| Elasticity | Correlation | Elasticity | Correlation | |
|---|---|---|---|---|
| Denmark | 0.071 | 0.089 | 0.034 | 0.045 |
| Finland | 0.173 | 0.157 | 0.080 | 0.074 |
| Norway | 0.155 | 0.138 | 0.114 | 0.084 |
| Sweden | 0.258 | 0.141 | 0.191 | 0.102 |
| UK | 0.306 | 0.198 | 0.331 | 0.141 |
| US | 0.517 | 0.357 | 0.283 | 0.160 |
Source: Table 2
8. Intergenerational mobility
KAT.TAL.322 Advanced Course in Labour Economics
Intergenerational mobility
Do children “inherit” their outcomes from parents?
Model of intergenerational mobility
Simplified Becker and Tomes (1979)
Maximise intergenerational utility (Cobb-Douglas)
\[ \max_{I_{t - 1}, C_{t - 1}} \left(1 - \alpha\right) \log C_{t - 1} + \alpha \log y_t \]
\(E_t\) are non-investment determinants (randomness?) that is known to the parent
Simplified Becker and Tomes (1979)
The first-order condition for \(I_{t - 1}\) implies
\[ I_{t - 1} = \alpha y_{t - 1} - \frac{(1 - \alpha) E_t}{1 + r} \]
Plug it back to the investment technology equation:
\[ y_t = \alpha(1 + r) y_{t - 1} + \alpha E_t \]
If \(E_t \perp y_{t - 1}\) and \(Var(y_t) = Var(y_{t - 1}) \Rightarrow \text{Corr}(y_t, y_{t - 1}) = \alpha (1 + r)\)
Simplified Becker and Tomes (1979)
Intergenerational correlation
Suppose \(E_t = e_t + u_t\), where \(e_t\) is endowment and \(u_t\) is randomness.
Endowment is passed down the generations: \(e_t = \lambda e_{t - 1} + v_t\)
\[ y_t = \alpha(1 + r) y_{t - 1} + \alpha e_t + \alpha u_t \]
Assuming \(y_t\) is stationary,
\[\text{Corr}(y_t, y_{t - 1}) = \delta \alpha(1 + r) + (1 - \delta) \frac{\alpha(1 + r) + \lambda}{1 + \alpha(1 + r) \lambda}\]
where \(\delta = \frac{\alpha^2 \sigma_u^2}{(1 - \alpha^2 (1 + r)^2)\sigma_y^2}\).
Together with explanations on the next slide, point out different components and build story.
Simplified Becker and Tomes (1979)
Intergenerational correlation
Even the simple model highlights important channels:
Importance \(\alpha\) of child’s future earnings on parent’s utility
Return to investments \(r\) (e.g., returns to education)
Strength of intergenerational transmission of endowments \(\lambda\)
Magnitude of market luck relative to endowment luck \(\delta\)
Notice \(\uparrow r\) (a measure of income inequality) implies higher correlation between generations, or lower mobility.
This relationship is captured by the Great Gatsby curve.
The Great Gatsby curve
Simplified Becker and Tomes (1979)
Limitations
Ignores transfer of assets (revisited Becker and Tomes 1986)
Single parent \(\Rightarrow\) ignores assortative mating
Single child \(\Rightarrow\) ignores intrahousehold allocation
Arbitrary functional forms
- For example, additive \(I_{t - 1}\) and \(u_t\) imply offsetting
Suppose, public investment \(\uparrow \Rightarrow u_t \uparrow \Rightarrow I_{t - 1}^\star \downarrow\) - Data does not support (Head Start experiment)
- For example, additive \(I_{t - 1}\) and \(u_t\) imply offsetting
Measurement
Basic framework
Simple regression (ignoring process on endowments)
\[ y_t = \beta y_{t - 1} + \varepsilon \]
where \(y_t\) and \(y_{t - 1}\) are log earnings and \(\beta\) is IGE elasticity.
