Channing Arndt and Finn Tarp

Print publication date: 2016

Print ISBN-13: 9780198744801

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198744801.001.0001

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Keep It Real

Measuring Real Inequality Using Survey Data from Developing Countries

Chapter:
(p.274) 17 Keep It Real
Source:
Measuring Poverty and Wellbeing in Developing Countries
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198744801.003.0017

Abstract and Keywords

The chapter investigates how two effects drive wedges between nominal and real inequality estimates. The effects are caused by (1) differences in the composition of consumption over the income distribution coupled with differential inflation of consumption items; and (2) quantity discounting effects for the non-poor. Household-specific deflators are estimated using fifteen surveys collected in six countries in the period 1999–2011. In some countries (Mozambique, Tanzania, Malawi, and Pakistan), nominal inequality is lower than real inequality, as it is defined in this chapter. In other countries (Ethiopia and Madagascar), no differences are found. Finally, the chapter argues that poverty estimation based on national accounts consumption means and estimates of inequality from consumption surveys should employ real, rather than nominal, inequality estimates.

17.1 Introduction

Measures of inequality are often used to direct and evaluate policy. In developing countries, inequality estimates are typically based on a consumption module included in nationally representative surveys. Based on this, a consumption aggregate is constructed. This aggregate is a measure of the value of consumption by a household. There are some technicalities involved with estimating the consumption aggregate: housing costs are often imputed, the cost of durable goods must be spread out over multiple years, etc. (Grosh and Deaton 2000; Deaton and Zaidi 2002). Nevertheless, at its heart, the value of consumption is reached by multiplying current prices with quantities. As such, the standard consumption aggregate is a nominal concept. Inequality indices derived from nominal consumption aggregates are therefore also nominal in their nature.

There are at least two reasons why basing inequality estimates on a real consumption aggregate—and thereby estimating what I will refer to as real inequality—is relevant. First, the poorest households tend to dedicate a higher share of their spending towards basic food items, the prices of which have been rising faster than other prices in recent years. I refer to this as the composition effect. Second, if there is a systematic difference in the prices faced by households over the income distribution, nominal inequality will differ from real inequality. Specifically, this can arise when the poor tend to purchase items in smaller quantities which can lead to higher prices. I refer to this as the quantity discounting effect. This chapter aims to empirically estimate deflators of these two effects, (p.275) proceed to estimate real consumption aggregates, and use these to compute estimates of real inequality. Many types of deflation can lead to different types of real consumption aggregates on which real inequality can be estimated. For example, nominal consumption is often both temporally and spatially deflated to arrive at a real consumption measure with implications for inequality. In this chapter, I use the term ‘real’ to denote nominal consumption deflated to account for the composition effect and the quantity discounting effect. This conversion from a nominal to a real value is described in detail in section 17.2.

I overcome the substantial data requirements for this task by building on the set of country-specific databases which were constructed as part of the Growth and Poverty Project (GAPP) conducted under the auspices of UNU-WIDER. Using fifteen surveys from six different countries (Ethiopia, Madagascar, Malawi, Mozambique, Pakistan, and Tanzania), collected in the period 1999 to 2011, and covering over 220,000 households, I construct household-specific indices of the composition and the quantity discounting effects.

The chapter proceeds by investigating how real inequality estimates affect poverty figures when estimated using a method developed in series of papers by Sala-i-Martin and Pinkovskiy. This method finds poverty rates by fitting two-parameter consumption distributions using inequality estimates obtained from survey data and national accounts information on income per capita (Pinkovskiy and Sala-i-Martin 2009, 2014; Sala-i-Martin 2006; Sala-i-Martin and Pinkovskiy 2010). I refer to this approach as the SiMP methodology. Using this approach, the authors find that poverty is falling much faster than what is observed by other methods of poverty estimation. Pinkovskiy and Sala-i-Martin (2014) state that the discrepancy is mainly caused by differences in the growth rates of mean per capita consumption observed in the surveys and the mean per capita GDP observed from the national accounts. These differentials are not disputed; however, this chapter shows that using the proper inequality estimates also matters.

The strength of the two estimated effects differs substantially across countries. In some countries, the poorest households were subject to a double penalty which is the result of a combination of high food inflation rates for the consumption bundle of the poor, and of the poor buying in smaller quantities. In continuation of this, the decline in poverty using the SiMP methodology may be overestimated, and the level of poverty underestimated. This chapter therefore explains part of the gap between the very optimistic results of Pinkovskiy and Sala-i-Martin (2014) and other, more mixed findings.

17.2 Empirical Framework

This section explains how the two effects described briefly in section 17.1 arise and how they are estimated.

