BLS WORKING PAPERS 

 U.S. Department of Labor 

U.S. Bureau of Labor Statistics

Office of Employment and Unemployment Statistics 

How to Think About Time-Use Data: What Inferences Can We Make About Longand Short-Run Time Use from Time Diaries?

 Harley Frazis, U.S. Bureau of Labor Statistics

Jay Stewart, U.S. Bureau of Labor Statistics

Working Paper 442

November 2010

All views expressed in this paper are those of the authors and do not necessarily reflect the views or policies of the

U.S. Bureau of Labor Statistics.
How to Think About Time-Use Data: What Inferences Can We Make About 

Long- and Short-Run Time Use from Time Diaries? 

October 2010 

Harley Frazis 

U.S. Bureau of Labor Statistics 

2 Massachusetts Ave., NE 

Washington, D.C. 20212 

Frazis.Harley@bls.gov

Jay Stewart 

U.S. Bureau of Labor Statistics 

2 Massachusetts Ave., NE 

Washington, D.C. 20212 

Stewart.Jay@bls.gov

Any views expressed in this article are ours and do not necessarily reflect those of the Bureau of 

Labor Statistics. We thank participants at the 2010 meetings of the International Association for 

Time Use Research for their comments. 
How to Think About Time-Use Data: What Inferences Can We Make About 

Long- and Short-Run Time Use from Time Diaries? 

Abstract 

Time-use researchers are typically interested in the time use of individuals, but time use data are 

samples of person-days. Given day-to-day variation in how people spend their time, this 

distinction is analytically important. We examine the conditions necessary to make inferences 

about the time use of individuals from a sample of person-days. We also discuss whether and 

how surveys with multiple household members or multiple days are an improvement over singlediary surveys. 

JEL codes: C81, D13, C83 

Keywords: Time use, survey methods, estimation. 
Introduction 

In recent decades, there has been an increased interest in using time diaries to analyze 

how people spend their time. The distinctive feature of time-diary data is the short reference 

period—usually one or two 24-hour periods—compared to reference periods of a week or more 

for most household surveys. The shorter recall period results in more accurate data, and because 

time diaries ask respondents to list all of their activities rather than asking about a few select 

activities, they are also relatively free of social desirability bias. These data would seem to be 

ideal for answering a number of questions about the time spent in many activities, including 

childcare, household work, and job search, that are of interest to policymakers. However, 

policymakers are typically interested in long-run time use—that is, the amount of time that 

individuals spend in an activity over the course of a month or a year. Thus a drawback to time 

diaries over retrospective questions is that the shorter reference period combined with the 

considerable day-to-day variation in the time spent in different activities means that an 

individual’s time diary does not necessarily reflect his or her long-run time use. Put another 

way, there is a mismatch between the reference period of the data (one or two days) and the time 

period that is typically of interest to the researcher. This feature of time-diary data has important 

implications for its analysis. 

To date, many studies that analyze time-diary data have failed to recognize the 

importance of the reference-period mismatch. As a result, many recent papers have analyzed 

time-diary data inappropriately. The published literature contains examples both of researchers 

estimating statistics that, if properly interpreted, have little analytic interest and of researchers 

failing to estimate easily-calculated statistics that are of interest. 
2

The purpose of this paper is to provide guidance to time-use researchers on what can and 

cannot be estimated from time-diary data. For the most part, we focus on data collected for a 

single day from a single member of a household as is done in the American Time Use Survey 

(ATUS).1 This framework brings out the statistical issues in sharpest relief. We begin by 

examining the most common type of analysis, where time spent in an activity is the dependent 

variable. We then turn to analyses that are becoming more common in which time use is an 

explanatory variable. Finally, we consider issues related to survey design, such as what 

researchers can learn from time-use surveys that collect data from multiple household members 

or for multiple days compared with surveys that do not collect this information. 

Time-Use as a Dependent Variable 

The time-use of a population of individuals can be thought of as a collection of persondays. For example, in 2008 the civilian non-institutional population of the U.S. ages 15 and 

older was 238 million, which translates into 87 billion person days. It is straightforward to use 

data collected for a single day per respondent to estimate summary measures over the population 

of person-days. Taking means and medians as examples of summary measures and using 2008 

ATUS data, we estimate that the mean time spent doing household activities was 106 minutes 

per person-day and the median time was 60 minutes. However, researchers are usually interested 

in time use over a period of time that is long enough to reflect the long-run decision making of 

individuals and households—that is, researchers are typically interested in person-months or 

person-years, rather than person-days. Given this mismatch between the period of interest and 

 

1

 To briefly describe the ATUS: One respondent is chosen from each sample household. The respondent is asked to 

take the interviewer through his or her day for one 24-hour period (beginning at 4 AM in the ATUS). The 

respondent describes each activity, which the interviewer records. For each episode the duration of the activity is 

also recorded. The activity descriptions are then coded. 
3

the reference period of the data, it is important to know what summary measures can be 

estimated from person-day data that allow us to make inferences about time use over a personyear. 

