the inheritance of inequality - thomas pikettypiketty.pse.ens.fr/files/bowlesgintisjep2002.pdf ·...

The Inheritance of Inequality

Samuel Bowles and Herbert Gintis

P eople differ markedly in their views concerning the appropriate role ofgovernment in reducing economic inequality Self-interest and differencesin values explain part of the con ict over redistribution But by far the most

important fault line is that people hold different beliefs about why the rich are richand the poor are poor Survey data show that peoplemdashrich and poor alikemdashwhothink that ldquogetting ahead and succeeding in liferdquo depends on ldquohard workrdquo orldquowillingness to take risksrdquo tend to oppose redistributive programs Conversely thosewho think that the key to success is ldquomoney inherited from familyrdquo ldquoparents and thefamily environmentrdquo ldquoconnections and knowing the right peoplerdquo or being whitesupport redistribution (Fong 2001 Fong Bowles and Gintis 2002) Handing downsuccess strikes many people as unfair even if the stakes are small while differencesin achieved success may be unobjectionable even with high stakes as long as theplaying eld is considered level

How level is the intergenerational playing eld1 What are the causal mechanismsthat underlie the intergenerational transmission of economic status Are these

1 See Bowles and Gintis (2001) for the relevant formal models and other technical aspects of thisresearch also available at httpwwwsantafeedus publicationsworking-papershtml ArrowBowles and Durlauf (1999) and Bowles Gintis and Osborne (forthcoming) present collections of recentempirical and theoretical research

y Samuel Bowles is Professor of Economics at the University of Siena Siena Italy andDirector of the Economics Program Santa Fe Institute Santa Fe New Mexico HerbertGintis is a member of the External Faculty Santa Fe Institute Santa Fe New MexicoBoth authors are Emeritus Professors of Economics University of Massachusetts AmherstMassachusetts Their e-mail addresses are bowlessantafeedu and hgintisattbicom and their websites are httpwww-unix oitumassedu bowles and httpwww-unixoitumassedu gintis

Journal of Economic PerspectivesmdashVolume 16 Number 3mdashSummer 2002mdashPages 3ndash30

mechanisms amenable to public policies in a way that would make the attainment ofeconomic success more fair These are the questions we will try to answer

No one doubts that the children of well-off parents generally receive more andbetter schooling and bene t from material cultural and genetic inheritances Butuntil recently the consensus among economists has been that in the United Statessuccess is largely won or lost in every generation Early research on the statisticalrelationship between parentsrsquo and their childrenrsquos economic status after becomingadults starting with Blau and Duncan (1967) found only a weak connection andthus seemed to con rm that the United States was indeed the ldquoland of opportu-nityrdquo For example the simple correlations between parentsrsquo and sonsrsquo income orearnings (or their logarithms) in the United States reported by Becker and Tomes(1986) averaged 015 leading the authors to conclude ldquoAside from families vic-timized by discrimination [a]lmost all earnings advantages and disadvantages ofancestors are wiped out in three generationsrdquo Becker (1988) expressed a widelyheld consensus when in his presidential address to the American EconomicsAssociation he concluded (p 10) ldquo[L]ow earnings as well as high earnings are notstrongly transmitted from fathers to sonsrdquo

But more recent research shows that the estimates of high levels of intergen-erational mobility were artifacts of two types of measurement error mistakes inreporting income particularly when individuals were asked to recall the income oftheir parents and transitory components in current income uncorrelated withunderlying permanent income (Bowles 1972 Bowles and Nelson 1974 AtkinsonMaynard and Trinder 1983 Solon 1992 1999 Zimmerman 1992) The highnoise-to-signal-ratio in the incomes of both generations depressed the intergenera-tional correlation When corrected the intergenerational correlations for eco-nomic status appear to be substantial many of them three times the average of theUS studies surveyed by Becker and Tomes (1986)

The higher consensus estimates of the intergenerational transmission ofeconomic success has stimulated empirical research The relevant facts onwhich most researchers now agree include the following brothersrsquo incomes aremuch more similar than those of randomly chosen males of the same race andsimilar age differences the incomes of identical twins are much more similarthan fraternal twins or non-twin brothers the children of well-off parents obtainmore and higher quality schooling and wealth inheritance makes an importantcontribution to the wealth owned by the offspring of the very rich On the basisof these and other empirical regularities it seems safe to conclude that theintergenerational transmission of economic status is accounted for by a heter-ogeneous collection of mechanisms including the genetic and cultural trans-mission of cognitive skills and noncognitive personality traits in demand byemployers the inheritance of wealth and income-enhancing group member-ships such as race and the superior education and health status enjoyed by thechildren of higher status families

However the transmission of economic success across generations remainssomething of a black box We nd that the combined inheritance processes

4 Journal of Economic Perspectives

operating through superior cognitive performance and educational attainments ofthose with well-off parents while important explain at most three- fths of theintergenerational transmission of economic status Moreover while genetic trans-mission of earnings-enhancing traits appears to play a role the genetic transmissionof IQ appears to be relatively unimportant

It might be thought that the black box is an artifact of poor measurement ofthe intervening variables relative to the measurement of the income or earnings ofparents and offspring But this does not seem to be the case Years of schooling andother measures of school attainment like cognitive performance are measuredwith relatively little error Better measurements will of course help but we are notlikely to improve much on our measures of IQ and recent improvements in themeasurement of school quality have not given us much illumination about whatrsquosgoing on inside the black box The fundamental problem is not that we aremeasuring the right variables poorly but that we are missing some of the importantvariables entirely What might these be

Most economic models treat onersquos income as the sum of the returns to thefactors of production one brings to the market like skills or capital goods But anyindividual trait that affects income and for which parent-offspring similarity isstrong will contribute to the intergenerational transmission of economic successIncluded are race geographical location height beauty or other aspects of physicalappearance health status and personality Thus by contrast to the standard ap-proach we give considerable attention to income-generating characteristics thatare not generally considered to be factors of production In studies of the inter-generational transmission of economic status our estimates suggest that cognitiveskills and education have been overstudied while wealth race and noncognitivebehavioral traits have been understudied

Measuring the Intergenerational Transmission of Economic Status

Economic status can be measured in discrete categoriesmdashby membership inhierarchically ordered classes for examplemdash or continuously by earnings incomeor wealth The discrete approach allows a rich but dif cult-to-summarize represen-tation of the process of intergenerational persistence of status using transitionprobabilities among the relevant social ranks (Erikson and Goldthorpe 1992 thisissue) By contrast continuous measures allow a simple metric of persistence basedon the correlation between the economic status of the two generations Moreoverthese correlations may be decomposed into additive components re ecting thevarious causal mechanisms accounting for parent-child economic similarity Bothapproaches are insightful but here we will rely primarily on the continuousmeasurement of status For reasons of data availability we use income or earningsas the measure of economic status though income (the more inclusive measure) ispreferable for most applications

We use subscript p to refer to parental measures while y is an individualrsquos

Samuel Bowles and Herbert Gintis 5

economic status adjusted so that its mean y is constant across generations by is aconstant and laquoy is a disturbance uncorrelated with yp Thus

y 2 y 5 by~yp 2 y 1 laquoy

that is the deviation of the offspringrsquos economic status from the mean is by timesthe deviation of the parent from mean economic status plus an error term In theempirical work reviewed below earnings income wealth and other measures ofeconomic success are measured by their natural logarithm unless otherwise notedThus by termed the intergenerational income elasticity is the percentage changein offspringrsquos economic success associated with a 1 percent change in parentsrsquoeconomic success The in uence of mean economic status on the economics statusof the offspring 1 2 by is called regression to the mean since it shows that one mayexpect to be closer to the mean than onersquos parents by the fraction 1 2 by

(Goldberger 1989)The relationship between the intergenerational income elasticity and the

intergenerational correlation is given by

ry 5 by

syp

sy

where sy is the standard deviation of y If y is a natural logarithm its standarddeviation is a common unit-free measure of inequality Thus if inequality isunchanging across generations so syp

5 sy then ry 5 by However the intergen-erational income elasticity exceeds ry when income inequality is rising but is lessthan ry when income inequality is declining In effect the intergenerationalcorrelation coef cient r is affected by changes in the distribution of income whilethe intergenerational income elasticity is not Also r2 measures the fraction of thevariance in this generationrsquos measure of economic success that is linearly associatedwith the same measure in the previous generation

Estimates of the intergenerational income elasticity are presented in Solon(1999 this issue) and Mulligan (1997) The mean estimates reported in Mulliganare as follows for consumption 068 for wealth 050 for income 043 forearnings (or wages) 034 and for years of schooling 029 Evidence concerningtrends in the degree of income persistence across generations is mixed Moststudies indicate that persistence rises with age is greater for sons than daughtersand is greater when multiple years of income or earnings are averaged Theimportance of averaging multiple years to capture permanent aspects of economicstatus is dramatized in Mazumder (forthcoming) He used a rich US SocialSecurity Administration data set to estimate an intergenerational income elasticityof 027 averaging sonrsquos earnings over three years and father earnings averaged overtwo years But the estimate increases to 047 when six years of the fathersrsquo earningsare averaged and to 065 when 15 years are averaged


