1 Time trends in food consumption economies of scale in Sri Lanka: An equivalence scales based analysis Maneka Jayasinghe*, Christine Smith, Andreas Chai, Shyama Ratnasiri Abstract When making welfare comparisons across different households, the possibilities for household consumption scale economies must be taken into consideration. The ability of household members to enjoy scale economies may not only depend on the household size, but also on the household spending capacity. While there exists the difference in food consumption patterns among the rich and the poor at a given point of time, the food consumption patterns may also drastically change, with changing income levels, advancing technologies and increasing mobility, over time. This study attempts (1) to discover the intertemporal trends in food consumption scale economies in Sri Lanka during the period of 1990/91 to 2009/10, (2) to examine what factors have contributed to such time trends in food economies of scale, and (3) to examine the extent to which the historical poverty rate patterns, based on per-capita income (PCI), vary significantly after food consumption scale economies are allowed for. The Engel equivalence scale approach is used for the analysis. The results reveal that equivalence scales have decreased over time, suggesting that households enjoy greater economies of food consumption in the present than in the past, except for among urban residents. We find that the changes in the household food consumption patterns together with electrification have made substantial contributions towards enhancing greater food scale economies in recent times. Our finding that the household enjoy greater food economies at present than in the past implies that actual poverty rates have declined even more over the last two decades than conventional poverty measurements suggest. Keywords: Equivalence scales, food consumption economies of scale, intertemporal trends Article Classification: D12 I32 D63 D19 * Corresponding Author
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1
Time trends in food consumption economies of scale in Sri Lanka: An equivalence scales
based analysis
Maneka Jayasinghe*, Christine Smith, Andreas Chai, Shyama Ratnasiri
Abstract
When making welfare comparisons across different households, the possibilities for
household consumption scale economies must be taken into consideration. The ability of
household members to enjoy scale economies may not only depend on the household size, but
also on the household spending capacity. While there exists the difference in food
consumption patterns among the rich and the poor at a given point of time, the food
consumption patterns may also drastically change, with changing income levels, advancing
technologies and increasing mobility, over time. This study attempts (1) to discover the
intertemporal trends in food consumption scale economies in Sri Lanka during the period of
1990/91 to 2009/10, (2) to examine what factors have contributed to such time trends in food
economies of scale, and (3) to examine the extent to which the historical poverty rate patterns,
based on per-capita income (PCI), vary significantly after food consumption scale economies
are allowed for. The Engel equivalence scale approach is used for the analysis. The results
reveal that equivalence scales have decreased over time, suggesting that households enjoy
greater economies of food consumption in the present than in the past, except for among
urban residents. We find that the changes in the household food consumption patterns
together with electrification have made substantial contributions towards enhancing greater
food scale economies in recent times. Our finding that the household enjoy greater food
economies at present than in the past implies that actual poverty rates have declined even
more over the last two decades than conventional poverty measurements suggest.
Keywords:
Equivalence scales, food consumption economies of scale, intertemporal trends
Article Classification:
D12 I32 D63 D19
* Corresponding Author
2
1. Introduction
When making welfare comparisons across different households, the possibilities for
household consumption scale economies must be taken into consideration. Household size
has been well proven and commonly acknowledged as the basis of consumption scale
economies (Lanjouw and Ravallion, 1995; Meenakshi and Ray, 2002; Nelson, 1993; Ray,
2000). These economies of scale may be generated through the sharing of household goods,
bulk purchases, and increasing returns to scale in home production (Nelson, 1988). They
result in the cost per person to maintain the same material wellbeing to decline as household
size increases. Accordingly, doubling of household size does not require a twofold increase in
income to achieve the same standard of living. In the literature, household equivalence scales
have commonly been used to capture these consumption scale economies (Balli and Tiezzi,
2013). As equivalence scales measure the cost of an additional household member, taking the
consumption scale economies into consideration, lower equivalence scales reflect higher
economies of scale.
Nevertheless, the ability of household members to enjoy economies of scale may not only
depend on the household size, but also on their spending capacity. While some studies claim
that equivalence scales, and hence economies of scale, are independent of income (Pendakur,
1999), other studies suggest that they are indeed dependent on household income (Balli and
Tiezzi, 2013; Donaldson and Pendakur, 2003; Koulovatianosa et al., 2005; Logan, 2011).
However, there is no consensus, so far, on whether economies of scale are positively or
negatively correlated with income. For example, some studies show that consumption scale
economies are increasing with income (Balli and Tiezzi, 2013; Donaldson and Pendakur,
2003; Koulovatianosa et al., 2005), while other studies reveal that they are decreasing with
income (Beatty, 2010; Burch and Matthews, 1987; Griffith et al., 2009; Leibtag and
Kaufman, 2003; Logan, 2011) due to various reasons attributed to household consumption
patterns based on their spending capacity. An important implication of income dependent
equivalence scales is that it suggests that rich and poor households face different costs for an
additional household member as they enjoy different levels of economies of scale.
