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 betweenhousehold 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 betweenhousehold 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
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.
The methodology consists of finding a loglinear model with good fit to explain a contingency table with the distribution of income by percentile (plus one category containing zeroincome observations). Then, one can compute predicted frequencies after removing certain regressors to reproduce counterfactual situations.
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.
As for Greenwood et al. (2014), we hereby refer to the revised findings published in the corrigendum.
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 \(\mathcal {W}(A,\sigma )\).
In addition, in CPS waves before 1976, there is no state variable at the household level. Only broad geographical areas are reported.
The 5level 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.
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.
Comparing summary statistics before and after 1971 suggests that most Hispanics declared themselves as White, whereas the category Others mostly contains Asians before 1988.
We also exclude students aged more than 23 by combining data on school attendance and reasons for not participating to the labor market.
More precisely, each cohort t of young men matches with the cohort t + 1 of young women.
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/timeseries/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.
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.
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.
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 crosssection. We do the same for women.
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.
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).
Precisely, we replace wages by the variable log(1 + w^{a}) where w^{a} are (possibly 0) annual earnings.
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.
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.
However, the effect is small and is not displayed in Fig. 14.
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 IPUMSCPS, 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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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:
The first component is x^{′}By: 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:
and plug it into the accounting constraints:
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 variancecovariance 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 comoments to the empirical counterparts, we pick a random subsample whose comoments 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:

Step 0.
Compute the empirical variancecovariance \(\hat {V}\equiv E[XY]\) with the full sample

Step 1.
Draw a subsample of size n < N and compute the empirical variance covariance matrix \(\hat {V}_{n}\)

Step 2.
Check if \(\hat {V}V_{n}<\epsilon \times \hat {V}\) for a given level of precision 𝜖.

Step 3.
If step 2 is satisfied, use V_{n} and the corresponding subsample to estimate the affinity matrix, otherwise repeat steps 1–3.
Appendix C: Samples
Appendix D: Additional figures
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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/s00148019007394
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DOI: https://doi.org/10.1007/s00148019007394
Keywords
 Matching
 Assortative mating
 Marital preferences
 Betweenhousehold inequality
JEL Classification
 D1
 I24
 J12