Work-leisure balances are beneficial to society (Driver et al., 1991; Guest 2002; Krueger, 2009), as they improve employees’ well-being (Judge and Watanabe, 1993; Pouwels et al., 2008; Erdogan et al., 2012; Bannal and Tamakoshi, 2014) and enhance labor productivities (White et al, 2003; Beauregard and Henry, 2009; Oswad et al., 2015; Pencavel, 2015; Collewet and Sauermann, 2017). Previous surveys reported that workers were generally dissatisfied with their working hours (Best, 1980; Cogan, 1981; Moffit, 1983; Kahn and Lang, 1991; Zabel, 1993; Feather and Shaw, 1999; Merz, 2002; Bloemen, 2008; Reynolds and Aletraris, 2010). Policymakers should know how individuals value their leisure and how many hours they desire to work. In this paper we answer these questions in the context of a partial equilibrium job search model. The model assumes that job providers determine work schedules. Job seekers accept a job offer provided that the offered wage is high enough to compensate the cost induced by any undesirable working time. Having said that, workers can adjust their working hours to their desired level by searching for a new job or holding more than one job at the same time (multiple job holding). By extending the job search model (Burdett, 1978; Flinn and Heckman, 1982) to incorporate desired working hours and multiple jobholding, we identify how individuals value their leisure time and estimate empirically the gaps between the desired and the actual working hours. In short, this paper builds on and contributes to three strands of literature, including the job search model, multiple jobholding, and valuation of leisure time.
Studies on the value of leisure dated back to the neoclassical static labor supply model (Heckman, 1974; Blundell and MaCurdy, 1999). It assumes that job seekers have discretion to choose their working hours. Observed hours in the market reflect workers’ optimal choices and the market wages represent the value of leisure. Parameters revealing leisure preferences are identified from the observed wages and hours. This model was challenged empirically by a series of survey studies that found persistent work-leisure mismatches in the past decades. An early survey in 1978 found that 28% of the respondents in the U.S. preferred to work more and earn more, while 11% preferred to work less (Best, 1980). Feather and Shaw (1999) found that half of the respondents desired longer working hours, while another half desired fewer. Bloemen (2008) noticed that more than 30% of the workers were not satisfied with their working times. Reynolds and Aletraris (2010) observed that only 20% of the workers wanted the same hours. Work-leisure mismatches happened in other countries as well (Kahn and Lang, 1991; Merz, 2002; and Reynolds and Aletraris, 2010). For instance, 33% of Canadian workers reported working too short, while 17 % too long (Kahn and Lang, 1991). These survey data, though insightful, reported workers’ subjective assessments, which were vulnerable to measurement errors and the outcomes varied considerably by questionnaire designs and interviewees’ interpretations (Paxon and Sicherman, 1994; Kahn and Lang, 2001; Bloemen, 2008). The goal of this paper is to estimate work-leisure mismatches empirically based on a structural model.
To explain the discrepancies between the actual and desired working hours, static labor supply models incorporating minimum hours constraints were developed (Cogan, 1981; Moffit, 1982; Zabel, 1993). In these models, job seekers enter into the labor market only if their desired working hours are longer than their required minimum. Identifications of these Tobit-type models require exclusion restriction: different sets of covariates are used to explain the desired hours and the offered hours (Zabel, 1993). Alternative strategies reckoned on available information about multiple jobholding were introduced (Shishko and Rostker, 1976; Krishnan, 1990; Abdukadir, 1992; Paxon and Sichermen, 1996; Feather and Shaw, 1999). These models assume that people use the second job to adjust their working time when their first job does not provide enough wage income. Under this circumstance, observed hours for the second job coincide with the desired hours. Identifications are achieved by deriving the optimal hours for the second job and fitting them empirically with the observed hours. Although hours constraint is deemed as the only reason for multiple job holdings in these models, other reasons were suggested in the literature (Conway and Kimmel, 1998; Averett, 2001; Kimmel and Conway, 2001; Dickey et al., 2011). As an example, people hold the second job to obtain nonpencuniary benefits unprovided by the first job (e.g., enjoyment or insurance against unemployment risks). Kostyshyna and Lalé (2022) found that there was an increasing trend of multiple job holdings, two-thirds of which were caused by hours constraints and one-third were caused by nonpencuniary benefits. Models considering both reasons for multiple job holdings were discussed in Oaxaca and Renna (2006) and Hlouskova et al. (2017).
