happiness inequality

8/8/2019 Happiness Inequality

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Can a rise in income inequality improve welfare? *

Ricardo Nicols Prez Truglia Department of Economics

Universidad de San Andrs

This Draft: December 2007

Abstract

While in homogenous societies income can only buy traditional goods (e.g. food,clothes), this paper claims that in heterogeneous societies income can also buy non-

market goods (e.g. respect, friends). Such transactions take place through thesignaling of unobservable characteristics via conspicuous consumption. Thetheoretical model shows that: i. Conspicuous consumption is an efficient allocationmechanism for some non-market goods; ii. There is an efficiency loss associated to aprogressive redistribution of incomes; iii. The loss is particularly important in more"meritocratic" societies. Then I test my conjectures based on panel data on lifesatisfaction for 10,000 respondents in Russia for 2000-2002, exploiting twoidentification strategies. The following results emerge: i. Expenditure inequalitywithin reference groups does increase the marginal utility derived fromconsumption; ii. The "direct" distaste for inequality has been considerablyunderestimated by the literature; iii. The model provides a micro-foundation for the

idea of a utility function first concave and then convex. The results remainunchanged after controlling for the income equivalence scale elasticity and a widerange of recent theories on Economics of Happiness.

JEL Codes : D01, D31, D69, H00, I31.Keywords : Income inequality, conspicuous consumption, life satisfaction.

* I want to recognize the precious support and guidance of Walter Sosa Escudero and Federico Weinschelbaum. Forhelpful comments, I thank Martin Rossi, Daniel Heymann, Martin Gonzalez-Eiras, Mara Edisa Soppelsa and MartinTetaz. The usual disclaimer applies. Universidad de San Andrs, Vito Dumas 284, (B1644BID) Victoria, Provincia de Buenos Aires, [email protected] | http://www.ricardotruglia.com.ar


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1. IntroductionEconomic condition was extremely important in the early stages of economic development,

when the fulfillment of basic needs was in the centre of every discussion. Nowadays, the role ofincome in life satisfaction is more frequently related to factors such as conspicuous consumption andsocial comparisons. This paper re-examine the welfare discussion on income inequality taking into

account the growing preponderance of such relative concerns.I will discuss a particular definition for conspicuous goods (throughout this paper,interchangeable with status goods). For now, consider them provisionally as those observable goods(and services) with prices above how much the consumer would have paid if the consumption hadnot been observable1 (further details in Section 2). It is easy to propose lots of goods that may satisfysuch conditions. A $20,000 gold watch, luxurious cars and expensive cell phones might serve aspreliminary examples.

The first explanations for the existence of such goods were based on envy, arrogance,greediness and similar manifestations of relative concerns. They argue that the difference betweenthe valuations for observable and unobservable consumptions mirrors that people enjoy showingtheir successes to everyone else, that people enjoy from the envy of their neighbors, and other similarexplanations. Since such goods are not thought to provide intrinsic utility, many economists arguedthat these relative concerns take individuals to a high level of social competition (i.e. to a "rat race")and then to an unnecessary waste on status goods.

However, conspicuous consumption may have a second (indirect) effect (Postlewaite, 1998). Iclaim that people care about relative standings not just because of their arrogance and greed but, atleast to some extent, because relative standings indirectly affect the goods and services (in a widesense) ultimately consumed by them. I propose that the gap between observable and unobservablevaluations is reflecting the increase in the probability of getting a different good. The implications ofthe latter explanation are diametrically different.

The signaling mechanism will be proposed as an allocation mechanism for some goods and

services (in a wide sense) that people consume but cannot be purchased through standard markets.Those goods have been proposed as a substantial part of the totality of goods in the economy (Cole etal., 1992a, 1992b, 1998). Consider friendship, sex or respect as obvious examples: they cannot beeither sold or bought, at least not without receiving a social or even legal reprimand.

Then, those non-market goods must be allocated through some kind of matching mechanism,which has to select among a set of candidates (demanders) with some relevant characteristics "to payin exchange". For instance, people have time to spend with others, and in exchange they prefer to "bepaid" with chats about topics of their same interest. The mechanism has to overcome a problem ofasymmetric information: the aspirants have non-observable characteristics, and they might not revealtruthfully their type. Something marvelous about formal markets is that they synthesize all theinformation needed in a single vector of relative prices. In the same spirit, the prices of status goods

will be proposed as a vector of implicit prices for non-market goods.Income is one of the unobservable characteristics in which the supplier of the non-market

good may be (directly or indirectly) interested. For instance, a man might be interested in marrying arich woman. However, income does not have to be a relevant characteristic per se . The selection ofrich individuals just because they are rich (because of greediness, relative concerns, and so forth) is

1 Besides "intrinsic" gains from observability, such as functionality (e.g. a sign has to be seen to execute its function)and esthetic valuation (e.g. people want beautiful clothes for attracting others and for self-satisfaction).


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not the main concern of this paper. Conspicuous consumption can signal any desirable characteristicof the "demanders", as long as it is (conditionally on observables) positively correlated with income.Following the previous example, the man may want to marry a rich woman not because he wants toenjoy her money, but because he thinks that, conditional on the observable information, the incomeof a woman is positively associated with her loyalty and other desirable characteristics. This subtleperception is the foundation for the main departures from the usual results.

Consider the pricing of graduate programs in business (e.g. an MBA). One of the mostvaluable benefits of attending an MBA is the possibility of getting in contact with other businessmento deal in the future, or just to share experiences and knowledge with. Thus, the most talentedmanagers will want to be in the same business programs. Notice that, since in the business worldmaking money is the main aspiration, income seems to be a good indicator of individual skills.

Suppose that the gains from the program are substantially above the marginal cost ofeducation, both for bad and good managers. In addition, suppose that good managers are seriouslydistressed when bad businessmen participate into the program. For instance, a good manager maylose money and valuable time when doing business with a bad manager.

Conditional on the characteristics reliably observed by the admission committee, the best

MBA's will set entrance fees high enough as to deter bad managers from entering the program. Sinceeveryone else is also a good manager, each talented manager will be glad to pay the expensive fee.However, as business programs can be offered for much lower prices, competition among differentprograms may suggest that the fees would be eventually reduced. But if one good program loweredthe fee, then bad managers would be able to enter into it and good managers would prefer to moveto one of the remaining expensive programs. Setting prices equal to marginal costs is not the optimalsolution, since a gap is needed to allow for the signaling of business skills.2

In order to study this phenomenon profoundly, I join together a theoretical model ofconspicuous consumption3 with an empirical application using life satisfaction data.4 The maintheoretical finding is that income inequality makes room to the allocation of non-market goods.Consequently, income inequality should increase the marginal utility from (overall) consumption.Additionally, this paper demystifies the traditional linkage between status goods and diamonds.Conspicuous consumption is expected to be more important not in the richest reference groups, butin the most heterogeneous-in-income (present in both tails of the income distribution). This wouldrationalize the consumption of "luxury" goods by the "prosperous" poor.

Two empirical identification strategies are proposed. First, expenditure inequality within thegeographical area is proposed as a multiplicative-augmenter for the effect of consumption on lifesatisfaction. Afterward, in order to exploit more information on the expenditure distribution, anonparametric estimate of the regional expenditure density distribution is proposed as a better proxyto measure inequality within reference groups.

2

Of course, there are some extra points to take into consideration for this particular example: graduate programs alsoinvolve education, the relation between business talents and income may not be so clear (because of inheritances andcredit frictions), etc.3 Status concerns have been long recognized not only by economists (for early contributions see Veblen, 1899; andThurow, 1971), but also by sociologists (Weber, 1978), and even in bio-sciences (Mazur et al., 1980).4 Essentially, I focus on economic literature which uses large-scale survey data on subjective well-being.Notwithstanding, there are other interesting ways to study that relationship. For example, Camacho-Cuena et al.(2002) provided a comparative experimental study of risky prospects and income distributions, and Carlsson et al.(2001) measured preferences for risk and inequality through experimental choices between hypothetical societies andlotteries.


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The results indicate that intra-reference-group expenditure inequality indeed increases themarginal utility derived from consumption. The indirect effect is observed only for the expenditure-related variables (observable), and not for the income-related variables (unobservable), what will beproposed as a robustness exercise. This paper fills a gap in the literature, as it can explain why manypapers have found either a null or positive relationship between income inequality and lifesatisfaction. I also show that the results can account for a utility function initially concave and thenconvex. In this sense this paper is intended to propose a micro-foundation to the concave-convexutility function proposed by Friedman et al. (1948), and consequently it provides a subtle support tothe idea of a "natural rate of inequality" (a.k.a. "manufactured inequality").

