Sleep and the Allocation of Time
Author(s): Jeff E. Biddle and Daniel S. Hamermesh
Source: Journal of Political Economy, Vol. 98, No. 5, Part 1 (Oct., 1990), pp. 922-943
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/2937618
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Sleep and the Allocation of Time
Jeff E. Biddle
Michigan State University
Daniel S. Hamermesh
Michigan State University and National Bureau of Economic Research
Using aggregated data for 12 countries, a cross section of microeconomic
data, and a panel of households, we demonstrate that increases
in time in the labor market reduce sleep. Our theory of the
demand for sleep differs from standard models of time use by assuming
that sleep affects wages by affecting labor market productivity.
Estimates of a system of demand equations demonstrate that
higher wage rates reduce sleep time among men but increase their
waking nonmarket time by an equal amount. Among women the
wage effect on sleep is negative but very small.
The study of sleep is wonder. [BURGESS 1982, p. 95]
I. Introduction
Sleeping occupies our scarce time more than any other single activity.
Economists have devoted immense effort to studying how consumers
allocate time but have almost entirely ignored the empirical study of
choices about time spent sleeping. 1 For example, Kooreman and KapHelpful
comments on previous drafts were received from two referees, John Owen,
Frank Stafford, and participants in seminars at McMaster, Michigan, Michigan State,
Princeton, Kentucky, and Pittsburgh. Neil Bjorksten provided excellent research assistance.
All the data files used in this project are available on diskette from the authors.
' Some humorous notes (e.g., Hoffman 1977) did examine sleep from one economic
perspective without developing or testing any predictions. Mullahy (1989) examines
alternative econometric techniques using data from a telephone survey of respondents'
previous night's sleep.
Journal of Political Economy, 1990, vol. 98, no. 5, pt. 1]
? 1990 by The University of Chicago. All rights reserved. 0022-3808/90/9805-0002$01.50
922
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ALLOCATION OF TIME 923
teyn (1987) estimate a demand system for seven categories of leisure
time use. Sleep is mentioned only once in this study, when it is noted
that time spent sleeping is grouped with various waking activities in a
"personal needs and care" (italics ours) category. Stafford and Duncan
(1980) note a negative correlation between wages and time spent
sleeping among men but dismiss it as a reflection of unmeasured
interpersonal differences. We have essentially banished roughly onethird
of humankind's available allotment of time from our analysis of
scarcity.
The failure to consider sleep is widespread in other social sciences.
A monumental compilation of studies of time use (Szalai 1972) reports
briefly on time spent sleeping but devotes none of its analytical
effort to this use of time. A recent comprehensive study of the United
States (Juster and Stafford 1985) examined a variety of quantitatively
less important uses of time but never considered sleep.
Only a very naive view of what determines how long a person sleeps
can justify neglecting sleep in an economic model of time allocation.
One could assume that sleep time is fixed for reasons unrelated to any
of the variables in the economic model. For example, one could assume
that the need for sleep is biologically determined. This would
leave each person with an endowment of waking time to divide between
work and various consumption activities. Even if endowments
differed, aggregation across a population would generate a total endowment
of waking time that was independent of economic shocks.
Many studies of labor supply implicitly assume that the representative
consumer has a fixed amount of time to allocate between work and
waking leisure. This assumption is explicit in Michael (1973, p. 325)
and Heckman and MaCurdy (1980, p. 59).
It seems more plausible to assume that the amount of time at an
individual's disposal is variable because time spent sleeping changes
from week to week and year to year. More important, some variation
in time spent sleeping may result from conscious choice in response to
changing economic incentives. These may operate directly, as the
price of time and the utility of sleep vary, or indirectly, as other
factors that affect the demand for waking leisure change. Some of the
variation is beyond the individual's control, but some may respond to
variations in labor-leisure choices and in the value of time. If so-if
decisions about sleep are not separable from decisions about labor
supply-the vast literature on labor supply that ignores sleep contains
a difficulty that could have important consequences for understanding
the allocation of time between the home and the market.
In this study we use several sets of data to explore whether variations
in time spent sleeping represent an important part of people's
shifting patterns of time allocation. A more specific question is
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924 JOURNAL OF POLITICAL ECONOMY
whether sleep time is under the individual's control and thus is related
to the economic variables that affect other decisions about time
allocation. In essence, we examine whether an individual's weekly
endowment of waking hours is endogenous, a task analogous to the
study of the endogeneity of length of life through suicide in Hamermesh
and Soss (1974). Section II presents evidence on the distribution
and socioeconomic correlates of sleep time and establishes the existence
of a relationship between sleep time and market work. In Section
III we construct a simple model of time allocation that includes
sleep as a choice variable, and in Section IV we present estimates of
the demand equation for sleep implied by this model. Section V draws
conclusions about the economic implications of our findings.
II. What Do We Know about Sleep, and Is Sleep
Economically Important?
The most striking fact that biopsychologists have demonstrated about
sleep is its diversity. Kleitman (1963) summarizes evidence on the very
wide range of sleep duration among adults. Authenticated examples
of nonpathological short sleepers exist (Meddis 1977, chap. 3).
"There is no more a 'normal' duration of sleep, for either children or
adults, than there is a normal heart rate, or height, or weight" (Kleitman
1963, p. 120). Sleep is clearly a major expenditure of time that
exhibits substantial variation within every population that has been
studied.
