0.32 0.15

4 -0.08 -0.75 0.67 0.20 0.26 0.05 0.01 0.04 0.12

C. Spending

1 15.46 0.66 14.80 1.79 4.80 2.17 1.44 2.37 2.23

2 6.52 0.50 6.01 -0.28 2.98 0.02 1.59 0.59 1.12

3 -6.20 -3.54 -2.66 -2.91 0.56 -0.25 0.73 -0.53 -0.27

4 -6.43 -3.36 -3.07 -0.65 -0.33 -0.69 -0.42 -0.57 -0.41

Notes:

1. Column 2 of panel A: This contains the index of the quality of food consumption,

28η,q i 1 i i iy Σ w η 1 log q log Q , where

i

28

i i i 1 i iw p q Σ p q

is the proportion of food expenditure

devoted to item i; i is the within-food income elasticity of this good; and 28i 1 i ilogQ w logq is the

food volume index. 2. Columns 3 and 4 of panel A: Dividing the food group into six groups and using equation (6.4), total

food quality can be decomposed into between- and within-group components:

g6 6

ig g g g i i g

g 1 g 1 i g,q

Within groupBetween group

qQW 1 log W w 1 log

Q Q(T7.4.1) y .

S

Here, gW and g are the budget share and income elasticity of food group g, respectively;

g

gi i ilogQ w logq S and 6 g 28

g 1 g i 1 i ilogQ W logQ w logq are the volume index of group g and

food as a whole; g

S is the set of goods in food group g; and iw and i are the budget share and

income elasticity of good i within group g. Columns 3 and 4 contain the above between- and within-components, averaged over countries.

3. Columns 5-10 of panel A: Contain each of the six elements of the within-group components of equation (T7.4.1) above, averaged over countries. These elements sum to the within component of column 4.

4. Panels B and C: The entries in these panels are defined analogously to those of panel A. 5. All entries are ×100.

44

Figure 2.1 Food and income, 128 countries in 2005

Notes: 1. The food budget share is the proportion of total consumption devoted to food. Income (total consumption) is

in $US per capita, as in note 2 to Table 2.1. 2. Standard errors in parentheses.

0

20

40

60

80

300 600 1,200 2,400 4,800 9,600 19,200 38,400

Income

Food budget share 100

y = –10.80 log(x) + 120.72 (0.64) (5.52)

45

Figure 3.1 Specialisation in Staples

A. Rice, Cereals and Other

B. Bread, Rice and Other

C. Bread, Cereals and Other

Notes: This figure plots for each of the 128 countries, the conditional budget shares of staples, that is, the shares of the three components in total expenditure on staples. As the shares have a unit sum, each budget-share vector can be represented as a point in an equilateral triangle. The shares are expressed in percentage terms. Note that as the “other” category is a residual, its definition changes across the three panels. The figures in boxes represent the percentage shares of the 128 countries falling in the each region.

Other

Rice Cereals

Other

Other

100 50 100

50 50

100

7055%

128

14%

18%

13%

14%

45%

16%

25%

13%

39%

16%

32%

Cereals Bread

Rice Bread

46

Figure 4.1 Price-Quantity Correlations for Food, Cumulative Distribution

0

50

100

150

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Number of countries

Correlation

Mean = -0.53

47

Figure 4.2 Food Diversity and Income

A. Quantity variance

B. Budget-share variance

C. Price variance

Notes: The quantity variance for country c is 228

qc i 1 ic ic cw log q log Q

, where

icw is the proportion of food

expenditure devoted to food item i, ic

q is the per capita quantity of i consumed in c and 28

c i 1 ic iclog Q w log q

is a

volume index of total food consumption. The variance of the budget shares and prices are defined analogously. Income is real income (consumption) per capita, defined as log M P as in note 2 of Table 2.1. All variances

are × 100.

0

100

200

300

400

5 6 7 8 9 10 11

0

50

100

150

200

250

5 6 7 8 9 10 11

0

25

50

75

5 6 7 8 9 10 11

y = -28.88x + 347.76 (2.87) (24.91)

y = -16.85x + 211.89 (1.98) (17.19)

y = -6.18x + 70.92 (0.50) (4.35)

Log income

Log income

Log income

Variance

Variance

Variance

48

Figure 5.1 Summary of Variance Decompositions

First Second Third Fourth All

Within Groups Between Groups

Income quartile

Percent of total

D. Price-Quantity Covariance

C. Quantities

B. Prices

A. Budget shares

0

20

40

60

80

100

0

20

40

60

80

100

0

20

40

60

80

100

0

20

40

60

80

100

49

Figure 5.2 Diversity of the Staples Budget and Income

A. Quantity variance

B. Budget-share variance

C. Price variance

Notes: The quantity variance for staples in country c is

g

2

i ic ic gcw log q log Q , S where gS is the set of

goods in staples, group g;ic gcicw w W is the share of group expenditure devoted to gi S ;

ggc i icW w S is the

budget share of group g; icq is per capita consumption of item i within staples; and ggc i ic iclog Q log qw S is an

index of the volume of staples. The variance of the budget shares and prices are defined analogously. Income is real income (consumption) per capita, defined as log M P as in note 2 of Table 2.1. All variances are × 100.

0

100

200

300

5 6 7 8 9 10 11

0

50

100

150

200

5 6 7 8 9 10 11

0

25

50

75

5 6 7 8 9 10 11

y = -7.39x + 143.79 (3.30) (28.57)

y = -8.35x + 125.74 (1.79) (15.52)

y = -3.95x + 50.63 (0.83) (7.21)

Log income

Log income

Log income

Variance

Variance

Variance

50 Figure 7.1 Quality of Food Consumption, Prices and Spending, Differences across Countries

A. Consumption c d,q ,qy y

B. Prices c d,p ,py y

C. Spending c d,pq ,pqy y

Note: Each panel is a histogram of the pairwise differences between countries c and d in the respective quality index of food c dy y , c,d 1, ,128. Indexes are 100.

.

0

1,000

2,000

3,000

4,000

5,000

-80 -60 -40 -20 0 20 40 60 80

0

1,000

2,000

3,000

4,000

5,000

-80 -60 -40 -20 0 20 40 60 80

0

1,000

2,000

3,000

4,000

5,000

-80 -60 -40 -20 0 20 40 60 80

Mean = 0 SD = 14.73

Mean = 0 SD = 17.60

Mean = 0 SD = 5.75

> 25 = 4.4%

> 20 = 8.7%

51

Figure 7.2 Quality of Food Consumption, Differences by Income Quartile

← RICHER POORER → First quartile Second quartile Third quartile Fourth quartile

←

Poo

rer

RIC

HE

R

→

Fir

st q

uart

ile

Sec

ond

quar

tile

Thi

rd q

uart

ile

Fou

rth

quar

tile

Note: Each histogram refers to c d

,q ,qy y , c < d, c quartile r, d quartile r , r r , where r, r 1,..., 4. Countries are ranked in terms of decreasing income, so country c is richer than d

when c < d. Indexes are × 100.

0

250

500

-40 -20 0 20 40 600

250

500

-40 -20 0 20 40 600

250

500

-40 -20 0 20 40 600

250

500

-40 -20 0 20 40 60

0

250

500

-40 -20 0 20 40 600

250

500

-40 -20 0 20 40 600

250

500

-40 -20 0 20 40 60

0

250

500

-40 -20 0 20 40 600

250

500

-40 -20 0 20 40 60

0

250

500

-40 -20 0 20 40 60

Mean = 3.12 SD = 11.05

Mean = 7.59 SD = 10.64

Mean = 17.17 SD = 13.08

Mean = 16.57 SD = 8.61

Mean = 2.82 SD = 9.68

Mean = 9.58 SD = 12.51

Mean = 8.98 SD = 7.72

Mean = 5.79 SD = 13.71

Mean = -0.61 SD = 10.84

Mean = 1.00 SD = 4.50

52

Figure 7.3 Quality of Food Consumption and Distance between Countries

Note: This figure gives the relative frequency that country c consumes a higher-quality food basket than does the poorer country c x x 1;, that is, the frequency of c c x

,q ,qy y , where x 1 is the “distance”

between countries, for c 1,...,127. Countries are ranked in terms of decreasing income, so country c is richer than d when c < d.

