Bright and Wealthy:Exploring Assortative Mating in Italy

VALERIO FILOSO∗

November 28, 2007

Abstract

While current literature on marital sorting focusesalternatively on the role of schooling or on the roleof wages, we argue that both variables simulta-neously determine the level of assortative mating,since schooling and wages are never perfectly corre-lated. Using data from the Bank of Italy’s Surveyon Household Income and Wealth (SHIW), withfamilies tracked longitudinally from 1989 to 2004,we estimate a system of simultaneous mating equa-tions for wages and schooling. We find evidencethat cross-effects of these variables account for be-tween 4,6% and 7,3%.

1 Introduction

In a monogamous marriage market, assortativemating is the pattern of traits’ pairings observedbetween partners. In his first work on marriagemarkets, Becker (1973) noted that sorting be-tween traits of married couples is not a randomphenomenon. People prefer to match accord-ing to personal characteristics, like age, beauty,wages, education. Assortative mating can eitherbe negative or positive. For example, assumethat in the marriage market the only relevant

∗Department of Economic Theory and Applications,University of Naples “Federico II”, Italy, and CHILD(Centre for Household, Income, Labour and Demographiceconomics), Turin, Italy. E-mail: filoso@unina.it

trait in pairing is labor productivity: under pos-itive assortative mating couples will be formedby individuals endowed with similar productiv-ity, while under negative assortative mating willbe formed by spouses’ whose productivity in la-bor activities tend to be different1. When pos-itive assortative mating prevails, the correlationbetween the spouses’ productivity displays a pos-itive sign.

When it comes to matching on more thana single variable, interpreting cross correlationsbecomes remarkably trickier. Since the work ofBenham (1974), the positive empirical relation-ship between spousal education and one’s earn-ings has become a focal point for applied researchin family economics (Boulier and Rosenzweig,1984). Given a high degree of educational mat-ing in the marriage market, a simple OLS re-gression of the effect of spousal education onwages – no matter how many controls are intro-duced by the statistician – cannot reveal a causa-tion, since the estimated coefficient could merelycapture a systematic tendency toward marry-ing the likes. According to game theory (Roth

1The observed degree of assortative mating dependsalso on the marginal distribution of traits in the two sidesof the market, since a given degree of assortative mating isalways observed in the data because of random matching.Using marriage-market-level data, it is possible to disentan-gle random and systematic sorting. See Sundaram (2004)and Liu and Lu (2006).

1

2. BACKGROUND LITERATURE

and Sotomayor, 1990; Gusfield and Irving, 1989;Knuth, 1997 [1981]; Gale and Shapley, 1962),the outcome of the marriage market mechanismis such that more educated members of one sextend to marry more educated members of theother sex: the observed cross correlations aresimply a by-product of mating on education.However, it may well be that spousal educationhelps partners accumulating human capital andincreasing earnings, since couples with high lev-els of eduction are more likely to share ideas, val-ues, and tastes within the family and this homo-geneity may impact positively also upon marketproductive traits (Huang, Li, Liu, and Zhang,2006).

Whereas the cross-productivity hypoth-esis has some straightforward implicationsfor spousal earnings, the implications of theselective-mating hypothesis are not so clear-cut.The problems here are similar to those faced inthe human capital literature with regard to alter-native explanations for the positive correlationbetween schooling and earnings i.e., a problemof mutual causation. Higher education couldeither signal high skilled individuals (Spence,1973) or a deliberate attempt to increase the levelof human capital (Becker, 1964): in this contextof multiple causality, devising a test to disentan-gle the relative importance of selectivity fromthat of cross-productivity is still an open issue,since finding genuinely exogenous variables isfar from simple in this context.

We enter this debate pointing out that, priorto cross-effects, also the level of sorting betweenspouses adjusts to schooling and labor condi-tions. Our approach explicitly takes into ac-count that the marriage market jointly deter-mines assortative mating on schooling and onwages, i.e., market and household productivity,because schooling and wages are partly substi-tutable in the marriage market, as emphasizedby the theory of compensating differentials inmarriage (Grossbard-Shechtman and Neuman,1988). Accordingly, we adopt the methodology

