Can a rise in income inequay imrove wefare? * Ricardo Nicoás Pérez Trugia γ Deartment of Economics niversidad de San Andrés Abstract Wie in omogenous societies income can ony buy tradiona goods e.g. food, cotes, tis aer caims tat in eterogeneous societies income can aso buy nonmarket goods e.g. resect, friends. Suc transactions take ace troug te signaing of unobservabe caracteristics via consicuous consumtion. Te teoretica mode sows tat: i. Consicuous consumtion is an efficient aocation mecanism for some non-market goods; ii. Tere is an efficiency oss associated to a rogressive redistribution of incomes; iii. Te oss is articuary imortant in more "merocratic" societies. Ten I test my conjectures based on ane data on ife satisfaction for 10,000 resondents in Russia for 2000-2002, exoing two identification strategies. Te foowing resuts emerge: i. Exendures inequay win reference grous do increase te margina utiy derived from consumtion; ii. Te "direct" distaste for inequay as been consideraby underestimated by te erature; iii. Te mode rovides micro-foundations for te idea of a utiy function first concave and ten convex. Te resuts remain uncanged after controing for te income equivaence scae easticy and a wide range of recent teories on Economics of Hainess. Bot te teoretica and emirica findings suggest, for exame, tat te government of a merocratic society suc as te ned States soud not worry about art of te rise in income inequay exerimented in te ast decades. JEL Codes : D01, D31, D69, H00, I31. Keywords : Income inequay, ainess, consicuous consumtion. * Tis is a work in rogress. I want to recognize te recious suort and guidance of Water Sosa Escudero and Federico Weinscebaum. For efu comments, I tank artin Rossi, artin Gonzaez-Eiras, aría Edisa Soesa and artin Tetaz. Te usua discaimer aies. γ niversidad de San Andrés, Vo Dumas 284, B1644BID Victoria, Provincia de Buenos Aires, Argentina. ricardotrugia@gmai.com tt://www.ricardotrugia.com.ar 1
1. Introduction Economic condion was extremey imortant in te eary stages of economic deveoment, wen te fufiment of basic needs was in te centre of every discussion. Nowadays, te roe of income in ife satisfaction is more frequenty reated to factors suc as consicuous consumtion and socia comarisons. Tis aer re-examine te wefare discussion on income inequay taking into account te growing reonderance of suc reative concerns. I introduce a articuar definion for consicuous goods trougout tis aer, intercangeabe w status goods: tose observabe goods and services w rices above ow muc te consumer woud ave aid if te consumtion ad not been observabe besides estetic or functiona features; furter detais in Section 2. It is easy to roose ots of goods tat may satisfy suc condions. A $20,000 god watc, uxurious cars and exensive ce ones migt serve as reiminary exames. Te first exanations for te existence of suc goods were based on envy, arrogance, greediness and simiar manifestations of reative concerns. Te difference between te vauations for observabe and unobservabe consumtions may be just mirroring tat eoe enjoy sowing teir successes to everyone ese, aso may be refecting tat eoe enjoy from te envy of teir neigbors, among oter simiar exanations. Since suc goods are not tougt to rovide intrinsic utiy, many economists argued tat tese reative concerns take individuas to a ig eve of socia cometion i.e. to a "rat race" and ten to an unnecessary waste on status goods. However, consicuous consumtion may ave a second indirect effect Postewae, 1998. I caim tat eoe care about reative standings not just because of teir arrogance and greed but, at east to some extent, because reative standings indirecty affect te goods and services in a wide sense utimatey consumed by tem. Te ga between observabe and unobservabe vauations is refecting te benefs from te signaing of income, due to te increase in te robabiy of getting a different second good. Te imications of te atter exanation may be diametricay different. Furtermore, tat signaing mecanism wi be roosed as an aocation mecanism for some goods and services in a wide sense tat eoe consume but cannot be urcased troug standard markets. In fact, tose goods ave been roosed as a substantia art of te totay of goods in te economy Coe et a., 1992a, 1992b, 1998. For instance, friendsi, sex and resect cannot be eer sod or bougt, at east not wout receiving a socia or even ega rerimand. Tose non-market goods and services must be aocated troug some kind of matcing mecanism, wic as to seect among a set of candidates demanders w some reevant caracteristics "to ay in excange". For instance, eoe ave time to send w oters, and in excange tey refer to "be aid" w cats about toics of teir same interest. Te mecanism ten as to overcome a robem of asymmetric information: te asirants ave non-observabe caracteristics, and tey migt not revea trutfuy teir tye. Someting marveous about forma markets is tat tey syntesize a te information needed in a singe vector of reative rices. In te same sir, te rices of status goods wi be roosed as a vector of imic rices for non-market goods. Income is one of te unobservabe caracteristics in wic te suier of te non-market good may be directy or indirecty interested. For instance, a man migt be interested in marrying a ric woman. However, income does not ave to be a reevant caracteristic er se. Te seection of ric individuas just because tey are ric because of greediness, reative concerns, and so fort is not te main concern of tis aer. Consicuous consumtion can signa any desirabe caracteristic of te "demanders", as ong as tis attribute is condionay on observabes correated w income 2