While there exists differences in food consumption patterns between the rich and the poor
at a given point of time, food consumption patterns may also drastically change, with
changing income levels, over time. Rapidly growing economies together with steadily rising
real per-capita income among the rich and the poor as well as increasing time scarcity can
give rise to dramatic changes in household food consumption patterns over time (Du et al.,
2004; Kearney, 2010; Popkin, 1999). Additionally, increased use of efficient energy sources
such as electricity, increased use of food storage facilities such as refrigerators, advancements
in food preparation and processing technologies, and increased mobility and accessibility
3
during the last several decades may have contributed to households enjoying more economies
of scale and thereby stretching their food dollars (Pena and Ruiz-Castillo, 1998; Reardon et
al., 2003; Tuttle, 2011). Logan (2011), for example, finds that in United States household
income plays a distinctive role in determining food scale economies at a given point of time
and over a period of time. More specifically, while low-income people enjoy more food
economies of scale in a particular period of time, there appeared to be fewer food economies
scale in the past than in the present, irrespective of lower per-capita incomes in the past. This
observation suggests that there may be other factors that override the effects of household
income on economies of scale over a period of time.
Sri Lanka has undergone many socio-economic changes in the past two decades, resulting
in significant changes in household consumption patterns. The objective of this study is three-
fold: (1) to discover the intertemporal trends in food consumption scale economies in Sri
Lanka during the period of 1990/91 to 2009/10, (2) to examine what factors have contributed
to such time trends in food economies of scale, and (3) to examine the extent to which the
historical poverty rates patterns based on per-capita income (PCI), vary significantly after
food consumption scale economies are allowed for. We argue that food economies of scale
have been increasing over time. Firstly, we test this hypothesis at the national level, using
Household Income and Expenditure Survey (HIES) data for 1990/91, 2001/02, and 2009/101.
over time. Secondly, we suggest that changes in food consumption patterns together with
technological advancements in domestic activities may have contributed to such increased
food scale economies. In this study, we use access to electrification as a proxy for
technological advancements in domestic activities. To test this hypothesis, we estimate the
differences in food scale economies in households with and without access to electricity. In
Sri Lanka, we observe that there have been significant improvements in the number of
households who have access to electricity during the last decade. Finally, we estimate poverty
rates using income per equivalent adult, i.e., using income adjusted for food consumption
scale economies. The conventional poverty rates that are based on per-capita income have
declined significantly over time in Sri Lanka (Department of Census and Statistics, 2011a).
Nevertheless, we expect the intertemporal poverty rates to decline, even further, when food
consumption economies of scale are allowed for, as households enjoy greater food scale
economies at present than in the past.
The rest of the paper is organised as follows. Section two presents the existing literature on
1 We verify the robustness of the observed national level intertemporal trends by checking whether similar patterns
are also found at the sectoral level – that is for the urban, estate and rural sectors over time. All results, relating to
sectoral levels, are given in the Appendix. Urban sector refers to the areas governed by either Municipal Council
or Urban Council. Estate sector refers to plantation areas, which are more than 20 acres of land and having not less
than 10 residential laborers. Rural sector refers to residential areas, which do not belong to the urban or estate
sectors (Department of Census and Statistics, 2011a).
4
equivalence scale, economies of scale, and the time trends in food consumption scale
economies. Section three describes the methodology adopted while section four describes the
data used in this study. Section five discusses our empirical results. Section six makes some
concluding remarks.
2. Literature Review
Different approaches can be employed to estimate equivalence scales (Deaton and
Muellbauer, 1986; Kakwani and Son, 2005; Muellbauer, 1977; Pollak and Wales, 1979). The
Engel (1895) method, which is based on the idea that two households with identical
expenditure shares on food are equally well off, represents a widely used such approach. This
is particularly due to its minimal data requirements and the simplicity of the associated
estimation procedure 2. Additionally, this method has received endorsement by Deaton (1981)
as the most appropriate approach to estimate equivalence scales for developing countries
using single cross sectional data. Nevertheless, the Engel method has also been criticised by
various scholars, due to a lack of plausibility of its assumptions and the weaknesses of its
theoretical base (Deaton and Muellbauer, 1980, 1986; Nicholson, 1976). Nicholson (1976) for
example, argues that although foodshares provide a numerical approach to compare standard
of living of households ‘of the same composition’, the indicator loses its intuitive appeal
when comparing households of different compositions. .Deaton and Muellbauer (1986) for
example assert that under Engel method, restoration of the foodshare of a household in the
presence of an additional child implies ‘overcompensation’. Additionally, the lack of an
answer to Pollak and Wales’ (1979) issue of under-identification has been identified as a
problem associated with the Engel method of measuring economies of scale. Another major
objection to the Engel method relates to its implicit assumption of identical levels of
economies of scale for every commodity.
