PRI Discussion Paper Series (No.20A-03)

Intertemporal Elasticity of Substitution with Leisure Margin

Senior Economist, Policy Research InstituteTakeshi Yagihashi
Associate Professor, Department of Economics, Strome
College of Business, Old Dominion University and
Lecturer, Faculty of Global Management, Chuo University
Juan DuMarch 2020

The views expressed in this paper are those of theauthors and not those of the Ministry of Finance or
the Policy Research Institute.

Research Department Policy Research Institute, MOF
3-1-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8940, JapanTEL 03-3581-4111

Intertemporal Elasticity of Substitution with Leisure Margin†

Takeshi Yagihashi* and Juan Du**First draft: March 2016
This version: March, 2020

Abstract

This paper investigates whether the estimation of the intertemporal elasticity of substitution of
consumption (IES) would be affected when leisure time is allowed to vary. To this end, we
adopt a utility specification that allows interactions between consumption and leisure andestimate IES using a pair of Euler equations. We find that the IES estimates that allow leisure
to respond to the market interest rate are consistently lower than the IES estimates using theconventional method that keeps leisure constant. We show that time spent on home
production explains majority of the difference between the two IES estimates due to thehigher substitutability of home production time, particularly the childcare component,
compared with other leisure time. When we exclude home production from nonmarket time,
we find the IES estimates become larger. Our findings demonstrate the importance of time
allocation when individuals make decisions on consumption and saving.

Keywords: time allocation, labor supply, earning
JEL code: E21 (Consumption), D91 (Intertemporal household choice), J22 (Time allocationand labor supply)† We thank the session/seminar participants at American Economic Association 2019 Annual Conference, Western Economic
Association International 2017 Conference, Society of Economics of the Household 2017 Conference, Hitotsubashi
University, Keio University, and Tohoku University for providing us with valuable comments and feedbacks. The views
expressed here are those of the authors and do not necessarily represent the views of Policy Research Institute.
*
Corresponding author. Address: Policy Research Institute, Ministry of Finance Japan, 3-1-1 Kasumigaseki, Chiyoda-ku,
Tokyo 100-8940, Japan; email: takeshi.yagihashi@mof.go.jp.
**
Address: Department of Economics, Old Dominion University, 5115 Hampton Boulevard, Norfolk, VA 23529; Faculty of
Global Management, Chuo University, 742-1 Higashinakano, Hachioji, Tokyo 192-0393.

1

I. Introduction
Intertemporal elasticity of substitution for consumption (hereafter IES) is widely
regarded as one of the key mechanisms that influence consumption and saving behavior
observed in the aggregate economy and has been extensively studied during the past four
decades.1 According to Friedman (1957), consumers allocate consumption over their lifetime
based on their projected lifetime income and the relative price of consumption over time. IES
indicates how strongly consumption responds to changes in the relative price, which is often
represented by the market interest rate.
One puzzle in this literature is that the level of consumption exhibits a pronounced
hump around mid-life, which is at odds with the Friedman-type life-cycle model that predicts
a relatively flat consumption profile over the lifetime. Heckman (1974) argues that once
leisure time and consumption are treated as additively nonseparable components in the utility
function, the path of consumption becomes dependent on both the interest rate and the wage
rate and can potentially explain the hump-shaped consumption. Motivated by Heckman’swork, a few studies (which we will discuss later in more detail) have incorporated
nonseparable preference in the utility specification and estimated IES while including laborrelated variables in their Euler equations.2 While this approach is clearly an improvement overstudies that entirely ignore the role of labor supply, one limitation is that labor-related
variables are effectively treated as exogenous. If consumption and leisure were to act as either
substitutes or complements in raising utility as Heckman argues, it is natural to assume that an

1 According to Havranek et al. (2015), over 300 academic papers have estimated IES during the same period: of the 169

published papers, 21 were published in the 1980s, 62 in the 1990s, and 86 during 2000-2014.
Past studies that emphasized the general importance of nonseparable preference in the context of consumption/saving
behavior, but did not specifically focus on obtaining the IES estimate, see for example, Aguiar and Hurst (2005), Altonji andHam (1990), Attanasio (1995), Attanasio and Browning (1995), Attanasio and Weber (1993), Blundell et al. (1994, 2016),
Browning and Meghir (1991), Eichenbaum et al. (1988), Ham and Reilly (2002), Mankiw et al. (1985), and Ziliak andKniesner (2005). Attanasio and Weber (1995) and Blundell et al. (1994) have included labor in the Euler equation estimation.

22

individual would adjust both consumption and leisure in response to the interest rate. If so,treating labor as exogenous may result in biased IES estimates.
The main goal of this paper is to examine whether IES estimates would be affected
when we treat leisure time as endogenous. Our approach is different from the existing
literature in two aspects. One is that we use a utility specification that directly allows
interaction between consumption and leisure. The second is that we examine the componentsof leisure time and identify the component that matters the most in consumption smoothing.
In the first half of this paper, we compare IES estimates when leisure is held constant
and when it is not. To this end, we employ a utility function of the King-Plosser-Rebelo form
(King et al., 1987), in which consumption and leisure are additively non-separable, an
extension of the CRRA utility function used in many macro studies. When estimating model
parameters, we utilize two intertemporal efficiency conditions for consumption and leisure.
We use the Consumer Expenditure Survey (CEX) for this analysis because the CEX has
information on both consumption and work hours. Work hours are converted to nonmarket
time, which serves as a proxy for leisure. For estimation, we construct a synthetic panel basedon birth-year cohort and estimate the IES using the Generalized Methods of Moments(GMM). We find that the leisure-varying IES is 0.115 and the leisure-held-constant IES is0.327. The almost threefold gap between the two IES estimates suggests that the leisuremargin plays an important role in smoothing consumption over the lifetime. That leisurevarying IES is lower than leisure-held-constant IES also holds for other forms of utility
function we experimented with (i.e., Jacob, 2007).
In the second half of the paper, we attempt to identify the leisure component(s) that
could explain the gap between the leisure-varying and leisure-constant IES by decomposing

3

nonmarket time into pure leisure (which we refer to as nonwork time) and those including
some form of home production. One could argue against using nonmarket time on several
grounds. First, leisure activities are heterogeneous in nature. For example, much of thehousehold chores (e.g., cooking, cleaning) and childcare can be either purchased from themarket or produced at home by spending one’s own time (Baxter and Jermann, 1999),
whereas other leisure activities (e.g., eating, sleeping, socializing) do not have market
alternatives. Second, activities that involve continued time investment, such as childcare, havethe nature of “durable goods” that produce a constant flow of utility in the future (Kydland
and Prescott, 1982).3 Finally, different leisure components are associated with different
utilities and respond differently to the wage rate. 4 Therefore, we explore several alternative
leisure measures that represent more “pure” leisure than nonmarket time.
Empirically this exercise requires information on detailed leisure time, which is notavailable in the CEX. We employ an imputation method that predicts time uses for individuals
in the CEX with information in the American Time Use Survey (ATUS) in which detailed
time use variables are available. We find that the leisure-varying IES estimated using“nonwork time” defined as nonmarket time less home production is 0.240, about twice thesize of the IES estimated using nonmarket time. This demonstrates that home production
accounts for much of the gap between leisure-varying and leisure-constant IES.

3 We note that similar argument is often employed in justifying the use of nondurable goods and services as the relevant

consumption measure when estimating the IES. This is because the change in durable goods and services spending (e.g.,purchase of cars, education, and health care) would not necessarily reflect the contemporaneous effect that interest rate has onthese expenditures.
4 Kahneman et al. (2004) and Krueger (2007) find that time spent on education and childcare is less pleasurable than otherleisure activities. Also, different leisure components are known to respond differently to the wage rate. See, for example,
Kimmel and Connelly (2007) for childcare time; Du and Yagihashi (2017) for exercise and medical/personal care time;
Biddle and Hamermesh (1990) for sleep time; Du and Leigh (2015) for smoking.

4

Our results offer new and important insights to the literature. First, when
consumption-leisure substitution is accounted for, the IES estimates become smaller. Ourpreferred IES estimate is 0.115, which is much lower than the median estimate of 0.5 asreported in the meta-study of Havernek et al. (2015). The studies included in Havernek et al.
largely ignore the role of labor/leisure. The few studies that incorporate labor-related variables
in IES estimation only report leisure-held-constant IES.5 In later analysis, we compare ourestimates of the leisure-held-constant IES with theirs. To our knowledge, this paper is the firstto provide IES estimates allowing for adjustment of the leisure margin and to compare withthe leisure-held-constant IES often seen in the literature.
Second, we explore the heterogeneous nature of the leisure time by examining
substitutability of different leisure components with consumption. We show that the IES
estimates become larger when housework and/or childcare time are excluded from nonmarket
time. This result is consistent with the change of a single parameter that measures thesubstitutability between consumption and leisure time. This parameter value becomes larger
when we include housework and childcare time in our leisure measure, either individually or
jointly. Our work is the first in pointing out the importance of home production, particularly
the childcare component, in smoothing consumption over the lifetime.
This paper is organized as follows. In Section II we discuss the theoreticalframework. Section III provides details on the data and the estimation method. Section IV
reports the main result and Section V conducts further analysis using predicted time use.
Conclusions follow in section VI.

5

These studies include Attanasio and Weber (1995), Blundell et al. (1994), Jacobs (2007), Basu and Kimball (2002),
Kilponen (2009).

5

II. Theoretical Framework
II.A. Individual’s Optimization Problem
In our model, individuals maximize their lifetime utility subject to constraints
associated with budget and time. Specifically, their time-separable lifetime utility can be
written as
max
where

is consumption,

,

,

1

1 is the time discount factor. We follow Becker

is leisure, and(1965) and assume that consumption and leisure act as substitutes in producing utilityyielding “commodities” by selecting a period utility function of the King-Plosser-Rebelo form
(King et al., 1987):
,
where

and

,

(2)

are curvature parameters associated with consumption and leisure, which areassumed to be nonnegative. These parameters capture how quickly people become satiatedwith increased consumption (whenis fixed) or leisure (whenis fixed). Whenisnonzero, the value of one variable would affect the marginal utility of the other. Thisparameter also influences the extent of substitutability between consumption and leisurebecause it enters the cross-partial derivative:
1,

The sign of,is determined bypositive values. If

1

1

.

