Equality of opportunity and the distribution oflong-run income among Swedish men and

women

Karin Hederos Eriksson 1 Markus Jäntti2 Lena Lindahl3

Draft – not for quotationApril 8, 2013

1Stockholm School of Economics2Swedish Institute for Social Research (SOFI), Stockholm University3Swedish Institute for Social Research (SOFI), Stockholm University

Abstract

In this paper we explore equality of opportunity in long-run incomes for Swedishmen and women. We decompose inequality into two parts; one that is due to dif-ferences in circumstances (e.g. gender, IQ and parental income) and one thatstems from differences in effort. The key idea is that a society has achieved equal-ity of opportunity if all income inequality can be attributed to differences in effort.We find that most of the variation in long-run incomes in Sweden can be accountedfor by differences in effort. When analyzing the male and female samples sepa-rately we find that IQ, non-cognitive abilities, parental income, parental educationand variations in the distribution of effort between groups of individuals who havethe same circumstances are important determinants of inequality of opportunity.When we pool the male and female samples gender explains up to one-fifth ofinequality in long-run incomes. This means that gender is the most importantcontributor to inequality of opportunity in long-run incomes in Sweden.

Keywords: Equality of opportunity, income distribution, gender, register data

1 IntroductionA large interest in economic inequality has generated a number of empirical ap-proaches to measuring its level and distribution in different parts of the world.Even though the economics literature has centered around outcome inequality, inrecent years there has been an upsurge of interest in opportunity inequality (seefor example Almås et al., 2011; Björklund, Jäntti, and Roemer, 2012; Checchiand Peragine, 2010; Ferreira and Gignoux, 2011). The equality of opportunity lit-erature leans on the basic idea that individual outcomes depend on circumstancesthat are beyond a person’s control (such as standard of living when growing upand parental education) as well as individual effort. The core argument is thatinequality stemming from differences in effort is ethically defensible by a percep-tion of fairness, while inequality due to circumstances is not. Since the amountof effort that an individual provides may partly depend on her circumstances, asociety is said to have achieved equality of opportunity if circumstances do nothave any influence on outcomes, neither directly nor through effort.

A general distinction in the literature is made between ex ante and ex postperspectives on equality of opportunity. According to the ex ante perspective, asociety offers equal economic opportunities if all individuals, regardless of theircircumstances, have the same income prospects. This perspective is typically con-nected to responsibility or reward principles defined for groups with identical cir-cumstances (Fleurbaey and Peragine, 2013).

The ex post perspective, on the other hand, stipulates that there is equality ofopportunity if all individuals who provide the same degree of effort have the sameincome. Here the compensation principle is rather to reduce inequality betweenindividuals who show the same level of effort, but face different circumstances.Fleurbaey and Peragine (2013) show that the ex post and ex ante versions of thecompensation principles are in fact incompatible.

Methodologically, Ramos and Van de gaer (2012) summarize the empirical ap-proaches in the literature into three groups: studies comparing standard inequalitymeasures, studies using direct measures that calculate the inequality when all dif-ferences due to effort are removed and finally studies using indirect measures thatcompare inequality in an actual income distribution to that in a counterfactual onewhithout inequality of opportunity.

Sorting under the third category, Björklund, Jäntti, and Roemer (2012) esti-mate lower bounds on the inequality of opportunity in Sweden by partitioningSwedish men into a number of different types, depending on parental incomeand education, family structure, body mass index, and own IQ measured at age

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18. They find that, depending on the inequality index, roughly one third of theinequality in long-run income among Swedish men can be attributed to these ob-served circumstances.

In much of the literature on equality of opportunity, one obvious circumstance,namely gender, is ignored. Clearly, if concern is with inequality within the overallpopulation, analyses of men and women separately can be highly misleading. ForSweden, Björklund, Jäntti, and Roemer (2012) analyze only men because they usemilitary enlistment test data to measure IQ.

We complement existing studies by providing a systematic analysis of genderand ex ante equality of opportunity in long-run incomes. Sweden is an interest-ing case where the average gender wage gap is relatively small in an internationalcomparison (Blau and Kahn, 2003), while there is evidence of a strong glass ceil-ing effect at the top of the income distribution (Albrecht, Björklund, and Vroman,2003). We thus address the question of to what extent the fairly high level ofgender equality in labor market outcomes translates into gender equality in labormarket opportunities. Björklund, Jäntti, and Roemer (2012) find that the two mostimportant factors for inequality of opportunity in long-run incomes for Swedishmen are parental income and IQ. We investigate whether inequality of opportu-nity for Swedish women can be attributed to the same circumstances and, moreimportantly, how important gender is in comparison to other circumstances for ex-plaining inequality of opportunity in the overall population. We also contribute tothe literature by including non-cognitive abilities in the vector of circumstances.

We account for gender using two different approaches. First, we estimatethe levels and shares of equality of opportunity for men and women separately,in order to assess whether it is the same in the male and the female population.Using this approach we also observe if the same circumstances are important inexplaining inequality of opportunity in the two populations.

The second approach is to pool the male and female samples and include gen-der in the vector of circumstances. This analysis gives us an estimate of the levelof inequality of opportunity in the overall population and it addresses the questionof too what extent inequality of opportunity can be attributed by gender. It alsoallows us to compare the importance of gender to that of the other circumstances.

