POLICY RESEARCH WORKING PAPER 156.1 Public Disclosure Authorized

Income Inequality No evidenceis found to support the notion that and AggregateSaving incomeinequaltyaffects aggregate saving across

countries- neitherin Public Disclosure Authorized The Cross-CountryEvidence developingnor inindustriat

countries. Klaus Schmidt-Hebbel Luis Serven Public Disclosure Authorized Public Disclosure Authorized The World Bank Policy Research Department Macroeconomics and Growth Division January 1996 POLICY RESEARCH WORKING PAPER 1561

Summary findings

Schmidt-Hebbel and Serven empirically review and Schmidt-Hebbel and Serven present new econometric analyze the link between income distribution and evidence on the link between saving and inequality using aggregate savings. new data on income distribution for a large cross- Recent research has focused on the impact of income country sample. inequality and growth. Less attention has been paid to The results provide no evidence that income inequality the link between inequality and saving. Once the affects aggregate saving across countries. This conclusion conventional representative-agent framework is holds for both industrial and developing countries and is abandoned, consumption theory brings out channels robust to changes in measures of saving, in income through which income inequality can affect aggregate distribution indicators, and in functional forms. saving.

This paper-a product of the Macroeconomics and Growth Division, Policy Research Department-was prepared as part of ongoing research on the determinants of saving. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Emily Khine, room NI 1-061, telephone 202-473-7471, fax 202-522- 3518, Internet address [email protected]. January 1996. (35 pages)

The Policy PesearchWorkPng Paper Series disseminates the findingsof workin progressto encouragethe exchangeof ideasabout develo pment issues. An objective of the series Is to get the findingsout quickly, even if the presentationsare less than fully polished. The papers carry the namnesof the authors and should be used and cited accordingly. The findings, interpretations, and conclusionsare the authors' own and should not be attributed to the World Bank, its Executive Board of Directors, or any of its member countries.

Produced by the Policy Research Dissemination Center INCOME INEQUALITY AND AGGREGATE SAVING: THE CROSS-COUNTRY EVIDENCE

Klaus Schmidt-Hebbel

Luis Serven

Policy Research Department

The World Bank

We are gratefulto Klaus Deinmgerand Lyn Squirefor kindlymaking available to us their databaseon income distribution.We thankSteve Marglin, Branko Milanovic, and Vito Tanzifor usefulcomments and suggestions on an earlierversion. Excellentresearch assistance by WanhongHu is gratefullyacknowledged.

1. Introduction If all individualswere identicalin regard to their saving behavior,then aggregatesaving would be triviallyrelated to individualsaving -- it wouldjust equalthe savingof a representativeagent multipliedby the population.Naturally, such a simplisticview of aggregatesaving would be highly misleading.It is hard to understandaggregate consunption and savingpatterns without considering that they reflectdissimilar behavior by heterogeneousindividuals who differ in preferences,resources, and/or institutionalconstraints. Indeed, consumptionand saving are amongthe few areas in macroeconomicswhere theoreticaldevelopments have occasionallyleft the safe -- but severely restrictive -- haven of representative-agent models' to venture into the wildernessof agentheterogeneity, collecting along the way valuableanalytical and empirical insights -- such as thosederived, for example,from the life-cycleconsumption model. One particulardimension of heterogeneitythat has receivedincreased attention from the macroeconomic viewpointin recentyears is thatof incomedistribution. Recent analytical and empiricalwork has focusedon the relationshipbetween income inequality, growth and investment.2 Less attentionhas beenpaid, however,to the linksbetween income distribution and saving. These links are the focus of this paper. More specifically,its objectiveis to ascertainthe impact on aggregatesaving of changesin the distnbutionof incomeamong groups of savers,after takinginto consideration the effectsof other standardvariables such as aggregateincome and its growthrate. The paperconcentrates on the channelsthrough which distribution affects saving. Yet feedbackeffects fromsaving to distributioncannot be ruledout a priori, and indeedthey are centralto someof the savinghypotheses (notably those emphasizing the functionaldistribution of income)that will be reviewedbelow. Of course,the possibilityof two-waycausation is not exclusiveto incomedistribution; it applies as well to other standarddeterminants of saving(income, interestrates, etc.) for whichthere is a strongpresumption that causalitymay run in both directions.While our discussiontouches upon these issues,we do not explorethem at length in this paper. Themain conclusion of thepaper - supportedby empiricalevidence based on new incomedistribution dataconstructed by Deiningerand Squire (1995) -- isthat cross-countrydata do not revealany strongassociation betweenincome distribution and saving ratios. After controlling for other savingdeterminants, aggregate saving ratiosdo not appearto be significantlyrelated to standardincome distribution indicators. This conclusion holds for a largecross-country sample, as well as for its industrialand developing-countrysubsamples, and is robust to alternativesaving measures, income distribution indicators, and functionalforms.

I SeeKirman (1992) for a recentsharp criticism of therepresentative-agent paradigm.

2 Seefor exampleGalor and Zeira (1993), Alesinaand Rodrik(1994), Persson and Tabellini(1994), Perotti (1995),and Alesinaand Perotti(1996). 2

Thepaper is organizedas follows.Section 2 presentsthe stylizedfacts on saving,income, growth and distributionusing data for a large numberof industrialand developingcountries, and relates the empirical regularities present in our sample to those reported in the literature.Section 3 providesa brief survey of alternativeviews of saving determination,with emphasison the saving consequencesof differentincome distributionprofiles. Section 4 reviewsprevious empirical studies of the impactof incomedistribution on saving, and Section5 presentsnew cross-coutry econometric evidence using our data set. Finally,Section 6 concludes.

II. Savingand Distribution: the StylizedFacts Webegin by reviewingthe empirical regularities on saving,income and distribution.To do this, we use annual macroeconomicdata on 52 industrialand developingcountries from the World Bank databases,and incomedistribution data froma new databaserecently constructed by Deiningerand Squire(1995). In principle the data coverthe years 1965to 1994 -- althoughfor somecountries some of the variablesof interest(notably incomedistribution data) arenot availableevery year withinthis time span. The discussionfocuses on the cross- countrydimension of thedata, making use of the averagesof the relevantvariables over the three-decadeperiod above.' Unlessotherwise noted, here and in therest of thepaper we use the term 'saving' ('savingratio') to refer to grossnational saving (respectively, its ratio to GNP).We choosenational saving and nationalproduct data as therelevant variables because they are closerto the relevantunits (householdsor individuals)for whichincome distributiondata is availablethan the domesticsaving and domestic product measures. In this respectwe differ frommost empirical studies, that are basedon the less adequatedomestic measures. A preliminaryissue that meritscomment is thatof measurementerror. As is wellknown, this is a central problemin empiricalstudies of saving,due not onlyto the inadequacyof the very savingconcept used by the NationalAccounts (which, for example,exclude capital gains fromthe definitionof income,and treat human capitalexpenditures as consumption)but also to the unreliabilityof measuredsaving, which stems largelyfrom the fact that savingis often computedas the residualfrom another residual (consumption). The upshotis that saving measuresmay containlarge errors, particularlyin poorer countries(see Schmidt-Hebbel,Serv6n and Solimano1996 for furtherdiscussion). Measurement error is evena more seriousproblem in the case of income

3The samplecountries were selected on thebasis of availabilityof incomedistribution data (kindly made availableto us byKlaus Deininger and Lyn Squire) and the following criteria. The 1965-94average for eachcountry is computedover those years for which the informationis available.To ensure the long-term nature of theaverages, the sampleincludes only those countries with at leastone income distribution observation in eachof twoof thethree decadesthat span the 1965-94period. This leaves us with20 industrialand 32 developingcountries, out of the20 industrialand 66 non-transitiondeveloping countries in thedata base of Deiningerand Squire. More details are givenin thedata appendix in this paper. 3 distributionstatistics. The latter are primarilyderived from household survey data, whichtypically understate the incomeof the richerhouseholds. As a result, incomeinequality is likelyto be underestimated.Although no firm evidenceis available,most observerswould probably agree that such underestimationagain is probablymore severein poorercoutries, becausethe statisticalapparatus involved in the collectionof householddata is likely to be weaker. Keepingin mindthese limitations of the availabledata, we turn to the reviewof the stylizedfacts. Since our incomedistribution information is new, we first providesome summary statistics (a detaileddescription is given in Deiningerand Squire 1995). Table 1 presentsmeans and standarddeviations of three conventional indicatorsof inequality:the Gini coefficient,the ratio betweenthe incomeshares of the richest 20 percentand poorest40 percentof thepopulation, and the income share of the 'middleclass', definedas the middle60 percent of the population(which is oftenused as an indicatorof equality).The statisticsare computedfor three country groups:industrial countries, developing cntries, and,as a subsetof the latter, the so-called'take-off' countries. Thelatter group is definedas consistingof thosedeveloping countries that duringthe sampleperiod successfully shiftedfrom a low to a high savingand growthpath. 4 As Table1 shows,developing countries are moreunequal than industrialcountries by any of the three indicatorspresented. Take-off countries, however, possess on averagean incomedistribution more equitablethan the rest of developingcountries, also by all three indicatorsconsidered.