(3)

because consumption and leisure can only takeis negative, then consumption and leisure are substitutes.

In maximizing the lifetime utility (1), individuals face two constraints: the budget
constraint and the time constraint. The budget constraint can be expressed as

6

,

,

represents savings that pay a predetermined real interest rate

where
,

(4)
in the next period.

is the after-tax income
,

where

1

,

≡ 1

,

(5)

,

, is the real wage rate for the individual and the spouse, and,are the time,spent on market work by the individual and the spouse, respectively. Parameter
progressivity of the tax system, and0). A larger

captures theis the tax rate when the tax system is proportional (i.e.,

implies higher penalty for working longer hours, which could affectconsumption-leisure decisions at the margin. The time constraint is expressed as
,
where

(6)

is the total endowed time that is constant and the same across individuals (e.g., 24

hours a day).

is the time that generates neither utility nor income, which we treat as

exogenous. Under this framework, individuals decide how to split time between leisure and). Deriving the first-order necessary conditions andwork out of the “available” time (combining them yield a pair of intertemporal efficiency conditions:11where before-tax income

,

≡

,

,

7
,
,

,

8

, . Equation (7) is the conventional

consumption Euler, whereas equation (8) is the leisure Euler, which describes intertemporal
substitution of leisure demand.

7

Equation (7) implies that when leisure is held constant, the intertemporal elasticity of
substitution for consumption is≡. When leisure is allowed to vary in response to theinterest rate while keeping the wage rate fixed, the intertemporal elasticity of substitution of
consumption (IES) becomes
≡

1

,

(9)

which follows directly from Swanson (2012) after substituting the partial derivatives of theutility function in Equation (2). The expression in Equation (9) implies that under a special
case where≡ , that is, the marginal utility of consumption is= 0 we have

independent of leisure. For a nonnegative value of ,When

1 (log-utility),

influence IES, we need both

and

and

will be positively associated.

both become one. Thus, for the leisure margin to
0 and

1.

III. Data and Estimation Strategy
We estimate the IES using the log-linearized version of Equations (7) and (8). Theseequations contain the growth rate of three variables (consumption, leisure, and wage rate). We
first describe how these variables are defined and then explain the estimation methodology.

III.A. Consumer Expenditure Survey
Our data source is the 1996-2014 Consumer Expenditure Survey (CEX) conducted by
the Bureau of Labor Statistics. The survey primarily records expenditures of a given“Consumer Unit (CU)” on a wide variety of items on a quarterly basis.6 Each household isinterviewed five times (four of them available to the public) over the course of one year and

6

A CU is defined as: (1) two or more people related by marriage, blood, adoption, or other legal arrangement who make joint
financial decisions; (2) a person living alone, or sharing a house with others but is financially independent.

8three months. In each quarter, the survey replaces 20% of the households with newly selectedhouseholds. In addition to consumption, the CEX also collects data on wages, earnings, andwork hours for each CU member. While consumption data are recorded at the CU level, wage
rate and work time are available at the member level.
To estimate parametersandin Equations (7) and (8), we use the synthetic cohort

approach to capture cohort fixed effects arising from each generation’s common lifetime
experience.7 We focus on employed individuals in their prime working years and restrict oursample to five birth-year cohorts (1951–1955, 1956–1960, 1961–1965, 1966–1970, and
1971–1975).8 To be eligible for our sample, the individual must appear in both the second andthe fifth waves of the interview and report positive wage rates (defined below). To mitigate
measurement errors, households with zero food expenditures and those with negative entries
for other nondurable goods are excluded.9

III.B. Definition of Main Variables
Nondurable consumption is defined as the sum of consumption on all nondurable
goods and services.10 We convert it into real values using the Consumer Price Index (CPI).
We assume the consumption growth rate to be the same for everyone in the same CU because
we cannot distinguish each CU member’s consumption in the CEX. Major consumption
decisions are usually made collectively within a household, and it is conceivable that the7

Other advantages are described in Chamberlain (1984) and Hayashi (1987). For examples of the synthetic cohort approach,see Attanasio and Weber (1995), Ghez and Becker (1975), and Rupert et al. (2000).
8 Thus the age range in our sample is 21-45 in 1996 and 39-63 in 2014.
9
By applying these sample selection criteria, we lose 3936 observations (3893 with zero food expenditure, 43 with negative
entries for other nondurable goods).
10 Nondurable consumption includes food, alcoholic beverages, tobacco and smoking, apparel and services, household
operation, utilities and fuels, gasoline, maintenance and repairs, vehicle-related expenses, public transportation, reading, fees
and admissions, maintenance and insurance, baby day care, domestic services, and personal care. Rent, education, andhealth-related goods and services are not included in our definition.

9

growth rate does not differ much among CU members. Following Attanasio and Weber(1995), we only consider consumption in the month immediately before the interview month.
This helps to avoid complicated error structures arising from having a monthly spending
covering different quarters as well as helping to reduce recall bias.
In our baseline analysis, leisure time is defined as total time minus work time (i.e.,“nonmarket time”). Specifically, we use total hours available in a year (8736 hours = 24hrs
7days

52weeks) minus the product of hours worked per week and weeks worked per year.

This number is multiplied by 0.75 for the 9-month period that consumption is measured.
For the wage rate, each CU member in the CEX is interviewed about their gross pay inthe last pay period and the period that this payment covers (one week, two weeks, month,quarter, and year). CU members are also asked about their wages and salary income before
deductions over the past twelve months. Our first wage measure is constructed by dividing
the gross pay by the corresponding work hours during the reference period. This is ourpreferred measure, because it closely represents the wage rate paid at the time of theinterview. For the second measure, we use annual wage and salary earnings divided by annual
work hours. Whenever the first wage measure is missing, we replace the missing with thesecond wage measure.11
For the nominal interest rate, we use the 3-month treasury bill rate, which is common in
the IES literature.

III.C. Estimation

The linearized Euler equations (7) and (8) are as follows:11

Ham and Reilly (2002) use a similar approach when constructing the wage rate in the CEX.

10∑ ∆ln

,

1

,

′ ∑ ∆
∑ ∆ln

,

∑ ∆ln
′ ∑ ∆
where

,

,

,

∑ ∆ln

,

∑ ∆ln

(10)

,

∆ln

,

,

,

,

,,

,

(11)

≡ 1⁄ is the leisure-held-constant IES and I is the number of observations of acohort in a given quarter (“cell size”). The interest rate and the wage rate are both adjusted for
inflation using the CPI. Vector z includes the number of adults (adults), the number ofchildren less than age 18 (children), marital status (single), whether the spouse works fulltime (spouse fulltime), spouse’s nonmarket hours (spouse nonmkt), spouse’s before-tax labor
income (spouse salary), and before-tax labor income of other CU members (other CU
salary).12

represents seasonal dummies.

Cohort-based growth rates for consumption, leisure, and wage rate are obtained byfirst taking the growth rate for each respondent between the second and the fifth interview (9month period), and then taking the average of these growth rates for a given cohort in eachquarter.13 By aggregating in this way, we can reduce the bias caused by serially correlated
errors. This approach also ensures that the growth rate is constructed using the same
individual across two periods so that any change in consumption growth is not caused bychanges in sample composition due to lifetime events, such as marriage, divorce, andchildbirth.

12 Spouse nonmarket hours is calculated in the same way as the main leisure variable.
13
We note that since our sample consists of those having positive wages in the second and fifth interview waves, anindividual could exit and re-enter the labor market between the waves. Our measure of annual nonmarket time may capturesome of the changes due to these entries and exits.

11

The linearized version of Equation (5) allows us to obtain an estimate for .
upon the (log of) before-tax

Specifically, we regress the (log of) after-tax income

income using Ordinary Least Squares. After-tax income is computed as before-tax CU income
net of federal, state, and social security taxes. These taxes are simulated jointly using
TAXSIM 9.0 software provided by the National Bureau of Economic Research.14 Our
estimate foris 0.081, which is similar to Heathcote et al. (2010, 2014)’s estimates.

Equations (10) and (11) are jointly estimated using GMM. Identification is achieved
using lagged variables as instruments. Specifically, we include the second, third, and fourthlags of the endogenous variables (consumption growth, leisure growth, nominal interest rate,inflation, and labor income growth), the second and third lags of the number of CU members(adults, children, and adults older than 64), age, age squared, and three seasonal dummies.
Four observations are lost for each cohort because four lags are used to construct instruments.
The total number of observations is 360 (= 5

(76

4)).

The average cell size of our sample exceeds 100 for all cohorts (see Table 1), whichhelps to reduce the risk of a spurious MA(1) error structure induced by limited cell size.15 The
fact that one CU member only appears once in the sample reduces autocorrelation withincohorts over time. To further mitigate the problem, we apply a weight matrix that controls forboth autocorrelation and potential heteroscedasticity arising from different cell sizes (i.e., thenumber of observations for each cohort in a quarter is different). Finally, clustered standard
errors are applied at the cohort level.

14 For simplicity, we treat each CU as a single tax unit and do not consider cases in which CU members file their taxes
separately. The income used as input in the tax simulation is the sum of all members’ labor income, self-employment income,and incomes from other sources such as rent, alimony, child support, estates, trusts, royalties, interest, social security, andtransfer income. We largely follow the code and procedures provided by Lorenz Kueng on the NBER website:
http://users.nber.org/~taxsim/to-taxsim/cex-kueng/cex.do.
15
A spurious MA(1) structure in the error term would generally make the first lagged endogenous variables invalid
instruments. See Attanasio and Weber (1995) for more details.

12III.D. Check on Concavity/Substitutability
We conduct statistical tests on the concavity of the utility function. For the utility
function to be concave, the estimated parameters must satisfy three conditions: (1)negative; (2)is negative; (3)equivalent to

0,

1

is

is nonnegative. In our model, this is1

0. If one of these null

0, andhypotheses is rejected at the 1% significance level, the concavity assumption is violated. We
also conduct hypothesis tests on whether consumption and leisure act as substitutes ingenerating utility. Specifically, we examine the sign of the cross-elasticity of equation (3),which depends on the sign of1. If the null

1

0 is rejected, thesubstitutability assumption can potentially be violated. Both tests serve as a check on theplausibility of the point estimates ofand .