There is remarkably little evidence on the determinants of individual
differences in sleep duration. There is some evidence that women
sleep more than men (cited in Kleitman [1963]) and still weaker indications
that sleep duration declines with age among adults (Morgan
1987). Beyond this and substantial unexplained individual variation,
previous studies offer few guidelines about how to begin an empirical
examination of sleep duration. One basic indicator of its importance
as an economic variable might, however, be its relationship to time
supplied to the labor market. As a by-product of examining this relationship,
we provide the first comprehensive set of demographic correlates
of sleep duration.
Evidence from International Surveys
One source of data on the sleep-work relationship is Szalai (1972, p.
618), who reports average sleep duration from time diaries collected
at 15 different sites or sets of sites in 12 countries in the mid-1960s.2
2 Diaries came from sites in Belgium, Bulgaria, Czechoslovakia, France, two from the
Federal Republic of Germany, the German Democratic Republic, Hungary, Peru, Poland,
two from the United States, the Soviet Union, and two from Yugoslavia.
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ALLOCATION OF TIME 925
TABLE 1
SLEEP (Minutes per Day) AND EMPLOYMENT STATUS, 15 STUDIES
Means and Parameter
Standard Deviations Estimates*
(1) (2)
Sleep 503
(47)
Minutes worked 511 - .109
(by workers, on weekdays) (21) (.01)
Children .35 - 11.18
(.48) (4.15)
Male .35 17.84
(.48) (2.66)
Married .71 -8.52
(.46) (5.83)
Workday .53 - 30.28
(.50) (5.37)
'R2 .70
* Based on data in Szalai (1972). The means and standard deviations are unweighted. The data cover 249 cells.
The estimates are from regressions that use the numbers of persons in each cell as weights. Standard errors of the
regression parameters are in parentheses here and in tables 3-6.
Average sleep duration is reported by employment and marital
status, presence of children, and sex and whether the diary is kept for
a weekday or a weekend. Underlying each usable cell are time diaries
of at least 10 people.
Column 1 of table 1 presents the means of the variables included in
a regression of minutes of sleep per day on control variables and on
daily minutes of work in the market.3 The means are unweighted; the
regression coefficients reported in column 2 are based on weights that
are inversely proportional to the square root of the number of people
in each cell. Average sleep duration is nearly 81/2 hours per day,
somewhat above the mean durations reported in clinical studies.
While this discrepancy is not easily explicable, there is no reason to
assume that whatever produced it biases the estimated effect of work
time on sleep duration.
Webb (1985) examined differences in mean sleep time within several
pairs of demographic categories in these data and showed that
people sleep less on workdays and that women sleep less than men on
weekends. The regression estimates presented here are mostly consistent
with these comparisons and with casual observations (though
there is no previous multivariate evidence on sex differences in sleep
behavior). Thus the presence of children reduces sleep duration, and
3 Minutes of work per day are an average for all workers on workdays in the particular
country study, not the average for each sex-marital status cell. These latter data
were not available. The results were qualitatively the same when a dummy variable
measuring employment status, which contains less information, was used instead.
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926 JOURNAL OF POLITICAL ECONOMY
people sleep less on workdays than on weekends. The only inconsistency
with the clinical results is the significantly longer sleep duration
among men. Since we have controlled for time spent working and the
presence of children, this difference may reflect differing allocations
of time in household production.
With other factors held constant, each additional hour of work
reduces time spent sleeping by about 7 minutes. Alternatively, employed
people sleep roughly 1 hour less per day on workdays than
those who do not work in the market. At the very least, this aggregate
evidence suggests that changes in work-leisure choices are related to
changes in the amount of time individuals have available for sleep.
Evidence from the 1975-76 Time Use Study
The 1975-76 Time Use Study obtained data from four days of time
diaries kept by 1,519 households. The days were at 3-month intervals,
with two being weekdays, one a Saturday, and the fourth a Sunday.
The data on time use are combined into "synthetic weeks," which we
use in estimating the relation between sleep duration and hours of
work. Of the respondents, 421 were excluded because they were
above age 65 or below age 23, or because they did not have complete
information on main sleep time in each of the interview waves. Others
were disqualified if one of the control variables of interest was missing
or if there were severe inconsistencies in the data.4 This left a usable
sample of 706 individuals, of whom 400 were men.
The 86 categories of time use in the 1975-76 diaries included night
(or main) sleep, naps and resting, and miscellaneous personal activities.
This last category does not include washing or dressing, but
presumably includes time spent in sexual activities and affection.
Since there is some scope for people to include sleep in any one of
these categories, we analyze increasingly broad definitions of sleep
time that add the last two categories successively to main sleep time.
We measure work time as minutes spent in normal work (excluding
on-thejob leisure) plus work at a second job.5
Table 2 shows descriptive statistics for the three definitions of sleep
time and for minutes of market work in the sample and two subsamples.
The mean weekly sleep durations imply an average daily main
4 Thirty-three individuals were excluded who reported earnings in 1974 that exceeded
their reported family income.
5 In these data we define market work as normal work time on the main and the
secondary jobs. Leisure time at work and travel to work are excluded. Hamermesh
(1990) shows that on-the-job leisure is less than 10 percent of total time spent at the job
and that its effects on wages are very small. This suggests that it makes sense to exclude
it from time spent working and to include it instead in waking nonmarket time.