Measurement error
Measurement error
Using father’s education as an instrument for father’s single-year earnings
So, the idea is that by using an instrument, they can also approximate lifetime earnings potential even when using single-year measures
Permanent income
Lifecycle bias
Haider and Solon (2006)
\[ \begin{align} y^\text{parent}_a &= \mu_a y^\text{parent} + v \\ y^\text{child}_a &= \lambda_a y^\text{child} + u \end{align} \]
In this case, IGE elasticity estimator \(\hat{\beta}\) is inconsistent:
\[ \text{plim}~\hat{\beta} = \beta \lambda_a \theta_a \]
where \(\theta_a = \frac{\mu_a \text{Var}(y^\text{parent})}{\mu_a^2 \text{Var}(y^\text{parent}) + \text{Var}(v)}\)
Intergenerational elasticity across countries
Jäntti et al. (2006)
Mechanisms
Mechanisms
Black and Devereux (2011): recent studies focus on causal mechanisms
What is the “optimal” amount of intergenerational mobility?
Returns to skills
High \(H\) parent invest more in child’s \(H \Rightarrow\) high IG correlation
Unequal access
Type of policy depends on channel:
- public education/health
- democratic hiring policies
- …
Intergenerational mobility and education
Pekkarinen, Uusitalo, and Kerr (2009)
School reform in Finland 1972-77: selective \(\rightarrow\) comprehensive
The reforms also
increased academic content of curriculum (more math and sciences)
one foreign language became compulsory
\(\Rightarrow\) new curriculum is
more demanding for those who would have stayed in vocational track
less demanding than in old secondary school! (because more heterogeneous students)
Plus, abolished private schools and imposed centralized control.
Intergenerational mobility and education
Pekkarinen, Uusitalo, and Kerr (2009)
Standard IGE elasticity regression
\[ \log(y_\text{son}) = a + b_{jt} \log(y_\text{father}) + e \tag{1}\]
Effect of reform on IGE elasticity
\[ b_{jt} = b_0 + \delta R_{jt} + \Omega D_j + \Psi D_t \tag{2}\]
where \(R_{jt}\) indicates if reform in municipality \(j\) affected cohort \(t\).
Write out the full regression equation
\[ \begin{align} \log(y_\text{son}) = &a + b_0 \log(y_\text{father}) + \\ & + \delta R_{jt} \log(y_\text{father}) + \left(\Omega D_j + \Psi D_t\right)\log(y_\text{father}) + \\ & + \Phi D_t + \Pi D_j + \gamma R_{jt} + e_{ijt} \end{align} \]
Intergenerational mobility and education
Pekkarinen, Uusitalo, and Kerr (2009)
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| Father’s earnings | 0.277 | 0.297 | 0.298 | 0.296 |
| (0.014) | (0.011) | (0.010) | (0.014) | |
| Reform | −0.063 | −0.019 | ||
| (0.012) | (0.021) | |||
| Father’s earnings \(\times\) reform | −0.055 | −0.069 | −0.066 | |
| (0.009) | (0.022) | (0.031) | ||
| Obs. | 20 824 | 20 824 | 20 824 | 20 824 |
| \(R^2\) | 0.05 | 0.05 | 0.05 | 0.06 |
| Cohort FE | Yes | Yes | ||
| Father’s earnings \(\times\) cohort FE | Yes | Yes | ||
| Region FE | Yes | Yes | ||
| Father’s earnings \(\times\) region FE | Yes | Yes | ||
| Cohort FE \(\times\) region FE | Yes | |||
| Region-specific trend | Yes |
Source: Table 3
Last column add fully interacted FEs \(\Rightarrow\) main effect of the reform is no longer identified
BUT interaction is still identified and is consistent with other columns!
Improving access to education promotes intergenerational mobility
Intergenerational spillovers in education
Do educational reforms have spillover effects on children?
Black, Devereux, and Salvanes (2005)
School reform in Norway in 1960-71: compulsory edu 7 \(\rightarrow\) 9 years
IV approach
\[ \begin{align} E &= \beta E^p + \gamma X + \gamma_p X^p + \epsilon \\ E^p &= \alpha {REFORM}^p + \delta X + \delta_p X^p + v \end{align} \]
Limited IG spillover of school reform at the bottom
Intergenerational spillovers in education
Suhonen and Karhunen (2019)
Expansion of Finnish university system in 1955-75
The third map shows 1995 (mostly expansion in student numbers)
Intergenerational spillovers in education
Suhonen and Karhunen (2019)
University access measures based on distance from municipality of birth
Event study and IV approach
\[ \begin{align} E^c_{ijmc} &= \beta_0 + \beta_1 E^p_{ijmc} + \beta_2 X_{ijmc} + \theta_m + \mu_c + \varepsilon_{ijmc} \\ E^p_{ijmc} &= \alpha_0 + \alpha_1 {UniAccess}_{ijmc} + \alpha_2 X_{ijmc} + \gamma_m + \delta_c + \vartheta_{ijmc} \end{align} \]
\(i\) - child, \(j\) - parent, \(m\) - parent birth municipality, \(c\) - parent birth cohort.
