Imperfect Commitment, Social Constraints

and Household Time Allocation

Cristina Fernandez Almudena Sevilla-Sanz

IESE Business School University of Essex, ISER

December, 2005

Abstract

Economic theories of the household predict that increases in rel-

ative female human capital lead to increases in female labor force

participation and, symmetrically, to decreases in the female time de-

voted to household production. However, both at the longitudinal

and cross-sectional level we observe that, despite the decline in the

wage gender gap, specialization in home production continues to be

high, with women providing most of household produced goods and

services. We develop a simple model that recognizes the imperfect

commitment associated to the contractual processes over household

time allocation. In the light of the model, imperfect commitment

is characterized as a constraint on the household division of labor

1

beyond what is considered to be "socially acceptable". The model

predicts that imperfect commitment problems are stronger (and thus

the social constraint more likely to bind) (1) the higher the woman’s

relative wage and (2) the less credible threats available. We test the

model using the 2002-2003 Spanish Time Use Survey, a time diary

survey with information on the time devoted to household production

activities by both partners. Empirical findings support the proposed

model of imperfect commitment in the allocation of household time.

Although a woman’s home time decreases as her wage goes up, this

effect is less pronounced as her wage is higher. Furthermore, the time

devoted to those household activities where no credible threats exist

(such as those involving care) are less elastic to an increase in the

relative female wage.

JEL classification: D13, J0, J1, J2, Z13

1 Introduction

Contrary to the predictions of comparative advantage or bargaining theories

of the household, higher female human capital has not led to a more egal-

itarian allocation of time within the household.1 The determinants of how

spouses allocate time to household production are based on the predictions

1Time spent producing goods and services within the household has been recognized as

important since Becker (Becker, 1965). However, the time devoted to household production

continues to be overlooked in most household economic models (Juster and Stafford, 1991).

2

of either the unitary household production models (Becker, 1991) or bargain-

ing models (McElroy and Horney, 1981). In the unitary framework family

members cooperate to produce utility for all, either through the purchase

of market goods and services with earnings from market work or through

household production. Specialization is thus efficient and the spouse with the

lowest opportunity cost (i.e. the lowest human capital or the highest home

productivity) contributes the most to household production and the least to

market work. Bargaining theories reach the same conclusion but are based

on the concept of threat points determined by either the cost of falling out

of marriage ((McElroy and Horney, 1981)) or of a non-cooperative marriage

((Lundberg and Pollak, 1993)).2 However, empirical findings using time-use

data contradict the prediction of both theories. For example, when a wife

works more hours than her husband outside the home, she still undertakes

a larger share of housework (Ackerlof and Kranton, 2000). Similarly, men’s

unpaid work increases with his wife’s wage but only up to the point where

the wife contributes as much as the husband to the household income. Be-

yond that point, the wife’s contribution to housework starts increasing again

2Chiappori (Chiappori, 1992) and (Browning and Chiappori, 1997) unified both set of

theories into a "collective" approach to the household, where efficiency in the household

maximization problem is secured due to spousal transfers of private consumption. Incor-

porating household production into the collective framework requires further restrictions

on preferences and technology in order to identify the sharing rule and raises questions on

the dichotomization of time into leisure and market work in household economic models

(Apps and Rees, 1996) and (Apps and Rees, 1997).

3

(Bittman et al., 2001). Furthermore, the unequal allocation of household

time persists after observable characteristics are taken into account (Alvarez

and Miles, 2003).

We present a simple household model that reconciles the theory and em-

pirical findings by recognizing that decisions over time allocation migtht be

subject to imperfect commitment mechanisms. These imperfect commit-

ment processes can be traced back to a couple’s inability to reach binding,

legally-enforceable agreements about future behavior because of the non-

observability by third parties (see (Basu, 2001) and (Rasul, 2002)) or the

inability to fullfil informal contracts because the lack of credible threats (Fol-

bre and Bittman, 2004). Imperfect commitment is usually characterized in a

dynamic bargaining setting as the inability of one spouse to make transfers

of private consumption to compensate the other partner for utility losses.

Thus inefficiencies may arise such as in Lundberg 2001 (Lundberg and Pol-

lak, 2001). The theory presented in this paper focuses on the inability of

potential partners to credibly commit to make transfers of time, rather than

private consumption. We characterize the imperfect commitment as a con-

straint on the household division of labor beyond what is considered to be

"socially acceptable". The model has two predictions. First, whereas the

constraint on household division of labor is not likely to bind for low wage

women where specializsation is high, it becomes binding for women with a

higher relative wage. Second, the model predicts that the constrain is more

likely to bind for those household actitivities where commitment failures are

4

more important (such as caring activities).

Empirical studies that test the theories of the household have focused

the identification of unitary from bargaining models of the household, which

assume efficiency inhousehold decisions. Studies that attempt to empirically

identify inefficient outcomes within the household are rare (An exception is

that of Mazzocco (Mazzocco, 2003)). We test the predictions of the model

using the 2002-2003 Spanish Time Use Survey, a time diary survey with in-

formation on the time devoted to household production activities by both

partners. Empirical findings support the proposed model of inefficient al-

location of household time. First, consistent with the presence of social

constraints in the division of household labor we find that a woman’s relative

time allocation to household production services decreases with her relative

wage up to a certain level, and remains constant afterwards. Second, we find

that for those household tasks subject to greater commitment problems (for

example childcare) the constraint binds for lower female relative wages.

The paper is organized as follows. Section 2 presents a simple model of

time allocation and household production. Section 3 specifies the empirical

methodology. Section ?? describes the data set used in the analysis. Section

?? presents the empirical results and section ?? concludes.

5

2 Theoretical Model

To begin a baseline model of the household is presented that focuses on two

specific aspects of the gains associated to a union: efficiency gains from spe-

cialization in household production and the consumption of market public

goods.3 We then present a model where imperfect committment is as a so-

cial constraint on the household division of household labor beyond what is

"socially acceptable".4 The rationale behind imperfect committment are the

non-observability by third parties of spouse’s time devoted to household pro-

duction and the absence of credible threats for certain household production

activities (especially those related to caring activities (Folbre and Bittman,

2004)). Once the surplus from the union is defined, prospective mates need

to form some notion as to whether families realize the potential gains and

how those gains are divided. However, while the division of household sur-

plus is done efficiently under the baseline model, inefficient allocations arise

in the presence of imperfect commitment and social constraints.

