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This paper studies the link between working hours and productivity using daily information on working hours and performance of a sample of call centre agents. We exploit variation in the number of hours worked by the same employee across days and weeks due to central scheduling, enabling us to estimate the effect of working hours on productivity. We find that as the number of hours worked increases, the average handling time for a call increases, meaning that agents become less productive. This result suggests that fatigue can play an important role, even in jobs with mostly part-time workers.
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Research Centre for Education and the Labour Market | ROA
ROA-RM-2017/4
Working hours and productivity
Marion Collewet
Jan Sauermann
ROA Research Memorandum
Researchcentrum voor Onderwijs en Arbeidsmarkt | ROA
Research Centre for Education and the Labour Market | ROA
Working hours and productivity
Marion Collewet
Jan Sauermann
ROA-RM-2017/4*
April 2017
* The ROA Research Memorandum Series was created in order to make research results available for discussion,
before those results are submitted for publication in journals.
Research Centre for Education and the Labour Market
Maastricht University
P.O. Box 616, 6200 MD Maastricht, The Netherlands
T +31 43 3883647 F +31 43 3884914
secretary-roa-sbe@maastrichtuniversity.nl
www.roa.nl
Abstract
Working hours and productivity**
This paper studies the link between working hours and productivity using daily
information on working hours and performance of a sample of call centre agents. We
exploit variation in the number of hours worked by the same employee across days and
weeks due to central scheduling, enabling us to estimate the effect of working hours
on productivity. We find that as the number of hours worked increases, the average
handling time for a call increases, meaning that agents become less productive. This
result suggests that fatigue can play an important role, even in jobs with mostly part-
time workers.
JEL classification: J23, J22, M12, M54
Keywords: working hours, productivity, output, labour demand
Marion Collewet
Centre for Operations Research and
Econometrics (CORE)
Université Catholique de Louvain
Voie du Roman Pays, 34 - L1.03.01
B-1348 Louvain-la-Neuve
Belgium
marion.collewet@uclouvain.be
and ROA, Maastricht University
Jan Sauermann
Swedish Institute for Social Research
Stockholm University
Universitetsvägen 10 F (oors 8 and 9)
SE-106 91 Stockholm
Sweden
jan.sauermann@sofi.su.se
and ROA, Maastricht University and IZA
** The authors would like to thank Jordi Blanes-I-Vidal, Alexandra de Gendre, Andries De Grip, Annemarie Künn-
Nelen, John Pencavel, two anonymous referees, and seminar participants at the Paris School of Economics, and
audience at EALE 2016 for valuable comments and suggestions. Jan Sauermann gratefully acknowledges financial
support from the Jan Wallanders och Tom Hedelius Stiftelse for financial support (Grant number I2011-0345:1).
1 Introduction
Hours worked vary substantially between countries, but also within countries,
e.g. due to the prevalence of part-time work and working hours regulations or
agreements (Bick et al., 2016; OECD, 2016). Understanding how the num-
ber of hours worked affects labour productivity is an important element of
understanding labour demand, and has important implications for the regu-
lation of working hours and firm management. Still, a lot remains unknown
about the effect of working hours on labour productivity. In theory, there
could be two opposite effects. On the one hand, longer hours can lead to
higher productivity if a worker faces fixed set-up costs and fixed unproduc-
tive time during the day, or if longer hours lead to better utilisation of capital
goods (Feldstein, 1967). On the other hand, worker fatigue could set in af-
ter a number of hours worked, so that the marginal effect on productivity
of an extra hour per worker starts decreasing (Pencavel, 2015). If neither
of these effects apply, or if both cancel each other out, it could also be the
case that marginal productivity does not change with working time, so that
output is proportional to the number of hours worked. Identifying the effect
of working time on productivity is not straightforward for two main reasons.
First, unobservable characteristics of industries, firms, jobs and individuals
are likely to influence both working time and productivity, so that the cor-
relation between the two variables is likely to be a biased estimate of the
effect of working time on productivity. Second, external shocks could in-
fluence both working time and productivity, which again leads to a biased
estimation of the effect.
In this paper, we study the influence of the daily number of hours worked
on workers’ productivity using panel data from a call centre in the Nether-
lands from mid-2008 to the first week of 2010 (cf. De Grip and Sauermann,
2012; De Grip et al., 2016). For each of the 332 workers in our sample, the
data contain detailed information on the number of daily working hours, and
workers’ individual performance, as measured by the average handling time
of calls. The panel structure of our data set allows us to correct for time-
invariant unobserved characteristics of individuals that may influence both
1
working time and productivity. Moreover, the exact number of hours worked
by a worker on a given day is determined by central planning. Expected cus-
tomer demand determines the scheduling process, and schedules are hardly
related to individual preferences. This enables us to obtain estimates of the
effect of working time on productivity.
Estimating a model controlling for individual fixed effects and several
types of time fixed effects, we find that an increase in working hours by
1 percent leads to an increase in output by only 0.9 percent, measured as
the number of calls answered. This finding suggests that fatigue sets in
as working time increases. The corresponding decrease in productivity is
mild in this sample where most employees work part-time, but it suggests
that fatigue effects would be much stronger if agents would work full-time.
We find evidence of more strongly decreasing returns to hours for workers
with shorter tenure, a result that is not driven by worker attrition. Using
additional data on service quality, we find that longer working hours are
associated with a moderate increase of call quality in working hours, a result
that partly offsets the negative effect on the number of calls answered.
This paper contributes to a rich literature that studies the link between
working time and productivity. Studies estimating production functions
based on industry-level data find mixed evidence for the returns to work-
ing hours. Whereas some studies find increasing returns to hours (Feldstein,
1967; Craine, 1973; Leslie, 1984), which could be the result of not taking
capacity utilisation rates into account (e.g. Tatom, 1980), or be due to ag-
gregation bias (e.g. DeBeaumont and Singell, 1999), other studies conclude
that output is roughly proportional to hours worked per worker (Hart and
McGregor, 1988; Anxo and Bigsten, 1989; Ilmakunnas, 1994). The majority
of studies, however, find evidence of decreasing returns to hours (e.g. Leslie
and Wise, 1980; Tatom, 1980; DeBeaumont and Singell, 1999; Shepard and
Clifton, 2000). Typically, studies using aggregate data deal with the endo-
geneity of working time by using panel data and including industry fixed
effects, and by instrumenting for working time using lagged values or ranks.
The validity of such instruments, however, can be questioned, and the mea-
2
surement of working time and output at these aggregate levels is likely to be
subject to error.