In the empirical analyses, we use the same basic data as Björklund, Jäntti,and Roemer (2012), but in order to include women and still use military enlist-ment data, we approximate women’s IQ and non-cognitive ability by those of theirbrothers.

We find that depending on which inequality measure we use the circumstancesjointly explain between 16 and 40 percent of the estimated level of inequality in

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the male sample. This means that between 16 and 40 percent of inequality in out-comes can be attributed to inequality of opportunity. When estimating inequalityof opportunity for women using their brothers’ IQ and non-cognitive abilities asproxies for their own, we find that the share of inequality in outcomes that isaccounted for by circumstances ranges from 5 to 19 percent.

The most important circumstances for both men and women are IQ, non-cognitive abilities, parental income, parental education and variations in the distri-bution of effort between groups of individuals who have the same circumstances.When we pool the male and female samples and include gender in the vector ofcircumstances gender explains up to one-fifth of inequality in long-run incomes.This result implies that gender is the most importantant contributor to inequalityof opportunity in long-run incomes in Sweden.

2 Literature reviewEquality of opportunity literature Most previous studies in the empirical liter-ature on economic equality of opportunity are based on data that do not allow foran analysis of gender differences. There are however a few groups of exceptionswhich we summarize below (we focus only on papers in which income is the out-come measure and consequently we leave out papers on equality of opportunityin education or health).

Using German and US data, Niehues and Peichl (2011) report results both formen and women separately and for pooled samples (including gender as one ofthe circumstances). They propose a new estimator of ex ante inequality of oppor-tunity based on a fixed effects panel model and argue that this estimator shouldbe considered an upper bound on the contribution of circumstances to income in-equality. Results from this estimation are contrasted by lower bound estimateson the share of ex ante inequality due to circumstances. When computing thelower bound estimates Niehues and Peichl (2011) include gender, height at birth,year of birth, dummies indicating place of birth, race (only for the US), degree ofurbanization of the place where the individual was born, father’s occupation andfather’s education in the vector of circumstances.

The data they use come from the German Socio-Economic Panel Study (SOEP)and from the Panel Study of Income Dynamics (PSID). As outcome measures theyuse annual and permanent labor earnings expressed in both gross and net terms.To compute the lower bound estimates Niehues and Peichl (2011) follow Bour-guignon, Ferreira, and Menéndez (2007) and Ferreira and Gignoux (2011) who

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both use a parametric estimation procedure. To estimate the upper bound on in-equality of opportunity Niehues and Peichl (2011) run fixed effects estimations ofthe earnings equations using panel data. Log earnings are regressed on the observ-able effort variables allowing for individual specific effects. The intuition is thatthe individual specific effects capture all (observable and unobservable) circum-stances. As these individual specific effects may also comprise time-constant-effort variables, the unit effects provide an upper bound on the importance ofcircumstances for inequality. The individual specific effects are used as circum-stances in a reduced-form cross-sectional earnings equation. Niehues and Peichl(2011) predict earnings using the coefficients from this equation and the levelsand shares of inequality of opportunity are computed from these distributions. Asinequality measure Niehues and Peichl (2011) use the mean logarithmic deviationas inequality measure.

The main finding is that for both Germany and the US, there are large androbust differences between the upper and the lower bound estimates of inequalityof opportunity. This result holds for both gross and net earnings and annual andpermanent earnings. The authors suggest that the existing lower bound estimatesunderestimate the true level of inequality of opportunity, which in turn may resultin too low levels of redistribution.

Regarding the importance of gender Niehues and Peichl (2011) find that whenestimating the lower bound estimates of inequality of opportunity separately formen and women both the level and the share of inequality of opportunity is lowerthan when the male and female samples are pooled and gender is included asa circumstance. This is true both for Germany and for the US, for annual andpermanent incomes, and for gross and for net incomes. Niehues and Peichl (2011)conclude that this result indicates that gender is an important driving force ofinequality of opportunity and argue that most of the effect of gender on inequalityof opportunity is due to the fact that women are more likely to work fewer hours.

Niehues and Peichl (2011) do not comment on whether men and women sufferfrom equal degrees of inequality of opportunity, but the results they present inTable 4 allow for such an analysis. For both countries most lower bound estimatesof inequality of opportunity are higher for men than for women. This is true bothfor levels and shares of inequality of opportunity. For the upper bound estimatesof inequality of opportunity there seems to be a gender difference in opportunityinequality in the opposite direction.

Finally, Niehues and Peichl (2011) do not analyze whether there are genderdifferences in the importance of the different circumstances included in the com-putation of the lower bound estimates, and no such conlusions can be drawn from

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the results presented in the paper.Checchi and Peragine (2010), Bourguignon, Ferreira, and Menéndez (2003)

and Nilsson (2005) estimate equality of opportunity separately for men and women.Using data from the Survey on Income and Wealth of Italian Households (SHIW),Checchi and Peragine (2010) measure circumstances by the highest obtained edu-cation of the parents. The individuals’ relative position in the earnings distributionconditional on parental education is used as a measure of effort. Individuals arecategorized into ten different tranches according to their relative position in theearnings distribution. To analyze ex post inequality of opportunity, the authorsremove inequality between tranches by proportionally scaling the tranches so thateach of them has the same mean income as the mean income in the entire popu-lation. All remaining inequality then stems from inequality within tranches. Thescaled distribution is used to compute the levels and shares of ex post inequalityof opportunity. To analyze ex ante inequality of opportunity Checchi and Peragine(2010) remove inequality within types by replacing the income in each cell by themean income in the type to which the cell corresponds. The new distribution isconsequently used to compute the levels and shares of ex ante inequality of op-portunity. The authors find that 15 percent of income inequality (measured by themean logarithmic deviation) can be attributed to inequality of opportunity mea-sured in this way. The corresponding figure is 20 percent when they use the expost approach to equality of opportunity.

