Time trends in food consumption economies of scale in Sri Lanka: … · 2015-07-09 · rates using income per equivalent adult, i.e., using income adjusted for food consumption scale

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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. 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

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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).

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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.

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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

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(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

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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.

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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

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(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-

4 These categories comprise cereal, prepared food, pulses, vegetables, yams, meat, fish, dried fish, eggs, coconuts,

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).

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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.

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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.

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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

Total HH expenditure 23,422 28,546 20,857 21,176 26,104 38,641 23,662 18,960 28,731 36,421 27,129 21,669

Food and beverages* 14,004

(60%)

16,314

(57%)

12,803

(61%)

13,393

(63%)

12,465

(48%)

15,898

(41%)

11,726

(50%)

11,242

(59%)

12,375

(43%)

14,146

(39%)

11,953

(44%)

10,898

(50%)

Non-food items 7,810

(33%)

11,251

(39%)

6,240

(30%)

4,938

(23%)

13,001

(50%)

22,069

(57%)

11,335

(48%)

6,792

(36%)

15,684

(55%)

21,563

(59%)

14,575

(54%)

9,730

(45%)

Alcohol 1,608 981 1,814 2,845 638 674 601 926 672 712 601 1,041

Health and Personal care 863 1,124 750 605 1,160 1,756 1,054 719 1,289 1,642 1,235 900

Housing 3,751 5,885 2,792 1,860 5,423 11,007 4,335 2,248 5,850 9,567 4,989 3,180

Clothing 1,022 1,142 970 978 817 1,127 754 663 902 989 890 778

Transport and communication 897 1,252 750 331 1,692 2,774 1,527 595 3,028 3,675 3,035 1,572

Recreation and education 597 883 473 294 845 1,466 736 369 1,121 1,594 1,027 600

Other 680 965 502 869 3,064 3,939 2,929 2,198 3,494 4,096 3,399 2,700

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5. Results and Discussion

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)

1990/91 2001/02 2009/10

Household

size

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

Rs.14, 194 Rs.23, 422 Rs.28, 818 Rs.13, 358 Rs.26, 105 Rs.32, 274 Rs. 16, 014 Rs. 28, 646 Rs. 35, 491

Panel A: Equivalence Scales for Food

1,0

0.53

(0.001)

0.53

(0.002)

0.52

(0.000)

0.58

(0.000)

0.57

(0.001)

0.56

(0.002)

0.58

(0.000)

0.57

(0.002)

0.57

(0.000)

2,0

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

3,0

1.41

(0.001)

1.43

(0.000)

1.43

(0.002)

1.29

(0.000)

1.32

(0.002)

1.33

(0.001)

1.29

(0.003)

1.30

(0.001)

1.31

(0.000)

4,0

1.76

(0.001)

1.81

(0.000)

1.82

(0.000)

1.48

(0.000)

1.54

(0.002)

1.56

(0.000)

1.47

(0.001)

1.52

(0.000)

1.52

(0.002)

Panel B: Marginal Equivalence Scales for Food

1,0 to 2,0

0.47

(0.001)

0.47

(0.001)

0.48

(0.001)

0.42

(0.002)

0.43

(0.000)

0.44

(0.001)

0.42

(0.001)

0.43

(0.000)

0.43

(0.001)

2,0 to 3,0

0.41

(0.002)

0.43

(0.001)

0.43

(0.001)

0.29

(0.001)

0.32

(0.001)

0.33

(0.002)

0.29

(0.000)

0.30

(0.002)

0.31

(0.002)

3,0 to 4,0

0.35

(0.000)

0.38

(0.000)

0.39

(0.002)

0.19

(0.001)

0.22

(0.000)

0.23

(0.002)

0.18

(0.002)

0.20

(0.000)

0.21

(0.001)

18

There are several factors that may explain the increasing trend in food consumption scale

economies. They are related to technological advancements in terms of food storage,

preparation, preservation, and processing over time, together with increased energy usage

such as electrification and improved transport facilities (Pena and Ruiz-Castillo, 1998;

Reardon et al., 2003; Tuttle, 2011). Due to an increase in the percentage of households who

have refrigerators together with access to electricity, households have been able to store

perishable food items for a longer time as well as to reduce food waste. Furthermore, due to

advances in the technology in terms of food preparing, processing and preservation, again

with electrification, households may prepare food at home more efficiently than they used do

in the past. In this study, we test the impact of technological advancements on food

consumption scale economies using data on household electrification. We use household

access to electricity as a proxy variable for technological advancements in domestic activities.

