Will you ‘quasi-marry’me? The Rise of Cohabitation and Decline of Marriages E¤rosyni Adamopoulou Universidad Carlos III de Madrid
12th Annual Congress of the European Economic Association Glasgow, Scotland 23-26 August 2010
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Introduction
Family and household structure changed drastically in the last couple of decades: Marriage rate declined sharply in Europe and the US Divorce rate increased People turned to more ‡exible forms of union)quasi marriages (formal/informal cohabitation) Cohabitation can be dissolved easily with minor costs and its dissolution rate is higher than the divorce rate
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Introduction Dramatic increase in female labor force participation over the past decades. Two of the factors that have been identi…ed behind the increase of female labor force participation: 1 2
The narrowing of the gender wage gap (Jones et al., 2003). The improvement in the household production technology (Greenwood et al., 2005).
These factors may also a¤ect agents’incentives to get married: 1
2
E¤rosyni Adamopoulou
Narrowing of the gender wage gap )" women’s bargaining power and # the value to specialization within marriage Improvements in household technology ) further # in the returns to specialization, and in the oppurtunity cost of not getting married.
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Question
The question we try to investigate is the e¤ect of the narrowing of the gender wage gap and the improvement in household production technology on the rise of cohabitation. To do so, we build a model of marriage and cohabitation with household production technology and the presence of gender wage gap in the labor market. The model can account for the changes in cohabitation and deliver cross-sectional facts.
(extra at p.22)
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Data
Austria Belgium* Denmark Finland France Germany Ireland Italy Netherlands Norway Spain Sweden UK US
Cohabiting couples as percentage of all couples 1990's 2000's 1997 9.11 2007 15.35 2007 11.10 1996 24.81 2006 24.37 1995 18.49 2007 24.19 1995 14.58 2004 19.61 1996 8.52 2005 11.71 1995 4.67 2006 14.14 1995 3.08 2006 4.47 1996 13.88 2008 19.25 2008 22.44 2005 4.26 1995 23.35 2005 26.82 1996 10.00 2006 15.99 1996 5.07 2008 10.43
% change 68.50 NA -1.77 30.83 34.50 37.44 202.78 45.13 38.69 NA NA 14.86 59.90 105.72
Definition: two persons of different sex that share the same house and identify themselves as a couple (it excludes roommates, siblings etc) Age group: All ages Source: UNECE and National Statistical Services of each country
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Cross country evidence
Unbalanced panel for 15 OECD countries in the period 1990-2008. Main speci…cation
(cohabitation rate)it = α + β0 (relative price of home appliances)it + β1 (gender wage gap)it + β2 (controls)it
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Cross country evidence
(extra at p.23) (extra at p.25) E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Model
There is a continuum of males (m ) and females (f ), each of measure one. There is heterogeneity in wages among men and among women. They live for 2 periods, and they discount future utility at rate 0 < β < 1. Additively separable utility U (c, h) = µ log(c ) + (1 µ) log(h), with µ > 0. c is a market good and h is a good produced at home.
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Model
There is a labor market where both men and women can work. Men’s wages wm are drawn from a distribution Fw m with support [w , w ] . Women’s wages are drawn from a distribution Fw f with support [τw , τw ] and τ 2 (0, 1) ) gender wage gap (exogenous). Married/cohabiting men devote all of their available time to market work (there is no leisure). Married/cohabiting women distribute their time between market work lf and house work (1 lf ).
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Model
There is a household production technology 1/ρ h = A [θd ρ + (1 θ )(1 l )ρ ] with 0 < ρ < 1. d is the stock of household durables which are purchased in price q. Durables purchased in the 1st period depreciate fully by the beginning of the 2nd period. The good produced at home is a shared good for the couple with equivalence scale γe 12 , 1 .
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Model: 1st period
There is a marriage market where single people meet potential partners of the opposite sex (random matching). Upon meeting, the man makes take-it or leave-it o¤ers to the woman. i , l i , d i , c i , l i , d i where Each o¤er consists of a sextuple c1f 2 1 2f 2f 1f i is the type of marital institution (marriage or cohabitation).
The o¤er is renegotiation-proof. The woman can either accept the o¤er and enter into a union with the man, or reject the o¤er and remain single.