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ALLOCATION OF TIME 927
TABLE 2
SLEEP AND WORK TIME (Minutes per Week), 1975-76 TIME USE STUDY
(Means and Standard Deviations)
Sleep,
Sleep Naps, and
and Personal
Sleep Naps Activities Work
All respondents 3,266 3,383 3,438 2,122
(444) (499) (520) (947)
Men 3,252 3,360 3,409 2,435
(435) (492) (505) (848)
Women 3,285 3,413 3,476 1,715
(456) (507) (539) (916)
sleep of around 73/4 hours, more consistent with clinical reports than
the mean in table 1 was. Adding rest and naps raises the daily average
to slightly over 8 hours, while adding miscellaneous personal activities
increases the total to nearly 81/4 hours. The standard deviation of
sleep time is large; 12 percent of the sample sleep more than 9 hours
per night, while 10 percent sleep less than 61/2 hours per night on
average.
For the average respondent, sleep clearly occupies a larger fraction
of the total time endowment than market work. What is more striking
is that this is true for a huge majority of the people in the sample:
Only 67 of the 400 men report working more than their main sleep
time, and only 20 of the 306 women do so.6 That sleep is the largest
single use of time by most people makes it a worthwhile subject for
economic analysis.
Consider some of the estimated effects of the variables used as
controls in the regressions. To save space, these are presented in table
3 only for the regressions describing time spent sleeping and napping
(resting). The dummy variables listed in the table are selfexplanatory.
The results on the effects of age are mixed. The evidence
suggests an inverse U-shaped sleep-age profile among men
(with a peak at age 46) but a U-shaped sleep-age profile among
women (with a minimum at age 36). For both men and women, including
only a linear term in age yields insignificant positive effects.
This runs counter to the sparse clinical evidence and may perhaps be
due to our multivariate analysis that controls for time spent in the
labor market. More interesting, increased educational attainment reduces
sleep duration. It is difficult to imagine that greater schooling
6 Only 58 of the men worked more than their combined time sleeping and resting,
and only 55 worked more than their total sleep, rest, and miscellaneous personal time.
The comparable figures among the 306 women are 17 and 17.
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928 JOURNAL OF POLITICAL ECONOMY
TABLE 3
PARAMETER ESTIMATES, SLEEP AND NAPS EQUATIONS, 1975-76 TIME USE STUDY
All Respondents Men Women
Work time -.199 -.219 -.169
(.02) (.03) (.03)
Married 16.04 -43.15 92.50
(57.27) (82.71) (82.20)
Years married - 2.59 2.43 - 7.62
(2.31) (3.13) (3.49)
Age 1.86 24.52 - 24.81
(12.80) (16.20) (21.17)
Age squared .02 -.26 .35
(.15) (.19) (.25)
Years of schooling - 14.30 - 18.28 -9.09
(6.71) (8.55) (10.83)
Male 99.42 ... ...
(39.07)
Excellent or -94.16 - 123.79 -59.66
good health (59.16) (80.75) (89.05)
Children < 3 - 35.42 39.03 - 153.00
years old (56.44) (67.72) (102.60)
Protestant 86.15 90.87 93.97
(37.45) (47.99) (60.04)
Black -69.17 -110.65 -43.95
(80.62) (114.41) (115.63)
jR2 .141 .176 .108
reduces the taste for sleep; rather, we interpret this as operating
through wages and thus as reflecting a price effect7 (see Sec. IV).
Finally, given their market work time, Protestants sleep more than
adherents of other faiths (in this sample, mostly Roman Catholics).
As in the estimates in table 1, men sleep more than women. The
difference in mean sleep time (see table 2) is more than accounted for
by differences by sex in characteristics, particularly employment
status and work hours. An otherwise identical woman sleeps between
3 and 5 percent less than her male counterpart, depending on the
definition of sleep that is used, a difference of around 20 minutes per
night. (This is remarkably close to the coefficient on the male dummy
variable in table 1.) There is some evidence that women who are in the
labor market work more hours (in the home and the market) than
men (Cain 1984). Our results show that part of the cushion for this
sex difference in hours worked is provided by reductions in hours of
sleep. It is not clear whether this represents discrimination due to
male dominance in household decision making or optimal responses
7Mullahy's (1989) data do not measure wages, but yield negative correlations of sleep
with age, education, and total income. All these correlations could be due to a negative
wage effect on sleep.
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ALLOCATION OF TIME 929
TABLE 4
PARAMETER ESTIMATES, OTHER SLEEP MEASURES AND WORK
TIME, 1975-76
DEPENDENT VARIABLE
Sleep, Naps,
and Personal
Sleep Activities
All respondents -.164 -.214
(.018) (.021)
R2 .116 .147
Men -.184 - .239
(.025) (.028)
jR2 .146 .190
Women - .134 - .179
(.028) (.033)
jR2 .082 .101
NOTE.-Includes all the variables listed in table 3.
to the differing capacities of men and women to reduce sleep without
reducing household and market productivity. Also noteworthy are
the various effects on parents' sleep time of having young children in
the household.8 Fathers' sleep duration is essentially unaffected, but
young children substantially reduce mothers' sleep time.
Estimates of the relationship between sleep time and work time are
presented in the first row of table 3 and in table 4. Each hour of
additional work reduces sleep by roughly 10 minutes. The effects on
total sleep and nap time are slightly greater than those on sleep alone,
and those on all possibly sleep-related time are greater still.9 None
of these coefficients is changed appreciably if we base them on a
bivariate regression of minutes sleeping on minutes of market work.
The estimated effect of additional work time on sleep duration is 50
percent larger than what we inferred from the cross-section international
averages in table 1. This discrepancy is not explicable by differences
in average working hours, nor does it differ if only the control
variables in table 1 are used. It may be due to differences in the
instructions to the participants in the various studies about keeping
their diaries or to greater measurement error in the 1-day diaries in
the international samples than in the 4-day diaries in the Time Use
Study. Also, the aggregation over individuals that produced the cell
means underlying the estimates in table 1 may have removed the
8 A child is coded as being less than 3 years old if he or she was at most 2 yea
9 Tests of sex differences in the response of the sleep measure to additional minu
of market work yield t-statistics of 1.39, 1.33, and 1.50 for the three variables that
measure sleep.
