The Relationship Between Spouses’Wages Over Time
Margaret Carroll
University of Wisconsin

Hyunjae Kang
Stony Brook University

Steven Stern
Stony Brook University

July 2021

Abstract
Using predicted wages from 18 CPS data waves between 1962 and 2019, we use local linear regression estimates of each
spouse’s predicted wage as a function of his/her spouse’s wage and show how they have changed over time. We look further
into issues such as how much of assortative mating on wages can be explained by assortative mating on education andwhen, in a couple’s lifetime, wages should be observed. We …nd strong evidence of assortative mating in both wages andeducation with assortative mating in education explaining much of the assortative mating in wages. We …nd that using
wages at the time of marriage causes signi…cant measurement problems as they do not re‡ect the true long-term expectedvariation in wages. Finally, we …nd that most of the assortative mating occurs at relatively low values of wages.

1

Introduction

In many ways, marriage has become more equal between partners, especially in labor market characteristics. Recent researchsupports the idea of positive assortative mating, that equilibrium in the marriage market results in positive correlation
between the earnings of spouses (e.g., Cancian et al.,1993; Blackburn and Bloom, 1995; Cancian and Reed, 1999; Hyslop,
2001; Nakosteen and Zimmer, 2001; Schwartz, 2010; Bredemeier and Juessen, 2013), and this may be a result of a change inthe structure of marriage itself. Instead of labor market specialization within families, we see more cooperative households
that have more equal distributions of …nancial power (e.g., Cancian et al., 1993; Blackburn and Bloom, 1995; Gray, 1997;
Cancian and Reed, 1999; Hyslop, 2001; Bianchi, Robinson, and Milkie, 2006). Alternatively, intra-family equality could be
due to the changing role of women in the workforce; women’s labor force participation has increased since the 1960’s as has
women’s levels of education and wage levels (Goldin, 2006).
There are some papers in the literature that use only two or three points in time (Blackburn and Bloom, 1995; Hyslop,
2001; Zimmerman and Nakosteen, 2001; Bredemeier and Juessen, 2013); others use multiple years (Cancian and Reed, 1999;
Schwartz, 2010). This paper examines assortative mating trends comprehensively, using frequent cross-sections back to 1962.
The existing research predominantly focuses on earnings when determining the association between spouses’ labor market
characteristics (e.g., Nakosteen and Zimmer, 2001). However, as we discuss later, given the evidence for the e¤ect of marriage
on labor force participation for women especially in the early to mid-20th century (e.g., Bredemeier and Juessen, 2013), it isless useful to look at earnings as it is a function of time spent working.1 In fact, assortative mating is a story about wages(Becker, 1973), and hours is a story about household specialization (Becker, 1973);2 the two together determine earnings.
We instead predict underlying wages of each spouse and measure association along labor market characteristics in terms of
how spouses’underlying wages relate to each other.
We also examine how much sorting with respect to wages can be explained by education. Part of the motivation forthis further analysis is the potential role education plays in marriage: that the social component of schooling leads many
This project started as a research project by Carroll in Stern’s undergraduate econometrics class. Carroll did all of the heavy lifting throughout
the project until she became ill. We would like to thank Marina Azzimonti, Gabriel Mihalache, David Wiczer, and especially Yiyi Zhou for excellent
suggestions. Stern is the corresponding author: (631)632-1328; steven.stern@stonybrook.edu.
1 Lundberg, Pollak, and Wales (1997), Blundell et al. (2005), and Pollak (2005) argue that wages are also the most relevant measure associatedwith bargaining because earnings re‡ect hours decisions. Chiappori, Fortin, and Lacroix (2002) show how bargaining power can a¤ect labor supply
within a household. Phipps and Burton (1998) use income but spend no time justifying its use over wage. Lundberg, Startz, and Stillman (2003)
use retirement (which is equivalent to using earnings in the context of this discussion) and also do not address income’s endogeneity.
2 The existence of household specialization and/or bargaining issues might a¤ect female education and, therefore, wages (e.g., Konrad andLommerud, 2000; Chiappori, Iyigun, and Weiss, 2009; Ge, 2011; Gihleb and Lifshitz, 2013) or might a¤ect which women marry (e.g., Van derKlaauw, 1996; Mazzocco, Ruiz, and Yamaguchi, 2007).

1

couples to meet in that environment, leading to a natural correlation between spouses’education levels and therefore wages.
If positive assortative mating along labor market characteristics is primarily driven by association in spouses’ education,then it is possible that couples are actually sorting along social characteristics rather than marginal productivity in the labormarket (Charles, Hurst, and Killewald, 2013).
Section 2 provides a literature review. Section 3 describes the data. It provides information on how the data sets foreach year were constructed and shows moments and trends of some of the key variables. Section 4 describes the methodologyof the paper. We start o¤ using a standard Heckman (1979) 2-step estimation procedure to estimate log wage equations andpredict log wages. Then, we describe how to use local linear regression to measure the relationship between the wages andeducation of husbands and wives and how they change over time. Finally, we propose how to test for positive assortative
mating. Section 5 provides empirical results, and Section 6 concludes.

2

Literature Review

The changes in wage association come in part from changes in family roles: a movement away from a more traditional,
specialized family structure towards a collaborative one. Becker’s (1973) theoretical model of the traditional family structure
included a head of household, typically male, who specializes in the labor market, and a partner, typically female, who
specializes in home production. This model of family structure leads to economic characteristics of partners being negatively
correlated, especially earnings, but non-economic characteristics that are positively correlated as people seek spouses similar
to themselves in other ways (Becker, 1973, 1991). However, Becker (1973, 1991) provides no empirical support for the theory,
so we look to other research to assess the validity of his claims.
Empirical analysis shows specialization becoming less common over time (Bianchi, Robinson, and Milkie, 2006; Bredemeierand Juessen 2013). Fertility, education, and labor market participation decisions have moved away from the gender roles
outlined by Becker, and increasingly families are composed of dual-earners with spouses entering the marriage with similarearnings capabilities and maintaining that equality throughout the relationship (Schwartz, 2010). Goldin (2006) describes
this change as one from women as secondary workers, whose labor supply was highly elastic with regard to household income,to one in which women’s identities were formed before partnering, an identity that “placed career ahead, or on equal footing,as marriage.”
These profound changes in 20th century women’s economic lives have had implications for their social lives as well. The
correlation between spouses’ education levels has increased by 25% between 1960 and 2003 (Schwartz and Mare, 2005).
Because high-productivity women get more education and have higher labor force participation rates, high-productivity
couples have more opportunities to meet at school or work. Meanwhile, low-productivity men are less likely to meet highproductivity women, and low-productivity women are less likely to meet high-productivity men. This naturally results insome similarities in the underlying wages among couples.
Much of the existing research on assortative mating on labor market characteristics focused on its rami…cations forinequality. Schwartz (2010) estimates that spousal matchings across di¤erent earnings percentiles accounts for 25% to 30%of the earnings inequality among households; other estimates range from 17% to 51% (Cancian et al. 1993; Blackburn andBloom 1994; Cancian and Reed 1999; Hyslop 2001, Schwartz 2010). Chiappori et al. (2020a, 2020b) and Greenwood et al.
(2014) focus on constructing Gini coe¢ cients under counterfactual matching patterns and …nd similar increases. However,this increase in inequality across families is paired with a decrease in inequality within a marriage (Chiappori, 1992; Cancian
and Reed, 1998; Schwartz, 2010; Greenwood et al., 2014). Greenwood et al. (2014) perform a straightforward analysis of
the change in inequality over time. Using the Gini index, they observe the changes in household income distribution in 2005
with 2005 mating preferences, 1960 mating preferences, and random mating, with either 2005 level labor force participationor 1960 level labor force participation. The authors observe that the positive assortative mating trends in 2005 increases
the Gini coe¢ cient relative to what it would be given 1960 mating patterns from 0:35 to 0:43. Furthermore, given the 1960
mating patterns, imposing the female labor force participation rates of the 1960’s increases the Gini coe¢ cient from 0:35 to
0:44, implying the 2005 female labor force participation rates had a dampening e¤ect on household inequality. We focus
on the similarity between spouses’underlying wages, rather than total earnings, to avoid the e¤ects of joint decision making
over hours. We do so comprehensively, taking advantage of the age of the ASEC and CPS surveys to look at repeated crosssections of data over time since 1960.
There is a large and growing literature discussing the implications of inequality within a household. Friedberg and Webb(2005) …nd that the distributions of wages, earnings, and unearned income between spouses a¤ects allocation of chores andleisure. Some …nd that children in the family receive more care when the wife has more bargaining power (e.g., Schultz, 1990;
Thomas, 1990, 1994; Haddad and Hoddinott, 1994; Du‡o,2003; Du‡o and Udry, 2004). Others …nd other e¤ects of within-2

family bargaining power on household consumption, with increases in women’s income increasing consumption of goods likechildren’s clothing and women’s clothing relative to men’s (Lundberg, Pollack, and Wales, 1997; Phipps and Burton 1998;
Lundberg, Startz, and Stillman, 2003; Du‡o and Udry, 2004).
A small but growing literature discusses the dynamics of assortative mating. Gihleb and Lifshitz (2013) provide evidence
that dynamic human capital accumulation plays an important role in the assortative mating issue. Van der Klaauw (1996)
endogenizes the marriage decision and shows that it has signi…cant e¤ects on estimates of wage e¤ects on female labor supply.
Ge (2011) suggests that the e¤ect of education on …nding a good mate has signi…cant explanatory power in explaining women’s
education choices, and Chiappori, Salanié, and Weiss (2017) show evidence of increasing returns to women’s education in
marriage markets.
Presently, Siow (2015) and papers such as Graham (2011) and Chiappori, Salanié, and Weiss (2011) provide methods tomeasure and test for assortative mating. We think there is still room for discussion about how to measure the amount ofassortative mating, and we focus on many of the issues we see as unresolved. These include what variable to focus on (e.g.,
education, wage, earnings); how to measure the variable (e.g., levels, percentiles); when to measure the degree of assortative
mating (e.g., the time of marriage, in a particular band of age, or not controlling for duration of marriage or age); and how
to test for assortative mating. These are the issues discussed in this paper.

3

Data

The data are from the Annual Social and Economic Supplement (ASEC) to the Current Population Survey (CPS), a monthly
survey conducted by the Bureau of Labor Statistics. They cover the years 1962, 1967, 1970, 1972, 1975, 1978, 1980, 1985,
1990, 1995, 2000, 2005, 2007, 2010, 2014, 2015, 2018, and 2019. We choose these years to capture incremental changes, withmore detail for the years before and after the Great Recession. The year 1972 is included as a comparison point to deal witha change in the availability of important explanatory variables that year. We use the data sets available from the Integrated
Public Use Microdata Series.
We include only heterosexual married couples within the ages 16 - 64.3 Selection rules and their e¤ects on sample size aredetailed in Table 1. The marriage restriction is the most important source of selection. Due to the increasing non-married
population, the e¤ect of the selection rule concerning marital status rises over time. The impact of the selection rules changes
signi…cantly between 1967 and 1970. In 1967, the proportion of observations lost to not married 4 was 0:268, while, in 1970,
it was 0:487. The proportion of observations lost to the age restrictions is relatively stable over time, which is 0:077 on
average. The important selection rules concern age and marital status excluding more than half of the sample. The impactof the selection rules changes signi…cantly between 1962 and 1970. In 1962, the proportions of observations lost to <16 years,>64 years, and not married were 0:056, 0:134, and 0:265, while, in 1970, they were 0:321, 0:093, and 0:196, respectively.
From 1970 on, the proportion of observations lost to <16 years declines by 0:6% annually, the proportion lost to >64 years
increases by 0:6% annually, and the proportion lost to not married rises by 1:1% annually. We exclude government workers,
self-employed people, and people in the armed forces. The sample sizes are very large, resulting in precise estimation of
the relevant parameters. For each year of data, it is necessary to construct the wage variable from last year’s salary, weeks
worked, and usual hours worked variables: hourly wage = annual earnings(hours/week*weeks/year).5 Implausibly low
wages, which we de…ne as wages less than the real minimum wage in the given year, are omitted from the estimation sample.
Wages are measured in 2014 real dollars.
Table 2 contains moments for each variable across each year, including a disaggregation by sex for the labor market
variables. Real log wages are conditional on working. With respect to explanatory variables, there is a notable rise in the
proportion of the sample that is Hispanic, rising from 4:5% in 1972 to 20:6% in 2019. The age distribution of Hispanics does
not change much over the years. But the never-married/single proportion changes from 0:24 in 1972 to 0:41 in 2019. This isa bigger increase than the same change in the whole population which is from 0:23 to 0:35. The variable Has Children Under
5 is not available until 1970, and Hispanic is not available until 1972. The increase of the Hispanic population is associatedwith the surge of Mexican immigrants (Borjas ,2006).
Also, the composition of education levels change signi…cantly, as seen in Figures 1 and 2. Over the sample period, the3 The CPS data started capturing same-sex marriage presumably due to the legalization of same-sex marriage in 2014. Although there is nosame-sex marriage observed prior to 2019, unmarried same-sex couples have been included in the data since 1990. The proportion of same-sex
marriage in 2019 is around 0:008, and the proportion of same-sex couples is around 0:015. Jepsen and Jepsen (2002) use data from 1990 Census
data to look at inequality within gay marriages.
4 Variable names, such as not married, are displayed in a di¤erent font.
5 There exists inconsistency within the variables used in constructing wage. The weeks-worked and the income variables are the information on
the previous year while the hours-worked variable represents the average hours worked in the week before the survey.

