NBER WORKING PAPER SERIES
WORKING OVER TIME:
DYNAMIC INCONSISTENCY IN REAL EFFORT TASKS
Ned Augenblick
Muriel Niederle
Charles Sprenger
Working Paper 18734
http://www.nber.org/papers/w18734
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
January 2013
We are grateful for many helpful discussions including those of Steffen Andersen, James Andreoni,
Colin Camerer, Yoram Halevy, David Laibson, Matthew Rabin, Georg Weizsacker and participants
at the Stanford Institute for Theoretical Economics. We thank Wei Wu for helpful research assistance and
technological expertise. Support is gratefully acknowledged from the NSF and also from the Department
of Economics and the Haas School of Business at Stanford University. The views expressed herein
are those of the authors and do not necessarily reflect the views of the National Bureau of Economic
Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peer-
reviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2013 by Ned Augenblick, Muriel Niederle, and Charles Sprenger. All rights reserved. Short sections
of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full
credit, including © notice, is given to the source.
Working Over Time: Dynamic Inconsistency in Real Effort Tasks
Ned Augenblick, Muriel Niederle, and Charles Sprenger
NBER Working Paper No. 18734
January 2013
JEL No. C9,D12
ABSTRACT
Experimental tests of dynamically inconsistent time preferences have largely relied on choices over
time-dated monetary rewards. Several recent studies have failed to find the standard patterns of time
inconsistency. However, such monetary studies contain often discussed confounds. In this paper, we
sidestep these confounds and investigate choices over consumption (real effort) in a longitudinal experiment.
We pair those effort choices with a companion monetary discounting study. We confirm very limited
time inconsistency in monetary choices. However, subjects show considerably more present bias in
effort. Furthermore, present bias in the allocation of work has predictive power for demand of a meaningfully
binding commitment device. Therefore our findings validate a key implication of models of dynamic
inconsistency, with corresponding policy implications.
Ned Augenblick
Haas School of Business - EAP Group
545 Student Services Building, 1900
Berkeley, CA 94720-1900
Muriel Niederle
Department of Economics
579 Serra Mall
Stanford University
Stanford, CA 94305-6072
and NBER
Charles Sprenger
Department of Economics
Stanford University
Stanford, CA 94305
An online appendix is available at:
http://www.nber.org/data-appendix/w18734
1 Introduction
Models of dynamical l y inconsistent time preferences (Strotz, 1956; Laibson, 1997; O’Donoghue
and Rabin, 1999)areapillarofmodernbehavioraleconomics,havingaddedgenerallyto
economists’ understanding of the tensions involved in consumption-sav i n gs choices, task per-
formance, temptation, and self-control beyond the standard model of exponential disco u nting
(Samuelson, 1937). Given the position of present-biased preferences in the behavioral litera-
ture, there is clear importance in testing the model’s central falsifiable hypothesis of diminishing
impatience through time. Further, testing a u x i l i a r y predictions such as individuals’ potential
to restrict future activities through commitment devices can deliver critical prescriptions to
policy makers. In this paper we present a test of dynamic inconsistency in consumption and
investigate the demand for a meaningfully binding commitment device.
To date, a notably large body of laboratory research has been generated focused on identify-
ing the shape of time preferences (for a comprehensive review to the early 2000s, see Frederick,
Loewenstein and O’Donoghue, 2002).
1
The core of this experimental literature has id entified
preferences from t i m e-d a t ed monetary payments. A paradigmatic example would have a sub-
ject state the monetary payment received today, $X,thatmakesherindi↵erentto$50received
in one months’ time, then would have her state the monetary payment received in one months’
time, $Y ,thatmakesherindi↵erentto$50receivedintwomonths’time.
2
Non-equivalence in
the stated indi↵erent values is often taken as evidence of dynamic inconsistency, and $X<$Y is
taken as evidence of a present-biased shape of discounting. Though conducted experiments dif-
fer along many dimensions including payment horizons, methods, subject pools, and potential
1
Though much of the literature has focused on laborat or y samples, there is also a growing body of research
attempting to identify the shape and extent of discounting from real world choices and aggregate data such as
durable goods pu r chase, annuity choice, and consumption patterns (Hausman, 1979; Lawrance, 1991; Warner
and Pleeter, 2001; Gourinchas and Parker, 2002; Cagetti, 2003; Laibson, Repetto and Tobacman, 2003, 2005).
2
A popular methodolgy for eliciting such ind i↵erences is the Multiple P r i ce List technique (Coller and
Williams, 1999; Harrison , Lau and Williams, 2002) asking individuals a series of binary choices between time
dated payments, identifying interval s in which $X and $Y lie. Psychology has often relied on an alternative
method to identify dynamic inconsistency, asking subjects a series of questions involving increasing delay lengths
and examining whether the implied discount factors nest exponentially (see, for example Kirby, Petry and Bickel,
1999; G i or d an o, Bickel, Loewenstein, Jacobs, Marsch and Badger, 2002).
2
transaction costs, a stylized fact has emerged that many subjects are dynamically inconsistent
and the majority of inconsistencies are in the direction of present bias (Frederick et al., 2002).
3
Several confounds exist for identifying the shap e of time preferences from experimental
choices over time-dated m o n eta r y payments, muddying t h e strict interpretations of behavior
provided above. Critically, issues of payment reliability and risk preference suggest that if in-
formation is to be gleaned from such choices, it m ay be linked to the subject ’ s assessment of
the experimenter’s reliability.
4
Recent work validates this suspicion. Andreoni and Sprenger
(2012a), Gine, Goldberg, Sil verman and Yang (2010), and Andersen, Har r i so n , Lau and Rut-
strom (2012) all document that when closely controlling transactions costs and payment re-
liability, dynamic inconsistency in choices over monetary payments is virtually eliminated on
aggregate. Further, when payment r i sk is added i n an experimentally controlled way, non-
expected utility risk preferences deliver behavior observationally equivalent to present bias as
described above (Andreoni and Sprenger , 2012b).
5
Beyond these operational issues, there is reason to question the use of potentially fungible
monetary payments to identify the parameters of models defined over time-dated consump-
tion. Clear arbitrage arguments exist indicating that nothing beyond the interval of subjects’
borrowing and lending rates should be revealed in choices over monetary payments.
6
Chabris,
3
For example, Ashraf, Karlan and Yin (2006) find that rou gh l y 47% of t h ei r su bjects are dynami cal l y
inconsistent over hypotheti cal time-dated monetary payments and around 60% of the inconsistencies are in
the direction of present bias. Similarly, Meier and Sprenger (2010) find that roughly 45% of their subjects
are dynamically inconsistent over incentivized time dated payments and 80% of the inconsistencies are in the
direction of present bias.
4
This point was originally raised by Thaler (1981) who, when considering the possibility of using incentivized
monetary payments in intertemporal choice experiments noted ‘Real money experi ments would be interesting
but seem to present enormous tactical problems. (Woul d subjects believe they would get paid in five years?)’
5
Specifically, Andreoni and Sprenger (2012b) show that when sooner payments are certain while future pay-
ment s are delivered only with 80%, subjects prefer the certain sooner payment. When payments at both time
periods are made uncer t ain , occurring with 50% sooner and 40% in the future, subject s appear more patient,
violating discount ed expected utility. The observation that non-expected utility risk preferences generate dy-
namic inconsistencies was previously thoughtfully analyzed theoretically by Machina (1989). Halevy (2008)
makes t h e lin k between pr ospect theory probability weighting and diminishin g imp at i en ce thr ou gh time citing
psychology experiments conducted by Keren and Roelofsma (1995) and Weber an d Chapman (2005)whoshow
in an original experiment and a par t i al repro d u ct i on, respectively, that when payment risk is added to binary
choi ces over monetary payments, dynami c inconsistency is reduced in some experimental contexts.
6
This poi nt has been thoughtfully t aken into account in some studies. For example, Harrison et al. (2002)
explicitly account for potential arbitrage in their calculations of individual discount rates by measuring indivi d u al
borrowing and saving rates and incorporating these values in estimation . Cubitt and Read (2007)provide
3
Laibson and Schuldt (2008)describethedifficultyinmappingexperimentalchoicesovermoney
to corresponding model parameters, casting skepticism over monetary experiments in general.
The model is one of consumption, so falsifyin g the key prediction of diminishing i m p at ien ce
through time m ay be more convincing when done in the relevant domain, consu mp t i o n .
7
There
are only a few exp erimental tests of dynamic inconsistency for consumption. Key contributions
include Read and van Leeuwen (1998)whoidentifydynamicinconsistencyinthesurprisereal-
locations of snack choices, and McClure, Laibson, Loewenstein and Cohen (2007)andBrown,
Chua and Camerer (2009), who document dynamic inconsistency in brief intertemporal choices
over squirts of juice and soda.
In thi s paper we attempt to move out o f the domain of mo n et a r y choices and into the
domain of consumption, while maintaining a portable design that allows individual parameters
of dynamic inconsistency to be estimated. With 10 2 UC Berkeley Xlab subjects, we intro d u ce
asevenweeklongitudinalexperimentaldesignaskingsubjectstoallocateandsubsequently
reallocate units of e↵ort (i.e., negative leisure consump t i o n ) over time at various gross interest
rates. Subject responses are incentivized by requiring completion of the tasks from either
one initial allocation or one subsequent reallocation. Subjects receive a one-time completion
bonus of $100 in the seventh week of the experiment, fixing the monetary dimension of their
e↵ort allocation choices. The tasks over which subjects make choices ar e tr an scr i pt i on of
meaningless greek texts and completion of pa r t i a l tetris games. Allocations are made in a
convex decision environment permitting identification of both cost functi o n and discounting
parameters. Di↵erences between initial allocations and subsequent reallocation s all ow for the
identi fi ca t i o n of dynamic inconsistency.
The repeated interaction of our seven-week study allows u s to complement measures of e↵ort
excellent recent discussion of the arbitrage arguments and other issues for choices over monetary payments.
One counterpoint is provided by Coller and Williams (1999), who present experimental subject s with a fully
articulated arbitrage argument and external interest rate information and docu ment only a small treatment
e↵ect.
7
Though our objective in the present study is the exploration of present bias separate from issues of fungibility,
recent develop ments in the field have led t o another impor t ant facet of the debate: why and when do monetary
discounting studies deliver measures of present bias with predictive validity despite their potential flaws? This
question lies outside the scope of thi s paper but clearly represents an important avenue for future research.
4
discounting with measures of monetary discounting taken from Andreoni and Sprenger (2012a)
Convex Time Budget (CTB) choices over cash paym ents received in the laboratory. In these
choices, subjects allocate money across time at various gross interest rates. We can compare
dynamic inconsistency measured over work and money at both th e aggregate and individual
level.