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930 JOURNAL OF POLITICAL ECONOMY
correlated extreme values of both the sleep time and work time variables,
so that the estimate of their partial correlation was reduced.
Evidence from Panel Data
We have shown that there is a significant negative partial correlation
between sleep time and work time that is robust to the location in
which the sampling occurs and to the characteristics of the workers
sampled. It does not, however, demonstrate a causal relationship.
Consider a situation in which sleep has no effect on productivity or
utility, provided that the individual satisfies a biologically required
need for sleep. Suppose also that this need varies among individuals.
Then economic theory predicts that (under most circumstances) individuals
requiring less sleep would divide the extra waking time between
work and leisure. This would lead to a negative correlation
between work and sleep in cross-section data, even though sleep time
would be irrelevant to changes in time allocation.
This extreme example illustrates a possible individual-effect bias in
the estimates in tables 1, 3, and 4. Consider the equation
Tsit = xTwit + PXjt + VI + Edty (1)
where Tszt is the time spent sleeping by individual i in perio
the time spent working, X is a vector of control variables, a and , are
parameter vectors, v is an unobserved individual-specific effect that is
time invariant, and E is a random term that varies across individuals
and time. If we interpret vi as an individual-specific "need for sleep,"
then it will be positively correlated with Tszt and negatively correlated
with Twit. Cross-section estimates of a from equations such as (1) will
be negatively biased. Despite the remarkable consistency of our estimates,
we may have shown only that there are some people who are
innately sleepless workaholics.
To examine this possibility, difference (1) over time:
ATS, = QATwi + PAX, + A\,y (2)
where A denotes a change between times t - k and t. Estimating (2)
using a panel of observations on the same people eliminates possible
biases in & that may be caused by unobserved individual effects that
are correlated with both Tw and Ts. Even though total time available is
fixed, a is not necessarily negative. There are many other uses of time
besides sleeping that can change to compensate for a change in market
work time.
Fortunately, a 1981 follow-up study to the 1975-76 Time Use
Study allows us to estimate (2). The 1975-81 Time Use Longitudinal
Panel Study collected data similar to those collected in the 1975-76
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ALLOCATION OF TIME 931
study, so that k = 6. Time diaries were kept for 4 days (again, at 3month
intervals) by 620 of the households included in the 1975-76
survey. The same age disqualified used in the 1975-76 data reduced
the sample to 507 observations. Missing data on the variables of interest
reduced it to 278 respondents, while inconsistencies between reported
incomes and earnings in 1974 or 1980 reduced it to a final size
of 239 people, of whom 95 are women.
The 1981 data allowed for 223 separate uses of time, including
night sleep (main sleep of the day), naps and resting, sex or making
out, personal or private activities, and affection. The first two categories
are the same as those in the 1975-76 cross section; the last three
can be viewed as subcategories of the group miscellaneous personal
time that was used in the 1975-76 cross section. We therefore formed
the same three dependent variables that we used in the cross-section
analysis. The individuals in this subsample from the panel study did
not differ significantly in their sleep or work times from the larger
1975-76 cross-section sample.'0 That there is potentially interesting
variation in the panel data is shown by noting that only 93 of the
sample participants changed their average main sleep time between
the two synthetic weeks by less than 30 minutes, while 81 changed it
by more than 1 hour. This is not simply measurement error: The 6year
correlations of sleep time are positive and significant.
We use a "within" estimator (Judge et al. 1980) to produce the
consistent estimates of a from (2) that are presented in table 5. Included
as control variables are all the measures for which AX =$ 0 for
some observations: health status, presence of young children, marital
status, years of schooling, and age. " l These "within" estimates of a are
remarkably similar to the cross-section estimates shown in tables 3 and
4. Neither for the sample as a whole nor for men and women separately
does the estimate of a differ significantly from the cross-section
estimates from the large 1975-76 sample.' 2 Again we find that
10 The means in 1975-76 for the three sleep classifications and work time we
3,246, 3,370, 3,410, and 2,184 minutes for the entire sample of 239 people. Among
women they were 3,278, 3,410, 3,458, and 1,750, while among men they were 3,225,
3,343, 3,378, and 2,470. A comparison with table 2 shows that, at least along these
dimensions of time use, the individuals in the longitudinal data were remarkably similar
to the people included in the sample from the 1975-76 Time Use Study.
1 "Since a quadratic in age is included in eq. (1), a linear term belongs in eq. (2).
12 The estimates of a from (2) are also very similar to cross-section estimates of a
based on this smaller sample. For example, for sleep and naps, & estimated over the 239
people in this panel and based on (1) for 1975-76 is -.212. Estimating the same
equation for these people using 1981 data produces & = -.100. Among men, the
analogous estimates are - .242 and - .129; among women, they are - .185 and - .065.
With the exception of the (small) subsample of women in 1981, all these estimates differ
significantly from zero.
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932 JOURNAL OF POLITICAL ECONOMY
TABLE 5
PARAMETER ESTIMATES, SLEEP TIME AND WORK TIME, 1975-76, 1981
(Within Estimates)
Sleep, Naps,
and Personal
Sleep Sleep and Naps Activities
All respondents - .175 - .224 - .234
(.031) (.037) (.037)
R2 .108 .123 .133
Men - .154 - .229 - .237
(.039) (.045) (.045)
jR2 .090 .129 .138
Women - .210 - .224 - .233
(.053) (.064) (.065)
jR2 .115 .092 .105
NOTE.-Includes variables measuring age and change in health status, presence of young children, educational
attainment, and marital status.
aTs/aTW increases in absolute value the more broadly we define sleep
time.
