Working Over Time: Dynamic Inconsistency in Real
Effort Tasks ∗
Ned Augenblick
†
Muriel Niederle‡
UC Berkeley, Haas School of Business
Stanford University and NBER
Charles Sprenger§
Stanford University
First Draft: July 15, 2012
This Version: January 26, 2015
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 present bias. However, such monetary studies contain oftendiscussed confounds. In this paper, we sidestep these confounds and investigate choices
over consumption (real effort) in a longitudinal experiment. We pair this effort study 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.
JEL classification: C91, D12, D81
Keywords: Time Discounting, Demand for Commitment, Real Effort, Convex Time Budget
∗
We are grateful for many helpful discussions including those of Steffen Andersen, James Andreoni, Colin
Camerer, Yoram Halevy, David Laibson, Matthew Rabin, and Georg Weizsäcker. We thank Wei Wu for helpful
research assistance and technological expertise.
†
University of California Berkeley, Haas School of Business, University of California, Berkeley, 545 Student
Services Building, 1900, Berkeley, CA, 94720-1900. ned@haas.berkeley.edu
‡
Stanford University, Department of Economics, Landau Economics Building, 579 Serra Mall, Stanford, CA
94305; niederle@stanford.edu, www.stanford.edu/∼niederle
§
Stanford University, Department of Economics, Landau Economics Building, 579 Serra Mall, Stanford, CA
94305; cspreng@stanford.edu.
1
Introduction
Models of dynamically inconsistent time preferences (Strotz, 1956; Laibson, 1997; O’Donoghue
and Rabin, 1999, 2001) are a pillar of modern behavioral economics, having added generally to
economists’ understanding of the tensions involved in consumption-savings choices, task performance, temptation, and self-control beyond the standard model of exponential discounting
(Samuelson, 1937). Given the position of present-biased preferences in the behavioral literature, there is clear importance in testing the model’s central falsifiable hypothesis of diminishing
impatience through time. Further, testing auxiliary predictions such as sophisticated individuals’ potential to restrict future activities through commitment devices can distinguish between
competing accounts for behavior and deliver critical prescriptions to policy makers.1 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 focused on identifying the shape
of time preferences (for a comprehensive review to the early 2000s, see Frederick, Loewenstein
and O’Donoghue, 2002). The core of this experimental literature has identified preferences
from time-dated monetary payments.2 Several confounds exist for identifying the shape of
time preferences from such monetary choices. Issues of payment reliability and risk preference
suggest that subject responses may be closely linked to their assessment of the experimenter’s
reliability rather than solely their time preferences.3 Furthermore, monetary payments may not
1
Sophistication is taken to mean the decision-maker’s recognition (perhaps partial recognition) of his predilection to exhibit diminishing impatience through time. Appendix section A outlines the model which follows the
framework of O’Donoghue and Rabin (2001).
2
Recent efforts using time dated monetary payments to identify time preferences include Ashraf, Karlan and
Yin (2006), Andersen, Harrison, Lau and Rutstrom (2008), Dohmen, Falk, Huffman and Sunde (2010), Tanaka,
Camerer and Nguyen (2010), Benjamin, Choi and Strickland (2010) Voors, Nillesen, Verwimp, Bulte, Lensink
and van Soest (2012), Bauer, Chytilova and Morduch (2012), Sutter, Kocher, Glatzle-Ruetzler and Trautmann
(2013), and Dupas and Robinson (2013).
3
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 experiments would be interesting but
seem to present enormous tactical problems. (Would subjects believe they would get paid in five years?)’. Recent
work validates this suspicion. Andreoni and Sprenger (2012a), Gine, Goldberg, Silverman and Yang (2010),
and Andersen, Harrison, Lau and Rutstrom (2012) all document that when closely controlling transactions
costs and payment reliability, dynamic inconsistency in choices over monetary payments is virtually eliminated
on aggregate. Further, when payment risk is added in an experimentally controlled way, non-expected utility
2
be suitable to identify parameters of models defined over time-dated consumption. Arbitrage
arguments imply that choices over monetary payments should only reveal subjects’ borrowing
and lending opportunities (Cubitt and Read, 2007).4 Chabris, Laibson and Schuldt (2008)
describe the difficulty in mapping experimental choices over money to corresponding model
parameters, casting skepticism over monetary experiments in general.
In this paper we attempt to move out of the domain of monetary choice and into the
domain of consumption. Our design delivers precise point estimates on dynamic inconsistency
based upon intertemporal allocations of effort and provides an opportunity to link parameter
measures with demand for commitment. Delivering such a connection and contrasting present
bias measured over money and over consumption are key contributions of our study.
There are few other experimental tests of dynamic inconsistency in consumption. Leading examples document dynamic inconsistency in brief, generally a few minutes, intertemporal
choices over irritating noises and squirts of juice and soda (Solnick, Kannenberg, Eckerman and
Waller, 1980; McClure, Laibson, Loewenstein and Cohen, 2007; Brown, Chua and Camerer,
2009). On a larger time scale, perhaps closer to everyday decision-making, there are two key
contributions. Read and van Leeuwen (1998) identify dynamic inconsistency between choices
over snack foods made one week apart. Ariely and Wertenbroch (2002) document demand
risk preferences deliver behavior observationally equivalent to present bias as described above (Andreoni and
Sprenger, 2012b).
4
In a monetary discounting experiment, subjects often make binary choices between a smaller sooner payY
ment, $X, and a larger later payment, $Y. The ratio, X
, defines a lab-offered gross interest rate. An individual
who can borrow at a lower rate than the lab-offered rate should take the larger later payment, finance any
sooner consumption externally, and repay their debts with the later larger payment they chose. An individual
who can save at a higher rate than the lab-offered rate should take the smaller sooner payment, pay for any
sooner consumption and place the remainder in their savings vehicle. These two strategies deliver a budget
constraint that dominates the lab-offered budget constraint. Hence, monetary discounting experiments should
reveal only external borrowing and lending opportunities. And, unless such opportunities change over time,
one should reveal no present bias. The logic extends to the convex decisions of Andreoni and Sprenger (2012a).
Subjects should allocate only at corner solutions and such solutions should maximize net present value at external interest rates. This point has been thoughtfully taken into account in some studies. For example, Harrison,
Lau and Williams (2002) explicitly account for potential arbitrage in their calculations of individual discount
rates by measuring individual borrowing and saving rates and incorporating these values in estimation. Cubitt
and Read (2007) provide 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
subjects with a fully articulated arbitrage argument and external interest rate information and document only
a small treatment effect.
3
for deadlines for classroom and work assignments, a potential sign of commitment demand for
dynamically inconsistent individuals. Though suggestive, neither exercise allows for precise
identification of discounting parameters, nor delivers the critical linkage between present bias
and commitment demand. With the exception of Ashraf et al. (2006) and Kaur, Kremer and
Mullainathan (2010) virtually no research attempts to make such links. Ashraf et al. (2006)
employ monetary discounting measures and link them to take-up of a savings commitment
product. Kaur et al. (2010) use disproportionate effort response on paydays to make inference
on dynamic inconsistency and link this behavior to demand for a dominated daily wage contract. There are several major differences between our research and this prior work, which are
discussed in detail in Section 3.4. Most important is the measurement of dynamic inconsistency.
As opposed to monetary measures or measuring potential correlates of present bias, our effort
allocations yield precise parametric measures linked directly to the theory of present bias.
102 UC Berkeley students participated in a seven week longitudinal experiment. Subjects
allocated units of effort (i.e., negative leisure consumption) over two work dates. The tasks over
which subjects made choices were transcription of meaningless Greek texts and completion of
partial Tetris games. Allocations were made at two points in time: an initial allocation made in
advance of the first work date and a subsequent allocation made on the first work date. We then
randomly selected either an initial allocation or a subsequent allocation and required subjects
to complete the allocated tasks. This incentivized all allocation decisions. Differences between
initial and subsequent allocations allow for precise measurement of dynamic inconsistency. A
first block of the experiment, three weeks in length, was dedicated to this measurement effort.
In a second block of the experiment, also three weeks in length, the design was augmented
to elicit demand for a commitment device. The commitment device of the second block allowed
subjects to probabilistically favor their initial allocations over their subsequent allocations in the
random selection process. Hence, commitment reveals a subject’s preference for implementing
the allocations made in advance of the first work date. We investigate demand for our offered
commitment device and correlate identified dynamic inconsistency with commitment demand.
4
The repeated interaction of our seven-week study allows us to complement measures of
effort discounting with measures of monetary discounting taken from Andreoni and Sprenger
(2012a) Convex Time Budget (CTB) choices over cash payments received in the laboratory. In
these choices, subjects allocated money over two dates. Variation in whether the first payment
date is the present delivers identification of monetary present bias. Hence, we can compare
dynamic inconsistency measured over work and money at both the aggregate and individual
level within subjects. A second study, essentially a between-subjects replication exercise, was
also conducted to provide corroboration of the within-subject conclusions.
We document three primary findings. First, in the domain of money we find virtually no
evidence of present bias. Monetary discount rates involving present dates are effectively indistinguishable from those involving only future dates. Further, subjects appear to treat money
received at different times as perfect substitutes, suggesting they treat money as fungible. Second, in the domain of effort we find significant evidence of present bias. Subjects allocate
roughly nine percent more work to the first work date when the allocation of tasks is made in
advance compared to when it is made on the first work date itself. Corresponding parameter
estimates corroborate these non-parametric results. Discount rates measured in advance of the
first work date are around zero percent per week while discount rates measured on the first
work date are around eleven percent per week. We reproduce these two primary study results
in our between-subjects replication exercise with an additional 200 UC Berkeley students. Our
third finding is that 59 percent of subjects demand commitment at price $0, preferring a higher
likelihood of implementing their initial pre-work date allocations. We show that the choice
of commitment is binding and meaningful in the sense that initial preferred allocations differ
significantly from subsequent allocations for committing subjects. Importantly, we show that
present bias measured in the first block of the experiment is predictive of this (later) commitment choice. A corresponding investigation on the extent of sophistication and commitment
demand indicates that subjects potentially forecast their present bias. This link delivers key
validation and support for our experimental measures and well-known theoretical models of
5
present bias.
We draw two conclusions from our results. First, our results show evidence of present bias
in the domain of consumption with a design that eliminates a variety of potential confounds
and provides precise parameter estimation. Second, our subjects are at least partially aware of
their dynamic inconsistency as they demand binding commitment.
The paper proceeds as follows: Section 2 provides details for our longitudinal experimental
design. Section 3 presents results and section 4 concludes.
2
Design
To examine dynamic inconsistency in real effort, we introduce a longitudinal experimental
design conducted over seven weeks. Subjects are asked to initially allocate tasks, subsequently
allocate tasks again, and complete those tasks over two work dates. Initial allocations made
in advance of the first work date are contrasted with subsequent allocations made on the first
work date to identify dynamic inconsistency.
If all elements of the experiment are completed satisfactorily, subjects receive a completion
bonus of $100 in the seventh week of the study. Otherwise they receive only $10 in the seventh
week. The objective of the completion bonus is to fix the monetary dimension of subjects’
effort choices and to ensure a sizable penalty for attrition. Subjects are always paid the same
amount for their work, the question of interest is when they prefer to complete it.
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 decision environment in which allocations were made. The third subsection describes the elicitation of commitment demand. The
fourth subsection addresses design details including recruitment, selection, and attrition. The
fifth subsection presents the complementary monetary discounting study. In addition to this
primary within-subjects study, we also conducted a between-subjects replication exercise. The
between-subjects design is discussed primarily in section 3.5 and note is made of any design
differences.
6
2.1
Jobs
The experiment focuses on intertemporal allocations of effort for two types of job. In Job 1,
subjects transcribe a meaningless Greek text through a computer interface. Panel A of Figure
1 demonstrates the paradigm. Random Greek letters appear, slightly blurry, in subjects’ transcription box. By pointing 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.5 In the first week, subjects completed a
task from Job 1 in an average of 54 seconds. By the final week, the average was 46 seconds.
In Job 2, subjects are asked to complete four rows of a modified Tetris game, see Panel B
of Figure 1. Blocks of random shapes appear at the top of the Tetris box and fall at a fixed
relatively slow speed. Arranging the shapes to complete a horizontal line of the Tetris 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 credit for the 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. In contrast to a standard Tetris game,
one cannot accelerate the speed of the falling shapes, and one does not pass through ‘levels’ of
progressive difficulty. Hence, our implementation of Tetris should not be thought of as being
as enjoyable as the real thing.
2.2
Experimental Timeline
The seven weeks of the experiment are divided into two blocks. Weeks 1, 2, and 3 serve as the
first block. Weeks 4, 5, and 6 serve as the second block. Week 7 occurs in the laboratory and is
only used to pay subjects. Subjects always participate on the same day of the week throughout
5
Our measure of accuracy is the Levenshtein Distance. 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, deletion or change of a single
character. As the strings of Greek characters used in the transcription task are 35 characters long our 80
percent accuracy measure is equivalent to 7 edits or less or a Levenshtein Distance ≤ 7.
7
Figure 1: Experimental Jobs
Panel A: Job 1- Greek Transcription
Panel B: Job 2- Partial Tetris Games
the experiment. That is, subjects entering the lab on a Monday allocate tasks to be completed
on two future Monday work dates. Therefore, allocations are made over work dates that are
always exactly seven days apart.
Weeks 1 and 4 occur in the laboratory and subjects 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
8
and complete their work by 2am the following morning.
At each point of contact, subjects are first given instructions about the decisions to be
made and work to be completed that day, reminded of the timeline of the experiment, given
demonstrations of any unfamiliar actions, and then asked to complete the necessary actions.
The second block of the experiment, Weeks 4, 5, and 6, mimics the first block of Weeks
1, 2, and 3, with one exception. In Week 4, subjects are offered a probabilistic commitment
device, which is described in detail in subsection 2.4. Hence, we primarily describe Weeks 1,
2 and 3 and note any design changes for Weeks 4, 5 and 6. To summarize our longitudinal
effort experiment, Table 1 contains the major events in each week which are described in detail
below.
Table 1: Summary of Longitudinal Experiment
Week
Week
Week
Week
Week
Week
Week
2.3
1
2
3
4
5
6
7
(In Lab):
(Online):
(Online):
(In Lab):
(Online):
(Online):
(In Lab):
10 Effort Minimum
Allocations
Work
x
x
x
x
x
x
x
x
x
x
Allocation-ThatCounts Chosen
Complete
Work
x
x
x
x
x
x
Commitment Receive
Choice
Payment
x
x
Effort Allocations
In Week 1, subjects allocate tasks between Weeks 2 and 3. In Week 2, subjects also allocate
tasks between Weeks 2 and 3. Subjects were not reminded of their initial Week 1 allocations in
Week 2. Note that in Week 1 subjects are making decisions involving two future work dates,
whereas in Week 2, subjects are making decisions involving a present and a future work date.
Before making decisions 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.
9
2.3.1
Allocation Environment
Allocations are made in a convex environment. Using slider bars, subjects allocate tasks to
two dates, one earlier and one later, under different interest rates.6 Figure 2 provides a sample
allocation screen. To motivate the intertemporal tradeoffs faced by subjects, decisions are
described as having different ‘task rates.’ Every task allocated to the later date reduces the
number of tasks allocated to the sooner date by a stated number. For example, a task rate of
1:0.5 implies that each task allocated to Week 3 reduces by 0.5 the number in Week 2.7
For each task and for each date where allocations were made, subjects faced five task rates.
These task rates take the values, R ∈ {0.5, 0.75, 1, 1.25, 1.5}. The subjects’ decision can be
formulated as allocating tasks e over times t and t + k, et and et+k , subject to the present-value
budget constraint,
et + R · et+k = m.
(1)
The number of tasks that subjects could allocate to the sooner date was capped at fifty such
that m = 50 in each decision in the experiment.8
2.3.2
Minimum Work
In each week, subjects are required to complete 10 tasks of each Job prior to making allocation
decisions or completing allocated tasks. The objective of these required tasks, which we call
“minimum work,” is three-fold. First, minimum work requires a few minutes of participation
at each date, forcing subjects to incur the transaction costs of logging on to the experimental
website at each time.9 Second, minimum work, especially in Week 1, provides experience for
6
The slider was initially absent from each slider bar and appeared in the middle of the bar once a subject
clicked on the allocation. Every slider bar was thus clicked on before submission, avoiding purely passive
response.
7
We thank an anonymous referee for noting a small error in our instructions which inverted the task rates
when first introducing them. Though this appears not to have affected response as allocations move appropriately with task rates, we do correct this error in our replication exercise and document very similar behavior.
See section 3.5 for detail.
8
We use R for present value budget constraints of the form et + R · et+k = m, and P for future value budget
constraints of the form P · et + et+k = m.
9
A similar technique is used in monetary discounting studies where minimum payments are employed to
eliminate subjects loading allocations to certain dates to avoid transaction costs of receiving multiple payments
10
Figure 2: Convex Allocation Environment
subjects such that they have a sense of how effortful the tasks are when making their allocation
decisions. Third, we require minimum work in all weeks before all decisions, and subjects are
informed that they will have to complete minimum work at all dates. This ensures that subjects
have experienced and can forecast having experienced the same amount of minimum work when
making their allocation decisions at all points in time.
2.3.3
The Allocation-That-Counts
Each subject makes 20 decisions allocating work to Weeks 2 and 3: five decisions are made
for each Job in Week 1 and five for each Job in Week 2. After the Week 2 decisions, one of
these 20 allocations is chosen at random as the ‘allocation-that-counts’ and subjects have to
complete the allocated number of tasks on the two work dates to ensure successful completion
of the experiment (and hence payment of $100 instead of only $10 in Week 7).
The randomization device probabilistically favors the Week 2 allocations over the Week 1
allocations. In particular, subjects are told (from the beginning) that their Week 1 allocations
will be chosen with probability 0.1, while their Week 2 allocations will be chosen with probability
or cashing multiple checks (Andreoni and Sprenger, 2012a).
11
0.9. Within each week’s allocations, every choice is equally likely to be the allocation-thatcounts.10 This randomization process ensures incentive compatibility for all decisions. This
design choice was made for two reasons. First, it increases the chance that subjects experienced
their own potentially present-biased behavior. Second, it provides symmetry to the decisions
in Block 2 that elicit demand for commitment.
2.4
Commitment Demand
In the second block of the experiment, Weeks 4, 5, and 6, subjects are offered a probabilistic
commitment device. In Week 4, subjects are given the opportunity to choose which allocations
will be probabilistically favored. In particular, they can choose whether the allocation-thatcounts 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. Subjects who choose to
commit and who differ in their allocation choices through time can find themselves constrained
by commitment with high probability.
In order to operationalize our elicitation of commitment demand, subjects are asked to
make 15 multiple price list decisions between two options. In the first option, the allocationthat-counts will come from Week 4 with probability 0.1. In the second option, the allocationthat-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.11
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
submit their Week 5 allocation decisions. Given this randomization procedure, an individual
choosing commitment in all 15 decisions will complete a Week 4 allocation with probability
10
For the description of the randomization process given to subjects please see instructions in Appendix F.
We chose not to have the listed prices ever take negative values (as in a cost) to avoid subjects viewing
paying for commitment as a loss.
11
12
0.9. Each row at which a subject chooses flexibility reduces this probability by 5.3 percent.12
Hence a subject choosing to commit at price zero (the eighth row) and lower will complete an
initial allocation with probability 0.53. Naturally, if subjects treat each commitment decision
in isolation, the incentives are more stark as each decision moves the probability of facing an
initial allocation from 0.1 to 0.9.13 This isolation is encouraged as subjects are told to treat
each decision as if it was the one going to be implemented (See Appendix F.4 for detail).
Figure 3: Commitment Demand Elicitation
Our commitment demand decisions, and the second block of the experiment, serve three
purposes. First, they allow us to assess the demand for commitment and flexibility. Second, a
key objective of our study is to explore the theoretical link, under the assumption of sophistication, between present bias and commitment demand. Are subjects who are present-biased more
likely to demand commitment? Third, a correlation between time inconsistency and commitment validates the interpretation of present bias over other explanations for time inconsistent
choices. For example, a subject who has a surprise exam in Week 2 may be observationally
indistinguishable in her Week 2 effort choices from a present-biased subject. However, a subject
12
Each row changes the probability of implementing an initial allocation by (1/15 * (0.9 - 0.1)) = 0.053.
In assessing the value of commitment we make this assumption, ignoring the second stage randomization
inherent to the commitment demand elicitation.
13
13
prone to such surprises should favor flexibility to accommodate her noisy schedule. In contrast,
a sophisticated present-biased subject may demand commitment to restrict her future self.
2.5
Design Details
102 UC Berkeley student subjects were initially 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.14 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 bonus. The 12 subjects who selected out of the experiment do not
appear different on either initial allocations, comprehension or a small series of demographic
data collected at the end of the first day of the experiment.15 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 responses. In particular, if subjects have no variation in allocations in
response to changes in R in some weeks, then attempting to point identify both discounting and
cost function parameters is difficult, yielding imprecise and unstable estimates. In our sample,
nine subjects have this issue for one or more weeks of the study.16 For the analysis, 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 A9, we re-conduct the aggregate
analysis including these nine subjects and obtain very similar findings.
14
Student subjects were recruited from the subject pool of the UC Berkeley Experimental Laboratory, Xlab.
Having subjects informed of the seven week design and payment is a potentially important avenue of selection.
Our subjects were willing to put forth effort and wait seven weeks to receive $100. Though we have no formal
test, this suggests that our subjects may be a relatively patient selection.
15
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 where available does qualitatively alter the analysis or conclusions.
16
Appendix Tables A5 and A6 provide estimates for each individual based on their Block 1 data. The
9 individuals without variation in their responses in one or more weeks are noted. Extreme estimates are
obtained for individuals without variation in experimental response in one of the weeks of Block 1.
14
2.6
Monetary Discounting
Subjects were present in the laboratory in the first, fourth, and seventh week 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 additional questions allocating monetary
payments to Weeks 1, 4, and 7. In Week 1, we implement three Andreoni and Sprenger (2012a)
Convex Time Budget (CTB) choice sets, allocating payments across: 1) Week 1 vs. Week 4; 2)
Week 4 vs. Week 7 (Prospective); and 3) Week 1 vs. Week 7. Individuals allocate monetary
payments across the two dates t and t + k, ct and ct+k , subject to the intertemporal constraint,
P · ct + ct+k = m.
(2)
The experimental budget is fixed at m = $20 and five interest rates are implemented in each
choice set, summarized by P ∈ {0.99, 1, 1.11, 1.25, 1.43}. These values were chosen for comparison with prior work (Andreoni and Sprenger, 2012a).17 In Week 4, we ask subjects to allocate
in a CTB choice set over Week 4 and Week 7 under the same five values of P . 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
as Week 4 vs. Week 7 (Prospective). Hence, subjects complete a total of four CTB choice sets.
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), we have minimum payments of $5 at
each payment date to ensure equal transaction costs in each week, such as waiting to get paid.
Appendix F provides the full experimental instructions.
While the monetary discounting experiment replicates the design of Andreoni and Sprenger
(2012a) to a large extent, there are two important differences. First, Andreoni and Sprenger
(2012a) implement choices with payment by check. Our design implements payment by cash
17
Additionally, P = 0.99 allows us to investigate the potential extent of negative discounting.
15
with potentially lower transaction costs. Second, Andreoni and Sprenger (2012a) implement
choices with present payment received only by 5:00 p.m. in a subject’s residence mailbox. If
these payments are not construed as the present, one would expect no present bias. Here, we
provide payment immediately in the lab.
In both Weeks 1 and 4, the monetary allocations are implemented after the more central
effort choices. The monetary choices were not announced 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
Results
The results are presented in five subsections. First, we present aggregate results from the monetary discounting study and compare our observed level of limited present bias with other recent
findings. Second, we move to effort related discounting and provide both non-parametric and
parametric aggregate evidence of present bias. Third, we analyze individual heterogeneity in
discounting for both work and money. Fourth we present results related to commitment demand, documenting correlations with previously measured present bias and analyzing the value
of commitment. Lastly, a fifth subsection is dedicated to a between-subjects replication exercise of the results concerning differences in discounting when comparing choices over monetary
rewards to effort chocies.
3.1
Monetary Discounting
Figure 4 presents the data from our monetary discounting experiment. The mean allocation
to the sooner payment date at each value of P from P · ct + ct+k = 20 is reported for the 75
subjects from the primary sample for whom we have all monetary data. The left panel shows
three data series for payments sets with three-week delay lengths while the right panel shows
the data series for the payment sets with a six-week delay length. Standard error bars are
16
clustered at the individual level.
Figure 4: Monetary Discounting Behavior
6 Week Delay
0
5
10
15
Dollars Allocated to Early Date
20
3 Week Delay
1
1.2
1.4
1
1.2
1.4
P
(from Pct+ct+k=20)
Week 1 vs. Week 4
Week 4 vs. Week 7
SE
Week 4 vs. Week 7 (Prospective)
Week 1 vs. Week 7
k
e
n
o
ym
sb
h
p
ra
G
We highlight two features of Figure 4. First, note that as P from P · ct + ct+k = 20
increases, the average allocation to the sooner payment decreases, following the law of demand.