0.50

0.60

0.70

0.80

0.90

1.00

0 10 20 30 40 50 60 70 80

Distance x

P (quality in c > quality in c+x)

53

Figure 7.4 Food Quality and Income, Differences across Countries

A. Consumption

B. Prices

C. Spending

Note: Each panel plots against the pairwise difference in income between countries c and d the corresponding difference in the respective quality index c dy y , c,d 1, ,128, c d. Countries are ranked in terms of

decreasing income, so country c is richer than d when c < d. Income is real income (consumption) per capita,

defined as log M P as in note 2 to Table 2.1. Quality indexes are 100.

-60

-40

-20

0

20

40

60

80

0 1 2 3 4 5

-40

-30

-20

-10

0

10

20

30

40

0 1 2 3 4 5

-60

-40

-20

0

20

40

60

80

0 1 2 3 4 5

y = 4.76x + 1.70 (0.13) (0.21)

y = 1.68x + 0.28 (0.05) (0.09)

y = 6.43x + 1.98 (0.14) (0.23)

c d,q ,qy y

c dlog M P log M P

c dlog M P log M P

c dlog M P log M P

c d,p ,py y

c d,pq ,pqy y

54

Figure 7.5 Quality and Dispersion of the Food Budget

A. Perspective I

B. Perspective II

Note: Both panels of this figure contain a bivariate histogram for the quality and dispersion of the food budget

for all pairs of countries, that is, c d,q ,qy y and c d

,q ,q , c,d 1,...,127,c d . Both variables are ×

100.

Dispersion Quality

Count

Dispersion Quality

Count

55

Figure 7.6 Quality of Food Subgroups and Income

A. Staples B. Meat and Seafood

C. Dairy D. Fruits and Vegetables

E. Sweet things F. Other Foods

Note: The variable on the vertical axis is a percentage share. For the food subgroup g g 1, ,6 , this share is

defined as

g

6h 1 h

a100 ,

Σ a

with ig g g i i g

i g

qa W w 1 log ,

Q

S

where the notation is defined in the notes to Table 7.4. The term ga is the contribution of subgroup g to the

within-group component of the quality of food consumption, with the sign disregarded. For details, see equation (T7.4.1) in the notes to Table 7.4.

0

50

100

6 7 8 9 10 110

50

100

6 7 8 9 10 11

0

50

100

6 7 8 9 10 110

50

100

6 7 8 9 10 11

0

50

100

6 7 8 9 10 110

50

100

6 7 8 9 10 11

y = -5.52x + 66.66 (1.04) (9.00)

y = -0.67x + 18.56 (0.90) (7.81)

y = -0.26x + 15.63 (0.64) (5.57)

y = 4.81x - 19.05 (1.12) (9.76)

y = -0.06x + 16.62 (1.04) (9.04)

y = 1.70x + 1.57 (0.86) (7.46)

56

APPENDICES

A1. THE ICP DATA

The basic data comprise 129 disaggregated components of GDP shown in Table A1.1.

These are unpublished ICP data supplied on a confidential basis by the World Bank. The first

116 categories fall under total consumption and within these, categories 1–29 are food items.

Detailed descriptions of the food items are given in Table A1.2.

Some countries have little to no PPP real expenditure per capita on certain food items,

be it for income, geographical or religious reasons. The most prominent example is pork in

many West Asia countries. Table A1.3 contains a summary of the extent of the problem, by

commodity.

The issue of zero or very small expenditure can be partially “solved” by combining

the “Pork” and “Lamb, mutton and goat” groups. To maintain internal consistency when we

combine, expenditures (in both domestic currency units and in US dollars, that is, real

expenditures) are summed over the sub-components, whilst the purchasing power parity of

the combination is the ratio of nominal to real expenditures. However, as in 16 countries real

expenditure per capita for at least one good was still $0.01 , these countries were dropped.

These 16 countries are Angola, Bangladesh, Bhutan, Chad, Colombia, Comoros, Congo Dem.

Rep., Djibouti, Ethiopia, Lao PDR, Lebanon, Maldives, Mali, Netherlands, Thailand and

Togo. A further two countries -- Burundi and Zimbabwe -- were removed as they did not

submit national accounts data to the ICP. Our final sample thus contains 146 16 2 128

countries. These 128 countries are listed in Table 2.1.

A2. MEASURING FOOD CONSUMPTION

The food volume index for country c is

(A2.1) 28

c ic ici 1

logQ w logq ,

where icw is the proportion of food expenditure devoted to food item i and icq is per capita

consumption of i. This index is a weighted average of the consumption of the 28 items, where

the weights are the expenditure shares.

The quantities are in terms of US dollars, so they are comparable across commodities.

Thus, a reasonable alternative approach to measuring food consumption might be just to add

57 the q ′s over commodities, or to make this comparable with index (A2.1), average them by

then dividing by 28:

(A2.2) 28

ii 1

1q .

28

Figure A2.1 is a scatter plot of the logarithm of index (A2.2) against (A2.1) for the 128

countries and shows that the two are closely related and roughly proportional. Although the

estimated elasticity is somewhat above unity at 1.1, it is sufficiently close to confirm that the

indexes are roughly proportional, so the two approaches would yield very similar results.

A3. THE PRICE-QUANTITY COVARIANCE

The results for the group-wise decomposition of the price-quantity covariance are

given in Table A3.1. Similar to the results of for the budget shares, prices and quantities of

Table 5.2, the within-group component of the covariances here are around two-thirds of the

total. The covariances for staples, meats and seafood, and fruits and vegetables are among the

highest.

A4. THE INCOME ELASTICITIES

This appendix gives details of the income elasticities used in Section 7.

A Demand System

To estimate the income elasticities while controlling for the influence of prices, we

use the CBS model (Keller and van Driel, 1985), the th i equation of which is

(A4.1) ii i i i *

pw logQ log .

P

with real income and the relative price defined in logarithmic terms as

n n ni

i i i i i i*i 1 i 1 i 1

plogQ log M w log p , log log p log p , 1.

P

 

This model is linear in real income and the relative price and is easy to interpret and estimate.

Note that the price elasticities play no role in the analysis – the objective of using model

(A4.1) is to control for prices when estimating income elasticities.

Let i i ip q M be the marginal share of good i. This i answers the question,

when income rises by one dollar, by how much does spending on i increase? To derive the

implied marginal share, multiply both sides of (A4.1) by M to give

58

n n

i i i i i i i i i ii 1 i 1

p q M log M w log p log p log p

so that

i i i i i

1w M w .

M

The income elasticity of i is defined as i i i ilogq log M w . Thus, model (A4.1)

implies an income elasticity of the form

(A4.2) ii

i

1.w

Next, suppose the 28 items of food are aggregated into a composite. What can be said

about the demand for this composite good? To answer this question, we first define a

logarithmic index of the price of food as a weighted average of the 28 prices with weights

that are proportional to the i in the original index *log P :

28 28* iF i F i

i 1 i 1F

log P log p , with .

Then, if we add both sides of (A4.1) over i = 1,...,28, we obtain

(A4.3) *F

F F F F *

PW log Q log ,

P

where 28F i 1 iW w is the food budget share, while 28 28

F i 1 i F i 1 iA and B are

parameters.  Equation (A4.3) states that the demand for food as a group depends on real

income and the relative price of food, * *Flog P P . This equation is just an “uppercase”

version of (A4.1), the demand for an individual item of food.

Proceeding as before, the marginal share of food is

28i 1 i i

F F F

p qW B

M

and the corresponding income elasticity is

(A4.4) 28 28 28

F i 1 i i i iF i

i 1 i 1F F F i F

w w.

W W W w W

In words, the group income elasticity is a weighted average of the elasticities of the

components, where the thi weight is the conditional budget share of this component, that is,

the share of food item i in total expenditure on food.

59 Estimation

For i 1,..., 29 commodities (28 foods and 1 non-food), equation (A4.1) satisfies the

budget constraint in the form 29i 1 iw 1 if 29

i 1 i 1 , 29i 1 i 0 and 29 *

i 1 i ilog p P 0.

This is a singular system so one equation must be omitted in estimation. A problem is that the

price index in the model, *log P , depends on the unknown weights i. This can be solved by

a simple iterative process:

Step 1: Set the initial values of i to be all equal and define the corresponding price index

29

(0) (0) (0)i i i

i 1

1, log P log p .

29

Step 2: Estimate as a SUR system (1) (1) (1)i i i, , in

(1) (1) (1) icic i i c i ic(0)

c

pw log Q log , i 1, ,29 goods; c 1, ,128 countries,

P

where (1)(1)i i is estimated as a free composite coefficient and ic is a disturbance

term. As the weights i sum over i 1,..., 29 to unity, it follows that 29i 1 i . Thus, the

first-round estimates of i and can be recovered as

(1)29

(1) (1) (1) ii i (1)

i 1 i

, .