This replication of the cross-section results on panel data suggests
that at the individual level part of any change in time spent in market
work is taken from nonmarket work and leisure, while the remainder
is taken out of sleep time. For the entire sample the panel results
imply that each 1-hour increase in work time results in a 13-minute
reduction in sleep duration and a 47-minute decline in waking nonmarket
time. In elasticity terms, the sleep-market work elasticity is
-.14, while the waking nonmarket time-market work elasticity is
-.36. It is certainly not the case that there is a fixed amount of
nonsleep time that individuals divide among other uses. It is also clear
that the greater part of any increase in market work is met by a
reduction in waking nonmarket time, though sleep time is also reduced
significantly.
We have not strictly established the direction of causation, if any,
between sleep time and labor supply. It may be that variations in
individuals' sleep time are beyond their control and that their labor
supply changes in response to these variations. For this explanation to
be plausible, exogenous changes in sleep would have to be both predictable
and persistent enough to engender a labor supply response.
It seems reasonable, however, to believe that the correlation between
sleep time and work time reflects in part people's ability to alter the
time spent sleeping in response to the same economic factors that
affect labor supply. Indeed, certain results of this section, particularly
our findings of differences in sleeping on workdays and weekends
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ALLOCATION OF TIME 933
and of the effect of young children on parents' sleep behavior, imply
that people are able to adjust their sleep behavior to changing circum-
stances.
The totality of our results suggests that, at the least, time spent
sleeping is changed by the indirect impacts of economic and demographic
factors on decisions about work and leisure. We have already
seen that education affects sleep duration independently of the
amount of time spent working in the market, which may reflect a
direct effect of wages on sleep. This finding and the strength of the
indirect effects justify constructing and testing a utility-based model
with sleep as a choice variable.
III. The Demand for Sleep: A Theoretical Model
Fitting sleep into a model of consumer choice can proceed at the
simplest level if we assume that individuals derive no utility from
sleep and that it has no impact on their market or household productivity.
In that case the consumer's choice is simple: Sleep duration will
equal the biological minimum, T*; it will be unaffected by other
choices about time allocation and by changes in exogenous factors
that affect consumer demand. At a more complex level, we can assume
that sleep is a completely time-intensive commodity whose consumption
yields utility just as other commodities do. In that case, it
can be analyzed in the same way as any other commodity. Under this
assumption, sleep is the obverse of work: It takes no goods, only time,
reducing the amount of time available for producing other commodities
or earning a wage.
At the most complex level, we can assume that sleep adds to an
individual's productivity. This view is consistent with Becker's (1965,
p. 498) argument that some sleep is necessary for efficiency and is
required even if the goal is to maximize money income. The idea that
sleep and productivity or job performance are related is supported by
evidence from sleep researchers. Experimental studies indicate that
severe sleep deprivation leads to lapses in efficiency, especially in
nontrivial but repetitious tasks (Meddis 1977, pp. 58-59), and that for
healthy subjects with normal sleep habits, an increase in nightly sleep
enhances alertness and daytime functioning (Roehrs et al. 1989). A
committee of the Association of Professional Sleep Societies (Mitler et
al. 1988) surveyed studies of performance failures in actual work
settings and concluded that "inadequate sleep, even as little as one or
two hours less than usual sleep, can greatly exaggerate the tendency
for error" (p. 107) during certain times of the day, especially late
afternoon. Other sleep researchers have placed at $50 billion the
annual reduction in manufacturing productivity as a result of "sleep
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934 JOURNAL OF POLITICAL ECONOMY
problems," including irregular work schedules and inadequate rest
(Wall Street Journal [July 7, 1988], p. 25).
We can model the worker's demand for sleep to allow for the possibility
that sleep enhances both productivity and utility. Let the worker's
market wage Wm be
Wm = WI + W2Ts, (3)
where we have dropped the i subscript, and W1 and W2 are positive
parameters. Assume that the individual's utility is defined over Ts and
a commodity Z,
U = U(Z, TS), U. > O. UZI < O. (4)
and that the worker's endowment of time is divided as T* = T, +
Ts + Tw, where TZ = bZ is time spent producing commodity Z. Production
of Z also requires the input of goods X such that X = aZ.13
The price of X is P. Thus the individual's goods constraint is the standard
PX = WmTw + I, where I is nonlabor income. Combining this
constraint with the individual's time constraint and the technology for
producing Z yields
(W1 + W2Ts)(T* - Ts - Tz) + I = aPZ. (5)
The individual maximizes (4) subject to (5), which yields
U1 - aP + bWm (6)
U2 W1 + W2(Ts - Tw)
Equation (6) states that the ratio of the marginal utilities of consumption
and sleep must equal the ratio of their prices. The price of a unit
of Z reflects the cost of the goods required to produce it and the
shadow price of the time needed for production. The price of a unit
of sleep is the wage rate minus any addition to labor income that
occurs as a result of the effect of extra sleep on productivity.