Studies using firm-level data, or data from workers in individual firms
or in specific sectors are typically better at dealing with the endogeneity of
working hours. A few studies use panels of firms to estimate the link between
working time and firm or establishment productivity (Cr´epon et al., 2004;
Schank, 2005; Kramarz et al., 2008; Gianella and Lagarde, 2011). They
tend to find that output is roughly proportional to the number of hours
worked.1Due to the data structure, these studies are able to control for the
endogeneity of working time caused by time-invariant firm characteristics.
However, shocks that would affect both working time and productivity could
still form a potential source of bias.
Studies using data about individual workers in a firm, or about work-
ers in comparable firms date back to the early 20th century, when studies
descriptively analysed the relationship between working hours and output,
or compared output before and after a change in working hours (Goldmark,
1912; Vernon, 1921; Kossoris, 1947).2More recent studies, however, exploit
exogenous sources of variation in working hours to address the relationship
between hours and worker level productivity. An early example is the study
of citrus harvesters by Crocker and Horst (1981), who use the size of the
grove worked on as a source of variation in working time. Brachet et al.
(2012) conduct a difference-in-differences analysis to compare performance
of paramedics working on short and long shifts. Using data from munition
plants in Britain during the First World War, Pencavel (2015) uses vari-
ation in working time coming from the demand for shells to estimate the
effect of working time on productivity. Dolton et al. (2016) use data from
the Hawthorne experiments (conducted between 1924 and 1932) to exploit
1Cr´epon et al. (2004) and Kramarz et al. (2008) find positive effects on productivity
of participating in a working time reduction scheme for French firms, but this effect is
due to the reorganisation of work that took place as a consequence of the working time
reduction. Work allocation as a mechanism to explain the link between part-time work and
productivity has been studied by K¨unn-Nelen et al. (2013), Specchia and Vandenberghe
(2013), Garnero et al. (2014), and Devicienti et al. (2015).
2See Nyland (1989) for an overview of these and other studies.
3
the fact that workers were subjected to different working times in different
periods. While Crocker and Horst (1981) find that output is proportional
to hours worked, Brachet et al. (2012), Pencavel (2015), and Dolton et al.
(2016) find evidence of decreasing returns to hours. A contrasting result is
found by Lu and Lu (2016), who exploit changes in mandatory overtime laws
for nurses. They find that the introduction of overtime laws actually reduced
the quality provided by nurses, an effect that can be explained by changes in
staffing policies of permanent and contractual (temporary) nurses.3We con-
tribute to this literature by exploiting exogenous variation in working hours,
which is due to the call centre’s central scheduling.
Most of the studies that are able to exploit exogenous variation in working
time to identify the effect of working hours on productivity have concentrated
on either manual workers from the first half of the 20th century (Pencavel,
2015; Dolton et al., 2016)4, or on the health sector using more recent data
(Brachet et al., 2012; Lu and Lu, 2016). In this paper, we provide evidence
about call agents in a call centre. Our results can have informative value for
a broader range of medium-skilled level jobs in the service sector, and are
relevant for policies such as working time regulation.
The remainder of the paper is structured as follows. In the next section,
we outline our conceptual framework. Section 3 presents the empirical model
we estimate and our identification strategy. Section 4 describes the data we
use. Section 5 presents our main estimation results. In Section 6, we conduct
a number of robustness checks, and we formulate conclusions in Section 7.
3In addition to these studies, there are more studies for the health sector, typically
finding decreasing returns to working hours. These studies, however, are either based on
indirect performance measures (psychometric tests, simulations of work tasks, self-report
questionnaires; for a review, see Kodz et al., 2003), or on correlations and before-after
comparisons (Rogers et al., 2004; Hart and Krall, 2007; McClay, 2008). There is also a
related literature that has analysed the link between long working hours and health (e.g.
van der Hulst, 2003) and between long hours and occupational injuries (e.g. Vegso et al.,
2007; Lee and Lee, 2016). These studies suggest that working long hours is detrimental
for health and therefore may have negative effects on productivity.
4The relation between working time and productivity might have changed as the nature
of jobs evolved. Pencavel concludes his paper stating that “it would be valuable if the
analysis here could be repeated on contemporary data that contain information on workers’
output and their working hours” (p. 2074).
4
2 Conceptual framework
2.1 Model
Typically, studies of the relation between working time and productivity
estimate a model of the type:
Y=f(H, X) + (1)
where Yis a measure of output, Ha measure of hours worked, Xis a
set of variables which are also relevant for output (the capital stock being
a typical candidate), and is the error term. Very often, the relationship
between log output and log hours is estimated assuming a Cobb-Douglas
production function. Because we focus on productivity at the level of the
individual worker, for whom capital use is constant (namely one workstation),
the Cobb-Douglas function can be estimated as
ln(Y) = α·ln(H) + γ·X+(2)
In our setting, call centre management uses a specific measure to evaluate
the performance of its agents: average handling time (AH T ), which is based
on the time taken by an individual agent to answer each call during a given
day or a given week. If output Yis defined as the number of calls made on
a given day, it can be expressed as
Y=H
AHT (3)
Inserting Equation (3) into (2) gives:
ln(AH T ) = (1 α)·ln(H)γ·X(4)
Average handling time is a negative measure of productivity, since indi-
viduals who take more time to answer calls are less productive (cf. De Grip
and Sauermann, 2012). To facilitate direct interpretation of our estimation
results, we multiply Equation (4) by 1, which allows us to rewrite it to
5
ln 1
AHT = (α1) ·ln(H) + γ·X+(5)
and to use 1/AHT as a measure of productivity: an increase in 1/AH T can
therefore be interpreted as an increase in productivity.
In this model, a coefficient on ln(H) equal to zero indicates that work-
ers’ productivity does not vary with working hours, which is equivalent to
constant returns to hours. A positive coefficient corresponds to increasing
returns to hours, and a negative one to decreasing returns. The magnitude
of the coefficient on log hours is also directly interpretable: as hours increase
by 1 percent, output increases by αpercent. If we define the coefficient on
ln(H) to be β=α1, output increases by β+ 1 percent as hours increase
by 1 percent.
We estimate the model both at the day and at the week level to address
potential heterogeneity in the returns to working hours at the day and week
level: at the week level, workers have time to recover from one day to another,
so that returns to hours might be more positive than at the day level (cf.
Pencavel, 2016). Moreover, comparing returns to hours at the day and at the
week level can tell us whether productivity can be increased by distributing
weekly working hours differently across days.
2.2 Mechanisms
Before turning to estimating the model, we want to pay closer attention to
the mechanisms that link working hours to labour productivity. Why exactly
would we expect labour productivity to rise or fall as working hours increase?
Potential reasons for increasing returns to hours are fixed unproductive
time and better capital utilisation rates. In our setting, unproductive time
cannot play a role because we study effective working time (excluding breaks,
see Section 4). Capital utilisation rates are not relevant either because we
focus on the level of the individual worker, who always uses exactly one
workstation consisting of a phone and a computer. One possible mechanism
that could lead productivity to increase with working time is what Vernon
(1921) calls “practice-efficiency”, i.e. the fact that one gets better at a task
6
as one “warms up”.5It is an open question whether what he describes for
physical work may also apply to call centre agents.