The paper is arranged as follows. In Section 2 a signaling-type model is presented, along witha theoretical discussion. The specification of the econometric model and a succinct description of thedata can be found in Section 3. The estimation results are shown in Section 4. Section 5 concludes.

2. Theoretical ModelThis paper argues that since part of the consumption is observable, it may provide

information on incomes. Conditional on observables, that information can be transformed in priors

about some underlying characteristics, such as labor skills, charisma and honesty, which are veryvaluable to make important decisions. Depending on the particular example under consideration,this phenomenon may be modeled in several ways: a search model, a model of adverse selection, amodel with informational externalities, etc. I will focus on a signaling model in order to stress therelationship between the size of the conspicuous expenditure and the size of the non-market good.

There are many examples of signaling within the theoretical literature. Workers can signaltheir ability to employers through status consumption (Frank, 1985a, 1985b) or social culture (Fang2001). People can also spend money on fashions to signal skills in a dating game (Pesendorfer 1995)or they can signal wealth just to match wealthier mates (Cole et al., 1992a). In the same vein asHopkins (2006b), my model marries aspects of both Spences (job market signaling) and Beckers(marriage matching) models (Spence, 1973; and Becker, 1973).

Maybe the most motivating examples of non-market "services" are personal, emotional andprofessional relationships. Indeed, recent empirical evidence shows that relational goods are a majorsource of life satisfaction (Becchetti, 2007). Even recognition (envy, jealousness, etc.) can be seen asnon-market good, what implies that the relative deprivation theory is a particular case of this model.

Human beings continuously have to pick a small number of individuals from a wide set ofcandidates: people looking for a job or a particular position inside a corporation, businessmen insearch of business partners, teenagers in search of new friends, etc. Seldom decision-makers canobserve every relevant aspect to make the right choice, and then they might want to rely on signalingmechanisms. The following model exploits that idea. Nevertheless, it is clear that mating neither isthe only nor the most important problem regarding conspicuous consumption. Indeed, this game isnot thought to take place explicitly in the real world but in a subtler way in many activities regardinghuman action. This subtleness is probably the main reason why this allocation mechanism has beensystematically disregarded.

2.1. Prince Charming's Model

Two individuals play a game. The first individual (hereinafter referred as to "the maiden") ischosen randomly by Nature from a population of two possible types: poor or rich (subscriptsl andh respectively), differentiated by their incomes ( 0>> lh M M ). The fraction of rich types in the


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population is . There are two varieties of goods, referred to as standard good and conspicuousgood. Let 0 x be the quantity consumed of the standard good by the maiden chosen by Nature,which has a constant price normalized to 1. Let z be the quantity purchased of the conspicuousgood, and suppose it is binary (each type consume one unit or nothing).5 Let 0> p be the price ofone unit of z . Just for the sake of simplicity, suppose that only the standard good enters into theutility function: ()U , with 0()' >U and 0()'' is larger the more important is the activity under consideration (i.e. the utilityassociated with marrying Prince Charming is larger than the utility associated with walking alongthe park with him).

Consider the allocation of a given activity (with a associated) through a certain status good(with a p associated). In order to sustain a separating equilibria, there are two necessary conditions:the rich type maiden must buy the conspicuous good, and the poor type must not have incentives topurchase it. Since the utility function is strictly increasing, every type choose to consume their entireincome. Hence, the two conditions can be expressed in the following way:

)()( ll M U p M U + (1)

)()( hh M U p M U + (2)

First consider the case of p is fixed. For a pair of incomes );( hl M M we have:

ull p M U M U = )()( (1a)

5 The vector of prices of the conspicuous goods and the vector of purchased quantities will not be important. Whatwill only matter is simply the total spending on conspicuous goods. Having one conspicuous good with binaryconsumption is just a simple way to synthesize that information.6 Accordingly, Prince Charming will be in the following lines for non-market goods what the walrasian auctioneer isfor traditional goods.7 Observability is one salient feature of positional goods. The only survey evidence I am aware of, Carlsson et al.(2003), supports that belief: an automobile (highly observable) was found to be a positional good, while leisure andcar safety (highly unobservable) were found non-positional.


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bhh p M U M U = )()( (2a)

The concavity of the utility function guarantees that bu > : the incentive compatibilityconditions for both poor and rich types can hold simultaneously, and in particular if (1a) holds withequality then (2a) must necessarily hold (see Proof 1 in the Appendix). For a price of the conspicuousgood h M p < and a pair of incomes );( hl M M there is a range of activities with a ],[ ub associated that comprises a perfect Bayesian separating equilibria in pure-strategies: only the richtype buys the status good, and Prince Charming performs the activity if he sees that the maidenconsumes z . In sharp contrast to the literature, this innovative formulation of conspicuousconsumption highlights the joy of marrying Prince Charming, . Keeping up the romanticatmosphere, the range of activities that can be achieved in equilibrium ranges from going out withPrince Charming ( b = ) to marrying him ( u = ).

Observe that 0>dpd u and 0>dpd b : more expensive conspicuous goods canrationalize activities with larger 's associated, although at the same time smaller 's are beingruled out (e.g. the purchase of diamonds can rationalize marrying, but it cannot rationalize going tothe cinema). The other way around is also valid (e.g. the purchase of bijouterie can rationalize goingthe cinema, but definitively it cannot rationalize getting married). Notice as well, using Jensen'sinequality, that 0


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spending (since b p is going down). As I want to emphasize that this effect might be significant, I willshow that under weak conditions the second (positive) effect may even prevail over the first(negative).

Nevertheless, if both and p were fixed there would be no way to exploit the greaterpotential welfare due either to the rise inu or to the decrease in b p .9 I will allow the rich type to

extract the highest possible surplus through the endogenous selection of one parameter. Henceforth,two scenarios will be taken into consideration: fixed p with endogenous , and fixed withendogenous p . A third scenario, allowing endogeneity for both p and , will not be considered because of uninteresting technical details.10 Different situations correspond to each one of the twoscenarios. The following analysis is provided for both scenarios.

Even though the results are pretty similar in both formulations, the two-stage mechanismsthat will be introduced below would not be necessary in the latter.

2.1.1. Fixed p

If every type could choose a pair ),( ii z , the poor type would choose ai as large as to ruleout the separating equilibria. In the above analysis both types should make the same offer),( p ,

and then i z could be enough as to identify each type. But ifi is different for each individual, PrinceCharming needs further information to distinguish among types. That information can be obtainedin various ways, depending on the particular nature of the game under consideration. The mostradical simplification would be to assume that Prince Charming knows thei of each type, and thenhe will perform the activity if the maiden offers the lowesti (i.e. the individual that is willing toreceive the lowest activity for a given conspicuous expenditure). This would be achieved if, forinstance, one maiden of each type were confronted simultaneously to Prince Charming, who would be able to see the offers of every type.

But the interesting exercise is to keep the signaling structure of the game. We need to designa mechanism to let Prince Charming learn about thei 's. For instance, if the game was repeated thenPrince Charming would simply employ a past-dependant strategy.11 Just to simplify the analysis, Iwill introduce a mechanism that solves almost trivially the identification problem. This mechanism justifies an initial "screening" by Prince Charming (e.g. if you are in a bar trying to get a rich-typedate, then you first have to go around and listen to the offers).

In a first stage, maidens of both types must offer to Prince Charming an activity to performwith him (characterized byh and l for the rich and poor types respectively). In the separatingequilibrium Prince Charming in the second stage should choose to perform the activity only if thei declared by the maiden corresponds to the lowest offer from the first stage.

fixed and exogenous, the achievability of smaller 's could be a welfare-improving channel as well. For instance, if was fixed below b , the separating equilibria would not be achievable. Thus, a rise in income inequality (through afall in b ) would make it possible to perform the activity in equilibrium.9 Nevertheless, if the values of and/or p were exogenous but chosen at random, it would be possible to shown aweaker result in expected value.10 For instance, it would be necessary to introduce an upper bound for .11 As soon as Nature chooses a rich-type maiden, she will be able to "show" to Prince Charming the non-market goodlinked to rich-type maidens.


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The strategy for an individual of rich type in the first stage will be to choose the highest that comprises a separating equilibria in the original game, )(* puh = , since she will want to get as

much pleasure as possible from the (fixed) incurred expense, p . Thus, in the subgame perfectequilibria Prince Charming chooses to perform the activity if the conspicuous good is purchased, thepoor type chooses not to make an offer in the first stage (or offers )(* pul ), only the rich type buys the status good in the second stage, and she offers in the first stage the largest activity thatmakes binding the incentive compatibility restriction of the poor, )(* puh = .12

Recall the example of graduate programs in business. In the short run, the entrance fee for aprogram is fixed. Once accepted to the program, a businesswoman can meet another manager andpropose her a business deal, . If were too high, it would make the entrance to the MBAprofitable even for a bad manager. Then, the talented-type manager will have to find out what is therange of business proposals ( 's) that can sustain a separating equilibria. In particular, she will beinterested in offering the maximum business proposal.