To illustrate, consider the two measures of central tendency mentioned above—the mean 

and the median. Estimates of long-term mean time use follow immediately from the short-term 

estimates. Estimated mean annual time spent by individuals in household activities in 2008 is 

clearly 366 x 106 minutes per year. In contrast, it is impossible to estimate median annual time 

use from daily data because there is no necessary relationship between the percentiles of the 

distribution of daily time use and the distribution over longer periods. To illustrate, suppose that

every person in the population does a certain activity only once per week. The median time 

spent in the activity is zero for the population of person days even though every person in the 

population spends time doing the activity each week. 

More generally, we seek to provide guidelines as to when it is possible to make 

inferences about the time use of individuals from a sample of person days. To generalize from 

the above examples, let 

a

id t

denote total time spent in an activity of interest a 

Aa )(

by person i 

(i = 1,...,I) on day d (d = 1,...,D). Let 

A

id t

denote the vector whose elements are 

a

id t

for all 

Aa , 

A

TID

denote the set of 

A

id t

for all activities for all person days in the population, and let Ti

A

A

TID

denote the set of days for person i, where 

A

ID

I

i

A  id TT

1

. The population 

A

TID

describes the 

sampling frame of the ATUS and many other time use surveys, which typically collect only one 

or two diaries per person. As our interest will be in one or two activities at a time, for the most 

part we confine our discussion to the population 

a

TID —the time spent engaged in activity a—and 
4

omit the superscript except where necessary for clarity. Finally, let g(T) be a statistic of interest 

to the researcher that is defined over a set of days, T. 

We would like to know the conditions under which the statistic 

)(Tg ID

calculated over a 

sample of person-days can be used to make inferences about the long-run time use of individuals. 

Let 

ID TTTT I

,,,

21



denote the long-run time use by the I individuals in the population, 

where 

iiii

,,, tttT

and 

D

d

i id t

D

t

1

1

. Put another way, 

Ti

is an artificial construct that 

represents the time spent in the activity by person i that would result if there were no day-to-day 

variation and he or she spent the same amount of time (his or her long-run average) in the 

activity every day. We can estimate average long-run time use from a sample of person days if: 

(1) 

()( ). ID TgTg ID

 

This condition simply states that it is possible to make inferences about individuals’ long-run 

time use from a sample of person days if the day-to-day variation does not affect the value of the 

statistic. 

A couple of examples will illustrate the point. The mean clearly satisfies this condition: 

( ). 1 11 1)(

1 1 1 1 1

ID

I

i

i

I

i

D

d

id

I

i

D

d

ID id Tgt

I

t

DI

t

DI

Tg

The earlier example of the once-per-week activity makes it clear that the median does not satisfy 

this property. The variance is another example of a function that does not satisfy this property. 

To see this, decompose tid as follows: 

(2) 

id i id emt

where mi = Ed(tid) is the long-run average deviation of individual i’s time spent in the activity of 

interest and eid is the deviation from mi for a given day. Note that mi and eid are orthogonal, that 
5

(2) is true by construction, and that we have made no assumptions about the time-series structure 

of the disturbances. Letting g(T) = Var(T) and noting that eid = 0 for each 

Ti

, then: 

 

()()()()()( ), ID i id i id i TgmVareVarmVaremVarTg ID

which means that we cannot estimate the variance of the long-run time use of individuals from a 

population of person-days. 

However, even though point estimates of the variance of long-term time use are not 

identified, it is possible to bound the variance. The addition of covariates X will help establish 

the lower bound, so we modify (2) to include covariates: 

(2′) 

id ii id )( emXLt , 

where L(X) is the long-run mean of tid conditional on X, mi is redefined to equal the long-run 

average deviation of individual i’s time use from L(X), and eid is the deviation from (L(X) + mi) 

for a given day. Note that L(X), mi, and eid are all mutually orthogonal. It is clear from equation 

(2′) that the residual components mi and eit are not identified in cross-sectional data. Letting 

)(

i

tVar

denote the variance of long-term time use across individuals, consider two polar cases. 

If there is no day-to-day variation, then eid = 0 for all members of the population, 

)(

i

tVar

= 

Var(L(Xi)) + Var(mi), and all variation in the data reflects permanent differences between 

individuals. If on the other hand mi = 0 for all members of the population, then 

)(TVar ID

= 

Var(L(Xi)) and all residual variation is day-to-day variation, which vanishes as averages are 

taken in the long run. This implies: 

(3) Var(L(Xi)) ≤ 

)(

i

tVar

≤ 

)(

id tVar . 

The lower bound can be estimated by computing the variance of predicted time use from a 

regression of the tid on the Xi. An illustration of this bounding, and an extension to multi-person 
6

households, can be found in Frazis and Stewart (2009) in the context of incorporating household 

production into income inequality measures. 

