ESTIMATING INCOME ELASTICITIES OF LEISURE ACTIVITIES USING
CROSS-SECTIONAL CATEGORIZED DATA
Jorge González Chapela*
Centro Universitario de la Defensa de Zaragoza
Address: Academia General Militar, Ctra. de Huesca s/n, 50090 Zaragoza, Spain
Email: [email protected] – Tel: +34 976739834
Abstract
The empirical classification of daily activities as luxuries, necessities, or inferior activities is
useful for predicting the impact of economic development, the life cycle, or social mobility on
the organization of people’s time. This paper conducts an empirical examination of three
broad leisure categories plus their main subcategories using a cross-section of time-use
observations for the United States. Estimation takes account of the form of the data in which
the income variable was recorded. Comparison of income elasticities with those reported by
previous studies is also made.
Keywords: Engel aggregation; Empirical time-demand function; Time-use income elasticity;
American Time Use Survey.
*
I am grateful to Dan Hamermesh, Robert Hill, Nancy Mathiowetz, and Frank Stafford for
helpful comments. Financial support from research project CREVALOR, funded by the
Diputación General de Aragón and the European Social Fund, is gratefully acknowledged.
1
1. INTRODUCTION
Ever since the seminal works of Mincer (1963) and Becker (1965), the notion that the
consumption of market goods calls for the consumer’s time has spread among economists to
reach, nowadays, the status of a common research tool. Coinciding with the diffusion of that
idea, leisure per adult in the United States increased dramatically (Aguiar and Hurst 2007),1
and demand analysis, which was fundamentally concerned with the demand for market goods,
has become increasingly interested in the demand for leisure (see for example Owen 1971,
Gronau 1976, Wales and Woodland 1977, Juster and Stafford 1985, Kooreman and Kapteyn
1987, Solberg and Wong 1992, Robinson and Godbey 1997, Hamermesh 2002, Kimmel and
Connelly 2007, Datta Gupta and Stratton 2010, Mullahy and Robert 2010, and Sevilla et al.
2012).
Still, certain aspects of the demand for leisure are not well understood. Americans, for
example, have preferences about the way their leisure time is spent, preferring as a rule
talking with friends to watching television (Juster 1985c) and socializing after work to using
the computer at home (Kahneman et al. 2004). Hence, one would expect that, ceteris paribus,
the demand for different leisure activities reacted differently to improvements in the standard
of living, moving as a whole towards a more enjoyable composition of total leisure.
Nevertheless, the empirical verification of this conjecture has proved elusive. Stafford and
Duncan (1985) developed estimates of income effects on time use to different activities for
208 working males included in Juster et al.’s (1978) 1975-76 Time Use Study (TUS). Their
standard errors appeared generally large relative to the coefficients except for meals out,
whose estimated elasticity at the mean was .20. Also using the TUS, Kooreman and Kapteyn
(1987) found negligible income responses in the demand for seven types of non-market
activities by 242 couples, and Biddle and Hamermesh (1990) obtained no evidence of income
1
The increase over the whole 20th century was smaller (Ramey and Francis 2009).
2
effects in the demand for non-market time by 706 individuals. For non-disaggregated leisure,
but also considering cross-sectional household data, Kimmel and Connelly (2007) estimated a
positive effect of husband’s earnings on his wife’s leisure in a large sample of 4,552 mothers
drawn from the American Time Use Survey (ATUS). While husband’s earnings played the
role of nonlabor income from the wife’s point of view, it could be also capturing a cross-price
substitution effect whereby the true income effect would be larger if husband’s and wife’s
leisure were complements (as found in Connelly and Kimmel 2009).2 In any case, if the
quantity of leisure increases with the standard of living, how can the demand for many
specific leisure activities appear generally as unaffected?
Additional research on the demand for disaggregated leisure was conducted by Juster
(1985a), Robinson and Godbey (1997), and Dardis et al. (1994). Juster (1985a) analyzed the
amount of investment time (i.e., time whose satisfaction derives from the activity’s end
product and not from the process of carrying it out) present in active, passive, and social
entertainment, concluding that investment time increased with household income. Table 17 of
Robinson and Godbey (1997) arrayed major background variables related to the allocation of
time. Household income appeared as a significant predictor of free time activities, but as the
authors recognized its predictive power could be the result of composition effects. Dardis et
al. (1994) considered a related issue. Using 1988-89 Consumer Expenditure Survey data on
active, passive, and social entertainment, they estimated expenditure elasticities in the range
of .40 to .72, indicating that goods consumed in the course of those activities (hereafter,
2
Solberg and Wong (1992) found that the husband’s and the wife’s leisure were negatively
related to commuting times. Although in the time allocation model of Gronau (1977)
increases in commuting time cause negative income effects, the critical predictions of
Gronau’s model were contradicted by Solberg and Wong (1992).
3
recreation goods) were necessities.3 But unless goods and time are consumed in fixed
proportion, the analysis of consumer expenditure is of limited utility for assessing the
variation of activity times. Thus, for example, there is evidence that expenditure on recreation
goods increases, but time allocated to leisure production decreases, with the consumer’s
education (Gronau and Hamermesh 2006).
This study is aimed at estimating income elasticities of demand for several leisure
activities in the United States. The knowledge of income elasticities is useful for predicting
which leisure activities will grow or decline on average as the economy develops, over an
individual’s life cycle, or across a nation’s income strata. This study departs from previous
disaggregated leisure analyses in two respects. First, the data source is the ATUS, which
allows a much larger sample than the 1975-76 TUS. Second, the form of our income measure
plus its treatment in estimation avoids some problems of parameter estimation. The income
variable used in Kooreman and Kapteyn (1987) was constructed by adding up the amounts
given to questions about the size of several nonlabor income sources. As the authors
recognized, the resulting measure could contain substantial measurement error. Stafford and
Duncan (1985) and Biddle and Hamermesh (1990) computed midpoints of income intervals
(as I also did in a previous version of this paper),4 but estimators computed from midpoints
are biased (e.g., see Haitovsky 1973), and Beaumont’s (2005) corrections are not workable
when intervals are of uneven width. Instead, the approach used here is that of Hsiao and
Mountain (1985a) in their study of the income elasticity of demand for electricity: To
approximate the distribution of categorized income by a continuous probability function,
3
Pawlowski and Breuer (2012) estimated expenditure elasticities of demand for leisure
services in Germany.
4
I thank Dan Hamermesh and Frank Stafford for clarification on the form of their income
measure.
4
using it to evaluate the conditional mean or compute the covariance between income and
other explanatory variables. In this way, the resulting regression output is known to be
consistent.
The rest of the paper is organized in four sections. Section 2 briefly discusses two
theoretical underpinnings to this investigation: A straightforward implication for the
allocation of time of the linear time-budget constraint that is analogous to the Engel
aggregation condition for commodity demand functions, and some issues involved in the
specification and estimation of a time-demand regression function. Section 3 describes the
data and the estimation method. Estimation in particular will be conducted assuming that all
consumers faced the same recreation goods prices, but, as in Mincer (1963), it will hold
constant consumers’ opportunity cost of time to avoid misinterpreting the estimated income
effects. Results are presented in Section 4. The final section summarizes the main
conclusions.
2. PRELIMINARIES
2.1 An Engel aggregation condition for the allocation of time
Suppose a consumer purchases goods and combine them with time to maximize satisfaction.
The allocation of time on a given day must obey the constraint
J 1
t
j 0
j
 t J  1, 440 ,
(1)
where t j is minutes spent on activity j and t J working time. Assume that demand functions
exist:
t j  t j  p, q, x  ,
j  0,, J 1 ,
(2)
J 1
t J  1, 440   t j  p, q, x   t J  p, q, x  ,
j 0
5
(3)
where (3) is the derived labor supply function. In these expressions, p represents a vector
with the unit prices of the goods consumed, q a vector with other relevant characteristics, and
x the log of full household income. For simplicity, the same determinants are assumed to
appear in each activity (which will hold in our empirical application).
Since (2) and (3) must satisfy (1), changes in x will cause rearrangements in the
consumer’s activities such that
J 1

