Inequality, Education and Marital Sorting Preliminary Version

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Inequality, Education and Marital
Sorting(Preliminary Version)

• R. Fernandez, NYU
• N. Guner, Queens University
• J. Knowles, Penn

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Background

• Does marital sorting affect income inequality?
• No large changes in marital sorting imply small
  changes in income inequality Kremer (1997) .
• Yes borrowing constraints and endogenous return
  to skill mean higher sorting leads to higher
  inequality Fernandez and Rogerson (1999).
• What determines the degree of marital sorting?
• Theory Becker (1991) predicts negative
  assortment by wage.
• In U.S. correlation between husband and wifes
  income grew from -.034 in 1973 to 0.102 in 1987
• Education correlations generally much stronger
  than income correlations.

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Theory of Sorting-Inequality

• Hypotheses of model
• People care about
• Money potential income of spouses.
• Love quality of match.
• Parental income affects childrens education.
• Skill premium declining in ratio of skilled to
  unskilled workers.

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The Model

• Adults live 2 periods
• infinite sequence of overlapping generations
• continuum of agents in each period of life
• agents are skilled or unskilled, care about
  marriage quality, fertility and consumption.
• 1st period choose education (borrow if
  necessary), then meet 1st match
• 2nd period meet 2nd match (if unmarried), repay
  student loans, make fertility decisions

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Matching Structure

• Match randomly when young
• Educational types are common knowledge.
• Match quality q is random, revealed after
  education decision.
• Meet someone of their own type in 2nd round
• if they dont marry 1st-round match.
• Quality q has distribution Q on 0,q
• E(q) ?
• independent of skill level

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Decisions

• Education become skilled?
• depends on returns to skill in labor and marriage
  markets, cost of education, parental income.
• Marriage marry 1st-round match?
• depends on match quality, partners incomes.
• Household fertility, consumption
• depends only on income.

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Couples Problem
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Skilled Matching Decision

• Skilled agent determines whether mixed marriage
  occurs
• solve for q that makes skilled indifferent
• Note Q(q ) correlation coefficient

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Education

• Cost of education
• idiosyncratic psychic cost ?i , distribution ?(
  ?i)
• monetary cost d
• Payoff from becoming skilled Vs - Vu
• return to skill in both labor and marriage
  markets
• Define skill ratio ? Ls /Lu
• In equilibrium kids want to be skilled if
• ?i

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Effect of higher skill premium

• Increase in skill premium raises q
• increases earnings of skilled
• makes skilled spouse more attractive
• Ambiguous effect on unskilled
• reduces probability of finding skilled spouse
• increases benefit of skilled spouse
• Raises the relative desirability of being skilled

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The Labor Market

• CRS prodn function Y F( LS, LU )
• Wages
• Higher skill ratio lowers the wage premium.
• So an increase in ? lowers degree of sorting..

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Figure 1 No Borrowing Constraints
?
?(l) Vs(l)-Vu(l)
?-1 (l)
?
l
l
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Borrowing Constraints

• Kids can borrow up to some fraction Z( I ) of
  parental income to become skilled.
• Let solve
• Fraction of kids that become skilled
• Unconstrained
• Constrained

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Figure 2 Borrowing Constraints
?
?(lt1)
?-1 (l, lt1)
?-1 (l, lt0)
?-1 (l)
?
l
l
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Multiple Steady-States

• Assume low ratio of skilled workers
• Low wages for unskilled high for skilled.
• Skilled people less likely to marry unskilled.
• Low-skill parents less able to pay to educate
  their children.
• Low rate of children becoming skilled workers.
• Result low ratio of skilled workers
• Implications
• inequality depends on initial conditions
• one-time redistribution may have permanent
  effects.

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Empirical Analysis

• Test for positive relationship between skill
  premium and degree of marital sorting.
• How much of cross-country inequality can sorting
  model explain?
• Method construct measures of sorting and
  inequality by country.
• Husband-wife education correlation
• Skill premium

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Data

• Latin America
• household surveys collected by IADB
• 13 countries, report years of education.
• Europe, Taiwan, Australia and North America
• surveys collected by Luxembourg Income Study.
• 22 countries.
• Education units vary across countries.
• Restrict sample to ages 36-45
• wages reflect lifetime income, marital decisions
  recent.

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Empirical Issues

• Comparing education across different systems
• want skill 1 to reflect beyond high-school
  education.
• Mapped LIS Levels onto years skilled 12
  years
• Some countries do not record partial higher educ.
• Annual income by skill level
• lifecycle differences, growth rates differ.
• use alternative measure lifetime income.
• Some countries report income net of tax, others
  gross.

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Sample Characteristics

• Skilled percent of husbands ranges from 8 for
  Paraguay to 60 for U.S. and Canada.
• Mean 0.24 for men, 0.21 for women.
• Skilled percent of wives highly correlated with
  that of husbands.
• Corr(men,women) 0.93.
• Skilled-marriage as of skilled men
• from 34 in U.K. to 78 for Belgium.

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Sorting Measures
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Inequality Measures

• Inequality wage-skill premium for men
• ratio of skilled to unskilled earnings.
• Mincer coefficient ln(y) a bd f(exp)
• y labor income from all sources.
• d years of schooling
• Sorting correlation of spouses educations
• education years of schooling.
• Alt correlation of indicator for skill.

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Inequality Measures
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Basic Results
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Log of Wage Ratio
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Mincer Results
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Excluding Russia
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Sorting and GDP
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Results Summary

• Data supports positive relationship between
  sorting and wage inequality
• weaker in sub-samples, but still significant.
• robust to specification different measures of
  skill premium, dummy for Latin America.
• Model does not account for all of difference
  between Latin America and rest of sample.
• Negative relationship between sorting and pc GDP

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Conclusion

• Model of sorting and inequality predicts
• more inequality associated with more sorting.
• Higher fertility differentials in more unequal
  countries
• Borrowing constraints lead to multiple
  steady-states
• high-sorting, high-inequality SS
• low-sorting, low-inequality SS
• Data consistent with 2 main predictions
• countries with lower sorting have lower
  inequality.
• countries with lower GDP have more sorting.

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Future Research

• Empirical
• Test fertility-differentials vs inequality
• Can we test whether sorting causes inequality?
• Can we distinguish multi-SS world from one where
  all countries are simply on transition to same
  SS?
• Theoretical
• Conditions that generate multiple steady states?