an engel curve for variety: household food consumption and welfare

An Engel Curve for Variety: Household foodconsumption and welfare in India

Nicholas Li∗

U.C. Berkeley

November 9, 2009 – Version 0.3Preliminary - Do Not Cite

Abstract

What are the welfare gains to Indian households from consuming an in-creasingly diverse basket of goods over the last two decades? How muchbetter off are urban households compared to rural households that consumemore monotonous diets? How important are income effects in explainingchanges in the range of goods consumed by households? To answer thesequestions I develop a new framework for comparing living standards acrossspace and time. I modify a standard representative agent CES framework toinclude fixed costs, generating positive income-variety correlation or “EngelCurve for Variety.” Using data from India’s National Sample Survey overthe 1983-2005 period, I estimate the parameters of the model and calculatewelfare gains due to greater food variety. In comparison to a standard cost-of-living index, accounting for variety makes urban households 2% betteroff than rural households and makes the average household 3.5% better offin 2005 than in 1983.

∗I am grateful to Pierre-Olivier Gourinchas, Chang-Tai Hsieh, and Ted Miguel for many valu-able discussions and to participants of the Berkeley Macro and Development lunches. I grate-fully acknowledge financial support from the Social Sciences and Humanities Research Councilof Canada and the Institute for Business and Economics Research at UC Berkeley. All errors aremy own. Comments welcome. [email protected]

http://works.bepress.com/nicholas_li/

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1. Introduction

What are the welfare gains to Indian households from consuming a more di-verse basket of goods over the last 25 years? How much better off are urbanhouseholds compared to rural households that consume more monotonous di-ets? How important are income effects in explaining differences in the range ofgoods consumed by households? These questions lie at the center of attempts tomeasure consumer welfare, growth and inequality.

While comparing nominal household incomes and expenditures is a straight-forward exercise, measuring and aggregating prices in order to construct a cost-of-living index that captures “real” income and expenditures is not. Goods thatappear similar - such as rice or wheat - may vary in terms of quality and othercharacteristics. When households do not consume identical sets of goods, asis usually the case when we go beyond the representative household abstrac-tion and examine consumption survey data, one is forced to exclude the relativeprices of non-overlapping goods from the cost-of-living index. In most analysisof cost-of-living across space and time, goods that are non-overlapping are sim-ply dropped from the analysis. The effect of quality and variety differences onthe cost-of-living are complicated by the fact that variety and quality are not ex-ogenous and vary with income. How, then, can we think about large differencesin the variety of foods consumed by the typical Indian household across spaceand time?

I address this question through several contributions. First, I develop a modelof consumer behavior to analyze consumption patterns at the household leveland capture the relationship between income and variety consumption. Themodel is motivated by some facts about Indian consumption patterns and in-troduces the concept of a variety Engel curve. Second, I estimate the parametersof the model using data from the Indian National Sample Survey and use it to es-timate changes in welfare over time and space arising from differences in varietyconsumption.

Specifically, I propose an otherwise standard model of Constant Elasticity ofSubstitution (CES) preferences that incorporates a fixed cost to consuming eachgood. The presence of a fixed cost counteracts the normal implication of CES

AN ENGEL CURVE FOR VARIETY 3

preferences, which is that each household consumes every good available due todiminishing marginal utility for each good. Instead, households consume a finiteset of goods that increases with income. This result is achieved without needingto assume an infinite reservation price. The overall consumption pattern gener-ated can be described as hierarchical or pyramidal, in the sense that consumersbegin to consume marginal goods as their income increases but simultaneouslyincrease consumption of infra-marginal goods(i.e. the base of the pyramid getslarger as it gets taller). The log-linear Engel curve for expenditure and varietyprovides a good approximation to the patterns observed in the data, as does thehierarchical/pyramidal relationship of marginal and infra-marginal goods. Themodel thus provides a tractable approach to analyzing welfare that is consistentwith a broad set of stylized facts.

Under a set of assumptions about unobserved heterogeneity in tastes, I esti-mate the main parameters of the model: the variety Engel curve slope, the changein the ratio of expenditures on inframarginal versus marginal goods as the num-ber of varieties increases, and the elasticity of substitution between varieties. Iuse these parameter estimates to show how changes in variety consumption inIndia affect the cost-of-living index and hence measurement of household wel-fare. By controlling for income effects explicitly, my approach avoids confound-ing endogenous changes in variety consumption due to income differences withexogenous changes in variety consumption due to different market conditions. Italso makes it possible to compare the cost-of-living indexes that result from dif-ferent assumptions - with and without controls for variety effects, and with andwithout controls for income effects.

The paper reports two main sets of results from the food cost-of-living in-dexes. First, accounting for greater urban variety lowers the food cost-of-livingfor urban households by about 2% relative to rural households. Second, account-ing for variety growth over time lowers the All India food cost-of-living index byabout 3.5% over the 1983-2005 period, concentrated mainly in the period since1988. I discuss the implications of these results for measurement of consumptiongrowth and inequality.

I probe the robustness of the results in three ways. First, I use an alternate ag-gregation scheme based on ten groups of goods rather than four. Second, I allow

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some of the parameters to vary by state and sector, which reduces the medianwelfare effect from variety slightly but does not eliminate it. Third, I providesome evidence that tastes alone cannot account for the variety differences by ex-amining district level proxies for market access and data on immigrants. I alsoexamine a range of parameter estimates to show how the welfare gains are drivenby assumptions about substitutibility between varieties.

This paper is related to a growing literature that uses economic theory to im-prove measurement of cost-of-living indexes over time. The literature on varietyhas typically used homothetic preferences and a representative agent framework.The seminal paper by Feenstra (1994) shows how a CES cost-of-living index canbe adjusted to take account of non-consumption of certain varieties in some pe-riods by using data on quantities and prices and by estimating the elasticity ofsubstitution. Broda and Weinstein (2006, 2007) implement this framework usingAmerican data on imports and household scanner data and find significant wel-fare gains due to increases in import variety and the appearance of new goods.Unlike these papers, my paper relaxes the representative agent framework. Thishas two main effects: (1)income effects matter and failing to account for themoverstates the welfare effects of variety growth over time, and (2)household be-havior is conceptually distinct from aggregate behavior and large changes in theconsumption patterns of the typical household do not show up when they areaggregated.

The paper is also closely related to a series of recent papers that use cross-sectional Engel curves to compute bias in cost-of-living indexes like the CPI.Costa (2001) and Hamilton (2001) use shifts in the intercept of food Engel curvesin an Almost Ideal Demand System to argue that CPI bias leads to an over-statement of inflation over time. A fall in the food share over time for a given(mismeasured) level of real income implies that the denominator of real income(the cost-of-living index) is biased upwards. Bils and Klenow (2001) use cross-sectional unit value Engel curves to calculate the extent of quality bias for durablegoods. They show that prices rise more rapidly for goods that have steepercross-sectional ‘quality’ Engel curves and estimate that two-thirds of the qual-ity growth for these goods shows up mistakenly as inflation. Unlike Costa andHamilton, my paper directly analyzes one particular bias in the cost-of-living


index and is not subject to the criticism that relative food/non-food prices aremismeasured or that food requirements have fallen for reasons unrelated to realincome growth. Unlike Bils and Klenow, my paper examines variety and notquality, and uses information on quantities to build a direct theoretical link to thecost-of-living index rather than a reduced form estimate of inflation bias. Unlikeall of the papers cited above, my paper also analyzes cross-sectional variation incost-of-living, which is an important extension of techniques that have mostlybeen developed to analyze changes over time.

I focus on India both because there is high quality consumption data at thehousehold level and because the increase in food variety consumption in Indiahas been particularly dramatic. While food expenditures in real terms have beenstagnant Indian households consume a much more diverse basket of food todaythan they did a few decades ago. There are also large differences between urbanand rural households that may be unique to India’s relatively undeveloped retailsector and often poor rural infrastructure. Some researchers have focused on thenegative caloric implications of greater food variety, which usually comes at thecost of lower consumption of the cheapest staples. This makes it important toconsider the other side of the equation - gains to consumer welfare that coincidewith decreased calorie consumption and greater variety. As food is such a largepart of household expenditures in India and India is such a large and poor coun-try, small changes in a cost-of-living index for food have major implications formeasurement of consumption growth, regional inequality, and poverty.

Section 2 describes the Indian National Sample Survey data and documents aset of stylized facts that present challenges for existing approaches that measurethe effect of variety on the cost-of-living. Section 3 presents the model motivatedby those facts. Section 4 describes the empirical issues associated with parameterestimation. Section 5 presents the main results for cost-of-living index over timeand across urban and rural areas and discusses some implications for measure-ment of growth and inequality. Section 6 presents robustness checks along witha discussion of the nature of the fixed costs and Section 7 concludes.

2. Data and stylized facts

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2.1. National Sample Survey

India’s National Sample Survey (NSS) collects household expenditure data us-ing a 30-day recall based survey. The number of households surveyed varies byround, but the “thick” survey rounds used in this paper - 38th (1983), 43rd (1987-88), 50th (1993-1994), 55th (1999-2000), and 61st (2004-2005) collect data for over100,000 households. The survey is meant to be representative at the state/sectorlevel, though over time the sampling scheme and weights have been adjusted tooversample (and down-weight) wealthier households. The number of differentgoods varies over the years as the National Sample Survey Organization (NSSO)adds new goods to its list or combines goods into a single category. The level ofdetail varies across consumption categories. For example, there is a single cat-egory for “chair, stool, bench, table” but 13 different kinds of pulses and pulseproducts.

The level of detail is much greater for food. The survey records quantitydata for most of the goods in the food, intoxicants, fuel and light, clothing andfootwear categories. The survey is designed to measure consumption, not expen-ditures, so home-produced goods and gifts have their prices imputed at ex-farmand local retail prices respectively. The ability to calculate unit values, definedas expenditure divided by quantity, is an important aspect of the survey - goodswith unit values make up from 67% to 83% of total expenditures over the 1983-2005 period. This enables the construction of price indexes for comparing pricesacross space and time. As food makes up 48% to 65% of the average budgetshare over this period, the relationship between food prices and the overall cost-of-living is likely to be quite tight, especially for poor households. Deaton (2008),Deaton and Kozel (2005), and Deaton and Tarozzi (2005) all use NSS data to ad-vance our understanding of growth and poverty in India by using unit valuesand aggregate expenditure shares to construct price indexes. Deaton and Dreze(2008) have also used the food quantity data to examine the puzzle of decliningcalories and slowly improving nutritional indicators during a period of relativelyrapid expenditure growth in India.


2.2. Variety growth

An aspect of the NSS data that has received little attention is the dramatic in-crease in the number of different goods consumed by households, what I call theincrease in consumption variety. Table 1 presents the total number of goods in thesurvey and the number of goods consumed by the survey-weighted ‘average In-dian household’ in a number of categories over time. I restrict the analysis to the17 biggest states and New Delhi and define good categories to be consistent overtime, which means collapsing several goods into a single good when necessary. 1

Consistency across rounds also requires special treatment of the 55th surveyround, which used a different methodology. Instead of the 30 day recall period ofother surveys the 55th round included a 7 and a 30 day recall period for food con-sumption. Numerous researchers have argued that this biased food consumptionestimates upwards, which resulted in the 61st survey round returning to a single30 day recall period (see Deaton and Kozel (2005) for an overview). As a result Ionly use data for the 55th round when total expenditure and total food expendi-ture are not being compared over time. I assume that consumption variety is stillwell-measured, and that relative consumption of different foods is not distortedby this change in methodology, but omitting this round does little to affect theresults.

Table 1 shows that there has been a large increase in the average number of va-rieties consumed by Indian households. The increase is particularly large in thefood, durables and miscellaneous categories, while there has been little changeor even a slight decline in the fuel and light and the intoxicants categories. Table2 shows that there is also a sizeable gap between urban2 In fact, rural households

1There are a number of “other” categories as well. I consider positive consumption in an“other” category as a single good. There may be increases or decreases in the number of differentgoods consumed in the other category that are not captured in the data. Similarly, there may bedifferent varieties for many of the goods in the survey, like chicken, bread and rice that are notcaptured by the survey.

2The NSS surveys follow the Indian census in defining urban areas as follows: (a) All statutoryplaces with a municipality, corporation, cantonment board or notified town area committee, etc.(b) A place satisfying the following three criteria simultaneously: i) a minimum population of5,000; ii) at least 75 per cent of male working population engaged in non-agricultural pursuits;and iii) a density of population of at least 400 per sq. km. (1,000 per sq. mile). For identification ofplaces which would qualify to be classified as ’urban’ all villages, which, as per the 1991 Censushad a population of 4,000 and above, a population density of 400 persons per sq. km. and

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seem to behave like urban households but with a lag - the consumption pat-terns of a rural household one period later look very similar to the consumptionpatterns of an urban household in the previous period. and rural households,particularly for food and miscellaneous, with urban households consuming awider range of goods. Perhaps not surprisingly, there are also large differencesin the expenditures of the average Indian household over time and between sec-tors that are positively correlated with the variety of goods consumed. Table 3presents evidence that nominal and real expenditures have been increasing overtime. I use both the official consumer price index and a price index that uses theunit values from the survey. The unit-value index only covers goods that about75% of household expenditures so is incomplete, but it has numerous advantagesover the official price index as well (see Deaton and Tarozzi (2005) for a discus-sion). When using the unit-value indexes I use a separate food index for foodexpenditures and use the more comprehensive index for all other goods. Usingthe official Indian CPI to deflate nominal expenditures leads to much smallergrowth in expenditures over time and even a decline in food expenditures, whileusing the survey based price index leads to much larger increases in real expen-ditures and roughly constant real food expenditures. Table 4 uses sectoral priceindexes calculated using unit values from the survey. Urban areas have higheraverage nominal and real expenditures than rural areas, for food and all goods.

2.3. Engel curve for variety

Taken together, the evidence in Tables 1 through 4 indicate that there is a positivecorrelation over time and space between the level of expenditures and the num-ber of distinct goods consumed. What is the nature of the relationship betweenthem? Figure 1 presents non-parametric locally-weighted regressions of the rela-tionship between log expenditures (deflated using the CPI) and the log numberof goods consumed for four survey rounds. Figure 2 repeats Figure 1 but onlyexamines food variety and food expenditures (deflated using median survey unitvalues). I use only households with five members to control for one major source

having at least 75 per cent of male working population engaged in non-agricultural activity wereconsidered. To work out the proportion of male working population referred to above againstb)(ii), the data relating to main workers were taken into account.


of household heterogeneity. This empirical relationship has conceptual similar-ities with the Engel curves traditionally analyzed by consumer theory, such asa non-unitary income elasticity/non-homothetic preferences. I call this relation-ship an Engel curve for variety.3 Several features of the variety Engel curvesare immediately apparent. First, the expenditure elasticity of variety is less thanone. If there is a positive expenditure elasticity for quantity and/or quality withrespect to total expenditures, we would generally expect a less than unitary elas-ticity for variety. Second, the relationship is quite linear over a large range ofexpenditures. The relationship is concave at higher expenditure levels, but thelinearity over a large range of expenditures will inform the theory presented inthe next section and facilitate the empirics. Third, there has been a marked shiftupwards of the variety Engel curve over time. At a given level of real expen-diture, Indian households are consuming about 40% greater variety of goods in2005 than they were in 1983, and 25% more food goods.