All models discussed above took the static neoclassical labor supply model as the point of departure. In this paper we apply the dynamic job search model that shares some similarities and differences with the static models. Similar to above, we assume that multiple job holding is a device to adjust working hours to the desired level, and we use the observed wages and hours of the second jobs to identify individual preference of leisure. However, workers make their optimal choice once and for all at the prevailing market wage in the static models. The optimal solution depends crucially on whether the first job is hours constrained or not (Conway and Kimmel, 1998). In the dynamic models, in contrast, workers have the option to perform job search continuously (Burdett, 1978; Flinn and Heckman, 1982). Wages and hours of the arriving new offers are not fixed but are drawn randomly from some distribution functions. This option has two implications. First, optimal hours are not constant values but change with the offered wage of the new jobs. Whether the new jobs are hours constrained or not is an endogenous outcome generated in the dynamic model, but not an assumption required to set up the model. Differences in the motivations for multiple jobholding play no role here. Second, the possibility of job search creates option value that improves workers’ utility. This option value increases the values of leisure in the dynamic model and the optimal working hours are shorter relative to the static models. Ignoring job searching behaviors understates the value of leisure and overstates the wage elasticities of labor supply.
There are some recent works analyzing multiple jobholding in the framework of job search models (Compton, 2019; Mancino and Mullins, 2019; Lalé, 2020). As far as we are aware, identifications of leisure value and desired leisure time in this setting have not been fully addressed along the lines that we set out below. Compton (2019) developed a general equilibrium model that permits multiple jobholding. Optimal working hours are not the subject of interest in his model, as working hours are fixed exogenously at 20 hours a week for part-time jobs and 40 hours a week for full-time jobs. The general equilibrium model introduced by Lalé (2020), in contrast, considers working hours as endogenous, which are chosen jointly by the job seekers and job providers to maximize their joint surplus. The resulting working times are generally different from the job seekers’ desired hours implied by the model's structural parameters. Comparisons of these two figures reveal the extent of work-leisure mismatches. The key structural parameter that measures leisure preference was calibrated to generate a predefined high (0.60) and low (0.30) values of the Frisch elasticity of labor supply. As a result, the estimated proportion of workers wanting more hours and fewer hours varied considerably by the chosen calibrated values. For instance, the proportion of male single-job holders wanting more hours increased from 8% to 26% when the assumed Frisch elasticity increased from its low to high value, while the proportion of female multiple-job holders wanting more hours increased from 20% to 48%. All structural parameters are estimated directly without calibration in our partial equilibrium model.
Different from the two general equilibrium job search models discussed above, job profiles are determined by the job providers and are not negotiated with the job seekers in the partial equilibrium models. The standard partial equilibrium models usually ignore working hours in the job profiles. Exceptions are Gørgens (2002) and Bloemen (2008). However, they did not consider multiple jobholding, which makes their models different from ours in two important ways. First, multiple job holdings are in all respects different from single job holdings. According to our results, multiple jobholders value their leisure 33% less than single jobholders, whereas their demand for leisure is 50% more elastic. Ignoring multiple jobs would underestimate the value of leisure by almost one-third. Second, the single-job models cannot exploit information from multiple jobs for identifications. Identifications are accomplished by assuming that there are no hours constraints in the single jobs, of which the observed hours are equal to the optimal hours. Work-leisure mismatches cannot be explained under this assumption. To solve this problem, Bloemen (2008) used self-reported desired hours available in his dataset as the second identification strategy. Results obtained from these two methods were pretty different. The estimated optimal hours ranged from 48 to 60 hours a week, while the self-reported desired hours ranged from 36 to 40 hours a week. Bloemen's results provide further insights on the (un)reliability of subjective data. He found that interviewees declared dissatisfied with their working hours only when the difference between their desired and actual hours was larger than some threshold values. The estimated threshold values had a mean of 16 hours a week with a standard deviation of 13 hours. We conclude that surveys’ results using subjective assessments quite likely underestimate the degree of work-leisure mismatches and the outcomes vary considerably by individual's interpretations. Closest to our paper is Mancino and Mullins (2019), who used partial equilibrium model to study multiple jobs. Their model is identified by the indirect inference method that necessitates more assumptions than ours. In their model, working hours are assumed to take two values only, i.e., 20 hours a week for part-time jobs and 40 hours for full-time jobs. Moreover, the offered wages for part-time jobs relative to full-time jobs are assumed to be a fixed ratio that applies to all individuals. Since working hours are fixed exogenously, identifying optimal working hours is out of scope of their model.