Indeed, at the individual level 98% of choices are monotonically decreasing in P , and only
1 subject exhibits more than 5 non-monotonicities in demand in their monetary choices.18
This suggests that subjects as a whole understand the implied intertemporal tradeoffs and the
decision environment.
Second, Figure 4 allows for non-parametric investigation of present bias in two contexts.19
18
Subjects have 16 opportunities to violate monotonicity comparing two adjacent values of P in their 20 total
CTB choices. 63 of 75 subjects have no identified non-monotonocities. 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-monotonicities in demand are somewhat less than the similar behavior of multiple switching in standard
Multiple Price List experiments.
19
Though the six-week delay data are used in estimation, our non-parametric tests only identify present bias
from choices over three-week delays. Without parametric assumptions for utility our data do not lend themselves
naturally to the method of identifying present bias where short horizon choices are compared to long horizon
17
First, one can consider the static behavior, often attributed to present bias, of subjects being
more patient in the future than in the present by comparing the series Week 1 vs. Week
4 and Week 4 vs. Week 7 (Prospective). In this comparison, controlling for P , subjects
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) made in Week 1 to the Week 4 vs. Week 7 choices made in Week 4. This measure
is similar to the recent work of Halevy (2012). Ignoring income effects associated with having
potentially received prior payments, this comparison provides a secondary measure of present
bias. In this comparison, controlling for P , subjects allocate on average $0.47 (s.e = 0.32) more
to the sooner payment when it is in the present, F (1, 74) = 2.08, (p = 0.15).20 Table 2, Panel
A provides a corresponding tabulation of behavior, presenting the budget share allocated to
the sooner payment date and the proportion of choices that can be classified as present-biased.
Budget shares for the sooner payment are calculated as (P · ct )/m for each allocation. Across
all values of P subjects allocate around 38% (s.e. = 1.73) of their experimental budget to the
sooner payment date when the sooner date is in the future (t 6= 0) and around 41% (1.34) to the
sooner payment date when the sooner date is in the present (t = 0), F (1, 74) = 3.50, (p = 0.07).
Further, across all values of P , seventy-eight percent of choices are dynamically consistent, 13%
are present-biased, and 9% are future-biased.
We find limited non-parametric support for the existence of a present bias over monetary payments. To provide corresponding estimates of present bias we follow the parametric
assumptions of Andreoni and Sprenger (2012a) and assume quasi-hyperbolic (Laibson, 1997;
O’Donoghue and Rabin, 2001) power utility with Stone-Geary background parameters. Hence,
the quasi-hyperbolic discounted utility from experimental payments at two dates, ct , received
choices to examine whether discount factors nest exponentially (see, for example Kirby, Petry and Bickel, 1999;
Giordano, Bickel, Loewenstein, Jacobs, Marsch and Badger, 2002).
20
Additionally, this measure is close in spirit to our effort experiment where initial allocations are compared to
subsequent allocations. To get a sense of the size of potential income effects, 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 P , 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 negligible income effects.
18
Table 2: Aggregate Behavior By Interest Rate
Panel A: Monetary Choices
P
0.952
1
1.11
1.25
1.429
Overall
t 6= 0
t=0
Budget Share Budget Share
(1)
(2)
t-test
(p-value)
(3)
Proportion
Present-Biased
(4)
Proportion
Dynamically Consistent
(5)
Proportion
Future-Biased
(6)
0.073
0.813
0.113
0.200
0.660
0.140
0.180
0.733
0.087
0.113
0.853
0.033
0.100
0.847
0.053
0.133
0.781
0.085
0.924
(0.228)
0.774
(0.368)
0.102
(0.259)
0.051
(0.177)
0.053
(0.182)
0.923
(0.189)
0.813
(0.323)
0.148
(0.300)
0.087
(0.239)
0.077
(0.228)
0.07
(p=0.94)
1.32
(p=0.19)
1.86
(p=0.06)
1.97
(p=0.05)
1.40
(p=0.16)
0.381
(0.461)
0.410
(0.458)
1.87
(p=0.07)
Panel B: Effort Choices
R
0.5
0.75
1
1.25
1.5
Overall
Initial
Subsequent
Budget Share Budget Share
(1)
(2)
t-test
(p-value)
(3)
Proportion
Present-Biased
(4)
Proportion
Dynamically Consistent
(5)
Proportion
Future-Biased
(6)
0.294
0.444
0.263
0.356
0.363
0.281
0.237
0.656
0.106
0.388
0.444
0.169
0.369
0.425
0.206
0.329
0.466
0.205
0.787
(0.180)
0.717
(0.206)
0.541
(0.134)
0.324
(0.239)
0.289
(0.242)
0.761
(0.219)
0.690
(0.245)
0.489
(0.183)
0.250
(0.222)
0.222
(0.226)
1.76
(p=0.08)
1.70
(p=0.09)
3.65
(p<0.01)
4.12
(p<0.01)
3.67
(p<0.01)
0.532
(0.286)
0.482
(0.311)
3.86
(p<0.01)
Notes: Panel A tabulates t 6= 0 and t = 0 budget shares for sooner payments for each P in money. Each row
calculates from 75 t 6= 0 allocations (one at each interest rate in the Week 4 vs. Week 7 prospective choices) and
150 t = 0 allocations (one at each interest rate in the Week 4 vs. Week 7 actual and Week 1 vs. Week 4) choices.
Paired t-tests with 149 degrees of freedom presented. Panel B tabulates initial and subsequent budget shares
for sooner tasks for each R in effort. Each row calculates from 160 initial allocations (one each for tetris and
greek at each task rate) and 160 subsequent allocations. Paired t-tests with 159 degrees of freedom presented.
Overall tests in both panels come from regression of budget share on allocation timing with standard errors
clustered on individual level. Test statistic is t-statistic testing the null hypothesis of no effect of allocation
timing, which controls for multiple comparisons.
at time t, and ct+k , received at time t + k, is
U (ct , ct+k ) = (ct + ω)α + β 1t=0 δ k (ct+k + ω)α .
19
(3)
The variable 1t=0 is an indicator for whether or not the sooner payment date, t, is the present.
The parameter β captures the degree of present bias, while the parameter δ captures long run
discounting. β = 1 nests the standard model of exponential discounting. The utility function
is assumed to be concave, α < 1, such that first order conditions provide meaningful optima.
Here, ω is a Stone-Geary background parameter that we take to be the $5 minimum payment
of the monetary experiment.21 Maximizing (3) subject to the intertemporal budget constraint
(2) yields an intertemporal Euler equation, which can be rearranged to obtain
log(
log(β)
log(δ)
1
ct + ω
)=
· (1t=0 ) +
·k+(
) · log(P ).
ct+k + ω
α−1
α−1
α−1
(4)
Assuming an additive error, this functional form can be estimated at the aggregate or individual level.22 One important issue to consider in estimation is the potential presence of corner
solutions. We provide estimates from two-limit Tobit regressions designed to account for the
possibility that the tangency condition implied by (4) does not hold with equality (for discussion, see Wooldridge, 2002; Andreoni and Sprenger, 2012a). Discounting and utility function
parameters can be recovered via non-linear combinations of regression coefficients with standard errors estimated via the delta method. Appendix A provides a detailed discussion of
identification and estimation of discounting parameters for both monetary and effort choices.
21
Andreoni and Sprenger (2012a) provide detailed discussion of the use of such background parameters and
provide robustness tests with differing values of ω and differing assumptions for the functional form of utility
in CTB estimates. The findings suggest that though utility function curvature estimates may be sensitive to
different background parameter assumptions, discounting parameters, particularly present bias, are virtually
unaffected by such choices.
22
An additive error yields the regression equation
log(
ct + ω
log(β)
log(δ)
1
)=
· (1t=0 ) +
·k+(
) · log(P ) + .
ct+k + ω
α−1
α−1
α−1
The stochastic error term, , is necessary to rationalize any discrepancies between our theoretical development
and our experimental data. One simple foundation for such an error structure would be to assume that indict +ω
viduals exhibit random perturbations to their log allocation ratios, log( ct+k
+ω ). A more complete formulation
might follow macroeconomic exercises such as Shapiro (1984), Zeldes (1989), and Lawrance (1991). With a
time series of consumption, one assumes rational expectations such that Euler equations are satisfied up to a
mean zero random error, uncorrelated with any information available to the decisionmaker. Assuming constant
relative risk aversion, as we do, this forecast error provides the structure for estimating utility function curvature
and recovering discounting parameters in a way very similar to our exercise.
20
23
Table 3: Parameter Estimates
Monetary Discounting
Effort Discounting
(1)
All Delay
Lengths
(2)
Three Week Delay
Lengths
(3)
Job 1
Greek
(4)
Job 2
Tetris
(5)
Combined
Present Bias Parameter: β
0.974
(0.009)
0.988
(0.009)
0.900
(0.037)
0.877
(0.036)
0.888
(0.033)
Weekly Discount Factor: (δ)7
0.988
(0.003)
0.980
(0.003)
0.993
(0.027)
1.007
(0.029)
0.999
(0.025)
Monetary Curvature Parameter: α
0.975
(0.006)
0.976
(0.005)
1.624
(0.114)
1.557
(0.099)
1.589
(0.104)
800
80
800
80
1600
80
Yes
Cost of Effort Parameter: γ
# Observations
# Clusters
Job Effects
1500
75
1125
75
H0 : β = 1
χ2 (1) = 8.77
(p < 0.01)
χ2 (1) = 1.96
(p = 0.16)
H0 : β(Col. 1) = β(Col. 5)
χ2 (1) = 6.37
(p = 0.01)
H0 : β(Col. 2) = β(Col. 5)
χ2 (1) = 7.36 χ2 (1) = 11.43 χ2 (1) = 11.42
(p < 0.01)
(p < 0.01)
(p < 0.01)
χ2 (1) = 8.27
(p < 0.01)
Notes: Parameters identified from two-limit Tobit regressions of equations (4) and (6) for monetary discounting
and effort discounting, respectively. Parameters recovered via non-linear combinations of regression coefficients.
Standard errors clustered at individual level reported in parentheses, recovered via the delta method. Effort
regressions control for Job Effects (Task 1 vs. Task 2). Chi-squared tests inlast three rows.
In Table 3, columns (1) and (2) we implement two-limit Tobit regressions 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 with our non-parametric
evidence. Across specifications we identify weekly discount factors of around 0.99. The 95%
confidence interval in column (1) for the weekly discount factor implies annual discount rates
between 40% and 140%.24 In column (1) of Table 3 we estimate β = 0.974 (s.e. = 0.009),
23
The notation of Appendix A is slightly altered to discuss allocation timing and make links to partial
sophistication and the value of commitment for effort choices.
24
In Appendix A, we discuss identification of all parameters and note that discount factors are identified
from variation in delay length, k. Our ability to precisely identify aggregate discounting was not a focus of
21
economically close to, though statistically different from dynamic consistency, H0 : β = 1:
χ2 (1) = 8.77, (p < 0.01). In column (2), focusing only on three week delays, we find β =
0.988 (0.009) and are unable to reject the null hypothesis of dynamic consistency, H0 : β = 1:
χ2 (1) = 1.96, (p = 0.16). These estimates demonstrate limited present bias for money and
hence confirm the non-parametric results.
In both specifications, we estimate α of around 0.975 indicating limited utility function
curvature over monetary payments. Finding limited curvature over money is important in its
own right, as linear preferences over monetary payments are indicative of fungibility. There
is no desire to smooth monetary payments as there might be for consumption, with subjects
treating money received at different points in time effectively as perfect substitutes. Supporting
these estimates, note that 86% of monetary allocations are corner solutions and 61% of subjects
have zero interior allocations in twenty decisions.25
Our non-parametric and parametric results closely mirror the aggregate findings of Andreoni
and Sprenger (2012a) and Gine et al. (2010).26 A potential concern of these earlier studies that
carefully control transaction costs and payment reliability, is that a payment in the present
was implemented by a payment in the afternoon of the same day, e.g. by 5:00 pm in the
subjects’ residence mailboxes in Andreoni and Sprenger (2012a). In this paper, because subjects
repeatedly have to come to the lab, a payment in the present is implemented by an immediate
cash payment. The fact that we replicate the earlier studies that carefully control for transaction
costs and payment reliability alleviates the concerns that payments in the afternoon are not
treated as present payments.
To summarize, we confirm the finding of limited present bias in the domain of money. This
the experimental design and is compromised by limited variation in delay length. In monetary discounting
experiments it is not unusual to find implied annual discount rates in excess of 100%.
25
A consequence of limited utility function curvature is that even a small degree of present bias can lead
potentially to sizable changes in allocation behavior through time as individuals may switch from one corner
solution to another. Hallmarks of this are seen in Table 2, which tabulates behavior across interest rates.
Though a wide majority of observations are dynamically consistent, some significant changes in budget shares
are seen at specific interest rates.
26
In both of these prior exercises substantial heterogeneity in behavior is uncovered. In subsection 3.3 we
conduct individual analyses, revealing similar findings.
22
could be either because the good in question, money, is fungible, a hypothesis for which we
find some evidence (recall that we estimate α to be around 0.975). Alternatively, it could be
because present bias in the form provided by models of dynamic inconsistency does not exist
or exists in only very limited form. This motivates our exploration of choices over effort, which
we believe is closer to consumption than money is.
3.2
Effort Discounting
Subjects make a total of 40 allocation decisions over effort in our seven week experiment.
Twenty of these decisions are made in the first block of the experiment, and twenty in the second
block. One focus of our design is testing whether participants identified as being present-biased
in Block 1 demand commitment in Block 2. Hence, we opt to present here allocation data from
only the first block of the experiment. This allows the prediction of commitment demand to
be conducted truly as an out-of-sample exercise. In Appendix E.5 we present results of present
bias from both blocks of the experiment and document very similar findings.
In Figure 5, we show for each value of R from et + R · et+k = 50, the amount of tasks
allocated to the sooner work date, Week 2, which could range from 0 to 50.27 We contrast
initial allocations of effort made in Week 1 with subsequent allocations made in Week 2 for the
80 subjects of the primary sample. Standard error bars are clustered at the individual level.
As with monetary discounting, subjects appear to have understood the central intertemporal
tradeoffs of the experiment as both initial and subsequent allocations decrease as R is increased.
At the individual level, 95% of choices are monotonically decreasing in R, and only 5 subjects
exhibit more than 5 non-monotonicities in their effort choices.28 This suggests that subjects as
27
The data are presented as a function of R from et + R · et+k = 50, as opposed to relative price, to provide
a standard downward sloping demand curve. Recall that R ∈ {0.5, 0.75, 1, 1.25, 1.5}. When R is low, sooner
tasks are relatively cheap to complete, and when R is high, sooner tasks are relatively expensive to complete.
28
Subjects have 32 opportunities to violate monotonicity comparing two adjacent values of R in their 40 total
CTB choices. 41 of 80 subjects are fully consistent with monotonicity and only 5 subjects have more 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 indicating upward
sloping sooner effort 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 effort relative
to money has several sources. Subjects may actually enjoy the tasks, they make more choices for effort than
23
Figure 5: Real Effort Discounting Behavior
Tetris
10
20
30
Tasks Allocated to Early Date
40
Greek Transcription
.5
1
1.5 .5
1
1.5
R
(from et+Ret+k=50)
Initial Allocation
Mean
Subsequent Allocation
Mean
SE
ytk
sb
h
p
ra
G
a whole understand the implied intertemporal tradeoffs and the decision environment.
Apparent from the observed choices is that at all values of R average subsequent allocations
lie below average initial allocations. Controlling for all R 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 tasks to the sooner work date than
they subsequently allocate (26.59 initial vs. 24.12 subsequent).29 Table 2, Panel B provides a
corresponding tabulation of behavior, presenting the budget share allocated to the sooner work
date and the proportion of choices that can be classified as present-biased. Budget shares for
the sooner work date are calculated as et /m for each allocation. Across all values of R, subjects
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).
29
The behavior is more pronounced for the first block of the experiment. For both blocks combined subjects allocate 25.95 tasks to the sooner date, 1.59 more tasks than they subsequently allocate (24.38 tasks),
representing a difference of around 6%, F (1, 79) = 15.16, (p < 0.01). See Appendix E.5 for detail.
24
initially allocate around 53% (s.e. = 0.97) of their experimental budget to the sooner work date
and subsequently allocate around 48% (1.02) to the sooner work date, when that sooner work
date is in the present, F (1, 79) = 14.87, (p < 0.01). Across all values of R, forty-seven percent
of choices are dynamically consistent, 33% are present-biased, and 21% are future-biased.30
Motivated by our non-parametric analysis we proceed to estimate intertemporal parameters.
Subjects allocate effort to an earlier date, et , and a later date, et+k . We again assume quasihyperbolic discounting and a stationary power cost function with Stone-Geary background
parameters to write the discounted costs of effort as
(et + ω)γ + β 1t=0 δ k (et+k + ω)γ .
(5)
Here γ > 1 represents the stationary parameter on the convex instantaneous cost of effort
function. The Stone-Geary term, ω, could be interpreted as some background level of required
work. For simplicity, we interpret ω as the required minimum work of the experiment and set
ω = 10 for our effort analysis. The variable 1t=0 is an indicator for whether or not the sooner
work date, t, is the present. As before, the parameter β captures the degree of present bias and
the parameter δ captures long run discounting.
Maximizing (5) subject to (1) (et,t + R · et+k,t = 50) yields an intertemporal Euler equation,
which can be rearranged to obtain
log(
log(β)
log(δ)
1
et + ω
)=
· (1t=0 ) +
·k−(
) · log(R).
et+k + ω
γ−1
γ−1
γ−1
(6)
As before, we assume an additive error structure and estimate the linear regression implied
by (6) using two-limit Tobit regression. The parameters of interest are again recovered from
non-linear combinations of regression coefficients with standard errors calculated via the delta
method. Appendix A provides detailed discussion of identification for such choices.31
30
Appendix Table A3 provides identical analysis using both blocks of data and reports very similar results.
The notation of Appendix A is slightly altered to discuss allocation timing and make links to partial
sophistication and the value of commitment for effort choices.
31
25
Table 3 columns (3) through (5) present two-limit Tobit regressions with standard errors
clustered on the individual level. In column (3) the analyzed data are the allocations for Job 1,
Greek Transcription. We find an estimated cost parameter γ = 1.624 (0.114). Abstracting from
discounting, a subject with this parameter would be indifferent between completing all 50 tasks
on one work date and completing 32 tasks on both work dates.32 This suggests non-fungibility in
the allocation of tasks as individuals do desire to smooth intertemporally. A further indication
of non-fungibility is that in contrast to the monetary choices, only 31% of allocations are at
budget corners and only 1 subject has zero interior allocations. The weekly discount factor of
δ = 0.993 is similar to our findings for monetary discounting.
In column (3) of Table 3 we estimate an aggregate β = 0.900 (0.037), and reject the null
hypothesis of dynamic consistency, χ2 (1) = 7.36, (p < 0.01). In column (4), we obtain broadly
similar conclusions for Job 2, the modified Tetris games. We aggregate over the two jobs in
column (5), controlling for the job, and again document that subjects are significantly presentbiased over effort.33 The results of column (5) indicate that discount rates measured in advance
of the Week 2 work date are around zero percent per week while discount rates measured on the
Week 2 work date are around eleven percent per week. We therefore confirm our non-parametric
findings on effort choices.
Finally, our implemented analysis allows us to compare present bias across effort and money
with χ2 tests based on seemingly unrelated estimation techniques. We reject the null hypothesis
that the β identified in column (5) over effort is equal to that identified for monetary discounting
in column (1), χ2 (1) = 6.37, (p = 0.01), or column (2), χ2 (1) = 8.27, (p < 0.01). Subjects are
significantly more present-biased over effort than over money.34
32
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.
33
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 individuals
are significantly less patient in their subsequent allocation decisions compared to their initial allocation decisions.
Appendix Table A10 provides estimates.
34
In Appendix E.5 we conduct identical analysis using both Blocks 1 and 2 and arrive at the same conclusions.
See Appendix Table A11 for estimates.
26
3.3
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 the individual level to understand the
extent to which present bias over effort and money is correlated within individual.
In order to investigate individual level discounting parameters we run fixed effect versions
of the regressions provided in columns (2) and (5) of Table 3.35 These regressions assume no
heterogeneity in cost or utility function curvature and recover individual parameter estimates
of β e , present bias for effort, and β m , present bias for money, as non-linear combinations
of regression coefficients. The methods for identifying individual discounting parameters are
discussed in Appendix A.36 Appendix Tables A5 and A6 provide individual estimates of β e and
β m along with a summary of allocation behavior for both effort and money for each subject.37
Figure 6 presents individual estimates and their correlation. First, note that nearly 60%
of subjects have an estimated β m close to 1, indicating dynamic consistency for monetary
discounting choices. This is in contrast to only around 25% of subjects with β e close to 1. The
mean value for β m is 0.99 (s.d. = 0.06), while the mean value for β e is 0.91 (s.d. = 0.20). The
difference 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 effort, they deviate in the
direction of present bias.
Since correlational studies (e.g., Ashraf et al., 2006; Meier and Sprenger, 2010) often use
35
We choose to use the measures of present bias based on three week delay choices for the monetary discounting
for continuity with our non-parametric tests of present bias. Further, when validating our individual measures,
we focus on allocations over three week delay decisions as in the presentation for the aggregate data. Very
similar results are obtained if we use the fixed effects versions of Table 3, column (1).
36
One technical constraint prevents us from estimating individual discounting parameters with two-limit Tobit
as in the aggregate analysis. In order for parameters to be estimable at the individual level with two-limit Tobit,
some interior allocations are required. As noted above, 86% of monetary allocations are at budget corners and
61% of the sample has zero interior allocations. For effort discounting, 31% of allocations are at budget corners
and 1 subject has zero interior allocations. To estimate individual-level discounting, we therefore use ordinary
least squares for both money and effort. Nearly identical aggregate discounting estimates are generated when
conducting ordinary least squares versions of Table 3. Curvature estimates, however, are sensitive to estimation
techniques that do and do not recognize that the tangency conditions implied by (6) and (4) may be met with
inequality at budget corners. Se Andreoni and Sprenger (2012a) for further discussion.
37
Appendix Tables A5 and A6 include data from the 9 subjects excluded from the primary study sample for
having no variation in experimental response in one or more weeks of the study. These subjects are noted along
with an explanation of which weeks they provided no variation in response.
27
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 β 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 ‘Present-Biased’m of 1. The difference in proportions of individuals classified
as present-biased over work and money is significant, z = 2.31, (p = 0.02).38
0
Fraction
.2 .4 .6
Figure 6: Individual Estimates of Present Bias
.75
Work Present Bias
1
1.25
1.5
.5
.75
Monetary Present Bias
1
1.25
1.5
.5
.75
Work Present Bias
1
1.25
1.5
Monetary Present Bias
.8 .9 1 1.11.2
0
Fraction
.2 .4 .6
.5
Two important 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
consistency of preferences across domains. Significant correlations would suggest that there may
be some important preference-related behavior uncovered in monetary discounting studies.39
38
Further, one can define future bias in a similar way. 17% of subjects are future biased in money while 29%
of subjects are future biased over effort. Similar differing proportions between present and future bias have
been previously documented (see, e.g., Ashraf et al., 2006; Meier and Sprenger, 2010). Two important counterexamples are Gine et al. (2010) who find almost equal proportions of present and future biased choices and
Dohmen, Falk, Huffman and Sunde (2006) who find a greater proportion of future-biased than present-biased
subjects.
39
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, produces similar neural
images to discounting over monetary rewards (McClure, Laibson, Loewenstein and Cohen, 2004; McClure et
28
Figure 6 presents a scatterplot of β m and β e . In our sample of 75 subjects with both complete
monetary and effort discounting choices, we find that β e and β m have almost zero correlation,
ρ = −0.05, (p = 0.66). Additionally, we find that the binary measures for present bias,
‘Present-Biased’e and ‘Present-Biased’m are also uncorrelated, ρ = 0.11, (p = 0.33).40
The second question concerning our estimated parameters is whether they can be validated
in sample. That is, given that β e and β m are recovered as non-linear combinations of regression
coefficients, to what extent do these measures predict present-biased allocations of tasks and
money? In order to examine this internal validity question, we generate difference measures for
allocations. For effort choices we calculate the budget share of each allocation for Week 2 effort.
The difference in budget shares between subsequent allocation and initial allocation is what we
term a ‘budget share difference.’41 As budget shares are valued between [0, 1], our difference
measure takes values on the interval [−1, 1]. Negative numbers indicate present-biased behavior
and values of zero indicate dynamic consistency. Each subject has 10 such effort budget share
difference measures in Block 1. The average budget share difference for effort is -0.049 (s.d.