Thestylizedfads The first stylizedfact concernsthe relationshipbetween saving ratios and levelof development-- as measuredby real per capitaGNP. Figure I presentsthe scatterplot of the 1965-1994averages of these two variablesfor the samplecountries; using per capita incomeat the initialyear of the sample insteadof its average value yields a very similarpicture. In the figure,countries appear clustered in rough correspondenceto their developmentlevel. On average,saving rates are lowerfor developingcountries than for industrialcountries. The exceptionare the take-offeconomies in our sample, whose savingratios exceedeven the industrial-country average. Thefigure shows that savingrates tendto risewith per capitaincome: the correlationcoefficient between the two variablesis .31, significantlydifferent from zero at the 5 percentlevel, and is even higher(.60) among developingcountries. (See the matrixof correlationsbetween the savingrate and relatedvariables in Table2).

4 Thegroup includes China, seven market-economy East-Asian countries (Hong-Kong, Indonesia, Korea, Malaysia,Singapore, Thailand and Taiwan (China)), Chile, and Mauritius. 4

A similarassociation has beenfound in a numberof empiricalstudies of saving (e.g.,Collins 1991;Schmidt- Hebbel,Webb and Corsetti1992; Carroll and Weil 1994; Masson,Bayoumi and Samiel1995; Edwards 1995). The figurealso suggests that at high levelsof per capita incomesaving ratios appear to leveloff -- i.e., the relationshipis not linear,and possibly not evenmonotonic. As a more formalcheck on this, the solid line in FigureI plotsthe fitted valuesfrom regressing the savingrate on a quadraticpolynomial in per capita income; the estimated coefficientsare significantat conventionallevels. The fitted curve shows that the positive associationbetween saving and developmentappears indeed to be confinedto the early stagesof development, ceasesto hold at about $8,000 per capita GNP ( in 1987US$), andturns into a negativeassociation at higher incomelevels. A secondstylized fact is the strongpositive association between saving ratios and real per capita growth, which has been amplydocumented in cross-countryempirical studies. 5 However,its structuralinterpretation remains controversial,as it has been viewedboth as proof that growthdrives saving(e.g., Modigliani1970, amongmany other studies)and that savingdrives growth through the saving-investmentlink (e.g., Levineand Renelt1992; Mankiw, Romer and Weil 1992).6 As Figure2 shows,our dataconform to thesefindings. Aggregate saving ratios andreal per capita GNP growthare positively associated, and their correlationcoefficient equals .63, significantlydifferent from zero at the 5 percentlevel. However, the figurealso suggeststhat this relationshipmight be drivenby the fast-growing, high-savingtake-off economies, most of whichare clustered at theupper-right corner of the graph.In fact, if these countriesare removedfrom the sample,the correlationdrops to .40, but stillremains significant. Is the associationbetween saving and income distribution as clear-cutas that betweensaving and income (or its growthrate) ? Figure3, whichplots saving ratios againstGini coefficients of incomedistribution, shows a less clear-cutpattem than the precedingtwo figures.Nevertheless, the full-samplecorrelation between both variablesis -.28, just statisticallysignificant at the 5 percentlevel. The correlationpattern is, however,rather differentin the industrial(.10) and developing-country(-.26) subsamples;in neitheris it significantlydifferent fromzer. Interestingly,the figurealso reveals a sharp distinctionbetween both sets of countriesfrom the point of viewof inequality:virtually all non-take-offdeveloping countries possess a more unequalincome distribution (as measuredby the Ginicoefficient) than that of the most unequalOECD country. The above facts lead to the much-discussedrelationship between income inequalityand level of

5 Seefor exampleModigliani (1970), Maddison (1992), Bosworth (1993) and Carroll and Weil (1 994).

6 Onthe saving-growthcausality see the recent overviews by Carrolland Weil (1994), Deaton (1995), and Scbmidt-Hebbel,Serven and Solirnano (1996). 5 development- withthe latter measuredas beforeby real per capita GNP. Accordingto the well-knownfinding by Kuznets(1955), the relationship between these variables follows an inverted-Ushape: inequality rises in the earlystages of development,and then decreases as percapita income continues to rise.This stylizedfact has been replicatedto varyingextents in a numberof cross-countrystudies (for recentexamples see Bourguignonand Morrison1990, and Clarke 1991),but its interpretationis far fromclear (see .Adelmanand Robinson 1989, for a discussion).' Figure4 showsthat our samplefits the Kuznetscurve. Keeping with convention,the figureplots Gini coefficientsagainst the logof per capitaincome (with both variables measured by their 1965-92averages). The curved line in the graphdepicts the fittedvalues fromregressing the Gini coefficienton the log of per capita incomeand its square;the estimatedcoefficients are highly significant. As can be seenfrom the figure,developing countriesaccount for the upward-slopingportion of the empiricalcurve, and industrialcountries cluster along the decliningportion. Onemethodological issue that arisesis whetherthe abovefindings are sensitiveto our choiceof the Gini coefficientas the relevantstatistic. A numberof altemativeindicators are foundin the literature-- e.g., Theil's index,the coefficient of variationof incomeacross households, the incomeshare of the poorest20 or 40 percent of the population,the ratio of the latterto the incomeshare of the richest20 percent,or the incomeshare of the middleclass. 8 Amongall them, the Gini coefficient,Theil's index or the coefficientof variationare generally preferablebecause they use moreinformation than the commonly-encounteredquintile-based indicators. At the same time, the Gini index has the well-knowndrawback that it is not uniquelyrelated to the shape of the underlyingdistribution, so that verydifferent redistribution schemes can be reflectedin the same changein the Ginicoefficient. Finally, income shares (in levels)and Ginicoefficients may pose cross-countrycomparability problems,likely to be minimizedby the use of shareratios (Deiningerand Squire,1995). In practice,however, the informationalcontent of all theseindicators is usuallyvery similar, as shown by the fact that they typicallyare veryhighly correlated -- even thoughthey mayyield differentorderings for a fewsample observations (see for exampleClarke 1991). This applies also in our case. Byway of example,Figure 5 plotsthe Ginicoefficient against the ratioof the incomeshare of the richest 20 percentof the populationto that of the poorest40 percent,for thosecountries in our samplefor whichboth kindsof data are available.The plot revealsa strong positiveassociation between both distributionmeasures; indeed, their correlationcoefficient

7 As iswell known, Kuznets' explanation of hisempirical finding was based on theshift of populationfrom traditionalto modern activities. See Anand and Kanbur (1993) for ananalytical reassessment of thisview. For a discussionof theproperties of theseindices see for exampleCowell (1971). 6 equals .95, so that they are virtuallyindistinguishable. To sunmarizethis section,our dataconform to three stylizedfacts found in cross-countrystudies. First, saving rates appear to rise with development(as measuredby per capita GNP) -- at least at its early stages. Second,saving rates and growthrates are positivelycorrelated across countries.Third, income inequality seems to riseat earlystages of development,and decline beyond certain levels of per capita income,as predictedby the 'Kuznetscurve'. Forthe overall sample, we alsofind a negativeassociation between aggregate saving rates and standard measuresof incomeinequality, although the relationshipappears weaker than the above 'stylizedfacts', and is not robustacross subsamples.More importantly,this refersonly to the simplecorrelation between saving and incomedistribution. The more substantive question is whetherthe associationbetween both variablescontinues to holdonce other standardsaving detenninants are taken intoconsideration. To answerthis question,we need to examinethe theoretical underpinnings of thesaving-inequality link, and placethe latter in a broaderframework encompassingother relevant determinants of saving.This task is undertakenin the next section.