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Model: 2nd period
In the 2nd period single men/women make/receive take-it or leave-it o¤ers as in the 1st period. Agents who are single in the beginning of the 2nd period did not match in the 1st period waiting for a di¤erent match (in terms of wages). Agents who matched in the 1st period and entered a union (marriage or cohabitation) face an exogenous probability of divorce 0 π i 1. Divorced/separated agents do not rematch.
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Model: Cohabitation/marriage VS singlehood
The reasons why agents would prefer entering a marital institution to singlehood are 1
Specialization: The woman will work in the household production, the man in the market.
2
Increasing returns to scale in the household good.
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Model: Cohabitation VS Marriage
Cohabitation di¤ers from marriage with respect to the cost and the probability of dissolution: 1
2
The divorce cost entailed with marriage (φ > 0) is higher than the one entailed with cohabitation due to the law (we normalize the separation cost of cohabitors to zero). Cohabitation is more unstable than marriage π c > π m .
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Optimal marriage proposal in the 1st period
max
cf1,m >0,0 0,
µ ln(cm1,m ) + (1
µ) ln(γh1,m )
c 2,m >0,0 0 f f
h + β (1
π m ) µ ln(cm2,m ) + (1
µ) ln(γh2,m ) + π m Umd (wm )
subject to cm1,m + cf1,m cm2,m
+ cf2,m 1,m h
h
E¤rosyni Adamopoulou
2,m
= wm + wf lf1,m = wm + wf lf2,m = A(d
1,m θ
= A(d
2,m θ
Universidad Carlos III de Madrid
) (1 ) (1
i
qd 1,m
(BC1)
2,m
(BC2)
qd
lf1,m )1 θ lf2,m )1 θ
Will you ‘quasi-marry’me?
(HPT1) (HPT2)
Optimal marriage proposal in the 1st period
(1 + β)Ufs (wf )
µ ln(cf1,m ) + (1
+ β[(1
µ) ln(γh1,m )
π m ) (µ ln(cf2,m ) + (1
+π m Ufd (wf )]
µ) ln(γh2,m )) (WPC1)
and Ufs (wf )
E¤rosyni Adamopoulou
µ ln(cf2,m ) + (1
Universidad Carlos III de Madrid
µ) ln(γh2,m ).
Will you ‘quasi-marry’me?
(WPC2)
Numerical Example
Preferences Public good parameter Household production technology Wages Dissolution
Parameters µ β γ A ρ q w τ πm πc φ
go to p.27
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Values 0.5 0.96 1/1.7 20 0.2 5!2 [10, 20, ..., 100] 0.6 ! 0.8 0.30 0.50 3
The e¤ect of the gender wage gap (1st period)
Optimal marital status with narrow gender wage gap 100
90
90
80
80
70
70
60
man's wage
man's wage
Optimal marital status with wide gender wage gap 100
marriage
50
40
marriage
60
50
cohabitation
40
cohabitation 30
30
singlehood 20
20
singlehood 10
6
12
18
24
30
36
42
48
54
60
10
8
16
24
woman's wage
(rob. check at p.29) Universidad Carlos III de Madrid
40
48
woman's wage
(cross sectional at p.28)
E¤rosyni Adamopoulou
32
Will you ‘quasi-marry’me?
