Present or Future Incentives?
On the Optimality of Fixed Wages With Moral Hazard
Rosario Macera
∗ †
February 2017
Abstract
This paper studies whether principals should use present or future payments, or both, to optimally motivate
present effort in a principal-agent setting. Using a laboratory experiment it shows that, in contrast to the
classical model prescribing that present and future payments must be made contingent on present outcomes
to motivate current effort at the least cost, an incentive scheme making only future payments contingent on
current outcomes—and thus paying a fixed wage today—implements the same level of present effort, at the
same expected cost, and is strictly preferred by a larger proportion of workers. Even though this result cannot
be explained by risk aversion, I estimate a model based on Kőszegi and Rabin (2006) preferences to show
that it is consistent with loss aversion.
JEL Classification: D03, D86, D90, J33
Key words: fixed wages, dynamic moral hazard, reference-dependent preferences, loss aversion.
∗
This paper is an extension of one of my dissertation chapters at UC Berkeley named “Intertemporal Incentives Under Loss
Aversion”. I am thus indebted to my advisors Botond Kőszegi and Matthew Rabin for their guidance and support. I am also
grateful to Ben Hermalin, Paul Heidhues, and Joaquı́n Poblete fro useful feedback on the model. I also thank Fondecyt Grant
Iniciación #11140101 for funding and Joseé Tomás Ambrus, Hugo Correa, Alejandro Guin-Po, Guillermo Irarrázabal, Amina
Merlez and specially Marı́a Cristina Riquelme for excellent research assistance.
†
Business School, Pontificia Universidad Católica de Chile. E-mail: [email protected]
1
Introduction
Payment schemes using fixed wages and thus totally deferring incentives into future payments are common in
the labor market. For instance, future incentives in the form of wage growth and promotions (Baker, Jensen,
and Murphy (1988), Baker, Gibbs, and Holmstrom (1994), Gibbons and Waldman (1999)), and dismissals and
layoffs (Lazear (1986), Kwon (2005), Brookman and Thistle (2009)) are widespread in the workplace, while
present incentives in the form of piece rates, commissions and other payments tied to current performance are
less prevalent (Lemieux, MacLeod, and Parent (2009)).
The observation that current wages can be insensitive to current performance is, however, puzzling when
output is observable and easily tied to compensation.1 The standard principal-agent model with observable
outcomes prescribes that both present and future payments must be contingent on current performance to
implement a desired level of effort at the least cost. The intuition behind this result lies on the agents’ risk
aversion: using present and future payments to incentivize current effort decreases the amount of risk the agent
bears thus decreasing the risk premium the principal pays (Rogerson (1985)).
This paper provides evidence on the optimality of fixed wages coupled with deferred incentives. It presents
a two-period real-effort laboratory experiment where subjects choose between two payment schemes that allocate incentives for first-period effort differently across first and second-period payments. Periods are set one
month apart. The Fully-Contingent scheme makes first and second-period payments contingent on first-period
performance, as prescribed by the principal-agent model with observable outcomes. In contrast, the Deferred
scheme makes only second-period payments contingent on first-period performance and thus pays a fixed wage
in the first period. The two schemes have the same expected cost for the principal. The data shows that 17.9%
more subjects choose the Deferred over the Fully-Contingent scheme and productivity is not hampered by the
Deferred scheme.
After empirically showing that deferred incentives are preferred by workers at no expense on productivity
or expected cost, I suggest a new explanation for why this preference can optimally lead to current fix wages:
loss aversion. Using a simple principal-agent model, I first show that when workers have reference-dependent
preferences and their reference point is their rational expectations as in Kőszegi and Rabin (2006), they strictly
prefer the Deferred scheme over the Fully-Contingent one. Intuitively, the reference-dependent expected utility
from wage uncertainty is negative due to loss aversion; whenever comparing actual and expected wages, the
prospect of being painfully disappointed outweighs that of being pleasantly surprised. A present fixed wage,
therefore, eliminates the disutility from uncertainty in current wages, increasing utility from the Deferred
1
I review the evidence indicating that commissions and piece rates are infrequent even in jobs where performance is observable
in Section 3.2
1
scheme vis-a-vis the Fully-Contingent one. Second, I show that if second-period payments are made sufficiently
contingent on first-period outcomes, the Deferred scheme can also implement the same level of effort of the FullyContingent scheme. Intuitively, by increasing the sensitivity of the second-period payments, future incentives
can perfectly replace the present incentives that were lost due to the present fixed wage without increasing the
expected cost. Using an exogenous measure of loss aversion, I structurally estimate the model to confirm that
loss aversion is related to contract choice.
This paper contributes to the literature on incentives by providing novel evidence on the optimality of fixed
wages coupled with deferred incentives. This is provoking as it challenges the standard principal-agent model,
which based on the risk-incentive trade-off, dictates that present payments must be contingent on present
outcomes whenever outcomes are observable. To the contrary, the laboratory evidence presented in this paper
suggests that a firm’s preference for paying fixed wages and delaying incentives in jobs where using present
incentives is feasible can be the reflection of the firms’ optimal behavior.
This paper also adds to the empirical literature studying the risk-incentives tradeoff. After Prendergast’s
(2002, 2000) assertion that the link between risk and incentives is tenuous, Bandiera, Prat, Guiso, and Sadun
(2015) use exogenous measures of risk attitudes to show that risk tolerance and the intensity of incentives are
positively related. Even though their measure of incentives mixes present and future incentives, their paper, as
well as this one, show that risk attitudes are a key driver behind the optimal provision of incentives.
Moreover, it also contributes to the empirical literature on the role of loss aversion in effort decisions when
workers have expectation-based reference-dependent preferences. Abeler, Falk, Goette, and Huffman (2011)
and Gill and Prowse (2012) provide direct evidence that effort provision is mediated by loss aversion where
the reference point corresponds to the workers’ expectations.2 Crawford and Meng (2011) apply this idea to
study the effects of exogenous wage changes on labor supply to rationalize negative wage-effort elasticities in
cab drivers’ labor supply.3 This paper enriches this literature by taking the loss-averse agent’s effort decision
as given to study its implication on the optimal shape of incentives from the principal’s perspective.4
Finally, this paper further contributes to the growing theoretical literature on the role of reference-dependent
preferences on hidden-action models. deMeza and Webb (2007) study the implications of several reference-point
specifications on a static moral hazard model. They find that optimal contracts have intervals where payments
are insensitive to performance and that rewards are more frequently used than punishments. Jofre, Repetto,
2
See Banerji and Gupta (2014) for evidence in auctions and Gneezy, Goette, Sprenger, and Zimmermann (forthcoming) for an
exploration of the limits of expectation-based reference-dependent preferences.
3
Goette, Huffman, and Fehr (2004) and Fehr and Goette (2007) also study the implication of loss aversion on labor supply but
using fixed reference points. In a different vein, Pope and Schweitzer (2011) show that loss aversion is important for effort provision
in the context of professional golfers’ performance.
4
See Kőszegi (2014) for a review of the theoretical literature studying the impact of loss aversion on optimal contracts.
2
and Moroni (2011) set a dynamic moral hazard model where the reference point is past consumption and they
find that the optimal contract is not monotonic and that it can be robust to savings. The model of Herweg,
Müller, and Weinschenk (2010) is most closely related to this paper’s theoretical model. They build a model of
static moral hazard with static reference-dependent preferences as in Kőszegi and Rabin (2006). They conclude
that the optimal contract has two levels of payments when the agent has a linear consumption utility. The
theoretical model in this paper differs from theirs mainly in its dynamic nature, which allows me to focus on
the intertemporal allocation of incentives rather than on the contract’s complexity.5
2
The Experiment
This section describes the laboratory experiment and its results. The experiment shows that a larger proportion
of workers strictly prefer to defer incentives for present performance at no expense on productivity or expected
cost. Therefore, even in a task with a well defined outcome—where using present incentives is feasible—a
principal will optimally choose to fully defer incentives into future payments.
2.1
The experimental design
(1) Recruitment. One hundred and twenty one students from nine different high-education institutions were
recruited to participate in a two-period study on productivity.6 Recruitment took place through campus flyers
and online postings providing background information and a contact email address for interested subjects who
were 18 years or older. Once a student sent an email, a research assistant blind to the research hypothesis
replied with a standardized response inviting them to participate. They were further informed that payments
were contingent on performance, though there was a minimum payment of $7,000 CLP (Chilean Pesos, with an
approximate exchange rate of $650 CLP per US dollar at the time of the implementation).7
(2) Task. The task was to find the two numbers that add up to 10 in a four by three matrix containing one or
two-decimal numbers. The program determined at random the number of decimals, with two-decimal numbers
having a probability of 0.8. Subjects, who were aware of the randomness in the number of decimals, were asked
to solve as many matrices as possible in a four-minute window, with a maximum of 20 matrices. There was a
counter showing the number of correctly solved matrices and a chronometer displaying the elapsed time at the
5
Moreover, the formal approach to solve the principal’s problems are also different. Herweg, Müller, and Weinschenk (2010)
use a continuous action set up with a linear specification of the conditional probability distribution and thus they rely on the
first-order approach. To the contrary, I use the discrete approach of Grossman and Hart (1983) and impose no restrictions over
the probability distribution. Iantchev (2005) and Daido and Itoh (2005) also build models of static moral hazard with referencedependent preferences to explain the Pygmalion effect and contract complexity respectively.
6
There were subjects from five different universities, three technical and one vocational institution.
7
See Appendix B.1 for the invitation email. The participation fee was split in a $2.000 fee for the first period and $5.000 for
the second period.
3
top of the page.8
This task was chosen for two reasons. First, it has an observable and verifiable outcome: every time
the subject solved the four-minute task, the program recorded the total number of matrices correctly solved.
Therefore, it would be easy for a principal to write down a contract based on output. Second, it resembles a
moral hazard problem where effort is not observable but it is—greatly though imperfectly—correlated with the
outcome, which is observed only after effort has been exerted.9
(3) Periods. Crucially, the study had two periods, the second occurring approximately one month after the
first. Subjects were aware of the two periods since recruitment. Both periods of the study took place in a
computer lab and were implemented completely through an online platform requiring almost no intervention
of the research assistants who were monitoring the room. Subjects worked in individual cubicles to avoid peer
effects. See Appendix B.2 for the full online platform.