(p.276) 17.2.1 The Composition Effect

The composition effect occurs when the relatively poor spend a larger part of their income on basic food items and there are disproportionate increases in the prices of these items. This effect has been studied in some detail for developed countries (see, for instance, Muellbauer 1974; Cage, Garner, and Ruiz-Castillo 2002; Leicester, O’Dea, and Oldfield 2008). A higher consumption share of food items by the poor has also been found in developing countries, even though the impact on inequality has not been the focus of the majority of this body of work (Pritchett, Suryahadi, Sumarto, and Suharso 2000; Deaton 2003; Günther and Grimm 2007; Aksoy and Isik-Dikmelik 2008).

The hike in food price inflation after 2000, culminating in the price spike of the food price crisis of 2007–9, provides a rationale for estimating the magnitude of such effects (Mitchell 2008; Wiggins, Keats, and Compton 2010). A few recent papers have explored the link between the composition effect and inequality in developing countries more directly (Goñi, López, and Servén 2006; Mohsin and Zaman 2012). The work most closely related to this chapter in its approach to estimating the composition effect is Arndt et al. (2015). The authors find that the structure of consumption bundles varies across the income distribution. Due to more rapid inflation in the prices of basic goods, nominal inequality was found to underestimate real inequality by several Gini points for Mozambique in 2008.

In this chapter, I follow the method proposed by Arndt et al. (2015).1 Consumption items are divided into three groups: core food items, non-core food items, and non-food items. A household-specific Paasche price index which takes into account differential inflation rates of these three groups of items is then given by:

$Display mathematics$
(17.1)

$pat$ is the index price in year t of group a products, where a can be either core (c), non-core (nc), or non-food (nf). $sai,t$ is the share of consumption used for group a products purchased by household i in year t.2

(p.277) There are two principal challenges associated with implementing this approach consistently across countries. The first is how to choose which food items should be included in the core and the non-core food groups, respectively. This choice should be country-specific since food consumption patterns vary substantially between countries. It should also be general since cross-country results can only be meaningfully compared if the decision rule is consistent across countries. An option which fits both of these criteria is to define the core food items as those included in the food poverty lines estimated by the Growth and Poverty Project in year t of each country. The poverty food basket is chosen consistently across countries, and across surveys within countries, in order to represent the most important food items for the poor. This makes this group of products an ideal candidate for the core food group. I do not use the inflation rates of the food poverty line as an estimate of the temporal change in $pct$, since items are allowed to move in and out of the food poverty bundle over time, and since the prices used to estimate the poverty lines are often estimated specifically for the poor. Instead, I re-estimate weights and price increases for the food items in the food poverty bundle directly from the survey data. Since the poverty lines vary at the subnational level, and since this chapter is concerned with estimating food inflation at the national level, a procedure to reconcile this difference is needed. I choose to keep only items which are present in the poverty lines of two or more spatial domains of year t, and also present in the first survey ($t=1$), though not necessarily part of the poverty basket in the first survey. In order to increase precision of the estimated unit prices, I further restrict the group of food items to those items where each survey has at least 200 recorded purchases.

The second challenge is to estimate price changes of core foods, non-core foods, and non-food items separately. It is not feasible to estimate all price changes from survey information alone due to missing prices and few purchases of some goods. Furthermore, detailed CPI information at the product level is not always available, especially for rural areas. For the core food items, the surveys contain sufficient information to calculate price changes directly from the survey. However, this is not the case for the non-core food items and the non-food items. The non-core food items are not observed as frequently in the data, and using the survey prices is not an option. The non-food items are typically only reported as (nominal) values, not as prices and quantities. Instead of using the survey data, I use external sources of CPI information which is available separately for food and non-food items. For the non-food group of items, the non-food CPI series can be directly used.

For the non-core food items, I proxy the non-core food inflation by the total food CPI series. One can think of the total food CPI series as a weighted average of core food and non-core food CPI series. Therefore, estimation of (p.278) the core food inflation from the household data means that the direction of the bias of the non-food inflation index is known. As will become clear, the bias will tend to attenuate the magnitude of the composition effect; the estimates presented here can therefore be seen as a lower bound on the true effect sizes.

17.2.2 The Quantity Discounting Effect

The quantity discounting effect arises when the poor purchase smaller amounts at a time, thereby missing out on quantity discounts. There are several potential explanations for why the poor would do so: the poor consume less and lack capacity to securely store perishable foods; the poor may be credit-constrained and the poor may lack transport options to transport larger amounts.

The quantity discounting effect has been studied using unit prices, i.e. prices calculated from quantities and values reported by households. The main pitfall with this approach is that the quality of the consumed items is variable and unobserved. A specific item code in the consumption module of a questionnaire must by necessity cover a variety of qualities but higher-quality items will have higher unit prices. This is difficult to separate from a potential quantity discounting effect when high- and low-quality items share the same survey code. The problem of separating quality issues from true price variation has been referred to as the unit value problem (Deaton 1988; Crawford, Laisney, and Preston 2003; Chung, Dong, Schmit, Kaiser, and Gould 2005; Beatty 2010; McKelvey 2011).