Henceforth, the utility derived from the activity with Prince Charming can be expressed as:)()(* p M U M U llh = ; with marginal utility 0)('

* >= p M U p lh and0)(''2*2 >= p M U p lh .

Let SW be the expected utility for the maiden chosen by Nature from the population ofindividuals of poor and rich types, and consider the subgame perfect equilibrium with )(* puh = and, just for the sake of simplicity, 21= (rich and poor types are equally frequent). The change inexpected total surplus can be expressed by differentiating with respect to both incomes:

),()()(2 p M d p M dU M dU dSW luhl ++=

12 For the poor type )(* pul is best response, since she is not purchasing the conspicuous good anyway. If)( pul > the poor type would not want to buy the conspicuous good, as she would not perform the activity with

Prince Charming. If she offers )(* pul = , since she is indifferent between buying or not the conspicuous good inthe second stage, we will assume that she does not buy it. Nevertheless, with )( pul < the separating equilibriawould not be valid any more. If a poor-type individual liked harming a rich-type individual (what does not happen inthis model), during the first stage she would be able to place an offer as low as to break the "good" equilibria (if in thesecond stage the poor type is chosen by Nature, she will simple have zero conspicuous expenditure). The existence ofsuch equilibria is a subtle departure from the model of two individuals of different types facing Prince Charmingsimultaneously.

U ia

x

U(x)

MhaMha-pMlaMla-p

Ula

Uha

a

FIGURE Ia


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After a symmetric redistribution ( lh dM dM = ), the greater spread of incomes allows the

rich type to increase her in ),( p M d lu . A dispersion of incomes will increase expected totalwelfare if and only if (Proof 4):

2)(')('

)('p M U p M U

M U lhl+

<

That is, if the mean between marginal utilities from traditional consumption and conspicuousconsumption for the rich type exceeds the marginal utility from traditional consumption for the poortype. If lh M p M > , then l M could be expressed as a linear combination with positive weights of

p M h and p M l , and then Jensen's inequality guarantees that the condition would hold if andonly if 0()''' >U . Alternatively, if 0()''' >U the following would be a sufficient condition:

2)(lh

M M p > (Proof 5).Figure Ia and Figure Ib illustrate the changes in welfare. In Figures 1a to 1c, the second

subscript indicate what is the situation under consideration. For instance,a is the activity reached by the rich type in the initial situation, depicted in Figure 1a, whileb and c are the activitiesreached after the increase in income inequality for the situations with fixed p and endogenous ,depicted in Figure 1b, and with fixed and endogenous p , depicted in Figure 1c, respectively.

The standard consumption for both types before redistribution are displayed in Figure Ia,along with the non-market good obtained by the rich type when chosen by Nature,

)()( p M U M U llh = . When redistributing from the poor to the rich type (Figure Ib) the lattergains b , while the poor losesa . The concavity of the utility function guarantees that 0U guarantees that

cd is also decreasing in )( lh M M . Then, the condition simply states that for given spread ofincomes there is a price large enough for the gain in total welfare to hold.

FIGURE IbU ib

x

U(x)

MhbMhb-pMlbMlb-p

Ulb

Uhb

b

a c

b

ddM ldM h


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Moreover, the analysis can be extended to a population of numerous types. Suppose that fora number of times two types,i and j , are randomly chosen to play the game (with replacement)from a sample of various types (characterized by different incomes). Before the change in the incomedistribution, the expected gain from a particular game realization for typei is:

[ ]),()()()()()( p M p M U M M P M U M M P M G jui jii jii +>+


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In the second stage Prince Charming will choose to perform the activity only if thei p declared by the individual was the highest offered to him during the first stage. In addition, the poortype chooses ** hl p p , Prince Charming chooses to perform the activity if the conspicuous goodpromised during the first stage is purchased, only the rich type buys the status good, and she offersthe conspicuous good with the highest price that makes the incentive compatibility restriction of thepoor type binding, =)( *hu p . The implicit price of the conspicuous good can be expressed as:

))((1* = llh M U U M p ; with 0* > h p and 0

2*2


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Figure Ic shows thedp needed to remain with the fixed after the income redistribution(i.e. to make ac = ). Thedp is then used to find the new level of utility for the rich,hcU , after thesaving in conspicuous expenditure. The utility of the poor type decreases ina , )(' l M U , while theutility of the rich type rises inb , ( )lh dM dp p M U + 1)(' .

Finally, the same results hold when the game is extended to a population of numerous types.

In addition, the (paretian) welfare-improving collusion is almost the same: the rich type sells to thepoor type a coupon equal to l M , and then she can get the by consuming a conspicuous good withan infinitesimally positive price.

2.2. Discussion2.2.1. Ruling out pooling equilibria

The leading assumption behind the striking results is the absence of pooling equilibria. Forinstance, if Prince Charming preferred to perform the activity with any type at random instead of notperforming it, then there would be a trivial solution for the social planner: Prince Charming choosesto perform the activity regardless of the conspicuous consumption, and both types choose zeroconspicuous expenditure. The activity is always performed and there is not a wasteful expense in

conspicuous goods.17

That probably happens with a lot of non-market goods. But I claim that for many non-marketgoods the separating equilibria is a necessary condition for the provision of the non-market good.Pooling equilibria is discarded not because it does not exist, but simply because the interesting casesare only those games where (conditional on observables) the expected values of skills are low enoughas to deter Prince Charming from mating someone at random. Since it helps to identify the talentedagent, adding some heterogeneity may create mating possibilities, and the consequently gain inwelfare will arise.

Recall the model with individuals of a continuum of types and suppose that their incomes( i M ) follow a density distribution with support in . Moreover, assume that there is a perfectcorrespondence between income and skills: the utility of Prince Charming equals the income of hispartner. In the pooling equilibria, Prince Charming would face two independent draws from thedistribution of incomes and then he would perform the activity with one of them at random (whichis the same than picking directly one single draw). Then, the non-market good would be provided ifand only if 0)( i M E . In the separating equilibria Prince Charming faces two independentrealizations of incomes from the same distribution and then he recognizes the greatest (throughconspicuous consumption). As a consequence, the non-market good would be provided if and only if

0}),(max{ ji M M E . Since }),(max{ ji M M E is significantly higher than )( i M E , there aresituations where the separating equilibria guarantees the provision of the non-market good while thepooling equilibria does not.18

17 It would be convenient to think about fixed and endogenous p , since the alternative scenario without arestriction on makes no sense (both individuals could have chosen a arbitrarily big). Additionally, there could bea pooling equilibria where Prince Charming performs the activity if the maiden is consuming the conspicuous good,and both types buy it.18 Notwithstanding, there are also situations where before the redistribution there was only possible to have a("good") pooling equilibria, while after the redistribution the separating equilibria is also possible. The sign of thewelfare change will respond to the comparison between the informational gain for Prince Charming (since he nowperforms the activity with the poor type with zero probability) against the loss in conspicuous expenditure for the richtype and the loss for the poor type (as now she does not perform the activity).


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However, when incomes are perfectly homogeneous there are not such things as poor andrich types. Prince Charming's preferences are not defined, and thus cardinal preferences must beaddressed. To do so, a crucial issue of this model would have to be defined. Up to this point, it wasirrelevant if Prince Charming cares directly about the relative income of his potential partner, or if hecares about some pleasant (unpleasant) trait positively (negatively) correlated with individuals'income. The spirit of this paper goes definitively in the second direction. For instance, the happinessof Prince Charming may depend positively on the charisma of his partner. Since, conditional onobservables, more charismatic businessmen are expected to make more money, then PrinceCharming will indirectly care about his partner's income.

Let's follow the simple and effective representation of American and European culturesintroduced in Di Tella et al. (2006). Societies (generally speaking) can be in an equilibria where firmpay workers' efforts and workers make efforts (i.e. USA) or, on the contrary, where firms do not payefforts and workers shirk (i.e. Europe). If Americans make efforts, then it will be easier to infer theirskills from the information provided by their ranks in the income distribution. Thus, the correlation between income and (unobservable) skills should be stronger in more "meritocratic" societies.