The main reason why productivity would decrease as working hours in-
crease is worker fatigue.6The origins of the literature on fatigue and the
link between working hours and labour productivity lie in the study of the
manufacturing industry in the early 20th century (Goldmark, 1912; Vernon,
1921), with physically demanding jobs and very long hours. But fatigue is
still relevant in today’s service economy with shorter hours. Indeed, Ny-
land (1989) emphasizes that the fall in working hours over the course of the
twentieth century has been accompanied by an intensification of work due
to the rise of scientific management, so that the optimal number of working
hours has most probably dropped below levels that were recommended at the
beginning of the twentieth century. In fact, the majority of studies on the
link between working hours and productivity still finds decreasing returns
to hours. Moreover, physical demands are not the only demands of a job.
Goldmark (1912) already emphasises the important role played by speed and
complexity of a task.7Bakker et al. (2003) find that job demands are related
to exhaustion and repetitive strain injury in call centre agents. The agents
we study were exposed to a constant flow of incoming calls and had to solve
problems that were potentially different for every single call. The manage-
5“The complex chain of central nervous system, neuro-muscular mechanisms, nerves
and muscles involved takes time to work up to its maximum efficiency, and to get into
thorough running order. In fact, this efficiency is unattainable except by practice, hence
I have termed it practice-efficiency.” (Vernon, 1921, p. 13).
6Vernon (1921) cites the definition by the British Association Committee on Fatigue
from the Economic Standpoint: it sees fatigue as the “diminution of the capacity for work
which follows excess of work or lack of rest, and which is recognised on the subjective side
by a characteristic malaise.” (p.1). More recently, in the occupational health literature,
fatigue is defined by van Dijk and Swaen (2003) as “the change in the psychophysiological
control mechanism that regulates task behaviour, resulting from preceding mental and/or
physical efforts which have become burdensome to such an extent that the individual is
no longer able to adequately meet the demands that the job requires of his or her mental
functioning; or that the individual is able to meet these demands only at the cost of
increasing mental effort and the surmounting of mental resistance.”
7Interestingly, she takes telephone operators as an example, and reports that a medical
commission deemed a 7-hours workday too long for “telephone girls”. Of course, it has to
be said that the work of telephone operators was much more physically demanding than
the work of call centre agents today.
7
ment of the call centre seemed well aware of the intensity and difficulty of the
task agents had to perform: without having actually measured the relation
between working hours and productivity, they expected a full-time contract
to be sub-optimal in terms of productivity and preferred to offer part-time
contracts to their employees for that reason.
3 Empirical strategy
Using panel data, our empirical model can be written as
ln 1
AHTit =φ+β·ln(Hit) + γ·Xit +δ·Tt+µi+it (6)
where the subscript istands for an individual agent, and trepresents the
time period (day or week) examined. In this section, we first discuss how we
control for potential confounders, and second how we exploit scheduling as
a source of exogenous variation in working hours.
3.1 Controlling for potential confounders
As mentioned above, there are several factors that can result in a biased esti-
mate of the effect of hours on productivity ( b
β). First, the estimate could be
biased due to characteristics of individuals that influence both their working
time and their productivity, such as preferences or ability. As far as these
individual characteristics are time-invariant, they can be controlled for by
the individual fixed effect µiin our model. Taking account of this unob-
served heterogeneity takes away an important part of the potential bias in
the coefficient on ln(Hit).
Second, the timing of work might be important as well. If variation
in types or amounts of customer calls varies over time, and this variation
results in changes of agents’ productivity, it is important to control for when
individuals work.8In estimations at the day level, we control for day of the
8Note that, although we have precise information on when and how long agents are
working, the data only contain information on performance on the daily level, but not by
the hour.
8
week dummies (as part of Tt) and for hours dummies for the time during
which an individual works on a given day (as part of Xit); in estimations
at the week level, we control for 168 dummies that represent each hour of
the week. There might also be shocks on specific days or weeks, e.g. if
there are technical problems that both induce agents to stay longer hours
and affect their productivity because the shocks influence the time taken to
help customers or the pressure experienced by agents. To control for this
possibility, our model includes day fixed effects in regressions based on daily
data, or week fixed effects in regressions based on weekly data.
Third, tenure is a potential confounder. Differences in tenure between
individuals at the beginning of the observation period are captured by the
individual fixed effect. However, as individuals become more experienced,
their productivity is likely to increase, and their working time might also
evolve. If this is the case, some of the effect of tenure will unduly be attributed
to working time. We therefore include a general time trend in the model.
Further, in Section 6, we run additional regressions including individual-
specific time trends, i.e. interactions of the individual fixed effect with the
time trend. This allows us to provide evidence against the hypothesis that
call centre management could give different contracts or schedules to workers
who learn faster.
Fourth, attrition may also be a problem. There is relatively high turnover
in our sample, resulting in that individuals who stay for relatively long in
the sample may be overrepresented in our data. If more productive individ-
uals stay longer, and if they are therefore overrepresented, we will tend to
overestimate returns to hours. We address this problem by estimating our
model for a balanced sub-sample in Section 6. This analysis shows that the
bias caused by attrition is only limited.
Finally, the team in which an individual works may also be a confounder,
in the sense that a team with more positive characteristics (more cohesive,
better team leader, etc.) may both induce an agent to be willing to work
longer hours and make him or her more productive. This would lead to an
underestimation of the fatigue effect, i.e. an overestimation of the returns to
hours. To rule this out, we include team fixed effects in our model.
9
3.2 Exogeneity of working hours due to central schedul-
ing
In our data, variation in an agent’s working time from day to day or from
week to week arises because contractual weekly working time does not need
to be exactly enforced every week. Rather, average working time over a
period of three months should be equal to contractual working time. An
agent’s working time for a given day is defined by the planning department,
on the basis of an algorithm that forecasts customer demand, i.e. the number
of incoming calls. A first version of an agent’s schedule for a given day is
communicated five weeks in advance, but it can be revised up to the last
moment. We also know that earlier performance of agents does not influence
future schedules. In principle, this ensures that the exact number of hours
worked by an individual on a given day is not related to shocks affecting this
individual, so that Hit is not correlated with it, the idiosyncratic error term.