One way of reducing the confounding of quality effects and quantity discounting effects is to use a survey instrument specifically tuned to separate different qualities of the same product into different questionnaire items (Rao 2000; Aguiar and Hurst 2007). However, such specialized datasets are often not available, especially in developing countries. Alternatively, one could limit the study to reasonably homogenous items (Attanasio and Frayne 2006). However, when the topic of interest is national inequality, it is necessary to use a method which works with all items of consumption and in addition to use the nationally representative surveys which exist.

In the following, I develop such a method which exploits information about the size of the purchases. By exploiting this information, one can non-parametrically estimate a household-specific price index which at least partially controls for quality differences. As the point of departure, I take the expensiveness index of Aguiar and Hurst (2007). The authors construct a household-specific expensiveness index in order to compare how expensively households bought their specific basket of goods. The index is given by: (p.279)

$Display mathematics$
(17.2)

Here, $pmi$ is the price paid for product m by household i, $p¯mi$ is the average price paid for product m in a geographical area where i resides, and $qmi$ is the quantity household i bought of product m. This measure compares actual expenditures of household i with the cost of this bundle of food items, priced at the average prices. If the index is larger than one, the household is paying more for its bundle than the average household would have done. Next, I introduce product-specific quantity bins. Using these bins, a more specific version of the index can be calculated, where u denotes the quantity bin of each purchase:

$Display mathematics$
(17.3)

This version of the index only compares products which were in the same quantity bin. Both (17.2) and (17.3) are affected by quality in the same way. The quantity discounting effect can now be isolated by taking the ratio of the two indices and exploiting that the numerator in both (17.2) and (17.3) is total household expenditure. This gives the final household-specific quantity discounting price index:3

$Display mathematics$
(17.4)

The necessary assumption for the quantity discounting index to exactly isolate the quantity discounting effect is that the quantity of purchase is uncorrelated with quality. If there is a correlation between quality and quantity of purchase it will continue to affect (17.4). Since one can expect richer households to buy higher-quality items, this effect will bias results in the opposite direction of quantity discounting. Therefore, if it is found that the poor pay more for their food, the estimated effect can be seen as a lower bound on the true effect size. I construct four bins separated at the twenty-fifth, fiftieth, and seventy-fifth percentile of the product-specific unit price distribution.

The index of (17.4) makes use of all variation in prices in the survey. However, if there is real price variation between geographical areas (Deaton 1988), the performance of the quantity-adjusting index can be improved by estimating average prices at a smaller geographical area than the national level. This will matter if the poor are disproportionately likely to live in either high- or low-price areas. The final index is shown in equation (17.5). Here, $p¯m,ug$ denotes the average price of unit-size u of item m in geographical area g which (p.280) household i lives in. In this version, the household-specific deflator of household i is based only on variation within the geographical area of household i.

$Display mathematics$
(17.5)

The geographical area employed in the remainder of the chapter is the survey stratum. This means that any differences in prices between strata do not affect the quantity discounting effect. The number of strata is survey-specific; the surveys used in this chapter have between eight and thirty-one strata.

17.2.3 Estimating Inequality

The deflated consumption aggregate for household i in year t is estimated as:

$Display mathematics$
(17.6)

Where $ya$ denotes nominal consumption aggregates of core, non-core, and non-food consumption, respectively and $Yreali,t$ is real consumption. All other notation is the same as above. Using population weights, nationally representative real Gini coefficients are estimated.