3.1) First period. In the first period subjects solved the task three times. First, in the In-Lab-Practice stage
subjects solved the task in order to familiarize themselves with it. Second, in the Piece-Rate stage subjects
solved the task under a piece rate of $400 CLP—approximately 0.6 dollars—per correct matrix to obtain a
baseline measure of productivity. Third, in the Choice stage subjects were not assigned a payment scheme, but
rather chose a payment from two options, which determined not only the payments for this first-period Choice
stage, but also for the stage coming in the second period. The two possible schemes are described in (4) below.
3.2) Second period. In this period subjects solved the task only one time and they were paid according to the
scheme previously chosen in the first-period Choice stage. This is called the Second-Period stage.
(4) Payment schemes. The scheme choices available to subjects were,
4.1) A Fully-Contingent scheme, where the number of correct matrices in the Choice stage determined payments
in the Choice and Second-Period stages. This scheme, thus, sets incentives for first-period effort using present
and future payments, as prescribed by the classical theory.
4.2) A Deferred scheme, where the number of correct matrices in the Choice stage only determined payments
in the second period. This scheme, thus, sets incentives for first-period effort using only future payments, while
fixing the wage in the first period.
(5) Calibration of the payment schemes. Table 1 shows each payment scheme in detail. Both payment schemes
are bonus contracts that were calibrated using the model in Section 4.1. In both schemes the threshold for
8
This task replicates that in Ariely, Gneezy, Loewenstein, and Mazar (2009), except for the randomness in the decimals.
Subjects do not know how hard a matrix is until they have solved it. This is because of the uncertain position of the two correct
numbers: matrices where the correct numbers are close together are easier. The randomness of the decimals was important to ensure
that subjects were aware that there was uncertainty whenever making their effort plans (i.e., when reading the instructions). This
is crucial for the theoretical model in Section 4.1.
9
4
success was defined as the number of successes in the Piece-Rate stage minus one.10
UC Study
Table 1: Payment Schemes Choices
DEFERRED SCHEME
FULLY-CONTINGENT SCHEME
Success = Make X correct matrices or more
First-Period payments
They depend only on the number of correct matrices in the first period.
$13,000 if successful in the first period.
$3,000 if not successful in the first period.
$10,000 independent of whether
successful in the first period.
Second-Period payments
They depend on the number of correct matrices in the first and second periods.
$18,000 if successful in the first
and second periods.
$14,000 if successful in the first but not
in the second period.
$14,000 if successful in the second
but not in the first period.
$9,000 if not successful in either period.
$21,000 if successful in the
first and second periods.
$17,000 if successful in the first but
not in the second period.
$7,000 if successful in the second but
not in the first period.
$2,000 if not successful in either period.
I choose payment scheme 1
I choose payment scheme 2
A summary of the key aspects behind payments in Table 1 are as follows. First, the fixed-wage payment in
I am indifferent: Please, choose on my behalf
the Deferred scheme was approximately the
expected value of the first-period payments in the Fully-Contingent
making my decision, I rather read
more the instructions
scheme assuming the probability ofBefore
success
is around 0.7.11once
Second,
as the model in Section 4.1 shows, for the
Deferred scheme to replace the incentives lost due to the first-period fixed wage, it must be the case that the
second-period payments are more extreme than those in the Fully-Contingent scheme. Third, given secondperiod payments in the Fully-Contingent scheme, second-period payments in the Deferred scheme had to obey
several intuitive criteria: no negative or zero payments, only round numbers, the maximum payment in each
of the two schemes could not to be too different, and the summation of payments in each possible scenario
had to be the same across schemes. These restrictions were made to avoid salient features of the schemes that
would distract subjects from making a thoughtful intertemporal decision. Fourth, and most importantly, the
payments were chosen so that both schemes would have the same expected cost for any probability of success.12
10
In case the correct number of matrices in the Piece-Rate stage was zero or one, the threshold was set at one.
Using each subject’s baseline productivity to set the threshold for success also allows me to assume a common probability of
success, even in a population with heterogenous productivity. In the experiment, the actual common probability of success under
the Fully-Contingent scheme was 0.77 (see column (1) in Table 5).
12
Ex-ante, the expected cost of the Fully-Contingent scheme was 0.7 ∗ [13, 000 + (0.7 ∗ 18, 000 + 0.3 ∗ 14, 000)] + 0.3 ∗ [3, 000 +
(0.7 ∗ 14, 000 + 0.2 ∗ 9, 000)] = 27.360 while that of the Deferred contract was 0.7 ∗ [10, 000 + (0.7 ∗ 21, 000 + 0.3 ∗ 17, 000)] + 0.3 ∗
[10, 000 + (0.7 ∗ 7, 000 + 0.3 ∗ 2, 000)] = 27.360. The two payment schemes have the same expected cost for any probability of success
because the summation of payments in each possible scenario was the same across schemes.
11
5
Finally, in the Choice stage, after reading the scheme options and before working on the task, subjects
had to declare whether they preferred the Fully-Contingent scheme, the Deferred one, or whether they were
indifferent between the two. The indifferent option was important to ensure subjects’ preference was strict.
Before finishing the first period, subjects also had to choose which of the two payment schemes they would
use to motivate another worker to perform the same study. To do so, after the conclusion of the experiment two
subjects were randomly chosen, one as an employer and the other as an employee. The employee was chosen
among those who preferred not to play any lotteries. The employer was chosen among the whole subject pool.
The randomly chosen employer received $1,000 CLP—approximately 1.4 dollars—for each matrix the employee
solved correctly (adding matrices in the Choice and Second-Period stages). As before, each subject had to
declare whether they would rather use the Fully-Contingent scheme or the Deferred scheme, or if they were
indifferent between the two, in order to motivate another worker.
(5) Payment delivery. At the recruiting period and in the experimental instructions, subjects were explicitly
told that payments for each period would be paid in cash at the end of the corresponding period. This was
important to make the incentive deferral meaningful.13
(6) Conditions. The 121 subjects recruited to participate were randomly assigned to two conditions.
6.1) Decision Condition. 95 subjects (79%) were assigned to the study as previously described, i.e., they chose
a scheme defining payments in the Choice and Second-Period stages. Because beliefs about success will be
important to test the role of loss aversion in subjects’ scheme choice, a random subsample of 40 subjects in
this condition (42% of the 95 subejcts) were allowed to practice the task beforehand. Subjects in this Practice
treatment practiced from home before the the study took place through an online platform. The platform was
active during 3 and a half days before the first period so subjects could practice as many 4-minute tasks as
desired.14 The other 50 subjects (58% of subjects in the Decision condition) performed the task for the first
time the day the first period took place (No-Practice treatment).
6.2) Fixed-Payment Condition. To obtain a baseline measure of productivity absent of any incentives, the
other 26 subjects (21%) did not choose a scheme, but rather worked on the task in the Choice and in the
Second-Period stages for a fixed payment of $10,000 CLP in each.15
13
At the end of the first period subjects were offered the possibility of collecting first and second period payments together at
the end of the study. Only seven out of 95 subjects took this option (7.37%).
14
The platform was protected with a password and it was only available until right before the first period.
15
Subjects in this condition participated in the study before subjects in the other conditions. They were part of an initial version
of this study where only payments schemes in the Decision condition were slightly different and thus are not reported here. All of
these subjects belong to the same higher education institution where I recruited 52% of the 95 subjects in the Decision condition.
6
2.2
Results
This section presents the results of the experiment. I show that a larger proportion of subjects choose the
Deferred scheme vis-a-vis the Fully-Contingent one and they produce a higher number of correct matrices than
subjects who are paid fixed in both periods and the same or higher than subjects choosing the Fully-Contingent
scheme. I further show that these results are not driven by selection on skills nor on beliefs about success.
Rather, Section 4 will propose risk attitudes as a more likely explanation.
Result 1 A larger proportion of subjects strictly prefer the Deferred scheme over the Fully-Contingent one.
Table 2 columns (1) and (2), show that among the 95 subjects in the Decision condition, 58.95% chose the
Deferred scheme, while 41.05% chose the Fully-Contingent scheme (no subject was indifferent between the two
schemes). The 17.9% difference between the proportion of subjects choosing the Deferred and Fully-Contingent
schemes is statistically significant both in a Binomial as well as a Proportion test (p-value of the difference
equal to 0.001 and 0.000, respectively). Columns (3) and (4) show that the majority also chose the Deferred
scheme to motivate another worker: 51.06% chose the Deferred scheme, while 42.55% chose the Fully-Contingent
one (6.38% were indifferent). The 8.51% difference is statistically significant both in a Binomial as well as a
Proportion test (p-value of the difference equal to 0.024 and 0.001, respectively).16
Having shown that a larger proportion of subjects have a strict preference for the Deferred scheme, Result 2
and Result 3 show that subjects’ preference for the Deferred scheme does not come at the expense of lower
productivity.
Result 2 The Deferred scheme does not induce lower productivity relative to the Fully-Contingent scheme.
Table 3, column (1) shows that, if anything, subjects choosing the Deferred scheme produce more rather than
less correct matrices than those choosing the Fully-Contingent scheme. The number of correct matrices in the
Choice stage is 8.70 for those choosing the Deferred scheme, and 7.03 for those choosing the Fully-Contingent
one, a 1.67 difference. This difference is significant at the 10% level in a Mann Whitney test (p-value of the
Mann-Whitney test equal to 0.095). Adjusting for baseline productivity, defined as productivity in the PieceRate stage while clustering standard errors at the subjects’ high-education institution strengthens this result:
a difference of 1.61 correct matrices, which is statistically significant (p-value equal to 0.000).
Table 4 complements Result 2 by showing that productivity in the Choice stage under the Deferred scheme
is also higher than productivity in the Fixed-Payment condition were subjects are paid fixed in the Choice and
16
Appendix Table A1 shows that this preference is even stronger when considering subjects only in the No-Practice treatment.
7
Second-Period stages. Column (1) shows that, after adjusting for baseline productivity proxied by productivity
in the Piece-Rate stage, those who chose the Deferred scheme make 1.54 more correct matrices in the Choice
stage relative to those in the Fixed-Payment condition. This difference is highly significant (p-value equal to
0.000) once correcting for baseline productivity.17
After showing that subjects’ preference for the Deferred incentive does not harm productivity in the first
period, Result 3 shows that the same is true for the second period.
Result 3 In the second period the Deferred and the Fully-Contingent schemes induce the same productivity.