3

Table 1: Data Selection
1962
71,741

1967
1970
1972
1975
CPS Sample Size
68,676 145,023 140,432 130,124
Cause of Exclusion
Age > 64 or Age of Spouse > 64
6,556
6,002
8,832
8,952
8,954
Age < 16 or Age of Spouse < 16
26
24
32
16
32
Not Married
18,521
18,43670,64867,89662,181Same-sex spouse
14
0
0
0
0
Unmarried Partner
0
0
0
0
0
Government, Self-Employed,
13,587
12,586
18,961
18,951
17,595and Armed Forces
Other Variable Missing
3,226
2,734
3,798
3,893
3,806
Remaining Sample Size
Total*
25,282
25,21436,21434,326
31,390# Employed
14,725
15,546
22,684
21,276
18,822# Employed with Plausible Wage
8,498
12,606
19,455
18,621
16,133
Note: Total includes sample with implausible wage, which we exclude for estimation

1978
155,706

1980
181,488

1985
161,3621990
158,079

10,53220
75,1590022,225

12,842
26
87,7960026,36911,942
24
78,3710022,16912,422
2
77,3820023,598

4,744

5,094

4,544

4,274

35,62022,654
19,372

40,62626,367
22,68335,942
23,84921,53531,87622,204
20,770

Table 1: Data Selection (Continued)
CPS Sample Size
Cause of Exclusion
Age > 64 or Age of Spouse > 64
Age < 16 or Age of Spouse < 16
Not MarriedSame-sex spouse
Living with unmarried partner
Government, Self-Employed,and Armed Forces
Other Variable Missing
Remaining Sample Size
Total
# Employed# Employed with Plausible Wage

1995
149,642

2000
133,710

2005
210,6482007
206,6392010
209,8022014
199,556

2015
199,0242018
180,0842019
180,101

11,7148
74,287
7
183
21,62910,34418
67,5225
231
17,92013,404
12
111,62115
377
29,742

13,556
4
108,9458
363
29,15014,674
10
112,20138
441
27,747

16,926
12
105,56354341
24,427

17,060
16
105,127
69
389
23,933

17,502
8
93,401
172
344
21,013

18,398
4
92,585505
346
20,725

3,842

3,402

5,128

5,212

5,235

4,906

4,772

4,298

4,123

29,734
20,957
19,47627,216
19,68418,18741,07029,53028,01740,31829,19027,464

39,83027,56325,38337,204
26,14824,33137,012
26,112
24,21532,55423,542
22,19632,49623,764
22,636

1978
0.350
2.896
(0.431)0.844
3.326(0.479)2.336
40.064
0.930
0.051
0.089
0.350
0.431
0.154
0.083
0.041
0.230
0.277
0.262
0.726
30,426

1980
0.385
2.879
(0.455)0.839
3.321(0.492)2.313
39.745
0.924
0.051
0.089
0.364
0.440
0.161
0.091
0.045
0.218
0.283
0.246
0.735
34,712

1985
0.464
2.798
(0.496)0.817
3.227(0.555)2.031
40.225
0.916
0.053
0.109
0.357
0.439
0.171
0.110
0.056
0.229
0.301
0.244
0.721
32,380

1990
0.546
2.804
(0.529)0.825
3.183(0.569)1.855
40.157
0.901
0.059
0.130
0.350
0.428
0.188
0.120
0.058
0.243
0.304
0.234
0.771
29,858

Table 2: Sample Moments
Variable
Female Employment

1962
1967
0.223
0.242
2.738
2.835
Female Real log Wage
(0.436)(0.414)
Male Employment
0.891
0.909
3.093
3.216
Male Real log Wage
(0.440)(0.453)National log(Real Minimum Wage)
2.208
2.325
Age
39.54639.830
White
0.931
0.938
Black
0.063
0.055
Hispanic----Has Children Under 5----High School Diploma
0.349
0.405
Some College
0.095
0.106
College Degree
0.055
0.062
Post-Graduate Degree
0.019
0.022
Northeast
0.289
0.278
South
0.246
0.258
Midwest0.304
0.299
Metropolitan
0.713
0.716
# Obs
22,39821,002
Note: Numbers in parentheses are standard deviations.

1970
0.281
2.864
(0.402)0.902
3.291(0.465)2.334
39.7550.931
0.062--0.435
0.423
0.119
0.063
0.025
0.265
0.272
0.300
0.703
31,222

4

1972
0.298
2.835
(0.424)0.883
3.280(0.481)
2.235
39.956
0.931
0.060
0.045
0.409
0.434
0.122
0.067
0.029
0.260
0.277
0.293
0.722
30,314

1975
0.303
2.884
(0.430)0.822
3.342(0.484)2.310
39.919
0.927
0.060
0.050
0.363
0.438
0.137
0.076
0.036
0.247
0.295
0.291
0.718
27,276

Table 2: Sample Moments (continued)
Variable
Female Employment

1995
2000
0.570
0.586
2.856
2.931
Female Real log Wage
(0.580)(0.608)
Male Employment
0.815
0.837
3.161
3.225
Male Real log Wage
(0.615)(0.647)National log(Real Minimum Wage)
1.914
1.990
Age
40.82741.655
White
0.873
0.893
Black
0.054
0.059
Hispanic
0.147
0.195
Has Children Under 5
0.342
0.322
High School Diploma
0.362
0.343
Some College
0.260
0.263
College Degree
0.150
0.165
Post-Graduate Degree
0.061
0.066
Northeast
0.241
0.198
South
0.306
0.312
Midwest0.233
0.235
Metropolitan
0.778
0.795
# Obs
27,53024,994
Note: Numbers in parentheses are standard deviations.

2005
0.588
2.972
(0.635)0.836
3.266(0.681)1.864
42.008
0.851
0.066
0.165
0.345
0.324
0.27
0.19
0.083
0.204
0.299
0.248
0.803
38,976

2007
0.592
3.005
(0.652)0.836
3.289(0.699)1.926
42.508
0.846
0.068
0.178
0.348
0.311
0.267
0.198
0.09
0.195
0.308
0.238
0.819
37,874

2010
0.576
3.066
(0.645)0.783
3.328(0.681)2.079
43.128
0.833
0.073
0.174
0.331
0.300
0.273
0.210
0.098
0.203
0.305
0.235
0.823
36,536

2014
0.575
3.040
(0.617)0.809
3.281(0.689)1.996
43.899
0.823
0.072
0.188
0.295
0.282
0.27
0.219
0.117
0.186
0.314
0.232
0.833
34,542

2015
0.573
3.062
(0.671)0.816
3.286(0.703)1.981
43.925
0.820
0.071
0.196
0.305
0.284
0.262
0.222
0.117
0.170
0.348
0.204
0.832
34,206

2018
0.593
3.101
(0.684)0.835
3.330(0.709)1.946
44.088
0.809
0.072
0.207
0.295
0.275
0.258
0.238
0.125
0.155
0.368
0.198
0.844
30,698

2019
0.609
3.103
(0.665)0.840
3.338(0.711)1.921
44.156
0.814
0.070
0.206
0.303
0.270
0.257
0.240
0.129
0.159
0.362
0.201
0.845
31,020percentage of the sample with some post-high school education increases from 13:7% in 1962 to 65:1% in 2019 for women andfrom 20:1% in 1962 to 59:9% in 2019 for men. From 1962 to 1970, the big increase is in the proportion of people who …nishhigh school. In later years, the increase is all of the other education levels. For example, the change in the percentage withat least a college degree is from 4:5% in 1962 to 38:4% in 2019 for women and from 10:2% in 1962 to 35:3% in 2019 for men.
Figures 3 and 4 show how employment rates and mean log real wages change over the sample period based on the moments
in Table 2. Women’s employment rates rise dramatically between 1962 and 1990 as documented in the literature (e.g., Goldin,
2006, Blau and Kahn, 2007; Bailey, Hershbein, and Miller, 2012). But, this by itself does not a¤ect our analysis because ourmeasure of analysis is wage rather than employment. On the other hand, Figure 4 shows large increases in wages for women,both absolutely and relative to men. However, unlike employment, most of the increase occurs between 1985 and 2010. Thechange in the log wage gap is shown in Figure 5 and is consistent with the literature (e.g., Blau, 1998; Eckstein and Nagypal,
2004; Blau and Kahn, 2017). The trend in log wages is the relevant one for this paper.
The weeks-worked variable in the CPS data before 1978 are collected by categories: 1 13 weeks, 14 26 weeks, 27 39
weeks, 40 47 weeks, 48 49 weeks, and 50 52 weeks. Papers using the CPS use the midpoint of each interval to represent the
weeks-worked (e.g., Bailey, DiNardo, and Stuart, 2020). Derenoncourt and Montialoux (2020) use the midpoint and smooththe measure using random numbers generated from the uniform distribution. Using the fact that weeks-worked variablesof later years are collected both as continuous and categorical variables, we identify the measurement errors from using thebracketed variable. Then we adjust the measurement errors in the weeks-worked variable nonparametrically. Using locallinear regression, we regress the measurement errors on total hours worked using later years’data, then use the prediction
for the adjustment. For both female and male respondents, there exist unignorable errors whose annual hours worked wereless than 2000. The magnitude of the measurement errors is displayed in the appendix.

4

Methodology

The goal of our work is to examine how the relationship between spouses’wages has changed over time. Our procedure does
this in two stages separately for each year of investigation: …rst, we predict of underlying wages using a Heckman two-stepprocedure, and, second, we use local linear regression methods to examine the relationship between spouses’predicted wages.
We consider at what point in across couples’marriage is a good time to measure assortative mating and consider measuring
it in log wage levels and in percentiles from the joint wage distribution. Afterwards, we estimate how much of the sorting
over wages is due to sorting over education and test for assortative mating against the null hypothesis of random sorting.