j 0
t j  p, q, x 
x

t J  p, q, x 
 0.
x
(4)
Defining
e jx 
t j  p, q, x  1
,
x
tj
(5)
eJx 
t J  p, q, x  1
,
x
tJ
(6)
bj as the share of full household income spent indirectly (i.e. through the foregoing of money
income) on activity j , and bJ as the share of labor earnings, (4) leads to the following
elasticity formula:
J 1
b e
j 0
j
jx
 bJ eJx  0 .
(7)
This restriction expresses that the weighted sum of income elasticities is zero, whereby either
all elasticities are zero or there must be at least one positive and one negative elasticity.
Estimates of eJx tend to be negative (e.g., see Juster and Stafford 1991, Blundell and
MaCurdy 1999, Klevmarken 2004, and Kimmel and Connolly 2007), whereby we would
expect at least one e jx to be positive. By analogy with the analysis of expenditure patterns
(e.g., see Deaton and Muellbauer 1980), if e jx  1 activity j would be a luxury. Since bj will
increase with income if and only if e jx  1 , a luxury is therefore an activity that takes up a
6
larger share of full household income as this increases. When an activity takes up a lower
share of full household income as this increases it is a necessity. In other words, a necessity is
an activity for which 0  e jx  1 . Inferior activities are those which take up a lower quantity of
time as income increases. In that case, e jx  0 . This study focuses on estimating income
elasticities of demand for leisure or free-time activities. As argued by Robinson and Godbey
(1997), these are activities that allow maximum opportunities for choice, pleasure, and
personal expression, and facilitate recovery from work-related effort.
2.2 Specification and estimation of a time-demand regression function
The e jx 's cannot be derived from time-use observations in share form when the share’s
denominator does also react to changes in the explanatory variables. If, for example, total
non-market time were in the share’s denominator, the share elasticity would be given by e jx
minus the elasticity of total non-market time, so that e jx could not be identified without
knowing the latter. Hence, I shall work with observations in level form.


Choosing a specification and estimation method for E t j p, q, x is complicated by
the presence of diaries with zeros. Presumably, zeros pertain to two kinds of individuals:
those who never do j (non-doers), and doers who, on the observation day, spent no time on
j (called reference-period-mismatch zeros by Stewart 2013). As shown by Stapleton and
Young (1984), the latter type introduces measurement error in t j , which renders the Tobit
estimator inconsistent. Stapleton and Young’s (1984) alternative estimators relied on the
possibility of separating doers from non-doers, which is not feasible in this study. Two-part
and exponential Type II Tobit models (e.g., see Wooldridge 2010) were also discarded
because those models’ first-stage regression represents whether
j was done on the
observation day, which is quite different from whether j is done or not.
7
While the ordinary least squares (OLS) estimator is inconsistent in the Tobit context,
Stoker (1986) found that with normally distributed regressors OLS consistently estimates
Tobit’s marginal effects. The same conclusion was reached by Greene (1981), whose Monte
Carlo study further suggested that that result is robust in the presence of uniformly distributed
and binary regressors, but is distorted by the presence of skewed regressors.5 The reason
behind the apparent robustness of OLS is that the presence of (random) measurement error in
t j is inconsequential when the estimating model is linear. The combination of a linear