Compared to less meritocratic societies (i.e. with distorted mechanisms of incentives), in the

former individuals make more efforts not only because they can withhold a bigger part of theirproduction to buy market good, but also because their signal of skills is stronger and they can buymore non-market goods (or, similarly, they can buy the same non-market goods but cheaper).19 Therefore, in meritocratic societies an increase in income inequality will probably reflect a spreadingof the returns to skills, which consequently would increase the provision of non-market goods andthus raise total welfare. In less meritocratic societies an increase in income inequality cannot berelated to such an increase in total welfare.20 Indeed, the findings of Di Tella et al. (2004) areconsistent with this conjecture: people in America do not seem to be harmed by income disparities,while there is a clear apathy towards inequality in Europe. Later this paper will be proposed as anew interpretation for that finding.

The adaptation of the model from ordinal to cardinal preferences is straightforward.21 Moreover, cardinal preferences can also allow for the inclusion of the utility of Prince Charming intothe social welfare function. As in homogeneous populations there is no matching, the effect of a risein income inequality on social welfare would be even more positive (or at least less negative). Inaddition, cardinal preferences may allow for a strategic choice of or p by Prince Charming(depending on which is fixed in the particular scenario), as to maximize his expected utility (during azero-stage, to be solved in a backward-induction fashion). For example, in the admission to graduateprograms in business this would be an interesting way to describe the underlying pricing process.

Even though ordinal preferences were proposed only as a practical way to focus onseparating equilibria, there are some arguments to justify their existence. Firstly, the poorest and

19

An extended version of this model would include a noise parameter. For instance, income could be a truthful signalwith a fixed probability, or maybe the model could take into consideration the joint distribution of income and thedesired or undesired underlying characteristic.20 Nevertheless, if income inequality increased orthogonally to the distribution of talents, then the informational gainswould not take place.21 For instance, if the utility function was strictly increasing in the income of his partner, Prince Charming would havea cut-off point: he would derive positive utility by sharing the activity with every type with an income above thatthreshold, and he would not want to perform the activity with types with incomes below it. Therefore, the ordinalpreferences would be applicable for two types around that cut-off point. Whether status is modeled as an ordinal orcardinal magnitude may be a major issue (Bilancini, 2007).


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richest individuals of a population are rarely found struggling for a good or service. As will bediscussed in the empirical section, individuals struggle for resources and compare to each otherwithin the so-called reference groups. Inside those clusters it is likely to find people with similarincomes. Then, Prince Charming should be sensitive to small variations in income relatively to themean variation in the entire population of incomes.

Secondly, behavioral mechanisms behind relative concerns may be mostly hard-wired, theresults of both biological and sociological evolution.22 As long as it worked well during evolution, avery rigid mating-rule such as "marry the richest no matters how much richer she is" could haveeasily arisen and survived until present. The subtleness of the mechanism may be even a historicaldirect product of the same kind of social intolerance that originally disqualified the direct trading ofthe non-market goods and services.

2.2.2. Towards a definition of conspicuous consumption

There are no particular goods and services always or sometimes, partially or totally dedicatedto conspicuous consumption. One good may be very conspicuous for an individual and anything butconspicuous for another. Furthermore, individuals do not rely only on conspicuous consumption for

signaling purposes, as probably they have a portfolio of different signaling instruments to choosefrom.The division between status goods and non-status goods is a degree matter. A particular

good must satisfy the following necessary conditions to be considered conspicuous: i. It must beobservable; ii. It should be distinguished from a fake23; iii. It should not be socially condemned (e.g. burning money). These conditions guarantee that Prince Charming will be (physically) able toidentify the consumption of the conspicuous good when deciding whether to perform the activity ornot.

There are a couple of additional conditions that arise from the mechanics of the game. Firstly,notice that the incentive compatibility restrictions do not require Prince Charming to know the priceof the conspicuous good. However, in the two stages game the individuals must declare theirexpected conspicuous expenditure. Therefore, the prices of the conspicuous goods must be public.24

Secondly, in the literature the status goods are always associated with expensive goods thatprovide little intrinsic utility25. For instance, a $50,000 watch seems to be a good exemplar becausethe intrinsic utility of watching the time and wearing a fashion accessory cannot explain by itself itsprice. But regarding our signaling game, if the benefits from the non-market good are the same for both types, the only requirement is that the cost of the "conspicuous action" must be higher for thepoor type.

The signaling does not require an intrinsic utility necessarily low. For instance, the"conspicuous action" may be consuming observable goods in a sub-optimally way. It does not matterhow much is the utility loss from the action (e.g. consuming a good that does not provide utility at

22 Some evolutionary arguments for relative concerns can be found in Postlewaite (1998) and Samuelson (2004). Thetheories go from natural selection (Brosnan et al., 2003) to the production of serotonin (Moldovanu et al., 2007).23 An interesting fact is that, when purchasing deliberately fake cloths of well-known brands, people are willing topay extra for falsified authenticity marks.24 As a consequence, for instance, Mercedes Benz should find convenient to inform non-customers about the highprices of its cars.25 Relative concerns such as envy and avarice may be considered intrinsic gains. If they are not so, they will be part ofthe non-market goods.


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all), but what matters is that the "conspicuous action" must be (a lot) less costly for the high type.26 Itis very important to notice that in the model p is in fact the monetary loss in utility related to theconsumption of a suboptimal set of goods. Then, a luxury car of $50,000 can be reflecting a monetaryloss of just $10,000, while a bag of $15,000 could be mirroring a monetary loss of $14,000.

However, the literature has been focused on goods that do not provide intrinsic utility for a

good reason. If we repeated the model using two different utility functions for z

, where the first didnot provide intrinsic utility while the second provided some, we would find that in the former muchmore non-market goods are allocated. Then, it is obvious that status goods with such characteristicswill arouse much easier.

In the real world there are plenty of observables goods, and it would be impossible for PrinceCharming to monitor every one of them. In each reference group only a relatively small set ofobservable goods can be considered conspicuous. Some of those goods may have arousedevolutionarily, but a great part of them must be the product of a complex process of coordination between princes and maidens.

In addition, the heterogeneity and variation of the goods are considerable, and then theprinces must frequently update the set of conspicuous goods. If Prince Charming sees p , ( )U z (at

least by guess) and other relevant characteristics (the frequency of exposition), then he can decidewhich goods to consider as conspicuous. I will not analyze further the process of selection ofconspicuous goods, since such a mechanism would demand an entire section to be developed.

To sum up, consider as an example a donation to an American university: the amount ispublic (Glazer et al., 1996), its price is arguably below the intrinsic utility derived from altruisticsatisfaction, it cannot be falsified and it is even socially supported. Secondly, consider an expensivedress: people can see if you are wearing it and it is not disapproved by society; but it is difficult todecide whether it is a fake or not, and since it makes you feel better with yourself its intrinsic utilitymay be considerable high.

There are other reasons to be careful: for instance, for durable goods the complete discountedflow of benefits must be taken into consideration, and not only the current benefits. If there were nocredit frictions, the actual cost of a very expensive golden watch would be solely the opportunity costof the capital, as after its use it maintains completely its resell value. In the real world, credit marketsare not perfect and hence a $50,000 gold watch can successfully signal the absence of financialconstraints.

The level of observability is continuous as well. For example, different status goods areobserved by the rest of the population with different probabilities (e.g. my car is observed morefrequently than the painting hanging in my room), and with different frequency. After some minormodifications, the model could have included imperfect publicity to show that, for a given amount ofconspicuous expenditure, the relation between the likelihood of observing the status good and thestrength of the signal.

26 There are special non-market goods that, in addition to the direct utility they provide, increase the marginal utilityfrom traditional consumption. For instance, a membership to a high-class club gives access to goods and services thatare not available to those with low status (as in Becker, 2007). In that case the good is far from lacking intrinsic utility.On the contrary, the separating equilibrium would be sustained by a convexity in the utility function. The poor typewould like to consume her entire income outside the club instead of entering the club and consuming her (little)remaining income. The rich, besides , prefer entering the club and consuming their remaining income instead ofconsuming their entire income outside the club.


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Additionally, people are not aware of how much intrinsic utility every individual derivefrom each good in the economy. Then, each individual should find optimal to signal wealth withthose status goods with a greater difference between how much intrinsic utility she derives from andhow much everyone else think she derives from.27

2.3. Empirical Identification

The objective of the next section is to identify econometrically the augmenting effect ofinequality on the marginal utility from consumption using life satisfaction data. Nevertheless, otherimplications of the model could have been tested, and the life satisfaction data could have beenskipped as well.28 The main explanation for those choices is that the theory may solve a quiteinteresting puzzle in the happiness literature: the positive relation between income inequality andreported well being. Ravallion et al. (2000), Clark (2003), Senik (2004) and Ohtake (2004) retrievenonnegative effects of inequality on individual happiness. Schwarze et al. (2003) found that incomeinequality reduction by the state does not increase wellbeing. Camacho-Cuena et al. (2002) found thatthe "transfer principle" is largely violated. In Luttmer (2005) and Di Tella et al. (2004) variousmeasures of regional inequality did not seem to affect the well being of Americans.