The poverty rate is the share of people who consume less than a given poverty line. A standard approach to estimating national poverty lines is to use information on consumption from nationally representative surveys and a caloric requirement in order to estimate the cost of consuming the caloric requirement, given the actual consumption structure of the poor. Subsequently, non-food requirements are estimated. The sum of the food and non-food requirements equals the total poverty line. This is the so-called cost of basic needs (CBN) approach (Ravallion and Bidani 1994; Tarp, Simler, Matusse, Heltberg, and Dava 2002). The CBN methodology can be made robust to both the composition and the quantity discounting effects. The composition effect is implicitly handled since the poverty line is by definition the cost of a certain amount of the consumption bundle consumed by the poor. It is therefore price changes of the poor which influence the intertemporal change in the poverty line. The quantity discounting effect can be handled by pricing the consumption bundle using the prices paid by the poor, which is frequently done in practice. Another common approach is to impose an exogenously defined poverty line. The leading example of such a poverty line is 1.25 PPP-adjusted US$in 2005 prices, proposed by Ravallion, Chen, and Sangraula (2009). (p.281) Recently, Sala-i-Martin and Pinkovskiy (SiMP) have proposed a third approach (Pinkovskiy and Sala-i-Martin 2009, 2014; Sala-i-Martin and Pinkovskiy 2010). This approach uses inequality estimates and national accounts information on GDP to fit a two-parameter consumption distribution for each country. For most developing countries (and all countries considered in this chapter), the inequality information is based on the same consumption surveys used to estimate poverty. Using the fitted distribution and the US$1.25-a-day poverty line, Pinkovskiy and Sala-i-Martin (2014) estimate poverty using the cumulative distribution function. The US$1.25-a-day poverty line is measured in real 2005 international (PPP-adjusted) prices. For this reason, Pinkovskiy and Sala-i-Martin (2014) use a real measure of GDP to anchor the income distribution. If all households face the same prices, it is unnecessary to deflate inequality estimates, because the Gini coefficient is unaffected by scalar multiplications. However, the deflator need not be constant over the income distribution. Therefore, if one wants to take seriously the notion of estimating poverty using a fitted distribution, the use of a real inequality estimate is necessary. In section 17.4.3 we therefore investigate the impact of using real inequality poverty rates when following the baseline methodology of Pinkovskiy and Sala-i-Martin (2014), i.e. by fitting a log-normal distribution using mean GDP per capita from the World Bank World Development Indicators and estimates of inequality.4 In addition to those we have discussed, there are several other differences between the CBN and the SiMP methodologies (see Guénard and Mesplé-Somps 2010; Arndt, Tarp, and McKay 2016; as well as the working paper version of the current chapter). Comparing the two directly is like comparing apples and oranges and I refrain from doing so in this chapter. Instead, I compare SiMP measures of poverty using nominal and real consumption aggregates. 17.3 Data The various data sources used for this chapter, as well as some descriptive statistics, are detailed in Table 17.1. As mentioned previously, the results build upon work done in relation to the GAPP project. Building on this body of work, I have compiled a standardized database of consumption information which allows real inequality measures to be computed at the household level (p.282) (p.283) for the more than 220,000 household observations in the database. In particular, the consumption aggregates used to calculate poverty rates are used to calculate the Gini coefficient. Nationally representative consumption questionnaires are often collected over an extended period of time, typically an entire year. Since prices change within this time frame, all prices and consumption aggregates presented are deflated using a temporal (within-survey) price index. Such an index is available for each of the GAPP country studies.5 Since prices also vary spatially, I also deflate consumption aggregates by the spatial indices. The countries cover a range of different experiences. Consider the survey mean consumption, converted to constant 2005 US$ using the PPP-adjusted exchange rate. The mean per capita consumption of Pakistan in 2007/8 was more than double that of Tanzania (in 2007) and three times that of Madagascar (in 2005). Trends also differ. At one end of the spectrum is Madagascar where the mean per capita consumption in 2001 was US$0.91 dollars a day; this fell slightly to US$0.83 in 2005. At the other end of the spectrum are Ethiopia and Pakistan where mean per capita consumption increased annually by 4 per cent from the first to the last survey (from US$1.4 to US$2.07 in Madagascar; from US$1.74 to US$2.52 in Pakistan). The picture in terms of trends is generally consistent if one instead looks at GDP per capita; however, the level is generally substantially higher. This difference in levels is consistent with the existing literature (Pinkovskiy and Sala-i-Martin 2014).

Table 17.1. Data sources and descriptive statistics

2005 PPP USD

Country and survey years

Household survey reference

CPI reference

No. of households

No. of EAs

No. of strata

Survey mean (consumption)

GDP per capita (nat. accounts)

10th percentile/mean cons.

90th percentile/mean cons.

National poverty rate

Ethiopia

Stifel and Woldehanna (2016)

NBE (2014); CSA (2015)

- HICES (1999/2000)

17,332

1264

20

1.40

1.44

0.48

1.60

46.8

- HICES (2004/5)

21,595

1548

18

1.69

1.74

0.46

1.58

46

- HICES (2010/11)

27,830

1966

20

2.07

2.56

0.42

1.64

23.8

Stifel, Razafimanantena, and Rakotomanana (2016)

instat.mg (2015)

- EPM (2001)

5080

303

12

0.91

2.54

0.27

2.06

57.8

- EPM (2005)

11,781

561

12

0.83

2.38

0.31

1.83

59.1

Malawi

Pauw, Beck, and Mussa (2016)

NSO (2015)

- IHS2 (2004/5)

11,280

564

30

1.33

1.77

0.35

1.72

47

- IHS3 (2010/11)

12,271

768

31

1.89

2.17

0.29

1.78

38.8

Mozambique

Arndt, Jones, and Tarp (2016)

INE (2015)

- IHS2 (2004/5)

8700

857

11

1.29

1.60

0.31

1.78

54.1

- IHS3 (2010/11)

10,832

1060

11

1.51

2.12

0.31

1.75

54.7

Pakistan

Nazli et al. (2015)

MoF (2015)

- HIES (2001/2)

14,649

1050

8

1.74

5.05

0.51

1.60

21.4

- HIES (2005/6)

15,374

1109

8

2.21

5.87

0.51

1.61

23.0

- HIES (2007/8)

15,441

1113

8

2.54

6.36

0.51

1.65

26.0

- HIES (2010/11)