= 0.115) indicating that subjects allocate around 5% less of their work budget to the sooner
work date when allocating in the present.42 At the individual level, 49 of 80 subjects have an
average budget share difference of less than zero, 13 have an average difference of exactly zero,
and 18 have an average difference greater than zero, demonstrating a modal pattern of present
bias.
A similar measure is constructed for monetary discounting choices. Taking only the three
week delay data, at each value of P we take the difference between the future allocation (Week 4
vs. Week 7 (Prospective)) budget share and the present allocation (Week 1 vs. Week 4 or Week
al., 2007).
40
Interestingly, when using both Blocks 1 and 2 of the data, we come to a slightly different conclusion. Though
β m and β e remain virtually uncorrelated, with the additional data we uncover a substantial and significant
correlation between Present-Biased’e and ‘Present-Biased’m ρ = 0.24, (p = 0.03). Further, ‘Present-Biased’m
is also significantly correlated with the continuous measure β e , ρ = −0.27, (p = 0.02). More work is needed to
understand the relationship between monetary and effort present bias parameters.
41
Specifically, given an initial Week 1 allocation of e2 of work to be done in Week 2 and a subsequent allocation
e0 −e
0
of e2 in Week 2 of work to be done in week 2, the budget share difference is 250 2 .
42
As noted previously, this average value deviates significantly from the dynamically consistent benchmark
of 0, F (1, 79) = 14.87, (p < 0.01).
29
4 vs. Week 7) budget share. This measure takes values on the interval [−1, 1], with negative
numbers indicating present-biased behavior. Each subject has 10 such monetary budget share
difference measures. The average budget share difference for money is -0.029 (s.d. = 0.134).43
At the individual level, 28 of 75 subjects have an average budget share difference of less than
zero, 32 have an average difference of exactly zero, and 15 have an average difference greater
than zero, demonstrating a modal pattern of dynamic consistency.
The non-parametric budget share difference measures are closely correlated with our parametric estimates at the individual level. The correlation between β e and each individual’s
average budget share difference for effort is ρ = 0.948, (p < 0.01). Of the 49 individuals with
negative average budget share differences for effort, 47 have estimates of β e < 1. Of the 18 individuals with positive average budget share differences for effort, all 18 have estimates of β e > 1.
Of the 13 individuals with zero average budget share differences for effort, 11 have β e = 1 and
2 have β e = 1.003 . The correlation between β m and each individual’s average Budget Share
Difference for money is ρ = 0.997, (p < 0.01). Of the 28 individuals with negative average
budget share differences for money, all 28 have estimates of β m < 1. Of the 15 individuals with
positive average budget share differences for money, all 15 have estimates of β m > 1. Of the 32
individuals with zero average budget share differences for money, all 32 have β m = 1.44 This
apparent internal validity gives us confidence that our parameter estimates for present bias are
indeed tightly linked with present-biased data patterns, appropriately capturing the behavior.
In the next section we move out-of-sample to investigate commitment demand. The investigation of commitment demand is critical to ruling out potential alternative explanations for
time inconsistency in effort allocations. Our preferred explanation is the existence of a present
bias in individual decision-making. However, many alternative explanations exist for rationalizing these data patterns. Chief among these alternatives are the existence of unanticipated
shocks to the cost of performing tasks (either in general or specific to tasks in Week 2), resolv43
As noted previously, this average value differs marginally significantly from the dynamically consistent
benchmark of 0, F (1, 74) = 3.50, (p = 0.07).
44
Appendix Tables A5 and A6 provide all the corresponding estimates and average budget share data.
30
ing uncertainty between allocation times, and subject exhaustion or error. These alternative
explanations are considered in detail in Appendix C. Importantly, we show in Appendix C that
under none of these alternatives would we expect a clear link between the behavioral pattern of
reallocating fewer tasks to the present and commitment demand. This is in contrast to a model
of present bias under the assumption of sophistication. Sophisticated present-biased individuals
may have demand for commitment. In the next section we document commitment demand on
the aggregate level and link commitment to measured present bias.
3.4
Commitment
In Week 4 of our experiment, subjects are offered a probabilistic commitment device. Subjects
are asked whether they prefer the allocation-that-counts to come from their Week 4 allocations
with probability 0.1 (plus an amount $X) or with probability 0.9 (plus an amount $Y), with
either $X=0 or $Y=0. The second of these choices represents commitment and $X - $Y is
the price of commitment.45 We begin by analyzing the simple choice between commitment
and flexibility at price zero ($X=0 and $Y=0) and in subsection 3.4.1 we explore the value
of commitment and choices when X or Y are not zero. In the simple choice where neither
commitment nor flexibility were costly, 59% (47/80) of subjects choose to commit. We define
the binary variable ‘Commit (=1)’ which takes the value 1 if a subject chooses to commit in
this decision.
Figure 7 presents Block 1 task allocation behavior separated by commitment choice in
Block 2. Immediately apparent from Figure 7 is that experimental behavior separates along
commitment choice. Subjects who choose commitment in Week 4 made substantially presentbiased task allocations in Week 2 given their initial Week 1 allocations. Controlling for all task
rate and task interactions, subjects who choose commitment allocate 3.58 fewer tasks to the
sooner work date when it is the present, F (1, 46) = 12.18, (p < 0.01). Subjects who do not
45
To avoid cutting the sample further, here we consider all 80 subjects in the primary sample. 4 of 80 subjects
switched multiple times in the commitment device price list elicitation. Identical results are obtained excluding
such individuals.
31
Figure 7: Commitment Choice and Allocation Behavior
Panel A: Commit (=0)
Tetris
10
20
30
Tasks Allocated to Early Date
40
Greek Transcription
.5
1
1.5 .5
1
1.5
R
(from et+Ret+k=50)
Initial Allocation
Mean
Subsequent Allocation
Mean
SE
ytk
sb
h
p
ra
G
Panel B: Commit (=1)
Tetris
10
20
30
Tasks Allocated to Early Date
40
Greek Transcription
.5
1
1.5 .5
1
1.5
R
(from et+Ret+k=50)
Initial Allocation
Mean
Subsequent Allocation
Mean
SE
ytk
sb
h
p
ra
G
demand commitment make more similar initial allocations and subsequent allocations of effort.
Controlling for all task rate and task interactions, they only allocate 0.89 fewer tasks to the
sooner work date when it is the present, F (1, 32) = 4.01, (p = 0.05). Furthermore, subjects
who demand commitment in Week 4 altered their allocations by significantly more tasks than
32
subjects who did not demand commitment, F (1, 79) = 5.84, (p = 0.02).46
Table 4 generates a similar conclusion with parametric estimates. In columns (3) and (4), we
find that subjects who choose commitment in Block 2 are significantly present-biased over effort
in Block 1, χ2 (1) = 9.00, (p < 0.01). For subjects who do not choose commitment, we cannot
reject the null hypothesis of β = 1 at conventional levels, χ2 (1) = 2.64, (p = 0.10). Further,
we reject the null hypothesis of equal present bias across committers and non-committers,
χ2 (1) = 4.85, (p = 0.03).47
In columns (1) and (2) of Table 4 we repeat this exercise, predicting commitment choice
for effort using present bias parameters from monetary decisions. While subjects who demand
commitment also seem directionally more present-biased for monetary decisions than subjects
who do not demand commitment, the difference is not significant, (p = 0.26).
These findings indicate that present bias in effort is significantly related to future commitment choice. Individuals who are present-biased over effort are substantially more likely to
choose commitment at price zero. An important caveat for this exercise is that correlation
is far from perfect. For example, the raw correlation between β e and commitment choice is
ρ = 0.225, (p = 0.04), implying an R-squared value of around 5%. Substantial variance in the
choice of commitment remains unexplained. There are several potential reasons for this lack of
46
When including the 9 subjects with insufficient variation, this relationship between commitment and presentbiased reallocations is no longer significant. Committers reallocate 0.90 (clustered s.e. = 1.32) fewer tasks to the
sooner work date when the sooner work date is the present compared to non-committers, F (1, 88) = 0.46, (p =
0.49). We believe this is due to the fact that the nine subjects with insufficient variation lie at the extremes of
changes in allocations in Block 1. Two of the nine would lie below the 5th percentile in budget share differences
(leading to β e estimates of 0.24 and 0.25) and one would lie above the 95th percentile (leading to a β e estimate
of 2.63). Removing these three extreme subjects, we find that committing subjects reallocate 2.19 (1.12) fewer
tasks to the sooner work date when it is the present compared to non-committers, F (1, 88) = 3.86, (p = 0.05).
47
These results are stronger for the first block of the experiment prior to the offering of the commitment
device, though the general patterns holds when we use both blocks of data. Appendix Table A12 provides
analysis including the data from both blocks. It is worth noting that the estimates of weekly discount factors, δ
also differ across committing and non-committing subjects. This difference is identified from differences in initial
allocations. Non-committing subjects have an average initial budget share for sooner tasks of 50.7% (clustered
s.e. = 1.6) and an average subsequent budget share of 49.0% (1.7), while committing subjects have an average
initial budget share of 54.9% (1.3) and an average subsequent share of 47.7% (1.4). Committing subjects’
behavior is consistent with δ > 1. However, we hesitate to draw any firm conclusions from this observation
as our experiment provides no variation in delay lengths to help identify δ. As discussed in Appendix A, δ is
identified from the constant one week delay between work dates. Hence, any level differences across subjects
are revealed as differences in estimated δ parameters.
33
Table 4: Monetary and Real Effort Discounting by Commitment
Monetary Discounting
Commit (=0) Commit (=1)
Effort Discounting
Commit (=0)
Commit (=1)
(1)
Tobit
(2)
Tobit
(3)
Tobit
(4)
Tobit
Present Bias Parameter: β
0.999
(0.010)
0.981
(0.013)
0.965
(0.022)
0.835
(0.055)
Weekly Discount Factor: (δ)7
0.978
(0.003)
0.981
(0.005)
0.917
(0.032)
1.065
(0.039)
Monetary Curvature Parameter: α
0.981
(0.009)
0.973
(0.007)
1.553
(0.165)
1.616
(0.134)
Cost of Effort Parameter: γ
# Observations
# Clusters
Job Effects
420
28
-
705
47
-
660
33
Yes
940
47
Yes
H0 : β = 1
χ2 (1) = 0.01
(p = 0.94)
χ2 (1) = 2.15
(p = 0.14)
χ2 (1) = 2.64
(p = 0.10)
χ2 (1) = 9.00
(p < 0.01)
H0 : β(Col. 1) = β(Col. 2)
χ2 (1) = 1.29
(p = 0.26)
H0 : β(Col. 3) = β(Col. 4)
χ2 (1) = 4.85
(p = 0.03)
Notes: Parameters identified from two-limit Tobit regressions of equations (4) and (6) for monetary discounting
and real effort discounting. Parameters recovered via non-linear combinations of regression coefficients. Standard errors clustered at individual level reported in parentheses, recovered via the delta method. Commit (=1)
or Commit (=0) separates individuals into those who did (1) or those who did not (0) choose to commit at a
commitment price of zero dollars. Effort regressions control for Job Effects (Job 1 vs. Job 2). Tested null hypotheses are zero present bias, H0 : β = 1, and equality of present bias across commitment and no commitment,
H0 : β(Col. 1) = β(Col. 2) and H0 : β(Col. 3) = β(Col. 4).
explanatory power. A natural first possibility is substantial naivete. Though our results suggest
at least partial sophistication, on average, many subjects may be naive with respect to their dynamic inconsistency. Further, among partially sophisticated individuals, there may be limited
correlation between behavior and beliefs such that individuals with both high and low values
of β e may share similar beliefs as to their future behavior. Third, there may be uncertainty
in the work environment uncontrolled by the researcher. Even sophisticated present-biased
34
individuals may wish to remain flexible. In subsection 3.4.1 and Appendix D we discuss uncertainty and the benefits of flexibility in detail, noting that the value of commitment is likely
influenced by the unmodeled benefits of flexibility. Fourth, the allocation decisions may be
subject to substantial noise, leading at least partially to a misestimation of preferences and a
misclassification of subjects. Each of these forces may be at play to certain degree, reducing our
ability to tightly measure present bias and the extent of sophistication. However, our finding
of a significant present bias and a correlation between present bias and commitment demand
points to at least partial sophistication for some subjects.
It is comforting for a theory of sophisticated present bias to find that present bias predicts
commitment demand. However, the result is only meaningful if we can show that commitment
places a binding constraint on subjects’ behavior. Do individuals who demand commitment
actually restrict their own activities, forcing themselves to complete more work than they
instantaneously desire?48 Given the nature of our commitment device, commitment will bind
whenever initial allocations differ from subsequent allocations. Two such comparisons are
considered. First, we consider the first block of the experiment when no commitment contract
is available. How many more tasks would subjects have been required to complete in Week 2
had commitment been in place? To answer this question we examine budget share differences
for Block 1. Non-committers have a mean budget share difference 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 difference of −0.072 (0.020),
allocating 7 percentage points less to Week 2 when deciding in the present. While both values
are significantly different from zero (F (1, 79) = 4.14, (p = 0.05), F (1, 79) = 12.39, (p <
0.01), respectively), the difference between the two is also statistically significant, F (1, 79) =
5.88, (p = 0.02). Hence, had commitment been in place in Week 2 and had subjects made the
48
Though our offered commitment contract allows individuals only to meaningfully restrict themselves, this
need not be the case. One example would be to have individuals commit to completing at least 1 task at the
sooner work date. As virtually all initial allocations and subsequent allocations satisfy this condition anyways,
such commitment would not be meaningful and as such, should not serve as evidence for the theoretically
predicted link between sophisticated present bias and commitment demand.
35
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 difference of 0.011 (0.017) while committers have a mean difference
of −0.030 (0.013). The difference for committers remains significantly different from zero,
F (1, 79) = 5.57, (p = 0.02), and the difference between the two remains significant at the
10% level F (1, 79) = 3.68, (p = 0.06).49 Hence, in the presence of commitment in Week 5,
committed subjects are required to complete significantly more work than they instantaneously
desire and are more restricted than non-committed subjects.
We are aware of two prior exercises exploring the potential extent of present bias and its
correlation with commitment demand. Kaur et al. (2010) link the apparently present-biased
behavior of working harder on paydays with demand for a dominated wage contract wherein
individuals choose a work target. If the work target is not met, an individual receives a low piecerate wage, while if it is met or exceeded the individual receives a higher piece rate wage. As the
dominated wage contract can be viewed as a commitment to complete a certain amount of work,
this represents a potential link between commitment and present bias. Commitment levels are
chosen by individuals themselves and are set to around one-sixth of daily production on average.
Calculations indicate that committing subjects would have missed their target with probability
around 0.091 in the absence of commitment, and do miss their target with commitment in
place with probability 0.026. Hence, commitment can viewed as binding in about 7.5 percent
of cases, effectively forcing an individual to do more work than they instantaneously desire.
Ashraf et al. (2006) consider hypothetical intertemporal choices over money, rice and ice cream
and link those to take-up of a savings commitment device. The authors show that present bias
in the hypothetical monetary decisions is significantly correlated at the 10% level with take-up
for women.
We contrast two dimensions of our study with these prior findings. The first concerns the
49
The difference for non-committers is no longer significantly different from zero F (1, 79) = 0.39, (p = 0.53).
36
techniques used to measure dynamic inconsistency, and the second is the extent to which subjects are bound by commitment. As opposed to monetary discounting measures or dynamic
inconsistency inferred from payday effects, we attempt to measure discounting directly with
intertemporal allocations of effort delivering identification. As opposed to commitments with
somewhat limited binding probabilities, our committing subjects are clearly bound by commitment.
3.4.1
The Value of Commitment
A natural question is how much should subjects be willing to pay for commitment. In Appendix
A we present the value of commitment, V , as the utility difference between the discounted
costs of commitment and flexibility. Given our experimental structure we can only assess
the monetary value of commitment. Virtually nobody is willing to pay more than $0.25 for
commitment, with 91 percent of subjects preferring flexibility when the price of commitment
is $0.25. Likewise, nobody is willing to pay more than $0.25 for flexibility, with 90 percent of
subjects preferring commitment when the price of commitment is -$0.25. Taking the midpoint
of each person’s price list switching interval, the data thus imply a median valuation of $0.125.50
For committers and non-committers, the median valuation is $0.125 and $-0.125, respectively.
What do these monetary valuations imply for the extent of V and correspondingly for the
extent of sophistication? In Appendix A, we theoretically investigate the valuation of commitment through the lens of the partially sophisticated quasi-hyperbolic model of O’Donoghue and
Rabin (2001). We recover the valuation of commitment, V , for stationary cost functions. This
analysis shows that the value of commitment is linked to the extent of sophistication, which
b reflecting an individual’s assessment of their future
is governed by sophistication parameter β,
b = 1, an individual is perfectly naive, and if β
b = β, an individual is perfectly
present bias. If β
b ∈ {β, 1} correspond to partial sophistication. That present bias
sophisticated. Values of β
is predictive of commitment demand at price zero indicates at least partial sophistication on
50
For this measure we exclude the four individuals with multiple switching.
37
b < 1.
average, β
b = β,
The level of V can be calculated directly for the fully sophisticated benchmark of β
which implies a perfect forecast for present-biased behavior. Using the parameters estimates of
Table 4, columns (3) and (4) and the actual allocations at R = 1, we can calculate the fullysophisticated value of commitment for committing and non-comitting subjects. For comitting
subjects, we calculate VC=1 = 1.23, which can be expressed in equivalent number of tasks as
c−1 (1.23) = 1.14 tasks. For non-comitting subjects, we calculate VC=0 = −2.06, which can be
expressed in equivalent number of tasks as -1.59 tasks.
To relate the value of roughly two tasks to mooney, note that on average, using minimum
work completion rate, subjects complete approximately 60 tasks per hour. Assuming earnings
of around $12 per hour and a constant task value, a subject would be willing to complete 1
task for around $0.20.51 Hence the monetary value of commitment should be around $0.23 for
committing subjects and the value of flexibility should be around $0.32 for non-committing
subjects. These values compare favorably to the monetary valuations reported above. Hence,
assuming complete sophistication and no additional benefits to flexibility, we predict monetary
commitment valuations reasonably close to the valuations expressed by subjects.52
We are hesitant to draw strong conclusions beyond the plausibility of sophistication from
our commitment valuation data. First, given the ex-post parameter estimates, our elicitation
procedure clearly was not optimized for fine price differentiations. Second, it is possible that
subjects largely followed the money in the elicitation, preferring either commitment or flexibility depending on which option provided additional payment. A direct experiment precisely
b is a clear next step that research in this vein should take.
identifying β
51
The assumption of constant per task reservation value is important. With convex costs an individual should
have a lower reservation value for the first task than the sixtieth. We opt to present the average valuation
recognizing the possibility that valuations could be either higher or lower. Appendix D analyzes the value of
commitment demand at a wide range of potential per task valuations to provide sensitivity analysis.
52
If individuals are fully sophisticated, monetary valuations for commitment should be close to those observed.
Naturally, evaluating β̂ > β lowers the value of commitment and for β̂ = 1 commitment should be worth exactly
zero. In Appendix D we analyze specific values of β̂ and corresponding valuations for commitment under various
assumptions for the transformation of V to dollars. This analysis also considers all allocations, not only those
at one interest rate. Clear from this exercise is that under the assumption of no additional benefits to flexibility,
only in extreme cases should commitment be worth more than a dollar.
38
3.5
Between Subjects Replication Exercise
A key contribution of our data is the documentation of limited present bias in the domain of
money and more substantial present bias in the domain of work. One interpretation is that
models of dynamic inconsistency are validated when tested in their relevant domain (consumption) and that choices over fungible monetary payments cannot easily speak to such models’
predictions.
However, in our within-subjects study, several design choices were made that might muddy
this interpretation. First, subjects faced different interest rates and forms of budget constraint
for effort and for money.53 Second, the delay lengths for money were three to six weeks, while
the delay lengths for effort were only one week. Third, subjects always completed their effort
allocations prior to completing their monetary allocations. Fourth, present bias is identified for
effort from only a dynamic choice, while present bias is identified for money from a combination
of static and dynamic choices.54 Fifth, for effort one allocation was chosen to be the allocationthat-counts from the initial and subsequent allocations with an asymmetric probability, while
for money each allocation could be the alllocation-that-counts with equal probability. Further,
the Week 4 monetary choices were paid separately from the Week 1 choices. Though each
design choice has a natural motivation, including our desire to replicate prior exercises, one
could potentially imagine them influencing the degree of dynamic inconsistency.55
To alleviate these concerns, we conducted a between subjects replication exercise. 200
subjects, again from the UC Berkeley Xlab subject pool, were randomized into two conditions:
53
That is, the constraint for effort was of a present value form, et + Ret+k = 50, while the constraint for
money was of a future value form, P ct + ct+k = 20.
54
That is, for effort to identify present bias one compares the Week 1 allocations over Weeks 2 and 3 to the
Week 2 choices over Weeks 2 and 3. For money to identify present bias one compares the Week 1 allocations
over Weeks 4 and 7 to the Week 4 choices over Weeks 4 and 7, the Week 1 allocations over Weeks 1 and 4
to the Week 1 allocations over Weeks 4 and 7, and the Week 1 allocations over Weeks 1 and 4 to the Week 1
allocations over Weeks 1 and 7.
55
The specific rationale for each choice, respectively: first, we expected substantially more curvature for effort
than money, which suggests different interest rates to avoid corner solutions. Second, we organized the monetary
choices around dates the subjects would come to the lab to equalize transactions costs. Third, our primary focus
was the effort choices, hence we sought to ensure theses data were collected. Fourth, we wished to replicate the
standard static evidence on present bias in money and benefited from an opportunity in Week 4 to additionally
generate dynamic evidence. Fifth and sixth, we did not wish to burden the subjects with another, potentially
complicated, procedure for determining which monetary decision would be implemented.
39
one in which allocations were made for money and one in which allocations were made for greek
transcription. In both conditions subjects selected into a four week study on decision-making
over time and were informed that their earnings would be approximately $60 if all aspects of the
study were completed. The main goal of the replication exercise is to keep allocation decisions
identical, with the only difference being whether allocations are over money or effort.
Mirroring our effort study, in Week 1 of the replication exercise subjects make allocations
over Weeks 2 and 3. In Week 2, subjects again make allocations over Weeks 2 and 3. All
allocations are made on a study website either in the lab in Week 1 or on any computer with
internet access in Week 2. In Week 2, one of the Week 1 or Week 2 decisions is chosen at
random, with each having equal probability, and the corresponding allocation is implemented.
For both effort and money, allocations are made using budgets of the form,
P a2 + a3 = m.
Where a2 refers to an allocation of either effort or money to Week 2 and a3 refers to
an allocation of either effort or money to Week 3.
For both effort and money P ∈
{0.66, 0.8, 0.91, 0.95, 1, 1.05, 1.11, 1.25, 1.54}, covering the interest rates used for both money
and effort from our initial experiment. For money m = $20 and for effort m = 60 tasks,
such that units are easily matched by dividing by three. Following our prior study, minimum
payments of $5 and minimum work of 10 tasks are implemented in Weeks 1, 2, and 3.
We attempt to put precise time stamps on both the completion of tasks and the collection of
money. For effort, subjects are told they must complete their tasks from the chosen allocation
on a study website between 9 am and 6 pm on the relevant day in Weeks 2 and 3. For
money, subjects are told they must collect their payments from the chosen allocation at the
UC Berkeley Xlab between 9 am and 6 pm on the relevant day in Weeks 2 and 3. To make
the Week 2 allocations as immediate as possible, subjects are additionally told in advance they
will have to either complete their Week 2 tasks or collect their Week 2 funds within two hours
of making their Week 2 allocations. Appendix G has the full study instructions.
40
If subjects complete all aspects of the study, including collecting their money or completing
their tasks on each relevant date within the relevant time window, they are eligible for a
completion payment paid in the fourth week of the study. For effort, the completion payment
is $60 with a non-completion payment of $5. For money, the completion payment is $30 with a
non-completion payment of $5. All payments, including those from monetary allocations, are
made in cash at the Xlab by a single research assistant who remained in place from 9 am to 6
pm on the relevant dates. All 200 subjects began the study on Thursday April 17, 2014. Of
these a total of 194 completed the study on Thursday May 1, 2014, with 95 from the effort
condition and 99 from the money condition.
In this between subjects design, we can directly compare present bias across conditions.
Figure 8 plots the amount of money in Panel A (out of $20) or the number of tasks in Panel B
(out of 60) and allocated to Week 3 for each level of P . Separate series are provided for when
the allocation is made in Week 1 and in Week 2. Note that because the budget constraints are
identical, Week 3 tasks are decreasing in P , while Week 3 money is increasing in P . Note as well
that due to the form of the budget, it is the constant-value Week 3 units that are graphed.56
Figure 8 closely reproduces our prior within-subject findings. For money mean behavior
appears almost perfectly dynamically consistent. Controlling for P , subjects allocate $0.14
(clustered s.e. = 0.12) less to Week 3 in Week 2 relative to Week 1, F (1, 98) = 1.37, p = 0.25.
