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.

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 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:

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

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:

• Step 0. Compute the empirical variance-covariance $\hat {V}\equiv E[XY]$ 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

Table 1 Robustness checks

Appendix D: Additional figures

Fig. 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

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

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

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

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

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

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

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

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