There are two potential ways in which individual preferences could in the-
ory still influence working time on a given day or a given week. First, agents
are allowed to state preferences about their schedule, both general prefer-
ences and preferences for specific days or weeks, without having a guarantee
that these preferences can be respected. While general preferences stated
by an agent about his or her schedule are captured by the individual fixed
effect, preferences concerning a specific day or week are not. Second, in case
of unexpectedly high or low demand at the last minute, agents are asked to
stay longer or leave earlier on a voluntary basis, with a corresponding ad-
justment in their pay. In theory, these two factors leave some room for the
agents to work more on days on which they expect to be more productive,
leading to an overestimation of the returns to hours. However, these poten-
tial sources of bias do not appear to play an important role in practice. In
Section 6, we present estimations including scheduled hours (or deviations
from schedules) as an additional control variable. This enables us to check
whether, conditional on the actual number of hours worked, schedules (or
deviations from schedules) are still related to productivity, which would hint
at self-selection by agents. We show that there is only very limited evidence
10
of self-selection, and that taking it into account barely changes our results.
We conclude that, conditional on our set of fixed effects, scheduling can be
considered an exogenous source of variation in working hours.
4 Data
4.1 Description of the context
We use rich company data on call agents employed in a call centre located
in the Netherlands. This customer service centre handles calls from current
and prospective customers of a mobile telecommunication company. The call
centre comprises five departments, which are segmented by customer groups.
To focus on workers which have comparable performance, we limit the sample
to the largest department, for customers with fixed contracts.
In this department, all call agents have the same task, answering cus-
tomer calls. Customers call the call centre in case of problems, complaints or
questions and are routed to available agents. Typically, at a given moment,
the number of incoming calls exceeds the number of available agents, gen-
erating non-zero waiting time for customers. Agents who have completed a
call faster are automatically linked to the next customer waiting. This means
that fast agents do not have longer breaks and do not need to wait for the
next customers. Therefore, agents have little slack time when on the job.
In other words, the number of hours that agents spend answering calls, our
main measure of working time, is very close to the number of hours during
which agents are available for calls.
Agents are incentivised to perform, and in particular to handle calls fast.
Agents are organised in 19 teams, each of which is led by a team leader.
The main task of team leaders is to monitor and evaluate the agents of his
or her team. For this purpose, team leaders receive weekly scorecards with
detailed information of their agents’ performance (including average handling
time), and regularly listen to the calls of their agents. Agents receive a fixed
11
wage per hour.9Following a performance appraisal of the team leader, the
agent receives a grade from 1 (worst) to 5 (best), which determines both
the size of an annual wage increase and an annual bonus. This grade is
determined by both the performance over the year, but also by other, more
subjective factors, such as the behaviour towards co-workers. The maximum
wage increase depends on the firm performance, and does not exceed 8% for
agents with the highest grade.10 Otherwise, there are no explicit incentives
based on agents’ performance, such as piece rates or bonuses upon their daily
or weekly performance.
Our data comprise daily performance information for each agent work-
ing in the call centre. In total, our analysis includes 332 agents on 33,123
agent-working days, over an observation period from week 36/2008 to week
1/2010. Descriptive statistics for the estimation sample are provided in Ta-
ble 1. Besides information on performance, the data also contain information
on the working hours and on some basic characteristics of the agents. The
majority of the agents is female, only 35% of all agents are men. Agents are
on average 29 years old, and the average tenure over all observations is about
140 weeks.11
4.2 Measuring performance
The main measure of performance used by the call centre is average handling
time (AHT). It is defined as the time taken for talking to the customer, plus
9Barzel (1973) studies how working hours are determined by the interplay of supply
and demand when the remuneration of an extra hour of work varies together with the
product of that extra hour. In our setting, workers are paid a constant hourly wage rate,
and therefore face the linear budget constraint which is usually assumed in the standard
model of labour supply. Therefore, our findings about the relation between hours and
labour productivity are mainly relevant for the demand side of the labour market.
10We observe the results of the annual performance appraisals only for a subsample of
agents. In these data, only very few agents receive the worst and the best grade (1: 1.3%;
5: 0.7%), while most agents receive a 2 (29.9%), 3 (54.6%), or 4 (13.6%), respectively.
The criteria for performance appraisals are agents’ performance scorecards throughout
the year, as well as the behaviour of the agent towards co-workers and team leader.
11The firm’s administrative data includes a small number of outliers. We therefore kept
only observations with positive values for hours and performance, and excluded from the
sample half a percentile at the top of the performance and the working hours distribution.
12
time taken for logging the information in the firm’s database. On average,
agents take 322 seconds, or 5.35 minutes, to handle a call. Figure 1 shows
the density of average handling time and shows that the distribution is right-
skewed. Earlier studies using performance data of call agents have used
similar measures to estimate the impact of training and learning on-the-
job on performance (Liu and Batt, 2007; De Grip and Sauermann, 2012;
Breuer et al., 2013; De Grip et al., 2016). Panel (a) of Figure 2 depicts the
descriptive relationship between our measure of productivity (1/AHT) and
daily working time. Longer working hours seem to be associated with slightly
lower productivity, i.e. slightly longer average handling times.
While it is relatively straightforward to measure how long agents take for
an average call, it is more difficult to measure the quality of these calls. We
use two different measures of quality. The first is the share of repeat calls.
The system tracks when customers are calling again within seven days after
the last call. Based on this information, the system calculates the share of
customers who call back within 7 days, relative to all customers an agent had
contact with. The higher the share of repeat calls, the lower service quality.
Zero repeat calls indicates that none of the customers an agent had contact
with was calling back within seven days. A value of 1 would indicate that
every customer would have called back.12
A second variable, which is used to assess the quality provided by agents,
is front line completion. This variable is based on the inbound and outbound
calls. Since the main task of agents is to receive inbound calls, and outbound
calls should only be necessary if an agent could not complete a case, a lower
front line completion rate is an indicator of lower quality. Completion is
defined as the difference between an agent’s number of inbound calls and
outbound calls, divided by the number of inbound calls. The measure is 1
if an agent does no outbound calls at all. Thus, a value of 1 reflects high
problem-solving ability of the agent.
12One disadvantage of this measure is that customers might have called back for a
different reason, which might be unrelated to the original call. In this case, the “repeat”
call would be wrongly attributed to an agent.
13
4.3 Measuring working time
Working time is calculated as the number of calls handled by an individual
agent, times the agent’s average handling time. It thus measures the time
during which an agent is directly working on his or her main task, answering
customer calls. By definition, this measure does not comprise any non-call
related time, such as breaks, slack, or training hours. We choose this measure
because it serves as a precise measure of effective working time. If we used
a measure which includes slack time and breaks, part of what would be
counted as working time would actually be recovery time. This would lead
to an underestimation of the fatigue effect. Moreover, slack time or time
for breaks is most probably not proportional to the time spent answering
calls. Rules about breaks, for instance, prescribe different break schemes for
different discrete values of time spent at the workplace. Therefore, the share
of time spent in breaks is not constant across values of time spent at the
workplace. This could also lead to bias in the estimated fatigue effect if we
used a measure of working time which includes breaks.13
To analyse how important our choice of the definition of working hours is,
we also consider two alternative measures of working time in our estimations
in the next section. The first is a measure of hours during which the agent is
available to answer calls at his or her desk. The second is a measure of the
time spent by the agent at the workplace, and includes training, the unpaid
lunch break, etc. They are not, however, precise enough to yield reliable
information about slack time and time spent in breaks.