specification for E t j p, q, x with an OLS estimator is therefore a reasonable choice when
the regressors adopt the format recommended by Greene (1981) and Stoker (1986).
3. DATA AND METHODS
3.1 Data selection and construction of key measures
The data for this study come from the ATUS. The ATUS is drawn from a subset of
households that have completed their participation in the Current Population Survey (CPS). In
each selected household, an individual aged 15 or older is interviewed over the phone, who is
asked to report on her activities over the previous 24 hours, beginning at 4 am. The ATUS
also asks for basic labor market information (including labor force status, earnings, and hours
of work), but an important range of socio-demographic measures (such as household income)
are carried over from the final CPS interview, which takes place two to four months before
the ATUS interview. Hamermesh et al. (2005) offer a more complete description of the
ATUS.
5
Stewart (2013) has simulated the behavior of the OLS estimator with time-diary data and
produced results consistent with Greene’s (1981). The regressors in Stewart’s data-generating
process were a dummy and two uniformly distributed variables.
8
The ATUS data selected for this study were collected evenly during 2011. Particular
of that year in the United States was that the price of recreation goods remained virtually
constant. I assume that this fact plus the inclusion of within-year and spatial controls allows
us to treat the relationship between income and leisure in isolation from p . The final size of
the 2011 ATUS was 12,479 individuals. In any study of the allocation of time, a crucial
control is the opportunity cost of time. Since this is generally approximated by the hourly
wage rate in the case of workers, only wage-earners aged 23-64 were included in the analyses
(the 2011 ATUS did not ask for earnings of the self-employed). I also removed individuals
whose household income was imputed or whose earnings were updated in the ATUS
interview. (Since household income was imputed primarily from longitudinal assignments, it
may be so far apart that might have changed; also, household income may become
mismeasured when earnings were updated.) After discarding cases with other missing or
inconsistent data, the usable sample comprised 3,239 persons. Of these, 1,907 did not live
with a spouse/partner or lived with a spouse/partner who was not working (for brevity, “single
earners”), and 1,332 lived with a spouse/partner who was also working (“dual earners”).
I focus on three broad leisure aggregates: active leisure, passive leisure, and social
entertainment, plus their main component activities. These three aggregates were identified as
major types of leisure by Hill (1985) and Juster (1985b), and were also studied by Kooreman
and Kapteyn (1987) and Dardis et al. (1994). The following definitions are taken from Hill
(1985) (the specific activities involved are listed in Appendix A). Active leisure includes a
wide assortment of recreational activities requiring active physical or mental exertion, plus
some domestic crafts. Passive leisure comprises television viewing plus a variety of activities
including relaxing, exposure to other media, and communication with others. Social
entertainment is composed of spectator and participation-oriented activities, the latter
9
including meals out. All uses of time include the associated travel and are measured in
minutes.
Table 1 presents descriptive statistics on the dependent and the explanatory variables.6
The controls included in q are: The respondent’s sex, age, educational attainment,
race/ethnicity, disability status, and w , the log of the ratio of usual weekly earnings to usual
hours of work;7 indicators for the presence of a spouse/partner in the household, of children
6
All income measures are recorded before payments.
7
The wage rate was assumed to be exogenous in Solberg and Wong (1992), but was treated
as endogenous in other time-use studies. I tested for the endogeneity of w using two different
sets of instrumental variables. The first set was taken from Biddle and Hamermesh (1990) and
included dummy variables for union membership and for one-digit occupation and industry.
The second set was taken from Kimmel and Connelly (2007) and Connelly and Kimmel
(2009), and included age squared, education squared, age times education, and the statemonth unemployment rate. Both sets of instruments appeared to be weakly related to w
(particularly the second set), though their validity was hardly questioned by Hansen’s (1982)
J test of overidentification restrictions. The endogeneity of w was tested using Hayashi’s
(2000, p. 220) C statistic and having dummy variables for the observed income categories in
place of the unobserved x . Overall, instrumenting received little empirical support. As to the
first set of instruments, and with a 95% of confidence, w was endogenous only in the
regression for spectator activities among single earners and in the regression for activities
requiring mental exertion among dual earners. In both cases, its estimated coefficient was
positive (ranging from 14 to 17 minutes, S.E. around 6.5). Considering the second set, w was
endogenous only in the regressions for passive leisure and TV viewing among dual earners. In
both cases, the estimated wage effect was huge (around -300) but measured imprecisely (S.E.
around 160).
10
aged 0-5 and 6-12, and of other adults beyond the spouse/partner; and indicators for region of
residence, metropolitan status, day of the week, work day, and season of the year. Pursuant to
Greene (1981) and Stoker (1986), the average hourly wage is included in log form and the
remaining controls as (sets of) binary variables. When the respondent lived with an employed
spouse/partner, q also includes the (log of the) spouse’s average hourly wage so as to control
for possible cross-substitution and power effects within the couple (e.g., see Solberg and
Wong 1992, Kimmel and Connelly 2007, and Datta Gupta and Stratton 2010). Region,
season, and metropolitan status are intended to control for possible differences in the price of
recreation goods. As in Datta Gupta and Stratton (2010), a work day is a day on which the
respondent spent more than 2 hours working.
The ATUS does not ask for the amount of nonlabor income, which complicates the
construction of a measure of full household income. Hence, x will be measured as the log of
annual household income. Annual income differs from full income in the inclusion of the
number of actual hours worked, instead of the maximum possible hours of work. But because
of the short period of time analyzed for each individual, there is little reason to believe that
the number of hours worked in the year is related to t j , especially after controlling for the
work/non-work character of the observation day. The income level of each household was
recorded in one of 16 intervals of uneven width. Figure 1 shows that its distribution in the
sample is skewed to the right.
3.2 Estimation method

Estimation of E t j q, x

is conducted using the conditional mean (CM) and pseudo-
instrumental variable (PIV) methods developed by Hsiao and Mountain (1985a). Let


E t j q, x be specified in error form as
t j   j  γ j q   j x  u j ,
11
(8)
where  j , γ j ,  j  are unknown parameters and u j is iid with mean zero and variance  u2j . x
falls in one of 16 mutually exclusive intervals, indicated by the dummy variables z h ,
h  1,,16 . To facilitate the interpretation of the income response, Hsiao and Mountain
decided against replacing x in (8) with these dummies. Instead, they approximated the
marginal distribution of household income by a lognormal distribution (as suggested for
example by Aitchison and Brown 1957), using it to evaluate the mean of x in each interval or
to compute the covariance between x and q . In this way, income has a format recommended
by Stoker (1986). Additionally, with the inclusion of income and the wage rate in log form,
the estimating equation adopts the semi-log specification of Kooreman and Kapteyn (1987)
and Biddle and Hamermesh (1990),8 which facilitates the comparison with previous studies.9
Let θ denote the mean  and variance  x2 that characterize the marginal distribution


of x , and let θ̂ be its interval regression estimator. Then, mˆ h  E x zh  1, θˆ is a consistent
estimate for mh  E  x zh  1 . The CM method replaces x in (8) with mˆ h , and then regresses
t j on a constant, q , and mˆ h . Unless
 x  mˆ h 
and q are correlated, the resulting CM
estimates of  j , γ j ,  j  are consistent and have as asymptotic variance matrix the expression
given in (2.6) of Hsiao and Mountain (1985a). When  x  mˆ h  and q are correlated, mˆ h is
8
Stafford and Duncan (1985) used a log-linear model because their time-use data presented
almost no zeros: The TUS obtained four time diaries at three-month intervals from each
respondent, which were then combined into “synthetic weeks”.
9
Nevertheless, the shape of activity Engel curves could vary, for example, by activity or with
the amount of leisure available, as the variety of expenditure Engel curves suggests (see
Lewbel 2008).
12
not substituted for x in (8), but  q, mˆ h  are used as instruments for  q, x  . Although the
ˆ
ˆ
sample covariance estimates Σ
qx and  mx cannot be directly computed because x is
unobserved, they can be approximated by observed quantities, yielding
 γˆ PIV
j
 PIV
 ˆ
j
ˆ
 Σ
qq

