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Erschienen in: Demography 4/2020

07.07.2020

Does Opportunity Skip Generations? Reassessing Evidence From Sibling and Cousin Correlations

verfasst von: Ian Lundberg

Erschienen in: Demography | Ausgabe 4/2020

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Abstract

Sibling (cousin) correlations are empirically straightforward: they capture the degree to which siblings’ (cousins’) socioeconomic outcomes are similar. At face value, these quantities seem to summarize something about how families constrain opportunity. Their meaning, however, is complicated. One empirical set of sibling and cousin correlations can be generated from a multitude of distinct theoretical processes. I illustrate this problem in the context of multigenerational mobility: the relationship between the incomes of an ancestor and a descendant separated by several generations in a family. When cousins’ outcomes are similar (an empirical fact), prior authors have favored the particular theoretical interpretation that extended kin affect life chances through pathways not involving the parents of the focal individual. I show that this evidence is consistent with alternative theories of latent transmission (measurement error) or dynamic transmission (a parent-to-child transmission process that changes over generations). Theoretical assumptions are required to lend meaning to a point estimate. Further, I show that point estimates alone may be misleading because they can be highly uncertain. To facilitate uncertainty estimation for the key test statistic, I develop a Bayesian procedure to estimate sibling and cousin correlations. I conclude by outlining how future research might use sibling and cousin correlations as effective descriptive quantities while remaining cognizant that these quantities could arise from a variety of distinct theoretical processes.

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Fußnoten
1
The measurement error that biases sibling and cousin correlations is error in the outcome variable. This makes the problem distinct from econometric work on the use of proxies for latent predictor variables (e.g., Lubotsky and Wittenberg 2006).
 
2
I focus on a theoretical model that assumes only one income variable in each generation, even though a given person has two sets of grandparents, four sets of great-grandparents, and so on. This simplification is similar to the assumption in many demographic studies of a one-sex population. In the setting of multigenerational mobility, Becker and Tomes (1979:1183) motivated it as an assumption of perfect assortative mating on social origins; under this assumption, all the grandparents here have the same family incomes and can be represented by a single variable. Extending the Becker-Tomes model to allow some independence between social origins is beyond the scope of this article but may be an important topic for future work.
 
3
The Becker-Tomes model is overidentified if we assume that β > 0; because β enters formulas only in squared form, the data would be equally consistent with β < 0 of equal magnitude.
 
4
Empirical evidence can sometimes cast doubt on the latent transmission model because one subspace of parameters (cousin correlations less than the squared sibling correlation) is impossible in this model.
 
5
I use .5 to follow the recommendations of Gelman et al. (2008) to place continuous variables on a scale that works well with the default priors they proposed.
 
6
This procedure takes several hours on a Windows cluster computer with 512 GB of RAM and an Intel Xeon CPU E7-4850 v3 @2.20 GHz processor.
 
7
The slightly higher coefficient required for grandparent-parent transmission is consistent with a supplemental result. Following a procedure analogous to the main model, I estimate the parent-generation sibling correlation to be .51 (95% CI: .46–.55), slightly higher than the estimate of .38 (95% CI: .32–.44) in the offspring generation.
 
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Metadaten
Titel
Does Opportunity Skip Generations? Reassessing Evidence From Sibling and Cousin Correlations
verfasst von
Ian Lundberg
Publikationsdatum
07.07.2020
Verlag
Springer US
Erschienen in
Demography / Ausgabe 4/2020
Print ISSN: 0070-3370
Elektronische ISSN: 1533-7790
DOI
https://doi.org/10.1007/s13524-020-00880-w

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