The Engel curve for variety is seen again in Figures 3 and 4, only here I onceagain plot rural and urban differences for 1983 and 2004-2005 and use a survey-based urban-rural price index to deflate urban expenditures. Urban householdswith an equivalent level of real expenditure in 1983 consume about 10% morevarieties and 15% more food varieties. For both food and non-food we see theurban-rural gap narrowing over time. These Engel curves exhibit less linearity,especially at the upper end of the expenditure distribution. It appears that theurban-rural variety gap is increasing in total expenditures, and that the gap hasdiminished slightly over time.4

Figures 1 through 4 reveal that part of the increase in variety over time shownin Tables 1 and 2 can be attributed to the rise in real expenditures observed in Ta-bles 3 and 4. However, much of the difference remains unexplained by increasingexpenditures. A model consistent with this data therefore requires a positive ex-penditure elasticity of variety in addition to some other variety demand shifter.

3Bils and Klenow (2001) study what they call quality Engel curves that capture the cross-sectional relationship between household expenditures and unit values for consumer durables.

4Though I ignore this for the main results and use a linear approximation, I plan to study rural-urban gaps at different percentiles of the expenditure distribution to account for this difference,relying on local linearity rather than the stronger global linearity assumed below.

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2.4. Consumption hierarchy

Another important characteristic of the data is the hierarchical ordering of vari-eties. Demand for the different varieties is asymmetric, with just a few varietiesaccounting for a majority of expenditures. These varieties make up a large shareof aggregate expenditures in part because of high consumption along the exten-sive margin of consumers - a larger share of households have positive consump-tion. They also tend to be more important along the intensive margin of con-sumers - conditional on positive consumption, these varieties have larger budgetshares. In other words, there is a positive correlation across varieties between theprobability of positive consumption and the individual budget share (or expen-diture) conditional on positive consumption. Figures 5 and 6 show scatter plotsof this relationship (including a regression line and 95% confidence band) for afour and a ten group classification. The four group classification is (1)grains andpulses, (2)meat, milk and oil, (3)fruits and vegetables, (4)spices, beverages andprocessed foods. The ten group classification uses the ten individual groups.Theten group classification also happens to coincide with the survey group headings,though I lump sugar and salt with other spices and combine fruit with dry fruitand nuts.

For some groups the relationship is very strong, while for others it is weaker.This results from the presence of some goods, like salt, that are consumed bymost households but in small quantities, as well as from large regional variationsin consumption for some commodities, or certain meats, which are consumed byrelatively few Indian households (many of which are vegetarian) for whom theyare important. For example, in the 2004-05 survey Jowar (sorghum) is an impor-tant staple in the states of Maharashtra and Karnataka where it is consumed by40% and 45% of sample households (and in large quantities), but it is consumedby less than 1% of households in 13 other states. Different states also have partic-ular oils that are the main staple for cooking (coconut oil in the south, mustard oilin the north). Regional taste heterogeneity is an important aspect of the data thatmakes comparisons across regions difficult. Consequently this paper examinesurban-rural gaps within states and changes over time in particular states, sectorsand regions but does not attempt an interregional comparison. When disaggre-gating by region, the general hierarchical pattern of variety consumption - that


varieties consumed by more households are consumed in greater quantities bythose households compared to other varities - is only strengthened.

This hierarchical pattern of consumption holds across the expenditure distri-bution as well. Figures 7 and 8 show that the fraction of households with positiveconsumption and the mean expenditure conditional on consumption are increas-ing in expenditure for most varieties in the grains and pulses group. As we sawwith the Engel curves, richer households consume more varieties (they are morelikely to consume each particular variety) but they also consume more on the in-tensive (quantity) margin. Some of the higher expenditures by rich householdsmay arise from quality upgrading, as these households tend to pay more perunit. However, quantity unambiguously increases in expenditure as well. Asdiscussed by Deaton and Dreze (2008), this results in positively sloped calorieEngel curves. The goods on the X-axis in Figures 7 through 8 are ordered interms of aggregate expenditure shares, and the figures make it clear that an ag-gregate expenditure share based ordering has a much tighter correspondence tothe extensive margin (share of consuming households) than to the intensive mar-gin (mean expenditures conditional on consumption).

2.5. Limitations of CES and other frameworks

The preceding stylized facts about the Engel curve for variety and the consump-tion hierarchy are perhaps not very surprising, but they present several chal-lenges to existing approaches to modeling consumer behavior in the literature.The standard CES approach to modeling variety consumption does not feature apositive expenditure elasticity of variety consumption or a relationship betweenthe probability that a variety is consumed and its conditional expenditure share.In a standard new trade model with fixed exporting costs, there will be a correla-tion between market size and the number of varieties imported, but income percapita is not relevant and it is difficult to relate these models to a within-countryenvironment where households in the same village or block consume very dif-ferent sets of varieties.

Flexible demand systems like the translog and Almost Ideal Demand Sys-tems typically abstract from zero consumption at the household level by either

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(a)aggregating across households, (b)dropping and/or aggregating individualvarieties to ensure positive consumption for all households, or (c)ignoring theproblem of zero consumption altogether and simply estimating conditional de-mand functions. These flexible approaches can easily deal with non-homotheticity,but generally feature a number of parameters that that rises very rapidly in thenumber of different goods, exhibit complicated aggregation properties, and havetrouble dealing with the combination of continuous quantity choice and discretevariety choice. These models could only explain a dramatic increase in varietythrough a large change in the price distribution interacting with income-varyingreservation prices, and the complexity of the resulting demand system for a largenumber of goods is overwhelming.5

While there is some potential for using a discrete choice framework this is im-practical given the extremely large combination of different variety and quantitycombinations that are observed. Discrete choice models that do not feature anintensive margin or non-homotheticity would have trouble modeling the factsthe above. There is no simple pattern of substitution from lower quality varieties(tapioca, jackfruit seed) to higher quality varieties (rice, wheat). 6

To get a sense of the limitations of the CES framework for explaining house-hold variety consumption and demand patterns in India, I apply the cost-of-living index based on CES preferences and non-identical sets of goods developedby Feenstra (1994) and used by Broda and Weinstein (2006,2007) to analyze con-sumer gains from trade and new products. Feenstra (1994) showed that a CESexpenditure function with non-overlapping varieties can be broken down intotwo components - a price index similar to a conventional price index like a Fisheror a Tornqvist index (the Sato-Vartia ideal log change index is exact for CES pref-erences) and a variety index reflecting welfare effects of non-overlapping variety,which is based on the theoretical properties of the CES price index when the

5Feenstra (2009) estimates a homothetic translog expenditure function with non-overlappingvarieties and finite reservation prices, but is forced to impose symmetry on the elasticities ofdifferent varieties and does not consider non-homothetic demand.

6Even the non-homothetic logit model developed by Allenby, Garratt and Rossi (2008) haslimitations in this context. Their model allows for non-homotheticity in a logit demand systemthrough trade-up. Higher quality goods have a higher elasticity of substitution due to incomeeffects. But their model does not feature an additional intensive margin or allow for the simulta-neous consumption of low and high quality varieties.


reservation price of non-consumed varieties goes to infinite.I construct all indexes using the richest household in each urban block and ru-

ral village as the base and use expenditures and variety for the four food groupsconsidered earlier. Figure 9 shows the relationship between the log of food ex-penditures and the logs of (a)the unit value index, (b)the variety index devel-oped by Feenstra, and (c)the cost-of-living based on the CES expenditure func-tion with non-overlapping varieties, which is simply the product of (a) and (b).I use village and urban block fixed effects, so the slope of the different quadraticregression functions can be interpreted as the average elasticity of the index withrespect to expenditures within a narrow geographic area. Figure 9 shows thatricher households pay higher prices within a particular village or urban block.This could be a result of unmeasured quality differences - richer households payhigher unit values because the varieties in the survey (like rice or wheat) are het-erogeneous with respect to quality. It could also be the result of discounts givento poor households through the Public Distribution System and more intensivebargain-hunting by poor households. The result that unit values vary with totalexpenditures within a village or urban block is thus ambiguous in terms of its im-plications for of cost-of-living of living differences and “real inequality” withinvillages.

There is also a large positive welfare effect on richer households due to greatervariety consumption, even within villages and urban blocks. Figure 9 uses threeseparate values for the elasticity of substitution - two, five and ten - that showthe sensitivity of variety-based welfare effects to this parameter. The welfare ef-fect is massive using the low elasticity of substitution of two, with an elasticity ofcost-of-living to expenditure of about -.52 which implies that a given nominal ex-penditure differences only results in half as big a “real” difference. Higher valuesfor the elasticity of substitution of five and ten result in more modest elasticitiesof -0.065 and -0.027. The size of these effects is non-trivial. Households livingin the same area presumably have access to the same set of local retailers, yetrich households consume significantly more varieties. The Feenstra approach as-cribes the entire difference in variety consumption between poor and rich house-holds in the same village to exogenous factors. In effect, the poor are assumedto face an infinitely high price for these goods (an infinite reservation price is

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required for non-consumption in a homothetic CES demand system) while richhouseholds that consume the good face a finite price. If retailers had to pay afixed cost to sell to households (analogous to exporting firms selling to anothercountry in the new trade literature) and households could not seek out addi-tional varieties themselves this would be the correct way to measure welfare.But this aspect of Feenstra’s approach is unappealing in this case, as commonsense suggests that rich and poor households face a similar retail environmentand a similar cost to consuming additional varieties.

It is households themselves that go to seek out varieties for consumption, andthey have access to a nearly unlimited number of varieties provided they arewilling to search long enough and travel far enough. If households in the samearea face identical costs to purchasing marginal varieties, the CES approach tomodeling variety would lead to an overstatement of the relative welfare of rich topoor households and a widening of intra-village inequality. The effects of vari-ety growth on consumer welfare over time would also be overstated if there issimultaneous growth in expenditures. Finally, the effect of urban-rural varietydifferences on consumer welfare would be overstated given the higher real in-comes in urban areas. The Engel curve for variety is thus an important factor toconsider when thinking about intra-area differences (is nominal expenditure in-equality sufficient for measuring welfare inequality?) and across-area and perioddifferences (how much of the variety differences are endogenous or exogenouswith respect to expenditure growth?).

The other main issue raised by the CES approach and many other approachesto modeling variety growth is aggregation. When variety consumption is mea-sured by constructing an aggregate set for households in a particular area, dif-ferences in variety and the resulting differences in welfare implied by theory arehighly sensitive to the size of the areas used. Table 5 provides evidence on thenumber of goods with positive consumption by any household at different levelsof aggregation. At the national level in India, there is positive consumption of allthe varieties that are listed in the National Sample Survey. Any differences in theset of varieties consumed over time is a direct result of changes in the definitionsof the goods or the addition of new goods. Even at the state level, there is positiveconsumption of almost all of the goods in the survey. However, when we look at


a more disaggregated level, the number of varieties with positive consumptionfalls dramatically and the size of variety gaps widens. While the state at the 10thpercentile of the variety distribution consumes 94% of the varieties consumedin the state at the 90th percentile, the equivalent gap for districts is 73% and forvillages/urban blocks it is 56%.

Aggregation across households at any level of geography can thus mask largedifferences in the variety consumption of the typical household, and the mea-sured level of variety will be negatively correlated with the number of aggre-gated households and the level of geographic aggregation used. The “represen-tative” household in the economy behaves nothing like the “average” or “me-dian” household when it comes to variety consumption. Given the large increasein household-level variety consumption and the stable set of varieties consumedat a more aggregated level, the CES approach to modeling would lead to an un-derstatement of variety differences and their effects on welfare. The main reasonthis issue has been ignored in previous work is that the focus has been on “new”varieties arising due to importation or invention and on measuring variety dif-ferences over time. While aggregation across households in this case will obscurepotentially heterogeneous impacts of new varieties, it does not obscure the mea-surement of new varieties. When examining the trends in India - rising house-hold consumption of a stable set of existing varieties - a count-based measure ofvariety at the household level has some advantages over a set-based measure atan aggregate level.

3. Model

Motivated by the facts presented in the last section, I develop a model of con-sumption hierarchy with non-homothetic demand for variety. The model is anasymmetric CES demand function with a continuum of goods extended to in-clude a fixed utility cost of consuming each variety. The fixed costs generate theincome elastic demand for variety, while the asymmetry of prices and preferencesacross goods generates the hierarchy. The model is then extended to include mul-tiple goods each featuring a continuum of varieties.

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3.1. Discussion

Consider a household that consumes multiple goods but receives diminishingmarginal utility from consuming greater quantities of the same good. This ideais the building block of Dixit-Stiglitz or Constant Elasticity of Substitution (CES)preferences but also most preferences studied in economics. The household wouldconsume as many varieties as possible in small amounts unless there was boundedmarginal utility or some friction that created a cost to consuming additional va-rieties. Bounded marginal utility ensures limited variety consumption becausea marginal variety will only be consumed when the marginal utility of existingvarieties is driven down to the upper bound for the marginal variety. Linear de-mand curves are one example of bounded marginal utility and have been usedby Melitz and Ottaviano (2007) to endogenize the number of varieties and the de-gree of competition across markets. Fixed costs for additional varieties are ubiq-uitous on the supply side of CES general equilibrium models, where a fixed costis necessary to limit the number of firms that sell differentiated products. Suchcosts are almost never modeled on the demand side, which implies that the con-sumer (which is typically a representative consumer in these models) consumesall the varieties available through domestic production or trade. One exceptionis Arkolakis (2008) which features an additional fixed cost that firms must pay tosell to each individual consumer. The fixed cost is motivated as marketing andadvertising expenditures and results in a “household” extensive margin for firmsales as well.

In the context of food consumption by Indian households, a fixed consumer-side cost of consuming additional varieties that varies over tiem and space hasseveral desirable properties. First, households in the same time and place fac-ing identical fixed costs could still exhibit different variety consumption due toincome differences. A drawback of modeling variety differences across house-holds through fixed costs paid by firms is that it is difficult to imagine how firmscould target certain richer households while excluding poorer households. Mostforms of marketing, advertising, or even transport costs would likely have a sim-ilar impact on all households in the same area. It is more natural to think of richerhouseholds expending greater effort and expense to seek out and purchase ad-ditional varieties than to think of firms specifically targeting these households.


Second, modeling variety choice due to frictions is more interesting than mod-eling variety choice due to differences in marginal utility bounds, which repre-sent different preferences. The welfare implications of changing preferences areunclear as it is not possible to construct theory-based cost-of-living indexes forhouseholds with different preferences. I later provide some evidence later thatpreferences are unlikely to account for a substantial part of the variety differencesbetween urban and rural areas. I also show that observable district-level proxiesfor market access can explain a substantial share of the geographic variation invariety consumption. However, like any non-experimental study of householdconsumption behavior it is difficult to rule out that differences in observed con-sumption patterns come from unobserved preference heterogeneity, rather thanobservable price, income, demographic and geographic variables.

The fixed costs facing households that seek to consume more varieties repre-sent a combination of

∙ Minimum scale and indivisibility: households may not be able to consumeinfinitesimally small quantities of a good. This is more pertinent to durablegoods and big-ticket items but it could also apply to nondurables, especiallyin poor countries. Without perfect rental/sharing/second-hand markets itis impossible or at least costly to consume 1/2 of a restaurant meal, articleof clothing, egg, car, fridge, etc. In addition to indivisibilities, fixed costshere also have a bulk discounting interpretation as they can lead to averageprice per quantity that declines in quantity. A household might have toconsume too large a quantity of a good to purchase it at an acceptably lowaverage price. Denser retail environments may facilitate consumption ofsmall quantities.