Step 3: Replace (0)i in Step 1 with (1)

i to give (1)ilog P . Re-estimate the model in Step 2 with

(1)ilog P to give the second-round estimates (2)

i , (2)i and (2)

i .

Step 4: Continue until convergence, that is, when (k 1) (k)i i , (k 1) (k)

i i and (k 1) (k)

i i .

Using our 128-country data, this procedure converges in under 100 iterations and the

results are in Table A4.1.26 The vast majority of the food items have negative i , indicating

they are necessities, as is to be expected. Only cheese and confectionary etc. (items 14 and

24) have significantly positive i. It is reasonable that these goods are luxuries, which

accords with the finding of Section 2 that their shares increase with income in some cases.

The i are weights in the price index *log P . As can be seen from column 5 of the table, all

but one of the estimated weights for the food items are positive.27 The majority of the weights

26 For the price of non-food, we divide the sum of nominal expenditure of all non-food items by the sum of their real expenditures. 27 The negative semi-definiteness of the substitution matrix does not depend on all the weights being positive.

60 are estimated quite precisely. The weights for rice, bread and potatoes are all large;

interestingly, these goods also have large budget shares. The weight for non-food is negative.

Finally, the estimated value of the parameter λ is -8.35  1100 .

Table A4.2 gives the implied income elasticities by income quartile, evaluated using

budget shares from Table 2.2. The several negative elasticities in the upper quartiles reflect

the low budget shares for these goods and should not be taken at face value. The income

elasticity of all food as a composite is a weighted average of the elasticities of the 28

components, as indicated by (A4.4), which, from (A4.2), takes the form

2828i i i 1 i 29

Fi 1 F i F F

w1 1 1,

W w W W

where the last step follows from 29i 1 i 0. The estimate of the income coefficient for non-

food, given as the last element of column 3 of Table A4.1, is 8.73 1100 . Using the

negative of this value in the above expression gives the income elasticity for food. This

elasticity, for each quartile, is given in the second last row of Table A4.3. These values agree

reasonably well with those from Gao (2012), given in the last row. The only notable

difference is the elasticity for the first quartile – this is now 0.03, whereas Gao obtained 0.31.

The Final Elasticities

Whilst the income elasticities for all food agree tolerably well with Gao (2012), the

difficulty is that several commodities have negative income elasticities, including rice and

other cereals for the higher income groups. This result cannot be ruled out, especially for rich

consumers; but as these are fairly broad items, it seems unlikely that they are inferior goods.28

Large negative income elasticities of the order of -7 can certainly be ruled out as implausible. 28 Ito et al. (1989) study per capita consumption of rice in 14 Asian countries for the 25 years up to the mid-1980s. They use a demand model with an inverted U-shaped income response. Thus, consumption grows with income as long as income is below some critical value; thereafter, consumption falls and the good becomes inferior. In 5 of the 14 countries, the income elasticity changes from positive to negative over the sample period; and in two cases (Nepal and Bangladesh), the elasticity is always negative. A more general result is that in almost all cases, the elasticity declines over time. The decline in the income elasticity of a necessity as income grows is plausible on economic grounds. Several points need to be noted about this study, however. First, apparent consumption of rice is used and there are well-known problems with this residual measure associated with uncertain estimates of stock holdings. Second, some of the changes in the income elasticity over time are large, perhaps too large to be entirely plausible. The largest change is for Malaysia, where the elasticity falls from 0.33 in 1961 to -0.71 in 1984. The falls for Japan, Singapore and Thailand are of a similar order of magnitude. Third, the elasticity is always negative in Nepal. The inferiority of rice in one of Asia’s poorest countries would not seem to agree well with the model that says the good is normal for low levels of income. A similar issue applies to Bangladesh, although its elasticity is much closer to zero. Fourth, in controlling for the influence of prices on consumption, the world prices of rice and wheat (a substitute for rice) are used, not the domestic prices. In short, the study raises the possibility of the inferiority of rice, but the findings need to be interpreted with due care in light of these issues.

61 As a way to avoid the above problems, we use prior studies as a guide to amending the

elasticities in Table A4.2. Our approach involves five steps. First, we start with the Table

A4.2 elasticities. Second, the negative values for rice are replaced with 0.1. In Appendix A5

below, we summarise prior estimates and while there is considerable dispersion, the value 0.1

is not inconsistent with this previous evidence. It seems reasonable to suppose that in the eyes

(mouths?) of consumers other cereals are fairly close to rice, so we assume the two

commodities are sufficiently similar to have the same income elasticity, 0.1 in this step.

Third, the negative values for other food items are also replaced with 0.1. In most cases, the

initial values are close to zero, and, most likely, insignificantly different from 0.1; thus, this

step is in all probability innocuous. Fourth, the bread elasticities are replaced with 0.5, on the

basis of previous estimates summarised in Appendix A5. Fifth, the elasticities are

renormalised such that a budget-share weighted average equals unity. Most of the above

adjustments pertain to the first and second quartiles. The only changes for the third and fourth

quartiles involve setting the bread elasticity at 0.5 and the renormalisation.

The new set of income elasticities is given in Table A4.4, which is used in Section 7.

As can be seen, only three food items have elasticities greater than unity – other meats (item

number 9), cheese (14) and confectionary, chocolate and ice cream (25). It is plausible that

these three are luxuries, although none is a strong luxury.

A5. PREVIOUS INCOME ELASTICITIES FOR RICE AND BREAD

Table A5.1 lists prior estimates of income elasticities for rice and bread. In order to

compare these estimates with ours, we convert income per capita of the prior studies into our

concept of income that is measured in term of international dollars of 2005. Our income is the

sum of individual consumption by households, non-profit institutions’ expenditure on

households and individual government expenditure on households. We use 1960-2015 data

from the World Bank’s World Development Indicators (WDI) to calculate this for the

previous studies. Whilst the first two components of income are readily available, the third

requires some inferences as the WDI only provides total government expenditure. To do so,

we use education and health as a proxy for individual government spending. For missing

years, we use the long-term average share of education and health in GDP multiplied by GDP

in the relevant year. This yields income per capita for the year applicable to the previous

study. We then inflate this to domestic 2005 dollars using the change in the country’s

consumer price index. To convert to real income, we deflate nominal income by the country’s

62 cost-of-living index n

c i i ilog P w log p . Finally, we allocate countries to income quartiles.

This assignment of countries is given in column 5 of Table A5.1.

Panel A of Table A5.2 summarises the prior elasticities of the rice income elasticities.

In total there are 42 and from column 7, the mean and median are 0.11, but there is

substantial dispersion (SD = 0.38). Of the 42 estimates, 32 can be cross classified by income

(columns 2-6). Panel B of the table gives the same information for bread. Here the income

elasticities are higher, at least on average, and on the order of 0.5. But it is to be noted that

there are much fewer estimates for bread.

A6. MUHAMMAD, SEALE, MEADE AND REGMI

Muhammad et al. (2011) use the 2005 ICP data to estimate income elasticities with

food is split into seven groups plus an eighth, “Beverages & Tobacco”. In this appendix, it is

shown that when we aggregate our results and weight them to make commodities

representative of spending patterns, the two sets of elasticities are reassuringly reasonably

close to each other.

Table A6.1 contains a comparison of our results, after appropriate aggregation of

commodities, with those of Muhammad et al. With the exception of staples and meat in high-

income countries, the elasticities in panel A are similar in the two studies. The last row of the

table gives the weighted sum of the income elasticities, which is the elasticity for food as a

whole. For the richest countries in this study is 16.18 100 (column 2), which is similar to

Muhammad et al.’s 17.88 100 (column 7). This is also true for the poorest countries:

136.51 100 vs. 132.89 100 . Table A6.2 gives the intermediate calculations underlying

Table A6.1.

Figure A6.1 plots the two sets of weighted income elasticities (which are given in

panel C of Table A6.1), and, except for other food, the agreement is fairly close.

A7. QUALITY GROUPS

Equation (6.1) defines the quality index for all n goods as

(A7.1) n

,q i i ii 1

y w 1 logq logQ ,

where, for good i, iw is the budget share, i the income elasticity, iq the quantity demanded

and ni 1 i ilogQ w logq is the volume index. The n goods are divided into G n groups,

63 written 1 G,..., ,S S where each good belongs to one group only. Equation (6.4) decomposed

this index into between- and within-group components:

(A7.2) gn G G

i ii i g g g g i i g

i 1 g 1 g 1 i g

q Q qw 1 log W 1 log W w 1 log .