In doing so, we compare the differences in food economies of scale in households with and

without access to electricity. The estimated Engel curves for food for households with and

without electricity are summarised in Table 611.

Table 6: Food Engel curve estimates for households with and without electricity

(national level)- 2009/10


Table 7 reports the marginal equivalence scales for households with and without

electricity. Panel A shows the equivalence scales for households with electricity, while Panel

11 Corresponding results for the sectoral level are given in Table 5 in the appendix

Variable Households

with

electricity

Households

without

electricity

(𝜷𝟎) Constant 1.657

(0.000)

-1.420

(0.017)


𝒏 -0.038

(0.267)

0.681

(0.000)


𝒏)𝟐 -0.009

(0.000)

-0.051

(0.000)

(𝜸𝟏) 𝒏𝒂 -0.030

(0.000)

-0.036

(0.000)

(𝜸𝟐) 𝒏𝒄 -0.042

(0.000)

-0.042

(0.000)

(𝜸𝟑) 𝒏𝒂𝒏𝒄 0.008

(0.000)

0.009

(0.000)

Number of observations 14,797 2,243

Root MSE 0.106 0.118

R-squared 0.536 0.336

19

B shows those for households without electricity. The results reveal that in the majority of

cases, the households with access to electricity show lower equivalence scales (except for the

1st income quartile in the national level), than those of the households who do not have access

to electricity12. This result implies that the households who have access to electricity enjoy

greater food consumption economies of scale.

Table 7: Marginal equivalence scales of the households with and without electricity

(national level)-2009/10


Figure 1 shows that, since 1990/91, there has been a significant increase in the percentage

of households with access to electricity. In 1990/91, for example, the percentage of

households with electricity, at the national level records 29 per cent, while it is 63 and 85.3

per cent in 2001/02 and 2009/10 respectively. Accordingly, we can expect the increasing

economies of scale over time have been mainly attributed to the increased storage facilities,

reduced food waste and increased food preparing and processing technologies that are

associated with electrification.

12 Similar patters are found at the sectoral level, except for the urban sector. The results are reported in Table 6 in

the appendix.

1st quartile Sample mean 3rd quartile

Rs. 15,665 28,598 35,266

Panel A: Marginal equivalence scales of the households

with electricity

1,0-2,0 0.42

(0.001)

0.43

(0.002)

0.43

(0.001)

2,0-3,0 0.30

(0.000)

0.31

(0.001)

0.31

(0.000)

3,0-4,0 0.19

(0.000)

0.20

(0.000)

0.21

(0.000)

4,0-5,0 0.11

(0.000)

0.13

(0.001)

0.13

(0.000)

Panel B: Marginal equivalence scales of the households

without electricity

1,0-2,0 0.42

(0.002)

0.44

(0.000)

0.44

(0.002)

2,0-3,0 0.28

(0.000)

0.32

(0.000)

0.34

(0.001)

3,0-4,0 0.15

(0.001)

0.23

(0.000)

0.24

(0.001)

4,0-5,0 0.05

(0.001)

0.14

(0.001)

0.16

(0.002)

20

Figure 1: Percentage of households with access to electricity by survey year

Note: The data on sectoral level percentages access to electricity is not available for 1990/91

Finally, we examine the extent to which the convectional poverty rates, estimated using

per-capita income (PCI) (as proxied by per-capita expenditure), vary when income equivalent

adult (IPEA) is used. As the increase in the marginal equivalence scales in the presence of

adult is considerably less than unity, the poverty levels under IPEA, given in Table 12, are

significantly different than those based on conventional PCI. In all three survey years, the

conventional poverty rates decline noticeably when food consumption scale economies are

accounted for. This reduction in poverty rates, when economies of scale are taken into

consideration, is in accordance with those results found in the literature (Lanjouw and

Ravallion, 1995; Meenakshi and Ray, 2002; Nelson, 1993; Ray, 2000). Nevertheless, due to

the variations in overall family size in Sri Lanka and the countries that have been investigated

in other studies, the magnitude of the reduction of poverty rates may be different.