 ˆ
  Σ mq
ˆ ˆ 
Σ
qm

ˆ m2 
1
ˆ
Σ
qt
 j
 ˆ
 mt j
ˆ PIV
 t j  γˆ jPIV q  ˆ jPIV x ,
j

,


(9)
(10)
where ˆ  ˆ x2 ˆ m2 and t j , q , and x are sample means. The PIV estimator is consistent and
has asymptotic variance matrix given by expression (2.13) of Hsiao and Mountain (1985a).10
The interval regression estimates of  and  x2 were 10.9564 and .6203. I tested the
appropriateness of the lognormal assumption using a chi-squared goodness-of-fit test. The test
statistic was 243.53. The critical value at 10% significance level with 13 df is 19.81. Clearly,
the null hypothesis that the distribution of household income in our sample is lognormal
cannot be accepted. The largest contributor to the criterion was the lowest income class (see
Table 2, which was constructed analogously to Table 1 of Hsiao and Mountain 1985a).
Following Hsiao and Mountain, I proceeded by removing observations in that class and
approximating the remaining observations’ income distribution by a lognormal curve. After
adjusting a truncated interval regression and redoing the test, the result was still a strong
rejection of the null, which stemmed again primarily from the lowest surviving income class.
I repeated the process eliminating each time the lowest/highest surviving income class that
contributed the most to the criterion. I stopped when the 5 lowest and the highest original
10
An element of that matrix was corrected in Hsiao and Mountain (1985b). The asymptotic
variance of ˆ
PIV
j
is calculated as 
2
uj
 γˆ PIV
j
N   q, x  var  PIV
 ˆ
 j
13

  q, x  , N being the sample size.


income classes had been removed. Then, the truncated interval regression estimates for  and
 x2 were 11.0706 and .5526. The predicted number of households in each income category is
given in Table 2 under the heading of Model 2. The chi-squared statistic was 9.87. Since the
critical value at 10% significance level with 7 df is 12.02, the lognormal assumption cannot
be rejected. Estimations, therefore, will ignore cases with household income below $15,000 or
above $150,000.11 The surviving sample comprised 2,781 persons, of whom 1,127 lived with
a spouse/partner who was also working.
4. EMPIRICAL RESULTS