III. Saving and Income Distribution: A Brief Survey Aggregatesaving is the outcomeof individualsaving efforts by heterogeneousmembers of different classesof savers. Heterogeneityamong savers is a key featurethat helps understandhow aggregatesaving is affectedby changesin savingdeterminants, including policies. Heterogeneity may be relatedto the fact that differenttypes of individualsdetermine their consumption/savingplans accordingto differentobjectives (i.e., their preferencesare not identical).Altematively, even if all individualspossess identicalpreferences, their behaviormay differbecause they face differentinstitutional constraints (e.g., in their accessto borrowing),or behavior may vary dependingon the values of exogenousvariables relevant for their consumption/saving decisions(e.g., no savingcan be made belowa certainthreshold of incomeneeded for subsistence). Heterogeneityis of courseimportant because when agentsare dissimilarthe aggregatelevels of those variablesrelevant for individualsaving decisions are not sufficientto determineaggregate saving -- the latter also dependson the distributionof such variablesacross individualsavers. Even if all agents had identical preferences,distribution still matters as long as their (common)decision rule for savingis not linearin the relevantvariables. In suchcase, a givenchange in the aggregatevalue of a savingdeterminant (such as disposable incomeor wealth)can have very differentconsequences for aggregatesaving depending on how it impacts differenttypes of savers.Likewise, purely redistributive policies can have an impacton aggregatesaving -- e.g., public transfers to the poor financedby taxes on the rich may reducetotal savingif the formerhave a higher propensityto spendthan the latter. 7

Belowwe reviewbriefly the literatureon consumptionand savingdetermination, with a focus on income (orwealth) distribution in particular.We adopt an aggregateperspective, although some referenceis madeto the distinctionbetween private and public saving,or firm and householdsaving, where relevant. Our approachis seectiverather than exstive. We first examinethe relationshipbetween saving and three basic determinants: income,the rate of retum, and uncertainty9. Then we highlightdifferent channels through which distribution affectsthe relationshipbetween these two basic variablesand aggregatesaving. We concludewith somebrief remarks on the influenceof standardeconomic policies on saving,discussing how their impactis affectedby distributivefactors.

I1I.1 Basicsaving determinants Income Incomeor wealthis the main drivingforce behindconsumption (and hence saving)and thereforehas attractedthe largestattention among all potentialsaving determinants. But beyondthis very generalstatement thereis verylittle in commonamong different saving theories. The differencesstart with the appropriatemeasure of income:current income (in the conventionalKeynesian hypothesis, henceforth KH), permanent income net of taxesover the life-cycle(the life-cycle hypothesis, LCH), permanentincome net of taxes over an infinitehorizon (the permanent-incomehypothesis, PIH) or, as a variant of the latter, pemanent incomenet of govenment spendingover an infinitehorizon (REH, the Ricardian-equivalencehypothesis). As a startingbenchmark consider either the PIH or its REHvariant for a representativeconsumer.'° A risein net permanentincome leads to a propoftionalincrease in consumptionlevels without any effecton saving. Temporalyincome changes are smoothedout through appropriate levels of saving.If both currentand permanent incomerise by the same amount,consumption and savingratios to currentincome remain unaltered; in turn, purelytemnporary income changes result in movementsof the saving(consumption) ratio in the same(opposite) direction. Accordingto the PIH,income growth -- i.e., the increaseof futureincome relative to currentincome levels -- must reduce savingrates, as consumersraise currentconsumption in anticipationof higher future income.This, however, is at oddswith the positivesaving-growth correlation observed in the data and reviewed

9 Uncertaintyrefers basically to the variabilityof incomeand the rate of return,and therefore is reallynot a separatevariable. However, because the literature emphasizes the distinction between the effects on savingof income (or rateof return)variability and those of theirrespective levels, we treatthem separately. 10See Friedman (1957), Hall (1978) and Flavin (I1981). 8 in theprevious section, and has promptedseveral lines of researchattempting to explainwhy rationalconsumers mayfail to adjusttheir consumptionlevels in the face of risingincome. ' The explanationsare mostly basedon non-standardpreferences incorporating consumption habits (wiuch prevent rapid changesin consumptionlevels), subsistenceconsumption levels (below which no savingwhatsoever takes place, so that the savingpropensity is effectivelyzero) or wealthas an argumentof the utility function(the classical"capitalist spirit" model).Under eachof thesefomlulations, higher income can generate inceases insaving, at least transitorily.On the other hand, as we shall see later, once the representative-agentframework is abandoned,some of these preference specificationsprovide possible channels through which income distribution could affect overall saving. Atthe otherend of thetheoretical spectrum is the LCH of Modiglianiand Brumberg (1954, 1979) -- the maincompetitor of thePIH-REH theories. As opposedto the representative-agentframework of the latter, agent heterogeneityis the cornerstoneof the LCH. Aggregatesaving results from the additionof savingby different age-specificcdoorts. Each cohort smooths consumption over a finitehorizon, given lifetime resources that -- in the simpleLCH hypothesis -- arenot transferredacross generations. Over the life cycle,saving and consumption followhump-shaped patterns, with dissavingat youngage, the peak of savingat workingage, and dissaving duing re=remut as householdsrun down their accumulated assets. Hence saving propensities depend on age and differsystematically across cohorts. The impactof growthon savingin the LCH framneworkis ambiguous. On the one hand,the earningsand savingof theworking-age population will rise relativeto retirees' dissaving,thus pushing up aggregatesaving. On the other hand, however,workers will anticipatehigher earningsduring their workingage, and this will depresstheir savingjust like in the PIHframework. The overalleffect is thereforeindeterminate. As mentionedearlier, there is of coursean altemativeinterpretation of whystandard models of saving have such a hard time generatinga positivegrowth-saving association. Rather than savingbehavior, the latter could just reflect the combinationof two well-establishedempirical facts: the positiveassociation between investmentand growth (Levine and Renelt 1992) and the equally positive saving-investmentcorrelation (Feldsteinand Horioka 1980, Feldstein and Bachetta 1990), often interpretedas evidenceof intemationalcapital immobility(see Schmidt-Hebbel,Serven and Solimano1996).

T7herate of return Thesecond key factorgoverning the intertemporalallocation of consumption,and hence saving,is the rate of return. However,its impacton savingin the representative-agentframework of the PIH is ambiguous,

II SeeCarroll and Weil (1994) and Deaton (1995). 9 becausechanges in the rate of returnhave both incomeand substitutioneffects, whichrun in oppositedirections (exceptin particularcases, like whenthe consumeris a net debtor).The situationis similarlyambiguous in the LCHfraewvrk Herechanges in interestrates entailtransfers among cohorts, and the net impacton aggregate consumptionand saving depends on the differentcohorts' saving propensities as wellas on their relativesize (see Deaton 1992). In practice,empirical studies support these theoreticalambiguities, and typicallyfail to find significanteffects of interestrate changeson saving. Recentwork by Ogaki,Ostry and Reinhart (1994) adds a new dimensionto the effectof the rate of return on saving.They present a modelin whichthe elasticityof intertemporalsubstitution (and hence the interestrate sensitivityof saving)rises withthe levelof income.Empirical estimation of the modelon a cross-countrydata set providessome support for this view.

Uncertainty Recentwork on savinghas movedaway from the simpleversions of the PIH and LCH modelstoward broaderframeworks incaporating uncertainty about future income, the rate of return to savings,the lengthof life, etc. One line of work has relaxedthe certainty-equivalentutility functionof Hall's (1978) PIH, allowingthe marginalutility of consumptionto be nonlinear,typically convex. This convexitycreates precautionary motives for savingwhenever uncertainty about future consumption is introduced:it is prudentfor individualsto limit borrowingand not consumetoo muchuntil they knowmore about their future-- an effectthat is strongerthe greaterthe uncertaintyabout lifetimeincome. 2 Tlheexistence of the precautionarymotive for savingsis less in doubtthan its actualmagnitude. While empiricaltesting has been limited,it is likelythat precautionarysaving may represent well the short-term consumption-smoothingbehavior of the averageconsumer, but not explainthe bulk of saving,which in most societiesappears to be carriedout by a relativelysmall number of wealthierhouseholds (see Carroll and Summers 1991and Deaton 1995).