In the literature on equivalence scales, there exists a notion that equivalence scales can be
estimated with the assumption that the income needed by one household relative to another
household of different size is independent of the base income at which the expenditure
comparisons are made. If for example, the income needs of a household in relation to another
satisfy base independence, then the equivalence scales do not vary across household income
levels. The theoretical plausibility of deriving equivalence scales under these assumptions has
been independently explored by Lewbel (1989) and by Blackorby and Donaldson (1993).
Blundell and Lewbel (1991), Pendakur (1999) and Gozalo (1997) each find that Engel
2 See Watts (1967), Seneca and Taussig (1971) for the United States, Deaton (1981) for Sri Lanka, Deaton and
Muellbauer (1986) for Sri Lanka and Indonesia, Binh and Whiteford (1990) for Australia, Tsakloglou (1991) for
Greece, Bosch-Domènech (1991) for Spain, Phipps and Garner (1994) for Canada and Valenzuela (1996) for
Australia, Thailand and Philippines inter alia for example.
5
equivalence scales are not base independent, and hence, that these scales vary with total
expenditure. Additionally, several studies document clear evidence of nonlinearities in Engel
curves (Betti, 2000; Lewbel, 2008; Moneta and Chai, 2014). An important implication of
non-linearity in Engel curves is that the cost of an additional household member (measured
using equivalence scales) for richer households can be different from that of the poorer
(Blackorby and Donaldson, 1991; Donaldson and Pendakur, 2003; Lewbel, 1989; Murthi,
1994).
Accordingly, several studies have attempted to investigate the existence of base-dependent
equivalence scales. However, there is no unanimity about whether the equivalence scales
positively or negatively correlated with income. For example, Logan (2011) shows that
equivalence scales for some commodities, including food, increase with income in the United
States. This implies that economies of scale decrease as household income increases. Burch
and Matthews (1987) and Timmer (1997), based on a descriptive analysis on developed
countries, support the argument that poorer households enjoy greater economies of scale.
Beatty (2010) and Griffith et al. (2009) using United Kingdom data, Leibtag and Kaufman
(2003) and Wiig and Smith (2009) using data on the United States and Dh́aese and
Huylenbroeck (2005) using data on South Africa further confirm that poorer households
enjoy greater food consumption scale economies than the rich. In contrast, Balli and Tiezzi
(2013) using data on Italy, Donaldson and Pendakur (2003) using Canadian data,
Koulovatianosa et al. (2005) using data on Germany and France, and Majumder and
Chakrabarty (2008) using Indian data observe decreasing with income equivalence scales.
This observation suggests that the scale economies are higher among the richer households.
One likely reason that explains these differing results is that there are many ways in which
household income is thought to affect economies of scale and household food consumption
behaviours. These include sharing of public goods (Burch and Matthews, 1987; Deaton and
Paxson, 1998; Kakwani and Son, 2005; Logan, 2011; Nelson, 1988), sharing of private goods
such as food (up to a certain extent) (Beatty, 2010; Byrne et al., 1996; Deaton and Paxson,
1998; Griffith et al., 2009; Lazear and Michael, 1980; Ma et al., 2006; Nelson, 1988; Vernon,
2005), bulk purchases (Beatty, 2010; Griffith et al., 2009; Leibtag and Kaufman, 2003; Wiig
and Smith, 2009), increasing returns to household production (Byrne and Capps, 1996;
McCracken and Brandt, 1987; Vernon, 2005), and other likely behavioural changes that are
associated with increased purchasing power, such as alteration of consumption basket towards
more of luxury goods and healthy eating (Caraher et al., 1998; Timmer, 1997).
The rapidly expanding economies and rising per-capita income levels have been
accompanied by significant changes in the household dietary patterns across the globe (Du et
al., 2004; Kearney, 2010). In Sri Lanka, for example, the nominal average household income
per month has increased rapidly from Rs. 3,549 in 1990/91 to Rs. 36,451 in 2009/10
6
(Department of Census and Statistics, 2011a). Consequently, the household food consumption
patterns also have undergone significant changes during the period (Wijesekere, 2015).