Do intergenerational elasticities of this magnitude mean that ldquorags torichesrdquo is no more than a fantasy for most poor children The intergenerationalcorrelation is an average measure and may be unilluminating about the prob-abilities of economic success conditional on being the child of poor or richparents Calculating these conditional probabilities and inspecting the entiretransition matrix gives a more complete picture The results of a study by Hertz(2002) appear in Figure 1 with the parents arranged by income decile (frompoor to rich moving from left to right) and with adult children arranged byincome decile along the other axis The height of the surface indicates thelikelihood of making the transition from the indicated parentsrsquo decile to thechildrenrsquos decile

Though the underlying intergenerational correlation of incomes in the dataset Hertz (2002) used is a modest 042 the differences in the likely life trajectoriesof the children of the poor and the rich are substantial The ldquotwin peaksrdquo representthose stuck in poverty and af uence (though we do not expect the term ldquoaf uencetraprdquo to catch on) A son born to the top decile has a 229 percent chance ofattaining the top decile (point D) and a 407 percent chance of attaining the topquintile A indicates that the son of the poorest decile has a 13 percent chance ofattaining the top decile and a 37 percent chance of attaining the top quintile Cindicates that children of the poorest decile have a 312 percent chance of occu-pying the lowest decile and a 507 percent chance of occupying the lowest quintilewhile B shows that the probability that a child of the richest decile ends up in thepoorest decile is 24 percent with a 68 percent chance of occupying the lowestquintile Hertzrsquos transmission matrix and other studies suggest that distinct trans-mission mechanisms may be at work at various points of the income distribution(Corak and Heisz 1999 Cooper Durlauf and Johnson 1994 Hertz 2001) Forexample wealth bequests may play a major role at the top of the income distribu-tion while at the bottom vulnerability to violence or other adverse health episodesmay be more important Mobility patterns by race also differ dramatically (Hertz2002) Downward mobility from the top quartile to the bottom quartile is nearly vetimes as great for blacks as for whites Thus whatever it is that accounts for theirsuccess successful blacks do not transmit it to their children as effectively as dosuccessful whites Correspondingly blacks born to the bottom quartile attain thetop quartile at one half the rate of whites

Sources of Persistence Cultural Genetic and Bequest

Economic status does persist substantially across generations We seek touncover the channels through which parental incomes in uence offspring in-comes We do this by decomposing the intergenerational correlation (or theintergenerational income elasticity) into additive components re ecting the con-tribution of various causal mechanisms This will allow us to conclude for example

The Inheritance of Inequality 7

that a certain fraction of the intergenerational correlation is accounted for by thegenetic inheritance of IQ or by the fact that the children of rich parents are alsowealthy

It is a remarkable fact about correlation coef cients that this can be doneMoreover the technique we use does not require that we introduce variables in anyparticular order Suppose that parentsrsquo income (measured by its logarithm yp) andoffspring education (s) affect offspring income (also measured by its logarithm y)Like any correlation coef cient this intergenerational correlation rypy can beexpressed as the sum of the normalized regression coef cients of measures ofparental income (bypy) and offspring education (bys) in a multiple regressionpredicting y each multiplied by the correlation between yp and the regressor(which of course for parental income itself is just 1) A normalized regressioncoef cient is the change in the dependent variable in standard deviation unitsassociated with a one standard deviation change in the independent variable Thedirect effect of parental income is the normalized regression coef cient of parentalincome from this regression The education component of this decomposition of

Figure 1Intergenerational Income Transition Probabilities

Notes The height of the surface in cell (i j) is the probability that a person whose parentsrsquohousehold income was in the ith decile will have household income in the jth decile as an adultThe income of the children was measured when they were aged 26 or older and was averaged overall such years for which it was observed (an average of ten years) Parentsrsquo income was averaged overall observed years in which the child lived with the parents (an average of 94 years)Source From PSID data Hertz (2002) The 10 3 10 transition matrix on which this gure is based isavailable at httpwww-unixoitumassedu gintis


the intergenerational correlation is called an indirect effect2 Figure 2 illustrates thisbreakdown which gives

r yyp 5 byp y 1 ryp sbys

intergenerational correlation 5 direct effect 1 indirect effect

As long as the multiple regression coef cients are unbiased the decomposition isvalid whatever the relationship among the variables Speci cally it does not requirethat the regressors be uncorrelated This decomposition allows us to be moreprecise about our ldquoblack boxrdquo claim in the introduction We mean that the directparental effect is a substantial fraction of the intergenerational correlation in anumber of studies allowing this comparison (Bowles 1972 Bowles and Nelson1974 Atkinson Maynard and Trinder 1983 Mulligan 1999)

Our strategy is to estimate the size of these direct and indirect effects Note thatthe decomposition uses correlations between parental incomes and othervariablesmdashschooling in the examplemdashthought to be causally related to the income-generating process These correlations with parental income need not re ectcausal relationships of course But the above decomposition can be repeated forthe correlations between parental income and the causes of offspring income insome cases permitting causal interpretations For example a study of the role ofwealth in the transmission process could ask why parental income and offspringwealth are correlated Is it bequests and inter vivos transfers or the culturaltransmission of savings behaviors that account for this correlation Or do we simplynot know why parent and offspring wealth is correlated and as a result should avoidgiving the data a causal interpretation Similarly parent-offspring similarity inhuman capital may be due to genetic or cultural inheritance of whatever it takes topersist in schooling and to acquire skills and behaviors that are rewarded in thelabor market Unlike the models of parental and child behavior accounting forpersistence pioneered by Becker and presented in this issue by Grawe and

2 This decomposition can be found in Blalock (1964) and is described in the Appendix to this paperGoldberger (1991) describes the standard regression model with normalized (mean zero unit standarddeviation) variables on which it is based

Figure 2Representing a Correlation as the Sum of Direct and Indirect Effects


Mulligan our approach is more diagnostic not giving an adequate causal accountof the transmission process but indicating where to look to nd the causes Thenext sections of this paper will explore such decompositions

The Role of Genetic Inheritance of Cognitive Skill

One of the transmission channels deserves special attention not only becauseof its prima facie plausibility but also because of the extraordinary attention givento it in popular discussions of the subject This is the genetic inheritance ofcognitive skill The similarity of parentsrsquo and offspringsrsquo scores on cognitive tests iswell documented Correlations of IQ between parents and offspring range from042 to 072 where the higher gure refers to measures of average parental andaverage offspring IQ (Bouchard and McGue 1981 Plomin et al 2000) Thecontribution of cognitive functioning to earnings both directly and via schoolingattainment has also been established in a variety of studies that estimate determi-nants of earnings using IQ (and related) test scores The direct effect of IQ onearnings is estimated from multiple regression studies that typically use the loga-rithm of earnings as a dependent variable and estimate the regression coef cientsof a variety of explanatory variables including performance on a cognitive testyears (and perhaps other measures) of schooling a measure of parental economicandor social status work experience race and sex The indirect effect of IQoperating through its contribution to higher levels of educational attainment isestimated using measures of childhood IQ (along with other variables) to predictthe level of schooling obtained

We have located 65 estimates of the normalized regression coef cient of a testscore in an earnings equation in 24 different studies of US data over a period ofthree decades Our meta-analysis of these studies is presented in Bowles Gintis andOsborne (2002) The mean of these estimates is 015 indicating that a standarddeviation change in the cognitive score holding constant the remaining variables(including schooling) changes the natural logarithm of earnings by about one-seventh of a standard deviation By contrast the mean value of the normalizedregression coef cient of years of schooling in the same equation predicting thenatural log of earnings in these studies is 022 suggesting a somewhat largerindependent effect of schooling We checked to see if these results were dependenton the weight of overrepresented authors the type of cognitive test used at whatage the test was taken and other differences among the studies and found nosigni cant effects An estimate of the causal impact of childhood IQ on years ofschooling (also normalized) is 053 (Winship and Korenman 1999) A roughestimate of the direct and indirect effect of IQ on earnings call it b is then b 5015 1 (053)(022) 5 0266

Do these two factsmdashparent-child similarity in IQ and an important direct andindirect causal role for IQ in generating earningsmdashimply a major role for geneticinheritance of cognitive ability in the transmission of intergenerational economic


status One way to formulate this question is to ask how similar would parental andoffspring IQ be if the sole source of the similarity were genetic transmission Alsohow similar would the incomes of parents and offspring be if there were no othertransmission channel