IV. Result
IV.A. Summary Statistics
Table 1 shows cohort summary statistics. Americans spend roughly 39 hours on work
per week or 128 hours on nonmarket time. Nonwork time (nonmarket time less home
production) occupies roughly 86% of the nonmarket time.16 Consumption at the CU level isthe highest for the cohort born between 1961-65 ($2,314), which reflects both the relatively
large household size (3.40 person, second highest) and the average before-tax CU income($78,709.32, second highest). The average wage rate is the highest for the oldest cohort born
between 1951-55 ($35.46/hour).

16

Details on how home production time is calculated is explained in Section V.

13

Figure 1 plots the average cohort nonmarket time, nondurable consumption, andhourly wage rate by age with a 5-year interval. Each line segment represents the average ofeach cohort. In panel (a), we see a mild U-shape for nonmarket time. This is expected as work
time tends to be high in the middle ages and low for the very young and the very old.
Consumption peaks around the middle ages17 and the wage rate keeps rising until close to theretirement age, which are in concordance with the cohort-based summary statistics.

IV.B. Baseline Estimation
Table 2 reports IES estimates for different sets of control variables. Column (a) shows
the result with no controls. The leisure-varying IES estimate
held-constant IES

is 0.091 whereas the leisure-is 0.304, which is more than three times the size of. The substitution

parameter , which explains the gap between the two IES estimates are positive andstatistically significant. The Sargan criterion suggests that the instruments used in theestimation are valid.
The importance of household characteristics in the context of IES estimation has been
noted in the literature (e.g., see Attanasio and Weber, 1995). Schirle (2008) and others showthat adults’ labor supply decisions often depend on their spouse’s labor market participation.
Column (b) adds the number of household members (adults, children) and column (c) further
adds marital status (single) and spouse’s labor market variables (spouse fulltime, spouse

17
Factors that explains the hump-shaped age profile other than household size include for example liquidity constraints,
income uncertainty, and work-related expenses. For more on this topic, see, for example, Aguiar and Hurst (2013), Attanasio
et al. (1999), Carroll (1994), and Hubbard et al. (1995).

14

nonmkt). In Column (b),increases from 0.091 to 0.115 and0.327. In Column (c), the estimates for, , andincreases from 0.304 toremain close to those in Column (b).18

Studies have repeatedly shown that the presence of a secondary earner in thehousehold provides indirect insurance against unforeseen lifetime events that negatively
impact the primary earner (Low, 2005).19 To check whether such an effect is present, weconsider two separate income variables. Column (d) adds spouse’s salary and column (e)replaces spouse’s salary in (d) with salary of the other CU members in case there are multiple
earners in the household. In Column (d), the estimates forunchanged from (b). In Column (e), the estimates forand, , andremain almost

go up slightly to 0.120 and

0.343, respectively.
In sum, we find that the leisure-varying IES to be consistently lower than the leisureheld-constant IES regardless of which control variables are used and that the substitutability
parameteris positive and statistically significant. This result suggests that consumption-

leisure substitution is important in understanding individuals’ consumption decisions over the
lifetime. The IES estimates in (b)-(e) are slightly higher compared to (a). To keep the model
simple, we use the specification in (b) as our baseline specification in subsequent analyses.20

IV.C. Comparison with existing studies

18

In later analysis, we experiment with an alternative utility specification in which the spouse’s leisure enters differently into
the individual’s maximization problem.
19
Blundell et al. (2016) specifically examine the effect of working spouses as an insurance against wage shocks. They findthat wives’ labor supply increases by 1.7 percentage points for a permanent 10% decrease in husbands’ wages. See also
Stephens (2002), which examines how labor supply of wives changes in response to husbands’ job losses.
20
We have also experimented whether the above result hold when proportional tax is assumed, which sets
0. Comparedto our baseline specification in column (b), the IES estimates
falls from 0.115 to 0.093. Since the change is quantitatively
minor, we do not report the full estimation result in the main text.

15

Past studies that allow for consumption-leisure (or labor) interactions have mainly
taken two different approaches: one uses fully-specified macroeconomic models to estimate
model parameters,21 and the other uses a more parsimonious model with fewer parameters.
Here we compare our results with the latter.
One of the most commonly applied utility functions takes the exponential form of
,
where

exp
′

satisfies the property of

1

0, ′′

,

(12)

0 (increasing disutility oflabor).22 Basu and Kimball (2002) proposed an approach that does not require

to beparametrically specified. Instead, they imposed an economic restriction that labor income tospending ratio must be constant, which also means that the variation of labor hours in
response to the wage rate is suppressed. The estimating equation becomes the following
modified consumption Euler equation,
∑ ∆ln

∑ ∆ln

,

,

∑ ∆ln

,

where

,

,

,

represents the labor-held constant IES. Using US macro data, they findwithin the range of 0.61 (for0.4) and 0.74 (foris1.2). Kilponen (2012) repeats thesame exercise using household-level data in Finland and estimate
Appendix Table A.1 reports the estimates of(13)

to be 0.23 (for0.5).

for Basu and Kimball’s specification

using our micro-data. The IES estimates range between 0.408 (with demographic controls)
and 0.646 (without any controls). Both values are reasonably close to Basu and Kimball’s

21

See, for example, Dotsey et al. (2014), Fujiwara et al. (2011), Smets and Wouters (2005, 2007).

22 For example, within the macroeconomics literature it is common to assume, where0. However, theestimation ofoften encounters identification problem and requires this parameter to be either calibrated or impose a priordistribution in the estimation.

16

original estimates. We note that Basu and Kimball’s approach cannot be used to obtain laborvarying IES, as we do in this paper.
Jacobs (2007) has used utility functions similar to ours,
,

,

(14)

where consumption and leisure are further assumed to be homogeneous of degree one. The
linearized Euler equation for consumption is given as
∑ ∆ln

,

,

1

∑ ∆ln

,

,

,

(15)

is the leisure-held constant IES.23 The Euler equation for leisure can be written as

where

∑ ∆ln

,

∑ ∆ln

,

1

∑ ∆ln

,

,

,

,

(16)

where

reappears in the leisure Euler equations. Jacobs (2007) only estimated Equation (15)and finds

to be within the range of 0.036-0.224. He also provided implied parameter values

for

and

estimate,based on the estimates ofand 1.24 For comparison purpose, weusing one Euler equation (consumption Euler only) as well as with two Euler

equations (consumption and leisure Euler).25 Appendix Table A.2 reports the result. We
estimate thatis 0.281 for single-equation estimation and 0.339 for two-equations

estimation. The latter is remarkably close to our baseline estimate (varying IES

0.327). The leisure-is 0.170 for the single-equation estimation and 0.185 for the two-equations

and 1
1 .
24
He takes this approach because the nonlinearity in parameters combined with the homothetic preference makes theparameters , difficult to be directly estimated in the estimating model.
25
We set0 to stay close to their original specification.
23 We note that this equation is observationally equivalent to our baseline specification, with17

estimation, which is also reasonably close to our baseline estimates. However, both the oneequation and two-equations IES estimates are not statistically significantly different fromzero. In addition, the estimates forandare negative in the two-equations case, which

violates the assumption of concave utility.
Lastly, we note that Low (2005) extends Heckman’s (1974) model by introducing
uncertainty and a precautionary motive of work. Low finds that consumption profiles
becomes less responsive to exogenous shocks once labor is allowed to vary. While we do nothave the uncertainty component in our model, our finding is consistent with Low (2005) inthe sense that labor supply serves as an additional adjustable margin to consumption
fluctuations.

V. The Role of Home Production
V.A. Constructing Alternative Leisure Measures
Our next objective is to understand the nature of substitution between consumption
and leisure. As we noted in the introduction, it is difficult to substitute some leisure activities(e.g., eating and sleeping time) with consumption, whereas it is relatively easy to outsource
home production activities to market-based goods and services. We define home production
as the combination of housework (e.g., cooking, cleaning) and childcare (primary,educational, recreational), both of which have market-based alternatives.
In this section, we re-estimate the IES by replacing nonmarket time with alternative
leisure measures. Particularly, we use nonmarket time less housework, nonmarket time lesschildcare, and nonmarket time less home production (“nonwork time”).26 The first two are26

We note that nonwork time includes both “core” leisure activities such as sleeping, eating, socializing, relaxing, andvolunteering as well as “quasi” leisure activities such as medical care, religious/civic activities, care for adult household

18

used to identify which of the two components of home production matters in IES estimation.
These alternative leisure measures are not readily available in the CEX. To overcome thisissue, we apply an imputation method that allows us to incorporate the detailed time use datain the ATUS. The ATUS is conducted by the US Census Bureau and primarily collects
information on how Americans spent their time on a given day using a diary format. The
imputation involves estimating the ratio of the alternative leisure measures and nonmarket
time in the ATUS, and then using the predicted ratios and nonmarket time in the CEX to
impute the alternative leisure measures. The observable individual characteristics are very
similar across the two datasets, which allows us to impute leisure time on an individual basis.
To ensure good quality of imputation, we tried many model specifications of the regression
model and selected the one with the lowest AIC or BIC. The details of the imputation method
are available in Appendix A. We also conducted several checks to ensure that our imputation
works properly. First, the predicted share of nonwork over nonmarket time is 86.7% in the
CEX, which is close to 86.6% reported in the ATUS. Second, we plotted the age and cohort
profile of nonmarket and nonwork time in the two datasets and find that they track each otherclosely.27 We regard these as a comforting sign that the imputation is working well.

V.B. Preliminary Analysis
Figure 2 presents the life-cycle profile of four different leisure measures (housework,
childcare, nonmarket time less housework, nonmarket time less childcare) plotted in five-year
age groups. Housework and childcare (top two panels) have an “inverted” U-shape. The peakmembers, and education. Online Appendix Table O.2 provides the complete definition of the time use variables in this paper
based on the ATUS code.
27
Both dataset show that the lifecycle profile of nonwork time exhibits U-shape whereas the birth-year cohort profile ofnonwork time exhibits a monotonically increasing trend from the oldest to the youngest cohort. See Online Appendix for
more details.