56
64
72
80
Female labor supply by marital status (1st period)
Female market labor supply by marital status with narrow gender wage gap
Female market labor supply by marital status with wide gender wage gap 0
0
0
0
0
0
0.04 0.12 0.19
0
0
0
0
0
0.04 0.15 0.23 0.29 0.34
0
0
0
0
0
0.11 0.2 0.27 0.33 0.37
0
0
0
0
0
0
0.01 0.11 0.18 0.24
0
0
0
0
0
0
0.09 0.17 0.24 0.29
0
0
0
0
0.05 0.17 0.26 0.32 0.37 0.41
0
0
0
0
0
0.06 0.16 0.24 0.3 0.34
0
0
0
0
0.13 0.24 0.31 0.37 0.41 0.45
0
0
0
0
0.03 0.15 0.24 0.3 0.35 0.39
0
0
0
0
0.14 0.24 0.31 0.37 0.41 0.44
man's wage
man's wage
0
0
0
0
0.07 0.21 0.3 0.37 0.41 0.45 0.48
0
0
0
0.17 0.29 0.37 0.42 0.46 0.49 0.52
0
0
0
0.12 0.24 0.33 0.39 0.43 0.47 0.49
0
0
0
0.1 0.26 0.35 0.42 0.46 0.5 0.69 0.70
0
0.02 0.26 0.38 0.45 0.5
0.07 0.29 0.39 0.46 0.68 0.69 0.69 0.69 0.70
0
0.23 0.39 0.48 0.68 0.69 0.69 0.70 0.70 0.70
0
0
0.12 0.27 0.37 0.43 0.48 0.51 0.70 0.70 0.69 0.70 0.70 0.70
0.022 0.36 0.66 0.67 0.68 0.68 0.69 0.69 0.69 0.70
0.191 0.44 0.67 0.68 0.68 0.69 0.69 0.70 0.70 0.70
woman's wage
woman's wage
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
The e¤ect of the price of home appliances (1st period)
Optimal marital status with low price of home appliances 100
90
90
80
80
70
70
60
man's wage
man's wage
Optimal marital status with high price of home appliances 100
marriage
50
40
50
cohabitation
40
cohabitation
30
30
20
10
marriage
60
20
singlehood 6
12
18
24
30
36
42
48
54
singlehood 60
10
6
12
18
24
woman's wage
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
30
36
woman's wage
Will you ‘quasi-marry’me?
42
48
54
60
Conclusions
1
The rise of cohabitation is associated with the narrowing of the gender wage gap and the improvement in the household production technology.
2
Women in cohabiting units do not specialize fully at home and they work more hours in the market than married women who earn the same wage.
3
In the data both the price of home appliances as a proxy of household production technology and the gender wage gap have a strong negative e¤ect on cohabitation.
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Related Literature
Brien, Lillard and Stern (2006): Learning of match quality Gemici and Laufer (2010): Assess ine¢ ciencies due to lack of commitment Cigno (2007), Matoushek and Rasul (2008): Game-theoretical approach Kalmjin (2007), Wydick (2007): Female labor force participation
(back to p.4)
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Gender wage gap and cohabitation
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Price of home appliances and cohabitation
(back to p.7) E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Religion and cohabitation rate
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Religion and cohabitation rate
(back to p.7) E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
How parameter values are picked Parameter Value µ = 0.5 β = 0.96 γ = 1/1.7 ρ = 0.2 A = 20 q=5!2 w = [10, 20, ..., 100] τ = 0.6 ! 0.8 π m = 0.30 π c = 0.50 φ=3 !
Justi…cation same weight on c and h standard OECD equivalence scale McGrattan, Rogerson & Wright (1997) Average share of expenditure on durables=21% (Baxter & Rotz, 2009) normalization US Census Bureau Stevenson & Wolfers (2007) Bumpass & Kennedy (2008) Cohabitation rate=15%
(back to p.17) E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Cross sectional facts Percentage of housewives Cohabiting women Married women Austria 11.89 26.36 Denmark 2.76 2.73 Finland 4.24 4.46 France 4.92 16.38 Germany 2.77 17.40 Ireland 9.52 39.07 Netherlands 10.53 32.19 Norway 6.62 7.37 Spain 15.71 49.60 Sweden 0.00 1.13 UK 14.79 16.90 US 15.56 26.25 Source: ISSP 2002 (own calculations) Age group: all ages
(back to p.18) E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Robustness I The man supplies a …xed amount of time to housework
(back to p.18)
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Robustness II The woman makes the take-it or leave-it o¤er
The woman tries to maximize her utility by choosing the hours she will work in the market and the amount of consumption good and durable good she will o¤er to the man. She has to take into account the man’s participation constraint in her decision (she should be able to convince him to cohabit/get married to her). The assumption that the man works full time in the market is maintained.
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
Robustness II The woman makes the take-it or leave-it o¤er
Results 1
The numerical example mitigates the optimal marital status that is obtained when the man makes the take-it or leave-it o¤er.
2
The only di¤erence lies on the fact that the utility of the woman is higher in marriage or cohabitation than in singlehood while the utility of the man is always the same as his participation constraint is binding.
(back to p.18)
E¤rosyni Adamopoulou
Universidad Carlos III de Madrid
Will you ‘quasi-marry’me?
