Journal of Public Economics 97 (2013) 272–281

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Journal of Public Economics

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The price and utility dependence of equivalence scales: Evidence from Indonesia☆

Joppe de Ree a,⁎, Rob Alessie b,c, Menno Pradhan d,e

a The World Bank, Jl. Jenderal Sudirman Kav 52-53, Jakarta 12190, Indonesiab University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlandsc Netspar, P.O. Box 800, 9700 AV Groningen, The Netherlandsd VU University Amsterdam, De Boelelaan 1105, 1081 HV, Amsterdam, The Netherlandse University of Amsterdam, De Boelelaan 1105, 1081 HV, Amsterdam, The Netherlands

☆ We thankMaarten Bosker, Adriaan Kalwij, Ines LindnSoest and Bastian Westbrock for helpful comments and dto thank one anonymous referee for very helpful comm⁎ Corresponding author.

E-mail address: joppederee@gmail.com (J. de Ree).

0047-2727/$ – see front matter © 2012 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.jpubeco.2012.09.006

a b s t r a c t

a r t i c l e i n f o

Article history:Received 16 September 2010Received in revised form 11 August 2012Accepted 25 September 2012Available online 23 October 2012

JEL classification:D11D12

Keywords:Equivalence scalesIndependence of baseConsumer demandSubjective wellbeing

The purpose of this research is to estimate equivalence scales and evaluate their price and utility dependen-cies. To do this we unify two strands of the empirical literature on this topic, one that relies on demand dataand one that relies on subjective evaluations of wellbeing. This way we are able to employ the strengths ofboth kinds of information. Equivalence scales are not identified from demand data alone. This is becausechanges in demographics could affect wellbeing directly, i.e., in ways that are not revealed by changes in be-havior. The demand-based literature rules out such effects a priori and restricts parameters that measurethem. In this paper we do not rely on such restrictions and instead use subjective evaluations of wellbeingas an additional source of information. Because demand data are highly informative about some of theother parameters of the model its use increases efficiency. This becomes critical once we specify complexpreference structures that allow for the equivalence scale's dependence on price and utility. Our modelnests the typical models used in the subjective and the demand literature and we are able to test downboth kinds. We find evidence for direct utility effects. This rejects the validity of some of the restrictions ap-plied by the demand literature within the Indonesian context. We estimate equivalence scales that are of rea-sonable magnitude and decrease in utility. We also find that the scales increase in the food to nonfood priceratio for poor households, whereas we do not find price dependence for more affluent households.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Household expenditures per capita are widely used as indicatorsof welfare in all kinds of applied welfare analysis. Expenditures percapita however are imperfect measures of welfare by disregardingthe potential for household economies of scale. Two person house-holds can share (to a certain extent) the house, the washing machineand the car. Indeed, a two person household needs more than a singleindividual to reach the same level of utility, but generally, not twice asmuch. For making welfare comparisons across households of differentsizes and compositions it is important to take this into account.

Equivalent expenditures xe are ordinal money-metric measures ofutility that take possibilities for household economies of scale explicitlyinto account by scaling household expenditures (or income) x with anhousehold specific equivalence scale I, i.e., xe=x/I. Equivalence scales

er, Giacomo Pasini, Arthur vaniscussions. We also would likeentary.

rights reserved.

depend in general on demographic variables, commodity prices andon utility itself and are defined as follows.

I z;p;uð Þ ¼ c z;p; δ u; zð Þð Þcr p;uð Þ ð1Þ

where c is the household cost function measuring the minimum cost ofreaching utility level u for given demographic characteristics z andprices p. cr measures the minimum cost of reaching the same utilityu for a reference household, facing the same prices p. The referencehousehold in our study is a single individual.1

Expenditures per capita can be seen as a special case of equivalentexpenditures where the equivalence scale is equal to the size of thehousehold. Because of the potential for economies of scale howeverequivalence scales should generally be smaller than household size it-self. Equivalence scales increase (decrease) when less (more) econo-mies of scale can be reached. Poor households in Indonesia spend alarge percentage of their income on foods, which are rival goods.For this reason, poor households might not benefit much from

1 c(zr,p,δ(u,zr))=cr(p,u) where zr is the household composition of the referencehousehold.

273J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

economies of scale. This would imply that equivalence scales decreasein utility.

The purpose of this research is to estimate equivalence scales andevaluate its utility and price dependencies. It is well known howeverthat equivalence scales are not identified from observed demand re-sponses (Pollak and Wales, 1979). To describe the problem we haveintroduced a δ function in Eq. (1). The parameters of c, excludingthose of δ, are defined to uniquely describe indifference curves ingoods space conditional on household composition z and prices. Bydefault, then, the parameters of δ measure how the utility level ofeach of these indifference curves depends on z.2 Demands can onlyidentify the parameters of c up to the δ function, whereas equivalencescales, in general, depend on all parameters of the cost function, includ-ing those of δ. This captures the idea that demographic shifts may affectwellbeing in ways that are not reflected through changes in demands.Blundell and Lewbel (1991) show that in fact only the price dependenceof equivalence scales can be uniquely identified from demands.

In this paper we unify two strands of the empirical literature onequivalence scales that each have their unique strengths and weak-nesses. Combining them provides a way of utilizing the strengths ofboth. A demand literature investigates the boundaries of what canstill be identified from demands, but must apply restrictions on thecost function which subsequently permit unique identification ofthe scales. These restrictions include ruling out the possibility that de-mographic changes affect utility directly, i.e., δ(u,z)=δ(u).3 The sub-jective literature is not subject to the identification problem discussedin the previous paragraph, but its modeling tradition is usually moread hoc in nature and tends to impose strong restrictions on theirmodels for other, perhaps practical, reasons.4

The use of subjective evaluations of wellbeing circumvents theneed of restricting δ(u,z)=δ(u). Demand data provides additionalvariation that substantially increases the precision with which pa-rameters are estimated. Indeed, demands cannot identify the param-eters of the δ(u,z) function, but they are highly informative about theremaining parameters of the cost function.

In our empirical application we specify a translated quadraticalmost ideal demand system (Lewbel, 2003). We then generalizethis model by introducing a set of parameters that is not identifiedfrom demands, i.e., the δ parameters. We use data on self reportedwellbeing and demands in combination with data on prices and de-mographics and jointly estimate the parameters of the cost functionusing a two equation quasi maximum likelihood model, one equationfor the subjective evaluations of wellbeing and one equation for the

2 Equivalence scales are usually expressed as functions of utility. For operationalpurposes it can be useful to express the equivalence scale in terms of expenditures x.Inverting the cost function with respect to u obtains the indirect utility functionu=u(z,p,x). Imputing u(z,p,x) back into Eq. (1) gives the equivalence scale in termsof expenditures x.

