Increasing Inequality in Parent Incomes and Children’s Completed Schooling Greg J. Duncan University of California- Irvine Greg J. Duncan University of California- Irvine Ariel Kalil University of Chicago Ariel Kalil University of Chicago Kathleen M. Ziol-Guest Cornell University Kjetil Telle Statistics Norway

Sir Frank Holmes

Russell Sage and Spencer Foundations, 2011 Whither Opportunity? Rising Inequality, Schools, and Children’s Life Chances Edited by Greg J. Duncan and Richard J. Murnane

Family income relative to 1979 Source: Authors’ calculations based on data from the U.S. Bureau of the Census. Shaded areas indicate recession years Top 1%: ↑ 2.69

NZ and US family income inequality Source: Perry (2012); US Census Bureau NZ US

Race and income-based gaps in reading achievement in SAT-type units High/low income advantage Reardon (2011)

Race and income-based gaps in reading achievement in SAT-type units High/low income advantage Reardon (2011)

College graduation rates for high and low income children in NLSs Bailey and Dynarski (2011) using NLSY

Key question: Can changing income gaps account for changes in attainment gaps between high and low income children? 9

Reardon’s evidence: Maybe not: Timing of income inequality changes don’t match timing of changes in test score gaps Indications that increases in the importance of income matters more than increases in the income gap itself 10

Our paper: Gaps in attainment (completed years of schooling) rather than achievement Use panel data linking teenage income to early adult attainment Draw from a single, consistent data set (the PSID) Consider gap trends in income + parent education, family size and structure 11

PSID data: All individuals turning 14 in and observed at age 24; non-immigrant ~200 per year; 6,141 in all Years of completed schooling at age 24 Gaps between top and bottom quintiles of the income distribution 12

PSID data: Income (2010$) and single-parent family status averaged over ages Parent (head’s) education, # siblings Gender, first born, race/ethnicity Weight for sampling and attrition; cluster on family ID 13

Are PSID data comparable with other sources? 14

College graduation rates for high and low income children in NLS and PSID Bailey and Dynarski (2011) for NLSY; authors’ calculations for the PSID

Suppose: Child schooling = β 1 Family income + β 2 Family structure + β 3 Parent education + β 4 Family size + Race/ethnicity, parity status 17

Accounting for the gaps Changes in schooling gaps (Y) are a function of: Changes in gaps in Xs: ∆X · β + Changes in coefficients: ∆β · X 18

Trends in PSID gaps in: 19 Children’s completed schooling Parent income Family structure Parent education Family size

Top minus Bottom Income Quintile Differences in Children’s Years of Completed Schooling Schooling gap in years between top and bottom income quintiles Year Turned 14

Top minus Bottom Income Quintile Differences in Family Income Income gap (in $10,000s) between top and bottom income quintiles Year Turned 14

Top minus Bottom Income Quintile Differences in ln Family Income Ln income gap between top and bottom income quintiles Year Turned 14

Top minus Bottom Income Quintile Differences in Single Parent Family Structure Year Turned 14 Gap in percent in single parent families between top and bottom income quintiles

Top minus Bottom Income Quintile Differences in Parent Schooling Year Turned 14 Gap in years of parental schooling between top and bottom income quintiles

Top minus Bottom Income Quintile Differences in Number of Siblings Year Turned 14 Number of siblings gap between top and bottom income quintiles

Scorecard: 26 High income kids: Children’s completed schooling Parent income Family structure Low income kids: Parent education Family size Changes in gaps favoring:

Changes in gaps in Xs: ∆X · β 27

What about the importance of parent income, etc.? 28

All cohorts Dependent variable: completed schooling Bivariate log family income 1.164*** [.39] Single parent family (% of years, age 14-16) -.820*** [.21] Number of siblings -.228*** [.25] Parent years of education.301*** [.46] Standardized coefficient

All cohorts Dependent variable: completed schooling BivariateFull controls Full controls - standardized log family income 1.164*** [.39].708***.24 Single parent family (% of years, age 14-16) -.820*** [.21] Number of siblings -.228*** [.25] -.110*** -.12 Parent years of education.301*** [.46].208***.32

Accounting for Increases in the Schooling Gap for Children in the Top and Bottom Quintiles, Last 6 yrs – 1 st 6 yrs

Sensitivity test: last half of period only

Top minus Bottom Income Quintile Differences in Children’s Years of Completed Schooling Schooling gap in years between top and bottom income quintiles Year Turned 14

Top minus Bottom Income Quintile Differences in ln Family Income Ln income gap between top and bottom income quintiles Year Turned 14

Top minus Bottom Income Quintile Differences in Parent Schooling Year Turned 14 Gap in years of parental schooling between top and bottom income quintiles

Sensitivity test: last half of period only

What about changes in the importance of parent income, etc.? 37

Standardized coefficients No controls for other interactions (four separate regressions) Incl. controls for other interactions ln income * CY turned *** (.003) (.003) Single parent * CY turned *** (.003) -.015*** (.003) Head education* CY turned *** (.002).014*** (.003) # of sibs * CY turned * (.003).012** (.004)

Linear Trends In Effects Of Demographic Measures Plus Family Income (All Standardized) On Children’s Years Of Completed Schooling Single parent

Sensitivity test: End-of-period coefficients Use end-of-period coefficients

Summary Schooling gaps have widened by ~ ½ year between top and bottom quintiles Income gaps have widened as well, but so have differences in family structure; Parent education and family size gaps have narrowed Increasing income gaps account for: o 80% of the schooling gaps over three decades o 25%-35% of gaps more recently Importance of income has not increased, but importance of family structure and parent education have 41

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Extra slides 43

∆Xs so far: Gaps have widened for o income o single-parent family structure but narrowed for: o parent education o family size What is the value of these X variables in predicting children’s schooling? 44

Linear Trends In Effects Of Demographic Measures But Not Family Income (All Standardized) On Children’s Years Of Completed Schooling

Accounting for Increases in the Schooling Gap for Children in the Top and Bottom Quintiles, Middle 6 yrs – 1 st 6 yrs

Accounting for the gaps Changes in schooling gaps (Y) are a function of: Changes in gaps in Xs: ∆X · β + Changes in coefficients: ∆β · X 47