111.2Income distribution and saving Let us now focus in more detailon the impactof changesin the distributionof income(or wealth)on aggregatesaving. We examinefour topics:(i) linksbetween saving and the unctionaldistribution of income;

2 UnRlikein the sirnple PIH, in this framework intertemporal transfers of resourcesthat leave the present value of lifetimeincome unaffected can stillaffect saving behavior. Higher present taxes with lower future taxes lead to a declinein consumptionif individuals have to rebuildtheir precautionary balances (and cannot borrow against the future taxbreak). 10

(ii) links betweensaving and the personal distributionof income;(iii) liquidityconstraints, distribution and saving;and (iv) indirecteffects of distributionon saving.

Fundionaldistribution and saving The link betweenthe functionaldistribution of incomeand saving(and growth)is at the heart of the neoclassicalgowth model(Solow 1956), as well as the neo-Keynesiangrowth models of Lewis(1954), Kaldor (1957) and Pasinetti(1962). These models are general-equilibriumin nature, with both savingand income distributionas endogenousvariables. Unlike the neo-Keynesianmodels, in the neoclassicalframework workers and capitalists do not necessarily differ in their saving patterns. Aggregate saving behavior in conjunctionwith production characteristicsdetermines income distribution. The reasonis that saving influencesinvestment and thus the capitalstock. An increasein the propensityto savewill increasethe long-runcapital-labor ratio, andcapital's incomeshare will rise or fall dependingon whetherthe elasticityof factor substitutionis greateror smallerthan one, respectively. Bycontrast, the neo-Keynesiangiwth modelsof Lewisand Kaldorassume from the outsetthat workers and capitalistshave differentsaving behavior." 3 Lewis(1954) arguesthat most savingcomes from the profits of the entrepreneursin the modem, industrialsector of the economy,who save a high fractionof their incomes, whileother groups in the economysave less. The morefervent the activitiesof the capitalists,the fasterdoes the distributionof incometilt towardprofits, increasing the aggregatesaving ratio. Incomeredistribution from the low-savinggroup to the entrepreneursraises aggregate saving. Likewise,in the simplestform of Kaldor's(1957) model, workers spend what theyearn (theirpropensity to saveis zero)and the shareof profitsin nationalincome depends positively on the investment-outputratio and inverselyon the propensityto saveof thecapitalists. Thus, like in Lewis' model, an increasein investmentraises the incomeshare of profitsat the expenseof the wageshare, and the more the capitalistsspend, the morethey earn -- the "widow'scruse" is neverempty. Pasinetti(1962) assumes that savingpropensities differ among classes of individuals,rather than classes of ineone. Workers'saving is not zero; indeed,they are assumedto own shares on the capitalstock and receive part of the profits.Nevertheless, the implicationsfor the shareof profits in incomeare the same obtainedby

13See Marglin (1984) for in-depthanalyses of theclassical, neoclassical, no-Marxian, and neo-Keynesian approaches. I1

Kaldcr.The fact that workers save does influence the distributionof incomebetween capitalists and workers,but does not influencethe distributionof incomebetween profits and wages. While these neo-Keynesianmodels establish a clear relationbetween the functionaldistribution of incomeand saving,it is worth noting that their implicationsin terms of the inequality-savinglink are less automatic.The reasonis that in manysocieties wage earners do not necessarilyrepresent the poorersegments of the population,which are likely to includeinstead small rural landowners and self-employedindividuals in the informal sector. As a result, the associationbetween the functionaland personaldistributions of incomeis empiricallyrather weak(Atkinson 1994).

PersonalDistribution and Saving With consumerheterogeneity, standard consumptiontheories also generatelinks betweenpersonal incomedistribution and aggregate saving that, unlikethe classicaltheories just referredto, do not dependon the exogmousdistinction of two groupsof savers and non-savers.These links result from a non-linearrelationship between individualsaving and income,which can have differentsources, but in most cases -- althoughnot invariably-- leadsto a positiverelationship between inequality and aggregatesaving. A startingpoint is again the LCH,amended to includebequests. The latter were absentfrom the early formulationsof the LCH becausethey were thought insignificant.Only 20 percentof total U.S. wealth was believedto come frombequests, with the remaining80 percentdue to the savingof livingindividuals. More recentstudies have virtuallyreversed this 20-80 rule to 80-20 (Kotlikoffand Summers1981, 1988).This is an i.nportantfinding from the theoretical viewpoint because, with a fullydeveloped intergenerational bequest motive, the distinctionbetween the LCH andthe PIHvirtally vanishes,as differentage cohortsbecome mutually linked. Theview that bequestsas a savingmotive are moreimportant than life-cycleconsiderations, and that the elasticityof bequestswith respect to lifetimeresources exceeds unity helps explain a numberof empirical puzzleson the LCHmodel (see Deaton 1992 and 1995for furtherdiscussion and references).First, there is little evidencethat the olddissave, as impliedby the simpleLCH; on the contrary,their savingrates appearto be as high or evenhigher than thoseof younghouseholds. Second, if bequestsare a luxury(at least over a relevant wealthrange), saving rates shouldbe higheramong wealthier consumers and richercountries than in the rest, whichempirically seems to be the case. Third,the fact that savingappears to be concentratedamong relatively fewricher households, who may be accumulatingmostly for dynasticmotives, is also in agreementwith a central roleof bequestsin drivingsaving. If bequestsby the wealthyare a chiefforce behind saving, as thisliterature suggests, the situationis close to that describedby the "capitalistspirit" modelmentioned earlier, in whichwealth is accumulatedfor its own 12 sake(see, for example,Zou 1993),and higher wealth prompts further accumulation -- becauseconsumption and wealthare gross substitutes in the agent's utilityfunction. More generally,the apparentconcentration of saving in a small groupof richer individualssuggests that a betterunderstanding of their savingbehavior is essential to understandaggregate saving patterns. The keyissue is that if the elasticityof bequestswith respect to lifetimeresources is greaterthan unity (so that bequestsare a lwaurygood), inoorne redistribution from rich to poor will unambiguouslyreduce aggregate saving(Blinder 1975).As we shall seelater, this viewhas receivedsome empirical support. An altemativeroute through which income distribution may matterfor aggregatesaving was suggested by Becker(1975). If thereare decreasing returns to humancapital, the poor will investrelatively more in human capital than the rich. Sincehuman capital expendituresare consideredas consumptionin standard national accounting,the neasuredsaving rates of the poor will appear lowerthan thoseof the rich, even if their "ovaall" savingrates (includinghuman capital accumulation) are identical. In turn,precautionary saving also impliesa link betweendistribution and saving. Consumers with low assetstend to compressconsumption to avoidrunning down their precautionarybalances, so that their marginal propensityto consumeout of incomeis higherthan that of thoseconsumers holding large asset stocks -- they woulddevote most of anyextra income to consumption.Thus redistributionfrom the wealthyto the poor would depressoverall saving. The oppositecould happen, however, if the poor face greateruncertainty, are more risk- averse,or have more limitedaccess to risk diversificationthan the rich; in such circumstances,a transferfrom the latter to the formerwould lead to higheraggregate saving. A relatedview, advanced by Friedman(1957), holdsthat, if the cross-sectionaldistribution of incomereflects future income uncertainty, then greaterincome inequalityshould raise precautionarysaving. Consumptionhabits, whose theoretical interest lies mainlyin their abilityto generatepositive saving- growth correlationsthrough the slow adjustmentof consumption'4 , also have implicationsfor the saving- distribution link. This can be most clearlyseen in an LCH framework.Consumption is costlier for young households-- becausethe habitit induceshas to be fed for the rest of life -- and cheaperfor old consumers.Thus theyoung will tend to savemore than the old, and incomeredistribution from the latter to the formerwill raise overallsaving. Redistribution from rich to poor can also raise savingunder the (not too implausible)assumption that habits make it more difficultto adjust futureconsumption down than up. In such case, richerconsumers would reduce their consumptionlevel by the full amount of the transfer,while poorerconsumers would be reluctantto raise their consumptionby the same amount.