16,295

1180

8

2.52

6.60

0.53

1.57

27.0

Tanzania

Arndt, Hussain, Leyaro, Jones, and Tarp (2013)

CountrySTAT (2015)

- HBS (2000)

22,176

1158

20

0.83

2.37

0.38

1.79

35.7

- HBS (2007)

10,407

447

20

1.13

3.15

0.37

1.79

33.6

Source: Author’s compilation based on the following consumption surveys: HICES is the Ethiopia Household Income, Consumption, and Expenditure Survey (HICES, multiple years). EPM is the Enquête Périodique auprès des Ménages (INSTAT 2002, 2006). IHS is the Integrated Household Survey (NSO (National Statistics Office Malawi) 2005, 2012). IAF is the Inquérito aos Agregados Familiares (MPF et al. 2004). IOF is the Inquérito ao Orçamento Familiar (MPF et al. 2010). HIES is the Household Integrated Economic Survey (FBS 2003, 2007, 2009, 2013) and estimates exclude Azad Jammu and Kashmir, Federally Administered Tribal Areas, and Northern Areas (PBS 2006, 2007, 2009, 2013). HBS is the Household Budget Survey (NBS 2002, 2011), and covers only mainland Tanzania (excludes Zanzibar). The poverty rates are from the sources listed above, except for Tanzania, where the estimates are from Arndt, Demery, McKay, and Tarp (2016). PPP conversion factors and national accounts information are from World Bank (2012).

The level of inequality also varies across countries: Madagascar and Malawi are the most unequal; here, the tenth percentile of the population consumes between 0.27 and 0.35 of mean income, whereas the ninetieth percentile consumes between 1.72 and 2.06 of mean income. There are differences in inequality trends as well: while the consumption spread has decreased in Madagascar, it has increased in Malawi. Pakistan is the least unequal of the countries: the tenth and ninetieth percentile consumed respectively 0.50 and 1.65 of mean consumption in the latest survey round.

Information on nominal inequality in the form of Gini coefficients can be readily obtained from the WIDER World Income Inequality Database, or WIID (UNU-WIDER 2014). However, I use nominal Gini coefficients estimated directly from the household-level consumption aggregates of the database. This is necessary since only by using the micro-level datasets can the household-specific deflators be applied. For the estimation of poverty using the SiMP methodology, I obtain time series of PPP-adjusted GDP per capita in constant 2005 dollars from the 2012 version of the World Bank’s World (p.284) Development Indicators (World Bank 2012). The same data sources were used by Pinkovskiy and Sala-i-Martin (2014). Therefore, the inequality estimates are the only source of difference.

17.4 Results

17.4.1 The Composition Effect

Table 17.2 shows the CPI indices used for the price changes of core food, non-core food, and non-food inflation. Taking the first survey in each year as the baseline, the core food items are rising in price faster than the non-core food (proxied by the food CPI) items in all countries except Ethiopia and Madagascar. Since total food inflation is a weighted average of core and non-core food inflation rates, in the four (two) countries where core inflation is higher (lower) than total food inflation, the use of total food inflation as a proxy measure of non-core food inflation overestimates (underestimates) the true rate of non-core inflation.

Table 17.2. Food and non-food CPIs

Country and year

Core food

Non-core Food

Non-food

Ratio (CF/NCF)

Ratio (CF/NF)

Ethiopia

- 1999/2000

100.0

100.0

100.0

1.00

1.00

- 2004/5

98.9

145.7

112.8

0.68

0.88

- 2010/11

249.0

315.8

254.7

0.79

0.98

- 2001

100.0

100.0

100.0

1.00

1.00

- 2005

152.4

176.3

149.9

0.86

1.02

Malawi

- 2004/5

100.0

100.0

100.0

1.00

1.00

- 2010/11

248.5

177.6

188.2

1.40

1.32

Mozambique

- 2002

100.0

100.0

100.0

1.00

1.00

- 2008

228.2

200.4

139.8

1.14

1.63

Pakistan

- 2001/2

100.0

100.0

100.0

1.00

1.00

- 2005/6

132.0

131.1

124.4

1.01

1.06

- 2007/8

182.8

144.6

131.9

1.26

1.39

- 2010/11

290.3

279.2

207.1

1.04

1.40

Tanzania

- 2000

100.0

100.0

100.0

1.00

1.00

- 2007

199.1

158.8

131.4

1.25

1.52

Note: Non-core and non-food inflation are calculated by the author based on the sources listed in Table 17.1. All CPIs are normalized to 100 in the first survey year.

Source: Core CPIs are calculated by the author based on survey data

Why do core food prices in Ethiopia and Madagascar behave differently? Between 2000 and 2005, Ethiopia experienced several good harvests which put downward pressure on food prices (Durevall, Loening, and Ayalew Birru (p.285) 2013). In particular, prices of domestically produced foods, which constitute the majority of core food items, were subjected to downward pressure. From 2004/5 to 2010/11, core food prices rose faster than non-core food prices. A partial explanation in the Malagasy case could be that in 2004, due to a partially failed harvest of rice, the main staple of Madagascar, the Malagasy government intervened in the rice market by slashing import tariffs and by importing state-bought rice (Dorosh and Minten 2006). This, combined with a better domestic rice harvest in 2005, contributed to downward pressure on rice prices near the end of 2005, which is when the second Malagasy survey was conducted.

