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Nobody to play with?The implications of leisure coordination

Stephen P. Jenkins ISER, University of Essex, UK

Email: stephenj@essex.ac.uk

Lars OsbergEconomics Department, Dalhousie University, Canada

Email: osberg@dal.ca

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The paper in one slide

• The core hypothesis: – Each individual’s time use choices are contingent on

the time use choices of others– The utility derived from leisure time often benefits

from the presence of companionable others (an externality argument)

• The paper presents:– A model of time use, and– Shows that it is consistent with the behaviour of British

working couples in the 1990s

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The core hypothesis• What people do in their non-work time …

– often involves other people– often distinctly more pleasurable if done with others– often impossible without others

• Heterogeneity of leisure tastes means that individuals face the problem of locating Suitable Leisure Companions – ‘somebody to play with’ – and of scheduling simultaneous free time

when paid work absorbs more of other people’s time, each person will find their own leisure time scheduling & matching problem more difficult to solve, – i.e. own leisure hours will be of less utility

externality to individual labour supply choices, implying possibility of multiple, sometimes Pareto-inferior, labour market equilibria

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Relationship to literature• Cf. standard household labour supply model

(‘leisure time of husbands and wives as complementary goods’)

• Corneo (2001) re private & social leisure (TV); Weiss (1996) re work hour coordination; etc.

• Evidence of spousal synchronisation of work schedules (Hallberg, 2003, S; Hamermesh, 2002, USA; Sullivan, 1996, GB; van Velzen, 2001, NL)

• This paper: Model + Evidence about (1) spousal work synchronisation, and (2) the role of others outside the household (measures of Suitable Leisure Companion availability) in determining propensities for associative leisure activities

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Outline• Theoretical model illustrating idea of interdependencies of time

use choices within and outside the household (Section 2)

• Overview of British Household Panel Survey data and key variables (Section 3)

• Preliminary evidence of externalities in likelihood of associational activity – social groups and sports clubs (Section 4)

• Synchronisation and scheduling of spousal work time – regressions (Section 5)

• Probability of engagement in associative leisure activities, and dependence of that of what others do – regressions (Section 6)

• Some implications: the welfare effects of longer work hours

(Section 7)

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The conventional model of time useConventional unitary household model for couple:

Max U = u(C, Lm, Lf)

subject to Hm + Lm = Hf + Lf = T

C wmHm + wfHf

C = household goods consumption (assume there is a sharing rule);

Lm, Lf = non-work time for husband and wife;

Hm, Hf = work hours;

wm, wf = hourly wages;

T = total time available

Optimal choice of

work hours for

husband (or wife):

MUHMUL

H*

u

U

0 T

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Our model of time use choice• Time use options: work (H hours), or non-work time spent either alone (A

hours) or in social leisure (S hours). [Household production time ignored.] • To enjoy social leisure, each individual must arrange a leisure match with some

other individual (or group of individuals) from among the list of possible contacts that they have at the start of each period.

• Each period, individuals first must commit to specific duration & timing of work hours H, and then after that they arrange their social lifeH household money income utility from material consumption (via sharing rule)

• Ex ante, utility from social life is uncertain:– search for Suitable Leisure Companions involves uncertainty, since some desired

matches may not be feasible.

• Time spent alone not working, A, is the residual after work and social

commitments are honoured. U = u(C, Am, Af, Sm0, Sm1, …, Smn, Sf0, Sf1, …, Sfn)

where i indexes possible Suitable Leisure Companions; social leisure time each partner spends with each other indexed by 0 (hence Sm0 = Sf0). Other social matches subscripted by 1,…,n and 1,…,n where n and n are the number of realized social leisure matches for each partner.

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Solving the model of time use choice• Arranging one’s social life cannot be done unilaterally

– It involves a discrete matching process – It is constrained by the social contacts available to each person, and by

the availability of other people. # social contacts/couple = km + kf .

• Expected utility of specific social leisure match = pi u(Si)

– i indexes each potential SLC, pi is Pr(social match with i) and u(Si) is utility associated with that match.

• Unitary couples maximise expected utility:max (U) = u(Cf) + u(Cm) + pi0[um(S0) + uf(S0)]

+ ikm+kf { pimum(Sim) + pifuf(Sif)}

+ uAm[T – Hf – pi0uf(Si0) – ikm+kf pimum(Sim) ]

+ uAf [T – Hm – pi0um(Si0) – ikm+kf pifuf(Sif) ]

where uAm and uAf are the utilities of non-work time spent alone.