Interestingly, Logan (2011) finds that there were fewer food consumption scale economies in
the past than in the present. There are several studies, which discuss the likely reasons that
may explain the increasing trends in food consumption economies of scale over time. For
example, studies have shown that food bulk purchases have been on the rise in recent years
due to increased use of storage facilities of perishable food items (such as refrigerators and
freezers) together with electrification and increased access to transport (own automobiles and
public transport services) (Pena and Ruiz-Castillo, 1998; Reardon et al., 2003; Tuttle, 2011).
Furthermore, the considerable reduction in food preparation, preservation and processing time
and costs, with technological advancements, may contribute to increasing returns to scale in
the home production of food (Popkin, 1999). This would in turn be expected to reduce the
marginal cost of food of an additional household member, reflecting greater economies of
scale.
The time trends in equivalence scales and economies of scale in food consumption may
exert significant implications when measuring poverty and inequality. For example, higher
consumption economies of scale in the recent years than in the past, as suggested by Logan
(2011), imply not only that the conventional poverty measures overstate the prevailing
poverty levels, but also that they do not capture adequately the actual decline in poverty rates
in a country over time. This is because the traditional poverty measures do not acknowledge
that the marginal cost of an additional household member is lower nowadays than it was in
the past. On the other hand, if economies of scale are lower in the present times than they
were in the past, the poverty rates in the present times are underestimated and the reduction in
actual poverty rates may have been overstated under traditional poverty measurements. In this
study, firstly, we examine the time trends in economies of scale in food consumption.
Secondly, we examine changes in poverty rates when food consumption scale economies are
taken into account.
3. Methodology
The specification of the Engel curve for food, with two demographic characteristics (adults
and children), used in this study is as follows
𝑤𝑓 = 𝛽0 + 𝛽1ln𝑥
𝑛+ 𝛽2(ln
𝑥
𝑛)2 + 𝛾1𝑛𝑎 + 𝛾2𝑛𝑐 + 𝛾3𝑛𝑎𝑛𝑐 (3.1)
where 𝑤𝑓 refers to aggregate food budget share, 𝑥 to household income (proxied by
expenditure), 𝑛 to household size (including children), 𝑛𝑎 to number of adults and 𝑛𝑐 to
children in the household. The variable ln𝑥
𝑛 is the logarithm of PCI and (ln
𝑥
𝑛)
2is the square
7
of the logarithm of PCI. The variable 𝑛𝑎𝑛𝑐 is an interaction term of 𝑛𝑎 and 𝑛𝑐 , which
estimates the joint effect of adults and children on foodshare. Accordingly, 𝛽0, 𝛽1 , 𝛾1, 𝛾2and
𝛾3 are parameters to be estimated. Following Deaton and Muellbauer (1986) we use a simple
logarithmic transformation of PCI for two reasons. Firstly, the problem of heteroskedasticity
commonly encountered with cross-sectional data can be reduced via such a transformation.
Secondly, this form of transformation reduces non-linearity in the data. In this study, we use
PCE as a proxy for PCI due to the enhanced reliability of expenditure data.3
We test base independence using the Pendakur (1999) approach to examine whether the
household preferences (as manifested in foodshare equations) are consistent with the
existence of base independent equivalence scales.
If
𝑤𝑓1 = 𝛽01 + 𝛽11ln𝑥
𝑛+ 𝛽21(ln
𝑥
𝑛)2 + 𝛾11𝑛𝑎 + 𝛾21𝑛𝑐 + 𝛾31𝑛𝑎𝑛𝑐 (3.2)
and
𝑤𝑓2 = 𝛽02 + 𝛽12ln𝑥
𝑛+ 𝛽22(ln
𝑥
𝑛)2 + 𝛾12𝑛𝑎 + 𝛾22𝑛𝑐 + 𝛾32𝑛𝑎𝑛𝑐 (3.3)
where 𝑤𝑓1 and 𝑤𝑓2 are the quadratic food Engel curve for households with one-adult and
two-adults respectively. We then obtain the differences in coefficient estimates of second
order terms in the two log-quadratic regressions ((ln𝑥
𝑛)2) i.e., 𝛽22 − 𝛽21. The standard errors
and p-values of the difference (𝛽22 − 𝛽21) are calculated using the bootstrapping approach
with 1000 replications. If the second order term differences are significantly different from
each other, the hypothesis of base independence has to be rejected. This necessitates us to
estimate income dependent equivalence scales.