Additionally, the significant decline in marginal cost of an adult from 1990/91 to 2001/02,

observed earlier, is reflected in the estimated difference of poverty rates based on PCI and

IPEA. For example, the difference in 2001/02 is 15.43, while it is 7.6 and 8.58 in 1990/91 and

2009/10 respectively. Moreover, as household enjoy more economies of scale in 2009/10 than

in 2001/02, the decline in IPEA based poverty rates between 1990/91 and 2009/10 is greater

than that between 1009/91 and 2001/02. Interestingly, despite the differences in sectoral level

food consumption scale economies mentioned above, we observe that the poverty headcount

ratio based on IPEA give similar rankings of sectoral level poverty to those based on PCI.

0

20

40

60

80

100

Na onal Urban Rural Estate

percentage

Percentage of households with access to electricity by survey year

1990/91 2001/02 2009/10

21

Table 8: Poverty Headcount ratios under per-capita income and income per equivalent adult

Source: Author’s calculation based on Department of Census and Statistics (1991, 2001, and 2011)

1990/91 2001/02 2009/10

Per-

capita

income

Income

per

equivalent

adult

Decline

in

poverty

rates

Per-

capita

income

Income

per

equivalent

adult

Decline

in

poverty

rates

Per-

capita

income

Income

per

equivalent

adult

Decline

in

poverty

rates

National 24.0

(0.002)

16.44

(0.003)

7.6

22.83

(0.012)

7.4

(0.021)

15.43

10.58

(0.001)

2.00

(0.001)

8.58

Urban 14.68

(0.003)

9.08

(0.002)

5.6

6.9

(0.002)

1.4

(0.001)

5.5

3.68

(0.003)

0.88

(0.001)

2.80

Rural 27.13

(0.003)

18.7

(0.010)

8.4

24.65

(0.021)

8.4

(0.002)

16.25

11.06

(0.004)

1.86

(0.002)

9.20

Estate 16.78

(0.011)

13.72

(0.001)

3.1

30.22

(0.002)

10.29

(0.001)

19.29

19.3

(0.003)

4.94

(0.006)

14.36

22

6. Concluding remarks

This study has examined the intertemporal trends in food consumption scale economies in

Sri Lanka during the period of 1990/91 to 2009/10, using Engel equivalence scales and likely

reasons that explain difference, if any. Sri Lankan data show that equivalence scales are

dependent on income levels and hence, we estimated income dependent equivalence scales,

for each survey year, to examine the time trends in food economies of scale. We find that at

the national level, the equivalence scales have decreased over time, in all income levels. This

suggests that households enjoy greater economies of food consumption in the present than in

the past. Therefore, at present, households spend lower marginal costs for an additional adult

than they did in the past. We find that this trend is attributed to the changes in the household

food consumption patterns that have been taking place during the last several decades. In

particular, this trend is linked with increased access to electrification and increased use of

food storage facilities such as refrigerators, and advancements in food preparation and

processing technologies. Similar patterns can be seen in the rural and the estate sector.

Our results also indicate that the poverty headcount ratios decline significantly when the

possibilities for scale economies are allowed for, confirming the widely held argument that

the traditional poverty measurements routinely categorise larger households as contributing

disproportionately to overall poverty. Our finding that the household enjoy greater food

economies at present than in the past implies that the actual poverty rates have declined even

more than the conventional poverty measurements suggest, during the last two decades. As a

future research direction related to this study, we suggest examination of the effects of bulk

purchases and transportation on economies of scale over time.

23

Appendix

Table 1: Food and non-food items removed from each survey year

Source: Author’s specification based on Department of Census and Statistics (1991, 2001,

2011)

2009/10 2001/02 1990/91

Food items

Rice flour Rice flour Kurakkan

Kurakkan flour kurakkan Cut fruits

Ulundu flour Kurakkan flour Peanuts

Kekiri Kekiri Meat-liver

Mullet Mora Tinned meat

Cuttle fish dried Cuttle fish dried Canned beef

Cutlets/pastries Cutlets/pastries Mullet

Liquid milk Soya oil Mora

Palmyrah products Food beverages Soya oil

Bottled water Ice packets Food beverages

Ice packet Water

Saruwath

Non-food items

Solar power Donation Buckets

Spectacles Beauty care

Ayurvedic medicine Grinding cost

Email/internet Buckets

Educational newspapers Mats and pillows

Grinding cost Washing machine

Day care charges Telephone

Elderly care charges

Mats and pillows

Washing machine

Telephone

24

Table 2: Test of base-independence (sectoral level)-2009/10

Source: Author’s compilation based on Department of Census and Statistics (1991, 2001,