Finally, once subjects have experi en ced the tasks for several weeks, we elicit their demand
for a commitment device. Specifically, we allow subjects to probabil i st ical l y favor their initial
allocations over their subsequent reallocations of work. We investigate the aggregate demand
for our o↵ered commi t ment device and correlate identified dynamic inconsisten cy over both
e↵ort and money with commitment demand.
We document three primary findings. First, in the domain of money we find virtually
no aggregate evidence of present bias using immediate in-lab cash payments. Second, in the
domain of e↵ort we find significant evidence of present bias. Allocations of tasks made one
week in advance exceed those made on the date of actual e↵ort by approximately 9%, on
average. Corresponding parameter estimates corroborate these non-parametric results. Third,
we find that the elicited demand for commitment is limited to price zero, at which price 59%
of subjects would prefer a higher likelihood of implementing one of their initial allocations
over their subsequent reallocations. More importantly, we show that subjects we identified as
present biased choose the commitment device, while others do not. We show that the choice
of commitment is binding and meaningful in the sense that initial preferred allocations di↵er
significantly from subsequent reallocat i on s. This provides key validation and support for our
experimental measures and well-k n own theoretical models of present bias.
Despite recent negative findings for models of dynamic inconsistency with time-dated pay-
ments, we find support for the model’s central prediction of di m in i sh i n g impatience th r o u g h
time in the dom a i n of consumption. Further, the auxiliary pr ed i ct i o n s of both the potential
demand for commitment and the link between commi t m ent demand and present bias are also
validated.
5
The pap er proceeds as follows: Secti on 2 provides details for our longitudinal experi m ental
design. Section 3 describes identification of intertemporal parameters based on experimental
choices over both e↵ort and money . Section 4 presents results. Section 5 is a discussion and
section 6 concludes.
2Design
To examine dynamic inconsistency in real e↵ort , we introduce a longitudinal experimental
design conducted over seven weeks. In the experiment, subjects are asked to allocate, sub-
sequentl y reallocate and complete task s for two jobs. If all elements of the ex periment are
completed satisfactorily, subjects receive a completion bonus of $100 in Week 7 of the study.
Otherwise they receive only $10 in Week 7. The objective of the completion bonus is to fix the
monetary dimensi o n of subjects’ e↵ort choices. Subjects are a lways paid the same amo u nt for
their completed work, the question of interest is when they prefer to exert e↵ort.
Having individuals make intertemporal choices over e↵ort allows u s to circumvent many of
the key concer n s t h a t p l a g u e mo n et a r y d i sco u nting experiments. First, subjects cannot borr ow,
save or substitute units of tasks o u t si d e of the exper im ent, removing opportunit i es of arbitrage.
8
Second, the precise date of consumption is known to both the researcher and the subject at the
time of decision, allowing for precise identification of discounting parameters. Third, individuals
select into a seven week exper im ent with a $100 completion bonus in the seventh week, reducing
issues of payment reliability. This also separates e↵ort allocation decisions from payment . And
lastly, we implement a minimum work requirement. This equalizes transaction costs over time
as subjects are forced to participate and complete minimum e↵ort on all dates.
We present the design in five subsections. First, we describe the Jobs to be completed.
Second, we present a timeline of the experiment and the convex decision environment in which
allocations were made. The third subsection describes the design of the commitment device
8
Though this removes substitutabi l i ty of the task at hand, subjects may alter their allocations of other ,
extra-lab con su mp t i on . As a first pass we ignore this possi b i l i ty and the possibility that subjects subcontr act
their experi mental task s. Section 6 pr ovides addi t i on al discussion.
6
for which demand was elicited once subjects had gained experience with t h e tasks. The fourth
subsection addresses design details includ i ng recruitment, selection and attrition. The fifth
subsection presents the complementary monetary discounting study facilitated by the repeated
interaction with subjects during the experiment.
2.1 Jobs
The experiment focuses on intertemporal allocat i o n s of e↵ort. Subjects are asked to allocat e,
subsequently reallocate and complete tasks of two jobs. In Job 1, subjects transcribe a mean-
ingless greek text thr o u g h a computer interface. Fig u r e 1, Panel A demonstrates the paradigm.
Greek letters appear in random order, slightly blur r y, in subjects’ transcr i p t i o n box. By point-
ing and clicking on the corresponding keyboard below the transcription box, subjects must
reproduce the observed series of Greek letters. One task is the completion of one row of Greek
text with 80 percent accuracy as measured by the Levenshtein Distance.
9
In the first week,
subjects com p l et ed a task from Job 1 in an average o f 54 seconds. By the final week , the
average was 46 seconds.
In Job 2, subjects are asked to complete four rows of a standard tetris game. Figure 1,
Panel B demonstrates the paradigm. Blocks of random shapes appear at the top of the tetris
box and fall at fixed speed. Arrangin g the shapes to complet e a horizontal line of the tet r i s
box is the game’s objective. Once a row is complete, it disappears and the shapes above fall
into place. One task is the completion of four rows of tetris. If the tetris box fills to the top
with shapes before the four rows are complete, the subject begins again with cr ed it for th e rows
already completed. In the first week, subjects completed a task from Job 2 in an average of 55
seconds. By the final week, the average was 46 seconds.
9
The Levenshtein Distance is commonly used in computer science to measure the distance between two
strings and is defined as the minimum number of edits needed to transform one string into the other. Allowable
edits are insertion, del et i on or change of a single character. As the strings of Greek character s used in the
transcription task are 35 characters long our 80 p er cent accuracy measure is equivalent to 7 edits or less or a
Leven shtein Distance 7.
7
Figure 1: Experim ental Jobs
Panel A: Job 1- Greek Transcription
Panel B: Job 2- Partial Tetris Games
2.2 Experimental Timeline and Allocation Environment
2.2.1 Timeline
The seven weeks of the experiment are divided int o two blocks. Weeks 1, 2, and 3 serve as
the first block. Weeks 4, 5, and 6 serve as the second block and mirror the first block with
the addition o f a commitment decision discussed below. Week 7 occurs in the laboratory and
is only used to distribute payment to the subjects. Subjects always par t i ci p a t e on the same
8
day of the week throughout the experiment. That is, subjects entering the lab on a Monday
allocate tasks to be compl et ed on future Mondays. Therefore, the time frame over which e↵ort
choices are made is exactly seven days in all choices.
Weeks 1 and 4 occur in the laboratory and sub jects are reminded of their study time the
night before. Weeks 2, 3, 5, and 6 are completed online. For Weeks 2, 3, 5, and 6, subjects
are sent an email reminder at 8pm the night before with a (subject-unique) website address.
Subjects are required to log in to this website between 8am and midnight of the day in question
and complete their work by 2am the following morning.
At each point of contact, subjects are first given instructions about the decisio n s to be
made and work to be completed that day, reminded of th e timeline of the experiment, given
demonstrations of any unfamiliar actions, and then asked to compl et e the necessary actions.
In each week, subjects are required to complete 10 tasks of each Jo b p r i o r t o m a k i n g
allocations decision or completing allocated tasks. The objective of this pair of 10 tasks,
which we call “minimum work,” is two-fold. First, minimum work requires a few minutes of
participation at each date, forcing subjects to incur the transaction co st s of logging on to the
experimental websit e at each time.
10
Second, minimum work, especially in Week 1, provides
experience for subjects such that they have a sense of how e↵ortful the tasks ar e when making
their allocation decision s. We require minimum work in all weeks before all decisions and
provide this information to subjects to control for issues related to projection bias (Loewenstein,
O’Donoghue and Rabin, 2003). This ensures that subjects have experienced and can forecast
having experienced the same amount of e↵ort when making their allocation decisions at all
points in time.
10
A similar technique is used in monetary di scou nting studies where minimum payments are employed to
eliminate subjects loading allocation s to certain dates to avoid transaction costs of receiving multiple payments
or cash i n g multiple checks (Andreoni and Sprenger, 2012a).
9
2.2.2 Allocation Environment
In Week 1, subjects allocate tasks between Weeks 2 and 3. Hence, subjects are choo si n g how
much work to complete at two future dates. In W eek 2, subjects also allocate tasks between
Weeks 2 and 3. Note that in Week 1 subjects a r e making d eci si o n involving two fu t u re dates,
whereas in Week 2, subjects are making decisions involving the present a n d a future date.
Before making the choice in Week 1, subjects are told of the Week 2 decisions and are aware
that exactly one of all Week 1 and Week 2 allocation decisions will be implemented.
11
Initial allocations and subsequent reallocations for Jobs 1 and 2 are made in a convex
decision environment. Using slider bars, subjects allocate tasks to two dates, one earlier and
one later, under di↵erent gross interest rates.
12
Figure 2 provides a sample allocation screen.
To motivate the intertemporal tradeo↵s faced by subjects, decisions are described as having
di↵erent ‘task rates’ such that every task allocated to the sooner da t e reduces the nu mber of
tasks allocated to the later date by a stated number . For example, a ta sk rate of 1:0.5 implies
that each task allocated to Week 2 reduces by 0.5 the number allocated to Week 3. It is
important to note t h a t the mini mum 10 tasks required fo r each job detailed in the previ o u s
section are separate fr o m this allocation decision and are not counted toward the allocations.
The subjects’ decision can be formulated as allocati n g tasks e over times t and t + k, e
t
and
e
t+k
,subjecttothepresent-valuebudgetconstraint,
e
t
+
1
p
· e
t+k
= m, (1)
where 1/p represents the provided task rate. For each task and for each date where allo cations
were made, subjects faced five task rates, 1/p 2{0.5, 0.75, 1, 1.25, 1.5}.Thenumberoftasks
that subjects could allocate to the sooner date was fixed at fifty such that m =50inevery
decision in the experim ent. Note that as the task rate falls, the relative cost of a task in Week
11
Subjects were not shown their initial al l ocations when making their subsequent reallocations.
12
Passi ve allocations are avoided in the design as the slider s’ initial location was in the middle of the slider
bar and subjects were required to click on every slider bef or e submitting their answers.
10
2(theearlierweek)falls,alteringintertemporalincentives.
Figure 2: Convex Allocation Environment
In Weeks 1 and 2 each subject makes 20 allocation decisions: five for each Job in Week
1 and five for each Job in Week 2. After the Week 2 decision s, one of these 20 allocations is
chosen at random as the ‘allocation-that-counts’ and subjects have to complete the allocated
number of ta sk s to ensu r e successful co m p l et i o n of t h e experiment. However, the random-
ization dev i ce probabilistical l y favors the Week 2 allocat io n s over the Week 1 allocatio n s. In
particular, subjects are told (from the beginning) that their Week 1 allocations will count with
probability 0.1, while their Week 2 reallocations will count with probability 0.9. Within each
week’s allocations, every choice is equally likely to be the allocation-that-counts.
