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The Economics of Time Use D.S. Hamermesh and G.A. Pfann (Editors) © 2005 Elsevier B.V. All rights reserved. DOI: 10.1016/S0573-8555(04)71003-2

CHAPTER 3

The Timing and Flexibility of Housework and Men and Women's Wages

Jens Bonkea, Nabanita Datta Gupta3 and Nina Smithb

"Danish National Institute of Social Research, Herluf Trollesgade 11, DK-1052 Copenhagen, Denmark E-mail address: jeb@sfi.dk; ndg@sfi.dk

bCIM, IZA, DIW and Aarhus School of Business, Prismet, Silkeborgvej 2, DK-8000 Aarhus C, Denmark

E-mail address: nina@asb.dk

Abstract

We analyze the wage effects of housework by estimating quantile regressions on a Danish time-use survey merged to register data. Housework has negative effects on women's wages and positive effects on men's wages, except at the top of the conditional wage distribution. The timing and flexibility of housework are more important than the amount, and women, particularly at the high end of the distribution, who time their housework immediately before or after market work or perform contiguously spaced home tasks earn significantly lower wages. These effects are even stronger for couples and for workers on fixed as opposed to flexible time schedules.

Keywords: wages, housework, time use, quantile regressions

JEL classifications: D13, J16

3.1. Introduction

Despite the fact that Danish women's participation in the labor market has increased rapidly since the 1970s, the division of work within the household still remains unequal. Currently in the 25-45 age group, almost 84% of women participate in the labor market, compared to 90% of men; but Danish time-use data from 1987 show that men still spend less time on

44 J. Bonke, N. Datta Gupta and N. Smith

housework on weekdays compared to women in coupled households: 81 min a day for men and 171 min for women. Although these figures have become more equal over time, the different roles of men and women within the household may still be expected to influence the amount of effort and their achievement on the job. For the US, Hersch (1991), Hersch and Stratton (1997, 2000), Noonan (2001) and Stratton (2001) have documented that the amount of time spent on housework has a negative effect on wages. For Canada, Phipps et al. (2001) also find that the amount of housework has a negative effect on the earning capacity of women.

The effect of housework activities may vary across the wage distribution. Especially for men and women in higher ranking positions holding demanding jobs, it may be impossible to combine the job with a large amount of housework or inflexible housework tasks. The very compressed wage structures in the Scandinavian countries and high tax levels imply that the price of market services (domestic help, restaurant visits, etc.) is very high. The market for private services may not even exist in the Scandinavian countries, contrary to the US, which has a fairly well- functioning market for most household services. This may induce even high-income families in Scandinavia to undertake more housework and do- it-yourself work compared to families in, for instance, the US. However, it may not be the amount of housework alone, which influences the labor market performance of men and women. The timing and flexibility of housework may also have negative effects on earnings and careers, especially at the higher end of the qualification distribution, and thus this may be one explanation of an increasing unexplained gender wage gap at the upper end of the wage distribution in Denmark and Sweden (Albrecht et al., 2003; Datta Gupta et al, 2003).

Earlier studies, mainly from the US, have documented that housework has a different effect on male and female wages and that the type of housework also matters (Hersch and Stratton, 2000; Noonan, 2001; Stratton, 2001). However, none of these previous studies has incorporated timing and flexibility aspects of housework and their effects on wages. When housework is done during the day may be just as important for wages as the amount of housework.1 Housework that is timed relatively close to market work hours may have more punitive effects on wages than housework that is timed farther away from market work hours, because

There are a number of other questions for which the issue of timing can be important. For instance, Hamermesh in this volume analyzes the demand for temporal variety or its absence, routine, and finds that economic incentives are important in decisions of timing of daily activities.

The Timing and Flexibility of Housework and Men and Women's Wages 45

individuals may need to interrupt their market work hours in order to undertake such activities or experience higher levels of stress or fatigue while trying to balance the conflicting needs of the job and the household.

In this study, we examine the wage effects of having flexibility with respect to one's housework and test whether or not these effects differ for men and women. Most previous studies have constrained the effect of housework to be the same at all points in the wage distribution. We estimate a traditional human capital model of hourly wages augmented by different aspects of housework responsibilities, including timing and flexibility as well as job characteristics. In contrast to the previous literature, we fully characterize the housework-wage relationship along the conditional wage distribution by using a quantile regression approach.

Unlike some of the previous studies in this area (Hersch and Stratton, 1997, 2000), we do not model the endogeneity of housework. Clearly, housework (both the amount and timing) may be potentially endogenous to wages, as those with higher wages typically do less housework and more market work, and this biases the coefficient of housework in a wage regression that treats housework as exogenous. We were unable to find suitable instruments for housework hours in the data we have available (see Section 3.5). Therefore, we concentrate here on introducing the notion of flexibility and timing of housework and testing their effects at different points along the conditional wage distribution. The analysis is based on merged register and survey data, i.e. the Danish 1987 Time-Use Survey (TUS) for information on household activities and market work, and on administrative registers for information on wages and labor market characteristics for the period 1987-1991 for the individuals included in the TUS.

In Section 3.2, we sketch a theoretical model which states a relationship between market wages, the amount of housework and the flexibility of time devoted to market work and housework and discusses the implications of this model. In Section 3.3, the time use and register data applied in the study are described, and Section 3.4 presents some descriptive analyses of Danish time-use patterns. In Section 3.5, an empirical model is presented. The results from the estimation are presented in Section 3.6, and Section 3.7 offers a conclusion.

3.2. Theoretical model

In one of his seminal papers, Becker (1985) discusses the importance of the allocation of home time and the resources and effort devoted to market work:

Earnings in some jobs are highly responsive to changes in the input of energy, while earnings in others are more responsive to changes in the amount of time.... Persons

46 / . Bonke, N. Datta Gupta and N. Smith

devoting much time to effort-intensive household activities like childcare would economize on their use of energy by seeking jobs that are not effort intensive, and conversely for persons who devote most of their household time to leisure and other time-intensive activities (Becker, 1985, p. S49).

The allocation of time within the household is assumed to be determined by comparative advantage. Women are assumed to be more productive in certain types of housework, especially child production and childcare. A key assumption in the Becker model is that the individual allocates a given amount of time and effort to different activities, for instance housework, leisure time and market work. Becker shows that given these assumptions, the individual will devote less effort to the job the more housework is done at home, and this explains that usually women earn lower market wages than men.

The Becker model has been criticized because of the assumption of a given amount of effort. It could be that individuals, who derive utility from their job and devote a lot of effort to the job, also devote more effort at home. Or the other way around, some individuals who spend many hours on housework activities spend few hours on passive leisure activities, for instance watching television, and may devote more effort to their job (Bielby and Bielby, 1988; Stratton, 2001). Thus if the amount of effort is not exogenously given, the implications of the Becker model become more ambiguous. Since the causality in the Becker model is that housework affects effort, which affects wage rates, one should expect that, controlling for effort, the direct effect of housework on wages might disappear. However, empirical studies which combine information on effort variables, housework and wage rates indicate that including information on effort does not reduce the significance of housework (see Stratton, 2001).

Instead of focussing on effort, we turn our attention to the importance of timing and flexibility of housework in this study. Many housework activities have to be performed at regular points in time each day. If there are babies or young children in the family, a number of tasks, such as preparing food, eating, bathing the children, preparing the children for school, etc. are time-inflexible tasks that have to be done each day at fairly rigid points in time. The same holds for activities like picking up children from day care centers, sport activities, etc. which may imply that the parent has to leave the job earlier in the afternoon. If employees are required to be present at meetings in the morning and late in the afternoon, this may have consequences for job and career. Other types of household activities, such as do-it-yourself work, are much more time flexible and can even be done on weekends. Therefore, it is important to focus on the

The Timing and Flexibility of Housework and Men and Women's Wages 47

flexibility and the timing of housework activities and not just on the amount of housework. If due to tradition, comparative advantage or other reasons women more often undertake daily routine tasks that need to be done at regular points in time, while men do housework tasks that can be relegated to weekends or late in the evening, women will tend to be less flexible with respect to their market jobs and have less potential for career advancement than men.