To our knowledge, our paper is the first to consider multiple jobholding in the partial equilibrium job search model that investigates the value of leisure and optimal working times. We believe that this makes a useful contribution to the literature concerning work-life balance. We applied our model to panel data collected from the National Longitudinal Surveys in the U.S. covering 1997 to 2015 for young adults aged 25 to 35 years. People in their early stages of adult life are more likely to take a second job (Wu et al., 2009; Dickey et al., 2011), so this data sample is appropriate for analyzing multiple jobs. We found evidence of remarkable work-leisure mismatches, both underwork and overwork. The estimated value of leisure is approximately three times the average hourly wage, and it drops by one-third when multiple jobs are taken. Workers are more willing to sacrifice their leisure time for obtaining multiple jobs than single jobs. Consistent with previous findings (Blundell, et al., 1998; Blundell and MaCurdy, 1999; Kudoh and Sasaki, 2011; Bils et al., 2012; Attanasio et al., 2018), age, education, and industry were the most important factors in determining leisure values, while gender and having kids play secondary roles. In particular, female, parents, older employees with more education who work in public or professional industries value leisure more than the others and are less elastic in their demand for leisure. Policies promoting more flexible work schedules (for reviews of similar policies see Lewis, 2003; Plantenga et al., 2009; Messenger, 2018) should facilitate desirable work-life balances.
The remainder of this paper is organized as follows: Section 2 introduces the theoretical model; Section 3 discusses the data and estimation methods; Section 4 provides the main results and extensions; the conclusion is presented in Section 5.
Central to our model is the optimal time allocation devoted to work and leisure. Available hours for each individual are 24 × 7 = 168 hours a week. Week is used as the time unit because the dataset contains employees’ weekly working hours but not daily working hours. We normalize the weekly time endowment to one, which is allocated as working hours
Individuals can hold more than one job simultaneously. When an individual holds one job only, it is a ‘single job spell’. When an individual holds more than one job at the same time, it is a ‘multiple job spell’. Let
Individuals derive their instantaneous utility
Let the dollar value per unit leisure time be
Since leisure time is complemented to working time, i.e.,
There are three job statuses in our model: single job spell, multiple job spell, and unemployment spell. Workers change their job status upon the arrival of stochastic events that arrive at a Poisson stream at different rates. To facilitate discussions, we need a system to define the job index.
In a single job spell workers hold one job, which is called job 1. The wage and working time associated with job 1 is defined as
We emphasize that jobs 1 and 2 are defined merely by chronological order, as job 2 is always accepted after job 1. This chronological order is essential in modeling the dynamic of changing job statuses. Our definitions of jobs 1 and 2 do not distinguish the differences between full-time and part-time jobs. For instance, workers can hold a part-time job in a single job spell (job 1) and switch to a multiple job spell by accepting another part-time second job (job 2) later. In fact, when we use 40 hours a week as the cutting line to distinguish a part-time and a full-time job, 20% of the multiple job spells in our dataset are holding two part-time jobs at the same time, while 27% of them are holding two full-time jobs simultaneously; and only 53% are holding one full-time and one part-time job.
Multiple job holders have two possible changes in job status. The first one is separating from job 1 with a separation rate of
Unemployed people may accept a job offer. To indicate that it is a change from an unemployment spell to a single job spell, we call it a ‘post-unemployment offer’. Since the unemployed people hold one job only after accepting this offer, we call it job 1 again. The wage and the working hours associated with this offer is denoted respectively as
We finish this section by introducing some notations. We define
In this section we discuss a variation of the standard partial equilibrium job search model (Burdett, 1978; Flinn and Heckman, 1982) that allows workers to hold multiple jobs. It extends the static multiple job model in Conway and Kimmel (1998) to a dynamic setting. The Bellman equations we discussed below are similar to those in Mancino and Mullins (2019). We let
The Bellman equation for single job holders is
The conditional wages
The conditional wages are functions depending on the current wage income
Equation (1) can be interpreted as follows: the expected present value for holding job 1 is discounted by the interest rate
When we derive the optimal working hours in Section 2.4, we need to differentiate this option value with respect to
The option value for searching a second job, i.e., the last item in (1), is derived similarly using Corollary 1(ii). Remarkably, the feasible set of the working time for the second job
The Bellman equation for multiple job holders is
It includes the wage income from both jobs
The Bellman equation for unemployed people is
The conditional reservation wage
This conditional reservation wage is a function depending on the offered wage
Tradeoffs between work and leisure are discussed in Corollaries 1 to 4 below. Their proofs are found in Appendix. To start with, we introduce additional notations for the sake of simplicity. We let
The (unconditional) acceptance probability for a second job offer and a post-unemployment job offer is respectively
We denote
Corollary 1(i) and (ii) state that a higher current wage increases the payoff of working at any given working hours. These corollaries ensure that there is a unique solution for
Corollary 1(i) leads to Corollary 1(iii) because a higher current wage implies a higher current expected value, which reduces the potential gain from searching another single job. Corollary 1(iv) is less obvious when workers are searching for a second job. On the one hand, the current wage
The optimal working time for a single job spell with a given wage
By taking the first order condition of
Interpretation of (14) is straightforward. The marginal gain of increasing working time in job 1 is the wage rate
The optimal working time for job 1, denoted as
Corollary 2(iv) states that the uncompensated wage elasticity of optimal leisure time (ɛ
Using
We have derived the optimal working time for a single job holder in the last section. Nevertheless, workers might not be able to find a single job that offers
By taking the first order condition of (19), the properties of
The marginal gain of increasing working hours in job 2 is the wage rate
The conditional reservation wages defined in (2) and (3) depend on the offered working hours in the following manners:
Corollary 4 implies that job seekers require a higher reservation wage to compensate the loss due to unattractive working hours, In particular, the conditional reservation wage has a U-shaped against the offered hours. Workers require the least reservation wage when the offered hours are equal to the optimal value. This result is consistent with the findings of Altonji and Paxson (1988), and Bloemen (2008).