13
This ran-
domization process e↵ectively favors flexibility while maintaining incentive compatibility in a
comprehensible manner. This design choice was made for two reasons. First, it increased the
chance that subjects experienced their own potentially present-biased reallocations. Second,
it provides a greater symmetry to the decisions in the second block of three weeks that elicit
demand for commitment.
13
For a complete descr i p t i on of the randomization process please see instructions in Appendix C.
11
The second block of the experiment, Week s 4, 5, and 6, mimics the first block of Weeks 1, 2,
and 3, with one exception. In Week 4 , subjects are o↵ered a probabilistic commitment device,
which is described in detail in the following subsection.
2.3 Commitment Demand
In the second b l ock of the experiment, Weeks 4, 5, and 6, once subjects have gained experience
with the tasks and the experimental design, they are o↵ered a probabilist i c commit m ent de-
vice. In the first block of the experiment, the allocation-that-counts is taken from the Week 1
allocations with probability 0.1 and from the subsequent Week 2 reallocations with probability
0.9, favoring the later reallocations. In Week 4, subjects are given the opportunity to choose
which allocations will be p rob ab i l i sti cal l y favored. In parti cul ar , they can choose whether t he
allocation-that-counts comes from Week 4 with probability 0.1 (and Week 5 with probability
0.9), favoring flexibility, or from Week 4 with probability 0.9, favoring commitment. This form
of commitment device was chosen because of its potential to be meaningfully binding. Sub-
jects who choose to commit an d who di↵er in their allocation choices through time can find
themselves constrained by commitment with high probability.
In o r d er to operation a l i ze our elicitation of commitment demand, subjects are asked to
make 15 multiple price list decisions between two options. In the first option, the allocation-
that-counts will come from Week 4 with probability 0.1. In the second option, the allocation-
that-counts will come from Week 4 with probability 0.9. In order to determine the strength
of preference, an additional payment of between $0 and $10 is added to one of the options for
each decision.
14
Figure 3 provides the implemented price list. One of the 15 commitment
decisions is chosen for implementation, ensuring incentive compatibility. Subjects are told that
the implementation of the randomization for the commitment decisions will occur once they
submitted their Week 5 allocation d ecisi on s.
Our commitment demand decisions, and the second block of the experiment, serve three
14
We chose not to have the listed prices ever take negative values (as in a cost) to avoid subjects viewing
pay i n g for commitment as a loss.
12
Figure 3: Commitment Demand Elicitation
purposes. First, they allow us to assess t h e demand for commitment and its extent. If i n d i -
viduals demand commitment, it is impo r t a nt to know both how much they are willi n g to pay
for the opportunity t o restrict their future activities and to help separate commitment demand
from simple decision error. Second, a key objective of our study is to explore the theoretical
link, under t h e a ssu m p t i o n of sophistication, between present bias an d commitment demand.
Are subjects who are pr esent biased comparing initial allocations to su b seq u ent reallocations
more likely to demand commitm ent? With the excep t i o n of Ashraf et al. (2006)andKaur,
Kremer and Mullainathan (2010)virtuallynoresearchteststhiscriticalimplicationofmodels
of dynamic inconsistency. We will com p a r e our results to those p a pers in subsection 4.4. Fi-
nally, a correlation between time inconsistency and commitment validates the interpretation of
present bias over o t h er explanations for time inconsistent e↵ort choices.
To summarize our longitudin a l e↵ort experiment, Table 1 contains the m ajor events in each
week.
13
Table 1: Summary of Longitudinal Experiment
Minimum 10 E↵ort All ocation-That- Complete Commitment Receive
Work Allocations Co u nts Chosen Work Choice Payment
Week 1 (In Lab): x x
Week 2 (Online): x x x x
Week 3 (Online): x x
Week 4 (In Lab): x x x
Week 5 (Online): x x x x
Week 6 (Online): x x
Week 7 (In Lab): x
2.4 Design Details
102 subjects from the UC Berkeley Xlab subject pool were ini t i a l l y recruited into the experiment
across 4 experimental sessions on February 8th, 9th and 10th, 2012 and were told in advance
of the seven week longitudinal design and the $100 completion bonus.
15
Subjects did not
receive an independent show up fee. 90 subjects completed all aspects of the working over time
experiment and received the $100 completion bonu s. The 12 subjects who select ed out of the
experiment do not appear di↵erent on either initial allocations, comprehensi on or a small series
of demographic data collected at the end of the first day of the experiment.
16
One more subject
completed initial allocations in Week 1, but due to computer error did not have their choices
recorded. This leaves us with 89 subjects.
One critical aspect of behavior limits our ability to make inference for time preferences
based on experimental r esponses. In particular, if subjects h ave no variation in allocations
in response to gross interest rate changes in some weeks, then at t em p t i n g to point identify
both discounting and cost function parameters is difficult or impossible, yielding imprecise and
unstable estimates. Similar to multiple price list experiments, if a subject always chooses a
15
This is a potentially important avenue of selection into the experiment. Our subject s were willing to put
forth e↵ort and wait seven weeks to receive $100. Though we have n o formal test, this suggests that our subj ect s
may be a relatively patient selection.
16
3 of those 12 subjects dropped after the first week while the remaining 9 dropped after the second week.
Including data for these 9 subjects whe re available does not qualitatively alter the analysis or conclusions.
14
specific option, only one-sided bounds on parameters can be obtained. Here, the problem is
compounded by our e↵orts to identify both discounting and cost function parameters. In our
sample, nine subjects have this issue for one or more weeks of the study. For the analysi s, we
focus on the primary sample of 80 subjects who completed all aspects of the experiment with
positive variation in their responses in each week. In Appendix Table A2,were-conductthe
aggregate analysis incl u d i n g these nine subjects and obt a i n very similar finding s.
2.5 Monetary Dis counting
Subjects were present in the UC Berkeley X-Laborat o r y in the first, fourth, and seventh weeks
of the experiment. This repeated interaction facilitates a monetary discounting study that
complements our main avenue of analysis. In Weeks 1 and 4 of our experimental design, once
subjects complete their allocation of tasks, they are invited to respond to addition a l qu est i o n s
allocating monetary payments to Weeks 1, 4, and 7. In Week 1, we implement three Andreoni
and Sprenger (2012a)ConvexTimeBudget(CTB)choicesets,allocatingpaymentsacross:1)
Week 1 vs. Week 4; 2) Week 4 vs. Week 7 (Prospective); and 3) Week 1 vs. Week 7. Individuals
are asked to allocate monetary payments c across the two dates t and t + k, c
t
and c
t+k
,subject
to the intertemporal budget constraint,
r · c
t
+ c
t+k
= m. (2)
The experimental budget is fixed at m =$20andfivegrossinterestratesareimplementedin
each choice set, r 2{0.99, 1, 1.11, 1.25, 1.43}. These gross interest rates were chosen for com-
parison with prior wo r k (And r eo n i and Spren g er , 2012a).
17
Such question s permit ident i fi ca t i o n
of moneta r y discountin g parameters fol l owing Andreoni and Sprenger (2012a). In Week 4, we
ask subjects to allocate in a CTB choice set over Week 4 and Week 7 under the same five gross
interest rates. We refer to these choices made in Week 4 as Week 4 vs. Week 7 and those made
in Week 1 over these two dates a s Week 4 vs. Week 7 (Prospect i ve). Hence, subjects co m p l et e
17
Additionally, r =0.99 allows us to investigate the potential extent of negative discounting.
15
atotaloffourCTBchoicesets.
The CTBs implemented in Weeks 1 and 4 are paid separately and independently from the
rest of the experiment with one choice from Week 1 and one choice from Week 4 chosen to be
implemented. Subjects are paid according to their choices. Subjects are not told of the Week
4 choices in Week 1. As in Andreoni and Sprenger (2012a), miniminum payments of $5 at each
payment date are enacted to eliminate transaction cost issues similar to those discussed above.
Appendix C provides the full experimental instructions.
The implemented mon et ar y discou nting experiments have two nuan ces relat i ve to Andreoni
and Sprenger (2012a). First, Andreoni and Sprenger (2012a)implementCTBswithpayment
by check. Our design implements payment by cash with potentially lower transaction costs.
Second, Andreoni and Sprenger (2012a) implement CTBs with present payment received only
by 5:00 p.m. in a subject ’ s residence mailbox. Here we provide paym ent immediately in the
laboratory limiting arguments about the relevant epoch of the present.
In both Weeks 1 and 4, the monetary all ocations are implemented after the more central
e↵ort choi ces. The monetary choices were not annou n ced in advance and subjects could choose
not to participate; five did so in either Weeks 1 or 4. In our analysis of monetary discounting,
we focus on the 75 subjects from the primary sample with complete monetary choice data.
3 Identification
In the intertempora l alloca t i o n of e↵ort and money, discounting and additional parameters can
be identified at either the aggregate or individual level under various structural assumptions. In
the following two subsections we describe which experimental variation provides identification
of specific parameters of interest and lay out methodology for estimation at both the aggregate
and individual level.
16
3.1 E↵ort Discounting
In the working over time experiment, subjects allocate e↵ort to an earlier date, e
t
,andalater
date, e
t+k
, subject to the intertemporal budget constrai nt described in (1). Hence, th e subject’s
decision problem is
min
e
t
,e
t+k
C(e
t
,e
t+k
) s.t. e
t
+
1
p
e
t+k
= m,
where C(e
t
,e
t+k
)isageneralcostfunction,assumedtobegloballyconvexsuchthatstandard
constrained optimization yiel d s m ea n i n g fu l first or d er conditions. We assume that the cost
function is time separable, that the in st antaneous cost function is stationary and takes an
exponential form, and that discounting follows the quasi-hyperbolic form proposed by Laibson
(1997). Under these struct u r a l assumptions we can wri t e
C(e
t
,e
t+k
)=(e
t
+ !)
+
1
t=0
k
(e
t+k
+ !)
, (3)
where >1representsthestationaryparameterontheconvexinstantaneouscostofe↵ort
function. The present-bias parameter, ,activatedwhenthetimeperiodt is the present, 1
t=0
,
captures the extent to which individual’s dispropor t ion at el y discount the future when viewed
from the present. The parameter captures the daily d i scou nt factor over the k =7daysof
each considered allocation . The additive term ! in the cost function could be interpreted as
aStone-Gearyminimumorassomebackgroundlevelofrequiredwork. Suchparametersare
used in monetary discounting studies (Andersen, Harri so n , Lau and Rutstrom, 2008; Andreoni
and Sprenger, 2012a), and are either taken from some external data source on background
consumption or est i m at ed from experimental choices. For simpl ici ty, we interp r et ! as the
required minimum work of the experiment and set ! =10.