The effect on sleep of a change in nonlabor income is given by
a_ = {U11[WI + W2(Ts - TA)] - U12(aP + bWm) + bU1W2ai
(7)
13 We adopt a fixed-coefficients specification of household production technology for
expositional convenience and also to highlight the fact that consumption activity requires
waking as opposed to sleeping leisure. Indeed, this is one important reason for
treating the two types of leisure as distinct categories. In the text we discuss certain
implications of the perfect complementarity of market goods and waking leisure embodied
in the specification. These results should be seen as extreme expressions of
tendencies present when there is any complementarity between X and T7. The basic
results are not affected if our assumption that the enjoyment of sleep requires no
expenditure on market goods is replaced with the more realistic assumption that it
requires some fixed expenditure on goods (e.g., a bed).
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ALLOCATION OF TIME 935
where D < 0. The first two terms in the expression are standard. If
sleep enhances the utility of consumption, as one might expect, both
terms exert a positive influence on the effect of income on sleep. The
third term, which is present only if sleep raises productivity, works in
the opposite direction. Its negative sign results from the assumption
that Z is produced using a fixed-coefficients technology. The market
goods purchased with an addition to income can enhance utility only
if T, is also increased. The increase in Tz, combined with the ten
for T, to increase in response to the added income, implies a reduction
in T,. From (6) one can see that, if sleep is productive, a fall in T
raises the price of sleep. Thus the third term in (7) can be viewed as a
second-order substitution effect working against the pure income effect
captured by the first two terms.
The demand for sleep is also affected by changes in the parameters
of the wage function in (3):
-a__ = [(U1 - bU2)(aP + bWm)]D + TW aI (8a)
and
a T5 7 = TSa Ts - (aP + bWm)UiTwD-. (8b)
Equation (8a) is the Slutzky equation describing the demand for sleep.
The first term differs from the usual substitution effect because it
includes - bU2. This appears because a change in the wage also
changes the price of Z; one can show, though, that (U1 - bU2) is
always positive. An analogous expression for aT,/aWI can be de
and it is interesting to note that the substitution effect of a change in
W1 on waking leisure is positive. This results from the complementarity
of T, and X in producing Z. If W1 increases, the goods purchased
with the extra income can be enjoyed only if T, increases as well.
However, the substitution effect of a change in W1 on total nonmarket
time, Ts + Tz, is negative, just as in the standard labor supply model.
Equation (8b) shows the effect on the demand for sleep of a change in
the productivity of sleep. As one would expect, an increase in W2 has a
less negative (more positive) impact on sleep than an increase in WI.
Note from (6) that the demand for sleep may be affected by
changes in any other exogenous factors that could be included as
affecting tastes for sleep or the composite commodity Z. This means
that, in general, any exogenous factor that shifts the demand for
commodities will affect the demand for sleep and the (residual) supply
of labor. Whether estimating separate wage effects for T7 and Tz
provides different implications for the wage elasticity of the demand
for leisure, T1 (= Ts + Tz), compared with what has been produced i
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936 JOURNAL OF POLITICAL ECONOMY
the standard work that does not make the distinction between sleep
and waking leisure, is an empirical question.
IV. The Demand for Sleep
Estimation of a Complete Model
The theoretical model implies a demand equation for sleep that is
analogous to the commodity demand and labor supply equations typically
estimated in the literature. The demand for sleep is a function of
the individual's wage rate and nonlabor income. We estimate such a
demand equation using the subsample of consumers we have extracted
from the 1975-76 Time Use Study. Along with it we estimate
a similar demand equation for T,. Market work is the commodity
deleted from the system of demand equations. The estimating equations
are analogues of equations that have become standard in the
literature on labor supply:
T = Yij + 'Y2AWm + Y31I + PIOX + VL1, (9)
where = s, the sleep equation, orj = z, the nonmarket waking time
equation; the y4, are parameters to be estimated; Wm is the logarithm
of the wage rate; I is the logarithm of the respondent's household's
other income; and ,u. is an independent and identically distributed
error term. Except for its exclusion of years of schooling, which we
assume affected the results in table 3 only through its effect on wages,
X is the same vector of demographic variables whose coefficients were
presented in table 3.
We measure Wm as the logarithm of the respondent's self-reported
monthly earnings divided by 4.3 times his or her self-reported weekly
hours. This hours measure is a response to a question and is not part
of the time diaries that yield the measures of Ts and Tz. Any bias
induced by error in this wage measure due to errors in reported
hours is removed by the use of instrumental variables. Other income I
is measured as the logarithm of the difference between the respondent's
reported 1974 household income less a spouse's expected 1975
earnings and 12 times the respondent's monthly earnings.
To estimate (9) we need to circumvent the standard problem that
the market wage rate is not observed for nonworkers (174 of the 706
sample members). We do this by first estimating a probit over the
entire sample of 706 observations, relating the probability of labor
force participation to a number of variables that might affect it: age
and its quadratic, religious preference, health status, sex, marital
status, and the presence of young children.'4 The inverse Mills ra-
14 This model is basically an extension of what Killingsworth (1983) has called "second-generation"
models of labor supply.
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ALLOCATION OF TIME 937
tio, f (-J)/[1 - F
unit normal distribution for an observation, was then entered into a
second-round equation describing the logarithm of wages in the sample
of 532 workers. As is common in the labor supply literature, the
inverse Mills ratio added little to the wage equation. We abandoned
this approach and estimated (9) using the prediction of the logarithm
of hourly earnings from wage equations that excluded this ratio. 15
By using instrumental variables for Wm,. we are implicitly viewing
the equations for T, and T, as part of a simultaneous system, because
of the possible impact of both T7 and T, on the wage rate. The time us
equations are identified by their exclusion of several variables used in
the wage equation-education, union status, large SMSA, and region-and
of the occupation and industry dummy variables.'6
The estimates of Y2j and y31 for demand equations describing T,
and T, are shown in table 6. The results are presented for the entire
sample and separately for equations estimated for men and women.