14 SeeCarroll and Weil (1994) and Carroll, Overland and Weil (1994). 13

Borrowingconstraints, saving and distribution The inabilityof some consumersto borrow forges a powerfullink betweenincome distribution and saving.Consumption models with borrowingconstraints divide consumers into saversand non-savers.Unlike in the classicalmodels of functionalincome distribution, however, this does not arise from the exogmous distinctionof two classesof peopleor preferwes, but fromthe distribution of preferencesamong the population, interestrates, the variabilityof earnings,and their rate of growth. Borrowingconstraints act in a way similarin manyrespects to the precautionarysaving motive. Given the inabilityto borrow,consumers use assets to bufferconsumption, accumulating when times are good and running them down to protect consumptionwhen earnings are low. In the theoreticalmodels, bofrowing constraintsmostly affect impatient consumers who facehigh earningsgrowth (Deaton 1991). Theempirical relevance of borrowingconstraints is wellestablished However,they help explainmostly short-termsaving for consumptionbuffering, not long-termsaving for old-ageor for bequests.For example, Hayashi(1985) finds that for a significantfraction of the Japanesepopulation the behaviorof consumptionover tie is consistentwith the existenceof creditrationing and differential borrowing and lendingrates. Borowing cmnstraitsappear particularly imrtant withregard to savingfor housingpurchases. Jappelli and Pagano(1994) showthat credit constaints reflected in housingnortgage regulations are an importantexplanatory factor behind cross-countrydifferences in saving. In practice,bcrrowing constraints affect mostly poorer households, and not the rich who holdlarge asset stocks. Thus, like the precautionarysaving motive, borrowing constraints likely are a chief force behindthe savingbehavior of lower-and middle-income groups, but not richer households. Income redistribution away fron thelatter makes the bcowing constraintsless likelyto bind and reducesthe importanceof buffer-stocksaving, thuslowering aggregate saving rates.

Indirect links Otherrecent literature brings out someindirect links between distribution and savingoperating through third variablesthat affect saving.One particularlyactive line of researchis the "politicaleconomy" literature, whichhas underscoredthe positiveassociation between income equality and economicgrowth in a framework of endogenousgrowth and endogenouseconomic policy' 5 . In this approach,causality runs fromdistribution to

5 Fora generaloverview of thedifferent strands of the literatureon incomedistribution and growh, se Solimno (1995). 14 growthvia investment.In addition,these models include a politicalmechanism which provides a link between incomeinequality and economic policy. The main line of argumentis that a highlyunequal distribution of incomeand wealth causes social tensionand political instability (violent protests, coups, etc.); the resultis a discouragementof investmentthrough imaeaseduncutaity, alongwith adverse consequences for productivityand thus growth (Perssonand Tabellini 1994,Alesina and Rodrik 1994,Perotti 1995, Alesinaand Perotti1996). In addition,income distribution may affectgrowth also throughtaxation and governmentexpenditure: in a more unequal societythere is greater demand for redistributionand thereforehigher taxation, lower returns to investmentsin physicaland human capital,and less investmentand growth. Thesearguments have received some empircal support. From the pointof viewof saving,the implication is that if savingis positivelydependent on growth-- or, alternatively,if savingreflects in part the investment decisions of firms -- then higher inequalitywill, throughthe above channels,depress aggregatesaving -- in contrastwith the positiveimpact of inequalityon savingimplied by most of the theoriesexamined so far. Additionally,distributive inequality may alsotend to lowerpublic saving,as govemrmentsengage more actively in redistributiveexpenditures -- as in the populistexperiences examined by Dombuschand Edwards(1991). It is importantto note that the existenceof an inverserelationship between inequality and investment, as suggestedby the above literature,could also imply a negativeassociation between inequality and saving throughfirms' earnings retention. The latteris typicallythe primarysource of financingfor privateinvestment, so that if higherinequality lowers investment it shouldalso reducefirm saving.What happenswith aggregate saving,however, depends on whetherfirm owners (i.e., households) can pierce the "corporateveil" that separates houscholdand firm decisions. If this is the case, a fall in firm savingcould be fullyoffset by a rise in household saving,leaving aggregate saving unaffected.

IV Empirical Studies Empiricaltests of the impactof incomedistribution on saving are rather scarce. Someearly studies followedthe Kaldor-Lewisapproach and focusedon the functionaldistribution of income.Along these lines, Houthakker(1961), Williamson (1968), Kelleyand Williamson (1968) and Gupta(1970) foundsome evidence that the propensityto save fromnon-labor income exceeds that fromlabor income. Morerecent empirical studies focus on the effectof personalincome inequality on saving.For the most part,they find eitdr no effectsor a positiveimpact, although in the latter case the estimatesoften are statistically insignificantat conventionallevels. 15

Blinder (1975) uses U.S. time-seriesdata for 1949-1970to estimate an equation for aggregate consunptionincluding income distribution indicators. He finds that higherinequality appears to raise aggregate consumption(and thus lowersaving), although the estimatedeffect is in generalstatistically insignificant. He attributes this result to the lack of correspondencebetween his analyticalframework -- which predicts the oppositeresult -- andhis empirical model, and proposesas a preferableempirical test the estimationof separate consumptionequations by incomeclass. This suggestionis takenup by Menchikand David(1983), who use disaggregatedU.S. data to testdirectly whether the elasticityof bequeststo lifetimeresources is largeror smaller for the richthan for otherincome groups. They findthat the marginalpropensity to bequeathis unambiguously higherfor the wealthy,so that higherinequality leads to higherlifetime aggregate saving. A relatedapproach is that of Bunting(1991), who uses consumerexpenditure survey data for the U.S. to estimateconsumption as a functionof incomelevel and distributionby incomequintile. He finds strong evidencethat householdspending depends on both the leveland distribution of income: the estimatedmarginal propensitiesto cansumeuniformly decline (and propensities to savetherefore rise) as the quintileshare of income rises. The coefficientsare highlysignificant, and the model explainsover half of the variationin household consumptionin the sample. Two early studiesby DellaValle and Oguchi(1976) and Musgrove(1980) use cross-countrydata on bothindustrial and developing countries to investigatethe relationshipbetween saving and incomedistribution. In bothcases the results show no statisticallysignificant effect of incomedistribution on saving. The exception arethe OECDcountries included in the studyby DellaValle andOguchi, for whichthey find someevidence that increasedinequality may increasesaving; Gersovitz (1988) suggeststhat their failureto obtain a similarresult for the developingcountries may be due to poor qualityof the correspondingincome distribution data. In turn. Lim(1980) finds that inequalitvtends to raise aggregatesaving rates in a cross-sectionsamnple of developing countries,but his coefficientestimates are significantat conventionallevels only in somesubsamples. Venierisand Gupta (1986) examine the patternof averagesaving propensities across incomegroups in a cross-sectionsample of 49 countries,using an econometricspecification that includesalso politicalinstability as a savingdeterminant. Their results show that poorerhouseholds have the lowestsaving propensities, but somewhatsurprisingly they also find that thehighest average saving propensity corresponds to the middle-income group,so thatredistribution against the rich may raise or lowerthe aggregatesaving ratio dependingon whether the favoredgroup is the middleclass or the poor, respectively.However, the interpretationof their results is somewhatunclear due to their use of constant-pricesaving as the dependentvariable, whichhas no clear analyticaljustification. 16

Sahota(1993) tests a reduced-formrelationship between saving and incomedistribution controlling for theeffects of per capitaincome on saving.Using data on 65 industrialand developingcountries for the year 1975, he regressesthe saving/GDPratio on the Gini coefficientand a quadraticpolynomial in per capitaincome (he includesalso regional dummy variables to remove cultural and habit effects). The parameterestimate on the Gini coefficientis foundto be positive,implying a positiveimpact of inequalityon aggregatesaving, but the estimate is somewhatimprecise and significantlydifferent from zero onlyat the 10%level. Morerecently, Cook (1995) presents estimates of the impactof inequalityon aggregatesaving ratios in LDCsfrom a conventionalsaving equation including also the leveland growthrate of real income, dependency ratios,and a measureof capitalinflows. A dummyfor Latin Americancountries is also addedto the regressions, althoughits justification is unclearsince no other regionaldummies are included.Using decade averages for the 1970s for 49 developingcountries, he finds a positiveand significanteffect of inequalityon saving,which appearsrobust to somechanges in specificationand to the choiceof alternativeindicators of incomeinequality. Finally,Hong (1995) reportseconometric results on the effectof incomeinequality on gross domestic savingratios in cross-countrysamples of 56 to 64 developingand industrialcountries, using 1960-85averages for eachcountry. He findsthat the incomeshare of the top 20% of the populationhas a positiveeffect on saving rates, controllingfor old-agedependency, income (and/or education) level, and incomegrowth.