For this we need some genetics (the details are in the Appendix and in Bowlesand Gintis 2001) and a few termsmdashphenotype genotype heritability and thegenetic correlationmdash unfamiliar to many economists A personrsquos IQmdashmeaning atest scoremdashis a phenotypic trait while the genes in uencing IQ are the personrsquosgenotypic IQ Heritability is the relationship between the two Suppose that for agiven environment a standard deviation difference in genotype is associated witha fraction h of a standard deviation difference in IQ Then h2 is the heritability ofIQ Estimates of h2 are based on the degree of similarity of IQ among twins siblingscousins and others with differing degrees of genetic relatedness The value cannotbe higher than 1 and most recent estimates are substantially lower possibly morelike a half or less (Devlin Daniels and Roeder 1997 Feldman Otto and Chris-tiansen 2000 Plomin 1999) The genetic correlation is the degree of statisticalassociation between genotypes of parents and children which is 05 if the parentsrsquogenotypes are uncorrelated (ldquorandom matingrdquo) But couples tend to be moresimilar in IQ than would occur by random mate choice (ldquoassortative matingrdquo) andthis similarity is associated with an unknown correlation m of their genotypes Theeffect is to raise the genetic correlation of parent and offspring to (1 1 m) 2

Using the method of decomposition introduced in the previous section thecorrelation g between parental and offspring IQ that is attributable to geneticinheritance of IQ alone is the heritability of IQ times the genetic correlation Thuswe have g 5 h2(1 1 m) 2 The correlation between parent and offspring incomethat is attributable to genetic inheritance of IQ is this correlation times thenormalized (direct and indirect) effect of IQ on the income of parents times theanalogous effect for the offspring or gb2 Another way to see this is to note that thecorrelation between parental income and offspring IQ that we would observe werethe genetic inheritance of IQ the only channel at work is gb and this times theeffect of offspring IQ on earnings which is b gives the same result

Using the values estimated above we see that the contribution of geneticinheritance of IQ to the intergenerational transmission of income is

~h2~1 1 m2~02662 5 035~1 1 mh2

If the heritability of IQ were 05 and the degree of assortation m were 02 (bothreasonable if only ballpark estimates) and the genetic inheritance of IQ were theonly mechanism accounting for intergenerational income transmission then theintergenerational correlation would be 001 or roughly 2 percent the observedintergenerational correlation Note the conclusion that the contribution of geneticinheritance of IQ is negligible is not the result of any assumptions concerningassortative mating or the heritability of IQ the IQ genotype of parents could be


perfectly correlated and the heritability of IQ 100 percent without appreciablychanging the qualitative conclusions The estimate results from the fact that IQ isjust not an important enough determinant of economic success

Might the small contribution of genetic inheritance of IQ to parent-offspringsimilarity of incomes be the result of measurement error in the cognitive measuresThere are two issues here First what is the reliability of the test whatever the testmeasures does it measure well Second what is the validity of the test does the testmeasure the right thing The concern that the tests are a very noisy measure ismisplaced In fact the tests are among the more reliable variables used in standardearnings equations where reliability is measured by the correlation between testsand retests between odd and even numbered items on the tests and by moresophisticated methods For the commonly used Armed Forces Quali cation Test(AFQT) for examplemdasha test used to predict vocational success that is often used asa measure of cognitive skillsmdashthe correlation between two test scores taken onsuccessive days by the same person is likely to be higher than the correlationbetween the same personrsquos reported years of schooling or income on two successivedays

The second concern that the tests measure the wrong thing is weightier andless easy to address with any certainty Could it be that cognitive skills not measuredon existing test instruments are both highly heritable and have a major impact onearnings thereby possibly explaining a more substantial fraction of the transmis-sion process The search for general cognitive measures that are substantiallyuncorrelated with IQ and predictive of success in adult roles began with EdwardThorndikersquos (1919) paper on ldquosocial intelligencerdquo Some alternative test instru-ments such as Robert Sternberg and collaboratorsrsquo ldquopractical intelligencerdquo predicteconomic success in particular occupations (Sternberg et al 1995 Williams andSternberg 1995) But despite the substantial fame and fortune that would haveaccrued to success in this area the quest that Thorndike launched three genera-tions ago has yielded no robust alternative to IQ let alone one that is highlyheritable Thus the possible existence of economically important but as yet un-measured heritable general cognitive skills cannot be excluded but should at thisstage be treated as speculation

Indeed we are inclined to think that available estimates overstate the impor-tance of general cognitive skill as a determinant of earnings since in many respectstaking a test is like doing a job Successful performance in either case results froma combination of ability and motivation including the disposition to follow instruc-tions persistence work ethic and other traits likely to contribute independently toonersquos earnings This is the reason we eschew the common label of a test score asldquocognitive skillrdquo but rather use the more descriptive term ldquocognitive performancerdquoEysenck (1994 p 9) a leading student of cognitive testing writes ldquoLow problemsolving in an IQ test is a measure of performance personality may in uenceperformance rather than abstract intellect with measurable effects on the IQ AnIQ test lasts for up to 1 hour or more and considerations of fatigue vigilancearousal etc may very well play a partrdquo Thus some of the explanatory power of the


cognitive measure in predicting earnings does not re ect cognitive skill but ratherother individual attributes contributing to the successful performance of tasks

Genetic and Environmental Inheritance

Although the genetic inheritance of IQ explains little of the intergenerationaltransmission process this says nothing about the possible importance of othergenetically transmitted traits Indeed the remarkable income similarity of identicaltwins compared to fraternal twins suggests that genetic effects may be importantWe will use the similarity of twins to estimate the genetic heritability of income aswell as the environmental component of intergenerational transmission

But two words of caution are in order First as we will demonstrate ourestimates are quite sensitive to variations in unobserved parameters Second it issometimes mistakenly supposed that if the heritability of a trait is substantial thenthe trait cannot be affected much by changing the environment The fallacy of thisview is dramatized by the case of stature The heritability of height estimated fromUS twin samples is substantialmdashabout 090 (Plomin et al 2000) Moreover thereare signi cant height differences among the peoples of the world Dinka men inthe Sudan average 5 feet and 11 inchesmdasha bit taller than Norwegian and USmilitary servicemen and a whopping 8 inches taller than the Hadza hunter-gatherers in southern Africa (Floud Wachter and Gregory 1990) But the fact thatNorwegian recruits in 1761 were shorter than todayrsquos Hadza shows that even quiteheritable traits are sensitive to environments What can be concluded from a nding that a small fraction of the variance of a trait is due to environmentalvariance is that policies to alter the trait through changed environments willrequire nonstandard environments that differ from the environments on which theestimates are based

Consider the case of South Africa where in 1993 (the year before NelsonMandela became president) roughly two-thirds of the intergenerational transmis-sion of earnings was attributable to the fact that fathers and sons are of the samerace and race is a strong predictor of earnings (Hertz 2001) That is adding raceto an equation predicting sonsrsquo earnings reduces the estimated effect of fathersrsquoearnings by over two-thirds Because the traits designated by ldquoracerdquo are highlyheritable and interracial parenting uncommon we thus nd a substantial role ofgenetic inheritance in the intergenerational transmission of economic status Yetit is especially clear in the case of South Africa under apartheid that the economicimportance of the genetic inheritance of physical traits derived from environmen-tal in uences What made the genetic inheritance of skin color and other racialmarkers central to the transmission process were matters of public policy nothuman nature including the very de nition of races racial patterns in marriageand the discrimination suffered by nonwhites Thus the determination of thegenetic component in a transmission process says little by itself about the extent towhich public policy can or should level a playing eld


Estimates of heritability use data on pairs of individuals with varying degrees ofshared genes and environments For example identical and fraternal twins areexposed to similar environments during their upbringing but fraternal twins areless closely related genetically than identical twins Under quite strong simplifyingassumptions (explained in the Appendix) one can exploit the variation in geneticand environmental similarities among pairs of relatives to estimate heritability of atrait such as income years of schooling or other standard economic variablesTaubman (1976) was the rst economist to use this method The model underlyingthe following calculations assumes that genes and environment affect humancapital which produces earnings as the equation below indicates but the effects ofwealth and other contributions to income are unaffected by genes and environ-ment and will be introduced subsequently

Here are the assumptions First genes and environments have additiveeffectsmdash genes and environment may be correlated but the direct effect of ldquogoodgenesrdquo on earnings (its regression coef cient) is independent of the quality of theenvironment and conversely Thus an individualrsquos earnings can be written

earnings 5 h~genes 1 b~environment 1 idiosyncratic effects

Second within-pair genetic differences (for the fraternals) are uncorrelated withwithin-pair environmental differences (for example the good-looking twin doesnot get more loving attention) Third the environments affecting individual de-velopment are as similar for members of fraternal pairs of twins as for the identicaltwins pairs Fourth the earnings genotypes of the two parents are uncorrelated(ldquorandom matingrdquo) Given these assumptions we show in the Appendix that theheritability (h2) of earnings is twice the difference between the earnings correla-tions of identical and fraternal twins As the difference between these two correla-tions is 02 in best data sets availablemdashthe Swedish Twin Registry studied byBjorklund Jantti and Solon (forthcoming) and a smaller US Twinsburg data setstudied by Ashenfelter and Krueger (1994)mdashthese assumptions give an estimate ofh2 equal to 04