Minimizing (3) subject to (1) yields the intertemporal Euler equation
(
e
t
+ !
e
t+k
+ !
)
(1)
(
1
(1
t=0
)
k
)=p.
17
Rearranging and taking logs yields
log(
e
t
+ !
e
t+k
+ !
)=
log()
1
· (1
t=0
)+
log()
1
· k +(
1
1
) · log(p), (4)
which is linear in t h e key experimentally varied parameters of whether allocations involve the
present, 1
t=0
,andalogtransformofthetaskrate,log (p).
From the intertemporal Euler equation above, identification of discounting and the cost
function is straig htforward. The task rate delivers identification of the cost funct i o n , ;the
choice being made in the present (Week 2 decision) rather than the future ( Week 1 decision)
delivers identification of present bias, ;andthedelaylengthgivesidentificationofthediscount
factor, .
18
In order to estimate discounting and cost function parameters from aggregate data, we
assume an additive error structure and estimate the linear regression implied by (4). The
parameters of interest can be recovered from non-linear combinations of regression coefficients
with standard errors calcul at ed via the delta method.
19
One important issue to consider in
the estimation of (4) is the potential presence of corner solutions. We provide estimates from
two-limit to b i t regressions designed t o account for the possibility that the tangency condition
implied by (4) does not hold with equality (Wooldridge, 2002).
Estimating (4) is easily extended to the study of individual parameters. To b egin , (4) can
be estimated at the individual level.
20
However, with limited numbers of individual choices
it is helpful to consider alternative, more structured approaches. In particular, we allow for
heterogeneous discounting across individuals, but assume all individuals have the same cost
18
Of course, with only one delay length of seven days considered in the experiment, we have limited confi d en ce
that our estimate of can be extrapolated to ar b i t r ar y delay lengths.
19
To be sp eci fi c, the regression equation is, for k = 7,
log(
e
t
+ !
e
t+k
+ !
)
i
= ⌘
0
k + ⌘
1
· (1
t=0
)
i
+ ⌘
2
· log(p)
i
+ ✏
i
,
and we recover the paramet er s of interest as
ˆ
= exp(ˆ⌘
1
/ˆ⌘
2
) and ˆ =1+1/ˆ⌘
2
. Note that
ˆ
= exp(ˆ⌘
0
/ˆ⌘
2
)is
recovered f r om the constant as only one delay length was used in the experimental design.
20
Broadly similar conclusions are reached when estimating (4) at the individual level, however, parameter
precision is greatly reduced and substantial estimate instabil i ty is uncovered in some cases.
18
function. Consider a vector of fixed e↵ects (1
j
)
i
which take the value 1 if observation i was
contrib u ted by individual j. This leads to the fixed e↵ects formulation
log(
e
t
+ !
e
t+k
+ !
)
i
=
log(
)
1
· k +
(log(
j
) log())
1
· (1
j
)
i
· k +
log(
)
1
· (1
t=0
)
i
+
(log(
j
) log())
1
· (1
t=0
)
i
· (1
j
)
i
+
1
1
· log (p)
i
,
where
, refer to sample means, and
j
,
j
refer to individual-specific discounting param-
eters. With an additive error str u ct u r e this is easily estimable.
21
The individual fixed e↵ect
interacted with the decision b eing made in the present provides identification of the individual-
specific
j
. In Appendix A we conduct simulation exercises under v arious correlation structures
for th e true parameters of interest and document that t h e implemented estimation methods
perform well both at the aggregate and individual level.
3.2 Monetary Dis counting
Our methods for recovering monetary discounting parameters at both the aggregate and indi-
vidual level closely follow those for e↵ort. Following most of the literature, we abstract from
standard arbitr a g e arguments for monetary di sco u nting and assume laboratory administered
rates are the relevant ones.
22
In particular, for m on et ar y payments, c
t
and c
t+k
,allocated
subject to th e constraint (2), we assume a quasi-hyperbol ic constant relative risk averse utility
function,
U(c
t
,c
t+k
)=(c
t
+ !)
↵
+
1
t=0
k
(c
t+k
+ !)
↵
. (5)
Here, the uti l i ty function is assumed to be concave, ↵<1, such that first order conditions
provi d ed mean i n g fu l opt i m a . Here, the parameter ! is a background parameter that we take
21
We allow both and to vary across individuals such that the implemented regression is a standard
interaction with bot h level and slope e↵ects.
22
One prominent exception to this tradition is Harrison et al. (2002), who measure and account for extra-lab
borrowing and savings opportunities.
19
to be the $5 minimum payment of the monet a r y experiment.
23
Maximizing (6) subject to the intertempor al budget constraint (2) yields an intertemporal
Euler equation similar to that above fo r e↵ort. Taking logs and rearranging we have
log(
c
t
+ !
c
t+k
+ !
)=
log()
↵ 1
· (1
t=0
)+
log()
↵ 1
· k +(
1
↵ 1
) · log(r), (6)
which can again be estimated at the aggregate or individual level via two-limit Tob i t . Discount-
ing and utility function parameters can be recovered via non-linear combinations of regression
coefficients as above with sta n d a r d errors estimated again via the del t a method.
4 Results
The results are presented in three subsectio n s. First, we present results from the monetary
discounting study and compare our observed level of limited present bias with other recent
findings. Second, we move to e↵ort related di sco u nting and provide both non-parametric and
parametric evidence of present bias. In a thir d subsection we present results related to commit-
ment demand and document correlations between identified present bias over work and money
with the demand for our lab-o↵ered commitment d ev i ce.
4.1 Monetary Dis counting
Figure 4 presents the data from our monetary discounting experiment. The mean allocation
to the sooner payment date at each interest rate is reported for the 75 subjects from the
primary sample for whom we have all monetary discounting data. Four data series are provided
separated by delay length corresponding to the four payment sets over which subjects made
allocations. Standard error bars are provided, clustered at the individual level.
23
Andreoni and Sprenger (2012a) provide detailed discussion of the use of such background p ar amet er s and
provide robustness tests with di↵ering values of ! and di↵ering assumptions for the functional form of utility
in CTB estimates. The findings suggest that though utility function curvature estimates may be sensitive to
di↵erent background parameter assumptions, discounting parameters, particularly present bias, are virtually
una↵ected by such choices.
20
Figure 4: Monetary Discounting Behavior
0 5 10 15 20
1 1.2 1.4 1 1.2 1.4
3 Week Delay 6 Week Delay
Week 1 vs. Week 4 Week 4 vs. Week 7 Prospective
Week 4 vs. Week 7 Week 1 vs. Week 7
SEM
Mean Sooner Allocation
Gross Interest Rate
Graphs by moneyk
We highlight two features of Figure 4. First, note that as the gro ss interest rate increases
the average allocation to the sooner payment decreases, following the law of demand. Indeed,
at the individual level 98% of choices are monotonica l l y decreasing in interest rate, and only
1subjectexhibitsmorethan5non-monotonicitiesindemandintheirmonetarychoices.
24
This suggests that subjects as a whole understand the implied intertemporal tradeo↵s and the
decision environment.
Second, Figure 4 allows for non-parametric investigation of present bias in two contexts.
25
First, one can consider the static behavior, often attributed to present bias, of subjects being
24
Subjects have 16 opport u n i t i es to violate monotonicity comparing two adjacent interest rates in their 20
total CTB choices. 63 of 75 subjects have no identified non-monotonoci t i es. Andreoni and Sprenger (2012a)
provide a detailed discussion of the extent of potential errors in CTB choices. In particular they note that
prevalence of non-mon ot on i ci t i es in demand are somewhat less than the similar behavior of multiple switching
in standard Multip l e Price List experiments.
25
Though the si x -week delay data are used in estimation, our non-parametric tests only identify present bias
from choices over three-week delays. We ignore here the met h od of identifying present bias frequently used in
psychology where short horizon choices are compared to long horizon choices.
21
more patient in the future than in the present by comparing Week 1 vs. Week 4 to Week 4 vs.
Week 7 (Prospective). In this comparison, controlling for interest rate fixed e↵ects, sub jects
do allocate on average $0.54 (s.e =0.31) more to the sooner payment when it is in the present
F (1, 74) = 2.93, (p =0.09). A second measure of present bias is to compare Week 4 vs. Week
7(Prospective)madeinWeek1totheWeek4vs.Week7choicesmadeinWeek4. This
measure is similar to the recent work of Hal evy (2012). Ignoring income e↵ects associated with
having potentially received prior experimental payments, this comparison provides a secondary
measure of present bias. In this comparison, control l i n g for interest r a t e fixed e↵ects, subjects
allocate on average $0. 47 (s.e =0.32) more to the so o n er payment when the sooner payment
is in the present, F(1, 74) = 2.08, (p =0.15).
26
Over moneta r y payments, we find limited non-parametric support for th e existen ce of a
present bias. In Table 2,columns(1)and(2)weprovidecorrespondingparameterestimates
implementing two-limit Tobit regressions of (6), with standard errors clustered at the individual
level. In column (1) we use all 4 CTB choice sets. In column (2) we use only the choice sets
which have three-week delays for continuity wit h both our n o n-p a r a m et r i c evidence and the
comparisons generally made in exp er i m ental economics. In both cases we estimate ˆ↵ of around
0.975 indicating limited utility function curvature over monetary payments. Further, we identify
daily discount factors of around 0.998. The 95% confidence interval in column (1) for the daily
discount factor implies annual discount rates between 40% and 140%.
27
In column (1) of Table 2 we estimate
ˆ
=0.974 (s.e . =0.009), close to dynamic consistency.
Though we do reject the null hy pothesis of =1,
2
(1) = 8.77, (p<0.01), our estimated
value for is economically close to 1. In column (2), focusing only on three week delay data,
we find
ˆ
=0.988 (0.009) a n d are unable to reject the null hypo t h esi s of dynamic consistency,
26
Additionally, this measure is close in spirit to our e↵ort exper i ment where in i t i al allocation s are compared
to subsequent reallocations. To get a sen se of the size of potential income e↵ects, we can also compare the
Week 1 vs. Week 4 choices made in Week 1 to the Week 4 vs. Week 7 choices made in Week 4. Controlling for
interest rate fixed e↵ects, subjects allocate on average $0.07 (s.e =0.31) more to the sooner payment in Week
1, F (1, 74) = 0.05, (p =0.82), suggesting negli gi b l e income e↵ects.
27
Admittedly, our ability to precisely identify aggregate discounting was not a focus of the experimental
design and is compromised by limited variation in delay length and interest rates. In monetary discounting
experiments it is not unusual to find implied an nual discou nt rat es in excess of 100%.