of simultaneous estimation for two equations:educational mating and wage mating, under theassumption that both decisions are strongly re-lated. The model is estimated for the Italian mar-riage market in which schooling and market pro-ductivity are important traits which jointly con-tribute to the process of marital sorting. As-suming that prospective partners have rationalexpectations and private information on eachother that can be revealed only gradually acrosstime, we estimate a non-recursive system ofequations which allows to appreciate how mar-riage markets work. The data are extracted fromthe Bank of Italy’s Survey on Household In-come and Wealth (SHIW), with families trackedlongitudinally from 1989 to 2004. The tempo-ral structure of the dataset permits an estima-tion of long-run performances in the job marketand in the educational system which cannot befully disclosed at the beginning of marriage, butwhose expected value is relevant for spouse’s se-lection. Our key finding indicates that wage haspredictive power in forecasting educational mat-ing and that education also helps predicting wagesorting. The inclusion of these cross variablessignificantly decreases the level of observed cor-relations: these cross effects account from 4,6%to 7,3%.

The next section of this article is devoted tosurveying the literature on cross-effects of wageand schooling between partners. Then, we in-troduce a stylized model of the marriage marketwhich can account for multidimensional sort-ing. Various estimates for the model are pro-vided and the resulting evidence is discussed,along with possible directions for further re-search.

2 Background Literature

The phenomenon of spousal matching over per-sonal traits has a long research tradition in thefields of biology, economics, and sociology. Ep-

2

2. BACKGROUND LITERATURE

stein and Guttman (1984), in one of the most ex-tensive study on this topic to date, observe pos-itive assortative mating for ages, wages, educa-tion, religion, heights, IQ scores, and ethnicity.As noted earlier, the applied economic literatureon the cross-effects of education dates back tothe work of Benham (1974) who finds that wife’seducation increases husband’s wage by 3% inthe US. According to Tiefenthaler (1997), wife’seducation increases husband’s wage by 5–7%in Brazil, while husband’s education increaseswife’s wage by roughly 5%, though the estima-tion does not explicitly control for assortativemating. Also, significant benefits are found toarise from role specialization in the family andassociation, i.e., working in the same marketsector. In their study on Chinese twins, con-trolling for selectivity in the marriage marketand for family background, Huang, Li, Liu, andZhang (2006) find that husband’s education in-creases wife’s earnings by 3.5%, but cannot findany significant effect running in the opposite di-rection. They provide evidence that the increasein wife’s earnings is explained by a positive effecton hourly wage.

Empirical results universally show a positivesign for the correlation between spouses’ wages.In their study of assortative mating, Zhang andLiu (2003) discover that wives’ schooling impactspositively on her husband’s wage, but a simi-lar effect does not work the other way around.Their major finding is that the correlation be-tween potential wages is statistically non signif-icant, so that the main gains from marriage de-rive from role specialization, as in Becker (1991[1981]). This evidence is partly consistent withthe work of Smith (1979) who comes across lowcorrelation levels between wage residuals oncethe estimation procedure takes into account sam-ple selection. To date, the only result of negativeassortative mating on wages has been obtainedby Zimmer (1996) with a negative coefficientfor North-American blacks, even though Becker(1991 [1981], pp. 118–119) cites unpublished

negative coefficients obtained by Gregg Lewis.Grossbard-Shechtman and Neuman (1991), us-ing the 20% sample from 1983 Census of Israel,find evidence of reciprocal influence of spouses’levels of schooling and significant complemen-tarities in earnings-related measures. Hours ofwork have also received interest within this re-search field: Pencavel (1998) tests whether themarket work hours of husbands and wives arecorrelated with their spouses’ schooling levels.Using the 1990 Census for US, he finds that hus-bands are little influenced by their wives school-ing, while women married to a college-educatedman work 4% fewer market hours than womenmarried to high-school dropouts, and the ef-fect is almost doubled when the couple has chil-dren aged less than six years. This suggeststhat college-educated husbands substitute someof their own hours of work with their wives’hours in the market.

Another stream of literature makes explicitthat the process of mating involves variableswhich the researcher can hardly fully controlfor. In this perspective, unobserved componentsof educational and income mating are employedto infer about the systematic patterns of mar-riage. Rupert and Cornwell (1997) find weakevidence of cross-productive effects in marriage:according to their estimation based on the Na-tional Longitudinal Survey of Young Men, themarriage premium – the observed positive dif-ference in the wage level between married andunmarried men – is attributable to unobserv-able individual effects that are correlated withmarital status and wages. Nakosteen and Zim-mer (2001), using unobservable components ofhourly wages observed before and immediatelyafter marriage, find evidence of positive assor-tative mating on the basis of earnings for thesubjects observed in the Panel Study of IncomeDynamics (PSID). Behrman, Birdsall, and De-olalikar (1995) employ an educational matingequation to estimate unobservable skills whichare found to impact significantly on the wage

3

3. THE MARRIAGE MARKET

of Indian husbands. In their recent contribu-tion, Brynin and Francesconi (2004) have ex-tended the same econometric methodology towives and found several measures of market suc-cess associated with unobservable componentsof human capital.