Because due to the assumption of random mating the correlation of genes forthe fraternal twins is 05 the implied correlation of fraternal twinsrsquo earningsbecause of genetic factors is h2 2 The fact that the observed correlation of twinsrsquoearnings exceeds this estimate is explained by the fact that twins share similarenvironments Thus once we know h2 we can use information about the degree ofsimilarity of these environments to estimate how large the environmental effectswould have to be to generate the observed earnings correlations

The assumptions concerning random mating and common environments areunrealistic and can be relaxed First we need an estimate of my the correlation ofparentsrsquo earnings genotypes The relevant measure is the earnings potential (thecorrelation of actual earnings would understate the degree of assortation becausemany women do not work full time) The degree of assortation on phenotype islikely to be considerably larger than on genotype for the simple reason that the


basis of the assortation is the phenotype not the genotype (which is unobservable)and the two are not very closely related for the case of earnings as we will seeAssuming that the genotype for potential earnings of parents is half as similar as arethe actual incomes of brothers the correlation would be about 02

Second note that because it was assumed that the environments experiencedby the two identical twins are not on the average more similar to the environmentsof the two fraternal twins the fact that within-twin-pair earnings differences are lessfor the identical twins must be explained entirely by their genetic similarity But ifthe identical twins experience more similar environments (because they lookalike for example) than the fraternals the estimate will overstate the degree ofheritability

It is likely that identical twins share more similar environments than fraternaltwins and other siblings (Loehlin and Nichols 1976 Feldman Otto and Chris-tiansen 2000 Cloninger Rice and Reich 1979 Rao et al 1982) Estimates of theextent to which the environments of identical twins are more similar than those offraternal twins are quite imprecise and we can do no better than to indicate theeffects of using plausible alternative assumptions Just how sensitive the estimatesare to reasonable variations in the assumptions concerning differences in thecorrelations of twinsrsquo environments can be estimated by assuming some degree ofstatistical association of genes and environment with the correlated but not iden-tical genes of the fraternal twins giving them less correlated environments than theidentical twins

Table 1 presents estimates based on various magnitudes of this genes-environment effect As the assumed correlation between genes and environmentincreases the correlation of the environments of the identical twins rises andbecause this then explains some of the earnings similarity of the identical twins theresulting estimate of heritability falls3 We take the third numerical column ofTable 1 as the most reasonable set of estimates On this basis two striking conclu-sions follow First the heritability of earnings appears substantial Second theenvironmental effects are also large The normalized regression coef cient ofenvironment on earnings is be 5 038 which may be compared with the normal-ized regression coef cient for a measure of years of schooling in an earningsequation from our earlier meta-analysis which is 022 Thus while educationalattainment captures important aspects of the relevant environments it is far fromexhaustive

What is the intergenerational correlation of earnings implied by our estimateof be and h To answer this question in addition to h and be we require thecorrelation of parentsrsquo earnings with genes (which is already implied by ourestimates) and the correlation of parentsrsquo earnings with environment The rst

3 The Swedish Twin Registry data set assembled by Bjorklund Jantti and Solon (forthcoming) has datanot just on twins but on many pairs with varying degrees of relatedness (half-siblings for example) andmay allow more robust estimates using the methods developed by Cloninger Rice and Reich (1979)Rao et al (1982) and Feldman Otto and Christiansen (2000)


column in Table 2 gives our estimates The genetic contribution is simply h timesthe correlation between parental earnings and offspring genotype orh2(1 1 m) 2 The environmental contribution similarly is be times a correlationof parentsrsquo earnings and environment (namely 074) selected to yield a totalintergenerational earnings correlation of 04

The estimate that genetic inheritance may account for almost one-third of theintergenerational correlation is somewhat unexpected in light of our negative ndings concerning the inheritance of IQ The surprising importance of bothenvironment and genes point to a puzzle If the genetic contribution is not stronglyrelated to IQ and if the environmental contribution is much larger than thecontribution of years of schooling what are the mechanisms accounting for per-sistence of income over the generations We shall return to this puzzle but will turnto data other than twins studies rst to show that the same puzzle arises

Human Capital

Because schooling attainment is persistent across generations and has clearlinks to skills and perhaps other traits that are rewarded in labor markets anaccount of the transmission of intergenerational status based on human capital hasstrong prima facie plausibility The data already introduced allow a calculation ofthe portion of the intergenerational income correlation accounted for by the factthat offspring of high-income parents get more schooling (measured in years) Thisis the correlation of parent income and offspring schooling (about 045) multipliedby the normalized regression coef cient of schooling in an earnings equation (022from our meta-analysis) or 010 This correlation is substantial particularly in thelight of the fact that it is restricted to the effects of years of schooling operatingindependently of IQ (because our estimate of 022 is from earnings functions in

Table 1Estimating the Heritability of Earnings

Assumed Correlation of Genes and Environment 000 050 070 080Heritability of Earnings (h2) 050 029 019 013Normalized Regression Coef cient

Genes on Earnings (h) 071 054 044 036Environment on Earnings (b) 029 033 038 044

Correlation of EnvironmentsFraternal Twins 070 070 070 070Identical Twins 070 080 090 097

Notes The association of genes with environment is represented by the normalized regression coef cientof genes on environment This table assumes that parental earnings-determining genes are correlated02 and the correlation of fraternal twinsrsquo environment is 07 We use the correlations of income foridentical twins of 056 and of fraternal twins of 036 taken from the US Twinsburg Study and assumethat these are also the correlations of earnings


which the regressors include the AFQT test or a similar instrument) The fullcontribution including the effect of schooling on IQ and its effect on earnings aswell as the direct effect of schooling on earnings holding constant IQ is 012

It used to be commonly assumed that once adequate measures of schoolingquality were developed the only effects of parental economic status on offspringearnings would operate through effects on cognitive functioning and schoolingwith the direct effect of parental status on offspring earnings vanishing But even asthe measurement of school quality has improved over the years the estimateddirect effect of parental incomes (or earnings) on offspring earnings has turnedout to be remarkably robust For example Mulligan (1999) using early 1990s datafrom the (US) National Longitudinal Study of Youth rst estimated the effect ofa change in the logarithm of parental earnings on offspringrsquos logarithm of earningswithout controlling for any other factors and then controlled for a number ofmeasures of school quality as well as the AFQT and standard educational anddemographic variables He found that between two- fths and one-half of the gross(unconditional) statistical relationship of parental and offspring earnings remainseven after controlling for the other factors These results just reaf rm the black boxpuzzle using entirely different data and methods more than two- fths of theintergenerational transmission coef cient is unaccounted for4

Taking account of the fact that the children of the well-to-do are muchhealthier than poor children (Case Lubotsky and Paxson 2001) along with the factthat poor health has substantial effects on incomes later in life (Smith 1999) wouldprobably account for a substantial part of the intergenerational transmission pro-cess The role of health in the process is particularly striking because parentalincomes appear to have strong impacts on child health that are not accounted forby either the health status of the parents nor by the genetic similarity betweenparents and children

4 It is also true that we can typically statistically account for less than half of the variance of the earningsor income using the conventional variables described above But this fact does not explain our limitedsuccess in accounting for the intergenerational correlation as this correlation measures only that partof the variation of earnings that we can explain statistically by parental economic status

Table 2Contribution of Environmental Genetic and Wealth Effects to IntergenerationalTransmission

Earnings Income

Environmental 028 020Genetic 012 009Wealth 012Intergenerational correlation 040 041

Notes The income column and the estimated contribution of wealth are discussed below The environ-mental versus genetic breakdown assumes the gures in the third numerical column in Table 1


Wealth Effects

Economic success can be passed on in a family through the inheritance ofwealth as well as inter vivos wealth transfers to children Remarkably little scholarlyattention has been given to this mechanism in part because no representativepanel data set with adequate measures of other earnings determinants exists forwhich the second generation has reached the age at which the inheritance ofwealth typically has been completed The only study of which we are aware thataddresses this problem by following the second generation to their deaths estimatesa much higher intergenerational wealth correlation than those reported by Mulli-gan above (Menchik 1979) But while inheritances of wealth clearly matter for thetop of the income distribution we doubt whether such transfers play an importantrole for most families Very few individuals receive inheritances of signi cantmagnitude Mulligan (1997) estimates that estates passing on suf cient wealth to besubject to inheritance tax in the United States constituted between 2 and 4 percentof deaths over the years 1960ndash1995 Even though this gure leaves out some quitesubstantial inheritances as well as transfers that occur during life it seems unlikelythat for most of the population a substantial degree of economic status is transmit-ted directly by the intergenerational transfer of property or nancial wealth

It thus seems likely that the intergenerational persistence of wealth re ects atleast in part parent-offspring similarities in traits in uencing wealth accumulationsuch as orientation toward the future sense of personal ef cacy work ethicschooling attainment and risk taking Some of these traits covary with the level ofwealth for example less well-off people may be more likely to be risk averse todiscount the future and have a low sense of ef cacy Because of this correlation ofwealth with the traits conducive to wealth accumulation parent-offspring similarityin wealth may arise from sources independent of any bequests or transfers