Before we discuss them, it is worth noting that the responses of T,
T, to wages are not really very different from each other. For th
entire sample, a test of the hypothesis that '2s = 2z yields the statistic
X2(l) = 1.38. For the samples of men and women, the corresponding
x2-values are 1.46 and 0.61. Except for the hypothesis that the entir
vectors of coefficients (including the control variables) in the two
equations are equal, none of the hypotheses that impose equal responses
of T, and Ts to the independent variables can be rejected
conventional significance levels. However, the directions of the differences
in the parameter estimates, the two X2-statistics that exceed
unity, and the significant negative p, the contemporaneous correlation
of ps and uz, indicate that this approach to disaggregating nonwork
time can be profitable.
If we hold the respondent's other household income constant, people
with higher predicted wages sleep less.'7 In the sleep and naps
equation for the entire sample, '25 is significantly negative at the 95
percent level of confidence. (The sleep-wage elasticity is -.042.) Indi-
15 Wage equations included education and experience and dummy variables for sex;
marital, union, and health status; race; region; large standard metropolitan statistical
area (SMSA); and one-digit occupation and industry. The R2's were .37 for the full
sample, .18 for men, and .28 for women. Complete results are available from the
authors and are comparable to those common in the literature.
16 We explored the possibility that sleep affects productivity by estimating a wage
equation that included a measure of sleep. Our model suggests that to do this properly,
sleep, waking nonmarket leisure (or hours of work), and wages would have to be
treated as endogenous. Unfortunately, our data are not sufficient to allow us to identify
convincingly such a wage equation: there are not enough variables that are strongly
correlated with sleep time and work time that can be excluded from the wage equation.
17 Qualitatively similar results on Wm are obtained when the equation systems are
reestimated using either sleep or sleep, naps and rest, and personal time as one of the
three uses of time.
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938 JOURNAL OF POLITICAL ECONOMY
TABLE 6
WAGE AND INCOME EFFECTS, DEMAND SYSTEMS, 1975-76 TIME USE DATA
Dependent Variable Wage Income R p
All Respondents
Sleep and naps - 141.44 - 1.78 .024
(77.35) (4.80) - 24
Waking nonmarket time 132.18 -1.71 .162
(129.37) (8.09)
Men
Sleep and naps -181.68 - 2.88 .040
(120.88) (5.77)
Waking nonmarket time 233.34 -6.69 .050 - .23
(193.67) (9.30)
Women
Sleep and naps - 64.30 1.55 .018
(93.44) (8.43) - 27
Waking nonmarket time - 262.42 14.44 .053
(166.99) (14.80)
NOTE.-Each equation also includes all the variables listed in table 3. The standard errors are adjusted using the
correction of Murphy and Topel (1985)
viduals whose time is more valuable substitute away from the relatively
time-intensive commodity sleep, a commodity that yields utility
but no direct income. While our results do suggest the existence of
this most basic of economic effects on the demand for sleep, they are
not overwhelming. We believe that they are strong enough, though,
to demonstrate that time spent sleeping is scarce and subject to variations
produced by the same economic factors that affect other choices
about allocating time.'8
The wage effect on sleep is especially large for men and mirrors the
wage effect on waking nonmarket time. The amount of time that men
spend in the market is unaffected by an increase in the wage rate, but
that increase induces them to switch time from sleeping to leisure and
nonmarket production. This could be a reflection of the complementarity
between waking leisure and consumption that we highlighted in
Section III. Among women, changes in the value of time have little
18 Kooreman and Kapteyn (1987), who use the 1975-76 Time Use Study to estim
their time allocation model, report that women "substantially reduce the amount of
time spent on personal care if their wage rate goes up" (p. 241). This result, with its
counterintuitive implication that highly paid women are less attentive to their health
and appearance, makes more sense when one recognizes the importance of sleep in
their personal care category. (Our broadest measure of sleep makes up 80 percent of
their category.) The decreased time devoted to personal care is recognizable as the
wage effect on the demand for sleep that we have found.
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ALLOCATION OF TIME 939
effect on sleep but lead to reallocation of time between market and
nonmarket work. This sex difference in the response of sleep to wage
changes may arise because women have more opportunities than men
for substituting between market and nonmarket work.
Taken together, the results of estimating this demand system are
consistent with the mass of prior research showing that men's supply
of work to the market is much less sensitive to wage rates than women's.
The implied labor supply elasticity for men is -.021, essentially
zero, while for women it is .191, positive but not very large (in this
sample in which an unusually large fraction of women are in the labor
force).
The standard errors of the estimated income effects j3 are too
large to permit reliable inferences about their signs, but the effect of
income on sleep appears to be economically insignificant. This could
be caused by the nonsuperiority of sleep that is induced by the second-order
substitution term in (7), or it could merely stem from problems
in our measure of other income. In any case, together with the
evidence (summarized by Killingsworth [1983]) that income effects on
the supply of hours of work are very small, these findings suggest that
the receipt of additional unearned income does not affect T, Implicitly,
the entire impact of extra nonlabor income is to shift the
typical consumer to the production of relatively more goods-intensive
commodities through purchasing more goods, not through reducing
the total time spent producing those commodities.