w a define sign. Foowing te revious exame, te man may want to marry a ric woman not because e wants to enjoy er money, but because e tinks tat, condiona on te observabe information, te income of a erson is associated w er oyaty and oter desirabe caracteristics in a artner. Tis subte ercetion is te foundation of te main deartures from te usua resuts. Consider te ricing of graduate rograms in business e.g. an BA. One of te most vauabe benefs of attending an BA is te ossibiy of getting in contact w oter businessmen to dea in te future, or just to sare exeriences and knowedge w. Tus, te most taented managers wi want to be in te same BA. Notice tat, since in te business word making money is te main asiration, income seems to be a good indicator of individua skis. Suose tat te gains from te rogram are substantiay above te margina cost of education, bot for bad and good managers. In addion, suose tat good managers are seriousy distressed wen bad businessmen articiate into te rogram. As a resut, condiona on te caracteristics reiaby observed by te admission commtee, in some BAs te entrance fees wi be set ig enoug as to deter bad managers from entering te rogram. In tose BSs, since everyone ese is aso a good manager, eac taented manager wi be gad to ay te exensive fee. As business rograms can be offered for muc ower rices, cometion among different rograms coud suggest tat te fees woud be eventuay reduced. However, if te entrance fee for one of te best rograms were owered, ten bad managers woud be abe to enter into and as a consequence good managers woud refer to move to one of te remaining exensive rograms. Setting rices equa to margina costs is not te otima soution, since a ga is needed to aow for te signaing of business skis. 1 In order to study tis enomenon rofoundy, I join togeter toos from te teoretica erature on consicuous consumtion 2 and from te emirica erature on Economics of Hainess. 3 Te main teoretica finding is tat income inequay, as ong as corresonds to differences in skis, makes ace to te aocation of non-market goods. Consequenty, income inequay soud increase te margina utiy from consumtion. Addionay, tis aer demystifies te tradiona inkage between status goods and diamonds. Consicuous consumtion is exected to be more imortant not in te ricest reference grous, but in te most eterogeneousin-income resent in bot tais of te income distribution. Tis woud rationaize te consumtion of "uxury" goods by te "roserous" oor. Two emirica identification strategies are roosed. First, exendures inequay win te geograica area is roosed as a mutiicative-augmenter for te effect of consumtion on ife satisfaction. Afterward, in order to exo more information on te exendures distribution, a nonarametric estimate of te regiona exendures densy distribution is roosed as a better roxy to measure inequay win reference grous. 1 Of course, tere are some extra oints to take into consideration for tis articuar exame: graduate rograms aso invove education, te reation between business taents and income may not be so cear because of inerances and cred frictions, etc. 2 Status concerns ave been ong recognized not ony by economists for eary contributions see Veben, 1899; and Turow, 1971, but aso by socioogists Weber, 1978, and even in bio-sciences azur et a., 1980. 3 Essentiay, I focus on economic erature wic uses arge-scae survey data on subjective we-being. Notwstanding, tere are oter interesting ways to study tat reationsi. For exame, Camaco-Cuena et a. 2002 rovided a comarative exerimenta study of risky rosects and income distributions, and Carsson et a. 2001 measured references for risk and inequay troug exerimenta coices between yotetica societies and otteries. 3
Te resuts indicate tat intra-reference-grou exendures inequay indeed increases te margina utiy derived from consumtion. Te indirect effect is observed ony for te exenduresreated variabes observabe, and not for te income-reated variabes unobservabe, wat wi be roosed as a robustness exercise. Tis aer fis a ga in te erature, as can exain wy many aers ave found eer a nu or osive reationsi between income inequay and ife satisfaction. I aso sow tat te resuts can account for a utiy function iniay concave and ten convex. In tis sense tis aer is intended to rovide a subte suort to te idea of a "natura rate of inequay" a.k.a. "manufactured inequay". Te aer is arranged as foows. In Section 2 a signaing-tye mode is resented, aong w a teoretica discussion. Te secification of te econometric mode and a succinct descrition of te data can be found in Section 3. Te estimation resuts are sown in Section 4. Section 5 concudes. 2. Teoretica ode Tere are many exames of signaing win te teoretica erature. Workers can signa teir abiy to emoyers troug status consumtion Frank, 1985a, 1985b or socia cuture Fang 2001. Peoe can aso send money on fasions to signa skis in a dating game Pesendorfer 1995, or tey can signa weat just to matc weatier mates Coe et a., 1992a. In te same vein as Hokins 2006b, my mode marries asects of bot Sence s job market signaing and Becker s marriage matcing modes Sence, 1973; and Becker, 1973. aybe te most motivating exames of non-market "services" are ersona, emotiona and rofessiona reationsis. Human beings continuousy ave to ick a sma number of individuas from a wide set of candidates: eoe ooking for a job or a articuar osion inside a cororation, businessmen in searc of business artners, teenagers in searc of new friends, etc. Sedom decisionmakers can observe every reevant asect to make te rigt coice, and ten tey migt want to rey on signaing mecanisms. Te foowing mode exos tat idea. Neverteess, is cear tat mating neer is te ony nor te most imortant exemar of consicuous consumtion. Indeed, tis game is not tougt to take ace exicy in te rea word but in a subter way in many activies regarding uman action. Tis subteness is robaby te main reason wy tis matcing mecanism as been systematicay overooked in te erature. 2.1. Prince Carmings ode Two individuas ay a game. Te first individua ereinafter referred as to "te candidate" is cosen randomy by Nature from a ouation of two ossibe tyes: oor or ric subscrits and resectivey, differentiated by teir income > > 0. Te fraction of ric tyes in te ouation is λ. Tere are two varieties of goods, referred to as standard good and consicuous good. Let x 0 be te quanty consumed of te standard good by te candidate cosen by Nature, wic as a constant rice normaized to 1. Let z be te quanty urcased of te consicuous good, and suose is binary eac tye consume one un or noting. 4 Let > 0 be te rice of one un of z. Just for te sake of simicy, suose tat ony te standard good enters into te utiy function:, w > 0 and < 0, identica for bot tyes. 4 Te vector of rices of te consicuous goods and te vector of urcased quanties wi not be imortant. Wat wi ony matter is simy te tota sending on consicuous goods. Having one consicuous good w binary consumtion is just a sime way to syntesize tat information. 4