The importance of timing and flexibility in household activities depends on how easy it is to substitute between the time of household members and market services. Despite young children being time consuming and implying time inflexibility, parents are in principle able to substitute part of the care. The same holds for other household activities. For example, sending children to childcare centers during working hours or hiring a nanny are possible strategies, as are visiting restaurants, employing a cleaner to take care of daily cleaning tasks, etc. However, substitution depends, among other things, on the prices of services bought in the market. A compressed wage structure and a high indirect tax rate imply high prices of most household services in Denmark. Thus many households cannot afford much substitution for their housework time, and high-income families who can afford these services often face thin and poorly functioning service markets.2 For these reasons, we expect that timing and flexibility of daily housework tasks like childcare, food preparing, cleaning, etc. are important factors affecting career develop- ment, especially in families with younger children whose needs are particularly time inflexible.

It is not an easy task to define flexibility, since the notion may have a number of dimensions to it, such as variability or stability over time, uncertainty with respect to future work requirements, etc. For instance, temporal stability with respect to the timing of housework activities may imply that the individual has a high degree of certainty with respect to when she is able to undertake market activities. On the other hand, temporal stability can also imply that she is inflexible and, for instance, has to leave the job early in the afternoon each day in order to pick up children. Further, the concept of flexibility depends on whether flexibility is viewed from the perspective of the employer or the employees.

2 The typical marginal income tax even on low-skilled workers exceeds 50%, VAT is 25%, and thus the tax wedge is high. In an empirical analysis based on German and US data, Schettkat (2003) demonstrates that a much larger tax wedge in Germany compared to the US may explain why the Germans undertake much more housework and do-it-yourself work and less market work compared to Americans.

48 J. Bonke, N. Datta Gupta and N. Smith

Flexibility from the employer's perspective will typically mean inflexi- bility from the employee's perspective.3

According to these considerations, we have the following definition for flexibility: the ease with which an individual can alter the timing of daily work or housework according to the needs of the employer (flexibility devoted to market work) or the family (flexibility devoted to non-market activities). Thus the amount of flexibility that the individual has at his or her disposal for work depends in part on the nature and type of work or housework, in part on family background characteristics, in part on job characteristics and in part on unobserved factors such as tastes for work. We assume that each individual can allocate a given amount of flexibility to market work, housework or to leisure activities, personal care, sleep, etc. Thus, besides allocating a fixed amount of time each day to market work, housework and leisure, the person has to decide how flexible he or she wants to be at the job and how much flexibility he or she reserves for the family, household tasks and leisure time. Thus flexibility which is devoted to the job or to housework can be thought of as an additional input, which increases the value of each hour spent working in the market or at home.

Assume, in line with the Becker model, that the individual can distribute the total time allocation, f, to three activities, market work (m) and two types of housework activities ( j = 1 , 2 ) where activity 1 is much more flexible than activity 2, i.e. activity 1 demands to a much larger extent than activity 2 that it is undertaken at given times during the day. For instance, activity 1 may be routine tasks like food preparing and cleaning, while activity 2 is do-it-yourself work.4

' i + ' 2 + fm = f (3-1)

Further, parallel to the time constraint the individual is assumed to have a given amount of flexibility (normalized to 1), which can be allocated to the three activities,

Fl+F2 + Fm=l. (3.2)

3 However, in some cases the employer and the employee may bargain more or less explicitly about the timing and flexibility of market work, for instance by having flex-time working schedules where the worker is allowed to decide when to come to work in the morning or when to leave the job, or the worker may be allowed to work at home (distance work) during part of the working time. If there exists this type of (implicit) contract between the employer and the employees, the negative trade-off between flexibility at work and flexibility at home may be loosened, as is the case in most academic jobs. 4 We abstract away from the leisure choice which is irrelevant for the purposes of our model.

The Timing and Flexibility of Housework and Men and Women's Wages 49

We assume that the output or the value (/,) of each of the housework activities and market work depends on the human capital acquired for each of these production processes, HCj(j = m, 1,2). Further, the value depends on the time (hours) and flexibility devoted to the activity (/y and Fj). For simplicity, we assume a Cobb-Douglas production function for the value of time and flexibility devoted to the housework and market work activities

Ij^UCjFptj-* 0' = m,l,2)

where o-j is the flexibility intensity of activity j . Denoting/- = F;/ry, i.e. the flexibility per hour, which can be shown to be a constant because of the Cobb-Douglas assumption, one gets the hourly wage rate in activity./ as

Wj = HCjf? U = m , l , 2 ) .

The size of oj is crucial for determining the endogenous variable j j . We assume <Tj < 1, fory = m, 1,2, and further that o-j > <r2 and <rm > a2. Thus, non-market activity 1 and market work are assumed to be less flexible than non-market activity 2. The ranking between non-market activity 1 and market work depends on which types of activities and jobs are considered. If the job is very demanding with much responsibility, <rm is large (though smaller than 1 in order to be sure that more hours of work always imply a higher market income, If), while less demanding jobs are represented by lower values of crm. Analogously, if there are young children in the household, household activities may be relatively time inflexible. In the Becker model, oj is treated as exogenous, but in a more general model the variables reflecting flexibility intensities should be considered endogenous. The flexibility intensity of non-market activities may be determined by endogenous fertility, and the flexibility intensity of market work by endogenous sector and occupational choices.

By introducing a traditional home production function approach for the two household goods (j = 1,2), see Appendix A3, and maximizing utility defined over these two goods subject to income, time and flexibility constraints, one can derive the demand and supply functions for market goods and services (xj), time devoted to the market and housework activities (/,), and flexibility in market and housework activities (fj) as functions of the endowment of human capital in different activities (HC;), flexibility intensities, OJ, prices and non-wage income. Focussing only on market wages, the observed market wage may be written as

wm = wm(HCm, crm, fm(a-i, <r2, <rm, Z)) (3.3)

where Z is a vector of the additional variables that determine flexibility (/m) devoted to market work. Parallel to the Becker model, one can show

50 J. Bonke, N. Datta Gupta and N. Smith

that the amount of flexibility devoted to the job is a negative function of the flexibility intensity demanded in the housework activities:

| ^ = n a m , 2 < 0 , (3-4)

ba) o-m(l - o-m)<r/

i.e. the relative flexibility devoted to the job is larger the smaller the o}, because the housework activities are less flexibility demanding. For a given value of <7m, i.e. for a given type of job, a person who undertakes flexibility-intensive non-market activities, o) close to 1, will devote less flexibility to the job than a person who engages in non-market activities with a low value of aj. This effect is larger, the more demanding the job is, i.e. the larger is trm.

3.3. Data

Our main data source, the Danish TUS, 1987 is a simple random sample of about 3600 adult Danish people aged 16-74. It contains demographic and socio-economic information on the current work behavior in the labor market for all persons, i.e. the amount of hours, including overtime and hours in supplementary jobs, in a normal working week. The sample used here includes employed individuals who filled out a time diary during a working weekday or during a weekend day. For the sample with information on a working weekday, we exclude individuals with less than 1 \ h of continuous work during the diary day. For individuals observed on a weekend, we apply the general restriction that they must be employed, but place no restriction on the hours typically worked on a weekend day. This leaves us with a sample of 2102 employed individuals, 1356 observed on working weekdays and 746 individuals observed during a weekend day.

In the time diary the respondents record the main activity (i.e. work, sleep, recreation, housework, etc.) in 15 min intervals for the full 24 h period prior to the interview day. In addition to market work 10 different categories of housework and several categories of leisure activities are identified among the 39 activities (see Appendix B3).