∙ Transport and search costs: households may incur large search and trans-port costs to purchase particular varieties. Discovering which varieties bestmatch their needs and locating them could entail substantial time costs.Transport to and from sellers could require substantial expenditures andconsiderable amounts of time. Better transportation links, dense and com-petitive retail environments, and modern retail formats like supermarketsmay all facilitate variety consumption by reducing these search and trans-

18 NICHOLAS LI

portation costs.

In the model that follows I interpret these fixed costs in terms of utility insteadof expenditure. One reason for this is that many of the relevant expenditures -fuel, transportation services, imputed service flow from transportation durables,imputed service flow from other durables like refrigerators - are either unob-served or separate from expenditures on the good whose expenditure-variety re-lationship is being modeled. Given that the fixed costs are not directly observed,treating the fixed cost as a budgetary rather than a utility cost introduces addi-tional ambiguity in calculation of budget shares, total expenditures, etc. Anotherreason for this is that unless the fixed budgetary cost is scaled appropriately by afunction of local prices and expenditures, the indirect utility function is not HD0 in expenditure and prices and the expenditure function is not HD 1 in prices.78

3.2. Basic model

Consider households that face the following problem:

maxn,qi

(∫ n

0

q�−1�

i di

)− (nF )� (1)

subject to∫ n

0qipidi ≤ X . where n is the number of varieties consumed, qi is the

quantity of variety i consumed, pi is the price of variety i, X is the total expendi-ture of the household, and F is a fixed cost in terms of utils that consumers must

7In a separate appendix I develop the fixed-budget cost version of the model and discuss someof these issues in greater detail. Both models deliver log linear relationships between varietyand expenditures and hierarchical demand, and both depend on similar parameters to measurewelfare gains from variety differences. As a result the quantitative implications of the model forwelfare are very similar.

8Another possible modeling approach would be to replace the fixed costs with an additionalterm in the utility function that maximizes some other objective, like quantity. If householdsmaximize consumption variety and total quantity simultaneously and some varieties are moreexpensive per quantity unit, this will bound variety demand endogenously. A reduction in theweight placed on the quantity part of the utility function would then result in greater variety at agiven level of expenditures, analagous to a decrease in fixed costs in the model. Since the growthin food variety in India has been accompanied by constant real expenditures a decrease in calories(quantity), this approach has some merit. However, the impact of a decreased weight on quantityand a fall in fixed costs are observationally equivalent in terms of their effect on variety choiceand welfare when the first part of the utility function is CES.


pay to consume a unit measure of varieties. The elasticity of substitution param-eter � governs the extent of diminishing returns for each individual variety. The� parameter allows for the fixed cost of variety consumption to be increasing ordecreasing in the number of varieties.

For a given number of varieties n = n, this problem has the familiar CESsolution -

qi =X

pi

(pi

P (n)

)1−�

(2)

where P (n) = (∫ n

0p1−�i di)

11−� is the CES price aggregator.

This allows us to re-write the problem in an unconstrained form that dependsonly on the choice of n:

maxn

(X

P (n)

)− (nF )� (3)

The first order condition for the problem is given by:

XP (n)−2∂P (n)

∂n= �F (nF )�−1 (4)

If the fixed cost was zero, the household would consume an infinite num-ber of varieties or the maximum number of differentiated varieties in existence.As the fixed cost is not zero, the household trades off the marginal utility fromconsuming additional varieties (the left hand side) against the marginal cost (theright hand side). The optimal choice of n is increasing in the level of expendituresbecause richer households consume greater quantities and hence receive lowermarginal utility from inframarginal units. Spreading their expenditure across agreater number of varieties is a way to partially counteract the effect of diminish-ing returns. 9

To solve the model it is necessary to assume a functional form for the distribu-tion of prices facing the household. Consider a simple exponential parametriza-

9Note that in this type of model, arbitrarily restricting the number of varieties that can be con-sumed only hurts households who would consume more varieties in the absence of constraints -the poorest households that consume only a handful of basic varieties derive no benefit from theexistence or non-existence of additional varieties. Given that no households consume all avail-able varieties I do not consider this case, but it may be relevant for some goods in some times andplaces.

20 NICHOLAS LI

tion of the price distribution used in the trade and growth literature:

pi = Ωi1� (5)

Facing this distribution of prices, we can order the varieties from 0 to n from low-est to highest price, with the variety indexed by 0 being consumed in the highestquantity and the variety indexed by n being consumed only in an infinitesimalquantity. As � increases, the dispersion in the prices of the different varieties de-creases and in the limit all varieties have the same price given by Ω. It is straight-forward to introduce a variety specific taste or quality parameter into this model,so that quantities consumed are not solely determined by relative prices but alsoby taste and quality, which I do later in the estimation section.

The above parameterization of prices gives rise to a consumption hierarchy.Households begin by consuming the cheapest and/or most preferred goods. Astheir expenditures increase, they consume those goods in higher quantities butalso begin consuming more expensive goods. Figure 10 provides a visual repre-sentation of the consumption pyramid where the area of the pyramid is equal tototal expenditures. Panel A shows that as total expenditures increase, variety nincreases (the triangle gets taller) but expenditure per variety also increases (thebase of the triangle expands and the area of each inframarginal variety also in-creases). Panel B depicts a downward shift in fixed costs, which preserves totalexpenditures (the total area of the two triangles is the same) but leads to morevariety and less expenditure per variety (represented by the taller pyramid withthe smaller base).

Given the specified distribution of prices, the solution to the household’sproblem is given by:

n =

([X

Ω

]1

F �(� − 1)�

) 1�−

(6)

where = 1�−1− 1

�. Quantity, qi, is then determined according to equation (2).

The elasticity of n with respect to X equal to ��− , and it is greater if the elasticity

of substitution between varieties (�) is lower or if the rate of price increase formarginal varieties (�) is lower.

To match the observed elasticity of variety with respect to expenditures, which


is always between zero and one, we need the following restriction on the param-eters:

�i > ( i + 1) (7)

The expenditure function is then given by:

X(U , �, ,Ω, F ) ≡ ΩF (U) �−

� (� − 1) [( �)

�− − ( �)

��−

]= ΩF Q (8)

where I define Q ≡(U) �−

� (� − 1) [( �)

�− − ( �)

��−

]as the “quantity” index

and ΩF is the “price” index that takes into account the impact of the fixed costson welfare.

The model provides a method of comparing welfare across households andareas. By comparing the “price” term, we can compare the cost of achieving a ref-erence utility level across two different areas or time periods provided the param-eters � and are common. While the demand system is clearly non-homothetic- budget shares for different varieties vary with total expenditures and can beequal to zero - the expenditure function can still be written in the formQ(U)P (Ω, F ),which makes aggregation at higher levels straightforward.

3.3. Multiple groups and varieties

Consider a demand system where utility is additively separable in G groups.Households maximize:

U =G∑g=1

gu�gg (9)

subject to∑G

g=1Xg(ug,Ωg, Fg) ≤ X . Here Xg measures total group expendituresand X measures total expenditures, while ug is the subutility function for group g.Additive separability allows us to analyze the group demand problem separatelyand use two-stage budgeting. By define a quantity index for group g Q = Qg anda price index for group g ΩgF

gg = Pg, we can re-write the problem above as:

maxQ1,...,Qg

G∑g=1

∗gQ�∗gg (10)

22 NICHOLAS LI

subject to∑G

g=1 PgQg ≤ X , where

∗g ≡ g

((�g − 1) g

[( g�g)

g�g− g − ( g�g)

�g�g− g

])− �g�g− g

(11)

and�∗g ≡ �g

�g − g�g

(12)

are functions of parameters from the intergroup problem ( g and �g) and thegroup problem ( g, �g).

These preferences, called direct addilog preferences by Houthakker (1960),are a generalized non-homothetic version of CES preferences. There is no explicitsolution for the group quantity index Qg, which also makes it impossible to solveexplicitly for budget shares. However the demand system does feature relativeEngel curves given by:

(�∗i − 1) lnxi =

(�∗i

∗i

�∗j ∗j

)+ (�∗j − 1) lnxj +

(�∗i�∗j

)lnPi/Pj (13)

Groups with higher values of the parameter �∗g are luxuries with a positiveincome elasticity of budget share, while those with lower values are necessities.Ceteris paribus, groups that feature a higher elasticity of variety with respectto group expenditures will have a higher elasticity of group expenditure withrespect to total expenditures, as will groups with less dispersed prices (high �)and groups with more differentiated varieties (low �). However, the functionalform for utility given in equation 13 allows for a group to have both a low overallincome elasticity and a high within-group variety elasticity.

In addition to allowing a two-stage budgeting procedure, the direct addilogpreference structure also facilitates the construction of an exact quantity index.10

Sato (1972) shows that for the non-homothetic addilog, an exact quantity indexis given by:

lnQ =G∑i=1

�i ln(qi1/qi0) (14)

10Assuming homothetic CES intergroup preferences makes things even easier, as we can usethe ideal-log change price index directly as an exact index.


where �i is the ideal log-change weight given by

�i =wi1−wi0

lnwi1−lnwi0∑Gi=1

wi1−wi0lnwi1−lnwi0

(15)

where wi1 is the budget share of group i in area/period 1 and wi0 is the budgetshare of group i in area/period 0. For a given level of expenditures this also de-fines the implicit price index lnP . One can also use other price indexes like aTornqvist or Fisher index as an approximation, as in practice these usually coin-cide closely with the ideal log-change index. In either case, the advantage of thisfunctional form is clear - one can calculate a welfare based cost-of-living indexwith data on Pg and group budget shares without having to estimate the param-eters of the intergroup demand system.

4. Estimation

Taking the model of the last section to the data requires estimating four key pa-rameters - �, �, � (or equivalently ) and Ω. This allows the recovery of a fifthparameter, the fixed cost F that feeds into the expenditure function ΩF Q. Theapproach I adopt here is to estimate three of the parameters - �, �, � - using re-lationships implied by the model, while using an approximation of the fourthparameter Ω.

These parameters are all estimated at the level of groups, where I treat thedifferent goods within a group as CES varieties. The baseline estimation con-siders four groups - (1) grains and pulses, (2)dairy, meat, and oil, (3)vegetablesand fruits, (4)spices (including sugar and salt), beverages and processed food.These groupings are inevitably arbitrary, although I follow the order of goods asthey are presented in the survey and the first group includes the most basic sta-ples and sources of carbohydrates in the Indian diet, the second group includesthe main sources fats, and the fourth group includes mainly goods with limitednutritional value that contribute taste and flavor to meals.

In the robustness section I also consider a more disaggregated grouping thatbreaks these groups into ten subgroups that follow the survey headings even

24 NICHOLAS LI

more closely. Larger group sizes present goods that are less likely to be closesubstitutes, violating the CES assumption of the model, but smaller group sizeslead to more consumption zeros and less variation in variety consumption.This isimportant because I do not allow for non-consumption of an entire group. At theten group level there are often many households with zero consumption withina group, while this almost never occurs for the four group level.

After estimating parameters for the individual groups, the overall food priceindex can be calculated by aggregating the groups, using the ideal log changeindex from the last section or another index formula. Throughout this section Ipool all households across the 38th, 43rd, 50th, 55th and 61st NSS rounds exceptwhere otherwise noted. Two issues that potentially affect all of the parameterestimates are non-linearities and parameter heterogeneity. I deal with parame-ter heterogeneity by considering Indian states separately and also examining thestability of these parameters over time. In future work I will address the non-linearities using subsamples of the population grouped by income, which onlyassumes approximate local linearity.

4.1. Variety choice

The key equation summarizing variety choice can be derived by taking logs ofequation (6), the optimal number of varieties:

lnngℎt = [(�g − 1)�g]1

g−�g +1

�g − glnXgℎt−

1

�g − gln Ωgℎt−

�g�g − g

lnFgℎt (16)

where h indexes households, g is a grouping of varieties, and t is an index ofarea or period shared by some households. The slope coefficient on log groupexpenditure is the slope of the variety Engel curve. The model indicates that weneed to control for the price level Ωgt and the level of fixed costs Fgℎt to accuratelyestimate the theoretical slope coefficient. The Engel curves estimated in Figures1 through 4 are illustrative but they potentially confound the effect of householdexpenditures with differences in prices and fixed costs that are correlated withexpenditures. Households that are richer on average may live in more expensiveareas or in areas with greater retail density that feature lower fixed costs.


Assuming that the level of prices and fixed costs is the same for householdsliving in the same village or urban block, we can get an unbiased estimate of theEngel curve slope 1

�g− g by using village and urban block dummies, using intra-village and intra-block variation in expenditures for identification. In practiceone could also use dummies for larger areas, depending on whether one is will-ing to believe the assumption that prices and fixed costs are similar throughoutthe area. If all households in the same area face the same set of prices there is noneed to include Ωgt in the regression when using area dummies.

Table 6 provides estimates of 1�g− g for each the four groups. Column one

presents the results without any geographic controls, column two uses state/sectordummies, and column three uses village/urban block dummies. It turns outthat geographic controls do not make much difference except for the first group,where the increase in slope implies that higher expenditure households tend tolive in areas with higher prices or fixed costs for consuming grains and pulses.Group 2 (which has the least number of total varieties) and group 3 (which hasthe most) have the highest elasticity of variety with respect to expenditure.

Even with geographic controls there is potential endogeneity and omittedvariable bias. When estimating equation (16) there is an error term that combinesall the unobserved preference heterogeneity, household heterogeneity, and mea-surement error that affect variety choice and group expenditure. I try to addressthis issue using a large set of household controls and instrumental variables. Thefourth column of Table 6 provides estimates of 1

�g− g using village/block fixedeffects and a number of household controls that might be correlated with ex-penditures and variety demand - dummies for household sizes 1 through 13,household type (defined by the NSS to identify households involved in agricul-tural wage labor, farming, casual labor, and non-agricultural enterprises), mo-torized vehicle ownership, religion, and schedule caste/tribe. Where possible Ialso include a dummy for use of the Public Distribution System which providessubsidized goods at below market costs to lower income households (thereby in-validating the constant price within-village assumption). However this data ismissing for some of the survey rounds. The use of household controls changesthe estimated coefficients slightly but not by much and the ranking across groupsis preserved. The notable exception is for group 4, where the the coefficient falls

26 NICHOLAS LI

by 33%. Note that given the sample sizes (five rounds and about 100,000 house-holds per round) these coefficients are always estimated precisely with minisculestandard errors, so we can typically reject equality of coefficients that differ by0.01 at the 95% level.

There are few good instruments for group expenditures in a non-experimentalsetting. Many of the likely candidates - total expenditures, income, land owner-ship - have major drawbacks. Only one of the NSS rounds is liked to an employ-ment survey that records income, and this is only useful for a subset of (mostlyurban) families. Land data is available for all of the survey rounds but may becorrelated with other determinants of variety consumption and excludes urbanhouseholds and non-agricultural rural households.

Total expenditure is available for all households but suffers from potential en-dogeneity of its own. However, total expenditures will reduce bias from one par-ticular type of endogeneity. As the extension of the model to multiple groups sug-gests, the group cost-of-living index ΩgF

gg will affect the intergroup allocation of

expenditures. As such, unobserved differences in Ωg or Fg across households -perhaps due to preference shocks or some omitted variable - will be correlatedwith group expenditures through the budget allocation mechanism. Using totalexpenditures or land ownership as instruments for group expenditures can elim-inate this particular bias unless they too are correlated with group level shocksto Ωg or Fg.