3 Perhaps the most well-known example of this is the Independence of Base(Lewbel, 1989) or Equivalence Scale Exactness (Blackorby and Donaldson, 1993) re-striction, which imposes that equivalence scales are independent of utility. SeePendakur (1999), Donaldson and Pendakur (2004, 2006) for some other importantexamples.

4 See Van Praag and Kapteyn (1978), Pradhan and Ravallion (2000) and Schwarze(2003) for examples of the subjective literature. All three introduce preference func-tions that are additive in expenditures or incomes, household demographics andprices. These systems are therefore Cobb–Douglas, thereby being inconsistent withthe patterns typically observed in demand data (Banks et al., 1997). Their restrictionsalso imply that equivalence scales are independent of prices and utility. See alsoKoulovatianos et al. (2005) and Olken (2005) for other creative variations on the sub-jective method. Koulovatianos et al. (2005) have put forward survey questions whichdirectly measure the respondent's estimates of equivalence scales at different (partlyhypothetical) income levels and demographic situations. Olken (2005) uses Indone-sian data to estimate the equivalence scale based on discretionary allocations of wel-fare benefits to households, the subjective assessment of welfare therefore comesfrom local leaders who allocate welfare benefits. Alessie et al. (2006) use subjective da-ta on financial satisfaction to estimate “indifference scales” a concept introduced byBrowning et al. (2006).

demand system.5 Our model nests some of the main specificationsused in the demand and subjective literatures and is thus able to sta-tistically evaluate the validity of these separate approaches.

The main findings of our analysis are summarized as follows. First,the equivalence scales we estimate are of reasonable magnitude.With a single person household as the reference we find equivalencescales of around 1.5, 1.9, 2.3, and 2.7, for 2, 3, 4, and 5 person house-holds respectively. Second, we find that our model greatly outper-forms the additive Cobb–Douglas type model typically used in thesubjective literature. Third, we find statistically significant price andreference utility effects. Equivalence scales increase in the food tonon-food price ratio for poor households, whereas we find hardlyany price dependence for more affluent households.6 Moreover, wefind that equivalence scales decrease in utility on the whole pricedomain, indicating that more affluent households benefit more fromeconomies of scale. A final result is that we find evidence for theexistence of direct utility effects that are not reflected through de-mands, i.e., δ(u,z)≠δ(u). This rejects the demand based approachesat least within the context of our model specification and our data.

The paper is organized as follows. Section 2 describes the model,discusses the various restrictions on this model that have beenapplied in both the demand and subjective literatures, and discussesidentification. Section 3 describes the data we use and a number ofrelevant stylized facts. Section 4 presents the regression results,tests on the various restrictions applied the literature, the equiva-lence scales we calculate based on the regression results, and theresults of an overidentification test on the identification strategy.Section 5 concludes.

2. Models and restrictions

We specify an indirect utility function that is essentially a straight-forward extension of the translated quadratic almost ideal demandsystem, or translated QUAIDS (Lewbel, 2003):

u z;p; xð Þ ¼ δ0 zð Þ ln x−d p; zð Þð Þ−ln a p; zð Þb p; zð Þ

� �−1þ λ p; zð Þ

� �−1

þ δ1 zð Þ

ð2Þ

where x denotes total expenditures. The parameters δ0(z) and δ1(z)are key preference parameters that are not identified from demandanalysis.

The household cost function, the building block of the equivalencescale, can be constructed by deriving the inverse of the indirect utilityfunction (2) with respect to total expenditures x. Cost functions, then,are imputed in the formula for the equivalence scale (1):

I z;p;uð Þ ¼exp b p; zð Þ u−δ1 zð Þ

δ0 zð Þ

� �−1−λ p; zð Þ

� �−1

þ ln a p; zð Þ" #

þ d p; zð Þ

exp br pð Þ u−δ1rδ0r

� �−1−λr pð Þ

� �−1

þ ln ar pð Þ" #

þ dr pð Þ

ð3Þ

where br(p)=b(p,zr), δ0r=δ0(zr), δ1r=δ1(zr), λr(p)=λ(p,zr), ar(p)=a(p,zr), and dr(p)=d(p,zr), where zr is the composition of the referencehousehold, i.e., a single individual. The equivalence scale, in general, willdepend on the parameters δ0(z) and δ1(z). In Section 2.1 we willsee that demand analysis will not reveal these parameters. Themethod-ology we describe in the rest of the sections does.

5 We analyze food and nonfood consumption expenditures in a two good demandsystem, which amounts to only a single demand equation. The approach described inthis paper can be straightforwardly extended to a multi-good model.

6 The difference in price responses of demand between the rich and the poor is atopic of current research, e.g., Blundell et al. (2011) and Lewbel and Pendakur (2009).

274 J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

In the empirical application we consider two composite goods,food and non-food consumption expenditures, in a two-good demandsystem. The functions a, b, λ and d are defined as follows:

ln a p; zð Þ ¼ α0 zð Þ þ α1 zð Þln pf

pnfþ ln pnf þ 0:5γ ln

pf

pnf

!2

ð4aÞ

b p; zð Þ ¼ pf

pnf

!β1 zð Þð4bÞ

λ p; zð Þ ¼ λ1 zð Þ lnpf

pnf−λ0

!ð4cÞ

d p; zð Þ ¼ d1 zð Þpf þ d2 zð Þpnf ð4dÞ

where pf is the price of food and pnf is the price of non-food. Thefollowing model parameters are permitted to depend on demo-graphics z (in our empirical operalization z is household size)7,8:

α0 zð Þ ¼ α00 þ αz

0ln z ð5aÞ

α1 zð Þ ¼ α01 þ αz

1ln z ð5bÞ

β1 zð Þ ¼ β01 þ βz

1ln z ð5cÞ

λ1 zð Þ ¼ λ01 λz

1� �ln z ð5dÞ

di zð Þ ¼ d0i þ dzi ln z ∀i ¼ 1;2 ð5eÞ

δ0 zð Þ ¼ δ00 δz0� �ln z ð5fÞ

δ1 zð Þ ¼ δ01 þ δz1ln z ð5gÞ

2.1. Identification from demand data

Only a specific set of the parameters of Eq. (2) can be identifiedfrom demand analysis. Applying Roy's identity to Eq. (2) yields thefollowing Marshallian budget share demand equation for food con-sumption.

wf z;p; xð Þ ¼x−d p; zð Þ

xd1 zð Þpf

x−d p; zð Þ þ α1 zð Þ þ γ lnpf

pnfþ β1 zð Þln mþ λ1 zð Þ

pf =pnf

� β1 zð Þ ln mð Þ20B@

1CA

ð6Þ

7 The parameters λ1(z) and δ0(z) are parameterized differently than the others. Themodel parameters depend on price normalizations: changing base price year, orchanging the size of the commodity basket will affect size and significance levels ofthe parameter estimates. This has implications. It, for example, limits the ways inwhich parameters are permitted to be interacted with household size without affectingthe fundamental predictions of the model. For this reason we have also introduced aparameter λ0 in Eq. (4c). This parameter does not appear in the demand system, butis an important nuisance parameter for when we use subjective data. It is beyond thescope of this paper to further elaborate on this issue, but analytical results are availableupon request.