Table 3, column (2) shows that in the second-period stage, the Deferred scheme implements the same output as
the Fully-Contingent one. The number of correct matrices in the second-period stage is 8.12 for those choosing
the Deferred scheme, and 7.50 for those choosing the Fully-Contingent one, a difference of 0.62 correct matrices,
which is not statistically significant (p-value of the Mann-Whitney test equal to 0.509). Adjusting for baseline
productivity, defined as productivity in the Piece-Rate stage, and clustering standard errors at the subjects’
high-education institution level does not change this result: in this case there is a non significant difference of
0.46 correct matrices (p-value equal to 0.171).
As before, Table 4 complements Result 3 by showing that second-period productivity under the Deferred
scheme is also higher than productivity in the Fixed-Payment condition. Column (2) shows that, after controlling for differences in baseline productivity, those who chose the Deferred scheme make 1.50 more correct
matrices relative to those who were paid fixed in the Choice and Second-Period stages. This difference is highly
significant (p-value equal to 0.000).18
Result 1 to Result 3 jointly posit a puzzle for the classical principal agent model with observable outcomes.
Namely, a well stablished result in the standard principal-agent model is that the Fully-Contingent scheme is
optimal: given agents are risk averse, the principal must use present incentives to smooth the risk over periods
and thus decrease the premium paid to the agent for bearing risk. As a consequence, if the agent prefers the
17
Because subjects in the Fixed-Payment condition did not practice from home, the Deferred scheme sample in Table 4 contains
only subjects in the No-Practice treatment in the Decision condition. Moreover, because subjects in the Fixed-Payment condition
belong to only one high-education institution, columns (3) and (4) show that in this case there are differences in baseline productivity
across groups. This indicates that meaningful productivity comparisons between groups can only be obtained if we control for these
differences. Table A2 in appendix repeat the analysis restricting the Deferred scheme sample to subjects only in the same higheducation institution. It shows that the results are the same once we adjust by productivity differences to gain power due to
the smaller sample sizes (26 subjects in the Fixed-Payment condition and 21 subjects in the Decision condition who chose the
Deferred payment). In this more restrictive case, subjects choosing the Deferred scheme still do 1.56 more matrices than those in
the Fixed-Payment condition, difference which is significant (robust p-value equal to 0.056).
18
As described in footnote 17, only results corrected by baseline differences in productivity are meaningful as in this case
productivity in the Piece-Rate and In-Lab-Practice stages is different across conditions. See Table 4, columns (3) and (4). As
before, Table A2 in the appendix show that this result is robust to restricting the Deferred scheme sample to subjects only in
the same high-education institution. In this case, subjects choosing the Deferred scheme do 1.54 more matrices than those in the
Fixed-Payment condition, difference which is significant at the 10% level (p-value equal to 0.096).
8
equally costly Deferred scheme, it must be the case that he is less productive if paid with it. If the agent is
not less productive under the Deferred scheme, then the principal could cut the fixed first-period wage until
the agent is indifferent between schemes, thus decreasing the Deferred scheme’s expected cost. This, however,
implies that the Deferred scheme induces the same productivity and at a lower expected cost, which violates
the optimality of the Fully-Contingent scheme. Formally, risk aversion can relax the participation constraint
of the Deferred scheme, but at the cost of failing on the incentive compatibility restriction given that the two
schemes have the same expected cost. Thus, even though risk aversion can explain Result 1, it cannot explain
that, given that Result 1 holds, Result 2 and 3 also hold.
The model in Section 4.1 will argue that even though risk aversion can not account for Result 1 to 3, an
alternative explanation based on loss aversion can. Before, however, Result 4 to 6 explore other potential drivers
behind subject’s preference for the Deferred scheme: selection based on skills and on beliefs about success to
conclude that neither of them seem to be a driving force.19
Result 4 Subjects choosing the Deferred scheme have the same skills as those choosing the Fully-Contingent
scheme.
If higher ability subjects self-select into the Deferred scheme then higher productivity due to higher skills can
offset the shortage in incentives making the Deferred and Fully-Contingent scheme look equally effective.20
Table 3, columns (3) rule out, however, that this is the case. In the Piece-Rate stage, the unadjusted difference
in productivity between those choosing the Deferred and the Fully-Contingent schemes is very small, 0.08
and not significant (p-value of the Mann-Whitney test equal to 0.744). Correcting by baseline productivity
(measured by productivity in the In-Lab-Practice stage) and clustering standard errors at the high-education
institution level does not change this result: a -0.38 difference in correct matrices (p-value equal to 0.615). The
same conclusion holds using productivity In-Lab-Practice stage as a proxi for skills (Table 3, column (4)).
Result 5 Subjects choosing the Deferred scheme are not more pessimistic about their likelihood of success in
the first period than those choosing the Fully-Contingent scheme.
A second type of selection arises if subjects choosing the Deferred scheme are more pessimistic about their
chances of success in the first period vis-a-vis those choosing the Fully-Contingent scheme. Lower probability of
success in the first period can explain subjects’ preference for the Deferred scheme as it could make it optimal to
19
Recall that classical explanations for deferred incentives or fixed payments reviewed in Section 3.1 do not apply in the experiment
as outcomes are observable and the environment is constant across all subjects.
20
This, however, goes against the proposition that fixed-payments induce self-selection of low rather than high skill workers
(Lazear (1986, 2000), Eriksson and Villeval (2008), Dohmen and Falk (2011)).
9
choose the scheme ensuring a fixed payment, at least in the first period. I thus compare the actual probability of
success of subjects who chose the Fully-Contingent scheme to that of subjects who chose the Deferred scheme.
Table 5 shows that the first-period probability of success in the Choice stage is actually higher—rather than
lower—under the Deferred vis-a-vis the Fully-Contingent scheme. Column (1) shows that the probability of
success for those who chose the Deferred scheme is 0.86, while for those who chose the Fully-Contingent scheme
is 0.77, leading to a difference of 0.07, which, even though not statistically significant using a Mann-Whitney
test (p-value of the Mann-Whitney test equal to 0.274), is significant once adjusting for baseline productivity
with clustered standard errors (p-value equal to 0.037).
The result that the probability of success is higher under the Deferred scheme also holds for subjects in
the Practice treatment, who should hold accurate beliefs thanks to their from-home training. First, subjects in
this treatment did train extensively. Table 6, column (1) shows that on average, subjects practiced 9.15 tasks
with a standard deviation of 8.45 and a maximum of 41 tasks. Second, Table 5, column (3) shows that for
subjects in this treatment, the probabilities of success having chosen the Deferred and the Fully-Contingent
schemes are 0.95 and 0.74 respectively, leading to an statistically significant 0.22 difference (p-value of the of
the Mann-Whitney test equal to 0.060). Clustering standard errors and correcting by baseline productivity
does not change this result (difference of 0.21 with a p-value equal to 0.028). Thus, subjects’ preference for the
Deferred scheme is unlikely driven by pessimism on the likelihood of success in the first period.
Result 6 Subjects choosing the Deferred scheme have the same belief about their likelihood of success in the
second period as those choosing the Fully-Contingent scheme.
A second type of selection on beliefs arises if subjects choosing the Deferred scheme are more optimistic about
their chances of success in the second period. This form of optimism can explain subjects’ preference for the
Deferred scheme as, for any given belief of first-period success, they can prefer the scheme that has greater
payments in the second period. Table 7 shows, however, that attrition—the natural proxi for beliefs about
success in the second period—is the same for those choosing the Deferred and Fully-Contingent schemes. Column
(2) shows that the attrition rate among those choosing the Deferred scheme is 8.93%, while those choosing the
Fully-Contingent scheme is 12.82%, a 3.89% difference, which is not statistically significant (p-value of the of
the Mann-Whitney test equal to 0.545).21
21
Table 8 shows that subjects in the Practice and No-Practice treatments have similar attrition rates, while only subjects in the
Fixed-Payment condition have higher attrition.
10
3
Mechanisms
To provide context for this paper’s null hypothesis on the optimality of fixed wages coupled with deferred
incentives when workers are loss averse, Section 3.1 reviews existing theories for fixed wages and deferred
incentives. It argues (1) that most of these theories rely on the non-observability of outcomes, and (2) that,
even though not mutually exclusive, no existing theory can simultaneously explain fixed wages and deferred
incentives. Section 3.2 further argues that other explanations to fixed wages coupled with deferred incentives
must go beyond solely job characteristics.
3.1
Current Explanations for Fixed Wages and Deferred Incentives
(1) Why are real-world contracts far less contingent on present performance than predicted? 22
I first review the most prominent explanations: monitoring costs, multitasking, relational contracts, relative performance and cooperation, and social preferences. I highlight that most of them build on the non-observability
of the performance measure, while arguing that none of them, without further assumptions, can simultaneously
explain the optimality of deferred incentives with fixed wages.23
1.1) Monitoring costs. Following Lazear (1986), one of the most prominent reasons why firms do not use
pay-for-performance is monitoring costs, which whenever sufficiently large, render output-contingent payments
suboptimal. Despite that monitoring costs can account for why wages can be optimally fixed by assuming
outcomes are not perfectly observable or verifiable, they cannot explain why incentives are deferred. Without
an additional assumption on how monitoring costs can decrease over time, they cannot explain why it might
be optimal for principal to delay incentives into future payments.
1.2) Multitasking. Holmström and Milgrom (1991) extended the classical moral-hazard problem to incorporate
the idea that jobs have multiple tasks or dimensions. They showed that whenever effort in one task increases
the marginal cost in another task whose output is non-observable or hard to measure, it is optimal to pay fixed
wages.24 Intuitively, if the principal wants to allocate effort in both tasks, incentives are counterproductive
because they distort effort away from the task with the unobservable outcome.25 Multitasking, however, cannot
explain why incentives in real-world contracts are deferred. Namely, if present incentives drive effort away from
22
This question has a long history. More than thirty years ago, Holmström and Milgrom (1991) already noticed that “it remains
a puzzle for [agency] theory that employment contracts so often specify fixed wages and more generally that incentives within firms
appear to be so muted”, while Baker, Jensen, and Murphy (1988) argued that “explicit financial rewards in the form of transitory
performance-based bonuses seldom account for an important part of a worker’s compensation”.
23
Explanations are reviewed in alphabetical order.