Intergenerational spillovers in education
Suhonen and Karhunen (2019)
| Child's years of education | ||||
|---|---|---|---|---|
| Full sample | Grandparent nonmissing | |||
| OLS | IV | |||
| (1) | (2) | (3) | (4) | |
| Mother's years of education | 0.345*** | 0.522*** | 0.540*** | 0.697*** |
| (0.004) | (0.133) | (0.143) | (0.120) | |
| F-stat (IV) | 4.1 | 14.2 | 21.3 | |
| Obs. | 1 239 331 | 1 239 331 | 1 239 331 | 628 230 |
| Father's years of education | 0.305*** | 0.400** | 0.535*** | 0.612*** |
| (0.003) | (0.161) | (0.171) | (0.143) | |
| F-stat (IV) | 3.7 | 12.7 | 19.6 | |
| Obs. | 1 195 008 | 1 195 008 | 1 195 008 | 710 677 |
| Additional controls | Yes | Yes | ||
Source: Table 7
1 extra year of mother education leads to 0.5-0.6 year of child education
1 extra year of father education leads to 0.4-0.5 year of child education
the complier parents are mainly low-income and low-educated \(\Rightarrow\) IG spillovers could lead to higher mobility of their children as well
Intergenerational spillovers in education
Suhonen and Karhunen (2019)
Strong positive spillover from parent’s to child’s education
Suggestive evidence that
assortative mating between parents can account for >50% of effects
higher parental income could also contribute to the results
IG transmission present in pre-uni school outcomes
Important for mobility discussion: complier parents mainly from low-educated and low-income families
Intergenerational mobility and neighbourhoods
Chetty and Hendren (2018a)
IGE mobility varies geographically (Chetty et al. 2014)
Intergenerational mobility and neighbourhoods
Chetty and Hendren (2018a)
Geographic variation in IGE mobility may stem from:
selection into neighbourhoods
causal effect of neighbourhoods
Do children moving to higher mobility area have better outcomes?
Endogenous moving \(\Rightarrow\) exploit timing of move
Intergenerational mobility and neighbourhoods
Chetty and Hendren (2018a)
Moving to a more mobile place improves success in proportion to exposure!
children who move at age 9 would pick up 56% of the observed difference in permanent residents’ outcomes between their origin and destination CZs
extrapolating: being born in a better area - pick up about 80% of the difference!
Intergenerational mobility and neighbourhoods
Chetty and Hendren (2018b)
What makes neighbourhoods generate good outcomes?
- Segregation (maps)
Racial and income segregation \(\sim\) lower upward mobility - Income inequality
“Areas with greater income inequality generate less upward mobility” - School quality
\(\uparrow\) test scores, \(\downarrow\) school dropout rates, \(\uparrow\) # of colleges per capita - Social capital
\(\uparrow\) participation in community activities, \(\downarrow\) crime rate
Together explain 58% of variation in CZ causal effect
Social capital = participation in civic organiziations, bowling centers, golf clubs, fitness centers, sports organizations, religious organizations, political organizations, labour, business and professional organizations.
Intergenerational mobility and genetics
Rustichini et al. (2023)
How much of IGE elasticity driven by nature vs nurture?