Consider a second individua ereinafter "Prince Carming" wo as to coose weter to erform or not an activy w te candidate e.g. marry er. Tis activy wi be te non-market good. Accordingy, Prince Carming wi be in te foowing ines for non-market goods wat te warasian auctioneer is for tradiona goods. I wi suose tat Prince Carming wants to sare te activy ony w te ricer of te two tyes. Te reason is not ertinent yet: e may ike being w te ricest artner merey because se is ric, or e may beieve tat tere is a desirabe attribute osivey correated w income. Hence, consider te simest suation: Prince Carming refers stricty erforming te activy w te ric tye over any oter outcome, and e refers stricty not erforming te activy over carrying out te activy w te oor tye w osive robabiy. Te ast condion, a key eement of te anaysis, is a very straigtforward way to discard ooing equiibria. Later I wi sow tat ooing equiibria indeed is not interesting wen Prince Carming cares about te skis needed to earn te money and not about te money sef. Prince Carming can ony observe te quanty of te consicuous good consumed by te candidate, because neer er income nor te quanty consumed of te standard good x are ubicy observabe. Hencefort, ony consicuous consumtion can otentiay serve as a signa of weat. 5 Te utiy of being seected to erform te activy enters ineary into te utiy function of te candidate: is x + θ if te individua carries out te activy, and merey x oterwise, were θ > 0 is arger te more imortant is te activy under consideration i.e. te utiy associated w marrying Prince Carming is arger tan te utiy associated w waking aong te ark w im. Consider te aocation of a given activy w a θ associated troug a certain status good w a associated. In order to sustain a searating equiibria, tere are two necessary condions: te ric tye must buy te consicuous good, and te oor tye must not ave incentives to urcase. Since te utiy function is stricty increasing, every tye coose to consume teir entire income. Hence, te two condions can be exressed in te foowing way: + θ 1 + θ 2 First consider te case of is fixed. For a air of incomes ; we ave: θ = ω u 1a θ = ω 2a Te concavy of te utiy function guarantees tat b ω u > ω b : te incentive comatibiy condions for bot oor and ric tyes can od simutaneousy, and in articuar if 1a ods w equay ten 2a must necessariy od see Proof 1 in te Aendix. For a rice of te consicuous < and a air of incomes ; tere is a range of activies w a θ ω b, ω ] [ u good associated tat comrises a erfect Bayesian searating equiibria in ure-strategies: ony te ric tye buys te status good, and Prince Carming erforms te activy if e sees tat te candidate 5 Observabiy is one saient feature of osiona goods. Te ony survey evidence I am aware of, Carsson et a. 2003, suorts tat beief: an automobie igy observabe was found to be a osiona good, wie eisure and car safety igy unobservabe were found non-osiona. 5
consumes z. In sar contrast to te erature, tis innovative formuation of consicuous consumtion igigts te joy of marrying Prince Carming, θ. Keeing u te romantic atmosere, te range of activies tat can be acieved in equiibrium ranges from going out w Prince Carming θ = ω b to marrying im θ = ω u. Observe tat dω u d > 0 and dω b d > 0 : more exensive consicuous goods can rationaize activies w arger θs associated, atoug at te same time smaer θs are being rued out e.g. te urcase of diamonds can rationaize marrying, but cannot rationaize going to te cinema. Te oter way around is aso vaid e.g. te urcase of bijouterie can rationaize going te cinema, but definivey cannot rationaize getting married. Notice as we, using Jensens inequay, tat dω u d < 0 and dω b d < 0 : as income disary grows u te θs uer boundary goes u wie te inferior boundary goes down e.g. increased income inequay makes acievabe bot, someting worse tan going to te cinema and someting better tan marrying. Consider now te case w θ fixed. For a air of incomes ; we ave: 1 = 1 = b θ 1b θ 2b Once again, te concavy of te utiy function guarantees tat u > b Proof 2. For a given activy θ and a air of incomes ; tere is a range of rices b, ] tat u [ u comrises a erfect Bayesian searating equiibria in ure-strategies: ony te ric tye buys te status good, and Prince Carming erforms te activy ony if e observes tat te candidate is consuming te consicuous good. Tis formuation igigts te roe of te consicuous exendure,. Te revious resuts can be extended to tis case: firsty, dθ > 0 and d b dθ > 0 ; secondy, d > 0 and > 0 u d d see Proof 3. b d Consider a bentamian aggregation of individua wefares te ossibiy of a aretian imrovement wi be considered furter. If tere is a searating equiibria, ten exected socia * wefare can be exressed as foows: SW = 1 λ + λ + λθ, were is te utiy reaced * by te oor tye, is te utiy reaced by te ric tye and enjoyed by te ric tye wen se is cosen by Nature. Te ast term as been consistenty ignored by te erature. One te one and, by rising inequay e.g. decreasing and increasing by te same amount tere is an obvious oss reated to te diminising margina utiy, since a socia anner woud refer a more egaarian scenario. On te oter and, tere is a gain reated to consicuous consumtion. If was fixed, te ric tye woud be abe to acieve a arger θ since ω is going u u. 6 On te oter and, if θ was fixed, te ric tye woud gain from a fa in er consicuous sending since is going down. As I want to emasize tat tis effect migt be significant, I wi b sow tat under weak condions te second osive effect may even revai over te first negative. d u θ is te vaue of a articuar θ 6 In te equiibriums described beow, te θs are aways te argest ossibe, and te consicuous exendures are aways te east ossibe. However, if te eve of avaiabe activies and/or te rices of consicuous goods were fixed and exogenous, te acievabiy of smaer θs coud be a wefare-imroving canne as we. For instance, if θ was fixed beow ω b, te searating equiibria woud not be acievabe. Tus, a rise in income inequay troug a fa in ω woud make ossibe to erform te activy in equiibrium. b 6