Regression Functional Forms and Reporting 

The ability to estimate means of long-run time use from a sample of daily observations 

implies that researchers can estimate the effect of covariates on time use using regression 

analysis. That said, the distinctive features of time-use data have implications for the functional 

form of regression functions. For some activities it makes sense to assume that L(X) in (2′) is 

strictly greater than zero. This would be the case for activities such as childcare done by parents 

and time spent working by the employed. Now let Sd(X) denote the corresponding expectation 

for a given day d. While it is obvious that the functional form of the Sd(·) implies a functional 

form for L(·), the reverse is also true. If, as is commonly assumed, L(X) is linear, then the Sd(X)

function will also almost always be linear.2

This implies that the long-term expectation, L(X), can be consistently estimated using 

OLS on a sample of person-day data, tid.

3

 This is true despite the possibility that a large 

proportion of tid observations have a zero value. In contrast, and somewhat ironically, estimation 

techniques for limited dependent variables that assume a non-linear functional form, such as the 

Tobit, will be inconsistent. For a comparison of OLS and Tobit, see Stewart (2009). 

Another specification issue is whether to estimate means and regression coefficients 

separately for weekends and weekdays. This is sometimes done on the grounds that these days 

are very different from each other. Although separate estimation can be justified, it raises the 

issue of how to report results. It is not uncommon for researchers to report means and 

 

2

 One can construct cases where the non-linearities of different Sd functions exactly cancel each other out. However, 

this will only happen coincidentally. 

3

 OLS, however, will be inefficient due to the non-normality of the residuals. 
7

regression coefficients separately for weekends and weekdays with no mention of overall means 

or the effect of covariates on overall time use (for example, Kalenkoski, Ribar, and Stratton, 

2007; Kimmel and Connelly, 2007; Connelly and Kimmel, 2009; and Vernon, 2010). Yet there 

is no reason not to report overall effects. Assuming (for convenience) time use is homogenous 

within weekdays and weekend days, it is a straightforward consequence of the linearity of means 

that weekly mean time use can be estimated as 

)(2)(5)( D iD E iE tStStw

, where S denotes the 

daily mean, D denotes weekday and E denotes weekend. More importantly, it is not clear how 

one should interpret the separate coefficients. The effect of a covariate on, say, weekend time 

use can be thought of as the combined effect of the effects of the covariate on overall time use 

and on the weekday-weekend distribution of time spent in the activity. Overall time-use is 

relevant for most policy-related questions, and substitution effects can shed light on how people 

rearrange their schedules in response to outside influences. But it is not clear what questions the 

combined effects address. 

Short-run Time Use 

Focusing on short-run time-use is appropriate when the researcher is interested in the 

shifting of activities between days. For example, Connolly (2008) uses ATUS data to examine 

how workers shift work and leisure activities in response to changes in the weather.4 She finds 

that people shift work activities from sunny days to rainy days, while leisure activities are shifted 

in the opposite direction. To illustrate the use of single-day data in analyzing substitution, 

consider the following regression equation: 

 

4

 Other researchers (Hamermesh, et al, 2008 and Stewart, 2010) have examined the timing of activities within a day. 

Hamermesh, et al, examined how light cues, television schedules, and the synchronization of work activities across 

time zones affect the timing of work and leisure activities. Stewart examines how work schedules affect when 

during the day that mothers spend time with their children and how mothers adjust their schedules to spend time 

with their children at more-preferred times of day. 
8

(4) 

id i id i i id )( emXXXt

where Xi denotes the mean value of covariate X across time and Xid denotes the value on day d. 

The person fixed-effect mi may be correlated with Xi –in the Connolly (2008) example, persons 

who spend above-average time in leisure may migrate to low-precipitation areas—but the 

parameter of interest will be consistently estimated if (Xid − Xi) is uncorrelated with eid. 

Because Connolly is interested in the short-run responsiveness of time-use to shocks in a 

covariate, there is no mismatch between the reference period and the period of interest. 

Accordingly, summary measures that do not satisfy equation (1), such as coefficients from 

median regressions or the probability that tid > 0, may be of analytic interest. 

Time Use as an Independent Variable 

Several recent studies have included time use as an explanatory variable (Pinkston and 

Stewart 2009, Christian 2009, Hersch 2009, Hamermesh 2010). This use of the data opens up 

new avenues of research, but there are potential problems with using time use as an independent 

variable. 