8 It is often seen that the b(p,z) function has also a β0(z) term, for example, in the

following way: b̃ p; zð Þ ¼ β0 zð Þ pf

pnf

� �β1 zð Þ. The terms β0(z), δ0(z) and λ1(z) would not

be separately identified however. For ease of exposition we chose to normalize sucha model by imposing β0(z)=1, rather than discuss composite parameters. The normal-ization has no fundamental implications and does not affect the estimates and testspresented in the remainder of the text. See also Donaldson and Pendakur (2004) fora discussion.

where ln m= ln(x−d(p,z))− ln a(p,z). The parameters δ0(z), λ0 andδ1(z) donot appear in thedemand system. Because equivalence scales de-pend on these parameters it shows that equivalence scales are not identi-fied from demand data alone. It should be clear however that demanddata is highly informative about the parameters that do appear in Eq. (6).

The demand literature on equivalence scales typically relies onspecific assumptions on preferences that permit unique identificationof the scales. We consider three kinds of these restrictions. Perhapsthe most well known restriction on preferences is the independenceof base (IB) restriction (Lewbel, 1989) or otherwise known as equiv-alence scale exactness (ESE) (Blackorby and Donaldson, 1993). Underthis restriction equivalence scales are independent of utility. TheIB/ESE restriction is the following:

IB=ESE → βz1 ¼ d01 ¼ dz1 ¼ d02 ¼ dz2 ¼ δz1 ¼ 0; λz

1 ¼ δz0 ¼ 1andλ01≠0

ð7Þ

An important implication of IB/ESE is that it restricts the parame-ters δ1z=0 and δ0z=1, which are not identified from demand analysis.This is the central assumption that permits complete identification ofIB/ESE scales from demand data under the additional requirementthat preferences are not PIGLOG.9

Obviously, the restrictions δ1z=0 and δ0z=1 can never be testedwithin a demand framework either, even if the IB/ESE restrictionsare tested in a semiparametric setting like in Pendakur (1999). TheIB/ESE hypothesis can only be tested partially by evaluating the re-strictions on the parameters that are identified from demand. Becausewe use subjective data an additional source of information we areable to run a full test on the IB/ESE concept.

On the basis of theoretical considerations and empirical evidence ithas been recognized that IB/ESE is perhaps too strict (see e.g.,Donaldson and Pendakur (2004, 2006)). It is conceivable that equiva-lence scales decrease in utility for example.10 Poor households mightbenefit less from economies of scale as a large fraction of total expendi-tures is allocated to rival goods like food.

To accommodate this possibility Donaldson and Pendakur (2004,2006) have introduced generalized equivalence scale exactness, orGESE, and generalized absolute equivalence scale exactness, or GAESE.Within the context of our model GESE and GAESE are maintained if:

GESE → d01 ¼ dz1 ¼ d02 ¼ dz2 ¼ δz1 ¼ 0; δz0 ¼ λz1 andλ

01≠0 ð8Þ

GAESE → βz1 ¼ δz1 ¼ 0; λz

1 ¼ δz0 ¼ 1andλ01≠0 ð9Þ

Similarly to IB/ESE, GESE and GAESE also restrict the parameters δ0z

and δ1z .Note that GESE is not nested in GAESE or vice versa. Both GESE and

GAESE relax IB/ESE and both allow equivalence scales to depend onutility, but in different ways. GESE and GAESE maintained scales canonly be uniquely identified from demands under the additional re-quirement that the reference cost function is not PIGLOG (GESE andGAESE) or Gorman polar form (GAESE).

The final set of restrictions we introduce relates to the equivalencescale's dependence of price. It can be easily derived that equivalencescales do not depend on prices if compensated budget shares areequal across household sizes, for each utility level and prices.

∂ ln I z;p;uð Þ∂ ln pf

¼ ∂ ln c z;p;uð Þ∂ ln pf

−∂ ln cr p;uð Þ∂ ln pf

¼ wf z;p;uð Þ−wrf p;uð Þ ¼ 0

ð10Þ

9 The indirect utility function (2) is not PIGLOG if λ10≠0.

10 This intuition is confirmed in survey study conducted by Koulovatianos et al.(2005). According to this survey people believe that equivalence decline withexpenditures.

275J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

wherewfr(p,u) is the food budget share of the reference household.With-

in the context of our model specification this condition is satisfied if atleast one of three different restrictions on the parameters is satisfied:

1. β10=β1

z=λ10=d1

0=d1z=d2

0=d2z=α1

z=0. This is a Cobb–Douglasspecification, yet more general than the typical model used in thesubjective literature.

2. d10=d1z=d2

0=d2z=α1

z=β1z=δ1z=0 and δ0z=λ1

z=1. This restric-tion corresponds to Engel scales.

3. α0z=α1

z=β1z=d1

z=d2z=δ1z=0 and λ1z=δ0z=1. For completeness

we also report this condition. The condition implies that all equiva-lence scales are equal to 1, and thus are also independent of prices.

These restrictions indicate that only in very special circumstancesequivalence scales are independent of prices.

2.2. Identification from subjective data

A change in household demographics could affect utility inways thatare not revealed by changes in demands. Within the context of ourmodel such effects are captured by the δ parameters. Because these pa-rameters do not appear in the demand systemweneed additional infor-mation to estimate them. A solution proposed in the literature is tomeasure utility directly using subjective evaluations of wellbeing.

The existing empirical literature on self reported wellbeing tendsto rely on rather elementary empirical specifications and usuallypresents utility functions that are additively separable in x, z and p.These preference systems are Cobb–Douglas and predict budgetshare demand equations that are constants, and simultaneously as-sume that equivalence scales are independent of prices and utility.See for example Van Praag and Kapteyn (1978), Schwarze (2003)and Pradhan and Ravallion (2000) within the context of equivalencescales, but also Blanchflower and Oswald (2004), out of many, withinthe broader subjective wellbeing literature.

The typical Cobb–Douglas type model is also nested in ourmodel Eq. (2):

typical subjective model → d01 ¼ dz1 ¼ d02 ¼ dz2 ¼ γ ¼ β01 ¼ βz

1

¼ αz1 ¼ λ0

1 ¼ 0; δz0 ¼ 1

Such extreme restrictions on Eq. (2) are not strictly necessary forthe theoretical identification of equivalence scales based on subjec-tive evaluations of utility.11

The subjective information we use in this paper comes from thefollowing questions, which were asked to a sample of Indonesianhousehold heads12,13:

Q1. In the past month, has your food consumption been adequatefor your household needs?