Checchi and Peragine (2010) do not comment on gender differences in levelsor shares of inequality of opportunity. However, the results they present in Tables4 and 5 provide us with some information on this topic. Their results seem tosuggest that circumstances are more important for men than for women. However,the differences are small and, while we do not have standard errors for the overallimportance of circumstances, the t-ratios for men and women would need to bevery large – back of the envelope calculations suggest 12-20 – for the differencesbetween them to be statistically significant.

Bourguignon, Ferreira, and Menéndez (2003) analyze ex ante inequality ofopportunity in Brazil using the 1996 wave of the Brazilian household surveyPesquisa Nacional por Amostragem a Domicilio (PNAD). They use parental ed-ucation, father’s occupation, race and region of origin as circumstance variables,and schooling, schooling squared and migration as effort variables. First, theauthors estimate separate earnings equations for men and women of log earn-ings on all circumstance and effort variables. To capture the indirect effect ofcircumstances on earnings through effort, they also estimate separate equationsfor men and women of schooling on the circumstances. Using the estimates of

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the coefficients from these regressions they compute what would be the earningsdistributions were all the circumstances equalized. To analyze the direct effectof circumstances on individual earnings, they equalize circumstances only in theearnings equations. To see both the direct effect on earnings and the indirect effectthrough effort they equalize circumstances in both the earnings equation and in theschooling equation. To get an estimate of the degree of inequality of opportunitythey compare the Gini and Theil coefficients in the hypothetical distributions tothe corresponding coefficients for the actual distributions. The authors concludethat when cirumstances are equalized the Gini for individual earnings decreaseswith 8-10 percentage points for both men and women.They do, however, not men-tion whether there is a gender difference in the shares of total income inequalitythat can be attributed to inequality of opportunity (and it is difficult to draw anyconclusions about this by looking at the graphs in which the results are presented).

Regarding gender differences in the importance of particular circumstances,the authors show that parental education plays the largest role for both genders.They conclude that to equalize opportunities in Brazil, the most effective measurewould be to reduce the importance of parental education for child schooling andearnings, and that this is particularly true for women.

Nilsson (2005) analyzes inequality of opportunity in incomes for Swedish menand women born in 1965. Nilsson (2005) uses data from several registers fromStatistics Sweden and he employs two different measures of income; average la-bor income 1994-1999 and average disposable income from the same years. Ascircumstances he includes a wide range of parental characteristics (e.g. parentalincome and age) and family characteristics (e.g. number of siblings). In contrastto the other papers summarized in this section Nilsson (2005) does not base theanalysis of inequality of opportunity on inequality measures.To test whether Swe-den has achieved equality of opportunity Nilsson (2005) estimates OLS regres-sions of income on the circumstances. He concludes that since the circumstancesinfluence income, equality of opportunity does not exist. Nilsson (2005) also es-timates indirect opportunity sets. In the first part of this analysis he finds thatindividuals whose parents belong to the 25th percentile in the income distributionmust exert more effort to reach the average labor income than individuals whoseparents belong to the 75th percentile in the income distribution. In the second partof the analysis Nilsson (2005) finds that when indivdual effort is held constant atthe 50th percentile, then individuals whose parents belong to the 75th percentilehave a higher average labor income than individuals whose parents belong to the25th income percentile.

Nilsson (2005) does not focus on gender differences, but since he performs

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separate analyses on men and women his results may give us some indicationson gender differences in equality of opportunity in Sweden. In the section onindirect opportunity sets he tests whether the opportunity set of labor incomesfor individuals whose parents belong to the 75th income percentile is differentfrom that of individuals whose parents belong to the 25th percentile. The nullhypothesis of equal distributions can be rejected for men but not for women. As togender differences in the importance of particular circumstances, Nilsson (2005)concludes from the OLS regressions that whether the mother is divorced, whetherthe mother received social assistance and whether the individual was living witha social parent at the age of 20 is more important for women’s than for men’sdisposable incomes.

Ferreira and Gignoux (2011) and de Barros et al. (2009) analyze equality ofopportunity pooling the male and female samples and including gender in the vec-tor of circumstances. Ferreira and Gignoux (2011) develop a scalar measure of thelower bound on ex ante inequality of opportunity and use it to analyze inequalityof opportunity in Brazil, Colombia, Ecuador, Guatemala, Panama and Peru. Foreach country they use data from one wave of a nationally representative survey.1.As outcome measures, Ferreira and Gignoux (2011) use household income percapita, household consumption expenditures per capita (not available for Brazil)and individual labor earnings. The circumstance vector includes ethnicity, father’soccupation, father’s education, mother’s education, birth region and gender (gen-der is included as circumstance only when individual labor earnings is used asoutcome measure).

Ferreira and Gignoux (2011) report levels and shares of inequality of oppor-tunity as well as partial shares of inequality of opportunity for specific circum-stances. The levels and shares of inequality of opportunity are estimated usingboth the non-parametric ex-ante approach of Checchi and Peragine (2010) andusing a version of the parametric ex ante approach in Bourguignon, Ferreira, andMenéndez (2007). The partial shares are estimated using the parametric approachby constructing counterfactual distributions in which only one circumstance isequalized across individuals at a time.