Most fundamentally, where the dependent variable is a long-term outcome such as 

obesity (Pinkston and Stewart 2009) or wages (Hersch 2009), OLS estimates of the coefficients 

on short-term time-use cannot be interpreted causally. Consider the equation 

(5) 

utXY ,

ii id

where Yi is a long-term outcome (such as obesity) for person i, Xi is a vector of covariates, tid is 

time-use in an activity of interest (such as exercise) by person i on diary-day d, and u is a 

residual. By itself we would expect a single day’s exercise (tid) to have a negligible effect on 

obesity (Yi).
9

Even though daily time use has little effect on Yi, it can be considered a proxy for the true 

variable of interest, ti, the long-term average time-use of person i. As implied by the 

decomposition in equation (2), tid will differ from mi by the residual eid which is uncorrelated 

with mi. Thus use of tid rather than mi is an example of classical measurement error. If there is a 

single time-use variable in the regression, we have the familiar errors-in-variables result that the 

coefficient on tid will be attenuated toward zero. 

With multiple time-use variables on the RHS, in general nothing can be said about the 

direction of the bias. Klepper and Leamer (1984) show that in the case where the measurement 

errors of the different variables are uncorrelated, the true coefficients can be bounded only if (5) 

and the reverse regressions formed by regressing one of the tid variables on Y and the other tid 

variables all imply the same signs on the γ vector. The bounds are the regression and reverseregression coefficients. With time-use variables the situation is even less favorable, as the eid

variables for different activities will usually be correlated with each other. In this case, the 

bounds will be looser than those of Klepper and Leamer. It is straightforward to construct 

examples where the probability limit of an estimated coefficient will have an incorrect sign even 

when the regression and all reverse regressions imply the same sign on all time-use variables. 

We suggest two solutions. The first is to group the data into cells based on observed 

characteristics (for example, age, education, and sex) and estimate (5) using cell means rather 

than individual data. It is important to make sure that cells are sufficiently large and that the 

day-of-week representation is correct. Faberman (2010) provides an example of this approach. 

The second is to use instrumental variables (IV). IV has the added advantage that it also 

corrects for any reverse causality between Y and ti. It is important to note that the instruments 

should predict long-term time-use rather than short-term. For example, Pinkston and Stewart 
10

(2009) use climate information (average temperature and rainfall) as instruments for time spent 

watching TV in their analysis of obesity, rather than using the weather on the diary day. 

Some interesting issues arise when time spent in one activity is an explanatory variable 

for time spent in another activity (for example, Christian 2009). Consider the equation 

(6) 

id

b

id

a

id utt ,

where time spent in activity a (exercising in Christian’s example) is a function of the time spent 

in activity b (commuting in Christian’s example) and, for simplicity, no other covariates. From 

(2), 

a

id

a

i

a

id emt

and 

b

id

b

i

b

id emt

, so defining as the population linear regression coefficient 

we have 

 (7) 

)()(

)()(

)()(

),(),(

)(

),(

b

id

b

i

e

b

m id

b

i

b

id

b

i

b

id

a

id

b

i

a

i

b

id

b

id

a

id

eVarmVar

eVarmVar

eVarmVar

eeCovmmCov

tVar

ttCov

where 

)(

),(

b

i

b

i

a

i

m

mVar

mmCov

and 

)(

),(

b

id

b

id

a

id

e

eVar

eeCov

are the coefficients from regressions of

a

mi

on 

b

mi

and of 

a

id e

on

b

id e

, respectively. Thus the coefficient estimated by OLS using ATUS-type 

time-diary data is a weighted average of the coefficient showing the linear relationship of long 

run variation between the two activities and the coefficient showing the relationship of day-today variation. The different coefficients answer different questions— m shows the extent to 

which people who spend more total time commuting spend more or less total time exercising, 

while e shows the extent to which people spend time exercising and commuting on the same 

days conditional on long-run total time in the activities. Either coefficient may be of interest, but 

it is hard to imagine what question the weighted average (with the value of the weights 

unknown) would answer. 
11

Instrumental variables may be used to estimate either m or e. Christian (2009) uses 

daily traffic accidents, which are presumably dominated by short-term variation, as an instrument 

for short-run variation in commuting, thus estimating e. Longer-run exogenous factors could be 

used as instruments for m. 

Survey Design Issues 

As mentioned in the introduction, time-use surveys outside the United States typically 

interview more than one household member, interview across multiple days, or both. Surveys in 

South Africa and Thailand interview multiple household members for a single day. The UK, 

German and Australian time-use surveys collect data on multiple household members for 

multiple days. In contrast, the ATUS collects data on one household member for one day, which 

Connelly and Kimmel (2009) describe as a ―near-fatal flaw.‖ 

Multiple Household Members 

At first glance, the availability of data on spouses would seem to allow researchers to 

estimate how the spouse’s time use affects own time use (this is the goal of Connelly and 

Kimmel 2009, for example). However, we face essentially the same issue as we do when an 

individual’s own time use is on both sides of the regression equation. Consider the following 

modification of (6): 

(6′) 

id

W

id

H

id utt ,

where here i denotes a household rather than an individual, the H superscript denotes the 

husband and W denotes the wife. An OLS regression of (6′) will estimate a weighted average of 

m, which in this context is the long-run association between husband’s and wife’s time in a 
12

given activity, and e, which measures the association between husband’s and wife’s deviations 

from their long-run means for that activity.5

As above, IV estimation may be used to estimate either m or e. But note that it is not 

necessary to have data on both the husband and the wife to apply IV. Predicted values (either of 

long-run means or of deviations from means) can be generated from a sample of husbands 