Whatever their source for families with signi cant income from wealthparent-offspring wealth similarities can contribute a substantial fraction to theintergenerational persistence of incomes Using the same decomposition methodsas above this contribution is the correlation of parent income and child wealthtimes the normalized regression coef cient of wealth in an income equation Weuse data from the Panel Study of Income Dynamics analyzed by Charles and Hurst(2002) The correlation between parent income and child wealth (both in naturallogarithms) in this data set is 024 The average age of the children is only 37 yearsso this correlation does not capture inheritance of wealth at death of the parentsTo get a rough idea of the normalized regression coef cient one way to proceedis by starting with the percentage change in income associated with a 1 percentchange in wealth this elasticity will range from virtually zero (for those with littleor no wealth) to one (for those with no source of income other than wealth) Aplausible mean value (based on average factor income shares) for the US popu-lation is 020 We convert this to a normalized regression coef cient by multiplyingby the ratio of the standard deviation of log wealth to the standard deviation of logincome also from the PSID data set provided by Charles and Hurst (2002) This


calculation suggests that the fact that higher income parents have wealthier chil-dren contributes 012 to the intergenerational correlation of incomes

This gure while substantial may be an underestimate as it is based on datathat for the reasons mentioned above do not capture a key transmission processnamely inheritance of wealth upon the death of onersquos parents Moreover theestimate should be adjusted upward to take account of the fact that those withgreater wealth tend to have higher average returns to their wealth (BardhanBowles and Gintis 2000 Yitzhaki 1987) Greater parental or own wealth may alsoraise the rate of return to schooling and other human investments but we have noway of taking account of this empirically For a sample of very rich parents thecontribution of wealth to the intergenerational correlation would be much higherof course For a sample of families with very limited wealth the contribution wouldbe nearly zero The difference in the contribution of wealth effects across theincome distribution is a re ection of the heterogeneous nature of the transmissionprocess mentioned earlier Because of the very skewed distribution of wealth thefamily with the mean level of wealth (to which our estimates apply) is considerablywealthier than the median family

Group Membership and Personality

Thus far we have followed the production function approach which under-pins most economic approaches to intergenerational transmission seeking todetermine the contribution of parent-child similarity in ownership of factors ofproduction We have complemented the usual choice-based approach by includingthe in uence of genetic inheritance But other traits are persistent across genera-tions and are arguably as importantmdashfor example race rst language number ofchildren number of siblings and others For example obesity is a predictor of lowearnings for women while height predicts high earnings for men Good lookspredict high earnings for both men and women the latter independently ofwhether they hold jobs interacting with the public (Hammermesh and Biddle1993) Bowles Gintis and Osborne (2002) provide a survey of empirical evidenceconcerning these and many other nonskill determinants of economic success

Two such variables illustrate the potential importance of nonskill factors inthe intergenerational transmission of economic status group membership andpersonality

Suppose that economic success is in uenced not only by a personrsquos traits butalso by characteristics of the group of individuals with whom the person typicallyinteracts Groups may differ in a variety of dimensions average level of schoolingeconomic success cognitive functioning and wealth level Groups may be residen-tial neighborhoods ethnic or racial groups linguistic groups citizens of a nation orany other set of individuals who typically interact with one another Group effectson economic success are well documented and may arise for a number of reasonsincluding discrimination conformist effects on behavior differential access to


information and complementarities in production (Cooper Durlauf and Johnson1994 Durlauf 2001 Borjas 1995)

Race apparently plays a signi cant role in the intergenerational transmissionof economic success This is suggested by the fact that for the United States thecorrelation among brothersrsquo earnings estimated by Bjorklund et al (2002) namely043 falls by 010 when the sample is restricted to whites Apparently what brothersalmost always have in common namely race accounts for much of their similarityof income The same is true of parents and their children In the data set under-lying Figure 1 the elasticity of offspring family income with respect to parentsrsquofamily income is 054 but the same elasticity for whites only is 043 and for blacksonly is 041 (Hertz 2002) Parent-offspring similarity in income is explained inimportant measure by the fact that ldquoracerdquo is transmitted across generations UsingHertzrsquos estimates we nd that race (that is the correlation of parents income withoffspring race) contributes 007 to the intergenerational correlation While thisestimate is a bit lower that those suggested by the above data it may nonetheless bean overestimate as it is based on an income equation with the standard regressorsbut without a measure of cognitive performance the inclusion of which wouldprobably lower the race coef cient somewhat

A second example of traits not found in a conventional production functionbut that contribute to intergenerational status transmission are dispositions such asa sense of personal ef cacy work ethic or a rate of time discount (present orien-tation) The importance of these aspects of personality stems from the fact that ina large class of exchanges including the hiring of labor borrowing and lending orthe exchange of goods of uncertain quality it is impossible to specify all relevantaspects of the exchange in a contract enforceable by the courts Where this is thecase the actual terms of the exchange are in uenced by the degree of trusthonesty hard work and other dispositions of the parties to the exchange Forexample a very present-oriented employee will not value the employerrsquos promise ofcontinued employment in the future conditional on hard work now Instead suchan employee will require a higher wage to motivate hard work in the present andtherefore is less likely to be employed As another example fatalistic workers whobelieve that the probability of job termination is unaffected by their own actions willbe costly to motivate under this type of labor contract (Bowles Gintis and Osborne2002) The empirical importance of these traits is suggested in a number of studies(Duncan and Dunifon 1998 Heckman and Rubinstein 2001 Kuhn and Wein-berger 2001 Heckman forthcoming)

Osborne (forthcoming) has studied the economic importance and intergen-erational persistence of fatalism as measured by the Rotter Scale a commonmeasure of the degree to which individuals believe that important events in theirlives are caused by external events rather than by their own actions Her study of asample of US men and their parents found that the score on the Rotter Scalemeasured before entry to the labor market has a statistically signi cant and largein uence on earnings Moreover the Rotter score is persistent from parents tooffspring The normalized in uence of the Rotter Scale on earnings in Osbornersquos


study is somewhat larger (in absolute value namely 202) than the average in u-ence of IQ in our meta-analysis of 65 studies discussed earlier The estimatedcorrelation of parental income with child fatalism is 2014 The contribution of thefatalism channel to the intergenerational correlation is the correlation of parentincome to child fatalism multiplied by the correlation from child fatalism tosubsequent income 0028mdashthat is (202)(2014)

Osborne (forthcoming) also studied a sample of women in England and foundthat measures of social maladjustment taken at age eleven (the Bristol SocialAdjustment Scale) such as aggression and withdrawal are strong predictors ofearnings at age 33 The normalized in uence of personality traits of aggression andwithdrawal on earnings is considerably larger than the in uence of IQ There areno measures of intergenerational persistence of personality traits in the OsbornersquosEnglish data set but other studies suggest that parent-child similarity in measuresof social maladjustment may be quite high For example Duncan et al (forthcom-ing) found that deviant forms of behaviors of US mothers were strong predictorsof the same behaviors in daughters including drug use violent behaviors early sexsuspension from school and criminal convictions Osbornersquos work thus suggeststhat the intergenerational transmission of personality traits (whether genetic orcultural) may be an important channel explaining the intergenerational persis-tence of income

We know relatively little about the workings of the intergenerational transmis-sion process for personality traits relevant to economic success other than cognitivefunctioning However Kohnrsquos (1969) study of child rearing values of parentssuggests that at least for some traits parentsrsquo experiences in the workplace aregeneralized and passed on to children Kohn categorizes his parent sample by thedegree of self-determination that each experiences on the job ranging from thosewho are relatively unsupervised to those who are closely directed by superiors Kohnfound that parents with high levels of what he termed ldquooccupational self-directionrdquoemphasize curiosity self-control happiness and independence as values for theirchildren Those who are closely monitored by supervisors at work emphasizeconformity to external authority Kohn concluded ldquoWhether consciously or notparents tend to impart to their children the lessons derived from their own socialclass and thus help prepare their children for a similar class positionrdquo The work byOsborne suggests that the degree of self-direction has signi cant effects on earn-ings later in life Other work by Yeung Hill and Duncan (2000) shows that parentalbehavior including church attendance membership in social organizations andsuch precautionary behavior as seat belt usage have signi cant impacts on theirchildrenrsquos earnings

Conclusion

Recent evidence points to a much higher level of intergenerational transmis-sion of economic position than was previously thought to be the case America may


still be the land of opportunity by some measures but parental income and wealthare strong predictors of the likely economic status of the next generation

Our main objective has been to assess the extent of intergenerationaltransmission and the mechanisms accounting for it Table 3 summarizes ourbest estimates of the relative importance of the main causal channels we havebeen able to identify The only entry not previously explained is the rst whichis an estimate of the correlation between parental income and child IQ multi-plied by our estimate of the normalized effect of IQ on earnings conditionedon among other things years of schooling The estimates for IQ schooling andpersonality in the income column are simply those in the earnings columnadjusted to take account of the effect of earnings differences on incomedifferences suitably normalized as described in Bowles and Gintis (2001) Thuswe do not take account of the way that these earnings determinants may affectthe rate of return to onersquos wealth By contrast we assume that the race effect isof the same magnitude in determining the returns to both human capital andconventional wealth (if the race effect on incomes worked solely via an effect onearnings its contribution to the intergenerational earnings correlation wouldbe signi cantly greater)

