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The role of evolving marital preferences in growing income inequality

Abstract

In this paper, we describe mating patterns in the USA from 1964 to 2017 and measure the impact of changes in marital preferences on between-household income inequality. We rely on the recent literature on the econometrics of matching models to estimate complementarity parameters of the household production function. Our structural approach allows us to measure sorting along multiple dimensions and to effectively disentangle changes in marital preferences and in demographics, addressing concerns that affect results from existing literature. We answer the following questions: Has assortativeness increased over time? Along which dimensions? To what extent can the shifts in marital preferences explain inequality trends? We find that, after controlling for other observables, assortative mating in education has become stronger. Moreover, if mating patterns had not changed since 1971, the 2017 Gini coefficient between married households would be 6% lower. We conclude that about 25% of the increase in between-household inequality is due to changes in marital preferences. Increased assortativeness in education positively contributes to the rise in inequality, but only modestly.

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Notes

  1. The survey of Stevenson and Wolfers (2007) tracks the changes that the institution of the family has gone through in recent decades, and presents several significant research questions that need to be answered.

  2. Two related works are those by Chiappori et al. (2017) and Greenwood et al. (2016), but both focus on educational sorting. Their findings are discussed in Section 5.

  3. Both Fernández and Rogerson (2001) and Fernández et al. (2005) use the skill premium as a measure of inequality.

  4. The methodology consists of finding a log-linear model with good fit to explain a contingency table with the distribution of income by percentile (plus one category containing zero-income observations). Then, one can compute predicted frequencies after removing certain regressors to reproduce counterfactual situations.

  5. Schwartz (2010) uses the ratios between the median income of the top 20% households (high class) over the median income of the middle 60% (medium class) or the median income of the top 20% (low class) as measures of inequality.

  6. As for Greenwood et al. (2014), we hereby refer to the revised findings published in the corrigendum.

  7. Alternatively, one could put an additional restriction on the parameters σ, for instance σ = 1 on each market. Ciscato et al. (forthcoming) propose to normalize the social gain \(\mathcal {W}(A,\sigma )\).

  8. In addition, in CPS waves before 1976, there is no state variable at the household level. Only broad geographical areas are reported.

  9. The 5-level variable is constructed as follows: (1) below high school degree, (2) high school degree, (3) some college, (4) college degree, and (5) 5+ years of college. With 4 levels only, we distinguish: (1) below high school degree, (2) high school degree, (3) college degree, and (4) 5+ years of college.

  10. The number of weeks working in the past year is usually available as a continuous variable. However, it is sometimes only available as a grouped variable, which we use to proxy the number of weeks worked in the past year.

  11. Comparing summary statistics before and after 1971 suggests that most Hispanics declared themselves as White, whereas the category Others mostly contains Asians before 1988.

  12. Similar simple selection criteria by age are common in the literature. See Schwartz and Mare (2005) (where the wife must be between 18 and 40) or Schwartz and Graf (2009) (where both partners must be between 20 and 34).

  13. We also exclude students aged more than 23 by combining data on school attendance and reasons for not participating to the labor market.

  14. More precisely, each cohort t of young men matches with the cohort t + 1 of young women.

  15. The trends for the median age at first marriage have been estimated with CPS data by the Fertility and Family Statistics Branch of the US Census Bureau and are available online: https://www.census.gov/data/tables/time-series/demo/families/marital.html. Details about the estimation method can be found in ?[ ()Chapter 9]siegel2004methods. The 1970 and the 1980 Census and the American Community Survey (ACS) contain survey data about the year of marriage: a comparison of the estimated CPS trends with these data sources reveals that the estimates are indeed accurate.

  16. The graph also shows the discrepancy in the education variable in 1992, as a large share of the population previously categorized as having a high school degree now appears in the “Some College” category.

  17. The share of employed people may appear extremely high in some cases (for men at the beginning of the period for example), but this may be due to our sample selection criteria based on age and marital status. In addition, we consider a person as employed as long as we are able to compute a wage, that is, as long as she worked in the past year.