(wives) and applied in a 2SLS regression of wives’ (husbands’) time-use. Thus there is little that 

can be learned from time diary data surveys that collect diaries from multiple household 

members compared to surveys that collect diaries from only one person per household.6

Multiple Days 

Many time-use surveys collect data on multiple days from either a single respondent or 

multiple household respondents. The most common arrangement is for respondents to be 

interviewed on two days, either consecutive days or one weekday and one weekend day.7 The 

2006 Netherlands survey collected data for seven consecutive days, but this is the only example 

we are aware of a large-scale survey collecting more than two days per respondent. High 

response burden and the resulting high non-response rate are obvious deterrents to this type of 

endeavor. 

Given that long-term means and total time-use are already identified in single-diary 

datasets, surveys that collect multiple days add nothing along this dimension for summary 

measures of long-run time-use that satisfy equation (1). Further, the periods collected are also 

 

5

 A brief examination of the literature did not reveal many cases of time-use data on couples being used to estimate 

(6'). Hook (2004) is one example. 

6

 Surveys with diaries from multiple household members can answer questions about how parents schedule work 

and family time within a day. 

7

 Australia, Japan, and Norway interview for two consecutive days. Sweden, Turkey, Latvia, Lithuania, Poland, and 

Denmark interview for one weekday and one weekend day. 
13

typically too short to be considered measures of long-run time use from the viewpoint of 

estimating statistics that do not satisfy equation (1). 

One rationale offered for collecting multiple days is to estimate variability in activities 

over time. The guidelines to the Harmonised European Time Use Surveys (Eurostat 2009) 

recommend collecting multiple days and state ―Using only one diary day will also be acceptable, 

but in that case it is impossible to get any idea of intra-personal variation.‖ However, we cannot 

learn much about intra-personal variability given the design of most multiple-day time-use 

surveys. 

Estimation of parameters describing intra-personal variation in time-use with data 

collected for two days is only possible if time use can reasonably be assumed to be uncorrelated 

between the days sampled. Extrapolating equation (2) to two days, d and d′, note that the 

variance of tid is Var(mi) + Var(eid) and that the covariance of time-use between days d and d′ is

Var(mi) + Cov(eid, eid′). In general, Cov(eid, eid′) is unknown unless we can safely assume that it 

is zero. We can estimate Var(tid), Var(tid′), and Cov(tid,tid′) from a two-day-per-person sample, 

but the underlying parameters Var(mi), Var(eid), Var(eid′), and Cov(eid,eid′) are not identified. 

For most existing surveys that sample two days, independence is unlikely for two 

reasons. First, the days sampled are typically close to each other in time, which may result in 

either positive or negative covariances depending on the activity. Busy periods at work that 

require longer hours may extend over several days and cause positive covariances for market 

work. On the other hand, household tasks may only be necessary periodically, so if observed on 

one day they would be unlikely to be observed on surrounding days, with a consequent negative 

covariance. 
14

The second, more subtle, reason is that some surveys intentionally sample two different 

days of the week, for example one weekday and one weekend-day. With this type of sampling, 

even for days that are widely separated from each other, time-use may be correlated if persons 

have regular weekly schedules that vary across the population. 

We first examine what can be estimated if activities on the sampled days are 

uncorrelated. As before, we decompose time use on a diary day into its components. 

Specifically, we redefine d to be a day of the week (d=1,...,7), let w denote a specific week, and 

rewrite the decomposition in equation (2) as follows (again omitting covariates for simplicity): 

(2′′) 

di id idw

idw i id

enNmM

emt



 

where M is the population mean time spent in the activity; 

Mmm )(

ii



is the deviation of 

individual i’s time use from the population mean, M; 

Nd



is the population mean deviation from 

M on a particular day of the week d; and 

id n



is the average deviation from the person i mean 

time mi on day of the week d net of the population day effect (

id i NmMtn di



 

), and eidw is 

the residual from the day-of-the-week mean. Note that by construction, 

0

1

I

i

mi

 , 

0

7

d 1

Nd



, and 

0

7

d 1

d

n . 

It is plausible to assume that 

0),(

idw id w''

eeCov

for two weeks, w and w', that are 

sufficiently widely separated in time. Thus the covariance between the widely separated days, d 

and d', is: 

),( (( )( )) ( )

'

2

idw id w'' i id iidw idid w''' i idid

 nnmEenmenmEttCov 

),()(

i idid '

nnCovmVar  .
15

Consider sampling two days at random from two weeks that are widely-separated in time 

each with probability 1/7. The average covariance between pairs of days is

 

.0

7

)(

7

1

...

7

1

7

1

7

1

...