Q Q Q

S

Here, gg i iW Σ w S is the budget share of group g;

gg i i iη Σ w η S is the income elasticity of

g, with i i gw w W the conditional budget share of good gi ;Sg

gi i ilogQ Σ w logq S is the

volume index for group g; and i i gη η η is the conditional income elasticity of gi .S In

this appendix, we derive equation (A7.2).

Rewrite the right-hand side of equation (A7.1) as

(A7.3)

n n

i i i i i i g gi 1 i 1

n n

i i g i i i gi 1 i 1

w 1 logq logQ w 1 logq logQ logQ logQ

w 1 logQ logQ w 1 logq logQ .

The first component of the second line of (A7.3) can be expressed as

n G

i i g i i gi 1 g 1 i g

G

g i i ig 1 i g i g

G

g g g gg 1

gG G

g g g g gg 1 g 1

w 1 logQ logQ w 1 logQ logQ

logQ logQ w w

logQ logQ W W

QW 1 logQ logQ W 1 log .

Q

This is the between-group component, the first term on the right of equation (A7.2).

Next, use i i gw w W and i i g to express the second component of the second

line of (A7.3) as

n G G

i i i g i i i g i i gi 1 g 1 i g g 1 i g

G G

i g i g i g i g i gg 1 i g g 1 i g

G G

g g i i i g g i i gg 1 i g g 1 i g

w 1 log q log Q w log q log Q w log q log Q

w W log q log Q w W log q log Q

W w log q log Q W w log q log Q

Since i g i i gw logq logQ 0, it is convenient to write the final term in the last line above as

G G

g i i g g g i i gg 1 i g g 1 i g

W w logq logQ W w logq logQ ,

64 so that

n G G

i i i g g g i i i g g g i i gi 1 g 1 i g g 1 i g

G

g g i i i g i i gg 1 i g i g

G

g g i i i gg 1 i g

w 1 log q log Q W w log q log Q W w log q log Q

W w log q log Q w log q log Q

W w 1 log q log Q .

This is the within-group component, the second term on the right of equation (A7.2). This

verifies equation (A7.2).

The above approach formulates the quality index in terms of the levels of quantities.

Theil (1975/76, Chaps. 11 and 14), by contrast, considers quality using a differential

approach in which quantities are expressed in terms of discrete changes over time. His

decomposition is analogous to the above.

65

APPENDIX REFERENCES

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Coelho, A. B., D. R. D. de Aguiar and J. S. Eales (2010). “Food Demand in Brazil: An Application of the Shonkwiler and Yen Two-Step Estimation Method.” Estud. Econ. 40: 186-211.

Chern, W. S., K. Ishibashi, K. Taniguchi and Y. Tokoyama (2003). “Analysis of Food Consumption of Japanese Households.” Food and Agriculture Organisation of the United Nations, Italy: Rome.

Food and Agricultural Policy Research Institute, FAPRI (2008). “Elasticity Database.” United States. Available at: http://www.fapri.iastate.edu/tools/elasticity.aspx [verified 16 September 2015].

Gao, G. (2012). “World Food Demand.” American Journal of Agricultural Economics 94: 25-51.

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Ito, S., E. W. F. Peterson and W. R. Grant (1989). “Rice in Asia: Is it Becoming an Inferior Good?” American Journal of Agricultural Economics 71: 32-42.

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Meyerhoefer, C. D., C. K. Ranney and D. E. Sahn (2005). “Consistent Estimation of Censored Demand Systems Using Panel Data.” American Journal of Agricultural Economics 87: 660-72.

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Theil, H. (1975/76). Theory and Measurement of Consumer Demand. Two Volumes. Amsterdam: North-Holland Publishing Company.

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Analysis.” Applied Economics 27: 509-15.

66

Table A1.1 ICP Categories

No. ICP Category No. ICP Category 1. 1101111 Rice 66. 110711 Motor cars 2. 1101112 Other cereals and flour 67. 110712 Motor cycles 3. 1101113 Bread 68. 10713 Bicycles 4. 1101114 Other bakery products 69. 110722 Fuels and lubricants for personal transport equip. 5. 1101115 Pasta products 70. 110723 Maint. and repair of personal transport equip. 6. 1101121 Beef and veal 71. 110724 Other services -personal transport equip. 7. 1101122 Pork 72. 110731 Passenger transport by railway 8. 1101123 Lamb, mutton and goat 73. 110732 Passenger transport by road 9. 1101124 Poultry 74. 110733 Passenger transport by air 10. 1101125 Other meats and preparations 75. 110734 Passenger transport by sea and inland waterway 11. 1101131 Fresh or frozen fish and seafood 76. 110735 Combined passenger transport 12. 1101132 Preserved fish and seafood 77. 110736 Other purchased transport services 13. 1101141 Fresh milk 78. 110810 Postal services 14. 1101142 Preserved milk and milk products 79. 110820 Telephone and telefax equipment 15. 1101143 Cheese 80. 110830 Telephone and telefax services 16. 1101144 Eggs and egg-based products 81. 110911 Audio-visual, photographic and information

processing equipment 17. 1101151 Butter and margarine 82. 110914 Recording media 18. 1101153 Other edible oils and fats 83. 110915 Repair of audio-visual, photographic and

information processing equipment 19. 1101161 Fresh or chilled fruit 84. 110921 Major durables for outdoor and indoor recreation 20. 1101162 Frozen, preserved or processed fruits 85. 110931 Other recreational items and equipment 21. 1101171 Fresh or chilled vegetables 86. 110933 Gardens and pets 22. 1101172 Fresh or chilled potatoes 87. 110935 Veterinary and other services for pets 23. 1101173 Frozen or preserved vegetables 88. 110941 Recreational and sporting services 24. 1101181 Sugar 89. 110942 Cultural services 25. 1101182 Jams, marmalades and honey 90. 110943 Games of chance 26. 1101183 Confectionery, chocolate and ice cream 91. 110950 Newspapers, books and stationery 27. 110119 Food products n.e.c. 92. 110960 Package holidays 28. 110121 Coffee, tea and cocoa 93. 111000 Education 29. 110122 Mineral waters, soft drinks, fruit and vegetable juices 94. 111110 Catering services 30. 1102111 Spirits 95. 111120 Accommodation services 31. 1102121 Wine 96. 111211 Hairdressing & personal grooming establishments 32. 1102131 Beer 97. 111212 Appliances, articles and products for personal care 33. 110220 Tobacco 98. 111220 Prostitution 34. 1103111 Clothing materials and accessories 99. 111231 Jewellery, clocks and watches 35. 1103121 Garments 100. 111232 Other personal effects 36. 1103141 Cleaning and repair of clothing 101. 111240 Social protection 37. 1103211 Footwear 102. 111250 Insurance 38. 1103221 Repair and hire of footwear 103. 111261 FISIM 39. 110410 Actual and imputed rentals for housing 104. 111262 Other financial services n.e.c 40. 110430 Maintenance and repair of the dwelling 105. 111270 Other services n.e.c. 41. 110440 Water sup. and misc. services relating to the dwelling 106. 111300 Net purchases abroad 42. 110442 Miscellaneous services relating to the dwelling 107. 130221 Compensation of employees 43. 110451 Electricity 108. 130222 Intermediate consumption 44. 110452 Gas 109. 130223 Gross operating surplus 45. 110453 Other fuels 110. 130224 Net taxes on production 46. 110511 Furniture and furnishings 111. 130225 Receipts from sales 47. 110512 Carpets and other floor coverings 112. 130421 Compensation of employees 48. 110513 Repair of furniture, furnishings and floor coverings 113. 130422 Intermediate consumption 49. 110520 Household textiles 114. 130423 Gross operating surplus 50. 110531 Major household appliances whether electric or not 115. 130424 Net taxes on production 51. 110532 Small electric household appliances 116. 130425 Receipts from sales 52. 110533 Repair of household appliances 117. 140111 Compensation of employees 53. 110540 Glassware, tableware and household utensils 118. 140112 Intermediate consumption 54. 110551 Major tools and equipment 119. 140113 Gross operating surplus 55. 110552 Small tools and miscellaneous accessories 120. 140114 Net taxes on production 56. 110561 Non-durable household goods 121. 140115 Receipts from sales 57. 1105621 Domestic services 122. 150110 Metal products and equipment 58. 1105622 Household services 123. 150120 Transport equipment 59. 110611 Pharmaceutical products 124. 150210 Residential buildings 60. 110612 Other medical products 125. 150220 Non-residential buildings 61. 110613 Therapeutical appliances and equipment 126. 150230 Civil engineering works 62. 110621 Medical Services 127. 150300 Other products 63. 110622 Dental services 128. 160000 Change in inventories and valuables 64. 110623 Paramedical services 129. 80000 Balance of exports and imports 65. 110630 Hospital services Source: World Bank (unpublished).