We describes the dataset and the empirical models we utilize to estimate the structural parameters of the above-presented model in the next section.
We extracted data from the National Longitudinal Surveys managed by the U.S. Bureau of Labor Statistics. This survey followed a cohort of American youth born between 1980 and 1984. Respondents aged 12–16 years were first interviewed in 1997. Follow-up surveys were done yearly until 2011 and biyearly afterward. We considered observations with age ≥ 25, as teenage workers presumably have stronger job frictions that would affect their labor supply elasticity and value of leisure. Our sample includes 7,573 individuals, with the oldest respondent aged 35. The dataset contains information about respondents’ employment and unemployment spells over the sample period. Starting and ending calendar week are available for each of these spells. We construct the entire career history of each respondent using this information.
The way we managed multiple jobs needs further discussion. Suppose an individual works for job A from week 1 to week 6 while holding job B between weeks 4 and 10, this working spell is split into three parts. The first part is a single job spell for job A that takes place from weeks 1 to 4, and job A is defined as job 1. The second part is a multiple job spell that includes the spell for the current job A (job 1) and the spell for the second job B (job 2) between weeks 4 and 6. This multiple job spell ends with the termination of job A (job 1). The last spell is a single job spell between weeks 6 and 10 for job B, which is defined as job 1 as it is the only job held during this time interval.
24,675 working spells are constructed in our sample consequently. 20,959 (85%) of them are single job spells, and 3,716 (15%) are multiple job spells. Among the single job spells, 6,953 (33%) are terminated by unemployment, 4,938 (21%) are terminated by accepting a new single job, 2,820 (13%) are terminated by taking a second job, and 6,803 (32%) are right-censored at the last date of the interview in the sample. Among the multiple job spells, 2,052 (55%) are terminated by a separation in job 1 and 1,664 (45%) by a separation in job 2. As was mentioned in Section 2.2, 4% (151) of these multiple job spells are followed by another multiple job spells, as workers take another second job immediately after quitting either one of the multiple jobs. Such an extension will be discussed in Section 4.2.4. Lastly, there are 6,953 unemployment spells.
Information about wages, working hours, and individual characteristics for each working spell were updated in the dataset at each interview date. We collected this information when there is a change in job status. For example, when an individual accepts a job at calendar time
Table 1 provides descriptive statistics. Average working hours for single job spells are 36.6 per week, while that for multiple job spells are 62.1 per week. It is consistent with the findings of Kostyshyna and Lalé (2022), as they found that two-thirds of the multiple job spells are used to increase working hours. Average employment duration for single job spells (106 weeks) is longer than multiple job spells (34 weeks), suggesting that multiple job holdings are short-term in nature. Similar patterns were observed in Kimmel and Conway (2001). A recent study in Hahn, Hyatt, and Janicki (2021) found that job movers are more likely to increase their working hours than job stayers and the growth rates range from 0.5% to 1.4%. We have similar findings as the average hours for new single job offers (39.1 per week) are longer than the current single jobs (36.6 per week) by around 7%.
Descriptive statistics.