V EconometricResults In this sectionwe presentnew empiricalresults on the cross-countryrelationship between saving and incomedistribution. Our objective is to assessthe impacton savingof alternativeincome distribution indicators, after controllingfor incomeand demographic variables. Our basic sampleincludes 52 countries(see the data appendix). We limit ourselvesto variantsof simplespecifications found in comparablecross-country studies of saving(see e.g. Edwards1995, and Masson,Bayoumi and Samiel1995). The basic equationto be estimatedis the following:

(1) GNS/GNP= ao + a, gnp + a2 (gnp)2 + a3growth + a4 old + a.,young + a6 distrib

whereGNSIGNP is theratio of current-pricegross nationalsaving to current-pricegross domestic product, gnp is real per capita gross nationalproduct, growth is the (geometric)average annual rate of growthof real per capitagross national product, old is theold-age dependency ratio (ratio of populationof age 65 and above to total 17 population),young is the young-agedependency ratio (ratio of populationof ages0 to 15 to total population), and distribis an incomedistribution variable. The basic specificationin (1) embedsboth a linearand a quadraticterm in real per capita incometo encompassthe non-linearrelation between the savingrate and incomedescribed in section11; accordingly, we 6 shouldexpect a, > 0, a:2< 0. Allother variables enter linearlyin our basic equation". The majorityof empirical studiessuggest that the coefficienton growth shouldbe positive,while those on the dependencyratios should be negative,according to standardlife-cycle arguments." As incomedistribution indicator we use the Ginicoefficient, although we presentalso someregressions using insteadthe ratio of the incomeshare of the poorest40 percentof householdsto that of the richest 20 percent,and the incomeshare of the middle60 percentof the population.The latter variables,however, are availableonly for a smallersample. The correlationmatrix of our basic set of regressorsin Table2 shows three strikingfeatures. First, as mentioned above, all three incomedistribution indicators are very highly correlatedwith each other, with correlationcoefficients in all casesexceeding .90 in absolutevalue. Second, the (negative)correlation between young-ageand old-agedependency ratios is also vely large (-.93). Third,both dependencyratios are closely correlatedwith real per capita income(the correspondingcorrelation coefficients exceed .88). It will be useful to keepin mindthese featuresof the data for the discussionof the empiricalresults below. Table3 showsestimation results using the basic equationfor a varietyof samples.As a benchmark,the first columnreports parameterestimates using a specificationexcluding income distribution indicators. As expected,the second and third rows show that savingratios rise with incomelevels (a result also foundby Carroll and Weil 1994 and Edwards 1995) but taper off at high income,as indicatedby the negativecoefficient on squaredGNP per capita. Specifically,the estimatesin columnI implythat, if the other variablesare set at their samplemeans, the savingrate peaks(at a levelaround 22 percent)when per capitaincome reaches $9,000 (in 1987dollars). In turn,the fourthrow in the table indicatesthat savingratios are positivelyassociated across countries withper capita GNP growthrates. A 1-percentincrease in real growthraises the nationalsaving ratio by about

16 Allvariables (except the variabilityof incomedefined below) are measured by theirmeans over 1965-1994 (or theavailable sample, if shorter).

17 SeeLeff (1969) and Modigliani (1970). The dependency ratio is often defined to includealso the population under15. See Gersovitz (1988) for ananalytical discussion of theeffects of theseand other demographic variables on saving. 18

1.5percentage points. Finally, it can be seen from the fifth and sixth rows in column 1 that both young and old- age dependency ratios have the expected negative effect on national saving rates. The simple specification in column I accounts for nearly 60 percent of the observed cross-country variationin nationalsaving rates. However,the estimatedcoefficients on per capita income and its square, as well as on the young-age dependency ratio, have rather large standard errors. The obvious reason for this lack of precisionis the strong cross-correlation between age-dependencyratios and real income described in Table 2.'" Indeed,a joint F-testof the null hypothesisthat young-agedependency, real income and real income squared have no impact on saving yields a test statistic of 5.49, which overwhelmninglyrejects the null at the I percent level. Columns2-4 in Table 3 augmentthe specificationin the first columnusing the Gini coefficient as income distribution indicator in different country samples. The sign pattern of the parameter estimates in the first six rows remainsunchanged, and the full-sample estimates in column 2 are virtually identical to those in column 1. However,the saving-growthrelationship does not appearrobust across country groups: it is much stronger among industrialcountries (column3) than in developing countries (column 4) -- the same cross-country pattem found bv Carrolland Weil (1994). Controlling for other factors, a I percent increase in the growth rate raises national saving ratiosby 3.3 percentage points among OECD countries, and by only 1.I percentage point among LDCs. The seventh row reports the parameter estimates for the Gini coefficient. They are positive for the full sample and the OECD subsample, and negative for LDCs. In all three cases, however, they are insignificantly differentfrom zero.As before, real income,its square, and the dependency ratios are not individually significant, but F-tests cannot reject their joint significance even at the I percent level. Columns 5 through 7 use as income distribution indicator the ratio of the income shares of the top 20 and bottom fortypercent of the population. This results in a loss of seven observations (two industrial countries and fivedeveloping countries) due to unavailability of the share data. Apart from a general loss of precision, the estimationresults are otherwise very sumilarto those obtained usmg the Gini coefficient, as should be expected in view of the very high correlation reported above between the two income distribution indicators. Columns 8 and 9 of Table 3 show the results of excluding from the sample the group of take-off developingcountries, which some might argue are 'exceptional' from the viewpoint of saving (and also growth). For both the full and LDC samples in columns 8 and 9, the main consequence is that the estimated coefficient on growth loses all significance, a finding similar to that reported by Carroll and Weil (1994) when excluding from their sample the East-Asian 'tigers'. In addition, in the LDC sample (column 9) the estimated coefficient on the income distribution indicator becomes larger in absolute value and closer to statistical significance,

Is Thecorrelation between real per capitaGNP and its square,not presentedin Table2, equals.98. 19 suggestinga negativeeffect of inequalityon saving.The interpretationof this result, however,is a bit unclear. Bydropping the take-offcountries, we are eliminatingeight of the ten highest-savingcountries (see Figure 1), so that in effectwe are truncatingthe sample from above.It is well knownthat in such circumstancesOLS estimatesare biased,although the directionof the bias is not knownin general(e.g., Maddala 1983). Next we check the robustnessof our main result -- that incomeinequality does not affectaggregate saving-- by estimatingaltemative specifications that havebeen used in previousstudies. Table 4 presentsthe resultsusing the full sample.The first two columnsexplore possible non-linear effects of incomedistribution, interactingthe Ginicoefficient with real per capita incomeand addinga quadraticterm, respectively.Neither specificationproved successful. Column 3 adds incomevariability to the basic set of regressors,with variability measured by the standarddeviation of real per capita GNP aroundtrend relativeto the averageGNP level; accordingto the precautionarysaving motive, it shouldhave a positiveimpact on savingratios. In fact, the estimatedcoefficient is negativebut insignificant.The likelyreason is that aggregateincome variability is very differentfrom -- actuallymuch lowerthan -- individualincome variability, as shown by Pischke(1995). Column4 introducesregional dummies, as donefor exampleby Sahota(1993), with industrialcountries as the omittedcategory. However, the durmniesare not significant,either individually or jointly(a joint F-testyields F(3, 42)=0.681, far below conventionalsignificance levels). The last two columnsin Table 4 investigate alternativeinequality indicators: column 5 uses the incomeshare of the middleclass, and column6 adds to this the ratioof incomeshares of the top 20 and bottom40 percentof the population.In neithercase do we find any significanteffects on saving. As a final checkon our results,and alsoto facilitatecomparability with other empiricalstudies, Table 5 presentsestimation results using gross domesticsaving and real per capita GDP as the relevantmeasures of saving and income,respectively. The first two columnsestimate our basic specificationon the full and LDC sample, respectively.As can be seen,the main differencewith the estimationresults in Table3 is the loss of significanceof incomegrowth as a savingdeterminant. For the full sample,the parameterestimate on the Gini coefficientis verysimilar to that reportedby Sahota( 1993),but falls far short of statisticalsignificance. For the LDCsample, the estimateturns positive(recall that it was negativewhen using the nationalsaving ratio as the dependentvariable), but its precisionis extremelypoor. Theremaining columns in Table5 reportalternative specifications adding income variability (computed nowon thebasis of realGDP), regional dummies, and using the ratio of incomeshares as indictorof distribution. Themain novelties are that theestimated coefficient on incomevariability has the correct(positive) sign, and the 20 regionaldummies are individuallysigmficant. In every specification,however, we fail to find any significant effectsof incomedistribution on saving.'9 Our findingsstand in starkcontrast to someof the recentempirical literature reviewed above (including Lim 1980,Venieris and Gupta 1986,Sahota 1993, Cook 1995,and Hong 1995)that finds a positiveeffect of incomeconcentration on saving.Our deviationfrom this literature-- that seemsrobust to altemativesaving measuresand specifications-- is likelydue to our use of the new andbetter cross-countrydata set on income distributionconstructed by Deiningerand Squire(1995).