4.1

Heckman Procedure

We need to compare wage rates of all spouses, including those not in the labor force. The decision to work is determinedin part by the wage a person would earn if she worked, thus causing the wage distribution of those who work to di¤er from5

Female Education Level Proportions
1
0.9
0.8
0.7
0.6
Post-Graduate Degree

0.5College Degree
Some College

0.4High School Diploma

0.3
0.2
0.1
0
1962 1967 1970 1972 1975 1978 1980 1985 1990 1995 2000 2005 2007 2010 2014 2015 2018 2019

Year

Figure 1: Female Education Level Proportions

Male Education Level Proportions
1
0.9
0.8
0.7
0.6
Post-Graduate Degree

0.5College Degree
Some College

0.4High School Diploma

0.3
0.2
0.1
0
1962 1967 1970 1972 1975 1978 1980 1985 1990 1995 2000 2005 2007 2010 2014 2015 2018 2019

Year

Figure 2: Male Education Level Proportions

6

Male and Female Employment
1.0
0.8
FemaleEmployment

0.6

Male
Employment

0.4
0.2
0.0
1960

1970

1980

1990

2000

2010

2020

Year

Figure 3: Male and Female Employment

Male and Female Real Log Wage
3.4
3.3
3.2
3.1
3.0

Female Real log Wage

2.9

Male Real log Wage

2.8
2.7
2.6
1960

1970

1980

1990

2000

2010

2020

Year

Figure 4: Male and Female Real log Wages

7

Wage Gap: log Men's - log Women's
0.7

0.6

0.5

0.4

Married People
Blau & Kahn (2017)
Blau (1998)

0.3

Eckstein & Nagypal (2004)
0.2

0.1

0.0
1960

1970

1980

1990

2000

2010

2020

Figure 5: Wage Gap: log Men’s - log Women’s
Notes: The solid (blue) curve, labeled “Married People,” is based on our data. The other three curves, each covering part of therelevant period, come from the literature. Blau and Kahn (2017) is based on the second panel of Table 1. Blau (1998) is based on
Table 4. Eckstein and Nagypál (2004) is based on means in Figure 2. Eckstein and Nagypál (2004) requires a translation from theindex in Eckstein and Nagypál (2004) to log wag gaps using 1980 as a matching year where the index is translated to log wages using
Blau and Kahn (2017) as a match.

the wage distribution of those who do not work. Estimating wage equations using solely the people who work would lead tobiased estimates (Heckman, 1979), and predicting potential wages of those who do not work even with consistent estimatesstill would lead to upward-biased predictions (e.g., Maddala, 1983). Thus, it is necessary to correct for selection bias during
both estimation and prediction.
We use the Heckman (1979) two-step procedure to correct for selection bias. There is some evidence that estimates fromthe Heckman procedure are sensitive to the necessary joint normality assumption (e.g., Arabmazar and Schmidt, 1982; Lee,
1982; Olsen, 1982; Duncan and Leigh, 1985; Lalonde, 1986; Mroz, 1987; Newey, Powell, and Walker, 1990; Coslett, 1991;
Ichimura, 1993; Stern, 1996). Some researchers have proposed semi-parametric methods to avoid the sensitivity (Lee, 1982;
Olsen, 1982; Newey, Powell, and Walker, 1990; Coslett, 1991; Ichimura and Lee, 1993; Ichimura, 1993; Stern, 1996; Blundell
et al., 2007; Escanciano, Jacho-Chavez, and Lewbel, 2016). However, the focus of this study is on the wage curves themselves,
and we try to use standard methods to construct the wage curves. The Heckman procedure is used also, for example, by
Hersch (1991) and Mulligan and Rubinstein (2008).
Despite it ubiquity, we provide notation for the Heckman procedure to aid in further discussion. Let
ytij = Xtijyt + utij(1)

be the value of working for person j in family i from year t where Xtij is a set of exogenous explanatory variables andutij
iidN (0; 1). Let j = 1 for husband and j = 2 for wife. Included in Xtij are a constant, a quadratic polynomial inage, dummies for race and education, the presence of any children under 5 years of age,6 regional dummies, and an urban
dummy.7 Recall that our data are repeated cross-sections; thus, family i in year t is not the same family as family i in adi¤erent year. We ignore the joint decision-making nature of the family’s labor force participation decision (e.g., Gustman
and Steinmeier, 1986; Chiappori, 1988; Blundell et al., 2005) and assume the binary participation decision for family member
j isytij = 1 ytij > 0 :(2)We estimate using probit.
The log wage one would receive if she8 worked is modeled as
wtij = Ztij t + uw
tij

(3)

6 Mulligan and Rubinstein (2008) use number of children times a dummy for marital status.
7 One might worry about the endogeneity of young children (e.g., Rosenzweig and Wolpin, 1980; Schultz, 1990, 2010; Huber and Mellace, 2011)or education (e.g., Gihleb and Lifshitz, 2013). For education, there is much more concern about the endogeneity of education with respect to wage
(e.g., Card, 2001). But neither issue is the point of the paper.
8 We use “she” as the generic pronoun throughout.

8where Ztij is a set of exogenous explanatory variables,yuw
tij j utijyis the correlation of (uwtij ; utij ).

andAs in Heckman (1979),

iidN

yt et utij ;

2
et

1

2
t

;

Included in Ztij are the variables in Xtij excluding the presence of young children.9
E(wtij j ytij = 1) = Ztij t +

t

(Xtij

t)

(4)

where ( ) = ( )/ ( ) is the inverse Mills ratio and t = t et . Following Heckman (1979), we estimate the log wage equation
parameters for each year ( t ; t ) using OLS and then adjust standard errors appropriately.
Given probit estimates b t and OLS estimates (bt ; bt ; bet ), we can predict log wages for each person in the sample, whether
or not she works, as(
Ztij bt + bt bet (Xtij b t ) if ytij = 1(5)
wtij =
Ztij bt + bt bet (Xtij b t ) if ytij = 0

where(Xtij b t ) = E uw
tij j ytij = 0 =1

Xtij b t

Xtij b t:

We use predicted log wages for each sample person, even if log wage is observed. In some sense, this has the opposite‡avor of Nakosteen and Zimmer (2001) and Zhang and Lui (2003). Both papers measure whether there is assortative
mating associated with residuals because Becker (1973) focuses on assortative mating over wages after controlling for othercharacteristics. However, residuals capture e¤ects not observed by the researcher. There is no reason why potential couples
would distinguish between those characteristics observed by the researcher and those not observed by the researcher. If thedata became a little better (e.g., one more variable was added), do we think couples’behavior would change? On the other
hand, it might be that couples sort based on some characteristics not observed by the researcher. Consider a wage equation
similar to equation (3),wtij = Ztij1 1t + Ztij2 2t + Ztij3 3t + uw
(6)
tijwhere Ztij in equation (3) is decomposed into (Ztij1 ; Ztij2 ; Ztij3 ) and where Ztij1 is observed in the data and observed bypotential partners, Ztij2 is not observed in the data but is observed by potential partners, and Ztij3 is neither observed in
the data nor by potential partners. The true object used for sorting is Ztij = Ztij1 1 + Ztij2 2 which is di¤erent from both
Ztij1 b1t (which we use) and wtij Ztij1 b1t (which is what Nakosteen and Zimmer (2001) and Zhang and Lui (2003) use).

4.2

Local Linear Estimation

After performing the two-step Heckman procedure to predict log wages, we use a local linear regression estimator to predict
expected spouse’s wage conditional on own predicted wage and spouse’s gender, using the predicted wages for both those
who work and those who do not.10 Using a local linear regression estimator is a simple and ‡exible way to examine theorelationship between spouses’wages and still see the variation in association over wage levels.11 In particular, let w
btij
be j’ssso“own” predicted log wage and w
btij be j’s spouse’s predicted log wage. We de…ne, for some arbitrary value w
btj ; wbtj
of acouple’s predicted log wage as
s
o
o
b w
E
btj
jw
btj
={
b 0t wbtj(7)
where12

o
{
b0 w
btj
o
{
b1 w
btj

=

"
X

K

i

"
X
i

K

o
w
btij

o
w
btij

b

b

o
w
btj

o
w
btj

1
o
w
btij
1
o
w
btij

1
s
w
btij

#

o
w
btij

# 1

(8)

9 Common examples of variables included only in the participation equation are husband’s income (e.g., Mroz, 1987; Zabel, 1993; Huber andMellace, 2011) and characteristics of children (e.g., Martins, 2001; Mulligan and Rubinstein, 2008; Lee, 2009; Chang, 2011; Huber and Mellace,2011).
1 0 Suen and Lui (1999) and Fernandez, Guner, and Knowles (2005) use correlations between husbands’ and wives’ education levels to test for
positive assortative mating.
1 1 One could also test hypotheses of interest using nonparametric testing methods (e.g., Hardle, 1992).
1 2 See, for example, Ichimura and Todd (2007) or Hansen (2021).

9

andK (x) = exp

:5x2

(9)

b [ j ] is an estimate of the expected wage of a spouse given one’s wage.
is the kernel function and b is the bandwidth.13 Eoob [ j ] can be evaluated over all w
E
btj 2 Wtj where Wtjo is a closed set bounded within the set of own predicted log wages
b [ j ] curves can vary across gender and across years thus allowing us toobserved in the year-t/gender-j sample. The E
observe how assortative mating changes over time.14

4.3

Measuring the Amount of Wage Sorting Due to Education Sorting

As wage is highly correlated with other factors over which couples sort, we next determine how much of sorting over wages
can be explained by sorting over education. We do this by regressing each individual’s predicted wage given their spouse’s
predicted wage on (from the local linear regression estimation exercise) evaluated at deciles of the distribution of genderspeci…c education.
First, we order husbands by their level of education in each year t, and then we de…ne husband k as the husband withm
the kth decile of education, k = 1; 2; ::; 20. Next, we de…ne (with a slight abuse of notation) w
btf (w
btk) as the predicted log

fm
btk
analogously
wage of the wife of husband k conditional on his predicted log wage w
btk
from equation (8). We de…ne w
btm w

for the husbands. Similarly, we de…ne ebft (emtk ), using a local linear regression estimator similar to equation (8) as the wife’s
predicted level of education conditional on her husband’s level of education15 and ebm
eftk analogously.16t
The OLS regression equations are thenmw
btf (w
btk
)

f
w
btm w
btk

=

f
0 +

=

m
0 +

f f
f
bt (emtk ) + "tk ,
1e
m m
bt
1 e

"ftk

m
eftk + "mtk , "tkiid 0;

f2"

iid 0;;

m2":

These allow us to estimate how much of the assortative mating trends are due to sorting over wages and how much is due
to sorting over education. Because education is highly correlated with wages as well as between spouses due to the social
context of marital sorting, we expect to see a positive relationship between the two.

4.4

Testing for Positive Assortative Mating

Siow (2015) and associated papers (e.g., Graham, 2011; Chiappori, Salanié, and Weiss, 2011) suggest methods based on
empirical representations of supermodularity to test whether a matching process exhibits positive assortative matching. Siow(2015) suggests that a “positive correlation test”is a weak test because it is unclear how low the correlation should be before
the theory is rejected.”
To understand our proposed test, let nmf be the number of observations
in a sample where a type-m male, m = 1; 2; ::; M ,P
is matched with a type-f female, f = 1; 2; ::; F , and de…ne N = mf nmf as the total number of sampled marriages. Let
pmf be the probability that a randomly sampled marriage is of type mf . The inclusion of some unobserved preferences
causes the sample proportions to be random.17 The unrestricted log likelihood function isXL=
nmf log pmf :m;fno
The unrestricted MLE of p is pbu = pbumf with pbumf = nmf =N . Siow (2015) and others argue that the way to test for positive
assortative mating is to also estimate pb under the restrictions imposed by positive assortative mating and then perform a

1 3 We produce results both using …xed bandwidth (0:5) and the bandwidth based on least square cross-validation (the rule of thumb).
Thisprocess chooses the constant bandwidth which minimizes the conditional weighted mean integrated squared error (Fan and Gijbels, 1996). Whilethe cross-validation approach is used to provide the minimized integrated mean squared errors, the generated curve is sometimes hard to interpret.
1 4 Asadi and Zarezadeh (2020) suggest an alternative measure to analyze the relationship between two random variable, X and Y , with marginal
distributions Fx and Fy . They measure the correlation between X and Fx 1 (Fy (Y )).
1 5 We use the same kernel function as in equation (8), and the bandwidth be is chosen using the cross-validation method.
1 6 For this procedure, we de…ne education as the semi-continuous variable highest grade level, as opposed to the distinct categorical variables
used in equations (1) and (4).
1 7 Siow (2015) uses iid Extreme Value errors. Papers such as Graham (2011) show that the methodology can be used even without specifying afunctional form for the distribution of the errors.