19for housework time occurs between ages 46-50, whereas the peak for childcare time occurs
between ages 31-35.28 The difference in peak timing is also reflected in the lifecycle profilesof the leisure measures that exclude housework or childcare from nonmarket time (bottom
two panels).
Figure 3 shows the time series plots of aggregate leisure measures averaged acrossemployed individuals. As we move from the most broadly defined nonmarket time (top panel)
towards the most narrowly defined nonwork time (bottom panel), the series become lessvolatile. Nonwork time shows a clear upward trend whereas nonmarket time does not. The
upward trend for nonwork time is consistent with the findings in Aguiar and Hurst (2007).
To examine the statistical association between consumption and leisure, we estimate
the following regression model,
Δ

Δln

,

,

Δln

Δln

,

,

Δ

,

(17)

,

where
component,,

represents the percentage of nonmarket time spent on a specific leisure,

is nonmarket time, and,is the vector of other control variables(marital status, whether the spouse works fulltime, spouse’s nonmarket hours, family size,
number of children).29 We include individuals who are born between 1951 to 1975 to beconsistent with the GMM estimation.

represents the association between consumption andthe leisure component. Figure 4 reports the estimates of
estimate offor selected leisure time. The pointis negative for childcare (-0.048), care for others (-0.038), and housework (-28
We also observe that housework time does not overlap one another compared with childcare time. Part of this can be
attributed to technology improvement as well as lifestyle changes that reduced time spent on housework more drasticallyover the sample period (1996-2014).
29
The regression is similar to Aguiar and Hurst (2013) that explore the effect of labor supply on how consumption isallocated conditional on a given level of spending. We further utilize the short-panel nature of the CEX data to account forunobserved characteristics of individuals.

20

0.003), but positive for other leisure time, such as medical and personal care (0.002), sleepand eat (0.007), and exercise (0.035). The different signs indicate the heterogeneous nature ofleisure time. The strength of substitution between consumption and leisure time is also
different, with childcare showing the strongest substitution and exercise showing theweakest.30

V.C. IES Estimation with Different Leisure Measures
In this subsection, we examine how sensitive IES estimates are when alternative
leisure measures are used. Results are shown in Table 3. First, we observe that the leisureheld-constant IES

remains within a narrow range (0.342-0.377) and is not much different

from the baseline case when nonmarket time is used (0.327). Second, we find that the leisurevarying IES

for nonwork time is twice as large as the

0.115). Finally, the leisure-varying

for nonmarket time (0.240 vswhen nonwork time is used remains smaller thanunder the same leisure definition (0.240 vs 0.377), consistent with our baseline result
presented in the last column of Table 3.
In the third and fourth columns of Table 3, we show that

increases from 0.115(baseline) to 0.133 when we exclude housework from nonmarket time, and increases to 0.190
when we exclude childcare. The change in the estimate ofcan be used to infer thesubstitutability between leisure and consumption. When childcare is excluded fromnonmarket time, the estimate ofhousework is excluded

falls from 2.726 (baseline) to 1.222, whereas whenfalls from 2.726 (baseline) to 2.483. This implies that time spent onchildcare is more substitutable with consumption compared with housework.

30
It should be further noted that the negative coefficient on housework is not statistically significant. Detailed estimation
result is available in Online Appendix Table O.3 (home production time use) and O.4 (nonwork time use).

21

There are two possible explanations for this result. First, when leisure is definedbroadly to include all nonmarket activities (i.e., nonmarket time), it is relatively easy for
individuals to find the optimal mix of consumption and leisure. Second, in contrast tohousework and childcare, some leisure activities are inherently more time-intensive and are
more difficult to be substituted by consumption (e.g., sleeping and eating), whereas others
require both consumption and time input (e.g., taking group exercise classes, visiting doctor’s
office, and getting a haircut). Childcare in contrast has readily available substitutes in themarket such as daycare and baby-sitters.

V.D. Subsample Analysis
In this subsection, we examine whether our results on nonmarket and nonwork time
hold for subsamples and whether the subsample differences are consistent with the literature.
We select gender, the level of education, and stock-holding status as our subsample criterion.
While there are no studies looking into the IES gap across gender, literature has provided
ample evidence on how men and women differ in labor supply behavior and how theypotentially affect consumption.31 The IES gap across education levels and stock-holding
status has been studied extensively in the literature.32 For subsample analysis, we estimate theconsumption and leisure Euler equations jointly for a pair of subsamples and test whether thedifference in the IES estimates between the two subsamples are statistically significant.33

31

For example, see Apps and Rees (2005), Bishop et al. (2009), Blau and Kahn (2007), and Kumar and Liang (2016).
For example, Attanasio and Borella (2014) study how IES varies by education and find that IES tend to be higher for thehigher-educated. There is a large body of work that study the effect of financial market participation on IES, which find that
IES tends to be higher for those who hold market-based financial assets. See, for example, Attanasio and Browning (1995),
Attanasio and Paiella (2011), Blundell et al. (1994), Gorbachev (2011), Guvenen (2006), and Vissing-Jorgenson (2002).
33
Yagihashi and Du (2015) use a similar method to examine the relationship between IES and risk aversion.
32

22

The results are shown in Figure 5.34 For each subsample, we provide (leisure-varying)
IES estimates using both nonmarket and nonwork time represented by two separate columns,
with the gap between subsamples shown in the last set of columns. Women are found to havenotably larger IES than men for both nonmarket time (0.18 vs 0.02) and nonwork time (0.24
vs 0.11), which can be linked to the higher(0.302-0.322 for women vs 0.092-0.246 formen). College-educated individuals have a larger IES estimate than lesser-educatedindividuals, though the gap appears to be small (0.05 vs 0.04 for nonmarket time and 0.12 vs0.09 for nonwork time, only statistically significant for the latter). Similarly, stockholders
have a marginally larger IES estimate than non-stockholders (0.063 vs 0.056 for thenonmarket time and 0.14 vs 0.11 for the nonwork time).35 While there are no studies thatallows comparison with regard to gender, those of education and stockholding are in line withthe literature.
In all six subsamples, the leisure-varying IES is strictly lower than the leisure-constantIES. Figure 5 further shows that the IES estimate for nonmarket time (dark-colored column) issmaller compared with that for nonwork time (light-colored column) in all cases, consistent
with the overall sample. Most notably, IES for the men falls sharply from 0.11 (nonworktime) to 0.02 (nonmarket time), which suggests that men actively substitute consumption andhome production time. For women, the change appears somewhat less apparent (0.24 for
nonwork vs 0.18 for nonmarket). The result may be related to socio-economic differences
between gender.36

34 For full estimation result, see Online Appendix Tables O.5-O.7.
35
To define stockholding status, we follow Cogley (2002) to include not only those who reported a positive value for theirstockholding, but also those who made investment in a private retirement account or IRA and those who reported positive
income from interest and dividend. By including these additional categories, we have 61.09% of the sample categorized as
stockholders.
36
Possible reasons include, but not limited to, (a) the types of home production activities that women primarily engage (e.g.,breastfeeding) have either limited market substitutes or makes them less eager to pay for it, (b) many women work in

23

V.E. Robustness Analysis
In Section III, we find that spouse’s leisure (spouse nonmkt) is one of the highly
significant explanatory variables, though including it in estimation did not affect the IES
estimates much. It is possible that our baseline specification of Equations (10) and (11) fails
to fully embrace the psychological effect that spouse’s leisure has on one’s
consumption/leisure choices. We now consider a slightly different model in which anindividual internalizes the spouse’s leisure in the following manner,
,

,

,

where

,

is the “composite” leisure,

,

,

,

(18)

,

is the spouse’s leisure, andthe individual’s own leisure. The optimality condition implies that

(19)
1 is the weight forequals the share of one’s

own labor income within the household.37 We estimate our model under the following two
scenarios: (a) nonmarket time is applied to,, , and (b) nonwork time is applied to,, .

From the individual’s perspective, specification (a) is less restrictive than specification (b) inthe sense that it adopts a broader leisure measure that includes home production.
Table 4 shows the estimation result. We observe that the leisure-held-constant IES islower in both cases compared with the baseline:

is 0.024 when nonmarket time is used and0.263 when nonwork time is used. This indicates that spouse’s leisure serves as anindependent channel of consumption smoothing. We note that the gap between

and

still

occupations with limited overtime hours that would give them less flexibility for work time adjustment, and (c) women tend
to use labor adjustment at the extensive margin (find/quit work) more frequently than men, which would not be fully captured
in our employed sample pool.
37
Further details of this specification and the linearized Euler equations are provided in Appendix B.

24

exists. For nonmarket time, substitutability parameter

slightly increases from 2.726(baseline) to 2.906, which contributes in pushing down the leisure-varying IES from 0.115(baseline) to 0.006. The same applies when nonwork time is used ( increases from 0.916 todecreases from 0.240 to 0.147). This result shows that consumption-leisure1.452;

substitutability increases when spouse’s leisure is included in the utility function.
In sum, the leisure-varying IES is somewhat lower when spouse’s leisure isinternalized, suggesting spouse’s leisure serves as an additional adjustment margin in married
couples.

VI. Conclusions
This paper provides estimates for the intertemporal elasticity of substitution (IES)
when leisure is allowed to vary. We utilize a utility function that allows interaction between
consumption and leisure to identify model parameters and show that the IES estimates thatallow adjustment of the leisure margin are consistently lower than leisure-held-constant IES.
This result holds for various robustness analysis and subsamples.
To further understand the source of the gap between the two IES measures, weincorporate detailed time use data to decompose nonmarket time. We find that the IES
estimate is larger when we exclude home production from nonmarket time. We further showthat this result is driven by the higher consumption-leisure substitutability for childcare andhousework compared with other leisure components. The findings in this paper indicate thatany public policies that affect labor supply decisions (such as taxation and childcare
subsidies) could have unintended spillover effects on individuals’ consumption/saving
decisions.