1. no2. yes3. more than adequate4. do not know

11 See also Kapteyn (1994) and Van Praag and der Sar (1988) for examples of moreflexible parameterizations within the context of the literature on the individual wel-fare function of income.12 Questions on self-rated consumption adequacy have already been part in varioussurveys across developing countries. Pradhan and Ravallion (2000) for example useconsumption adequacy data from Jamaica and Nepal to estimate subjective povertylines. Such questions are of the type where individuals are asked to rate their own in-come, consumption of welfare level as above or below a certain subjective value. Thecommonly asked satisfaction question — how satisfied are you with your life as awhole, on a scale from 1 to 10? — also fits within this description. Such questions in-tend to evaluate the current situation of the respondent and do not attempt to measurewellbeing in hypothetical situations (like in e.g., Van Praag and Kapteyn (1978) orKoulovatianos et al. (2005)).13 Only a small fraction of the households report 3.more than adequate. We thereforegroup the households who report 2. adequate and 3. more than adequate together inestimation.

Q2. In the past month, has your nonfood consumption been ade-quate for your household needs?

1. no2. yes3. more than adequate4. do not know

In what follows we will show that under some assumptions theparameters of model (2) can be identified on the basis of only oneof these questions. The fact that we have two of these questionsallows us to test the identifying assumptions.

Intuitively, identification comes from the feasibility of calculating thefraction of households that report consumption adequacy frac(z,p,x) foreach combination z,p,x. This permits the construction of a kind of equiv-alence scale that compares themonetary costs associatedwith each fracfor households that differ in terms of their demographics. We canmakethese comparisons for different levels of f rac z;p; xð Þ and therebyallowing equivalence scales to vary with frac for example. This would,in a sense, measure the equivalence scale's dependence on utility.14

It is important however to establish a link between the broaderutility concept, the adequacy questions, and the fraction of consump-tion adequate households. The literature typically interprets ques-tions like Q1 and Q2 as follows: food consumption adequacy (Af=1)means that u(z,p,x)>Tf, where Tf is a threshold, non-food consump-tion adequacy (Anf=1) means that u(z,p,x)>Tnf (see e.g., Pradhanand Ravallion (2000)). We show that under some assumptions thefraction of consumption adequate households frac(z,p,x) is also ameasure of utility.

frac(z,p,x) is an unbiased nonparametric estimator of the probabil-ity of consumption adequacy, conditional on z,p,x. We can further de-rive:

P�Ak ¼ 1 z;p; x

¼ P

�u z;p; x�

> Tk z;p; x

∀k ¼ f ;nf

¼ FTk jz;p;x u z;p; xð Þð Þ ∀k ¼ f ;nf

ð11Þ

where FTk z;p;xj is the conditional CDF of the threshold Tk. The key iden-tifying assumption we make in paper is that the utility function iscorrectly specified by Eq. (2) and that the thresholds Tf and Tnf areidentically and independently distributed conditional on z,p,x.Under these assumptions we can derive that the fraction of consump-tion adequate households frac(z,p,x) is an unbiased nonparametricestimator of a monotonic transformation of utility u:

E frac z;p; xð Þ z;p; xj � ¼ FTku z;p; xð Þð Þ

hð12Þ

Because FTkis a monotonically increasing transformation of utility

u, FTku x; z;pð Þð Þ itself is proper measure of utility. In principle we do

not need specific functional assumptions on FTkfor identification. In

this paper however we impose normality on FTk.15

The above shows that under some assumptions equivalence scalesare fully identified from only a single question on consumption ade-quacy. These assumptions might not be appropriate. We have how-ever two consumption adequacy questions, one for food and one for

14 ln x(frac,z)− ln x(frac,z0) could be derived for different levels of frac.15 In line with the demand based literature on equivalence scales we assume thatthere is no randomness in the utility function. The randomness comes from the thresh-olds Tk, the heterogeneity in reporting behavior. We could also allow for randomness ein the utility function, in addition to just randomness in the thresholds Tk and still ob-tain a useful interpretation of the equivalence scales we estimate in this paper. Obvi-ously, the introduction of randomness in the utility function prevents us fromestimating separate utility function for each household: two households with exactlythe same characteristics z,p,x could have different utilities. If e is weakly separablefrom z,p,x and identically and independently distributed conditional on z,p,x ourequivalence scale estimates still have a clear and useful interpretation. Our equivalencescales, then, are expected utility equivalence scales, which can be used for welfarecomparisons on average. The proof of this is presented in Appendix A.

Table 1Reporting statistics on food and non-food consumption adequacy.

276 J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

non-food. Following the logic above it must be true that bothFTf

u z;p; xð Þð Þ and FTnfu z;p; xð Þð Þ are both (different) monotonic trans-

formations of the same underlying utility concept. Equivalence scalesthat are estimated on the basis of either food or non-food consumptionadequacy, therefore, must be the same. We test this overidentifyingrestriction in Section 4.2.

2.3. Unifying subjective and demand data in one integrated econometricframework

In this section we present a way of unifying both subjective anddemand information in one econometric framework. The previoussections have identified two theoretical models, the indirect utilityfunction Eq. (2) and, based on that, the model for the budget shareof food consumption Eq. (6).

We estimate the parameters of those two models with a twoequation quasi maximum likelihood procedure. The first equation uti-lizes the relationship between the consumption adequacy data andthe utility function Eq. (2) based on Eq. (11).

P Ait ¼ 1 zit ;prt ; xitj Þ ¼ P u zit ;prt ; xitð Þ > Tit zit ;prt ; xitj Þðð ð13Þ

where Ait is an observed binary indicator of consumption adequacy,u(zit, prt, xit) is the utility function specified in Eq. (2), and Tit is a ran-dom threshold.

The second empirical model is a single-equation demand system:

wfit ¼ wfit zit ;prt ; xitð Þ þ vit ð14Þ

where wfit is the observed budget share of food consumption ofhousehold i at time t, wfit(zit, prt, xit) is the theoretical model specifiedin Eq. (6) and vit is an individual and time specific error term.16

Both Eqs. (13) and (14) are estimated jointly with maximum like-lihood. We impose the following assumptions on the random thresh-old Tit and the idiosyncratic error term in the demand system vit:

Titvit

� �zit ;prt ; xit ∼ NID 0

0

� �;

1 00 σ2

v

� �� � ð15Þ

Without loss of generality, the variance of the threshold Tit is nor-malized to one.17

In estimation we allow the random components Tit and vit to becorrelated within villages and over time, using a clustering command.This means that we are estimating a marginal likelihood function(that is correctly specified for a single household in one period). Thestandard errors are adjusted afterwards. We use the following mar-ginal likelihood function in estimation:

Lit ¼ g Ait zit ;prt ; xit ; θd; θs

� h wf it zit ;prt ; xit ; θ

d;σ2

v

��ð16Þ

h is the conditional density associated with the food budget sharemodel and g is a conditional Bernoulli distribution associated with thebinary outcome variable Ait. θd are the model parameters that aretheoretically identified from demand analysis, hence, the parametersthat appear in the demand Eq. (6). θs are the additional parametersthat are only identified from using subjective data, hence, the param-eters δ0, δ1 and λ0.