In contrast to previous literature, this arti-cle argues that marital sorting operates not onlyalong the educational dimension but also on theincome dimension. However, since educationand labor income are not perfectly correlated,both correlations need to be taken into accountwhen studying marital sorting. In this perspec-tive, we contribute to clarify the missing linkin the applied literature between the job marketand the marriage market, a point which has re-cently received attention in a theoretical articleby Chiappori, Iyigun, and Weiss (2006). As oftoday, a joint estimation of market productivityand educational sorting for married couples hasnot been tempted yet and will be the theme ofthe next sections.

3 The Marriage Market

The marriage market model presented here isbased on the assumption that schooling producesmonetary effects because more educated peopleusually have better jobs, obtain higher salarieson the job market, and have greater chances ofmoving upward socially (Kalmijn, 1994). Non-monetary effects also follow from schooling,since education generally provides broader per-spectives on world visions and relaxes strictnessfrom inherited cultural values. Married individ-uals can gain from a higher level of their spouses’education because of the monetary and the non-monetary benefits from schooling: couples inwhich both spouses share the same backgroundvalues enjoy higher utility from the productionof public household goods. In an ideal settingin which schooling and wages are perfectly cor-related, and no significant heterogeneity exists

between people, the same marital sorting wouldprevail with regard to education and to wages,since the choice variable would make no differ-ence.

In contrast, the real world is characterizedby imperfect correlations between schooling andwages: this impacts the labor market as wellas the marriage market. Explanations for theimperfect correlation in the labor market arenot particularly relevant, since here we focus onwhat happens in the marriage market and onthe heterogeneity observed inside and among thecouples. This heterogeneity in sorting patternsis mainly due to: (1) different personal tastes to-ward the monetary and the non-monetary ben-efit which follow from education, and (2) un-observable factors which the social scientist canhardly control for.

Assuming that utility is transferable betweenpartners, as in the classical Becker’s model, part-ners can make themselves attractive compensat-ing a low level of a personal trait with a highlevel of another valuable personal trait. Af-ter marriage, this compensation can take theform of monetary transfers, like in the modelof Grossbard-Shechtman and Neuman (1988),but to a certain extent this compensation oftraits can take place also in the marriage market:for example, a prospective husband endowedwith low market productivity could make him-self more attractive when endowed with rel-atively higher education. If this holds true,schooling and income are partly substitutablein women’s eyes. As a result, marital sortinghappens not only along the educational dimen-sion, but partly also on the income dimension.Dual matching – with regard to education andjob prospects – and simultaneity are the corner-stones of the present model. We also assumethat, when people meet in the marriage market,they form expectations on each other’s chancesto obtain education and wage. Obviously, anyfamily can benefit from high levels of wage andfrom high levels of education, but imperfect cor-

4

3. THE MARRIAGE MARKET

relation and personal tastes introduce the possi-bility of substitution between the two inputs ofhousehold production.

Formally, actual household production for ageneric family can be written as:

F = F (v) (1)

where F is the total value of household-producedgoods,

v≡ [ew eh sw sh]′ (2)

is a vector containing the levels of education(e) and the levels of wages (s ) of the wife (w)and of the husband (h). F is assumed to be in-creasing in the level of each observable indepen-dent variable. Further, assuming competitionamong women and among men to marry thebest partners, the marriage market mechanismmaximizes the sum of the expected value of (1)across all possible matches (Becker, 1991 [1981],pp. 82–84).

Competition in the marriage market is basedon the assumption that matching is not com-pletely random. Then, the possibility of mar-rying a man of a given educational level de-pends, among other things, upon a person’s ed-ucational and wage levels. This systematic rela-tion between one’s traits and his/her partner’s istermed mating function and has been introducedin the context of family economics by Boulierand Rosenzweig (1984). While current litera-ture on human capital (Brynin and Francesconi,2004; Behrman, Birdsall, and Deolalikar, 1995)estimates mating functions only with regard toschooling, we allow for simultaneous determi-nation of educational and income sorting. Fi-nally, to enable simultaneous estimation of mat-ing equations, we With all the assumptions pre-viously stated, the resulting mating equation sys-tem can be written as follows:

D v+X′β+Ω= 0 (3)

where

D≡

1 −d1 0 −d2−d3 1 d4 0

0 −d5 1 −d6−d7 0 −d8 1

(4)

is the matrix of coefficients for the endogenousvariables, X is a matrix of exogenous variables,β is a vector of estimated parameters for the ex-ogenous variables, and

Ω≡ [ωew ωe

hω s

w ω sh]′ (5)

is a vector of i.i.d. error terms.To make things clearer, let us consider the

mating equations for wife’s education and wage.These can be written as:

ew = d1eh + d2 sh +xehβ

eh +ω

ew (6)

sw = d5eh + d6 sh +xshβ

sh +ω

sw (7)

where the terms for the exogenous characteris-tics x are allowed to vary across equations. Thehypotheses that

d1 > 0 (8)d6 > 0 (9)

have been tested in the literature under the as-sumption that d2 = d5 = 0 and found true. In-stead, we are interested in testing whether

d1, d2 > 0 (10)d6, d5 > 0 (11)

i.e., if there is any possibility of trade betweenschooling and market productivity. To sum up,this structure for marital mating is based onfour equations: two for schooling of husbandand wives and two more for wages of the samespouses. Each mating equation implies that wageand schooling of a man jointly determine theexpected levels of schooling and of wage of hisprospective wife and the same causal relation

5

4. ESTIMATION AND DATA

holds true also for women. This implies the pos-sibility that education and wage can impact dif-ferently prospective spouse’s wage and school-ing; furthermore, those effects need not to besymmetric with regard to gender and can pro-vide interesting sources of imbalances in the mar-riage market. In statistical terms, we are inter-ested in testing the positive signs for the coeffi-cients in the D matrix.

4 Estimation and Data

4.1 The Dataset

The data used for estimation originate fromthe Bank of Italy’s Survey on Household In-come and Wealth (SHIW) sample, containingobservations on families and individual compo-nents tracked longitudinally from 1989 to 2004.Though SHIW’s data collection actually datesback to 1977, it is only from 1989 that data oneducation are collected also for nonworking in-dividuals. Apart from observations from 1977to 1987, other groups were dropped: (1) cou-ples for which education is missing, (2) couplesfor which job status is missing, (3) couples inwhich spouses are retired, (4) couples in whichhusbands are older than 65 and wives are olderthan 60. As a result of this process of selection,the sample reduces to 18,459 couples. All in-come and wealth measures are adjusted to 2004-equivalent euros. Education and wages are inlogarithms, with the censoring point for wage(originally set equal to zero) being shifted byone euro to obtain non-missing values for pre-dicted wages also in case of individuals who donot work. In our sample, the percentage of wivesworking and receiving a salary is 43%, while theproportion of husbands is 91%. According tothese figures, the problem of censoring for wivesis particularly acute, so it is tackled from the be-ginning, performing a Heckman estimation overthe subsamples of wives and husbands and us-ing the resulting equations to predict notional

wages for the censored observations, as describedin Cahuc and Zylberberg (2004, p. 34–35). Re-sults are reported in tables 3 and 4, with furtherdetails provided in the estimation section of thispaper.

To check the basic relations between the vari-ables of interest, i.e., wages and schooling, pair-wise correlations on the censored sample are tab-ulated in table 1 and contrasted with the co-efficients calculated over the uncensored sam-ple, reported in table 2. Correlation betweenspouses’ schooling is around 64%, a value whichis fairly higher than the average 50% as reportedby Lam (1988) for the US, while correlation be-tween wages goes from 41% in the censored sam-ple to 29,7% in the uncensored sample2. Also,we employ the method of quantile regressions,as described in Koenker (2005), since we areinterested not only in the strength of the lin-ear relation around the mean, but also in whatis happening in other sections of the distribu-tion of the dependent variable. Graph 1 showsthe relation between the log of husband’s yearsof schooling on his wife’s years of schooling.On the x-axis we have the quantiles of the de-pendent variable and on the y-axis the value ofthe estimated coefficients. The straight line isthe value of the OLS estimator, being used asa benchmark, surrounded by confidence bandsat 95%. The kinked line, surrounded by grey-shaded confidence bands, shows the values ofquantile regression coefficients obtained at dif-ferent points of the distribution of the depen-dent variable. The awkward shape of this partic-ular curve is due to the discrete nature of the dataon schooling, which are available only for classesof completed education levels. The resulting re-ciprocal elasticity ranges from 35% in the highestquantile to 100% in the 30-60% quantiles.