Real wage (cent) in current job | 452 | 261 | 1 | 1858 |
Real wage (cent) in new single job offer | 517 | 267 | 9 | 1636 |
Real wage (cent) in new second job offer | 434 | 239 | 39 | 1623 |
Real wage (cent) in post unemployment job offer | 409 | 212 | 67 | 1644 |
Weekly working hours in current job (one job) | 36.6 | 11.7 | 0 | 168 |
Weekly working hours in current jobs (two jobs) | 62.1 | 19.5 | 0 | 168 |
Weekly working hours in new single job | 39.1 | 8.77 | 1 | 168 |
Weekly working hours in new second job | 29.8 | 13.7 | 1 | 140 |
Weekly working hours in post unemployment job | 35.0 | 11.0 | 1 | 144 |
Weekly leisure hours | 127 | 16.0 | 0 | 168 |
Duration (week) for employment spell (one job) | 106 | 133 | 1 | 1346 |
Duration (week) for employment spell (two jobs) | 34.2 | 47.1 | 1 | 630 |
Duration (week) for unemployment spell | 49.5 | 65.6 | 1 | 631 |
Previous work experience (week) | 391 | 197 | 1 | 1646 |
Number of jobs held prior to change in job status | 7.25 | 4.67 | 1 | 36 |
Age | 29.2 | 3.13 | 25 | 35 |
Female (dummy) | 0.50 | 0.50 | 0 | 1 |
White (dummy) | 0.51 | 0.50 | 0 | 1 |
Black (dummy) | 0.28 | 0.45 | 0 | 1 |
Married (dummy) | 0.32 | 0.47 | 0 | 1 |
Parenthood (dummy) | 0.72 | 0.45 | 0 | 4 |
Net worth (thousand dollars) | 61 | 136 | −300 | 600 |
Non high school qualification or lower (dummy) | 0.15 | 0.35 | 0 | 1 |
Industry - public sector (dummy) | 0.22 | 0.41 | 0 | 1 |
Industry- professional services (dummy) | 0.21 | 0.41 | 0 | 1 |
Real interest rate (percent) | 1.80 | 1.90 | 0.50 | 6.02 |
The different components in the model are estimated separately. Let
The observed wage distribution is truncated at the conditional reservation wage
The estimated conditional minimum wages are consistent estimates of the actual conditional minimum wages when
Table 2 shows the estimated conditional reservation wages using some selected values of
Estimated conditional reservation wages (cent). The proportion of observed accepted wages
Estimated conditional reservation wages,
|
57 | 82 | 113 | 158 | 191 | 231 |
Pr( |
0.6 | 0.7 | 1.0 | 1.6 | 2.3 | 3.4 |
Acceptance probability of single job offers,
|
0.89 | 0.87 | 0.78 | 0.61 | 0.41 | 0.20 |
Acceptance probability of second job offers,
|
0.86 | 0.84 | 0.76 | 0.60 | 0.53 | 0.24 |
Acceptance probability of post-unemployment offers,
|
0.93 | 0.90 | 0.85 | 0.72 | 0.54 | 0.20 |
We use
After estimating the conditional reservation wage
We assume that
The computed value of
Let
Histograms for working hours in single job.
The job offer and separation rates are
The hazard rate of accepting a new offer for job
Single job holders have three possible changes in job status: accepting a new job, accepting a second job, and job separation. Since these three possible changes are competing risks, the probability of these three transitions at time
The only risk for unemployed individuals is accepting a new offer. Its sub-density function is
For multiple job holders, the two possible changes are separations from either job. A job separation at time
The probability of separation in job
The likelihood for all spells (indexed as
After
We consider the case of
The marginal effect is individual specific and has the same sign as
As discussed in the introduction, observed working hours
After α is estimated, we estimate the optimal working time for each single job spell
The estimated optimal hours
In this section we summarize the main results. Detailed reports are provided in supplements upon request.
Table 3 shows the summary statistics for the estimated conditional reservation wages. To facilitate comparisons, we report the observed offered wages as well. The estimated conditional reservation wages are highest in single job offers and lowest in post-unemployment offers, whereas the second job offers are somewhere in between. The observed offered wages have the same patterns. We reason that unemployed people have zero wage income and have a lower opportunity cost to accept new offers relative to working people who perform on-the-job search. Conditional reservation wages for second job offers are lower than single job offers as the former are a device to adjust the working hours to the optimal level.
Observed offered wages and estimated conditional reservation wages for different types of job, measured in cent
Mean | 517 | 434 | 408 | 218 | 154 | 125 |
Median | 446 | 355 | 338 | 206 | 139 | 124 |
S.D. | 268 | 239 | 212 | 121 | 113 | 53 |
Figure 2 provides the histograms of the estimated reservation wages and the observed offered wages. The observed offered wages are skewed to the right, arguably due to truncations by the reservation wages from below. Since different observations have different reservation wages, the truncation points are also different for different observations. We plot the fitted truncated models for using three truncation points: the mean, 10th percentile, and 90th percentile of the reservation wages. The models fit the data quite well except that the estimated densities are underestimated at the mode for the post-unemployment offers. To evaluate whether
Offered wages and reservation wages - Fitted truncated models and histograms.