25

The major contribution of this paper is that we have endogenized labor/leisure in
estimating IES and compare our leisure-varying IES with leisure-held-constant IES typicallyestimated by existing studies in the literature. Another contribution is that we are able todecompose nonmarket time to examine the leisure component that matters in the IES
estimates. Our result points out that the substitutability of home production time (in particularchildcare) matters the most in the magnitude of IES estimates. Lastly, micro data employed inthis study allows us to examine IES estimates for various subsamples, such as gender,
education, and stock holding status. We find that the IES estimate is higher for women thanmen, and higher for stockholders than non-holders.
One of the limitations of this paper is that time use data are noisy. In addition,measurement errors can be induced by the imputation process. These measurement errors arelikely to be non-classical due to the non-linear nature of our imputation method. It is in
general not possible to predict the sign of the bias caused by this type of measurement error(Chen et al., 2011).
One possible extension of this paper is to endogenize other time uses (such as, home
production, education, or medical care) that are neither market work nor pure leisure. Whilemodeling time spent on home production is relatively straightforward, it is difficult toincorporate it empirically. This is because imputing a small fraction of leisure time such as
housework and childcare time would accompany substantial measurement errors. In addition,in order to calculate the growth rate accurately, we would also need home production timesurveyed at different timings, which requires longitudinal time use data. Likewise, modelingtime spent on education and medical care would be an interesting venue, though testing the26

empirical relevance of such models would also call for a dataset that tracks individuals morethan just a few years.

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Appendix A: Imputation Method
Our proposed method consists of the following steps: (1) estimate the ratio of a specific timeuse over nonmarket time using the American Time Use Survey (ATUS); (2) predict leisuretime in the Consumer Expenditure Survey (CEX) by using the estimated ratio in (1), nonmarket
time available in the CEX, and other observables in the CEX.

A.1 American Time Use Survey (ATUS)
ATUS is a nationally representative time diary survey that records detailed individual
time use data in the past 24 hours. About 50% of the sample is randomly assigned to weekdays

31and 50% to weekends. Respondents are required to identify the primary activity when multiple
activities are performed at the same time; therefore, all activities sum up to 24 hours.
In Appendix Table A.3, we present summary statistics for the variables used inestimating time use in the CEX sample (1996 - 2014) and in the ATUS sample (2003 - 2014)
for employed individuals. While the CEX and the ATUS are conducted independently, thestatistics are similar once sample weights are adjusted for: for example, in the CEX theaverage age is 42.21 years, 52% of the sample are male, and 62% of them are collegeeducated, whereas the corresponding averages in the ATUS are 41.22 years, 53%, and 64%.

A.2 Fractional logistic regression
For each of the three leisure measures, we estimate the ratio of the leisure measure andnonmarket by using the ATUS and then predict the ratio using the same variables in the CEX.
Specifically, we define the ratio of leisure time and nonmarket time as
≡

.

A. 1

We apply a fractional logistic regression (Papke and Wooldridge, 1996) to predict
for each individual i on a given day. The advantage of the fractional regression comparedwith Least Square regressions is that it takes into account boundary values and restricts thefitted values to be between 0 and 1, which avoids generating implausible values for thefraction of time use. In addition, we can choose the most appropriate functional form for theconditional mean for each leisure measure separately by weekday and weekend. The

32

functional forms include Cauchit, Logit, Probit, Log-Log, and Complementary Log-Log.38
The estimation model is specified as
,

,

V
where

,

,

,

,

(A. 2)

represents the fraction of leisure time for individual i in year t. The variable

represents dummy variable for marital status and the vector

represents thenumber of children for different age groups (0-2 years old, 3-6 years old, 7-18 years old). The
vector V includes other socioeconomic and demographic characteristics, which are gender,
age, age squared, race (white, black, hispanic, other), education (less than high school, highschool diploma, college degree), self-employment, occupation (manager and professional,
administrative, sales, protective services, personal care services, other services, laborer,
construction, and farming)39, regional dummies (Northeast, Midwest, South, West), and an
indicator for whether the interview was conducted during the summer months (June, July, andAugust).

represents the interview year dummies. We estimate equation (A. 2)

separately for weekdays (day = wd) and weekends (day = we).

A.3 Predicting Leisure TimeWe predict individual’s daily leisure time in the CEX using estimated coefficients ofEquation (A.2). We then convert the predicted daily leisure measure to an annual measure38
We tested the goodness-of-functional-form of five link functions (Cauchit, Logit, Probit, Log-Log, Complementary LogLog) by using two different test statistics (RESET-LM, GOFF-Ramalho). We used the RESET-LM test which is theheteroskedasticity robust version of the original RESET test proposed by Ramsey (1969). The GOFF test was proposed by
Ramalho and Ramalho (2011), who show that the GOFF test performs better than RESET-LM in terms of size and power.
We used version 1 of the GOFF test in Ramalho and Ramalho (2011) and results were similar when using other versions of
the test. In a few cases where all link functions were rejected, we chose the distribution that has the smallest test statistics (orthe largest p-value).
39
The occupation codes do not match exactly across the two datasets. The ATUS has 22 categories while the CEX has 18
categories. See Appendix Table A.4 for the matching of the occupation codes between the two datasets.

33

based on additional information in the CEX. The CEX records how many hours each memberof the CU worked during a given week (Nweek) and how many weeks they worked in the past
year (Hyear). Using this information, we compute leisure time for the work week and thenonwork week separately.40 Leisure time i during an average work week is computed as
,

5 24

,

2 24

,

,

, ,

(A. 3)

whereas leisure time during an average nonwork week is computed as
7

,

24

(A. 4), .

Annual measure for leisure time i is calculated as the sum of leisure time during the work andthe nonwork weeks as
,

,

52

(A. 5), .

Appendix B: Including Spouse’s Leisure in Time Allocation
We assume that a “composite” leisure consists of one’s own leisure and the spouse’s
leisure, as described in Equation (19), i.e., the individual internalizes the spouse’s leisure time
when deciding his/her own time use. Parameterin Equation (19) represents the weight of

one’s own leisure in the composite leisure. We assume that within a given period a couple
jointly minimizes the opportunity cost associated with time, i.e.,
condition implies that

equals the share of one’s own labor income in a two-earnerhousehold. If the person is single or has a non-working spouse,
and. The optimality

is automatically set to unity. Thus, both singles and married individuals can be included in the same

estimation.

40
Since the CEX does not provide the breakdown of how work hours are split between weekdays and weekends, we take anagnostic stance and evenly split work hours into seven days.

34

The first-order necessary conditions that describe the intertemporal substitution in
consumption and leisure are modified as,
1

,

,

,

,

,

(B.1)
,

,

1

,

(B.2)

and the linearized version of Equations (B.1) and (B.2) can be expressed as
∑ ∆ln

1

,

,

′ ∑ ∆ln
∑ ∆ln

,

∑ ∆ln

,

∑ ∆ln

,,

′ ∑ ∆ln

∑ ∆ln

,,

,

,

,

∑ ∆ln

,

(B.3)
,

B. 4

,

,

where the growth rate of the composite leisure for each individual i is calculated as
∆ln

,,

∆ln

,

1

∆ln

,,

.

(B.5)

Appendix References
Papke, Leslie E., Jeffrey M. Wooldridge (1996), “Econometric methods for fractional
response variables with an application to 401(K) Plan participation rates,” Journal of Applied
Econometrics, 11(6), 619-632.
Ramalho, Esmeralda A. and Joaquim J.S. Ramalho (2011), “Alternative estimating andtesting empirical strategies for fractional regression models,” Journal of Economic Surveys
25(1), 19–68.
Ramsey, James B. (1969), “Tests for specification errors in classical linear least-squares
regression analysis,” Journal of the Royal Statistical Society: Series B (Methodological),
31(2), 350-371.

35

Table 1 Cohort Summary Statistics
Birth-year

1951-1955

1956-1960

1961-1965

1966-1970

1971-1975

age in 1996
age in 2014

41-45
59-63

36-40
54-58

31-35
49-53

26-30
44-48

21-25
38-43

Work time, weekly
Nonmkt.time, weekly
Nonwork time, weekly
Consumption, monthly
Wage rate, hourly# of adults# of children below18
CU income, annual
Observations

39.7
128.3
112.0
2,217.81
35.46
2.25
0.54
77,466.62
10,212

39.6
128.4
110.6
2,293.38
34.57
2.25
0.88
80,330.85
12,206

39.7
128.3
109.2
2,314.20
30.41
2.17
1.23
78,709.32
12,170

39.2
128.8
109.3
2,219.36
31.43
2.10
1.37
74,657.05
10,703

38.9
129.1
110.3
2,093.47
27.71
2.06
1.30
70,987.89
8503

ave. cell size

138

165

164

145

115

Note: The sample consists of employed individuals who have positive wages in both the second and the fifth
waves of the interview in the Consumer Expenditure Survey. Sample period is 1996Q1-2014Q2. Average cellsize is the number of observations for a given cohort in each quarter, and it is calculated as the total number ofobservations for a given cohort divided by the number of quarters (74 quarters). Leisure and work time aremeasured in hours per week for convenience of understanding. Consumption is defined as average nondurable
consumption per CU over one month, measured in 2014 dollar. Wage rate is the average hourly wage measured
in 2014 dollar. CU income is (before-tax) labor income per CU over one year measured in 2014 dollar.

36

Table 2 IES Estimates with Different Control Variables(a)0.091***(b)0.115***(0.000)(0.000)(0.000)(0.000)(0.000)0.304***

0.327***

0.323***

0.324***

0.343***(0.000)(0.000)(0.000)(0.000)(0.000)

3.358

***

(0.000)Δ ln (adult)

2.726(0.000)0.241

Δ ln (children)

***

***

(c)
0.113***

2.734

***

(d)
0.115***

2.708

***

(e)
0.120***

2.824***(0.000)(0.000)(0.120)

0.001

0.035

0.031

(0.000)(0.496)(0.484)(0.986)-0.072***-0.023-0.030-0.024***(0.000)(0.293)(0.104)(0.253)Δ single

0.525

Δ spouse fulltime***(0.000)(0.000)**-0.148**(0.014)(0.039)-0.203

Δ spouse nonmkt

0.375

***

***

(0.000)0.460***(0.000)-1.818-2.060-0.828***(0.000)(0.000)(0.000)

Δ spouse salary***

0.829******-0.107(0.000)Δ other CU salary-0.039***(0.000)Sargan criterion
Concave utility?
C and L are
substitutes?