Having estimated the Engel curve for food, the estimated coefficients of the quadratic
Engel curves are used to construct income dependent equivalence scales. We estimate
equivalence scales for year 1990, 2001, and for 2009 to observe the time trends in
equivalence scales and thereby economies of scale in food consumption. Following Deaton
(1981) and Lelli (2005) an analytical solution can be derived using a basic mathematical
approach to solve quadratic equations as follows. We take a two-adult and no-children
household, (2,0) as the reference household. If
𝑤ℎ = 𝛽0 + 𝛽1ln𝑥ℎ
𝑛ℎ + 𝛽2(ln𝑥ℎ
𝑛ℎ)2+𝛾1𝑛𝑎 + 𝛾2𝑛𝑐+𝛾3𝑛𝑎𝑛𝑐 (3.4)
and
𝑤𝑟 = 𝛽0 + 𝛽1 ln (𝑥𝑟
𝑛𝑟) + 𝛽2(ln𝑥𝑟
𝑛𝑟)2 + 2𝛾1 (3.5)
3 As noted by Summers (1959), the Engel curve, when modelled on household expenditure, may suffer from
endogeneity. To allow for possible effects of endogeneity, following Banks et al. (1997) we used log per-capita
income and its square as instrumental variables for log of per-capita expenditure and its square during the actual
estimation.
8
then at any chosen level of income 𝑥𝑟, equation (3.5) generates the budget share of the
reference household 𝑤𝑟. The application of the Engel assumption, 𝑤ℎ= 𝑤𝑟, to equations (3.4)
and (3.5) creates a quadratic equation. This equation gives two roots for 𝑥ℎ for any given 𝑛ℎ,
𝑛𝑎ℎ and 𝑛𝑐
ℎ. From the two possible solutions for 𝑥ℎ the larger value of 𝑥ℎ corresponds to the
relevant part (or downward sloping side) of the Engel curve. An equivalence scale is the ratio
between 𝑥ℎ and 𝑥𝑟, such that dividing 𝑥ℎ by the initially selected 𝑥𝑟 yields the equivalence
scale.
In our study, we estimate equivalence scales for food expenditure at three different income
levels; sample mean, and bottom and top income quartiles, for each year. First, we estimate
the Engel curves and equivalence scales for the entire dataset of each year; which yields
national level estimates. Secondly, we disaggregate the data sets of three years into three
sectors, i.e. rural urban and estate sectors. This enables us to verify the consistency of our
hypothesis and test the robustness of the national level results at the sectoral level during the
period of last 20 years. Additionally, we estimate equivalence scales for households with and
without access to electricity for 2009/10 data. We also perform bootstrapping with 1000
replicates to estimate standard errors associated with our equivalence scales. In this study, we
consider that all of the adults in the households have identical tastes, irrespective of their
gender and age.
Finally, we estimate poverty headcount ratio using conventional method and equivalence
scale based method, for all three survey years, to examine the effects of food consumption
scale economies on poverty measurements. Poverty head count ratio is the percentage of
households fall below the poverty line. Under conventional method, we obtain the percentage
of households whose PCI (proxied by household total expenditure) fall below the official
poverty line. The inflation adjusted official poverty line in Sri Lanka for 1990/91, 2001/02,
and 2009/10 is Rs.3000, Rs.3165 and Rs.3028 real total expenditure per person, respectively
(Department of Census and Statistics, 2004, 2011b). Under the equivalence scale based
method, we estimate the percentage of households whose income per equivalent adult (IPEA)
falls below the official poverty line. The IPEA is obtained by dividing household income
(proxied by household total expenditure) by equivalence scales, estimated at the mean income
of each year, taking the one-adult household as the reference household. The next section
presents a brief explanation on the data used in this study.
4. Data
The analysis in this study is based on the 1990/91, 2001.02 and 2009/10 Household Income
and Expenditure Surveys (HIES) conducted by the Department of Census and Statistics
9
(DCS) in Sri Lanka. Table 1 given below summarises the profile of each survey sample.
Table 1: Profile of the three survey samples
Survey
Survey Period
Number of
Households
District
surveyed
Full
sample
Sample
use in the
analysis
HIES 1990/91 June 1990-May 1991 18,462 18,187 17
HIES 2001/02 Jan 2002-Dec 2002 16,924 16,654 17
HIES 2009/10 July 2009-June 2010 19,958 17,021 22
Source: Author’s compilation based on Department of Census and Statistics (1991, 2002, and
2011)
The 1990/91 HIES, which conducted during June 1990-May 1991, consists of 18,462
households. Nevertheless, the removal of outliers, using trimming under three standard
deviations from the mean as advocated by Miller (1991), and missing values reduced the
sample used in this study to 18,187. Similarly, the 2001/02 HIES sample, which collected
during January to December 2002 is reduced to 16,654 households. Both samples do not
cover the Northern province (which covers Jaffna, Mannar, Vavuniya, Mullativu, and
Killinochchi districts) and Eastern province (which covers Batticaloa, Ampara, and
Traincomalee) due to the prevailing civil war condition in the area during that period. This
excludes about 14 per cent of the total population in the country from the sample. The
2009/10 HIES full sample comprises 19,958 households and excludes only three districts
(Mannar, Killinochchi and Vavuniya) due to resettlement activities took place after the civil
war. After dropping outliers and missing values, the sample size reduced to 19,804, which we
have used for the test of base independence. However, the sample used in the intertemporal
comparison is further reduced to 17,021 as we dropped Jaffna, Vavuniya, Batticaloa, Ampara,
and Traincomalee districts from the 2009/10 sample to match the geographic coverage
associated with the 1990/91 and 2001/02 survey samples.