Furthermore, the finding is not at odds with the most recent theoretical literature. Forinstance, in the model introduced in Hopkins et al. (2004, 2006a) an increase in equality rises thedegree of social competition, diminishing the utility of the poor. Becker et al. (2005) also found thatreducing inequality may be inefficient because of the existence of self-generated inequality.29 Rege(2007) found similar results about the inefficiency behind income redistributions.

3. Econometric Model and Data3.1. Main Framework

The socio-economic changes that have taken place in Russia during the past decade havecaused this country to become an authentic laboratory for the social sciences. A period characterized by deteriorated living conditions and dramatic economic uncertainty began in 1991. Over one thirdof the population was living below the official poverty line by the end of 1995. Notwithstanding, thefinancial crisis of 1998 was a turning point. It was followed by a gradual recovery, with real incomegrowing up and unemployment rates steadily falling. A comprehensive analysis of the economic andsocial spheres of Russia following transition years can be found in Braithwaite et al. (1998).30

27 Therefore, there is an additional loss related to the over-taxation or prohibition of status goods. The followingsituation should be illustrative: facing the absence of markets to meet interesting friends, an individual decide to flightin first class in order to signal business skills. If the government opts to ban the first class, he by no means will stoppreferring some companions above others. He will be just not able to get new friends through flight tickets, and hewill merely make use of another status good (e.g. expensive cell phones). Since the latter was not his first choice, theintervention is inefficient. Paying taxes do not provide intrinsic utility. Taking that into consideration Bagwell et al.(1996) and Rege (2007) suggested that they may serve as conspicuous goods. What they did not take into

consideration is that the selection of the goods that will be considered status goods is very complex. For instance, thetax rate should be public and credible (e.g. this may work properly with specific taxes).28 For instance, I could have measured the impact of inequality on Engel curves for highly observable and highlyunobservable consumptions (inspired in Kerwin Kofi et al., 2007).29 Additionally, Glazer et al. (1996) pointed out that people may be interested in making donations (for signalingwealth) only if income is not homogeneous. The consequences were worthy of note: universities should be interestedin giving scholarships to the middle class in order to increase the heterogeneity of their student body and then raisefuture donations by rich alumni.30 An emerging economy like Russia can guarantee enough variation along the features of interest: life satisfactionand the distribution of income. In fact, Frijters et al. (2008), based on the same database, found that changes in real


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I focus on life satisfaction via 3 rounds (9 to 11, covering the period 2000-2002) of thehousehold-level Russian Longitudinal Monitoring Survey (RLMS).31 The analysis is limited torespondents aged over 18, reaching a sample size of just over 23,500 observations on 9,200individuals (after discarding missing values). The average number of observed rounds is over 2.5(out of 3).

The RLMS was designed as a repeated sample of each household dwelling. Consequently,instead of following individuals or households from one year to the next, the interviewers merelyreturn to the same residences sampled in the previous year. All households who move areautomatically lost to follow-up, and the new tenants of the sample dwellings are invited to join thesurvey.32

Just to mention some basic statistics about the sample, at October 2000 the average age was45, 44% were male, 54% were married, 66% had a high school diploma, 50% were working, 32%received a pension, 29% reported to be in good or very good health, 5% had been hospitalized during

the last three months, 32% smoked, and almost 30% (5%) of the respondents had at least one car(personal computer) in their household. The average of the monthly real household income was8,000 roubles (approximately US$284), with a standard deviation of 12,000 roubles, and the averageof the monthly real household expenditure was 6,100 roubles (US$216), with a standard deviation of7,400 roubles. Table I reports the mean and standard deviation of the main variables for the fivegroups of individuals with each level of life satisfaction.

The least squares specification is:

household income can explain up to a third of the large swings in life satisfaction within Russia accounted between1996 and 2000.31

Information about the RLMS can be found at the following address: www.epc.unc.edu/projects/rlms. Some detailsabout the project (and an interesting overview of the data) can be found in Mroz et al. (2004). I use only those rounds because they are freely accessible.

32 New entrants are not dropped. As fixed effects estimators demand at least two observations on each individual to be considered into the estimation, the new entrants included are only those who enter the sample during the secondround and remain in the third. Without considering missing values, 1,243 of the 9,074 individuals in the round 9 hadleft the sample at round 10, and 177 individuals were the new entrants. Only 767 of the 8,008 individuals present atround 10 left the sample before round 11. As usual, I threw away data with missing values. Ferrer-i-Carbonell (2005)recounted that, within the literature, none of the authors that reweigh data reports that reweighting makes adifference.

TABLE I

Mean SD Mean SD Mean SD Mean SD Mean SDSat. with Economic Condition 1.22 0.59 1.80 0.72 2.34 0.91 2.81 1.11 3.29 1.39Comparison Life Satisfaction -1.18 0.44 -0.35 0.36 0.50 0.36 1.36 0.42 2.16 0.60

HH Expenditures Real 6195 9657 7036 8182 8796 11859 10156 13183 17319 31601HH Income Real 4746 5373 5761 5967 6904 8679 7734 9841 8480 9336F(Expenditures) 0.46 0.29 0.54 0.27 0.59 0.27 0.64 0.27 0.68 0.26f(Expenditures) 4.12 2.04 3.84 2.14 3.69 2.33 3.24 2.23 3.80 2.82F(Income) 0.47 0.28 0.55 0.28 0.60 0.28 0.64 0.27 0.63 0.28f(Income) 4.34 2.11 3.99 2.11 3.81 2.31 3.44 2.25 4.15 2.73Gini(Expenditures) 0.46 0.06 0.46 0.06 0.46 0.06 0.46 0.06 0.47 0.06Gini(Income) 0.44 0.07 0.44 0.07 0.44 0.07 0.44 0.07 0.44 0.06

3 4 5

Notes: Means and standard deviations (at individual level) for the Round 9 observations included in equation (1), Table III.

Life Satisfaction1 2


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it it it it it Z X H ++++= 21

Where it H is a measure of life satisfaction,it X is a matrix of individual time-varying controlvariables, it Z is the vector containing the variables of interest related to income and expenditure,t denotes year effects, i corresponds to individual fixed effects, andit corresponds to the remainingerror term.

As more than 50% of the variation in individuals' reported well-being might be explained bygenetics (Lykken et al., 1996), we can not ignore fixed effects33. Fixed effects estimators help us toconcentrate on the longitudinal nature of the data, focusing only on the intra-individual variations inhappiness. Beyond obvious unchanging characteristics (such as gender, ethnic group or birthplace),fixed effects are supposed to account for key static variables, such as personal traits, individualaspiration towards life and, as will be shown below, internal and external comparison incomes.

Following McBride (2001), individuals compare their income to their "external norm" whenthey look at the people in their cohort (of similar age, gender, race, location, etc). On the other hand,the "internal norm" is based on the individual's personal consumption path. For instance, a particularamount of present income will probably make an individual who was raised in a wealthy

environment less happy than an individual with a record of poverty.Suppose that income raises well being as a logarithmic transformation, ) / ln( iit Nor Inc ,where it Inc is the income of the individuali at time t and i Nor is the individual's comparisonincome (internal, external, or a combination of both). If both norms were expressed approximately asconstant across time, we would be able to ignore the comparison income and focus solely on thelogarithm of income, as fixed effects would be controlling for the norms:

iit iit iit Inc Nor Inc Nor Inc +== )ln()ln()ln() / ln(

Income by itself is far from being the only indicator of material standard of living. Headey etal. (2004) used household economic panel data from five countries to find that in the two countrieswhere consumption data were available, non-durable consumption expenditure appeared to be atleast as important to happiness as income. As a matter of fact, if only one of the two variables(income or expenditure) was included in each regression of this paper, the remaining coefficientwould show a large bias.

It is not very clear what part of material standard of living is captured separately by eachvariable, and it is even less clear what part do each one explain when both income and expenditureare included jointly as regressors. Income may be associated with economic security, or assets thatindeed generate a real flow of benefits (e.g. having a more comfortable house). Income also enablesto borrow money for investment purposes and for coping with bad times (Headey et al., 2004).Income may even make people happier just because they experience a feeling of self-realization (i.e.they love money itself).

The expenditure variable has been created to measure consumption (in fact, this variable ispartially constructed based on questions about consumption). Since the expenditure variable might be missing some information on consumption, income would be able to capture partially theresidual. For instance, in household surveys there are not questions about the quality of goods.