7

1

7

1

)(

2

2

7

1

', ' 1 2 7 1 2 7

d

i d

dd i di d i i i i i i

n

nnEnnEE nnn En



 

Thus for randomly-selected pairs of days in widely separated weeks, the covariance of time-use 

after subtracting day-of-week effects is: 

)(),(

idw d id dw ''' mVarNtNtCov i





, which means that 

day-to-day variation in time use can be disentangled from long-run variation.

Now consider a sampling scheme that is similar to those used in some existing surveys 

where one weekend-day (d= 1,2) and one weekday (d'=3,...,7) are chosen at random. We have: 

,0

52

)(

7

3'

2 '

7

3'

'1

', '

d

i id

d

i id

dd idid

nnnn

EnnEE

so long-run variation in time-use is no longer identified. 

If the survey design is such that time use on the days sampled is uncorrelated between 

days, one can identify both βm and e in equation (7). In the regression 

(8) 

' ''

)(

idd

B

id

B

id

A

id

A

id tt vtt ,

the coefficient βδ will equal βe in this case. As noted above, the 

)(mVar i



and 

)(

id eVar

parameters (or rather 

( ), idw id neVar 

in the notation of (2′′)) can also be identified in this case, so 

βm can be identified by estimating (5) and substituting e, )(mVar i



and 

)(

id eVar

into (6). 

If time use on the days sampled is correlated, the regression in equation (8) will not 

identify βe: 
16

,

),()(

),(),(

)(

),(

)(

),(

'

'

'

' '

'

' '

B

id

B

id

B

id

B

id

A

id

B

id

A

id

B

id

B

id

B

id

B

id

A

id

A

id

B

id

B

id

B

id

B

id

A

id

A

id

eeCoveVar

eeCoveeCov

eeVar

eeeeCov

ttVar

ttttCov

(using the decomposition (2) instead of (2'') for simplicity). The non-zero cross-day covariances 

),(

'

B

id

A

id eeCov

and 

),(

'

B

id

B

id eeCov

prevent identification of βm and βe.

Even with time-use correlated between days, collecting multiple days will tighten the 

upper bound of the long-run variance of ti described in (3). This bound will be tighter (on a perday basis) with more days surveyed per respondent. 

Multiple Household Members on Multiple Days 

Several time-use surveys obtain data from multiple household members on multiple days. 

The issues arising from this design are similar to those in previous sections. The short- and longrun regression coefficients βe and βm in (6′) can be identified by the equivalent of (8) if time-use 

on the days sampled is uncorrelated between days, but not otherwise.

How Prevalent are these Issues in the Literature? 

To answer this question, we conducted a brief review of the literature to see how often 

these issues arise in published papers. To keep the review to a manageable size, we focused on 

26 papers that use ATUS data, were written by researchers outside of BLS, and were published 

in economics journals or conference volumes.8

 We examined three issues. First, when it was 

long-run time use that was of interest, did the authors report any statistics that did not satisfy 

equation (1)? Second, did the authors only report time use for weekends and weekdays even 

though they were interested in long-run time use? And third, in cases where time-use was an 

 

8

 The papers are Aguiar and Hurst (2007a,b), Burda and Hamermesh (2010), Burda, Hamermesh, and Weil (2008), 

Connelly and Kimmel (2009), Connolly (2008), Davis and You (2010), Folbre and Yoon (2007, 2008), Guryan, 

Hurst, and Kearny (2008), Hamermesh (2007, 2008a, 2008b, 2010) , Hamermesh, Myers and Pocock (2008), Hersch 

(2009), Kalenkoski, Ribar, and Stratton (2007), Kimmel and Connelly (2007), Krueger (2007), Landefeld, 

Fraumeni, and Vojtech,(2009), Meyer and Sullivan (2008), Price (2008), Vernon (2009), Ward-Batts (2008), Zick 

and Bryant (2008), Zick, Bryant, and Srisukhumbowornchai (2008). 
17

independent variable, did the authors use aggregation or instrumental variables to mitigate the 

mismeasurement of long-run time-use? 

The results confirm that these three issues frequently arise in the literature. Out of the 26 

papers we reviewed, 15 had one or more issues. Of the 22 papers concerned with long-run timeuse as a dependent variable, 6 reported statistics that do not satisfy (1) (in every case, the authors 

reported percentiles). Four papers out of the same 22 did not report totals where relevant. Of the 

7 papers where time-use was an independent variable, 5 did not use any methods to mitigate 

measurement error. In many cases the suspect analysis is only a minor part of the overall paper.9

But it is clear that time-diary data are frequently used as if they were an accurate measure of the 

respondent’s long-run time use. 

Conclusion 

Time diary data provide researchers with a detailed look at how people spend their time 

over a 24-hour period. However, the short reference period combined with the large amount of 

day-to-day variation in time use implies that any given time diary is a poor indicator of that 

individual’s long-run time use. Although short-run time use is sometimes of interest, for most 

policy-related questions it is long-run time use that is relevant. This mismatch between the 

reference period of the data (a person-day) and the period of interest (a person-month or personyear) has important implications for the analysis of time diary data. These implications have not 

been fully appreciated by many researchers. 