All three HIES samples consist of data on both food and beverage and non-food
expenditures of households. Expenditure on food and beverages (hereafter referred to as
expenditure on food) covers 18 sub-categories4. Expenditure on non-food items covers 10
additional sub-categories5. The total expenditure in this study consists of both food and non-
condiments, other foods, milk & milk products, fats & oils, sugar, fruits, confectionery and non-alcoholic
beverages (Department of Census and Statistics, 2011a). 5 These categories comprise housing & household services, fuel & lighting, personal care, health care, transport,
communication, recreation, education, clothing & footwear and other ad hoc expenditure. Certain non-food
expenditure items include some imputed expenditure elements (e.g. the rental value of owner-occupied housing
and the value of free housing, particularly in the estate sector) (Department of Census and Statistics, 2011a).
10
food expenditure, excluding the expenditure on purchase of motor vehicles6. Expenditures on
some non-food items are measured on an annual or bi-annual basis to avoid seasonal effects
on spending. Hence, in this analysis all of the expenditure figures are converted to monthly
data to match other expenditure categories as necessary. Furthermore, the expenditure
subcategories, under both food and non-food items, that are not available for all three survey
years were also removed during the intertemporal analysis (refer Table 1 in appendix for
detailed explanation on removed expenditure subcategories). Additionally, the Engel curves
and equivalence scales are estimated using the expenditure values adjusted for inflation using
the consumer price index (CPI) (2005=100) and therefore, the effect of prices on equivalence
scales is eliminated (Central Bank of Sri Lanka, 1991, 2002, 2010).
Table 2 provides mean total expenditure, expenditure on food, and non-food items by
sector. During each survey period, the lowest foodshare is recorded in the urban sector (57%,
41%, and 39% in 1990/91, 2001/02 and 2009/10 respectively) followed by the rural sector
(61%, 50%, and 44% in 1990/91, 2001/02 and 2009/10 respectively). Since 1990/91, there
has been a significant decline in the food expenditure share in all three sectors, while the
largest decline is seen during the period of 1990/91 to 2001/02. In particular, the national
average of food expenditure share has declined from 60 per cent in 1990/91 to 48 per cent in
2001/02. By 2009/10, the national average food expenditure share has further dropped to 43
per cent. On the other hand, it is observed that the non-food expenditure share has increased
considerably over time since 1990/91. For example, the national level average of non-food
expenditure share has increased from 33 per cent (in 1990/91) to 55 per cent (in 2009/10).
Table 2 shows that the lowest non-food expenditure share is reported in the estate sector
(23%, 36%, and 43% in 1990/91, 2001/02 and 2009/10 respectively), followed by the rural
sector (30%, 48%, and 54% in 1990/91, 2001/02 and 2009/10 respectively).
The household size and the composition of each given household represent important
considerations in this study. We mainly focus on households with a single-adult to four-
adults. Table 3 presents the number of households in each household type at the national level
and the sector level in each survey period. In all survey periods, the two-adult household type
has the highest number of observations followed by the three-adult household.
The richness in the three HIES datasets, with detailed information on household food
expenditures, provides a splendid opportunity to examine time trends in food consumption
economies of scale. This study represents the first attempt at analysing these matters using
data from a developing country like Sri Lanka. The next section presents the results of the test
6 We exclude expenditure on motor vehicle from this analysis as it is lifetime expenditure for many households
and inclusion of it in the total expenditure increases total expenditure of those households who own motor vehicles
significantly.
11
of base independence and the results of empirical analysis where we investigate the time
trends in food consumption scale economies in Sri Lanka from 1990/91 to 2009/10.
12
Table 2: Average monthly household expenditure by sector and survey year
Source: Author’s compilation based on Department of Census and Statistics (1991, 2002, and 2011)
1990/91 2001/02 2009/10
National Urban Rural Estate National Urban Rural Estate National Urban Rural Estate
Firstly, in order to examine the validity of the hypothesis of base independence in the
context of Sri Lanka, we undertake Pendakur’s (1990) test of base independence using
2009/10 data. Table 3 shows that, at the national level, the second order terms in the
household type specific log-quadratic equations are significantly different from each other in
ten cases either at the 95% significance level or at the 90% significance level7. This suggests
that the hypothesis of base independence is rejected for these cases.