24
As Dewatripont, Jewitt, and Tirole (2000) highlight, however, a multitasking problem can arise even if all tasks’ output are
measurable but one is noisier than others.
25
Dumont, Fortin, Jacquemet, and Shearer (2008) provide evidence of effort reallocation across multiple tasks in response to
changes in the compensation scheme of physicians. Further evidence for multitasking can be found in Slade (1996).
11
the task with the non-observable outcome, so will future incentives. Both, present and future incentives are
thus counterproductive and the principal should choose not to provide formal incentives in any period.
1.3) Relational contracts. In a repeated principal-agent relationship, whenever the outcome measure is nonobservable or non-verifiable, the principal can use self-enforced informal agreements to provide incentives (e.g.
MacLeod and Malcomson (1989), Levin (2003)). Namely, the principal can offer an informal contingent bonus to
motivate effort, which will be honored if the continuation value of the relationship is high enough. In this case,
because incentives are set implicitly, the formal contract can take the form of a simple fixed-wage contract.26
Despite that relational contracts can account for fixed wages, they cannot explain the optimality of deferred
incentives: because in relational contracts both parties are risk neutral, present and future incentives are perfect
substitutes, and thus the optimal relational contract takes a stationary form in which the same compensation
scheme is used in every period (Levin (2003)).27
1.4) Relative performance and cooperation. Lazear (1989) showed that whenever workers are paid according to
their relative performance and there are sabotage opportunities, wage compression might be optimal. Indeed,
wage differentials create incentives to work but they also create incentives to sabotage others’ output. Paying
the same to winners and losers—a fixed wage—might thus be optimal if the costs of sabotage fully offset the
benefits of competition.28 Relative performance and cooperation can account for fixed wages but it cannot
account for the optimality of deferred incentives. As it is the case with multitasking, there is no reason why
the counterproductive effects of wage dispersion change across periods. As a consequence, if the present costs
of sabotage offset the present benefits of competition, the same should apply to future costs of sabotage and
future benefits of competition.
1.5) Social preferences. In a static moral-hazard model, Englmaier and Leider (2012) showed that fixed wages
can be optimal if agents have reciprocal preferences. A reciprocal agent is motivated by standard contingent
incentives and also by a generous fixed wage, which he returns with high effort to maximize utility. Whenever
reciprocal concerns are sufficiently strong and agents are risk averse—rendering pay-for-performance expensive—
the risk-neutral principal can implement effort at a cheaper cost by relying only on a generous fixed wage to
motivate the worker.29 Reciprocal preferences, however, cannot explain why incentives in real-world contracts
26
Brown, Falk, and Fehr (2004, 2012) present experimental evidence that implicit contracts arise spontaneously in the context
of long-term trading interactions. Johnson (1985) showed that fixed-wage contracts with layoffs are socially optimal (even though
not optimal for any individual firm) whenever risk-neutral workers have heterogenous search costs of looking for an alternative job
and their marginal product is stochastic.
27
This conclusion depends crucially on the risk neutrality assumption. Since in the static moral-hazard model with classical
preferences and observable outcomes, risk aversion predicts that present and future incentives are complements, it is reasonable to
expect that this property will be preserved in the case of relational contracts with risk aversion.
28
Drago and Garvey (1998) provided empirical evidence that helping efforts among coworkers are reduced whenever promotion
incentives are strong.
29
Relatedly, von Siemens (2013) shows that contingent contracts can have perverse effects on performance whenever the agent’s
12
are deferred. Indeed, unless preferences—and in particular, reciprocal preferences—dwindle over time, there is
no reason why it could be optimal for the principal to delay incentives for present effort.
(2) Why firms use future instead of present payments to motivate effort today?
Next, I review the main explanations for deferring incentives to motivate present effort. As before, I argue that
none of them, without further assumptions, predict fixed wages.
2.1) Career concerns. Fama (1980) argued that reputation concerns are a perfect substitute for present contingent incentives: firms can pay present fixed wages and trust that the market will make future payments
depending on current performance. Similarly, Lazear and Rosen (1981) showed that a contract paying according to the worker’s ordinal rank in the firm can be optimal relative to a standard output-based contract.30
Career concerns, however, are not a perfect substitute for present incentives: Holmström (1999) formalized
Fama’s intuition and showed that motivating through pure reputation concerns is probably suboptimal because
of the agents’ risk aversion. Gibbons and Murphy (1992) enriched Holmström (1999) to show that the optimal
contract optimizes the sum of both types of incentives: implicit coming from reputation and explicit coming
from the formal contract, where the importance of the latter increases as retirement approaches.31 In Gibbons
and Murphy’s framework, therefore, present and future incentives are complements rather than substitutes and
thus career concerns cannot predict the optimality of fixed wages.
2.2) Incentives through the life-cycle. Lazear (1979, 1981) presented a model where workers are paid below
their marginal productivity when young and above it when old. Lazear showed that this deferred payment
scheme creates stronger incentives for effort relative to paying a worker his spot marginal productivity because
it increases the opportunity cost of shirking. The optimal incentive scheme trades off this benefit with the
firm’s perverse incentive to dismiss workers at an early date.32 Lazear’s analysis, however, assumes the wage
is fixed within periods, an assumption disproved by Akerlof and Katz (1989), who showed that in Lazear’s
environment, deferred incentives are not a perfect substitute for present incentives. This implies that for deferred
compensation to be optimal, there must be some form of non-observability or monitoring cost preventing the
use of present contingent payments.33
reciprocal type is his private information. Reciprocal preferences were proposed in the seminal work of Rabin (1993) and further
developed by Dufwenberg and Kirchsteiger (2004) and Falk and Fischbacher (2006). For an extensive summary of the evidence on
reciprocal preferences see Fehr and Fischbacher (2002) and Fehr, Goette, and Zehnder (2009).
30
Chevalier and Ellison (1999) presented empirical evidence of the effects of dismissal over fund managers’ performance.
31
The original Holmstrom article was published in 1982 in Essays in Economics and Management in Honor of Lars Wahlbeck.
32
Huck, Seltzer, and Wallace (2011) provided experimental evidence that credible deferred compensation does increase effort
relative to a non-credible deferred compensation. Related, Loewenstein and Sicherman (1991) provided survey evidence that
workers have a taste for increasing wage profiles. Using a laboratory experiment, Sliwka and Werner (forthcoming) showed that
these wage profiles raise worker’s performance whenever agents are not aware of the increasing profile.
33
Hutchens (1987) presented evidence that jobs associated with better monitoring tend not to have characteristics associated
with delayed payment contracts.
13
2.3) Retention. Salop and Salop (1976) proposed that deferred compensation can be used as a self-selection
device to minimize turnover costs and maximize retention. Deferring incentives into the future can thus be
optimal when workers are heterogeneous in non-observable dimensions and screening is imperfect or costly. In
their analysis, however, payments are assumed to be fixed within periods.
2.4) Rewarding long-term returns. Assuming that (noisy) signals about executives’ performance are only available in the future, Eaton and Rosen (1983) proposed that deferring compensation is optimal to solve short-run
agency problems, as future incentives “bond” executives to their firms. Present fixed wages in this model,
therefore, arise due to the assumption over the temporal observability of the performance measure and thus
this explanation cannot account as to why deferred incentives are coupled with fixed wages.
3.2
The need for an alternative to existing models
As argued in Section 3.1, most of the previous explanations for fixed wages and deferred incentives lie on the
impossibility of tying present payments to present performance. Multitasking and relational contracts assume
outcomes are hard to observe or verify; monitoring costs, relative performance and cooperation, and incentives
through the life cycle assume monitoring is expensive. I argue, however, that focusing solely on the nonobservability of outcomes provides an incomplete explanation to fixed wages coupled with deferred incentives.
First, present payments are not formally tied to present outcomes even in highly repetitive tasks where
output is easily-measurable and thus likely observable and verifiable. Namely, evidence shows that present
incentives are not used even in blue and pink-collar jobs where performance measures are readily observable.
For instance, using the Quality of Employment Survey, MacLeod and Parent (1999) document that 84% of
precision machine operatives declare that their job is repetitive, while having the lowest rate of learning among
all the surveyed occupations. Despite this, 0% of them are paid using commissions or piece rates, the two most
common forms of pay for present performance. This finding is similar for office machine operators and laborers
(except farm).34 Similarly, Lemieux, MacLeod, and Parent (2009) show that only 30% of craftsmen are paid
using commissions, piece rates or bonuses.35 Petersen (1992) studies the compensation structure of a sample of
more than 62,000 sales persons in 264 retail stores in the United States. He documents that more than half of the
sample is paid independently of present performance. Using representative data of the manufacturing industry
in Germany, Jirjahn and Stephan (2004) find that less than 25% of the blue-collar workers use contingent
payments in the form of piece rates. Moreover, they document that in sectors like services, mining, energy,
water and construction, piece rates are not used at all. This evidence, therefore, suggests that not only the
34
35
See Tables 2.A and 3.A.
Their definition of bonuses, however, admit long-term bonuses, such as yearly ones.
14
outcome observability is at play when considering the optimality of fully deferred incentives.
Second, if the non-observability of the outcome is the main driver behind fixed wages and deferred incentives,
then we should observe that the same job within a given industry is incentivized using similar contracts across
different firms, as all of these jobs should have the same level of outcome observability.36 To the contrary, there
is evidence that the same job within an industry is paid using different incentive schemes across firms. For
instance, Gerhart and Milkovich (1990) examine whether organizations facing similar conditions make different
compensation decisions regarding fixed pay, bonuses and long-term incentives. Using data on 14,000 middle
to top managers in 200 organizations in the US, they conclude that compensation differences between firms
remain after differences in employees, jobs, industry, size and financial performance are accounted for.
If outcome observability is not the only determinant of the optimal allocation of incentives between present
and future payments, another possible explanation lies in the agents’ risk preferences, as suggested by the
classic risk-incentive trade-off. A concave consumption utility, however, cannot fully account for how firms and
managers set incentives across periods. As explained before, the dynamic moral-hazard model with a concave
utility function predicts that contracts should use more contingent payments rather than less whenever agents
are risk averse: because making present and future payments contingent in the present outcome allows the agent
to smooth consumption, a fully contingent contract increases the agent’s total utility, allowing the principal
to pay lower wages (Lambert (1983), Rogerson (1985), Murphy (1986), Malcomson and Spinnewyn (1988),
Chiappori, Macho, Rey, and Salanié (1994)).37
The idea that risk aversion is not sufficient to explain the optimal temporal allocation of incentives relates
to the findings in Macpherson, Prasad, and Salmon (2014). Using a laboratory experiment with 10-period
sessions, they show that subjects have a preference for an efficiency wage profile (i.e., a constant fixed wage
above the outside option) over a deferred compensation one (i.e., an increasing fixed wage above the outside
option), which cannot be rationalized by risk aversion. Even though their focus is on efficiency wages while my
study focuses on the standard pay-for-performance predicted by the classical moral hazard model, their results
support the idea that more than just risk aversion is needed to explain subjects’ preferences on how to spread
risk across present and future payments.