Using the non-parametric approach Ferreira and Gignoux (2011) find that theshare of total inequality (measured by the mean logarithmic deviation) in house-

1The Brazilian Pesquisa Nacional por Amostra de Domicilios (PNAD) 1996, the ColombiaEncuesta de Calidad de Vida (ECV) 2003, the Ecuadorian Encuesta Condiciones de Vida (ECV)2006, the Guatemalan Encuesta Nacional sobre Condiciones de Vida (ENCOVI) 2000, the Pana-manian Encuesta Niveles de Vida (ENV) 2003 and the Peruvian Encuesta Nacional de Hogares(ENAHO) 2001)

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hold income per capita that can be accounted for by opportunity inequality rangesfrom 25 percent for Colombia to 36 percent for Guatemala. Controlling for all theother circumstance variables, gender accounts for between 0.2 percent (Colom-bia) and 5.8 percent (Guatemala) of total inequality in individual labor earnings.These results suggest that gender is much less important than family backgroundvariables such as parental education and father’s occupation in accounting for in-equality of opportunity in individual labor earnings. To put the importance ofgender into perspective, it can be compared to that of mother’s education whichaccounts for between 9.4 percent (for Panama) and 11.9 percent (for Brazil) oftotal inequality in individual labor earnings.

Ferreira and Gignoux (2011) also point out that including gender in the cir-cumstance vector does not seem to affect neither the shares of inequality of op-portunity nor the importance of family background variables in accounting forinequality of opportunity in any substantial manner. Note however that Ferreiraand Gignoux (2011) do not include any interaction effects between gender andthe other circumstance variables. That is, they do not allow the share of totalinequality that is accounted for by family background variables such as parentaleducation and father’s occupation to differ between men and women.

In the book Measuring Inequality of Opportunities in Latin America and theCaribbean de Barros et al. (2009) provide a comprehensive review of inequal-ity of opportunity in Latin America. In one of their chapters they analyze eco-nomic inequality of opportunity in Brazil, Colombia, Ecuador, Guatemala, Mex-ico, Panama and Peru.2 In contrast to Ferreira and Gignoux (2008) and Ferreiraand Gignoux (2011), de Barros et al. (2009) include Mexican data from the 2002wave of the Mexican Encuesta Nacional sobre Niveles de Vida de los Hogares(MxFLS) in the analysis. Using a non-parametric approach on the Mexican data,the share of total inequality accounted for by opportunity inequality amounts to 21percent for household income per capita, 27 percent for household consumptionper capita and 23 percent for individual labor earnings. Turning to the importanceof gender, de Barros et al. (2009) find that in Mexico gender accounts for 3-4percent of overall inequality in individual labor earnings. In comparison to theimportance of the family background variables, gender thus plays a small role inexplaining opportunity inequality in individual labor earnings.

Almås et al. (2011), Devooght (2008), Almås (2008) and Checchi, Peragine,and Serlenga (2010) also pool the male and female samples and include gender in

2This chapter is based on Ferreira and Gignoux (2008) which is the working paper version ofFerreira and Gignoux (2011).

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the vector of circumstances. However, in these studies it is not reported to whatextent gender accounts for the observed level of inequality of opportunity.

3 DataIn order to examine the role of circumstances and effort on the distribution oflong-run income, we must define the data and variables that allow such an anal-ysis. Thus, we start with a sample of Swedish men and women who have beenlinked to their parents, with rich data on the incomes, education and other socio-economic characteristics of both generations. The key concept is that of circum-stance. Circumstances are captured by partitioning the population (and sample)into discrete types, each of which has a particular set of circumstantial backgroundcharacteristics. The key idea is that an individual should not be held accountablefor outcomes that vary because of type.

Samples and source registers In order to achieve our goals, we exploit a com-bination of Swedish administrative register data sets. A first and basic source isStatistics Sweden’s so-called Multi-generational register. This is a register of allpersons who were born 1932 and onward, and who have ever received a uniquenational registration number from 1961 and onward.3 For the Swedish popula-tion defined in this way, the register contains information about biological (andadoptive) parents and their national registration number. From this information,one can also infer which individuals are related as siblings; full siblings are thosewho have the same father and mother, half siblings are those who only have oneparent in common. Our analysis sample is a 35 percent random sample of theSwedish population born 1955-67 defined in this register. We also use the Multi-generational register to identify parents and siblings.

The second source is the set of bidecennial censuses conducted from 1960to 1980. We can identify our main sample of offspring in the households ofthese censuses as well as other persons in the household. Thus we can deter-mine whether our offspring generation lived with their biological parents or not inthe fall of these census years.

The third source is Statistics Sweden’s income register, which in turn comesfrom the Swedish tax assessment procedure. A limitation is that such data are

3The requirement that the persons must have been registered in Sweden from 1961 and onwardimplies that persons who died between 1932 and 1960 are not included. For our purposes, however,this is not a problem since we want to observe outcomes in the 1990s and 2000s.

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available only from 1968 onwards. From that year the income register providesdata on total income from all sources of income, from work, self employment,capital, real estate as well as some transfers (from 1974 onward). We use suchincome data for both parents and children. The earlier data for parents stem fromtheir own compulsory tax assessments. In later years, when we measure children’sincomes, the source of the data is compulsory reports by employers to the taxauthorities.