This section presents the estimated income elasticities at the means of the data ˆ j t j
 for
active leisure, passive leisure, social entertainment, and their main component activities. The
complete set of time-demand regression estimates is given in Appendix B. The income
elasticities are shown in Table 3 separately for single and dual earners, as well as for the PIV
and CM estimation methods. Since the covariance of  q, x  was similar to that of  q, mˆ h  ,
differences between the PIV and CM estimates were very small.12 For comparison purposes,
Table 3 also presents elasticities obtained using midpoints of income intervals as a proxy for
x.
The estimated income elasticities for the three leisure aggregates ranged from -.09 to
.45. For their main component activities, they ranged from -.20 to .61. The highest elasticity
values were obtained for social entertainment: .30 and .45 for single and dual earners,
respectively. These estimates attained statistical significance at or around 5%. For single
11
Aitchison and Brown (1957, p. 116) discuss the systematic discrepancy from lognormality
at the ends of the income scale.
12
Expression (2.10) of Hsiao and Mountain (1985a) shows that Σ qx can be approximated as
ˆ ˆ . In this study, ˆ  1.0188 .
Σ
qm
14
earners, the main contributor to the reaction of social entertainment was the set of spectator
activities (.61). For dual earners, however, the main contributor was the category of
participation-oriented activities (.51). The magnitude of the income elasticity for active leisure
was similar for single (.20) and dual earners (.17). However, for the former group the main
contributor to the response was the set of activities requiring physical exertion (.47), whereas
for the latter it was domestic crafts (.45). Passive leisure was slightly inferior for single (-.09)
and dual earners (-.04). For single earners this response attained statistical significance at
10%, and TV viewing (-.11) was the main contributor to the reduction. The estimated
elasticities yielded by the midpoint technique were, as a rule, substantially smaller, and some
of them were of incorrect sign.
Our estimated income elasticities for passive leisure and social entertainment agree
with the claim that Americans prefer talking with friends or socializing after work to watching
TV or using the computer at home. The elasticity for participation-oriented activities among
single earners (.19) is remarkably similar to that obtained by Stafford and Duncan (1985) for
meals out among working males (.20). However, the presence in the household of an
employed spouse/partner increased that elasticity to .51. The expenditure elasticities for nonsalary income observed by Dardis et al. (1994) in a sample of households where two thirds
had income from salary from the household head, were higher and ranged from .40 for active
leisure to .59 for passive leisure and .72 for social entertainment. In combination with ours,
their results suggest that recreation goods and leisure time are not consumed in fixed
proportion, but that, holding other factors fixed, consumers endowed with more income
increase the quality (i.e., the goods intensity) of the leisure activities consumed.
The coefficient associated to w is representing both a substitution and a traditional
income effect, the latter created by variation in the consumer’s real full income when w
changes. The estimated effect of w was generally small and insignificant, with the exception
15
of the demand for passive leisure among single earners, which shrank 16 minutes per week
when the wage rate increased by 10%. As in Connelly and Kimmel (2009), the results showed
little effect of the spouse/partner’s wage on the individual’s leisure demands. The estimated
effect of education on the demand for leisure was also insignificant, which suggests that the
positive association between education and physical activity among working-age individuals
found by Mullahy and Robert (2010) stemmed from a positive income effect.
5. CONCLUSION
A straightforward implication of the linear time-budget constraint is that the weighted sum of
income elasticities of demand for the set of daily activities has to be zero, whereby either all
the elasticities are equal to zero or at least some of them is positive and other is negative. This
paper focused on estimating income elasticities of demand for leisure activities. The results of
fitting a linear model with a categorized income variable to a sample of workers taken from
the 2011 ATUS suggest that social entertainment increases moderately with income (the
elasticity ranged from .30 to .45). The effect however is larger for spectator activities among
single earners (.61) and for participation-oriented activities among individuals living in dualearner couples (.51). Active leisure is slightly normal (.17 to .20), although the effect is larger