Neverteess, if bot θ and were fixed tere woud be no way to exo te greater otentia wefare due eer to te rise in ω or to te decrease in u. b 7 I wi aow te ric tye to extract te igest ossibe surus troug te endogenous seection of one arameter. Hencefort, two scenarios wi be taken into consideration: fixed w endogenous θ, and fixed θ w endogenous. A tird scenario, aowing endogeney for bot and θ, wi not be considered because of uninteresting tecnica detais. 8 Different suations corresond to eac one of te two scenarios. Consider te case of graduate rograms in business. First notice tat, in te sort run, te entrance fee for a rogram is fixed. Once se entered into te rogram, a businesswoman can meet anoter manager and roose er a business dea θ.if θ were too ig, woud make te entrance to te BA rofabe even for a bad manager. Ten, te taented-tye manager wi ave to find out wat is te range of business roosas θs tat can sustain a searating equiibria. Conversey, consider te foowing exame for te second scenario: wen cometing for a job, te vauation of every candidate θ are fixed and equa. If te candidates income was correated to er exerience w foreign anguages e.g. young workers raised in ric famiies robaby went to biingua scoos and traveed around te word, te ric-tye candidate woud ike to signa er income troug consicuous consumtion in order to get te job. As tey are two equivaent robems, te foowing anaysis is rovided for bot scenarios. In tis formuation an individua is randomy samed from a ouation of agents of two tyes, and ten se is confronted to Prince Carming. In anoter ossibe formuation two individuas, aso differentiated by teir income, are directy confronted to Prince Carming wout any saming, wo can see te consicuous consumtion of bot. Even toug te resuts are retty simiar in bot formuations, te two-stage mecanisms tat wi be introduced beow woud not be necessary in te atter. 2.1.1. Fixed If every tye coud coose a air θ, z to offer to Prince Carming, a tecnica detai woud emerge: te oor tye coud coose a θ as arge as to rue out te searating equiibria. Hence, I roose te foowing setu: in a first stage, candidates of bot tyes must offer to Prince Carming an activy to erform w im caracterized by θ and θ for te ric and oor tyes resectivey. For aving a searating equiibrium, Prince Carming in te second stage soud coose to erform te activy ony if te θ decared by te candidate corresonds to te owest i offered during te first stage. 7 Neverteess, if te vaues of θ and/or were exogenous but cosen at random, woud be ossibe to sown a weaker resut in exected vaue. 8 For instance, woud be necessary to introduce an uer bound for θ. 7
ia FIGRE Ia a x θ a a a - a a - a x Te strategy for an individua of ric tye in te first stage wi be to coose te igest θ * tat comrises a searating equiibria in te origina game, θ = ω u, since se wi want to get as muc easure as ossibe from te fixed incurred exense. Tus, in te subgame erfect equiibria Prince Carming cooses to erform te activy if te consicuous good is urcased, te * oor tye cooses not to make an offer in te first stage or cooses θ ω u, ony te ric tye buys te status good, and se offers in te first stage te argest activy tat makes binding te * incentive comatibiy restriction of te oor, θ =. 9 ω u Reca te BA exame: te taented-tye manager soud offer to er coeague te maximum business roosa θ se can offer tat is consistent w a searating equiibria. As te game is not reeated, tis two-stage mecanism is one way among many for Prince Carming to earn wic is te maximum θ tat coud be offered ony by te ric tye. As I reviousy igigted, if te game were between Prince Carming and two candidates not one candidates of two ossibe tyes, te former woud be abe to see te θ offered by bot candidates, and te twostages mecanism woud be no onger needed. Hencefort, for te ric tye te utiy derived from te activy w Prince Carming can * be exressed as: θ =. Te margina utiy from te consicuous exendure is ten. Let SW be te exected utiy for te candidate cosen by Nature from te ouation of individuas of oor and ric tyes. Just for te sake of simicy, consider te case w λ = 1 2 ric and oor tyes are equay frequent. Te exected cange in tota surus can be exressed by differentiating: 2 dsw = d + d + dω, After a symmetric redistribution d ric agent to increase er θ in dω, wefare if and ony if Proof 4: u d u =, te greater sread of incomes aows te. A disersion of incomes wi increase exected tota < + 2 9 * For te oor tye θ ω u is best resonse, since se is not urcasing te consicuous good anyway. If θ > ω u te oor tye woud not want to buy te consicuous good, as se woud not erform te activy w Prince Carming. Neverteess, w θ < te searating equiibria woud not be vaid any more. ω u 8
FIGRE Ib ib b b x a c b θ b d d d b - b b - b x Tat is, if te mean between te margina utiy from tradiona consumtion and te margina utiy from consicuous consumtion for te ric tye exceeds te margina utiy from tradiona consumtion for te oor tye. Furtermore, if > 0, a sufficient condion woud be: > 2 Proof 5. Figure Ia and Figure Ib iustrate tat resut. Te standard consumtion for bot tyes before redistribution are disayed in Figure Ia, aong w te θ reaced by te ric agent, θ =. In Figures 1a to 1c, te second subscrits indicate wat is te suation under consideration. For exame, θ is te activy reaced by te ric tye in te inia suation, a deicted in Figure 1a, wie θ and b θ are te activies reaced after te increase in income c inequay for te suations w fixed and endogenous θ, deicted in Figure 1b, and w fixed θ and endogenous, deicted in Figure 1c, resectivey. Wen redistributing from te oor to te ric tye Figure Ib te atter gains b, wie te oor oses a. Te concavy of te utiy function guarantees tat b a < 0. However, since te sread of incomes as been increased, te ric individua can now get a iger θ, wic grows in d c osive due to te concavy of te utiy function. Hence, te cange in tota wefare is b a + d c. Lets interret te condion > 2. Foowing Figure Ib, te concavy of te utiy function ensures tat bot band d are increasing in, and tus d c and b a are increasing in. On te oter and, a, c and d are decreasing in, wie bis decreasing in. As a resut, b a is decreasing in, and > 0 guarantees tat d c is aso decreasing in. Tus, for given sread of incomes tere is a rice arge enoug as to guarantee a gain in tota wefare. oreover, te anaysis can be extended to a ouation of numerous tyes. Suose tat for a number of times two tyes, i and j, are randomy cosen to ay te game w reacement from a same of various tyes caracterized by different incomes. Before te cange in te income distribution, te exected gain from a articuar game reaization for tye is: [ + ω, ] G = P < + P > i i j i i j If income inequay is increased but te rank of every singe tye in te income distribution is reserved, ten te robabiies in te revious exression remain uncanged. If in addion te i u j 9