36
I thank a thoughtful referee for suggesting this testable implication.
The consumption smoothing argument lies crucially on the agent’s liquidity restrictions. Intuitively, if the risk-averse agent
can save or borrow in the capital market, he can transfer consumption across periods on his own, i.e., independently of the contract.
For blue-collar jobs, however, it is reasonable to assume that credit constraints are active. For instance Solis (forthcoming) provides
evidence of credit constraints among low-income Chilean students, who most likely will perform blue-collar jobs in the future.
Similar results can be found for the United States in Teng Sun and Yannelis (2016). Moreover, even if the agent can save, a whole
literature in behavioral biases might prevent optimal smoothing. For instance, agents with present-biased preferences can choose a
contract that smooths consumption as a commitment device instead of using the capital market to do so. See footnote 13 for details
on how the laboratory study addressed this issue.
37
15
4
An Explanation Based on Loss Aversion
This section proposes an explanation to the experimental results based on loss aversion. Section 4.1 presents
the basic mechanism in the most simple case of bonus contracts in a two-effort and two-outcome environment.38
Section 4.2 tests the relationship between subjects’ scheme choice and loss aversion using the laboratory data
to show that loss aversion induces self-selection of subjects into the Deferred scheme.
4.1
The basic mechanism under loss aversion
(1) Setting. A principal (she) offers a contract S to an agent (he) to implement high effort in two periods.
High effort, eh , costs c to the agent in each period. Normalize the cost of low effort, e` , to zero. To isolate the
role of loss aversion, I assume the principal and the agent are risk neutral. Furthermore, to keep the utility
specifications simple, second-period effort is assumed observable so the principal can contract upon it. In the
first period, however, she can only contract on an observable outcome X, as first-period effort is not observable.
Assume the first-period outcome can be high or low, X ∈ {xh , x` }, xh < x` , where 0 < πe < 1 denotes the
conditional probability of xh given first-period effort. Let x denote any possible realization of X.
The timing is as follows. In an initial period, the principal offers the contract S to the agent, who accepts
or rejects. If he accepts, he commits to working during both periods. Considering the contract he just signed,
the agent forms his effort expectations for the two upcoming periods. In a first period he exerts effort, observes
the outcome realization, receives his payment and consumes it. Given that the outcome realization brings news
to the agent, at the end of the first period he uses such information to update his effort plans for the second
period. Then in the second period he exerts effort, receives his payment and consumes it.
In this simple environment, the principal’s problem reduces to choose first and second-period payments to
implement first-period effort at a minimum expected cost.39 To motivate first-period effort, however, the principal can choose between making first-period or second-period payments contingent on the outcome realization
observed in the first period. In this section I show that, to the contrary of what would be predicted by standard
preferences, deferring incentives implements first-period effort at a lower expected cost without decreasing the
incentives for first-period effort.
(2) Preferences. Agents have reference-dependent preferences as in Kőszegi and Rabin (2006). Therefore, they
experience two types of utility: standard consumption utility and reference-dependent utility from payments
and effort. Reference-dependent utility compares each possible outcome realization with a reference point, which
38
The model is a particular case of the general model in Macera (2016). The general model uses a dynamic rather than a static
version of reference-dependent preferences and N outcomes instead of a two-outcome model.
39
Indeed, because second-period effort is observable, the continuation contract defined by second-period payments will ensure
that the agent will exert high effort in the second period.
16
corresponds to the agent’s rational expectations about outcomes. In this case, because the agent’s expectations
are shaped by the contract, the reference point is possibly stochastic. Thus, following Kőszegi and Rabin, I
assume he compares each posible realization of the reference point with each possible outcome. The agent’s
utility from comparing actual outcomes with expected ones is given by a function µ, which—as is standard in the
literature—is assumed to be piece wise linear, i.e., µ(x) = x if x > 0, µ(0) = 0 and µ(x) = λx if x < 0, where λ >
1 is the loss aversion parameter reflecting how much losses hurt than same-sized gains please. Finally, the total
utility the agent gets from a contract S whenever planning and exerting high effort in both periods corresponds
to the discounted sum of the utility he gets in both periods, EU (S) = EU1 (eh |eh ; S) + δEU2 (eh |eh ; x, S) where
δ < 1 is a standard discount factor.40
(3) Payment schemes. Following the experimental design, the two payment schemes or contracts the principal
can use to implement high effort in both periods are,
3.1) Fully-Contingent scheme (S F C ). This scheme consists of a first-period payment S1F C , which depends on
first-period outcomes and a second-period payment S2F C , which depends on second-period performance. That
is,
S1F C =


sh
if X = xh

s < s
`
h
if X = x`
and S2F C =


(UR + c)
if e = eh

−∞
if e = e`
where UR is the outside option and the second-period contract is defined in terms of the second-period effort
because of the observability assumption. I assume sh and s` are such that they implement high effort at the
least cost for an agent with classical preferences, i.e., for λ = 1.
3.2) Deferred scheme (S D ). This scheme consists of a modification of the Fully-Contingent one: it has the same
expected cost but, crucially, it uses only future incentives to motivate the agent. The contract offers a fixed
first-period wage equal to the expected value of S1F C given high effort. To replace the incentives lost due to the
fixed first-period payment, the contract makes second-period payments depending on the first-period outcome
realization. Thus the first and second-periods payments, S1D and S2D , are,
S1D = E(S1F C |eh ) = πh sh + (1 − πh )s` ∀x
and S2D



(UR + c) + ρh



= (UR + c) − ρ`





−∞
if X = xh and e = eh
if X = x` and e = eh
if e = e` for any x
where sh , s` are defined in S F C , and ρh > 0, ρ` > 0 are such that contracts S F C and S D have the same expected
40
I explicitly add for readers to see that the key driver behind the optimality of deferred incentives is not discounting.
17
cost,
πh ρh − (1 − πh )ρ` = 0
(1)
(4) Which payment scheme does the agent choose? To answer this question, I explore which contract provides the
agent a higher overall utility (the individual rationality restriction). I show that because agents with referencedependent preferences experience disutility from payment variation, they are strictly better off choosing the
Deferred scheme, as proven in the laboratory experiment in Result 1.
(4.1) Individual-rationality restriction of the Fully-Contingent scheme. The total expected utility the agent gets
from contract S F C whenever he plans and implements high effort is,
n
o
EU (eh , |eh ; S F C ) = πh sh + πh µ(sh − sh ) + (1 − πh )µ(sh − s` ) − c + δ(UR + c − c)
n
o
+ (1 − πh ) s` + πh µ(s` − sh ) + (1 − πh )µ(s` − s` ) − c + δ(UR + c − c)
= πh sh + (1 − πh )s` − c + (1 − λ)πh (1 − πh )(sh − s` ) +
|
{z
} |
{z
}
E(consumption ut.)
E(referent-dependent ut.)< 0
δUR
|{z}
(2)
Second-period utility
The first bracket shows first-period expected consumption utility in payments and effort, the standard
expected utility source in agency models.
The second bracket, which is negative for loss averse agents, is the crucial one. It shows the expected
reference-dependent utility from payments, capturing the utility the agent gets from comparing actual payments
with expected ones in the first period. If λ = 1 then this term is zero. If λ > 1, i.e., if the agent is loss averse,
this term reflects the disutility the agent gets from payment variation: the prospect of being disappointed by
the actual payment realization outweighs the prospect of being pleasantly surprised by it. A fixed first-period
wage therefore, would save the agent from this disutility.41
Consider now second-period utility. Since in the contract S F C second-period payments do not depend on
the first-period outcome and second-period effort is observable, the continuation contract contains no payment
uncertainty: the agent knows that in the second period he will exert high effort and thus knows how much he
is going to be paid. As a consequence, all reference-dependent terms in second-period utility are zero and the
agent only experiences consumption utility in wages and effort.
(4.2) Individual-rationality restriction of the Deferred scheme. The total expected utility the agent gets from
41
Notice that there is no reference-dependent utility from effort in equation (2), as in equilibrium the agent plans and implements
high effort and thus there are no departures from expectations in this domain.
18
contract S D offering a fixed first-period payment, whenever he plans and implements high effort is,
n
o
n
o
EU (eh |eh ; S D ) = πh S1D − c + δ(UR + c + ρh − c) + (1 − πh ) S1D − c + δ(UR + c − ρ` − c)
= S1D − c + δ UR + (πh ρh − (1 − πh )ρ` )
(3)
where the most important difference between equations (2) and (3), is that, because of the fixed first-period
wage, the latter has no disutility form payment variation.42
I now can show that the agent is strictly better-off under the Deferred scheme. Using equation (1), which
ensures that S F C and S D have the same expected cost, and the definition of S1D as the expected consumption
utility of contract S1F C , we can compare equation (3) to (2),
EU (eh |eh ; S D ) = S1D − c + δUR ± (1 − λ)πh (1 − πh )(sh − s` )
= EU (eh |eh ; S F C ) − (1 − λ)πh (1 − πh )(sh − s` )
> EU (eh |eh ; S F C )
(4)
As the agent strictly prefers the Deferred contract to the Fully-Contingent one, he is strictly better-off deferring
incentives for present effort. Intuitively, because S D pays a fix first-period payment, it saves the agent from
first-period disutility from payment variation while providing the same second-period utility.
(5) Does the Deferred scheme induce the same effort as the Fully-Contingent one? I now show that if the
principal chooses the parameters ρh and ρ` appropriately, the agent will also exert high effort under the Deferred
scheme (as in the Fully-Contingent one), as also in the laboratory experiment, Result 2. Using only future
incentives, therefore, the Deferred scheme is able to provide the same incentives for first-period effort as the
Fully-Contingent scheme.