The fourth source is the Swedish Military Enlistment Battery, which providesa measure of intellectual capacity. As military service in Sweden only appliesto men, these data are only available for men. The purpose of these tests is toclassify Swedish men to different military positions with different demands ongeneral intellectual capacity. For the cohorts who now are adults, military servicewas compulsory in Sweden with only few exceptions. Generally, the tests weredone during the year when men turned 18 years of age. The Enlistment Batterycontained four cognitive tests: instructions, synonyms, metal folding and technicalcomprehension. The subtests were designed to measure the primary IQ factorsInduction, Verbal Comprehension, Spatial Ability and Technical Comprehensionrespectively. We use a summary measure of intellectual ability based on the fourtests provided by the military organization that runs the tests.4 The EnlistmentBattery also provides measures of height and weight, which we use to calculatethe body mass index, BMI.

Military enlistment tests provide our data on cognitive (IQ) and non-cognitive(NC) ability. Only men had national service in Sweden, so these measures areunavailable for women. We measure the cognitive and non-cognitive skills ofwomen using the information for their brothers as proxies for their own. In themain analysis, we only use men and women who have at least one brother forwhom the enlistment data are available, and measure the abilities of both men andwomen by those of their brothers.

To construct our analysis sample, we make use of the fact that all four datasources contain the unique Swedish national registration number, by means ofwhich we can merge the information from the four sources.

Variables As our outcome variable for children we use a measure of total marketincome before taxes provided by Statistics Sweden. It includes income from allsources, that is, labor, business, capital, realized capital gains as well as some

4Mårdberg and Carlstedt (1998) and Carlstedt (2000) provide more information on the cogni-tive tests we use. See also Björklund, Eriksson, and Jäntti (2010) for additional information.

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taxable social transfers such as unemployment insurance, sickness pay, parentalleave payment, and pensions. We use the average of real total income over theyears when sons and daughters were 32-38 years of age. At these ages, we arelikely to get a good estimate of long-run income (see Böhlmark and Lindquist,2006). Further, averaging over as long a period as seven years is likely to eliminatemost transitory income variation that is not relevant for our purposes.

Our 6 background characteristics are

1. parental income quartile group (4 groups)

2. parental education group (3 groups)

3. family structure/type (2 groups)

4. number of siblings (3 groups)

5. IQ quartile groups (4 groups)

6. Non-cognitive skill quartile groups (4 groups)

the combination of which gives us T = 1152 types.For parental income we apply the same income concept as for sons and daugh-

ters. We use a multi-year average of the sum of the two biological parents’ in-comes during the years when the child was 13-17 years old. We treat an incomeobservation of SEK 100 or lower (in 2005 prices) as missing, so the over-time av-erage is only taken for non-zero income. This measure we divide into four quartilegroups of equal size.

To measure parental education, we make use of the fact that the 1970 censusmade special effort to collect information about education. We use the educationallevel of the biological parent who has the highest educational level according theinformation in the census. This level in turn, we split into three groups: onlycompulsory school, more than compulsory school but no college, and at leastsome college.

We also use the censuses to construct a family type indicator. This is equal toone if the child lived with both biological parents during its first three censuses inlife. For example, for the cohort born in 1955 this implies that we require that thechild lived with both biological parents in the 1960, 1965, and 1970 censuses. Ifthis condition is not fulfilled, the indicator takes on the value zero.

We use data from the Multi-generational register to compute the number offull biological siblings. We split the observations into three groups: 0, 1-2 or 3+siblings.

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For IQ, we split the summary measure of intellectual ability from the MilitaryEnlistment Battery into four quartile groups The use of own IQ as a circumstance,as opposed to effort, is potentially controversial, for several reasons. First, cogni-tive test scores at age 18 are very likely affected by educational choices up to thatage. Moreover, to some extent such choices, and performance within the choseneducational path, reflect effort on the part of the young individual making them.However, the key here is the following. We define as a circumstance factors thataffect socio-economic outcomes, but for which we do not hold the individual re-sponsible. Your actions and effort prior to the age of 18, even if they in part reflectyour ambitions and motivations, are not something we would hold you responsiblefor.

Our measure of non-cognitive skills (NC) is based on a structured interviewconducted during military enlistment by a psychologist charged with rating a per-son’s suitability for military service (for detailed discussion of this variable, seeLindqvist and Vestman, 2011).

The definitions imply that we need to make some sample restrictions. Wefocus on persons born in Sweden, as the information on the parents of foreign-born inhabitants can be quite sketchy and unreliable. We also only include personsfor whom both the biological mother and biological father are non-missing in theMultigeneration register.

To measure IQ and NC for women, we use the characteristics of their brothers.This means that we need to limit our main analysis samples to persons who haveat least one brother with non-missing information on both IQ and NC. Thus, wehave eliminated singletons from our main samples. In cases a person has morethan one brother, we take the average across all brothers as the measures of IQand NC.

4 MethodsThe approach we take is originally based on Keane and Roemer (2009), Betts andRoemer (2007) and Lee (2008), and follows very closely Björklund, Jäntti, andRoemer (2012). We are interested in what fraction of the inequality of long-runincome, Y , which has distribution FY , can be attributable to circumstances andwhat can be attributable to effort. Circumstances are captured by partitioning thepopulation (and sample) into discrete types, each of which has a particular setof circumstantial background characteristics. The key idea is that an individualshould not be held accountable for outcomes that vary because of type.