The TUS is matched to administrative income-tax registers and registers on labor-market attachment for each of the years 1987-1991. Thus we are able to trace career development for a period of 4 years after the survey was collected. The register data include information on the person interviewed in 1987, and on the spouse in a couple household. For each of the years 1987-1991 we have information on annual earnings and other income, actual labor-market experience, sector (public or private), occupational

The Timing and Flexibility of Housework and Men and Women's Wages 51

position, education, number and age of children, and information on spousal income and labor market variables. If the interview person changes civil status (and spouse) and/or acquires more children, this is registered, and information on new spouse or child is included in the data. In Appendix C3, sample means for the years 1987 and 1991 are shown for the variables included in the estimation.

The register information allows us to calculate hourly wage rates by dividing annual earnings by annual employed hours. Thus, our earnings measure suffers from the traditional weakness attributed to this measure, i.e. measurement error in hours is transmitted to the wage variable. The wage rate variable (which is measured in 1987 prices, Danish Kroner) includes overtime payments but excludes pension payments not included in registered annual earnings. The Danish pension payments rules changed over the period, and these changes affect the level of measured wage rates. Therefore in the empirical model presented below we include year-specific indicators in order to catch these changes in the overall level of the observed wage rates.

3.4. The amount and timing of housework activities

Table 3.1 shows the number of minutes spent on different activities during the day distributed by quartiles of the male and female wage distributions. The upper figures show hours on working weekdays (Monday-Friday), and the lower figures show hours on weekend days (Saturday-Sunday). On working weekdays, men in the upper quartile of the wage distribution spent on average 8.9 h on paid work, while women spent about 6.6 h. For men, there is a clear pattern, in that the higher the position in the wage distribution, the more the market work, whereas for women, we do not observe this tendency. Women in the upper wage quartile do not have more paid work on average than women in the second and third quartiles. Looking at housework, women in the upper quartile do slightly less housework, about 2.7 h compared to the lower quartiles (3 h in the lower quartile) on working weekdays.5 For men, we do not observe this pattern. Men in the lowest quartile work slightly fewer minutes than men in the other quartiles.

5 Gronau and Hamermesh (2001) find that the amount of housework decreases with educational level for married women in all countries included in their study. Interestingly, the only exception from this pattern is Sweden, where the most educated women do more housework than women with a medium level of education.

s to § IT

§

I s

Table 3.1. Average number of minutes spent on different activities ? during a working weekday (Monday -Friday: upper figures) and a weekend day (Saturday-Sunday: lower figures), 1987

Activity Men Women

Quartile in Male Wage Distribution 1987 (Min/Day) Quartile in Female Wage Distribution 1987 (Min/Day)

1st Quartile 2nd and 3rd Quartiles 4th Quartile All 1st Quartile : 2nd and 3rd Quartiles 4th Quartile All

Housework (4-10,24,35,36) 70 91 73 81 180 170 164 171 107 136 148 132 196 188 190 191

Food preparation (4,5) 23 27 25 25 66 65 61 64 26 37 40 35 73 71 69 71

Cleaning, etc. (6,7) 6 5 5 5 40 38 37 38 12 11 10 11 43 46 50 46

Childcare and child transp. 5 11 11 10 21 25 17 22 (8,24) - direct 4 8 21 10 23 22 9 21

Childcare and child trans. 39 101 96 84 151 150 155 151 (8,24) - indirect 144 208 209 193 234 276 318 277

Shopping, services, etc. (35,36) 16 21 15 18 30 26 26 27 23 18 25 21 19 15 25 19

Do-it-yourself work and 21 27 17 23 24 15 22 19 gardening (9,10) 42 61 53 55 37 34 27 33

Paid work, incl. transp. 457 489 536 493 350 398 396 386 (11,25,28) 55 88 109 85 48 67 67 62

Number of observations 180 343 181 704 156 333 163 652 95 223 90 408 83 166 89 338

Only individuals who were employed during th« i survey week are included. The numbers given in parentheses refer to activity types, see Appendix B3. Childcare and child transportation - indirect is i not included in total housework.

The Timing and Flexibility of Housework and Men and Women's Wages 53

Looking at the different housework activities, there is a clear gender division of work. Women tend to engage in food preparation and cleaning activities, while men do more do-it-yourself activities, particularly on the weekends.6 This raw empirical evidence confirms the hypothesis that women tend to have more routine activities which are rather inflexible, in the sense that they have to be done each day, while men tend to have more time- flexible activities. During weekend days women and men increase their housework activity, especially in the upper wage quartile. Women, mainly in the upper wage quartile, seem to do the cleaning work on the weekend, while men do a lot of do-it-yourself work and gardening on the weekend.

In order to look more closely at the timing of housework activities and market work, we calculate the distribution of time spent on market work, housework and other activities (sleep, personal care, leisure time) at each quarter of the day. Figure 3.1 shows these distributions for men and women on working weekdays and weekend days. The housework profile is clearly double-peaked: during the morning (about 10AM) and about dinner time (6PM) a relatively large proportion of women's time (30-40%) is spent on housework, both on weekends and working weekdays. For men, the pattern is different. They spend only about 10% of their time on housework during the morning on working weekdays, but on weekends it is mainly during the morning that men work at home. During working weekdays, men tend to do more market work than women early in the day and late in the afternoon, while women on average do more housework early in the morning and late in the afternoon.

The observed pattern in Figure 3.1 may confirm that women are less flexible at their jobs, since they tend to time more market work late in the morning and early in the afternoon (when the children are probably at school or at a day care center) compared to men. However, we do not know

6 Time spent on (direct) caring for children is surprisingly small, partly due to the fact that both parents and non-parents are included in the sample (see for instance Gronau and Hamermesh, 2001, where the time allocation in six countries, Australia, Israel, the Netherlands, Sweden, the US, West Germany, is shown). Danish men and women seem to spend much less time on their children compared to these countries. Another reason is that parents typically record a lot of activities done simultaneously with childcare in other categories than childcare (as housework, leisure or other). As the survey contains explicit information on who in the family is present when the different activities are performed, we are able to identify a much larger amount of indirect childcare (childcare performed as the secondary activity), as shown in Table 3.2. The definition of housework used in this paper includes only direct childcare. However, in Table 3.6 we test the robustness of our results to an expanded definition of housework in which time spent on both direct and indirect childcare is included.

54 J. Bonke, N. Datta Gupta and N. Smith

whether the people would have been able to time their market work and housework differently, and whether it is the timing of housework or market work that determines the allocation of time during the day. Instead, in Table 3.2 below we try, by combining the type of activity and timing information from the time diaries, to identify different indicators of the flexibility of housework and market work activities.

According to Table 3.2, women do more housework before they go to work and more housework just after they have left their jobs than men. On average, women spend 37 min doing housework before they start at their job (including travel) and 100 min after they leave the job. For men the same figures are 14 and 44 min. Men have longer breaks between their job

The Timing and Flexibility of Housework and Men and Women's Wages 55

and their housework, and a much larger proportion of men than women do not undertake any kind of housework before their paid work (65% of men and 33% of women). The majority of housework is done after the paid work has been finished, but 52% of the males and 22% of the females do not undertake any housework when they arrive home after paid work.

This evidence gives some indirect empirical support to our hypothesis that women tend to be more inflexible in their jobs because they have more housework tasks that need to be done at inflexible points in time. In fact, much casual evidence supports these findings that women more than men hurry home after work to pick up children or do the shopping. In Denmark shopping hours are limited, and most

Si 60

.8*

I B & a

3"

Table 3.2. Housework before and after market work and breaks between housework and market work during a working weekday (Monday-Friday), 1987

Men Women

Mean (Min) Standard Deviation Mean (Min) Standard Deviation

Housework before market work8

Housework after market work* Morning break, conditional on doing housework

before market workb

Afternoon break, conditional on doing housework after market work6

14 44 42

66

34 66 55

79

37 100 34

48

56 87 35

68

No housework before or after market work 0 < break < 30 min 30 min < break ^ 60 min 60 min < break ^ 90 min Break > 90 min

Before (Morning) (%) 65 22 10 2 1

After (Afternoon) (%) 52 26 9 6 7

Before (Morning) (%) 33 47 15 3 2

After (Afternoon) (%) 22 54 11 6 7

All 100 100 100 100

"Paid work is restricted to a period of more than 90 min including transportation time. bTime between household work and first period of paid work (paid work restricted to a period of more than 90 min of work) cTime between last period of paid work (paid work restricted to a period of more than 90 min of work) and housework.