Graph 2 displays the relation between the logof husband’s wage and wife’s wage, provided that

2For more details on the structure of mating in Italy seeFiloso (2007).

6

4. ESTIMATION AND DATA

both work in the marketplace. Conditioning onhusbands’ wage quantiles, the strength of the lin-ear relation between the two variables displaysa non-linear trend, with steadily decreasing val-ues until the last quantiles, where the relation isjumping back to the same values observed for thelow-wage wives. Correcting for selectivity re-stores a U-shaped curve between the two wages,as it is evident from graph 3.

Lastly, graphs from 4 to 7 show the elasticitybetween schooling and wage, for husbands andwives, in the case of censoring and in the caseof imputed potential wages to nonworking in-dividuals. Correcting for censoring shows thatwomen increasingly benefit from education allalong the distribution of wages, even thoughpart of this effect could be due to the effectof notional wages. The returns from schoolingfor husbands tell a different story. Husbands’schooling has an increasing positively impact onwages until highest quantiles, where the widerconfidence bands show greater variability com-pared to lower quantiles: thus, very high levelsof wage are explained by schooling only at a lim-ited extent. Given the very small degree of cen-soring for husbands, the two graphs look almostidentical.

All these econometric investigations showthat the relationship between the variables of in-terest do not closely match the assumption ofnormality, since the estimates for the quantileregressors systematically depart from OLS esti-mates. This suggests that the phenomena un-der study involve significant substantial censor-ing and nonlinearities, two aspects that will ad-dressed in the empirical section of this article.

4.2 Estimation Technique

The estimation procedure is structured as fol-lows:

1. The first problem to tackle when estimat-ing the effects of sorting on observed laborbehavior is obtaining reasonable estimates

of the expectations of ei and si as they en-ter in the evaluation that prospective part-ners make while dating. We assume thatprospective partners have rational expecta-tions on each other’s achievements, both inthe educational system and in the job mar-ket. This implies that the observed valuesin the data for ei and si can be used to re-cover their expected levels, provided thatsome sort of temporal smoothing is oper-ated in order to obtain the expected val-ues as computed before marriage. Since thedata in SHIW have a panel structure, i.e.repeated observations across the years forthe same couples, we can exploit this fea-ture to obtain estimates of the variables rele-vant for the mating system. For computingexpected education, we use the maximumlevel of schooling observed in the data. Forcomputing expected salary, we use the me-dian salary.

2. Since salary s j is not observed for peopleunemployed or out of the labor force, wehave left censoring for this variable:

s j =¨

s∗j if s j > 00 if s j ≤ 0

with j ∈ w, h. We use Heckman’s model(Heckman, 1979) to account for censoringand estimate potential wages for nonwork-ing wives and husbands. The regressors forwives’ wages are schooling, expertise, exper-tise squared, professional qualification, andproductive sector. The selection equationfor wives includes age, age squared, school-ing, schooling squared, number of children,dummies for geographical location, prox-ies for house ownership, non-labor income,and husband’s wage. The squared term areinserted since the high degree of nonlineari-ties in wives’ behavior. The equations forhusbands parallel those for wives, except

7

5. RESULTS

for spouse’s wage and professional qualifica-tion which are not included in the selectionequation.

3. Using predicted wages, we perform Three-Stage Least Squares procedure for the hus-bands’ mating equations and another onefor wives’ mating equations. As a compar-ison, we also estimate a SUR model withall the four equations computed simultane-ously. Along with direct and cross effects,mating equations contain controls for per-sonal wealth (approximated by house own-ership and income from capital), InverseMills’ Ratio, job qualification, and numberof children. Moreover, wife’s wage matingequation also controls for notional wages.

5 Results

The results from the Heckman model for sam-ple selection, obtained by Maximum LikelihoodEstimation and displayed in tab. 3, highlight theconcave effect of age on the probability of en-tering the job market. For women, the proba-bility of being employed is maximized around35 years. Merging this information with thesignificantly negative impact of children on la-bor market participation, it comes out that preg-nancy and child rearing do impact the workingposition. The concavity of education on wives’wage is also confirmed by high estimated Stu-dent’s t .Also, the same wage equation showsthat expertise exerts a weak influence on wives’wage: while Becker (1991 [1981]) argues that thehigher the husband’s wage, the lower must re-sult wives hazard for participation, Lam (1988)has proved that this holds true only when house-hold production does not include public goods.The positive estimated coefficient in the presentmodel supports the hypothesis that labor partic-ipation decisions of wives are mainly driven bypublic goods considerations.