Extension of standard model:
genetic transmission and assortative mating
skill transmission: genetic factors, parental investments, family environment and idiosyncratic events
Minnesota Twin Family Study (income, skills, genotypes + parents)
Intergnerational mobility and genetics
Rustichini et al. (2023)
PGS as measure of genetic endowment affects significantly the income
hence endowment plays an important role
most of the PGS effect is mediated via education variables
so, it is possible that PGS determines the investments they get
also part of the PGS effect carries the weight of assortative mating
- observed PGS correlation between twins - expected correlation = 0.083
Intergenerational mobility and genetics
Rustichini et al. (2023)
The last panel (equation of education years of children) shows that
PGS of parents completely mediated through family environment variables such as parent education and family income
PGS of child remains highly significant and large, so genetic endowment continue to play an important role
Multigenerational mobility
Colagrossi, d’Hombres, and Schnepf (2020)
Typical regression of parent-child pairs
\[ \ln y^\text{child} = \beta_{-1} \ln y^\text{parent} + \varepsilon \]
Similar estimation across \(k\) generations
\[ \ln y^\text{child} = \beta_{-k} \ln y^{k \text{ ancestor}} + \vartheta \]
Iterated regression fallacy: \(\beta_{-k} \neq \left(\beta_{-1}\right)^k\)
Multigenerational mobility
Colagrossi, d’Hombres, and Schnepf (2020)
Multigenerational mobility
Stuhler (2012)
Possible explanations of iterated regression fallacy:
Multigenerational mobility
Barone and Mocetti (2021)
Current individuals in Florence \(\leftrightarrow\) ancestors in 1427 based on surnames
Multigenerational mobility
Collado, Ortuño-Ortín, and Stuhler (2023)
Horizontal approach: Grandparent-grandchild \(\rightarrow\) cousin-cousin
blood relationships: intergenerational processes
in-law relationships: assortative processes
Swedish registry: “up to 141 distinct kinship moments”
Multigenerational mobility
Collado, Ortuño-Ortín, and Stuhler (2023)
\[ \begin{align} y_t &= \beta \tilde{y}_{t - 1} + \gamma \tilde{z}_{t - 1} + e_t + v_t + x_t + u_t \\ \tilde{y}_{t - 1} &= \alpha_y y_{t - 1}^m + \left(1 - \alpha_y\right) y_{t - 1}^f \\ \tilde{z}_{t - 1} &= \alpha_z z_{t - 1}^m + \left(1 - \alpha_z\right) z_{t - 1}^f \end{align} \]
\(\beta\) and \(\alpha_y\) measure direct transmission
\(\gamma\) and \(\alpha_z\) measure indirect transmission
\(u_t\) is white noise (market luck)
\(v_t\) is white noise in latent factor (endowment luck)
\(x_t\) is shared sibling component
\(e_t\) is latent sibling component
Multigenerational mobility
Collado, Ortuño-Ortín, and Stuhler (2023)
| \(\beta\) | \(\gamma\) | \(\alpha_y\) | \(\alpha_z\) | \(\sigma_y^2\) | \(\sigma_u^2\) | \(\sigma_z^2\) | \(\sigma_x^2\) | \(\sigma_e^2\) | |
|---|---|---|---|---|---|---|---|---|---|
| Men | 0.144 | 0.664 | 0.389 | 0.660 | 4.648 | 1.975 | 2.072 | 0.180 | 0.657 |
| Women | 0.129 | 0.566 | 0.018 | 0.775 | 4.465 | 2.333 | 1.559 | 0.244 | 0.712 |
- Indirect transmission dominates direct (\(\beta < \gamma\))
- Shared sibling component \(x\) explains ~5%, \(e\) ~ 15% of \(\sigma_y^2\)
- Spousal correlation in latent factor > observed factor
Summary
Vast literature on intergenerational mobility
- Earlier works concentrated on measuring mobility precisely
- Later works focus on determinants of mobility
Improving access to education promotes mobility
- The effect may spillover to children
Geographic variation in mobility; largely causal
- Lower segregation, inequality, better schools and social cohesion
Genetic endowment and assortative mating important components
Multigenerational mobility slower than predicted
References
Barone, Guglielmo, and Sauro Mocetti. 2021. “Intergenerational Mobility in the Very Long Run: Florence 1427–2011.” The Review of Economic Studies 88 (4): 1863–91. https://doi.org/10.1093/restud/rdaa075.
Becker, Gary S., and Nigel Tomes. 1979. “An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility.” Journal of Political Economy 87 (6): 1153–89. https://www.jstor.org/stable/1833328.
———. 1986. “Human Capital and the Rise and Fall of Families.” Journal of Labor Economics 4 (3): S1–39. https://www.jstor.org/stable/2534952.
Black, Sandra E., and Paul J. Devereux. 2011. “Recent Developments in Intergenerational Mobility.” In Handbook of Labor Economics, 4:1487–1541. Elsevier. https://doi.org/10.1016/S0169-7218(11)02414-2.