(5.1) Incentive-compatibility restriction of the Fully-Contingent scheme. Given contract S F C and having planned
to exert high effort—as warranted by the individual-rationality restriction—the agent will exert high effort only
if the utility of carrying his plan through is greater than that of deviating towards low effort, EU (eh |eh ; S F C ) −
42
Notice that this is even more striking: in equation (3) all reference-dependent terms are zero. For present payments this
is straightforward: in the payment domain there are no departures from expectations because the payment is fixed, while in
the effort domain rational expectations ensure the agent foresees he will exert high effort. For future payments there are no
departures from expectations either, as once x has been observed at the end of the first period, the agent knows with certainty
what will be his second-period payment given his effort choice. To see this last point, notice that EU (eh |eh ; S D ) = πh S1D −
c + δU (eh |eh ; xh , S D ) + (1 − πh ) S1D − c + δU (eh |eh ; x` , S D ) where the second-period utility having observed xh corresponds to
U (eh |eh ; xh S D ) = ((UR + c) + ρh − c) + µ((UR + c) + ρh − ((UR + c) + ρh )) + µ(−c − (−c)) = (UR + c) + ρh − c. A similar computation
shows that U (eh |eh ; x` S D ) = (UR + c) − ρ` − c.
19
EU (e` |eh ; S F C ) > 0.43
Using equation (2) to compute EU (e` |eh ; S F C ) and then taking differences, under contract S F C the agent
exerts high effort if,
EU (eh |eh ; S F C ) − EU (e` |eh ; S F C ) =
(πh − π` )(sh − s` )
{z
}
|
Incentives from consumption ut.
+ [(1 − πh ) + λπh ](πh − π` )(sh − s` ) − µ(c) > c
|
{z
}
Incentives from ref.dependent ut.
(5)
Equation (5) shows that under contract S F C there are two sources of incentives, both coming from firstperiod payments (second-period payments do not depend on the outcome realization). The first is incentives
from consumption utility: implementing high effort increases the probability of getting the high payment and
decreases the probability of a low one, as it is the case in standard moral-hazard models.
The second bracket shows incentives coming from first-period reference-dependent utility: carrying through
the high-effort plan increases the probability of a gain and decreases the probability of a loss in the payment
domain but it also forgoes the positive surprise of having to exert less effort than planned.44
(5.2) Incentive-compatibility restriction of the Deferred scheme. Given contract S D and having planned to
exert high effort—as warranted by the individual rationality restriction—the agent will exert high effort only
if the utility of carrying his plan through is greater than that of deviating towards low effort, EU (eh |eh ; S D ) −
EU (e` |eh ; S D ) > 0.
Using equation (3) to compute EU (e` |eh ; S D ) and then taking differences, under contract S D the agent will
exert high effort if,
EU (eh |eh ; S D ) − EU (e` |eh ; S D ) =
−µ(c)
| {z }
Present ref.dependent ut.
+ δ(πh − π` )(ρh + ρ` ) > c
|
{z
}
(6)
Future consumption ut.
Equation (6) shows that under contract S D there are two sources of incentives, one coming from present
payments and another from future payments. Given the first-period payment is fixed in this contract, present
payments only trigger a reference-dependent incentive coming from the forgone utility of exerting less effort
than planned, which discourages high effort. Further, to the contrary of equation (5), there are no incentives
coming from present reference-dependent utility from payments.
The second bracket represents the incentives from future payments that are particular to the Deferred
scheme, which will be in charge of replacing the incentives that were lost by fixing the first-period payment.
43
This is Kőszegi and Rabin (2006)’s Personal Equilibrium concept, where an action is an equilibrium only if the agent is willing
to implement it having planned it.
44
Notice that because S F C does not make future payments contingent on first-period performance, there are no incentives coming
from second-period wages.
20
In particular, these incentives come from second-period consumption utility: if the agent executes high effort
in the first period, he increases the probability of getting the high second-period payment instead of the low
one.45
Using equations (5) and (6), it is easy to see that S D will replace the incentives lost by fixing the first-period
wage if ρh and ρ` satisfy,
(ρ∗h + ρ∗` ) =
1
1 + [(1 − πh ) + λπh ] (sh − s` )
δ
(7)
Finally, noticing that equations (1) and (7) form a system of two equations with two unknowns, we have that
if the principal sets ρh and ρ` as,
ρ∗h =
(1 − πh ) 1 + [(1 − πh ) + λπh ] (sh − s` )
δ
and ρ∗` =
πh 1 + [(1 − πh ) + λπh ] (sh − s` )
δ
the contract S D implements high effort and at the same expected cost than S. As overall utility is higher under
the Deferred scheme, then the principal can decrease the first-peril fixed wage, implement high effort in both
periods and lower the expected cost relative to the original contract S F C .
Finally, notice that the model highlights that the key driver behind the optimality of deferred incentives is
loss aversion and not discounting. As shown in equations (2) and (3), second-period utility is constant across
payment schemes and thus discount plays no role in the intertemporal allocation of incentives. Intuitively,
ρ∗` and ρ∗h strategically increase the distance between the continuation contracts (i.e., the contracts after a
first-period realization) without affecting the distance of payments across first-period outcome realizations.46
4.2
Loss aversion and scheme choice in the laboratory experiment
This section tests the prediction that loss aversion is related to subjects’ scheme choice. It shows that, as
predicted by the model, whenever loss averse subjects face uncertainty in their probability of success, they are
more likely to choose the Deferred scheme than the Fully-Contingent one.
45
Importantly, second-period consumption utility is the only source of future incentives: because there is no uncertainty in
payments in the second period once the first-period outcome is observed, there are no departures from expectations and referencedependent utility cannot help setting incentives. The general model in Macera (2016) relaxes this by assuming that agents experience
in period one the anticipation of changes in future payments, as proposed by Kőszegi and Rabin (2009), to show that even in this
general case agents prefer the Deferred scheme at no cost to performance or expected cost.
46
In Macera (2016) I show that deferring incentives into future periods is optimal even if the agent experiences disappointment
from anticipating changes in future wages, which implies the agent will experience disutility from payments across first-period
outcomes realizations. Even though this adds great technical complexity to the analysis as it requires working with dynamic
preferences, I show that the main forces still hold.
21
According to equation (4), subjects prefer the Deferred scheme over the Fully-Contingent one if,
EU (Deferred scheme) − EU (Fully-Contingent scheme) = (λ − 1)π(1 − π)(sh − s` ) > 0
(8)
where π is the likelihood of success in the Choice stage. The inequality in equation (8) shows that loss aversion
is necessary but not sufficient to define which scheme is preferred: the Deferred scheme is preferred to the
Fully-Contingent one only if the subject is loss averse and he perceives first-period payments as uncertain. To
see this, notice that loss averse subjects who perceive π = 1 or π = 0, will be indifferent between the two
schemes, as π(1 − π) = 0. This is a distinctive feature of the Kőszegi and Rabin (2006) preferences: because it is
uncertainty what triggers departures from the reference point, loss aversion is reflected in behavior only in risky
situations. Testing the model, therefore, requires a measure of loss aversion and a measure of the probability
of success in the Choice stage.47
bi . Before starting the study, subjects participated in a series of lottery choices
(1) The loss aversion measure, λ
designed to measure their aversion to losses. In the task, they had to accept or reject 11 lotteries, each offering
equal chance of winning $5,000 CLP (approximately $7.5 dollars) or losing an amount that ranged from $0 to
$5,000 CLP in increments of $500 CLP.48 The loss aversion index was normalized so that those who were loss
neutral—accepted all lotteries—displayed an index equal to one, while those who accepted lotteries up to that
offering to lose $2,500 CLP (half of the possible gain) displayed an index equal to two. Notice that anyone
with an index strictly higher than one displays some level of loss aversion.49 This measure of loss aversion
follows Rabin (2000) where rejection of small-scale risks is the reflection of loss aversion, and is related to
the measures of risk attitudes in e.g., Dohmen, Falk, Huffman, Sunde, Schupp, and Wagner (2011), Toubia,
Johnson, Evgeniou, and Delquié (2013). Figure 1 shows the histogram of the loss aversion index for all subjects
in the Decision condition.50
(2) The probability of success, π
bi . To measure the probability of success in the Choice stage, I estimate a probit
model where the likelihood of success in the Choice stage depends on the scheme’s threshold, the task difficulty
47
For notational simplicity, equation (8) suppresses the subscript h from π in equation (4). Also, in the model this probability
of success corresponds to that under the Fully-Contingent scheme. Table A3 in the appendix shows, however, that the scheme
choice does not affect the probability of success, since—as shown in the model—both incentive schemes induce maximum effort.
The probability of success, therefore, is only determined by exogenous variables as proposed in equation (9) below.
48
See the exact task description in Section B.2
49
The loss aversion index was computed as 1 + 15 ∗number of rejected lotteries. This normalization is, however, innocuous as it
only scales the original index adding the number of rejected lotteries.
50
Twenty one subjects out of the 95 subjects in this condition made inconsistent choices by reversing back to acceptance once
having rejected a lottery. In this case, the program warned them of their inconsistency and encouraged them to revise their choices.
Only their consistent measures are used in the analysis. I show that no result is affected by dropping these subjects.
22
and the subject’s characteristics,
π
bi = α0 + α1 thresholdi + α2 difficulty + α3 Xi + (9)
where threshold i is the number of correct matrices required to succeed in the Choice stage; difficulty represents
the difficulty of the task in the Choice stage, proxied by two variables: the proportion of matrices where the
correct numbers have two decimals instead of zero or one, and the relative position of the two correct numbers
in the matrix; and Xi is a set of individual characteristics such as skills (measured by productivity during
In-Lab-Practice practice for subjects in the No-Practice treatment and practice from home for subjects in the
Practice condition), fastness (measured as the total number of solved matrices), and gender.