Evidence from the mating equations, dis-played in tables 6–5 show overall significance forboth structural models, with R2s higher for ed-ucational mating. Checks for multicollinearity,not attached here but available upon demand,show tolerable values around 1.19 in the Vari-ance Inflation Factor for all the four equations.To correct for spurious correlations induced bycensoring, the Inverse Mills’ Ratio and a dummyfor censored observations were introduced andfound significant for wives and for husbands.

All endogenous variables are estimated to berelevant in each equation, with some asymme-tries across gender and the sharpest effects be-ing the direct links between schooling levels andwage levels across partners. The strong statisti-cal and economic significance of cross-effects sup-ports our hypothesis about the possibility of substi-tution between education and wages in the mar-riage market. Wage impacts positively the educa-tional mating equation, both for women and formen, as well as schooling impacts wage mating.The elasticity of an additional year of schooling,calculated around the mean, is 0.045 for womenand 0.073 for men; moreover, the correspond-ing t values are found higher for men. Proba-bly, since men are expected to provide the mostpart of family income, the effect of their wage isstronger when compared to women and allowsmen with higher wages to afford more educatedwives. Contrasting these results with the crudeestimates presented in tab. 2, it is a striking evi-dence that a structured model of marital sortingdecreases observed schooling correlation from64% to 42%. The issue of simultaneity is alsorelevant for the results: using as a benchmark acompanion model of the same four equations ob-tained through SUR technique reported in tab.7, assuming only links between error terms andnot between variables, the 3SLS-estimated equa-tions display non trivial differences between esti-mated coefficients. This also supports our initialconjecture that wages and eduction jointly im-pact the sorting between spouses and that simul-

8

5. RESULTS

taneity does matter.Interestingly, the Inverse Mills’ Ratio (λ), rep-

resenting the hazard rate of nonparticipation,is also negatively related to prospective hus-band’s and wives’ expected education; in otherwords, ceteris paribus, women or men withhigher probability of entering the job market aremore likely than others to marry highly edu-cated partners. Wages are sorted positively be-tween partners, estimates say, and the effect isstronger from a prospective wife’s standpoint,with a value of 30% for women and 16% formen. This is consistent with previous litera-ture (Ermisch, 2003), since generally husbandstransfer resources to their wives in exchange forhousehold production. Accordingly, wives areexpected to rely more on her husband’s wagethan the opposite. Minor findings show that bet-ter job positions impact positively on the prob-ability of wage matching. Since the omitted cat-egory in the models is worker, results show thatwomen are more responsive than men to job po-sitions, because their estimated coefficients areuniformly higher than the corresponding figuresfor men.

It is instructive to compare our results withthose obtained by Behrman, Birdsall, and Deola-likar (1995) and Brynin and Francesconi (2004).These authors estimate a mating equation of thetype

ew = d1eh +xehβ

eh +φ+ω

ew (12)

where φ is an unobservable component of hu-man capital to be estimated consistently fromthe post-regression residuals ew − ew . They findthat φ impacts positively on wages. Our re-sults show that part of this unobservable vari-able depends upon wage, since marital sortingis multidimensional and education is not theonly variable that prospective spouses may con-sider. If our interpretation holds true, then,the expected return of unobservable human cap-ital to wages should be lower than Behrman’sestimates. Lastly, on obvious way to extend

the present econometric exercise would be em-ploying a technique of simultaneous quantile re-gressions, as indicated by Chernozhukov andHansen (2006) and Kim and Muller (2004): al-though still in its infancy, this approach looksextremely promising for modeling complex andnonlinear links like those observed in the mar-riage market.

9

A. STATISTICAL TABLES

ASt

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Tabl

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s–

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aria

bles

Wife

’sSc

hool

ing

Hus

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645

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382

0.30

61.

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age

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60.

388

0.41

21.