The Timing and Flexibility of Housework and Men and Women's Wages 57

stores close by 5:30 or 6:00 PM, while day care centers close at 5:00 PM. As it is typically women who are responsible for shopping and picking up the children, the effect of these restricted hours may reduce women's flexibility more than men's.7

3.5. Empirical model

According to the theoretical model above, the hourly wage rate observed is given by wm = wm(HCm,<rm, fm{<ru<r2,(rm,Z)). Thus, we estimate a human capital wage function, where we successively include more detailed information on housework activities (HW) and job-specific and household- specific factors which capture a), i.e. explain flexibility-intensity aspects (F)- The wage functions are estimated by quantile regression methods (Koenker and Bassett, 1978; Buchinsky, 1998), where we specify the 0th quantile of the conditional wage distribution given X and housework variables HW as a linear function of the covariates

GrfLn(Wa|Xa),HW,)

= )3o(0)+Xl-,i3(0+HWIr 1(0+^72(0), ^=(0.1,0.5,0.9)

<2e(e,rlX,/,HW,-,F,-,)=0, Xit is a vector of (time-varying) explanatory variables included in traditional human capital functions, HW,- a vector of time-use variables from 1987, Fit a vector of time-varying variables determining flexibility intensity, and j3(0), «f(Q) and ^(0) are parameter vectors to be estimated. The subscripts i = l , . . . , n and t— 1987,...,1991, index the individual and time, respectively, and eit is an error component. The use of quantile regressions allows the marginal effect of housework to vary across the quantiles of the conditional wage distribution, consistent with the evidence suggested by the raw data in Table 3.1. Standard errors are obtained through 200 bootstrap repetitions, based on Koenker and Bassett (1978) algorithms.

As individuals are observed repeatedly over time, the data should in principle be corrected for individual effects. However, a simple differencing technique cannot be applied here, because differencing the quantiles of the conditional wage distribution would yield the effect of additional HW, e.g. on the 0th quantile of the conditional distribution of

A study of the lifting of shopping hours constraint in the Netherlands shows that women are most affected by the relaxation of such laws and increase their market hours the most following the change, both due to their employment in the retailing sector and also due to their increased work hours in other sectors (Jacobsen and Kooreman, this volume).

58 J. Bonke, N. Datta Gupta andN. Smith

within-person wage differences, rather than the effect of HW on the conditional wage distribution. The quantile estimates obtained from differenced data are not equivalent to quantile estimates from data on levels (Arias et al., 2002). In a survey on quantile methods Koenker and Hallock (2001) also caution against additive random effects, as the quantile of convolutions of random variables is likely to be intractable. Thus as of yet, quantile methods have not been applied to panel data, although one study by Chay (1995) applies minimum distance methods to unrestricted quantile regressions of several cross-sections.

Another consideration is that time use is observed only in 1987. We assume that the 1987 time allocation gives a reliable picture of the allocation of time for the 4 consecutive years after, or at least we assume that the allocation of time in 1987 had effects on the consecutive wage development. Thus we analyze how time allocation affects wages in the medium run. Note that this means that each person's time-use measure appears multiple times in the quantile regression equation, leading to the random disturbance in the regression being correlated within person groups. As pointed out by Moulton (1990), the consequence may be that standard errors are biased downwards (and f-statistics biased upwards), leading to spurious conclusions about the significance of the aggregate time-use measure in the wage equation. While a test of the importance of this correlation and correction of standard errors could be attempted in an OLS wage regression, the quantile method is not yet as well developed to take account of this problem. However, we devise an informal test of the significance of this problem below.8 Further, in Table 3.6, Model 3b, we explore the sensitivity of our findings to this assumption when we replicate the analysis on the sub-sample of individuals who remain married or

As an informal test, we have estimated the basic model (Model 1, see below, including the housework variable) on two different samples. Sample 1 contained one-third of the observations (about 635 individuals) observed repeatedly in the years 1987,1989 and 1991. Sample 2 contained the pooled sample of the first third of the individuals observed in 1987, the second third of the individuals observed in 1989 and the last third of the individuals observed in 1991, i.e. a pooled sample consisting of three independent cross-section samples observed in either 1987,1989 or 1991 (about 1300 distinct individuals). When we compare the estimated standard errors from these two samples, we do not find any systematic differences. For instance, the estimated standard error on the coefficient of the amount of housework at thelOth percentile is 0.017 (0.016) for women (men) in Sample 1, while the same figure in Sample 2 is 0.007 (0.010). For none of the estimated variables do we find large differences between results from the two samples. We take this as (imprecise) evidence that our standard errors are not greatly underestimated, despite estimating our model on a pooled sample of highly dependent cross-sections.

The Timing and Flexibility of Housework and Men and Women's Wages 59

cohabiting throughout the sample period, as for these individuals, we expect little change in housework duties to occur over the sample period.

Yet another problem is that the housework variables may be endogenous. Those with higher market wages may do fewer hours of housework and more market work, and we may therefore obtain biased estimates of the wage effects of housework (see Hersch and Stratton, 1997, 2000). We have therefore experimented with instrumenting the housework variables. As instruments we used a number of register variables for the years 1986 and 1987 (number of rooms in the house, number and age of children, number of adults in household, own unemployment experience during the year, different characteristics of the spouse, household income and the square value of all these variables).9 However, our tests on the validity of our instruments in all the different specifications we tried came out negatively, i.e. we were unable to find valid instruments according to the test procedure described in Bound et al. (1995).10

3.6. Results

3.6.1. Amount of housework

The results from estimating simple quantile regression wage functions including the amount of housework are shown in Tables 3.3 and 3.4. First, a basic human capital model, Model 1, including the total amount of housework, is shown in Table 3.3. In this model, as well as in the following models that extend it, we pool the samples of men and women and interact all human capital variables (which include education, experience and paid work hours), housework variables, family, sector and occupational variables by the gender variable. Year indicators, the regional indicator variable and the constant term are not interacted with gender. Further, we include an indicator variable, 'woman,' in order to get an estimate of how much the constant term for women deviates from the male constant.

9 Following Arias et al. (2002), we use a two-stage quantile regression estimator, in which the first stage is described above, where we project endogenous HW on the space spanned by the instruments which are assumed to be uncorrelated with the error term. In the second stage we estimate a quantile regression of log wages on the projected HW obtained in the previous stage and on the other exogenous regressors. The two-stage quantile estimator has been shown to be asymptotically consistent in previous studies. The correction of the standard errors requires the estimation of a sparsity function using non-parametric techniques or bootstrapped versions of the same. 10 Hersch and Stratton (1997) also test for endogeneity of housework and conclude that they cannot reject that the amount of male housework is exogenous to their model, while they reject exogeneity for female housework.

s

s to

b

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Table 3.3. Model 1: human capital variables and observed amount of housework on working weekdays

10th Quantile 50m Quantile 90th Quantile

Women Men Women Men Women Men

Educational level 2 0.039* (0.016) 0.126* (0.017) 0.032* (0.009) 0.051* (0.010) 0.006 (0.019) 0.018 (0.026) Educational level 3 0.160* (0.024) 0.121* (0.022) 0.146* (0.018) 0.109* (0.021) 0.068* (0.034) 0.014 (0.047) Educational level 4 0.208* (0.017) 0.221* (0.025) 0.146* (0.010) 0.168* (0.020) 0.098* (0.032) 0.193* (0.062) Educational level 5 0.473* (0.022) 0.473* (0.022) 0.408* (0.032) 0.463* (0.025) 0.340* (0.034) 0.451* (0.047) Experience, years 0.042* (0.005) 0.065* (0.004) 0.012* (0.003) 0.040* (0.004) --0.009(0.007) 0.027* (0.007) Experience squared/100 -0.096* (0.018) --0.166* (0.013) -0.010(0.009) --0.104* (0.012) 0.065* (0.029) --0.072* (0.021) Market work, daily hours 0.001 (0.002) 0.006* (0.002) -0.001 (0.001) 0.009* (0.002) --0.001 (0.002) 0.006 (0.003) Housework, daily hours -0.003(0.004) 0.011* (0.004) -0.006* (0.002) 0.000 (0.002) 0.010* (0.004) --0.014* (0.006) Constant term, year dummies, Yes Yes Yes

woman indicator and region

Pseudo R2 0.235 0.196 0.187 t

Number of observations 7718

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Table 3.4. Model 2: human i capital variables, household, occupational and r sector variables, and amount of housework on working weekdays