3Other dimensions to marriage such as risk pooling or consumption smoothing are left

out of the analysis for exposition purpuses.

4Similarly to Lundberg and Pollak (Lundberg and Pollak, 1993) and Ackelof et al.

(Ackerlof and Kranton, 2000).

6

2.1 Baseline Model: Efficient Allocation of Household

Time

A household is denoted by the superscript U (union) and is assumed to

be formed by two individuals a man m and a woman f . The joint house-

hold utility depends on the consumption of two public goods: household

maintenance (which is privately produced by the household members) and

a composite consumption good (which is purchased in the market). The

composite consumption good includes market consumption goods that are

jointly consumed by the household C (such as groceries, housing, child care,

etc.) and can be acquired in the market at a normalized price p = 1. For

the remainder of the paper we will refer to C as the market public good. The

household joint utility also depends on the production (and consumption) of

a particular public good, household chores or household public good, Z (these

are the "commodities" in Becker’s language (Becker, 1965) such as a cleaned

house or home-made meals). Consider Z as a lower bound for the amount

of household production that needs to be done in the household which differs

from C in that it cannot be purchased in the market and is produced using

both partners’ time in household production Hi for i = m, f such that

Z = afHf + amHm

with ai being the man’s and woman’s productivity in household produced

7

goods.5 Thus, whereas the output Z is consumed jointly by both partners,

each partner privately contributes to its production. I assume that each part-

ner derives disutility f(Hi) from the time devoted to household production

Hi for i = m,w, where f(.) is an increasing and convex cost function. I

normalize 0 ≤ Hi ≤ 1.

The household’s utility is defined as the sum of individual utilities such

that:

V = U(C) + U(Z)− f(Hm)− f(Hf)

and the household’s maximization problem is:

maxCi,Hi

U(C) + U(Z)− f(Hm)− f(Hf)

st.

Z ≥ afHf + amHm

C =X(1−Hi)wi

at the optimum the household consumes all the joint disposable income

and produces the needed amount of household production. The amount of

time that each partner devotes to household production Hi is given by the

first order conditions:

Hi : −U 0(C)wi + aiU0(Z)− f 0(Hi) = 0

5For the reminder of this paper lets assume that af = am. This assumption is made for

exposition purposes only. The results are robust to general specifications of the production

function, which include market goods as inputs and other forms of substitutability.

8

The standard prediction follows thatHUf > HU

m as long as wm > wf . Further-

more the relative amount of housework Hf

Hf+Hmis decreasing on the female

wage wf .6

It is important to note that in this household there is a unique distri-

bution of individual utilities. This derives from the assumption that the

only private goods are essentially the disutility of time devoted to household

production. Thus, unlike collective (Browning and Chiappori, 1997) or non-

cooperative models of the household (Lundberg and Pollak, 1993), transfers

of private consumption between partners cannot compensate for time devoted

to household production. This distinction, which bares the substitutability

assumption between time spent at household production and money, is im-

portant on theoretical and empirical grounds. Empirically, time-use survey

data shows low levels of household services outsourcing, suggesting low sub-

stitution between time spent in household production and money spent in

market goods.7 On the theoretical front, Apps and Rees (Apps and Rees,

6Under the assumption of interior solution, the second order conditions are satisfied

such that:

Hi : 2U”(CU )w2i + 2aiU

”(ZU )− f”(HUi ) ≤ 0

for i = m, f .

7Using Australian time-use data, Bittman shows that during the period 1984-94 real

expenditure in outsourcing for cleaning, for instance, did not increase (Folbre and Bittman,

2004) (p.229-230). Moreover, only 4 percent of the households bought any cleaning services

during the two-week period of the survey. Similar evidence exists for the case of Britain

9

1996) and (Apps and Rees, 1997) extensively discuss the theoretical limi-

tations of the perfect substitutability assumption necessary to identify the

sharing rule in collective models of the household (Browning and Chiappori,

1997).8

2.2 Imperfect commitment, social constraints and in-

efficient allocation of household time

This section builds on the baseline model of section 2.1 by analyzing the role

of imperfect commitment processes associated to household production. Im-

perfect commitment is characterized as a constraint that effectively prevents

potential partners to perfectly contract upon the efficient division of house-

hold labor. Thus, the amount of time each partner devotes to household

production Hm and Hf is the value dictated by what is socially acceptable.

and the United States, where despite increases in income inequality the demand for paid

domestic services has not increased. Such low levels of outsourcing are also found in the

1994 and 2002 ISSP in this paper.

8Apps and Rees (Apps and Rees, 1997) point out that most of the goods consumed

within the household, except for arguably leisure, are public goods. They also show

that the range of goods where consumption differs significantly across individuals in the

household is relatively small. Similarly, Fella et al. (Fella et al., 2004) use the non-

divisibility of public consumption goods within marriage to explain the relevance of divorce

laws on the probability of divorce. In this setting, the allocation of private allocation of

time, rather than private consumption, becomes the variable of interest.

10

The household maximization problem becomes:

maxCi,Hi

U(C) + U(Z)− f(Hm)− f(Hf)

st.

Z ≥ Hm +Hf

C =X(1−Hi)wi

Hm ≤ Hm

where the constraint is characterized by the fact that the male partner

cannot increase his time to household production above what is imperative

by gender roles Hm (or symmetrically, that a woman cannot decrease the

amount of time devoted to household production below what is prescribed

by the existing social norms Hf). If the constraint is not binding we are

in the baseline model presented above, however when the constraint binds

the solution is straigth forward given that ZU is fixed and ZU = HU

m +HUf ,

HUf = H

U

f and CU =X(1−H

U)wi.

Imperfect commitment has two effects: First, it diminishes the household

utility and second, it alters the distribution of household surplus. First,

household utility is lower because partners are constrained from reaching

optimal time allocations. Second, the distribution of the surplus is altered.

The decrease in total surplus occurs despite increases in the consumption

11

of the market public good.9

CU

Imp erf ect commitment = (1−HU

m)wm+(1−HU

f )wf > CUBaseline = (1−HU

m)wm+(1−HUf )wf

Under imperfect commitment in the way characterized above a man has

no incentive to deviate from what is constrained once the union is formed.