for activities requiring physical exertion among single earners (.47) and for domestic crafts
among dual earners (.45). Passive leisure is slightly inferior (-.04 to -.09), including TV
viewing among single earners (-.11). These estimates are larger than those of previous studies
in which a measure of income obtained either by adding up several nonlabor income sources
or by computing midpoints of income intervals was utilized. They are, however, smaller than
the corresponding leisure expenditure elasticities, and suggest that consumers endowed with
more income consume leisure activities of higher quality.
16
A
COMPONENTS OF ACTIVITIES WITH ATUS ACTIVITY CODES
Active Leisure (ACT)
Requiring physical exertion (PHY)
Sports and exercise as part of job
Participating in sports, exercise, or recreation
Travel related
Requiring mental exertion (MEN)
Taking class for personal interest
Playing games
Hobbies
Writing for personal interest
Travel related
Domestic crafts (DOM)
Sewing, repairing, and maintaining textiles
Lawn, garden, houseplants, animals, and pets
Travel related
Passive Leisure (PAS)
Television viewing (TV)
Other passive leisure (COM)
Conversations with family/friends/neighbors/acquaint.
Relaxing, thinking
Tobacco and drug use
Listening to/playing music
Computer use for leisure (exc. games)
Reading for personal interest
Phone calls to/from family/friends/neighbors/acquaint.
Travel related
Social Entertainment (SOC)
Spectator activities (SPE)
Arts and entertainment (other than sports)
Attending sporting/recreational events
Travel related
Participation-oriented activities (PAR)
Attending social events with coworkers/bosses/clients
Eating/drinking at others’ home, bar, or restaurant*
Attending or hosting social events
Travel related
1st-tier
2nd-tier
3rd-tier
05
13
18
02
01
13
03
01
06
12
12
12
18
01
03
03
03
06 (12)
02
07
09,10,11
13
01 (03)
02
02
18
01
05,06
02
03
05,06
12
03
03,04
12
12
12
12
12
12
16
18
01
03
03
03
03
03
01
12
01
02
05,06
08
12
01,02
01,03
12
13
18
04
02
12 (13)
04 (02)
05
11
12
18
02
01
02
11 (12)
01 (02)
*: Time spent eating/drinking at a bar/restaurant is included whenever the respondent was not
alone.
17
B
COMPLETE ESTIMATION OUTPUT
TABLE B1.a—TIME USE (MINUTES). PSEUDO-INSTRUMENTAL VARIABLE ESTIMATES. SINGLE EARNERS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Independent variables ACT S.E. PHY S.E. MEN S.E. DOM S.E. PAS S.E. TV S.E. COM S.E. SOC S.E. SPE S.E. PAR S.E.
Constant
-21
57
-44
39
-15
31
38
32 572 106 388 97
184
77
-46
57
-40
36
-6
45
ln wage
3
6
-3
4
2
3
4
4
-23
12
-17
11
-6
9
-2
6
-3
4
1
5
Male
17
5
7
3
4
2
6
3
33
8
37
8
-4
6
-4
5
-2
3
-3
4
Age 31-40
-7
7
-6
5
-2
4
1
4
34
13
11
12
24
9
-15
7
1
4
-16
5
Age 41-50
-12
7
-14
5
-3
4
4
4
39
13
26
12
13
10
-19
7
3
4
-22
6
Age 51-64
-3
7
-10
5
-5
4
12
4
54
13
33
12
21
9
-22
7
-3
4
-19
5
Exactly high school
0
10
0
7
1
6
-2
6
-7
19
-3
18
-4
14
2
10
3
7
-1
8
Some college
4
11
0
7
0
6
4
6
-18
20
-21
18
3
14
-1
11
2
7
-3
8
College graduate
5
11
2
8
0
6
3
6
-33
20
-39
19
6
15
7
11
4
7
3
9
Pres. of spouse/partner
3
6
1
4
-3
3
5
3
3
11
6
10
-3
8
-9
6
-5
4
-4
5
Pres. of children 0-5
-16
7
-5
5
-3
4
-9
4
-28
13
-12
12
-17
10
-8
7
-3
5
-5
6
Pres. of children 6-12
-12
6
-3
4
-4
3
-5
3
-44
11
-32
10
-12
8
8
6
1
4
6
5
Pres. of other adults
-6
6
0
4
0
3
-5
3
-5
10
1
10
-6
8
-4
6
-3
4
-1
4
Black
-18
6
-10
4
-2
3
-6
4
28
12
30
11
-1
8
-12
6
-4
4
-8
5
Hispanic
-9
7
-1
5
-5
4
-4
4
-22
13
5
12
-26
9
-11
7
-7
4
-4
5
Disabled
0
11
-3
8
8
6
-5
6
22
21
14
19
8
15
-8
11
3
7
-11
9
Work day
-34
6
-16
4
-9
3
-9
3
-149 10
-91
9
-58
7
-32
6
-10
3
-22
4
Sunday
-6
6
-10
4
-2
3
6
4
17
12
16
11
0
9
5
6
-4
4
9
5
Friday
0
8
-2
5
0
4
1
4
15
14
0
13
15
10
25
8
5
5
20
6
Saturday
9
6
1
4
4
4
4
4
4
12
-9
11
13
9
34
7
10
4
24
5
Winter
-28
6
-14
4
-2
3
-11
3
29
11
43
10
-13
8
-15
6
-8
4
-7
5
Spring
-15
6
-10
4
-1
3
-4
3
29
11
19
10
10
8
-11
6
-3
4
-8
5
Autumn
-18
6
-11
4
-2
3
-6
3
26
11
35
10
-9
8
-11
6
-7
4
-4
5
Midwest
9
7
3
5
8
4
-2
4
-5
13
-5
12
0
9
1
7
2
4
-1
5
South
17
6
9
4
4
4
4
4
-3
12
-5
11
2
9
-1
6
2
4
-3
5
West
19
7
10
5
5
4
3
4
-17
13
-19
12
2
9
-5
7
0
4
-6
5
Metropolitan area
-14
6
-6
4
-1
3
-7
4
15
12
12
11
2
9
7
6
3
4
4
5
ln household income
9
6
9
4
2
3
-3
4
-22
12
-17
11
-5
9
11
6
6
4
5
5
Notes: The number of observations is 1,654 in all columns. Unreported age: 23-30. Activity abbreviations are defined in Appendix A.
18
TABLE B1.b—TIME USE (MINUTES). CONDITIONAL MEAN ESTIMATES. SINGLE EARNERS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Independent variables ACT S.E. PHY S.E. MEN S.E. DOM S.E. PAS S.E. TV S.E. COM S.E. SOC S.E.
Constant
-20
58
-43
41
-14
33
37
28 568 103 385 89
183
79
-44
59
ln wage
3
7
-3
5
2
3
4
2
-24
11
-18
9
-6
9
-2
6
Male
17
5
7
3
4
3
6
2
32
9
37
8
-4
6
-4
4
Age 31-40
-7
6
-6
5
-2
3
1
3
34
12
11
11
24
9
-15
7
Age 41-50
-12
6
-14
5
-3
4
4
3
39
13
26
12
13
9
-19
8
Age 51-64
-3
7
-10
5
-5
4
12
3
54
13
33
12
21
9
-22
7
Exactly high school
0
10
0
8
1
4
-2
4