67

Table A1.2 Composition of Food Items

Food classes

ICP Basic Headings

ID Name ID Name Description

(1) (2) (3) (4) (5)

1. STAPLES

11 Bread and cereals

Includes farinaceous-based products prepared with meat, fish, seafood, cheese, vegetables or fruit.

11.1 Rice Rice in all forms except flour

11.2 Other cereals and flour Maize, wheat, barley, oats, rye and other cereals in the form of grain, meal or flour; cereal preparations (cornflakes, oat flakes, etc.) and other cereal products (malt, malt flour, malt extract, potato starch, tapioca, sago and other starches); includes couscous; rice flour; excludes sweetcorn.

11.3 Bread Fresh bread and special bread.

11.4 Other bakery products Bakery products such as crispbread, rusks, toasted bread, biscuits, gingerbread, wafers, waffles, crumpets, muffins, croissants, cakes, tarts, pies, quiches and pizzas; includes mixes and doughs for the preparation of bakery products; excludes meat pies; fish pies.

11.5 Pasta products Pasta products in all forms.

2. MEAT AND SEAFOOD

12 Meat

Includes animals and poultry purchased live for consumption as food.

12.1 Beef and veal Fresh, chilled or frozen meat of bovine animals, excludes edible offal.

12.2 Pork Fresh, chilled or frozen meat of swine; excludes edible offal.

12.3 Lamb, mutton and goat Fresh, chilled or frozen meat of sheep and goat; excludes edible offal.

12.4 Poultry Fresh, chilled or frozen meat of poultry (chicken, duck, goose, turkey, guinea fowl); includes edible poultry offal.

12.5* Other meats and preparations

Fresh, chilled or frozen meat of hare, rabbit, game (antelope, deer, boar, pheasant, grouse, pigeon, quail, etc.), marine mammals (seal, walrus, whale, etc.), horse, mule, donkey, camel, ostrich, kangaroo, alligator, etc.; fresh, chilled or frozen edible offal; excludes edible poultry offal.

Dried, salted or smoked meat and edible offal (sausages, salami, bacon, ham, pâté, etc.); other preserved or processed meat and meat-based preparations (canned meat, meat extracts, meat juices, meat pies, etc.); excludes frogs, land and sea snails; lard and other edible animal fats; soups, broths and stocks containing meat.

(continued on next page)

68

Table A1.2 Composition of Food Items (continued)

Food classes

ICP Basic Headings

ID Name ID Name Description

(1) (2) (3) (4) (5)

13 Seafood 13.1 Fresh or frozen fish and seafood

Fresh, chilled or frozen fish and seafood (crustaceans, molluscs and other shellfish, sea snails); includes land crabs, land snails and frogs; fish and seafood purchased live for consumption as food.

13.2 Preserved fish and seafood

Dried, smoked or salted fish and seafood; other preserved or processed fish and seafood and fish and seafood based preparations (canned fish and seafood, caviar and other hard roes, fish pies, etc.); excludes soups, broths and stocks containing fish or seafood.

3. DAIRY

14 Milk, cheese and eggs

Includes non-dairy milk substitutes such as soya milk; excludes butter and butter products.

14.1 Fresh milk Raw milk; pasteurised or sterilised milk; includes whole and low fat milk; recombined or reconstituted milk; soya milk.

14.2 Preserved milk and milk products

Condensed, evaporated or powdered milk; yoghurt, cream, milk-based desserts, milk-based beverages and other similar milk-based products; includes milk, cream and yoghurt containing sugar, cocoa, fruit or flavourings.

14.3 Cheese Cheese and curd.

14.4 Eggs and egg-based products

Eggs and egg products made wholly from eggs.

15 Oils and fats 15.1* Butter and margarine Butter and butter products (butter oil, ghee, etc.).

Margarine; includes “diet” margarine.

4. FRUIT AND VEGETABLES

16 Fruit 16.1 Fresh or chilled fruit Fresh or chilled fruit; includes melons and water melons; excludes vegetables grown for their fruit such as aubergines, cucumbers and tomatoes.

16.2 Frozen, preserved or processed fruits

Frozen fruit; dried fruit, fruit peel, fruit kernels, nuts and edible seeds; other preserved fruit; processed fruit; fruit-based products; excludes jams, marmalades, compotes, jellies, fruit purees and pastes; parts of plants preserved in sugar; fruit juices.

(continued on next page)

69

Table A1.2 Composition of Food Items (continued)

Food classes

ICP Basic Headings

ID Name ID Name Description

(1) (2) (3) (4) (5)

17 Vegetables 17.1 Fresh or chilled vegetables

Fresh or chilled vegetables cultivated for their leaves or stalks (asparagus, broccoli, cauliflower, endives, fennel, spinach, etc.), for their fruit (aubergines, cucumbers, courgettes, green peppers, pumpkins, tomatoes, etc.), and for their roots (beetroot, carrots, onions, parsnips, radishes, turnips, etc.); includes olives; garlic; pulses; sweetcorn; sea fennel and other edible seaweed; mushrooms and other edible fungi; excludes lentils; culinary herbs (parsley, rosemary, thyme, etc.) and spices (pepper, pimento, ginger, etc.).

17.2 Fresh or chilled potatoes Fresh or chilled potatoes; includes other tuber vegetables (manioc, arrowroot, cassava, sweet potatoes, etc.).

17.3 Frozen or preserved vegetables

Frozen vegetables; dried vegetables; other preserved vegetables; processed vegetables; vegetable-based products; includes frozen preparations such as chipped potatoes; lentils; products of potatoes and other tuber vegetables such as flours, meals, flakes, purees, chips, crisps, etc.; excludes potato starch, tapioca, sago and other starches; soups, broths and stocks containing vegetables; vegetable juices.

5. SWEET THINGS

18 Sugar, jam, honey, chocolate and confectionery

18.1 Sugar Cane or beet sugar, unrefined or refined, powdered, crystallised or in lumps; includes artificial sugar substitutes.

18.2 Jams, marmalades and honey

Jams, marmalades, compotes, jellies, fruit purees and pastes, natural and artificial honey, maple syrup, molasses and parts of plants preserved in sugar.

18.3* Confectionery, chocolate and ice cream

Chocolate in bars and slabs, chewing gum, sweets, toffees, pastilles and other confectionery products; cocoa-based foods and cocoa-based dessert preparations; excludes cocoa and chocolate-based powder. Edible ice, ice cream and sorbet.

(continued on next page)

70

Table A1.2 Composition of Food Items (continued)

Food classes

ICP Basic Headings

ID Name ID Name Description

(1) (2) (3) (4) (5)

6. OTHER FOODS

15 Oils and fats 15.3 Other edible oils and fats Edible oils (olive oil, corn oil, sunflower-seed oil, cotton-seed oil, soybean oil, groundnut oil, walnut oil, etc.); edible animal fats (lard, etc.); edible vegetable fats (peanut butter, etc.); excludes cod or halibut liver oil

19 Food products n.e.c. 19.1 Food products n.e.c. Salt, spices (pepper, pimento, ginger, etc.), culinary herbs (parsley, rosemary, thyme, etc.), sauces, condiments, seasonings (mustard, mayonnaise, ketchup, soy sauce, etc.), vinegar; prepared baking powders, baker's yeast, dessert preparations, soups, broths, stocks, culinary ingredients, etc.; homogenised baby food and dietary preparations irrespective of the composition; excludes soya milk; milk-based desserts; artificial sugar substitutes; cocoa-based dessert preparations.

21 Coffee, tea and cocoa 21.1 Coffee, tea and cocoa Coffee, whether or not decaffeinated, roasted or ground; tea, maté and other plant products for infusions; cocoa, whether or not sweetened, and chocolate-based powder; includes instant coffee; coffee substitutes; extracts and essences of coffee; tea substitutes; extracts and essences of tea; cocoa-based beverage preparations; excludes chocolate in bars or slabs; cocoa-based foods and cocoa-based dessert preparations.

22 Mineral waters, soft drinks, fruit and vegetable juices

22.1* Mineral waters, soft drinks, fruit and vegetable juices

Mineral or spring waters; all drinking water sold in containers.