income distances were increased for every air of tyes 10, te new robem woud equa tat of twotyes and te wefare imications woud be aso identica. oreover, as every tye from te ouation excet te oorest wi be te ric tye w osive robabiy in te two-tyes-game, a tyes in exected vaue wi exeriment an utiy gain from te increase in income inequay. In articuar, te gain wi be greater te ricer te individua. 11 Since adding utiies may be unersuasive, I wi sow tat a Pareto imrovement can be reaced as we by a articuar cousion among agents. Suose tat in a revious stage of te twotyes-game te candidate of ric tye can se to te candidate of oor tye a discount couon to ay in advance for a fixed quanty C of uns of good x. As te oor tye knows tat in te future se wi not be abe to erform te activy w Prince Carming, se wi accet to buy te couon for nonnegative discounts. Notice tat te se of te couon raises te sread of incomes disosabe for status consumtion, even wen te sread of reaized consumtion of good x woud be even reduced for osive discounts. C > Just for te sake of simicy suose tat te discount is zero. If a couon for uns of x were sod, in te second eriod te oor tye woud not be abe to buy te consicuous good and tus te ric individua woud be abe to reac a θ as arge as ossibe. Tat woud undoubtedy imy a Pareto imrovement, as te ric tye woud be muc better wout arming te oor tye wo woud be even better if te discount was osive. 12 2.1.2. Fixed θ It seems natura to suose, at east in te sort term, tat tere is a fixed and exogenous continuum of vaues for to coose from. 13 In a simiar fasion of te revious scenario, eac tye in a first stage must sow to Prince Carming wat consicuous good se wants to roose w a associated. Since an individua of ric tye wants to send as ess as ossibe in consicuous consumtion to reac te searating equiibria w a fixed θ, se wi find otima to make te comatibiy restriction of te oor tye binding: se cooses as to ave * * ω = θ u. In te second stage Prince Carming wi coose to erform te activy ony if te decared by te individua was te igest offered to im during te first stage. In addion, te oor * * tye cooses, Prince Carming cooses to erform te activy if te consicuous good romised during te first stage is urcased, ony te ric tye buys te status good, and se offers te consicuous good w te igest rice tat makes te incentive comatibiy restriction of te * oor tye binding, ω u = θ. Reca te exame of te two tyes of young workers aying for a osion inside a cororation: te ric-tye candidate woud ike to exend te east in consicuous goods in order to signa er income and get te job. Once again, tis two-stage mecanism is noting but a articuar earning device for Prince Carming. i 10 For instance, te income distribution may be mutiied by a scaar greater tan one and ten disaced downward as to recover te origina mean. 11 In addion, te direct effect of redistribution on tradiona consumtion wi increase te exected utiy of ric tyes and wi decrease te exected utiy of oor tyes. 12 Te cousion roosed above is obviousy ridicuous and as been exosed ony for exosory uroses. 13 In fact, wen a monooy soves te vertica differentiation robem, guarantees te existence of status goods. onooies do not subtract te θ as rofs because of te inter-market cometion: every vertica differentiated good can be used as a consicuous good. God watces comete as signaing device w fancy cars and a uge quanty of oter remium mercandises, and tus neer of tem can take te θ away. 10
FIGRE Ic ic c b x θ c =θ a c a d d d c - c c - c x Hencefort, te imic rice of te consicuous good θ can be exressed as: * 1 = θ. Let SW be te exected utiy for te candidate cosen by Nature, and consider te subgame erfect equiibrium w = * = b and λ = 1 2. Te cange in exected tota surus can ten be exressed by differentiating: After a symmetric redistribution if and ony if Proof 6: 2 dsw = d + d d d d =, te effect on socia wefare wi be osive < d d + 1 = 2 θ Tat is, te margina oss in utiy for te oor tye must be ess tan te sum of te margina gains for te ric tye bot from te increased income and from te savings in consicuous exendures. Even toug bot scenarios are simiar, notice tat te fina condion for te increase in wefare does not ave to be te same for bot cases. Indeed, teir difference coud be catured by anayzing te exression for dsw obtained in eac case. For te sake of variety, ets avoid te assumtion > 0. A sufficient condion for aving a wefare imrovement is: > Proof 7. Reacing by gives: θ > 2. b 11 Figure Ic sows te dneeded to remain w te fixed θ after te income redistribution i.e. to make θ c = θ a. Te dis ten used to find te new eve of utiy for te ric,, after te c saving in consicuous exendure. Te utiy of te oor tye decreases in a,, wie te utiy of te ric tye rises in b, 1+ d d. Finay, te same resuts od wen te game is extended to a ouation of numerous tyes. In addion, te aretian wefare-imroving cousion is amost te same: te ric tye ses to te oor tye a couon equa to, and ten se can get te θ by consuming a consicuous good w an infinesimay osive rice. 2.2. Discussion 2.2.1. Ruing out ooing equiibria
Te eading assumtion beind te striking resuts is te absence of ooing equiibria. For instance, w omogeneous incomes tere coud be a trivia soution for te socia anner: Prince Carming cooses to erform te activy regardess of te consicuous consumtion, and bot tyes coose zero consicuous exendure. Te activy is aways erformed and tere is not a wastefu exense in consicuous goods. 