He not only enjoys a higher level of market consumption good but also a

lower disutility from household labor.

VU

m = U(CU) + U(ZU)− f(H

U

m) < V Um = U(CU) + U(ZU)− f(HU

m)

A woman is however worse off as a higher consumption of the market

public good is not enough to compensate her for a higher amount of time

devoted to household production.10

VU

f = U(CU) + U(ZU)− f(H

U

f ) < V Uf = U(CU) + U(ZU)− f(HU

f )

3 Empirical Specification

First we test for the existence of rigidities associated to the division of house-

hold labor. The model predicts that the constraint is more likely to bind the9Under social constraints the man devotes less time to household production and more

to market labor. Given that the man’s wage is higher, the consumption of market public

good increases.

10Given that the household’s utility decreases in the presence of imperfect committment,

and that man’s utility increases, woman’s utility must necessarily decrease.

12

higher the female relative wage. Intiuitively this is so because the degree of

specialization within a household i is decreasing with the female wage, so that

as the female wage increases Hi,m increases and Hi,f decreases. Let’s denote

w the binding wage defined as the female wage associated with an optimal

value H∗i,m, such that H

∗i,m = Hm. Then the constraint becomes binding

for any wi,f > w. Thus, for female wages less than w the ratio Hi,f

Hi,f+Hi,mis

decreasing in the female wage but becomes constant for any wi,f > w.

Denote the optimal share of female housework in a given household i as

hi,f =Hi,f

Hi,f+Hi,m. We showed that hi,f is a function of both spouses wages

wi,f and wi,m, spouses productivities ai,f and ai,m, the minimum amount

of housework Zi and the socially constrained housework H so that hi,f =

h(wi,ai, Zi,H) where the minimum amount of housework Zi, and individual

productivities ai,f and ai,m are randomly distributed across households and

are a function of the household’s and spouses’ observable characteristics and

tastes such that Zi = Z(Vi;ωi) and aj = a(Xi;ui). We can use the following

linear regression equation to test this first implication of the model

hi,f = wlowi,f β

lowf + whigh

i,f βhighf + wi,mβm +Xiγ + εi (1)

where i denotes the household, wf is the woman’s wage, wm is the husband’s

wage, andXi controls for other household’s and spouses’ characteristics. The

coefficients of interest are βlowf and βhighf . The theory predicts both coeffi-

cients to be negative, i.e., as female relative wage increase hf should decrease.

However, if our theory is right hf has to level off once wf = w is reached.

13

This would imply |βlowf | ≈ |βhighf |. The variables in Xi control for both the

technology of household produced goods ai and for the tastes for the level

of household production in the household Zi. Among these variables are the

existence of outsourced household production and the presence of microwave

and other devices used for household production that might affect spouses’

productivity in household production. Other variables included in Xi are

spouses ages, education and household composition, as well as a dummy to

control for regional residence.

The second test of the theory attempts to identify the imperfect commit-

ment processes associated to household production activities. If imperfect

commitment is the underlying cause for social constraints in the division of

household labor, and different household activities are subject to different

imperfect commitment problems, we would expect the constraint to be dif-

ferent for different types of household production activities. Consider two

types of household production activities, activity k and activity j. If ac-

tivity k is more prone to suffer from imperfect commitment processes due,

for example, to the inexistence of credible threats (such is the case for car-

ing activities) then we would expect that the constrained level of housework

would be lower for activity k than for activity j, such that Hk < Hj and

thus wk < wj for any household i. That is, the constraint binds for lower

levels of female wages for activity k than what it does for activity j. We test

this hypothesis by running equation 1 for different household activities:

14

hik,f = wlowikf β

lowkf + whigh

ikf βhighkf + wikmβkm +Xikγk + εik (2a)

hij,f = wlowij,fβ

lowf + whigh

ijf βhighf + wijmβm +Xijγj + εjk (2b)

where k and j stand for two different household activities and wlowif are low

female wages and whighif are high female wages. If imperfect commitment is

associated to activity k and not to activity j then we expect that whereas

|βlowkf | ≈ |βhighkf | for activity k, for activity j |βlowj,f | < |βhighj,f |. This is, theamount of woman’s time devoted to childcare (task k) is more likely to be

less responsive to a woman’s wage w as the female wage increases than the

amount of woman’s time devoted to dish washing (task j). Furthermore, we

would expect that |βlowkf | ≈ |βlowj,f |, i.e. when the constraint is not bindingthe effect of the female wage on the division of housework is similar for both

activities.

4 Data: 2002-2003 Spanish Time Use Survey

The data used for the empirical analysis is drawn from the 2002-03 Spanish

Time Use Survey. The Spanish Time Use Survey is part of the Harmonized

European in Time Use Surveys (HETUS) launched by the EU Statistics Of-

fice (Eurostat). This is a representative data set directed at a sample of

20,603 households, which obtains information on daily activities by means of

the completion of a personal diary and household and individual question-

naires. The sample is evenly distributed over the year in order to represent

15

all days of the week and is potentiated on the weekend in order to capture

a greater variety in the population’s behavior.For this purpose, the sample

is subdivided in two sub-samples of equal size, one which must complete the

diary from Monday to Thursday and one which completes it from Friday to

Sunday.

The activities diary constitutes the most characteristic instrument of the

Survey. All members of the household 10 years old and over must complete

it on a selected day (the same day for all members of the household). The

diaries time frame occupies 24 consecutive hours (from 6:00 in the morning

until 6:00 the following day) and is divided into 10 minute intervals. In each

of the intervals, the informant must note the main activity, the secondary

activity carried out at the same time (given the case) and if at that time

they are in the presence of other known persons. These activities are coded

according to a harmonized list of activities from Eurostat, which considers 10

large groups: personal care, work, studies, household and family, volunteer

work and meetings, social life and recreation, sports and open air activities,

hobbies and games, means of communication, and non-specified travel and

use of time.

