Status Traps

Abstract

In this article, we explore nonlinearities in the intergenerational mobility process using threshold regression models. We uncover evidence of threshold effects in children's outcomes based on parental education and cognitive and noncognitive skills as well as their interaction with offspring characteristics. We interpret these thresholds as organizing dynastic earning processes into “status traps.” Status traps, unlike poverty traps, are not absorbing states. Rather, they reduce the impact of favorable shocks for disadvantaged children and so inhibit upward mobility in ways not captured by linear models. Our evidence of status traps is based on three complementary datasets; that is, the PSID, the NLSY, and US administrative data at the commuting zone level, which together suggest that the threshold-like mobility behavior we observe in the data is robust for a range of outcomes and contexts.

KEY WORDS:

• Inequality
• Intergenerational mobility
• Poverty traps
• Threshold regression

ACKNOWLEDGMENTS

Durlauf thanks the Vilas Trust and Institute for the New Economic Thinking for financial support. Kourtellos thanks the University of Cyprus for funding. Tan thanks the Greg and Cindy Page Faculty Distribution Fund for financial support. We would like to thank Kyriakos Petrou for excellent research assistance.

Notes

Chetty et al. (2014) measured spatial intergenerational mobility across US commuting zones using a rank–rank regression, which allows them to compare the rank of children to others in their birth cohorts with the rank of parents in relation to other parents with children in the corresponding cohorts. Another distinct feature of their study is that unlike previous studies, which are mainly based on survey data (e.g., PSID and NLSY), they employed a novel dataset based on federal income tax records for a core sample of 1980–1982 birth cohorts.

As shown by Solon (2004), a linear specification may be derived from the foundational Becker and Tomes (1979) model of intergenerational mobility under particular functional form assumptions. The work of Loury (1981) also nests a linear specification as a special case. The linearity finding, however, is not generic in the space of utility and production functions consistent with these models.

Table A.1 of the online appendix provides a detailed description of these studies.

Chetty et al. (2014) proposed two statistics that describe the relative and absolute mobility based on rank–rank regression. While their approach cannot be regarded as nonlinear, it turns out that the rank–rank relationship appears to be linear in their sample unlike the log–log specification.

Grawe (2004) challenged suggestions in Becker and Tomes (1986) and Corak and Heisz (1999) that a S-shaped relationship between parental and offspring income is a sign of credit constraints, since such a pattern may be replicated by certain wage processes. This is true, but is not germane in our context since our argument is that a class of theories suggests threshold approximations, not that there is a logical entailment of any particular functional form for mobility. We see our exercise as structuring the construction of evidence in a way that is sensitive to substantive theories of intergenerational mobility.

To see this, note that under the assumption that the intergenerational process of dynastic income is stationary then Equation (3(3) $$\begin{array}{ccc}\hfill y_{i,1}& =& \alpha +\beta y_{0,i}+{\theta }^{\text{'}}{z}_i+{\delta }_{\alpha }{d}_i\left(\gamma \right)+{\delta }_{\beta }{y}_{0,i}{d}_i\left(\gamma \right)\hfill \\ & & +{\delta }_{\theta }^{\text{'}}{z}_i{d}_i\left(\gamma \right)+e_i,\hfill \end{array}$$(3) ) suggests that the long-run conditional means for the lower and upper regimes are $E\left(y_i^{*}\right|z_i,q_i\le \gamma )=\frac{{\alpha }_1+{\theta }_1^{\text{'}}{z}_i}{1-{\beta }_1}$ and $E\left(y_i^{*}\right|z_i,q_i>\gamma )=\frac{{\alpha }_2+{\theta }_2^{\text{'}}{z}_i}{1-{\beta }_2}$, respectively.

We apply a 10% trimming.

Following Chetty et al. (2014), we focus on absolute upward mobility for two reasons: first, the outcomes of disadvantaged families is the focal point of government policy and second, because the outcomes of children from low-income families have more variation across areas than those from high-income families.

We also trimmed observations higher than $150,000 or less than $150 in 1967 dollars as in Lee and Solon (2009). The results were similar and available in the online appendix.

While Lee and Solon (2009) employed a method that estimates time-specific IGE's, we opted to follow Hertz (2007) and estimate cohort-specific IGE's. As Hertz (2007) argued, the Lee and Solon method is likely to give rise to biases because it assumes a fixed age-structure of income for the whole period, does not allow the inclusion of individual fixed effects, and omits other observable sources of heterogeneity (beyond age effects) such as education.

One implication of this predictive method for constructing the permanent income variables is that the key variable in Equation (1(1) $$\begin{array}{c}\hfill y_{1,i}=\alpha +\beta y_{0,i}+{\theta }^{\text{'}}{z}_i+e_i,\end{array}$$(1) ), namely, the logarithm of parents’ income is a generated regressor and as a result standard inference may be distorted. That is why, we opt to use averages of actual incomes for our baseline results.

In unreported exercises, we also considered exercises that used latent factors that were extracted from the entire set of variables, which includes the remaining five variables from TIPI (Quiet, Warm, Disorganized, Anxious, and Conventional) as well as the six variables from the Behavior Problems Index (Antisocial, Dependent, Headstrong, Hyperactive, Peer, Conflict, and Depressed).

http://www.equality-of-opportunity.org/

We also investigated relative mobility with similar findings.

The results for the other schooling variables are similar and available upon request.

See Almlund et al. (2011) for a detailed survey and Heckman and Mosso (2014) for discussion in the context of intergenerational mobility.

The size of the test for both levels is set 10%. In unreported exercises, we also investigated the effect of using a more conservative size of the test (set at 1%) in the second level without finding substantial differences.

In both the short and long regression exercises, we focus on the intergenerational mobility between mothers and daughters, but also consider the relationship between mothers and all their children (both daughters and sons) in the online appendix. The results between the two samples appear to be qualitatively similar, especially when we study the interactions between parental characteristics and offspring characteristics.

In the online appendix, we also consider the best model (according to BIC) from a universe of models obtained by appending the short model with all permutations of three groups of variables; that is, the set of daughter's cognitive abilities, the set of daughter's noncognitive abilities, and daughter's schooling. The findings of these “best among all” models are qualitatively identical to those for the corresponding best long regression models reported above except for the findings regarding the effects of daughter's noncognitive abilities on her earnings.

As discussed in Section 3, absolute upward mobility measures the expected income rank of children of parents in the bottom half of the national income distribution.

Given the fairly large model space, we first use the leaps and bounds algorithm to obtain a number of best models for each model size and then use BIC to select the best model. Alternatively, this model can be viewed as the posterior mode model in a Bayesian model averaging (BMA) analysis using linear models; see Kourtellos, Marr, and Tan (2015a) who employed BMA to identify robust predictors of spatial mobility.

Inference for the best BIC and the factor specifications is complicated by post-selection and estimation error concerns, respectively. We are unaware of a model selection correction that applies to this environment and note that similar issues arise in Chetty et al.'s reported results where models were selected based initially on a set of correlation exercises. The latter observation is not meant to be criticism, but simply to clarify parallels in terms of the difficulties faced here and in the existing literature. Nevertheless, the main findings are in agreement with the results that use individual variables.

In particular, the Racial Segregation, High School Dropout Rate, and Fraction Single Mothers are all statistically significant and negatively affect absolute upward mobility. The Social Capital Index is also statistically significant, but it is positively associated with absolute mobility. The Gini Bottom 99% does not appear to have a significant effect on mobility.