22
Table 2: Parameter Estimates
Monetary Discounting E↵ort Discounti n g
(1) (2) (3) (4) (5)
All Delay Three Week Delay
Job 1 Job 2 Combined
Lengths Lengths
Greek Tetri s
Present Bias Parameter:
ˆ
0.974 0.988 0.900 0.877 0.888
(0.009) (0.009)
(0.037) (0.036) (0.033)
Daily Discount Factor:
ˆ
0.998 0.997
0.999 1.001 1.000
(0.000) (0.000)
(0.004) (0.004) (0.004)
Monetary Curvature Parameter: ˆ↵ 0.975 0.976
(0.006) (0.005)
Cost of E↵ort Parameter: ˆ 1.624 1.557 1.589
(0.114) (0.099) (0.104)
#Observations 1500 1125 800 800 1600
#Clusters 75 75
80 80 80
Job E↵ects
Yes
H
0
: =1
2
(1) = 8.77
2
(1) = 1.96
2
(1) = 7.36
2
(1) = 11.43
2
(1) = 11.42
(p<0.01) (p =0.16)
(p<0.01) (p<0.01) (p<0.01)
H
0
: (Col. 1) = (Col. 5)
2
(1) = 6.37
(p =0.01)
H
0
: (Col. 2) = (Col. 5)
2
(1) = 8.26
(p<0.01)
Notes: Parameters identified from two-limit Tobit regressions of equations (6)and(4)for
monetary discounting and e↵ort discounting, respectively. Parameters recovered via non-linear
combinat i ons of regression coefficients. Standard er ror s clustered at individual level repor t ed
in parentheses, recovered via the delta met h od. E↵ort regressions control for Job E↵ects (Task
1 vs. Task 2). We use Chi-squared tests for the null hypoth eses in the last three rows.
2
(1) = 1.96, (p =0.16). For a fixed delay length and interest rate, subjects make virtually
identical allocations in the present and the future.
Our non-parametric and parametric results closely mirror the aggregate findings of Andreoni
and Sprenger (2012a)andGi n e et al. (2010).
28
Apotentialconcernoftheseearlierstudiesthat
carefully control transaction costs and payment reliability, is that a payment in the present
was implemented by a payment in the after n oon of the sam e day, e.g. by 5:00 pm in the
subjects’ residence mailboxes in An d r eo n i and Sprenger (2012a). In this paper, because subjects
28
In both of these prior exercises substantial heterogeneity in behavior is uncovered. In subsection 4.3 we
conduct individual analyses, revealing similar findings.
23
repeatedly have to come to the lab, a pay m ent i n the present is implement ed by an immediate
cash payment. The fact that we replicate th e ear l i er studies that careful l y control for transaction
costs and payment reliabil i ty alleviates the concer n s that payments in the afternoon are not
treated as present payments.
Confirming the find i n g of limited present bias in the dom a i n of money motivates our ex-
ploration of choices over e↵ort. Clear confounds exist for identifying or rejecting models of
dynamic inconsistency from moneta r y choices. In the next secti o n we attempt to test the
central hypothesis of dimin i sh i n g impatience without these confounds in the domain of e↵ort.
4.2 E↵ort Discounting
Subjects make a total of 40 allocation decisions over e↵ort in our seven week exp eriment.
Twenty of these decisions are initial allocations and reallocations made in the first block of the
experiment. The other twenty are made in the second block. Our design is focused on testing
whether participants identified as being present biased (in Block 1) demand commitment in
Week 4 (in Block 2). Hence, we opt to present here allocati o n data from only the first block of
the exp eriment, Weeks 1 and 2. This allows the prediction of Week 4’s commitment demand to
be cond u ct ed truly as an out-of-sample exercise. In Appendix B.3,wepresentresultsofpresent
bias from both blocks of the exp eriment and document very similar results.
In Fi g u r e 5 we show for each task rate the amount of tasks allocated to the sooner date,
Week 2, which could range from 0 to 50. We contrast initial allocations of e↵ort made in Week
1 at each task rate with subsequent reallocations made in Week 2 for the 80 subjects of the
primary sample. Standard errors bars are provided, clustered at the individual level.
As with moneta r y discounting, subjects appear to have understood the central intertemporal
tradeo↵s of the experiment as both initial allocations and subsequent reallocations decrease as
the task rate is increased. At the individual level 95% of choices are monotonically decreasing in
interest rate, and only 5 subjects exhi b i t more than 5 non-monotoniciti es in their e↵ort choices.
29
29
Subjects have 32 opport u n i t i es to violate monotonicity comparing two adjacent interest rates in their 40
total CTB choices. 41 of 80 subjects are fully consistent wit h monotonicity and only 5 subjects have more
24
Figure 5: Real E↵ort Discounting Behavior
10 20 30 40
.5 1 1.5 .5 1 1.5
Greek Transcription Tetris
Initial Allocation
Mean
Re-Allocation
Mean
SEM
Sooner Tasks
Task Rate
Graphs by task
This suggests that subjects as a whole understand the implied intertemporal tradeo↵s and the
decision environment.
Apparent from the observed choices is that at all task rates average subsequent reall ocations
lie b elow average initial allocations. Controlling for all task rate and task interactions, subjects
allocate 2.47 fewer tasks to the sooner work date when the sooner work date is the present
F (1, 79) = 14.78, (p<0.01). Subjects initially allocate 9.3% more to the sooner date than
they subsequently reallocate (26.59 initial vs. 24.12 reallocation).
30
Motivated by our non-parametric analysis we proceed to estimate intert em poral parameters.
Table 2 columns (3) through (5) present two-limit Tobit regressions based on (4). In column
(3) th e analyzed data are the allocations for Job 1, Greek Transcription. We find an estimated
than 5 non-monotonicities. Deviations are in general small with a median required allocation change of 3 tasks
to bring the data in line with monotonicity. Three subjects have more than 10 non-monotonicities indicat i n g
upwar d sloping sooner e↵ort curves. Such subjects may find the tasks enjoyable such that they prefer to do
more tasks sooner to fewer tasks later. We believe the increased volume of non-downward sloping behavior in
e↵ort relative to money has several sources. Subjects may actually enjoy the tasks, they make more choices
for e↵ort than for money, and half of their allocations are completed outside of the controlled lab environment.
Importantly, non-monotonicities decrease with experience such that in the second block of the experiment 97
percent of choices satisfy monotonicity while in the first block, only 93 percent do so, F (1, 79) = 8.34 (p<0.01).
30
The behavior is more pronounced for the first block of the experiment. For both blo cks combined sub-
jects allocate 25.95 tasks to th e sooner date, 1.59 more tasks than they subsequently real l ocate (24. 38 tasks),
representing a di↵erence of around 6%, F (1, 79) = 15.16, (p<0.01). See Appen d ix B.3 for detail.
25
cost parameter ˆ =1.624 (0.114). Abstracting from discounting, a subject with this parameter
would be indi↵erent between completing all 50 tasks on one experimental date and completing
32 tasks over two experimental dates.
31
The daily discount factor of
ˆ
=0.999 (0.004) is similar
to our findings for monetary discounting.
In column (3) of Table 2 we estimat e an aggregate
ˆ
=0.900 (0.037), and easily reject the
null hypothesis of dynamic consistency ,
2
(1) = 7.36, (p<0.01). In column (4), we obtain
broadly similar conclusions for Job 2, the partial tetris games. We aggregate over the two
jobs in column (5), controlling for the job, and again document that subjects are significantly
present-biased over e↵ort.
32
Finally, our implemented analysis allows us to compare present bias across e↵or t and money
with
2
tests based on seemingly unrelated estimation techniques. We reject the null hypothesis
that the identified in column (5) over e↵ort is equal to that identified for monetary discounting
in column (1),
2
(1) = 6.37, (p =0.01), or column (2),
2
(1) = 8.26, (p<0.01). Subjects are
significantly more present-biased over e↵ort than over money.
33
4.3 Individual Analysis
On aggregate, we find that subjects are significantly more present-biased over work than over
money. In this sub-section we investigate behavior at th e individual level to understand the
extent to which present bias over e↵ort and money is correlated within individual.
In order to investigate individual level discounting p aram et er s we run fixed e↵ect versions
of the regressions provided in columns (2) and (5) of Table 2.
34
As discussed in section 3,we
31
In many applications in economics and experiments, quadratic cost functions are assumed for tractability
and our analysis suggests that at least in our domain this assumption would not be too inaccurate.
32
For robustness, we run regressions similar to column (5) separately for each week and note that though the
cost function does change somewhat from week to week, present bias is still significantly identified as individ-
uals are signifi cantly less patient in their reallocation decisions compared to their initial allocation decisions.
Appendix Table A3 provides estimates.
33
In Appendi x B.3 we conduct identical analysis using both Blocks 1 and 2 and arrive at the same conclusions.
See Ap pendix Table A4 f or estimates.
34
We choose to use the measures of present bias based on three week delay ch oi ces for the monetary di scou nting
for continuity with our non-parametric tests of present bias. Further, when validating our individual measures,
we focus on reallocations over three week delay decisions as in the presentation for the aggregat e data. Very
similar results are obtained if we use the fixed e↵ects versions of Table 2, column (1).
26
identi fy discounting para m et er s at the individual level assuming no heterogeneity in cost or
utility function curvature. Indivi d u a l parameter estimates of
ˆ
e
,presentbiasfore↵ort,and
ˆ
m
,presentbiasformoney,arerecoveredasnon-linearcombinationsofregressioncoefficients
as described in section 3.
One technical constra i nt prevents us from estim a t i n g individual discounting parameters with
two-limit Tobit as in th e aggregate analysis. In order for p a r a m et er s to be estimable at the
individual level with two-limit Tobit, some interior allocations are required. As suggested by
our curvature estimates in Table 2 ,86%ofmonetaryallocationsareatbudgetcornersand61%
of the sample has zero interior allocations. This issue is not as severe for e↵ort discounting as
only 31% of allocations are at budget corners and only 1 subject has zero interior allocations.
For individual-level discounting, we therefore use ordinary least squares for both money and
e↵ort.
35
Figure 6 presents individual estimates and their correlation. First, note that nearly 60%
of subjects have an estimated
ˆ
m
close to 1, indicating dynamic consistency for monetary
discounting choices. This is in contrast to only around 2 5 % of subjects wit h
ˆ
e
close to 1. The
mean value for
ˆ
m
is 0.99 (s.d. =0.06), wh i l e the mean value for
ˆ
e
is 0.91 (s.d. =0.20). The
di↵erence between these measures is significant, t =3.09, (p<0.01). Second, note that for the
majority of subjects when they deviate from dynamic consistency in e↵ort, they deviate in the
direction of present bias.