In all countries except for Ethiopia, the prices of core foods outpace those of non-food, compared to the first survey of each country. The magnitude of the price differentials varies between countries. For instance, core prices in Mozambique rose 63 per cent faster than non-food prices from 2002 to 2008. However, in Madagascar, the difference was only 2 per cent from 2001 to 2005. To conclude, the data presented here shows that in many, but not all, of the included countries, food price inflation has been higher than non-food inflation in the period considered.

Figure 17.1 shows the mean consumption shares of the three groups of items for each percentile of the consumption distribution, across countries and surveys. The percentile-specific means are calculated for ease of illustration; deflators are household-specific as indicated by equation (17.1). A consistent picture, which matches what Arndt et al. (2015) found for Mozambique, emerges: as one moves up through the income distribution, the share of consumption expenditures allocated to core foods declines. Instead, the non-food share and in many cases also the non-core food share increases. The core food consumption profiles of Madagascar and Mozambique have somewhat more u-shaped curves, where the very poorest spend less on food and more on non-food than those who consume a little more.

Figure 17.1. Consumption shares by consumption percentiles

Note: Each dot represents a percentile of the consumption distribution.

Source: Author’s calculations

In all countries except Ethiopia, the non-core food share increases along the income distribution. This empirical regularity, combined with the use of the general food inflation index as the non-core food index which overestimates non-core inflation for all countries except Ethiopia and Madagascar, means the increase in inequality due to the composition effect is underestimated in all countries except Madagascar, where the composition effect may be overestimated.

Figure 17.2. Composition CPIs by country

Note: Each dot represents a percentile of the consumption distribution. A few percentile dots are outside the graph areas. The year of first survey for each country against which the effects are calculated are as follows: Ethiopia: 1999/2000; Madagascar: 2001; Malawi: 2004/5; Mozambique: 2002; Pakistan: 2001/2; Tanzania: 2000.

Source: Author’s calculations

Figure 17.2 shows the composition CPIs for each percentile of the consumption distribution. Results are as expected, given the inflation rates and the consumption shares reported above: in all countries except Ethiopia and Madagascar, the composition CPI index is highest for the lower part of the distribution. This indicates that the consumption structure of the poor combined with the observed price changes have resulted in higher price increases for the poor. The magnitudes of the effects are country-specific. For instance, (p.286) (p.287) there is only a slight slope over the consumption distribution in Malawi. In Pakistan for the 2005/6 survey, only the top percentiles are notably different.

17.4.2 The Quantity Discounting Effect

Figure 17.3. Quantity CPIs by country and survey

Note: Each dot represents a percentile of the consumption distribution. A few percentile dots are outside the graph area.

Source: Author’s calculations

Figure 17.3 shows the estimated quantity discounting CPIs by percentiles. In Mozambique, Tanzania, and Malawi, the estimated deflator is downward-sloping over the consumption distribution. In these countries, it appears that the quantity discounting effect is indeed at work in the sense that the poorest are paying higher unit prices solely due to the size of their purchase. On the other hand, Ethiopia, Pakistan, and Madagascar show no sign of a quantity discounting effect.6

17.4.3 Inequality and Poverty

Table 17.3 shows the real Gini coefficients estimated by applying the household-specific deflators presented in section 17.4.1 and 17.4.2. The first thing to note is that even the nominal Ginis of the WIID and the nominal Ginis from the GAPP database differ. In some cases, such as Malawi, this is partly caused by the re-estimation of the consumption aggregate by Pauw et al. (2016). Another source of variation is the temporal and spatial deflation of the nominal consumption aggregates. However, these differences are not driving the results in the following—the effects on the Gini coefficients would have been qualitatively similar if the household-specific deflators had been applied to consumption aggregates which exactly reproduce the WIID Ginis.

The composition effect means that real inequality is higher than nominal in all countries except Ethiopia and Malawi where the effect is slightly negative. For example, while one would draw the conclusion from the nominal Ginis that inequality in Mozambique was unchanged (or decreasing, using the WIID information), the real Gini show an increase of 44.3−41.5=2.8 Gini points. This is qualitatively consistent with the conclusion drawn by Arndt et al. (2015). In Tanzania, the nominal (GAPP) inequality measure increases by 1.1 Gini points from 2000 to 2007. However, applying the composition deflator increases this to 2.5 Gini points (36.7−34.2).