2011)

Singles vs

2 adults

Singles vs

3adults

Singles vs

4 adults

Urban Sector

2nd order term difference -0.041* -0.044* -0.034*


P-value 0.010 0.010 0.048

Rural Sector

2nd order term difference -0.023* -0.018** -0.015


P-value 0.024 0.060 0.168

Estate Sector

2nd order term difference -0.056* -0.055** -0.043


P-value 0.047 0.056 0.199

25

Table 3: Food Engel curve estimations

Source: Author’s calculation based on Department of Census and Statistics (1991, 2001,

2011)

Variable Urban Rural Estate

Panel A: 1990/91

(𝜷𝟎) Constant -1.054

(0.001)

-0.765

(0.001)

1.560

(0.049)


𝒏 0.571

(0.000)

0.477

(0.000)

-0.098

(0.606)


𝒏)𝟐 -0.043

(0.000)

-0.036

(0.000)

-0.001

(0.913)

(𝜸𝟏) 𝒏𝒂 -0.013

(0.000)

-0.007

(0.000)

-0.004

(0.614)

(𝜸𝟐) 𝒏𝒄 -0.015

(0.000)

-0.010

(0.000)

0.002

(0.554)

(𝜸𝟑) 𝒏𝒂𝒏𝒄 -0.015

(0.000)

0.001

(0.018)

0.001

(0.000)


Root MSE 0.113 0.113 0.217

R-squared 0.380 0.232 0.113

Panel B: 2001/02


(0.000)

0.266

(0.148)

-0.503

(0.508)


𝒏 -0.122

(0.041)

0.277

(0.000)

0.441

(0.015)


𝒏)𝟐 -0.004

(0.025)

-0.027

(0.000)

-0.035

(0.000)

(𝜸𝟏) 𝒏𝒂 -0.025

(0.000)

-0.028

(0.000)

-0.021

(0.001)

(𝜸𝟐) 𝒏𝒄 -0.030

(0.000)

-0.038

(0.000)

-0.032

(0.000)

(𝜸𝟑) 𝒏𝒂𝒏𝒄 0.006

(0.000)

0.007

(0.000)

0.007

(0.000)


Root MSE 0.107 0 .109 0.106

R-squared 0.543 0.510 0.345

Panel C: 2009/10


(0.000)

0.925

(0.028)

-1.647

(0.001)


𝒏 -0.171

(0.001)

0.128

(0.004)

0.729

(0.000)


𝒏)𝟐 -0.001

(0.672)

-0.019

(0.000)

-0.054

(0.000)

(𝜸𝟏) 𝒏𝒂 -0.024

(0.000)

-0.034

(0.000)

-0.030

(0.000)

(𝜸𝟐) 𝒏𝒄 -0.028

(0.000)

-0.049

(0.000)

-0.034

(0.000)

(𝜸𝟑) 𝒏𝒂𝒏𝒄 0.005

(0.000)

0.009

(0.000)

0.007

(0.000)


Root MSE 0.099 0.108 0.111

R-squared 0.540 0.492 0.390

26

Table 4.1: Equivalence scales for food in 1990/91 (sectoral level)


Urban Rural Estate

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

Rs. 16,903 Rs.28,546 Rs.36,747 Rs.13,188 Rs.20,856 Rs.25,617 Rs.14,473 Rs.21,176 Rs.25,965


1,0

0.53

(0.001)

0.53

(0.002)

0.52

(0.001)

0.53

(0.000)

0.53

(0.001)

0.52

(0.001)

0.52

(0.000)

0.52

(0.000)

0.52

(0.000)

2,0

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

3,0

1.41

(0.001)

1.43

(0.000)

1.43

(0.000)

1.41

(0.001)

1.42

(0.000)

1.43

(0.000)

1.45

(0.001)

1.45

(0.001)

1.45

(0.001)

4,0

1.76

(0.002)

1.81

(0.000)

1.82

(0.000)

1.76

(0.001)

1.80

(0.000)

1.82

(0.000)

1.86

(0.001)

1.86

(0.001)

1.86

(0.001)


1,0 to 2,0 0.47

(0.000)

0.47

(0.000)

0.48

(0.000)

0.47

(0.000)

0.47

(0.000)

0.48

(0.001)

0.48

(0.000)

0.48

(0.000)

0.48

(0.000)

2,0 to 3,0 0.41

(0.001)