Because the parameter vectors θd and θs are both present in g wecould at least in principle rely on data on self reported consumption

16 We introduce two indices i for household and t for time in order to highlight thelongitudinal nature of our dataset. Prices are region-time specific and are indexed withr and t.17 The arbitrary normalizations that are usually applied in binary outcome models,such as, for example, a normalization of the conditional mean and variance to 0 and1 respectively, are irrelevant for our final outcomes (i.e., equivalence scales). See alsoSection (4.2).

adequacy, prices, demographics and total expenditures alone to esti-mate all necessary parameters, using only the g part of the likelihoodfunction.

LSUBJECTIVEit ¼ g Ait zit ;prt ; xit ; θd; θs

�ð17Þ

Obviously, neglecting the h element of the likelihood function willsacrifice efficiency. In Section 4 we will estimate the parameters usingboth likelihood functions and show the importance of using demanddata, alongside data on consumption adequacy, for reasons of statisti-cal efficiency.

3. Data and stylized facts

For this research we use an unexploited micro consumption paneldata set drawn from the Indonesian National Socioeconomic Survey(henceforth SUSENAS). The SUSENAS is a nationally representativesurvey among Indonesian households and interviews about 200,000households on a yearly basis. Listings of consumption expenditureitems of this broad survey however are limited. From 2002 up to2004 the SUSENAS has selected a subset of about 10,000 householdsfrom the original SUSENAS to take part in a consumption panel. Inaddition to a more detailed set of consumption expenditures and de-mographic variables, these households were asked to rate their re-spective (levels of) food and non-food consumption as adequate orinadequate for their particular household's needs (only the 2003and 2004 wave). The exact phrasing of the questions is discussed inthe previous section. We exclude the households that reported donot know to either one of the two questions (about 8% of the observa-tions). After the selection we have 18,242 observations (from thewave 2003 and 2004).

Most households (85%) provided the same answer to both the foodand the non-food adequacy question (15,524 observations). In ourbaseline models we only use these observations. We will refer to(total) consumption adequate households when both food and non-food consumption are reported adequate. Consumption inadequatehouseholds report that both food and non-food consumption are notadequate for household needs. In Section 4.2 we use both food andnon-food adequacy data separately to test the overidentifying restric-tions the identification strategy prescribes. Table 1 presents the sum-mary statistics.

It is unlikely that all respondents have exactly the same concept inmind when they answer Q1 and Q2. This is another way of saying thatit is likely that there is some heterogeneity in the thresholds Tf and Tnf.Still, we expect that there is some general understanding about whatconsumption adequacy means. At the minimum, consumption ade-quacy should be positively associated with total expenditures, condi-tional on the size of the household. Furthermore, because morepeople means more mouths to feed, we expect that consumption ad-equacy is negatively associated with the size of the household, condi-tional on total expenditures. The left panel of Fig. 1 shows that this isindeed the case. It also shows that the curves for different householdsizes are converging for higher levels of total expenditures. Following

NONFOOD consumption adequacy

No Yes Total

FOOD consumptionadequacy

No 4658 517 5175Yes 2201 10,866 13,067Total 6859 11,383 18,242

Note. Total numbers of observations reporting food consumption adequacy andnon-food consumption adequacy.

.4.6

.81

frac

. con

sum

ptio

n ad

equa

cy

−1 −.5 0 .5 1log total consumption

1 prs. household

2 prs. household

3 prs. household

4 prs. household

by household sizeAdequacy in log total consumption

0.2

.4.6

.81

food

sha

re

−3 −2 −1 0 1 2log total consumption

1 prs. household

2 prs. household

3 prs. household

4 prs. household

by household sizeFood share in log total consumption

Fig. 1. Left panel: Fraction of consumption adequate households, as function of the log of total consumption expenditures. Right panel: Budget share Engel curves for food as func-tion of the log of total consumption expenditures.

277J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

the logic presented in Section 2.2, this is (nonparametric) support forthe idea that equivalence scales decrease in utility.18

The right panel of Fig. 1 shows the nonparametric relationship be-tween the food budget shares and the log of total expenditures(scaled with the food poverty line). The budget shares of food aredownward sloping and nonlinear functions of the logarithm of totalexpenditures. The nonlinearity is quite strong which is somewhatunusual. However, it supports the choice for a demand system thatallows for this nonlinearity. The nonlinearity in demands is importantsupport for the demand based literature on equivalence scales as IB/ESE, GESE, and GAESE based equivalence scales can only be uniquelyidentified if preferences are not PIGLOG. Moreover, the budgetshares consistently increase with household size for a given level ofexpenditures.

Another important observation is that budget shares seem to havethe same shape, in the sense that budget shares for different house-hold compositions are “related by a horizontal and vertical shift(Pendakur, 1999)”. Pendakur (1999) shows that IB/ESE restrictedutility functions predict budget shares that have this property. Theright panel of Fig. 1 therefore indicates that preferences could beIB/ESE. This contrasts, in some sense, the evidence we obtainedfrom the left panel of Fig. 1, which indicates that equivalence scalesdecrease in utility. Both pieces of information combined highlightthe value of our approach.

A final conclusion we can draw from the right panel of Fig. 1 is thatthe share equations are certainly not constant. This informally rejectsthe assumption of Cobb–Douglas preferences, the common model inthe empirical literature on subjective wellbeing.

In the analysis we use food poverty lines as a region and time spe-cific prices for food. The associated non-food prices are obtained usinga method similar to Ravallion and Bidani (1994).

4. Econometric results and equivalence scales

We report estimates of five different regression models in Table 2.The first four columns (1), (2), (3) and (4) only use subjective data inestimation (using the likelihood function Eq. (17)) and therefore dis-misses the information content of demand data.

Column (1) is a baseline specification and replicates the standardresult from the subjective literature. The significantly positive α0

z

parameter indicates that utility depends negatively on householdsize, after conditioning on x and p (see also Van Praag and Kapteyn(1978), Schwarze (2003) and Pradhan and Ravallion (2000)). As

18 ln x(frac,z)− ln x(frac,zr) tends to decrease in frac.

previously referred to, equivalence scales constructed from theseestimates would not depend on utility and prices.