Columns five and six of Table 6 provide the IV estimates for total expendituresand land, with household controls and area dummies still included. Note that Iuse log(land) as an instrument and hence drop many households that own noland, but this greatly increases the relevance of the instrument. The instrumentsare very relevant - for example, the first group features a t-stat of 413 for totalexpenditure and 67 for land. The IV estimated Engel curves for groups two andthree are not very different, but the slopes for groups one and four double. Thissuggests that bias operating through the intergroup allocation (the allocation oftotal expenditures into group expenditures) could be quite large for these groups.


4.2. Variety hierarchy

The key equation summarizing the slope of the variety hierarchy is equation (2).To fit the data, it is necessary to include differences in quality/taste for the differ-ent varieties. This is because varieties within a group are sometimes measuredusing different quantity units and because some varieties may be preferred orof higher quality. Quality and preference are isomorphic in this model, in thatboth manifest themselves in a willingness by households to spend more on somevarieties than others even if they have the same price. The aggregate varietyhierarchy - the ordering of varieties by aggregate expenditure shares - thus rep-resents a combination of price, taste, and quality attributes of the varieties. Con-sider a slight modification of the household’s direct utility function to include ataste/quality parameter, as is standard with asymmetric CES preferences:

maxn,qi

(∫ n

0

d1�i q

�−1�

i di

)− (nF )� (17)

subject to∫ n

0qipidi ≤ X where di is the taste/quality parameter. The demand

function in share form becomes:

si = di

(pi

P (n)

)1−�

(18)

Let pi = Ωi1�1 and parameterize the distribution of di by

di = zii1−��2 (19)

where ln zi is distributed normally with mean zero. Defining 1�≡ �1+�2

�1�2, we have

the original model except that now the ordering of goods from 0 through n isbased on a combination of price and preference/quality parameters.

Aggregate expenditure shares are still informative about the importance ofmarginal varieties, but depending on the variance of zi the correspondence of theaggregate hierarchy to an individual’s hierarchy could be considerably weaker.To deal with this I adopt two different approaches - one based on a low vari-ance of zi and aggregation, and the other based on a high variance of zi usinghousehold-level data.

28 NICHOLAS LI

First consider the extreme case where the variance of the idiosyncratic taste/qualityshock goes to zero, i.e. zi = z. All households rank goods from lowest to high-est index number (corresponding to highest to lowest budget share) in the sameorder as the aggregate expenditure shares. An expression for the cumulativebudget share of the first k goods is given by:

sℎ(k) ≡∫ k

0qipidi∫ n

0qipidi

=

(k

nℎ

) (�−1)

(20)

with sℎ(k) = 1 for k > nℎ. Note that the share of the first k goods dependson the household’s choice of variety nℎ and hence indirectly on the household’sexpenditures.

We can re-write this expression using the solution for nℎ as a function of ex-penditures as:

s(k)ℎ = k (�−1)E− (�−1)y− (�−1)

�− ℎ ifnℎ > k, 1 if nℎ ≤ k (21)

where E ≡([

1Ω

]1

F �(�−1)�

) 1�−

. If Ω and F are constant, only yℎ varies acrosshouseholds and affects s(k)ℎ. Suppose expenditures follow a Pareto distribu-tion with shift parameter ym and shape parameter � such that the pdf of yℎ is�y�my

−(�+1). We can then define the cumulative aggregate share of the first kgoods as S(k) ≡

∫∞yks(k, y)ydF (y) +

∫ ykymydF (y) so that

S(k) = k (�−1)�y�mE− (�−1)

∫ ∞yk

y− (�−1)�− −�dy +

∫ yk

ym

�y�my−�dy, (22)

where yk is the minimum income cutoff such that a household with yℎ = yk hasnℎ = k. To get the following useful log linear approximation

lnS(k) = � + [ (� − 1)] ln k + �k (23)

with unbiased error term �k, we need to ensure that the last term∫ ykym�y�my

−�dy isas small as possible. Note that if this term is small, the distribution of E, Ω and yaffect the share of each variety because they affect the choice of nℎ and the share ofan infra-marginal variety is always decreasing in nℎ. However, they do not affect


the relative share as their effects are absorbed into the constant. This means wedo not need to control for geographic effects in this case, though we can estimateequation (23) separately for different states (which I do in the robustness section).

To ensure that the bias from the∫ ykym�y�my

−�dy term is small, we can eitherdrop households with nℎ < k or pick a smaller range for k such that most or allhouseholds have nℎ > k. I adopt the latter approach and restrict attention to vari-eties with an index below the 90th percentile of the expenditure distribution. Thisis similar giving more weight to the most important varieties. While this partic-ular cutoff ensures that we have more than just one or two varieties to estimatethe slope and eliminates most marginal varieties, it still leaves many householdswith nℎ < k for some values of k. While this may still bias the slope downwards,the effect appears to be small, at least compared to the effect of dropping the mostmarginal varieties.11 Table 7 shows the results of estimating equation (23) on allvarieties with an (aggregate-share based) index number below the 90th percentileof the household variety distribution. The slope is very low for grains and pulsesand dairy, meat and oil, indicating that just a few varieties, like rice,wheat andmilk, dominate the group and the other varieties are relatively marginal. Fruitsand vegetables and spices, beverages, and processed foods have relatively steephierarchy slopes, indicating that there is greater symmetry between varieties. Allgroups fall significantly short of a slope of one, indicating a significant departurefrom a symmetric CES environment - prices, tastes, and quality all differ signifi-cantly across varieties in each group.

Consider now the case where the variance of the household preference shockzi is very large and consequently aggregate expenditure shares are not very in-formative about the relative expenditure shares of individual households. S(k)may not be very correlated with s(k)ℎ, which is defined as the cumulative shareof the k most important varieties from the perspective of each household. For exam-ple, households might have preferences over the varieties that are all randomlydrawn from the same distribution function. If these apparently large preferenceshocks were just caused by measurement and sampling error, it would be a mis-

11Using lower cutoffs appears to have little effect on the results, suggesting that the size of thebias is small. For example, using the 50th percentile cutoff results in slopes of 0.31,0.31,0.60,0.61for the four groups, which are very similar to the results in Panel B and within the 95% confidenceinterval.

30 NICHOLAS LI

take to use these individual slopes for welfare analysis. However, if they repre-sent real preference shocks, the slope of the individual’s variety hierarchy wouldbe the right parameter for a model of average individual welfare.

By picking some set k corresponding to the k most important varieties foreach household and calculating the cumulative share s(k)ℎ we can estimate:

ln s(k)ℎ = [ (� − 1) ln k]− [ (� − 1)] lnnℎ + �ℎ (24)

for all households with n ≥ k. Rather than varying k and holding the distributionand level of expenditures fixed, we fix a particular k and look across householdsthat have different levels of expenditures (and hence different values of nℎ). Thisidentifies the same parameter as in the aggregate case only with the oppositesign.

The error term �ℎ reflects the possibility that positive and negative preferenceshocks may not balance out for households so that some have an above or belowaverage share of the first k varieties. If these preference shocks are large enoughto affect the choice of n then nℎ is endogenous and estimates of (� − 1) fromthis regression will be biased. A good instrument in this case would be totalexpenditures, assuming that preference shocks that affect the relative share ofdifferent varieties have no effect on a household’s total expenditures. The theoryimplies that the choice of k is irrelevant but in reality the choice of k has twoeffects - choosing higher k will lead to households with n < k being droppedfrom the sample, and it will also affect the slope directly if the true distribution ofthe log cumulative share is non-linear in k. Table 8 provides estimates using the10th and 50th percentiles of the variety distribution as the value of k (implyingthat I drop 10% and 50% of sample households).

The IV slopes are below the OLS slopes suggesting that households withhigher preferences for the first k varieties tend to have lower n, as would bepredicted by the model. The coefficients are smaller than those in Table 7 as well,with the most notable difference being for spices, beverages and processed food.The difference could be from two sources. One possibility is that the variance ofindividual preferences is not that large and the difference is due to non-linearityin the variety hierarchy. The individual approach uses mostly marginal varieties


to identify the slope while the aggregate approach uses inframarginal varieties.The second possibility is that the variance of individual preferences is very large.This will move the individual slope closer to zero as the highest order statistics(the most important, lowest index number goods) dominate and the individual’sdistribution of expenditures is skewed towards just a few goods. These issuessuggest that the individual and aggregate approaches are complementary in thesense that they may provide reasonable bounds on the correct parameter to usefor welfare analysis. The aggregate approach puts all the weight on the house-hold with the mean of the preference shock parameter distribution (perhaps as-suming that most divergence is due to measurement and sampling error and nottrue preferences), while the individual approach gives equal weight to house-holds with (apparently) very different configurations of preferences.

4.3. Elasticity of substitution

A key feature of the data that enables estimation of � and an approximation of Ω

is that prices are observed directly in the form of unit values. I follow Deaton andTarozzi (2005) and use median unit values for a particular area/period as pricesafter eliminating obvious outliers and ensuring that good categories and units areon a similar scale over time. This ignores many factors that could affect measure-ment such as differences in quality - as Figure 9 reveals, the intra-village elasticityof unit value with respect to household expenditures is about 5%. While someof this may represent lower prices earned by the poor through greater bargain-hunting, the potential bias from quality is non-trivial. This is more of a concernfor estimation of Ω, as the method I use to estimate the elasticity of substitutionwill tend to minimize income effects.

To estimate the elasticity of substitution, take equation (2), the share equa-tion of the model and depart from previous practice and treat the share for aparticular variety and its price as discrete variables. The aggregate share Sit ≡∫∞yisi(pi, P (n), di)ydF (y) gives

Sit = p�−1i �y�mE

− (�−1)

∫ ∞yi

di(y)y− (�−1)�− −�dy (25)

32 NICHOLAS LI

where di(y) is an unobserved taste/quality parameter that may be correlatedwith expenditures and yi is the minimum expenditure of a household that pur-chases the good (the share for non-purchasing households is zero and the priceelasticity is also zero). As in the previous section, the bias introduced by non-consumption will be dealt with by putting more weight on goods that are widelyconsumed.

Taking logs of equation (25) and differencing with respect to a base variety,labeled B, gives:

lnSi − lnSB = (� − 1) [ln pi − ln pB] + �i (26)

where the term �i includes sampling error and also the effects of the taste/qualityparameters di(y) and dB(y). The impact of the taste/quality parameters will notdepend on the expenditure distribution if di and dB are independent of y, but ifnot then changes in the expenditure distribution holding the taste/quality parame-ters constant could still affect the aggregate share. Note however that absent vari-ation in the taste/quality parameters the expenditure distribution would haveno independent effect, as changes in aggregate expenditures scale the shares forvarieties by the same amount provided they are consumed by most households.Differences in relative prices across areas are almost certainly correlated with dif-ferences in relative taste/quality, as Atkin (2008) has shown recently using theIndian NSS data. This makes using cross-sectional relative price differences un-appealing - �i is almost certainly correlated with the relative price gap. Differ-encing over time will reduce this bias substantially as preferences, quality, andexpenditure distributions are relatively stable over short periods:

Δt (lnSit − lnSBt) = (� − 1) [Δt (ln pit − ln pBt)] + �it (27)

where �it = �it − �it−1 and Δt is the first difference operator. The estimate of �will still be biased if changes in tastes, quality, or expenditures over time are cor-related with price changes. I adopt one solution to this problem that avoids theneed for instruments by using the approach developed by Feenstra (1994) - giventhe assumption that all varieties share the same elasticity, a panel dataset with at


least three varieties is sufficient to identify the supply and demand elasticities. 12

The Feenstra approach assumes a reduced form supply curve in share form:

�it = (1− �)(Δtpit −Δt ln pBt)− [�/(� − 1)](Δt lnSit −Δt lnSBt) (28)

where � is the correlation between vertical shifts in the demand curve and thechange in the equilibrium price and we require 0 ≤ � < �−1

�< 1. Re-write

equation (27) as:

�it = (Δt lnSit −Δt lnSBt) + (� − 1)(Δtpit −Δt ln pBt) (29)

Feenstra’s approach depends critically on �it and �it being independent and ex-ploiting the moment condition E[�it�it] = E[uit] = 0. Shocks to demand and sup-ply must be independent. For example, a rainfall shock that increases the supplyof rice relative to wheat at a given relative price must not simultaneously increasethe relative demand for rice versus wheat.13 This alone would be insufficient toidentify the two parameters � and � due to non-uniqueness - the independence ofthe error terms provides only one moment condition when there are two param-eters to estimate. However, given multiple varieties and the assumption of a com-mon elasticity we have N-1 independent moment conditions, where N is the totalnumber of varieties and we subtract one to reflect the differencing with respectto a common base variety. This estimator corresponds to Hansen’s GMM, wherethe parameters are chosen to minimize the weighted sum of squared sample mo-ments E[uit]. The only additional requirement for consistency as the number of

12In separate work I adopt an IV approach using local rainfall shocks as instruments for pricechanges. The results generally lead to much lower estimates of the elasticity of substituion, butthe instrument is generally weak with an F-stat around 5 and there are other issues as well.

13One possible objection is that rainfall shocks affect the distribution of expenditures andexpenditure levels, which influences relative demand for varieties through the extensive mar-gin/variety Engel curve. The original application in Feenstra (1994) used trade data, where in-dependence is more plausible (but still arguable). Later applications (Broda and Weinstein 2007)used within country data. One way to achieve greater “separation” between demand and supply,in the spirit of the trade litereature, is to use only urban areas of regions. This makes it more plau-sible that supply and demand disturbances are independent, as the effect of agricultural supplyshocks on urban incomes is likely to be second order. Doing so has little impact on the elasticityestimates.

34 NICHOLAS LI

periods T goes to infinity is that there exist varieties i ∕= B and j ∕= B such that

(�2�i + �2

�B

�2�j + �2

�B

)∕=

(�2�i + �2

�B

�2�j + �2

�B

)(30)

This condition requires that there are differences in the relative variances of thedemand and supply curves across varieties. Provided these conditions are metthen we have consistent estimates of �. For a fuller discussion of this estimationtechnique, see Feenstra (1994). I follow Broda and Weinstein (2006) in weightingthe different varieties using their relative importance (budget shares in this case)- this minimizes the bias caused by non-consumption of marginal varieties andleads to a natural interpretation of the parameter estimates as a weighted averageelasticity for the different varieties in the group.

To estimate the elasticity of substitution, I divide the five survey rounds into62 different regions and four quarters (subrounds) per survey round. I take firstdifferences across quarters within a survey round and use the variety with thehighest aggregate budget share as the base variety. I weight all regions equallybut use aggregate budget share weights for different varieties within each group.Table 9 provides the main parameter estimates for the four group classification.Standard errors are calculated using the delta method. The elasticities range fromtwo for grains and pulses to six for fruits and vegetables. As an alternative I alsocalculate elasticities of substitution separately for the ten group classification andthen use aggregate budget weights to generate �g weighted. These weighted �g

are quite close to the ones from the more aggregated classification, suggestingthat using the more aggregated grouping does not introduce too much bias inthe estimation.14

14It is interesting to note that the elasticities from the more disaggregated ten group classifica-tion are not necessarily larger. This is different from the results in Broda and Weinstein (2006) buttheir result is based on much more disaggregated data and a large number of categories - thereis no mechanical relationship between the level of aggregation and the elasticities of substitutionestimated using Feenstra’s method.