0.43

(0.000)

0.43

(0.000)

0.41

(0.001)

0.42

(0.000)

0.43

(0.000)

0.45

(0.001)

0.45

(0.001)

0.45

(0.001)

3,0 to 4,0 0.35

(0.001)

0.38

(0.001)

0.39

(0.000)

0.35

(0.001)

0.38

(0.000)

0.39

(0.000)

0.41

(0.001)

0.41

(0.001)

0.41

(0.001)

27



Urban Rural Estate

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

Rs. 21,306 Rs.36,330 Rs.45,371 Rs.12,485 Rs.23,662 Rs.28,974 Rs.12,523 Rs.18,960 Rs.22,676


1,0

0.57

(0.001)

0.57

(0.002)

0.57

(0.001)

0.58

(0.000)

0.57

(0.001)

0.56

(0.001)

0.56

(0.000)

0.55

(0.000)

0.55

(0.000)

2,0

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

3,0

1.32

(0.001)

1.33

(0.000)

1.34

(0.000)

1.29

(0.001)

1.32

(0.000)

1.32

(0.000)

1.32

(0.001)

1.34

(0.001)

1.35

(0.001)

4,0

1.54

(0.002)

1.56

(0.000)

1.59

(0.000)

1.47

(0.001)

1.54

(0.000)

1.55

(0.000)

1.54

(0.001)

1.59

(0.001)

1.62

(0.001)


1,0 to 2,0 0.43

(0.000)

0.43

(0.000)

0.44

(0.000)

0.42

(0.000)

0.43

(0.000)

0.44

(0.001)

0.44

(0.000)

0.45

(0.000)

0.45

(0.000)

2,0 to 3,0 0.32

(0.001)

0.33

(0.000)

0.34

(0.000)

0.29

(0.001)

0.32

(0.000)

0.32

(0.000)

0.32

(0.001)

0.34

(0.001)

0.35

(0.001)

3,0 to 4,0 0.22

(0.001)

0.23

(0.001)

0.25

(0.000)

0.18

(0.001)

0.22

(0.000)

0.23

(0.000)

0.22

(0.001)

0.25

(0.001)

0.27

(0.001)

28



Urban Rural Estate

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

Rs. Rs. 21,137 Rs.38,641 Rs.50,240 Rs.15,301 Rs.27,037 Rs.33,518 Rs.13,092 Rs.20,777 Rs.25,531


1,0

0.56

(0.001)

0.56

(0.002)

0.56

(0.001)

0.59

(0.000)

0.58

(0.001)

0.58

(0.001)

0.57

(0.000)

0.56

(0.000)

0.55

(0.000)

2,0

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

1.00

(0.000)

3,0

1.33

(0.001)

1.34

(0.000)

1.34

(0.000)

1.27

(0.001)

1.29

(0.000)

1.30

(0.000)

1.30

(0.001)

1.32

(0.001)

1.33

(0.001)

4,0

1.57

(0.002)

1.58

(0.000)

1.60

(0.000)

1.42

(0.001)

1.47

(0.000)

1.49

(0.000)

1.47

(0.001)

1.51

(0.001)

1.53

(0.001)


1,0 to 2,0 0.44

(0.000)

0.44

(0.000)

0.44

(0.000)

0.41

(0.000)

0.42

(0.000)

0.42

(0.001)

0.43

(0.000)

0.44

(0.000)

0.45

(0.000)

2,0 to 3,0 0.33

(0.001)

0.34

(0.000)

0.35

(0.000)

0.27

(0.001)

0.29

(0.000)

0.30

(0.000)

0.30

(0.001)

0.32

(0.001)

0.33

(0.001)

3,0 to 4,0 0.24

(0.001)

0.24

(0.001)

0.25

(0.000)

0.15

(0.001)

0.18

(0.000)

0.19

(0.000)

0.18

(0.001)

0.19

(0.001)

0.20

(0.001)

29

Table 5: Food Engel curve estimates for households with and without electricity

(2009/10)


Variable Urban Rural Estate

Panel A: Households with electricity


(0.001)

1.524

(0.001)

-0.951

(0.109)


𝒏 -0.175

(0.001)

-0.003

(0.955)

0.570

(0.000)


𝒏)𝟐 -0.001

(0.675)

-0.012

(0.000)

-0.045

(0.000)

(𝜸𝟏) 𝒏𝒂 -0.023

(0.000)