In contrast, at each value of P , individuals appear present-biased for effort, allocating more
effort to the later date when the sooner date is the present. Controlling for P , subjects allocate
2.14 (clustered s.e. = 1.10) more tasks to Week 3 in Week 2 relative to Week 1, F (1, 94) =
3.82, p = 0.05. Appendix Table A4 provides a corresponding tabulation of behavior, presenting
budget shares and the proportion of choices that can be classified as present-biased.57
56
This is in contrast to the prior effort figures where earlier tasks had constant value and were graphed and
the prior money figures where earlier money was also graphed for ease of comparison.
57
For consistency with Table 2 and Appendix Table A3, Appendix Table A4 tabulates budget shares for the
sooner date, calculated as (P a2 )/m for each allocation. For money, subjects initially allocate around 51.4% (0.7)
of their experimental budget to the sooner payment and subsequently allocate around 51.9% (0.6) to the sooner
payment, F (1, 98) = 0.85, (p = 0.36). Eighty-three percent of individual choices are dynamically consistent,
10% are present-biased, and 7% are future-biased. For effort, subjects initially allocate around 52.4% (clustered
s.e. = 1.1) of their experimental budget to the sooner work date and subsequently allocate around 48.8% (1.7)
41
Figure 8: Between Subjects Replication Exercise
Panel B: Effort
0
15
20
Tasks Allocated to Later Date
25
30
35
Dollars Allocated to Later Date
5
10
15
40
20
Panel A: Money
.6
.8
1
1.2
P
(from Pa2+a3=20)
1.4
1.6
.6
Week 1 Allocation
Mean
.8
1
1.2
P
(from Pa2+a3=60)
Week 2 Allocation
Mean
1.4
1.6
SE
Non-parametric replication in hand, we now turn to estimation of aggregate utility parameters. In Table 5, we replicate the estimation exercise of Table 3 with the new between-subjects
data. The parameter values and corresponding conclusions are effectively unchanged. For
monetary present bias in column (1), we estimate β = 0.997 (clustered s.e. = 0.005), which
compares favorably to Table 3, column (2), which estimates β = 0.988 (0.009). Similar to
our within-subjects conclusion, we fail to reject the null hypothesis of dynamic consistency,
β = 1, for money, χ2 (1) = 0.50, (p = 0.48). Interestingly, we also find quite similar discount
factor and curvature estimates between Table 5, column (1) and Table 3, column (2). For effort
present bias in column (2), we estimate β = 0.892 (0.056), which compares favorably to Table
3, column (3) for greek transcription where β = 0.900 (0.037). Similar to our within-subjects
conclusion, we reject the null hypothesis of β = 1 for effort, χ2 (1) = 3.73, (p = 0.05). Again,
we find quite similar estimates for the auxiliary parameters between Table 5, column (2) and
to the sooner work date, F (1, 94) = 3.82, (p = 0.05). Twenty-five percent of individual choices are dynamically
consistent, 43% are present-biased, and 32% are future-biased.
42
Table 3, column (3). The analysis again allows us to compare present bias across effort and
money, and again we reject the null hypothesis that the β identified for money is equal to that
identified for effort, χ2 (1) = 3.50, (p = 0.06).58
Though these findings closely replicate our prior within-subjects data, it is important to
note that the data from this exercise yields somewhat less precise measures and test statistics
than our initial study. We hesitate to speculate as to the source of this imprecision, and draw
some comfort from the replication of the point estimates from our prior work.
Table 5: Replication Exercise Parameter Estimates
Monetary Discounting
Effort Discounting
Greek
(1)
(2))
Present Bias Parameter: β
0.997
(0.005)
0.892
(0.056)
Weekly Discount Factor: (δ)7
0.998
(0.001)
1.009
(0.005)
Monetary Curvature Parameter: α
0.952
(0.009)
Cost of Effort Parameter: γ
1.774
(0.167)
# Observations
# Clusters
1782
99
1710
95
H0 : β = 1
χ2 (1) = 0.50
(p = 0.48)
χ2 (1) = 3.73
(p = 0.05)
H0 : β(Col. 1) = β(Col. 2)
χ2 (1) = 3.50
(p = 0.06)
Notes: Parameters identified from two-limit Tobit regressions of equations (4) and (6) for monetary discounting
and effort discounting, respectively. Parameters recovered via non-linear combinations of regression coefficients.
Standard errors clustered at individual level reported in parentheses, recovered via the delta method. Chisquared tests used in last two rows.
58
Appendix Tables A7 and A8 provide individual estimates of β e and β m along with a summary of allocation
behavior for these subjects. Subjects with no variation in experimental response in a given week are also noted.
16 of 194 non-attriting subjects have no variation in experimental response in one or more weeks and 14 of these
subjects were in the effort condition. Importantly, the results of Table 5 are maintained if we eliminate such
subjects with no variation in one or more weeks. See Appendix Table A13 for detail.
43
4
Conclusion
Present biased time preferences are a core of behavioral research. The key hypothesis of diminishing impatience through time is able to capture a number of behavioral regularities at odds
with standard exponential discounting. Further, the possibility of sophistication provides an
important channel for policy improvements via the provision of commitment devices. With the
exception of only a few pieces of research, most evidence of dynamic inconsistency is generated
from experimental choices over time-dated monetary payments. When those are administered
in a way to keep transaction costs constant and uncertainty at bay, recent studies have found
limited evidence of dynamic inconsistency. However, such findings may not be appropriate to
reject a model defined over streams of consumption.
The present study attempts to identify dynamic inconsistency for choices over real effort.
We introduce a longitudinal design asking subjects to allocate and subsequently allocate again
units of effort 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, confirming earlier work. Second, in choices over effort, we find substantial
present bias. Subjects reallocate about 9% less work to the present than their initial allocation.
Corresponding parameter estimates generate a similar conclusion. Individuals are estimated to
be substantially present-biased in effort choices and significantly closer to dynamically consistent in choices over money. Third, we study commitment demand, documenting that at price
zero roughly 60% of subjects prefer commitment to flexibility. A key result is that these commitment decisions correlate significantly with previously measured present bias. Individuals
who demand commitment are significantly more present-biased in effort 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 meaningfully restricts activities.
Committed subjects are required to complete more effort than they instantaneously desire.
By documenting the link between experimentally measured present bias and commitment demand, we provide support for models of dynamic inconsistency with sophistication. Subjects
44
are potentially aware of their present bias and take actions to limit their future behavior.
We view our paper as providing a portable experimental method allowing tractable estimation of intertemporal preferences over consumption (effort) and correlating such preferences
with a meaningful, potentially constraining, 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 effort and, furthermore, is linked to
effort-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 not be well captured by models of dynamic inconsistency. For example, subjects
may wish to get a painful single experience over with immediately or postpone a single pleasure
(Loewenstein, 1987).59 Lastly and most importantly, though fungibility issues may be mediated
in the present design, the natural problems of arbitrage will still exist if subjects substitute
effort in the lab with their extra-lab behavior. The existence and use of such substitutes, like
avoiding doing laundry or homework in response to the experiment, will confound our measures
in much the same way as monetary studies. Discounting will be biased towards market interest
rates, present bias will be exhibited only if such rates change through time, and cost functions
will be biased towards linearity. Though our data suggest effort is less fungible than money,
one cannot say that extra-lab smoothing opportunities for effort are eliminated. Hence, one
should view our measures as lower bounds on the true extent of dynamic inconsistency and the
instantaneous cost of tasks. We want to, however, point out that to some extent such fungibility
will be present in many dimensions in which time inconsistency has been measured. Ultimately,
the best measure of time inconsistency will be one that predicts ecologically relevant decisions
across a broad set of environments. This suggests important avenues for future research.
59
This suggests a key anticipatory component of intertemporal behavior, potentially mediated by our design’s
use of minimum effort requirements and convex decisions.
45
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50
APPENDIX - NOT FOR PUBLICATION
A
Theoretical Structure and Identification Appendix
In the intertemporal allocation of effort and money, discounting and additional parameters can
be identified at either the aggregate or individual level under various structural assumptions.
In the following three appendix subsections we describe our theoretical environment, explore
the demand for commitment, demonstrate which experimental variation provides identification
of specific parameters of interest, and lay out methodology for estimation. A fourth subsection
presents estimation details for monetary discounting.
A.1
A.1.1
Effort Discounting
Allocation Timing
In the working over time experiment, subjects allocate effort to an earlier date, et , and a later
date, et+k , subject to the intertemporal budget constraint described in (1). Subjects make
allocations at two points in time, one at time s < t, and one at time t. The allocation-thatcounts is randomly implemented from time s with probability p and from time t with probability
1 − p.60 Let et,s be the allocation of effort to time t chosen at time s. Let es∗
t,t be the allocation
of effort to time t forecasted to be chosen at time t from the perspective of time s. That is, es∗
t,t
captures what an individual at time s believes they will optimally choose at time t.
A.1.2
Preferences
To develop our theory, we assume an instantaneous cost function, c(e), for effort, e, that is
time separable, stationary, and of an expected utility form with respect to the probability
that an allocation is implemented. To aid our development and foreshadow our empirical
60
We abstract from the fact that subjects make multiple allocations. Given the assumed separability over
time and in probabilities, this abstraction is innocuous.
1
implementation we also make a functional form assumption for the shape of c(·). We assume
c(e) = (e + ω)γ ,
where γ > 1 represents the stationary parameter on the convex instantaneous cost of effort
function. The additive term ω in the cost function could be interpreted as a Stone-Geary
minimum or as some background level of required work. Such parameters are used in monetary
discounting studies (Andersen et al., 2008; Andreoni and Sprenger, 2012a), and are either taken
from some external data source on background consumption or estimated from experimental
choices. For simplicity, we interpret ω as the required minimum work of the experiment and
set ω = 10 for our effort analysis.61
We assume discounting follows the quasi-hyperbolic partially sophisticated form proposed
by O’Donoghue and Rabin (2001). For two periods, t and t + k, discounting, D(t, t + k), is
captured by
D(t, t + k) =


 βδ k
if k > 0

 1
if k = 0.
The parameter β captures the degree of present bias while the parameter δ captures long run
discounting. β = 1 nests the standard model of exponential discounting. From period s < t,
the discounted costs of effort at times t and t + k can be written as
βδ t−s (et,s + ω)γ + βδ t+k−s (et+k,s + ω)γ .
61
Andreoni and Sprenger (2012a) provide estimates for ω based on non-linear least squares techniques and
analyze the extent to which different assumptions for ω influence remaining parameter estimates. Though utility
curvature and discounting are sensitive to varying assumptions for ω, present bias, β, is largely unaffected.
Andersen et al. (2008) also provide some sensitivity analysis.
2
Eliminating common terms, the decision problem at time s can be written as
p · [(et,s + ω)γ + δ k (et+k,s + ω)γ ] +
minet,s .et+k,s
k s∗
γ
γ
(1 − p) · [(es∗
t,t + ω) + δ (et+k,t + ω) ]
et,s + R · et+k,s = m,
s.t.
which yields the intertemporal Euler equation satisfied by the optimal allocation, (e∗t,s , e∗t+k,s ),
e∗t,s + ω γ−1 1
1
( ∗
)
= .
k
et+k,s + ω
R
δ
s∗
Note that the forecasted allocation, (es∗
t,t , et+k,t ), and the probability of implementation, p, do
not feature in the intertemporal Euler due to the assumed separability. Similarly, the decision
problem at time t can be written
minet,t .et+k,t
p · [(e∗t,s + ω)γ + βδ k (e∗t+k,s + ω)γ ] +
(1 − p) · [[(et,t + ω)γ + βδ k (et+k,t + ω)γ ]]
s.t.
et,t + R · et+k,t = m,
with corresponding Euler equation satisfied by the optimal allocation, (e∗t,t , e∗t+k,t ),
e∗t,t + ω γ−1 1
1
( ∗
)
=
k
et+k,t + ω
R
βδ
The prior allocation, (e∗t,s , e∗t+k,s ), and the probability of implementation do not feature in the
intertemporal Euler. Any differences in allocations between time s and time t are delivered by
the present bias term, β.62
62
A recent discussion of non-expected utility behavior in intertemporal settings has demonstrated that apparently present-biased behavior can be delivered by deviations from expected utility (see, e.g., Halevy, 2008).
Under discounted expected utility, allocations over two periods should depend on the ratio of probabilities with
which the allocations are realized. In two important conditions Andreoni and Sprenger (2012b) demonstrate in
the monetary domain that if sooner and later payments are paid independently with probability 0.5, behavior
deviates from the common ratio counterpart of all payments being certain. Under expected utility and atempo-
3
Combining our Euler equations we have
(
e∗t,D + ω γ−1
1
1
=
)
∗
1
k
et+k,D + ω
R
β D=t δ
(7)
where D ∈ {s, t} represents whether the allocation decision was made at time t or time s. Note
that for β < 1, an allocation made at time t at a given R will have a lower value of e∗t,D than
an allocation made at time s. A present-biased individual allocates less work to time t at time
t than they did at time s.
Naturally, the prediction that dynamically inconsistent behavior depends only on β relies
on the assumption of a stationary cost function. Changes in the cost function through time
could easily lead to differences in allocations between time s and t. Such changing costs could
be delivered by a variety of sources. For example, there could be permanent shocks to the cost
function, perhaps due to a misforecasting of task difficulty. There could also be temporary
shocks due to some random events that impose time constraints or leave subjects more tired
and exhausted than they normally are. In section C we address these concerns directly and
provide evidence that such possibilities are unlikely to drive observed behavior.
A.1.3
Partial Sophistication
We allow for the fact that individuals may be partially sophisticated with respect to their
own present bias. The nature of sophistication follows that of O’Donoghue and Rabin (2001),
b captures the belief an individual has on his future present bias: β
b = β represents full
where β
b = 1 represents full naivete, and β
b ∈ (β, 1) represents partial sophistication.
sophistication, β
ral applications of prospect theory, the deviations cannot be rationalized. An intuition for the effect is that the
independent payment probabilities give subjects the opportunity to hedge through time. Cheung (Forthcoming)
and Miao and Zhong (2012) demonstrate the importance of this intuition, as they show in the Andreoni and
Sprenger (2012b) setup that when one makes the two 0.5 realization probabilities perfectly correlated behavior
is closer to the expected utility benchmark. In our environment, the implementation probability applies equally
to both the sooner and later work date, creating perfect correlation through time. Hence, the effects of Andreoni
and Sprenger (2012b) are unlikely to be present. Additionally, because the same implementation probability
applies to both work dates, any non-linear treatment of p or 1 − p must be applied equally, and so drop out of
marginal conditions in exactly the same way that undistorted probabilities do. Further potential concerns with
respect to the asymmetry of p and 1 − p in the design are addressed in our replication exercise where initial and
subsequent allocations are implemented with equal probability. See section 3.5 for detail.
4
This means that allocations at time t, forecasted at time s < t are
s∗
γ
γ
∗
b k ∗
(es∗
t,t , et+k,t ) = argmin p · [(et,s + ω) + βδ (et+k,s + ω) ] +
γ
b k (es
(1 − p) · [(est,t + ω)γ + βδ
t+k,t + ω) ]
s.t.
est,t + R · est+k,t = m.
b ∈ (β, 1] an individual’s forecasted allocation, (es∗ , es∗ ) will not accord with their actual
If β
t,t t+k,t
subsequent allocation, (e∗t,t , e∗t+k,t ).
b is absent from the Euler formulations above. This is
Note the sophistication parameter, β
by construction both in the theory and the experimental design. An individual at time s may
forecast a level of present bias at time t but is incapable of controlling behavior at that point in
time. More importantly, this forecasted present bias at time t does not influence his behavior
at time s. The only actions available to the time t self is to complete the time s allocation
with probability p, complete the time t allocation with probability 1 − p, or opt out of the
experiment, foregoing $90. Given the high penalty, an individual at time s can appropriately
forecast the third action will not be taken. The individual is aware that he cannot control the
b absent
second action. Hence, he optimizes according to his time s preference as above with β
b will be important for our analysis of commitment in
from the formulation. The parameter β
which an individual at time s may indeed control time t behavior.
A.2
Commitment
In the second block of the experiment subjects are offered a probabilistic commitment device.
The commitment device favors the initial allocations made at time s over the subsequent
allocations made at time t by changing the time s implementation probability from p to 1 − p
(i.e. from 0.1 to 0.9).
Recall that intertemporal Euler equations and allocations are independent of implementation probabilities. Hence, the value of commitment can be arrived at by comparing discounted
5
costs. An individual prefers to commit if the discounted costs of the chosen allocation at time
s are smaller than the discounted costs of the forecasted allocation for time t at time s.63 The
value of commitment is given as
k
k
γ
s∗
γ
∗
γ
∗
γ
V = (1 − 2p) · βδ t−s · {[(es∗
t,t + ω) + δ c(et+k,t + ω) ] − [(et,s + ω) + δ c(et+k,s + ω) ]}.
Note that the value of commitment, V , depends upon both actual allocations and forecasted
allocations at time s. Hence, the value of commitment depends upon the degree of sophisticab = 1, (es∗ , es∗ ) = (e∗ , e∗ ). Actual and forecasted
tion. Clearly, for naive individuals with β
t,s t+k,s
t,t t+k,t
allocations are identical and the value of commitment is zero.
b ∈ [β, 1), actual allocations and forecasted allocations at
For sophisticated individuals, β
s∗
time s differ. By the definition of the minimum from the perspective of period s, (es∗
t,t , et+k,t )
yields higher discounted costs than (e∗t,s , e∗t+k,s ). This implies that the value of commitment
b diverges from 1, the value of
should be positive provided p < 0.5, as in the experiment. As β
commitment increases. Appendix D provides further detail and corresponding simulated values.
The extent of commitment demand, when combined with parametric measures for discounting
and costs, can be informative for the extent of sophistication.
Naturally, there may be intrinsic benefits to flexibility. These unmodeled benefits to flexibility could have many sources including future uncertainty in costs or task difficulty.64
63
The inequality between discounted costs
t+k−s
γ
γ
(1 − p) · [βδ t−s (e∗t,s + ω)γ + βδ t+k−s c(e∗t+k,s + ω)γ ] + p · [βδ t−s (es∗
c(es∗
t,t + ω) + βδ
t+k,t + ω) ] <
t+k−s
γ
γ
p · [βδ t−s (e∗t,s + ω)γ + βδ t+k−s c(e∗t+k,s + ω)γ ] + (1 − p) · [βδ t−s (es∗
c(es∗
t,t + ω) + βδ
t+k,t + ω) ],
reduces to the inequality,
k
γ
s∗
γ
(e∗t,s + ω)γ + δ k c(e∗t+k,s + ω)γ < (es∗
t,t + ω) + δ c(et+k,t + ω) ,
provided p < 0.5 as in the experiment. Subtracting the discounted costs one arrives at the value of commitment,
t+k−s
γ
γ
V = {p · [βδ t−s (e∗t,s + ω)γ + βδ t+k−s c(e∗t+k,s + ω)γ ] + (1 − p) · [βδ t−s (es∗
c(es∗
t,t + ω) + βδ
t+k,t + ω) ]} −
t+k−s
γ
γ
{(1 − p) · [βδ t−s (e∗t,s + ω)γ + βδ t+k−s c(e∗t+k,s + ω)γ ] + p · [βδ t−s (es∗
c(es∗
t,t + ω) + βδ
t+k,t + ω) ]}.
64
Note that in the presence of such factors even sophisticated present-biased subjects may have low or even
negative values for commitment. Hence, it is critical that our design elicits the demand for both flexibility and
6
The value of commitment, V , is measured in the same units as the discounted costs of
effort. A potential shortfall of our design is that our experiment does not measure V directly
but rather measures its translation into dollars. Hence, we provide potential bounds on V based
upon assumptions for the transformation of V to dollars.
A.3
Identification
From the intertemporal Euler equation, (7), identification of discounting and the cost function
is straightforward. Rearranging and taking logs yields
log(
log(β)
log(δ)
1
et,D + ω
)=
· (1D=t ) +
·k−(
) · log(R),
et+k.D + ω
γ−1
γ−1
γ−1
(8)
which is linear in the key experimental parameters of whether allocations are made at time
t, 1D=t , and the log transform, log(R). In our implementation, variation in log(R) delivers
identification of the cost function, γ; the allocation being made in Week 1 (D = s) rather than
Week 2 (D = t) delivers identification of present bias, β; and the delay length, k = 7 days,
gives identification of the discount factor, δ.65
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 (8). To be
specific, the regression equation is, for k = 7,
log(
et + ω
)i = η 0 k + η 1 · (1D=t )i + η 2 · log(R)i + i ,
et+k + ω
and we recover the parameters of interest as β = exp(η̂ 1 / − η̂ 2 ) and γ = 1 + 1/ − η̂ 2 . Note
that δ̂ = exp(η̂ 0 / − η̂ 2 ) is recovered from the constant as only one delay length was used in the
experimental design.
The parameters of interest can be recovered from non-linear combinations of regression
commitment to assess the possible presence of such factors.
65
Of course, with only one delay length of seven days considered in the experiment, we have limited confidence
that our estimate of δ can be extrapolated to arbitrary delay lengths.
7
coefficients with standard errors calculated via the delta method. One important issue to
consider in estimation is the potential presence of corner solutions. We provide estimates from
two-limit tobit regressions designed to account for the possibility that the tangency condition
implied by (8) does not hold with equality (Wooldridge, 2002).
Estimating (8) is easily extended to the study of individual parameters. To begin, (8) can
be estimated at the individual level.66 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
function. Consider a vector of fixed effects (1j )i which take the value 1 if observation i was
contributed by individual j. This leads to the fixed effects formulation
log(
log(δ)
(log(δ j ) − log(δ))
log(β)
et,D + ω
)i =
·k+
· (1j )i · k +
· (1D=t )i
et+k,D + ω
γ−1
γ−1
γ−1
+
(log(β j ) − log(β))
1
· (1D=t )i · (1j )i −
· log(R)i ,
γ−1
γ−1
where δ, β refer to sample means, and δ j , β j refer to individual-specific discounting parameters.
With an additive error structure this is easily estimable.67 The individual fixed effect interacted
with the decision being made in the present provides identification of the individual-specific
β j . In Appendix B we conduct simulation exercises under various correlation structures for the
true parameters of interest and document that the implemented estimation methods perform
well both at the aggregate and individual level.
A.4
Monetary Discounting
Our methods for recovering monetary discounting parameters at both the aggregate and individual level closely follow those for effort. Following most of the literature, we abstract from
standard arbitrage arguments for monetary discounting and assume laboratory administered
66
Broadly similar conclusions are reached when estimating (8) at the individual level, however, parameter
precision is greatly reduced and substantial estimate instability is uncovered in some cases.
67
We allow both β and δ to vary across individuals such that the implemented regression is a standard
interaction with both level and slope effects.
8
rates are the relevant ones.68 In particular, for monetary payments, ct and ct+k , allocated
subject to the constraint (2), we assume a quasi-hyperbolic constant relative risk averse utility
function,
U (ct,D , ct+k,D ) = (ct + ω)α + β 1D=t δ k (ct+k + ω)α .
(9)
Where D ∈ {s, t} refers to the same notation as before for when the allocation decision is made.
The utility function is assumed to be concave, α < 1, such that first order conditions provided
meaningful optima. Here, the parameter ω is a background parameter that we take to be the
$5 minimum payment of the monetary experiment.69
Maximizing (9) subject to the intertemporal budget constraint (2) yields an intertemporal
Euler equation similar to that above for effort. Taking logs and rearranging we have
log(
log(β)
log(δ)
1
ct,D + ω
)=
· (1D=t ) +
·k+(
) · log(P ).
ct+k,D + ω
α−1
α−1
α−1
(10)
Again, assuming an additive error structure, this can be estimated at the aggregate or individual
level via two-limit Tobit. Discounting and utility function parameters can be recovered via nonlinear combinations of regression coefficients as above with standard errors estimated again via
the delta method.
B
Simulation Appendix
This appendix focuses on two questions related to the estimation strategies laid out in Appendix A. First, we examine the extent to which the implemented estimators identify the true
68
The assumptions that individuals narrowly bracket time-dated experimental payments, treat money effectively as consumption, and ignore extra-lab arbitrage have been standard in the literature. One prominent
exception to this tradition is Harrison et al. (2002), who measure and account for extra-lab borrowing and
savings opportunities.
69
Andreoni and Sprenger (2012a) provide detailed discussion of the use of such background parameters and
provide robustness tests with differing values of ω and differing assumptions for the functional form of utility
in CTB estimates. They provide estimates for ω based on non-linear least squares techniques and analyze the
extent to which different assumptions for ω influence remaining parameter estimates. Though utility curvature
and discounting are sensitive to varying assumptions for ω, present bias, β, is largely unaffected. Andersen et
al. (2008) also provide some sensitivity analysis.