4.4. Price level and relative prices

The CES price aggregator given by P (n) =(∫ n

0dip

1−�i di

) 11−� which is equal to

Ωn− given our parameterization is not the same thing as a conventional CESprice index. When variety is endogenous every household effectively has a dif-ferent CES price aggregator that depends on the number of varieties it consumes,and the correct price index for comparing welfare takes fixed costs and expendi-tures into account as well. Furthermore the parameter includes both preferenceparameters like the elasticity of substitution � and the average relative taste slope(�2) as well as relative price dispersion (decreasing in �1 as pi = Ωi

1�1 ). The param-

eter is not calculated from the distribution of prices but rather from the varietyhierarchy analyzed in section 4.2.

The independent role of prices works through the term Ω. The term Ω op-erates like a conventional price index - it deflates nominal expenditures X inmany of the model’s equations and the expenditure function is HD 1 in Ω, aswe would expect from any reasonable price index. The difference is that Ω isthe part of the price index that is independent of relative prices. A conven-tional fixed weight price index could feature two vectors of prices p1 and p2

such that P (p1) = P (p2) even when p1 ∕= p2. There would be many mean-preserving spreads that would deliver the same index number despite shiftingrelative prices. In the context of this model, there is no such mean-preservingspread that delivers the same cost-of-living index. Changes in the dispersion ofprices affect and hence the variety Engel curve and the slope of the consump-tion hierarchy - the non-homotheticity of the model means changes in relativeprices have asymmetric impacts on the welfare of poor and rich households. Ofcourse this is true of many non-homothetic preferences, for which it is possibleto isolate a price level effect that scales the welfare/expenditure function of allhouseholds equally but for which a mean preserving spread would have asym-metric impacts on rich and poor households, even when the aggregate price in-dex is unchanged.

When making comparisons across time or space, I assume that householdsface the same combination of relative prices/tastes (and hence the same ) butallow Ω to differ to reflect differences in the “neutral” price level. Since the pa-rameter Ω does not have an obvious empirical counterpart, I use a conventional

36 NICHOLAS LI

price index with aggregate expenditure shares as an approximation. Any con-ventional price index will be highly correlated with Ω over long periods wheremost prices rise - though there may be some relative price changes as well, theireffect on the distribution of prices pi = Ωi

1�1 are likely to be swamped by the

component common to all varieties, Ω. Similarly, when comparing large pricedifferences between urban and rural areas, a conventional price index provides areasonable approximation to Ω.

There are many candidate price indexes to approximate Ω. The preferredspecification uses the Sato-Vartia log-change index, as this facilitates comparisonto the homothetic CES demand system and cost-of-living index used by Feen-stra. I also tried a Tornqvist index as it is common in applied work and satisfiessymmetry, but the difference is minimal.

4.5. Estimating fixed costs

Given estimates of �, , �, and Ω we return to equation (26) to back out an esti-mate of F:

lnFgℎt =

[�− �

]([(�g − 1)�g]

1 g−�g +

1

�− lnXgℎt/Ωgt

)(31)

When estimating F, I also subtract the fitted values of other household vari-ables that might influence the choice of variety but that I do not wish to interpretas fixed costs specific to a location or period (such as vehicle ownership, house-hold size, purchase at subsidized PDS prices, or farming). This leaves lnFgℎt as aresidual variety shifter not explained by expenditures, the price level, and otherhousehold controls. We can then calculate the mean, median, or other summarystatistic of the residual for the relevant period and area. Denoting the mean forgroup g and area t as Fgt, the group-level expenditure index for comparing ar-eas/periods t and s is given by:

Ωgt

Ωgs

(FgtFgs

) g(32)

Note that since[�− �

]is the same for both areas this term drops out of the ratio. In


fact, we could allow an additional term � to influence variety choice by param-eterizing Fgℎt ≡ �Cgtugℎt. As long as the idiosyncratic variety preference lnugℎt

has mean zero (and did not affect the estimates of the parameters earlier due tothe use of controls and/or instruments) and as long as basic variety preference �scales the fixed cost and households in both areas have the same preference, theratio ( Fgt

Fgswill be driven only by the ratio of the fixed costs ( Cgt

Cgs.

This suggests two potential sources of bias - dissimilar preferences �gt ∕= �gs

and unmeasured household heterogeneity that biases the fixed cost ratio up ordown. I address the first issue in section 6 by examining migrants - under the as-sumption that preferences are static or change slowly, the variety demanded bymigrants is informative about the degree to which differences in variety acrossspace are due to features of the local environment or due to systematic geo-graphic differences in preferences. I address the second issue by including nu-merous household-level controls and by showing how differences in the averagevariety residual are correlated with district-level covariates that proxy for marketaccess.

5. Results

5.1. Changes over time

Table 10 presents the parameter estimates used for the results in this section. Ifocus primarily on two sets of elasticity estimates and two sets of hierarchy slopeestimates. My low parameters use the Feenstra method point estimates of theelasticity of substitution from Table 9 and the lowest values of the hierarchy slope g(�g − 1) (corresponding to the IV estimate of the individual hierarchy exclud-ing the bottom 50% of households in Table 8). This gives the lowest values of ,the parameter that governs the elasticity of welfare with respect to differences infixed costs (and hence variety). The mid parameters use the same elasticities butthe higher values of the hierarchy slope from the aggregate slope in Table 7. Thisgives higher values of than the low parameters. The high parameters take anelasticity of two and use the aggregate hierarchy slope - this reflects the possi-bility that elasticities of substitution are even lower. Broda and Weinstein (2006)

38 NICHOLAS LI

report a median elasticity of substitution of 2.9 at the 3-digit SITC classificationand consider a value of 2 as well. The groups in my survey are even more aggre-gated, and correspond more closely to the 2-digit SITC classification, so a valueof 2 is not an unreasonable lower-bound elasticity of substitution.15 Across allthree specifications it is clear that differences in variety for grains and pulses willmatter a lot, but the mid specifications has a fairly large impact from the spices,beverages and processed food group and the high specification has a large impactfrom fruits and vegetables. In most specifications I use the within-village/urbanblock with controls estimate of the variety Engel curve slope (column (4) of Table6), though I present some results using the total expenditure IV specification.

Table 11 presents the main results for cost-of-living indexes over time between1983 and 2004-2005. The first column “normal” presents a conventional priceindex based on the log-change formula described earlier, without any varietyeffects. The second column presents the Feenstra index (which uses the aggregateratio of consumed to non-consumed goods) with an elasticity of substitution oftwo. The other columns present the results for the index developed in this paperbased on the group price index ΩgF

gg . Note that using the Feenstra methodology

(with low elasticity of substitution 2), which uses aggregate variety consumptionrather than household variety consumption, leads to no variety effect. This isdue to the positive aggregate consumption of all varieties in the 1983 and 2004-05 periods.

The first row presents the All India estimate, which pools all the householdsin the 17 most populous states and Delhi. By dividing the normal index bythe variety-augmented cost-of-living index we see the magnitude of the welfaregains from variety - one minus this ratio tells us roughly how much the aver-age household would be willing to pay (as a share of total food expenditures)to face the lower fixed costs of the later period. This varies from 1.93% for thelow estimate, 3.5% for the mid estimate, and 6.7% for the high estimate. Thuseven using conservative parameter estimates, the variety effect is non-trivial - thesignificantly higher number of varieties consumed in 2004-2005 versus 1983 byhouseholds with apparently the same level of real expenditure leads to a fairly

15Results from simple OLS regressions and those that use rainfall shocks as an instrument oftenfind elasticites between one and two.


large welfare gains. To put this estimate in perspective, Broda and Weinstein(2006) find a 28% effect of variety on the US import index over the 1972-20001period while Broda and Weinstein (2007) find a variety effect of 0.8% per yearover the 1994-2003 period using American scanner data covering 40% of hosue-hold expenditures. The gains here over a 22 year period appear quite small incomparison, but one should keep in mind that the data here is much more aggre-gated (so it could miss increases in variety occuring within good categories) andmy focus is on increased variety consumption of existing varieties at the house-hold level, not new goods at the aggregate level.

This welfare calculation only applies to food. If fixed costs are identical forother goods and households substitute between food and other goods, total wel-fare gains from variety will be lower. On the other hand the non-food goodscould see equal or even larger variety gains. Since food consumes a much largershare of the budget of poor households, if the variety effect is concentrated infood then it will disproportionately benefit poor households. The average bud-get share of food for Indian households is 57% over this period, so changes in thecost-of-living index for food have large impacts on the overall cost-of-living.

In the second last column I consider the effect of using the total expenditureIV, which has minimal effect on the results. In the last column, I consider whatwould happen if we ignored income effects and the gains from variety are large(the high parameter case). Ignoring the variety Engel curve makes the increase invariety in the later period look even larger, resulting in an overestimation of thegains to variety by 2.5%. This distortion gets smaller as the importance of varietydecreases, so if variety contributes little to welfare it is not important to controlfor income effects.16

The next four rows of Table 11 present the breakdown by individual groups. Ipresent the ratio of fixed costs, the F ratio (see equation 33). Most of the gains areconcentrated in grains and pulses and spices, beverages and processed food, asthese groups have the largest reductions in fixed costs (lower F ratios). The fixedcosts actually increase somewhat for the dairy, meat and oils category but the

16Note that real household food expenditures actually declined slightly over this period. How-ever, the expenditure effect varies by group and consumption of some groups increased relativeto others, explaining why ignoring expenditure effects could still generate an overestimate of theexogenous change in variety and its welfare effects.

40 NICHOLAS LI

effect on welfare is minimal as this group generally features the smallest effectof variety on welfare. Note that this does not mean that variety consumptiondecreased in this category, only that expenditure growth on this category overtime should have resulted in even greater variety growth based on the cross-sectional Engel curve.

Rows five and six consider rural and urban India separately. Prices rose morein urban than in rural India over this period, and rural India seems to have gaineda bit more from variety growth (about 0.5%). Rows seven and eight calculateprice indices and variety differences separately for the 17 states by sector andDelhi, and present the means and medians across the 35 observations. The mag-nitude of gains from variety is similar when we estimate the fixed costs and pricesseparately by state, though there is significant variation across states and sectorsin both the total increase in prices and the total gains from variety.

Table 12 breaks down the results by period for the normal price index and thevariety index that uses the mid parameters. I omit 1999-2000 from the analysisfor the reason stated earlier - the 55th NSS round used a different survey method-ology with different recall periods, and estimates of expenditure levels from thissurvey are difficult to compare with other survey rounds. The gains were quitesmall in the earlier, pre-reform period at 0.5% to 0.8%, and they were higher inthe 1987-88 to 1993-1994 period at 1.1% to 1.2% and higher still from 1993-94 to2004-2005 at 2.1% to 2.5%. The annualized gains appear to be similar since the43rd NSS round in 1987-1988.

To examine the variation in price level changes and variety effects across re-gions, the left panel of Figure 11 plots the increase in the normal cost-of-livingindex for food across 62 NSS regions between 1983 and 2004-2005 against thenominal food expenditure ratio. There is a significant positive correlation, indi-cating that regions with higher nominal food expenditure growth also had pricesthat rose more rapidly. Real food expenditure growth was more equitable thannominal food expenditure growth across Indian regions. The right panel of Fig-ure 11 shows the relationship between the welfare effect of greater variety usingthe mid parameters (as a share of food expenditures) against the expenditureratio. The relationship is negative but not very strong, implying that varietygrowth tended to favor faster growing areas and increase welfare inequality over


time relative to a scenario with no or equal variety growth. These plots also showthe wide range of price level changes and variety welfare effects. The correlationbetween these two effects is very weak but positive (0.065).

What are the implications for debates about growth and poverty in India?Deaton and Dreze (2009) show that per capita calorie consumption has been de-clining in India over the 1983-2005 period, from 2,240 to 2,047 calories in rural In-dia and 2,070 to 2,021 in urban India, while real food expenditures have remainedroughly constant (evident from Table 3). This implies an increase in real expendi-tures per calorie, consistent with a diet higher in fats and lower in cheap staples.This increase in real expenditures per calorie may occur partly through consump-tion of higher quality goods within a category, but also through expansion intomarginal, higher priced goods through the love of variety effect examined in thispaper. The evidence here suggests that even though real food expenditure percapita has remained roughly constant over this period, declining fixed costs thatmake it easier to consume more varieties may still lead to a substantial increasein household welfare from food consumption, on the order of 2 to 7 percent.

The lack of growth of real food expenditures explains why failing to con-trol for income effects does not have a major influence on the measured gainsfrom variety - even though the elasticity of food variety to real expenditures isquite substantial, there has been little increase in real food expenditures. Mostof the increase in food variety must be explained by other factors. Deaton andDreze (2008) suggest that the decrease in calories is a result of declining levelsof physical activity and improvements in the health environment. The evidencepresented here does not contradict their story, and provides an estimate of thepotential welfare gains from decreased physical activity and improved healthenvironments through one particular channel - consumption utility. Under thisinterpretation a decline in caloric requirements would be observationally equiv-alent to a decline in fixed costs, as both would result in greater variety and lowerconsumption of cheap high-calorie staples - in both cases there could be a sizeablewelfare gain from the greater food variety.

Small changes in cost-of-living indexes can have big effects on measured povertyrates. Deaton (2008) shows that using NSS data to measure food inflation over the1999-2005 period instead of the official Consumer Price for Agricultural Laborers

42 NICHOLAS LI

(CPIAL) changes measured food inflation from 10.6% to 14.3%, which increasesthe official poverty ratio from 28.3% to 31% in 2004-2005 rural India. It is difficultand controversial to interpret theory-based cost-of-living indexes from a publicpolicy point of view (evident in the debates about hedonic adjustment for the USCPI in the Boskin commission) and it is not clear that we want to incorporatequality and variety effects into the construction of poverty indexes given the nu-merous assumptions required to use theory-based tools for measuring welfare.However, the evidence presented in this paper is at least suggestive that therehave been some sizeable unmeasured welfare gains, even as calorie consump-tion has fallen. Even small changes in the cost-of-living index of a few percentmake a big difference to national and global poverty counts in a country such asIndia with such a large population centered around the poverty threshold.

5.2. Differences across space: Urban-rural gaps

Table 13 presents the main results for urban-rural cost-of-living indexes in 1983and 2004-2005. Urban areas have more expensive food than than rural areas, andthis gap has increased over time from about 10% to 19% over the sample period.The difference is generally higher for fruits and vegetables and smaller for dairy,meat and oils, though the gap for grains and pulses has increased over the sampleperiod as well. Once again we see that calculating the Feenstra index has littleeffect on the cost of living, because both rural and urban households consume allthe same varieties when they are aggregated sufficiently.

The variety effect on the urban-rural gap is mostly concentrated in grains/pulsesand fruits/vegetables, where urban households have much greater variety. Thisleads to a variety welfare effect of 2% to 4% in 1983 and 1.3% to 3.7% in 2004-2005. The variety gap appears to have closed in favor of rural households butonly a little over this period (consistent with slightly higher variety growth overtime for rural India). Factoring variety into the cost-of-living index significantlyreduces the urban-rural gap - urban households may pay higher prices for mostgoods but they are partly compensated by their easy access to a greater varietyof foods.

