Intergenerational mobility, intergenerational effects, sibling correlations, and equality of opportunity: a comparison of four approaches Markus Jäntti1 (with Anders BjÜrklund) 1
Swedish Institute for Social Research, Stockholm University
Conference on Social Mobility and Inequality in Israel Jerusalem, June 14, 2017
The four approaches
1. Intergenerational mobility (or transmission or persistance), (IGM) 2. Intergenerational effects, (IGEff) 3. Sibling correlations 4. Equality of opportunity, (EOp)
Our goal
Approach 1. Intergenerational mobility (or persistence) 2. Intergenerational effects 3. Sibling correlations 4. Equality of opportunity
Questions
Results
Our motivation 1. Research: 1.1 We want to know how important family background (broadly defined) is for inequality in outcomes that people tend to care about; (long-run) income and education. 1.2 The 4 approaches give very different answers to the question how important family background is. 1.3 The reason for 2 is that the approaches capture quite different mechanisms. By considering all four approaches we also learn about the importance of different mechanisms. 1.4 The four literatures are quite separated and have much to learn from each other.
2. Public policy: Is family background very important, or only somewhat important? Crucial when we evaluate our societies from an egalitarian point of view.
Roadmap
1. Intergenerational mobility: approach and findings 2. Intergenerational effects: approach and findings 3. Sibling correlations: approach and findings. 4. Equality of opportunity: approach and findings 5. Conclusions/synthesis: 5.1 Which family background mechanisms are important and which are not so important? 5.2 What is important to learn more about? 5.3 What can scholars in the four literatures learn from each other?
The presentation is not as comprehensive as it might look
1. We don’t cover structural modelling of, e.g., parental investments. But hopefully, we provide useful input for such modelling approaches. 2. We don’t consider social mobility, i.e., class mobility. We stick to: 2.1 long-run (log) income and earnings 2.2 years of education
3. The gender dimension is treated very poorly! (Which, alas, reflects much of the research!)
Outline
Intergenerational mobility Intergenerational effects Sibling associations Equality of opportunity Summing up
Intergenerational mobility
Meaning: The descriptive association between two (or more) generations.
Main claim: The intergenerational associations are not very strong and imply quite much mobility (except possibly in the very top when capital income is included).
Intergenerational mobility I
The prototypical (Galtonian) model: Y offspring = α + βY parent + e
I
I
IGE: the regression coefficient β measures persistence (when Y are on logarithms, the elasticity) IGC: the (Pearson) correlation coefficient ρ=β
I
σ parent σ offspring
many other measures (see Jäntti and Jenkins, 2015): I I I
(1)
additional terms to pick-up non-linearities rank (Spearman) correlations transition matrices etc
(2)
Cross-national results
I
IGEs: 0.15-0.50 (acc. to Corak’s (2013) version of the Great Gatsby Curve)
I
IGCs: possibly less variation (Corak, Lindquist, and Mazumder, 2013) but there is less comparable information about IGCs.
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Thus: R-squares (IGC2 ) from 0.02-0.25.
Swedish illustration 6-year averages for sons and parents, total income (including capital income); IGE: 0.24 and IGC: 0.16
o o Ran
p ng n ome
o o
lin. slope: 0.216
earnings
Ran
p ng n ome
Income
Some results, years of schooling
Country USA Denmark Finland Norway Sweden UK Netherlands Belgium Italy Source: Hertz et al. (2007)
Regression coefficient .46 .49 .48 .40 .58 .71 .58 .41 .67
Correlation coefficient .46 .30 .33 .35 .40 .30 .36 .40 .40
Main results
I
Income associations are not that strong. Correlations from 0.15 to 0.5 imply R2 of 0.02-0.25. I
I
Scatter plots also reveal a lot of mobility. Except possibly in the very top, when capital income is included.
Education associations are slightly higher 12
Outline
Intergenerational mobility Intergenerational effects Sibling associations Equality of opportunity Summing up
Intergenerational effects
I
Meaning: I
I
I
What are the causal effects of thought interventions that change parents’ income or education? This is something (potentially very) different from descriptive intergenerational mobility patterns
Main claim: I
Intergenerational effects are clearly smaller than IGM-estimates reveal
Intergenerational effects
Prototypical model Y offspring = α + β1 Y father + β2 Y mother + e
(3)
Intergenerational effects Empirical strategies to get causal effect
1. Twin-differences: ∆Y cousins = Îą + ∆Y twin parents + e I
takes some genetics and common environment out
2. Adoptive parents I
- eliminates genetic transmission (if random assignment) >
3. Instrumental Variables (IV; often reforms) I
gives exogenous variation in parental resources
(4)
General pattern in the results
I
Estimates of causal effects in general in the range 0- 60% of the IG-associations.