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Denote each of the J background characteristics by X j, which can take K j spe-cific values (see Section 3). Each type t consists of a particular cell or collectionof value t ∈ T , where the set T consists of elements Xt = (X1 = xt

1,X2 = xt2,X3 =

xt3,X4 = xt

4,X5 = xt5,X6 = xt

6,X7 = xt7). The type of a particular sample member is

Xti.

We now outline a version that takes effort to be the deviation of long-run in-come from the expected income of a person of type t, E[Y |Xt ] from actual incomeof that person. We measure effort by the residual of a regression of lnY on Xt :5

lnY ti =µ+

∑t

Ind[i is of type t]βt + εti⇔

lnY ti =µ+

∑j

X′jiβ j + εti,

(1)

where the second row uses the more conventional notation with each separatecharacteristic being a set of dummy variables. The two formulations are inter-changeable, but the latter is what we actually use in regressions.

We next measure the role of each circumstance, and of effort, by a Shapley-value decomposition of the inequality index I(FY ). The above implementationtakes the “raw” residual from an empirically estimated version of equation (1) asa measure of effort.

The problem with this is that the distribution of εti may vary across types, that

is, it can be heterogeneous. Each type is characterized by an expected/averageincome, captured in equation (1) as the deviation of that type’s income from theoverall average (i.e., E[lnY |Xt ] = µ+ Ind[i is of type t]βt . Each type may in ad-dition be characterized by a different distribution of effort εt , F t

ε . As a personshould not be held accountable for her circumstances (captured by type), and F t

ε

is a consequence of being of type t, variations in ε and therefore realized incomeY that are attributable to differences in F t

ε are also part of what a person can notbe held accountable for.

The solution to this in Betts and Roemer (2007) is to measure effort by being ata particular quantile p in the distribution of effort among type t, and standardizethe distribution of effort to be the same across all types. That solution is notavailable to us in this accounting exercise. In this paper, we follow Björklund,Jäntti, and Roemer (2012) and correct for the distribution of effort as follows.

5Note that we regress the natural logarithm of long-run income rather than its level on X as thisis conventional in earnings regressions. Results using the level rather than the natural logarithmare similar to those we report here.

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The heterogeneity takes the form of heteroscedasticity. That is, each type t hasits own variance σ2

t = Var[εt |Xt ]. We address this by adding and subtracting to theregression equation a residual term that has a homogenous variance. The mostnatural candidate for standardizing the distribution across types is to choose theoverall variance, which, since the expectation of the residual is zero in all groups isgiven by the weighted average of the variance within types as σ2 =

∑t ftσ2

t . Thisallows us to distinguish between a residual whose variance varies across types,and one that does not. It is this latter residual that we associate with individualeffort. Thus, we add one more background characteristic, namely the effect oftype on the variation of effort to our list of characteristics. Thus, we work with aregression equation of the form

lnY ti = µ+

∑j

X′jiβ j + εti

= µ+∑

j

X′jiβ j + εti− ε

ti/kσt︸ ︷︷ ︸

ui

+εti/kσt︸ ︷︷ ︸

ui

= µ+∑

j

X′jiβ j + ε̃ti +ui,

(2)

where k = (1/∑

t ftσ2t )−1/2 = 1/σ. Thus, ui has variance 1/k2 = σ2 across all

types. This separates between standardized effort ui that is measured in terms of acommon distribution, and that part of effort ε̃t

i = εti−ui that captures the influence

of type on the conditional variation of income around the expected value for eachtype.

Implementing this is quite straightforward and involves estimating in the firststep all β coefficients and then, based on the OLS residuals the type-specific vari-ances σ2

t . In practice, however, some types have very few observations and/orvery small estimated variances, leading to very large standardized residuals ui.For this reason, in our baseline case, we regress the estimated variances on thebackground characteristics, and use the fitted values from that regression as thebasis for εt

i/kσt . This procedure smooths out the more extreme values.A key difference between this paper and Björklund, Jäntti, and Roemer (2012)

is that we include also women, whose IQ and NC needs to be measured using in-formation for their brothers. For symmetry, we also measure these circumstancesfor men using information from their brothers, and compare the results with thoseobtained using own observations.

The use of proxy measures for IQ and NC has several consequences for ouranalysis. First, we need to restrict our main analysis to only those persons who

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have a brother who is also included in our data and who has taken the militaryenlistment test. Second, we need to make a strong assumption, which is that abrother’s IQ and NC abilities are equally good measures of his sister’s abilities asthey are for a brother. I.e., the measurement error is similar for mixed and same-sex siblings. We will (in a future version) use other data sources to examine theplausibility of that assumption. However, IQ sibling correlations in Bouchard andMcGue (1981) suggest brother-brother and brother-sister correlations in IQ arevery similar, lending plausibility to this hypothesis.

Third, our estimated regression coefficients will suffer from attenuation bias.This bias we will try to correct for (in a future version of this paper) in the esti-mations by using the estimated variance matrix of the ability measures. Finally,our shapley-value decomposition, which makes use of the empirical distributionof circumstances, will also be biased, because we use an error-ridden measure ofcircumstances. This source of error we will also correct for using the estimatedvariance matrix of the errors. Thus, we can adjust both coefficient estimates andthe inequality decomposition, subject to the assumed similarity of brother-brotherand brother-sister associations.