Figure 3 reports the histograms for the categorized weekly working hours and the estimated mixed Poisson models. Compared with single jobs, the proportion of second jobs offering the standard 40 hours (
Fitted distributions for working time.
Table 4 summarizes the estimated job offer rates
Estimated job offer rates λ
Mean | 0.78 | 0.55 | 2.18 | 1.24 | 1.71 | 61.0 | 59.8 | 72.4 |
1 percentile | 0.18 | 0.10 | 1.16 | 0.14 | 0.40 | 5.58 | 7.02 | 21.6 |
99 percentile | 7.36 | 5.86 | 7.62 | 14.1 | 5.31 | 98.9 | 98.9 | 99.7 |
Results are reported in Table 5. The estimated average minimum value of leisure ($16.8) is around 3.8 times the observed average offered real wage ($4.45). We compare this figure with a few previous studies that estimated similar objects. Bockstael et al. (1987) and Larson and Shaikh (2001) estimated the shadow values of time using static structural models with hours constraints, which are 3.5 to 7 times the wage. Using a reduced form Tobit model with hours constraints, Feather and Shaw (1999) found that the reservation wages are around 106% to 112% of the accepted wages. Allowing for intertemporal substitution in a structural model, Phaneuf et al. (2000) and Lloyd-Smith et al. (2019) found that the values of time are around 90 percent of the wages. It is reminded that the above studies used different theoretical and empirical approaches, which make comparisons not straightforward. In particular, the Tobit model concerns the extensive margin (work or not work) rather than the intensive margin (number of working hours) of labor supply. It is well-known that the extensive margin is more elastic than the intensive margin (see, e.g., Keane and Rogerson, 2012). A higher elasticity of labor supply is accompanied by a lower value of leisure according to Corollary 2(iii), which plausibly explains why the estimated value in Feather and Shaw (1999) is relatively small. For similar reasons, models allowing for intertemporal substitutions tend to provide smaller values of leisure, as the intertemporal elasticities of labor supply are larger than the non-intertemporal elasticities. For instance, Chetty et al. (2011) found that the former are about 3 times larger than the latter. The implied value of leisure would then be 3 times smaller than our estimated values.
Wage rate
|
|
||||||||
---|---|---|---|---|---|---|---|---|---|
Mean | 445 | 1680 | 1.02 | 0.67 | −0.26 | −0.40 | 39.0 | 46.5 | −7.50 |
S.D. | 239 | 410 | 0.01 | 0.11 | 0.12 | 0.22 | 8.39 | 17.4 | 17.7 |
1 percentile | 126 | 1101 | 1.00 | 0.40 | −0.71 | −1.27 | 12 | 14.4 | −57.9 |
99 percentile | 1345 | 3152 | 1.08 | 0.92 | −0.08 | −0.10 | 65 | 97.1 | 27.7 |
The estimated values of
Agreeing with Corollary (2)(iv) and Corollary (3)(iii), the estimated wage elasticities of leisure time, ɛ
Leisure
Next, we discuss the estimated working hours mismatch, defined as
Histogram for the dierences between actual and optimal working hours, Δ
Table 6 reports the disaggregated figures in detail. For our benchmark model using
Estimated values of leisure
|
|
|||||||||
---|---|---|---|---|---|---|---|---|---|---|
|
|
|||||||||
1595 | 46.6 | −7.6 | 0.36 | 41.7 | 32.4 | 9.3 | 37.5 | 54.7 | −17.2 | |
1655 | 46.6 | −7.6 | 0.36 | 41.7 | 32.9 | 8.8 | 37.5 | 54.6 | −17.1 | |
1655 | 46.8 | −7.8 | 0.36 | 41.7 | 32.6 | 9.1 | 37.5 | 54.7 | −17.2 | |
1680 | 46.5 | −7.5 | 0.37 | 41.5 | 33.1 | 8.5 | 37.5 | 54.4 | −16.9 | |
1681 | 47.5 | −8.7 | 0.34 | 41.2 | 33.5 | 7.8 | 37.5 | 54.8 | −17.2 | |
1693 | 48.0 | −9.2 | 0.34 | 41.1 | 33.8 | 7.3 | 37.5 | 55.2 | −17.7 |
Table 7 shows the estimated
Estimated parameter for the value of leisure (measured in
Constant | −857** | −2594 | −30665 | −793 |
Previous work experience (weeks) | 0.06 | 0.19 | 0.06 | 2.31 |
Number of previous jobs held | −8.90** | −27.0 | −318 | −8.23 |
Age (years) | 10.5** | 31.8 | 9.69 | 375 |
Female (dummy) | −27.4* | −83.1 | −980 | −25.3 |
White (dummy) | 17.7 | 53.6 | 16.3 | 632 |
Black (dummy) | −69.5** | −210 | −2486 | −64.3 |
Married (dummy) | 4.76 | 14.4 | 4.40 | 170 |
Parenthood (dummy) | −17.2* | −52.2 | −615 | −15.9 |
Net worth (thousands dollar) | 0.30** | 0.92 | 0.28 | 10.8 |
Non high school qualification or lower (dummy) | −146** | −440 | −5202 | −134 |
Industry - public sector (dummy) | 115** | 348 | 106 | 4124 |
Industry- professional services (dummy) | 63.2** | 191 | 58.4 | 2258 |
Table 7 shows that age and net worth have important roles in the value of leisure. When age increases from 25 to 35, the value of leisure increases by $3.20 (=$0.318 × 10) on average, which is approximately 20% of the average value of