VI ConcludingRemarks Recenttheoretical and empircal literature has examinedthe linksbetween inequality and investmentand inequalityand growth However,less attentionhas ben paid to the relationshipbetween saving and distribution. Yetit is hardto understandaggregate consumption and saving without taking into accountthe fact that they result from the behaviorof heterogeneousmicroeconomic agents, a fact that makesincome distribution a potentially importantfactor behind overall consumption and saving. Thispaper has reviewedanalyfically and empirically the link betweenincome distribution and aggregate saving.While systematic explorations of thisissue havebeen mostlyconfined to Neo-Keynesiangrowth models, the paper has arguedthat, once the conventionalrepresentative-agent framework is abandoned,consumption theorybrings out a numberof channelsthrough which income inequality can affectsaving. Further, in most cases the relationshipthat arisescan be expectedto be positive,so that on theoreticalgrounds higher inequality is, ceteris paribus, likelyto be associatedwith highersaving. Thepaper has alsopresented new econometric evidence on the saving-inequalitylink. Using a new data set on incomedistribution for a large cross-countrysample, on the wholewe do not find evidenceof any significant associationbetween standard inequalit- indicators and saving ratios, once other key saving determinantsare taken into consideration.This conclusionholds for a varietyof samples,income distribution indicators,and empiricalspecifications. There are, however,some caveats that make our empiricalresults tentative.First, because of the unavailabilityfor most countriesof longtime-series on incomedistribution, only the cross-countrydimension of the data has been exploitedhere. While this entailssome loss of information,it is well knownthat income distributionindicators generally display little variation over time relativeto that across countries,and thus on the

19The same resultwas obtained in otherregressions (not reported)using alternativelythe incomeshares of the top20, middle60, and bottom40 percentof the populationas inequalityindicators. 21 wholewe do not thinkthat omissionof the time dimensionhas any majorconsequences for our results.Second, ouremnpirical estimates -- like thosereported in the vast majorityof the literatureon saving-- are based on the implicitassumption that causalityruns from income,growth anddistribution to saving.While we are awareof thepotential simultaneity between these variables,we also believethat the searchfor validinstruments is not a trivialtask, and we leaveit for futurework Third,related to this, our empiricalestimates focus only on the direct effects of inequalityon saving ratios, ignoring possible indirect effects operatingthrough other saving

determinants- like, for example,the negativeimpact of inequalityon growththat the recentpolitical-economy literaturesuggests. To explore the total effectof inequalityon savingin a satisfactorymanner one wouldneed an analyticaland empiricalframework encompassing these indirectchannels. Ideally,the starting point to addressthe latter two caveatswould be to specifya completetheoretical modeldescribing, as a minimum,the determinationnot only of saving,but also of the distributionof incomeand its growthrate. This,however, is likelyto be a formidabletask, well beyondthe scopeof this paper.

DataAppendix

Thevariables introduced in sections II andV andtheir definitions and sources are the following:

VariableName Definitionand Source

Grossdomestic saving ratio grossdomestic savings relative to grossdomestic product in currentprices, average over 1960-94; The World Bank

Grossnational saving ratio grossnational savings including net currenttransfers relative to grossnational product in currentprices, average over 1965-94; TheWorld Bank

RealGDP per capita in constant 1987 U.S. dollars, average over 1960-94; The World Bank

Real GNPper capita in constant 1987 U.S. dollars, average over 1965-94; The World Bank

RealGDP per capita growth rate averageover 1960-94 22

Real GNP per capita growth rate average over 1965-94

Gini coefficient and Income Share of average over 1965-94; Deininger and Squire Top 20% / Bottom 40% of Population

Income share of Middle 60% of average over 1965-94; Deininger and Squire Population

Old age dependency ratio population aged 65 and over relative to total population, average over 1965-94; The World Bank

Young age dependencyratio population aged 14 and below relative to total population, average over 1965-94; The World Bank

GDP variability ratio of standard deviation of residuals of regression of real GDP per capita on time trend to real GDP; authors'calculation.

GNP variability ratio of standard deviation of residuals of regression of real GNP per capita on time trend to real GNP; authors'calculation.

The number of countries in the full sample is 52. The country classification is the following. OECD countries: Australia,Austria, Belgium, Canada, Dernmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Netherlands, New Zealand,Norway, Portugal, Spain, Sweden, United Kingdom, and United States. Take-Off countries: Chile, China, Hong Kong, Indonesia,Korea (Rep.), Malaysia,Mauritius, Singapore, Thailand and Taiwan, China. Other developing countries: Bangladesh, Brazil, Colombia, Costa Rica, Dominican Republic, Egypt, Guatemala, India, Jamaica, Mexico, Morocco, Pakistan, Panama, Peru, Philippines, Sri Lanka, Tanzania, Trinidad & Tobago, Tunisia, Turkey, Venezuela, Zambia.

Not all countrieshave Gini and Income Distribution measures available for each year. Countries are included in the sampleonly if theyhave at least one observationin each of two different decades. The distribution of countries according to the number of annual observations is the following: 38 (31) countries with less than 10 Gini (Income Distribution) observations,1 I (11) countries with 10 to 20 Gini (Income Distribution) observations, and 3 (3) countries with more than 20 Gini (Income Distribution) observations. 23

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Number of Income Share Redo Observatons Gini Coefficient of Top 20% to Bottom 40% Income Share of Middle 60%Y

Mean Std. dev. Mean Std. dev. Mean Std. dev.

World 52 39.62 2.70 2.72 0.04 0.48 0.02

OECD Countries 20 33.34 1.92 2.08 0.04 0.54 0.01

Developing Countries 32 43.68 3.17 3.65 0.03 0.45 0.05 of which: Take-Off Countries 10 40.31 2.87 2.63 0.04 0.47 0.02

Other Developing 22 45.21 3.31 4.00 0.05 0.43 0.03

Table 2

Correlation Matrix of Basic Regressors

GNS/GNP Per Capita Growth rate of Gini Income share Income share Old age GNP Per Capita GNP coefficient of top2O/bot4O of middle 60 dependency ratio

GNS/GNP Per Capita GNP 0.311 Growth rate of Per Capita GNP 0.632 -0.001 Gini coefficient -0.278 -0.551 -0.238 Income share of top 20%/bottom 40% -0.277 -0.469 -0.233 0.951 Income share of middle 60% 0.335 0.652 0.204 -0.957 -0.919 Old age dependency ratio 0.177 0.860 -0.012 -0.627 -0.536 0.705 Young age dependency ratio -0.394 -0.872 -0.211 0.683 0.603 -0.763 -0.933 Table 3

Cross-SectionEstimates of Saving Equations DependentVariable: GNS/GNP (t-statisticsin parentheses) Equation 1 2 3 4 5 6 7 8 9

Sample Full Full OECD LDC Full OECD LDC Full W/o Take- LDC w/o Take- Off Countries Off Countries

Constant 36.506 36.055 28.209 39.844 37.632 30.999 41.447 32.57 52.299 (2.762) (2.666) (1.261) (2.149) (2.708) (1.348) (2.144) (2.155) (2.616) Real GNP per capita 0.001 0.001 0.002 0.004 0.001 0.001 0.004 0.002 0.011 (1987constant dollar) (1.736) (1.667) (1.906) (1.151) (1.375) (1.196) (1.054) (2.165) (2.070) Real GNP per capita -5.67E-08 -5.5E-08 -7.22E-08-3.26E-07 -4.20E-08 -4.61E-08 -4.13E-07 -7.96E-08 -1.84E-06 squared (-1.429) (-1.376) (-1.603) (-0.727) (-0.979) (-0.823) (-0.730) (-1.903) (-1.475) Real GNPgrowth rate 1.479 1.495 3.265 1.074 1.502 3.202 1.107 0.923 0.341 c (3.055) (3.042) (2.757) (1.779) (2.843) (2.687) (1.738) (1.308) (0.729)