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Model equilibrium illustrated (for one of the spouses in a couple)

H* T

A* S*

u*

U

MUH

MUA

MUS

a

r

0

Equilibrium requires work hours H* such that u* = MUH*, and A*, S* such that MUA* = MUS* = MUH*.

MUS* , MUH* are ‘expected’ marginal utilities: uncertainty ex ante via pi

= Pr(social match with i)

pi is negatively associated with own work hours and with non-overlapping work hours of potential SLC i.

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The implications of longer (or less coordinated) work hours by others

MUH

MUA

MUS

MUS ‘

u*

H* H**

A*A**

0 T

Others’ work hours pi piu(Si) MUS

Given equilibrium condition, H* to H**, and S* to S**.

Effect on A* ambiguous.

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Further implications of the model• Increase in full income: may increase total leisure (A+S) if normal good,

but how solo leisure (A) and social leisure (S) each change is not clear• Increase in own hourly wage: effect on work hours H depends on

combination of income and substitution effects; effect on A and S also not determined (without extra assumptions)

• Overall, principal novelty = idea that when other persons increase their paid work hours, Pr(feasible and desirable leisure match) falls, which decreases own utility of non-work time. Also, …

– for given total hours of labour supply by each person, greater mismatch between the timing of work hours of work will decrease Pr(social leisure time match), lowering utility of non-work time.

– by reducing the utility of non-work time, both effects increase one’s own desired hours of paid work.

• Implication: the desired supply of labour of each person will be conditional on their expectations of the labour supply decisions of others (an externality hypothesis). Similarly, …

• Implication: own associative activity propensities depend on activities of others (SLC availability) empirical work

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Interdependencies between spouses in time use

• Spouse is a primary candidate for a Suitable Leisure Companion

• Conventional models of family emphasize interdependencies via household budget constraint … but …

• Spouses actually want to spend time together?

• Several theories suggest that the types of non-work activities by spouses is likely to be similar, but …

• Our point: conditional on preferences for type of activity and total work and leisure time, spouses derive utility from spending non-work time together. – Hence we expect to observe a correlation of the timing of working hours,

for any given level of working hours

empirical work on spousal synchronisation of work times

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Data: the BHPS• British Household Panel Survey, waves 1–9

(1991–9). Has time use variables, and can use panel to control for individual effects, large and representative samples (cf. TUS)

• Sample of working couples– each spouse gave full interview, co-resident

spouse, married or cohabiting, both aged 18–59, both in paid employment (neither self-employed)

– Unbalanced panel of c. 10,000 couple-years from c. 2,500 couples

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Key variables• Work hours: usual hours per week (including overtime)

• Hourly wage rate: usual gross pay usual hours

• Scheduling of work hours: ‘At what time of the day do you usually work? Is it: 1 mornings only; 2 afternoons only; 3 during the day; 4 evenings only; 5 at night; 6 both lunch/evenings; 7 other times/day; 8 rotating shifts; 9 varies/no pattern; 10 other; or 11 daytimes & evenings’.– Spousal synchronisation of work hours if variable code is same– Prevalence of ‘unsocial hours’ in region (pooled averages, codes 8&9)

• Associative activities (social leisure): whether reported activity in a (a) sports club, or (b) social group or working men’s club. (Most prevalent of 13 activities asked about.)– also used to derive measures of SLC availability: average activity rates

by age group (18–30, 31–50, 51–59) and region [pooling data across waves] Reported ‘membership’ gave similar results.

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Control variables in regressions• Age• Number of children aged less than 16 years, and

whether youngest child aged less than 6 years• Whether cohabiting rather than married• Educational qualifications (five categories)• Survey year (dummy variables)• Labour demand structure and level: prevalence of

unsocial hours, industry of main job (10 major SIC groups), and the unemployment rate in the local labour market (‘travel-to-work-area’); firm size (# employees)

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Preliminary evidence on extra-household interdependence in associative activity

• Positive externality hypothesis: each person’s likelihood of participating in associational life depends on what others in their local area have chosen to do – one cannot join a club that does not exist for lack of membership; and the

more members these organizations have, the more attractive they are to prospective members

expect that regions where a larger fraction of people participate in associational life will be regions where clubs and associations are more easily available, and more attractive to others

• Examine correlations between average rates by region across different age groups: – Figure 2: association between prevalence for middle-aged and youth of

activity in (a) sports club and (b) social group or working men’s club

• Positive correlation between associative activity of one cohort and another in each chart, i.e consistent with our externality hypothesis.

