1. 1 Nobody to play with? The implications of leisure coordination Stephen P. Jenkins ISER, University of Essex, UK Email: stephenj@essex.ac.uk Lars Osberg Economics Department, Dalhousie University, Canada Email: osberg@dal.ca

2. 2 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

3. 3 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

4. 4 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

5. 5 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)

6. 6 The conventional model of time use Conventional unitary household model for couple: Max U = u(C, L m, L f ) subject to H m + L m = H f + L f = T C  w m H m + w f H f C = household goods consumption (assume there is a sharing rule); L m, L f = non-work time for husband and wife; H m, H f = work hours; w m, w f = hourly wages; T = total time available Optimal choice of work hours for husband (or wife):

7. 7 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 life H  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, A m, A f, S m0, S m1, …, S mn, S f0, S f1, …, S fn ) where i indexes possible Suitable Leisure Companions; social leisure time each partner spends with each other indexed by 0 (hence S m0 = S f0 ). 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.

8. 8 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 = k m + k f. Expected utility of specific social leisure match = p i u(S i ) –i indexes each potential SLC, p i is Pr(social match with i) and u(S i ) is utility associated with that match. Unitary couples maximise expected utility: max  (U) = u(C f ) + u(C m ) + p i0 [u m (S 0 ) + u f (S 0 )] +  i  km+kf { p im u m (S im ) + p if u f (S if )} + u Am [T – H f – p i0 u f (S i0 ) –  i  km+kf p im u m (S im ) ] + u Af [T – H m – p i0 u m (S i0 ) –  i  km+kf p if u f (S if ) ] where u Am and u Af are the utilities of non-work time spent alone.

9. 9 Model equilibrium illustrated (for one of the spouses in a couple) Equilibrium requires work hours H* such that u* = MU H*, and A*, S* such that MU A* = MU S* = MU H*. MU S*, MU H* are ‘expected’ marginal utilities: uncertainty ex ante via p i = Pr(social match with i) p i is negatively associated with own work hours and with non-overlapping work hours of potential SLC i.

10. 10 The implications of longer (or less coordinated) work hours by others Others’ work hours   p i   p i u(S i )   MU S  Given equilibrium condition, H*  to H**, and S*  to S**. Effect on A* ambiguous.

11. 11 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

12. 12 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

13. 13 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

14. 14 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.

15. 15 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)

16. 16 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.

17. 17 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

18. 18 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!

19. 19 More likely if husband hours not ‘unsocial’ NB good correspondence in ‘% in cat’ for real and pseudo-couples: good matching How does synchronisation vary with husband’s work time? Table 1 (part)

20. 20 Synchronisation less likely, the more kids The 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: Table 1 (part)

21. 21 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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23. 23 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.

24. 24 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

25. 25 Example

26. 26 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)

27. 27 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?