9
parameters of interest, β, δ and γ at the aggregate and individual level. As our individual
estimates restrict γ to be constant across subjects, this exercise is conducted under various
correlation structures for β and γ to understand the sensitivity of our parameter estimates to
this restriction. Further, the correlation structure also helps to investigate the sensitivity of
identifying β via a non-linear combination involving γ in the aggregate estimates.
Second, we investigate the sensitivity of aggregate and individual estimates to uncertainty.
Subjects may make allocations in Week 1 that minimize their discounted expected cost in future weeks given the potential 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 allocations. To explore the extent to which this issue hampers identification of present
bias, we conduct simulations under several uncertainty structures.
Our procedure for conducting the first simulation exercise is straightforward. We draw 100
samples of 80 individuals with underlying true parameters drawn from distributions centered
roughly around our aggregate estimates. That is, for each sample β is drawn from a normal
distribution with mean 0.9 and standard deviation 0.2; δ is drawn from a normal distribution
with mean 0.99 and standard deviation 0.2; and γ is drawn from a normal distribution with
mean 1.6 and standard deviation of 0.2. We introduce five correlation structures for the relationship between β and γ, ρ(β, γ) ∈ {−0.75, −0.25, 0, 0.25, 0.75}. For simplicity and to focus
attention on the sensitivity of present bias we assume ρ(β, δ) = 0 and ρ(δ, γ) = 0 when drawing
each sample.
For each of these correlation structures we conduct two key analyses. First, for every sample
b b
b over the
we estimate the aggregate parameters, β,
δ and γ
b. The empirical distribution of β
b the empirical standard deviation, s(β).
b
100 samples is summarized by the empirical mean, β,
Similar values summarize the empirical distributions of b
δ and γ
b. We investigate the extent
b correspond to the underlying data generating process by
to which the estimated values for β
10
b to the true mean β of 0.9. We also provide a measure of type I error in the form
comparing β
of the probability of rejecting β = 0.9 from each of our 100 drawn samples, 0.9 ∈
/ CI(β), and
a measure of type II error in the form of the probability of rejecting β = 1, 1 ∈
/ CI(β). Table
A1, Panel A provide these analyses. With zero correlation structure we precisely estimate
all parameters close to the true underlying distribution. We reject the truth with probability
around 0.10 and remain powered to reject β = 1. With extreme negative correlation of ρ(β, γ) =
−0.75, this precision is largely unaffected, though with extreme positive correlation of ρ(β, γ) =
0.75 the aggregate estimator falters. We begin to overestimate the extent of present bias
and reject the truth with frequency. This exercise documents the sensitivity of our aggregate
estimates to extreme correlation structures.
Next, we focus on individual estimates. Table A1, Panel A provides the results. In each
sample of 80 observations, we estimate individual parameters based on the fixed effects regression described in section A. We consider the median and mean level of the individual estimate
b and β
bmed , and the correlation between the true draw of β and the estimated value β
b,
b,β
β
i
i
i
i
i
bi ). For each of the 100 samples, we construct a correlation coefficient, and present the
r(β i , β
average value. Across correlation structures, we estimate broadly correct average and median
values. Importantly, even when the accuracy of the level of behavior deteriorates due to exb
treme negative correlation between β and γ, we find the correlation between the true β i and β
i
remains above 0.9. This indicates that the individual estimates remain capable of identifying
differences across individuals in present bias, providing a solid foundation for our individual
analysis.
The remainder of Table A1 analyzes the effect of uncertainty. We focus on uncertainty in
γ realized only in Week 2. Hence the Week 1 allocations are made under uncertainty that is
resolved in Week 2. To operationalize this exercise we again have β and δ drawn from the
distributions above in advance. However, we assume that in Week 1, subjects do not know
their true γ but optimize subject to the knowledge that γ is drawn from a normal distribution
with mean 1.6 and standard deviation of σ. We consider five values of σ ∈ {0, 0.05, 0.1, 0.2}.
11
In Panel B, we provide aggregate and individual analysis.. Though the aggregate estimates
and error rates are unaffected for the lower value of uncertainty, as parametric uncertainty is
increased, we begin to overestimate β and reject the truth with frequency. A similar pattern
is observed in the individual estimates. Importantly, the presence of parametric uncertainty
bi which drops below 0.3 in
greatly reduces the correlation between between the true β i and β
the more extreme case.
A natural question is why parametric uncertainty leads towards upward-biased estimates of
β, pushing away from present bias. Intuitively, a subject with parametric uncertainty attempts
to avoid situations of high work under extremely convex cost functions that are rarely realized.
As this encourages subjects to spread their initial allocations, we estimate a more convex cost
function. When the uncertainty is realized, they allocate less evenly over time on average, but
the cost function is required by the estimator to remain constant. This change in behavior in
Week 2 winds up being captured partially in the form of an increased β in our parameter space
of interest.
Table A1: Simulation Exercises
Aggregate Estimates
Simulations: δ ∼ N (0.99, 0.2 ), β ∼ N (0.9, 0.2 ), γ ∼ N (1.6, 0.22 )
Correlation Structure: r(β, γ) ∈ {−0.75, −0.25, 0, 0.25, 0.75}
Panel A:
b
β
N
r(β, γ)=0
r(β, γ)=-0.25
r(β, γ)=-0.75
r(β, γ)=+0.25
r(β, γ)=+0.75
80x100
80x100
80x100
80x100
80x100
N
=0
= 0.05
= 0.1
= 0.2
b
s(β)
.8828 .0242
.8884 .0235
.9169 .0235
.8712 .0228
.8541 .0265
2
0.9 ∈
/ CI(β)
1∈
/ CI(β)
γ
b
b
δ
βbi
bmed
β
i
b)
r(β i , β
i
11%
11%
13%
19%
45%
95%
98%
86%
96%
96%
1.552
1.552
1.537
1.556
1.545
.9955
.9960
.9955
.9957
.9953
.9080
.9113
.9359
.8997
.8872
.9077
.9029
.9071
.9116
.9103
0.971
0.965
0.931
0.971
0.964
Simulations: δ ∼ N (0.99, 0.22 ), β ∼ N (0.9, 0.22 ), γ ∼ N (1.6, σ 2 )
Uncertainty Structure: σ ∈ {0, 0.05, 0.1, 0.2}, Unrealized at Initial Allocation
Panel B:
σ
σ
σ
σ
Individual Estimates
2
b
β
b
s(β)
80x100 .8800 .0202
80x100 .9001 .0287
80x100 .9593 .0369
80x100 1.186 .0823
0.9 ∈
/ CI(β)
1∈
/ CI(β)
γ
b
b
δ
βbi
bmed
β
i
bi )
r(β i , β
13%
7%
26%
98%
94%
92%
17%
58%
1.601
1.608
1.632
1.736
.9957
.9949
.9952
.9957
.9044
.9336
1.022
1.367
.9017
.9122
.9539
1.164
0.995
0.824
0.590
0.325
12
C
Discussion of Potential Confounds
Our effort discounting data address several key confounds present in monetary studies, such as
fungibility and arbitrage issues. In this appendix section we address whether we can attribute
the observed behavior for effort choices to dynamic inconsistency. Foremost, the ability to
predict commitment demand based on present-biased allocations gives a degree of confidence
that present-biased allocations are driven by dynamic inconsistency. In the following, we discuss
four additional hypotheses that can generate time inconsistent effort allocations. These are
(unanticipated) permanent shocks to the cost function of performing the tasks, unanticipated
shocks to the cost function in Week 2, general uncertainty in cost functions, and simple mistakes.
Though none of these explanations would predict a correlation between time inconsistency and
commitment demand, we can also address these hypotheses directly.
First, subjects may make present-biased allocations in Week 2 not because they are presentbiased, but because their cost function for the tasks changed permanently. Maybe upon returning to the tasks they find them to be more or less difficult than they previously envisioned. For
example, this could be because they have an injury that makes typing harder, have a bigger
and better (or smaller and worse) screen at home than in the lab, which makes the tasks less
(more) onerous, etc.70 Though we do attempt to give subjects a sense of the tasks, this is a
plausible and critical confound. Our environment is 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 value of R. Because both initial allocations and subsequent
allocations are made at various interest rates, the cost function is identified at multiple points
and time. In Appendix Table A10, we estimate cost functions and discounting parameters at
each point in time. We do not find evidence that cost functions change over time.71 This lends
70
We see this channel as distinct from the role of uncertainty, as such changes in difficulty need not have been
forecasted.
71
The analysis of Appendix Table A10 can be conducted separately for committing and non-committing
subjects to examine if those individuals identified to be dynamically inconsistent in their commitment choice
have varying cost functions or varying discounting parameters over time. For committing subjects the weekly
discount factor measured in Week 1 is 1.082 (s.e. = 0.051), while the weekly discount factor measured in Week 2
is 0.900 (0.037). This difference is significant at the 1% level, χ2 (1) = 6.38 (p = 0.01). For committing subjects
13
credence to the notion that changes in cost functions are not driving the observed behavior.72
Second, subjects may reallocate fewer tasks to the present due to an unforeseen, local shock
that resulted in an increase in the cost function in Week 2 only. This could be because the
subject is unusually busy in Week 2 because of a surprise exam, or finds himself unusually
exhausted and hence unusually irritated with the length of work to be done. There are several
ways to address this concern. First, a simple way in which subjects may find it unusually difficult
to complete the work in Week 2 is if they log on to the experimental website so late, just prior
to midnight, that they have only a very limited opportunity to complete their tasks. We can
check for this hypothesis because we recorded the time at which subjects made their allocations.
The median subject completed their allocations in Week 2 with 10.3 hours remaining before
the imposed midnight deadline. Only 4 of 80 subjects completed their allocations in Week 2
with less than 2 hours remaining before the imposed midnight deadline and 0 of 80 completed
their allocations with less than 1 hour remaining. We therefore do not find evidence that a
physical time constraint is a driving force in the allocations.
However, subjects logging on later may indeed be those who experienced an unanticipated
shock in costs (even if their timing does not entail a physical constraint). We therefore examine
whether subjects who log on to our experimental website later in the evening of their Week
2 work date exhibit more present bias. Individuals who log on with less than 4 hours before
midnight (20 percent of our sample) are no more present-biased and have virtually identical
allocation behavior as others.73
the cost function parameter measured in Week 1 is γ = 1.739 (0.184), and in Week 2 is γ = 1.519 (0.121). This
difference is not significant at conventional levels, χ2 (1) = 2.53 (p = 0.11). This indicates that for subjects
separately identified as present-biased through their commitment choice, changing behavior through time is
more clearly linked to changing discounting parameters and not changing cost functions. No differences in
either discounting or cost functions are observed between Weeks 1 and 2 for non-committing subjects.
72
Note that if cost functions would change over time, and this were the unique driver for changes in allocations
between Week 1 and Week 2, we would observe a specific pattern of allocations. If an individual moved from
having an almost linear cost function to a very convex one, the corresponding allocations would shift from being
very price sensitive to limited price sensitivity. When initial allocations asked for lot of work to be done in
Week 2, we would indeed see a change that amounts to a reduction of work in Week 2. However, for allocations
that asked for little work in Week 2, we would see an increase in work to be done in Week 2. This is not what
we observe. The data show a universal reduction of work to be allocated in Week 2.
73
Subjects logging on with more than 4 hours before midnight allocate an average of 23.80 (s.d = 15.91) tasks
to the sooner work date in Week 2, while subjects logging on with less than 4 hours allocate 25.43 (14.06). Even
14
As a final way to assess whether some subjects may have had unusual shocks to their cost
function (and whether these are subjects that generate our results of present-biased allocations),
we can find a proxy for the costs of the tasks in Week 2. Specifically, we examine the amount
of time it takes subjects to complete their minimum work in Week 2. Minimum work took
the median subject around 18 minutes to complete. Those subjects who take longer than 25.7
minutes (20 percent of our sample) are no more present-biased and have virtually identical
allocation behavior as others.74 Naturally, these analyses may not give a fully satisfactory
response to the potential confound presented by forecasting error and boredom. If indeed such
a possibility is the source of our present-biased data patterns, a final question is whether or
not such a hypothesis delivers the observed correlation between present-bias and commitment
demand. We believe the answer to this question to be no.
A third class of explanations which can generate a pattern of present-biased behavior in
the absence of time inconsistency concerns uncertainty in cost functions. When making initial allocations, subjects do so under a different informational environment than when making
their subsequent allocations. There could be uncertainty for initial allocations, which is partially resolved when allocations are again made one week later. Several aspects of uncertainty
warrant attention. 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 effort experiment such a preference may more naturally lead to a future bias.
without accounting for multiple observations this difference is not significant, t(798) = 1.19, p = 0.24. Subjects
logging on with more than 4 hours before midnight have budget share differences between Weeks 1 and 2 of
-0.049 (0.21), indicating they allocate around 5 percent less of the budget of tasks to the sooner work date in
Week 2 than they allocated in Week 1. Subjects logging on with less than 4 hours have budget share differences
between Weeks 1 and 2 of -0.052 (0.20). Even without accounting for multiple observations this difference is
not significant, t(798) = 0.15, p = 0.88. Note however, that in general, subjects that log in later may be more
present-biased, as they do everything a little later. And indeed, if we instead cut at the median log-in time, 10.3
hours before midnight, marginally significant differences are observed indicating that present-biased individuals
may be logging in later. However, such individuals do not appear to be those particularly close to the deadline.
74
Subjects taking less than 25.7 minutes allocate an average of 24.11 (s.d = 15.43) tasks to the sooner work
date in Week 2, while subjects taking more than 25.7 minutes allocate 24.15 (16.11). Even without accounting
for multiple observations this difference is not significant, t(798) = 0.03, p = 0.98. Subjects taking less than
25.7 minutes have budget share differences between Weeks 1 and 2 of -0.049 (0.20), indicating they allocate
around 5 percent less of the budget of tasks to the sooner work date in Week 2 than they allocated in Week
1.Subjects taking more than 30 minutes have budget share differences between Weeks 1 and 2 of -0.053 (0.22).
Even without accounting for multiple observations this difference is not significant, t(798) = 0.23, p = 0.82.
15
Subjects desiring to resolve uncertainty in their subsequent allocation choices could, in principle, choose to complete their tasks immediately when the present is available. Second, our
discounting 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 Table A10 help to alleviate some concerns, a deeper problem
may exist. Subjects may make allocations in Week 1 that minimize their discounted expected
cost in future weeks given the potential 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 allocations. To explore the extent to which this issue hampers identification
of present bias, we conduct simulations under a variety of uncertainty structures in Appendix
B. Uncertainty, unresolved at initial allocation and realized at the time of the subsequent allocation, does bias our estimates of β both at the aggregate and individual level. However,
the direction of bias is generally upward in the parameter regions of interest, leading to less
estimated present bias.75 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.
Fifth, present-biased allocations of effort may be a simple decision error. Hence, present
bias, or any dynamic inconsistency, may be an unstable phenomenon. The two blocks of our
experiment speak to this possibility. Subjects have two opportunities to exhibit present-biased
allocations. Indeed, present-biased behavior in Block 1 and Block 2 is significantly correlated.76
At the allocation level, a subject who is present-biased in Block 1 is 58% more likely than others
75
Intuitively, subjects with unresolved 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 allocations to be
frequently lower than subsequent allocations, particularly at higher interest rates. Appendix B provides greater
detail.
76
Though the behavior is significantly correlated when examined as indicators for present bias, future bias
and dynamic consistency; the budget share differences are not significantly correlated through time. This may
be due to the sheer volume of data with budget share differences equal to zero and the relative lack of stability
for future-biased behavior.
16
to be present-biased in Block 2, F (1, 79) = 6.94, (p = 0.010).77 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).78
This discussion helps to clarify some of the potential confounds for our observed effects.
We view it as unlikely that present-biased allocations of effort are driven by unanticipated
permanent or temporary shocks, uncertainty, or decision error. Further, that present bias over
effort exhibits stability and predicts commitment demand gives confidence that our observed
effects are generated by dynamic inconsistency.
D
Commitment Value and Sophistication
We analyze the relationship between commitment valuations and sophistication by calculating
k
k
γ
s∗
γ
∗
γ
∗
γ
V = (1 − 2p) · βδ t−s · {[(es∗
t,t + ω) + δ c(et+k,t + ω) ] − [(et,s + ω) + δ c(et+k,s + ω) ]}.
at the estimated parameter values from Table 3, column (3) of γ = 1.6, δ = 1, and β = 0.9
b Differing values of β
b deliver different forecasted
under various assumptions for the value of β.
s∗
b
allocations (es∗
t,t , et+k,t ) and hence different values of V . As β diverges from 1, forecasted alloca-
tions differ more dramatically from initial allocations and the value of commitment grows. For
each value of V we calculate the equivalent number of tasks as
T γ = V.
77
Test statistic from OLS regression of binary indicator for a present-biased allocation in Block 2 on matched
indicator for present-biased allocation 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).
78
Test statistic from OLS regression of binary indicator for a dynamically consistent allocation in Block
2 on matched indicator for a dynamically consistent allocation 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 0.342 (s.e. = 0.048). Interestingly, somewhat less precision is found for future biased allocations.
An individual who is future-biased 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 regression of binary indicator for a future-biased allocation
in Block 2 on matched indicator for a future-biased allocation 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).
17
It is useful to go through the calculation similar to that in the main text, solving for T
given a set of parameters. Consider a subject with parameter values γ = 1.6, δ = 1, β = .9, and
ω = 10 (our maintained assumption), optimizing at R = 1 with m = 50 and the experimental
implementation probability of p = .1. Optimization at time s yields e∗t,s = e∗t+k,s = 25. A
s∗
subject with βbe = .9 perceives that she will choose es∗
t,t = 21.9 and et+k,t = 28.1. V can then be
calculated as
V = (0.8) · 0.9 · {[(21.9 + 10)1.6 + (28.1 + 10)1.6 ] − [(25 + 10)1.6 + (25 + 10)1.6 ]} = T 1.6
Solving for T yields 1.32 tasks.
This calculation does not take into account the fact that subjects make 10 allocations at
time s. Hence, the value of commitment should be expressed as the expectation of V across
these 10 allocations,
10
X
1
T = E[V ] =
Vi .
10
i=1
γ
For simplicity, we ignore the fact that the elicitation of commitment demand entails a second
stage price list randomization procedure.
Using this calculation and the parameters above, it is possible to solve for the equivalent
b In Table A2, we calculate T for various values
number of tasks, T , for a given value of β.
b at the parameter values noted above. For each T we also provide the monetary value
of β
b decreases, the value of
of commitment at a wide range of per-task values, w. Note that as β
commitment increases and that only in the extremes do commitment valuations exceed one or
two dollars.
18
b=1
β
b = .9
β
b = .8
β
b = .7
β
b = .6
β
b = .5
β
b and Per Task Valuations
Table A2: Commitment Values, β
b
Value of Commitment Given Different β
Equiv. # of Tasks
Monetary
T
w = $0.10
w = $0.20
w = $0.30
w = $0.40
(˜$6/hour) (˜$12/hour) (˜$18/hour) (˜$24/hour)
0
$0.00
$0.00
$0.00
$0.00
1.2
$0.12
$0.23
$0.34
$0.46
2.9
$0.29
$0.59
$0.88
$1.18
5.3
$0.53
$1.06
$1.59
$2.12
8.2
$0.82
$1.64
$2.46
$3.28
11.7
$1.17
$2.35
$3.52
$4.69
19
w = $0.50
(˜$30/hour)
$0.00
$0.57
$1.47
$2.64
$4.10
$5.87
E
E.1
Additional Tables and Figures
Tabulations of Dynamic Consistency
The following tables provide tabulations of each experimental interest rate or task rate for
money and effort and two measures of dynamic inconsistency. First, the average budget share
to either the sooner payment or sooner work date is contrasted across allocation timing and,
second, the proportion of subjects who are present-biased, dynamically consistent, and futurebiased is provided. Separate tables are provided for the the full set of experimental data and
the replication exercise.
20
Table A3: Aggregate Behavior By Interest Rate, Full Data Set
Panel A: Monetary Choices
P
0.952
1
1.11
1.25
1.429
Overall
t 6= 0
t=0
Budget Share Budget Share
(1)
(2)
t-test
(p-value)
(3)
Proportion
Present-Biased
(4)
Proportion
Dynamically Consistent
(5)
Proportion
Future-Biased
(6)
0.073
0.813
0.113
0.200
0.660
0.140
0.180
0.733
0.087
0.113
0.853
0.033
0.100
0.847
0.053
0.133
0.781
0.085
0.924
(0.228)
0.774
(0.368)
0.102
(0.259)
0.051
(0.177)
0.053
(0.182)
0.923
(0.189)
0.813
(0.323)
0.148
(0.300)
0.087
(0.239)
0.077
(0.228)
0.07
(p=0.94)
1.32
(p=0.19)
1.86
(p=0.06)
1.97
(p=0.05)
1.40
(p=0.16)
0.381
(0.461)
0.410
(0.458)
1.87
(p=0.07)
Panel B: Effort Choices
R
0.5
0.75
1
1.25
1.5
Overall
Initial
Subsequent
Budget Share Budget Share
(1)
(2)
t-test
(p-value)
(3)
Proportion
Present-Biased
(4)
Proportion
Dynamically Consistent
(5)
Proportion
Future-Biased
(6)
0.291
0.494
0.216
0.375
0.384
0.241
0.231
0.653
0.116
0.297
0.509
0.194
0.278
0.525
0.197
0.294
0.513
0.193
0.796
(0.179)
0.729
(0.208)
0.533
(0.152)
0.293
(0.232)
0.244
(0.234)
0.768
(0.207)
0.694
(0.240)
0.494
(0.181)
0.260
(0.235)
0.222
(0.231)
2.95
(p<0.01)
3.11
(p<0.01)
3.87
(p<0.01)
2.74
(p<0.01)
1.81
(p=0.07)
0.519
(0.301)
0.488
(0.311)
3.90
(p<0.01)
Notes: Panel A tabulates t 6= 0 and t = 0 budget shares for sooner payments for each P in money. Each row
calculates from 75 t 6= 0 allocations (one at each interest rate in the Week 4 vs. Week 7 prospective choices)
and 150 t = 0 allocations (one at each interest rate in the Week 4 vs. Week 7 actual and Week 1 vs. Week 4)
choices. Paired t-tests with 149 degrees of freedom presented. Panel B tabulates initial and subsequent budget
shares for sooner tasks for each R in effort. Each row calculates from 320 initial allocations (one each for tetris
and greek at each task rate in each round) and 320 subsequent allocations. Paired t-tests with 159 degrees of
freedom presented. Overall tests in both panels come from regression of budget share on allocation timing with
standard errors clustered on individual level. Test statistic is t-statistic testing the null hypothesis of no effect
of allocation timing, which controls for multiple comparisons.
21
Table A4: Aggregate Behavior By Interest Rate, Replication Exercise
Panel A: Monetary Choices
P
0.666
0.8
0.909
0.952
1
1.053
1.111
1.25
1.538
Overall
Initial
Subsequent
Budget Share Budget Share
(1)
(2)
t-test
Proportion
(p-value) Present-Biased
(3)
(4)
0.932
(0.174)
0.929
(0.172)
0.917
(0.186)
0.908
(0.190)
0.621
(0.336)
0.105
(0.240)
0.086
(0.207)
0.064
(0.162)
0.062
(0.171)
0.935
(0.182)
0.945
(0.153)
0.917
(0.194)
0.901
(0.206)
0.695
(0.302)
0.084
(0.212)
0.088
(0.226)
0.064
(0.182)
0.048
(0.150)
0.39
(p=0.70)
1.77
(p=0.07)
0.03
(p=0.97)
0.55
(p=0.58)
2.37
(p=0.02)
1.05
(p=0.30)
0.25
(p=0.81)
0.07
(p=0.95)
1.71
(p=0.09)
0.514
(0.451)
0.520
(0.456)
0.92
(p=0.36)
Proportion
Dynamically Consistent
(5)
Proportion
Future-Biased
(6)
0.091
0.879
0.030
0.081
0.859
0.061
0.101
0.828
0.071
0.152
0.788
0.061
0.232
0.667
0.101
0.081
0.828
0.091
0.081
0.869
0.051
0.071
0.869
0.061
0.020
0.879
0.101
0.101
0.829
0.070
Proportion
Dynamically Consistent
(5)
Proportion
Future-Biased
(6)
0.400
0.305
0.295
0.421
0.242
0.337
0.453
0.189
0.358
0.474
0.221
0.305
0.337
0.358
0.305
0.463
0.200
0.337
0.474
0.211
0.316
0.400
0.253
0.347
0.400
0.305
0.295
0.425
0.254
0.322
Panel B: Effort Choices
P
0.666
0.8
0.909
0.952
1
1.053
1.111
1.25
1.538
Overall
Initial
Subsequent
Budget Share Budget Share
(1)
(2)
t-test
Proportion
(p-value) Present-Biased
(3)
(4)
0.337
(0.203)
0.385
(0.196)
0.432
(0.191)
0.458
(0.175)
0.522
(0.153)
0.581
(0.194)
0.618
(0.195)
0.658
(0.210)
0.727
(0.220)
0.318
(0.232)
0.361
(0.223)
0.405
(0.219)
0.418
(0.220)
0.507
(0.211)
0.554
(0.235)
0.566
(0.239)
0.603
(0.255)
0.667
(0.280)
1.09
(p=0.27)
1.25
(p=0.21)
1.21
(p=0.23)
1.96
(p=0.05)
0.58
(p=0.56)
1.18
(p=0.24)
2.37
(p=0.02)
2.29
(p=0.02)
2.38
(p=0.02)
0.524
(0.229)
0.489
(0.260)
1.95
(p=0.05)
Notes: Panel A tabulates initial and subsequent budget shares for sooner payments for P in money. Each row
calculates from 99 initial allocations and 99 subsequent allocations choices. Paired t-tests with 98 degrees of
freedom presented. Panel B tabulates initial and subsequent budget shares for sooner tasks for each P in effort.