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Figure 2. Activity rates (regional averages)(mean rate among 18–30 year-olds versus mean rate among 31–50 year olds)

(a) Active in a sports club (b) Active in a social group or working men’s club

InnerLon

OuterLon

restSE

SW

EAEM

WMconurb

restWM

GterMan

Mersey side

restNW

S Yorks

W Yorks

restYo&Hum

Ty ne&Wear

restNorth

Wales

Scotland

.04

.06

.08

.1.1

2.1

4M

ean

rate

by

regi

on, 1

8-30

yea

r ol

ds

0 .05 .1 .15 .2Mean rate by region, 31-50 year olds

InnerLon

OuterLon restSE

SW

EA

EMWMconurb

restWM

GterMan

Mersey side

restNW

S YorksW Yorks

restYo&Hum

Ty ne&Wear restNorthWales

Scotland

.15

.2.2

5.3

.35

Mea

n ra

te b

y re

gion

, 18-

30 y

ear

olds

.15 .2 .25Mean rate by region, 31-50 year olds

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Synchronisation of usual daily working time • In 51% of couples, spouses usually worked at the same time

of the day

• Greater prevalence than would be expected from a random match of a husband’s and a wife’s work times (Pearson test of independence: p-value = 0.0000)

• Greater prevalence than would be expected due to the inherent constraints on daily time-use imposed by the regularity of office hours, school hours, and the hours of darkness, etc.– Create ‘pseudo-couples’ by matching otherwise-similar single men

to married men, and otherwise-similar single women to married women (1:1 propensity score matching on age, education, work hours, kids): only 46% of pseudo-couples work at same time of day

– Match every husband with every wife: synch. rate was 46% too!

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More likely if husband hours not ‘unsocial’

NB good correspondencein ‘% in cat’ for real andpseudo-couples: good matching

Real couples Pseudo-couples% withsynch.worktimes

(row %)(1)

% incat.

(col %)(2)

% withsynch.worktimes

(row %)(3)

% incat.

(col%)(4)

All working couples 51.2 100.0 46.4 100.0Usual time of day for paidwork (husband)Mornings only 25.8 1.4 6.9 2.5Afternoons only 0 0.3 0 0.2During the day 67.1 71.8 62.5 72.0Evenings only 4.3 0.5 1.5 0.5At night 5.4 2.1 2.2 2.5Bothlunchtimes/evenings

23.8 0.2 0 0.4

Other times of theday

0 0.3 0 0.3

Rotating shifts 9.2 13.4 7.3 11.4Varies or no pattern 9.6 4.7 2.0 5.5Other 13.5 4.9 5.1 4.5Daytimes andevenings

16.6 0.3 0 0.3

How doessynchronisationvary with husband’swork time?

Table 1 (part)

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Synchronisation less likely, the more kidsThe more kids a couple has, the more likely spouses are to working at different times to save child care costs, or to give each parent quality time with kids:

Real couples Pseudo-couples% withsynch.worktimes

(row %)(1)

% incat.

(col%)(2)

% withsynch.worktimes

(row %)(3)

% incat.

(col%)(4)

All working couples 51.2 100.0 46.4 100.0Number of children aged <16 years in household

None 60.0 51.9 52.2 52.5 1 48.3 21.2 45.1 21.1 2 38.8 20.5 36.6 20.4 3 28.8 5.4 34.6 5.3 4 26.2 0.9 29.7 0.8

Table 1 (part)

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Pr(spousal synchronisation of usual work hours)

• Random effects probit regressions• Explanatory variables include (following previous

literature):– wage rates of each spouse

– work hours of each spouse

– whether husband works during the day

– regional prevalence of unsocial hours

– control variables cited earlier

• Table 2: separate models for childless couples and parents

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Table 2. The probability that a husband and wife work at same of the day, by whether household has children

Regressor No children aged < 16

Children aged < 16

MargEff |t| MargEff |t|

Husband’s wage rate –0.004 (1.00) 0.009 (2.16) Wife’s wage rate 0.033 (6.30) 0.015 (4.74) Husband’s work hours –0.001 (0.79) 0.000 (0.02) Wife’s work hours 0.010 (7.16) 0.019 (13.8) Husband worked during the day 0.895 (24.7) 0.612 (21.6) Proportion in region working

unsocial hours

Men 0.798 (0.93) 0.144 (0.17) Women –0.978 (0.92) –1.228 (1.02) Youngest child aged < 6 –0.012 (3.29) Number of children –0.067 (3.20) Mean of dep. var. 0.61 0.42 Log-likelihood –1,797 –1,698

Random effects probit estimates. Marginal effects evaluated at the mean values of the regressors. Other control variables also included.