61.10760.16660.86760.29062.011(0.740)(0.710)(0.747)(0.608)(0.712)

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Note:
is constructed based on Equation (9) and for the null hypotheses H0: θ =0, we use Wald-type of tests
and the delta method to estimate the standard errors. The number in the parentheses represents the p-value for the
test. ***, ** and * represent statistical significance at the 1%, 5%, and 10% level, respectively. The instrumentsin (a)-(c) include the second, third, and fourth lags of consumption growth, leisure growth, nominal interest rate,inflation, and labor income growth, and the second and third lag of the number of adults, children, and elderly(those older than 64), number of earners, single status, whether the spouse works full-time, spouse’s nonmarket
time, average age, age squared, and three seasonal dummies. The instruments in (d)-(e) further include thesecond, third, and fourth lags of spouse salary and salary of other CU members, respectively. In addition to thevariables presented in the table, three seasonal dummies are also included in estimation.

37

Table 3 IES Estimates with Different Leisure Measures

Nonwork
time

Nonmarket
time lesshousework

Nonmarket
time lesschildcarecf. Nonmarket time(baseline)

0.240***

0.133***

0.190***

0.115***(0.000)(0.000)(0.000)(0.000)0.377***

0.349***

0.342***

0.327***(0.000)(0.000)(0.000)(0.000)

0.916

***

(0.009)Δ ln (adult)
Δ ln (children)
Sargan criterion
Concave utility?
C and L are
substitutes?

0.253

2.483

***

(0.000)
***

0.270

1.222

***

(0.000)

0.202

***

2.726***(0.000)0.241***(0.000)(0.000)(0.000)(0.000)-0.073-0.073***-0.067***-0.072***(0.000)(0.000)(0.000)(0.000)60.31358.71660.67360.166(0.705)(0.755)(0.694)(0.710)

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Note:
is constructed based on Equation (9) and for the null hypotheses H0: θ =0 we use Wald-typeof tests and the delta method to estimate the standard errors. The number in the parentheses represents
the p-value for the test. ***, ** and * represent statistical significance at the 1%, 5%, and 10% level,
respectively. The instruments include the second, third, and fourth lags of consumption growth, leisure
growth, nominal interest rate, inflation, and labor income growth, and the second and third lag of thenumber of adults, children, and elderly (those older than 64), number of earners, single status, whether
the spouse works full-time, spouse’s nonmarket time, average age, age squared, and three seasonal
dummies. In addition to the variables presented in the table, three seasonal dummies are also includedin estimation.

38

Table 4 IES Estimates with Joint Leisure Utility Specification
Parameter estimates

Nonmarket
time as, ,0.006***

Nonworktime as, ,0.127***(0.000)(0.000)

0.024

***

(0.000)2.906**(0.000)Δ ln (adult)

0.012

***

(0.001)0.263***(0.000)1.452**(0.000)0.038***(0.000)Δ ln (children)-0.005(0.000)(0.000)Sargan criterion

61.25761.293(0.675)(0.674)

Yes
Yes

Yes
Yes

Concave utility?
C and L are
substitutes?

***-0.046***

Note: , , are own/spouse’s leisure, respectively.
is constructed based on Equation (9). For the
0 we use Wald-type of tests and the delta method to estimate the standard
null hypotheses H0:errors. ***, ** and * represent statistical significance at the 1%, 5%, and 10% level. P-values areincluded in parentheses. The instruments include the second, third, and fourth lags of consumption
growth, the corresponding leisure growth, nominal interest rate, inflation, and labor income growth, andthe second and third lags of the number of adults, children, and elderly (those older than 64), number of
earners, average age, age squared, and three seasonal dummies. In addition to the variables presented in
the table, three seasonal dummies are also included.

39

Figure 1 Life-cycle Profile of Nonmarket time, Consumption, and Wage Rate(a) Nonmarket time(b) Consumption(c) Wage rate

Note: The figure plots the average cohort nonmarket time, nondurable consumption, and hourly wage
rate by age. Each line segment represents one cohort and the sample period of 1996-2014 in theConsumer Expenditure Survey. Consumption represents nondurable nominal consumption deflated by
the Consumer Price Index and log transformed. The wage rate is the nominal wage rate deflated by theConsumer Price Index and log transformed. Consumption is measured at the household level and wage
rate is measured at the individual level. The sample consists of employed persons only.

40

Figure 2 Life-cycle Profile of Leisure Measures

Note: This figure plots the average cohort leisure by age. Each line segment represents one cohort andthe sample period of 1996-2014 in the CEX. All leisure measures are predicted using data from the
ATUS and the CEX and apply for employed persons.

41

Figure 3 Time-series Plots of Different Leisure Measures

Note: Leisure time is plotted over time from 1996 to 2014 at the annual frequency. Nonmarket time is calculated
from the CEX as total time minus annual work hours. Work hours are obtained as weeks worked per year times
hours worked per week. Remaining leisure measures (b)-(d) are predicted using data from the ATUS and theCEX. All measures are for employed persons.

42Figure 4 Relationship between Consumption and Specific Time Use

Value of
-0.06
Childcare

Care for others (incl.child)

Housework

Medical & personal care

Sleep & eat

Exercise

-0.04

-0.02

0.00

0.02

0.04

0.06

-0.048***-0.038***-0.003

0.002

0.007

0.035***

Note: The numbers reported are the coefficient of nondurable consumption ( ) in Equation (17). Standard
errors clustered at the individual level are included in the parentheses. *** indicates statistcal significance at the
1% level.

43

Figure 5 IES Estimates for Subsamples(a) By Gender
0.250
0.200

0.238***
0.179***

0.150

0.107***

0.156***
0.131***

0.100
0.023***

0.050
0.000
FemaleMale
Nonmkt.time

0.120

0.117***

Gap: Female ‐ Male

Nonwork time(b) By education
0.093***

0.090
0.060

0.045***

0.044***
0.024***

0.030

0.001

0.000
College educatedHigh school or less

Nonmkt.time

Gap: College ‐Highschool

Nonwork time(c) By stockholding
0.150

0.140***
0.106***

0.120
0.090

0.063***

0.060

0.056***
0.034***

0.030

0.007***

0.000
Hold stock

Do not hold stock
Nonmkt.time

Gap: Hold ‐ Nohold

Nonwork time

Note: The columns represent the IES estimates for subsamples using nonmarket time (dark color) and nonwork
time (light color), respectively. The last column shows the difference between the two subsamples presented in
the first and second column. For a given pair of subsamples, four equations (two times consumption and leisure
Euler) are jointly estimated. The control variables include the number of adults, the number of children, andseasonal dummies. A formal test with regard to the significance of the gaps are provided in the Online Appendix
Table O.5-O.7. *** indicates statistcal significance at the 1% level.

44Appendix Tables and Figures
Table A.1 Alternative Estimates with Basu and Kimball (2002)’s Utility Specifications

Δ ln (adult)No
controls
0.646**

With
controls
0.408***(0.046)(0.000)--0.461***(0.005)Δ ln (children)

-

0.034
(0.288)Sargan criterion

7.501

45.626(1.000)(0.026)

Note: Labor income to spending ratio is set to 0.8. Basu and Kimball (2002)’s specification does not
require wage rate, instead they use labor hours. Instruments include the second, third, and fourth lags ofconsumption growth, annual hours’ growth, nominal interest rate, inflation, and labor income growth,and the second and third lag of the number of adults, children, and elderly (those older than 64), numberof earners, single status, whether the spouse works full-time, spouse’s nonmarket time, average age, andage squared.

45

Table A.2 Alternative Estimates with Jacobs (2007)’s Utility Specifications,

Δ ln (adult)Oneequation
0.170(0.414)(0.414)0.281*

0.339***(0.100)(0.000)0.669-0.663(0.144)(0.138)4.828-1.934(0.349)(0.239)

0.094

0.055

(0.695)Δ ln (children)
Sargan criterionTwoequations
0.185

0.124

**

(0.685)0.107***(0.070)(0.006)32.48545.353(0.052)(0.548)

Note: Instruments include the second, third, and fourth lags of consumption growth, annual hours’
growth, nominal interest rate, inflation, and the second and third lag of the number of adults, children,
single status, whether the spouse works full-time, spouse’s nonmarket time, average age, and age
squared. The numbers in the parenthesis are p-values.

46

Table A.3 Summary Statistics of Consumer Expenditure Survey (CEX) and American Time
Use Survey (ATUS)
CEX

ATUS

Age

42.21

41.22

Less than high school

0.11

0.08

High school diploma

0.26

0.28

College degree

0.62

0.64

Gender (male = 1)

0.52

0.53

White, non-hispanic

0.71

0.70

Black, non-hispanic

0.10

0.10

Hispanic

0.12

0.14

Other race

0.06

0.06

Marital status (single = 1)

0.34

0.40

# of children, aged 0-2

0.08

0.13

# of children, aged 3-6

0.19

0.18

# of children, aged 7-18

0.60

0.54

210,861

84,996

Observation

Note: Samples are restricted to those between 21-64 years old and those who are employed.
All statistics are adjusted using sample weights.

47

Table A.4 Occupation Categories
Occupation categories
Manager and professional
Administrative support
Sales
Protective services
Private household services
Other services
Laborer (operator, assembler, inspector,
repairer, precision production)
Construction, mining
Farming, fishing, forestry, armed forces

ATUS code
1 - 1017
16
12
15
11, 13, 14
20 - 22

CEX code1 - 3, 7
4
5, 6
8
9
10
11 - 1419
18

15
16 - 18

Note: The occupation variable in the ATUS is trdtocc1. The occupation variable in the CEX is
occucode.

48

Additional Information(To be eventually published as “online appendix”)
Online Appendix A: Comparing Predicted Outcomes with those in the American Time
Use Survey (ATUS)
Here, we examine whether the predicted nonwork time is comparable with thosereported in the ATUS. These results are shown in Online Appendix Table O.1. The predictedlevel of nonwork time is somewhat larger than the ATUS counterparts. This is because our
imputation method predicts the ratio of nonwork and nonmarket time and then use thepredicted ratio to impute leisure time in the CEX. Because nonmarket time in the CEX issomewhat larger than that in the ATUS, and multiplying it with a predicted ratio will cause
predicted nonwork time to be larger as well.41 In the last two columns of Table O.1, we
calculate the ratio of nonwork time to nonmarket time. These ratios are almost identical(86.7% for CEX, 86.6% for ATUS).
Next, we compare the life-cycle profile of leisure time in the CEX and the ATUS. To
account for the differences in cohort, year, and household characteristics, we estimate thefollowing regression,
ln

,

,

,

,

, ,

O. 1

where dagegr is a vector of five-year age dummies (base = 41-45 years old), dcohort is avector of birth-year cohort dummies (base = those born in the years 1951-55), and dfamsize isfamily size dummies (base = 1).42 We restrict individuals in our sample to those who are

41 In the CEX, nonmarket time is calculated based on an annual basis using information on hours worked per week and weeks
worked per year, whereas in the ATUS nonmarket time is calculated based on a one-day time diary.
42
Because the CEX sample (1996-2014) is longer than the ATUS sample (2003-2014), the regression for the CEX sample
has more year dummies and cohort dummies.