Each row calculates from 95 initial allocations and 95 subsequent allocations. Paired t-tests with 94 degrees of
freedom presented. Overall tests in both panels come from regression of budget share on allocation timing with
standard errors clustered on individual level. Test statistic is t-statistic testing the null hypothesis of no effect
of allocation timing, which controls for multiple comparisons.
22
E.2
Individual Estimates
We contrast initial and subsequent allocations for work and for money within subjects for the
80 subjects in the primary study sample and the 75 subjects with complete monetary data.
Estimates of present bias for each subject are also provided. Corresponding allocations and
estimates also provided for between subjects replication study.
23
Table A5: Individual Estimates Subjects 1-45
Subject #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25∗
26
27
28
29
30
31
32∗
33
34
35
36∗
37
38
39
40
41
42
43
44
45
Effort Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(1)
(2)
.5
.496
.522
.534
.516
.514
.514
.576
.514
.5
.5
.5
.628
.462
.542
.5
.5
.468
.582
.504
.51
.482
.5
.832
.56
.52
.648
.642
.588
.552
.51
.432
.5
.526
.496
.516
.666
.792
.514
.516
.536
.6
.514
.522
.514
.5
.476
.516
.498
.402
.512
.514
.472
.5
.5
.52
.5
.486
.512
.414
.5
.4
.404
.296
.48
.424
.344
.51
.512
.518
.404
.514
.254
.51
.5
.498
0
.5
.478
.4
.522
.5
.746
.54
.516
.51
.6
.512
.514
.51
βe
(3)
1
.952
.983
.86
.731
.995
1
.742
.959
1
1.078
1
.664
1.143
.683
1
.725
.796
.437
.884
.739
.665
1.012
.426
.815
.731
.698
.319
.724
.851
.961
.249
1
.842
.723
1.045
.638
.879
1.072
1
.945
1
.995
.976
.991
Monetary Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(4)
(5)
.4
.527
.4
.309
.4
.4
.4
.
.
.4
.4
.4
.4
.3
.4
.4
.4
.4
.4
.4
.4
.4
.294
.4
.4
.
.2
.4
.2
.4
.3
.4
.4
.4
.2
.4
.3
.457
.51
.4
.206
.4
.4
.531
.4
.3
.537
.3
.354
.4
.4
.4
.
.
.4
.4
.4
.4
.456
.4
.4
.4
.3
.3
.4
.4
.4
.376
.415
.3
.
.407
.513
.3
.4
.4
.4
.4
.5
.35
.7
.35
.5
.45
.4
.428
.4
.666
.532
.3
βm
(6)
1.046
.999
1.046
.979
1
1
1
.
.
1
1
1
1
.934
1
1
1
1.046
1.046
1
1
1
.964
.999
1.046
.
.914
.961
.956
1
.956
1
1
.957
.935
.88
.978
.983
1.02
1
.91
1
.897
1
1.046
Notes: Tabulates initial and subsequent budget shares for both effort and money and corresponding present
bias estimates for subjects 1-45 of 89 non-attriting subjects and 84 subjects with complete monetary data. Nine
subjects excluded from primary sample marked with ∗ . Subject 25 provided no variation in response in Weeks
4 or 5. Subject 32 provided no variation in Week 2. Subject 36 provided no variation in Week 5.
24
Table A6: Individual Estimates Subjects 46-89
Subject #
46
47∗
48
49∗
50∗
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69∗
70
71
72∗
73
74
75
76
77
78
79
80
81
82∗
83
84
85
86
87
88
89
Effort Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(1)
(2)
.512
.34
.508
.514
1
.59
.548
.506
.5
.514
.354
.896
.512
.474
.24
.5
.518
.57
.55
.5
.604
.42
.546
.4
.47
.46
.22
.512
.5
.44
.544
.594
.52
.53
.72
.542
.754
.5
.512
.504
.46
.514
.51
.5
.36
.27
.518
.516
.844
.692
.5
.38
.5
.514
.444
.502
.504
.48
.21
.6
.5
.5
.6
.4
.524
.4
.552
0
.5
.476
0
.516
.5
.51
.506
.626
.5
.518
.056
.508
1
.49
.5
.538
.504
.458
.51
.5
βe
(3)
.654
.818
1.024
1.006
.603
1.174
.979
.686
1
1.003
1.32
.291
.983
1.027
.876
1.379
1.086
.788
1.174
.725
.788
.957
1.019
.238
1.132
1.092
.429
1.005
1
1.203
.802
1.114
.964
.973
.14
.912
2.629
.973
1.107
1.091
1.12
.935
1.003
1
Monetary Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(4)
(5)
.509
.4
.4
.4
.4
0
.4
.403
.4
.4
.201
.4
.203
.4
.4
.4
.4
.4
.2
.2
.4
.
0
.4
.6
.6
.539
.2
.4
.4
1
.2
.4
.52
.9
.499
.2
.
.4
.4
0
.4
.4
.4
.743
.3
.4
.4
.3
.2
.4
.306
.4
.147
.256
.4
.405
.4
.4
.4
.8
.45
.4
.3
.4
.
.471
.4
.4
.5
.851
.198
.4
.35
.5
.2
.4
.5
.959
.409
.1
.
.4
.4
.303
.4
.4
.5
βm
(6)
.91
1.046
1
1
1.046
.913
1
1.044
1
1.121
.976
1
.92
1
1
1
.842
.979
.914
.956
1
.
.814
1
1.092
1.045
.873
1.001
1
1.023
1.236
1
1
1.007
.973
1.041
1.047
.
1
1
.87
1
1
.957
Notes: Tabulates initial and subsequent budget shares for both effort and money and corresponding present
bias estimates for subjects 51-89 of 89 non-attriting subjects and 84 subjects with complete monetary data.
Nine subjects excluded from primary sample marked with ∗ . Subject 47 provided no variation in response in
Week 5. Subject 49 provided no variation in Week 5. Subject 50 provided no variation in Week 1. Subject 69
provided no variation in Week 2. Subject 72 provided no variation in Weeks 2, 4 or 5. Subject 82 provided no
variation in Weeks 2 or 5.
25
Table A7: Replication Study Individual Estimates Subjects 1-50
Subject #
1
2
3
4
5∗
6∗
7
8
9∗
10
11
12
13
14
15
16
17
18∗
19
20
21
22
23
24
25
26
27
28
29
30
31
32∗
33∗
34
35
36
37
38
39
40
41
42∗
43∗
44
45∗
46
47
48
49
50
Effort Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(1)
(2)
.444
.528
.556
.463
.072
.578
.575
.5
.258
.509
.542
.484
.427
.502
.579
.556
.693
.499
.665
.509
.526
.558
.494
.423
.508
.502
.402
.5
.529
.283
.551
.498
.509
.598
.518
.527
.604
.814
.509
.528
.507
.52
.747
.561
.68
.517
.486
.5
.568
.488
.556
.774
.552
.5
0
.258
.556
.5
.606
.501
.423
.523
.25
.502
.593
.444
.553
.504
.603
.362
.31
.441
.487
.475
.53
.506
.39
.5
.553
.486
.486
.83
1
.621
.505
.407
.659
.798
.52
.537
.506
0
0
.504
0
.598
.518
.502
.742
.51
βe
Subject #
(3)
1.502
2.126
.958
1.12
.753
.369
.888
1
2.835
.98
.703
1.129
.586
1
1.043
.666
.647
1.002
.84
.644
.527
.674
.976
1.144
1.076
1.022
.963
1
1.072
1.824
.827
2.87
6.087
1.103
.959
.727
1.181
.906
1.04
.98
.999
.153
.071
.818
.091
1.422
1.157
1.005
1.776
1.064
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20∗
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Monetary Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(4)
(5)
.499
.444
.55
.492
.522
.555
.555
.497
.555
.499
.489
.555
.555
.555
.301
.499
.555
.499
.507
.497
.345
.555
.5
.499
.499
.499
.499
.499
.555
.499
.444
.499
.499
.444
.499
.499
.555
.555
.499
.555
.444
.499
.494
.499
.555
.666
.499
.499
.444
.499
.555
.444
.495
.532
.527
.555
.666
.502
.555
.499
.499
.555
.555
.555
.444
.499
.555
.499
.438
.499
.363
.555
.501
.499
.555
.499
.499
.499
.418
.501
.555
.488
.555
.555
.499
.499
.499
.555
.499
.555
.555
.555
.555
.499
.555
.452
.499
.499
.444
.555
βm
(6)
.965
1
1.036
.978
.997
1
.932
.997
1
1
.991
1
1
1
.909
1
1
1
1.044
.999
.989
1
1
1
.965
1
1
1
1.097
.999
.931
1.006
.965
.931
1
1
1.036
1
1
1
.931
.965
.96
1
1
1.148
1
1
1
.965
Notes: Tabulates initial and subsequent budget shares and corresponding present bias estimates for both effort
and money for between subjects data for first 50 of 99 money subjects and first 50 of 94 effort subjects
26
Table A8: Replication Study Individual Estimates Subjects 51-99
Subject #
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77∗
78
79
80
81∗
82
83
84∗
85∗
86
87
88∗
89
90
91
92
93
94
95
Effort Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(1)
(2)
.505
.493
.632
.5
.411
.588
.296
.538
.574
.502
.574
.685
.794
.448
.554
.493
.5
.505
.574
.433
.489
.595
.496
.512
.462
.49
.67
.572
.755
.503
.283
.477
.634
.344
.667
.517
.497
.516
.505
.528
.503
.641
.514
.571
.581
.741
.493
.591
.502
.333
.542
.334
.526
.514
.499
.586
.654
.528
.46
.53
.491
.498
.516
.632
.348
.499
.551
.516
.176
.476
.603
.67
.553
.273
.512
0
.503
.341
.501
.667
.509
.48
.597
.504
.539
.401
.506
.495
.518
.243
Subject #
βe
(3)
2.438
1
.863
1
.805
.866
1.112
.924
.826
.985
1.027
.831
.369
1.043
.892
.992
1
1.03
1.188
.777
1.028
.885
1.053
.353
.994
1.39
1.011
.983
.231
1.016
.308
1.076
.424
1.577
1
.982
.955
1.321
.995
1.033
.753
.677
.951
.862
.364
51
52
53
54
55
56∗
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
Monetary Choices
Mean Initial Mean Subsequent
Budget Share
Budget Share
(4)
(5)
.503
.465
.555
.555
.493
.699
.555
.555
.555
.555
.555
.555
.555
.499
.555
.444
.555
.562
.499
.555
.444
.476
.555
.72
.444
.499
.444
.555
.555
.499
.777
.503
.499
.384
.555
.499
.444
.444
.555
.533
.289
.444
.555
.499
.499
.472
.499
.444
.666
.481
.536
.555
.555
.534
.337
.555
.555
.555
.555
.499
.555
.555
.499
.555
.499
.555
.617
.499
.545
.555
.515
.555
.749
.555
.555
.444
.555
.555
.499
.666
.512
.499
.477
.555
.499
.499
.499
.555
.533
.281
.555
.555
.499
.499
.383
.499
.444
.555
βm
(6)
1.013
.961
1
1
.977
1.199
1
1
1
1
1.036
1
1
1
1
.965
1
.971
1
1.009
.931
.973
1
.976
.931
.965
1
1
1
1
1.073
.995
1
.953
1
1
.965
.965
1
1.006
1.005
.931
1
1
1
1.048
1
1
1.073
Notes: Tabulates initial and subsequent budget shares and corresponding present bias estimates for both effort
and money for between subjects data for subjects 51-99 of 99 money subjects and first 51-94 of 94 effort subjects
27
E.3
Estimates Including Nine Subjects With Limited Effort Allocation Variation
We re-conduct the primary aggregate analysis including 9 subjects with limited variation in
their effort allocation choices.
Table A9: Parameter Estimates Including 9 Additional Subjects
Monetary Discounting
Effort Discounting
(1)
All Delay
Lengths
(2)
Three Week Delay
Lengths
(3)
Job 1
Greek
(4)
Job 2
Tetris
(5)
Combined
Present Bias Parameter: β
0.975
(0.008)
0.988
(0.008)
0.870
(0.045)
0.848
(0.042)
0.858
(0.040)
Weekly Discount Factor: (δ)7
0.988
(0.002)
0.979
(0.003)
0.996
(0.034)
1.014
(0.035)
1.002
(0.032)
Monetary Curvature Parameter: α
0.976
(0.006)
0.977
(0.005)
1.666
(0.122)
1.580
(0.101)
1.621
(0.109)
890
89
890
89
1780
89
Yes
Cost of Effort Parameter: γ
# Observations
# Clusters
Job Effects
1680
84
1260
84
H0 : β = 1
χ2 (1) = 9.09
(p < 0.01)
χ2 (1) = 2.12
(p = 0.15)
H0 : β(Col. 1) = β(Col. 5)
χ2 (1) = 11.45
(p < 0.01)
H0 : β(Col. 2) = β(Col. 5)
χ2 (1) = 8.41 χ2 (1) = 13.39 χ2 (1) = 12.23
(p < 0.01)
(p < 0.01)
(p < 0.01)
χ2 (1) = 13.79
(p < 0.01)
Notes: Parameters identified from two-limit Tobit regressions of equations (4) and (6) for
monetary discounting and effort discounting, respectively. Parameters recovered via non-linear
combinations of regression coefficients. Standard errors clustered at individual level reported
in parentheses, recovered via the delta method. Effort regressions control for Job Effects (Task
1 vs. Task 2). Tested null hypotheses are zero present bias, H0 : β = 1, and equality of present
bias across effort and money, H0 : β(Col. 1) = β(Col. 5) and H0 : β(Col. 2) = β(Col. 5).
28
E.4
Estimates For Effort Discounting By Week
We re-estimate parameters by week and test the null hypothesis of equality of discount rates
identified from initial allocations and subsequent allocations.
Table A10: Parameter Estimates By Week
Effort Discounting
(1)
Week 1
Initial Allocations
(2)
Week 2
Subsequent Allocations
(3)
Week 4
Initial Allocations
(4)
Week 5
Subsequent Allocations
Weekly Discount Factor: (δ)7
0.998
(0.029)
0.898
(0.025)
0.939
(0.019)
0.892
(0.024)
Cost of Effort Parameter: γ
1.668
(0.126)
1.521
(0.097)
1.463
(0.074)
1.528
(0.092)
800
80
Yes
800
80
Yes
800
80
Yes
800
80
Yes
# Observations
# Clusters
Job Effects
H0 : (δ)7 (Col. 1) = (δ)7 (Col. 2)
χ2 (1) = 7.02
(p < 0.01)
H0 : (δ)7 (Col. 3) = (δ)7 (Col. 4)
χ2 (1) = 4.10
(p = 0.04)
Notes: Parameters identified from two-limit Tobit regressions of equation (6) assuming β = 1 for
effort discounting. Parameters recovered via non-linear combinations of regression coefficients.
Standard errors clustered at individual level reported in parentheses, recovered via the delta
method. Effort regressions control for Job Effects (Task 1 vs. Task 2). Tested null hypotheses
are equal discounting in Weeks 1 vs. 2 and Weeks 4 and 5, H0 : (δ)7 (Col. 1) = (δ)7 (Col. 2) and
H0 : (δ)7 (Col. 3) = (δ)7 (Col. 4).
29
E.5
Full Effort Data Set Tables Figures
We reconduct all analyses using Block 1 and Block 2 data to identify effort discounting parameters.
Table A11: Parameter Estimates: Full Effort Data Set
Monetary Discounting
Effort Discounting
(1)
All Delay
Lengths
(2)
Three Week Delay
Lengths
(3)
Job 1
Greek
(4)
Job 2
Tetris
(5)
Combined
Present Bias Parameter: β
0.974
(0.009)
0.988
(0.009)
0.927
(0.022)
0.927
(0.021)
0.927
(0.020)
Weekly Discount Factor: (δ)7
0.988
(0.003)
0.980
(0.003)
0.978
(0.022)
0.979
(0.022)
0.977
(0.021)
Monetary Curvature Parameter: α
0.975
(0.006)
0.976
(0.005)
1.566
(0.090)
1.510
(0.081)
1.537
(0.084)
1600
80
Yes
1600
80
Yes
3200
80
Yes
Yes
Cost of Effort Parameter: γ
# Observations
# Clusters
Block Effects
Job Effects
1500
75
1125
75
H0 : β = 1
χ2 (1) = 8.77
(p < 0.01)
χ2 (1) = 1.96
(p = 0.16)
H0 : β(Col. 1) = β(Col. 5)
χ2 (1) = 5.46
(p = 0.02)
H0 : β(Col. 2) = β(Col. 5)
χ2 (1) = 11.1 χ2 (1) = 11.9 χ2 (1) = 13.94
(p < 0.01)
(p < 0.01)
(p < 0.01)
χ2 (1) = 8.61
(p < 0.01)
Notes: Parameters identified from two-limit Tobit regressions of equations (4) and (6) for
monetary discounting and effort discounting, respectively. Parameters recovered via non-linear
combinations of regression coefficients. Standard errors clustered at individual level reported in
parentheses, recovered via the delta method. Effort regressions control for Block Effects (Weeks
1,2,3 vs. 4,5,6) and Job Effects (Task 1 vs. Task 2). Tested null hypotheses are zero present bias,
H0 : β = 1, and equality of present bias across effort and money, H0 : β(Col. 1) = β(Col. 5)
and H0 : β(Col. 2) = β(Col. 5).
30
Table A12: Monetary and Real Effort Discounting by Commitment: Full Effort Data Set
Monetary Discounting
Commit (=0) Commit (=1)
Effort Discounting
Commit (=0)
Commit (=1)
(1)
Tobit
(2)
Tobit
(3)
Tobit
(4)
Tobit
Present Bias Parameter: β
0.999
(0.010)
0.981
(0.013)
0.989
(0.018)
0.880
(0.031)
Weekly Discount Factor: (δ)7
0.978
(0.003)
0.981
(0.005)
0.911
(0.030)
1.032
(0.029)
Monetary Curvature Parameter: α
0.981
(0.009)
0.973
(0.007)
1.485
(0.123)
1.579
(0.116)
Cost of Effort Parameter: γ
# Observations
# Clusters
Block Effects
Job Effects
28
47
33
Yes
Yes
47
Yes
Yes
H0 : β = 1
χ2 (1) = 0.01
(p = 0.94)
χ2 (1) = 2.15
(p = 0.14)
χ2 (1) = 0.34
(p = 0.56)
χ2 (1) = 15.12
(p < 0.01)
H0 : β(Col. 1) = β(Col. 2)
χ2 (1) = 1.29
(p = 0.26)
H0 : β(Col. 3) = β(Col. 4)
χ2 (1) = 9.35
(p < 0.01)
Notes: Parameters identified from two-limit Tobit regressions of equations (4) and (6) for monetary discounting and real effort discounting. Parameters recovered via non-linear combinations
of regression coefficients. Standard errors clustered at individual level reported in parentheses,
recovered via the delta method. Commit (=1) or Commit (=0) separates individuals into those
who did (1) or those who did not (0) choose to commit at a commitment price of zero dollars.
Effort regressions control for Block Effects (Weeks 1,2,3 vs. 4,5,6) and Job Effects (Job 1 vs. Job
2). Tested null hypotheses are zero present bias, H0 : β = 1, and equality of present bias across
commitment and no commitment, H0 : β(Col. 1) = β(Col. 2) and H0 : β(Col. 3) = β(Col. 4).
31
E.6
Replication Exercise Additional Tables
Table A13: Replication Exercise Parameter Estimates, Restricted Sample
Monetary Discounting
Effort Discounting
Greek
(1)
(2))
Present Bias Parameter: β
0.995
(0.004)
0.934
(0.035)
Weekly Discount Factor: (δ)7
0.989
(0.005)
1.077
(0.032)
Monetary Curvature Parameter: α
0.955
(0.009)
Cost of Effort Parameter: γ
1.733
(0.169)
# Observations
# Clusters
1746
97
1458
81
H0 : β = 1
χ2 (1) = 1.13
(p = 0.29)
χ2 (1) = 3.60
(p = 0.06)
H0 : β(Col. 1) = β(Col. 2)
χ2 (1) = 3.07
(p = 0.08)
Notes: Parameters identified from two-limit Tobit regressions of equations (4) and (6) for monetary discounting
and effort discounting, respectively. Parameters recovered via non-linear combinations of regression coefficients.
Standard errors clustered at individual level reported in parentheses, recovered via the delta method. Chisquared tests used in last two rows. Sample restricted to those individuals with positive variation in experimental
response in both weeks of replication exercise. Excluded subjects noted with ∗ in Appendix Tables A7 and A8
32
Figure A1: Real Effort Discounting Behavior: Full Effort Data Set
Tetris
10
20
30
Tasks Allocated to Early Date
40
Greek Transcription
.5
1
1.5 .5
1
1.5
R
(from et+Ret+k=50)
Initial Allocation
Mean
Subsequent Allocation
Mean
SE
ytk
sb
h
p
ra
G
0
Fraction
.2 .4 .6
Figure A2: Individual Estimates of Present Bias: Full Effort Data Set
.75
1
Work Present Bias
1.25
1.5
.5
.75
1
Monetary Present Bias
1.25
1.5
.5
.75
1
Work Present Bias
1.25
1.5
Monetary Present Bias
.8 .9 1 1.11.2
0
Fraction
.2 .4 .6
.5
33
Figure A3: Commitment Demand: Full Effort Data Set
Panel A: Commit (=0)
Tetris
10
20
30
Tasks Allocated to Early Date
40
Greek Transcription
.5
1
1.5 .5
1
1.5
R
(from et+Ret+k=50)
Initial Allocation
Mean
Subsequent Allocation
Mean
SE
ytk
sb
h
p
ra
G
Panel B: Commit (=1)
Tetris
10
20
30
Tasks Allocated to Early Date
40
Greek Transcription
.5
1
1.5 .5
1
1.5
R
(from et+Ret+k=50)
Initial Allocation
Mean
Subsequent Allocation
Mean
ytk
sb
h
p
ra
G
34
SE
F
Instructions
F.1
Week 1 Effort Instructions
Welcome:
Thank you for participating in our experiment. We will begin shortly.
Eligibility for this study:
To be in this study, you need to meet these criteria: You must be willing to participate for six
consecutive weeks. Participation will require your presence on six consecutive Thursdays for at
least 10 minutes per week for an average of 60 minutes. Weeks 1 (today) and 4 will occur in
the xlab. Weeks 2,3,5, and 6 will occur at any computer that has access to the Internet.
You must be willing to receive your payment from this experiment as one single completion
payment at the end of the study. Payments will be made one week after the final session, on
Thursday, March 22. You will return to the xlab to receive this payment.
If you do not meet these criteria, please inform us of this now.
Informed Consent
Placed in front of you is an informed consent form to protect your rights as a subject. Please
read it. If you would like to choose not to participate in the study you are free to leave at this
point. If you have any questions, we can address those now. We will pick up the forms after
the main points of the study are discussed.
Anonymity
Your anonymity in this study is assured. Your name will never be recorded or connected to
any decision you make here today. Your email will be collected in order to send reminder
emails. After the study, your email information will be destroyed and will not be connected to
your responses in the experiment.
1
Rules
Please turn your cell phones off. If you have a question at any point, just raise your hand.
Please put away any books, papers, computers, etc. There will be a quiz once we have finished
with the instructions. If it is clear that you do not understand the instructions when we review
your answers, you will be emailed and removed from the study.
Your Earnings
If you complete all six weeks of participation, a completion payment of $100 will be provided.
You may receive additional earnings during the experiment. If you choose to end your participation before the six weeks are complete, please report this to study administrators, and you
will receive a minimum payment of $10.
All payments will be made one week after the final session, on Thursday March 22. You
will return to the xlab to receive this payment.
Jobs
In this study there are two types of jobs, Job 1 and Job 2. These jobs will be completed over
time. Some portion of the jobs may be completed sooner, and some portion of the jobs may be
completed later depending on your choices and chance. Importantly, some tasks for each job
must be completed in each week. That is, as mentioned before, your participation is required
in each of the six consecutive weeks of the study.