The annualized change in the composition-adjusted Gini coefficient, compared to the annualized change in the nominal (GAPP) Ginis, varies from 0.06 (for Pakistan from 2007/8 to 2010/11) over 0.47 (for Mozambique from 2002 to 2008) to 1.08 (for Pakistan from 2005/6 to 2007/8). To give an idea about magnitudes, these figures can be compared to the average annual absolute (p.288) (p.289) (p.290) change in the nominal (GAPP) Gini coefficients, which is 0.5 Gini points. This means that composition adjustments of Gini coefficients are in some cases substantial, compared to the average change in the nominal Gini. This means that the composition effect severely alters the inequality track record in some, but not in all, countries.

The quantity discounting effect can also increase the level of inequality substantially. In Mozambique, the level of inequality increases by between 0.6 and 1.3 Gini points, depending on the survey. In Tanzania, the increase is between 0.6 and 0.9 Gini points. In Malawi, the effect is 0.8 Gini points in both survey rounds. However, the effect is not found in all countries—Pakistan and Ethiopia show no signs of quantity discounting effects.

Table 17.3. Gini coefficients using alternative deflators

WIID

GAPP

Quantity

Composition

Both

Quantity minus Nominal

Composition minus Nominal

Both minus Nominal

Ethiopia

- 1999/2000

30.0

28.9

28.9

0.0

- 2004/5

29.8

32.6

32.6

32.0

32.0

0.0

−0.6

−0.6

- 2010/11

29.8

32.1

32.3

32.0

32.2

0.0

−0.1

0.1

- 2001

45.3

45.4

45.6

0.2

- 2005

41.0

41.0

41.1

40.6

40.8

0.2

−0.4

−0.2

Malawi

- 2004/5

41.0

41.9

42.7

0.8

- 2010/11

39.3

44.5

45.3

45.4

46.2

0.8

1.0

1.7

Mozambique

- 2002

47.1

41.5

42.1

0.6

- 2008

41.4

41.4

42.7

44.3

45.4

1.3

2.8

4.0

Pakistan

- 2001/2

30.4

26.8

26.8

0.0

- 2005/6

32.7

28.5

28.5

28.7

28.7

0.0

0.2

0.3

- 2007/8

30.0

27.9

27.9

29.2

29.2

0.0

1.3

1.3

- 2010/11

30.6

26.0

26.1

27.2

27.2

0.1

1.1

1.2

Tanzania

- 2000

34.6

34.2

34.8

0.6

- 2007

35.0

35.3

36.2

36.7

37.6

0.9

1.4

2.3

Source: Author’s calculations

Results are robust to varying the number of bins as well as to using prices for the entire country instead of within-strata prices.7

Table 17.4. Poverty rates and changes using different inequality measures

WIID

GAPP

Quantity

Composition

Both

Quantity minus Nominal

Composition minus Nominal

Both minus Nominal

Ethiopia

- 1999/2000

50.3

49.5

49.5

0.0

- 2004/5

36.6

39.8

39.8

39.1

39.1

0.0

−0.6

−0.7

- 2010/11

14.6

17.6

17.8

17.5

17.7

0.2

−0.1

0.1

- 2001

34.2

34.3

34.5

0.2

- 2005

32.2

32.1

32.3

31.7

31.9

0.2

−0.5

−0.3

Malawi

- 2004/5

45.2

47.8

48.6

0.7

- 2010/11

41.2

40.4

41.3

41.4

42.2

0.8

1.0

1.8

Mozambique

- 2002

56.7

52.7

53.1

0.5

- 2008

38.1

38.1

39.5

41.1

42.4

1.4

3.0

4.2

Pakistan

- 2001/2

1.2

0.4

0.4

0.0

- 2005/6

1.1

0.3

0.3

0.3

0.3

0.0

0.0

0.0

- 2007/8

0.3

0.1

0.1

0.3

0.3

0.0

0.1

0.1

- 2010/11

0.3

0.0

0.0

0.1

0.1

0.0

0.0

0.0

Tanzania

- 2000

24.4

23.9

24.7

0.8

- 2007

13.1

13.5

14.6

15.2

16.2

1.1

1.7

2.7

Note: Poverty rates are reported in %.

Source: Author’s calculations

The rightmost column in Table 17.3 shows the results when both deflators are applied. In general, the combined effect is close to the sum of the two effects. The combination of the quantity discounting effect and the composition effect means that nominal inequality tends to underestimate the level of (p.291) inequality and overestimate reductions in inequality. Since country growth performance and policy effectiveness are often evaluated in the context of such changes, it is important to consider the possibility that nominal inequality measures may be severely downwards biased.