14 However, wen incomes are erfecty omogeneous tere are not suc tings as oor and ric tyes. Prince Carmings references are not defined, and tus cardina references must be addressed. To do so, a crucia issue of tis mode woud ave to be defined. to tis oint, was irreevant if Prince Carming cares directy about te reative income of is otentia artner, or if e cares about some easant uneasant tra osivey negativey correated w individuas income. Te sir of tis aer goes definivey in te second direction. For instance, te ainess of Prince Carming may deend osivey on te carisma of is artner. Since, condiona on observabes, more carismatic businessmen are exected to make more money, Prince Carming wi indirecty care about is artners income. Tis is a crucia oint. For instance, ets foow te sime and effective reresentation of American and Euroean cutures introduced in Di Tea et a. 2006. Societies generay seaking can be in an equiibria were firms ay workers efforts and workers make efforts i.e. SA or, on te contrary, were firms do not ay efforts and workers sirk i.e. Euroe. If Americans make efforts, ten wi be easier to infer teir skis from te information rovided by teir ranks in te income distribution. Tus, te correation between income and unobservabe skis soud be stronger in more "merocratic" societies. Indeed, te findings of Di Tea et a. 2004 are consistent w tis conjecture: eoe in America do not seem to be armed by income disaries, wie tere is a cear aaty towards inequay in Euroe. Later tis aer wi be roosed as a new interretation for tat finding. A necessary condion for aving ooing equiibria is tat te exected vaue for Prince Carming of erforming te activy w someone randomy samed from te ouation as to be osive. But tose cases are not interesting at a. Pooing equiibria is discarded not because I tink tat does not exist, but simy because te interesting cases are ony tose games were condiona on observabes te exected vaues of skis are ow enoug as to deter Prince Carming from mating someone at random. Since es to identify te taented agent, adding some eterogeney may create mating ossibiies, and te consequenty gain in wefare wi arise. Te easiest way to understand tis mecanism is te foowing: consider a mode w a continuum of tyes and suose tat teir incomes foow a densy distribution w suort in R. oreover, assume tat te utiy of Prince Carming is increasing in te income of is artner. In te ooing equiibria, Prince Carming woud face two indeendent draws from te distribution of incomes and ten e woud erform te activy w one of tem cosen randomy by Nature wic is te same tan icking directy one singe draw. Ten, te interesting case arises wen te exected utiy for tat exercise is negative. On te oter and, in te searating equiibria Prince Carming faces two indeendent reaizations of incomes and ten recognizes te greater, wat as noticeaby suerior exected vaue tan tat offered by te ooing equiibria. Ponero en ecuaciones y acarar as dos etaas. 14 It woud be convenient to tink about fixed θ and endogenous, since te aternative scenario wout a restriction on θ makes no sense bot individuas coud ave cosen a θ arbrariy big. 12
It woud not be difficut to extend te mode to cardina references. 15 oreover, cardina references can aso aow for te incusion of te utiy of Prince Carming into te socia wefare function. As in omogeneous ouations tere is no matcing, te effect of a rise in income inequay on socia wefare woud be even more osive or at east ess negative. In addion, cardina references may aow for a strategic coice of θ or by Prince Carming deending on wic is fixed in te articuar scenario, as to maximize is exected utiy during a zero-stage, to be soved in a backward-induction fasion. For exame, in te admission to graduate rograms in business tis woud be an interesting way to describe te underying ricing rocess. Even toug ordina references were roosed ony as a ractica way to discard ooing equiibria, tere are some exanations for te existence of suc discontinuous references. Firsty, te oorest and ricest individuas of a ouation are rarey found strugging for a good or service. As wi be discussed in te emirica section, individuas strugge for resources and comare to eac oter win te so-caed reference grous. Inside tose custers is ikey to find eoe w simiar incomes. Ten, Prince Carming soud be sensive to sma variations in income reativey to te mean variation in te entire ouation of incomes. Secondy, beaviora mecanisms beind reative concerns may be mosty ard-wired, te resuts of bot bioogica and socioogica evoution. 16 As ong as worked we during evoution, a very rigid mating-rue suc as "marry te ricest no matters ow muc ricer se is" coud ave easiy arisen and survived unti resent. Te subteness of te mecanism may be even a istorica direct roduct of te same kind of socia intoerance tat originay disquaified te direct trading of te non-market goods and services. 2.2.2. Towards a definion of consicuous consumtion Tere are no articuar goods and services aways or sometimes, artiay or totay dedicated to consicuous consumtion. Tis is a more oistic concet: is a sare of tota consumtion wat as a signaing urose. A good can be consicuous for an individua and not consicuous for anoter individua or for te same individua but in a different suation. Furtermore, individuas do not rey ony on consicuous consumtion for signaing uroses, as robaby tey ave a ortfoio of different signaing instruments to coose from. Tere is not a sar division between status goods and non-status goods: is a degree matter. A articuar good or service wi be considered more consicuous te more satisfies certain basic roerties: i. It must be observabe; ii. Oters individuas soud know s rice 17 and referaby soud be distinguised from a fake 18 ; iii. Its rice must be above wat woud be if consumtion was not observabe 19 wat I sometimes ca "intrinsic" utiy; iv. It soud not be sociay condemned e.g. burning money. 15 For instance, if te utiy function was stricty increasing in te income of is artner, Prince Carming woud ave a cut-off oint: e woud derive osive utiy by saring te activy w every tye w an income above tat tresod, and e woud not want to erform te activy w tyes w incomes beow. Terefore, te ordina references woud be aicabe for two tyes around tat cut-off oint. 16 Some evoutionary arguments for reative concerns can be found in Postewae 1998 and Samueson 2004. Te teories go from natura seection Brosnan et a., 2003 to te roduction of serotonin odovanu et a., 2007. 17 It is interesting to note tat as a consequence, for instance, ercedes Benz soud find convenient to inform noncustomers about te ig rices of s cars. 18 An interesting fact is tat, wen urcasing deiberatey fake cots of we-known brands, eoe are wiing to ay extra for fasified autenticy marks. 19 Besides "intrinsic" gains from observabiy. For instance: functionay e.g. a sign as to be seen to execute s function, estetic vauation e.g. eoe want beautifu cotes for attracting oters and for sef-satisfaction, etc. 13