10th Quantile 50th Quantile 90th Quantile

Women Men Women Men Women Men

Educational level 2 0.045* (0.019) 0.118* (0.019) 0.022(0.011) 0.029* (0.015) -0.011(0.021) -0.010(0.021) Educational level 3 0.150* (0.031) 0.156* (0.029) 0.121* (0.016) 0.119* (0.024) 0.013 (0.045) 0.079* (0.030) Educational level 4 0.212* (0.022) 0.188* (0.033) 0.100* (0.018) 0.100* (0.018) 0.057 (0.048) 0.035 (0.053) Educational level 5 0.410* (0.034) 0.464* (0.041) 0.217* (0.042) 0.272* (0.025) 0.175* (0.073) 0.265* (0.055) Experience, years 0.040* (0.005) 0.051* (0.005) 0.013* (0.003) 0.030* (0.003) -0.007(0.006) 0.020* (0.006) Experience squared/100 - 0 . 0 9 3 * (0.018) - 0 . 1 2 9 * (0.016) -0.016(0.012) --0.072* (0.010) 0.050* (0.024) -0.052* (0.020) Market work, daily hours -0.002(0.002) 0.006* (0.002) -0.002(0.001) 0.003* (0.001) -0.007* (0.003) 0.003 (0.002) Married or cohabiting 0.012 (0.017) 0.096* (0.018) -0.000(0.009) 0.019* (0.012) 0.036 (0.019) 0.043* (0.018) One child aged less than 10 years 0.010 (0.018) - 0 . 0 2 3 (0.017) -0.015(0.010) 0.024 (0.013) -0.015 (0.023) 0.042 (0.022) Two or more children aged 0.017 (0.019) 0.012 (0.020) -0.013(0.013) 0.023* (0.015) -0.023 (0.032) 0.016 (0.027)

less than 10 years Public sector -0.007(0.014) - 0 . 0 8 1 * (0.014) - 0 . 1 0 1 * (0.009) --0.160* (0.010) -0.187* (0.022) - 0 . 2 4 2 * (0.028) Salaried, high level 0.089* (0.022) 0.144* (0.026) 0.196* (0.028) 0.323* (0.023) 0.228* (0.067) 0.380* (0.042) Salaried, medium level -0.008(0.017) 0.087* (0.021) 0.087* (0.015) 0.133* (0.016) 0.098* (0.048) 0.084* (0.025) Skilled workers -0.084(0.092) -0.010(0.023) 0.042 (0.041) 0.097* (0.017) -0.045 (0.087) 0.056 (0.029) Unskilled workers, medium level 0.000 (0.022) 0.067* (0.019) 0.000 (0.013) 0.044* (0.021) -0.044(0.023) 0.014 (0.032) Unskilled workers, low level - 0 . 1 0 6 * (0.034) - 0 . 1 2 4 * (0.032) -0.034(0.025) 0.003 (0.023) 0.018 (0.057) 0.037 (0.057) Housework, daily hours -0.005(0.005) 0.013* (0.004) - 0 . 0 0 3 (0.003) 0.003 (0.004) 0.009 (0.006) -0.007(0.006) Constant term, year dummies, Yes Yes Yes

woman indicator and region

Pseudo R2 0.259 0.249 0.264 Number of observations 7718

•Denotes significance at the 5% level here.

62 J. Bonke, N. Datta Gupta and N. Smith

Since we estimate the coefficients of the pooled conditional wage distribution, the female indicator is interpreted as a partial measure of the unexplained gender wage gap in the model concerned.1 In the next step, we extend the basic model by adding job and household characteristics variables which are supposed to capture flexibility and flexibility-intensity aspects of different household and market activities (fj and oj in Model 2) in Table 3.4.

In the basic model in Table 3.3, the total number of hours spent on housework activities is investigated. This model is basically in line with Hersch (1991), except that we use a quantile regression approach. Table 3.3 shows that the amount of housework has a negative effect on the hourly wages of women and a positive effect on the hourly wages of men, except at the 90th percentile of the conditional wage distribution where this is reversed. However, the effect of housework on wages is only significant for women at the 50th and 90th percentiles and men at the 10th and 90th percentiles. For women at the 50th percentile, the results indicate that one more hour of daily housework reduces the hourly wage rate significantly by about 0.6%, and for men at the 90th percentile by about 1.4%. Therefore, the group that appears to be most strongly penalized is men at the high end of the conditional wage distribution. Surprisingly, for women at the upper end of the conditional wage distribution the effect is significantly positive. Compared to the US studies by Bielby and Bielby (1988), Hersch (1991), Hersch and Stratton (1997) and Stratton (2001), which do not find negative effects of housework for men but only for women, our results for Denmark are more mixed.12

11 By estimating gender-specific coefficients on the human capital variables, we implicitly assume away the part of the unexplained gap that is due to differences in returns to the human capital variables. Thus, the coefficient on the female indicator should be regarded as a lower bound on the true unexplained gap. Indeed, the agender gaps found in the data are smaller than those found in previous studies for Denmark, 0.8% at the 10th percentile, -0.01 % at the 50th percentile and - 1 2 % at the 90th percentile. Moreover, these gaps turn positive or disappear when market work hours are included in the wage regression.

We are hesitant to conclude that gender differences in paid work hours account for the wage gap in Denmark, in part because including paid work hours in the wage regression may introduce potential endogeneity, and in part because, from the argument above, significant gender differences still exist in the returns to human capital variables (see Table 3.4 below). These differences by convention should also be included in the unexplained gap. 12 To compare our findings more closely with those of the US studies mentioned above that employ simple or augmented OLS regressions, we also run the pooled OLS estimator of the model in Table 3.3. The coefficient of housework is negative and insignificant for women (-0.0002), and positive and insignificant for men (0.003). Thus in the pooled model, the signs match those found in the US studies.

The Timing and Flexibility of Housework and Men and Women's Wages 63

Looking at the other variables in the wage function, we find with a few exceptions that women receive a lower return on their human capital, education and experience and market work hours at all points of the conditional wage distribution. The wage profile across experience levels is steeper at the lower end of the conditional wage distribution, while at the upper end it is flatter for men but steeply increasing for women (significant and positive squared term to experience).

In the next step, we extend the basic model with variables that may capture flexibility-intensity aspects. The variables selected are indicators for one and two or more children aged less than 10 years, indicators for being married or cohabiting, occupational categories and employment in the public sector. The occupational indicators are expected to reflect that the level of flexibility demanded from the job, and thus the wage rate, varies according to occupational position. The public sector variable is expected to capture their more flexible working conditions (more care days for sick children, flexible working time schedules, more rights concerning parental leave, etc.). The public sector is typically less demanding regarding the flexibility of the workers. The interpretation of these additional variables should be handled carefully, however, since they may be endogenous to the model. However, for the same reason as for the housework variables, we have not instrumented them.