33 In fact, Frijters et al. (2008) observed that most of the life satisfaction studies involving panel data have tested theappropriateness of the random effects versus fixed-effects specifications, and the former was always rejected. A moredetailed methodological discussion on this issue will be developed in the next subsection.


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Conditional on expenditure and other variables, it would be natural to think that the quality of foodin richer households is greater.

Wealth may be another variable of interest. As fixed effects control for the initial level ofwealth, only changes in wealth are left as interesting candidates for regressors. Notwithstanding, it isdifficult to think about any source of changes in wealth other than income and consumption, already

included as regressors.Ravallion et al. (2001) found that household income is a much stronger predictor of lifesatisfaction than individual income. For the sake of simplicity, I will focus on income andexpenditure measures only at the household level, disregarding individual data.34 Accounting for thehousehold income (expenditure) composition has not been properly addressed in the literature, eventhough it can be a serious source of bias.

In fact, Bonke et al. (2003) found evidence on the rejection of income pooling, and provideddirect evidence that the distribution of income within the household does impact on the within-household distribution of welfare (see also Lundberg et al., 1996; and Phipps et al., 1998). Thehappiness of the household head may be decreasing in the income of his/her spouse, or at least not asincreasing as in his/her own income. Besides controlling for variables on household composition, the

income (expenditure) variables are going to be normalized to account for this household compositioneffect using a particular calculation of the income (expenditure) equivalence scale elasticity(addressed in Section 3.3.).

The expenditure and income variable are probably endogenous. For example, the direction ofcausality might be the opposite: happier people consume more and earn more money just becausethey are content.35 As there is no credible instrumental variable or natural experiment to carry on,the identification strategy consists in the inclusion of fixed effects and dozens of time varyingcovariates. However, this strategy clouds the interpretation of the interesting coefficients. Forinstance, income (and expenditure) provides life satisfaction through the purchase of health servicesand education. Therefore, including explanatory variables on education and health will surely biasits coefficient downward.36

In order to account for income (expenditure) relative concerns, I will propose to calculate theempirical cumulative income (expenditure) distribution function. For this purpose, each individualmust be matched to the group he/she compares to. Reference groups have been defined in a numberof different ways within the literature. Easterlin (1995) implicitly assumes that individuals comparethemselves with all the other citizens of the same country; Persky et al. (1990) assume that allindividuals living in the same region are part of the same reference group; McBride (2001) andFirebaugh et al. (1998) use some kind of age cohorts; Van de Stadt et al. (1985) and Ferrer-i-Carbone(2005) make use of a combination of various criterions (for a detailed discussion see Clark et al.,2006b).

34 One positive point about the database is the level of detail on income and expenditure information. As shown by Juster et al. (1999), meticulous questionnaires provide higher and nearly always more valid estimates for averagelevels of wealth.35 Nonetheless, as I care the most about the relevance of an interactive term, talking about conditional associations isnot a vital problem.36 The coefficient on income must be then read as "the satisfaction from income besides everything I am controllingfor". Something similar happens with the interactive term. For instance, one of the non-markets goods is respect, butin some specifications I include respect as an explanatory variable.


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Several papers have taken a geographic approach (e.g. Luttmer, 2005; Blanchflower et al.,2004). Based on the similarities between China and Russia, I consider the work of Knight et al. (2006as a valuable source of information. They simply asked Chinese people to whom they comparethemselves. The cross-sectional information confirmed that 70% of the sampled population really seetheir village as their reference group (and a third of that segment said that they compared themselvesspecifically to their neighbors).

Therefore, I define the reference group as those individuals within the same geographicalunit, which is defined as a parsimonious agglomeration of survey sites belonging to the samegeographical area (almost all are cities, most of them administrative centres). One key leadingcriterion for the election of the level of aggregation was the sample size. As a result, the maximumnumber of surveyed individuals within a geographical unit at a particular round is 548, while theminimum is 150. Then, the cumulative expenditure, )( it ExpF , is defined as the percent ofhouseholds within the geographical unit with less real household expenditure than individuali atyear t . The same idea is applied to household real income.

The usual functional form for income (expenditure) is the logarithmic transformation.37 Thecorrelation between )( it Exp Ln and )( it ExpF is greater than 0.9, and the same is true for income.

Including both variables, and their interactions with other variables, would involve a problem ofhigh multicollinearity.38 All specifications will include only the cumulative incomes and expenditure,and their subsequent interactions. Notwithstanding, all the results would remain unchanged if

)( it ExpF and )( it IncF were replaced by their logarithmic counterparts.It would be ideal to have measures of how much conspicuous is each good (in the sense

introduced in the theoretical model), and then separate between conspicuous and non-conspicuousconsumption. Even that experiment was not implemented, in my model the status market clears withpositive sorting: the conspicuous expenditure is higher the higher the total expenditure (see foranother example Becker et al., 2005). Thus, total expenditure can be seen as a valid proxy forconspicuous expenditure and there is no need to discriminate between conspicuous and non-conspicuous goods.

In the next subsections there is a discussion about the suitability of OLS (compared toordered logit), followed by the calculation of the income (expenditure) scale elasticity. Then the twoidentification strategies are finally introduced.

3.2. OLS vs. Ordered Logit

As discussed in Ferrer-i-Carbonell et al. (2005), the choice between least squares and orderedlogit can be reduced to the treatment of reported life satisfaction as either cardinal (OLS is suitable)or ordinal (ordered logit/probit is appropriate). The ordered logit/probit model will not be suitable because of the discreteness of the dependent variable, but because of the nature of the problem.Intuitively, the properness of OLS may be subsequently subdivided into two separated conditions: i.If for the same individual the difference in happiness between reported values of 3 and 4 is the samethan the difference between 6 and 7; ii. If the difference in happiness between reported values of 3and 4 is the same for any pair of randomly-chosen individuals.

If the first condition does not hold, OLS can remain suitable if the dependent variable isproperly transformed. For instance, if differences near the centre (5, in a 1 to 10 scale) were stronger,it would be enough to apply a U-shaped function on the reported-happiness variable (i.e. to

37 What entails dropping each nonpositive observation (around 50 for income).38 Nevertheless, the high collinearity also implies that if we included the wrong variable, the bias would be minor.


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transform it as to make the first condition hold). I have carried out several trials and found that thereare no major differences if the dependent variable is transformed in numerous ways.

Regarding the second condition, if the differences in happiness between 3 and 4 for a pair ofrandomly-chosen individuals were the same than the differences between 4 and 5 for the same twoindividuals, then fixed effects estimators would be suitable (as those differences are captured by

individuals' fixed terms).Besides the conditions exposed above, there are other two advantages commonly associatedto the choice of a nonlinear model (not necessarily ordered logit/probit). Firstly, in nonlinear modelspredictions "out of range" can be ruled out (i.e. if the happiness scale goes from 1 to 10, the modelforecasts in that span). For every specification I regressed, not only those presented in this paper,there was not a single prediction out of range. The second advantage of nonlinear models is thatmarginal effects can be variable. This is not a major issue, since this paper makes intensive use of setsof dummy variables. In addition, OLS marginal effects are linear in the parameters, and thenfunctional transformation of the variables and interactive terms can be used to get variable marginaleffects.

There are some practical difficulties associated with the ordered model. Firstly, estimation of

nonlinear models with fixed effects yields inconsistent estimates (see Greene, 2002). Even thoughFrijters et al. (2008) proposed a suitable model39 , it is not yet available in standard software packagesand thus its development demands time and effort. Secondly, the complex interpretation of marginaleffects is a major source of troubles. As noticed in Boes et al. (2004), marginal probability effects arrarely reported in practice.40 For instance, in Frijters et al. (2004) marginal effects are arbitrarilycalculated at the mean values of the explanatory variables as the change in the probability ofreporting high life satisfaction, either 9 or 10, relative to a value of 8 and below (in a 1 to 10 scale)Despite other measures can be adopted (e.g. the mean of the marginal effects over the entire sample,for each outcome), I would not recommend such room for arbitrary interpretations unless there is aclear reason to suspect that there are results "hidden" by nonlinearities.41

3.3. Elasticity to household sizeIn the literature of life satisfaction it is not usual to account for the income (expenditure)

elasticity to household size. I believe that this omission (even if including explanatory variables forhousehold composition) may likely lead to biased conclusions. I test if the results of this paper arerobust to a choice of an scale elasticity different from zero.