Column (2) extends the baseline model and allows for the param-eters δ0 and α1 to depend on household size. A statistically significantα1z would indicate that equivalence scales depend on prices, whereas

a significant δ0z would indicate that equivalence scales depend onutility. We do not find evidence for either of these effects here.Column (2) however is still Cobb–Douglas, and the predicted de-mands from this model clearly contradict the nonlinear patterns indemands, which we saw in the right panel of Fig. 1.

Column (3) extends the model to the QUAIDS specification definedby (2), by restricting the translation parameters d1

0, d1z, d20 and d2z to

zero. In line with the column (2) results, most of the relevant parame-ters are very imprecisely estimated. On the basis of the column (3) re-sults we can perform some of the tests described in Sections 2.1 and2.2 of this paper. The test results can be quickly summarized.We cannotreject IB/ESE (p−val=0.41), and we also cannot reject price indepen-dence as two out of three different independence of price restrictionscannot be rejected (1. p−val=0.83, 2. p−val=0.49, 3. p−val=0.00following the three conditions presented in Section 2.1). A naive conclu-sion of these findings would be that there is no evidence for the utilityand price dependence of equivalence scales.

We also cannot reject GESE (p−val=0.96). Testing GAESE withinthe context of the QUAIDS is not useful as the GAESE restrictions col-lapse to the IB/ESE restrictions when the d parameters are restrictedto zero. We do reject however, the Cobb–Douglas model presentedin column (1) (p−val=0.03).

Column (4) presents the results of estimating the full extendedtranslated QUAIDS model, but only with subjective data as the primarysource of identification. The likelihood procedure converges, but doesnot produce standard errors for some of the parameters. The model isclearly complex, and subjective data, demographic variables, total ex-penditures and prices alone are not sufficiently informative to differen-tiate between the different parameters of the model.

In column (5) we estimate the same model as in column (4), buthere we rely on demands as an additional source of information. Thishas important implications for the precision with which the modelparameters are estimated. On the basis of the column (5) results wereject IB/ESE (p−val=0.000). In other words we reject the equiva-lence scale's independence of utility. Independence of price is also deci-sively rejected (1. p−val=0.000, 2. p−val=0.000, 3. p−val=0.000following the three conditions presented in Section 2.1).

This exercise clearly motivates the theoretical and empirical rele-vance of our study. Excluding variation in demands is problematic fortesting the price and utility dependence of equivalence scales. Subjec-tive data theoretically identifies all the important parameters of thecost function, but is insufficiently powerful to do this with reasonable

Table 2Parameter estimates.

(1) Cobb–Douglassubjective data

(2) Cobb–Douglassubjective data

(3) QUAIDSsubjective data

(4) transl. QUAIDSsubjective data

(5) transl. QUAIDSsubjective+demand data

α00 −1.624 (−25.03)*** −1.604 (−22.56)*** −1.644 (−1.38) 0.968 (6.23)*** −2.598 (−5.54)***

α0z 0.610 (17.66)*** 0.592 (12.97)*** 0.622 (1.82)* −0.325 (−2.06)** −0.549 (−3.04)***

α10 0.139 (0.99) 0.319 (1.63) 0.361 (1.29) 0.600 (1.41) 0.299 (2.63)***

α1z – −0.140 (−1.06) −0.221 (−0.71) 0.157 (0.48) 0.024 (0.97)

β10 – – −0.184 (−0.54) 0.167 (NC) 0.279 (3.65)***

β1z – – 0.260 (0.73) −0.196 (−0.50) −0.016 (−1.06)

λ10 – – 0.015 (0.16) 0.066 (1.64) −0.086 (−6.86)***

λ1z−1 – – 3.506 (0.22) 3.264 (NC) −0.269 (−6.82)***

γ – – 2.216 (2.69)*** 1.697 (1.85)* −0.313 (−4.67)***d10 – – – −0.048 (−0.37) 0.059 (8.80)***

d1z – – – −0.628 (−1.32) 0.019 (1.85)*

d20 – – – 0.061 (0.55) −0.001 (−0.10)

d2z – – – 0.474 (1.56) 0.010 (1.90)*

λ0 – – 0.707 (0.78) 0.039 (0.21) −1.330 (−1.93)*δ00 1.051 (15.13)*** 1.115 (10.30)*** 1.175 (8.36)*** 1.188 (6.73)*** 0.601 (3.37)***δ0z−1 – −0.047 (−0.75) −0.101 (−0.64) 0.145 (1.38) −0.032 (−0.58)δ10 – – 0.013 (0.01) 3.131 (NC) −0.379 (−1.39)δ1z – – 0.044 (0.10) −1.255 (−8.42)*** −0.912 (−3.49) ***ln σv – – – – −2.244 (−166.80)***# observations 15524 15524 15524 15524 15524log likelihood −8254 −8253 −8197 −8191 4474# clusters 396 396 396 396 396

Note. Column (1), (2), (3) and (4) use only consumption adequacy data (in addition to data on prices and household size). The model estimated in column (4) converged, but didnot produce standard errors for three parameters (NC, for not computed). This indicates problems with multicollinearity. Column (5) uses consumption adequacy data and demanddata simultaneously. The parameters λ1

z and δ0z are transformed in estimation. Also, the nuisance parameter σv is transformed in estimation. Clustered z statistics are in parentheses.* significant at 10%; ** significant at 5%; *** significant at 1%. We cluster on the district-urban/rural level (396 clusters).

278 J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

precision. Based on the columns (1)–(3) results we would spuriouslyconclude that equivalence scales are independent both of prices andutility. When using demands as an additional source of variation weconclude the exact opposite.

Another important contribution of this paper is that we can testthe validity of some of the demand based approaches by runningfull tests on concepts like GESE (Donaldson and Pendakur, 2004)and GAESE (Donaldson and Pendakur, 2006). The tests thereforecan be used to validate (or invalidate) these approaches. Beforepresenting the test results we would like to draw attention to themassively significant δ1z parameter in column (5). It indicates that in-creases in household size has depressing effects on householdwellbeing in Indonesia, which cannot be measured through observedchanges in behavior. This finding is first evidence against conceptslike GESE, GAESE or IB/ESE.

Having said that, the first requirement for whether demand anal-ysis alone would have been sufficient for estimating IB/ESE, GESE, orGAESE maintained scales is that preferences are not PIGLOG. Prefer-ences cannot be PIGLOG if λ1

0≠0. The restriction λ10=0 is clearly

rejected. The nonzero λ10 picks up the nonlinearity in the budget

shares we already observed in Fig. 1.Both GESE (p−val=0.000) and GAESE (p−val=0.000) are

rejected at the 1% level. At least within the Indonesian context, andwithin the context of our model specification, concepts like GESE andGAESE seem not appropriate. Our results, in some sense, contrastsKoulovatianos et al. (2005) who do not find evidence against GESE.