Diary-based time use data avoids the biases associated to other time-use

surveys based on stylized questions where the total amount of time devoted

to a particular activity is recorded (Juster and Stafford, 1991), (Alvarez and

Miles, 2003) and (Kan, M. 2006). The Spanish Time Use survey proves

particularly useful for our study since, unlike other recent diary-based time

16

use surveys like the American Time Use Survey (ATUS), the Spanish Time

Use Survey contains information on time devoted to household production

by both spouses (as well as other members of the household).

Given the novelty of this data set, table ?? presents a comparison of

main variables to the Spanish Labor Force Survey (EPA), a well-known rep-

resentative panel data set of the Spanish labor market. We observe that the

main demographic and economic variables in both data sets resemble each

other. The education distribution is somewhat different between the two sur-

veys. This is likely to be due to a different classification method rather than

inherent differences in educational achievement. Labor force participation

confirms this hypothesis, as both data sets coincide in the percentage of men

and women in the labor force and unemployed.

17

EPA Time Use

Both Men Women Both Men Women from 16 to 19 5.43 5.73 5.14 5.55 5.68 5.42 from 20 to 24 8.43 8.86 8.02 8.46 8.91 8.03 from 25 to 29 10.08 10.58 9.62 10.58 11.12 10.08 from 30 to 34 10.13 10.63 9.66 9.75 10.26 9.27 from 35 to 39 9.75 10.15 9.37 9.94 10.23 9.66 from 40 to 44 8.94 9.22 8.68 8.95 9.18 8.74 from 45 to 49 7.85 8.04 7.67 7.95 8.23 7.7 from 50 to 54 7.09 7.22 6.97 7.13 7.2 7.07 from 55 to 59 6.65 6.68 6.61 6.54 6.62 6.46 from 60 to 64 5.56 5.49 5.63 5.59 5.43 5.74 from 65 to 69 5.86 5.44 6.25 6.43 6.09 6.76 more than 70 14.22 11.95 16.37 13.12 11.05 15.07Total 100 48.56 51.44 100 48.66 51.34

Both Men Women Both Men WomenSingle 31.05 35.19 27.15 30.27 33.76 26.96Married 58.61 60.32 57.00 59.55 61.39 57.8Widow 7.58 2.54 12.33 7.28 2.54 11.77Divorced 2.76 1.96 3.52 2.91 2.32 3.47Total 100 100 100 100 100 100

Both Men Women Both Men WomenNo Education 2.94 1.88 3.93 2.69 1.61 3.72Primary Education 35.61 33.31 37.79 28.61 26.53 30.57Secondary Education (1st. stage) 25.04 27.10 23.09 30.37 31.56 29.25Secondary Education (2nd. stage) 16.86 17.25 16.50 17.04 17.95 16.17Secondary Education (2nd. stage) 0.11 0.12 0.10 6.53 7.51 5.61College 19.19 20.01 18.43 14.29 14.18 14.41PhD 0.24 0.32 0.17 0.46 0.65 0.27Total 100 100 100 100 100 100Employment

Both Men Women Both Men WomenLabor Force Participation 54.87 67.28 43.15 56.19 68.53 44.49Unemployment 11.12 7.95 15.79 10.43 7.48 14.73

Marital Status Distribution

Education Distribution

Employment Status Distribution

Age Distribution

4.1 Sample and Descriptive Statistics

For the empirical analysis in Section ?? we restrict the sample to those indi-

viduals who are married or living as a couple. We also restrict the sample to

those households where both spouses report a "usual day" and focus on week-

days.11 Finally, we only keep those households where both spouses report

positive earnings. This leaves a sample of 1,894 housholds.

11We focus on usual days to avoid biases in our estimation results as in Bonke 2001.

18

Table 4.1 presents information on the socioeconomic variables that are

used in the empirical analysis for our sample. The average age difference

between spouses is of around 2 years, with men averaging 42 years old and

women 40. It is worth noting that although education is distributed evenly

between men and women, labor force participation differs as men tend to

work about 5 hours more than women. Whereas men devote more time to

market work, women spend almost four times more thanmen doing household

production activities (about 211 versus 68 daily minutes). This difference is

much greater for daily activities such as cooking or cleaning and is reduced

for childcare provision12. The average number of children is around 2 and

50% of our sample have children between 5 and 14 years old, whereas 37%

have children less or equal than 4 years of age. With respect to household

technology we see that almost all the households have a microwave, a wash-

ing machine and a fridge. However only about half have a dishwasher and

about 25% have a dryer or an independent freezer. The commonly outsourced

household activities are cooking and cleaning, with a percentage of 7% and

19% respectively.13 Also 23% of households outsource some type of child-

care. Other activities that are outsourced are shopping and clothes repair,

with about 4% of households outsourcing these services. In turn, household

12In the case of childcare we are reporting the average over all households, whether or

not they have children, which is about 80% of the sample.13Low reported outsourcing levels for others activities such as repairs or maintenance

strike as very low. This is because the question is whether the person being interviewed

received any outside help in the last four weeks, where outside helpd is defined as help

from a person, and not from a company or the public administration.

19

outsourcing levels are relatively low, which stresses the importance of sub-

stitution within household members rather than the exchange between the

family and the market.

20

Demographic and Economic Variables Mean Std. Dev. Min MaxWife's age 39.49 8.49 19.00 66.00Husband's wage 41.80 8.93 22.00 65.00Wife's schooling 1 39.66%Wife's schooling 2 13.41%Wife's schooling 3 17.03%Wife's schooling 4 29.90%Husband's schooling 1 44.04%Husband's schooling 2 13.86%Husband's schooling 3 19.11%Husband's schooling 4 22.99%Wife's usual weekly hours of work 36.10 5.60 2.00 56.00Husband's usual weekly hours of work 39.84 2.47 14.00 60.00No. of children 1.33 0.96 0.00 7.00No. of children 0-2 10.83%No. of children 2-4 15.76%No. of children 5-14 50.00%No. of children +15 (men) 29.63%No. of children +15 (women) 27.09%Household members 3.42 1.01 2.00 9.00No. Rooms 4.40 1.21 1.00 14.00Housework time (minutes per day):Wife: Housework 211.64 125.56 0 810Cooking 88.32 58.36 0 410Cleaning 56.83 57.35 0 640Clothes 23.92 38.87 0 370Gardening and Pets 3.04 14.26 0 170Maintenance and Repairs 1.07 12.67 0 310Shopping 37.67 54.02 0 510Household Management 0.79 9.67 0 170Childcare 64.07 101.66 0 730Husband: Housework 68.19 82.97 0 700Cooking 25.35 31.31 0 210Cleaning 13.23 34.78 0 460Clothes 1.04 6.95 0 180Gardening and Pets 6.35 26.13 0 380Maintenance and Repairs 3.81 24.05 0 440Shopping 17.52 40.90 0 290Household Management 0.91 8.03 0 200Childcare 27.52 55.95 0.00 450.00Household Technology:Microwave 85.77%Dishwasher 53.44%Washing machine 99.45%Dryer 25.20%Fridge 99.37%Independent freezer 26.26%Outside Help:Meal preparation 7.54%Household Mainteinance 18.71%Clothes 4.09%Gardening and pets 0.98%Repairs 1.93%Household shopping 3.10%Household management 1.32%Childcare 23.14%Observations: 1892