With the aim of calculating the value of the elasticity, I implement a method based onindividual panel data on income satisfaction (suggested by Schwarze, 2000). Because the databasedoes not include a specific question about the satisfaction with household income, I focus on the

39 Das et al. (1999) also developed an ordinal fixed effect estimator. Chamberlain (1980) proposed to collapse thehappiness scale into a binary variable (applied in Winkelmann et al., 1998; and Clark, 2003). Terza (1985) proposed an

ordered probit in which the value of the thresholds is a linear function of the included regressors (presented as theGeneralized Threshold Model in Boes et al., 2004). There is another alternative based on a sequence of binary choicemodels for the conditional probability of choosing a higher response category each period, what borrows conceptsfrom the literature on discrete duration models (Sequential Model, in Boes et al., 2004).40 The remark of Boes et al. (2004) is noble. Their main concern was that there was no evidence whether themagnitude of the income effect depends on the level of the individual's life satisfaction. Nonetheless, the results donot suggest that the differences are significant.41 Since we are interested in interactive terms, the additional work would be even greater. As Ai et al. (2003) pointedout, an interaction effect in nonlinear models does not equal the marginal effect of the interaction term: it can be evenof opposite sign, and its statistical significance is not calculated properly by standard software.


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economic rank variable: in which step of the 9-step ladder the respondent declares to stand, wherethe first step corresponds to the poorest and the ninth corresponds to the wealthiest. The model can be written as:

it t h

it

it it it

k k it k h

Y X S

++

+= +0ln21

Where it S is the self-evaluated economic rank,it X is a matrix of time-varying individualcontrol variables (a constant, respondent age, work status and hours in an average workday),t denotes year effects, and it corresponds to the remaining error term.it Y is the total householdincome, and the term in parentheses corresponds to the scaled income, whereit h is the householdsize. Its exponent, the scaling parameter, is compounded by a constant (0 ), and a linear

combination of the number of kids, teenagers, working age males and females, and post working agemales and females (eachk it h within the weighted sumk k it k h ). Rearranging:( ) ( ) ( ) it t it k k it k it it it it hhhY X S +++= lnlnln 20221

I regress it S on ( )it Y ln , ( )it hln and the interactions between ( )it hln and each k it h :

( ) ( ) ( ) it t it k k it k it it it it hhhY X S +++++= lnlnln 4321

Hence, I can recover the linear parameters of the elasticity to household size: 230 = ,and 24

k k = . The regression is shown in Table III, along with a replication using life

satisfaction as dependent variable. Both household income and household expenditure were

included as regressors. Therefore,2 is the sum of the coefficient on the logarithm of income and thecoefficient on the logarithm of expenditure.The coefficient 3 is negative, as expected (i.e. the more the people the less each one can

enjoy a fixed amount of money). The coefficientsk 4 show that the elasticity scale is decreasing inthe number of kids under seven years old (as expected), in the number of working age females, andin the number of post working age males. The scale is increasing in the number of working age malesand in the number of post working age females, while the effect for the number of teenagers in thehousehold is not statistically different from zero.

TABLE IIepen ent aria e:

Coefficient SE Coefficient SE

Ln(Expenditures) 0.301*** (0.014) 0.212*** (0.010)Ln(Income) 0.147*** (0.015) 0.151*** (0.010)Ln(No HH Members) -0.139*** (0.044) -0.236*** (0.033)Ln(No HH Members)*No of kids less than 7 years old 0.069*** (0.013) 0.049*** (0.009)Ln(No HH Members)*No of kids 7-18 years old 0.009 (0.010) -0.007 (0.007)Ln(No HH Members)*No of working-age males -0.023** (0.012) -0.023*** (0.008)Ln(No HH Members)*No of working age females 0.032*** (0.012) 0.018** (0.009)Ln(No HH Members)*No of post working age males 0.098*** (0.023) 0.082*** (0.017)Ln(No HH Members)*No of post working age females -0.039** (0.017) -0.009 (0.013)

Notes: Robust standard errors in parentheses. Star is significant at 10%; Double-Star is significant at 5%; Triple-Star is significant a t 1%. Datadefinitions in the Appendix. Both regressions include a constan t, year dummies and personal controls (respondent age, work status, and hours in

an average workday). Observations: 25074 and 25276 respectively.

(2) Satisfaction with Life(1) Economic Rank Ladder


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The scale proposed by the OECD assigns a weight of one to the first adult, 0.5 to furtheradults and 0.3 for children under 15 years of age, generating equivalence scales, for instance, rangingfrom 0.53 (2 adults and 2 kids) to 0.66 (4 adults). Schwarze (2000) suggested equivalent scales belowthe latter (0.40 and 0.31 respectively), and below every other standard scale. My calculations implyequivalence scales such as 0.21 for a working age woman with a kid, 0.29 for a working age couplewithout kids, and 0.38 for a post working age woman with a teenager. All the regressions will bereported with and without accounting for the income (expenditure) scale elasticity.

4. Results4.1. First identification strategy: regional inequality

The theoretical model proposed that consumption affects individual happiness through twochannels: i. A direct channel, related to the "intrinsic" utility derived from consumption; ii. Anindirect channel, related to a higher probability of being chosen by Prince Charming. The secondsource of happiness is (by construction) null in a perfectly homogeneous-in-consumption society,and grows as consumption heterogeneity rises (Prez Truglia, 2006).

The econometric specification is:

it it it it it it

it it it it it it

IncGini IncGini IncF IncF

ExpGini ExpGini ExpF ExpF X H

++++++++++=

)()()()(

)()()()(

765

4321

Where ()Gini is the Gini coefficient in the reference group. The more unequal inexpenditure is the geographical unit where the individual lives, the larger the effect of expenditureon happiness will be. Thus:

0)()( 3

>=

it it

it

ExpGini ExpF H

All the analysis began supposing that income is unobservable. If income variables did notcapture a residual effect of consumption (not accounted by expenditure), the indirect effect wouldhave to be identified for expenditure-variables and not for income-variables. In that case,6 should be zero. This is a key robustness check for both identification strategies.

As mean expenditure (income) within the reference group is correlated with regionalinequality, it is also included as a regressor. In some specifications I include the interactions betweenincome (expenditure) and a set of 7 dummies that indicate the eight geographical regions where theindividual may belong to. These region-specific()F 's control for any "interactive" variable constantthrough time within geographical regions.42

42 For example, consider two individuals in the first deciles of their respective reference groups. If the first society issignificantly richer than the second for every step of the economic ladder, the first individual would be happiersimply because being in the first decile in the first group means (in rubles) having more money than in the secondgroup. As mean income (expenditure) and income (expenditure) inequality are correlated, the estimate of6 ( 3 )might suffer from an omitted-variable bias. This is not a relevant concern when the logarithmic transformation isunder consideration (instead of the empirical cumulative distribution function).


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Table IV presents various specifications: the interactive terms appear in the second equation,

while the first equation will be analyzed in the next subsection. The second pair of equations is equalto the first pair, but using instrumental variables instead of ordinal least squares (as will be explainedlater). The third pair of equations is also equal to the first pair, but it accounts for income andexpenditure scale elasticity.

In equation (2) the coefficient3 is positive and statistically different from zero at the 1%level of significance. The hypothesis that6 is different from zero cannot be rejected at anyconventional level of significance. The coefficients on mean expenditure and mean income arenegative and significative. This is consistent with the empirical literature, which shows thatindividual happiness decreases as the reference group's income raises (Blanchflower et al., 2004;Luttmer, 2005; Ferrer-i-Carbonell, 2005; Clark et al., 2006a). The coefficient on the interaction betwemean income (expenditure) and real income (expenditure) is not statistically different from zero. The

coefficients 4 and 7 will be analyzed in the next subsection.I propose a set of instruments for income and expenditure inequality in order to lessen the

potential identification problems. The idea is basically to exploit the geographical structure of thedata. The happiness of a particular individual, conditional on the income (expenditure) inequality inhis own geographical unit, has not to be influenced by the income (expenditure) inequality in anyother geographical unit different from his own (and the same is true for the interactive term). On theother hand, income (expenditure) inequalities in different geographical units are expected to becorrelated between them due to exogenous common shocks on the distribution of incomes (e.g.weather, politics, etc). Therefore, income (expenditure) inequality in other geographical units canserve as instruments for income (expenditure) inequality in a given geographical unit.43

The results for instrumental variables are reported in the equation (4) from Table IV. Thecoefficient 3 remains positive and statistically different from zero at the 1% level of significance,although its value is slightly smaller.

Figure II shows the total effect of cumulative expenditure on happiness, using the estimatedvalues for coefficients 2 , 3 and 4 from equation (4). The marginal effect is given by:

43 For the interactive term between income (expenditure) inequality and cumulative income (expenditure) theinstruments are the interactions between the cumulative income (expenditure) and the set of instruments for income(expenditure) inequality.