-7
20
-3
19
-4
14
2
8
Some college
4
11
0
8
0
4
4
5
-18
20
-21
18
3
15
-1
9
College graduate
5
11
2
7
0
5
3
5
-33
20
-39
18
6
15
7
10
Pres. of spouse/partner
3
6
1
5
-3
2
5
4
3
10
6
9
-3
8
-9
5
Pres. of children 0-5
-16
7
-5
5
-3
3
-9
3
-28
13
-11
11
-17
9
-8
6
Pres. of children 6-12
-12
6
-3
4
-4
3
-5
3
-44
11
-32
9
-12
8
8
6
Pres. of other adults
-5
5
0
5
0
2
-5
2
-5
10
1
9
-6
8
-4
5
Black
-18
5
-10
3
-2
3
-6
3
29
13
30
13
-1
10
-13
6
Hispanic
-9
6
-1
5
-5
3
-4
3
-21
12
5
11
-26
9
-11
6
Disabled
0
13
-3
6
8
12
-5
4
22
23
14
24
8
17
-8
10
Work day
-34
5
-16
4
-9
2
-9
3
-149 11
-91
10
-58
8
-32
5
Sunday
-6
6
-10
4
-2
3
6
4
17
12
16
11
0
9
5
6
Friday
0
6
-2
5
0
3
1
3
15
13
0
11
15
10
25
7
Saturday
9
7
1
5
4
3
4
3
4
13
-9
11
13
10
34
7
Winter
-28
6
-14
5
-2
3
-11
3
29
11
43
10
-13
8
-15
6
Spring
-15
7
-10
4
-1
4
-4
3
29
11
19
10
10
9
-11
6
Autumn
-18
6
-11
5
-2
3
-6
3
26
11
35
10
-9
8
-11
6
Midwest
9
6
3
4
8
3
-2
3
-5
13
-5
12
0
9
1
7
South
17
6
9
4
4
2
4
3
-3
12
-5
11
2
8
-1
7
West
19
6
10
4
5
3
3
3
-17
12
-19
11
2
9
-5
7
Metropolitan area
-14
7
-6
5
-1
3
-7
4
15
12
12
11
2
9
7
5
ln household income
8
7
9
5
2
4
-3
3
-21
11
-16
10
-5
9
11
7
R-squared
.26
Notes: See notes to Table B1.a.
.14
.06
.15
.72
19
.55
.42
.23
(9)
SPE
-39
-3
-2
1
3
-3
3
2
4
-5
-3
1
-3
-4
-7
3
-10
-4
5
10
-8
-3
-7
2
2
0
3
6
(10)
S.E. PAR S.E.
33
-5
47
3
1
5
3
-3
4
4
-16
6
5
-22
6
3
-19
6
3
-1
8
4
-3
8
5
3
8
3
-4
4
4
-5
5
4
6
5
3
-1
4
4
-8
5
3
-4
5
8
-11
5
3
-22
4
4
9
5
4
20
6
5
24
5
4
-7
5
4
-8
5
4
-4
5
4
-1
6
4
-3
5
4
-6
6
3
4
4
4
5
5
.06
.21
TABLE B2.a—TIME USE (MINUTES). PSEUDO-INSTRUMENTAL VARIABLE ESTIMATES. DUAL EARNERS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Independent variables ACT S.E. PHY S.E. MEN S.E. DOM S.E. PAS S.E. TV S.E. COM S.E. SOC S.E. SPE S.E. PAR S.E.
Constant
-27
83
17
56
23
39
-67
54 385 130 272 113 113
92 -203 80
-34
45 -169 67
ln wage
5
7
6
5
-2
3
0
5
-9
11
-6
9
-2
8
11
7
2
4
8
6
Partner’s ln wage
2
7
4
5
2
3
-4
5
-12
12
-15
10
3
8
7
7
2
4
5
6
Male
21
6
12
4
5
3
3
4
30
9
31
8
-1
7
-11
6
-7
3
-4
5
Age 31-40
-17
9
-12
6
-10
4
5
6
32
14
20
12
12
10
13
9
1
5
12
7
Age 41-50
-15
10
-14
7
-10
5
10
7
23
16
21
14
2
11
-23
10
-9
6
-14
8
Age 51-64
-4
11
-10
7
-9
5
15
7
42
17
35
15
7
12
-10
11
-7
6
-2
9
Exactly high school
20
16
1
10
9
7
10
10
32
24
19
21
13
17
1
15
6
8
-5
13
Some college
18
16
1
11
7
7
11
10
-14
25
-28
22
14
18
13
15
8
9
5
13
College graduate
8
17
-1
11
7
8
3
11
-6
26
-32
22
26
18
9
16
12
9
-2
13
Married
-8
11
-3
7
-1
5
-4
7
-5
16
-6
14
1
12
-9
10
4
6
-13
8
Pres. of children 0-5
-13
7
-4
5
-2
3
-8
5
-46
11
-28
10
-18
8
-12
7
-11
4
-2
6
Pres. of children 6-12
6
6
2
4
2
3
2
4
-24
10
-17
9
-7
7
2
6
0
3
3
5
Pres. of other adults
-9
8
-8
6
2
4
-3
5
2
13
-2
11
4
9
5
8
4
4
1
7
Black
-31
12
-11
8
-6
5
-14
7
33
18
14
16
19
13
1
11
-4
6
4
9
Hispanic
0
10
3
6
-4
4
1
6
-13
15
-3
13
-9
11
12
9
5
5
7
8
Disabled
0
21
-12
14
0
10
12
13
5
32
-12
28
17
23
37
20
16
11
21
17
Work day
-48
7
-21
5
-9
3
-19
5
-115 11
-71
10
-43
8
-33
7
-8
4
-25
6
Sunday
-10
8
-7
6
-4
4
1
5
50
13
43
11
7
9
3
8
5
5
-2
7
Friday
0
10
-9
7
12
5
-3
6
13
15
3
13
10
11
13
9
6
5
7
8
Saturday
-3
8
-4
6
-1
4
2
5
15
13
-2
11
17
9
55
8
16
4
39
7
Winter
-17
8
-8
5
4
4
-13
5
32
12
34
11
-2
9
-18
8
-10
4
-8
6
Spring
2
8
-5
5
2
4
5
5
2
12
-1
10
3
8
-6
7
0
4
-6
6
Autumn
-6
8
0
5
4
4
-10
5
1
12
9
11
-8
9
-4
8
-2
4
-2
6
Midwest
3
9
2
6
0
4
1
5
-2
13
-12
12
10
9
6
8
0
5
6
7
South
-2
9
1
6
0
4
-2
5
-9
13
-18
12
9
9
-1
8
0
5
-1
7
West
4
9
-3
6
5
4
2
6
-21
14
-17
13
-4
10
4
9
6
5
-2
7
Metropolitan area
-9
7
-11
5
3
3
-2
5
8
12
8
10
-1
8
-13
7
-2
4
-11
6
ln household income
8
9
1
6
-2
4
9
6
-9
14
-5
12
-4
10
20
9
3
5
17
7
Notes: The number of observations is 1,127 in all columns. Unreported age: 23-30. Activity abbreviations are defined in Appendix A.
20
TABLE B2.b—TIME USE (MINUTES). CONDITIONAL MEAN ESTIMATES. DUAL EARNERS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Independent variables ACT S.E. PHY S.E. MEN S.E. DOM S.E. PAS S.E. TV S.E. COM S.E. SOC S.E.
Constant
-26
76
17
49
23
32
-65
51 384 140 271 123 113
90 -200 85
ln wage
5
7
6
4
-2
3
1
5
-9
10
-6
9
-2
7
11
7
Partner’s ln wage
2
7
4
5
2
3
-3
4
-12
12
-15
11
3
8
8
7
Male
21
6
12
4
5
3
3
4
30
9
31
8
-1
6
-11
6
Age 31-40
-17
11
-12
9
-10
5
5
4
32
14
20
11
12
10
13
8
Age 41-50
-14
12
-14
9
-10
7
10
5
23
16
21
13
2
11
-23
9
Age 51-64
-4
13
-10
10
-9
7
15
7
42
18
35
15
7
13
-10
10
Exactly high school
20
11
1
8
9
4
10
6
32
29
19
29
13
16
1
11
Some college
19
12
1
8
7
5
11
7
-14
29
-28
29
14
17
14
12
College graduate
8
12
-1
9
7
4
3
7
-7
29
-32
29
26
17
9
12
Married
-8
11
-3
7
-1
6
-4
7
-5
16
-6
13
1
11
-9
10
Pres. of children 0-5
-13
8
-4
5
-2
5
-8
3
-46
11
-28
9
-18
8
-12
7
Pres. of children 6-12
6
6
2
4
2
3
2
4
-24
10
-17
8
-7
7
2
6
Pres. of other adults
-9
8
-8
4
2
3
-3
6
2
14
-2
13
4
8
5
8
Black
-31
6
-11
4
-6
2
-14
4
33
21
14
20
19
16
1
10
Hispanic
0
10
3
6
-4
5
1
7
-13
15
-3
14
-9
10
11
10
Disabled
0
21
-12