One te one and, take as an exame a donation to an american universy: te amount is ubic since is ubised in graduate magazines, s rice is arguaby beow te intrinsic utiy derived from atruistic feeings, and is even sociay suorted see Gazer et a., 1996. On te oter and, consider a goden cain: eoe can see if you are wearing, and is not articuary disaroved by society; but easy to decide weter is a fake and makes you fee better w your image, wic make s intrinsic utiy considerabe ig. It is very imortant to notice tat in te mode is in fact te ga between te actua rice and wat woud ave been if consumtion was not observabe. For instance, a uxury car of $50,000 can be refecting a ga of just $10,000, wie a bag of $15,000 coud be mirroring a ga of $14,000. Tere are oter reasons to be carefu: for instance, for durabe goods te comete discounted fow of benefs must be taken into consideration, and not ony te current benefs. If tere were no cred frictions, te actua cost of a very exensive goden watc woud be soey te oortuny cost of te caa, as after being used maintains cometey s rese vaue. In te rea word, cred markets are not erfect and ence a $50,000 god watc can successfuy signa te absence of financia constraints. Addionay, eoe are not aware of ow muc "intrinsic" utiy every individua derive from eac good in te economy. Ten, eac individua soud find otima to signa er weat w tose status goods w a greater difference between ow muc intrinsic utiy se derives from and ow muc everyone ese tink se derives from. Te eve of observabiy is continuous as we. For exame, different status goods are observed by te rest of te ouation w different robabiies e.g. my car is observed more frequenty tan te ainting anging in my room. After some minor modifications, te mode coud ave incuded imerfect ubicy for consicuous consumtion to sow tat if te status good were observed w ower robabiy te signa woud be even stronger. As a consequence, tere is an addiona oss reated to te over-taxation or roibion of status goods. Take as an exame te foowing suation: facing te absence of markets to meet interesting friends, an individua decide to figt in first cass in order to signa business skis. In se of te wi of some autors, if te government ots to ban te first cass, tat erson by no means wi sto referring some comanions above oters. He wi be just not abe to get new friends troug figt tickets, and e wi merey make use of anoter status good e.g. exensive ce ones. Since te atter was not is first coice, te intervention must be seen as intrinsicay inefficient. 20 2.3. Emirica Identification In summary, te main resut is tat an increase in income inequay migt be consistent w a rise in tota wefare, as may make ace to te rovision of ots of non-market goods and services. Tis kind of finding is not at odds w te most recent teoretica erature. For instance, in te mode introduced in Hokins et a. 2004, 2006a an increase in equay rises te degree of socia cometion, diminising te utiy of te oor. Rege 2007 and Becker et a. 2005 aso found tat reducing inequay may be inefficient because of te existence of sef-generated inequay. 21 20 However, Bagwe et a. 1996 sowed tat rices on uxury goods may be demand driven, wic means tat uxury brands are sod by te tax-incusive consumers referred rice. As noticed by Rege 2007, a tax on status goods ten migt make te status signaing ess wastefu wout causing any efficiency oss in terms of ess efficient matcing. 21 Addionay, Gazer et a. 1996 ointed out tat eoe may be interested in making donations for signaing weat ony if income is not omogeneous. Te consequences were worty of note: universies soud be interested 14
Win te emirica erature, Scwarze et a. 2003 found tat income inequay reduction by te state does not increase webeing. Camaco-Cuena et a. 2002 found tat te "transfer rincie" is argey vioated. Ravaion et a. 2000 and Senik 2004 retrieved nonnegative effects of inequay on individua wefare. In Luttmer 2005 and Di Tea et a. 2004 various measures of regiona inequay did not seem to affect te we being of Americans. Furtermore, in Cark 2003 ife satisfaction was found osivey correated w reference grou income inequay. Income disersion seems to augment te imortance of income on individua we being. Te objective of te next section is to identify econometricay te existence and magnude of suc enomenon using ife satisfaction data. 3. Econometric ode and Data 3.1. ain Framework Te socio-economic canges tat ave taken ace in Russia during te ast decade ave caused tis country to become an autentic aboratory for te socia sciences. A eriod caracterized by deteriorated iving condions and dramatic economic uncertainty began in 1991. Sigty over one tird of te ouation was iving beow te officia overty ine by te end of 1995. Notwstanding, te financia crisis of 1998 was a turning oint. It was foowed by a gradua recovery, w rea income growing u and unemoyment rates steadiy faing. A comreensive anaysis of te economic and socia seres of Russia foowing transion years can be found in Brawae et a. 1998. 22 I focus on ife satisfaction via 3 rounds 9 to 11, covering te eriod 2000-2002 of te ouseod-eve Russian Longudina onoring Survey RLS. 23 Te anaysis is imed to resondents aged over 18, reacing a same size of just over 23,500 observations on 9,200 individuas after discarding missing vaues. An imortant feature is tat te same does not suffer from considerabe ane attrion, w an average number of observed rounds over 2.5 out of 3. in giving scoarsis to te midde cass in order to increase te eterogeney of teir student body and ten raise future donations by ric aumni. 22 An emerging economy ike Russia can guarantee enoug variation aong te features of interest: ife satisfaction and te distribution of income. In fact, Frijters et a. 2008, based on te same database, found tat canges in rea ouseod income can exain u to a tird of te arge swings in ife satisfaction win Russia accounted between 1996 and 2000. 23 Information about te RLS can be found at te foowing address: www.ec.unc.edu/rojects/rms. Some detais about te roject and an interesting overview of te data can be found in roz et a. 2004. 15