5 ResultsIn this section, we present our main results. We start by discussing the regressionresults that we use to decompose inequality into that due to circumstances and thatdue to effort. In presenting the findings on how much of long-run inequality can besaid to be due to circumstances and effort, respectively, we first examine results formen, measuring IQ and NC by the men’s own and their brothers’ characteristics,respectively. We then proceed to compare the role of particular circumstancesand effort for men and women, measuring in both cases IQ and NC by that ofthe person’s brothers’ characteristics. In the last set of results, we ask examine adifferent question, namely, when we pool men and women and include the samecircumstances as earlier to define type, but add gender to the definition of type,how much of long-run inequality is accounted for by each circumstance, includinggender.

Regression results We present the results from the regressions of long-run in-come on circumstances in Tables A1 and A2. In Table A1 we display the resultsfor men. The difference between the two columns in Table A1 is that we includethe men’s own IQ and NC abilities in the circumstance vector in the left column,

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while we use the IQ and NC abilities of their brothers in the right column. The co-efficients in these regressions have the expected signs and some of them are quitelarge. For instance, the coefficents on parental income type in the left columnindicate that having parents in the highest income group offers a 0.174 log pointincome advantage in comparison to having parents in the lowest income group.As expected, the influence of IQ and NC abilities on long-run incomes is largerwhen using the men’s own characteristics than when letting those of their brothersact as proxies.

In Table A2, we show the regression coefficients for both men (left column)and women (right column) when using their brothers’ IQ and NC abilities as prox-ies for their own. In the left column of Table A1 we thus present the same regres-sion results as in the right column of Table A2. The coeffcients on IQ and NCabilities are smaller for women than for men. This tendency is compatible withtwo different explanations. Either the female coefficients are smaller because IQand NC abilities are less important determinants of women’s than of men’s long-run incomes, and/or the measurement error caused by using their brother’s IQ andNC abilities as proxies for their own is larger for women than for men.

Inequality of opportunity and effort: men and women compared In this sec-tion, we want to compare the importance of circumstances in long-run income in-equality across men and women. We start by comparing results for men using ownand brother characteristics in Table 1. We use four different indices to measureinequality; the Gini coefficient, the mean log deviation (GE(0)), the Theil(1) index(GE(1)) and the squared coefficient of variation (CV2). We show the index valuesfor these measures as well as the corresponding shapley-value decompositions inTables 1 and 2.

In the top panel of Table 1, we display the results obtained when using themen’s own IQ and NC abilities. In this panel, we see that all circumstances, in-cluding type heterogeneity, jointly explain between 16 and 40 percent of the esti-mated level of inequality. In other words, between 16 and 40 percent of inequalityis accounted for by inequality of opportunity. Regardless of which inequalitymeasure we use, the three most important circumstances are IQ, NC abilities andtype heterogeneity. Together these three circumstances account for between 12percent (for GE(0)) and 36 percent (for CV(2)) of the observed level of inequality.Our results are in line with those of Björklund, Jäntti, and Roemer (2012), butwe provide new evidence on the importance of NC abilities before adulthood forinequality of opportunity.

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In the bottom panel, we display the results obtained when using the men’sbrothers’ IQ and NC abilities instead of their own. Doing this the joint contribu-tion of circumstances to inequality decreases slightly (they now explain between12 and 42 percent of the estimated level of inequality). Also, as expected, the rel-ative contributions of IQ and NC abilities decrease substantially (the bottom panelestimates of these contributions are never higher than half the size of the top panelestimates).

In the middle panel of Table 2, we present the index values and the resultsfrom the shapley value decompositions for women. In the female sample, thejoint contribution of all circumstances including type heterogeneity ranges from 5to 19 percent of the estimated level of inequality. Comparing these shares to thoseobtained for men when using the men’s brothers’ IQ and NC abilities instead oftheir own, we see that the joint contribution of circumstances to inequality is sub-stantially larger in the male than in the female sample. This result should howeverbe interpreted with caution since it does not necessarily imply that women ex-perience a lower level of inequality of opportunity than men. It may as well justreflect that the measurement error caused by using brothers’ IQ and NC abilities islarger for women than for men. Another potential explanation is that other circum-stances than those included in this analysis are important for women’s incomes.For women, the three most important contributors to inequality of opportunityamong the circumstances included in this analysis are parental income type, NCabilities and type heterogeneity.

Inequality of opportunity and effort: gender as a circumstance In our finalset analyses, we pool the male and female samples and include gender as oneof the circumstances. We display the results from this exercise in the bottompanel of Table 2. Using this sample the share of inequality that can be attributedto circumstances ranges between 18 and 36 percent depending on the inequalitymeasure. The most striking result when pooling the samples is that among the cir-cumstances, gender is the most important contributor to inequality (except whenCV(2) is used as inequality measure, then type heterogeneity is the most importantcircumstance, followed by gender). Using the Gini coefficient as measure of in-equality, gender explains 18 percent of the inequality in long-run incomes. Theseresults contrast sharply with those obtained by Ferreira and Gignoux (2011) andBarros et al. (2009) who find that in Latin America gender is much less importantfor inequality of opportunity than family background variables such as parentaleducation and father’s occupation.