Estimating equation (9) clustering standard errors at the high-education institution level shows that the
most important determinants for success in the Choice stage are the threshold, the difficulty of the task and
skills measured by baseline productivity. Table 9, column (1) shows that, in the whole Decision condition,
subjects with lower threshold are significantly more likely to succeed (p-value equal to 0.000). Moreover, easier
tasks—measured by the relative position within the matrix of the two correct numbers adding up to 10—make
it more likely to succeed (p-value equal to 0.000), and subjects with higher baseline productivity (measured by
their performance in the Piece-Rate stage) are also more likely to succeed (p-value equal to 0.002).51
(3) Econometric model and results. Define the dichotomous choice variable si as one if the subject chose the
Deferred scheme and zero if he chose the Fully-Contingent scheme. Following equation 8, I assume this choice
is the result of a latent variable s∗ = λπ − λπ 2 − π + π 2 + εi , were si = 1 if s∗ > 0 and si = 0 if s∗ 6 0. Then,
P(si = 1|λi , πi ) = P(s∗ > 0|λi , πi ) = P(β1 λπ + β2 λπ 2 + β3 π + β4 π 2 + εi > 0|λi , πi )
(10)
which can be estimated through a probit model. The theoretical model in Section 4.1 proposes the following
null hypothesis,
H0 :
β1 > 0
β2 < 0
β3 < 0 and β4 > 0.
(11)
Table 10 shows the probit estimates of equation (10) clustering standard errors at the high-education institution
level. The results cannot reject the model’s null hypothesis, confirming thus the role of loss on aversion on the
subjects’ scheme choice. Column (1) shows the results without controls. Row (1) shows that the parameter
estimate associated with λπ is positive and highly significant (p-value equal to 0.006), indicating that, given
uncertainty, more loss averse subjects are more likely to choose the Deferred scheme. From the model, the
51
Columns (2) and (3) show that the same is true if we consider the No-Practice and Practice treatments separately.
23
intuition behind this result is simple: the disutility from payment variation in the Choice stage is greater for
more loss averse subjects, who thus have greater gains from choosing the Deferred scheme over the FullyContingent one. Column (1), row (2), shows that, as predicted by the model, this effect is concave in the level
of uncertainty (βb2 , associated with λπ 2 , is negative and significant, p-value of the difference equal to 0.009).
Also, as predicted by the model, βb3 is negative (p-value equal to 0.000) and βb4 positive (p-value equal to 0.000).
Columns (3) and (4) repeat the analysis adding controls: column (3) shows that controlling by practice does
not change results, while column (4) shows that the same is true if one controls by baseline productivity.52
4) Alternative estimation for πi . I now explore the robustness of the results using a different specification for
the probability of success. To this end I build a proxi for πi , which resembles the information subjects have at
the moment of their choice: the comparison between their performance in the In-Lab-Practice stage against the
threshold they require for success. I hypothesize that subjects whose performance in the In-Lab-Practice stage
is greater than the threshold face less uncertainty than those in the opposite situation.
I now show that estimating the probit model in equation (10) using this alternative definition of the probability of success does not reject the null hypothesis in 11 either, confirming the role of loss aversion in scheme
choice. Clustering standard errors at the high-education institution level, Table 11, column (1) shows that
the parameter associated with λπ is again positive and highly significant (p-value equal to 0.007). Moreover,
the effect of loss aversion on scheme choice is once more concave in uncertainty, as the parameter associated
with λπ 2 is negative and significant (p-value equal to 0.002). As before, controlling for practice (column (3))
and baseline productivity and gender (column (4)) does not affect these results. Finally, in all regressions, the
parameters associated to π and π 2 are significant and have the predicted signs according to the model’s null
hypothesis in (11).53
5
Discussion
This paper explores the optimality of fixed wages coupled with deferred incentives. It presents a laboratory
experiment where a larger proportion of subjects have a strict preference for delaying incentives for present
effort to future payments at no expense to productivity nor expected cost. Then, it uses an exogenous measure
of loss aversion to show that, conditional on the uncertainty of the payment scheme, more loss averse subjects
are significantly more likely to choose to fully defer incentives into future payments. This result, therefore,
provides a new mechanism for why current wages are not conditional on current performance.
52
Table A4 in the appendix shows that the results, in terms of sign and significance, are the same excluding the 24 subjects who
made inconsistent choices in the loss aversion measure.
53
Table A5 shows that all results are preserved, both in sign and significance, excluding the 24 inconsistent subjects.
24
I emphasize that this paper’s loss-aversion rationalization to the laboratory evidence should be best viewed as
a complement rather than as a substitute to the classical theories for fixed wages and deferred incentives reviewed
in Section 3.1. Indeed, the preference-based rationalization presented in this paper is perfectly compatible with
explanations relying on the cost and unfeasibility of measuring output: both preferences and information
jointly determine real-world contracts. This explanation, however, is based on a substantial body of theoretical
and empirical work showing that reference-dependent preferences and loss aversion are relevant for economic
decisions. DellaVigna (2009) and Barberis (2013) review the existing evidence of these preferences for financial
decisions, insurance, consumption and saving, pricing, labor supply, etc. Moreover, recently, the laboratory and
empirical evidence on expectations as reference points have also flourished. For instance, Abeler, Falk, Goette,
and Huffman (2011), Ericson and Fuster (2011), Gill and Prowse (2012), Karle, Kirchsteiger, and Peitz (2015),
Imas, Sadoff, and Samek (forthcomig) all present laboratory evidence of the role of expectations as reference
points, while Card and Dahl (2011), Crawford and Meng (2011), Pope and Schweitzer (2011) and Lien and
Zheng (2015) provide empirical evidence.54
Moreover, loss aversion is not the only modification of classical preferences that has been explored to
rationalize evidence incompatible with the predictions of the classical moral-hazard model. For instance, there
is now a large body of experimental and theoretical research showing that social preferences, such as fairness
concerns (e.g., Cohn, Fehr, and Goette (2014)), reciprocity (e.g., Englmaier and Leider (2012)), inequality
aversion (e.g., Fehr, Klein, and Schmidt (2007)), desire for social esteem (e.g., Ellingsen and Johannesson
(2008)), etc. are important determinants of the optimal contract (MacLeod (2007), Fehr, Goette, and Zehnder
(2009)).
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30
A
Appendix: Tables
Table 2: Scheme Choice in the Choice Stage
Scheme Choice
Chosen Payment Scheme
Scheme Choice for Another Worker
N
%
N
%
(1)
(2)
(3)
(4)
Deferred Scheme
56
58.95%
48
51.06%
Fully-Contingent Scheme
39
41.05%
40
42.55%
Indifferent
0
0%
6
6.38%
95
100%
94
100%
Difference between Deferred and Fully-Contingent
17.90%
8.51%
P-Value H0: Difference=0 (Binomail test)
0.001
0.024
P-Value H0: Difference=0 (Proportion test)
0.000
0.001
Notes. Table 2 presents the share of subjects in the Decision condition who, in the Choice stage, chose the Deferred scheme, the
Fully-Contingent scheme and those indifferent between the two. It further shows the statistical significance of the difference in
percentage of subjects choosing the Deferred versus the Fully-Contingent scheme. The sample includes all subjects in the Practice
and No-Practice treatments in the Decision condition. Columns (1) and (2) show subjects’ scheme preference when the scheme
determined their own payment. Columns (3) and (4) show their scheme preference if they had to use the scheme to motivate another
worker. One subject in the Practice condition skipped the question on motivating another worker and thus column (3) highlights
that the sample size in this case is 94 rather than 95 subjects. The binomial test corresponds to a standard Binomial probability
test where the null hypothesis is that the proportion of choices of the Deferred scheme equals that of the Fully-Contingent scheme.
The Proportion corresponds to a standard test of proportions with the same null hypothesis as the Binomial test.
31
Table 3: Average Productivity Comparison Across Stages by Scheme Choice
Choice
Stage
(1)
Deferred Scheme
Second-Period Piece-Rate
Stage
Stage
(2)
(3)
In-Lab-Practice
Stage
(4)
8.70
8.12
6.52
6.73
7.03
7.50
6.44
6.13
Difference
1.67
0.62
0.08
0.60
P-Value H0: Difference = 0 (Mann-Whitney)
0.095
0.509
0.744
0.539
Difference adjusted by baseline productivity
1.61
0.46
-0.38
0.54
P-Value H0: Difference adjusted by baseline productivity = 0
0.000
0.171
0.615
0.283
N=56
Fully-Contingent Scheme
N=39
Notes. Table 3 displays the average productivity (number of correctly solved matrices in a four-minute task) across stages the
Decision condition (N=95) by scheme choice. Columns (1) and (2) compare the productivity across scheme choices in the Choice
and Second-Period stages, where subjects chose to be paid by the Deferred or Fully-Contingent schemes. Column (3) compares the
(baseline) productivity across scheme choices in the unpaid ln-Lab-Practice stage. Column (4) compares the (baseline) productivity
across scheme choices in the Piece-Rate stage where subjects were paid $400CLP (around $0.6 cents) for each correct matrix.
The sample size in column (4) is N=85 (Table 7 shows that attrition is not selective by scheme choice). The p-value for the null
hypothesis that the productivity difference between those choosing the Deferred and the Fully-Contingent scheme is zero correspond
to that of a standard non-parametric Mann-Whitney test for differences in means. The p-value adjusted by baseline productivity
correspond to the t-test using clustered standard errors at the high-education institution level in a regression of the number of
correct matrices in the corresponding stage with a dummy variable taking value 1 if the subject chose the Deferred scheme in the
fist-period Choice stage and 0 if the subject chose the Fully-Contingent one correcting by baseline productivity. In columns (1),
(2) and (4) baseline productivity corresponds to the number of correct matrices in the Piece-Rate stage, while in column (3) it
corresponds to productivity in In-Lab-Practice stage.
32
Table 4: Average Productivity Comparison Across Stages For Subjects Choosing the Deferred Scheme and
those in the Fixed-Payment Condition
Piece-Rate In-Lab-Practice
Stage
Stage
(4)
(3)
Choice
Stage
(1)
Second-Period
Stage
(2)
6.60
6.56
5.09
4.77
6.23
6.55
6.65
5.15
Difference
0.37
0.01
-1.57
-0.38
P-Value H0: Difference = 0 (Mann-Whitney)
0.924
0.835
0.037
0.428
Deferred Scheme
(Subset of Choice condition (N=35))
Fixed-Payment Scheme
(Whole Fixed-Payment condition (N=26))
Difference adjusted by baseline productivity
1.54
1.50
-0.74
0.58
P-Value H0: Difference adjusted by baseline productivity = 0
0.000
0.000
0.000
0.000
Notes. Table 4 displays the average productivity (number of correctly solved matrices in a four-minute task) of subjects in the
Decision condition, who chose the Deferred scheme vis-a-vis subjects in the Fixed-Payment condition, who were paid fixed in the
Choice and Second-Period stages (notice that in the Choice stage both groups are paid the same fixed amount, $10.000CLP, around
$14US). Columns (1) and (2) compare the productivity across scheme choices in the Choice and second-period stages. Column (3)
compares the (baseline) productivity across scheme choices in the unpaid In-Lab-Practice stage. Column (4) compares the (baseline)
productivity across scheme choices in the Piece-Rate stage where subjects were paid around $0.6 cents for each correct matrix. The
sample size in column (4) is N=79 (Table 7 shows that attrition is not selective by scheme choice). The p-value for the null
hypothesis that the productivity difference between those paid by the Deferred scheme and those in the Fixed-Payment condition
is zero correspond to that of a standard non-parametric Mann-Whitney test for differences in means. The p-value adjusted by
baseline productivity correspond to the t-test using clustered standard errors at the high-education institution level in a regression
of the number of correct matrices in the corresponding stage with a dummy variable taking the value of one if the subject was
paid with the Deferred scheme and zero if the subject was paid with the Fixed-Payment scheme correcting by baseline productivity.