While the estimates in Table 3 are quite imprecise the qualitative results arenot likely to be affected by reasonable alternative methods The results are some-what surprising wealth race and schooling are important to the inheritance ofeconomic status but IQ is not a major contributor and as we have seen above thegenetic transmission of IQ is even less important

A policymaker seeking to level the playing eld might use these results todesign interventions that would loosen the connection between the economicsuccess of parents and the economic prospects of their children But does a levelplaying eld entail no correlation between parental and child incomes (Swiftforthcoming) There are important values of family life and privacy that would be

Table 3The Main Causal Channels of Intergenerational Status Transmission in the US

Channel Earnings Income

IQ conditioned on schooling 005 004Schooling conditioned on IQ 010 007Wealth 012Personality (fatalism) 003 002Race 007 007Total Intergenerational

Correlation Accounted For 025 032

Notes For each channel the entry is the correlation of parent income with the indicated predictor ofoffspring income multiplied by its normalized regression coef cient in an earnings or income equationThe total is the intergenerational correlation resulting from these channels in the absence of a directeffect of parentsrsquo status on offspring statusSource Calculations described in text and Bowles and Gintis (2001)


compromised by any serious attempt to disconnect the fortunes of parents andchildren completely Rather than pursuing an abstract (and to our minds unattrac-tive) objective of zero intergenerational correlation a better approach might be toask which mechanisms of intergenerational transmission seem unfair and to directpolicies accordingly The role of race in transmitting status from generation togeneration is clearly unfair Many people regard the strong correlation betweenparental income and child health as morally suspect and many feel the same wayabout high levels of wealth inheritance Large majorities favor policies to compen-sate for inherited disabilities Other mechanisms of persistencemdashthe genetic in-heritance of good looks for examplemdashstrike most people as unobjectionable andnot an appropriate target for compensatory policy interventions Even if someconsensus could be formed on which of these mechanisms are morally suspect thepolicy implications would be far from clear For example the possible incentiveeffects on parental behaviors of reduced parental in uence on child success wouldhave to be estimated and considered

AppendixDecomposing Correlation Coef cients and Estimating Heritability

Suppose parental earnings yp directly affects offspring earnings y but offspringearnings is also affected by two variables v1 and v2 that are correlated withparental earnings5 Then if rypv1

and rypv2are the correlations of parental earnings

with v1 and v2 respectively and if the normalized regression coef cients of yp v1 and v2 predicting y are given by bypy

bv1 yand bv2 y

respectively we have

(1) r ypy 5 bypy 1 r ypv 1bv 1y 1 rypv 2

bv 2 y

This is the correlation between parental and offspring earnings decomposed intoits direct effect (the rst term) the effect via variable v1 (the second term) and theeffect via variable v2 (the third term) To derive this equation we write

(2) y 5 byp yyp 1 bv 1 yv1 1 bv 2 yv2 1 laquoy

where all variables are normalized to have zero mean and unit variance and laquoy isuncorrelated with the independent variables Then substituting the above expres-sion for y into the expectation E[ ypy] and noting that if two variables (eg y andyp) have zero mean and unit variance the correlation between these variables is theexpected value of their product we get

5 For previous treatments of this material see Rao Morton and Yee (1976) Cloninger Rice and Reich(1979) Rao et al (1982) and Otto Feldman and Christiansen (1994)


(3) ryp p 5 E yp y 5 E yp yp byp y 1 E v1 ybv 1 y 1 E v2 ybv 2 y

Since given our normalization E[ ypyp] 5 1 E[v1 y] 5 rv1y and E[v2 y] 5 rv2 y

we arrive at equation 16

We now apply this method to estimating heritability using data on similarity ofidentical and fraternal twins A more general treatment using pairs of varyingdegrees of relatedness is developed in Feldman Otto and Christiansen (2000)Suppose a family has two sons whose earnings y1 and y2 depend additively on theirgenotypes g1 and g2 and their environments e1 and e2 Thus

(4) y i 5 beei 1 hgi 1 laquoyi for i 5 1 2

where laquoyiis uncorrelated with the independent variables in the model and is chosen

such that the variance of yi is unity The variances of ei and g i are also normalizedto unity Note that the normalized regression coef cient of genotype is then h thesquare root of the heritability of earnings We assume the environment e i of brotheri depends both on his genotype gi and the common family environment E We thushave

(5) e i 5 bEE 1 bgeg i 1 laquoeifor i 5 1 2

where laquoeiis uncorrelated with the independent variables in the model and is chosen

such that the variance of ei is unity We interpret E as including the effect ofparental earnings education and any other environmental factor that affectsoffspring earnings and is shared by brothers For simplicity we include the fulleffect of genes on environment in the coef cient bge so gi is uncorrelated with EFinally the genotype g i of brother i is determined by the genotypes of the parentsgiven by

(6) g i 5 bggf 1 bggm

where g f and gm are the genotypes of father and mother and bg is the normalizedregression coef cient (path) of fatherrsquos (or motherrsquos) genotype predicting sonrsquosgenotype The structure of this model is illustrated in Figure 3

To show that bg is 12 suppose my is the correlation of maternal and paternalgenes Since we are assuming additivity (meaning that the total effect of thegenome is the sum of the effects of each gene) we can derive bg for a single locusWe label each possible gene at this locus with the amount x it contributes toearnings We normalized x so that E[x] 5 0 and E[ x2] 5 2 By basic genetics a son

6 Note that the same argument holds if we replace the expectations which refer to population valueswith the sample means variances and covariances In this case the statistical independence of the errorterms and the independent variables is assured by construction whereas on the population level thisindependence is assumed


inherits one copy of the gene at the locus from each parent say xf from the fatherand xm from the mother The value of genes at this locus for a son is then ( xf 1xm) 2 assuming that both genes have equal expected effect on economic successwhich we do here and throughout7 In addition to xf the father has another genewith value zf at this locus with the same mean 0 and variance 2 The correspondingvalue for the father is then ( xf 1 zf) 2 where x f and zf are uncorrelated Thecorresponding value for the mother is ( xm 1 zm) 2 where zm is the motherrsquos othergene at this locus and xm and zm are uncorrelated Because of assortative matingeach gene of the father x f zf is correlated my with each gene of the mother xm zmThe variance of the parentsrsquo genetic value at this locus is E[( xm 1 zm)24] 5E[( xf 1 zf)

24] 5 1 and the covariance of father and son is E[( xf 1 zf)( xf 1xm)4] 5 (1 1 my) 2 Therefore the correlation of fatherrsquos and sonrsquos geneticvalue at this locus is the quotient of the previous two expressions or

(7) rg f g i5 bge 1 bgemy 5

12

1my

2

The rst term in this expression represents the direct path from fatherrsquos genometo sonrsquos and the second is the correlation of fatherrsquos and motherrsquos genetic value atthe locus my multiplied by the direct path from mother to son at that locus To seethis recall that the least squares estimator of b1 in the regression equation

7 The actual value of a pair of genes at a locus can be higher or lower than their average value of courseas when one gene is dominant or recessive

Figure 3The Earnings of Brothers

Notes In this diagram gf and gm are the genotypes of father and mother g1 and g2 are the genotypesof brothers E is the common environment of brothers e1 and e2 are the total environment ofbrothers and y1 and y2 are the earnings of brothers Here my is the genetic relatedness of parentsbased on assortative mating and as explained below bg 5 1 2 while h2 is the heritability ofearnings The path labeled bge represents the tendency of genes to affect the environments (bge 0means that identical twins experience more similar environments than fraternal twins)


y 5 b1x1 1 b2x2 1 laquo where x1 x2 and y are normalized to mean zero and varianceunity and where laquo is uncorrelated with x1 and x2 is given by (Goldberger 1991)

(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2

In our case b1 5 bg rx1 y5 rx2 y

5 (1 1 my) 2 and rx1x 25 my Substituting in the

above expression we get bg 5 1 2To determine the correlation of fraternal twinsrsquo genotypes we multiply the

right sides of (6) for i 5 1 2 and take expectations giving

r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2

which consulting (7) con rms the standard result in genetics that fathers and sonson the one hand and nonidentical brothers with the same parents on the other areequally related To determine the correlation of environments of fraternal twins wemultiply the right sides of (5) for i 5 1 2 and take expectations giving

r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2

Finally multiplying the right sides of (4) for i 5 1 2 and taking expectations we get

r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE

2 1 ~1 1 my bge2 2 1 h2~1 1 my2 1 ~1 1 my bebgeh

In the case of identical twins the same gure is relevant but now the correlationof genotypes of brothers is rg1 g2

id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE

2 1 bge2 1 h2 1 2bebgeh


In the text we assume r e1e2

id 5 09 for identical twins (although our results are notvery sensitive to this assumption) so be 5 =09 2 bg