Old agedependency ratio -1.258 -1.253 -0.927 -1.36 -1.271 -0.878 -1.671 -1.188 -2.742 (-2.643) (-2.618) (-1.490) (-1.061) (-2.522) (-1.452) (-1.106) (-2.055) (-1.819) Youngage dependency -0.413 -0.439 -0.647 -0.402 -0.425 -0.593 -0.455 -0.426 -0.518 ratio (-1.620) (1.672) (-1.218) (-1.143) (-1.521) (-1.219) (-1.202) (-1.503) (-1.631)

Gini coefficient 0.035 0.105 -0.095 0.094 -0.238 (0.381) (0.982) (-0.734) (1.054) (-1.613) Incomeshare ratio of -0.019 0.222 -0.649 top 20%/bottom40% (4.033) (0.165) (-0.921)

AdjustedR 2 0.528 0.520 0.539 0.511 0.506 0.525 0.497 0.455 0.413 StandardError 3.875 3.912 2.691 4.446 4.092 2.817 4.742 3.681 3.458 Numberof Observations 52 52 20 32 45 18 27 42 22

Note:The abovet-statistics were computedusing heteroskedasticity-corrected standard errors. 29 Table 4

Cross-SectionEstimates of Saving Equations DependentVariable: GNSIGNP (t-statisticsin parentheses) Equation 1 2 3 4 5 6 Sample Full Full Full Full Full Full

Constant 38.740 23.249 41.816 33.354 35.140 27.395 (2.654) (1.480) (2.709) (2.425) (2.061) (1.170) Real GNP per capita 0.001 0.001 0.001 0.002 0.001 0.001 (1987 constantdollar) (0.517) (1.614) (1.211) (2.032) (1.402) (1.251) Real GNP per capita squared -5.33E-08 -5.63E-08 -3.76E-08 -6.99E-08 -4.22E-08 -3.84E-08 (-1.334) (-1.377) (-0.933) (-1.734) (-0.995) (1.251) Real GNP growthrate 1.420 1.453 1.291 1.234 1.497 1.504 (2.710) (2.912) (2.429) (2.065) (2.817) (2.765) Old age dependencyratio -1.241 -1.256 -1.349 -0.997 -1.273 -1.287 (-2.556) (-2.591) (-2.638) (-2.002) (-2.498) (-2.471) Young age dependencyratio -0.444 -0.484 -0.455 -0.485 -0.407 -0.411 (-1.656) (-1.794) (-1.655) (-1.736) (-1.445) (-1.439) Gini coefficient -0.024 0.763 -0.032 0.022 (-0.180) (1.541) (-0.347) (0.191) Incomeshare ratio of top 20% I bottom 40% 0.548 (0.526) Incomeshare of middle 60% 0.038 0.173 (0.218) (0.526) GNP variability -16.185 (-1.317) Multiplicationof GNP and Gini coefficient 2.15E-05 (1.099) Gini coefficientsquared -0.009 (-1.410) Latin Americaregional dummy 4.413 (1.129) Africa regionaldummy 3.975 (1.001) Asia regionaldummy 5.164 (1.403)

AdjustedR 2 0.516 0.520 0.535 0.508 0.507 0.496 StandardError 3.925 3.911 3.848 3.960 4.089 4.134 Numberof Observations 52 52 52 52 45 45

Note: The abovet-statistics were computedusing heteroskedasticity-correctedstandard errors. Table 6 Cross-SectionEstimates of Saving Equations DependentVariable: GDS/GDP (t-statisticsin parentheses) Equation 1 2 3 4 5 a Sample Full LDC Full Full Full Full

Constant 39.011 51.769 28.699 40.523 34.594 41.524 (2.444) (2.158) (1.857) (2.305) (2.116) (2.558) Real GDP per capita 0.002 0.005 0.002 0.002 0.003 0.002 (1987 constantdollar) (2.260) (1.615) (2.792) (1.199) (2.897) (1.965) Real GDP per capita squared -7.94E-08 -5.58E-07 -8.44E-08 -7.81E-08 -1.03E-07 -6.49E-08 (-1.822) (-1.198) (-2.008) (-1.777) (-2.304) (-1.353) Real GDP growthrate 0.430 -0.213 0.582 0.385 0.130 0.447 (0.664) (-0.251) (1.003) (0.558) (0.163) (0.688) Old age dependencyratio -1.695 -1.791 -1.574 -1.688 -1.196 -1.695 (-3.256) (-1.121) (-3.121) (-3.219) (-2.144) (-3.026) Young age dependencyratio -0.548 -0.716 -0.359 -0.552 -0.644 -0.480 (-1.812) (-1.589) (-1.210) (-1.780) (-2.000) (-1.443) o Gini coefficient 0.149 0.012 0.134 0.117 0.097 (1.368) (0.087) (1.219) (0.7340) (0.673) Income shareratio of top 20%/ bottom 40% 0.546 (0.726) GDPvariability 14.945 (1.760) Multiplicationof GDP and Gini coefficient 1.16E-05 (0.483) Latin America regionaldummy 9.324 (2.337) Africa regionaldummy 8.848 (1.952) Asia regionaldummy 9.176 (2.540)

AdjustedR2 0.355 0.323 0.385 0.342 0.373 0.290 StandardError 4.770 5.447 4.656 4.816 4.704 5.013 Numberof Observations 52 32 52 52 52 45

Nnta Tha nhnva tLctnatitfirc waro rnmnijfM aicinn hn*o,nok*,4aetipiij rrt_ e4.A,-A £rrnr. Figure 1

LONG-TERM WORLD SAVING AND INCOME LEVEL (Gross National Saving Rate Including Net Current Transfers and Real GNP Per Capita, 1965 - 94 Averages, by Countries) 35 _ .10

30

25

20A

10 O. I I- II

y -9E-08x2 +0.0016x + 17.967 2- 0.1806

0 2000 4000 6000 8000 10000 12000 14000 16000 Averge Real GNP Per C$ap | LDC (excl. Take-OffCouniries) *Take-Offcountnes AOECD:| Figure 2

LONG-TERM WORLD SAVING AND INCOME GROWTH (Gross National Saving Rate Including Net Current Transfers and Growth Rate of Real GNP Per Capita, 1965-94 Averages,by Countries)

35

30

23 A z

L*

y 2.05 73x + 16.034 R2 = 0.3779

-2 -1 0 1 2 3 4 5 6 7 8 9 Average Growth Rate of Real GNP Per Capita *LDC (excl. Take-OffCountries) mTake-Off countries A OECD Figure 3

LONG-TERM WORLD SAVINGAND INCOME DISTRIBUTION (Gross National Saving Rate Including Net Current TRansfers and Gini Coefficient, 1965-94Averages, by Countries)

35 A 30 U U

25 A AA *

20 *

15. .

10 |. D ec.Tk@fonres aeOfonnsOC U

5

0 25 30 35 40 45 50 55 60 Average Gili Coeffideut *LDC(excl. Take-Off Countries)u Take-off countriesA OECD Figure 4

LONG-TERM WORLD INCOME DISTRIBUTION AND DEVELOPMENT (Gini Coefficientand Log of Average GNP Per Capita, 1965- 94 Averages,by Countries)

60 - -- 2 * y -2.1861x+ 30.807x- 63.211 55 - R =0.4292

50

.;45 j40

35

30A

25 a A

20 I l 4.5 5.5 6.5 7.5 8.5 9.5 10.5 Log of Average GNPPer Capita

* LDC (excl. Take-OffCountries) * Take-Offcountries A OECD Figre 5

LONG-TERM WORLD INCOME DISTRIBUTION MEASURES (GiniCoefficient and Ratio of Income of Top 20% to Bottom 40% of Population, 1965-94Averages, by Countries) 60

55

50 -

45

40 U

35

30 --

25 a A

1 2 3 4 5 6 7 8 AverageIncome Ratio of Top 20% to Botom 40% F*LDC (excl. Take-OffCountires) a Take-Offcountries AOECD7

I

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