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Pr(spousal synchronisation of usual work hours)

• the impacts of each spouse’s wage rate, holding each spouse’s work hours constant: two opposing influences (Hamermesh 2002):– Higher wages ceteris paribus act like an increase in full earnings, so

expect the income effect to raise the work time synchronisation probability (the synchronisation-as-normal-good argument), versus

– Husbands and wives who wish to play together may be willing to accept a wage penalty in order to do so. Or, in order to induce husbands and wives to work at different times, employers need to pay them more (compensating differential argument)

• Evidence of synchronisation-as-normal-good for wives but only for husbands with children (insig. for childless husbands)

• Strong positive effect of husband working during day

• Regional prevalence of unsocial hours not stat. signif.

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Interdependencies in associative activities? • 4-variate probit regression estimates of a couple’s

activity propensities:Pr(husband active in social group or working men’s club, wife active in social group or working men’s club, husband active in sports club, wife active in sports club)

• Separate regressions by age group of husband: 18–30, 31–50, 51–59 years (Tables 3, 4, 5)

• Key measure of extra-household SLC availability: mean regional activity rates for other age groups

• Spouse-as-SLC effects picked up by cross-equation correlations

• Control variables cited earlier also in regressions

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Table 4. The probabilities of associative activity for husbands and wives (husbands aged 31–50)

Regressor Pr(active in a social group or working men’s club)

Pr(active in a sports club)

Husband (1)

Wife (2)

Husband (3)

Wife (4)

Coeff. |t| Coeff. |t| Coeff. |t| Coeff. |t|

Mean regional social group activity rate

18–30 years 5.221 (3.40) 2.368 (1.41) 51–59 years 1.458 (1.81) 0.137 (0.13) Mean regional sports club activity rate

18–30 years 0.847 (0.79) 1.907 (1.84) 51–59 years –0.927 (0.77) 2.222 (1.67) Cross-equation correlations

21 0.581 (15.44) 31 0.197 (5.04) 41 0.057 (1.29) 32 0.068 (1.46) 42 0.126 (2.47) 43 0.482 (14.91) Mean of dep. var. 0.16 0.08 0.30 0.16 Log pseudo-Likel. –6,305 N (couple-waves) 3,893

Multivariate probit estimates, derived by simulated maximum likelihood (number of random draws = 75), with standard errors adjusted to account for repeated observations per couple across waves. Each regression also included the controls listed in the note to Table 3.

Example

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Interdependencies in associative activities? Main results from Tables 3–6

• Some evidence of cross-cohort externalities in activity propensities (i.e. supportive of our core hypothesis).– E.g. young husbands were more likely to be active in a social club if

there was a higher rate of activity among middle-aged husbands, and the middle-aged husbands were also more likely to be active if there was more activity among the young husbands or old ones

– but no similar results for husband’s sports club activity. – Wives’ results differ: supportive evidence for the externality hypothesis

concerns sports club activity (and only for wives with husbands aged 31–50)

• Regressions for single householders aged 31–50 also showed some partial support for our externality hypothesis (not shown)

• Cross-equation correlation structure consistent with core hypothesis (but identification issue! – assortative mating)

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So what (if true)? The welfare effects of economy-wide increases in

work hours

• [Background: 1980–2000, average work hours higher in USA than Europe, and difference grew]

• If externality exists, then when average working time rises, aggregate well-being falls by more than the cost of foregone wages

• Model suggests multiple equilibria in labour supply, some with lower aggregate utility. Maybe Americans work more hours partly because they’re more likely to have nobody to play with, and are worse off as result?

• Model draws an explicit link between rising work hours and decreasing social contacts. If ‘social capital’ related to latter (Putnam and others), then additional costs of high-work/low-social-contact equilibrium?

Figure 1

Annual Number of Hours Worked per Person Aged 15-64 1

600

800

1000

1200

1400

1600

1800

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

year

annual h

ours Canada

France

Germany

Sweden

United Kingdom

United States

1 = Average hours worked per employed person *(Employment / pop. age 15-64) Canada and France 1999, 2000 and UK, US 2000 are extrapolations.Sources: hours of work: Key Indicators of the Labour Market 2001-2002, International Labour Office population and employment data: OECD Health Data 98 CDROM, "A Comparative Analysis of 29 Countries".