In general, when time use is the dependent variable, researchers can make inferences 

about the long-run time use of individuals from a sample of person-days only when the value of 

 

9

 For example, in one section of a substantial paper Aguilar and Hurst (2007b) discuss changes in percentiles of 

leisure, but otherwise analyze means. Price (2008) uses median regressions as a robustness check for his OLS 

regressions. 
18

the statistic is invariant to the amount of day-to-day variation in the data. For example, 

researchers can estimate mean (per person) time use for a population of individuals, but it is 

impossible to estimate how much time the median person spends in an activity. 

Several recent studies have included time use as an explanatory variable in regression 

equations. Long-run outcomes such as obesity can only be affected by time-use over a long 

period of time. But, as we have seen, time use on a randomly chosen diary day is not a good 

indicator of long-run time use. This implies that time-diary data measure the true variable of 

analytic interest with considerable error even if the respondent has made no recall errors. Using 

instrumental variables (IV) or entering time use as an aggregate (for example, cell means) are 

two ways of dealing with this measurement error. 

Lastly, our findings have implications for survey design. Time use researchers have long 

recommended that surveys collect time diaries from every person in the household and collect 

them for multiple days. Collecting time diaries from everyone in the household would seem to 

allow researchers to learn about the intra-household allocation of household work and leisure. 

But we have shown that users of single-day data from multiple household members face the 

problem of disentangling the day-to-day covariance of activities from the long-run covariance, 

which implies that there is little that one can learn by collecting diaries from everyone in the 

household that cannot be learned from single-person-per-household diaries. Collecting multiple 

diaries from respondents can be potentially valuable, but (given practical limits on the number of 

days sampled) only if the days are sampled so as to ensure that the activities on those days are 

independent. Without independence, between-day covariance makes it impossible to identify the 

within- and between-person variance. 
19

The increasing availability of time-diary data has allowed analysts to research a wide 

variety of questions whose investigation was previously limited by data that was either 

nonexistent or subject to substantial recall bias. We hope that future researchers will take 

account of the short-term nature of the data in their research designs while continuing to take 

advantage of the greater accuracy that time diaries offer. 
20

References 

Aguiar, Mark and Erik Hurst (2007a) ―Life-Cycle Prices and Production‖ American Economic 

Review 97(5), pp. 1533-1559. 

Aguiar, Mark and Erik Hurst (2007b) ―Measuring Trends in Leisure: The allocation of Time 

over Five Decades.‖ Quarterly Journal of Economics 122(3), pp.969-1006. 

Burda, Michael C. and Daniel S. Hamermesh (2010) ―Unemployment, market work and 

household production.‖ Economics Letters 107, pp. 131-133. 

Burda, Michael C., Daniel S. Hamermesh and Phillipe Weil (2008) ―The Distribution of Total 

Work in the EU and US.‖ In Working Hours and Job Sharing in the EU and USA: Are 

Europeans Lazy? Or Americans Crazy? Tito Boeri, Michael C. Burda, and Francis 

Kramarz, ed. New York: Oxford University Press, pp 13-91. 

Christian, Thomas J. (2009) ―Opportunity Costs Surrounding Exercise and Dietary Behaviors: 

Quantifying Trade-offs Between Commuting Time and Health-Related Activities.‖ 

Unpublished working paper. 

Connelly, Rachel and Jean Kimmel (2009) ―Spousal influences on parents’ non-market time 

choices.‖ Review of Economics of the Household 7(4), pp. 361-394. 

Connolly, Marie (2008) "Here Comes the Rain Again: Weather and the Intertemporal 

Substitution of Leisure." Journal of Labor Economics 26(1), pp. 73-100. 

Davis, George C., and Wen You (2010) ―The time cost of food at home: general and food stamp 

participant profiles‖ Applied Economics 42(20), pp. 2537-2552. 

Eurostat (2009) Harmonised European time use surveys 2008 guidelines. Eurostat 

Methodologies and Working Papers. Luxembourg: Office for Official Publications of the 

European Communities, p. 9.

Faberman, R. Jason (2010) ―Revisiting The Role Of Home Production In Life-Cycle Labor 

Supply.‖ Working Paper No. 10-3, Research Department, Federal Reserve Bank of 

Philadelphia. 

Folbre, Nancy and Jayoung Yoon (2007) ―What is Child Care? Lessons from time-use surveys 

of Major English-speaking Countries.‖ Review of Economics of the Household 5(3), pp. 

223-248.

Folbre, Nancy and Jayoung Yoon (2008) ―The Value of Unpaid Child Care in the United States 

in 2003,‖ in How Do We Spend Our Time? Evidence from the American Time Use 

Survey, Jean Kimmel, ed. Kalamazoo, MI: W.E. Upjohn Institute for Employment 

Research, pp. 31-56. 