We conclude this discussion by mentioning that we test GESE andGAESE within the context of a flexible, but nevertheless restrictiveparametric specification. It would be interesting to further evaluatesuch concepts in a nonparametric or semiparametric setting, likePendakur (1999) for example. However, still by making use of acombination of demand and subjective data.

4.1. Constructing equivalence scales (and evaluating their price andutility dependencies)

The evidence suggests that equivalence scales depend in somecomplexway on prices and utility (at leastmore complex than implied

by GESE or GAESE). The strong statistical rejections of independenceof price and IB/ESE do not imply however that these dependenciesare very important or relevant from a practical point of view. Thismatters as policy analysts might not be able to run a similar complexanalysis as presented here, perhaps simply because they do not haveaccess to the necessary data.

We construct equivalence scales on the basis of the parameterestimates of Table 2 column (5). Because equivalence scales are homog-enous of degree zero in prices they can be expressed in terms of priceratios. Fig. 2 presents equivalence scales for 2, 3, 4, and 5 person house-holds (with a single person household as the reference) as a function ofthe food to non-food price ratio. The price ratio used in estimationranges from 0.6 to about 1.8.

Each curve in each panel presents the equivalence scale for differentutility levels. The dashed–dotted curves are the equivalence scales forhigh utility households (the 90th percentile in the estimated utility dis-tribution), the solid curves are the equivalence scales for median utilityhouseholds and the dashed curves are the equivalence scales for poorhouseholds (the 10th percentile in the estimated utility distribution).The thick horizontal line represents the modified OECD scale that weuse as benchmark (de Vos and Zaidi, 1997).

We find that the scales are of reasonable magnitude and generallylarger than the OECD modified scales (which the exception of thescales of 2 person households, where the curve for median utility 2person households practically coincides with the modified OECDscale). This indicates that larger Indonesian household have less pos-sibilities to benefit from economies of scale than the modified OECDscales would suggest. This may be explained by the idea that theOECD scales are applicable to OECD countries, which are typicallyricher, and less dependent on rival goods like food. Our results indeedindicate that more affluent Indonesian households have more possi-bilities to benefit from household economies of scale, which amountsto smaller scales. The results presented in Fig. 2 are consistent withthe nonparametric evidence presented in the left panel of Fig. 1which also indicated that equivalence scales decrease in utility.

The magnitude of the scales is similar to the scales reportedby Donaldson and Pendakur (2006) and on the whole somewhatlarger than that reported by Donaldson and Pendakur (2004) and

0.6 0.8 1.2 1.4 1.6 1.8

p foodp nonfood

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3eq. scale 2 person household

0.6 0.8 1.2 1.4 1.6 1.8

p foodp nonfood

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3eq. scale 3 person household

0.6 0.8 1.2 1.4 1.6 1.8

p foodp nonfood

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3eq. scale 4 person household

0.6 0.8 1.2 1.4 1.6 1.8

p foodp nonfood

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3eq. scale 5 person household

Fig. 2. The figure presents equivalence scales as functions of prices and utility for 2, 3, 4, and 5 person households, where a one person household is used as the reference. Theupper-left panel presents the equivalence scales for 2 person households (upper-right panel (3 person), bottom-left panel (4 person), bottom-right (5 person)). In each panel,the food to non food price ratio is on the horizontal axis. The dashed–dotted curve is the equivalence scale for the 90th percentile of the utility distribution (more affluent house-holds), the solid curves are for median households and the dashed curves represent equivalence scales for the 10th percentile of the utility distribution (the poorest households).The thick horizontal line represents the modified OECD scale.

279J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

Koulovatianos et al. (2005). Interestingly we find that our scales aresmaller in magnitude than the ones estimated by Olken (2005),who also studies an Indonesian population. In terms of the directionof the utility dependence our results are consistent with the findingsof Donaldson and Pendakur (2004, 2006), and Koulovatianos et al.(2005). The economic magnitude of the utility effects are similar tothose reported by Donaldson and Pendakur (2004), larger thanDonaldson and Pendakur (2006), but smaller than reported byKoulovatianos et al. (2005).

We find that there are somewhat substantial price effects for lowutility households and hardly any price effects for high utility house-holds (the curves for high utility households are practically flat onthe whole price ratio domain).19 Clearly, price and utility effects arehighly interrelated in this context. When food prices rise, benefitsfrom economies of scale decline, but only for poor households. Thefinding of minor price effects for wealthier households, seems tosomewhat contradict the strong statistical evidence for price depen-dence we obtained in the previous section. We do however find eco-nomically meaningful price effects for poor households, hence thestatistical rejection of independence of price.

4.2. Robustness: testing overidentification

Section 2.2 discusses the identifying assumptions we exploit toestimate the parameters of the utility function on the basis of consump-tion adequacy data. If the thresholds for food consumption adequacy Tfand nonfood consumption adequacy Tnf are both identically and inde-pendently distributed conditional on z, p and x we can fully identifythe parameters of the utility function, and therefore the equivalencescales, on the basis of either one of these two pieces of information.Under the identifying assumptions the equivalence scales based onfood and nonfood consumption adequacy information should be thesame. Because we have information on both food and nonfood con-sumption adequacy we can perform a test on this assumption.

19 Pendakur (2002) also stresses the importance of using price dependent equiva-lence scales.

If we estimate the model on the basis of food or nonfood con-sumption adequacy we deal with two different distributions of thethreshold Tk∀k= f,nf.

P�Ak ¼ 1 z;p; x

¼ P

�u z;p; x�

> Tk z;p; x

¼ Pu−μk

σk> zjz;p; x

� �¼ Φ

u−μk

σk

� �∀k ¼ f ;nf

whereΦ(.) is the standard normal CDF, so that u−μk

σ k

� �is a monotonic

transformation of utility u and therefore a valid measure of utility it-self. The mean and the standard deviation of the thresholds will beabsorbed by the model parameters as follows:

u−μk

σk¼ δk0 zð Þ ln x−d p; zð Þð Þ−ln a p; zð Þ

pf =pnf

� β1 zð Þ

0B@

1CA

−1

þ λ1 zð Þ lnpf

pnf−λ0

!264

375−1

þ δk1 zð Þ

where

δk0 zð Þ ¼ δ0k0 δz0� �ln z ¼ δ00

σkδz0� �ln z

δk1 zð Þ ¼ δ0k1 þ δzk1 ln z ¼ δ01−μk

σkþ δz1σk

ln z

Under the identifying assumptions (including normality of thethresholds Tf and Tnf) we would obtain different estimates for δ00k, δ10k

and δ1zk, but not for the other model parameters, depending onwhetherwe use food or nonfood adequacy as the identifying source of informa-tion. The equivalence scales will also not differ in that case, as the differ-ent normalizations will cancel out when the scales are constructed.