Table 1 also provides summary statistics of these alternative measures of
working time. Both measures are very strongly correlated with the measure
we chose, in particular the time that agents are available for calls (ρ= 0.95).
Most agents working in the call centre work part time. On average, agents
spend 4 days a week and 6 hours per day at their workplace. Their effective
working time, however, only averages 4.6 hours per day, and 17.7 hours per
week.
13It would be very interesting to study the role played by slack time and breaks, and
whether they function as recovery time for workers (cf. Pencavel, 2016). However, the
data we have does not allow us to do so.
14
Table 2 shows that there is sufficient within-agent variation in the number
of hours worked per day and per week. Agents work days of about 5 effective
working hours about half (45.8 percent) of the time. However, during the
rest of the time, they work very different numbers of hours per day, ranging
from about 0 to about 8 hours. At the week level, the number of observations
peaks at around 24 hours a week. About 70 percent of agents in the sample
have at least one working week of that length, but there is still quite some
variation in the length of the working week across observations and agents.
In addition to the information on working hours, the data also contain
information on the total number of scheduled hours for each individual in
each week.
5 Estimation results
In this section, we present the results of estimating the relation between
working hours and productivity. We first address our main measure of pro-
ductivity, ln(1/AH T ), and then the two measures of the quality of calls. As
mentioned above, we conduct the estimations both at the daily and at the
weekly level.
5.1 Working hours and productivity
Table 3 presents estimation results of a regression of productivity on working
hours at the daily level, including different control variables. Regardless of
the specification, productivity appears to decrease slightly as working hours
increase. As the number of controls included in the model increases, the esti-
mated relationship between working time and productivity tends to become
less negative. In particular, controlling for the timing of shifts (day of the
week and hour dummies) leads to a lower estimate of the fatigue effect. This
is because shifts at atypical times, such as nights and weekends, tend to be
both shorter and more productive. There are two likely explanations for this.
First, agents have less calls to handle, creating slack time to rest between
calls. Second, the call centre is open only for very specific types of calls
15
during the night and during the weekend, which could be shorter by nature.
Consequently, fatigue is overestimated when timing is not controlled for.14
Our preferred specification is shown in Column (7). The interpretation of
the coefficient on ln(H), β, is that output increases by β+1 percent as hours
increase by 1 percent (see Subsection 2.1). Therefore, our estimation results
suggest that if working hours increase by 1 percent, the number of calls han-
dled will only increase by 0.9 percent. This suggests that, as agents work
longer hours, fatigue makes agents work slower. The log-log specification ap-
pears to fit the data. The R2statistic is higher for this specification than for
a linear or a quadratic one. Panel (b) of Figure 2, which plots the coefficients
obtained from a regression of productivity on a set of dummies for 15-minute
working time intervals, and therefore does not impose any functional form on
the data, also hints at a negative logarithmic relationship between working
time and productivity.15 In Column (8), we include individual-level charac-
teristics. The estimates show that, although agents perform less well with
increasing age, tenure significantly improves productivity (cf. De Grip et al.,
2016). The performance of male and female call agents does not, however,
differ significantly.
Table 4 presents regressions of productivity on working time at the week
level. The magnitude of the negative effect appears less important at the
week level, compared to the results at the day level. This could be explained
by the fact that people have the time to rest from one day to another. The
idea that agents have time to recover from one day to the other is further
supported by the fact that we find no relationship between productivity on a
14If we exclude observations, for which the shifts starts before 09:00 or ends after
21:00, we obtain very similar results, with a coefficient on log working hours of -0.105***.
Likewise, if we exclude observations from Saturdays and/or Sundays, the estimates are
almost identical to the ones shown in Column (7) of Table 3 (-0.113***).
15To allow for potential non-linearities in the effect of working hours on performance,
we also estimated the regression shown in Column (7) of Table 3, allowing for structural
breaks above/below which the effects of working hours could be stronger/weaker. We do
not find any significant structural breaks in our estimations. The results are available
upon request.
16
given day and the number of hours worked on previous days.16 Column (2)
in Table 4 indeed suggests that it is worth spreading hours worked over more
days. In that specification, total hours worked in a week are decomposed
into number of days worked and average number of hours worked per day
in that week. The returns to days per week seem to be slightly higher than
the returns to hours per day. The difference between both coefficients is,
however, not statistically significant.
Table 5 presents estimation results using the two alternative measures
of working time we have: (1) time available for calls and (2) time present
at the workplace. As hypothesised above, the estimated fatigue effects are
smaller if slack time is included in the measure of working time. They even
disappear when breaks are included. When using a measure of working time
which includes breaks, one would be inclined to conclude that output is
proportional to working time and that there are no fatigue effects. However,
the evidence presented in Tables 3 and 4 on the relationship between effective
working time and productivity shows that this would be misleading.
5.2 Working hours and call quality
Table 6 presents the estimation results of a regression of different quality
indicators on working time and a series of controls, at both the day and
the week level. Call quality, as measured by repeat calls and front line
completion, slightly increases in the number of working hours. Column (1)
shows that one additional working hour is related to a decrease in the share
of repeat calls by 0.005, which translates to a decrease by 6% of a standard
deviation. Since high shares of repeat calls are equivalent to low performance,
agents with longer hours improve on this quality measure. Column (2) shows
that one additional working hour is related to an increase in the front line
completion rate by 0.018, or 25% of a standard deviation. The effects on call
quality measured at the weekly level are of similar size.
16These results are available from the authors. Pencavel (2016) does find evidence
that long working hours negatively affect productivity in subsequent weeks for munition
workers. This does not seem to be the case for call centre agents.
17
Although the effect size is small, the results show that agents are providing
better calls if working longer hours. We can only speculate about the reason
for this observed increase in quality with working hours. First, this may
be due to a learning effect if many of the problems for which customers
are specific for a given day and agents learn how to resolve them during
the course of that day. Second, this may be the result of what Vernon
(1921) calls “practice-efficiency”, if call agents are better able to tune in
to customers’ demands as they spend more time at their desk, get used
to answering calls and leave other thoughts behind. For both arguments
to be true, however, the mechanisms should enable the agents to provide a
better solution to consumers’ problems but not enable them to help customers
quicker, otherwise we would observe a positive effect of working hours on
average handling time. A third possibility is that there is a trade-off between
speed and quality and that agents provide better quality because they slow
down has they have been working for a while.17
Taken together, the results show that, as agents work longer hours, they
become slower, meaning that they score worse on the quantity of output,
whereas quality slightly increases.