Table 17.4 shows the poverty rates calculated using the national accounts means and the Gini coefficients of Table 17.3. For the countries such as Mozambique and Tanzania where substantial differences in inequality were found, sizable differences in poverty are also found. For instance, the combination of the quantity discounting and composition effect raises the poverty rate by 4.2 percentage points in Mozambique in 2008, by 2.7 percentage points in Tanzania in 2007, and by 1.8 percentage points in Malawi in 2010/11. In Ethiopia and Madagascar, the estimated effect is smaller and sometimes even slightly negative, as expected from inspection of Figures 17.2 and 17.3. Since the composition effect builds up over time, the discrepancy in poverty estimates is bigger in later surveys. The composition effect alone raises the poverty estimate by 3.0 percentage points in the 2008 Mozambique survey and by 1.7 percentage points in the 2007 Tanzania survey. On this background, the optimistic picture of very fast poverty reduction in sub-Saharan African countries of Pinkovskiy and Sala-i-Martin (2014) (p.292) should be interpreted with caution: while the technique still shows substantial poverty reductions when real inequality estimates are used, the level is higher and the pace of reduction is slower overall.

17.5 Conclusion

This chapter shows how two different effects can drive wedges between estimates of nominal and of real inequality. The first effect works through the combination of differential consumption structures across the consumption distribution and differential price increases of different product groups. The second effect works through quantity discounting: the poor may pay more for their food consumption since they buy smaller quantities. Household-specific deflators are calculated for fifteen surveys from six different countries which cover a range of varying experiences in terms of consumption levels and trends over time. A key advantage of this method is that it relies only on information which is available in existing nationally representative surveys of developing countries.

A composition effect was found in Malawi, Mozambique, Pakistan, and Tanzania but not in Ethiopia and Madagascar. Non-negligible quantity discounting effects were found in Mozambique and Tanzania; a smaller effect was found in Malawi; and no effects were found in Pakistan, Madagascar, and Ethiopia.

In most cases, the estimated effects are lower bounds on the true effect sizes. Nonetheless, the impacts on inequality and on the derived poverty estimates are in some cases substantial. Estimated real Gini coefficients are between −0.6 and 4.0 Gini points higher than nominal Gini coefficients. In some countries (Malawi, Mozambique, Pakistan, Tanzania), real inequality is higher than nominal inequality. Using real inequality indices can also affect inference on the speed of inequality reduction (Malawi, Pakistan, Tanzania). In the most extreme cases, it can change the direction of inequality change so that a decrease in nominal inequality conceals an increase in real inequality (Mozambique). However, in some countries (Ethiopia, Madagascar), real inequality does not appear to be different from nominal.

Finally, the inequality estimates matter for estimating poverty based on national accounts means and an estimate of inequality. In countries where the composition and quantity discounting effects affect the Gini coefficients, the poverty rates are also affected. While the quantity discounting effect potentially affects inequality indices in every year, the composition effect builds up over time as prices diverge. This means that in the countries where later surveys are more heavily influenced by the composition effect, the use of (p.293) nominal inequality indices does not only introduce a source of bias in the level of poverty but may also overestimate the rate of poverty reduction.

The effects are highly country-specific. Why do effect sizes differ from country to country? For the composition effect, this is caused by differences in consumption structures and differences in inflation rates. Inflation rates are affected by a complex interaction of domestic conditions, such as harvests and government policies, as well as international changes in world market prices. Especially for the surveys conducted in the years of the food price crisis of 2007–9, world market prices of basic food items were very high. As new survey rounds become available it will be interesting to see if the composition effect shrinks, or if it is a longer-lasting phenomenon. For the quantity discounting effect, the cross-country differences are likely caused by a mix of real differences in the magnitude of quantity discounting present, and of differences due to varying survey instruments and methodologies.

Since the estimation of the composition and the quantity discounting effects requires only data which is generally available, and since the two effects are easily estimated, I suggest doing so for other countries, and whenever a new survey becomes available, in order to check whether keeping inequality in real terms matters in the country- and time-specific context.

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Notes:

(1) Arndt et al. (2015) also consider spatial differences in price levels. If poorer households are overrepresented in spatial domains with lower price levels, failing to correct for this will overestimate inequality. I do not consider spatial differences in prices in the estimation of the composition effect; instead, a spatial price index is applied throughout where available. Thus, the ‘nominal’ inequality estimates of this study contain spatial price corrections.

(2) Arndt et al. (2015) do not use a Paasche index. This study uses a true Paasche index as its properties are well known. Specifically, if there is substitution towards goods that become relatively cheaper, a Paasche index will underestimate the rate of inflation. This means that inflation estimates reported here are a lower bound on the true inflation rates in the presence of substitution. The Paasche index is written in share expenditure form to ease estimation.

(3) The index is subsequently normalized to have a mean of one.

(4) Pinkovskiy and Sala-i-Martin (2014) adjust estimates of consumption inequality to make them comparable with other surveys based on income. For the sake of simplicity, and since only consumption-based surveys are used in this study, I do not make an adjustment here.

(5) The Madagascar surveys and Ethiopia in 2000 and 2005 are exceptions where no such indices are used since those surveys were collected over a relatively short period of time, i.e. over a couple of months.

(6) For additional discussion of this finding, see the working paper version of this chapter.

(7) See the working paper version of this chapter for detailed results.