49

employed and between 21 and 63 years old in both datasets. For the CEX sample, we use only
information from the second wave to keep it consistent with the cross-section nature of the
ATUS.
The top panel of Appendix Figure O.1 plot the estimated regression coefficients of age
for nonwork time. The lifecycle profiles generated using the predicted leisure measures
show the same U-shape pattern as the actual measures in the ATUS and they trace each otherfairly closely. There are some noticeable differences among the older and younger age
groups: the CEX nonwork time is higher for the younger group and lower for the older group.
However, this is mostly due to the difference in the nonmarket time, as shown in the top panelof Figure O.2.
The bottom panel of Figure O.1 plot the regression coefficients of cohort. The

predicted nonwork time in the CEX again tracks the nonwork time in the ATUS fairly closely,
especially for those who are born between 1931-55 which shows a virtually flat profile. We
observe an upward trend for all three leisure measures, indicating younger cohorts have moreleisure time than older cohorts. The increase in leisure time for the younger cohorts is a bit
steeper in the ATUS than in the CEX, which again reflects the difference in nonmarket time
(Figure O.2, bottom panel).

50

Table O.1 Comparison of Leisure Time in Consumer Expenditure Survey (CEX) andAmerican Time Use Survey (ATUS)

Nonmarket time
Nonwork time
Share of nonwork time
Observation

CEX
1,132.48

ATUS
1,088.05(129.39)(279.93)982.21

942.57(121.11)(248.43)86.7%
210,861

86.6%
84,996

Note: Samples are restricted to those between 21-64 years old employed individuals. All
statistics are adjusted using sample weights. Time is expressed in minutes per day and share isin terms of nonmarket time The predicted values for nonwork time in the Consumer
Expenditure Survey are obtained using the constructed 9-month value (measured in hours)
divided by 270 to obtain daily value and multiplied by 60 to convert to minutes. Numbers in
the parenthesis represent standard deviations.

51

Table O.2: Leisure Measures and the Corresponding ATUS Codes(a) Primary childcare, educational childcare, recreational childcare for household children(“Childcare”)
ATUS categories

Primary childcare
Caring for and helping
hh children

Descriptions

Physical care for hh children; Organization & Planning forhh children; Looking after hh children (as a primaryactivity); Waiting for/with hh children; Picking
up/dropping off hh children; Caring for & helping hhchildren, n.e.c.*6-digitactivitycodes

Activities related to hh
children’s health

Providing medical care to hh children; Obtaining medicalcare for hh children; Waiting associated with hh children's
health; Activities related to hh child's health, n.e.c.*Travel related to caring
for & helping hhchildren
Educational childcare
Caring for and helping
hh children
Activities related to hh
children’s education

Travel related to hh children's health030101,030108,030109,030111,030112,030199030301,030302,030303,030399180303

Reading to/with hh children

030102Homework (hh children); Meetings and school conferences(hh children); Home schooling of hh children; Waiting
associated with hh children's education; Activities related
to hh child's education, n.e.c.*Travel related to caring
for & helping hhchildrenRecreational childcare
Caring for and helping
hh children

Travel related to hh children's education

030201,030202,030203,030204,030299180302

Travel related to caring
for & helping hhchildrenTravel related to caring for & helping hh children

Playing with hh children, not sports; Arts and crafts withhh children; Playing sports with hh children; Talking
with/listening to hh children; Attending hh children’s
events

030103,030104,030105,030106,030110180301(b) Caring for & helping household children, caring for & helping remaining household
members, caring for & helping non-household members (“Care for others”)
ATUS categories

Descriptions

6-digitactivitycodes

Caring for & helping household children

52Refer to the above section (a)Caring for & helping remaining household members
Caring for & helping hh
Caring for household adults
members, remaining
Helping household adults

Travel time

Travel related to caring for hh adults; Travel related tohelping hh adults; Travel rel. to caring for & helping
hh members, n.e.c.*Caring for & helping remaining non-household members
Caring for & helping
Caring for & helping nonhh children
nonhh members
Activities related to nonhh children’s education
Activities related to nonhh children’s healthCaring for nonhh adults
Helping nonhh adults
Caring for & helping nonhh members, n.e.c.*Travel time

Travel related to caring for & helping nonhh members

030401030499
030501030599
039999180304,180305,180399,040101040199
040201040299
040301040399
040401040499
040501040599
049999180401180499(c) Core nonmarket work, shopping/obtaining goods and services, and other home production(“Housework”)
ATUS categories

Core nonmarket work
Household activities

Descriptions

Housework
Food & drink prep., presentation, & clean-up
Interior maintenance, repair, & decoration
Household management, excl. mail/email

Traveling

Travel related to household activities

Shopping/obtaining goods and services
Consumer purchases
Shopping (store, telephone, internet)
Researching purchases

6-digitactivitycodes
020101020199
020201020299
020301020399
020901,020902,020905,020999180201,180202,180203070101070199
070201,070299Security procedures rel. to consumer purchases

53Professional services,excl. med. care

Consumer purchases, n.e.c.
Childcare services
Financial services and banking
Legal services
Real estate
Veterinary services (excl. grooming);

Traveling

Travel related to consumer purchases
Travel related to using professional services (excl. med.
care)

Other home production
Household activities

Exterior maintenance, repair, & decoration
VehiclesAppliances, tools, & toys

Household services

Household activities, n.e.c.*Household services (not done by self)
Home maint /repair/décor/construction (not done by self)
Pet services (not done by self, not vet)
Lawn and garden services (not done by self)
Vehicle maint. & repair services (not done by self)household services, n.e.c.

Traveling

Travel related to household activities

Travel related to using household services

070301,070399079999080101080199
080201080299
080301080399
080601080699
080701080799
180701180799,
180801,180802,180803,180806,180807020401020499
020701,020799020801,020899029999090101090199
090201090299
090301090399
090401090499
090501090599
099999180204,180207180299
180901180999(d) Own medical care, personal care services, and personal care activities that do not involve
market transaction (“Medical and personal care”)
ATUS categories

Descriptions

6-digitactivitycodes

54Own medical care
Medical and care services

Health-related self care
Travel related to using
Professional and Personalcare services
Personal care services
Personal care services

Using health and care services outside the home;
Using in-home health and care services; Waiting
associated with medical services; Using medical
services, n.e.c.*
Health-related self care; Self care, n.e.c.*Travel related to using medical services

Using personal care services; Waiting associatedw/personal care services; Using personal careservices, n.e.c.*Travel related to using
Travel related to using personal care services;
professional and personal care Travel rel. to using prof. & personal care services,
services
n.e.c.*;
Personal care activities that do not involve market transaction
Grooming
Washing, dressing and grooming oneself;
Grooming, n.e.c.
Personal activities
Personal / Private activities; Personal activities,
n.e.c.
Personal care emergencies
Personal emergencies; Personal care emergencies,
n.e.c.*; Personal care, n.e.c.*Travel related to personal care

Travel related to personal care; Travel related topersonal care, n.e.c.*080401,080402,080403,080499010301,010399180804080501,080502,080599180805,180899010201,010299010401,010499010501,010599,019999180101,
180199(e) Sleeping, eating, and personal care activities that do not involve market transaction(“Sleep & eat”)
ATUS categories

Descriptions

6-digitactivity
codes

Sleeping
Sleeping

Sleeping; Sleeplessness; Sleeping n.e.c.

010101,010102,010199EatingEating and drinking
Eating and drinking
110101,
Waiting associatedWaiting associated w/eating & drinking;110201,w/eating & drinking
Waiting associated w/eating & drinking, n.e.c.
110299Eating and drinking, n.e.c. Eating and drinking, n.e.c.
119999Travel related to eating
Travel related to eating and drinking
181101and drinking
Personal care activities that do not involve market transaction excl. personal care emergencies,
travel related to personal care
Grooming
Washing, dressing and grooming oneself;
010201,Grooming, n.e.c.
010299Personal activities
Personal / Private activities; Personal activities,
010401,n.e.c.
01049955

(f) Exercise
ATUS categories

Exercise
Participating in sports,
exercise, or recreation

Descriptions

6-digitactivitycodes

Doing aerobics; Playing baseball; Playing basketball;Biking; Playing Billiards; Boating; Bowling;
Climbing, spelunking, caving; Dancing; Participating
in equestrian sports; Fencing; Fishing; Playing
football; Golfing; Doing gymnastics; Hiking; Playing
hockey; Hunting; Participating in martial arts; Playing
racquet sports; Participating in rodeo competitions;
Rollerblading; Playing rugby; Running; Skiing, ice
skating, snowboarding; Playing soccer; Softball;Using cardiovascular equipment; Vehicle
touring/racing; Playing volleyball; Walking;Participating in water sports; Weightlifting/strength
training; Working out, unspecified; Wrestling; Doingyoga; Playing sports n.e.c.*130101,…,130136,130199(g) Core market work and work-related activities (used to construct nonmarket time in ATUS)
ATUS categories

Core market work
Working

Descriptions

6-digitactivity
codes

Work, main job; Work, other job(s); Security
procedures related to work; Waiting associated withworking; Working, n.e.c.*050101,050102,050103,050104,050199050301,050302,050303,050304,050305,050399180501,180503

Other income-generating
activities

Income-generating hobbies, crafts, and food; Incomegenerating performances; Income-generating services;
Income-generating rental property activities; Waiting
associated with other income-generating activities;
Other income-generating activities, n.e.c.*Travel related to coremarket work
Work-related activities
Work-related activities

Travel related to working; Travel related to incomegenerating activities;

Job search andinterviewing

Security procedures as part of job; Waiting associatedwith work-related activities; Work-related activities,
n.e.c.*
Job search activities; Job interviewing; Waiting
associated with job search or interview; Security
procedures rel. to job search/interviewing; Job searchand Interviewing, n.e.c.*050204,050205,050299050401,050403,050404,050405,05049956

Work and work-related
activities, n.e.c.
Using government services
Travel related to workrelated activities

Work and work-related activities, n.e.c.