Since correlational studies (e.g., Ashraf et al., 2006; Meier and Sprenger, 2010)oftenuse
binary measures of present bias, we define the variables ‘Present Biased’
e
and ‘Present Biased’
m
which take the value 1 if the corresponding estimate of lies strictly below 0.99 and zero
otherwise. We find that 56% of subjects have a ‘Present-Biased’
e
of 1 while only 33% of
subjects have a ‘ Pr esent-Biased’
m
of 1. The di↵erence in proportions of individuals classified
35
Nearly identical aggregate discounting estimates ar e generated when conducting ordinary least squares
ver si on s of Table 2. Curvatur e estimates, however, are sensitive to estimation techniques that do and do not
recognize that the tangency cond i t i ons implied by (4) and (6) may b e met with inequality at budget corners.
Andreoni and Sprenger (2012a) provides further discussion.
27
as present-biased over work and money is significant, z =2.31, (p =0.02).
36
Figure 6: Individual Estimates of Present Bias
0 .2 .4 .6
Fraction
.5 .75 1 1.25 1.5
Work Present Bias
0 .2 .4 .6
Fraction
.5 .75 1 1.25 1.5
Monetary Present Bias
.8 .9 1 1.11.2
Monetary Present Bias
.5 .75 1 1.25 1.5
Work Present Bias
Two import a nt questions with respect to our individual measures arise. First, how much
do these measures correlate within individual? The answer to this question is important for
understanding both the validity of studies relying on monetary measures and the potential con-
sistency of preferences across domains. If significant correlations are obtained it suggests that
there may be some important preference-related behavior uncovered in monetary discounting
studies.
37
Figure 6 presents a scatterplot of
ˆ
m
and
ˆ
e
.Inoursampleof75subjectswithboth
complete monetar y and e↵ort discounting choices, we find that
ˆ
e
and
ˆ
m
have almost zero
correlation, ⇢ = 0. 05, (p =0.66). Additionally, we find tha t the binary measures for present
36
Further, one can d efi n e future bias in a similar way. 17% of subjects are future biased in money while 29%
of subjects are future biased over e↵ort. Similar di↵ering proportions between present and future bias have
been previously documented (see, e.g., Ashraf et al., 2006; Meier and Sprenger, 2010). Two impor t ant count er -
examples are Gine et al. (2010) who find almost equal proportions of present and future biased choices and
Dohmen, Falk, Hu↵man and Sunde (2006) wh o find a greater proportion of future-biase d than present-biased
subjects.
37
Indeed psychology provides some grounds for such views as money generates broadly similar rewards-related
neural patterns as more primary incentives (Knutson, Adams, Fong and Hommer, 2001), and in the domain
of discounting evidence suggests that discounting over primary rewards, such as juice, pro d uc es similar neural
images to discounting over monetary rewards (McClure, Laibson, Loewenstein and Cohen, 2004; McClure et
al., 2007).
28
bias, ‘Present Biased’
e
and ‘Present Biased’
m
are also uncorrelated, ⇢ =0.11, (p =0.33).
38
Table 3: Validation of Individual Parameter Estimates
Dependent Vari a bl e: Budget Share Distance
E↵ort Discounting Monetary Discounting
(1) (2)
(3) (4)
Real E↵ort Present Bias Parameter:
ˆ
e
0.532***
(0.053)
Present Biased
e
(=1) -0.123***
(0.020)
Monetary Present Bias Parameter:
ˆ
m
2.393***
(0.052)
Present Biased
m
(=1) -0.201***
(0.026)
Constant -0.531*** 0.020***
-2.391*** 0.044***
(0.052) (0.007)
(0.049) (0.015)
Job E↵ects Yes Yes
--
Choice Set E↵ects - -
Yes Yes
#Observations 800 800 750 750
# Uncensored Observations 798 798
731 731
#Clusters 80 80
75 75
Notes: Coefficients from tobit regressions of budget share di st an ce 2 [1, 1] on identified in-
dividual disco u nting parameters. 10 reallocations per i n d i v i d u a l for e↵ort decisions and 10
reallocations per individual for monetary decisions. Standard errors clustered on individual
level in parentheses. Job fix ed e↵ects for e↵ort and choice set fixed e↵ects for monetary dis-
counti n g included but not reported. Discounting parameters identified fro m OLS regressions for
monetary discounting and real e↵ort discountin g with individual specific e↵ects for both
ˆ
and
ˆ
.Curvatureparameter,↵,andcostparameter,,assumedconstantacrossindividuals. E↵ort
regressions identifying parameters control for Job E↵ects (Job 1 vs. Job 2). Mon et a r y Present
Bias (=1) and E↵ort Present Bias (=1) calculated as individuals with estimated
ˆ
<0.99 in
the relevant domain. Levels of significance: *** p<0.01, ** p<0. 05, * p<0.10.
The second question concerning our estimated parameters is whether they can be validated
38
Int er est i n gl y, when using both Blocks 1 and 2 of the data, we come to a slightly di↵erent conclusion. Though
ˆ
m
and
ˆ
e
remain virtually uncorrelated, with the additional data we uncover a substantial and significant
correlation between Present Biased’
e
and ‘Present Biased’
m
⇢ =0.24, (p =0.03). Further, ‘Present Biased’
m
is also significantly correlated with the continuous measure
ˆ
e
, ⇢ = 0.27, (p =0.02). More work is needed to
understand the relat i ons hi p between monetary and e↵ort present bias parameters.
29
in sample. That is, given that
ˆ
e
and
ˆ
m
are recovered as non-linear combinations of regression
coefficients, to what ex t ent do these measures predi ct present-biased realloca ti o n s of tasks and
money? In order to examine this internal validity question, we generate distance measures for
reallocations. For e↵ort choices we calculate the budget share of each allocation for Week 2
e↵ort. The di↵erence in bud get shares between reallocation and initial al l ocation is what we
term a ‘Budget Share Distance.’
39
As budget sha r es are valued between [0, 1], our budget share
distance measure takes values on the interval [1, 1], with negative numbers indicating present-
biased reall ocations. Ea ch subject has 10 such e↵ort budget share distance measures in Block
1. A similar measure is constructed for monetary discounting choices. Ta k i n g only the three
week delay data, at each gross interest rate we take the di↵erence between the future allocation
(Week 4 vs. Week 7 (Prospective)) budget share and the present allocation (Week 1 vs. Week
4orWeek4vs. Week7)budgetshare. Thismeasuretakesvaluesontheinterval[1, 1], with
negative numbers indicating present-biased reallocations. Each subject has 10 such monetary
budget share distance measures.
Table 3 presents a validation table with tobit regressions of ‘Budget Share Distance’ for
e↵ort and money on our correspondi n g p ar am eter estimates.
40
Individuals who are identified
as present-biased by our parameter measures do indeed have more present-biased reallocations
for both work and money. Columns (1) and ( 3) demonstrate that individuals with lower values
of
ˆ
e
and
ˆ
m
make more present-biased reallocations, and those subjects with =1wouldbe
predicted to make virtually identical allocations through time. Columns (2) and (4) demon-
strate that subjects who are present-biased over e↵ort al l ocate 12 percent less of their budget
to the sooner date when the sooner date is the present. Subjects who are present-biased over
money allocate around 20 percent less of their budget to the sooner payment when the sooner
payment is in the future.
In the next section we move out-of-sample to investigate commitment dema nd . The inves-
39
Specifically, given an initial Week 1 allocation of e
2
of work to be done in Week 2 and a reallocation of e
0
2
in Week 2 of work to be done in week 2, the b u d get share distance is
e
0
2
e
2
m
.
40
Tobit regressions are implemented to account for the dependent variable being measured on t h e interval
[1, 1].
30
tigation of commitment demand is critical to ruling out potential alternative explanations for
time inconsistency in e↵ort allocations. Our preferred explanation is the existence of a present-
bias in individual decision-making. Many alternative explanations exist, which are considered
in detail in Section 5.Importantly,undernoneofthesealternativehypotheseswouldweex-
pect a clear link between the behavioral pattern of reallocating fewer tasks to the present and
commitment demand. This is in contrast to a mod el of present bias under the assumption of
sophistication. Present-bi a sed ind i v i d u a ls shoul d have demand for commitment. In the next
section we document commitment demand on the aggregate level and link commitment dema n d
to measured present-bias at both the aggregate and individual level.
4.4 Commitment Demand
In Week 4 of our ex periment, subjects are o↵ered a pr ob ab il i st i c commitment device. S u bjects
are asked whether they prefer the allocation-that-counts to come from their Week 4 allocations
with probabil i ty 0.1 (plu s an amou nt $X) or with prob a b i l i ty 0.9 (plu s an amo u nt $Y), with
either $X=0 or $Y=0. The secon d of these choices represents commitment and $X - $Y is t h e
price of commitment.
41
Virtually nobody is willing t o pay more than $0.25 for commi t m ent,
with 91 percent of subjects preferring flexibility when the cost of commitment ($X - $Y) is
$0.25. Likewise, nobody is willing to pay more than $0.25 for flexibility, with 90 percent of
subjects preferring commitment when the p r i ce of commitment ($X - $ Y) is -$0.25. It appears
that most subjects simply followed the money in the elicitation, preferring either commitment
or flexibility depending on which option provided additional payment.
42
We obtai n some heterogeneity in beh avior at price zero ($X=0 and $Y=0) where 59%
(47/80) of subjects commit, indicating substantial commitment demand. We define the binary
41
To avoid cutt i n g the sample further, here we consider all 80 subjects in the primary sample. 4 of 80 subjects
switched multipl e times in the commitment device price list elicitation. Identical results are obtained excluding
such individuals.
42
We are hesitant to draw strong concl u si on s based on price sensitivity for two reasons. First, the elicitation
procedure may not have been optimized for fine price di↵erentiations. Second, given the observed reallocations,
and t h e overall payment subjects received for units of work, it is not clear how much t h e option to reallocate
should be worth.
31
variable ‘Comm i t (=1 ) ’ whi ch takes the value 1 if a subject chooses to commit at price zero
and use this measure in the following analysis.
Figure 7: Commitment Demand
Panel A: Commit (=0)
10 20 30 40
.5 1 1.5 .5 1 1.5
Greek Transcription Tetris
Initial Allocation
Mean
Re-Allocation
Mean
SEM
Sooner Tasks
Task Rate
Graphs by task
Panel B: Commit (=1)
10 20 30 40
.5 1 1.5 .5 1 1.5
Greek Transcription Tetris
Initial Allocation
Mean
Re-Allocation
Mean
SEM
Sooner Tasks
Task Rate
Graphs by task
Figure 7 sep a r a t es Figure 5 showing the real e↵ort discounting behavior by commitm ent
demand at price zero. Immediately apparent from Figure 7 is that experimental behavior
separates along commitment demand. Subjects who demand commitm ent in Week 4 made
32
substantially present biased reallocations in Week 2 given their ini t i a l Week 1 e↵ort allocations.