TABLE I Life Sat.=1 Life Sat.=2 Life Sat.=3 Life Sat.=4 Life Sat.=5 ean SD ean SD ean SD ean SD ean SD Sat. w Economic Condion 1.22383 0.58551 1.80019 0.7237 2.34325 0.90756 2.80732 1.10526 3.28923 1.38868 Comarison Life Satisfaction -1.17873 0.43706-0.35117 0.3633 0.50409 0.3612 1.36375 0.41661 2.15638 0.60244 HH Exendures Rea 6195.33 9656.98 7035.58 8182.14 8796.19 11859 10155.7 13183.2 17318.9 31601.4 HH Income Rea 4745.92 5372.55 5760.91 5966.77 6903.86 8679.49 7734.13 9841.43 8479.56 9336.33 FExendures 0.4618 0.28746 0.54164 0.27124 0.59136 0.27219 0.63571 0.26696 0.67893 0.26341 fexendures 4.118 2.04027 3.8353 2.13934 3.68501 2.32987 3.24251 2.23319 3.79662 2.8151 FIncome 0.47034 0.2771 0.55382 0.27563 0.59963 0.27675 0.6383 0.27307 0.62714 0.27728 fincome 4.34341 2.10945 3.99267 2.1065 3.81389 2.31276 3.43829 2.24885 4.15146 2.73031 GiniExendures 0.46378 0.06399 0.46151 0.06316 0.45993 0.06027 0.46369 0.06074 0.47087 0.06392 GiniIncome 0.44358 0.06851 0.43977 0.0677 0.4417 0.06752 0.44468 0.06804 0.44221 0.0617 Notes: eans and standard deviations at individua eve for te Round 9 observations incuded in Equation 1, Tabe II. Te RLS was designed as a reeated same of eac ouseod dweing. Consequenty, instead of foowing individuas or ouseods from one year to te next, te interviewers merey return to te same residences samed in te revious year. A ouseods wo move are automaticay ost to foow-u, and te new tenants of te same dweings are inved to join te survey. 24 Just to mention some basic statistics about te same, at October 2000 te average age was 45, 44% were mae, 54% were married, 66% ad a ig scoo dioma, 50% were working, 32% received a ension, 29% reorted to be in good or very good eat, 5% ad been osaized during te ast tree monts, 32% smoked, and amost 30% 5% of te resondents ad at east one car ersona comuter in teir ouseod. Te average of te monty rea ouseod income was 8,000 roubes aroximatey S$284, w a standard deviation of 12,000 roubes, and te average of te monty rea ouseod exendures was 6,100 roubes S$216, w a standard deviation of 7,400 roubes. Te east squares secification is: H = 1X + β 2 β Z + Ψ + Σ + ε t i Were H is a measure of ife satisfaction, X is a matrix of individua time-varying contro variabes, Z is te vector containing te variabes of interest reated to income and exendures, Ψ denotes year effects, t Σ corresonds to individua fixed effects, and i ε corresonds to te remaining error term. As more tan 50% of te variation in individuas reorted we-being migt be exained by genetics Lykken et a., 1996, we can not ignore fixed effects 25. Fixed effects estimators e us to 24 New entrants are not droed. As fixed effects estimators demand at east two observations on eac individua to be considered into te estimation, te new entrants incuded are ony tose wo enter te same during te second round and remain in te tird. Wout considering missing vaues, 1,243 of te 9,074 individuas in te round 9 ad eft te same at round 10, and 177 individuas were te new entrants. Ony 767 of te 8,008 individuas resent at round 10 eft te same before round 11. As usua, I trew away data w missing vaues. Ferrer-i-Carbone 2005 recounted tat, win te erature, none of te autors tat reweig data reorts tat reweigting makes a difference. 25 In fact, Frijters et a. 2008 observed tat most of te ife satisfaction studies invoving ane data ave tested te aroriateness of te random effects versus fixed-effects secifications, and te former was aways rejected. A more detaied metodoogica discussion on tis issue wi be deveoed in te next subsection. 16
concentrate on te ongudina nature of te data, focusing ony on te intra-individua variations in ainess. Beyond obvious uncanging caracteristics suc as gender, etnic grou or moter tongue, fixed effects are suosed to account for key static variabes, suc as ersona tras, individua asiration towards ife and, as wi be seen beow, interna and externa comarison incomes. Foowing cbride 2001, individuas comare teir income to teir "externa norm" wen tey ook at te eoe in teir coort of simiar age, gender, race, ocation, etc. On te oter and, te "interna norm" is based on te individuas ersona consumtion at. For instance, a articuar amount of resent income wi robaby make an individua wo was raised in a weaty environment ess ay tan an individua w a record of overty. Suose tat income raises we being as a ogarmic transformation, n Inc / Nori, were Inc is te income of te individua i at time t and Nor is te individuas comarison i income interna, externa, or a combination of bot. If bot norms were exressed aroximatey as constant across time, we woud be abe to ignore te comarison income and focus soey on te ogarm of income, as fixed effects woud be controing for te norms: n Inc / Nor = n Inc n Nor = n Inc + Σ i i Income by sef is far from being te ony indicator of materia standard of iving. Headey et a. 2004 used ouseod economic ane data from five countries to find tat in te two countries were consumtion data were avaiabe, non-durabe consumtion exendures aeared to be at east as imortant to ainess as income. As a matter of fact, if ony one of te two variabes income or exendures was incuded in eac regression of tis aer, te remaining coefficient woud sow a arge bias. It is not very cear wat art of materia standard of iving is catured searatey by eac variabe, and is even ess cear wat art do eac one exain wen bot income and exendures are incuded jointy as regressors. Income may be associated w economic secury, or assets tat indeed generate a rea fow of benefs e.g. aving a more comfortabe ouse. Income aso enabes to borrow money for investment uroses and for coing w bad times Headey et a., 2004. Income may even make eoe aier just because tey exerience a feeing of sef-reaization i.e. tey ove money sef. Te exendures variabe as been created to measure consumtion in fact, tis variabe is artiay constructed based on questions about consumtion. Since te exendures variabe migt be missing some information on consumtion, income woud be abe to cature artiay te residua. For instance, in ouseod surveys tere are not questions about te quay of goods. Condiona on exendures and oter variabes, woud be natura to tink tat te quay of food in ricer ouseods is greater. A tird variabe of interest is weat. As fixed effects contro for te inia eve of weat, ony canges in weat are eft as interesting candidates for regressors. Notwstanding, I can not tink about any source of canges in weat oter tan income and consumtion, aready incuded as regressors. Ravaion et a. 2001 found tat ouseod income is a muc stronger redictor of ife satisfaction tan individua income. For te sake of simicy, I wi focus on income and i 17