Table 3.4 below shows that the housework coefficients become (numerically) slightly smaller and lose significance when family and job characteristic variables are included in the model, except at the lowest quantile.13 Men at the 10th percentile still experience a 1.3% increase in wages for every additional hour of housework. Further, in contrast to Table 3.3, women at the highest quantile no longer face a significant positive effect of housework on wages. The coefficients of the classic human capital variables are not altered much by the inclusion of more variables in the wage function. The additional variables reflecting family background are not significant for women. Married women or women with at least one child aged less than 10 do not earn less than single women or women without young children, whereas men get a marriage premium in the sense that they earn significantly higher wages than other men.14

Exactly the same patterns are found for Sweden (see Albrecht et al., 2003).

In the corresponding pooled OLS estimates of this model the coefficient on housework is 0.0005 (s.e. = 0.002) for women and 0.006 (s.e. = 0.003) for men. 14 The absence of a family gap in women's wages in Denmark has been documented by Datta Gupta and Smith (2002).

64 J. Bonke, N. Datta Gupta and N. Smith

Men as well as women who are employed in the public sector are strongly punished, especially at the high end of the conditional wage distribution.

The coefficient of the public sector variable is - 1 9 % for women and - 2 4 % for men at the 90th percentile. Since more than 50% of Danish women (about 20% of Danish men) are employed in the public sector, the public sector indicator variable to a large extent explains the gender wage gap. However, the public sector variable may capture that individuals who prefer a family friendly job to a demanding job with a high wage choose to work there.15 In the same way, the coefficients on the occupational variables that indicate large wage differentials between occupational categories may reflect the endogeneity of occupational status.16

3.6.2. Timing and flexibility of housework

In Tables 3.5 and 3.6, we try to measure flexibility of housework more directly. We also experiment with measuring flexibility and timing aspects in alternative ways. One indicator of having low flexibility on the job and giving higher priority to family tasks may be that the individual does housework both before and just after being at the job. Thus in Model 3 we add an indicator variable to the amount of housework, which assumes the value of one for persons who, based on their time diaries, are observed to fulfill this criterion.

In Nielsen et al. (2003) the wages of Danish men and women are analyzed in a switching regression approach where choice of sector is considered endogenous to the wage determination. The result is that the effects of young children and periods out the labor market turn significantly negative. 16 One further experiment splits housework activities into more detailed groups and analyzes whether there are significant differences in the wage effects of activities that are assumed to be more or less flexibility intensive. Housework categories are: food preparation, dish washing, etc.; cleaning, etc.; childcare and child transportation; do-it- yourself work; and shopping, services, etc. (see Table 3.1). Our expectation is that food preparation, cleaning and childcare are less flexible activities than do-it-yourself work, and therefore these activities may have more negative effects on the wage growth. (See Noonan, 2001 for similar evidence from US data.) The results show that our expectations are to some extent fulfilled. However, women at the high end of the conditional wage distribution are not penalized more for doing routine tasks like cleaning and food preparation activities. On the contrary, cleaning activities have a positive and significant effect on women's wages at the 90th percentile! One explanation for this may be that women with demanding jobs can move the more inflexible cleaning tasks to the weekend or purchase cleaning services in the market despite the high prices of these services, and that on weekdays they therefore only undertake time-flexible cleaning activities that are not damaging to wages.

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Table 3.5. Selected results from models reflecting timing and flexibility aspects, extended model, Model 2

10th Quantile 50th Quantile 90th Quantile

Women Men Women Men Women Men

Hours of housework Indicator for morning and

afternoon housework

Hours of housework Average spell length

of housework

Model 3: both morning and afternoon housework (No. of observations 7718) -0.002(0.004) 0.013* (0.004) -0.002(0.002) 0.004(0.004) 0.014* (0.005) -0.032* (0.014) -0.002(0.012) - 0 . 0 3 3 * (0.008) -0.020(0.011) -0.046* (0.018)'

Model 4: contiguity of housework spells (No. of observations 7718) -0.006(0.005) 0.002(0.007) 0.0005(0.003) -0.001(0.006) 0.019* (0.007)

0.028(0.051) 0.071* (0.029) -0.036(0.023) 0.018(0.021) -0.089* (0.041)

-0.006(0.005) - 0 . 0 3 7 * (0.021)

-0.010(0.006) 0.018 (0.029)

•Denotes significance at the 5% level here. Model 2, see Table 3.4.

ON

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Table 3.6. Specification tests involving flexibility of housework model, extended model, Model 2

10th Quantile 50th Quantile 90th Quantile

Women Men Women Men Women Men

Model 3a: Including interactions with work schedule flexibility (No. of observations 7718) Hours of housework -0.001(0.004) 0.014* (0.003) -0.002(0.002) 0.003(0.003) 0.011* (0.005) -0.006(0.006) Indicator for morning and 0.029(0.036) 0.108* (0.031) 0.076(0.065) 0.054* (0.025) 0.150* (0.040) -0.027(0.197)

afternoon housework X flexible work schedules

Indicator for morning and - 0 . 0 3 5 * (0.014) -0.004(0.015) -0.034* (0.008) - 0 . 0 3 1 * (0.012) - 0 . 0 5 3 * (0.019) -0.038(0.020) afternoon housework X fixed work schedules

Model 3b: married and cohabiting individuals only (No. of observations 5715) Hours of housework -0.007(0.005) 0.009* (0.004) -0.004(0.003) -0.002(0.004) 0.009(0.005) -0.006(0.005) Indicator for morning and - 0 . 0 4 3 * (0.017) -0.015(0.016) - 0 . 0 4 3 * (0.010) -0.012(0.012) - 0 . 0 6 3 * (0.019) - 0 . 0 4 8 * (0.023)

afternoon housework

Model 3c: housework including indirect childcare (No. of observations 7718) Hours of housework -0.004* (0.002) 0.007* (0.002) -0.001(0.001) 0.004* (0.002) 0.004(0.003) 0.002 (0.003) Indicator for morning and - 0 . 0 3 1 * (0.014) 0.007(0.013) - 0.032* (0.008) -0.024* (0.011) -0.038* (0.019) -0.035(0.021)

afternoon housework

•Denotes significance at the 5% level here. Model 2, see Table 3.4.

The Timing and Flexibility of Housework and Men and Women's Wages 67

The first two rows of Table 3.5 below show the results of this estimation. This aspect of timing and flexibility clearly has an effect on observed wages, and the effect is much more negative and significant for women than for men, except for men at the upper end of the conditional wage distribution. Further, the effect on wages of housework before and after work is considerably larger than the effect of the level of housework. The wages of women who do housework just before and after their job are on average 3.2% (3.3%) lower than for other women at the 10th (50th) percentile of the conditional wage distribution. At the 90th percentile, the effect is as large as —4.6% for women and —3.7% for men.

Apart from the timing aspect, another way to capture the notion of flexibility of housework is to measure the contiguity of housework spells, since some tasks need long periods of time in order to be completed satisfactorily. Thus, we try to come up with an objective measure of whether or not housework requires contiguous time blocks by taking an average over the individual's spells of housework over the course of the day. This variable, the average spell length of housework, is tried in place of the timing indicators but along with the quantity of housework in Model 4 which appears in the lower panel of Table 3.5 above. We expect that individuals who do tasks that appear to take more contiguous time (longer average housework spell) will be penalized more than people who have on average shorter spells of housework chores. The results from this model indicate particularly that women at the high end of the conditional wage distribution are penalized for having a higher average housework spell, and this penalty is large, around 9%. Other groups, however, appear not to be penalized for the contiguity of their housework spells.