Contro l l i n g for all task rate and task interactions, subjects who demand commitment allocate
3.58 fewer tasks to the sooner date when it is the present, F (1, 46) = 12.18, (p<0.01).
Subjects who do not demand commitment make more similar initial allo cations and subsequent
reallocations of e↵ort. Controlling for all task rate and task interactions, they only allocate 0.89
fewer tasks to the sooner date when it is the present, F (1, 32) = 4.01, (p =0.05). Furtherm o r e,
subjects who deman d commitment in Week 4 reallocated significantly more tasks than subjects
who did not demand commitment, F (1, 79) = 5.84, (p =0.02).
Table 4 generates a similar conclusion with parametric estimates. In columns (3) and (4),
we find that subjects who demand commitment in W eek 4 are significantly present biased over
e↵ort in Weeks 1-3,
2
(1) = 9.00, ( p<0 . 0 1 ) . For subjects who do not demand commitment,
we cannot reject the null hypothesis of =1atconventionallevels,
2
(1) = 2.64, (p =
0.10). Further, we reject the nu l l hypothesi s of equal pr esent bias across committers and non-
committers,
2
(1) = 4.85, (p =0.03).
43
In columns (1) and (2) of Ta b l e 4 we repeat this exercise, predicting commitment demand
for e↵ort using present bias param et er s from moneta r y decisi o n s. While subjects who demand
commitment also seem directionally more present-biased for monetary decisions than subject s
who do not demand com mi t m ent, the di↵erence is not si gni fi cant, (p =0.26).
In Table 5 we assess whether present bias identified at the individual level predicts com-
mitment demand. We show logit regressions wit h ‘Commit(=1)’ as the dependent variable and
measures of present bias over work and money as independent variables. In column (1) we fi n d
that the continuous value
ˆ
e
significantly predict s commitment demand. Column (2) shows that
while the binary measur e, Present Biased
e
, h a s the right sign, it fails to be significant.
44
There
43
These results are stronger f or the first block of the experiment prior to the o↵ering of the commitment
device, though the general patterns hold s wh en we use both blocks of data. Appendix Table A6 provides
analysis including t he data from both blocks.
44
In Appendix Table A7, we use parameter est i mat es from Blocks 1 and 2 combined and find that bot h the
cont i nuous and the binary measure are predictive. Indeed, marginal e↵ects indicate that individuals who are
present biased are 33 percentage points more likely to demand commitment, an increase of 56% f r om the mean.
That binary present bias identified from the combined data set has incr ease d predictive power may be related
to the arbitrary cuto↵ (
ˆ
e
< 0.99) employed for the measu re . For example, identifying binary present bias with
33
Table 4: Monetary and Real E↵ort Discounting by Commitment
Monetary Discounting E↵ort Discounting
Commit (=0) Commit (=1)
Commit (=0) Commit (=1)
(1) (2) (3) (4)
Tobit Tobit
Tobit Tobit
Present Bias Paramet er :
ˆ
0.999 0.981 0.965 0.835
(0.010) (0.013)
(0.022) (0.055)
Daily Discount Factor:
ˆ
0.997 0.997
0.988 1.009
(0.000) (0.001)
(0.005) (0.005)
Monetary Curvature Parameter: ˆ↵ 0.981 0.973
(0.009) (0.007)
Cost of E↵ort Parameter: ˆ 1.553 1.616
(0.165) (0.134)
#Observations 420 705 660 940
#Clusters 28 47
33 47
Job E↵ects - -
Yes Yes
H
0
: =1
2
(1) = 0.01
2
(1) = 2.15
2
(1) = 2.64
2
(1) = 9.00
(p =0.94) (p =0.14)
(p =0.10) (p<0.01)
H
0
: ( Col. 1) = (Col. 2)
2
(1) = 1.29
(p =0.26)
H
0
: ( Col. 3) = (Col. 4)
2
(1) = 4.85
(p =0.03)
Notes: Parameters identified from OLS regressions of equations (1) and (2) for monetary
discounting and real e↵ort discounting. Parameters recovered via non-linear combinations of
regression coefficients. Stand a r d err o r s cluster ed at indiv i d u a l level reported in parent h eses,
recovered via the delta method. Commit (=1) or Commit (=0) sepa r a t es individuals into those
who did (1) or those who did not (0) choose to commit at a commitment price of zero dollars.
E↵ort regressions control for Job E↵ects (Job 1 vs. Job 2). Tested null hypoth eses are zero
present bias, H
0
: = 1, and equality of present bias a cr o ss commi t ment and no commitment,
H
0
: (Col. 1) = (Col. 2) and H
0
: (Col. 3) = (Col. 4).
are again some suggestive, but statistically insignificant results, delivered by our measures of
monetary present bias in columns (3) and (4). In columns (5) and (6) we combine present bias
measures and note that where significant relations are achieved, present bi a s over e↵ort has
substant i all y more predictive power than present bias over money for explaining commitment
lower values of
ˆ
e
yields significance with only Block 1 data.
34
demand.
Table 5: Predicting Commitment Demand
Dependent Variable : Commit (=1)
(1) (2) (3) (4) (5) (6)
ˆ
e
-2.595** [-0.625] -3.157** [-0.725]
(1.170) (1.333)
Present Biased
e
(=1) 0.031 [0.008] 0.301 [0.070]
(0.459) (0.488)
ˆ
m
-3.146 [-0.735] -3.841 [-0.883]
(4.140) (4.008)
Present Biased
m
(=1) 0.622 [0.140] 0.588 [0.133]
(0.533) (0.537)
Constant 2.746** 0.336 3.635 0.323 7.262* 0.180
(1.087) (0.340) (4.092) (0.288) (4.259) (0.369)
#Observations 80 80 75 75 75 75
Log-Likelihood -52.031 -54.218 -49.280 -48.838 -46.529 -48.646
Pseudo R
2
0.040 0.000 0.006 0.014 0.061 0.018
Mean of Dependent Variable 0.59 0.59 0.63 0.63 0.63 0.63
Notes: Co effi ci ents from logistic regression of demand for commitment on identified individual
discounting parameters. Marginal e↵ects in brackets. Robust standard errors in parentheses.
Commit (=1) or Commit (=0) separates individuals into those who d i d (1) or those who did
not (0) choose to commit at a commitment price of zero dollars. Discounting parameters
identified from OLS regressions of equations (1) and (2) for monetary discounting and real
e↵ort discounting with individual specific e↵ects for both
ˆ
and
ˆ
.Curvatureparameter,↵,
and cost parameter, ,assumedconstantacrossindividuals. E↵ortregressionsidentifying
parameters control for Job E↵ects (Job 1 vs. Job 2). Pr esent Biased
m
(=1) and Present
Biased
e
(=1) calculated as individuals with estimated
ˆ
<0.99 in the relevant domain. Levels
of significance: *** p<0.01, ** p<0.05, * p<0.10.
These findings in d i cat e that present bias in e↵ort is signifi cantly related to future commit-
ment demand. Individuals who are present biased over e↵ort are substantially more likely to
demand commitment at price zero.
It is im portant to ensure that t h e desired commitment is meaningful in that it imposes a
binding const r a i nt. Specifica l l y, we ask whether in d i v i d u a l s who demand commitment actually
restrict their own activities through commitment, forcing themselves t o complete more work
than they instantaneously desire.
45
Given t h e n a t u r e of o u r commitment device, this seems at
45
Though our o↵ered commitment contract allows individuals only to meaningfully rest r i ct themselves, this
need not be the case. One example would be to have ind i v i d u al s commit to completing at least 1 task at the
sooner work date. As virtually all initial alloc ati on s and subseq u ent real l ocations satisfy this condition anyways,
35
least ex-ante plausible, and will be the case as long as initial alloca t i o n s di↵er from reallocations.
Two such comparisons a r e considered. First, we consider the first block of the experiment
when no commitment contract is available. How many more tasks woul d subjects have been
required to complete in Week 2 had the commitment contract been in place? To answer this
question we examine budget share distances for Block 1. Non-committers have a mea n budget
share distance of 0.018 (clustered s.e. = 0.009) allocating about 2 percentage points less of
each budget to Week 2 when deciding in the present. In contrast, committers have a mean
budget share distance of 0.072 (0 .020), allocating 7 percentage points less to Week 2 when
deciding in th e present. While both values are significantly di↵erent from zero (F (1, 79) =
4.14, (p =0.05), F (1, 79) = 12.39, (p<0.01), respectively), the di↵erence between the two
is also statistically significant, F (1, 79) = 5.88, (p =0.02). Hence, had commitment been
av ailable in W eek 2 and had subjects made the same choices, committers would have been
required to complete significantly more work than they instantaneously desired and would
have been more restricted than non-committers. The same analysis can be done for Block 2
focusing on required work in Week 5. Non-committers have a mean budget share distance
of 0.011 (0.017) while committers have a mean distance of 0.030 (0.013). The di↵erence
for committers remains signifi ca ntly di↵erent fro m zero, F(1, 79) = 5.57, (p =0.02), and
the di↵erence between the two remains significant at the 10% level F (1, 79) = 3.68, (p =
0.06).
46
Hence, in th e presence of commitment in Week 5, committers are required to complete
significantly more work than th ey inst antaneously desi r e and are more restr i ct ed th an non -
committers.
We are aware of two prior exercises exploring the potential extent of present bias and its
correlation with commitment demand. Kaur et al. (2010)linktheapparentlypresent-biased
behavior of working harder on pay d ays with d em a n d for a dominated wag e contract wherein
individuals choose a work target. If the work target is not met, an individual receives a
low piece-rate wage, while if it is met or exceeded the individual receives a higher piece rate
such commitment is not very meaningful.
46
The di↵erence for non-committers is no longer significantly di↵erent from zero F (1, 79) = 0.39, (p =0.53).
36
wage. As the domi n a t ed wage contract can be viewed as a commitment to compl et e a certain
amount of work, this represents a potential link between commitment and present bias. Though
compelling, the co m mi t m ent levels are ch o sen by individuals themselves and are set around 1/6
of average productivity.
47
Ashraf et a l. (2006)considerhypotheticalintertemporalchoicesover
money, rice and ice cream and link those to take-up of a savings commitment device. The
authors show that present bias in hypothetical monetary decisions is correlated with take-up
for wom en.
5 Discussion
Our e↵ort discounting data address several key confounds present in monetary studies, such as
fungibility and arbitrage issues. However, some discussion is required befo r e one can attribute
the observed behavior for e↵ort choices to dynamic i n co n si st en cy. Clearly, the ability to pre-
dict commitment demand based on present-biased reallocations gives a degree of confidence.