I
In some contexts, however, the causal income (education) effects might be very large.
Outline
Intergenerational mobility Intergenerational effects Sibling associations Equality of opportunity Summing up
Sibling correlation I
The prototypical model: Yij = ai + bij ,
I I
I
a⊥b
the “family effect” a shared by sibling in family i , variance σa2 the “individual effect” b unique to individual j in family i (orthogonal to a), variance σb2
the population variance of the outcome Y is σ 2 = σa2 + σb2,
I
(5)
(6)
the share of variance attributable to family background (its “R2 ”) is σ2 ρ= 2 a 2 (7) σa + σb which coincides with the Pearson correlation for sibling pairs
A sibling correlation captures more than an intergenerational correlation (IGC)
I
Sibling correlation = IGC2 + other shared factors that are uncorrelated with parental Y
I
An omnibus measure – captures both observed and unobserved family background (and neighborhood) factors
I
Yet it is a lower bound, because siblings don’t share everything from the family background!
Brother correlations in earnings and income
Country Denmark China Finland Germany Norway Sweden USA
Estimate 0.20 0.57 0.26 0.43 0.14 0.32 0.49
Source Schnitzlein (2013) Eriksson and Zhang (2012) Österbacka (2001) Schnitzlein (2013) Björklund et al. (2002) Björklund, Jäntti, and Lindquist (2009) Mazumder (2008)
Sibling correlations in years of schooling
Country Germany Germany Norway Sweden Sweden USA
Sibling type Brothers Sisters Mixed sexes Brothers Sisters Mixed sexes
Estimate .66 .55 .41 .43 .40 .60
Source Schnitzlein (2013) Schnitzlein (2013) Björklund and Salvanes (2011) Björklund and Jäntti (2012) Björklund and Jäntti (2012) Mazumder (2008)
These quite high numbers are only lower bounds. What is missing?
1. Full siblings have only about half of (initial) genes in common. But each individual has 100% of her (initial) genes from the parents. 2. Not all environmental experience and “shocks� are shared, only some. Thus some environmental stuff is missing. 3. Differential treatment by parents. Will not be captured if it creates differences, but is part of family background.
Raising the lower bound: MZ-twins?
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They share all (initial) genes (GOOD)
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They share more environment and more “shocks� (GOOD)
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They might interact more and affect each other in ways that have no counterpart in the general population (BAD) Because of (3), an MZ-correlation might be an upper bound of family background.
Sibling correlations for MZ-twins vs. full siblings: Swedish results
Outcome Earnings Schooling Schooling
Sibling type Brothers Brothers Sisters
Full sibling .22 .44 .40
MZ-twins .73 .75 .73
Raising the lower bound: differential treatment
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Birth order is one candidate: see below.
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Sibling correlation = IGC2 + other shared factors that are uncorrelated with parental Y
Sibling correlations vs. intergenerational correlations, Swedish estimates
Ď Brothers: Earnings Schooling Sisters: Schooling
IGC2 = R2
Other factors
.24 .46
.02 .15
.22 .31
.40
.11
.29
An extension
I
adding one more parent, or higher-order income terms, to the IGM-equation does not change the results very much.
Caution – education and income can move in different ways Source: Björklund, Jäntti, and Lindquist (2009) Baseline Brother corrrelation in schooling Constant return to schooling Control schooling
0.5
0.4
Constant return to schooling
Baseline
0.3
cohort
1962−1968
1959−1965
1956−1962
1953−1959
1950−1956
1947−1953
1944−1950
1941−1947
1938−1944
1935−1941
Control schooling
1932−1938
^ ρ
Brother corrrelation in schooling
Summing up about sibling correlations
1. Sibling correlations reveal a large role for something in the family (or the neighborhood). Unobserved factors, not captured by IGM-estimates, must be quite important. 2. Candidate unobserved factors: 2.1 parental skills, uncorrelated with parental income 2.2 sibling interaction effects 2.3 genes
3. And yet sibling correlations are lower bounds I
MZ-twin-correlations are possibly upper bounds, but not necessarily and suggest a very big role for family background
Outline
Intergenerational mobility Intergenerational effects Sibling associations Equality of opportunity Summing up
Equality of opportunity approach I
Highly stylized version: Y =α + βC + γ E + e
(8) E =δC + v
I
I
C: set of circumstances: factors beyond individual control, for
I
which individuals should not be held responsible (such as parental resources). E : set of effort variables: all choices for which society holds the individual accountable (such as labor supply). “Justifiable” inequality.