-0.033

(0.000)

-0.030

(0.000)

(𝜸𝟐) 𝒏𝒄 -0.015

(0.000)

-0.050

(0.000)

0.032

(0.000)

(𝜸𝟑) 𝒏𝒂𝒏𝒄 -0.005

(0.000)

0.009

(0.000)

0.006

(0.000)


Root MSE 0.099 0.107 0.112

R-squared 0.554 0.516 0.437

Panel B: Household without electricity


(0.056)

-2.262

(0.000)

-1.893

(0.052)


𝒏 -0.144

(0.580)

0.811

(0.000)

0.794

(0.001)


𝒏)𝟐 -0.003

(0.834)

-0.063

(0.000)

-0.058

(0.000)

(𝜸𝟏) 𝒏𝒂 -0.039

(0.000)

-0.039

(0.000)

-0.029

(0.001)

(𝜸𝟐) 𝒏𝒄 -0.030

(0.039)

-0.050

(0.000)

-0.036

(0.000)

(𝜸𝟑) 𝒏𝒂𝒏𝒄 0.003

(0.376)

0.012

(0.000)

0.006

(0.000)

Number of observations 184 1,557 502

Root MSE 0.114 0.109 0.112

R-squared 0.423 0.510 0.308

30

Table 6: Marginal equivalence scales of the households with and without electricity


National Urban Rural Estate

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

1st

quartile

Sample

mean

3rd

quartile

Rs. 15,665 28,598 35,266 20,638 36,206 44,703 14,972 27,005 33,318 12,849 20,735 25,331

Marginal equivalence scales of the households with electricity

1,0-2,0 0.42

(0.001)

0.43

(0.002)

0.43

(0.001)

0.44

(0.003)

0.44

(0.000)

0.44

(0.000)

0.41

(0.001)

0.42

(0.000)

0.42

(0.001)

0.43

(0.000)

0.44

(0.001)

0.44

(0.000)

2,0-3,0 0.30

(0.000)

0.31

(0.001)

0.31

(0.000)

0.34

(0.001)

0.34

(0.003)

0.34

(0.000)

0.28

(0.002)

0.29

(0.000)

0.29

(0.000)

0.29

(0.002)

0.32

(0.000)

0.32

(0.000)

3,0-4,0 0.19

(0.000)

0.20

(0.000)

0.21

(0.000)

0.25

(0.000)

0.25

(0.002)

0.25

(0.000)

0.17

(0.000)

0.19

(0.002)

0.19

(0.001)

0.18

(0.001)

0.18

(0.001)

0.22

(0.001)

4,0-5,0 0.11

(0.000)

0.13

(0.001)

0.13

(0.000)

0.18

(0.000)

0.18

(0.000)

0.18

(0.000)

0.08

(0.000)

0.10

(0.000)

0.11

(0.000)

0.09

(0.001)

0.17

(0.001)

0.18

(0.001)

Marginal equivalence scales of the households without electricity

1,0-2,0 0.42

(0.002)

0.44

(0.000)

0.44

(0.002)

0.39

(0.002)

0.40

(0.000)

0.40

(0.000)

0.42

(0.000)

0.44

(0.001)

0.40

(0.001)

0.43

(0.002)

0.45

(0.001)

0.45

(0.002)

2,0-3,0 0.28

(0.000)

0.32

(0.000)

0.34

(0.001)

0.24

(0.001)

0.24

(0.001)

0.24

(0.000)

0.26

(0.001)

0.32

(0.000)

0.33

(0.001)

0.31

(0.001)

0.35

(0.003)

0.36

(0.001)

3,0-4,0 0.15

(0.001)

0.23

(0.000)

0.24

(0.001)

0.12

(0.000)

0.13

(0.001)

0.13

(0.001)

0.13

(0.001)

0.22

(0.001)

0.24

(0.000)

0.19

(0.001)

0.25

(0.002)

0.27

(0.001)

4,0-5,0 0.05

(0.001)

0.14

(0.001)

0.16

(0.002)

0.04

(0.000)

0.04

(0.001)

0.05

(0.001)

0.01

(0.000)

0.12

(0.002)

0.15

(0.001)

0.10

(0.001)

0.18

(0.001)

0.20

(0.000)

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Time trends in food consumption economies of scale in Sri Lanka: … · 2015-07-09 · rates using income per equivalent adult, i.e., using income adjusted for food consumption scale