10likelihood ratio test. A simpler approach is to construct a “pseudo-Wald test,” requiring only the unrestricted estimates(Kang and Stern, 2021). This avoids the cost associated with imposing the positive assortive mating restrictions, and it
allows for more general tests. The condition for positive assortative mating is18
Rmf = (log pmf + log pm+1;f +1 )(log pm+1;f + log pm;f +1 ) > 0 8mf;

Note that one could test the null hypothesis that Rmf = 0 8m; f with power against the alternative of (positive or
negative) assortative mating as a Wald Test with
X
2
2
T =
Tmf
=b
s2mf
(10)
K
m;f

where

s2mf

Tmf = log pbumf + log pbum+1;f +1= V ar=(1

log pbumf + log pbum+1;f +1

log pbum+1;f + log pbum;f +1 ;log pbum+1;f + log pbum;f +1

pmf ) (1 pm+1;f +1 ) (1 pm+1;f ) (1 pm;f +1 )
+
+
+
;
npmf
npm+1;f +1
npm+1;fnpm;f +1andK = (M

1)(F

1)

(11)

is the number of restrictions (Kang and Stern, 2021). The results of this test statistic are reported in Section 5.5.
If one were interested in testing the null hypothesis of no assortative mating versus the alternative of positive assortative
mating (one-sided), then the distribution of T under either the null or alternative would be di¢ cult to evaluate. However, thesame is true of Siow (2015) because the restrictions are inequalities instead of equality restrictions (see, for example, Kudo,
1962; Gourieroux, Holly, and Monfort, 1982; Kodde and Palm, 1986). Siow (2015) uses parametric bootstrapping to simulate
critical values. The same can be done for T . Under positive assortative mating, T > 0, and, with total positive assortative
mating (TP2 in Siow, 2015), T ! 1 because pm+1;f pm;f +1 = 0. Under random sorting, where log pmf = log xm + log yf ,Rmf = 0 8m; f . In general, one can simulate a critical value bc such that
Pr[T > bcA j Rmf = 0 8m; f ] = :The advantages of the Siow (2015) test over our suggested pseudo-Wald test are a) it provides an estimate of p under the
restriction of positive assortative mating (and therefore also allows for simulation using pb) and b) it allows one to think of
the positive assortative mating model as the null hypothesis. Advantage (a) has signi…cant value, but advantage (b) is not
so valuable since it is not clear which of the two models should be taken as the null hypothesis model. In our case, since we
do not focus on the positive assortative mating parameters, our test seems advantageous, given its ease of use.
We can also construct a likelihood ratioP(LR) test. The unrestricted estimate of pmf is pbumf = nmf =n where nmf is thenumber of observations in cell mf and
P n = m;f nmf .PUnder the null hypothesis of random sorting, the restricted estimateof pmf is pbrmf = pbrm pbrf where pbrm = f pbumf and pbrf = m pbumf . Then, the LR test statistic is
3
2
X
X
Lu
nmf log pbumf
nmf log pbrmf 5
= 24
2 log
Lr
m;f
m;f
2
3
X
pbumf
= 24
nmf log r 5
pbmf
m;f
2
3
X
pbumf
2
= 24
nmf log P
K
P u 5
u
p
b
p
b
m;f
f mf
m mf
1 8 Note that R

ij > 0 8ij )log pij + log pi+k;j+m > log pi+k;j + log pi;j+m 8k; m

111:

Distribution of Pseudo-Wald Test Statistics for a = 0
1
0.9
0.8
0.7
0.6
n=500

Cumulative
0.5
Distribution

n=1000n=10000

0.4

Chi-sq Distn(81)

0.3
0.2
0.1
0
0

20

40

60

80

100

120

140

160

180

Wald Test Statistic

Figure 6: Distribution of Pseudo-Wald Test Statistic for=0

Distribution of LR Test Statistics for a = 0
1
0.9
0.8
0.7
0.6
n=500

Cumulative
0.5
Distribution

n=10000.4

n=10000

0.3

Chi-sq Distn(99)

0.2
0.1
0
0

50

100

150

200

LR Test Statistic

Figure 7: Distribution of LR Test Statistic for

=0

with
K = MF1which is larger than the degrees of freedom in equation (11) (Kang and Stern, 2021). This di¤erence exists because, for thepseudo-Wald test, one loses degrees of freedom at m = M and f = F which does not happen for the LR test. The resultsof these test statistics are reported in Section 5.5.
The application in Siow (2015) is about education which has a natural discreteness to it, while our application is about
log wage which is continuous. Dagsvick (1994) and Dupuy and Galichon (2014) suggest how to amend the Choo and Siow(2006a, 2006b) model for continuous variables. To operationalize the test statistic in equation (10), we divide the R R
space of log wages into cells where the boundaries of each cell are the deciles for men and women in each of our samples. By
construction, under the null hypothesis of random sorting, this implies that pbrmf = 1=100 8m; f . We also report results ofthe test statistics for education using 5 levels of education for men and women.

12Power
1
0.9
0.8
0.7
0.6

Wald Test, n=500
Wald Test, n=1000

0.5

Wald Test, n=10000

0.4

LR Test, n=500

0.3

LR Test, n=1000

0.2
0.1
0
0

0.2

0.4

0.6

0.8

1

1.2

Alpha

Figure 8: Power
Table 3: Female Participation Estimates
Variable
Constant
White
Black
Hispanic
Age/100

1962-2.772 ***-0.161-0.2021967-1.290 ***-0.354 *-0.356 *1970-0.620 **-0.011
0.246

7.199 ***

2.810 ***

0.919

1972
-0.487 **-0.1380.037-0.121 *
0.750

1975
-0.479 **-0.1110.050-0.0020.930

1985-0.695 ***-0.0360.154 *
-0.109 **3.976 ***

1990
-1.399 ***0.086
0.169 *
-0.117 ***7.966 ***

(Age/100)-8.235 ***-3.124 **-2.587 **-2.566 **-3.150 ***-4.883 ***-7.150 ***-7.903 ***HS Diploma
0.208 ***
0.331 ***
0.279 ***
0.304 ***
0.302 ***
0.362 ***
0.467 ***
0.444 ***
Some College
0.221 ***
0.268 ***
0.294 ***
0.284 ***
0.416 ***
0.422 ***
0.597 ***
0.645 ***
College Degree
0.134-0.0140.060
0.153 **
0.381 ***
0.437 ***
0.489 ***
0.660 ***
Post Grad Degree
0.562 ***
0.216
0.386 ***
0.312 **
0.709 ***
0.671 ***
0.558 ***
0.750 ***
# Children < 5-0.598 ***-0.631 ***-0.615 ***-0.601 ***-0.567 ***-0.503 ***Northeast
0.170 ***
0.100 *
0.095 **
0.128 ***
0.061
0.049
0.061 *
0.079 *
South
0.078
0.047
0.039
0.148 ***
0.057
0.033
0.001
0.046
Midwest
0.040
0.053
0.062
0.122 ***
0.056
0.046
0.098 ***
0.106 ***
Metro
0.187 ***
0.051
0.035
0.095 ***
0.083 **
0.059 *
0.080 ***
0.095 ***
# Obs
9,961
10,175
15,246
14,792
13,274
14,877
17,013
15,886
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-12.761 ***0.485 ***
0.647 ***
0.678 ***
0.757 ***
-0.471 ***0.116 ***
0.072 *
0.137 ***
0.064 *
14,6772

5

1978-0.344 *-0.164 *-0.008-0.0701.818 *

1980
-0.699 ***-0.128 *0.007-0.0093.537 ***

Results

In this section, we provide results using the methods described above. First, we show results from our use of the Heckman
2-stage procedure. We do this separately for men and women as we need to predict log wages for both and gender hasa large e¤ect on how other variables a¤ect labor force participation and wages. Next, we display, mostly graphically how
assortative mating works, both for wages and for education, and how it has changed from 1962 up to the present. In
particular, we look at the characteristics of men who marry women with speci…ed log wages and education, and then we lookat the characteristics of women who marry men with speci…ed log wages and education. We also perform a cohort analysis
to better measure the relationship between men and women at the time they are likely to marry. We …nish with the resultsof our proposed test statistics for positive assortative mating with respect to log wages and education.

5.1

Labor Force Participation Estimates

Tables 3 and 4 show estimates for the male and female participation equations de…ned in equations (1) and (2). The resultsin Tables 3 and 4 are largely as we would expect and are fairly consistent with probit labor force participation estimates,for example, for 1986 from Hersch (1991) and for the 1970’s and 1990’s from Mulligan and Rubinstein (2008). Labor force
participation increases with education level and with age up to around 50, depending on the year, after which it decreases.
An exception to the general results for education is that, for years 1970 and 1972, men with post-graduate degrees have lower
labor force participation rates relative to other education levels.

13

Table 3: Female Participation Estimates (continued)
Variable

1995

2000

2005

2007

2010

2014

2015

2018

2019

Constant
White
Black
Hispanic
Age/100-1.610 ***0.120 **
0.196 **
-0.176 ***8.656 ***

-1.963 ***0.171 **
0.298 ***
-0.124 ***9.911 ***

-1.629 ***0.087 **
0.139 **
-0.138 ***8.636 ***

-1.895 ***0.084 *
0.194 ***
-0.158 ***9.868 ***

-1.755 ***0.093 **
0.127 **
-0.171 ***8.071 ***

-2.039 ***0.128 ***
0.175 ***
-0.130 ***8.707 ***

-2.524 ***0.103 **
0.123 *
-0.118 ***10.618 ***-1.697 ***0.203 ***
0.262 ***
-0.166 ***7.411 ***

-1.561 ***0.195 ***
0.256 ***
-0.146 ***6.734 ***

(Age/100)-13.158 *** -14.137 ***-12.291 *** -13.465 *** -10.995 ***-11.301 ***-13.319 ***-10.108 ***HS Diploma
0.454 ***
0.478 ***
0.470 ***
0.442 ***
0.508 ***
0.504 ***
0.526 ***
0.415 ***
Some College
0.656 ***
0.658 ***
0.653 ***
0.629 ***
0.689 ***
0.698 ***
0.763 ***
0.622 ***
College Degree
0.656 ***
0.696 ***
0.649 ***
0.589 ***
0.698 ***
0.809 ***
0.882 ***
0.759 ***
Post Grad Degree
0.710 ***
0.743 ***
0.664 ***
0.747 ***
0.765 ***
0.912 ***
0.981 ***
0.951 ***
# Children < 5-0.423 ***-0.411 ***-0.382 ***-0.356 ***-0.331 ***-0.287 ***-0.279 ***-0.367 ***Northeast
0.083 *
0.099 **
0.152 ***
0.117 ***
0.139 ***
0.164 ***
0.125 ***
0.146 ***
South
0.036
0.064 *
0.017
0.018
-0.023-0.004-0.031-0.026Midwest0.241 ***
0.209 ***
0.211 ***
0.202 ***
0.236 ***
0.246 ***
0.279 ***
0.243 ***
Metro
0.081 **
0.045
-0.029-0.0040.027-0.027
0.035
0.055
# Obs
13,561
12,271
19,222
18,66418,04917,05016,87015,129Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-9.194 ***0.451 ***
0.656 ***
0.793 ***
0.976 ***
-0.327 ***0.124 ***
-0.0480.271 ***
0.037
15,291

2

Table 4: Male Participation Estimates
Variable
Constant
White
Black
Hispanic
Age/100

1962-1.902 ***0.277-0.24212.902 ***1967-1.653 ***0.236-0.10114.093 ***1970-2.079 ***0.313-0.01315.129 ***1972-2.296 ***0.286 *
-0.097-0.11215.809 ***1975-2.670 ***0.263 *
-0.156-0.127 *16.024 ***1978-2.421 ***0.328 ***
0.013
-0.082
16.596 ***1980-2.109 ***0.324 ***
0.016
-0.04814.912 ***1985-2.010 ***0.347 ***
-0.012-0.103 *14.004 ***1990-2.094 ***0.232 ***
-0.1170.048
15.456 ***(Age/100)-16.786 *** -19.288 ***-19.995 *** -20.505 *** -20.405 ***-22.305 ***-20.292 ***-19.701 ***HS Diploma
0.449 ***
0.409 ***
0.389 ***
0.389 ***
0.418 ***
0.404 ***
0.397 ***
0.325 ***
Some College
0.264 ***
0.357 ***
0.265 ***
0.336 ***
0.456 ***
0.531 ***
0.460 ***
0.460 ***
College Degree
0.551 ***
0.521 ***
0.410 ***
0.549 ***
0.786 ***
0.727 ***
0.807 ***
0.777 ***
Post Grad Degree
0.385 **
0.041
0.187 *
0.332 ***
0.662 ***
0.503 ***
0.699 ***
0.721 ***
# Children < 5
0.011
0.061 *
0.060 *
0.016
-0.072 **-0.039Northeast
0.120 *
0.281 ***
0.318 ***
0.127 **
0.158 ***
0.063
0.152 **
0.225 ***
South
-0.0350.120 *
0.197 ***
0.205 ***
0.138 ***
0.135 *
0.088
0.211 ***
Midwest0.201 ***
0.384 ***
0.381 ***
0.212 ***
0.175 ***
0.186 ***
0.130 *
0.075
Metro
0.318 ***
0.298 ***
0.259 ***
0.273 ***
0.205 ***
0.167 ***
0.144 ***
0.175 ***
# Obs
7,809
10,25815,456
15,042
13,536
15,102
17,232
16,088Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-21.867 ***0.409 ***
0.448 ***
0.685 ***
0.693 ***
-0.0240.124 ***
0.116 ***
0.103 *
0.171 ***
14,825