Job 1:
In Job 1 you are asked to transcribe letters from a greek text. Greek text will appear in
the Transcription Box on your screen. For each letter you will need to find and select the
corresponding letter and enter it into the Completion Box on your screen. One task is one row
of greek text. For the task to be complete your accuracy must be 80% or better.
2
Job 2:
In Job 2 you are asked to play a tetris game. Blocks of different shapes drop from the top of
the task screen into a box. Each block is made up of four small squares arranged to make a
larger square, an L-shape or a column. As the blocks fall they can be rotated (by pressing the
up arrow key), moved horizontally (by pressing the left and right arrow keys), or moved down
more quickly (by pressing the down arrow key). Your goal is to fill a entire horizontal line
with parts of the blocks. When a horizontal line is filled, that line is ”destroyed,” moving the
rest of the placed pieces down by one square. If a line remains incomplete, another line must
be finished above it. The more lines that stand incomplete, the higher the blocks above them
stack, reducing the space in which falling shapes can be manipulated. Eventually the blocks
reach the top of the screen and the game ends. One task will be 4 lines of blocks completed. If a
game ends before a task is complete, the completed lines will be counted in the subsequent game.
Practice: We will now spend a few minutes practicing both jobs on the computer.
Before
we continue, you will be asked to register using your email by clicking ”register” once you open
the experiment. Make sure that you enter a valid email address.
3
The Experiment Timeline
Now that you’ve tried Job 1 and Job 2, let’s consider the timeline of the study. Along the way
we will discuss a few important details of how the study works.
Note: Minimum Work for each week
In each week (including today), you are required to complete a minimum number of tasks of
both Job 1 and Job 2.
Today (Week 1):
Once your minimum work is complete, you will be asked to make a series of 5 decisions for each
job. In these decisions you are asked to allocate tasks between one week from today (Week 2)
and two weeks from today (Week 3). You will make 5 decisions for both Job 1 and Job 2.
In each decision you are free to allocate your tasks as you choose. Note that this allocation
decision does not include the minimum work for each week, which you must also complete.
You will choose by moving a slider to your desired allocation.
computer.
4
We will now practice on the
Task Rates:
In the example decision above every task you allocate to Week 2 reduces the number of tasks
allocated to Week 3 by one. This is what we will refer to as a 1:1 task rate. The task rate
will vary across your decisions. For example, the task rate may be 1:1.5, such that every task
you allocate to Week 2 reduces the number of tasks allocated to Week 3 by 1.5. Or, the task
rate may be 1:0.5, such that every task you allocate to Week 2 reduces the number of tasks
allocated to Week 3 by 0.5. For simplicity, the task rates will always be represented as 1:X,
and you will be fully informed of the value of X when making your decisions. Please practice
with the different allocations using the computer.
5
Week 2 (One Week From Today):
Week 2, one week from today, will occur online. You will receive an email with instructions on
how to access the website with the jobs. You will again complete your minimum work. You
will be asked again to make 5 allocation decisions for each job. Exactly one of your 20 total
allocation decisions will be implemented. That is, we will implement one decision from Week
1 for Job 1, or one decision from Week 2 for Job 1, or one decision from Week 1 for Job 2, or
one decision from Week 2 for Job 2.
We will discuss how this allocation decision is chosen shortly. We refer to this allocation
decision as the ”decision-that-counts.” The tasks you allocated to Week 2 in the decisionthat-counts must be completed. If you do not return or do not complete the tasks in Week
2, you cannot complete the study, and you will receive only the minimum payment of $10.
In order for your tasks in Week 2 to be counted, they must be submitted by midnight on
February 16th, 2012.
6
Week 3, Two Weeks From Today:
Week 3, two weeks from today, will occur online. You will receive an email with instructions
on how to access the website with the jobs. You will again complete your minimum work.
Then, you must complete the tasks you allocated in the decision-that-counts. If you do not
return or do not complete the tasks in Week 3, you cannot complete the study, and you will
receive only the minimum payment of $10. In order for your tasks in Week 3 to be counted,
they must be submitted by midnight on February 23rd, 2012.
Choosing the Decision-That-Counts:
To summarize: In Week 1 (today), you will make 5 allocation decisions for both Job 1 and Job
2 for different task rates. In Week 2, you will also make 5 allocation decisions for both Job 1
and Job 2 for different task rates.
Therefore, you will make 20 total allocation decisions. As stated above, we will choose
only one of these decisions as the decisions-that-counts. That is, we will either implement one
decision from Job 1 or one decision from Job 2, but not both.
There are three stages to determine the decision-that-counts.
1. First, we will choose if the decision-that-counts will come from Week 1 or Week 2. To do
this, we will pick a random number from 1 to 10. If the number is 1, then the decisionthat-counts will come from your Week 1 allocations. If the number is 2,3,4,5,6,7,8,9 or
10, then the decision-that-counts will come from your Week 2 allocations. Therefore, the
decision-that-counts will come from Week 1 with a 10 percent chance and the decisionthat-counts will come from Week 2 with a 90 percent chance.
2. Second, we will choose if the decision-that-counts will come from Job 1 or Job 2. To
do this we will pick a second random number from 1 to 2. If the number is 1 then the
decision-that-counts will come from Job 1. If the number is 2, then the decision-thatcounts will come from Job 2. Therefore, the decision-that-counts is equally likely to come
7
from Job 1 and Job 2.
3. Third, we will choose the decision-that-counts from the 5 allocations you made in the
chosen week and the chosen job. To do this, we will pick a third random number from 1
to 5. Therefore, within the chosen week and chosen job, every allocation is equally likely
to be chosen as the decision-that-counts.
For example, consider the following allocation examples. Imagine that your allocations
were shown in the following diagram for Weeks 1 and 2. Now, imagine that we determine the
decision-that-counts.
Week 1 Allocations
Week 2 Allocations
1. Following the first step above, we would first generate a random number from 1 to 10
to determine whether the Week 1 or the Week 2 allocations will be implemented. If the
8
number is 1, then the decision-that-counts will come from your Week 1 allocations. If
the number is 2,3,4,5,6,7,8,9 or 10, then the decision-that-counts will come from your
Week 2 allocations. Imagine the number is 7, such that your Week 2 allocations will be
implemented.
2. Following the second step above, we would generate a random number from 1 to 2 to
determine the job of the decision-that-counts. If the number is 1 then the decision that
counts will come from Job 1. If the number is 2, then the decision that counts will
come from Job 2. Imagine the number is 1, such that the your Job 1 allocations will be
implemented.
3. Following the third step above, we would generate a random number from 1 to 5 to
determine the decision-that-counts from your Week 2 allocations for Job 1. Imagine this
number is 3 such that the decision-that-counts would then be third allocation
decision from your Week 2 allocations for Job 1
In Week 2, you would be required to complete 27 tasks of Job 1 and in Week
3 you would be required to complete 23 tasks of Job 1.
Note that these tasks will be in addition to the minimum work that you will
be required to complete for both jobs in both weeks.
REMEMBER: EACH DECISION COULD BE THE
DECISION-THAT-COUNTS SO TREAT EACH DECISION AS IF IT WAS
THE ONE DETERMINING YOUR TASKS.
9
Recap:
• You will be participating in a six week study that requires participation one day per week
on six consecutive weeks.
• You will receive a completion payment of $100 at the end of the study by check one week
after Week 6. You will return to the xlab on March 22, 2012 to receive this payment.
• If you choose to no longer participate, or do not complete the jobs you chose, you will
receive only a minimum payment of $10 by check one week after Week 6. You will return
to the xlab on March 22, 2012 to receive this payment.
• There are two possible jobs in the study. Job 1 is transcription of greek letters. Job 2 is
a tetris game.
• In each week, you will be asked to complete minimum work for each job.
• In Week 1, today, you will be asked to make a series of allocation decisions for both Job
1 and Job 2. You will allocate tasks to Weeks 2 and 3 at various task rates.
• In Week 2, you will again make allocation decisions.
• One of your allocation decisions will be chosen at random as the decision-that-counts and
your allocation will determine the tasks that you complete in Weeks 2 and 3.
• One of your Week 1 allocations will be implemented with 10 percent chance while one of
your Week 2 allocations will be implemented with 90 percent chance.
• Weeks 4, 5, and 6 will mirror Weeks 1, 2, and 3. In Week 4 you will make allocation
decisions. In Week 5, you will again make allocation decisions and one of your allocation
decisions will be chosen at random as the decision-that-counts. Your allocation will
determine the jobs that you complete in Weeks 5 and 6.
10
• One week after week 6, you will receive your completion payment of $100. You will return
to the xlab on March 22, 2012 to receive this payment.
11
Consent
Now that we have explained the study, you are free to leave if you would like to choose not to
participate in the study. Otherwise, please sign the consent form and we will pick these up now.
Minimum Work
Now you will complete your minimum work for each job for this week. For each job, we ask
that you complete 10 tasks.
Reminder of Timeline
Today you will be asked to make a series of 5 allocation decisions for both Job 1 and Job 2. In
these decisions you are asked to allocate tasks between one week from today (Week 2) and two
weeks from today (Week 3).
In each decision you are free to allocate your tasks as you choose. The allocations do not
include the minimum amount of work for each job. You will choose by moving a slider to your
desired allocation.
Allocations
In the sliders on the screen, you will be asked to make 5 allocations for Job 1. Then, you will
be asked to make 5 allocation decisions for Job 2.
Remember each decision could be the decision-that-counts, so please make each decision as
if it were the one that determines your tasks.
12
F.2
Week 1 Money Instructions
Thank you for completing your allocations. On the following screens we would like to ask
you several additional questions allocating money over time. Your decisions in this portion of
the study are completely unrelated to your allocations over Job 1 and Job 2 and will be paid
separately.
You must be willing to receive your payment for this study by cash provided to you in the
xlab by Professor Ned Augenblick of the Haas School of Business. You will be required to
return to the xlab on the dates indicated to complete the study and so your choice of payments
will not require you to arrive any extra times.
Earning Money
To begin, you will be given a $10 thank-you payment, just for participating in this study! You
will receive this thank-you payment in two equally sized payments of $5 each.
The two $5
payments will come to you at two different times. These times will be determined in the way
described below.
In this portion of the study, you will make 15 choices over how to allocate money between
three possible dates:
1) February 9th (today - week 1),
2) March 1st (three weeks from today - week 4)
3) March 22nd (six weeks from today - week 7).
Note that these are all days that you will be in the xlab. In each decision, you will allocate
money between two of these dates. In the first set of five decisions, you will allocate money
between week 1 (today) and week 4. In the second set, you will allocate money between week
1 (today) and week 7. In the third set, you will allocate money between week 4 and week 7.
This means you could be receiving payments as early as today, and as late as the week 7.
Once all 15 decisions have been made, we will randomly select one of the 15 decisions as the
decision-that-counts. We will use the decision-that-counts to determine your actual earnings.
13
Note, since all decisions are equally likely to be chosen, you should make each decision as if it
will be the decision-that-counts.
When calculating your earnings from the decision-that-counts, we will add to your earnings
the two $5 thank you payments. Thus, you will always get paid at least $5 at the chosen
earlier time, and at least $5 at the chosen later time.
IMPORTANT: All payments you receive will be paid in cash in the xlab.
On the
scheduled day of payment, you will come to the xlab for the regular schedule of the study.
Hence, you will not be asked to make any special arrangements to receive payment from this
portion of the study. You will receive your payment from Professor Ned Augenblick.
On your desk are two envelopes: one for the sooner payment and one for the later payment.
Please take the time now to write your participant ID on them.
14
How It Works:
In the following three screens you are asked to make 15 decisions involving payments over time.
Each row is a decision and is numbered from 1 to 15.
Each row will feature a series of options. Each option consists of a sooner payment AND a
later payment. You are asked to pick your favorite option in each row by moving the slider to
your desired location. You should pick the combination of sooner payment AND later payment
that you prefer the most.
Note that there is a trade-off between the sooner payment and the later payment. As the
sooner payment goes down, the later payment goes up. All you have to do for each decision
is choose which combination of sooner and later payment you prefer the most by moving the
slider to that location.
Once all 15 of your decisions are complete, we will choose one at random to be the decisionthat-counts. Your chosen allocation will be implemented.
Consider if the decision-that-counts was the third decision, and in that decision, you
allocated $11 on February 9th and $10.50 on March 1st. Then, on February 9th, we would
place $11 along with your $5 minimum payment, making $16.00, into your first envelope. This
envelope will be given to you on February 9th (today) in the xlab. On March 1st, we would
place $10.50 along with your $5 minimum payment, making $15.50, into your second envelope.
This envelope will be given to you on March 1st when you return to the xlab. Recall that
this will not require you to make any special arrangements to receive payment as you will be
returning to the laboratory as part of the regular schedule of the study.
Once your payments have been determined, you will write the amounts and dates on the
inside of the two envelopes. When you receive your payments you can guarantee there have
been no clerical errors by checking against the amounts and dates you wrote.
15
Remember that each decision could be the decision-that-counts! It is in your interest to treat each decision as if it could be the one that determines your payment.
16
F.3
Week 1 Quiz
Quiz
Please complete the quiz in order to make sure that you understand the allocation decisions
and the timeline of the study.
Participant #
1. How many weeks are you required to participate?
2. In which weeks are you asked to come to the xlab to participate?
3. In which weeks are you asked to participate online and not come to the xlab?
4. Will you have to complete minimum work for each job in each week?
5. You will make allocation decisions for Weeks 2 and 3 both today and in Week 2. What
is the percent chance that one of your Week 2 allocations will be implemented?
6. If you face a 1:2 task rate for allocations between Weeks 2 and 3, every task you allocate
to Week 2 decreases by how many the number of tasks you allocate to Week 3?
7. You will make allocations for each job. Apart from your minimum work, will you complete
any tetris tasks if a transcription job allocation is chosen as the decision-that-counts.
17
F.4
Week 4 Effort Instructions
Welcome:
Thank you for returning to the experiment. We will begin shortly.
Eligibility for this study:
To continue in this study, you need to meet these criteria: You must be willing to participate for
three consecutive weeks. Participation will require your presence on three consecutive Fridays
for at least 10 minutes per week for an average of 60 minutes. Week 4 (today) will occur in the
xlab. Weeks 5 and 6 will occur at any computer that has access to the Internet.
You must be willing to receive your payment from this experiment as one single completion
payment at the end of the study. Payments will be made one week after the final session, on
Friday, March 23. You will return to the xlab to receive this payment.
If you do not meet these criteria, please inform us of this now.
Your Earnings
If you complete all six weeks of participation, a completion payment of $100 will be provided.
You may receive additional earnings during the experiment. If you choose to end your participation before the six weeks are complete, please report this to study administrators, and you
will receive a minimum payment of $10.
All payments will be made one week after the final session, on Friday March 23. You will
return to the xlab to receive this payment.
Jobs
In this study there are two types of jobs, Job 1 and Job 2. These jobs will be completed over
time. Some portion of the jobs may be completed sooner, and some portion of the jobs may be
completed later depending on your choices and chance. Importantly, some tasks for each job
must be completed in each week. That is, as mentioned before, your participation is required
18
in each of the six consecutive weeks of the study.
Job 1:
In Job 1 you are asked to transcribe letters from a greek text.
Job 2:
In Job 2 you are asked to play a tetris game.
19
The Experiment Timeline
Note: Minimum Work for each week
In each week (including today), you are required to complete a minimum number of tasks of
both Job 1 and Job 2.
Today (Week 4):
Once your minimum work is complete, you will be asked to make a series of 5 decisions for each
job. In these decisions you are asked to allocate tasks between one week from today (Week 5)
and two weeks from today (Week 6). You will make 5 decisions for both Job 1 and Job 2.
In each decision you are free to allocate your tasks as you choose. Note that this allocation
decision does not include the minimum work for each week, which you must also complete.
Task Rates:
For one example task rate, every task you allocate to Week 6 reduces the number of tasks
allocated to Week 5 by one. This is what we will refer to as a 1:1 task rate. The task rate
will vary across your decisions. For example, the task rate may be 1:1.5, such that every task
you allocate to Week 6 reduces the number of tasks allocated to Week 5 by 1.5. Or, the task
rate may be 1:0.5, such that every task you allocate to Week 6 reduces the number of tasks
allocated to Week 5 by 0.5. For simplicity, the task rates will always be represented as 1:X,
and you will be fully informed of the value of X when making your decisions.
Week 5 (One Week From Today):
Week 5, one week from today, will occur online and follows week 2 of the experiment. You will
receive an email with instructions on how to access the website with the jobs. You will again
complete your minimum work. You will be asked again to make 5 allocation decisions for each
job. Exactly one of your 20 total allocation decisions will be implemented. That is, we will
implement one decision from Week 4 for Job 1, or one decision from Week 5 for Job 1, or one
decision from Week 4 for Job 2, or one decision from Week 5 for Job 2.
We will discuss how this allocation decision is chosen shortly. We refer to this allocation
20
decision as the ”decision-that-counts.” The tasks you allocated to Week 5 in the decisionthat-counts must be completed. If you do not return or do not complete the tasks in Week 5,
you cannot complete the study, and you will receive only the minimum payment of $10. In order
for your tasks in Week 5 to be counted, they must be submitted by midnight on March 9th, 2012.
Week 6, Two Weeks From Today:
Week 6, two weeks from today, will occur online and follows week 3 of the experiment. You
will receive an email with instructions on how to access the website with the jobs. You will
again complete your minimum work. Then, you must complete the tasks you allocated in the
decision-that-counts. If you do not return or do not complete the tasks in Week 6, you cannot
complete the study, and you will receive only the minimum payment of $10. In order for your
tasks in Week 6 to be counted, they must be submitted by midnight on March 16th, 2012.
Choosing the Decision-That-Counts:
To summarize: In Week 4 (today), you will make 5 allocation decisions for both Job 1 and Job
2 for different task rates. In Week 5, you will also make 5 allocation decisions for both Job 1
and Job 2 for different task rates.
Therefore, you will make 20 total allocation decisions. As stated above, we will choose
only one of these decisions as the decisions-that-counts. That is, we will either implement one
decision from Job 1 or one decision from Job 2, but not both.
The decision-that-counts will be chosen using a similar method to the one used in Week 2.
However, this week, you will make a set of new decisions that affect the precise
way that the decision-that-counts is chosen. To understand these new decisions, please
recall how the decision-that-counts was chosen in Week 2:
How the decision-that-counts was chosen in Week 2
We used 3 steps to choose the decision-that-counts in Week 2.
21
1. First, we chose if the decision-that-counts came from the sooner week (Week 1) or the later
week (Week 2) allocations. To do this, we picked a random number from 1 to 10. If the
number was 1, then the decision-that-counts came from the allocations from the sooner
week (Week 1). If the number is 2,3,4,5,6,7,8,9 or 10, then the decision-that-counts came
from the allocations from the later week (Week 2). Therefore, the decision-that-counts
came from the sooner week with a 10 percent chance and the decision-that-counts came
from the later week with a 90 percent chance. This is the part of the choosing the
decision-that-counts that you will be able to affect in the new set of decisions
this week.
2. Second, we chose if the decision-that-counts came from Job 1 or Job 2. To do this, we
picked a second random number from 1 to 2. If the number was 1 then the decision-thatcounts came from Job 1. If the number was 2, then the decision-that-counts came from
Job 2. Therefore, the decision-that-counts was equally likely to come from Job 1 and Job
2.
3. Third, we chose the decision-that-counts from the 5 allocations you made in the chosen
week and the chosen job. To do this, we picked a third random number from 1 to 5.
Therefore, within the chosen week and chosen job, every allocation was equally likely to
be chosen as the decision-that-counts.
How the decision-that-counts will be chosen in Week 5
In Week 5, the decision that counts will be chosen in a similar way to Week 2 with one
important difference. Today, you will make a set of 15 decisions that can affect the first step
of the process.
In Week 2, there was a 10 percent chance that the decision-that-counts
would come from your sooner (Week 1) allocations. In Week 5, based on your decisions, there
will either be a 10 percent chance or a 90 percent chance that decision-that-counts will come
from your sooner (Week 4) allocations. That is, your decisions will change the likelihood that
one of your Week 4 allocations is chosen as the decision-that-counts.
22
For example, in one of the decisions, you will simply be asked to choose which option you
prefer:
1) a 10 percent chance that decision-that-counts will come from your Week 4 allocations
(and 90 percent chance that it comes from Week 5).
2) a 90 percent chance that decision-that-counts will come from your Week 4 allocations
(and 10 percent chance that it comes from Week 5)
This decision measures your preference about which choices will be allocated. For example,
if you would prefer that one of your week 5 allocations were chosen rather than a week 4
allocation, you should choose the first option.
Please take a second to think about this
decision.
The other decisions measure the strength of your preference about which choices will be
allocated. In these decisions, you will make this same decision but with additional payments
added to one of the two options. So, for example, you will be asked to choose which option
you prefer:
1) a 10 percent chance that decision-that-counts will come from your Week 4 allocations
(and 90 percent chance that it comes from Week 5).
2) a 90 percent chance that decision-that-counts will come from your Week 4 allocations
(and 10 percent chance that it comes from Week 5) plus $3.
For example, if you would very strongly prefer that one of your Week 5 allocations were
chosen rather than a Week 4 allocation, you might still choose the first option, even though
you could get an extra $3 for choosing the second option.
We will choose one of your 15
percentage decisions to be implemented at random. This implemented decision will be used
to determine the percentage chance that the decision-that-counts comes from your Week 4
allocations. Furthermore, if your implemented decision includes an additional payment, this
additional payment will be added to your final $100 completion check.
23
REMEMBER: EACH DECISION COULD BE IMPLEMENTED SO TREAT
EACH DECISION AS IF IT WAS GOING TO BE IMPLEMENTED.
24
Recap:
• You will be continuing in a study that requires participation one day per week on three
consecutive weeks.
• You will receive a completion payment of $100 at the end of the study by check one week
after Week 6. You will return to the xlab on March 23, 2012 to receive this payment.
• If you choose to no longer participate, or do not complete the jobs you chose, you will
receive only a minimum payment of $10 by check one week after Week 6. You will return
to the xlab on March 23, 2012 to receive this payment.
• There are two possible jobs in the study. Job 1 is transcription of greek letters. Job 2 is
a tetris game.
• In each week, you will be asked to complete minimum work for each job.
• In Week 4, today, you will be asked to make a series of allocation decisions for both Job
1 and Job 2. You will allocate tasks to Weeks 5 and 6 at various task rates.
• In Week 5, you will again make allocation decisions.
• One of your allocation decisions will be chosen at random as the decision-that-counts and
your allocation will determine the tasks that you complete in Weeks 5 and 6.
• You will be asked to make decisions about the percentage chance that the decisionthat-counts will come from your Week 4 allocations.
You will make a series of 15
decisions between (10% Week 4) and (90% Week 4) with additional payments potentially
added to the options. One of these decisions will be implemented. If the decision that
is implemented includes an additional payment, this will be added to your completion
payment.
• One week after Week 6, you will receive your completion payment. You will return to the
xlab on March 23, 2012 to receive this payment.
25
Minimum Work
Now you will complete your minimum work for each job for this week. For each job, we ask
that you complete 10 tasks.
Allocations
Today you will be asked to make a series of 5 allocation decisions for both Job 1 and Job 2. In
these decisions you are asked to allocate tasks between one week from today (Week 5) and two
weeks from today (Week 6).
In each decision you are free to allocate your tasks as you choose. The allocations do not
include the minimum amount of work for each job. You will choose by moving a slider to your
desired allocation.
In the sliders on the screen, you will be asked to make 5 allocations for Job 1. Then, you
will be asked to make 5 allocation decisions for Job.
Remember each decision could be the
decision-that-counts, so please make each decision as if it were the one that determines your
tasks.
Determining how the decision-that-counts will be chosen
in Week 5
On the screen you will be asked to choose between a 10% or a 90% chance that the decisionthat-counts comes from today’s allocations (Week 4) rather than the allocations you will make
next week (Week 5). In each decision, you are also given an additional payment for choosing
one of the two options. Remember each decision could be implemented, so please make the
decision as if it was determining the percent chance and your additional payment.
26
F.5
Week 4 Money Instructions
Thank you for completing your allocations. On the following screen we would like to ask you
several additional questions allocating money over time. Your decisions in this portion of the
study are completely unrelated to your allocations over Job 1 and Job 2 and will be paid
separately.
You must be willing to receive your payment for this study by cash provided to you in the
xlab by Professor Ned Augenblick of the Haas School of Business. You will be required to
return to the xlab on the dates indicated to complete the study and so your choice of payments
will not require you to arrive any extra times.
Earning Money
To begin, you will be given a $10 thank-you payment, just for participating in this study! You
will receive this thank-you payment in two equally sized payments of $5 each.
The two $5
payments will come to you at two different times. These times will be determined in the way
described below.