6 Robustness checks
In Section 3, we discussed potential sources of endogeneity in our estimations.
In this section, we check whether these potential problems indeed play a role
in our data.
6.1 Tenure and attrition
One potential confounder in the relationship between working time and pro-
ductivity is tenure. The results so far controlled for individual fixed effects
that should account for differences in tenure between individuals at the start
17An alternative explanation for the positive relation between working hours and call
quality would be that in times of high customer demand, customers would be less likely
to call back. Because results for both repeat calls and front line completion confirm our
interpretation, we do not think that this is a likely explanation.
18
of the observation period. If, however, more productive agents have lower
turnover than less productive agents, high-productivity agents could be over-
represented in the sample. In this case, we may overestimate the returns to
hours, or underestimate the effects of fatigue.
To account for potential differences in how fast individuals learn on the
job, we estimate a model in which we control for an individual-specific time
trend (i.e. an interaction of the individual fixed effect with the time trend).
Table 7 presents the estimation results, both at the day and at the week
level. The individual-specific time trends typically have positive coefficients,
confirming the idea that individuals learn on the job. Controlling for a (daily
or weekly) time trend at the individual level does not affect the estimated
coefficient on hours worked much, compared to the results in Tables 3 and 4.
This suggests that differences in learning speed between individuals are not
an important confounder.18
To check for the role of selective tenure, we estimate the model for differ-
ent sub-samples of our data: (1) including only shifts which take place during
the first year of tenure of an individual, (2) including only shifts which take
place after the first year of tenure of an individual, and (3) including only the
first half year of observation, and only shifts of individuals who are present
during all of this first half year, to proxy a balanced panel in terms of tenure.19
The results are presented in Table 8. The coefficient on hours worked is much
larger for individuals with short tenure than for individuals with long tenure.
This suggests that fatigue plays a much larger role for agents early in their
career than for experienced agents.20 This finding is consistent with evidence
that the need for recovery increases as workers’ skills are below what is re-
18Instead of assuming a linear individual time trend, we also estimated the same model
with fixed effects interacting the agent with months and year dummies to allow for non-
linear individual-specific time effects. The results, which are available from the authors,
result in a very similar point estimate as the ones presented in Table 7.
19The panel is not exactly balanced, because the individuals of this sub-sample are not
observed for exactly the same number of days. But this sub-sample is useful to check
whether the potential overrepresentation of individuals with long tenure in the data leads
to bias in the estimations.
20The results for a sub-sample of individuals who are in their first half year of tenure
are very similar to those for individuals in their first year.
19
quired for their job (Gommans et al., 2016). If workers learn on the job, they
should be less subject to fatigue as they become more experienced. But the
finding of smaller fatigue effects for agents with longer tenure is also consis-
tent with the idea that tenure is selective, in the sense that agents who are
less subject to fatigue are more likely to remain in the call centre. In any
case, the effect of hours estimated in Table 3 actually covers heterogeneous
effects which depend on the tenure of an agent. Further, the coefficient on
hours obtained in Column (3) of Table 8 is very similar to the one obtained
in Table 3. As our results are similar whether we use a balanced panel or
not, attrition does not seem to be an important source of bias.
In estimations at the week level, we also observe a much stronger fatigue
effect for agents with less than a year tenure than for agents with more than
a year of experience. The fatigue effect even seems to be entirely driven
by individuals in their first year of tenure, and to disappear entirely for ex-
perienced agents at the week level. A possible explanation could be that
experienced agents are better able to recover from one day to another. Esti-
mation of a balanced panel yields results similar to those obtained in Table
4, suggesting that attrition does not bias the results.21
6.2 Scheduling as a source of exogeneity in hours worked
In Section 3, we argued that scheduling by the planning department of the call
centre ensures that the number of hours worked by an agent on a given day or
in a given week is exogenous. We also mentioned potential objections to this
argument: individuals can express schedule preferences for a specific day or
week, and they may be asked to stay shorter or longer in case of unforeseen
changes in the number of incoming calls. We address these objections here.
In Table 9, we estimate our preferred models at the day and week level,
including additional controls for the number of hours scheduled (Columns
(1) and (3)) or the deviation from the number of hours scheduled, defined as
21Results available from the authors. For individuals in their first year of tenure and
for the balanced sample, the results described here are only found after the week fixed
effects and the time trend are dropped out of the model. Estimation of the model with
the full set of controls seems to be hampered as the number of observations is reduced.
20
the difference between actual hours worked and scheduled hours for a week
(Columns (2) and (4)).22
The positive coefficient on hours scheduled in Columns (1) and (3) of
Table 9 suggests that individuals are indeed more (less) productive in weeks
for which their expressed preferences ensured that they were scheduled for
longer (shorter) hours. However, controlling for the length of schedules does
not lead to important changes in the estimated magnitudes of the coefficients
on working time. They are only slightly more negative, hinting at a slight
underestimation of the fatigue effect due to selective scheduling.
The results in Columns (2) and (4) show that hours worked on top of
scheduled hours are negatively related to productivity. It suggests that fa-
tigue becomes even stronger if the effort to be made by agents is unexpected.
This is intuitive, and is evidence against self-selection of agents in the sense
that they would volunteer to work more hours on days on which they are
more productive. The coefficient on working time becomes slightly less neg-
ative in this specification, which is logical because the total fatigue effect (as
estimated in Tables 3 and 4) is now decomposed into “simple” fatigue due to
working more hours and additional fatigue during unexpected extra hours.
All in all, the evidence presented in Table 9 suggests that self-selection by
agents is not an important source of bias in our estimations. Rather, it seems
plausible that scheduling exogenously determines the hours actually worked
by agents.
7 Conclusions
In this paper, we have estimated the impact of working time on productivity,
both at the daily and at the weekly level. We have used panel data on indi-
vidual workers of a call centre in the Netherlands, which contain information
about the number of hours worked, the number of calls answered, the average
22The number of observations drops because information about scheduled hours is not
available for every agent. If we limit the estimation sample to agents with strictly positive
scheduled hours, the results remain very similar, only the coefficient on scheduled hours
becomes smaller. If we take up the log scheduled hours and log deviation in the models
instead of scheduled hours and deviation, the results remain virtually unchanged.
21
handling time of calls and indicators of call quality for every day worked by
an agent from mid-2008 until the first week of 2010. The panel character of
the data enables us to control for time-invariant unobserved heterogeneity.
Scheduling by the firm generates variation in the daily and weekly hours of
individual workers which is hardly related to individual time-varying char-
acteristics, since expected consumer demand is leading in making schedules.