2

Table 4: Male Participation Estimates (continued)
Variable

1995

2000

2005

2007

2010

2014

2015

2018

2019

Constant
White
Black
Hispanic
Age/100-1.849 ***0.305 ***
0.056
0.016
13.416 ***-1.692 ***0.291 ***
0.022
0.102 *
13.516 ***-2.108 ***0.122 **
-0.278 ***0.151 ***
15.182 ***-2.356 ***0.183 ***
-0.168 **0.160 ***
16.134 ***-2.351 ***0.140 ***
-0.226 ***0.083 **
14.401 ***-2.455 ***0.195 ***
-0.0980.152 ***
15.175 ***-2.553 ***0.150 ***
-0.146 **0.212 ***
16.180 ***-2.025 ***0.139 ***
-0.170 **0.219 ***
14.330 ***-2.064 ***0.111 **
-0.208 ***0.203 ***
14.840 ***(Age/100)-19.651 *** -19.898 ***-20.794 *** -22.188 *** -18.979 ***-19.716 ***-20.780 ***-18.950 ***HS Diploma
0.420 ***
0.366 ***
0.332 ***
0.412 ***
0.363 ***
0.313 ***
0.225 ***
0.230 ***
Some College
0.540 ***
0.444 ***
0.434 ***
0.545 ***
0.512 ***
0.378 ***
0.324 ***
0.349 ***
College Degree
0.728 ***
0.788 ***
0.679 ***
0.728 ***
0.852 ***
0.722 ***
0.612 ***
0.572 ***
Post Grad Degree
0.850 ***
0.664 ***
0.798 ***
0.926 ***
1.074 ***
0.830 ***
0.803 ***
0.670 ***
# Children < 5-0.0370.063 *
0.086 ***
0.067 **
0.070 **
0.071 **
0.113 ***
0.079 **
Northeast
0.030
0.059
0.011
0.044
0.071 *
0.102 **
0.034
0.037
South
0.096 *
0.001
0.048
0.037
0.049
0.056
0.043
0.049
Midwest0.144 ***
0.110 *
0.081 *
0.069 *
0.052
0.133 ***
0.161 ***
0.115 **
Metro
0.202 ***
0.203 ***
0.186 ***
0.206 ***
0.072 *
0.105 ***
0.115 ***
0.146 ***
# Obs
13,655
12,415
19,336
18,79718,087
17,106
16,94815,213
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-19.613 ***0.254 ***
0.334 ***
0.526 ***
0.680 ***
0.133 ***
0.028
0.030
0.129 **
0.162 ***
15,391

2

14

Education Effect on Participation
1.0

0.8

0.6

Female HS Diploma
Female College
Male HS Diploma

0.4

Male College Degree

0.2

0.0
1962

1969

1976

1983

1990

1997

2004

2011

2018

Figure 9: Education E¤ect on Participation
For women, whites tend to have a lower propensity to work than blacks; while, for men, whites and other races as well
as Hispanics have a higher propensity to work than blacks. This could be associated with the fact that the spouses of white
women earn more than the spouses of black women on average, which is likely to increase the reservation wage of white
women. The presence of children under age …ve greatly decreases a woman’s propensity to work, but it has no e¤ect on men.
Living in a metro area increases propensity to work for men and women except for women in the most recent years in which
it decreases propensity to work. With respect to changes in estimates over time, we focus on the education estimates andhas child under 5, and we focus on estimates in 1972 and after. Prior to 1972, has child under 5 was not available, causing
there to be a large break in estimates in that year. For has child under 5, while the e¤ect for women is large, over time, it
has declined (in absolute value) at a surprisingly steady annual rate.19
The changes in the estimated e¤ect of education on labor force participation, reported in Figure 9, are quite interesting.
Women’s labor force participation is more responsive to education than men’s, and women’s is growing at a faster rate thanmen’s. Figure 10 shows how the predicted variation in labor force participation for men can be decomposed into variationin parameter estimates across years and variation in covariates across and within years. Table 2 shows the variation acrossyears. The only two covariates with signi…cant variation are Hispanic and metropolitan. However, there is signi…cantvariation in all of the covariates within each year that causes variation in participation rates within each year. Meanwhile,
Tables 3 and 4 and Figure 9 show the variation in parameter estimates across years. Besides variation in education estimatesacross years, there is signi…cant variation in estimates especially for racial e¤ects, age e¤ects, and metro e¤ects. The …rst
two curves from the bottom are for men who did not complete high school, the next two are for men with a high school
degree, and the last two are for men with a college degree. The solid lines are expected participation rates using 1990
sample means but allowing parameter estimates to vary across years E ytij j X 1990;j t from equation (1) conditional on
gender and education, and the dashed lines use both variation in estimates across years and variation in covariates acrossand within years E ytij j Xtij t . The variation in the parameter estimates alone explains almost all of the variation inparticipation rates across years for men with at least a high school diploma. For men who did not …nish high school, thevariation in covariates other than just education explains a signi…cant amount of the variation in participation prior to 2005.
For women, the variation in parameter estimates alone (using 1990 sample means) explains almost all of the variation inlabor force participation rates.20
1 9 The slope of the OLS regression line is 0:0116, and R2 = 0:989.
2 0 The graph for women is available from the corresponding author.

15

Predicted Male Participation Conditional on Education andOther Covariates
1.00
0.95
0.90

< HS Diploma USING 1990
Means

0.85

<HS Diploma Cond
E(Participation)

0.80

HS Diploma Using 1990 Means

0.75
HS Diploma Cond
E(Participation)

0.70

College Degree Using 1990
Means

0.65
0.60

College Degree Cond
E(Participation)

0.55
0.50
1950

1960

1970

1980

1990

2000

2010

2020

2030

Figure 10: Predicted Male Participation Conditional on Eduction and Other Covariates

5.2

Log Wage Estimates

Log wage estimates are reported in Table 5 (for women) and Table 6 (for men). As is the case for the labor force participation
estimates in Tables 3 and 4, the log wage results are largely as we would expect and are fairly consistent with, for example,
Hersch (1991) and Mulligan and Rubinstein (2008). Log wages increase at a decreasing rate with age, maximized at around
50 to 60 years. As seen in Figure 11, log wages increase with education level with higher returns to education in more recent
years. E¤ects for women are slightly higher than for men, possibly helping to explain the large increase in the proportionof women getting more education (e.g., Goldin, 1990; Blau and Kahn, 2007; Bailey, Hershbein, and Miller, 2012). Ashworth
and Ransom (2019) and Ashworth et al. (2020) …nd evidence of ‡attening of education returns in the last 20 years, and our
results are somewhat consistent with their …ndings. The year 1962 for women is an exception for all of these results, which
may be due to the vastly di¤erent role education and work played in the lives of women then (e.g., Goldin, 1990).
The imprecise results in 1962-1972 are likely the consequence of the lack of information about household children in
those years. Without the variable about existing children under 5, when distinguishing the selection equation from the wage
equation, there is no exclusion restriction. As we have the ability to observe the dependent variable in the selection equation,
this does not interfere with the identi…cation of the inverse Mills ratio term. However, the lack of exclusion restriction
increases the degree of multicollinearity between the inverse Mills ratio and the other covariates. This multicollinearity
increases the standard errors on the estimated coe¢ cients, decreasing the precision of the estimates. In particular, the resultsof the Heckman two-step procedure in 1962 and 1967 su¤er from severe multicollinearity. The problem is …xed from 1970
onward with has child under 5 becoming available.21
The e¤ect of race on log wages is much stronger for men than for women. White men earn more than black men who earnmore than Hispanic men. For women, the results are similar but weaker, and the race terms are insigni…cant over several
years. Living in a metro area increases log wages for both genders, especially for the years after 1972.
For women, the inverse Mills ratio coe¢ cient estimates are signi…cant essentially in all years while the coe¢ cientestimates are generally insigni…cant for men. Selection bias is much stronger for women; i.e. more women self-select out of
the workforce because their wages would be lower than their unobserved reservation wage. Our results are in contrast to the
1980s results in Smith and Ward (1989) but are broadly similar to the results of Nakosteen and Zimmer (2001) and Zhang
2 1 Returning to the potential use of semiparametric estimation methods, for example, Escanciano, Jacho-Chavez, and Lewbel (2016) provide a
proof and Monte Carlo evidence that exclusion restrictions are not necessary for identi…cation in semiparametric two-step estimators. However,
it is not clear how relaxing a functional form assumption in a model that is behaving poorly without an exclusion restriction will perform better
than with the functional form assumption.

16

Table 5: Female log Hourly Wage Estimates
Variable
Constant
White
Black
Hispanic
Age/100

1962
2.019 ***
0.182 *
0.074--2.967 ***1967
2.570 ***
0.179 **
0.114--0.0631970
2.272 ***
-0.001-0.011--1.390 ***1972
2.200 ***
0.094
0.007
-0.106 **1.738 ***

1975
2.321 ***
-0.101 *-0.146 *-0.0692.219 ***

1978
2.099 ***
0.026
0.027
-0.087 ***2.825 ***

1980
2.225 ***
-0.014-0.010-0.070 ***1.639 ***

1985
1.758 ***
0.069 *
0.044
-0.099 ***3.111 ***

1990
1.411 ***
0.029
-0.017-0.096 ***4.207 ***

(Age/100)-3.494 ***-0.194-1.702 ***-2.154 ***-2.783 ***-3.528 ***-2.118 ***-3.705 ***HS Diploma
0.039
0.072 ***
0.123 ***
0.096 ***
0.078 ***
0.114 ***
0.134 ***
0.181 ***
Some College
0.086 *
0.211 ***
0.230 ***
0.202 ***
0.178 ***
0.186 ***
0.249 ***
0.345 ***
College Degree
0.121 *
0.244 ***
0.278 ***
0.271 ***
0.261 ***
0.281 ***
0.400 ***
0.472 ***
Post Grad Degree
0.675 ***
0.299 **
0.534 ***
0.369 ***
0.417 ***
0.371 ***
0.510 ***
0.693 ***
Northeast-0.127 **0.004-0.011-0.016-0.015-0.010-0.020-0.046 **South-0.166 ***-0.084 **-0.085 ***-0.096 ***-0.067 **-0.077 ***-0.074 ***-0.067 ***Midwest-0.146 ***-0.045-0.028-0.031-0.012-0.021
0.006-0.074 ***
Metro
0.045
0.078 ***
0.082 ***
0.125 ***
0.079 ***
0.062 ***
0.053 ***
0.071 ***
Inverse Mills Ratio
0.168 ***
0.073 *
0.121 ***
0.118 ***
0.212 ***
0.163 ***
Residual SE
0.000
0.000
0.000
0.000
0.000
0.000
# Obs
1,259
2,213
15,246
14,792
13,274
14,877
17,013
15,886
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-5.030 ***0.231 ***
0.446 ***
0.623 ***
0.767 ***
0.073 ***
-0.055 **-0.039 *0.132 ***
0.202 ***
0.000
14,677

2

Table 5: Female log Hourly Wage Estimates (continued)
Variable
Constant
White
Black
Hispanic
Age/1001995
1.127 ***
0.065 *
0.032
-0.076 ***5.211 ***

2000
1.152 ***
0.096 **
0.065
-0.160 ***5.050 ***

2005
1.068 ***
0.050 *
0.001
-0.146 ***5.588 ***

2007
0.946 ***
0.054 *
-0.002-0.182 ***5.978 ***

2010
1.069 ***
0.027
-0.054-0.158 ***5.362 ***

2014
0.548 **
0.076 ***
0.031
-0.136 ***6.334 ***

2015
0.826 ***
0.044 *
-0.002-0.159 ***5.784 ***

2018
1.401 ***
0.034
-0.041-0.187 ***4.058 ***

2019
1.298 ***
0.058 **
-0.040-0.181 ***4.108 ***

(Age/100)-6.245 ***-5.915 ***-6.482 ***-6.895 ***-5.888 ***-6.806 ***-6.341 ***-4.315 ***HS Diploma
0.263 ***
0.257 ***
0.265 ***
0.272 ***
0.311 ***
0.330 ***
0.289 ***
0.252 ***
Some College
0.423 ***
0.444 ***
0.467 ***
0.493 ***
0.515 ***
0.552 ***
0.505 ***
0.452 ***
College Degree
0.705 ***
0.702 ***
0.765 ***
0.767 ***
0.772 ***
0.880 ***
0.846 ***
0.790 ***
Post Grad Degree
0.894 ***
1.011 ***
1.050 ***
1.065 ***
1.132 ***
1.161 ***
1.141 ***
1.151 ***
Northeast
0.032
0.063 **
0.044 *
0.045 *
0.021
0.038
0.013
0.011
South
-0.065 ***-0.010-0.061 ***-0.036 *-0.073 ***-0.070 ***-0.068 ***-0.103 ***Midwest0.005
0.017-0.053 **-0.054 **-0.042 *-0.0020.009-0.050 *Metro
0.145 ***
0.136 ***
0.132 ***
0.163 ***
0.121 ***
0.138 ***
0.152 ***
0.091 ***
Inverse Mills Ratio
0.255 ***
0.254 ***
0.293 ***
0.314 ***
0.347 ***
0.495 ***
0.407 ***
0.308 ***
Residual SE
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
# Obs
13,561
12,271
19,222
18,66418,04917,05016,87015,129Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-4.339 ***0.236 ***
0.444 ***
0.786 ***
1.094 ***
0.019
-0.084 ***-0.0080.160 ***
0.323 ***
0.000
15,291