Soft drinks such as sodas, lemonades and colas; syrups and concentrates for the preparation of beverages; excludes non-alcoholic beverages which are generally alcoholic such as non-alcoholic beer.

Fruit and vegetable juices.

Notes: 1. The ICP Basic Headings are based on OECD Basic Headings. As some headings were considered too detailed by the ICP, they were combined as denoted by “*”. Basic

headings are reported as they appear in the confidential spreadsheet supplied by the World Bank and refer to consumption expenditure by households on food and non-alcoholic beverages.

2. The food products and non-alcoholic beverages considered here are those purchased for consumption at home. The data exclude food products sold for immediate consumption away from the home by hotels, restaurants, cafés, bars, kiosks, street vendors, automatic vending machines, etc.; cooked dishes prepared by restaurants for consumption off their premises; cooked dishes prepared by catering contractors whether collected by the customer or delivered to the customer’s home; and products sold specifically as pet foods.

3. The six panels represent the six food groups as defined in this paper. Source: World Bank (2003).

71

Table A1.3 Instances of Low Consumption

(Number of countries affected)

ICP Category

Cut-off (per capita real expenditure)

A. Original data

B. Pork and Lamb combined

$0 $0.01 $0.1 $1 $0 $0.01 $0.1 $1

(1) (2) (3) (4) (5) (6) (7) (8) (9) 1. 1101111 Rice - - 1 2 - - 1 2 2. 1101112 Other cereals and flour - - - 5 - - - 5 3. 1101113 Bread - - - 3 - - - 3 4. 1101114 Other bakery products 2 2 3 18 2 2 3 18 5. 1101115 Pasta products - 1 10 28 - 1 10 28 6. 1101121 Beef and veal - - - 3 - - - 3 7. 1101122 Pork 21 23 26 39

1 1 2 5 8. 1101123 Lamb, mutton and goat 4 4 9 23 9. 1101124 Poultry 1 1 1 13 1 1 1 13 10. 1101125 Other meats and preparations 1 1 2 28 1 1 2 28 11. 1101131 Fresh/frozen fish and seafood - - 1 5 - - 1 5 12. 1101132 Preserved fish and seafood 1 1 6 24 1 1 6 24 13. 1101141 Fresh milk 1 1 5 22 1 1 5 22 14. 1101142 Preserved milk and milk products - - 3 17 - - 3 17 15. 1101143 Cheese 2 4 23 49 2 4 23 49 16. 1101144 Eggs and egg-based products - - 1 19 - - 1 19 17. 1101151 Butter and margarine 1 2 6 28 1 2 6 28 18. 1101161 Fresh or chilled fruit - - - 7 - - - 7 19. 1101162 Frozen, preserved or processed fruits 5 7 13 43 5 7 13 43 20. 1101171 Fresh or chilled vegetables - - - - - - - - 21. 1101172 Fresh or chilled potatoes - - - 6 - - - 6 22. 1101173 Frozen or preserved vegetables 3 3 8 26 3 3 8 26 23. 1101181 Sugar - - - 8 - - - 8 24. 1101182 Jams, marmalades and honey 1 1 14 50 1 1 14 50 25. 1101183 Confectionery, chocolate and ice cream - 3 11 39 - 3 11 39 26. 1101153 Other edible oils and fats 1 1 2 7 1 1 2 7 27. 110119 Food products n.e.c. - - - 6 - - - 6 28. 110121 Coffee, tea and cocoa - - 1 15 - - 1 15 29. 110122 Min. waters, sft drinks, fruit & veg. juices - - - 14 - - - 14 Total 30 36 62 98 11 16 43 82

72

Table A3.1 Decomposition of Price-Quantity Covariances

Income quartile

Total covariance

Components Group covariances

Between group

Within group

Staples Meats and Seafood

Dairy Fruits and vegetables

Sweet things

Other food

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

1 -8.99 -3.00 -5.99 -6.86 -7.90 -7.61 -6.74 4.30 -0.83

2 -20.86 -7.39 -13.47 -30.68 -12.35 -5.07 -18.69 -1.25 -4.94

3 -33.20 -13.67 -19.53 -30.03 -26.55 -5.62 -21.66 -8.93 -4.70

4 -37.33 -17.55 -19.78 -18.07 -40.26 -8.14 -17.66 -1.93 -6.10

All -25.22 -10.46 -14.76 -21.52 -21.87 -6.60 -16.26 -2.00 -4.17

Notes: All entries are ×100. See notes to Table 5.2 for calculation details.

73

Table A4.1 A Demand System for Food and Non-food

icic i i c i ic*

c

pw logQ log

P , i 1,...,29 goods; c 1, ,128 countries

Item Intercept

i 100

Income coefficient

i 100

Price coefficient

i 100

Normalised price coefficient

29i i j 1 i 100

(1) (2) (3) (4) (5)

Food

1. Rice 14.52 (1.78) -1.55 (0.20) -1.72 (0.11) 20.57 (0.25)

2. Other cereals and flour 18.07 (1.60) -1.85 (0.18) -0.61 (0.05) 7.34 (0.28)

3. Bread -0.88 (0.83) 0.12 (0.09) -1.47 (0.09) 17.64 (0.23)

4. Other bakery products 0.55 (0.30) 0.00 (0.03) -0.05 (0.04) 0.63 (0.43)

5. Pasta products 1.08 (0.19) -0.09 (0.02) -0.38 (0.03) 4.52 (0.22)

6. Beef and veal 5.04 (0.89) -0.46 (0.10) -0.72 (0.05) 8.63 (0.27)

7. Pork, Lamb, mutton and goat 2.04 (0.75) -0.13 (0.09) -0.48 (0.04) 5.80 (0.27)

8. Poultry 2.59 (0.54) -0.18 (0.06) -0.31 (0.03) 3.74 (0.30)

9. Other meats and preparations 0.08 (0.76) 0.12 (0.09) -0.45 (0.04) 5.37 (0.26)

10. Fresh or frozen fish and seafood 3.49 (0.84) -0.33 (0.10) -0.75 (0.05) 9.02 (0.23)

11. Preserved fish and seafood 3.43 (0.55) -0.33 (0.06) -0.21 (0.02) 2.57 (0.25)

12. Fresh milk 3.52 (0.58) -0.32 (0.07) -0.70 (0.05) 8.39 (0.25)

13. Preserved milk and milk products 1.90 (0.41) -0.12 (0.05) -0.22 (0.03) 2.59 (0.34)

14. Cheese -0.61 (0.36) 0.13 (0.04) -0.12 (0.03) 1.49 (0.31)

15. Eggs and egg-based products 0.87 (0.26) -0.05 (0.03) -0.39 (0.03) 4.63 (0.27)

16. Butter and margarine 1.24 (0.41) -0.12 (0.05) -0.48 (0.04) 5.78 (0.27)

17. Fresh or chilled fruit 1.68 (0.65) -0.09 (0.07) -0.73 (0.05) 8.70 (0.29)

18. Frozen, preserved or processed fruits 0.86 (0.23) -0.07 (0.03) -0.23 (0.03) 2.72 (0.36)

19. Fresh or chilled vegetables 7.22 (0.90) -0.65 (0.10) -0.78 (0.06) 9.31 (0.34)

20. Fresh or chilled potatoes 8.24 (1.28) -0.86 (0.15) -0.81 (0.05) 9.71 (0.19)

21. Frozen or preserved vegetables 2.01 (0.49) -0.17 (0.06) -0.24 (0.04) 2.82 (0.41)

22. Sugar 5.41 (0.60) -0.54 (0.07) -0.33 (0.03) 3.95 (0.24)

23. Jams, marmalades and honey 0.21 (0.10) -0.01 (0.01) 0.00 (0.02) 0.02 (0.22)

24. Confectionery, chocolate and ice cream -0.47 (0.24) 0.12 (0.03) -0.11 (0.02) 1.29 (0.18)

25. Other edible oils and fats 5.56 (0.49) -0.53 (0.06) -0.43 (0.04) 5.13 (0.29)

26. Food products n.e.c. 6.46 (0.89) -0.60 (0.10) -0.24 (0.03) 2.90 (0.37)

27. Coffee, tea and cocoa 1.87 (0.42) -0.15 (0.05) -0.20 (0.03) 2.37 (0.30)

28. Min. waters, sft drnks, frit & veg. juices 1.23 (0.38) -0.03 (0.04) 0.05 (0.03) -0.66 (0.39)

Non-food 2.78 (5.12) 8.73 (0.58) 4.76 (0.30) -56.95 (0.00)