The rejection of the base independence for one of our datasets (2009/10), suggests that the
use of base-independent Engel equivalence scales is not appropriate in the case of Sri Lanka.
Therefore, we estimate income dependent equivalence scales for 1990/91, 2001/02 and
2009/10 to examine the time trends in food consumption scale economies. The next section
presents the results of the Engel curve estimates and equivalence scales for the three years.
Table 3: Test of base independence, single equations (National Level)- 2009/10
Source: Author’s calculation based on Department of Census and Statistics (2011)
Notes: Bootstrapped Standard errors are given in parenthesis
* and ** indicates the 2nd order term difference coefficients that are statistically
significantly different from each other at 95% and 90% level of significance
respectively
For the interest of brevity, we only present the difference of the square of PCI terms in
this table.
Table 4 presents the parameter estimates of the Engel curve for food at the national for
survey year 1990/91, 2001/02, and 2009/108. These results are derived from models that have
been corrected for heteroskedasticity. The R-squared values fall between 30 and 54 per cent
indicate that the estimated Engel curves for food fit reasonably well with our cross sectional
Sri Lankan data.
7 Similar results are found at the sectoral level as well. The results are given in Table 2 in Appendix. 8 The food Engel curves associated with sectoral level are given in Table 3 in Appendix.
Singles vs
2 adults
Singles vs
3adults
Singles vs
4 adults
2nd order term difference -0.030* -0.029* -0.019*
Std Error of the difference (0.007) (0.007) (0.008)
P-value 0.00 0.00 0.02
14
Table 4: Food Engel curve estimations (national level)
Source: Author’s calculation based on Department of Census and Statistics (1991, 2001,
2011)
With respect to family composition, the coefficients relating to the number of adults (𝛾1),
number of children (𝛾2) and the interaction term between the number of adults and the
number of children (𝛾3) are statistically significant at the 5 per cent level in all regression
estimates. The negative sign of the 𝛾1 and 𝛾2 coefficients implies that when the household
size increases by one adult (or child), the expenditure share on food declines. For example, at
the national level in 1990/91, an increase in household size by one adult reduces the
foodshare by 0.011 per cent, other things held constant. This inverse relationship between the
number of adults (𝑛𝑎) and children ( 𝑛𝑐) variables and the foodshare is in accordance with
our expectations This implies that due to food consumption scale economies, an additional
adult or child adds less than double to expenditure on food. The larger coefficient for 𝑛𝑎 than
for 𝑛𝑐 implies that the change in foodshare for an additional child is greater than that of an
additional adult. This observation is not surprising due to the fact that food consumption
needs of adults are greater than those of children. Moreover, we observe that the reduction in
food expenditure share is gradually increasing during the period. For example, while the
reduction in foodshare in 1990/91 is 0.010 per cent, it increases to 0.028 and 0.031 per cent in
2001/02 and 2009/10 respectively, for adults. This implies that when the household size
increases by one adult (or child), the food expenditure share decreases more in recent time.
This suggests that households economise more on food consumption in the recent years than
in the past. Additionally, our results suggest that the joint impact of the interaction term on
food expenditure share is negative. At the national level in Panel A, for example, if we
assume that number of adults is 1 then an increase in number of children by 1 child reduces
the foodshare by 0.008 per cent (-0.010+0.002) ceteris paribus. In the presence of food
Variable 1990/91 2001/02 2009/10
(𝜷𝟎) Constant -0.966
(0.000)
0.603
(0.000)
1.146
(0.000)
(𝜷𝟏) 𝐥𝐧𝒙
𝒏 0.531
(0.000)
0.198
(0.000)
0.075
(0.002)
(𝜷𝟐) (𝐥𝐧𝒙
𝒏)𝟐 -0.040
(0.000)
-0.022
(0.000)
-0.016
(0.000)
(𝜸𝟏) 𝒏𝒂 -0.010
(0.000)
-0.028
(0.000)
-0.031
(0.000)
(𝜸𝟐) 𝒏𝒄 -0.011
(0.000)
-0.037
(0.000)
-0.042
(0.000)
(𝜸𝟑) 𝒏𝒂𝒏𝒄 0.002
(0.000)
0.007
(0.000)
0.007
(0.000)
Number of observations 18,187 16,654 17,021
Root MSE 0.111 0.1091 0.106
R-squared 0.307 0.539 0.516
15
consumption scale economies, the joint negative effect of the interaction term on food
expenditure share is in line with our expectations.