Table 4.1: Summary Statistics21

Table 4.1 reports the percentage of net monthly earnings and the per-

formed by wife anddaily minutes devoted to household production by hus-

band and wife.14 Unfortunately the Spanish Time Use data does not contain

information on hourly wage, but rather net monthly earnings. This variable

is also reported in a scale fashion rather than a continuous manner. We see

that 50% of women have net monthly earnings between 500 and 1000 euros,

whereas the distribution is more disperse for men. There are more women

than men with earnings below 500 euros, which is likely due to a greater

percentage of women working part time. It is also worth noting that there

is a few percentage of both, men and women, with net monthly earnings

greater than 2000 euros. Despite variations in earnings housework time does

not seem to vary much with respect to the wife’s wage, especially fror men.

For women this variation is greater at the top and botton of the earnings

distribution, but almost constant within it (for earnings between 500 and

2500 the average daily minutes devoted to housework is around 230)

14We have excluded caring activities in this table. Household production activities are

cooking, cleaning, clothes, gardening and pets, repairs and maintenance, shopping and

household management.

22

Net Monthly Earnings %

Housework wife (daily

min.)

Housework husband (daily

min.)Wife: <500 18.55% 310 160

500-1000 42.65% 255 1311000-1250 16.39% 242 1251250-1500 8.84% 239 1251500-2000 9.05% 216 1102000-2500 2.93% 185 1032500-2900 0.60%>3000 1.00%

Husband: <500 3.03%500-1000 29.57%1000-1250 29.03%1250-1500 13.51%1500-2000 13.83%2000-2500 5.88%2500-2900 1.75%>3000 0.03389

Observations: 1892

Table 4.1: Spouses Net Monthly Earnings and Housework Division

5 Empirical Results

The analysis below presents the empirical results for estimating equations 1

and 2a. The dependent variable is the ratio of female daily time to both,

woman’s and man’s housework daily time. A weighted OLS procedure is

used, although a Tobit specification might be desirable results do not vary

much.15

As mentioned above, a potential problem with the Spanish Time Use

data is that it does not contain information on hourly wages, which difficults

the estimation of the equations above. We use information on net monthly

earnings, rather than the hourly wage, and although potentially endogenous,

15Tobit results can be obtained from the authors upon request.

23

we control for reported weekly hours of work in the LHS. Results do not vary

significanly when we omit hours of work. This is likely to be so because of the

little variation in hours of work in Spain Another problem is that net monthly

earnings is not reported as a continuous variable, but rather in a scale fashion

as described in the summary statistics. This does not necessarily play against

our interests, since we are interested in identifying the wage w at which the

constraint becomes binding and would be using a step specification anyway.

5.1 Imperfect Commitment and Female Wage

Table 5.1 shows the coefficients from a series of OLS regressions of the share

of time that a woman’s spends doing houseusehold production services on

different variables. We see that the female earning’s coefficients are negative,

meaning that the higher the female earnings the lower the amount of woman’s

share of time devoted to housework. The magnitude of these coefficients

is fairly small, although all of them are significantly different from 0. In

particular, an increase in the woman’s net monthly earnings from less than

500 euros to the next level (between 500 and 1000 euros) would mean a

reduction of her share of housework of 5 percentage points. Although the

reduction in the share might seem insignificant this can still translate into a

significant amount of time savings for the woman. In particular, a decrease

of the ratio from .66 (the average ratio for female wages lower than 500)

to .60 translates into a decrease of the daily minutes devoted to housework

activities from 310 (the average for a female wage lower than 500) to 240

24

(given that the man’s housework time remains unchanged). This is about

more than an hour time savings. However, we observe that the reduction in

the woman’s share of housework as she moves up in the earnings distribution

becomes smaller and smaller. In fact, for earnings greater than 1000 a test

at the 5% confidence level indicates that we cannot reject the hypothesis

that the coefficients are different from each other. This would suggest that,

consistent with the model, there is a constraint on the division of housework

and that this constraint binds for woman’s earnings greater than 1000, i.e.

w = 1000. These results are robust to different specifications that control for

wife’s and husband’s hours of market work, total household time devoted to

household production, household composition and household outsourcing.

25

Wife's share of housework time - Weekwife's net monthly earnings 500-999 -0.06 -0.05 -0.04 -0.04 -0.05 -0.04 -0.04

(5.15)*** (3.74)*** (3.63)*** (3.57)*** (3.71)*** (3.67)*** (3.25)***wife's net monthly earnings 1000-1249 -0.08 -0.07 -0.06 -0.06 -0.06 -0.06 -0.06

(5.86)*** (4.46)*** (4.39)*** (4.00)*** (4.17)*** (3.99)*** (3.80)***wife's net monthly earnings 1250-1499 -0.10 -0.09 -0.09 -0.08 -0.08 -0.08 -0.08

(5.97)*** (4.88)*** (5.12)*** (4.36)*** (4.41)*** (4.55)*** (4.31)***wife's net monthly earnings 1500-1999 -0.11 -0.10 -0.10 -0.09 -0.09 -0.09 -0.09

(6.51)*** (5.42)*** (5.71)*** (4.84)*** (5.02)*** (5.05)*** (4.82)***wife's net monthly earnings >2000 -0.15 -0.14 -0.14 -0.13 -0.13 -0.13 -0.13