2

Table 6: Male log Hourly Wage Estimates
Variable
Constant
White
Black
Hispanic
Age/100

1962
1.413 ***
0.212 **
-0.049--5.688 ***1967
1.955 ***
0.219 ***
0.057--3.879 ***1970
1.844 ***
0.259 ***
0.058--4.572 ***1972
1.481 ***
0.098 *
-0.122 **-0.196 ***6.912 ***

1985
1.858 ***
0.061 *
-0.148 ***-0.147 ***4.751 ***

1990
0.995 ***
0.145 ***
-0.045-0.198 ***7.469 ***

(Age/100)-6.125 ***-3.933 ***-4.983 ***-7.740 ***-4.894 ***-4.007 ***-4.579 ***-4.075 ***HS Diploma
0.148 ***
0.132 ***
0.142 ***
0.149 ***
0.119 ***
0.127 ***
0.119 ***
0.159 ***
Some College
0.218 ***
0.245 ***
0.238 ***
0.249 ***
0.195 ***
0.172 ***
0.160 ***
0.214 ***
College Degree
0.446 ***
0.416 ***
0.475 ***
0.464 ***
0.307 ***
0.337 ***
0.317 ***
0.408 ***
Post Grad Degree
0.464 ***
0.430 ***
0.448 ***
0.471 ***
0.349 ***
0.448 ***
0.409 ***
0.521 ***
Northeast-0.024-0.049 **-0.053 ***-0.022-0.023-0.079 ***-0.088 ***-0.068 ***South-0.125 ***-0.121 ***-0.139 ***-0.111 ***-0.079 ***-0.106 ***-0.094 ***-0.090 ***Midwest0.004-0.0180.006
0.010-0.006-0.043 ***-0.018-0.058 ***Metro
0.138 ***
0.137 ***
0.150 ***
0.161 ***
0.109 ***
0.065 ***
0.064 ***
0.058 ***
Inverse Mills Ratio
0.269-0.0120.174
0.282 *
-0.055-0.199 *-0.097-0.192
Residual SE
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
# Obs
7,809
10,25815,456
15,042
13,536
15,102
17,232
16,088Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-7.923 ***0.217 ***
0.327 ***
0.554 ***
0.658 ***
0.057 ***
-0.073 ***-0.007 ***0.162 ***
0.200
0.000
14,8252

17

1975
2.017 ***
0.083 *
-0.052-0.186 ***4.846 ***

1978
2.138 ***
0.089 **
-0.052-0.145 ***4.314 ***

1980
2.004 ***
0.124 ***
0.006
-0.157 ***4.736 ***

Table 6: Male log Hourly Wage Estimates (continued)
Variable
Constant
White
Black
Hispanic
Age/100

1995
0.583 **
0.108 ***
-0.073 *-0.176 ***9.119 ***

2000
1.500 ***
0.136 ***
-0.017-0.219 ***5.178 ***

2005
1.095 ***
0.144 ***
-0.081 **-0.211 ***6.960 ***

2007
1.073 ***
0.145 ***
-0.087 **-0.192 ***7.131 ***

2010
1.280 ***
0.139 ***
-0.068 *-0.169 ***6.273 ***

2014
1.431 ***
0.077 ***
-0.115 ***-0.159 ***5.607 ***

2015
1.631 ***
0.095 ***
-0.096 ***-0.189 ***4.700 ***

2018
2.146 ***
0.058 **
-0.122 ***-0.218 ***3.066 **

2019
2.150 ***
0.033
-0.154 ***-0.195 ***2.866 **

(Age/100)-10.108 ***-5.265 ***-7.497 ***-7.786 ***-6.774 ***-5.537 ***-4.565 ***-2.381HS Diploma
0.236 ***
0.175 ***
0.181 ***
0.221 ***
0.205 ***
0.182 ***
0.197 ***
0.171 ***
Some College
0.355 ***
0.320 ***
0.340 ***
0.352 ***
0.359 ***
0.310 ***
0.320 ***
0.301 ***
College Degree
0.651 ***
0.611 ***
0.657 ***
0.701 ***
0.710 ***
0.630 ***
0.660 ***
0.600 ***
Post Grad Degree
0.827 ***
0.871 ***
0.944 ***
1.017 ***
0.999 ***
0.950 ***
0.923 ***
0.868 ***
Northeast
0.048 **
0.008
0.033 *
0.016
0.033 *
-0.002-0.001-0.021South-0.041 **-0.013-0.020-0.055 ***-0.050 ***-0.025-0.025-0.073 ***Midwest-0.0030.008-0.024-0.050 ***-0.106 ***-0.042 *-0.075 ***-0.070 ***Metro
0.158 ***
0.146 ***
0.176 ***
0.172 ***
0.140 ***
0.106 ***
0.106 ***
0.076 ***
Inverse Mills Ratio
0.364 **
0.070
0.179
0.207
0.199
0.042
0.039
-0.298Residual SE
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
# Obs
13,655
12,415
19,336
18,79718,087
17,106
16,94815,213
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

-2.1260.175 ***
0.322 ***
0.633 ***
0.898 ***
-0.010-0.051 **-0.062 ***0.107 ***
-0.300 *0.000
15,391

2

Education Effect on log Hourly Wage
1.0

0.8

0.6

Female HS Diploma
Female College
Male HS Diploma

0.4

Male College Degree

0.2

0.0
1960

1970

1980

1990

2000

2010

2020

Figure 11: Education E¤ect on log Hourly Wage18

Predicted Husband's log Wage Conditional on Predicted
Wife's log Wage (Selected Years)
4.0
3.8
3.6
3.4
3.2
1962

Predicted
Husband's 3.0
log Wage

1970
1980

2.8

2000
2.6

2019

2.4
2.2
2.0
1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

Predicted Wife's log Wage

Figure 12: Predicted Husband’s log Wage Conditional on Predicted Wife’s log Wage (Selected Years)
and Lui (2003), which also used a Heckman selection model. They found no evidence for selection bias among men andevidence for positive selection bias for women for the years 1983-1991. While Nakosteen and Zimmer (2001) then went on touse an OLS regression for the men in their sample due to these results, we continue to use the estimates generated by the
Heckman two-step method to maintain consistency across years and gender.22

5.3

Local Linear Regression Estimation Results

5.3.1

log Wage Relationships

Using the wages predicted by equation (5) and the estimates from Tables 5 and 6, we next use equation (8) to construct
ws (wo ) curves in equation (7). The results are displayed in Figures 12 and 13 with 95% percentile intervals (see Cattaneo
and Jansson, 2018) at discrete points.23 One can see that all of the curves are measured with high precision. Figure 12
shows that, even in 1962, there is a positive relationship between spouses’wages. The relationship becomes a little weakerin more recent years, which we see in the change in the general slope of each successive year. The positive relationship isconstant across all levels of income. Except for 1962, husbands’wages are generally higher than their wives’, which we also
see in Figure 13.
One might wonder why the curves in Figures 12 and 13 are not transposed mirror images of each other. To gain some
intuition, consider a simple example where
wf
wm

f

N

m

;

ff

fm

fm

mm

:

2 2 Zhang and Lui (2003) use 2nd-stage log wages but only for the women who did not work. The wage equation they estimate is for men, so it isalso not clear how substituting the selection-corrected woman’s log wage has the properties described in Heckman (1979).
2 3 The standard errors used in constructing con…dence intervals ignore the fact that the predicted log wages are themselves random variables.
However, the standard errors associated with these estimates are quite small making the relevant adjustment negligible.

19

Predicted Wife's log Wage Conditional on
Predicted Husband's log Wage (Selected
Years)
3.3
3.1
2.9

Predicted
Wife'slog Wage

2.7
1962

2.5

1970

2.3

1980

2.1

2000

1.9

2019

1.7
1.5

1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00

Predicted Husband's log Wage

Figure 13: Predicted Wife’s log Wage Conditional on Predicted Husband’s log Wage (Selected Years)
Then
Ewm

j wf =mEwf

j wm =fand
E wf j Ewm j wf
is a weighted average of wf and

f

fm

+

fm

+

fm

=

ff

mm

wf

f

(wm

m

fm

wf + 1
ff

mm

;

(12)

);

fm

fm

mm

ff

f

. This is shown clearly in Figure 14 with
wf
wm

N

2
3

;

1
2

2
2

with = 0:4. The horizontal axis has wf and E wf j wm , and the vertical axis has wm and E wm j wf . The blue dashedcurve is E wm j wf , and the red solid curve is E wf j wm . Each of the conditional expectations move towards the mean.
Thus, a wife with a log wage of 4:0 has a husband with a conditional expected log wage of 4:13, and a husband with a log
wage of 4:13 has a wife with a conditional expected log wage of 2:32 (as seen by the arrows).
An interesting feature of Figure 12 is that, for all years, when the predicted wife’s log wage (PWLW) reaches 2:75 (wage= $15:64), the predicted husband’s log wage (PHLW) ‡attens with respect to the PWLW and converges across years. Since$15:64/hour is not that high a wage, this suggests that assortative mating is a stronger phenomenon at lower wages thanat higher wages. Figure 13 shows a somewhat di¤erent pattern where assortative mating exists over the whole period but
is signi…cantly stronger in later years (2000 and after). We still see some ‡attening out at log wages about 4:0 (wage =$54:60/hour). One might wonder how two …gures, both about matching over the same period of time and the same group ofpeople, can tell such di¤erent stories. The reason is that the two …gures are sorting the data in fundamentally di¤erent ways.
Figure 12 aggregates PWLWs that have similar PHLWs, while Figure 13 aggregates PHLWs that have similar PWLWs. Let
Af (wm ) be the function that aggregates PWLWs with similar PHLWs equal to wm , and let Am (wf ) be the function that
aggregates PHLWs with similar PWLWs equal to wf . It is only in special cases that Am (Af (wm )) = wm which is what isrequired for Figures 12 and 13 to provide equivalent curves.
20E[wf|E(wm|wf)]
6

5

4

E(wm|wf)
E(wf|wm)

wm,E(wm|wf) 3

2

1

0
0

1

2

3

4

5

6

wf,E(wf|wm)

Figure 14: E wf j E wm j wf
5.3.2

Percentile Relationships

Another way to look at the data is to turn predicted log wages of husbands and wifes into percentiles. Choo and Siow(2006b) assume this will happen implicitly and Burdett and Coles (1997) assume so explicitly. In particular, let Fbj wj
be the empirical distribution of predicted log wages of j = husband or wife, and use local linear regression for Fbj wj on
Fbj w j where j is the other member of the couple. The results of these regressions are displayed in Figures 15 and 16.
Figure 15 shows a monotone increasing relationship between the household member percentiles with the exception of low
income husbands in 1962. The relationship is very stable over time. The curves all come close to passing through (50; 50),
and they all have slopes less than 1. This implies sorting by percentile on average with some signi…cant deviations due toother sorting factors (e.g., emotional attraction). Barnett (1980) presents some bivariate uniform distributions of interest
that can be used to compare to Figure 15. For example, f (u; v) = 1 + (1 2u) (1 2v) for 0
1, discussed by
Schucany, Parr, Boyer (1978), has marginal standard uniform densities and exhibits positive assortative mating. For thiscase, E (U j v) = (1=2) + ( (1 2v) =6), implying a smaller slope than in Figure 15. An alternative is a bivariate Gaussian
coppula with density,f (u; v)

=

2

p

exp

1
1

2

2 (1

(u) (v)h12)and conditional expectation,
E (U j v) =

(13)
1

(u)

Z 1

2

1

0

2

(v)
p
1

1

1
2

1

(u)

(u)

!