  18. In practice, we first compute \((diag(E_{\hat {\pi }}[x_{1991}^{\prime }x_{1991}]))^{-1/2}\) for men’s population in 1991, and then use it as a scaling factor for every cross-section. We do the same for women.

  19. In fact, in spite of the increasing median age of first marriage, most people still get married before they turn 35. The share of married people in a cohort is indeed approximately constant after 35 (see Chapter 1, Browning et al. 2014.

  20. The difference between the median age for men and for women is approximately constant over the time period considered, and is around 2 years (see Fig. 1).

  21. Precisely, we replace wages by the variable log(1 + wa) where wa are (possibly 0) annual earnings.

  22. Alternatively, we could compare the counterfactual matching P(2017, 2017; 1971) with the actual frequencies observed in the data, rather than those predicted by the model. However, since the model does an excellent job in reproducing the actual frequencies, the two exercises yield similar results.

  23. The only trend that we find is a slight—and barely significant—decrease of the negative interaction between men’s wage and women’s working hours. This parameter may partly capture the wife’s wealth effect on labor supply.

  24. However, the effect is small and is not displayed in Fig. 14.

  25. As discussed by DG (see Appendix C in particular) and Ciscato et al. (forthcoming), the distributional assumption on the stochastic terms of the marital payoff functions is such that the choice model (1) is logit and benefits from the property of the independence of irrelevant alternatives. Under this assumption, treating the composition of the married population as exogenously given does not affect the empirical findings.

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Acknowledgments

The authors thank the editor and two anonymous reviewers for very helpful comments. Additionally, the authors acknowledge the insightful comments of Arnaud Dupuy, Alfred Galichon, Sonia Jaffe, Andreas Steinhauer, Frederic Vermeulen, Paul Vertier, and seminar participants at University of Chicago, Sciences Po Paris, and the RES Symposium of Junior Researchers. The data used in this paper are available from IPUMS-CPS, University of Minnesota, www.ipums.org.

Funding

Weber is grateful for financial support from the France Chicago Center Exchange Fellowship and for the hospitality of the CEHD at the University of Chicago where part of this paper was written.

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Correspondence to Edoardo Ciscato.

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Appendices

Appendix A: Neutrality of optimal matching

According to DG, the equilibrium matching is described by the function 2. Take the log of π(x,y) so that:

$$ \log\pi(x,y) = x^{\prime}\frac{A}{\sigma}y - \frac{a(x)}{\sigma} - \frac {b(y)}{\sigma}. $$

The first component is xBy: without the identification assumption with multiple markets described in Section (3.4), we are still able to identify B = A/σ unequivocally. In fact, under any assumption to disentangle A from σ, a sample (X,Y ) yields a unique estimate \(\hat {B}\).

As concerns the second and third components a(x)/σ and b(x)/σ, define \(\tilde {a}(x)=\exp (a(x)/\sigma )\) and \(\tilde {b}(x)=\exp (b(x)/\sigma )\). We can rewrite (2) as:

$$ \pi(x,y) = K(x,y;B)\tilde{a}(x)\tilde{b}(y) $$

and plug it into the accounting constraints:

$$ \begin{array}{@{}rcl@{}} f(x) & =& \tilde{a}(x){\int}_{\mathcal{Y}}K(x,y;B)\tilde{b}(y)dy \\ f(y) & =& \tilde{b}(y){\int}_{\mathcal{X}}K(x,y;B)\tilde{a}(x)dx. \end{array} $$

DG suggest solving this system by means of an IPFP algorithm. Notice that we can conclude that, for a given set of parameters B, there is a unique solution given by vectors \(\tilde {a}^{*}\) and \(\tilde {b}^{*}\), and thus a unique solution π.