(6.69)*** (5.70)*** (5.85)*** (5.17)*** (5.23)*** (5.27)*** (5.13)***husband's net monthly earnings 500-999 -0.01 -0.02 -0.01 -0.02 -0.01 -0.02 -0.02

-0.57 -0.76 -0.48 -0.62 -0.61 -0.70 -0.81husband's net monthly earnings 1000-1249 -0.02 -0.03 -0.02 -0.02 -0.02 -0.02 -0.02

-0.74 -1.02 -0.82 -0.85 -0.85 -0.98 -0.94husband's net monthly earnings 1250-1499 0.00 -0.01 0.00 0.00 0.00 0.00 0.00

-0.01 -0.26 -0.01 -0.09 -0.09 -0.03 -0.03husband's net monthly earnings 1500-1999 0.02 0.01 0.01 0.02 0.02 0.01 0.02

0.75 0.46 0.43 0.71 0.65 0.56 0.57husband's net monthly earnings >2000 0.01 0.00 0.00 0.00 0.00 0.00 0.00

0.40 0.08 0.08 0.18 0.05 0.05 0.06weekhourwife 0.00 0.00 0.00 0.00 0.00 0.00

(2.92)*** (2.62)*** (2.51)** (2.38)** (2.00)** (2.31)**weekhourhusband 0.00 0.00 0.00 0.00 0.00 0.00

(2.20)** (2.47)** (2.38)** (2.37)** (2.46)** (2.40)**age wife 0.00 0.00 0.00 0.00 0.00

1.07 1.42 1.39 1.30 1.31age husband 0.00 0.00 0.00 0.00 0.00

1.19 0.76 0.73 0.49 0.36wife's education yes yes yes yes

husband's education yes yes yes yes

cleaning service yes yes yes

children yes yes

region dummy yes

household technology yes

housework outsourcing yes

constant 0.76 0.70 0.56 0.57 0.57 0.54 0.54(32.63)***(9.38)*** (7.16)*** (7.07)*** (7.09)*** (6.31)*** (6.49)***

Observations 1892.00 1892.00 1892.00 1882.00 1882.00 1882.00 1877.00R-squared 0.04 0.05 0.07 0.07 0.08 0.09 0.1Absolute value of significant t statistics in parentheses* significant at 10%; ** significant at 5%; *** significant at 1%

Table 5.1.a: Binding Constraints on the Division of Housework

26

5.2 Heterogeneity in Household Production and Im-

perfect Commitment

The second test attempts to identify the imperfect commitment processes as-

sociated to different household production activities by exploiting the infor-

mation in the data regarding the different commitment problems associated

to different household activities. For this purpose we exploit three pieces of

information: The frequency of household production activities (whereas it is

a daily activity or a less frequent activity), when this household production

is undertaken (if during the working days or in the weekend) and the type of

household production activity (whether it is caring activities or housework

activities). In the first case we expect imperfect commitment problems to be

more important for those activities that are performed daily. In the second

case we expect imperfect commitment problems to be more important for

those activities performed during workdays. In the third case we expect im-

perfect commitment problems to be more important for caring rather than

other activities.

Frequent and infrequent household activities One would expect that

the type of housework done daily is that type of housework that "needs to

be done" and cannot be postponed. However, other type of housework, the

one that is done less often, is considered to be not such a necessity so people

can live without it. This would imply that whereas there might be some

credible threats availiable for non-daily housework, credible threats might be

27

more difficult to find for daily housework. If activity k is performed daily

and activity j non-daily, then Hk < Hj and thus wk < wj for any household

i. That is, the constraint binds for activity k (daily) for lower female wages

than what it does for activity j (non-daily).

We test this hypothesis by running equation 1 separately for daily and

non-daily activities. Daily activities are those that are done for more than

half of the sample and non-daily activities are those not done for more than

half of the sample in the day when they are interviewed. Daily activities

are thus cooking, cleaning, clothes and shopping. Non-daily activities are

household repairs and maintenance, household management and gardening.

The results of are presented in table

We observe that most of the variation observed in table ?? comes from

daily activities. The coefficients for daily activities are very similar to those

of total housework. As it was the case in ??, we cannot reject the hypothe-

sis that the female wage coefficients are not different from each other, which

would be consistent with the existence of constraints in the division of house-

hold labor.

28

Wife's share of housework time - Non-daily [1] [2] [3] [4] [5] [6] [7]wife's net monthly earnings 500-999 -0.11 -0.09 -0.09 -0.11 -0.11 -0.13 -0.12

(1.92)* -1.39 -1.42 (1.68)* (1.80)* (2.00)** (1.82)*wife's net monthly earnings 1000-1249 -0.02 0.00 0.00 -0.04 -0.04 -0.06 -0.07

-0.31 -0.05 0.00 -0.52 -0.58 -0.80 -0.88wife's net monthly earnings 1250-1499 0.04 0.06 0.06 0.00 -0.04 -0.04 -0.06

-0.49 -0.68 -0.65 -0.05 -0.37 -0.39 -0.55wife's net monthly earnings 1500-1999 -0.27 -0.24 -0.24 -0.27 -0.29 -0.28 -0.31

(2.95)*** (2.58)** (2.58)** (2.76)*** (2.91)*** (2.91)*** (3.14)***wife's net monthly earnings >2000 0.06 0.09 0.09 0.02 -0.02 -0.02 -0.03

-0.54 -0.75 -0.74 -0.19 -0.18 -0.18 -0.23husband's net monthly earnings 500-999 -0.28 -0.28 -0.27 -0.25 -0.24 -0.19 -0.27

(2.34)** (2.28)** (2.25)** (2.03)** (1.95)* -1.60 (2.13)**husband's net monthly earnings 1000-1249 -0.21 -0.21 -0.21 -0.20 -0.19 -0.14 -0.18

(1.75)* (1.72)* (1.69)* -1.59 -1.52 -1.10 -1.44husband's net monthly earnings 1250-1499 -0.38 -0.37 -0.36 -0.38 -0.36 -0.32 -0.31

(2.89)*** (2.81)*** (2.76)*** (2.81)*** (2.70)*** (2.41)** (2.29)**husband's net monthly earnings 1500-1999 -0.11 -0.11 -0.11 -0.15 -0.15 -0.10 -0.17