(v) +

1

(v)

2

i

du

with average @E (U j v) =@v varying from 0 (when = 0) to 1 (when = 1). The curves in Figure 15 are very similar to
those that would be generated by the joint density in equation (13) with
0:4.
Figure 16 is mostly a monotone increasing relationship with exceptions for low income husbands in 2019 and middle
income husbands in 1970 and 1980. The curves are not as similar as are those in Figure 15 and are not centered at (50; 50)
as in Figure 15. Also, globally, the slopes in Figure 16 are slightly steeper than in Figure 15. The large dip in the 1980 curvein the middle percentiles is due to the bimodal nature of the wive’s expected log wage density which is unique to 1980. The
other deviations from the smooth and similar behavior of curves in Figure 15 may be due to other, more subtle characteristicsof the marginal or bivariate distributions.

21

Expected Wife's Percentile Conditional on Husband's Percentile
90
80
70
60

Wife'sPercentile

1962
1970

50

1980
40

1990
2000

30

2010
2019

20
10
0
0

10

20

30

40

50

60

70

80

90

100

Husband's Percentile

Figure 15: Expected Wife’s Percentile Conditional on Husband’s Percentile

Expected Husband's Percentile Conditional on Wife's Percentile
90
80
70
60

Husband's
Percentile

1962
1970

50

1980
40

1990
2000

30

2010
2019

20
10
0
0

10

20

30

40

50

60

70

80

90

100

Wife's Percentile

Figure 16: Expected Husband’s Percentile Conditional on Wife’s Percentile

22

Predicted Husband's log Wage Conditional on
Wife's Predicted log Wage (20<Age<30)

4.0

3.5

Predicted
Husband's 3.0
log Wage

1962
1970
1980
2000
2019

2.5

2.0

1.5

2

2.5

3

3.5

4

Wife's log Wage

Figure 17: Predicted Husband’s log Wage Conditional on Wife’s Predicted log Wage (20<Age<30)
5.3.3

Cohort E¤ects

A potentially serious problem with the curves in Figures 12 and 13 is that they are based on all couples in the data while onlya small portion of couples in the data were married recently. Assortative mating is a statement about similarities with who
one marries. If people change over time, then a set of curves from a representative sample of people may not be similar tothe curves from a representative sample of people who recently married. Also, since the marriage market changes as people
age, it is probably important to focus on a cohort of people who recently married. Unfortunately, there is no exact way toconstruct a cohort of people who recently married using our data because, except for prior to and including 1970, we do notknow people’s age when they got married. The second best feasible alternative is to focus on cohorts of people within anage range when people usually marry (e.g., see Pencavel, 1998). Figures 17 and 18 focus on cohorts of men and women who
were between the ages of 20 to 30 in …ve di¤erent years. For example, the dark blue dashed curve (lower than the othercurves) in Figure 17 displays how PHLW changes with PWLW for the 20 to 30 year olds in 2000. The curves for the …veselected years have di¤erent vertical intercepts but similar slopes, suggesting that assortative mating among people ages 20
to 30 has not changed much over the 60 years included in the data. This result di¤ers from Greenwood and Guner (2008)
and Santos and Weiss (2016) but is consistent with Gayle, Golan and Soytas (2020) and Gihleb and Lang (2020).
The curves in Figure 18 show a more interesting picture. The earliest curve (1962) is an outlier showing no wage gaps
between men and women but still a signi…cant amount of assortative mating. This is probably caused by the poor performanceof the Heckman 2-step estimator for 1962 due to lack of plausible instruments. From 1970 to 2019, the curves are bunched
together, but the patterns of assortative mating vary by year. In 1970, the slope of the curve declines with the PHLW. In
2000, it increases with the PHLW. In 1990 it is ‡at, then declines, and then increases. In 2019, it is almost linearly increasingin PHLW. Overall, we still see positive assortative mating almost always, but in more varied patterns. The positive slope
con…rms earlier research. Positive assortative mating extends to wages, not just non-labor market characteristics. The generaltrend towards stronger positive relationships between spouses’wages supports our earlier hypothesis that spouses’wages are
more similar over time. However, the results contradict some of the theoretical discussions of marital sorting in the 1960’s
and 1970’s. For example, Becker (1985) and Becker(1991) both predict negative assortative mating over wages holding othercharacteristics constant, in the earlier years of the analysis. The results indicate that positive assortative mating in wages
existed even in 1962, if weakly. But they have nothing to say about correlation after controlling for other characteristics. It
is possible that negative assortative mating in wages existed prior to 1962 or that negative partial assortative mating has
always existed, but we do not have the data to consider the possibility.24
2 4 It is worth noting that Becker’s analysis was signi…cantly after 1962, the earliest year used in our analysis.

23

Predicted Wife's log Wage Conditional on
3.5Predicted Husband's log Wage (20<age<30)
3.0
2.5

2.0

Predicted
Wife'slog Wage 1.5

1962
1970
1980
2000

1.0

2019

0.5

0.0
1.0

1.3

1.5

1.8

2.0

2.3

2.5

2.8

3.0

3.3

3.5

3.8

4.0

4.3

4.5

Predicted Husband's log Wage

Figure 18: Predicted Wife’s log Wage Conditional on Predicted Husband’s log Wage (20<Age<30)
The main reason for looking at cohorts in Figures 17 and 18 instead of Figures 12 and 13 was assortative mating is astatement about similarities when marrying and the characteristics of couples can change as they age.25 To see how important
this concern is, we can look at how PHLWs and PWLWs change as they age. Figure 19 shows how the relationship between
PWLW and PHLW changes as a couple from the 1970 cohort ages from 20 30 years of age to 40 50 years of age. Figure
19 shows PHLW steadily increasing as a function of PWLW.
Figure 20 shows how the relationship between PHLW and PWLW changes as a couple from the 1970 cohort ages from20 30 years of age to 40 50 years of age. This …gure shows little assortative mating in 1970 among the 20 30 year oldcohort; PWLW is almost ‡at as a function of PHLW. But, by 1980, there is signi…cantly more assortative mating. Thissuggests that there was some characteristic, such as education, that had a small e¤ect on PWLW in 1970, at least for new
job entrants, but then later led to signi…cant increases in PWLW 10 years later and beyond. There is also a dip in the
curve for 40 50 years; we do not know how to interpret the dip. Altogether, this …gure suggests caution in using wages of
newly married couples to measure assortative mating as much of the variation in wages occurs later in life and in a somewhat
predictable way. A large literature on income generating processes, including Macurdy (1982), Baker (1997), Baker andSolon (2003), and Guvenen (2009), …nds signi…cant evidence of heterogeneous wage growth. An alternative set of work,
including Abowd and Card (1989), Deaton and Paxson (1994), Gottschalk and Mo¢ tt (1995), and Meghir and Pistaferri(2004), model the income process with permanent shocks and/or random walks. The …rst approach suggests that individuals
have much information about their future wages, and the second assumes future wages exhibit signi…cant shocks unknown
early in an individual’s life. Our results lend some support for the …rst approach.
5.3.4

Sharing Within Families

Chiappori, Fortin, and Lacroix (2002) use a collective model to estimate a transfer function from the husband to the wife,=

56:64 log wf

25:94 log wm + 20:06 log wf log wm+0:70v + 216:28s1 + 4:31s2 + (z) + "where log wf is the log wage of the wife, log wm is the log wage of the husband, v is non-labor income, s1 is the age/race/statespeci…c sex ratio, s2 is a measure of divorce law characteristics, (z) is an unidenti…ed e¤ect of other household characteristics,
and " is the error.26 Figure 21 shows how the share of household resources going to the husband (wm + )=(wm + wf + v)
2 5 Also, divorce rates varying over joint realizations of the husband’s and wife’s wages would change the amount of assortative mating as couples
age. For example, Bertrand, Kamenica, and Pan (2015) provide evidence that couples with the husband earning less than the wife are more likely
to divorce. This changes the nature of observed assortative mating as the divorces occur.
2 6 It is not clear how to interpret the error in Chiappori, Fortin, and Lacroix (2012). In fact, the structural equations in Chiappori, Fortin,and Lacroix (2012) are the labor supply equations, and they have no errors attached to them. The addition of errors might represent unobserved24Changes in Husband's Predicted log Wages Conditional on
Wife's Predicted log Wages for the 1970 Cohort
3.9
3.7
3.5

Husband's 3.3
Predicted
log Wages 3.1

Ages 20-30 in 1970
Ages 30-40 in 1980
Ages 40-50 in 1990

2.9
2.7
2.5
1

1.5

2

2.5

3

3.5

4

Wife's Predicted log Wages

Figure 19: Changes in Husband’s Predicted log Wages Conditional on Wife’s Predicted log Wages for the 1970 Cohort

Changes in Wife's Predicted log Wages Conditional on
Husband's Predicted log Wages for the 1970 Cohort
3.5
3.0
2.5

Wife's 2.0
Predicted
log Wages 1.5

Ages 20-30 in 1970
Ages 30-40 in 1980
Ages 40-50 in 1990

1.0
0.5
0.0
1

2

3

4

5

Husband's Predicted log Wages

Figure 20: Changes in Wife’s Predicted log Wages Conditional on Husband’s Predicted log Wages for the 1970 Cohort25Iso-Share Curves
3.0

Share=0.4
2.8

Share=0.5
2.6

Wife'slog
Wage

Share=0.6

2.4

Share=0.7

2.2

2.0

Share=0.8

1.8

1.6
1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Husband's log Wage

Figure 21: Husband’s Sharevaries with the wife’s log wage and the husband’s log wage.27 The contour curves presented in the …gure have slopes varying
from 0:6 when the husband’s wage is low relative to the wife’s wage to 0:85 when the husband’s wage is high relative to thewife’s wage. This implies a moderately small amount of sharing (and caring) consistent with results in Chiappori, Fortin,and Lacroix (2002) and in Friedberg and Stern (2014).
A concern with this approach is whether we can interpret the estimates in Chiappori, Fortin, and Lacroix (2002) as
the correct structure. Choo and Siow (2006a, 2006b) and Chiappori, Iyigun, and Weiss (2009) argue that one should notseparately analyze assortative mating and marital sharing. For example, part of the results seen in Figures 12 and 13 is dueto the increasing average educational attainment of women. On the one hand, this increases a woman’s log wage causing hertransfer to her husband to decline; this is the e¤ect measured in Figure 21. On the other hand, other women’s wages also
increase, thus improving the bargaining power of the husband. Since neither the average log wage of women nor the average
education level of women in the husband’s marriage market is included in the model, the model is not controlling for thissecond e¤ect.28 To some degree, these types of e¤ects are the meat of Greenwood et al. (2014). But neither Greenwood etal. (2014) nor its companion model in Greenwood et al. (2016) have anything to say about the household sharing rule.
A second concern is that some of the literature provides structural estimates showing that the gains to marriage forwomen decline with the woman’s wage (e.g., Van der Klaauw (1996); Mazzocco, Ruiz, and Yamaguchi, 2007). This suggeststhat a woman does not receive as much from a higher wage in marriage as she would if single. This contradicts the resultsin Chiappori, Fortin, and Lacroix (2002), and it implies a surface for Figure 21 with a less steep slope in the wife’s log wage,
reducing the gains associated with higher female wages.

5.4

Assortative Mating and Education

Smits, Ultee, and Lammers (1998), Fernandez, Guner, and Knowles (2005), Hou and Myles (2008), Siow (2015), Eika,
Mogstad, and Zafar (2017) …nd strong evidence of positive assortative mating in marriage by education.29 Also, Mare (1991)
and Pencavel (1998) provide evidence of changing degrees of assortative mating on education and suggest explanations forthe changes, Gihleb (2013) and Siow (2015) …nd that the degree of assortative mating on education has not changed muchover time, and Chiappori, Salanié, and Weiss (2011) argue that the US marriage market for individuals born between 1943
and 1972 can be described as having a constant value of a statistic (TP2) similar to T from equation (10) with time-varying
marriage rates. Eika, Mogstad, and Zafar (2017) …nd stronger assortative mating at lower levels of education than higher
levels of education; this is somewhat consistent with our results showing more assortative mating at low wages than atvariation in preferences, unobserved factors a¤ecting the transfer rule, or measurement error in hours data. Each of these possibilities would a¤ect
the transfer equation, and therefore the share equation, in di¤erent ways.
2 7 Wages are measured as hourly wages. All necessary assumptions are made based on sample averages provided in Table 1 of the paper.
2 8 The increased log wage of the wife also changes the optimal sharing of household production. Chiappori, Fortin and Lacroix (2002) control forthis e¤ect.
2 9 Arum, Roksa, and Budig (2008) present evidence that couples sort on the quality of the school where one attends college.