059999Using social services
Travel related to work-related activities; Travel
related to job search & interviewing; Travel related towork, n.e.c.*100102180502180504180599Note: The 6-digit activity codes are based on years after 2004.

57

Table O.3 Relationship between Consumption and Home Production Time Use

Δ ln (C)Δ ln (w)Δ ln (nonmkt)
R-squared# of IndividualsChildcare

Care for
OthersHousework-0.048***-0.038***-0.003(0.009)(0.000)(0.479)

0.004

0.002

-0.020(0.649)(0.760)0.097(0.041)(0.041)(0.000)0.655
53,7970.690
53,7970.128
53,7970.114**(0.000)**0.123***

Note: The numbers reported are the coefficient of nondurable consumption, real wage rate, andnonmarket time in equation (17) for different time uses. Standard errors clustered at the individual levelare included in the parentheses. ***, ** and * represent statistical significance at the 1%, 5%, and
10% level, respectively. In addition to the variables presented in the table, dummy for marital status(single), whether the spouse works fulltime (spouse fulltime), spouse’s nonmarket hours (spousenonmkt), 14 family size dummies (dfamsize), 3 number of children dummies based on age category(nchild0_2, nchild3_6, nchild7_18), 19 year dummies (dyear), three seasonal dummies (dseason) arealso included in estimation.

58

Table O.4 Relationship between Consumption and Nonwork Time Use

Δ ln (C)Δ ln (w)Medical &Personal
Care

Sleep & Eat

Exercise

0.002

0.007

0.035***(0.437)(0.225)

0.008

0.028

(0.000)Δ ln (nonmkt)
R-squared# of Individuals**(0.000)***(0.000)0.009***(0.001)***-0.007-0.216-0.068***(0.646)(0.000)(0.001)

0.172
53,7970.224
53,7970.065
53,797

Note: The numbers reported are the coefficient of nondurable consumption, real wage rate, andnonmarket time in equation (17) for different time uses. Standard errors clustered at the individual levelare included in the parentheses. ***, ** and * represent statistical significance at the 1%, 5%, and
10% level, respectively. In addition to the variables presented in the table, dummy for marital status(single), whether the spouse works fulltime (spouse fulltime), spouse’s nonmarket hours (spousenonmkt), 14 family size dummies (dfamsize), 3 number of children dummies based on age category(nchild0_2, nchild3_6, nchild7_18), 19 year dummies (dyear), three seasonal dummies (dseason) arealso included in estimation.

59

Table O.5 Subsample Analysis: By Gender(a) Nonmarket Time
Femalesubsample

Malesubsample

Test statistics(Null: same)

0.179***

0.023***

125.76***(0.000)(0.000)(0.000)0.322***

0.092***

375.64***(0.000)(0.000)(0.000)1.183
Δ ln (adult)
Δ ln (children)
Sargan criterion(common)Concave utility?
C and L are
substitutes?

***

3.395

***

57.50***(0.000)(0.000)(0.000)0.187***

0.062***

116.75***(0.000)(0.000)(0.000)******-0.079-0.018107.83***(0.000)(0.000)(0.000)67.129(1.000)

Yes
Yes

Yes
Yes

Femalesubsample

Malesubsample

Test statistics(Null: same)

0.238***

0.107***

54.01***(0.000)(0.000)(0.000)0.302***

0.246***

24.86***(0.000)(0.000)(0.000)(b) Nonwork Time

0.389

***

(0.000)Δ ln (adult)
Δ ln (children)
Sargan criterion(common)Concave utility?
C and L are
substitutes?

0.158

1.712

***

(0.000)

***

0.148

***

77.55***(0.000)0.42(0.000)(0.000)(0.515)-0.060***-0.045***12.44***(0.000)(0.000)(0.000)67.698(1.000)

Yes
Yes

Yes
Yes

Note: For a given pair of subsamples, four equations (two times consumption and leisure Euler) are
jointly estimated. The first two columns of numbers present the parameter estimates for the two groups.
The third column of numbers shows test statistics for the null hypothesis that the parameter values are
the same. ***, ** and * represent statistical significance at the 1%, 5%, and 10% level, respectively. Pvalues are included in parentheses. In addition to the variables presented in the table, three seasonal
dummies are also included in the estimation.

60

Table O.6 Subsample Analysis: By Education(a) Nonmarket Time
Collegesubsample

HS & lesssubsample

Test statistics(Null: same)

0.045***

0.044***

0.07(0.000)(0.000)(0.785)0.120***

0.259***

596.86***(0.000)(0.000)(0.000)1.922
Δ ln (adult)
Δ ln (children)
Sargan criterion(common)Concave utility?
C and L are
substitutes?

***

6.666

***

478.14***(0.000)(0.000)(0.000)0.062***

0.038***

36.37***(0.000)(0.000)(0.000)******-0.020-0.109358.74***(0.000)(0.000)(0.000)67.382(1.000)

Yes
Yes

Yes
Yes

Collegesubsample

HS & lesssubsample

Test statistics(Null: same)

0.117***

0.093***

4.37**(0.000)(0.000)(0.037)0.174***

0.288***

366.22***(0.000)(0.000)(0.000)(b) Nonwork Time

0.595

***

(0.000)

2.957

***

(0.000)185.31***(0.000)Δ ln (adult)

0.085(0.000)(0.007)(0.000)Δ ln (children)-0.024***-0.109***219.87***(0.000)(0.000)(0.000)Sargan criterion(common)Concave utility?
C and L are
substitutes?

***

0.012

***

106.48***66.920(1.000)

Yes
Yes

Yes
Yes

Note: For a given pair of subsamples, four equations (two times consumption and leisure Euler) are
jointly estimated. The first two columns of numbers present the parameter estimates for the two groups.
The third column of numbers shows test statistics for the null hypothesis that the parameter values are
the same. ***, ** and * represent statistical significance at the 1%, 5%, and 10% level, respectively. Pvalues are included in parentheses. In addition to the variables presented in the table, three seasonal
dummies are also included in the estimation.

61

Table O.7 Subsample Analysis: By Stock Holding(a) Nonmarket Time
Holdersubsample

Non-holder
subsample

Test statistics(Null: same)

0.063***

0.056***

7.50***(0.000)(0.000)(0.006)

0.195***

0.289***

183.75***(0.000)(0.000)(0.000)2.603
Δ ln (adult)
Δ ln (children)
Sargan criterion(common)Concave utility?
C and L are
substitutes?

***

5.875

***

325.96***(0.000)(0.000)(0.000)0.123***

0.157***

8.17***(0.000)(0.000)(0.004)******-0.044-0.07055.63***(0.000)(0.000)(0.000)67.578(1.000)

Yes
Yes

Yes
Yes

Collegesubsample

HS & lesssubsample

Test statistics(Null: same)

0.140***

0.106***

45.97***(0.000)(0.000)(0.000)0.239***

0.307***

39.58***(0.000)(0.000)(0.000)(b) Nonwork Time

0.928

***

(0.000)

2.736

***

(0.000)973.27***(0.000)Δ ln (adult)

0.135(0.000)(0.000)(0.065)Δ ln (children)-0.045***-0.066***823.29***(0.000)(0.000)(0.000)Sargan criterion(common)Concave utility?
C and L are
substitutes?

***

0.118

***

3.42*

67.775(1.000)

Yes
Yes

Yes
Yes

Note: For a given pair of subsamples, four equations (two times consumption and leisure Euler) are
jointly estimated. The first two columns of numbers present the parameter estimates for the two groups.
The third column of numbers shows test statistics for the null hypothesis that the parameter values are
the same. ***, ** and * represent statistical significance at the 1%, 5%, and 10% level, respectively. Pvalues are included in parentheses. In addition to the variables presented in the table, three seasonal
dummies are also included in the estimation.

62

Figure O.1 Comparison of Nonwork Time in Consumer Expenditure Survey (predicted) vs.
American Time Use Survey
by AgeCoefficient

0.1
0.08

CEX

0.06

ATUS

0.04
0.02
0
‐0.02
‐0.04

by Cohort
0.15
0.13
0.11
0.09
0.07
0.05
0.03
0.01
‐0.01
‐0.03
‐0.05

Note: The top panel plots the average log nonwork time by age, conditional on cohort, year, and family
charateristics. Each point represents the coefficient of the five-year age dummies in equation (O.1). The
omitted age group is 41-45 years old. The bottom panel plots the averaeg log nonwork time by cohort,conditional on age, year, and family charateristics. Each point represents the coefficients on the 5-year
cohort dummies in equation (O.1). The omitted cohort is the 1951-1955 birth-year cohort. The
Consumer Expenditure Survey (CEX) data are shown in squares and the American Time Use Survey(ATUS) data are shown in dots. Markers with solid fills represent statistical significance at the 5%
level. Full estimation result is available upon request.

63

Figure O.2 Comparison of Nonmarket Time in Consumer Expenditure Survey vs. American
Time Use Survey
by AgeCoefficient

0.1
0.08

CEX

0.06

ATUS

0.04
0.02
0
‐0.02
‐0.04

by Cohort
0.15
0.13
0.11
0.09
0.07
0.05
0.03
0.01
‐0.01
‐0.03
‐0.05

Note: The top panel plots the average log nonmarket time by age, conditional on cohort, year, andfamily charateristics. Each point represents the coefficient of the five-year age dummies in equation(O.1). The omitted age group is 41-45 years old. The bottom panel plots the averaeg log nonmarket
time by cohort, conditional on age, year, and family charateristics. Each point represents thecoefficients on the 5-year cohort dummies in equation (O.1). The omitted cohort is the 1951-1955 birthyear cohort. The Consumer Expenditure Survey (CEX) data are shown in squares and the American
Time Use Survey (ATUS) data are shown in dots. Markers with solid fills represent statisticalsignificance at the 5% level. Full estimation result is available upon request.

64