In this section we discuss four additional hypotheses which can generate time inconsistent ef-
fort allocations. Though non e of these exp l anat ion s would predict a correlation between time
inconsistency and commit m ent demand, we ca n also address these hy potheses directly.
First, subjects may reallocate fewer tasks to the present because of time constraints. Sub-
jects who log on to the experimental website just prior to midnight may have limited opportu-
nity to complete their tasks. Importantly, we recorded allocation times. On average, subjects
completed their allocatio n s i n Weeks 2 and 5 with around 8 hours remaining before the imposed
midnight deadline. Onl y 8 of 80 subjects completed their allocations in Weeks 2 or 5 with less
than 2 hours remaining before the imposed midnight deadline and only 2 of 80 completed their
allocations with less than 1 hour remaining. O f cour se, subjects that log in later may be more
likely to be present-biased, but the physical time constraint appears not to be a driving force
in the allocations.
48
47
The commitment may ser ve other purposes than constraining behavior that may still be desirabl e to ind i -
viduals who work harder on paydays.
48
Int er est i n gl y, in unreported post-hoc results, when splitting the sample at the median allocation completion
37
Second, subjects may make reallocations not because they are present-biased but because
they find the task to be more or less difficult than they previously envisioned.
49
Though we
do attempt to give subjects a sense of the tasks, this is a plausible and critical confound. Im-
portantly, our environment is po t entially able to address this confound as changes to perceived
cost functions are separable from time preferences. The shape of the cost function is identified
from changes in the exper i m ental task rates. Because both initial allocatio n s and subsequent
reallocations are made at various task rates, the cost function is identified at both points and
time. In Appendix Ta b l e A3, we estimate cost functions a n d discounting parameters at each
point in time, lending credence to the notion that changes in cost functions are not driving the
observed behavior.
50
Third, and relatedly, attention must be paid to the role of u n cer t a i nty in delivering a
present-b i a sed pattern of behavio r . When making initial allocations, subjects do so under a
di↵erent informational environment than when making their subsequent reallocations. There
could be u n cer tai nty for initial allocations, which is partially resolved when reallocations are
made one week later. Several aspects of uncertainty warrant attentio n . First, individuals may
carry preferences for the resolution of uncertainty (Kreps and Porteus, 1978; Epstein and Zin,
1989; Chew and Epstein, 1989). Unlike monetary designs, in our e↵or t experi m ent such a
preference may more naturally lead to a future bias. Subjects desiring to resolve uncertainty
in their reallocation choices could , in principle, choose to complete their tasks immedia t el y
when the present is available. Second, our discountin g estimates do not account for subjects’
potential uncertainty on their own parameters, such as uncertainty with regards to the future
costliness of the task. Though the weekly parameter estimates provided in Tabl e A3 help to
alleviate some concerns, a deeper problem may exist. Subjects may make allocations in Week
time we do find th at subjects who log in later are estimated to be more present-biased.
49
We see this channel as d i st i n ct from the role of uncertainty, as such changes in difficulty need not have been
forecasted.
50
The non-parametric analysis above also gives some sense of the validity of this concern. If changing cost
functions were to drive the behavior, one would observe a di↵erent pattern of reallocations. If an individual
moved from having an extremely convex to an almost linear cost function, the corresponding allocations would
shift from having limited price sensitivity to being very pr i ce sensitive. Hence, one would expect reallocations
to be hi gh er than initial allocations at some prices and lower at others.
38
1thatminimizetheirdiscountedexpected cost in future weeks given the potent i al realizations
of future parameters. This uncertainty may be subsequently resolved in Week 2, such that
subjects minimize their discounted cost at specific realizations of key parameters. As the
minimizer of the expectation need not be the expectation of the minimizer, such issues can
lead to inconsistencies between initial allocations and subsequent reallocations. To explore the
extent to which this issue hampers identification of present bias, we conduct simulations under
a variety of uncertainty structures in Appendix A. Uncertainty, unresolved at initial allocation
and realized at the time of reallocation, does bias our estimates of both at the aggregate and
individual level. However, the direction of bias is generally upward in the p a ra m et er regions of
interest, leading to less estimated present bias.
51
Importantly, a subject with future uncertainty
would benefit from flexibility, such that even if present bias was delivered by uncertainty of
some form one would not expect a correlation between present bias and commitment demand.
Fourth, present-biased reallocations of e↵o r t may be a simple decision error. Hence, present
bias, or any dynamic inconsistency, may be an u n st a b l e phenomenon . The two blocks of
our experiment speak to this possibility. S u bjects have two opportuni t i es to exhibit present-
biased reallocations. Indeed, present-biased behavior in Block 1 and Block 2 is significantly
correlated.
52
At the allocation level , a subject who is present biased in Block 1 is 58% more
likely than others to be present biased in Block 2, F (1, 79) = 6.94, (p =0. 010).
53
Additionally,
an individual who is dynamically consistent in Block 1 is 85% more likely to be dynamically
consistent in Block 2 than others F (1, 79) = 50.88, (p<0.01).
54
51
Int u i t i vely, subjects with unr e sol ved uncertainty on future parameters seek to avoid the extreme possibilities
of working under a very convex cost structure that is only rarely realized. This leads initial allocation s to be
frequently lower than subsequent reallocations, par t i cu l ar l y at higher task rates. Appendix A provides greater
detail.
52
Though the behavior is significant l y correlated when examined as indicators for present bias, future bias
and dynamic consistency ; the budget share distances are not significantly correlated through time. This may
be due to the sheer volume of data with budget share distances equal to zero and the relative lack of stability
for future-biased behavior .
53
Test statistic from OLS regression of binary indicator for a present-biased reallocation in Bl ock 2 on matched
indicator for present-biased reallocation in Block 1 with standard errors clustered on the subject level. The
estimated constant is 0.218 (s.e. =0.030) and the coefficient on Block 1 present bias is 0.128 (s.e. =0.049).
54
Test st at i st i c from OLS regression of binary indicator for a dynamically consistent reallocation in Bl ock 2
on match ed ind i cat or for a dynamical l y consi st ent reallocation in Block 1 with standard errors clustered on the
subject level. The estimated constant is 0.400 (s.e. =0.041) and the coefficient on Block 1 dynamic consistency is
39
This discussion helps to clarify some of the potential confounds for our observed e↵ects.
We view it as unlikely that present-biased reallocations of e↵ort are driven by time constraints,
unforeseen difficulty or uncertainty. Further, that present bias over e↵ort exhibits stability
and predicts commitment demand gives confidence that our observed e↵ects are generated by
dynamic inconsistency.
6 Conclusion
Present biased time preferences are a core of behav i or al research. The key hypothesis of dimin-
ishing impatience through time is able to capture a number of behavioral regularities at odds
with standard exponential discounting. Further, th e possibility of sophistication provid es an
important channel for policy improvements via the provision of commitment devices. With the
exception of only a few pieces of research, most evid ence of dynamic i n co n si st en cy is generated
from experimental cho i ces over time-d a t ed monetary payments. Such methods are subject to a
variety of critical confounds, muddying the resulting inference for a model defined over strea m s
of consumption.
The present study recognizes the key shortcomings of monetary discounting experiments
and attempts to identify dynamic inconsistency for choices over real e↵ort. We introduce a lon-
gitudinal design asking subjects to allocate and subsequently reallocate units of e↵ort through
time. A complementary monetary study is conducted for comparison. We document three key
findings. First, in choices over monetary payments, we find limited evidence of present bias.
This fin di n g supports recent work demonstrating that when transactions costs and payment
risk are closely controlled, monetary choices generate only limited present bias. Second, in
choices over e↵ort, we find substantial present bias. Subjects reallocate about 9% less work to
0.342 ( s.e. =0.048). Interestingly, somewhat less precision is found for future biased reallocations. An individual
who is f u t u r e-b i ased in Block 1 is 54% more likely to be future-biased in Block 2 than others F (1, 79) =
3.07, (p =0.08). Test statistic from OLS regr essi on of binary indicator for a future-biased reallocation in
Block 2 on mat ched indicator for a future-biased reallocation in Block 1 with standard errors clustered on
the subject level. The estimated constant is 0.162 (s.e. =0.025) and the coefficient on Block 1 future bias is
0.088 ( s.e. =0.050).
40
the present than their initial allocati o n . Corresponding parameter estimates generate a si m i l a r
conclusion. Indi v i d u a l s are estimated to be substantially present-biased in e↵ort ch o i ces and
significantly cl oser to dyn am i call y consistent in choices over m on ey. Third, we study commit-
ment demand, do cumenting that at price zero roughly 60% of subjects prefer commitment to
flexibility. A key result is that th ese commitment decisions correlate sig n i fi ca ntly with pre-
viously measured present bias. Individuals who demand commitment are significantly mo r e
present-biased in e↵ort than those who do not. This provides validation for our experimental
measures and helps to rule out a variety of potential confounds. Importantly, in our design
commitment meaningfull y restricts activities. Committed subjects are r eq u i red to complete
more e↵ort than they instantaneously desire. By documentin g the link between experimentally
measured present bias and commitment demand, we provide support for models of dynamic
inconsistency with sophistication. Subjects are apparently aware of their present bias and take
actions to limit their future behavior.
We v i ew our paper as provid i n g a portable experimental method allowing tract a b l e esti-
mation of inter t em poral preferences over consumpt i o n (e↵ort) a n d correlating such preferences
with a meaningful, potentially constr ai n i ng, commitment device. Though the implementation
here is with American undergraduates, we feel the design is suitable for field interventions.
We draw one conclusion and several words of caution from our findings. Our results indicate
that present bias is plausibly identified in choices over e↵ort and, furthermore, is linked to
e↵ort-related commitment demand. However, we caution using the estimated parameters at
face value as they are for a specific subject pool (self-selected to work for six weeks for final
payment in week seven) and a specific task. There may be other decision environments wherein
behavior may n o t be well captured by models of dy na m i c inconsistency. For example, subjects
may wish to get a painful single experience over with immediately or postpone a single pleasure
(Loewenstein, 1987).
55
Additionally, though fungibility issues may be mediated in the present
design, the natural problems of arbitrage will still exist if subjects substitute e↵ort in the
55
This suggests a key anticipatory component of intertemporal behavior, potentially mediated by our design’s
use of minimum e↵ort requirements and convex d eci si on s.
41
lab wit h their extra-lab behavior. The existence and use of such substitutes, like avoiding
doing laundry or homework in response to the experiment, may bias ou r d i sco u nting estimates.
Together th ese cautions sug g est important benefits to future research ex p l o r i n g the correlat i o n
between our measures and ecologically relevant decisions.
42
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