-0.85 -0.89 -0.82 -1.11 -1.11 -0.77 -1.20husband's net monthly earnings >2000 -0.29 -0.29 -0.28 -0.35 -0.35 -0.31 -0.38

(2.17)** (2.18)** (2.05)** (2.47)** (2.47)** (2.18)** (2.52)**weekhourwife 0.00 0.00 0.00 0.00 0.00 0.00

-1.09 -1.06 -0.88 -0.77 -0.68 -0.93weekhourhusband 0.00 0.00 0.00 0.00 -0.01 0.00

-0.46 -0.49 -0.13 -0.15 -0.71 -0.40age wife 0.00 0.00 0.00 0.00 0.00

-0.42 -0.38 -0.40 -0.16 -0.10age husband 0.00 0.00 0.00 0.00 0.00

-0.27 -0.48 -0.39 -0.15 -0.18wife's education yes yes yes yes

husband's education yes yes yes yes

cleaning service yes yes yes

children yes yes

region dummy yes

household technology yes

housework outsourcing yes

constant 0.66 0.94 0.99 0.74 0.75 0.78 0.82(5.60)*** (2.88)*** (2.73)*** (1.96)* (2.00)** (1.92)* (1.89)*

Observations 428.00 428.00 428.00 425.00 425.00 425.00 425.00R-squared 0.07 0.07 0.07 0.09 0.10 0.13 0.21Absolute value of significant t statistics in parentheses* significant at 10%; ** significant at 5%; *** significant at 1%

Table 5.2.b: Social Constraints in the Division of Housework. Daily vs. Non-daily Activities

29

However, for non-daily activities we observe that the coefficients on the

female wage are very different from those in table ??. A significant coeffi-

cient of -.11 denotes a big drop in the share when women move up from less

than 500 to between 500-1000 euros per month. The coefficients on higher

earnings are not significant, except for a significant coefficient of .3 for earn-

ings between 2000-2500. This would not suggest the existence of a social

constraint in housework for these activities.

Weekdays vs. weekend One would expect that individuals prefer to

postpone housework activities when possible to those days when there is

more time availiable.16 Thus, one would expect that during the weekend

individuals perform those types of housework that are more easily postponed

and not so important. In other words, one would expect that for housework

performed during the weekend there are credible threats availiable, and thus

commitment problems are less important. If activity k is performed during

the weekend and activity j during the week, thenHk > Hj and thus wk > wj

for any household i. That is, the constraint binds for higher levels of female

wages for activity k (weekend) than what it does for activity j (week). We

test this hypothesis by running equation 1 separately for week and weekend

housework shares.

Table 5.2 presents the amount of housework performed during the week-16This is true since the marginal utility of leisure is greater in those days when time

for leisure is scarce, such as working days. Thus, it is expected that individuals pospone

housework time during the week to the weekends in order to maximize their utility.

30

end by both wives and husbands, as well as the wife’s housework over total

housework ratio. We observe that when compared to 5.2 the amount of time

devoted to household activities is greater for almost all activities during the

weekend. However, the degree of specialization as measured by the ratio of

interest is slightly lower during the weekend than during the week.

Housework Activity Mean Std. Dev. Min Max RatioWife: Housework 250.41 145.00 0.00 830.00 0.66Cooking 100.28 67.10 0.00 480.00 0.73Cleaning 73.91 65.00 0.00 420.00 0.71Clothes 29.76 47.71 0.00 320.00 0.92Gardening and Pets 5.72 26.22 0.00 440.00 0.25Maintenance and Repairs 2.53 26.47 0.00 510.00 0.22Shopping 38.88 62.58 0.00 450.00 0.53Household Management 0.30 3.98 0.00 100.00 0.38Childcare 50.87 96.63 0.00 500.00 0.56Husband: Housework 127.78 122.80 0.00 750.00Cooking 36.55 48.80 0.00 380.00Cleaning 30.45 47.43 0.00 500.00Clothes 2.68 16.80 0.00 260.00Gardening and Pets 16.79 56.32 0.00 450.00Maintenance and Repairs 8.99 39.35 0.00 520.00Shopping 34.37 61.96 0.00 400.00Household Management 0.49 4.44 0.00 100.00Childcare 39.46 77.32 0.00 510.00Observations: 804Units: Minutes per day

Table 5.2: Summary Statistics, Weekend Housework Activities

Table 5.2 presents the results of running equation 1 for housework per-

formed during the weekend. We observe that the earnings coefficients are

all negative and significant for almost all the specifications, with magnitudes

ranging from half percentage to 1 percentage points. We also observe, unlike

5.2 a significant drop in the ratio of woman’s housework for the earnings level

31

of 1000-1250. However the ratio fails to decrease further after this level of

earnings. In fact, we cannot reject the hypothesis that the earnings coeffi-

cients are different from each other at the 5% level. This would suggest that

the constraint becomes binding not at an earnings level of 1000 as it was the

case during the week, but at an earnings level of 1250. In other words, the

constrained level of housework is higher during the weekend than during the

week, which is consistent with the theory.

32

Wife's share of housework time- Weekendwagewife999 -0.05 -0.05 -0.05 -0.04 -0.04 -0.04 -0.03

(3.10)*** (2.86)*** (2.85)*** (2.27)** (2.29)** (2.08)** (1.95)*wagewife1249 -0.10 -0.10 -0.11 -0.09 -0.09 -0.09 -0.09

(5.14)*** (4.75)*** (5.26)*** (4.22)*** (4.26)*** (4.11)*** (3.97)***wagewife1499 -0.12 -0.12 -0.12 -0.08 -0.08 -0.07 -0.07

(4.74)*** (4.53)*** (4.71)*** (2.99)*** (2.98)*** (2.75)*** (2.49)**wagewife1999 -0.08 -0.08 -0.09 -0.04 -0.04 -0.03 -0.03

(2.98)*** (2.84)*** (3.26)*** -1.28 -1.30 -1.20 -1.14wagewife2499 -0.10 -0.10 -0.11 -0.06 -0.06 -0.05 -0.03

(2.72)*** (2.65)*** (2.93)*** -1.51 (1.65)* -1.18 -0.73wagehusband999 -0.07 -0.07 -0.05 -0.04 -0.04 -0.04 -0.03