26

Table 7: Effects of Predicted Wife's Education on log Predicted Wife's Wage
Dependent variable: log(Predicted Wife's Wage)
Variable
1962
1967
1970
1972
Continuous Education
Predicted Wife's
0.026 ***
0.034 ***
0.034 ***
0.039 ***
(0.005)
Education(0.005)(0.005)(0.005)Constant
2.430 ***
2.449 ***
2.276 ***
2.303 ***
(0.056)(0.060)(0.058)(0.058)R squared
0.820
0.825
0.889
0.922
Discrete Diploma
Predicted Wife's
Education
Constant

0.042 ***
(0.003)
2.234 ***
(0.036)0.969

0.044 ***
(0.005)2.316 ***
(0.061)
0.957

0.044 ***
(0.007)2.143 ***
(0.079)0.933

0.047 ***
(0.005)2.194 ***
(0.057)
0.961

1975

1980

1985

1990

0.032 ***
(0.005)2.350 ***
(0.060)0.871

0.025 ***
(0.005)2.355 ***
(0.067)0.839

0.030 ***
(0.004)2.261 ***
(0.063)0.917

0.092 ***
(0.009)1.482 ***
(0.129)0.916

0.038 ***
(0.002)2.278 ***
(0.029)0.987

0.035 ***
(0.002)2.233 ***
(0.032)0.971

0.040 ***
(0.001)2.131 ***
(0.017)0.984

0.100 ***
(0.002)
1.356 ***
(0.031)
0.993

R squared
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

Table 7: Effects of Predicted Wife's Education on log Predicted Wife's Wage (Continued)
Dependent variable: log(Predicted Wife's Wage)
Year
Variable
1995
Continuous Education
Predicted Wife's
0.087 ***
Education(0.007)
Constant
1.527 ***
(0.097)R squared
0.948
Discrete Diploma
Predicted Wife's
Education
Constant

0.099 ***
(0.003)1.354 ***
(0.048)
0.990

2000

2005

2007

2010

2014

2015

2019

0.121 ***
(0.005)1.147 ***
(0.066)0.973

0.130 ***
(0.006)
0.992 ***
(0.079)0.980

0.134 ***
(0.010)0.946 ***
(0.135)0.962

0.139 ***
(0.007)0.878 ***
(0.096)0.973

0.152 ***
(0.006)0.520 ***
(0.100)0.985

0.151 ***
(0.004)0.611 ***
(0.058)0.987

0.105 ***
(0.002)
1.352 ***
(0.030)0.993

0.134 ***
(0.003)0.946 ***
(0.037)0.998

0.134 ***
(0.006)0.930 ***
(0.089)0.993

0.137 ***
(0.005)0.889 ***
(0.074)0.993

0.131 ***
(0.007)0.983 ***
(0.106)0.988

0.146 ***
(0.008)0.617 ***
(0.109)0.988

0.149 ***
(0.006)0.647 ***
(0.083)0.990

0.105 ***
(0.004)1.355 ***
(0.063)0.994

R squared
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

high wages. Gayle, Golan and Soytas (2020) show that the characteristics of assortative mating in education vary by race.
Meanwhile, Fernandez, Guner, and Knowles (2005) …nd some interesting variation in the amount of assortative mating acrosscountries and tie it to variation in country-speci…c skill premia.
To further examine the sorting trends in each year in our data, we analyze how much of the sorting over wages can be
explained by sorting over education. We use an OLS regression of the local linear regression predicted wages displayed in
Figures 12 and 13 on an analogous local linear regression predicted education term (as described in Section 4.3), both given
the spouse’s wage or education. The regression results are provided in Tables 7 and 8 and then graphed in Figure 22. Wife’s
education has very small e¤ects on log wage prior to 1980. From 1980 on, the e¤ect grows and becomes large, and it becomeslarger than for husbands.

5.5

Positive Assortative Mating Test Results

We perform two tests each for log predicted wages and education separately and for a range of sample years, displayed inTable 9. For the log predicted wage tests, we divide the space of log wages for men and women into deciles, implying that
M = F = 10 which, using equation (11), leads to degrees of freedomof 81. Using a normal approximation for the 281
p
distribution, the critical value for the LR test statistics is 81 + 1:96 162 = 105:9. For the education tests, M = F = 5 which
implies that the degrees of freedom are 16. The critical value for the LR test statistics is 26:3. For all years and all tests,
the test statistics are very large leading us to reject the null hypothesis of no assortative mating. The LR test statistics are
an order of magnitude larger than the Wald test statistics (see Kang and Stern (2021) for more discussion).

27

Table 8: Effects of Predicted Husband's Education on log Predicted Husband's Wage
Dependent variable: log(Predicted Husband's Wage)
Variable
1962
1967
1970
1972
Continuous Education
Predicted Husband's
0.081 **
0.048 ***
0.038 ***
0.069 ***
Education(0.029)(0.006)(0.006)(0.010)Constant
2.148 ***
2.688 ***
2.808 ***
2.405 ***
-0.312(0.074)(0.069)(0.118)R squared
0.711
0.839
0.934
0.940

1975

1980

1985

1990

0.037 ***
(0.007)2.904 ***
(0.082)0.873

0.019 ***
(0.003)3.103 ***
(0.030)0.917

0.045 ***
(0.004)2.704 ***
(0.054)0.959

0.080 ***
(0.004)2.112 ***
(0.058)0.946

Discrete Diploma
Predicted Husband's 0.107 *
0.066 ***
0.044 **
0.084 ***
0.044 ***
0.023 ***
0.051 ***
0.093 ***
Education(0.043)(0.004)(0.008)(0.006)(0.005)(0.001)(0.005)(0.002)
Constant
1.745 **
2.425 ***
2.717 ***
2.183 ***
2.791 ***
3.045 ***
2.615 ***
1.905 ***
(0.525)(0.054)(0.094)(0.070)(0.065)(0.008)(0.059)(0.030)R squared
0.702
0.971
0.915
0.986
0.962
0.996
0.975
0.998
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

Table 8: Effects of Predicted Husband's Education on log Predicted Husband's Wage (Continued)
Dependent variable: log(Predicted Husband's Wage)
Year
Variable
1995
Continuous Education
Predicted Husband's 0.092 ***Education(0.004)
Constant
1.822 ***
(0.055)R squared
0.969

2000

2005

2007

2010

2014

2015

2019

0.089 ***
(0.007)2.037 ***
(0.097)0.969

0.099 ***
(0.006)1.873 ***
(0.078)0.972

0.100 ***
(0.005)1.854 ***
(0.072)
0.983

0.092 ***
(0.007)1.964 ***
(0.088)0.973

0.077 ***
(0.006)2.193 ***
(0.074)0.963

0.084 ***
(0.003)
2.096 ***
(0.043)0.987

0.090 ***
(0.006)2.161 ***
(0.079)0.973

Discrete Diploma
Predicted Husband's 0.108 ***0.102 ***
0.109 ***
0.110 ***
0.101 ***
0.075 ***
0.083 ***
0.086 ***
Education(0.003)(0.007)(0.006)(0.007)(0.009)(0.005)(0.005)(0.008)Constant
1.593 ***
1.835 ***
1.718 ***
1.717 ***
1.846 ***
2.210 ***
2.112 ***
2.220 ***
(0.041)(0.083)(0.073)(0.086)(0.112)(0.064)(0.066)(0.108)R squared
0.997
0.989
0.992
0.990
0.978
0.987
0.990
0.980
Notes:
1) Single-starred items are statistically significant at the 5% level, double-starred items at the 1% level, and triple-starred at the 0.1% level.
2) Standard errors are available from the corresponding author.

Effect of Predicted Education on
Predicted log Wage
0.18

0.16

0.14

0.12
Wife's Continuous Education

0.10

Wife's Discrete Diploma
Husband's Continuous Education

0.08

Husband's Discrete Diploma
0.06

0.04

0.02

0.00
1960

1970

1980

1990

2000

2010

2020

Figure 22: E¤ect of Predicted Education on Predicted log Wage

28

Table 9: Assortative Mating Test Statistics
Year
1962
1967
1970
1972
1975
1978
1980
1985
1990
1995
2000
2005
2007
2010
2014
2015
2018
2019
# CellsDF

6

log Predicted Wage
Years of Education
Wald Test
LR test Wald Test
LR test525.5
7314.02443.65642.5773.3
6298.72981.75968.1604.15317.94453.58447.1497.97318.33952.18404.5269.1
4329.73456.17756.3318.5
2382.03857.48507.5672.93119.25022.210139.1
871.8
3101.75121.09977.7564.95818.56061.810134.3
451.1
5098.84344.78250.6544.95764.13799.67642.9631.38087.45372.711930.9654.3
7502.85108.611536.9807.47046.44525.010983.2
1004.08168.83654.210317.1
935.5
7930.83946.910395.8
1043.65283.82964.68854.51183.95208.02897.48604.3
10
5
81
99
16
24

Conclusion

This paper adds to the literature examining e¤ects of economic characteristics on marital sorting by using Current Population
Survey data with local linear regression to ‡exibly model the relationship between spouses’log wages and an OLS decomposition to examine the e¤ects of education on this sorting over wage. Our primary departure from existing research is to focus
on underlying wages, instead of earnings or labor supply, which we believe better captures the labor market characteristics ofeach spouse relevant to assortative mating. The local linear regression also allows us to examine how the association between
spouses’wages varies given wage level and to avoid endogeneity issues associated with the spousal labor market participation
decision.
We …nd evidence for positive assortative mating over wages, in concordance with the existing research, and extend that
research to compare the assortative mating patterns of recent years to the 1960’s and 1970’s. Our …ndings indicate theexistence of positive assortative mating even as early as 1962, contrary to Becker (1973). The education sorting analysis
across years shows an increasing percentage of sorting over wages is driven by the association between spouses’ educationlevels. Also, our results generally …nd more assortative mating at lower levels of education and wages than at higher levels.
We considered a number of other questions associated with estimating the degree of assortative mating. We explored
what was the best time in a marriage to measure assortative mating. Theoretically, because assortative mating involves how
couples sort themselves in marriage, it might seem that the relevant measure is assortativeness at the the time of marriage
or very early in a marriage. On the other hand, there might be factors that are important for sorting at the beginning of amarriage that become observable to an outside observer only much later. In particular, there might be important factors,
including level of and success in education that are observable to couples at the time of marriage that manifest themselves
into signi…cant heterogeneity in wages much later. We …nd strong evidence of this in that the degree of assortative mating
is much greater later in couples’marriages than at the time of marriage.
We also explore the value of transforming predicted log wages into percentiles. Most of the theoretical literature implies
that measuring assortative mating in terms of percentiles would be more informative than in terms of log wages. Our results
have nothing to say about which is preferred. But the percentile results are interesting in and of themselves and lead tomore understanding of the sorting process.
Finally, we suggest some new test statistics associated with assortative mating that are easier to use than those alreadyexisting in the literature. The test statistics imply rejection of the null hypothesis of no assortative mating in favor of theexistence of positive assortative mating, both for log predicted wages and level of education, for every CPS sample year.

7

Appendix: Weeks Worked Measurement Error

Figure 7 presents the measurement error of the weeks worked variable varying with annual hours worked of the person.
Maximum weeks worked overestimates the actual weeks worked. One can see that there exists unignorable measurement29

errors for people whose annual hours worked were less than 2000 hours. Using the fact that weeks worked variables of later
years are collected both as continuous and categorical variables, we identify the measurement errors from using the bracketedvariable. Then we adjust the measurement errors using local-linear regression. In particular, denote h as an arbitrary value ofctotal hours worked by an individual from year t, wit
as a weeks worked variable for person i in year t collected in a continuousdmanner, and wit as a weeks worked variable for person i in year t collected in a discrete manner. We calculate the weeks
worked error as
1X
b (h) ;E (mb j h) =T t 0
T is the number of sample years,andb0 (h)
b1 (h)

=

"

X

K

i

hit

h

1
hit

b

1

c
mit = wit

# 1"

hit

X

K

i

hit

h

1
hit

b

mit

#

d
wit

is the measurement error. Then, for t < 1978, we replace the weeks worked data with the error-adjusted weeks workeddinterpolating with h-points close to that consistent with wit.
Weeks Worked Measurement Errors
0.5
0.0
-0.5
-1.0
-1.5

1978

Avg Weeks-2.0Worked Error

1980

-2.5

2000

1990

2014
-3.0

2018

-3.5
-4.0
-4.5
0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Total Hours Worked

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