Reduced form:
Y = (β + γδ)C + γ v + e
(9)
EO-approach: implementation I I
Estimate the reduced form above Measure: I
I
Derive the inequality (according to a suitable measure of inequality) that is generated by circumstances. Compare this inequality with total inequality.: Ineq(due to circ.)/Ineq(total). Or the fraction of variance which is explained by circumstances: R2
I
Claim in the field: I
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lower bound of such inequality since only a subset of circumstances are observed in available data
Some empirical approaches consider the role of luck. Some try to measure effort and control for it in the outcome equation. Also other nice tricks.
Pros and cons of the EOp-approach Pros 1. Recognizes that ineq. of opp. cannot be measured by one SESindicator as the IGM-app. does. 2. Flexible about the measure of inequality. 3. Can include multiple measures of SES (cf. Clark). Also, mothers! 4. Can include grandparents that belong to a general IGM-model 5. Can include factors not shared by siblings, e.g., birth order. 6. Can include assortative mating as interactions.
Cons 1. Ideally requires a multivariate causal model. Else must assume that the omitted (but bu correlated) variables also capture circumstances. 2. Cannot account for unobserved family background variables as the sib-corr app. can 3. Requires rich data and large sample sizes.
EO-approach – results
EO-approach – results
EO-approach – new results (from Sweden)
How do the results compare to those from sibling correlations? Has the gap between IGM-estimates and the sib corr estimates been filled?
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In general clearly lower explanatory power than what sibling correlations predict (but the latter rarely reported).
I
And yet sibling correlations are lower bounds of the importance of family background. Note the omitted genetic influence captured by MZ-twins: clearly a circumstance according to Roemer!
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But are all factors shared by siblings really circumstances?
Major problem: are omitted variables effort or circumstances?
Variable
Results from causal effect studies
Are omitted variables circumstances?
Parental income and education
Intergenerational effects considerably lower than IGcoefficients. Effects lower than descriptive regression coefficients. Effects lower than descriptive regression coefficients.
Maybe, because that is what is controlled away by twinning and using adoptive parents. ?
Parental separation Family size, or number of siblings
?
Thus: the claim that the results are lower bounds on unjustifiable inequality does not (necessarily) hold.
Back to sibling correlations – same problem applies
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Are all factors shared by siblings really to be considered circumstances? I I
If unobserved parental skills: yes! If sibling spillover I I I
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of skills (Nicoletti and Rabe, 2010) of benefit use via information (Dahl et al. 2014) of effort ?
Maybe sibling spillover effects are circumstances since you have not chosen your siblings yourself.
To find out more, we have to understand the mechanisms that siblings share. A key challange for future research
Circumstance variables that have not been used
I
school and teacher quality
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health indicators from early childhood, including birth weight
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explicit genetic information. Difficult though.
Outline
Intergenerational mobility Intergenerational effects Sibling associations Equality of opportunity Summing up
Time to sum up and conclude about the four approaches
Factors captured by the various approaches Causal par income effects
Correlates of par income
Observed factors shared by sibs, uncorr. with par income
Unobs. factors shared by sibs, uncorr. with par income
Observed factors not shared by siblings
Unobserved factors not shared by siblings
IGM
Yes
Yes
No
No
No
No
IGEff
Yes
No
No
No
No
No
Sib corr
Yes
Yes
Yes
Yes, but cstances?
No
No
EOp
Yes
Yes, but cstances?
Yes
No
Yes
No
Magnitudes in terms of fraction of inequality (the variance), Sweden IGC2
IGM IGEff
0-0.03
Sib Corr
IGC2
EOp
IGC2
= 0.02-0.06
-
-
-
-
0-0.03
-
-
-
-
-
-
0.00 (birth order)
-
+ other factors = 0.25-0.30 (a lower bound)
+ our other Xs (incl. Grandparents, IQ and NC, etc.)=0.08
ca 0.20
Intergenerational mobility
1. Does not directly address the inequality-of-opportunity question! 2. But: provides an easy-to-understand picture that the public policy debate seems to appreciate: I I
it tells us about “the rise and fall of families�. the cross-country pattern has received a lot of public attention
3. Maybe easier to study and interpret country-differences and trends in intergenerational mobility than in the combined importance of a set of circumstances. 4. Associations are not that strong.