When considering the coefficient estimates of the ln𝑥
𝑛 and (ln
𝑥
𝑛)2 variables, the
coefficients are statistically significant at the 5 per cent level. According to the Engel’s law,
which suggests that the foodshare declines as household income increases, we expected the
𝛽1 and 𝛽2 coefficients, in our regression estimates, to be negative. Nevertheless, 𝛽1
coefficient is positive in all three cases indicating that the foodshare increases with PCI
(proxied by PCE). For example, at the national level in 1990/91, a 10 per cent increase in PCI
increases the foodshare by 53.1 per cent. The expected inverse relationship in 𝛽2 is observed
in all regression estimates. The negative signs of the 𝛽2 coefficients co-incident with positive
𝛽1 coefficients indicate that the foodshare increases at a decreasing rate. Our observations of
the signs of 𝛽1 and 𝛽2 coefficients are similar to those found by Deaton (1981).
The estimated equivalence scales based on the national level Engel curves for food are
reported in Table 5. Panel A of Table 5 reports the actual equivalence scales while Panel B
reports the marginal change in equivalence scales for an additional adult up to 4 adults. The
marginal equivalence scale refers to the change in the cost of remaining at the same welfare
level (measured in terms of food consumption) when household size increases by one adult.
Equivalence scales are estimated under three different income levels, of respective survey
years, proxied by household expenditure as mentioned in Table 5 below. The Rupee value of
each income level is given in the third row. In the household size column, the left hand side
figure indicates the number of adults while the right hand side figure indicates the number of
children. Accordingly, household size (1,0) is read as one-adult and no-children household.
The equivalence scale for the reference household (2,0) is 1.00, as shown in Panel A. In Panel
B, the marginal equivalence scale of 0.47 for 1,0-2,0 household implies that a single-adult
household requires only 47 per cent of the total income of a (2,0) household to be on the same
level of welfare as measured in terms of the budget share on food. The standard errors, given
in parenthesis, estimated using the bootstrapping method with 1000 replications indicate that
the equivalence scales are statistically different from each other9.
According to Table 5, we identify three trends in marginal equivalence scales at the
national level. Firstly, in each survey year, the marginal equivalence scales decline as
household size increases within each income level. At the bottom income decile in 1990/91
9 For example, in panel B, first income quartile, in household category 2,0 to 3,0, the marginal
equivalence scale is 0.17. When the income level increases to the mean income, the marginal
equivalence scale increases to 0.20. A hypothesis test based on the bootstrapped standard error
indicates that the null hypothesis (𝐻0) of “two equivalence scales are equal” can be rejected at the 5
per cent significant level as (𝛽−�̂�)
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟.> 1.96. Accordingly, we can conclude that these two
equivalence scales are significantly different from each other.
16
for example, the equivalence scale for 1,0-2,0 household is 0.47 and it declines gradually to
0.35 in the 3,0-4,0 household category. This suggests that the larger the household size, the
lower the marginal cost of an adult to remain in the same level of welfare, measured in terms
of the budget share on food, due to economies of scale in food consumption (Deaton and
Paxson, 1998; Lanjouw and Ravallion, 1995; Vernon, 2005).
Secondly, we observe increasing marginal equivalence scales with income at the national
level, in all three years. For example, the marginal equivalence scale in 2,0-3,0 increases from
0.41 in bottom income quartile (poorest) households to 0.43 in top income quartile (richest)
households, in 1990/91. Our results suggest that as household income increase, the scale
economies in food consumption gradually decline resulting in an increase in the marginal cost
of an additional household member. This contradicts with the results of the decreasing with
income equivalence scales observed by Meenakshi and Ray (2002), Balli and Tiezzi (2013)
and Donaldson and Pendakur (2003). However, our results support the arguments raised by
Beatty (2010), Griffith et al. (2009) and Leibtag and Kaufman (2003).
Thirdly, we observe that the equivalence scales, in all income levels, decline overtime,
where the highest decline is seen during the period of 1990/91 to 2001/02, despite the
increase in income levels (as proxied by expenditure given in Table 2). For example, in the
sample mean income level, the marginal equivalence scale for 2,0-3,0 household category
decreases from 0.43 in 1990/91 to 0.32 in 2001/02 and it further declines to 0.30 in 2009/10.
This observation implies that over time, food consumption scale economies gradually
increase resulting in a decline in the marginal cost of an additional adult. This result is similar
to that of Logan (2011), where he observed that there were fewer economies of scale in food
consumption in the past10.
10 Similar patters are found at the sectoral level as well, except for the urban sector. The results are given in Table
4.1, 4.2, and 4.3 in Appendix.
17
Table 5: Equivalence scales for food by survey year (national level)
Source: Author’s calculation based on Department of Census and Statistics (1991, 2001, and 2011)