FIGURE II

1.9

22.1

2.22.3

2.42.5

2.6

2.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1F(Expenditures)

I n c r e a s e

i n H a p p

i n e s s

0.4 0.425 0.45 0.475 0.5 0.525 0.55Gini(Expenditures):


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)(22.28.0)( it it it ExpGini ExpF H += .44 The contribution of the interactive term takes valuesfrom 0.8 to 1.21, corresponding to the 5th and 95th percentiles of the Gini coefficients in the sample(0.37 and 0.56, respectively). On the one hand, in the most homogeneous-in-expendituregeographical unit ( 4.0)( =it ExpGini ) an individual in the fist decile of the expenditure distributionthat increases his expenditure up to the highest decile experiments an increase in happiness of 0.1.On the other hand, in a very heterogeneous-in-expenditure geographical unit ( 55.0)( =it ExpGini )the impact on happiness is greater by a factor larger than 4. That illustrates the importance ofexpenditure inequality on the magnitude of marginal utility.

As shown in Figure II, the poorest two-fifths of the population would be discontented withan increase in expenditure inequality, whilst the richest three-fifths of the population would beconsiderably better. As ()F is the cumulative distribution function, the areas between lines inFigure II suggest that there would be a gain in total welfare from the increase in expendituredispersion. Nonetheless, this benthamian welfare improvement would be accompanied by a rise inhappiness inequality. The main results do not change neither if income (expenditure) is normalized by the elasticity scale, nor if()F is replaced by () Ln (not reported).

But the signaling theory is not the only valid explanation for that finding. The interaction

between real expenditure and expenditure inequality might be partially reflecting that a person in amore unequal group is in average more distant from his followers in the expenditure distribution.Following the theory of relative deprivation, rich individuals might feel better just because theirdistance in income to poorer individuals has been increased. Conversely, poor individuals might feelworse because their distance in income to richer individuals has been increased. In fact, the amountof average deprivation in a society can be written as the product of the Gini coefficient and the meanincome (see Yitzhaki, 1979).45

I previously pointed out that relative deprivation is in fact a particular case of the PrinceCharming Model where respect (or envy, admiration, etc.) is the non-market good to be allocated.Since I want to separate both explanations, I propose a second identification strategy to overcomesuch overlapping.

4.1.1. Inequality aversion revisited

The most striking finding of the literature on inequality and individual happiness is thatwell-being appears to be positively correlated with income inequality within the reference group(e.g. see Clark, 2003; Schwarze et al., 2003, 2006; Graham et al., 2005). For instance, Ravallion et (2000) and Senik (2004) claim to have found such positive association using the same Russiandatabase employed in this paper. In order to explain that finding, some papers have proposed effectsof indirect nature: inequality as an indicator of social mobility (Di Tella et al., 2004), and theformation of an informational tunnel effect (Ravallion et al., 2000). I propose that conspicuousconsumption may be the answer to the puzzle.

The derivative of happiness with respect to expenditure inequality is compounded by twoterms: 43 )()( += it it it ExpF ExpGini H . The first term, the indirect effect of consumption, is

44 With respect to potential identification problems, it is worth noticing that it is more probable to find an omittedvariable correlated to expenditure (income) inequality than finding an omitted variable correlated to the interaction between expenditure (income) inequality and real expenditure (income). The identification of4 and 7 are not themain concern of this paper, and thus the results that include those coefficients must be treated carefully.45 The sign of the total effect of consumption inequality on total welfare would be determined by the direction of theasymmetry between the upward and downward comparisons. For instance, Duesenberry (1949) suggested that onlyupward comparisons matter. In that case consumption inequality should noticeably decrease the welfare of all.


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always positive. Henceforth, if the interactive term were not included in the regression, a positivecoefficient could arise even though the direct effect of expenditure inequality on happiness (3 ) wasin fact negative. That can explain the nonnegative impact of income inequality on individual well being found by the papers introduced at the very end of the previous section.46 Indeed, in equation(1) from Table IV the interactive terms were "intentionally forgotten": a positive (though notsignificant) coefficient appeared for expenditure inequality (when in fact the direct effect is negative,as shown in the second equation). The result is the same for the IV estimates shown in the last pair ofequations.47

4.2. Second identification strategy: further distributional information

The previous empirical strategy exploits only the inter-geographical-unit variation in thedistribution of expenditure (and income). All the distributional information within the geographicalunits was collapsed into a single indicator, the Gini coefficient. In order to exploit more distributionalinformation, empirical densities of the household expenditure (incomes) were obtainednonparametrically (using an Epanechnikov kernel with optimal bandwidth) for every referencegroup (geographical unit) and for every year.

People continuously interact with other people from the same neighborhood, workplace,educational institution, etc. Reference groups are compounded mainly by people with similarpositions in the economic ladder. Those groups are in general much more homogeneous in purchasepower than the society as a whole. In particular, I argue that someone in a very "populated" step (e.g.with the "mode income") is likely to have a high proportion of friends and neighbors with similareconomic conditions. And someone in a very "unpopulated" step (e.g. unusually rich or poor) willprobably have many friends and neighbors coming from the adjacent steps.

The new identification assumption claims that the density of income (expenditure) at aparticular year is a good indicator of the degree of income (expenditure) heterogeneity within theindividual's reference group. Namely, an individual with a "frequent" income (the density of theincome distribution evaluated in her income is high) is expected to have a much more homogeneous-

in-income reference group than an individual with an "infrequent" income.This partially solves the differentiation with respect to the relative deprivation theory.

Inequality is not longer defined on differences in absolute income, but on the probability of "sharing"the reference group with individuals from other segments of the income distribution. For instance,consider the following two distributions of discrete incomes:{ }90,90,100,100,110,110 A = and

{ }60,60,100,100,130,130 B = . While the Gini coefficient is greater in the second, the incomedensities are exactly the same. Then, their interactive effect (contrary to the Gini coefficient) will no be capturing the income heterogeneity coming from the upward and downward mean incomedistances.48

The specification is:

46 As they do not include expenditure variables, income probably captures to some degree the effect of expenditure.47 Up to my knowledge, aside from Prez Truglia (2006), only Ravallion et al. (2005) have focused on interactive termsfor income. They simply noticed that, as income rises, if the effect of some variable (e.g. regional inequality) switchessign, then not including the interaction term (regional inequality by income) will insinuate a positive coefficient forregional inequality (even if it is indeed negative for a great share of the population).48 There is still a direct relationship between the reference group's inequality and the sum of the densities for all theindividuals. However, if the interactions with both the regional Gini coefficients and the individual densities wereincluded, only the coefficients corresponding to the latter would appear as statistically different from zero.


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it it it it it it

it it it it it it

Inc f Inc f IncF IncF

Exp f Exp f ExpF ExpF X H

++++++++++=

)()()()(

)()()()(

765

4321

Where )( it Exp f and )( it Inc f are the densities of total real expenditure and total realincome for individuali at year t , respectively.49 For an easier quantitative interpretation of theresults, () f was normalized to take values between 1 and 10. Percentiles 15th, 50th and 85th arerespectively 1.43, 3.21 and 5.96 for )( it Inc f , and 1.15, 3.33 and 5.7 for )( it Exp f . The impact ofexpenditure on happiness will be greater the more heterogeneous-in-expenditure is the referencegroup of the individual:

0)()( 3


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scale, as revealed by equations (1a) to (3a). As in the previous identification strategy, the results donot change after considering bootstrapped and clustered standard errors.

Figure IIIa shows the total effect of expenditure on life satisfaction, using the estimatedvalues for coefficients 2 , 3 and 4 from equation (2). The marginal effect can be expressed as:

)(057.033.0)( it it it Exp f ExpF H = . The contribution of the interactive term takes values

from 0.065 to 0.32, corresponding to the 15th and 85th percentiles of)(

it Exp f

in the sample (1.15and 5.7, respectively). In a very homogeneous-in-expenditure reference group ( 5)( =it Exp f ) anindividual in the fist decile of the expenditure distribution that increases his expenditure up to thehighest decile do not experiment a change in happiness. In contrast, in a very heterogeneous-in-expenditure reference group ( 2)( =it Exp f ) the increase in happiness would have been almost 0.3.A good measure for the relative importance of the indirect effect is the absolute value of the ratio ofthe interactive term to the non-interactive term, which ranges from 0.19 to 0.98, corresponding to the15th and 85th percentiles of the expenditure densities. The interactive effect is certainly veryimportant. Holding their ranks constant, a dispersion of the expenditures for people above

7.0)( =it ExpF would increase their welfare.The estimate of the coefficient on the term() f is significant only for expenditure. The

positive sign of 4 may be reflecting some kind of aesthetic valuation for homogeneity inexpenditure within reference groups.50 Since the coefficient7 is not statistically different from zero,the aesthetic valuation would not be ext

happiness inequality

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