Table 13 also presents results comparing rural and urban sectors for the 17


most populous states. The welfare effect of greater urban variety appears to besimilar if we calculate fixed costs on a state by state basis, as the mean and me-dian states have similar size effects. We also see that there is significant variationin urban-rural price gaps, from below 1 for Jammu and Kashmir in 1983 and 1.03for Kerala in 2004-2005 to as high as 1.249 for Karnataka in 2004-2005. Interest-ingly these extreme cases tend to have fairly small variety effects - Kerala typi-cally has the lowest price and variety gap of any state between rural and urbanareas, while urban Karnataka does not seem to have any variety advantage overrural Karnataka despite facing much higher prices. Figure 12 shows that stateswith higher urban-rural expenditure gaps also feature higher urban-rural pricegaps, so real urban-rural inequality is lower than nominal inequality. While thisis similar to the results for changes over time, in this case a higher urban-rural ex-penditure gap is associated with a smaller welfare gain from variety, although thecorrelation across the 17 states is low. Note that while this lowers the inequalityof urban-rural welfare gaps across states, the overall effect of variety is to increasegeographic inequality in India as urban areas are richer in real expenditure termsalready and they all get an extra benefit from variety.

The urban-rural variety gap raises an important issue in debates about ruralto urban migration and inequality measures. Many theories have been advo-cated to explain rural to urban migration in India and in the developing worldgenerally. While prospects for better employment and education are probablythe biggest pull factors, and rural displacement and landlessness are the biggestpush factors, one theory that is sometimes advanced is the “bright light” the-ory of migration. The bright light theory holds that the attraction of urban areasis due in part to the greater amenities and facilities that cities provide. Theseamenities are typically analyzed in economic models as unobserved variablesthat factor into migration equilibria along with observed wages and prices (usu-ally rent). The results of this paper indicate that it may be possible to observesome of these amenities directly and quantify their effect on welfare. The diver-sity of consumption opportunities is almost certainly greater in urban areas andis sometimes amenable to measurement, but existing theoretical frameworks arenot well suited to measuring these effects. One contribution of this paper is toshow that these perceived urban-rural variety differences appear to be real and

44 NICHOLAS LI

can have non-trivial effects on relative welfare measurement and hence on mi-gration flows and equilibria. It also suggests that while normal price measuresoften offset geographic inequalities in nominal incomes and expenditures, higherprices might often be associated with greater amenities like variety. Failing totake these into account may make it difficult to understand the motivation of mi-grants to the great (and relatively expensive) cities of the world like New Yorkor Mumbai. As supermarkets and modern retail formats continue to expand inurban areas and lag in rural areas, there is a potential for the urban-rural food va-riety gap to increase further in the future. The urban-rural variety gaps are likelyto be even larger for unmeasured variety differences within food categories - dif-ferent types of tomatoes or rice for example, and different types of restaurants inthe cooked meal category - and for many non-food items as well.

6. Robustness

6.1. Different variety aggregation

One way in which the results presented so far may be biased is through aggre-gation of goods into groups. The CES framework that underlies the theoreticalmodel is premised on the idea that varieties are substitutes and share a commonelasticity. While this is unlikely to be the case for almost any data, this assump-tion is less realistic when groups are more aggregated. Empirical trade studiesthat estimate these elasticities typically find that they are lower when using moreaggregated groups, consistent with the degree of substitution between goods de-creasing as more dissimilar varieties are lumped together in aggregation. Thefact that the elasticities of substitution estimated using a ten group classificationsometimes run lower than using a four group classification may be a cause forconcern here. In this section I present results where I use the �g estimated us-ing the Feenstra method for the ten group classification and also estimate thehierarchy slope g(�g) and the variety Engel curve slope 1

�g− g for the ten groupaggregation. It is not possible to disaggregate more given the 136 food itemsincluded in the NSS surveys, as disaggregating further typically results in toomany consumption zeros - all of the parameter estimates require multiple vari-


eties in a group for identification. I use the estimated �g from Table 9 and estimateaggregate hierarchy slopes for the goods, which is similar to the mid parameterestimates for the four group classification but uses relatively higher elasticity ofsubstitution estimates and relatively higher hierarchy slope estimates - the aver-age g is 0.29 across the 10 groups.

Table 14 presents the 1983-2004/05 cost-of-living index means and mediansacross 35 state/sectors (rural and urban sectors for 17 states plus Delhi) usingthe ten group classification. The mean and median variety effect on welfare is4.6% to 5.2%, between the mid and high parameter estimates from the four groupclassification. This is reassuring and indicates that the measurement of welfaregains is not overly sensitive to aggregation across varieties. The more detailedbreakdown of goods indicates that gains from variety are most concentrated inprocessed foods and fruits and nuts where the gain is about 10%, followed bygrains, pulses, meat, and spices at about 6% to 8%. Oil and dairy have a positiveF-ratio, indicating that variety growth in these groups was lower than would beexpected given expenditure growth in these categories. However, as these goodsboth have very high estimated elasticities of substitution, the decrease in varietyper real rupee of expenditure has virtually no effect on the overall food cost-of-living index.

Table 15 presents the urban-rural price index for the ten group classificationacross 17 states in 2004-2005. The total variety effect is about 2.1% to 2.4%, similarto the effect of the mid parameter estimate using four groups. Grains, pulses,and fruits and nuts are the groups with the lowest F ratios and as they featurerelatively high values of they explain most of the urban-rural variety gap.

6.2. Geographic variation in tastes

The welfare analysis of previous sections is made under the assumption thatwhile the price level Ω and the variety shifter F can vary across areas or overtime, the other parameters , �, and � are constant. This is taken into accountthrough estimation - to the extent that the parameters vary, pooling the data re-sults in averaging out these differences. It is difficult to estimate � for individualperiods and regions, as the estimates use aggregate data and the number of ob-

46 NICHOLAS LI

servations is very small when not pooling across survey rounds and regions. Theestimates of � vary substantially but the standard errors are very large. To con-sider how differences in and � might bias the results, the top panel of Table 16presents individual and aggregate estimates for the hierarchy slope g(�g − 1)

under the 4-group classification for the 38th, 43rd, 50th, 55th, and 61st NSS sur-vey rounds. The bottom panel presents the estimates of the Engel curve slope

1�− . While there are clearly changes over time and one can often reject equalityat conventional significance levels, the quantitative impact is likely to be quitesmall. Changes to the Engel curve slope have a minimal impact because real ex-penditures do not change that much, and a small change in the Engel curve slopecan only have a big impact on the fixed cost estimate if real expenditure changesover time are very large.

Changes in the hierarchy slope can potentially have a bigger impact. Thebiggest effects would come from the 33% decrease in the hierarchy slope fordairy, meat and oil for the aggregate hierarchy and the 40% increase in the slopefor spices, beverages and processed food for the individual hierarchy. Such achange in the hierarchy slope would have a proportionate impact on the varietywelfare gains for that particular group. Since the increases and decreases appearto balance out somewhat, the net effect is unlikely to be large. Adjusting the pa-rameters within this range is unlikely to greatly increase the roughly 4% rangebetween the low and the high parameter welfare estimates. Comparing welfareunder different parameter values is more difficult, as the price and quantity indexinterpretation of the group expenditure function becomes more complicated.

Table 17 turns to the geographic heterogeneity in the parameters, estimatingthe aggregate hierarchy slope for each state by sector. There is a lot of hetero-geneity in these parameters across the 17 major states and Delhi. The correlationbetween the hierarchy slope rural and urban sectors within states is very high forthe first three groups (0.88 to 0.93) but lower for spices, beverages and processedfood (0.35). Note that the average hierarchy slope is a bit higher in rural areasfor the first two groups but a bit lower in the last two. According to the model,this implies that higher rural price dispersion is unlikely to be the main reasonfor higher urban variety - higher rural price dispersion must manifest itself ina flatter hierarchy slope, as households consume relatively less of the marginal


expensive goods than urban households. The relative stability of the hierarchyslope across rural and urban areas of the same state (as well as over time) is someof the strongest evidence that unobserved factors like fixed search and transportcosts or declining caloric requirements explain the variety differences over timeand space rather than lower relative prices for marginal goods in urban areasand later periods. The Engel curves vary even less across states and the urbandifferences are typically very small.

Because the variation in hierarchy slopes across states is quite large and couldpotentially bias the welfare estimates, the upper panel of Table 18 re-calculatesthe 1983-2005 cost-of-living index for the 17 states and Delhi. I estimate one spec-ification that allows both the Engel curve slope (and all household covariates)and the aggregate hierarchy slope to vary state/sector, and another that only al-lows to vary. I still impose consistency over time. The results for the 17 statemean and the median suggest a slightly lower variety effect compared to Table11, with gains of 1.8% to 2.2% for the higher Feenstra elasticities and 3.3% to 3.8%for an elasticity of substitution of two, but the effect seems to stem mostly fromallowing Engel curve slopes and household covarites to vary flexibly by state.The lower panel of Table 18 estimates an analogous welfare effect across urbanand rural sectors, allowing the parameters to vary by state but restricting themto be the same for both sectors. The welfare effects for the mean and medianstate are also smaller, in the 0.5% to 1% range, compared to 1.4% to 2.7% whenimposing similar parameters for each state. The range is still large - over 8 statesare above 1%, with Himachal Pradesh featuring the a 2% urban-rural welfaredifference from variety - but there is a sizeable reduction in welfare gains.

These results emphasize the importance of allowing for heterogeneity in theparameters, especially across states and sectors. Since the g parameter capturesthe impact of both preference dispersion and price dispersion, it is not surpris-ing that there would be large differences in a country that is large and diverselike India with significant variation in tastes and markets. Allowing for variableEngel curves is also important, though some of the difference is driven by theeffects of conditioning household variables as well - since the variety effect is ahousehold residual, allowing more degrees of freedom will tend to minimize anyvariety differences measured with this methodology. This evidence also shows

48 NICHOLAS LI

the difficulty of inter-state comparisons. Restricting analysis of the welfare ef-fects of variety coming from unobserved fixed costs to urban-rural comparisonswithin states or changes in sector/state/region variety over time is justified bythe stability of behavioral parameters and relative prices that appear to be moresimilar (based on the hierarchy slope).

6.3. What are the fixed costs in the model? Immigrants, tastes,

and district-level analysis

The main purpose of this paper has been to quantify the welfare gains of exoge-nous differences in variety, i.e. differences in variety over time and space that arenot related to observable household characteristics, particularly income. How-ever, the source of these differences in variety - fixed costs in the model - arenot clear even though they are clearly related to changes over time and betweenurban and rural areas.

I first investigate whether taste differences between rural and urban house-holds could be one source of variety differences. If changing tastes are the mainexplanation for increased variety consumption in urban areas, the implicationsfor welfare are much less clear, although it is likely that changing tastes wouldbe endogenous to changes in market conditions and availability of different va-rieties. To examine what role tastes may play in variety consumption, I followAtkin (2008) and exploit the fact that the 43rd NSS round for 1987-1988 linkshousehold consumption to data on household migration status. Immigrants fromrural to urban areas or across states and regions are likely to bring their tasteswith them, even though their tastes may eventually adapt to local varieties. Thekey assumption underlying this strategy is that immigrant tastes are sticky andthat conditional on other observables immigrants have the same taste for variety asnon-immigrants - a rural Indian who moves to the city must have similar tastesto a rural Indian who remains in the village.

Table 19 presents the results for an OLS regression of log variety on the fullset of controls including expenditures for the four different food groups. Urbanexpenditures are discounted using urban-rural price deflators and I include anurban dummy and state fixed effects. The coefficient on the urban dummy cap-


tures the average (across 17 states) additional variety from living in an urbansector of a state relative to a rural sector. I also include a set of dummies forhouseholds whose head migrated within the same state, excluding householdswhose heads migrated across states. The intra-state migrants make up 78% ofrural to urban migrants (8.5% of all households in the survey), 73% of urban torural migrants (1.6% of the sample), 94% of rural to rural migrants (8.2% of thesample) and 72.4% of urban to urban migrants (6% of the sample). I focus onintra-state migrants because the object of interest is urban-rural variety differ-ences within states - there are large differences in tastes across states that makeinter-state comparisons difficult.

If taste is the only explanation for urban and rural variety differences, rural tourban immigrants in the sample should exhibit lower variety consumption thantheir urban peers - the coefficient on rural to urban migrants would be exactly thesame size and opposite sign as the coefficient on the urban dummy. Similarly, thecoefficient on the urban to rural dummy would be exactly the same size and thesame sign as the urban dummy. Table 19 shows that this is generally not the case.For the two groups with the biggest average urban-rural variety gap - grains andpulses and fruits and vegetables - there is virtually no effect of rural to urbanimmigration on variety consumption. In other words, migrants who move froma rural area of a state to an urban area of the same state consume around 10%more than their rural counterparts, exactly like the average urban household.However the effect is not symmetric - urban households that move to rural areasof the same state consume more varieties than rural households, and look closerto their urban counterparts. Rural-rural and urban-urban migrants also behavea bit differently, as both appear to have higher demand for variety than non-migrants. For the spices, beverages and processed food group there does appearto be a decline for rural to urban migrants, but the urban dummy is negative inthis case so there was no average urban-rural variety gap to begin with.

Similar results obtain if we estimate the regression state by state allowing theimmigrant dummies, the urban dummy and all covariates to have different ef-fects for each state. When the migration variable is defined as migration withinthe last year, there is no impact of rural to urban migration on variety for grainsand pulses and dairy, meat and oil, but a negative impact on fruits and vegeta-

50 NICHOLAS LI

bles that offsets the urban-rural gap. While there is thus some evidence that tastesmay explain part of the variety differences across urban and rural areas, there isaappear to be other factors at work as well. Understanding the source of chang-ing taste is an important topic for future research. Atkin (2008) provides evidencethat it has important caloric implications for trade liberalization in India, but un-derstanding how and why tastes differ and how they affect consumer welfare islikely to remain a fairly intractable topic for applied research.

If there are factors other than taste at work, they may be related to local marketcharacteristics that influence the availability of different varieties and the ease ofconsuming them, including search and transport costs related to shopping. I pro-vide some preliminary evidence by analyzing variation in food variety consump-tion across 267 Indian districts using the 1987-88 NSS survey. The 267 matcheddistricts come from 13 states. I match survey data by district to the World BankIndia Agriculture and Climate Data set which contains data on population densi-ties, distance from the coast, roads per square kilometer, the agricultural wage ofa male ploughman, and altitude. This can be combined with data on mean totalexpenditures per capita in the district from the survey, though it is important tonote that the NSS survey is not intended to be representative at the district level,only at the state/sector level. Table 20 presents two sets of OLS regression resultswith the same regressors but with two different dependent variables. The first isthe district median number of food varieties consumed, while the second is thevariety residual from a regression of food variety on food expenditure and thefull set of household controls. The second variety measure thus represents ‘ex-ogenous’ variety from the point of view of the household, and differences in thismeasure across districts cannot be attributed to differences in household foodexpenditures, household sizes, religion, farming/agricultural/casual labor, thepublic distribution system, scheduled tribe and caste, and vehicle ownership.