Intergenerational effects
1. This approach addresses well-defined questions of high scientific and public-policy importance. 2. Some approaches incorporate mothers. 3. But estimated effects are small in the sense that they explain very little of inequality of income and schooling: such effects do not violate egalitarian norms very much. 4. But effects might be large in other dimensions: the benefit-cost ratio of some interventions that change parental income and education might by be high.
Sibling associations
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A sibling correlation does not provide the answer to any well-defined scientific or public-policy questions
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A sibling correlation should rather be used as a warning signal (�benchmark�) whether researchers have missed important family background factors And the right light is on for this signal:
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I
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Considering that sibling correlations are lower bounds, the magnitudes can make persons with egalitarians attitudes really concerned! Key challenge: to understand what siblings share but is, so far, unobserved!
Equality of opportunity
1. Finding the explanatory power of circumstances is the natural correct approach to measuring inequality of opportunity! I
Ideally: a multivariate model of circumstances’ causal effects
2. Many important circumstances are not observed in typical data sets. And are probably not observable even with very ambitious data collection efforts. 3. Maybe one can find the most important circumstances I
That should ideally be done with a causal analysis.
4. Challenge: how to treat gender (mothers and daughters).
Björklund, Anders and Markus Jäntti (2012). “How important is family background for labour-economic outcomes?”. In: Labour Economics 19.4, pp. 465–474. doi: 10.1016/j.labeco.2012.05.016. url: http://dx.doi.org/10.1016/j.labeco.2012.05.016. Björklund, Anders, Markus Jäntti, and Matthew J Lindquist (2009). “Family Background and Income during the Rise of the Welfare State: Brother Correlations in Income for Swedish Men Born 1932–1968”. In: Journal of Public Economics 93.5–6, pp. 671–680. Björklund, Anders and Kjell G Salvanes (2011). “Education and Family Background: Mechanisms and Policies”. In: Handbook of the Economics of Education. Ed. by Eric A Hanushek, Stephen Machin, and Ludger Woessmann. Vol. 3. Amsterdam: North-Holland. Chap. 3, pp. 201–247. Björklund, Anders et al. (2002). “Brother correlations in Earnings in Denmark, Finland, Norway and Sweden Compared to the United States”. In: Journal of Population Economics 15.4, pp. 757–772.
Corak, Miles (2013). “Income Inequality, Equality of Opportunity, and Intergenerational Mobility”. In: Journal of Economic Perspectives 27.3, pp. 79–102. Corak, Miles, Matthew J Lindquist, and Bhaskar Mazumder (2013). “A Comparison of Upward and Downward Intergenerational Mobility in Canada, Sweden and the United States”. Paper presented at the 2013 EALE Conference, Turin. Eriksson, Tor and Yingqiang Zhang (2012). “The Role of Family Background for Earnings in Rural China”. In: Frontiers of Economics in China 7.3, pp. 465–477. Hertz, Tom et al. (2007). “The Inheritance of Educational Inequality: International Comparisons and Fifty-Year Trends”. In: The B.E. Journal of Economic Analysis & Policy 7.2, (Advances) Article 10. Jäntti, Markus and Stephen Jenkins (2015). “Income mobility”. In: Handbook of Income Distribution. Ed. by Anthony B Atkinson and François Bourguignon. Vol. 2. Elsevier. Chap. 10, pp. 807–935. Mazumder, Bhashkar (2008). “Sibling similarities and economic inequality in the US”. In: Journal of Population Economics 21.3, pp. 685–701.
Nicoletti, Cheti and Birgitta Rabe (2010). Inequality in pupils’ educational attainment: how much do family, sibling type and neighbourhood matter?. ISER Working Paper 2010-26. Colchester, UK: Uniersity of Essex. Österbacka, Eva (2001). “Family background and economic status in Finland”. In: Scandinavian Journal of Economics 103.3, pp. 467–484. Schnitzlein, Daniel D (2013). “How important is the family? Evidence from sibling correlations in permanent earnings in the USA, Germany, and Denmark”. In: Journal of Population Economics, pp. 1–21.