(1.88)* (1.89)* -1.34 -1.21 -1.20 -1.00 -0.84wagehusband1249 -0.09 -0.09 -0.07 -0.07 -0.07 -0.06 -0.06

(2.48)** (2.48)** (2.01)** (1.93)* (1.93)* (1.69)* -1.49wagehusband1499 -0.08 -0.08 -0.06 -0.04 -0.04 -0.03 -0.03

(1.94)* (1.92)* -1.42 -0.92 -0.89 -0.75 -0.71wagehusband1999 -0.05 -0.05 -0.04 -0.03 -0.03 -0.02 -0.01

-1.19 -1.16 -0.94 -0.69 -0.70 -0.55 -0.26wagehusband2499 -0.06 -0.06 -0.05 -0.04 -0.04 -0.04 -0.02

-1.39 -1.40 -1.26 -0.90 -0.99 -0.87 -0.46weekhourwife 0.00 0.00 0.00 0.00 0.00 0.00

0.15 0.61 0.21 0.22 0.42 0.39weekhourhusband 0.00 0.00 0.00 0.00 0.00 0.00

0.80 0.96 0.96 0.75 0.75 0.47age wife 0.01 0.01 0.01 0.01 0.01

(2.58)** (2.88)*** (2.94)*** (2.81)*** (2.92)***age husband 0.00 0.00 0.00 0.00 0.00

0.04 0.70 0.74 0.79 0.69wife's education yes yes yes yes

husband's education yes yes yes yes

cleaning service yes yes yes

children yes yes

region dummy yes

household technology yes

housework outsourcing yes

Constant 0.77 0.69 0.43 0.49 0.50 0.48 0.52(21.02)***(6.52)*** (4.01)*** (4.48)*** (4.59)*** (4.18)*** (4.34)***

Observations 804.00 804.00 804.00 798.00 798.00 798.00 798.00R-squared 0.06 0.07 0.12 0.16 0.16 0.18 0.21Absolute value of t statistics in parentheses* significant at 10%; ** significant at 5%; *** significant at 1%

Table 5.2.c: Social Constraints in the Division of Housework. Weekend vs. Weekday Activities

33

Caring activities Table 5.2 presents the results of running equation 1 for

caring activities. We observe that the earnings coefficients are all very close

to zero and insignificant for almost all the specifications, with magnitudes

ranging from half percentage to 1 percentage points. This would suggest that

the constraint is binding overall the wage distribution, which is consistent

with the model.

34

Wife's share of caring time- Care [1] [2] [3] [4] [5] [6] [7]wagewife999 0.00 0.03 0.02 0.01 0.00 -0.02 -0.01

-0.06 -1.38 -1.18 -0.59 -0.19 -1.29 -0.98wagewife1249 -0.01 0.02 0.02 0.00 -0.02 -0.01 -0.01

-0.39 -0.92 -0.84 -0.18 -0.63 -0.36 -0.41wagewife1499 0.00 0.04 0.05 0.03 0.00 0.00 0.00

-0.10 -1.15 (1.84)* -1.06 -0.08 -0.06 -0.07wagewife1999 -0.02 0.01 0.04 0.02 0.00 -0.01 -0.01

-0.60 -0.39 -1.23 -0.57 -0.03 -0.36 -0.44wagewife2499 -0.01 0.03 0.04 0.02 -0.03 -0.02 -0.02

-0.23 -0.65 -1.13 -0.56 -0.65 -0.56 -0.79wagehusband999 0.07 0.06 0.02 0.02 0.02 0.03 0.02

-1.60 -1.36 -0.60 -0.46 -0.51 -0.99 -0.56wagehusband1249 0.06 0.05 0.02 0.02 0.02 0.02 0.01

-1.44 -1.10 -0.55 -0.39 -0.41 -0.74 -0.20wagehusband1499 0.07 0.06 0.03 0.01 0.01 0.01 0.00

-1.59 -1.28 -0.59 -0.13 -0.13 -0.42 -0.07wagehusband1999 0.09 0.07 0.07 0.05 0.04 0.06 0.04

(1.99)** -1.56 (1.71)* -1.07 -0.98 (1.72)* -1.13wagehusband2499 0.13 0.11 0.13 0.10 0.07 0.07 0.05

(2.70)*** (2.25)** (2.87)*** (2.15)** -1.55 (1.95)* -1.30weekhourwife -0.01 -0.01 -0.01 -0.01 0.00 0.00

(3.98)*** (5.12)*** (4.67)*** (4.52)*** -1.07 -1.26weekhourhusband 0.00 0.00 0.00 0.00 0.00 0.00

-0.14 -0.52 -0.31 -0.24 -0.76 -0.50age wife -0.01 -0.01 -0.01 0.00 0.00

(4.66)*** (4.47)*** (4.50)*** -1.46 -1.55age husband 0.00 0.00 0.00 0.00 0.00

(1.79)* -1.30 -1.54 -0.55 -0.57wife's education yes yes yes yes

husband's education yes yes yes yes

cleaning service yes yes yes

children yes yes

region dummy yes

household technology yes

housework outsourcing yes

Constant 0.19 0.36 1.02 0.90 0.91 0.01 0.00(4.55)*** (2.73)*** (7.84)*** (6.75)*** (6.87)*** -0.11 -0.01

Observations 1885.00 1885.00 1885.00 1875.00 1875.00 1875.00 1870.00R-squared 0.01 0.01 0.14 0.14 0.17 0.55 0.56Absolute value of t statistics in parentheses* significant at 10%; ** significant at 5%; *** significant at 1%

Table 5.2.d: Social Constraints in the Division of Housework, Caring vs. Non-Caring Activities

35

6 Conclusion

Economic theories of the household predict that increases in female human

capital lead to increases in female labor force participation and, symmet-

rically, to decreases in the female time devoted to household production.

However, both at the longitudinal and cross-sectional level we observe that,

despite the decline in the wage gender gap, specialization in home produc-

tion continues to be high with women providing most of household produced

goods and services. We develop a model that recognizes the inefficiencies

inherent to household production activities. We test the model using the

2001 Spanish Time Use Survey, a time diary survey with information on the

time devoted to household production activities by both partners. Empirical

findings support the proposed model inefficient allocation of household time.

36

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