Education has the strongest effect among the dummy variables: workers without high school and degree qualifications have a lower value of leisure by $4.40 (26%). Types of industry also matter: workers in the public sector and professional services have a higher value of leisure by $3.48 (20.7%) and $1.91 (11.3%), respectively, than other industries. These results agree with Bils et al. (2012) as workers having different kinds of human capital value their leisure differently. Also, Kudoh and Sasaki (2011) found that industries requiring different levels of professional training have different search frictions that affect the costs of working. Generally speaking, workers who have better education and/or receive professional training have a higher opportunity cost for leisure, which makes them less elastic in labor supply.
Females value leisure $0.83 (4.9 %) less than males meaning that females are more elastic in labor supply. It is intuitive as female labors are usually regarded as more substitutable for domestic work than male labors (e.g., Blundell and MaCurdy, 1999), although female elasticities dropped by half over the two decades (Heim, 2007). Workers having at least one child value their leisure $0.52 (3.1%) less. It is in some way in line with Blundell et al. (1998) who found that the elasticity of labor supply for parents is the largest when their child is aged below four years old, as the young parents in our sample arguably have relatively small kids. The remaining results in Table 7 show that Black workers have lower value of leisure by $2.10 (12.5%) than white worker and Hispanics. The effect of previous job turnovers is weak, as the value of leisure drops by $0.27 (1.6%) only when workers have one more previous job. The effects of previous employment duration and marital status are insignificant.
We introduce some new variables in this section. The weekly time endowment is denoted as
Estimated value of leisure
|
|
||||||||
---|---|---|---|---|---|---|---|---|---|
|
1680 | −0.26 | −0.40 | 39.0 | 46.5 | 8.5 | −16.9 | ||
|
1508 | −0.28 | −0.51 | 39.0 | 42.1 | 9.0 | −13.7 | ||
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1485 | −0.32 | −0.59 | 39.0 | 38.3 | 0.6 | 0.53 | 9.9 | −10.1 |
We consider a simple case, in which
This extension would affect the empirical results. The reason is explained in the following. Our dataset provides us with the individuals’ working hours only, but not their leisure time. Leisure time is computed as the residual hours out of working, i.e.,
We have to fix
Consistent with our predictions, leisure is more elastic (changing from −0.26 to −0.32 for single job holdings and from −0.40 to −0.59 for multiple job holdings) while the value of leisure drops (from $16.8 to $14.9), when people have a smaller time endowment
We examine to what extent a policy enhancing working hours flexibility would alleviate working hours mismatches in this section. Policies promoting flexible hours have become popular in the last decades in European countries (see Lewis, 2003; Plantenga, 2009; Messenger, 2018, for reviews). These policies give employees the right to bargain with their employers so that they can have more flexibility in determining their working schedules. It was found that a quarter of workers had access to flexible schedules across 30 European countries by 2015 (Chung and Van der Lippe, 2020). Females with family responsibility were most benefited by these policies (Song and Gao, 2020). There are evidence that these policies increase workers’ leisure satisfaction and reduce their turnover intention (Kröll and Nüesch, 2019). A survey regarding the increasing practices of flexible work arrangements in the U.S. is found in Katz and Krueger (2019).
We start with a closer look on the nature of mismatches by studying the differences between actual and optimal hours in Figure 5. In our model hours distribution is exogenously determined by the employees and is featured by spikes at certain fixed value of hours (see the left panel of Figure 5). Most noticeably, the spike at the standard 40 hours occupies around 35% of the entire distribution. The desired hours in contrast are smoothly distributed. The middle panel of Figure 5 shows the distributions for the overworked group. It is apparent that most of the overworked workers prefer to work shorter than 40 hours while a lot of them have to work for 40 hours or longer. For the underworked group in the right panel of Figure 5, most of them prefer to work longer than 40 hours while a lot of them have to work for 40 hours or less. Mismatches occur as workers do not have enough choices to match their desired hours.