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Tabl

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Cor

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Sam

ple

Var

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ife’s

Scho

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gH

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0.63

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178

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270

0.36

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281

1.00

0

10

A. STATISTICAL TABLES

A.2 Heckman Equations

Table 3: WivesHECKMAN SELECTION MODEL

COEFFICIENTS STATSVARIABLES β t Mean σWife’s WageWife’s Schooling 0.141 7.368 2.264 0.511Expertise 0.003 1.419 24.370 10.866Expertise (Square) 0.981 2.113 0.071 0.056Freelancer 0.058 1.090 0.005 0.072Entrepreneur -0.035 -1.056 0.014 0.118Self-employed -0.244 -12.804 0.080 0.272Manufacturing 0.115 4.547 0.096 0.295Marketing/Catering 0.105 3.958 0.086 0.281Transportation/Communications 0.180 4.158 0.008 0.089Finance 0.259 7.303 0.015 0.123Public Administration/Service 0.240 9.538 0.238 0.426Out of Labor Force -0.103 -2.046 0.533 0.499Constant 3.127 50.911Selection EquationAge 0.139 14.519 40.511 8.985Age (Square) -0.002 -14.492 1721.886 732.141Wife’s Schooling -0.881 -13.390 2.264 0.511Wife’s Schooling (Square) 0.473 27.506 5.386 1.908Number of Children -0.150 -15.694 1.696 1.078Husband’s Wage 0.096 11.129 3.270 1.111Freelancer 6.039 0.000 0.005 0.072Entrepreneur 2.110 11.239 0.014 0.118Self-employed 0.635 17.044 0.080 0.272Constant -3.571 -18.354tanh(ρ)Constant -0.901 -27.075ln(σ)Constant -0.680 -52.043StatisticsSubjects 18,459

11

A. STATISTICAL TABLES

Table 4: HusbandsHECKMAN SELECTION MODEL

COEFFICIENTS STATSVARIABLES β t Mean σWife’s WageHusband’s Schooling 0.291 31.386 2.303 0.476Expertise 0.010 6.980 27.515 10.782Expertise (Square) -0.980 -3.706 0.087 0.062Freelancer 0.458 23.848 0.028 0.165Entrepreneur 0.170 11.395 0.048 0.214Self-employed -0.026 -2.828 0.208 0.406Manufacturing 0.172 11.292 0.366 0.482Marketing/Catering 0.117 6.936 0.144 0.351Transportation/Communications 0.230 12.172 0.065 0.246Finance 0.429 18.668 0.032 0.176Public Administration/Service 0.277 17.421 0.299 0.458Out of Labor Force -0.010 -0.248 0.041 0.199Constant 2.482 74.387Selection EquationAge 0.079 6.574 43.957 9.243Age (Square) -0.001 -7.311 2017.664 814.623Husband’s Schooling 0.337 12.517 2.303 0.476Constant -0.857 -3.312tanh(ρ)Constant 0.222 2.911ln(σ)Constant -0.870 -126.090StatisticsSubjects 18,459

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A. STATISTICAL TABLES

A.3 3SLS Estimation

Table 5: WivesDEPENDENT VARIABLES: Log of schooling years, Log of wage

COEFFICIENTS STATSVARIABLES β t Mean σWife’s SchoolingHusband’s Schooling 0.420 36.526 2.303 0.476Husband’s Wage 0.073 10.767 3.569 0.451House Ownership -0.004 -0.580 0.668 0.467Husband’s Inverse Mills’ Ratio (λ) -1.468 -19.014 0.174 0.068Wife’s Wage Censoring -0.205 -34.590 0.571 0.495Constant 1.411 34.780Wife’s WageHusband’s Schooling 0.059 10.899 2.303 0.476Husband’s Wage 0.165 29.180 3.569 0.451Income from Capital 0.003 4.665 6.970 3.387Executive 0.038 3.951 0.062 0.242Freelancer 0.069 4.822 0.028 0.166Entrepreneur 0.034 3.089 0.048 0.214Self-employed -0.002 -0.277 0.208 0.406Wife’s Wage Censoring 0.037 7.641 0.571 0.495Constant 2.709 129.763StatisticsSubjects 18,086R2 (Schooling) 0.444R2 (Wage) 0.093

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A. STATISTICAL TABLES

Table 6: HusbandsDEPENDENT VARIABLES: Log of schooling years, Log of wage

COEFFICIENTS STATSVARIABLES β t Mean σHusband’s SchoolingWife’s Schooling 0.420 51.563 2.264 0.511Wife’s Wage 0.046 5.427 3.482 0.321House Ownership -0.046 -4.730 0.087 0.277Wife’s Inverse Mills’ Ratio (λ) -0.257 -25.955 0.977 0.419Constant 1.445 37.254Husband’s WageWife’s Schooling -0.065 -6.642 2.264 0.511Wife’s Wage 0.287 29.345 3.482 0.321Number of Children 0.045 14.866 1.696 1.078Income from Capital -0.008 -7.545 0.989 2.706Executive 0.038 1.578 0.016 0.124Freelancer -0.150 -3.564 0.005 0.072Entrepreneur -0.139 -5.183 0.014 0.118Self-employed -0.155 -13.298 0.080 0.272Wife’s Inverse Mills’ Ratio (λ) -0.456 -33.756 0.977 0.419Constant 3.110 66.258StatisticsSubjects 18,424R2 (Schooling) 0.420R2 (Wage) 0.182