In this portion of the study, you will make 5 choices over how to allocate money between
two points in time:
1) March 2nd
2) March 23rd
Note that these are days that you will be in the xlab.
In each decision, you will allocate money between these dates. Once all 5 decisions have
been made, we will randomly select one of the 5 decisions as the decision-that-counts. We will
use the decision-that-counts to determine your actual earnings. Note, since all decisions are
equally likely to be chosen, you should make each decision as if it will be the decision-thatcounts.
When calculating your earnings from the decision-that-counts, we will add to your earnings
the two $5 thank you payments. Thus, you will always get paid at least $5 on March 2st, and
27
at least $5 on March 23nd.
IMPORTANT: All payments you receive will be paid in cash in the xlab.
On the
scheduled day of payment, you will come to the xlab for the regular schedule of the study.
Hence, you will not be asked to make any special arrangements to receive payment from this
portion of the study. You will receive your payment from Professor Ned Augenblick.
On your desk are two envelopes: one for the sooner payment and one for the later payment.
Please take the time now to write your participant ID on them and study time/date on them.
28
How It Works:
In the following screen you are asked to make 5 decisions involving payments over time. Each
row is a decision and is numbered from 1 to 5.
Each row will feature a series of options. Each option consists of a sooner payment AND a
later payment. You are asked to pick your favorite option in each row by moving the slider to
your desired location. You should pick the combination of sooner payment AND later payment
that you prefer the most.
Note that there is a trade-off between the sooner payment and the later payment. As the
sooner payment goes down, the later payment goes up. All you have to do for each decision
is choose which combination of sooner and later payment you prefer the most by moving the
slider to that location.
Once all 5 of your decisions are complete, we will choose one at random to be the decisionthat-counts. Your chosen allocation will be implemented.
Consider for example the first decision. If this was chosen as the decision that counts and
your preferred allocation was $11 on March 2st and $10.50 on March 23nd, this would then
be implemented. On March 2st, we would place $11 along with your $5 minimum payment,
making $16.00, into your first envelope. This envelope will be given to you on March 2st in the
xlab. On March 23nd, we would place $10.50 along with your $5 minimum payment, making
$15.50, into your second envelope. This envelope will be given to you on March 23nd when
you return to the xlab. Recall that this will not require you to make any special arrangements
to receive payment as you will be returning to the laboratory as part of the regular schedule
of the study.
Once your payments have been determined, you will write the amounts and dates on the
inside of the two envelopes. When you receive your payments you can guarantee there have
been no clerical errors by checking against the amounts and dates you wrote.
29
Remember that each decision could be the decision-that-counts! It is in your
interest to treat each decision as if it could be the one that determines your payment.
G
Replication Study Instructions
INSTRUCTIONS
Welcome
Thank you for participating in our study. We will begin shortly.
Eligibility and Study Requirements
Participation in this study will require activities lasting at least 30 minutes on four consecutive Thursdays, beginning today and ending three weeks from today: Apr-10, Apr-17, Apr-24,
May-1.
Your first activity for this study is choosing amounts of money to be received one week
from today, Thursday, Apr-17, and two weeks from today Thursday, Apr-24. You will make
nine such choices today and you will make nine such choices one week from today on Thursday,
Apr-17. The choices you make today will be referred to as your Week 1 choices. The choices
you make one week from today on Thursday, Apr-17, will be referred to as your Week 2 choices.
You will make your Week 1 choices today in the laboratory via the study website.
Next week, on Wednesday night, you will receive an email with the study website. This link
will be active at 9am on Thursday morning. You can then login and make your Week 2 choices
using any computer that has internet access. You must make these decisions by 4pm that day.
Your second activity for this study is collecting your chosen payments. Payments will be
collected at a table setup directly outside of the xlab. The Apr-17th payments must be collected
within 2 hours of making your decisions. The Apr-24th payments must be collected between
9am and 6pm.
In order to complete this study you must be willing to both choose amounts of money and
to collect these amounts on Thursday, Apr-17 and Thursday, Apr-24. If you complete these
elements, you will be eligible to receive a completion payment of $30. This can be collected
on Thursday, May-1 outside the xlab between the hours of 9 a.m. and 6 p.m. If you do not
complete all elements of the study, you will be eligible to receive only a payment of $5. This
can also be collected on Thursday, May-1 at the xlab between the hours of 9 a.m. and 6 p.m.
30
If you do not meet or understand the study requirements, please inform us of this now.
Your Earnings
All payments will be made by Professor Ned Augenblick and his assistants. All payments
will be made in cash. You will receive your payments only in designated locations, at
designated times, on designated dates.
Informed Consent
Placed in front of you is an informed consent form to protect your rights as a subject.
Please read it. If you would like to choose not to participate in the study you are free to leave
at this point. If you have any questions, we can address those now. We will pick up the forms
after the main points of the study are discussed.
Anonymity
Your anonymity in this study is assured. Your name will never be recorded or connected
to any decision you make here today. Your email will be collected in order to communicate
with you during the study. After the study, your email information will be destroyed and will
not be connected to your responses in the experiment.
Rules
Please turn your cell phones off. If you have a question at any point, just raise your hand.
Please put away any books, papers, computers, etc.
Registration
We will now begin the study. Please open the study interface and enter your e-mail address.
Make sure that you enter a valid e-mail address as this will be the method by which we contact
you throughout the study.
Study Activities
We will now discuss in detail the study activities. In this study there are two activities. The
first activity is choosing payments over time. You will make 9 such choices today, Thursday,
Apr-10. The choices you make today will be referred to as your Week 1 choices. You will make
9 such choices one week from today, Thursday, Apr-17. The choices you make one week from
today will be referred to as your Week 2 choices. In both your Week 1 and Week 2 choices, you
will be choosing an amount of money to be received on Thursday, Apr-17 AND an amount of
money to be received on Thursday, Apr-24.
31
Each choice is a series of options. Each option consists of a sooner payment (to be collected
on Thursday, Apr-17) AND a later payment (to be collected on Thursday, Apr-24). You are
asked to pick your favorite option in each choice by moving a slider to your desired location.
In the example sliders on the website, please explore the potential choices.
Note that there is a trade-off between the sooner payment and the later payment. When
the sooner payment goes down, the later payment goes up and vice versa. In each choice, the
trade-off will be summarized by an “exchange rate,” and will be expressed as a number 1 : X.
This means that if you increase the sooner payment by $1, the later payment will be decreased
by $X. In the example, the exchange rate was 1 : 1, meaning that if you increase the sooner
payment by $1, the later payment is decreased by $1.
Remember, all you have to do for each decision is choose which combination of sooner and
later payment you prefer the most by moving the slider to that location.
The second activity is collecting payments. You will collect the payments from one of
your choices. This means you will collect some amount of money on Thursday, Apr-17
and some amount of money on Thursday, Apr-24. The payment on Apr-17 must be collected within 2 hours of making your decision. The payment on Apr-24 can be collected
anytime between 9am and 6pm. Payments will be collected at a table setup outside of the xlab.
The Experiment Timeline
We will now discuss the timeline of the study.
important details of how the study works.
Along the way we will discuss a few
Note: Minimum Payments for Each Week. With the exception of the final completion
payment date, on each day of study participation (including today), you will receive a
minimum payment of $5. These payments are in addition to your chosen payments. This
payment will be paid in cash and be added to your experimental earnings. These payments
must be collected for successful completion of the study.
Week 1(Today: Apr-10)
Today you will make 9 choices. Each choice is a series of options. Each option will consist of
a sooner payment (to be collected on Thursday, Apr-17) AND a later payment (to be collected
on Thursday, Apr-24). In each choice, the “exchange rate” will be different.
You will be asked to pick your favorite option in each choice by moving a slider to your
desired location. You should pick the combination of sooner payment AND later payment that
you prefer the most.
Once your 9 choices are complete, you will receive your minimum payment of $5 and depart.
32
Week 2 (One Week From Today: Apr-17)
Next week, on Wednesday night, you will receive an email with the study website. This
link will be active at 9am on Thursday morning. You must log in to the study website between
9am and 4pm of next Thursday, Apr-17. You will also receive a reminder email on Thursday.
You will again make 9 choices. Each choice is a series of options. Each option will consist of
a sooner payment (to be collected on Thursday, Apr-17) AND a later payment (to be collected
on Thursday, Apr-24). In each choice, the “exchange rate” will be different.
You will be asked to pick your favorite option in each choice by moving a slider to your
desired location. You should pick the combination of sooner payment AND later payment that
you prefer the most.
Once your 9 Week 2 choices are complete, you will have made a total of 18 choices: 9 Week
1 choices and 9 Week 2 choices. We will then pick one of your 18 total choices at random
to be the decision-that-counts. Your earnings will be determined by your decision in the
decision-that-counts. You will receive the amounts specified in the decision-that-counts on the
designated dates, Thursday, Apr-17 and Thursday, Apr-24. Recall that these earnings are in
addition to your two $5 minimum payments. Thus, you will always pick up a payment on
Thursday, Apr-17 and $5 on Thursday, Apr-24 of at least $5.
REMEMBER: EACH DECISION COULD BE THE
DECISION-THAT-COUNTS SO TREAT EACH CHOICE AS IF IT WAS THE
ONE DETERMINING YOUR EARNINGS.
Consider if in the decision-that-counts your preferred choice was an $11 sooner payment (to
be collected on Thursday, Apr-17) AND a $10.50 later payment (to be collected on Thursday,
Apr-24). Then, on Thursday, Apr-17 outside the xlab, you would collect $11 along with your $5
minimum payment, making $16.00 in cash. On Thursday, Apr-24 outside the xlab, you would
collect $10.50 along with your $5 minimum payment, making $15.50 in cash.
You must collect your earnings on Apr-17 within two hours of making your decisions online.
You must collect your earnings on Apr-24 between 9am and 6pm.. If you do not collect your
payment on either Thursday, Apr-17 or Thursday, Apr-24, you will be removed from the study
and forfeit all future payments including your completion payment of $30. You will be eligible
only for the reduced payment of $5 at the end of the study. There will be no exceptions to this
rule.
REMEMBER:YOU MUST PICK UP YOUR PAYMENTS BETWEEN 9AM
AND 6PM.
33
YOU MUST PICK UP YOUR PAYMENT NEXT WEEK WITHIN 2 HOURS
OF LOGGING INTO THE WEBSITE.
Week 3, (Two Weeks From Today: Apr-24)
In Week 3, you will make no decisions. You will receive an e-mail the night before reminding
you of the study. You must pick up your payment for Thursday, Apr-24 along with your $5
minimum payment outside the xlab between 9am and 6pm. If you do not pick up your payment,
you will be removed from the study and forfeit your completion payment of $30. You will be
eligible only for the reduced payment of $5 at the end of the study. There will be no exceptions
to this rule.
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Week 4, (Three Weeks From Today: May-1)
In Week 4, you will make no decisions. You will receive an email reminding you to pick up
your completion payment outside the xlab between 9am and 6pm on Thursday, May-1. If you
have completed all elements of the study you are eligible to receive a $30 completion payment.
If you have not completed all elements of the study you are eligible to receive a $5 completion
payment.
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Recap:
• You will be participating in a four week study that requires participation for at least 30
minutes on four consecutive Thursdays.
• On Thursday, April-10, Thursday, Apr-17 and Thursday, Apr-24, you will receive minimum payments of $5. These minimum payments are in addition to your chosen payments
from the decision-that-counts. These payments must be collected for successful completion of the study.
• In Week 1, today, Thursday, Apr-10, you will be asked to make 9 choices. Each choice
is a series of options. Each option will consist of a sooner payment (to be collected on
Thursday, Apr-17) AND a later payment (to be collected on Thursday, Apr-24). In each
choice, the “exchange rate” will be different.
• In Week 2, one week from today, Thursday, Apr-17, you will again be asked to make
9 choices. These decisions will be made online between 9am and 4pm. Each choice is
a series of options. Each option will consist of a sooner payment (to be collected on
Thursday, Apr-17) AND a later payment (to be collected on Thursday, Apr-24). In each
choice, the “exchange rate” will be different.
• You will be asked to pick your favorite option in each choice by moving a slider to your
desired location. You should pick the combination of sooner payment AND later payment
that you prefer the most.
• You will make 18 total choices: 9 in Week 1 and 9 in Week 2. We will pick one of your
18 total choices at random to be the decision-that-counts.
• Once your Week 2 decisions have been made on Thursday, Apr-17 and the decisionthat-counts has been determined, a two hour window will begin. You must collect your
earnings for Thursday, Apr-17 from the decision-that-counts outside of the xlab within
this two hour window (and between 9 am and 6pm).
• In Week 3, two weeks from today Thursday, Apr-24, you must collect your earnings for
Thursday, Apr-24 from the decision-that-counts outside the xlab between 9am and 6pm.
• If you fail to collect your earnings from the decision-that-counts you will be removed
from the study and forfeit all future payments. You will be eligible only for the reduced
payment of $5 at the end of the study.
• In Week 4, three weeks from today Thursday, May-1, you will pick up your completion
payment outside the xlab between the hours of 9 a.m. and 6 p.m. to receive your
completion payment. If you have completed all elements of the study you are eligible for
a $30 completion payment. If you have not completed all elements of the study you are
eligible only for the reduced amount of $5.
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Consent
Now that we have explained the study, you are free to leave if you would like to choose not to
participate in the study. Otherwise, please sign the consent form and we will pick these up now.
Allocations
In the sliders on the screen, you will be asked to make 9 allocations.
Remember each decision could be the decision-that-counts, so please make each decision as
if it were the one that determines your payment.
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INSTRUCTIONS
Welcome:
Thank you for participating in our study. We will begin shortly.
Eligibility and Study Requirements
Participation in this study will require activities lasting at least 30 minutes on four consecutive Thursdays, beginning today and ending three weeks from today: Apr-10, Apr-17, Apr-24,
May-1.
Your first activity for this study is choosing amounts of work to be completed one week
from today, Thursday, Apr-17, and two weeks from today Thursday, Apr-24. You will make
nine such choices today and you will make nine such choices one week from today on Thursday,
Apr-17. The choices you make today will be referred to as your Week 1 choices. The choices
you make one week from today on Thursday, Apr-17, will be referred to as your Week 2 choices.
You will make your Week 1 choices today in the laboratory via the study website.
Next week, on Wednesday night, you will receive an email with the study website. This link
will be active at 9am on Thursday morning. You can then login and make your Week 2 choices
using any computer that has internet access. You must make these decisions by 4pm that day.
Your second activity for this study is completing your chosen work. The work in this study
will be completed via the study website and can be completed on any computer that has internet
access. The Apr-17th work must be completed within 2 hours of making your decisions. The
Apr-24th work must be completed between 9am and 6pm.
In order to complete this study you must be willing to both choose amounts of tasks and
to complete these tasks on Thursday, Apr-17 and Thursday, Apr-24. If you complete these
elements, you will be eligible to receive a completion payment of $60. This can be collected
on Thursday, May-1 outside the xlab between the hours of 9 a.m. and 6 p.m. If you do not
complete all elements of the study, you will be eligible to receive only a payment of $5. This
can also be collected on Thursday, May-1 at the xlab between the hours of 9 a.m. and 6 p.m.
If you do not meet or understand the study requirements, please inform us of this now.
Your Earnings
The completion payment will be made by check by Professor Ned Augenblick and his
assistants. You will receive your payment only in designated locations, at designated times, on
designated dates.
38
Tasks
The tasks in this study are transcriptions of letters from a greek text. Greek text will
appear in a Transcription Box on your screen. For each letter, you will need to find and select
the corresponding letter and enter it into the Completion Box on your screen. One task is one
row of greek text. For a task to be complete, your accuracy must be 80% or better. Each task
takes an average student between 40-60 seconds.
Informed Consent
Placed in front of you is an informed consent form to protect your rights as a subject.
Please read it. If you would like to choose not to participate in the study you are free to leave
at this point. If you have any questions, we can address those now. We will pick up the forms
after the main points of the study are discussed.
Anonymity
Your anonymity in this study is assured. Your name will never be recorded or connected
to any decision you make here today. Your email will be collected in order to communicate
with you during the study. After the study, your email information will be destroyed and will
not be connected to your responses in the experiment.
Rules
Please turn your cell phones off. If you have a question at any point, just raise your hand.
Please put away any books, papers, computers, etc.
Registration
We will now begin the study. Please open the study interface and enter your e-mail address.
Make sure that you enter a valid e-mail address as this will be the method by which we contact
you throughout the study.
39
Study Activities
We will now discuss in detail the study activities. In this study there are two activities.
The first activity is choosing amounts of work over time. You will make 9 such choices today,
Thursday, Apr-10. The choices you make today will be referred to as your Week 1 choices. You
will make 9 such choices one week from today, Thursday, Apr-17. The choices you make one
week from today will be referred to as your Week 2 choices. In both your Week 1 and Week 2
choices, you will be choosing an amount of work to be completed on Thursday, Apr-17 AND
an amount of work to be completed on Thursday, Apr-24. The amount of work on each date is
expressed as a number of tasks.
Each choice is a series of options. Each option consists of a sooner number of tasks (to be
completed on Thursday, Apr-17) AND a later number of tasks (to be completed on Thursday,
Apr-24). You are asked to pick your favorite option in each choice by moving a slider to your
desired location. In the example sliders on the website, please explore the potential choices.
Note that there is a trade-off between the sooner number of tasks and the later number of
tasks. When the sooner number of tasks goes down, the later number of tasks goes up and
vice versa. In each choice, the trade-off will be summarized by an “exchange rate,” and will be
expressed as a number 1 : X. This means that if you increase the sooner number of tasks by
1 task, the later number of tasks will be decreased by X tasks. In the example, the exchange
rate was 1 : 1, meaning that if you increase the sooner number of tasks by 1, the later number
of tasks is decreased by 1.
Remember, all you have to do for each decision is choose which combination of sooner and
later tasks you prefer the most by moving the slider to that location.
The second activity is completing work. This means you will complete some tasks on
Thursday, Apr-17 and some tasks on Thursday, Apr-24. The tasks on Apr-17 must be
completed within 2 hours of making your decision. The tasks on Apr-24 can be completed
anytime between 9am and 6pm. Tasks will be completed online using any computer that has
access to the Internet.
The Experiment Timeline
We will now discuss the timeline of the study.
important details of how the study works.
Along the way we will discuss a few
Note: Minimum Work for Each Week. With the exception of the final completion payment
date, on each day of study participation (including today), you are required to complete a
minimum number of 10 tasks. These tasks are in addition to your chosen numbers of tasks.
These tasks must be completed for successful completion of the study.
40
Week 1(Today: Apr-10)
Today you will make 9 choices. Each choice is a series of options. Each option will consist of
a sooner number of tasks (to be completed on Thursday, Apr-17) AND a later number of tasks
(to be completed on Thursday, Apr-24). In each choice, the “exchange rate” will be different.
You will be asked to pick your favorite option in each choice by moving a slider to your
desired location. You should pick the combination of sooner tasks AND later tasks that you
prefer the most.
Today you will complete your minimum work of 10 tasks, then make your 9 choices, and
depart.
Week 2 (One Week From Today Apr-17)
Next week, on Wednesday night, you will receive an email with the study website. This
link will be active at 9am on Thursday morning. You must log in to the study website between
9am and 4pm of next Thursday, Apr-17. You will also receive a reminder email on Thursday.
You will again complete minimum work of 10 tasks. Then, you will again make your 9
choices. Each choice is a series of options. Each option will consist of a sooner number of
tasks (to be completed on Thursday, Apr-17) AND a later number of tasks (to be completed
on Thursday, Apr-24). In each choice, the “exchange rate” will be different.
You will be asked to pick your favorite option in each choice by moving a slider to your
desired location. You should pick the combination of sooner tasks AND later tasks that you
prefer the most.
Once your 9 Week 2 choices are complete, you will have made a total of 18 choices: 9 Week
1 choices and 9 Week 2 choices. We will then pick one of your 18 total choices at random to
be the decision-that-counts. Your tasks will be determined by your decision in the decisionthat-counts. You will complete the tasks specified in the decision-that-counts on the designated
dates, Thursday, Apr-17 and Thursday, Apr-24. Recall that these tasks are in addition to your
10 tasks of minimum work. Thus, you will always login into the website and complete at least
10 tasks on Thursday, Apr-17 and 10 tasks on Thursday, Apr-24.
REMEMBER: EACH CHOICE COULD BE THE DECISION-THAT-COUNTS
SO TREAT EACH CHOICE AS IF IT WAS THE ONE DETERMINING YOUR
TASKS.
Consider if in the decision-that-counts your preferred choice was 30 sooner tasks (to be
completed on Thursday, Apr-17) AND 25 later tasks (to be completed on Thursday, Apr-24).
Then, on the study website, on Thursday, Apr-17, you would complete 30 tasks along with
41
your 10 tasks of minimum work, making 40 tasks. On Thursday, Apr-24, on the study website,
you would complete 25 tasks along with your 10 tasks of minimum work, making 35 tasks.
You must complete your tasks on Apr-17 within two hours of making your decisions online.
You must complete your tasks on Apr-24 between 9am and 6pm. If you do not complete your
tasks on either Thursday, Apr-17 or Thursday, Apr-24, you will be removed from the study and
forfeit the completion payment of $60. You will be eligible only for the reduced payment of $5
at the end of the study. There will be no exceptions to this rule.
REMEMBER:YOU MUST COMPLETE YOUR TASKS BETWEEN 9AM AND
6PM.
YOU MUST COMPLETE YOUR TASKS NEXT WEEK WITHIN 2 HOURS
OF LOGGING INTO THE WEBSITE.
Week 3, (Two Weeks From Today: Apr-24)
In Week 3, you will make no decisions. You will receive an e-mail the night before
reminding you of the study. You must login into the website between 9am and 6pm and you
must complete your tasks from the decision-that-counts for Thursday, Apr-24 along with your
10 tasks of minimum work on the study website. If you do not complete your tasks by 6pm,
you will be removed from the study and forfeit your completion payment of $60. You will be
eligible only for the reduced payment of $5 at the end of the study. There will be no exceptions
to this rule.
Week 4, (Three Weeks From Today: May-1)
In Week 4, you will make no decisions. You will receive an email reminding you to pick up
your completion payment in the xlab. If you have completed all elements of the study you are
eligible to receive a $60 completion payment. If you have not completed all elements of the
study you are eligible to receive a $5 completion payment. These payments will be available
outside of the xlab on Thursday, May-1 between the hours of 9 a.m and 6 p.m.
42
Recap:
• You will be participating in a four week study that requires participation for at least 30
minutes on four consecutive Thursdays.
• On Thursday, April-10, Thursday, Apr-17 and Thursday, Apr-24, you are required to
complete minimum work of 10 tasks. These tasks are in addition to your chosen tasks
from the decision-that-counts. These tasks must be completed for successful completion
of the study.
• In Week 1, today Thursday, Apr-10, you will be asked to make 9 choices. Each choice is a
series of options. Each option will consist of a sooner number of tasks (to be completed on
Thursday, Apr-17) AND a later number of tasks (to be completed on Thursday, Apr-24).
In each choice, the “exchange rate” will be different.
• In Week 2, one week from today Thursday, Apr-17, you will again be asked to make 9
choices. Each choice is a series of options. Each option will consist of a sooner number
of tasks (to be completed on Thursday, Apr-17) AND a later number of tasks (to be
completed on Thursday, Apr-24). In each choice, the “exchange rate” will be different.
• You will be asked to pick your favorite option in each choice by moving a slider to your
desired location. You should pick the combination of sooner tasks AND later tasks that
you prefer the most.
• You will make 18 total choices: 9 in Week 1 and 9 in Week 2. We will pick one of your
18 total choices at random to be the decision-that-counts.
• Once your Week 2 decisions have been made on Thursday, Apr-17 and the decision-thatcounts has been determined, a two hour window will begin. You must complete your tasks
for Thursday, Apr-17 from the decision-that-counts on the study website within this two
hour window (and between 9 am and 6pm).
• In Week 3, two weeks from today Thursday, Apr-24, you will again login to the website.
You must complete your tasks for Thursday, Apr-24 from the decision-that-counts on the
study website within two hours of logging in (and between 9am and 6pm).
• If you fail to complete your tasks from the decision-that-counts you will be removed from
the study. You will be eligible only for the reduced payment of $5 at the end of the study.
• In Week 4, three weeks from today Thursday, May-1, you will come outside the xlab
between the hours of 9 a.m. and 6 p.m. to receive your completion payment. If you have
completed all elements of the study you are eligible for a $60 completion payment. If you
have not completed all elements of the study you are eligible only for the reduced amount
of $5.
43
Consent
Now that we have explained the study, you are free to leave if you would like to choose not to
participate in the study. Otherwise, please sign the consent form and we will pick these up now.
Minimum Work
Recall that, each week, you must complete a mandatory number of 10 tasks. We will not
complete those tasks.
Allocations
In the sliders on the screen, you will be asked to make 9 allocations.
Remember each decision could be the decision-that-counts, so please make each decision as
if it were the one that determines your payment.
44