Appendix B: Improvements to the estimation procedure

Depending on the year, our samples may contain many individuals. However, for computational reasons, estimation can only be performed on a subset of the population. Doing so, we do not make full use of the data to compute the empirical variance-covariance matrix. If the subsample’s size is too small, this may even introduce some bias in the estimates. Since the estimation strategy relies on matching the theoretical co-moments to the empirical counterparts, we pick a random subsample whose co-moments of interest are close to those of the full sample. Hence, we use the following procedure to select the subsamples:

Procedure 1

Let N be the number of couples in the population:

  1. Step 0.

    Compute the empirical variance-covariance \(\hat {V}\equiv E[XY]\) with the full sample

  2. Step 1.

    Draw a subsample of size n < N and compute the empirical variance covariance matrix \(\hat {V}_{n}\)

  3. Step 2.

    Check if \(|\hat {V}-V_{n}|<\epsilon \times \hat {V}\) for a given level of precision 𝜖.

  4. Step 3.

    If step 2 is satisfied, use Vn and the corresponding subsample to estimate the affinity matrix, otherwise repeat steps 1–3.

Appendix C: Samples

Table 1 Robustness checks

Appendix D: Additional figures

Fig. 15
figure 15

Relevant cross-interactions. Sample used: baseline A. The figures display the estimated trends of the off-diagonal elements of the marital preference parameter matrix A that have some relevance in our decomposition exercise in Section 6.4. In the labels, the first trait is the husband’s and the second is the wife’s, e.g., Wage-Educ refers to the interaction between the husband’s wage rate and the wife’s education

Fig. 16
figure 16

Sample selection by median age. Sample used: check 1 (see Appendix C). The figures compare our baseline results on estimated trends of the diagonal elements of the marital preference parameter matrix A with those obtained using a subsample of couples where at least one partner is aged between the contemporaneous female median age at first marriage (minus 2) and the contemporaneous male median age at first marriage (plus 2)

Fig. 17
figure 17

Sorting on annual earnings. Sample used: check 2 (see Appendix C). The figures show estimated trends of the diagonal elements of the marital preference parameter matrix A when annual earnings are used instead of wages

Fig. 18
figure 18

All couples and working couples (where both partners work). Sample used: check 3 (see Appendix C). The figures compare our baseline results on estimated trends of the diagonal elements of the marital preference parameter matrix A with those obtained using a subsample of couples where both spouses work

Fig. 19
figure 19

All couples and childless couples. Sample used: check 4 (see Appendix C). The figures compare our baseline results on estimated trends of the diagonal elements of the marital preference parameter matrix A with those obtained using a subsample of childless couples

Fig. 20
figure 20

Sorting on potential income. Sample used: check 5 (see Appendix C). The figures compare our baseline results on estimated trends of the diagonal elements of the marital preference parameter matrix A with those obtained using a measure of potential wages

Fig. 21
figure 21

Decomposed taste for interracial marriage. Sample used: check 6 (see Appendix C). The figures describe trends for preferences for interracial marriage, decomposed by racial/ethnic category. We omitted findings for the category “Others,” which is by far the smallest in numbers (see Fig. 3)

Fig. 22
figure 22

Education omitted. Sample used: check 7 (see Appendix C). The figures compare our baseline results on estimated trends of the diagonal elements of the marital preference parameter matrix A with those obtained when purposefully omitting education

Fig. 23
figure 23

Cohabitating and married couples. Sample used: check 8 (see Appendix C). The figures compare our baseline results on estimated trends of the diagonal elements of the marital preference parameter matrix A with those obtained using a subsample of cohabitating couples. Data on cohabitating couples are only available since 1995 and the size of the sample is considerably smaller

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Ciscato, E., Weber, S. The role of evolving marital preferences in growing income inequality. J Popul Econ 33, 307–347 (2020). https://doi.org/10.1007/s00148-019-00739-4

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Keywords

  • Matching
  • Assortative mating
  • Marital preferences
  • Between-household inequality

JEL Classification

  • D1
  • I24
  • J12