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A. STATISTICAL TABLES

A.4 SUR Estimation

Table 7: SUR EstimationDEPENDENT VARIABLES: Log of schooling years, Log of wage

COEFFICIENTS STATSVARIABLES β t Mean σWife’s SchoolingHusband’s Schooling 0.797 83.397 2.303 0.475Husband’s Wage 0.062 11.084 3.569 0.451House Ownership -0.009 -1.752 0.669 0.466Husband’s Inverse Mills’ Ratio (λ) -0.793 -12.395 0.174 0.068Wife’s Wage Censoring -0.098 -19.907 0.571 0.495Constant 0.406 12.008Husband’s SchoolingWife’s Schooling 0.753 109.635 2.264 0.510Wife’s Wage 0.068 9.470 3.482 0.320House Ownership -0.025 -3.114 0.088 0.279Wife’s Inverse Mills’ Ratio (λ) -0.089 -10.629 0.977 0.420Constant 0.450 13.830Wife’s WageHusband’s Schooling 0.064 12.183 2.303 0.475Husband’s Wage 0.311 56.995 3.569 0.451Income from Capital 0.002 3.464 6.982 3.377Executive 0.030 3.192 0.062 0.242Freelancer 0.059 4.221 0.028 0.165Entrepreneur 0.026 2.495 0.048 0.214Self-employed 0.001 0.235 0.208 0.406Wife’s Wage Censoring 0.059 12.778 0.571 0.495Constant 2.167 106.857Husband’s WageWife’s Schooling 0.018 1.912 2.264 0.510Wife’s Wage 0.563 59.050 3.482 0.320Number of Children 0.039 13.375 1.696 1.079Income from Capital -0.006 -5.883 1.007 2.727Executive 0.038 1.615 0.016 0.124Freelancer -0.135 -3.291 0.005 0.072Entrepreneur -0.121 -4.604 0.014 0.118Self-employed -0.140 -12.212 0.080 0.272Wife’s Inverse Mills’ Ratio (λ) -0.368 -27.868 0.977 0.420Constant 1.881 41.150StatisticsSubjects 18,051R2 (Husband’s Schooling) 0.373R2 (Husband’s Wage) 0.348R2 (Wife’s Schooling) 0.051R2 (Wife’s Wage) 0.140

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B. GRAPHS

B Graphs

B.1 Educational Mating

0.20

0.40

0.60

0.80

1.00

1.20

Wife

’s S

choo

ling

0 .2 .4 .6 .8 1Quantile

Figure 1: Correlation between spouses’ schooling (Uncensored sample).

B.2 Wage Mating

0.30

0.35

0.40

0.45

0.50

0.55

Hus

band

’s W

age

0 .2 .4 .6 .8 1Quantile

Figure 2: Correlation between spouses’ wages (Censored sample).

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B. GRAPHS

0.10

0.20

0.30

0.40

Hus

band

’s W

age

0 .2 .4 .6 .8 1Quantile

Figure 3: Correlation between spouses’ wages (Uncensored sample).

B.3 Wives’ Returns to Schooling

0.30

0.40

0.50

0.60

0.70

Wife

’s S

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ling

0 .2 .4 .6 .8 1Quantile

Figure 4: The effect of wife’s schooling on her wage (Censored sample).

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B. GRAPHS

0.00

0.10

0.20

0.30

Wife

’s S

choo

ling

0 .2 .4 .6 .8 1Quantile

Figure 5: The effect of wife’s schooling on her wage (Uncensored sample).

B.4 Husbands’ Returns to Schooling

0.25

0.30

0.35

0.40

0.45

Hus

band

’s S

choo

ling

0 .2 .4 .6 .8 1Quantile

Figure 6: The effect of husband’s schooling on his wage (Censored sample).

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B. GRAPHS

0.25

0.30

0.35

0.40

0.45

Hus

band

’s S

choo

ling

0 .2 .4 .6 .8 1Quantile

Figure 7: The effect of husband’s schooling on his wage (Uncensored sample).

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