All variables are in logs and so the coefficients in Table 20 can be interpretedas elasticities of variety with respect to the district level covariates. The resultsindicate that road density and distance from the coast have large impacts on foodvariety in the expected direction - districts with greater road density and thosethat are closer to the coast appear to have greater food variety, even after control-ling for expenditures, with 1% greater road density associated with 0.06% greater


variety and 1% greater proximity to the coast associated with 0.1% greater foodvariety. Since these variables are often associated with measures of market accessand regional integration, these results support a market access view of the districtlevel fixed costs. Agricultural wages appear to have a negative effect on variety,which is puzzling. Altitude appears to have a positive effect on variety, after con-trolling for distance from the coast, which is also a bit puzzling although altitudeis not necessarily associated with terrain ruggedness. Some of the Northern In-dian states with high elevation like Punjab have relatively good infrastructure.The effect of population density is positive but not significantly different thanzero. Note that the effect of mean expenditures is much higher in the first spec-ification that uses log food variety. This is because the coefficient confounds theeffects of living in a richer area with the effects of richer households. The coeffi-cient on the residual variety effect effect is smaller because it already controls forhousehold food expenditures, and it implies something stronger - poor house-holds with low food expenditures will on average consume more food varietiesin richer districts than poorer districts.

In future work I plan to incorporate information on calorie consumption,caloric requirements, and shopping by converting food quantities into caloriesand integrating the data from the Indian Time-Use survey. This will improve ourunderstanding of the sources of variety-seeking behavior and quantify the con-tribution of decreased caloric requirements and transport/shopping costs. In-tegrating census data and extending the district covariates to a panel will alsoenable better identification of district-level sources of variety difference, sincea district-level cross-sectional regression suffers from potentially severe omittedvariable bias.

7. Conclusion

This paper revisits the classic question of how consumers benefit from greater va-riety and makes several contributions. First, the paper develops a novel frame-work for analyzing endogenous household-level variety demand with varietyEngel curves. Unlike previous models of variety growth and consumer welfare,variety growth in this model consists of households consuming a greater num-

52 NICHOLAS LI

ber of varieties for a given quantity of real expenditure, which means there therecan be variety growth even when the total number of varieties in the economyremains constant. The model is able to capture a particular stylized fact thathas not been considered in previous models. Second, the paper discusses howto estimate the key model parameters and calculate the welfare impact of ex-ogenous changes in variety. Third, the paper applies the model and estimatedmodel parameters to Indian household data to examine the welfare impact ofvariety differences over time and space.

I find that the food cost-of-living index that incorporates increased varietyleads to a welfare gain of about 3.5% (measured as a fraction of real food ex-penditures) over the 1983-2005 period. While the magnitude of the welfare gainseems small given the enormous changes occuring in India over this period, thisestimate only includes the effect of increased food variety consumption out ofexisting varieties. Increases in quality and new goods may lead to even largerunmeasured welfare gains over time that are complementary to these gains andoccur through different channels. Failing to account for the variety Engel curvecan potentially bias the results and overstate the rate of variety growth, althoughthe effect is muted in India because growth in real food expenditures has beenstagnant. Turning to urban-rural gaps, I find that these gaps average about 2%in favor of the urban sectors though there is large variation across states. Whileurban areas are more expensive, urban households appear to be partly compen-sated by easier access to a wider variety of food. The size of the urban-ruralvariety gap appears to have narrowed over the last 25 years but it is still sizeable.

Unmeasured welfare differences from variety have important implicationsfor how we think about growth, inequality, and migration equilibria. The re-sults suggest that welfare from food intake has increased by more than measuredreal food expenditure, and provide one way of measuring the welfare gain fromchanging food consumption patterns over time. Some authors have been puzzledby the decline in calorie intake in India over the last 25 years, which coincideswith stagnant real food expenditures and rising real expenditures per calorie.While declining caloric intake India is alarming given widespread malnutrition,the results of this paper provide some idea of how households may have bene-fited from this change in consumption patterns away from a few basic staples to


a more diverse basket of goods. Urban-rural variety gaps indicate that welfareinequality across space may be larger than previously thought - while correctingfor higher urban prices decreases inequality in India by shrinking the nominalexpenditure gap between urban and rural sectors, accounting for larger urbanvariety increases the welfare gap between the sectors. The paper provides a di-rect estimate of the welfare effects of an amenity that potentially makes urbanlocations attractive to rural immigrants.

While the paper provides some suggestive evidence, further research is neededinto the precise nature of the costs that constrain variety consumption. Relativeprices alone appear to be insufficient to explain the dramatic increase in vari-ety growth. One potential candidate is declining caloric requirements causedby a decline in physical activity levels and improvement in the health environ-ment. In this view the fixed costs of the model are interpretable as a penalty ina household’s utility function from consuming less calories, an inevitable resultof spreading a fixed amount of money over more varieties when these varietieshave a higher cost per calorie. Incorporating nutritional information into theanalysis is an important next step. A second potential candidate are costs relatedto transport, shopping, and market access. Adding additional geographic co-variates related to infrastructure and retail density is an important area of furtherresearch, as is directly measuring household shopping patterns using time-usedata. A final potential candidate is taste difference. There is not enough evidenceyet to categorically rule out taste differences as the main driver of variety growth.Disentangling taste differences from environmental factors would be useful butthe data requirements are exacting. Even if one could quantify the contributionof taste and other factors, understanding why tastes change and how to factorthem into a consumer welfare analysis are interesting and unresolved questions.

References

Arkolakis, Costas, Svetlana Demidova, Peter J. Klenow, and Andres Rodriguez-Clare, “Endogenous Variety and the Gains from Trade,” Working Paper, 2007.

Atkin, David, “Trade, Tastes and Nutrition in India,” 2009.

54 NICHOLAS LI

Bils, Mark and Peter J. Klenow, “Quantifying Quality Growth,” American Eco-nomic Review, 2001a, 91, 1006–1030.

and , “The Acceleration in Variety Growth,” American Economic Review,2001b, 91(2), 274–280.

Broda, Christian and David E. Weinstein, “Globalization and the Gains from Va-riety,” Quarterly Journal of Economics, 2006, pp. 541–585.

and , “Product Creation and Destruction: Evidence and Price Implications,”NBER Working Paper 13041, 2007.

and John Romalis, “Inequality and Prices: Does China Benefit the Poor inAmerica?,” Working Paper, 2008.

Costa, Dora L., “Estimating Real Income in the US from 1888 to 1994: CorrectingCPI Bias Using Engel Curves,” Journal of Political Economy, 2001, 109(6), 1288–1310.

Deaton, Angus, The Analysis of Household Surveys, John Hopkins University Press,1997.

, “Prices trends in India and their implications for measuring poverty,” 2008.

and Alessandro Tarozzi, “Prices and Poverty in India,” Working Paper, 2005.

and Jean Dreze, “Food and Nutrition in India: Facts and Interpretations,” Eco-nomic and Political Weekly, 2008.

and Valerie Kozel, “Data and Dogma: The Great Indian Poverty Debate,”World Bank Research Observer, 2005.

, Vivi Alatas, and Jed Friedman, “Purchasing Power Parity Exchange Ratesfrom Household Survey Data: India and Indonesia,” Working Paper, 2004.

Feenstra, Robert C., “New Product Varieties and the Measurement of Interna-tional Prices,” American Economic Review, 1994, 84(1), 157–177.

, “Measuring the Gains from Trade under Monopolistic Competition,” 2009.


Greg, Garratt Mark Allenby and Peter Rossi, “A Model for Trade-Up and Changein Considered Brands,” 2008.

Hamilton, Bruce W., “Using Engel’s Law to Estimate CPI bias,” American Eco-nomic Review, 2001, 91(3), 619–630.

Institute, McKinsey Global, “The Bird of Gold: The Rise of India’s ConsumerMarket.”

Melitz, Marc J. and Gianmarco I.P. Ottaviano, “Market Size, Trade, and Produc-tivity,” Working Paper, 2005.

Sato, Kazuo, “The Ideal Log-Change Index Number,” 1976.

Working, Holbrook, “Statistical Laws of Family Expenditure,” Journal of the Amer-ican Statistical Association, 1943, 38, 43–56.

8. Appendix: Feenstra model

In this appendix I detail the model used by Feenstra (1994) and Broda and Wein-stein (2004,2006,2008) to calculate a conventional exact price index and an idealprice index for overlapping sets of varieties, including their technique for empir-ically estimating the elasticities of substitution.

Let k denote the time period/area, g is the grouping within which we expectthe elasticity of substitution to be constant (there are G groupings in total) and iindexes varieties within each grouping. The utility function is:

Uk =

(G∑g=1

u1−�kg

) 11−�

(33)

and the subgroup utility function for area k, consumption group g is given byukg:

ukg =

⎛⎝∑i∈Igk

d1/�gkgi q

�g−1

�g

kgi

⎞⎠�g�g−1

(34)

56 NICHOLAS LI

where Ikg is the set of all varieties consumed (‘available’) in group g in area k, qkgiis the quantity of variety i of group g consumed in area k and dkgi is a quality ortaste parameter. Define a base area 0 and denote the set of varieties of group gthat are common to area k and 0 as Ig. We can then write the exact price index forarea k relative to area 0 as:

Pk =G∏g=1

(PkgP0g

)wkg(35)

where

Pkg =∏i∈Ig

(pkgip0gi

)wkgi (�kg�0g

) 1�g−1

(36)

and

�kg =

∑i∈Ig pkgiqkgi∑i∈Igk pkgiqkgi

(37)

wkg =

skg−s0gln skg−ln s0g∑g∈G

skg−s0gln skg−ln s0g

(38)

wkgi =

skgi−s0giln skgi−ln s0gi∑i∈Ig

skgi−s0giln skgi−ln s0gi

(39)

skg =pkgqkg∑g∈G pkgqkg

(40)

skgi =pkgiqkgi∑i∈Ig pkgiqkgi

(41)

Note that the necessary and sufficient condition for this is that dkgi = d0gi fori ∈ Ig and Ig ∕= ∅.

To calculate the elasticities, �g, for each group g the authors implement anidentification method that uses moment conditions based on the independenceof demand and supply shocks and panel data rather than instruments. Considerthe demand equation given by:

�i,t = (Δ ln si,t −Δ ln sk,t) + (� − 1)(Δ lnPi,t −Δ lnPk,t) (42)

where we have difference the CES share equation twice - once with respect to


time (Δ) and once with respect to a base variety k. We do the same for the supplyequation Δ lnPi,t = t + !

1+!Δ ln si,t + �it, yielding:

�i,t = − !

1 + !(Δ ln si,t −Δ ln sk,t) + (Δ lnPi,t −Δ lnPk,t) (43)

By multiplying these equations together we can take advantage of the assump-tion that Et(�i,t�i,t) = 0, that is, the supply and demand shocks are uncorrelated.We estimate an equation of the form:

Yi,t = �1X1i,t + �2X2i,t + ui,t (44)

where Yi,t = (Δ lnPi,t − Δ lnPk,t)2, X1,i,t = (Δ ln si,t − Δ ln sk,t)

2, and X2i,t =

(Δ ln si,t −Δ ln sk,t)Δ lnPi,t −Δ lnPk,t) and ui,t = �i,t�i,t. By averaging over time,we get Yi, X1i, X2i, the second moments of the changes in prices and expenditureshares, with ui the cross-moment of the errors in the demand and supply equa-tions. These errors are independent by assumption, so we can use E(ui) = 0 as amoment condition for identification. As T approaches infinity, then under weakconditions plim(ui) = 0 so the error ui vanishes. Using the estimates of �1 and �2

from running a regression of Yi on X1i and X2i for different varieties i (we need atleast three for identification) we can solve for the parameters � and �. The mainrequirement for consistency is that regressors are not collinear, which will occurif the relative variances of demand and supply vary across the different varieties.The equation is estimated using weighted-least squares, with weights equal tothe number of observations used for the average and the aggregate expenditureshare for each variety. The weighting scheme is motivated by a desire to givemore weight to important varieties and those with more observed price changes,and because less important varieties may be measured with more sampling andsurvey error.

58 NICHOLAS LI9. Figures

Table 1: Survey-weighted mean household number of varieties consumed overtime

Year Categories 1983 1987-88 1993-94 1999-00 2004-05

All goods 307 42.5 45.6 52.1 57.7 64.5

Food 136 22.8 24.8 28.0 28.7 33.4

Clothing 24 6.0 6.2 6.8 8.7 8.8

Intoxicants 20 1.9 1.9 1.7 1.3 1.4

Fuel and light 12 3.5 3.6 3.7 3.9 4.0

Durables 44 0.6 1.1 1.3 1.8 2.2

Miscellaneous 71 7.7 8.0 10.7 13.3 14.6

Households 109011 116002 100949 108258 108413


Table 2: Survey-weighted mean household number of varieties consumed by sec-tor and year

Year 1983 1987-1988 2004-2005

Sector rural urban rural urban rural urban

All goods 40.4 49.2 50.1 58.1 62.0 71.5

Food 21.5 26.8 26.6 32.0 31.8 37.9

Clothing 5.9 6.2 6.8 6.8 8.7 9.2

Intoxicants 2.0 1.5 1.8 1.2 1.6 1.0

Fuel and light 3.5 3.4 3.8 3.5 4.1 3.7

Durables 0.6 0.7 1.3 1.3 2.2 2.3

Miscellaneous 6.9 10.5 9.8 13.2 13.6 17.4

Households 71721 37290 61837 39112 68982 39431

60 NICHOLAS LI

Table 3: Survey-weighted mean household expenditures over time (in rupees).Real (survey) uses all goods with unit values

1983 1987-88 1993-94 1999-00 2004-05

Nominal All goods 608.1 891.6 1499.9 2821.5 3362.2

Food 397.8 544.7 929.3 1557.7 1615.4

Clothing 46.6 62.9 126.5 217.2 246.6

Intoxicants 17.5 26.4 44.3 69.9 72.8

Fuel and light 44.2 63.9 109.3 215.2 325.2

Durables 8.8 25.0 39.5 84.4 137.5

Miscellaneous 93.3 152.0 251.0 677.2 964.8

Real(CPI) All goods 2475.8 2508.8 2495.7 2877.0 2823.8

Base year 1999 Food 1619.5 1562.0 1546.3 1588.3 1356.7

Clothing 189.7 180.4 210.5 221.5 207.1

Intoxicants 71.2 75.6 73.7 71.2 61.2

Fuel and light 179.8 183.2 181.8 219.4 273.1

Durables 35.8 71.7 65.7 86.1 115.4

Miscellaneous 379.7 435.9 417.7 690.5 810.3

Real(Survey) All goods 2211.4 2399.7 2347.3 2821.5 2925.4

Base year 1999-00 Food 1452.6 1492.7 1466.8 1557.7 1448.6

Clothing 169.4 172.6 198.0 217.2 214.6

Intoxicants 63.6 72.3 69.3 69.9 63.4

Fuel and light 160.6 175.2 171.0 215.2 282.9

Durables 32.0 68.6 61.8 84.4 119.6

Miscellaneous 339.1 416.9 392.9 677.2 839.4

Share of goods with unit values 0.83 0.78 0.81 0.73 0.67


Table 4: Survey-weighted mean household expenditures for sectors (in rupees).The urban-rural price deflator uses all goods with unit values.