Additional Evidence on the Income Effect
We failed to find any evidence of income effects in the estimates of
the demand system. Contemplating this issue, though, leads to two
interesting extensions. The first involves examining the impact of
economic development on the demand for sleep. There is a general
notion that as the price of time increases and incomes rise, the demand
for sleep will fall.'9 This ignores the possibility that sleep yields
utility and that the higher incomes produced by rising wages can
overcome the pure price effects. This possibility does not seem consistent
with the results from the demand system; yet since its obverse is
the best way to reconcile cross-section and time-series estimates of
variations in labor supply, the argument is surely not outlandish.
We do not have time series on sleep duration. We can, though, use
measures of living standards along with the demographic variables in
the international data set described earlier to estimate a reduced-form
19 Linder (1970, p. 47) argues that "many people regard sleep as a waste of time. The
greater the demand for time, the more people come to accept this view."
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940 JOURNAL OF POLITICAL ECONOMY
Engel curve for sleep over a diverse sample of economies. Using gross
national product per capita in 1966 in that equation and dropping
minutes of work produce only minor (less than 10 percent) changes in
the coefficient estimates in table 1. Higher GNP per capita is associated,
though, with significantly longer sleep duration.20 The ef
small, with an increase in income over the entire range producing
only 21 extra minutes per day of sleep time for the average household
(and an increase of two standard deviations producing only 14 extra
minutes of sleep). Nonetheless, this contradicts the notion that economic
development must be associated with less time spent sleeping,
and it may provide some evidence for the existence of income effects
in the demand for sleep.
A second extension involves examining how people respond to a
hypothetical offer of an increase in full income through increased T*.
In three of its monthly polls (in 1978, 1983, and 1988) the Roper
Organization asked respondents to list two or three activities that they
would engage in if they had an additional 4 hours each day.2' Sleeping
was the seventh most frequently mentioned activity by the 776
people in the samples. Moreover, under the assumption that each
activity mentioned occupies the same share of the additional time, the
implied estimate of dTs/dT* is .045. Participants in the fourth wave of
the 1975-76 Time Use Study were asked how they would spend an
additional 2 hours per day. Most in our sample listed only one activity;
31 sample members out of the 671 who responded to this question
chose sleep. Assuming that these people would spend all this extra
time sleeping, we can infer a value of .046 for dTs/dT*. Although
these two remarkably similar results are based on a hypothetical question,
they do suggest that sleep is not inferior.
What sort of people would sleep more if the day were longer? The
sleep lovers in our sample sleep 1 1/2 hours more per week than the
other sample members and work less, but they are not significantly
different with respect to any other variable in the data set. The desire
to spend hypothetical surplus hours on sleep may reflect a constraint
on time allocation not captured by our model, for example, a
minimum hours constraint on the job. To examine this, we respecified
(9) to allow those wanting to sleep during the extra 2 hours
to have wage and income effects different from the rest of the sample.
20 The GNP data were constructed from materials in the United Nations Statistical
Yearbook and the International Financial Statistics. The coefficient on GNP per capita,
measured in thousands of 1966 U.S. dollars, was 6.14; its standard error was 1.87. The
range of GNP per capita in this sample was $356-$3,842, with a mean of $1,609 and a
standard deviation of $1,110.
21 We thank Sender Hoffmann of the Roper Organization for providing the underlying
data.
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ALLOCATION OF TIME 941
If a constraint were affecting their behavior, their sleep would be less
responsive to wage and income changes. There was no evidence of
differential responses. Either these 31 respondents have a pure preference
for sleep or sleep enhances their productivity more than it
does that of other respondents.
V. Conclusions and Implications
People spend close to one-third of their time sleeping, but it is wrong
to view these unconscious hours as a predetermined deduction from
their scarce allotment of time. We have shown that at least part of
sleep time is a reserve on which people can draw when economic
circumstances make other uses of time more attractive. Our results
suggest that it is not unusual for people's average daily sleep time to
differ by as much as 1 hour at different times in their adult lives. Such
variations are economically important, for they respond to economic
incentives: Time spent sleeping is inversely related to both the wage
and time spent in the labor market. In short, sleep is subject to consumer
choice and is affected by the same economic variables that
affect choices about other uses of time.
This fact has not been recognized in empirical studies of labor
supply and commodity demand. If sleep does not influence productivity,
then estimates of labor supply equations and "complete" systems
of labor supply and commodity demand (e.g., Abbott and
Ashenfelter 1976) that ignore sleep will yield unbiased estimates of
income and substitution parameters.22 The labor supply equation
proxies the complement of the demand for all nonmarket time (sleeping
and waking); since the price of that time is the wage rate, estimating
labor supply equations in standard ways is a legitimate application
of the composite commodity theorem. The realization that sleep is a
choice variable does lead to a subtle reinterpretation of estimated
labor supply elasticities, in that they can no longer be viewed as the
negative of elasticities of demand for leisure. For example, a substitution
effect on labor supply that is nearly zero may reflect the combination
of a positive price effect on waking leisure and a negative effect
on the demand for sleep. Indeed, that is what our results suggest is
the case for men.
If sleep affects productivity, as evidence from other fields strongly
suggests, the issue becomes more complex. The marginal price of
sleep differs from the marginal price of other uses of time. The
22 Estimated demand systems that ignore labor supply will produce biased p
estimates if sleep is not weakly separable from goods in the utility function, just as they
would if waking leisure time were not weakly separable.
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942 JOURNAL OF POLITICAL ECONOMY
impact of sleep on the wage rate makes the wage endogenous in the
labor supply function. Demand systems that are derived from parameterizations
of the direct or indirect utility function without accounting
for the role of sleep will produce biased estimates of the structural
parameters. This relationship clearly merits further investigation by
economists.
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