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Table 1 Contribution of types to overall inequality of long-run average incomefor men – own (Panel A) and brother’s characteristics (Panel B) – heterogeneouseffort controlled using smoothed residual variance

A. Own characteristicsGini GE(0) GE(1) CV2

Index valueineqest 0.256 0.149 0.149 0.703

Relative contributionsParentIncType 6.1 2.9 3.7 4.1ParentEducType 0.6 0.3 0.4 0.5SibType 0.6 0.0 0.0 −0.4FamilyType 1.0 0.2 0.2 0.4IQType 8.1 3.9 4.8 4.7NCType 9.4 4.6 5.7 5.9Type heterogeneity 6.6 3.7 9.1 25.2Residual 67.6 84.3 76.1 59.6

B. Brothers’ characteristicsGini GE(0) GE(1) CV2

Index valueineqest 0.256 0.149 0.149 0.703

Relative contributionsParentIncType 7.6 3.3 4.3 3.9ParentEducType 2.1 1.0 1.4 1.3SibType 0.8 0.0 0.0 −0.7FamilyType 1.3 0.3 0.3 0.9IQTypeB 3.3 1.3 1.7 1.6NCTypeB 4.4 1.7 2.2 2.5Type heterogeneity 6.5 4.0 9.5 32.1Residual 74.1 88.4 80.7 58.5

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Table 2 Contribution of types to overall inequality of long-run average incomeusing brothers’ characteristics – men (Panel A), women (Panel B), and both menand women (Panel C) – heterogeneous effort controlled using smoothed residualvariance

A. MenGini GE(0) GE(1) CV2

Index valueineqest 0.259 0.153 0.151 0.682

Relative contributionsParentIncType 7.4 3.3 4.3 4.8ParentEducType 1.9 0.9 1.2 1.4SibType 0.8 0.0 0.0 −0.3FamilyType 1.6 0.3 0.4 0.6IQTypeB 3.4 1.4 1.8 2.0NCTypeB 4.6 1.8 2.3 2.6Type heterogeneity 5.8 3.2 7.4 17.8Residual 74.4 89.2 82.7 71.2

B. WomenGini GE(0) GE(1) CV2

Index valueineqest 0.234 0.134 0.116 0.565

Relative contributionsParentIncType 6.8 2.3 3.6 6.0ParentEducType 1.8 0.6 1.0 1.3SibType 0.6 0.0 −0.1 −1.1FamilyType 0.8 0.1 0.2 0.7IQTypeB 1.6 0.5 0.8 1.6NCTypeB 2.4 0.7 1.1 2.3Type heterogeneity 5.2 0.8 3.2 5.9Residual 80.8 95.0 90.3 83.4

C. AllGini GE(0) GE(1) CV2

Index valueineqest 0.271 0.162 0.155 0.705

Relative contributionsgender 18.0 10.5 11.6 7.1ParentIncType 5.6 2.5 3.5 4.8ParentEducType 1.4 0.7 1.0 1.3SibType 0.6 0.0 0.0 −0.5FamilyType 1.0 0.2 0.2 0.6IQTypeB 2.0 0.8 1.1 1.7NCTypeB 2.9 1.1 1.5 2.2Type heterogeneity 4.9 2.3 5.8 13.4Residual 63.6 81.9 75.3 69.4

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6 ConclusionsTBA

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Table A 1 Regression results

Men – own IQ and NC Men – brother’s IQ and NC(Intercept) 12.015

(0.004)12.052(0.004)

FamilyType(omitted: 1) 2 0.054(0.006)

0.078(0.005)

IQTypeB(omitted: 1) 2 0.073(0.004)

0.042(0.004)

3 0.107(0.005)

0.059(0.005)

4 0.199(0.005)

0.100(0.005)

NCTypeB(omitted: 1) 2 0.128(0.004)

0.076(0.004)

3 0.172(0.005)

0.103(0.005)

4 0.233(0.005)

0.137(0.005)

ParentEducType(omitted: 1) 2 −0.003(0.004)

0.018(0.004)

3 0.022(0.006)

0.065(0.006)

ParentIncType(omitted: 1) 2 0.064(0.005)

0.071(0.004)

3 0.102(0.005)

0.113(0.005)

4 0.174(0.005)

0.201(0.005)

SibType(omitted: 1) 2 −0.027(0.006)

−0.039(0.005)

3 −0.054(0.007)

−0.079(0.006)

n 148952 172610k 15 15σ 0.617 0.64Adj R2 0.0739 0.0451

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Table A 2 Regression results for diagnostic purposes

Men Women(Intercept) 12.052

(0.004)11.762(0.004)

FamilyType(omitted: 1) 2 0.078(0.005)

0.039(0.006)

IQTypeB(omitted: 1) 2 0.042(0.004)

0.013(0.004)

3 0.059(0.005)

0.020(0.005)

4 0.100(0.005)

0.048(0.005)

NCTypeB(omitted: 1) 2 0.076(0.004)

0.037(0.004)

3 0.103(0.005)

0.050(0.005)

4 0.137(0.005)

0.075(0.005)

ParentEducType(omitted: 1) 2 0.018(0.004)

0.025(0.004)

3 0.065(0.006)

0.054(0.006)

ParentIncType(omitted: 1) 2 0.071(0.004)

0.047(0.005)

3 0.113(0.005)

0.096(0.005)

4 0.201(0.005)

0.166(0.005)

SibType(omitted: 1) 2 −0.039(0.005)

−0.012(0.006)

3 −0.079(0.006)

−0.047(0.006)

n 172610 163475k 15 15σ 0.64 0.638Adj R2 0.0451 0.0227

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