6
0
8
12
20
5
41
-12
35
17
30
37
31
Work day
-48
8
-21
5
-9
4
-19
5
-115 12
-71
11
-43
8
-33
6
Sunday
-10
10
-7
6
-4
3
1
7
50
14
43
12
7
9
3
7
Friday
0
8
-9
4
12
6
-3
4
13
13
3
10
10
9
13
8
Saturday
-3
10
-4
6
-1
4
2
6
15
14
-2
13
17
10
55
9
Winter
-17
7
-8
4
4
3
-13
4
32
13
34
11
-2
9
-18
7
Spring
2
8
-5
5
2
3
5
6
2
11
-1
10
3
9
-6
8
Autumn
-6
9
0
6
4
4
-10
5
1
12
9
11
-8
9
-4
8
Midwest
3
8
2
6
0
4
2
5
-2
14
-12
12
10
10
6
8
South
-2
8
1
6
0
4
-2
5
-9
14
-18
12
9
9
-1
8
West
4
10
-3
7
5
6
2
6
-21
14
-17
12
-4
9
4
10
Metropolitan area
-9
8
-11
6
3
2
-2
5
8
12
8
10
-1
9
-13
7
ln household income
8
8
1
5
-2
4
9
6
-9
15
-5
13
-4
10
19
9
R-squared
.27
.14
.06
.16
.70
.57
.38
.30
Notes: See notes to Table B2.a.
21
(9)
SPE
-33
2
2
-7
1
-9
-7
6
9
12
4
-11
0
4
-4
5
16
-8
5
6
16
-10
0
-2
0
0
6
-2
3
.10
(10)
S.E. PAR S.E.
46 -166 71
4
9
5
3
6
6
3
-4
5
5
12
7
6
-13
7
6
-2
9
4
-5
10
6
5
10
5
-2
11
4
-13
9
4
-2
6
3
3
5
5
1
6
5
4
9
7
6
8
15
21
30
3
-25
6
4
-2
6
4
7
7
5
39
8
4
-8
7
5
-6
6
5
-2
7
4
6
8
4
-1
7
5
-2
8
3
-11
5
5
17
7
.25
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26
TABLE 1. SAMPLE DESCRIPTIVE STATISTICS (3,239 INDIVIDUALS)
Mean
S.D.
Min
Max
Variable (minutes per day)
Active leisure
45
93
0
1050
Requiring physical exertion
20
61
0
860
Requiring mental exertion
9
48
0
1050
Domestic crafts
16
52
0
580
Passive leisure
224
178
0
990
TV viewing
139
151
0
990
Other passive leisure
85
116
0
800
Social entertainment
41
94
0
1075
Spectator activities
11
56
0
1075
Participation-oriented activities
30
74
0
750
Mean
S.D.
Min
Max
Variable ($)
Average hourly earnings
23.30
13.64
4.12
72.12
Spouse’s average hourly earnings*
23.55
13.01
4.50
72.12
%=0
60.2
82.2
92.7
78.3
7.3
23.9
35.1
71.6
95.0
74.5
Mean Variable (%)
Variable (%)
Male
48.6 Summer
Age 23-30
15.6 Autumn
Age 31-40
30.1 Sunday
Age 41-50
27.5 Friday
Age 51-64
26.8 Saturday
Less than high school
4.9
Work day
Exactly high school
24.4 Household income below $5,000
Some college
28.4
between $5,000 and $7,499
College graduate
42.3
between $7,500 and $9,999
Presence of spouse/partner
55.5
between $10,000 and $12,499
Presence of children 0-5
21.4
between $12,500 and $14,999
Presence of children 6-12
26.2
between $15,000 and $19,999
Presence of other adults
18.9
between $20,000 and $24,999
Black
12.4
between $25,000 and $29,999
Hispanic
12.8
between $30,000 and $34,999
Disabled
3.2
between $35,000 and $39,999
Northeast
16.9
between $40,000 and $49,999
Midwest
26.6
between $50,000 and $59,999
South
34.1
between $60,000 and $74,999
West
22.4
between $75,000 and $99,999
Metropolitan area
84.3
between $100,000 and $149,999
Winter
25.2
above $150,000
Spring
25.8
Notes: *: Persons living with a spouse/partner who is also working (1,332 individuals).
27
Mean
25.7
23.2
25.7
9.5
24.6
53.1
0.8
0.6
0.9
1.6
1.6
3.3
4.5
4.8
6.3
5.6
9.8
9.8
11.6
15.3
14.7
8.6
TABLE 2. COMPARISON OF FITTED AND ACTUAL DISTRIBUTIONS
Model 1, original
Model 2, removing the
Logarithm of income
income
5 lowest and the highest
range
Actual
categorizationa
income categoriesb
‒
  x  8.5172
25
3
‒
8.5172  x  8.9227
21
13
‒
8.9227  x  9.2103
30
27
‒
9.2103  x  9.4335
51
43
‒
9.4335  x  9.6158
52
58
9.6158  x  9.9035
108
150
108
9.9035  x  10.1266
145
179
144
10.1266  x  10.3090
155
193
166
10.3090  x  10.4631
204
194
178
10.4631  x  10.5966
183
189
180
10.5966  x  10.8198
319
347
348
10.8198  x  11.0021
319
298
313
11.0021  x  11.2252
376
358
391
11.2252  x  11.5129
495
410
465
11.5129  x  11.9184
477
418
488
‒
11.9184  x  
279
359
Total
3,239
2 statistic
 2 (critical value)
3,239
2,781
243.53
9.87
2
13df
 19.81
2
7df
12.02
10
10
Notes: a: x  N 10.9564, .6203 . b: x  N 11.0706, .5526
28
10
TABLE 3—INCOME ELASTICITIES OF DEMAND
Single earners
Dual earners
(1)
(2)
(3)
(4)
(5)
(6)
PIV
CM
Midpoint
PIV
CM
Midpoint
Leisure activity
Estimate S.E.
Estimate S.E.
Estimate
Estimate S.E.
Estimate S.E.
Estimate
Active leisure
.20
.15
.19
.16
-.01
.17
.19
.17
.17
.05
Physical exertion
.47**
.22
.46*
.26
.14
.05
.30
.05
.26
-.01
Mental exertion
.22
.36
.21
.39
-.11
-.19
.50
-.18
.42
-.14
Domestic crafts
-.20
.25
-.19
.20
-.15
.45
.29
.44
.29
.18
Passive leisure
-.09*
.05
-.09*
.05
-.01
-.04
.07
-.04
.07
-.02
TV viewing
-.11
.07
-.11*
.06
.01
-.04
.09
-.04
.10
-.10
Other passive
-.05
.09
-.05
.10
-.06
-.06
.13
-.05
.13
.13
Social entertainment
.30*
.17
.29*
.17
.21
.45**
.20
.44**
.20
.14
Spectator
.61
.41
.60*
.36
.64
.25
.46
.25
.44
.16
Participation
.19
.18
.19
.19
.06
.51**
.22
.50**
.23
.13
Notes: Elasticities are calculated at the means of the data. Standard errors are computed using the delta method. *: Significant
at 10%. **: Significant at 5%.
29
Figure 1. Household income distribution (wage earners aged 23-64)
Notes: Author’s calculations with data from the 2011 ATUS. When the original interval
width was greater than $10,000, households were assigned assuming that they were
uniformly distributed within the original interval.
30