Black, Sandra E., Paul J. Devereux, and Kjell G. Salvanes. 2005. “Why the Apple Doesn’t Fall Far: Understanding Intergenerational Transmission of Human Capital.” The American Economic Review 95 (1): 437–49. https://www.jstor.org/stable/4132690.
Chetty, Raj, and Nathaniel Hendren. 2018a. “The Impacts of Neighborhoods on Intergenerational Mobility I: Childhood Exposure Effects*.” The Quarterly Journal of Economics 133 (3): 1107–62. https://doi.org/10.1093/qje/qjy007.
———. 2018b. “The Impacts of Neighborhoods on Intergenerational Mobility II: County-Level Estimates*.” The Quarterly Journal of Economics 133 (3): 1163–1228. https://doi.org/10.1093/qje/qjy006.
Chetty, Raj, Nathaniel Hendren, Patrick Kline, and Emmanuel Saez. 2014. “Where Is the Land of Opportunity? The Geography of Intergenerational Mobility in the United States *.” The Quarterly Journal of Economics 129 (4): 1553–623. https://doi.org/10.1093/qje/qju022.
Colagrossi, Marco, Béatrice d’Hombres, and Sylke V Schnepf. 2020. “Like (Grand)parent, Like Child? Multigenerational Mobility Across the EU.” European Economic Review 130 (November): 103600. https://doi.org/10.1016/j.euroecorev.2020.103600.
Collado, M Dolores, Ignacio Ortuño-Ortín, and Jan Stuhler. 2023. “Estimating Intergenerational and Assortative Processes in Extended Family Data.” The Review of Economic Studies 90 (3): 1195–1227. https://doi.org/10.1093/restud/rdac060.
Corak, Miles. 2013. “Income Inequality, Equality of Opportunity, and Intergenerational Mobility.” Journal of Economic Perspectives 27 (3): 79–102. https://doi.org/10.1257/jep.27.3.79.
Gelber, Alexander, and Adam Isen. 2013. “Children’s Schooling and Parents’ Behavior: Evidence from the Head Start Impact Study.” Journal of Public Economics 101 (May): 25–38. https://doi.org/10.1016/j.jpubeco.2013.02.005.
Haider, Steven, and Gary Solon. 2006. “Life-Cycle Variation in the Association Between Current and Lifetime Earnings.” The American Economic Review 96 (4): 1308–20. https://www.jstor.org/stable/30034342.
Jäntti, Markus, Bernt Bratsberg, Knut Røed, Oddbjørn Raaum, Robin Naylor, Eva Österbacka, Anders Björklund, and Tor Eriksson. 2006. “American Exceptionalism in a New Light: A Comparison of Intergenerational Earnings Mobility in the Nordic Countries, the United Kingdom and the United States.” IZA Discussion Paper. Bonn, Germany. January 2006.
Mazumder, Bhashkar. 2005. “Fortunate Sons: New Estimates of Intergenerational Mobility in the United States Using Social Security Earnings Data.” The Review of Economics and Statistics 87 (2): 235–55. https://www.jstor.org/stable/40042900.
Pekkarinen, Tuomas, Roope Uusitalo, and Sari Kerr. 2009. “School Tracking and Intergenerational Income Mobility: Evidence from the Finnish Comprehensive School Reform.” Journal of Public Economics 93 (7): 965–73. https://doi.org/10.1016/j.jpubeco.2009.04.006.
Rustichini, Aldo, William G. Iacono, James J. Lee, and Matt McGue. 2023. “Educational Attainment and Intergenerational Mobility: A Polygenic Score Analysis.” Journal of Political Economy 131 (10): 2724–79. https://doi.org/10.1086/724860.
Solon, Gary. 1992. “Intergenerational Income Mobility in the United States.” The American Economic Review 82 (3): 393–408. https://www.jstor.org/stable/2117312.
Stuhler, Jan. 2012. “Mobility Across Multiple Generations: The Iterated Regression Fallacy.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2192768.
Suhonen, Tuomo, and Hannu Karhunen. 2019. “The Intergenerational Effects of Parental Higher Education: Evidence from Changes in University Accessibility.” Journal of Public Economics 176 (August): 195–217. https://doi.org/10.1016/j.jpubeco.2019.07.001.
Appendices
Head Start and absence of offsetting behaviour
US Racial Dot Map
White - blue
Black - green
Asian - red
Hispanic - yellow