Frazis, Harley and Jay Stewart (2009) "How Does Household Production Affect Measured 

Income Inequality?" Forthcoming in Journal of Population Economics.

Guryan, Jonathan, Erik Hurst, and Melissa Kearney (2008) ―Parental Education and Parental 

Time with Children,‖ Journal of Economic Perspectives 22(3), pp. 23-46. 

Hamermesh, Daniel S. (2007) ―Time to Eat: Household Production Under Increasing Income 

Inequality.‖ Journal of Agricultural Economics 89(4), pp. 852-863. 
21

Hamermesh, Daniel S. (2008a) ―Direct estimates of household production.‖ Economics Letters

98, pp. 31-34.

Hamermesh, Daniel S. (2008b) ―The Time of Our Lives.‖ in How Do We Spend Our Time? 

Evidence from the American Time Use Survey, Jean Kimmel, ed. Kalamazoo, MI: W.E. 

Upjohn Institute for Employment Research, pp. 11-30. 

Hamermesh, Daniel S. (2010) ―Incentives, time use and BMI: The roles of eating, grazing and 

goods.‖ Economics and Human Biology 8, pp. 2-15. 

Hamermesh, Daniel S., Caitlin Knowles Myers, Mark L. Pocock (2008) ―Cues for Timing and 

Coordination: Latitude, Letterman, and Longitude.‖ Journal of Labor Economics 26(2), 

pp. 223-246.

Hersch, Joni (2009) ―Home production and wages: evidence from the American Time Use 

Survey.‖ Review of Economics of the Household 7, pp. 159-178.

Hook, Jennifer (2004) ―Reconsidering the Division of Household Labor: Incorporating 

Volunteer Work and Informal Support.‖ Journal of Marriage and the Family 66(1), pp. 

101-117.

Kalenkoski, Charlene, David Ribar, and Leslie Stratton (2007) ―The Effect of Family Structure 

on Parents' Child Care Time in the US and the UK.‖ Review of Economics of the 

Household 5(4), pp. 353-384. 

Kimmel, Jean and Rachel Connelly (2007) ―Mothers’ Time Choices: Caregiving, Leisure, Home 

Production, and Paid Work.‖ Journal of Human Resources 42(3), pp. 643-681. 

Klepper, Steven and Edward E. Leamer, Edward E. (1984) "Consistent Sets of Estimates for 

Regressions with Errors in All Variables." Econometrica. 52(1), pp. 163-183.

Krueger, Alan B. (2007) ―Are We Having More Fun Yet? Categorizing and Evaluating Changes 

in Time Allocation.‖ Brookings Papers on Economic Activity 2007(2), pp. 193-215.

Landefeld, J. Steven, Barbara M. Fraumeni, and Cindy M. Vojtech (2009) ―Accounting for 

Household Production: A Prototype Satellite Account Using the American Time Use 

Survey‖. Review of Income and Wealth 55(2), pp. 205-225. 

Meyer, Bruce and James X. Sullivan (2008) ―Changes in the Consumption, Income, and WellBeing of Single Mother Headed Families.‖ American Economic Review 98(5), pp. 2221-

2241.

Pinkston, Joshua, and Jay C. Stewart (2009) ―How Does Time Use Affect the Probability of 

Becoming Obese?‖ Unpublished manuscript. 

Price, Joseph (2008) ―Parent-Child Quality Time: Does Birth Order Matter?‖ Journal of Human 

Resources 43(1), pp. 240-265. 

Stewart, Jay C. (2009) ―Tobit or not Tobit?‖ BLS Working Paper No. 432. 

Stewart, Jay (2010) "The Timing of Maternal Work and Time with Children," Industrial & 

Labor Relations Review. 64(1), pp. 181-200 

Vernon, Victoria (2010) ―Marriage: for love, for money ... and for time?‖ Review of Economics 

of the Household. Forthcoming. 
22

Ward-Batts, Jennifer (2008) ―Household Production, Consumption, and Retirement,‖ in How Do 

We Spend Our Time? Evidence from the American Time Use Survey, Jean Kimmel, ed. 

Kalamazoo, MI: W.E. Upjohn Institute for Employment Research, pp. 81-108. 

Zick, Cathleen D. and W. Keith Bryant (2008) ―Does Housework Continue to Narrow the 

Income Gap?‖ in How Do We Spend Our Time? Evidence from the American Time Use 

Survey, Jean Kimmel, ed. Kalamazoo, MI: W.E. Upjohn Institute for Employment 

Research, pp. 57-80. 

Zick, Cathleen D., W. Keith Bryant, and Sivithee Srisukhumbowornchai (2008) ―Does 

housework matter anyore? The shifting impact of housework on economic inequality.‖ 

Review of Economics of the Household 6(1), pp. 1-28.