2 The two equations for thecorrelations of brother earnings (8) and (9) together with the observed values ofthese correlations allow us to determine h and be for various values of bg

Equations (8) and (9) imply that the difference between the correlations ofearnings of identical and fraternal twins is given by

(10) r y1 y 2

id 2 r y1 y 2

fr 5 ~1 2 my~h 1 bebge 22

Note that assuming greater assortative mating raises the estimate of h2 whileassuming a stronger tendency for genes to effect environment (raising bge) has theopposite effect as one would expect In the literature it is often assumed that my 5

0 and bge 5 0 in which case we get the standard equation for estimatingheritability

(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr

If this is the case we can estimate h2 directly from this equation and then use thisestimate of h2 together with (8) to estimate be

y We would like to thank Jere Behrman Anders Bjorklund Kerwin Ko CharlesBradford De Long Williams Dickens Marcus Feldman James Heckman Tom HertzErik Hurst Arjun Jayadev Christopher Jencks Alan Krueger John Loehlin CaseyMulligan Suresh Naidu Robert Plomin Cecelia Rouse Michael Waldman and ElisabethWood for their contributions to this paper Bridget Longridge and Bae Smith for researchassistance and the John D and Catherine T MacArthur Foundation for nancialsupport

References

Arrow Kenneth Samuel Bowles and StevenDurlauf 1999 Meritocracy and Economic Inequal-ity Princeton NJ Princeton University Press

Ashenfelter Orley and Alan Krueger 1994ldquoEstimates of the Economic Return to School-ing from a New Sample of Twinsrdquo AmericanEconomic Review December 845 pp 1157ndash172

Atkinson A B A K Maynard and C G

Trinder 1983 Parents and Children Incomes inTwo Generations London Heinemann

Bardhan Pranab Samuel Bowles and HerbertGintis 2000 ldquoWealth Inequality Credit Con-straints and Economic Performancerdquo in Hand-book of Income Distribution Anthony Atkinson andFrancois Bourguignon eds Dortrecht North-Holland pp 541ndash604

Becker Gary S 1988 ldquoFamily Economics and


Macro Behaviorrdquo American Economic ReviewMarch 781 pp 1ndash13

Becker Gary S and Nigel Tomes 1986ldquoHuman Capital and the Rise and Fall of Fam-iliesrdquo Journal of Labor Economics July 43 ppS1ndash39

Bjorklund Anders Markus Jantti and GarySolon Forthcoming ldquoIn uences of Nature andNurture on Earnings An Early Progress Reporton a Study of Various Sibling Types in Swedenrdquoin Unequal Chances Family Background and Eco-nomic Success Samuel Bowles Herbert Gintis andMelissa Osborne eds New York Russell SageFoundation

Bjorklund Anders et al 2002 ldquoBrother Cor-relations in Earnings in Denmark Finland Nor-way and Sweden Compared to the UnitedStatesrdquo Journal of Population Economics Forth-coming

Blalock Hubert 1964 Causal Inferences in Non-experimental Research Chapel Hill NC Univer-sity of North Carolina Press

Blau Peter and Otis Dudley Duncan 1967The American Occupational Structure New YorkWiley

Borjas George 1995 ldquoEthnicity Neighbor-hoods and Human Capital Exernalitiesrdquo Ameri-can Economic Review June 853 pp 365ndash90

Bouchard T J Jr and M McGue 1981 ldquoFa-milial Studies of Intelligencerdquo Science 212 4498pp 1055ndash059

Bowles Samuel 1972 ldquoSchooling and In-equality from Generation to Generationrdquo Jour-nal of Political Economy MayJune 803 ppS219ndash51

Bowles Samuel and Herbert Gintis 2001ldquoThe Inheritance of Economic Status Educa-tion Class and Geneticsrdquo in International Encyclo-pedia of the Social and Behavioral Sciences GeneticsBehavior and Society Volume 6 Marcus Feldmanand Paul Baltes eds New York Oxford Univer-sity Press and Elsevier pp 4132ndash141

Bowles Samuel and Valerie Nelson 1974ldquoThe lsquoInheritance of IQrsquo and the Intergenera-tional Reproduction of Economic InequalityrdquoReview of Economics and Statistics February 561pp 39ndash51

Bowles Samuel Herbert Gintis and MelissaOsborne 2002 ldquoThe Determinants of IndividualEarnings Skills Preferences and SchoolingrdquoJournal of Economic Literature December 394pp 1137ndash176

Bowles Samuel Herbert Gintis and MelissaOsborne eds Forthcoming Unequal ChancesFamily Background and Economic Success NewYork Russell Sage Foundation

Case Anne Darren Lubotsky and Christina

Paxson 2001 ldquoEconomic Status and Health inChildhood The Origins of the Gradientrdquo NBERWorking Paper No W8344 June

Charles Kerwin Ko and Erik Hurst 2002ldquoThe Correlation of Wealth Across Genera-tionsrdquo University of Chicago Working Paper

Cloninger C Robert John Rice and Theo-dore Reich 1979 ldquoMultifactorial Inheritancewith Cultural Transmission and Assortative Mat-ing II A General Model of Combined Polygenicand Cultural Inheritancerdquo American Journal ofHuman Genetics 2931 pp 176ndash98

Cooper Suzanne Steven Durlauf and PaulJohnson 1994 ldquoOn the Evolution of EconomicStatus across Generationsrdquo American Economic Re-view 842 pp 50ndash58

Corak Miles and Andrew Heisz 1999 ldquoTheIntergenerational Earnings and Income Mobil-ity of Canadian Men Evidence from the Longi-tudinal Income Tax Datardquo Journal of Human Re-sources 343 pp 505ndash33

Devlin Bernie Michael Daniels and KathrynRoeder 1997 ldquoThe Heritability of IQrdquo NatureJuly 31 388 pp 468ndash71

Duncan Greg J and Rachel Dunifon 1998ldquolsquoSoft-Skillsrsquo and Long-Run Market Successrdquo Re-search in Labor Economics 17 pp 123ndash50

Duncan Greg et al Forthcoming ldquoThe Ap-ple Does Not Fall Far from the Treerdquo in Un-equal Chances Family Background and EconomicSuccess Samuel Bowles Herbert Gintis andMelissa Osborne eds New York Russell SageFoundation

Durlauf Stephen 2001 ldquoA Framework forthe Study of Individual Behavior and SocialInteractionsrdquo Sociological Methodology 311 pp47ndash 87

Erikson R and J H Goldthorpe 1992 TheConstant Flux A Study of Class Mobility in the In-dustrial Societies Oxford Oxford UniversityPress

Eysenck H J 1994 ldquoIntelligence andIntroversion-Extraversionrdquo in Personality and In-telligence Robert J Sternberg and Patricia Ruzgiseds Cambridge Cambridge University Presspp 3ndash31

Feldman Marcus W Sarah P Otto andFreddy B Christiansen 2000 ldquoGenes Cultureand Inequalityrdquo in Meritocracy and Economic In-equality Kenneth Arrow Samuel Bowles andSteven Durlauf eds Princeton NJ PrincetonUniversity Press pp 61ndash85

Floud Roderick Kenneth Wachter and An-nabel Gregory 1990 Height Health and His-tory Nutritional Status in the United Kingdom1750ndash1980 Cambridge Cambridge UniversityPress


Fong Christina 2001 ldquoSocial PreferencesSelf-Interest and the Demand for Redistribu-tionrdquo Journal of Public Economics 822 pp 225ndash46

Fong Christina Samuel Bowles and HerbertGintis 2002 ldquoReciprocity and the WelfareStaterdquo in Handbook on the Economics of GivingReciprocity and Altruism Jean Mercier-YthierSerge Kolm and Louis-Andre G9rard-Varet edsAmsterdam Elsevier Forthcoming

Goldberger Arthur S 1989 ldquoEconomic andMechanical Models of Intergenerational Trans-missionrdquo American Economic Review June 793pp 504ndash13

Goldberger Arthur S 1991 A Course in Econo-metrics Cambridge Mass Harvard UniversityPress

Hammermesh Daniel S and Jeff E Biddle1993 ldquoBeauty and the Labor Marketsrdquo NBERWorking Paper 4518 November

Heckman James Forthcoming The GEDHeckman James and Yona Rubinstein 2001

ldquoThe Importance of Noncognitive Skills Lessonsfrom the GED Testing Programrdquo American Eco-nomic Review May 912 pp 145ndash49

Hertz Thomas 2001 ldquoEducation Inequalityand Economic Mobility in South Africardquo Un-published PhD Dissertation University of Mas-sachusetts

Hertz Thomas 2002 ldquoIntergenerationalEconomic Mobility of Black and White Fami-lies in the United Statesrdquo Paper presented atthe Society of Labor Economists Annual Meet-ing May

Kohn Melvin 1969 Class and ConformityHomewood Ill Dorsey Press

Kuhn Peter and Catherine Weinberger 2001ldquoLeadership Skills and Wagesrdquo Institute for So-cial Behavioral and Economic Research De-cember