Sum 100 0 -8.35 (0.53) 100

74

Table A4.2 Income Elasticities of Demand

Food item Income quartile

First Second Third Fourth All (1) (2) (3) (4) (5) (6)

Food 1. Rice -7.659 -2.031 0.241 0.722 0.253 2. Other cereals and flour -8.817 -2.185 0.281 0.649 0.140 3. Bread 1.197 1.082 1.055 1.080 1.084 4. Other bakery products 1.004 1.003 1.004 1.003 1.003 5. Pasta products 0.543 0.699 0.816 0.792 0.746 6. Beef and veal -0.066 0.602 0.795 0.815 0.709 7. Pork, Lamb, mutton and goat 0.769 0.901 0.914 0.914 0.894 8. Poultry 0.622 0.832 0.900 0.845 0.841 9. Other meats and preparations 1.155 1.071 1.126 1.136 1.112 10. Fresh or frozen fish and seafood 0.408 0.450 0.808 0.843 0.735 11. Preserved fish and seafood -0.169 -0.239 0.206 0.756 0.430 12. Fresh milk 0.010 0.625 0.697 0.790 0.659 13. Preserved milk and milk products 0.711 0.868 0.892 0.868 0.856 14. Cheese 1.281 1.176 1.190 2.126 1.260 15. Eggs and egg-based products 0.598 0.891 0.935 0.889 0.889 16. Butter and margarine 0.037 0.663 0.790 0.821 0.721 17. Fresh or chilled fruit 0.885 0.939 0.954 0.950 0.940 18. Frozen/ preserved/processed fruits 0.603 0.639 0.808 0.829 0.755 19. Fresh or chilled vegetables -0.019 0.576 0.794 0.798 0.696 20. Fresh or chilled potatoes -4.882 -0.738 0.356 0.743 0.353 21. Frozen or preserved vegetables 0.388 0.663 0.652 0.809 0.685 22. Sugar -6.352 -0.212 0.455 0.705 0.354 23. Jams, marmalades and honey 0.887 0.961 0.949 0.932 0.942 24. Confec., chocolate and ice cream 1.194 1.175 1.189 1.437 1.217 25. Other edible oils and fats -1.961 -0.010 0.619 0.721 0.469 26. Food products n.e.c. -0.074 0.214 0.650 0.752 0.560 27. Coffee, tea and cocoa 0.462 0.726 0.822 0.828 0.764 28. Min. wtrs, sft drnks, f. & veg. juice 0.964 0.975 0.976 0.970 0.972 Non-food 1.098 1.111 1.134 1.157 1.121

Table A4.3 Food Budget Shares and Income Elasticities

Income quartile

Source (1)

First (2)

Second (3)

Third (4)

Fourth (5)

All (6)

A. Budget share FW 100

Table 2.2 11 21 35 44 28

Gao (2012) 11 21 35 46 28

B. Income elasticity FN

Implied by Table A4.2 0.03 0.55 0.77 0.83 0.74

Gao (2012) 0.31 0.53 0.74 0.90 0.62 Source: Gao (2012, Table 7), who uses the 2005 ICP data (World Bank, 2008).

75

Table A4.4 Modified Income Elasticities

Food item Income quartile

First Second Third Fourth All (1) (2) (3) (4) (5) (6)

Food 1. Rice 0.096 0.098 0.244 0.728 0.255 2. Other cereals and flour 0.096 0.098 0.284 0.655 0.141 3. Bread 0.478 0.489 0.506 0.504 0.504 4. Other bakery products 0.960 0.981 1.016 1.012 1.011 5. Pasta products 0.519 0.683 0.826 0.799 0.752 6. Beef and veal 0.096 0.589 0.805 0.822 0.715 7. Pork, Lamb, mutton and goat 0.736 0.881 0.925 0.922 0.901 8. Poultry 0.595 0.813 0.911 0.852 0.848 9. Other meats and preparations 1.105 1.047 1.140 1.146 1.121 10. Fresh or frozen fish and seafood 0.390 0.440 0.818 0.850 0.741 11. Preserved fish and seafood 0.096 0.098 0.208 0.762 0.434 12. Fresh milk 0.010 0.611 0.705 0.797 0.664 13. Preserved milk and milk products 0.680 0.849 0.903 0.875 0.863 14. Cheese 1.225 1.150 1.204 2.144 1.270 15. Eggs and egg-based products 0.572 0.871 0.946 0.897 0.896 16. Butter and margarine 0.035 0.648 0.799 0.828 0.727 17. Other edible oils and fats 0.096 0.098 0.626 0.727 0.473 18. Fresh or chilled fruit 0.847 0.918 0.965 0.958 0.948 19. Frozen/ preserved/processed fruits 0.577 0.625 0.818 0.836 0.761 20. Fresh or chilled vegetables 0.096 0.563 0.804 0.805 0.702 21. Fresh or chilled potatoes 0.096 0.098 0.360 0.749 0.356 22. Frozen or preserved vegetables 0.371 0.648 0.660 0.816 0.691 23. Sugar 0.096 0.098 0.460 0.711 0.357 24. Jams, marmalades and honey 0.848 0.940 0.960 0.940 0.950 25. Confec., chocolate and ice cream 1.142 1.149 1.203 1.449 1.227 26. Food products n.e.c. 0.096 0.209 0.658 0.758 0.565 27. Coffee, tea and cocoa 0.442 0.710 0.832 0.835 0.770 28. Min. wtrs, sft drnks, f. & veg. juice 0.922 0.953 0.988 0.978 0.980 All Food 0.563 0.653 0.744 0.821 0.715 Non-food 1.050 1.086 1.147 1.167 1.130

76

Table A5.1 Previous Income Elasticities of Bread and Rice

Country Income elasticity Year Source Assigned income group

(Income quartile) (1) (2) (3) (4) (5)

A. Bread

France 1.040 1994 Balcombe et al. (1999) First Japan 0.474 1997 Chern et al. (2003) First United States 0.578 1988 Huang and Lin (2000) First Romania 0.465 1995 Meyerhoefer et al. (2005) Third Australia 0.449 2002 Ulubasoglu et al. (2011) First

B. Rice

Vietnam 0.761 2004 Canh (2015) Third Brazil 0.838 2003 Coelho et al. (2010) Third Argentina 0.110 2008 FAPRI (2008) n/a Australia 0.430 2008 FAPRI (2008) First Brazil -0.050 2008 FAPRI (2008) Second Canada 0.470 2008 FAPRI (2008) First China -0.070 2008 FAPRI (2008) Third Egypt 0.300 2008 FAPRI (2008) n/a Hong Kong -0.190 2008 FAPRI (2008) n/a India -0.040 2008 FAPRI (2008) Fourth Indonesia -0.120 2008 FAPRI (2008) Third Iran 0.200 2008 FAPRI (2008) n/a Iraq 0.140 2008 FAPRI (2008) n/a Japan -0.260 2008 FAPRI (2008) First Malaysia 0.090 2008 FAPRI (2008) Second Mexico 0.460 2008 FAPRI (2008) Second Nigeria 0.250 2008 FAPRI (2008) n/a Pakistan 0.100 2008 FAPRI (2008) Third Philippines 0.150 2008 FAPRI (2008) Third Saudi Arabia 0.100 2008 FAPRI (2008) Second South Africa 0.470 2008 FAPRI (2008) Second Taiwan -0.030 2008 FAPRI (2008) n/a Turkey 0.400 2008 FAPRI (2008) Second United States 0.340 2008 FAPRI (2008) First Uruguay 0.500 2008 FAPRI (2008) Second Vietnam -0.230 2008 FAPRI (2008) Third China 0.133 1984 Ito et al. (1989) n/a India 0.125 1984 Ito et al. (1989) Fourth Indonesia 0.108 1984 Ito et al. (1989) Fourth Japan -0.708 1984 Ito et al. (1989) First Malaysia -0.671 1984 Ito et al. (1989) Third Nepal -0.346 1984 Ito et al. (1989) Fourth Philippines 0.121 1984 Ito et al. (1989) Fourth Singapore -0.599 1984 Ito et al. (1989) Second Sri Lanka 0.032 1984 Ito et al. (1989) Fourth Taiwan -0.594 1984 Ito et al. (1989) n/a Argentina 0.106 2000 Lema et al. (2007) n/a Bolivia 0.074 2000 Lema et al. (2007) Third Paraguay 0.067 2000 Lema et al. (2007) Third Indonesia 0.450 1978 Tyers and Rachman (1982) Fourth Australia 1.196 2002 Ulubasoglu et al. (2011) First China 0.370 1990 Wu et al. (1995) Fourth Notes: 1.On the basis of correspondence with Karen Kovarik from FAPRI, the FAPRI estimates are taken to refer to the year 2008. 2. The term “n/a” in column 5 indicates insufficient data from the WDI to assign the country to an income group.