In Table 3.6 we return to the first definition of flexibility and test the sensitivity of our findings to alternative specifications and alternative sample definitions. First, the notion of time flexibility introduced in Table 3.5 assumed that individuals who did housework before and after the job were constrained by its dictates to cut down their work hours, and therefore that the effects on productivity and hence wages of such behavior were necessarily negative. However, the causation could go the other way, in that some employees can bargain flexible work schedules with their employers, affording them the flexibility to time their work and housework according to the changing needs of the family or employer. In fact, this type of bargain could increase productivity and wages, because it may increase job satisfaction without conflicting with the demands of the employer. In order to try to distinguish between these hypotheses, we use additional information from the TUS in which

68 / . Bonke, N. Datta Gupta and N. Smith

individuals are asked whether or not their jobs require fixed work schedules or flexible work schedules that are a part of a bargain made with the employer.17

Around 6% of men and 3% of women report having flexible work schedules that are determined through bargaining with the employer. Model 3a in Table 3.6 shows that when the indicator for doing housework just before or just after the job is interacted with having fixed or flexible work schedules, exactly as predicted, negative effects arise for those (significant mostly for women) on fixed work schedules, while positive effects arise (significant mostly for men) for those who have flexible work schedules. Thus, it may be important to distinguish whether the. timing of housework just before or after work is flexibly chosen by the individual or enforced upon the individual as a result of time-inflexible household duties or family responsibilities.

Another way to analyze whether the flexibility of housework matters is to restrict the samples to groups that are more homogenous with respect to flexibility. One hypothesis is that married people face many more routine tasks that make them less flexible than single people because they have to coordinate the timing of housework tasks like food preparing, shopping, etc. with their spouse. We expect this effect to exist especially for women. For men, an opposite effect from being married can arise if the wife takes the main responsibility for activities at home. This may increase the flexibility that married men devote to their jobs. In Model 3b we therefore restrict the estimation to include only married or cohabiting persons.

One weakness of our sample is that the time-use information for 1987 is used for the subsequent 4 years. The allocation of time may, of course, be affected during the period if the person changes civil state (or undergoes other major changes). However, when restricting our sample to individuals observed as non-singles, we may partly take account of the lack of annual time-use information, and, if civil state affects the flexibility of work, we should expect to see stronger results with respect to the wage effects of housework, especially at the upper end of the female wage distribution. For men, we may find the opposite if their wives are mainly responsible for

17 The actual question is: do you have fixed work hours or variable work hours? The choices given are fixed daytime work hours, fixed evening/night work hours, variable daytime work hours and variable evening/night work hours. For those who answer some type of variable hours, a further question probes the actual nature of varying work hours, i.e. shift work (two shifts), shift work (three or more shifts with weekend breaks), shift work (three or more shifts without weekend breaks), varying according to employer's plan, varying according to the bargain with the employer, including flex-time. Only the last group is considered to be on flexible work schedules.

The Timing and Flexibility of Housework and Men and Women's Wages 69

time-inflexible housework. According to Table 3.6, this is in fact the case. Hours of housework become more negative for all groups and, in fact, are no longer significantly positive for women at the 90th percentile. Regarding time flexibility, the effects become stronger for women and slightly weaker (although still negative) for men except men at the 90th percentile. At the 90th percentile, the coefficient of morning and afternoon housework becomes large for married or cohabiting individuals, — 6.3% for women and —4.8% for men. The indicator for doing housework immediately before and after the job also becomes more negative for married women at the other points of the conditional wage distribution, although less negative for married men.

These findings indicate that, given the prevalence of assortative mating, at the high end of the distribution there is more sharing of housework between partners, so that both partners are affected by the coordination problem. At other points married women are penalized more and married men less, perhaps because in this case it is women who are mainly responsible for the 'balancing act/

As a final test of the robustness of results to alternative definitions, in Model 3c in Table 3.6 we experiment with a different measure of housework, one that includes both direct and indirect childcare activities, childcare that is done simultaneously with other housework or leisure activities. The mean values for indirect childcare can be seen in Appendix C. For example, while men (women) in 1987 spent 0.16 (0.36) h on direct childcare and child transportation, the numbers for indirect childcare are much higher, 2.07 (3.24) h. One reason for taking this into is that childcare activities are typically the most widespread type of secondary activity that individuals engage in and, as such, capture the wage effects of multi- tasking within the household. If such dual tasking increases stress or fatigue, we would expect more negative effects of the amount and timing of housework than when these activities are not accounted for. The results show, however, that the coefficients on the amount and timing of housework are not appreciably altered in Model 3c compared to Model 3. We conclude that recoding housework to include secondary activities that involve children as childcare does not change the results and that the wage effects of flexibility are not appreciably altered if tasks are done simultaneously with children.

3.7. Conclusion

In this study we analyze whether the amount and timing or flexibility of housework have negative effects on the wages of men and women. We find, as in US studies, that housework has negative effects on the wages of

70 J. Bonke, N. Datta Gupta and N. Smith

women and positive effects on the wages of men, except at the high end of the conditional wage distribution. At the 90th percentile housework has a positive effect on the wages of women and a negative effect on the wages of men. In fact, high-wage men receive the largest wage penalty for doing housework, namely, a wage loss of 1.4% for each additional hour of housework done during the weekday.

The coefficient on housework becomes numerically smaller and less significant when family and job characteristics are added to the model. These characteristics can be thought of as indirectly measuring flexibility intensity. Of these, public-sector employment is particularly important, especially at the high end of the conditional wage distribution. At the 90th percentile public-sector employed women earn 19% less than private- sector employed women, while the same figure for men is 24%. Since unions in the public sector prioritize non-wage benefits such as long maternity leave with full wage compensation, care days, flexible working schedules, and during recent years even reduced hours instead of wage increases, the large negative effect of public sector employment may indirectly reflect the importance of flexibility and home responsibilities.

When looking directly at timing and flexibility, we find evidence that they matter for wages, in fact considerably more than the quantity (amount) of housework. Women (and to a smaller extent men) who do housework activities immediately before or after their job have significantly lower wage rates, especially at the upper end of the conditional wage distribution, where the wage penalty for women is 4.6% and 3.7% for men. Further, high-wage women whose average housework spells requires contiguous blocks of time face a wage penalty of 9%. It is important, however, to distinguish whether the timing of housework just before or after work is flexibly chosen by the individual or enforced upon the individual as a result of time-inflexible household duties or family responsibilities that cannot be moved. Only the latter appear to be damaging to productivity and wages.

The wage effects of flexibility are numerically larger for married or cohabiting women but slightly smaller for men in such households, except at the 90th percentile. There the coefficient of morning and afternoon housework becomes large for both married men and married women, — 6.3% for women and - 4 . 8 % for men. This asymmetry may indicate that, assuming assortative mating behavior, there is more sharing of housework tasks at the high end of the distribution, so that both partners are negatively affected by the coordination problem, but that lower down the distribution women take more responsibility for coordinating home activities.

The Timing and Flexibility of Housework and Men and Women's Wages 71

Finally, we test the robustness of our housework measure to an alternative definition of childcare. The expanded definition includes both direct childcare as well as childcare that is recorded as a secondary activity done simultaneously with other housework or leisure activities. The results show that re-measuring housework to take into account secondary childcare activities does not alter the conclusions appreciably. Dual- tasking does not appear damaging to wages.

Our study is the first to try to quantify the effects of timing and flexibility of housework on the wages of men and women. The main finding seems to be that women more than men are penalized for inflexibility, and that this is most pronounced at the high end of the conditional wage distribution. Due to the very compressed wage structures in the Scandinavian countries and high tax levels, which in turn imply high prices of market services (domestic help, restaurant visits, etc.), even high-income families in Scandinavia undertake more housework and do-it- yourself work compared to families in the US, for instance. At the same time, the early closing of shops and day care institutions imparts a certain degree of inflexibility to women's daily schedules, which our study shows has negative effects on earnings and the career, especially at the higher end of the qualification distribution. This may be one explanation for the increasing unexplained gender wage gap at the upper end of the wage distribution in Denmark.

Acknowledgements

The project has received financial support from the Danish Social Research Council (FREJA). Thanks to Daniel Hamermesh, Jean Yeung, Joyce Jacobsen, Leslie Stratton and participants at the IZA conference, May 2002 and May 2003, and the EALE conference 2002, for many helpful comments. Astrid Wurtz has done most of the computational work.

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Arias, O., K. Hallock and W. Sosa-Escudero (2002), "Individual heterogeneity in the returns to schooling: instrumental variables quantile regression using twins data", pp. 7 - 4 0 in: B. Fitzenberger, R. Koenker and J.A.F. Machado, editors, Economic Applications of Quantile Regressions, Wurzburg: Physica Verlag.