Loehlin John and Robert Nichols 1976 He-redity Environment and Personality Austin TexasUniversity of Texas Press

Mazumder Bhashkar Forthcoming ldquoEarn-ings Mobility in the US A New Look at In-tergenerational Inequalityrdquo in Unequal Chanc-es Family Background and Economic SuccessSamuel Bowles Herbert Gintis and MelissaOsborne eds New York Russell Sage Founda-tion

Menchik Paul 1979 ldquoInter-GenerationalTransmission of Inequality An Empirical Studyof Wealth Mobilityrdquo Economica November 46184 pp 349ndash62

Mulligan Casey 1997 Parental Priorities andEconomic Inequality Chicago University of Chi-cago Press

Mulligan Casey 1999 ldquoGalton vs the HumanCapital Approach to Inheritancerdquo Journal of Po-litical Economy December Part 2 1076 ppS184ndash224

Osborne Melissa A Forthcoming ldquoPersonal-ity and the Intergenerational Transmission ofEconomic Statusrdquo in Unequal Chances FamilyBackground and Economic Success Samuel BowlesHerbert Gintis and Melissa Osborne eds NewYork Russell Sage Foundation

Otto Sarah P Marcus W Feldman andFreddy B Christiansen 1994 ldquoGenetic and Cul-tural Transmission of Continuous TraitsrdquoStanford University Morrisson Institute Work-ing Paper No 64

Plomin Robert 1999 ldquoGenetic and GeneralCognitive Abilityrdquo Nature December 4022 ppc25ndashc29

Plomin Robert et al 2000 Behavioral GeneticsNew York W H Freeman and Company

Rao D C N E Morton and S Yee 1976ldquoResolution of Cultural and Biological Inheri-tance by Path Analysisrdquo American Journal of Hu-man Genetics 28 pp 228ndash42

Rao D C et al 1982 ldquoPath Analysis UnderGeneralized Assortative Mating II AmericanIQrdquo Genetical Research 39 187ndash98

Smith James 1999 ldquoHealthy Bodies andThick Wallets The Dual Relation betweenHealth and Economic Statusrdquo Journal of EconomicPerspectives Spring 132 pp 145ndash66

Solon Gary R 1992 ldquoIntergenerational In-come Mobility in the United Statesrdquo AmericanEconomic Review June 823 pp 393ndash408

Solon Gary R 1999 ldquoIntergenerational Mo-bility in the Labor Marketrdquo in Handbook of LaborEconomics Volume 3A Orley Ashenfelter andDavid Card eds Amsterdam North-Hollandpp 1761ndash800

Sternberg Robert J et al 1995 ldquoTesting Com-mon Senserdquo American Psychologist November 5011 pp 912ndash27

Swift Adam Forthcoming ldquoJustice Luckand Family Values The IntergenerationalTransmission of Economic Status from a Nor-mative Perspectiverdquo in Unequal Chances FamilyBackground and Economic Success SamuelBowles Herbert Gintis and Melissa Osborneeds New York Russell Sage Foundation

Taubman Paul 1976 ldquoThe Determinants ofEarnings Genetic Family and Other Environ-ments A Study of White Male Twinsrdquo AmericanEconomic Review December 665 pp 858ndash70

Thorndike Edward L 1919 ldquoIntelligence andIts Usesrdquo Harperrsquos Monthly Magazine DecemberJanuary 140 pp 227ndash35


Williams Wendy M and Robert J Sternberg1995 Success Acts for Managers Florida HarcourtBrace

Winship Christopher and Sanders Korenman1999 ldquoEconomic Success and the Evolution ofSchooling with Mental Abilityrdquo in Earning andLearning How Schools Matter Susan Mayer andPaul Peterson eds Washington DC BrookingsInstitution pp 49 ndash78

Yeung Jean Martha Hill and Greg Duncan

2000 ldquoPutting Fathers Back in the Picture Pa-rental Activities and Childrenrsquos Adult Attain-mentsrdquo Marriage and Family Review Part I 292ndash3 pp 97ndash113

Yitzhaki Shlomo 1987 ldquoThe Relation Be-tween Return and Incomerdquo Quarterly Journal ofEconomics February 1021 pp 77ndash95

Zimmerman David J 1992 ldquoRegression To-ward Mediocrity in Economic Staturerdquo AmericanEconomic Review June 823 pp 409ndash29


mechanisms amenable to public policies in a way that would make the attainment ofeconomic success more fair These are the questions we will try to answer

No one doubts that the children of well-off parents generally receive more andbetter schooling and bene t from material cultural and genetic inheritances Butuntil recently the consensus among economists has been that in the United Statessuccess is largely won or lost in every generation Early research on the statisticalrelationship between parentsrsquo and their childrenrsquos economic status after becomingadults starting with Blau and Duncan (1967) found only a weak connection andthus seemed to con rm that the United States was indeed the ldquoland of opportu-nityrdquo For example the simple correlations between parentsrsquo and sonsrsquo income orearnings (or their logarithms) in the United States reported by Becker and Tomes(1986) averaged 015 leading the authors to conclude ldquoAside from families vic-timized by discrimination [a]lmost all earnings advantages and disadvantages ofancestors are wiped out in three generationsrdquo Becker (1988) expressed a widelyheld consensus when in his presidential address to the American EconomicsAssociation he concluded (p 10) ldquo[L]ow earnings as well as high earnings are notstrongly transmitted from fathers to sonsrdquo

But more recent research shows that the estimates of high levels of intergen-erational mobility were artifacts of two types of measurement error mistakes inreporting income particularly when individuals were asked to recall the income oftheir parents and transitory components in current income uncorrelated withunderlying permanent income (Bowles 1972 Bowles and Nelson 1974 AtkinsonMaynard and Trinder 1983 Solon 1992 1999 Zimmerman 1992) The highnoise-to-signal-ratio in the incomes of both generations depressed the intergenera-tional correlation When corrected the intergenerational correlations for eco-nomic status appear to be substantial many of them three times the average of theUS studies surveyed by Becker and Tomes (1986)

The higher consensus estimates of the intergenerational transmission ofeconomic success has stimulated empirical research The relevant facts onwhich most researchers now agree include the following brothersrsquo incomes aremuch more similar than those of randomly chosen males of the same race andsimilar age differences the incomes of identical twins are much more similarthan fraternal twins or non-twin brothers the children of well-off parents obtainmore and higher quality schooling and wealth inheritance makes an importantcontribution to the wealth owned by the offspring of the very rich On the basisof these and other empirical regularities it seems safe to conclude that theintergenerational transmission of economic status is accounted for by a heter-ogeneous collection of mechanisms including the genetic and cultural trans-mission of cognitive skills and noncognitive personality traits in demand byemployers the inheritance of wealth and income-enhancing group member-ships such as race and the superior education and health status enjoyed by thechildren of higher status families

However the transmission of economic success across generations remainssomething of a black box We nd that the combined inheritance processes














ry 5 by

syp

sy

































~h2~1 1 m2~02662 5 035~1 1 mh2






























Human Capital













Earnings Income




Wealth Effects




















Conclusion


















bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References





















































































ry 5 by

syp

sy

































~h2~1 1 m2~02662 5 035~1 1 mh2






























Human Capital













Earnings Income




Wealth Effects




















Conclusion


















bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References





































































































~h2~1 1 m2~02662 5 035~1 1 mh2






























Human Capital













Earnings Income




Wealth Effects




















Conclusion


















bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References




































































































Human Capital













Earnings Income




Wealth Effects




















Conclusion


















bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References














































































Earnings Income




Wealth Effects




















Conclusion


















bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References









































































Wealth Effects




















Conclusion


















bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References
























































































Conclusion


















bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References
























































































bv1 yand bv2 y



bv 2 y
























12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References



























































































12

1my

2







(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References










































































(8) b1 5rx1y 2 rx1x 2

rx 2y

1 2 rx1x 2





r g1 g2

fr 5 E g1g2 5 ~122E g f2 1 ~122E gm

2 1 2~122E gmgf

5 ~122 ~2 1 2my 5 ~1 1 my2


r e1 e2

fr 5 bE2 1 r g1 g 2

fr bge2 5 bE

2 1 ~1 1 mybge2 2


r y1 y 2

fr 5 be2r e1 e 2

fr 1 h2r g1 g 2

fr 1 2behrg1g 2bge

which expands to

(8) r y1 y 2

fr 5 be2~bE



id 5 1 We then

r e1 e 2

id 5 bE2 1 r g1 g 2

id be2 5 bE

2 1 bge2

and

r y1y 2

id 5 be2r e1e 2

id 1 h2r g1 g 2

id 1 behr e1 g 2

id 1 behr e 2 g1

id

which becomes

(9) r y1 y 2

id 5 bE2~bE







(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References













































































(10) r y1 y 2

id 2 r y1 y 2




(11) h2 5 2~r y1 y 2

id 2 r y1 y 2

fr



References









































































the inheritance of inequality - thomas pikettypiketty.pse.ens.fr/files/bowlesgintisjep2002.pdf ·...

Documents