77

Table A5.2 Summary of Previous Income Elasticities of Rice and Bread

Measure Income quartile

Not cross classified by income First Second Third Fourth All

(1) (2) (3) (4) (5) (6) (7)

A. Rice

Mean 0.245 0.171 0.090 0.103 0.142 0.119

Median 0.385 0.250 0.071 0.115 0.104 0.109

SD 0.600 0.351 0.420 0.229 0.412 0.382

Min -0.708 -0.599 -0.671 -0.346 -0.708 -0.708

Max 1.196 0.500 0.838 0.450 1.196 1.196

No. of estimates 6 8 10 8 32 42

B. Bread

Mean 0.635 - 0.465 - 0.601 0.601

Median 0.526 - 0.465 - 0.474 0.474

SD 0.239 - 0.000 - 0.224 0.224

Min 0.449 - 0.465 - 0.449 0.449

Max 1.040 - 0.465 - 1.040 1.040

No. of estimates 4 0 1 0 5 5

78

Table A6.1 Comparison of Income Elasticities, 7 Food Groups

Commodity I. Current study II. Muhammad et al. (2011) Income quartile

Income group

First Second Third Fourth All High Middle Low (1) (2) (3) (4) (5) (6) (7) (8) (9)

A. Income elasticities 1. Cereals 0.560 0.486 0.428 0.683 0.459 0.019 0.253 0.514 2. Meat 0.724 0.855 0.916 0.895 0.890 0.490 0.649 0.771 3. Fish 0.278 0.332 0.653 0.820 0.640 0.379 0.521 0.654 4. Dairy 0.665 0.854 0.899 0.891 0.880 0.506 0.671 0.798 5. Oils & Fats 0.085 0.209 0.659 0.758 0.528 0.097 0.297 0.531 6. Fruits & Vegetables 0.436 0.548 0.760 0.820 0.696 0.319 0.462 0.615 7. Other Food 0.665 0.749 0.909 1.030 0.870 0.636 0.882 1.42 B. Budget shares (×100) 1. Cereals 1.70 3.51 7.70 13.31 6.56 2.82 4.21 12.28 2. Meat 2.27 5.27 6.53 6.06 5.03 3.10 4.61 7.37 3. Fish 0.84 0.86 2.13 3.45 1.82 0.85 1.44 2.94 4. Dairy 1.33 2.98 3.66 3.05 2.75 1.82 2.62 4.03 5. Oils & Fats 0.30 0.87 1.96 2.57 1.43 0.44 0.84 2.36 6. Fruits & Vegetables 1.98 4.14 7.21 9.61 5.74 2.38 4.25 9.56 7. Other Food 2.37 3.73 5.50 6.42 4.51 6.70 8.18 6.07 C. Weighted income elasticities (×100) 1. Cereals 0.953 1.706 3.295 9.100 3.009 0.054 1.066 6.311 2. Meat 1.641 4.508 5.986 5.423 4.477 1.519 2.989 5.684 3. Fish 0.233 0.287 1.392 2.826 1.165 0.321 0.752 1.921 4. Dairy 0.882 2.544 3.291 2.721 2.424 0.920 1.756 3.214 5. Oils & Fats 0.026 0.183 1.289 1.948 0.753 0.043 0.251 1.254 6. Fruits & Vegetables 0.866 2.271 5.485 7.878 3.995 0.760 1.965 5.880 7. Other Food 1.577 2.795 5.000 6.616 3.922 4.259 7.211 8.624 Total 6.18 14.29 25.74 36.51 19.74 7.88 15.99 32.89 Notes: 1. The current study (columns 2-6): The 28 food items are aggregated into seven groups as follows: Cereals comprise items 1-5; meat, items 6-9; fish, 10-11; dairy, 12-15; oils and fats, 16 and 25; fruits and vegetables, 17-21; and other food, 22-24 and 26-28. The income elasticities in panel A are conditional-budget-share weighted averages of the elasticities in Table A4.4. The budget shares of panel B are derived from Table 2.2. 2. Muhammad et al. (2011) (columns 7-9): The income elasticities of panel A are from their Appendix Table 5. For details of the budget shares of panel B, see Table A6.2. 3. The weighted income elasticities in panel C are the income elasticities (panel A) multiplied by the budget shares (panel B).

79

Table A6.2 Intermediate Steps, Muhammad et al. (2011)

Income group Item High Middle Low (1) (2) (3) (4)

I. Unconditional marginal shares of total food (Muhammad et al., App. Table 7) 0.107 0.209 0.392 II. Conditional marginal shares of food groups (Muhammad et al., App. Table 8) Cereals 0.005 0.051 0.161 Meats 0.142 0.143 0.145 Fish 0.030 0.036 0.049 Dairy 0.086 0.084 0.082 Oils and Fats 0.004 0.012 0.032 Fruits and Vegetables 0.071 0.094 0.150 Food other 0.398 0.345 0.220 Beverages & Tobacco 0.265 0.234 0.162 III. Unconditional marginal shares of food groups (item I above × item II) Cereals [0.107 × 0.005; 0.209 × 0.051; 0.392 × 0.161] 0.001 0.011 0.063 Meats [0.107 × 0.142; 0.209 × 0.143; 0.392 × 0.145] 0.015 0.030 0.057 Fish 0.003 0.008 0.019 Dairy 0.009 0.018 0.032 Oils and Fats 0.000 0.003 0.013 Fruits and Vegetables 0.008 0.020 0.059 Food other 0.043 0.072 0.086 Beverages & Tobacco 0.028 0.049 0.064 IV. Unconditional income elasticities by food groups (Muhammad et al., App Table 5) Cereals 0.019 0.253 0.514 Meats 0.490 0.649 0.771 Fish 0.379 0.521 0.654 Dairy 0.506 0.671 0.798 Oils and Fats 0.097 0.297 0.531 Fruits and Vegetables 0.319 0.462 0.615 Food other 0.636 0.882 1.42 Beverages & Tobacco 0.613 0.839 1.325 V. Implied unconditional budget shares (item III ÷ item IV) Cereals 0.028 0.042 0.123 Meats 0.031 0.046 0.074 Fish 0.008 0.014 0.029 Dairy 0.018 0.026 0.040 Oils and Fats 0.004 0.008 0.024 Fruits and Vegetables 0.024 0.043 0.096 Food other 0.067 0.082 0.061 Beverages & Tobacco 0.046 0.058 0.048 VI. Weighted income elasticities (item IV × item V) Cereals 0.001 0.011 0.063 Meats 0.015 0.030 0.057 Fish 0.003 0.008 0.019 Dairy 0.009 0.018 0.032 Oils and Fats 0.000 0.003 0.013 Fruits and Vegetables 0.008 0.020 0.059 Food other 0.043 0.072 0.086 Note: Items III and VI are conceptually and algebraically identical.

80

Figure A2.1 Two Measures of Food Consumption

Notes: 1. Average food in country c is 28

i 1 icq 28 , where icq is per capita consumption of good item i, measured in terms of

$US, in country c (c = 1,..., 128). The volume index is 28c i 1 ic iclog Q w log q , where icw is the budget share of i

within food in c. 2. The solid line is the regression line. Standard errors in parentheses.

0

2

4

6

0 1 2 3 4 5 6

Log of average food consumption

Volume index log Q

y = 1.11x – 0.74 (0.02) (0.09)

81

Figure A6.1 Scatter Plots of Weighted Income Elasticities

A. High income and first quartile

B. Middle income and second quartile

C. Low income and third/fourth quartile

Note: Weighted income elasticities are from panel C of Table A6.1. As the low income group in Muhammad et al. (2011) encompasses 53% of their sample, the average of two lowest quartiles in the current study are used as a basis for comparison given in panel C of this figure.

0

1

2

3

4

5

0 1 2 3 4 5

0

2

4

6

8

10

0 2 4 6 8 10

0

2

4

6

8

10

0 2 4 6 8 10

Current study

Muhammad et al. (2011)

Current study

Muhammad et al. (2011)

Current study

Muhammad et al. (2011)

45°

45°

45°

Other Food

Other Food

Other Food

Cereals

Cereals

Cereals

Correlation = 0.746

Correlation = 0.513

Correlation = 0.815