Histograms for the preferred hours and actual hours, original data.
It is natural to ask to what extent the problem of hours mismatches is alleviated when the offered hours have more variety. We introduce flexibility in the offered hours distribution by adding random noises to the working hours. The random noises have a normal distribution with zero mean and we consider different values of the standard deviation defined as
Histograms for the preferred hours and actual hours, simulated data.
We report the numerical results in Table 9 using different values of
Actual working hours
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39.0 | 46.5 | −7.5 | 0.37 | 41.5 | 33.1 | 8.5 | 37.5 | 54.4 | −16.9 | |
39.8 | 46.5 | −7.1 | 0.37 | 40.5 | 33.3 | 7.2 | 38.8 | 54.3 | −15.6 | |
39.8 | 46.5 | −6.7 | 0.38 | 40.5 | 34.0 | 6.4 | 39.4 | 54.0 | −14.5 | |
40.7 | 46.5 | −5.8 | 0.38 | 42.8 | 36.2 | 6.6 | 39.3 | 52.8 | −13.5 |
From the policy's point of view, one would want to know the average size of the noises added to the working hours distribution. It is found that the random noises have an average absolute size of 6.5 hours when
We consider an extension where workers can hold more than two jobs in multiple job spells. We fix
Equation (6) is revised as
The conditional reservation wage
Comparing (6) with (39), the added item is the option value created by the search for job 3. Workers holding three jobs have three possible changes in their job status, i.e., separate from job 1 and hold jobs 2 and 3, or separate from job 2 and hold jobs 1 and 3, or separate from job 3 and hold jobs 1 and 2. The Bellman equation for a triple job spell is
Since
It is possible that multiple job holders take a second job by the same time they quit one of the two existing jobs. The Bellman equation for multiple job holders in (6) would be extended to
Let
We discuss the biases created in our estimates when multiple job searching is ignored. In the framework of our model, the effect of ignoring multiple job holdings can be replicated by fixing the job offer rate for the second job as zero, i.e.,
We consider the situation where unobserved heterogeneity
By controlling
Work-leisure balances are advantageous for individuals and society as a whole. This paper used a partial equilibrium job search model to explain the optimal work-leisure tradeoffs for single-job holders and multiple-jobs holders. Using a structural model, we derived several empirically testable implications regarding job search behaviors for both single and multiple jobs. We suggested identification strategies to estimate how individual characteristics determine the perceived values of leisure. By comparing the empirically computed optimal working hours with the actual hours, we estimated the patterns of work-leisure mismatch for single job holders.
Our theoretical model has several implications. First, optimal working hours that maximize individuals’ utility are unique. Workers accept jobs with unattractive hours provided that the wages are high enough to compensate for the loss of utility. Second, possibilities of job search create option values. Chances for taking multiple jobs increase the value of leisure for single-job holders. Models ignoring multiple jobs understate the value of leisure and overstate the optimal leisure time. Third, multiple job holders have smaller values of leisure and are more elastic in the demand of leisure than single job holders. Workers are more willing to sacrifice their leisure time to accept multiple jobs than a single job. Fourth, when workers are committed to more non-substitutable activities (e.g., childcare), their value for leisure would be smaller and their demand for leisure would be more elastic due to a smaller endowment for allocatable time.
We estimated our model empirically using a panel dataset containing young adults’ work history. Remarkable work-leisure mismatches were found, both overworked and underworked. 63% of the observations worked shorter than desired by an average of 16.9 hours a week, while the remaining 37% worked on average 8.5 hours longer than desired. Our results enriched survey studies based on workers’ subjective assessments on their optimal hours, which tended to understate the degree of work-leisure mismatch. The estimated minimum dollar value of leisure was about four times the average hourly real wage. The value of leisure dropped by one-third on average when multiple jobs were held. When workers required 6 hours per day (or 42 hours per week) in non-substitutable activities, the value of leisure dropped from $16.8 to $14.9, while the demand for leisure increased by 25% to 50%.
Age, education, and industry are the most important factors in determining leisure values, while gender and having kids play secondary roles. In particular, female, parents, older employees with more education who work in public or professional industries value leisure more than the others and are less elastic in their demand for leisure.
We found in a counterfactual experiment that policies promoting flexible working hours (e.g., allowing employees to adjust the working hours by ± 1.3 hours per day) alleviate the problem of working hours mismatches, as the discrepancy between the actual and desired hours would be reduced by one-fourth from 7.5 hours a week to 5.8 hours on average.