This yields estimates of the effect of working time on productivity that are
not biased by individual shocks.
Our results show that an increase in effective working time by 1 percent
leads to an increase in output, i.e. the number of calls answered, by about
0.9 percent. This corresponds to moderately decreasing returns to hours,
probably due to fatigue among agents. Given that agents in our sample
work on average 4.6 effective hours per day, this shows that the call centre
environment is demanding and that fatigue sets in early. The fatigue effects
would be larger if the call agents worked full-time. This study complements
the small number of studies which examine the effect of working time on
productivity using an arguably exogenous source of variation in working time
(Crocker and Horst, 1981; Brachet et al., 2012; Pencavel, 2015; Dolton et al.,
2016), by providing evidence for medium-skilled jobs in the service sector.
As we are able to isolate effective working time and concentrate on this
measure, our estimates form an upper bound for the fatigue effect. Our
finding of decreasing returns to hours seems to hold best for individuals with
shorter tenure, while we find much less evidence of fatigue effects among more
experienced agents. Various indicators of call quality show that call quality
does not suffer as the number of hours worked increase. On the contrary, call
quality seems to slightly improve.
Our findings are most relevant for part-time medium-skilled jobs in the
service sector. They suggest that increasing the effective working time in
these occupations would cause individual workers, in particular the relatively
inexperienced ones, to produce smaller quantities of output per hour, due to
fatigue. Such an increase in working time could, however, be beneficial for
the quality provided. These findings are informative for firm management
and for working time regulation policies. The total economic effects of such
22
policies, however, are dependent not only on the effect of working hours on
labour productivity at the individual level, but also on many more factors
such as work organisation and availability of qualified workers.
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Figures
Figure 1: Density of daily productivity
0.002 .004 .006
Density
0200 400 600 800 1000
Average handling time (in seconds)
Note: The figure shows how the density plot of daily productivity, as measured by the average handling
time (in seconds).
Figure 2: Productivity by working hours
(a) Descriptive results
0 .005 .01 .015
Productivity (1/AHT)
0 2 4 6 8
Daily working hours
(b) Estimation results
-.001 0 .001 .002 .003
Effect on productivity (1/AHT)
0 2 4 6 8
Daily working hours
Note: Panel (a) shows average productivity over working time for 15-minute intervals. The capped spikes
present the corresponding 5th and 95th percentile of the productivity distribution. Panel (b) shows the
coefficients on dummies for 15-minute working time intervals in a regression as in model (7) from Table
3. The capped spikes present the corresponding 95-percent confidence intervals. The reference category
is 21 quarters of an hour, i.e. 5 hours and 15 minutes.
28
Tables
Table 1: Descriptive statistics
Variable Mean Std. Dev. Min. Max. N
Day level
Average handling time (AHT) 321.613 111.012 3 910.364 33,123
Productivity (1/AHT) 0.004 0.003 0.001 0.333 33,123
Calls Answered 55.795 22.992 1 129 33,123
Daily working hours 4.621 1.516 0.001 7.747 33,123
Starting time 11.445 3.079 1 24 33,120
Share of repeat calls 0.164 0.084 0 1 33,123
Front line completion rate 0.956 0.072 0 1 32,831
Working hours 4.621 1.516 0.001 7.747 33,123
Hours available for calls 4.812 1.414 0.001 7.903 33,123
Hours present at the workplace 6.05 1.476 0.01 9.52 33,123
Week level
Average handling time (AHT) 319.314 100.133 5 910.364 8,641
Productivity (1/AHT) 0.003 0.002 0.001 0.2 8,641
Calls answered 213.876 114.138 1 645 8,641
Weekly working hours 17.712 8.458 0.001 43.046 8,641
Days per week 4.020 1.282 1 7 8,641
Tenure in weeks 149.58 191.623 1 691 8,587
Share of repeat calls over week 0.167 0.066 0 1 8,641
Front line completion rate over week 0.950 0.083 0 1 8,641
Working hours 17.712 8.458 0.001 43.046 8,641
Hours available for calls 18.447 8.334 0.001 42.929 8,641
Hours present at the workplace 23.191 9.775 0.02 50.56 8,641
Hours scheduled for the week 19.805 9.573 0 51 6,513
Agent level
N of agents 332
Male 0.351 0.478 0 1 305
Age 29.542 10.578 17 65 284
29
Table 2: Variation in daily and weekly working hours
Day level:
Working hours
h(rounded at 1)
Observations with
hhours
Individuals with h
hours at least once
Conditional on working hhours
at least once, share of days in
which individual works hhours
0 473 135 2.74
1 1211 192 6.13
2 1663 215 6.49
3 3228 276 11.1
4 5325 315 17.4
5 14372 317 45.84
6 3461 275 12.56
7 3211 202 17.24
8 179 70 3.51
Total 33,123
Week level:
Working hours h
(rounded at 4)
Observations with
hhours
Individuals with h
hours at least once
Conditional on working hhours
at least once, share of weeks in
which individual works hhours
0 187 92 7.25
4 725 227 13.6
8 997 224 17.2
12 1124 245 15.46
16 1262 247 17.68
20 1229 249 20.37
24 1621 232 27.02
28 968 189 19.95
32 350 114 13.1
36 171 66 11.78
40 6 6 8.11
44 1 1 9.09
Total 8,641
30
Table 3: Relationship between productivity and working time at the day level
(1) (2) (3) (4) (5) (6) (7) (8)
Log working hours -0.175*** -0.152*** -0.151*** -0.151*** -0.137*** -0.128*** -0.113*** -0.139***
(0.007) (0.013) (0.013) (0.013) (0.013) (0.012) (0.013) (0.011)
Trend 0.001*** 0.001*** 0.001*** 0.001*** 0.001*** 0.001***
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Day of the week dummies (reference: Monday)
Tuesday 0.004 0.007* -0.023 -0.452***
(0.004) (0.003) (0.024) (0.045)
Wednesday -0.000 0.001 0.029 -0.427***
(0.004) (0.004) (0.025) (0.052)
Thursday -0.001 0.001 0.066*** -0.609***
(0.004) (0.003) (0.025) (0.063)
Friday 0.004 0.006* 0.011 -0.424***
(0.004) (0.004) (0.026) (0.050)
Saturday 0.109*** 0.110*** -0.471*** -0.890***
(0.008) (0.007) (0.069) (0.074)
Sunday 0.809*** 0.417*** 0.806*** 0.608***
(0.058) (0.063) (0.039) (0.040)
Age -0.001***
(0.000)
Tenure 0.008***
(0.000)
Male -0.003
(0.004)
Individual fixed effects No Yes Yes Yes Yes Yes Yes No
Team fixed effects No No No Yes Yes Yes Yes Yes
Hour-of-the-day dummies No No No No No Yes Yes Yes
Day fixed effects No No No No No No Yes Yes
R-squared 0.085 0.094 0.152 0.160 0.198 0.285 0.385 0.403
N 33,123 33,123 33,123 33,123 33,123 33,123 33,123 31,525
Individuals 332 332 332 332 332 332 332
Note: * p<0.10; ** p<0.05; *** p<0.01; ordinary least squares regression; dependent variable =
ln(1/AHT ); robust standard errors in parentheses.