Becker, G.S. (1985), "Human capital, effort, and the sexual division of labor", Journal of Labor Economics, Vol. 3, pp. 33-58.

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The Timing and Flexibility of Housework and Men and Women's Wages 73

Appendix A3. Theoretical model - the maximization problem

We assume the household produces two services (j = 1,2), which are determined by two production functions that combine market goods or services bought in the market, *,-, with efficiency units of time, /,, y = 1,2:

Zj = Zj(Xj,Ij). (A3.1)

The individual is assumed to maximize her utility function which is a function of the produced goods and services Z\ and Z^

U=U(ZUZ2) (A3.2)

The budget constraint is given as

Pixi + p2x2 = wm(/m)fm + F, (A3.3)

where Y is the non-wage income of the household, which in this single- person model may include earnings of the spouse, since we do not model interactions between the spouses with respect to effort and time allocation.18

Maximization of Equation (A3.2) with respect to the choice variables xjtfjt and tj subject to the time and flexibility constraints (3.1), (3.2) and the production functions (A3.1) and (A3.3) gives the first-order conditions

~bZ'bxL" XxPj = Vxi " XxPj = ° f ° r ; = l ' 2

S § S " A ^ ^ = ^ " A ' " ^ = o for;,=l'2 A*wm - A, - \ffm = 0 (A3.4)

bU bZj blj % r dwj . _ . . " .

^ ^ ^ " V , = ^ " V > = 0 for;-1,2

Ktm-TT1 ~ A/rm = 0

where \x, An and Ay are the marginal utilities of income, time and flexibility. The second and third conditions state that the marginal utility of one extra hour spent on non-market activity j or market work must equal the marginal cost of the hour (A,) plus the flexibility cost related to

The sample does not include information on spouses, so we are unable to model time allocation between spouses.

74 J. Bonke, N. Datta Gupta and N. Smith

this hour (Ay, fj). The fourth and fifth conditions, which relate to one extra unit of flexibility spent on non-market activities and market work, Equation (A3.4) and the budget constraints define the demand and supply functions for Xj, fj, and tj as functions of endowment of human capital in different activities, flexibility intensities, prices and non-wage income.

The Timing and Flexibility of Housework and Men and Women's Wages 75

Appendix B3. Activities recorded in the Danish Time-Use Survey 1987

1. Sleep 2. Personal care 3. Eating 4. Food preparation 5. Dish washing 6. Household upkeep 7. Care for clothes 8. Childcare 9. Construction and repair 10. Gardening 11. Employment at home 12. Homework 13. Reading newspapers 14. Reading periodicals and books 15. Hobbies 16. Visit by family (at home) 17. Visit by friends and others (at home) 18. TV and video 19. Radio 20. Music 21. Socializing with family 22. Resting 23. Other at home (telephone, etc.) 24. Transporting a child 25. Travel to/from work 26. Travel to/from school or university 27. Other travels 28. Employment 29. School or university 30. Participatory activities 31. Sports 32. Trips 33. Visit family 34. Visit friends and others 35. Shopping 36. Services 37. Restaurant 38. Entertainment and culture 39. Others (outside home)

3

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Appendix C3

Table C3.1. Sample means

Men ^ Women

1987 1991 1987 1991

Log hourly wage rate 4.734 (0.349) 4.859 (0.333) 4.511 (0.301) 4.651 (0.293) Daily hours of

Total amount of housework, working weekdays 1.354 (1.720) 2.845 (2.129) Total amount of housework, weekend days 2.194 (2.286) 3.175 (2.419) Total amount of housework, new def, weekdays 2.753 (3.227) 5.368 (4.317) Total amount of housework, new def, weekend 5.411 (5.253) 7.789 (6.034)

Food preparing (4,5) 0.481 (0.652) 1.109 (0.936) Cleaning (6,7) 0.122 (0.436) 0.679(1.116) Childcare and child transportation (8,24) 0.162 (0.580) 0.363 (0.909) Childcare, indirect 2.066 (3.387) 3.235 (4.016) Shopping, services, etc (35,36) 0.319 (0.729) 0.402 (0.727) Do-it-yourself work (9,10) 0.581 (1.483) 0.393 (1.081) Paid work, working weekdays 8.217 (3.972) 6.430 (3.635) Paid work, weekend days 1.414 (3.393) 1.035 (2.651) Indicator for housework both before and after paid work 0.151 (0.358) 0.334 (0.472) Average spell length of housework 0.411 (0.471) 0.511 (0.347) Average spell length of paid work 1.613 (1.668) 1.283 (1.239) Indicator for flexible work schedules 0.062 (0.241) 0.028 (0.165) Education, 9-10 years 0.321 (0.467) 0.261 (0.439) 0.402 (0.491) 0.348 (0.477) Education, 11-12 years 0.488 (0.500) 0.530 (0.499) 0.365 (0.482) 0.390 (0.488) Education, 13-14 years 0.042 (0.201) 0.050 (0.217) 0.046 (0.210) 0.050 (0.218) Education, 15-16 years 0.096 (0.295) 0.104 (0.305) 0.164 (0.371) 0.186 (0.389)

3

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I a. ft 3 ft.

s 3 ft 3 ft.

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Education, 17-18 years 0.054 (0.226) 0.056 (0.229) 0.022 (0.147) 0.026 (0.158) Years of experience 13.954 (7.271) 16.875 (7.622) 10.336 (5.913) 13.440 (6.473) Years of experience squared/100 2.475 (2.031) 3.428 (2.572) 1.418 (1.431) 2.225 (1.924) Controls for Copenhagen 0.306 (0.461) 0.306 (0.461) 0.366 (0.482) 0.375 (0.484) Public employment 0.230 (0.421) 0.220 (0.414) 0.467 (0.499) 0.475 (0.500) One child aged 0 - 9 years 0.120 (0.347) 0.151 (0.358) 0.197 (0.398) 0.187 (0.390) Two or more children aged 0 - 9 years 0.096 (0.295) 0.113(0.317) 0.125 (0.331) 0.125 (0.331) Married 0.711 (0.453) 0.760 (0.427) 0.768 (0.422) 0.793 (0.406) Age < 25 0.150(0.357) 0.062 (0.242) 0.130(0.337) 0.028 (0.165) 25 =s age < 35 0.268 (0.443) 0.249 (0.433) 0.296 (0.457) 0.273 (0.446) 35 =s age < 45 0.263 (0.441) 0.289 (0.454) 0.296 (0.457) 0.318 (0.466) 45 < age < 55 0.203 (0.403) 0.251 (0.434) 0.186 (0.389) 0.261 (0.439) 55 ^ age 0.116(0.320) 0.149 (0.356) 0.091 (0.288) 0.120 (0.326) No. of rooms per adult in household 4.220 (1.588) 4.233 (1.567) 4.300 (1.648) 4.424 (1.568) No. of children aged 0 - 2 years 0.098 (0.309) 0.123 (0.357) 0.137 (0.369) 0.132 (0.354) No of children aged 0 - 2 years squared 0.105 (0.370) 0.143 (0.491) 0.155 (0.489) 0.143 (0.435) One adult in household 0.142 (0.349) 0.154 (0.361) 0.137 (0.344) 0.148 (0.356) Two adults in household 0.616 (0.487) 0.657 (0.475) 0.674 (0.469) 0.659 (0.474) More than two adults in household 0.242 (0.429) 0.189 (0.392) 0.189 (0.392) 0.193 (0.395) Other income 0.021 (0.064) 0.028 (0.074) 0.014 (0.024) 0.019 (0.037) Spouses income if present 84.245 (75.569) 112.790(90.308) 171.106 (143.350) 206.840 (172.085) Indicator for spouse present 0.289 (0.453) 0.240 (0.427) 0.232 (0.422) 0.207 (0.406)

Number of observations 1116 1009 999 897

Selected years: 1987 and 1991.

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