If the identifying assumptions are flawed however, like, whenthe distributions of the thresholds depend on z, or when the thresh-olds are not identically distributed, or when the utility function ismisspecified, there is no reason to suspect that the parameterschange exactly in the way described above.

280 J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

We have estimated the complete model— like the model reportedin column (5) of Table 2 — twice, using food consumption adequacyand nonfood consumption adequacy respectively. We then test thefollowing equality restrictions across both models20:

H0 : All model parameters; except for δ0k0 ; δ0k1 and δzk1 are the sameþ the ratio δ0k0 =δzk1 is the same

Ha : otherwise

We do not reject this null hypothesis (p−val=0.44). This resultsupports the approach we follow. An interesting additional result isthat we find some evidence for the idea that food consumption adequa-cy is reached at a lower level of utility than nonfood consumption ade-quacy, as the δ10k parameter is smaller when nonfood rather than foodconsumption adequacy is used in estimation. This indicates that μf b μnf.

It would be a promising avenue for further research whether thesefindings hold more generally. It could be argued for example that thestatistical test we introduce is not very powerful. Subjective questionsthat are further apart in the utility spectrum for example, could beused for a more powerful test.

5. Conclusions

Because equivalence scales are generally not identified from de-mands, the demand-based literature on equivalence scalesmust restrictpreferences in ways that are unsubstantiated. This paper analyzes theprice and utility dependence of equivalence scales, without relying onsuch restrictions. To do this we unify two strands of the literature onequivalence scales. A demand based approach typically introduces pref-erence systems that allow for complex interactions between the keyvariables expenditures, prices and demographics. The subjective litera-ture aims tomeasurewellbeing or utility directly and therefore does notsuffer from the identification problems introduced by Pollak andWales(1979). The subjective literature is however less technically developedand in a sense less embedded in economic theory. The modeling tradi-tion in this literature tends to be ad hoc and the typical empirical modelused is additively separable in expenditures/income, prices and demo-graphics, i.e., a Cobb–Douglas preference system which we estimate asa benchmark in column (1) of Table 2.

In this paper we extend the typical additive model from the sub-jective literature and introduce more realistic preference systemstypically used in the literature on consumer demand (in this paperwe introduce a straightforward extension of the translated quadraticalmost ideal system). These systems allow for equivalence scales todepend on prices and utility. At the same time, they accommodatethe typically observed nonlinear relationship between budget sharesand (the log of) total expenditures (see Banks et al. (1997) as wellas Fig. 1 of this paper).

In our paper we use both subjective data (for complete identifica-tion) and demand data (for efficiency) at the same time. We are ableto estimate and test the price and utility dependence of the equivalencescales, without applying restrictions like IB/ESE, GESE and GAESE intro-duced by the demandbased literature on equivalence scales (see Lewbel(1989), Blackorby and Donaldson (1993), Donaldson and Pendakur(2004, 2006) for examples).We reject IB/ESE, GESE andGAESE, and con-clude that these concepts do not hold within the Indonesian context.More specifically, we find evidence for the idea that increases in house-hold size has (negative) welfare implications, in ways that are not re-vealed through observed changes in behavior.

We estimate equivalence scales that are of reasonable magnitudeand generally larger than the widely used modified OECD scales.Equivalence scales decrease in utility, which supports common

20 A robust Hausman test is used for this purpose (see page 273 of Cameron andTrivedi (2005) for more details on how to compute the test statistic).

perception that poor households have less possibilities to benefitfrom household economies of scale as a large fraction of their incomeis spent on food, a rival good. Furthermore, we find that equivalencescales increase in food prices for poor households and are practicallyinvariant to price changes for more affluent Indonesian households.

To our knowledge, our analysis is the first that combines both sub-jective data and demand data to estimate a preference system that isconsistent with economic theory. However, it is our opinion thatthere exists no broad academic consensus about what the differentkinds of subjective information measure exactly, and how theyshould be used within a theoretical framework. We aim to contributeto this debate with this paper. For example, the assumptions weintroduce in Section 2.2 describe a way of using and interpreting sub-jective evaluations of consumption adequacy. Under our interpreta-tion only one adequacy question is sufficient for identifying the scales.We subsequently test these identifying assumptions in Section 4.2 andcannot reject.

It would be an interesting avenue for further analysis to investi-gate whether these findings hold up with different data sets, orwith other kinds of questions on subjective wellbeing. An additionalavenue for further research is to developways of using subjective and de-mand data simultaneously within a nonparametric or semiparametricsetting (such as Pendakur (1999)).

Appendix A. Allowing for some forms of randomness in theutility function

In our paper we assume that the utility function is correctly spec-ified by Eq. (2). The literature on equivalence scales typically assumesthat there is no randomness in the utility function. This implies thatequivalence scales are constants, conditional on demographics, pricesand utility. It is possible to allow for randomness in the utility func-tion while maintaining a useful interpretation of the equivalencescales we estimate in this paper.

Suppose that the utility function is defined by u(u∗(z,p,x),e) wheree is unobserved preference heterogeneity. The unobserved preferenceheterogeneity is assumed weakly separable from the structural com-ponents of the model z,p,x. If this is true, frac(z,p,x) would estimatethe following:

P�Ak ¼ 1 z;p; x

¼ P

�u u� z;p; x

� ; e

� > Tk z;p; x

¼ Fu−1 Tk ;eð Þ z;p;x u� z;p; xð Þ� �

If now the unobserved preference heterogeneity term e and thethreshold Tk are jointly and identically and independently distributedconditional on z,p,x, frac(z,p,x) is a nonparametric estimator of amonotonic transformation of u∗, rather than of u.

This is also useful. Consider the case where u∗=u∗(z,p,x)=u∗(z0,p,x0), so that naturally Fu−1 Tk ;eð Þ u� z;p; xð Þð Þ ¼ Fu−1 Tk ;eð Þ u� z0;p; x0ð Þð Þ. Ifu∗(z,p,x)=u∗(z0,p,x0) we must also have that

E u u� z;p; xð Þ; e� �z;p; xj � ¼ E u u� z0;p; x0ð Þ; e� �

z0;p; x0j ��� ðA:1Þ

So if u∗ is equal for a particular pair of households, expected utilityis also equal for that same pair. The equivalence scales we estimate inthis paper (the frac based equivalence scales), therefore, can beinterpreted as expected utility equivalence scales. In other words,the fraction of consumption adequate households (given z,p,x) is anonparametric estimator of expected utility given z,p,x (under theweak separability assumption and the independence assumptions).Again, in principle we do not need explicit distributional assumptionson the thresholds and the unobserved heterogeneity.

281J. de Ree et al. / Journal of Public Economics 97 (2013) 272–281

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