31
Table 4: Relationship between productivity and working time at the week
level
(1) (2)
Log weekly working hours -0.078**
(0.031)
Log days per week -0.066**
(0.032)
Log average hours per day -0.079**
(0.031)
Trend (weekly) 0.004*** 0.004***
(0.001) (0.001)
R-squared 0.345 0.345
N 8,641 8,641
Individuals 332 332
Note: * p<0.10; ** p<0.05; *** p<0.01; ordinary least squares regression; dependent variable =
ln(1/AHT ); robust standard errors in parentheses. All regressions include agent, week, and team fixed
effects. The regressions also include hour-of-the-week fixed effects, which are defined as 168 dummies for
each hour of the week during which an individual works.
Table 5: Alternative working time definitions and the relationship between
productivity and working time
(1) (2) (3) (4)
Day level Week level
Log daily hours available for calls -0.078***
(0.015)
Log daily hours present at the workplace -0.016
(0.015)
Trend (daily) 0.001*** 0.001***
(0.000) (0.000)
Log weekly hours available for calls -0.050
(0.035)
Log weekly hours present at the workplace -0.020
(0.029)
Trend (weekly) 0.004*** 0.004***
(0.001) (0.001)
R-squared 0.368 0.357 0.335 0.329
N 33,123 33,123 8,641 8,641
Individuals 332 332 332 332
Note: * p<0.10; ** p<0.05; *** p<0.01; ordinary least squares regression; dependent variable =
ln(1/AHT ); robust standard errors in parentheses. All regressions include agent and team fixed effects.
Regressions at the day level include day fixed effects, hour-of-the-day fixed effects and day-of-the-week
fixed effects. Regressions at the week level include week fixed effects and hour-of-the-week fixed effects.
Day-of-the-week (hour-of-the-week) fixed effects are defined as dummies for each hour of the day (week)
an individual works.
32
Table 6: Call quality and working time
(1) (2) (3) (4)
Day level Week level
Dependent Repeat Completion Repeat Completion
Variable calls rate calls rate
Daily working hours -0.005*** 0.018***
(0.001) (0.002)
Trend (daily) 0.000*** 0.000
(0.000) (0.000)
Weekly working hours -0.001*** 0.012***
(0.000) (0.001)
Trend (weekly) 0.002*** -0.000
(0.000) (0.000)
R-squared 0.200 0.079 0.237 0.223
N 33,123 32,831 8,641 8,641
Individuals 332 332 332 332
Note: * p<0.10; ** p<0.05; *** p<0.01; ordinary least squares regression; robust standard errors in
parentheses. All regressions include agent and team fixed effects. Regressions at the day level include day
fixed effects, hour-of-the-day fixed effects and day-of-the-week fixed effects. Regressions at the week level
include week fixed effects and hour-of-the-week fixed effects. Day-of-the-week (hour-of-the-week) fixed
effects are defined as dummies for each hour of the day (week) an individual works. Repeat calls are
defined as the share of customers to whom an agent spoke who call back within seven days and is defined
on a scale from 0 (best) to 1 (worst). Front line completion is defined as difference between an agent’s
number of inbound calls and outbound calls, divided by the number of inbound calls. It is defined on a
scale from 0 (worst) to 1 (best).
33
Table 7: Individual-specific time trends and the relationship between pro-
ductivity and working time
(1) (2)
Day level Week level
Log daily working hours -0.104***
(0.013)
Trend (daily) -0.000***
(0.000)
Log weekly working hours -0.071**
(0.034)
Trend (weekly) -0.001*
(0.001)
Agent-specific day trend Yes No
Agent-specific week trend No Yes
R-squared 0.479 0.496
N 33,123 8,641
Individuals 332 332
Note: * p<0.10; ** p<0.05; *** p<0.01; ordinary least squares regression; dependent variable =
ln(1/AHT ); robust standard errors in parentheses. All regressions team fixed effects. Regressions at
the day level include day fixed effects, hour-of-the-day fixed effects and day-of-the-week fixed effects.
Regressions at the week level include week fixed effects and hour-of-the-week fixed effects. Day-of-the-
week (hour-of-the-week) fixed effects are defined as dummies for each hour of the day (week) an individual
works.
Table 8: Tenure, attrition, and the relationship between productivity and
working time at the day level
(1) (2) (3)
Log daily working hours -0.141*** -0.078*** -0.100***
(0.022) (0.014) (0.023)
Trend (daily) 0.002*** 0.000*** -0.000
(0.000) (0.000) (0.000)
R-squared 0.421 0.430 0.499
N 15,664 17,326 9,366
Individuals 249 131 104
Note: * p<0.10; ** p<0.05; *** p<0.01; ordinary least squares regression; sample is restricted to
individuals with a year tenure or less (Column (1)), with more than a year tenure (Column (2)), and only
the first half year of observation and only shifts of individuals who are present during all of this first half
year (Column (3)); robust standard errors in parentheses. All regressions include agent, day fixed effects
and team fixed effects. Regressions also include hour-of-the-day fixed effects and day-of-the-week fixed
effects, which are defined as dummies for each hour of the day and day of the week an individual works.
34
Table 9: Relationship between productivity and working time, controlling
for weekly schedule
(1) (2) (3) (4)
Day level Week level
Log daily working hours -0.132*** -0.113***
(0.015) (0.014)
Log weekly working hours -0.091** -0.077*
(0.041) (0.040)
Hours scheduled for the week 0.004*** 0.005***
(0.000) (0.001)
Deviation from schedule -0.006*** -0.006***
(0.001) (0.001)
Trend (daily) 0.001*** 0.000***
(0.000) (0.000)
Trend (weekly) 0.003*** 0.003***
(0.001) (0.001)
R-squared 0.350 0.350 0.285 0.290
N 25,129 25,129 6,513 6,513
Individuals 319 319 319 319
Note: * p<0.10; ** p<0.05; *** p<0.01; ordinary least squares regression; dependent variable =
ln(1/AHT ); robust standard errors in parentheses. All regressions include agent and team fixed effects.
Regressions at the day level include day fixed effects, hour-of-the-day fixed effects and day-of-the-week
fixed effects. Regressions at the week level include week fixed effects and hour-of-the-week fixed effects.
Day-of-the-week (hour-of-the-week) fixed effects are defined as dummies for each hour of the day (week)
an individual works.
35
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