Year 1983 2004-2005

Sector rural urban rural urban

Nominal All goods 556.5 772.9 2817.9 4891.0

Food 377.8 461.6 1490.7 1965.7

Clothing 41.9 61.7 219.4 323.0

Intoxicants 16.9 19.3 71.5 76.6

Fuel and light 41.0 54.2 276.2 462.6

Durables 7.0 14.6 110.3 213.8

Miscellaneous 71.9 161.5 649.8 1849.4

Urban price All goods 556.5 673.6 2817.9 4073.7

deflator Food 377.8 419.7 1490.7 1653.4

Clothing 41.9 53.8 219.4 269.0

Intoxicants 16.9 16.8 71.5 63.8

Fuel and light 41.0 47.2 276.2 385.3

Durables 7.0 12.7 110.3 178.1

Miscellaneous 71.9 140.8 649.8 1540.3

62 NICHOLAS LI

Table 5: Number of food varieties with positive consumption at different levelsof aggregation in 2004-2005

Aggregation Units HH per unit Mean n Median n 10% n 90% n

All India 1 108413 136 136 136 136

State 18 6022.94 133.06 134 128 136

Region 63 1720.84 126.7 129 118 133

Subregion 175 619.5 110.94 119 75 128

District 532 203.78 101.1 102 85 116

Village/block 10875 9.97 56.72 56 42 72

Household 108413 1 34.37 34 22 48

Table 6: Engel curve slopes: OLS regression of log variety on log expenditure

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

Grains and pulses 0.19 0.25 0.26 0.30 0.62 0.69

Dairy, meats and oils 0.30 0.32 0.32 0.36 0.33 0.25

Fruits and veg. 0.44 0.44 0.44 0.48 0.43 0.42

Spice,bev.,processed 0.21 0.21 0.19 0.13 0.28 0.20

Geographic controls No State Village Village Village Village

Household controls No No No Yes Yes Yes

Instrument No No No No Expend. Land

All coefficients significant at 1% level. Poolinh 38th,43rd,50th,55th, and 61st rounds.

Household controls include household size dummies, farmer dummy, agricultural laborer dummy,

vehicle dummy, religion dummies, and schedule tribe/cast dummies.


Table 7: Aggregate Hierarchy Slope: coefficient from OLS regression of aggregateexpenditure share of K most important varieties on log K ( g(�g − 1))

Group Coefficient Number of varieties

Grains and pulses 0.25 9 of 31

(0.038)

Dairy, meats, oils 0.31 5 of 20

(0.014)

Fruits and vegetables 0.57 17 of 53

(0.009)

Spices,beverages,processed 0.57 15 of 32

(0.020)

Robust standard errors in parentheses. All coefficients significant at 1% level.

Pooling 38th,43rd,50th,55th, and 61st rounds and using all varieties below the 90th

percentile of the individual variety distribution.

64 NICHOLAS LI

Table 8: Individual Hierarchy Slope: coefficient from OLS regression of log cu-mulative expenditure share of K most important varieties for each household onlog total household variety (− g(�g − 1))

Group OLS coef. IV coef. K N-cutoff.

Grains and pulses -0.24 -0.19 3 10%

Grains and pulses -0.22 -0.17 5 50%

Dairy, meats, oils -0.44 -0.23 2 10%

Dairy, meats, oils -0.40 -0.23 3 50%

Fruits and vegetables -0.51 -0.43 4 10%

Fruits and vegetables -0.42 -0.36 9 50%

Spices,beverages,processed -0.29 -0.22 6 10%

Spices,beverages,processed -0.21 -0.15 10 50%

All coefficients significant at 1% level. N-cutoff is the percentile

of the variety distribution below which households are dropped due to N ≥ K requirement.

Instrument is total household expenditures. Pooling all survey rounds.


Table 9: Elasticity of substitution using Feenstra methodology

4 good grouping �g s.e. 95% CI weighted �g

Grains and pulses 2.01 0.24 (1.51,2.51) 1.92

Dairy, meats, oils 5.63 0.57 (4.51,6.76) 6.53

Fruits and vegetables 6.05 0.13 (5.80,6.30) 5.73

Spices,beverages,processed 3.71 0.34 (3.03,4.38) 2.51

10 good grouping �g s.e. 95% CI average share

Grains 1.86 0.34 (1.13,2.58) 0.36

Pulses 2.34 0.59 (1.01,3.67)) 0.06

Milk 5.44 10.93 (-29.36,40.23) 0.15

Meat 2.86 0.43 (1.02,4.71) 0.05

Oil 11.40 4.87 (-50.44,73.25) 0.07

Vegetables 6.88 1.02 (4.78,8.99) 0.09

Fruits and nuts 2.46 0.87 (0.64,4.28) 0.03

Spices 2.04 0.06 (1.92,2.17) 0.09

Beverages 3.24 2.55 (-3.33,9.81) 0.04

Processed 2.73 0.34 (2.06,3.40) 0.04

Pooling all rounds. Standard errors using the Delta Method.

Weighted �g uses aggregate share weights on ten group elasticities

Table 10: Summary of parameters

Parameters Low Mid High

Elasticity of substitution �g Feenstra Feenstra 2

Hierarchy slope (� − 1) Ind. IV above 50% Ind. IV above 50% Agg.

Grains and pulses 0.17 0.25 0.25

Dairy, meats, oils 0.05 0.07 0.33

Fruits and vegetables 0.07 0.11 0.57

Spices,beverages,processed 0.06 0.21 0.57

66 NICHOLAS LI

Table 11: Price indexes for 2004-2005 relative to 1983(=1)

Welfare gain as % of exp.

Normal Feenstra F-ratio Low Mid High High IV High IV, no X

Grains and pulses 3.530 0.000 0.805 0.036 0.052 0.052 0.062 0.039

Dairy,meat,oil 4.072 0.000 1.091 -0.004 -0.006 -0.027 -0.027 0.019

Veg. and fruits 4.330 0.000 0.640 0.031 0.047 0.188 0.193 0.261

Spices, bev, proc. 5.332 -0.003 0.758 0.017 0.055 0.135 0.132 0.142

All India 4.107 0.000 0.019 0.034 0.067 0.070 0.089

Urban India 4.451 -0.001 0.017 0.030 0.065 0.072 0.068

Rural India 4.020 0.000 0.023 0.039 0.070 0.072 0.101

State/sect. mean 4.214 -0.001 0.021 0.035 0.066 0.069 0.079

Region mean 4.140 0.001 0.021 0.036 0.067 0.069 0.087

Table 12: Price indexes over different periods using mid parameters, base year isfirst year for each period(=1)

1983-1987/88 1987/88-1993/94 1993/94-2004/05

Normal Variety gain Normal Variety gain Normal Variety gain

All India 1.324 0.005 1.732 0.012 1.758 0.021

Urban India 1.377 0.006 1.771 0.011 1.833 0.023

Rural India 1.316 0.008 1.669 0.011 1.786 0.025


Table 13: Urban price indexes for 1983 and 2004-2005 (Rural=1)

Welfare gain as % of exp.

1983 Normal Feenstra F-ratio Low Mid High High IV High IV, no X


Dairy,meat,oil 1.048 0.000 0.992 0.000 0.001 0.002 0.003 0.070

Veg. and fruit 1.185 0.000 0.819 0.014 0.021 0.090 0.089 0.143

Spice,bev.,proc. 1.103 0.000 0.970 0.002 0.006 0.015 0.001 0.074

All India 1.099 0.000 0.018 0.027 0.036 0.039 0.061

State mean 1.085 0.000 0.014 0.021 0.028 0.027 0.044

State min 0.984 -0.001 0.003 0.005 0.139 0.015 0.033

State max 1.179 0.000 0.007 0.010 -0.011 0.025 -0.006

2004-05 Normal Feenstra F-ratio Low Mid High High IV High IV, no X


Dairy,meat,oil 1.122 0.000 0.937 0.003 0.005 0.020 0.019 0.032

Veg. and fruit 1.232 0.000 0.879 0.009 0.014 0.059 0.058 0.050

Spices,bev,proc. 1.150 0.000 0.965 0.002 0.007 0.018 0.017 0.036

All India 1.188 0.000 0.011 0.017 0.030 0.038 0.030

State mean 1.134 0.000 0.009 0.014 0.026 0.029 0.026

State min 1.032 0.000 0.002 0.001 0.001 0.006 0.005

State max 1.249 0.000 0.006 0.008 0.007 0.014 0.011

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Table 14: Price indexes for 2004-2005 relative to 1983(=1) using ten groups and 35state/sectors

Means Normal F ratio g Variety gain

Grains 3.577 0.803 0.356 0.077

Pulses 5.363 0.792 0.377 0.085

Dairy 4.421 1.241 0.032 -0.006

Meat 5.154 0.853 0.407 0.063

Oil 3.617 1.107 0.086 -0.009

Vegetables 4.076 0.667 0.093 0.038

Fruits and nuts 4.845 0.789 0.478 0.108

Spices 5.351 0.841 0.374 0.066

Beverages 4.862 0.909 0.446 0.045

Processed 4.616 0.721 0.298 0.095

Food index mean 4.210 0.052


Table 15: Price indexes for urban relative to rural for 2004-2005 using ten groupsand 17 states

Means Normal F ratio Variety index

Grains 1.224 0.959 0.062

Pulses 1.034 0.932 0.018

Dairy 1.222 0.896 0.004

Meat 1.057 0.951 0.011

Oil 1.007 0.968 0.001

Vegetables 1.107 0.917 0.007

Fruits and nuts 1.105 0.889 0.022

Spices 1.054 0.986 0.009

Beverages 1.099 0.914 0.013

Processed 1.114 0.873 0.015

Food index mean 1.133 0.024

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Table 16: Changes in All India parameter estimates over time

Year 1983 1987-88 1993-94 1999-00 2004-05

Aggregate g(�g − 1)

Grains and pulses 0.31 0.31 0.28 0.31 0.33

Dairy,meat,oil 0.41 0.34 0.30 0.27 0.31

Veg. and fruit 0.53 0.63 0.64 0.63 0.58

Spices,bev.,proc. 0.66 0.62 0.56 0.60 0.61

Individual g(�g − 1)


Dairy,meat,oil 0.40 0.39 0.39 0.38 0.38

Veg. and fruit 0.37 0.39 0.40 0.42 0.42

Spices,bev.,proc. 0.15 0.18 0.18 0.20 0.21

Engel curve 1�g− g


Dairy,meat,oil 0.38 0.34 0.34 0.36 0.35

Veg. and fruit 0.43 0.48 0.52 0.47 0.52

Spices,bev.,proc. 0.14 0.14 0.15 0.11 0.10


Table 17: Differences in state/sector aggregate hierarchy slope estimates for 2004-2005

Group Grains and pulses Dairy,meat,oil Veg. and fruit Spices,bev.,proc.

Sector rural urban rural urban rural urban rural urban

Andhra Pradesh 0.09 0.12 0.53 0.42 0.69 0.71 0.60 0.52

Assam 0.08 0.12 0.62 0.64 0.58 0.63 0.61 0.61

Bihar 0.24 0.30 0.41 0.35 0.33 0.43 0.56 0.59

Delhi 0.25 0.23 0.62 0.64

Gujarat 0.55 0.32 0.34 0.33 0.63 0.77 0.47 0.61

Haryana 0.16 0.20 0.13 0.18 0.62 0.64 0.37 0.49

Himachal Pradesh 0.40 0.37 0.21 0.31 0.55 0.67 0.44 0.39

Jammu and Kashmir 0.21 0.24 0.34 0.36 0.50 0.64 0.55 0.63

Karnataka 0.37 0.27 0.44 0.37 0.54 0.59 0.58 0.46

Kerala 0.13 0.14 0.62 0.63 0.27 0.29 0.52 0.42

Madhya Pradesh 0.35 0.32 0.36 0.32 0.53 0.64 0.43 0.49

Maharashtra 0.58 0.41 0.53 0.38 0.67 0.85 0.41 0.58

Orissa 0.10 0.17 0.74 0.65 0.38 0.49 0.62 0.64

Punjab 0.18 0.20 0.15 0.17 0.61 0.66 0.35 0.52

Rajasthan 0.20 0.12 0.18 0.29 0.67 0.67 0.39 0.56

Tamil Nadu 0.13 0.15 0.56 0.39 0.59 0.65 0.55 0.45

Uttar Pradesh 0.27 0.28 0.29 0.25 0.37 0.46 0.45 0.56

West Bengal 0.11 0.19 0.69 0.66 0.39 0.46 0.69 0.64

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Table 18: Cost-of-living indexes allowing for differences in state/sector � and parameters

Welfare gains

Normal Mid High

Variable parameter � and Just � and Just

Over time 1983-2005 index

Food index mean 4.214 0.022 0.033 0.037 0.061

Urban-rural index 2004-2005

Food index mean 1.134 0.006 0.012 0.010 0.022


Table 19: Migration and urban dummy estimates by group

Group Grains/pulses Dairy,meat,oil Veg./fruit Spice,bev,proc.

log(real expenditure) 0.225 0.314 0.435 0.190

(0.002) (0.001) (0.002) (0.002)

Urban 0.113 0.054 0.114 -0.023

(0.004) (0.004) (0.004) (0.003)

Rural to Urban migrant 0.006 0.004 0.004 -0.081

(0.005) (0.004) (0.005) (0.006)

Urban to Rural migrant 0.143 0.067 0.085 0.053

(0.011) (0.009) (0.009) (0.009)

Rural to Rural migrant 0.053 0.029 0.050 -0.011

(0.004) (0.004) (0.004) (0.004)

Urban to Urban migrant 0.101 0.007 0.009 -0.034

(0.006) (0.005) (0.006) (0.006)

OLS with state fixed effects for 17 states in 1987-88. Robust standard errors in parentheses.

Uses all household controls from before plus PDS dummy.

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Table 20: OLS regression of food variety on district level covariates for 1987-1988.

Coefficient robust standard error

Dependent variable: log variety R2 = 0.48

Per capita expenditure 0.387∗ 0.041

Population. Density 0.009 0.013

Road density 0.036∗ 0.011

Agricultural Wage -0.026 0.024

Distance from coast −0.059∗ 0.011

Altitude 0.073∗ 0.024

Dep. variable: log residual variety R2 = 0.24

Per capita expenditure 0.280∗ 0.091

Population Density 0.030 0.034

Road density 0.059∗ 0.021

Agricultural Wage −0.170∗ 0.053

Distance from coast −0.106∗ 0.022

Altitude 0.145∗ 0.048

N=267 Indian districts. All variables in logs.

∗ denotes significant at the 1% level.


Figure 1: Total variety Engel curves over time for households with 5 members

Figure 2: Food variety Engel curves over time for households with 5 members

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Figure 3: Total variety Engel curves for rural/urban sectors and households with5 members

Figure 4: Food variety Engel curves for rural/urban sectors and households with5 members


Figure 5: Consumption ‘hierarchy’ for 4 group classification

Figure 6: Consumption ‘hierarchy’ for 10 group classification

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Figure 7: Grains and pulses: Share of consuming households by good and expen-diture quintile for Maharashtra in 2004-05. Goods ordered by aggregate expen-diture share.

Figure 8: Grains and pulses: Mean expenditures conditional on consumption bygood and expenditure quintile for Maharashtra in 2004-05. Goods ordered byaggregate expenditure share.


Figure 9: Quadratic fit of log of food unit value index, variety index, and Feen-stra index (unit value*variety) on log food expenditures. The base householdfor index construction is the richest household in each village and urban block.Estimation uses village and urban block fixed effects.

Figure 10: Graphical representation of consumption hierarchy, where total areaof the triangle is equal to total expenditures

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Figure 11: Scatter plot of nominal food expenditure ratio against price ratio andmid variety welfare effect for 62 regions over 1983-2004/2005

Figure 12: Scatter plot of nominal food expenditure ratio against urban-ruralprice ratio and mid variety welfare effect for 17 states, 2004-2005

an engel curve for variety: household food consumption and welfare

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