In columns (1), (2) and (4), baseline productivity corresponds to the number of correct matrices in the Piece-Rate stage, while in
column (3) it corresponds to productivity in In-Lab-Practice stage.
33
Table 5: Probabilities of Success in the Choice Stage
(1)
No-Practice
Treatment
(2)
Practice
Treatment
(3)
0.86
0.80
0.95
56
35
21
0.77
0.80
0.74
39
20
19
Difference
0.09
0.00
0.22
P-Value H0: Difference = 0 (Mann-Whitney)
0.274
1.000
0.060
Difference adjusted by baseline productivity
0.09
0.05
0.21
P-Value H0: Difference adjusted by baseline productivity = 0
0.037
0.462
0.028
Overall
Deferred Scheme
N
Fully-Contingent Scheme
N
Notes. Table 5 shows the actual probabilities of success in the Decision condition by scheme choice. Probabilities are calculated as
the proportion of subjects whose performance in the Choice stage was greater or equal to their threshold for success (defined as the
number of correctly solved matrices in the Piece-Rate stage minus one). Column (1) considers all subjects assigned to the Decision
condition, while column (2) and (3) show the probabilities of success for the No-Practice and Practice treatments, respectively.
The p-value for the null hypothesis that the difference in the probability of success between those paid by the Deferred and the
Fully-Contingent schemes is zero correspond to that of a standard non-parametric Mann-Whitney test for differences in means. The
p-value adjusted by baseline productivity correspond to the t-test using clustered standard errors at the high-education institution
level in a regression of a dummy variable taking value one if the subject succeed in his chosen payment scheme and zero otherwise
with a dummy variable taking the value of one if the subject chose the Deferred scheme and zero if he chose the Fully-Contingent
scheme correcting by baseline productivity measured as the number of correct matrices in the Piece-Rate stage.
34
Table 6: Summary Statistics for Tasks Practiced From Home
(1)
Standard
Deviation
(2)
Average
Min.
Max.
(3)
(4)
(1)
Average number of rounds
practiced from home
9.15
8.45
0.00
41.00
(2)
Average number of correct matrices
practiced from home
7.61
4.07
0.67
18.33
Notes. Table 6 displays the summary statistics for the tasks practiced from home for subjects in the Practice treatment (N=40).
Subjects in this treatment were randomly selected from the Decision condition and invited to practice the task during three and a
half days before the experiment through an online platform. Row (1) corresponds to the average number of tasks practiced from
home. Row (2) corresponds to the total number of matrices correctly solved during all practice days divided by the total number
of tasks practiced during all practice days, averaged across subjects. Since one invited subject did not practice from home the total
sample in row (2) is 39 subjects.
35
Table 7: Attrition by Scheme Choice
All subjects in
Decision condition
Chosen Payment Scheme
Deferred
Scheme
Fully-Contingent
Scheme
(1)
(2)
(3)
Total subjects in the first stage
95
56
39
Total subjects in the second stage
85
51
34
10.53%
8.93%
12.82%
Attrition rate (%)
% Difference
-3.89%
0.545
P-Value H0: Difference = 0 (Mann-Whitney)
Notes. Table 7 compares the attrition rates of subjects in the Decision condition by scheme choice. Column (1) provides the
baseline attrition from the first to the second period by pooling all subjects in the Decision condition. Columns (2) and (3) show
the attrition rates for subjects choosing the Deferred and the Fully-Contingent schemes, respectively. The p-value for the null
hypothesis that the difference in attrition rates between subjects choosing the Deferred and the Fully-Contingent schemes is zero
correspond to that of a standard non-parametric Mann-Whitney test for differences in means.
36
Table 8: Attrition by Condition
Decision Condition
Fixed-Payment
Condition
Practice
Treatment
No-Practice
Treatment
All
Subjects
(1)
(2)
(3)
(4)
Total subjects in the first stage
40
55
95
26
Total subjects in the second stage
37
48
85
20
7.5
12.7
10.5
23.1
Attrition rate (%)
Notes. Table 8 compares attrition rates by conditions. Column (1) and (2) show the attrition rates for treatments in the Decision
condition, while column (3) shows the overall attrition rate for the condition. Column (4) shows the baseline attrition rate for
subjects in the Fixed-Payment condition who were paid fixed in the Choice and Second-Period stages.
37
0
.2
Density
.4
.6
.8
Figure 1: Histogram of the Loss Aversion Measure
1
1.5
2
2.5
Loss aversion measure
3
Notes. Histogram of the loss aversion index for all subjects in the Decision condition (N=95). The loss aversion measure takes
value one if the subject accepted all 11 lotteries in the lottery task, each offering equal chance of winning $5,000 CLP (approximately
$7.5 dollars) or losing an amount that ranged from $0 to $5,000 CLP in increments of $500 CLP. Subjects accepting up to the
lottery offering to lose $2.500 receive a loss aversion index equal to two. Any index strictly above one displays some loss aversion.
38
Table 9: Determinants of the Probability of Success in the Choice Stage, π
bi
Dep. Variable: 1 if succeded in Choice round, 0 if not
Overall
No-Practice
Treatment
Practice
Treatment
(1)
(2)
(3)
-0.446***
-0.627***
-1.461***
(0.107)
(0.180)
(0.546)
-0.059
-1.620
11.61**
(1.559)
(2.691)
(5.742)
0.181***
0.279**
0.260
(0.036)
(0.113)
(0.467)
-0.147
-0.396*
0.401
(0.129)
(0.226)
(0.721)
0.415***
0.502***
0.899*
(0.133)
(0.185)
(0.521)
0.278
0.423
1.945
(0.396)
(0.292)
(1.747)
-0.373
1.327
-6.793*
(0.671)
(0.984)
(3.624)
N
95
55
40
Pseudo R2
0.356
0.429
0.666
Threshold
Difficulty (decimals)
Difficulty (position)
Fast
Productivity during practice
Gender
Constant
Notes. Probit estimates with standard errors clustered by high-education institution level, in parenthesis. Threshold corresponds to
the number of correct matrices required to succeed in the Choice stage, defined as the number of correct matrices in the Piece-Rate
stage minus one if productivity is higher than one, and one if productivity is equal to zero or one. Difficulty (decimals) is a proxy
of the level of difficulty of the task in the Decision condition, defined as the proportion of solved matrices where the two correct
numbers have two decimals (rather than zero or one). Difficulty (position) is a discrete proxy of the level of difficulty of the task
in the Decision condition ranging from one to three depending on the distance between the two correct numbers within the four by
three matrix. The higher the index, the closer to opposite borders of the matrix the two numbers are. Fast corresponds to the total
number of solved matrices in the Decision condition, irrespectively of whether they were correctly or incorrectly solved. Productivity
during practice corresponds to the number of correctly solved matrices during practice. For subjects in the No-Practice treatment,
this number is computed using the In-Lab-Practice stage, while for subjects in the Practice treatment it is computed as the average
number of correct matrices during the practice from home. Gender takes the value of one if the subject is female.
Level of significance: ∗ p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01
39
Table 10: Model Estimates for Scheme Choice
H0
(1)
λπ
(2)
(3)
(2)
(3)
(4)
+
3.068**
3.570**
3.456***
(1.477)
(1.431)
(1.332)
-4.001**
-4.432***
-4.332***
(1.731)
(1.609)
(1.499)
-10.777***
-12.092***
-11.654***
(4.127)
(3.313)
(3.380)
12.212***
13.315***
13.851***
(3.736)
(3.546)
(3.025)
-0.027*
-0.041**
(0.015)
(0.017)
-
π
(4)
(1)
-
λ π2
+
π2
Dep. Variable: 1 if chose Deferred scheme, 0 if
chose Fully-Contingent scheme
(5) Practice
(6) Baseline productivity
0.039
(0.046)
(7) Gender
-0.257
(0.302)
(8) Constant
N
P-Value Wald Test rows (1) to (4)
are jointly 0
Pseudo R2
0.975
1.147
0.920**
(0.711)
(0.628)
(0.453)
95
95
95
0.000
0.000
0.000
0.101
0.114
0.132
Notes. Probit estimates with standard errors clustered by high-education institution level, in parenthesis. Sample corresponds to
all subjects in the Decision condition. Null hypothesis from the model in column (1), estimates without controls in column (2),
additional controls in columns (3) and (4). Loss aversion, λ, corresponds to a continuous variable ranging from 1 to 5, where 1
denotes subjects who accepted all lotteries in the lottery task and 2 denotes subjects who rejected lotteries involving losing half
or more of the possible gain (see the exact task description in Section 4.2). Probability of success, π corresponds to the estimated
probability of success in Table 9. Practice takes a value zero for subjects in the No-Practice treatment, and the number of tasks
practiced in the Practice-from-Home stage for subjects in the Practice condition. Baseline productivity corresponds to the number
of correctly solved matrices in the Piece-Rate condition. Gender is a dummy variable taking the value of one if the subject is female.
Level of significance: ∗ p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01
40
Table 11: Model Estimate for Scheme Choice with Alternative Specification for the Probability of Success
H0
(1)
λπ
(2)
(3)
(2)
(3)
(4)
+
0.279***
0.286***
0.295***
(0.062)
(0.089)
(0.056)
-0.074***
-0.052***
-0.070***
(0.028)
(0.018)
(0.025)
-0.622***
-0.562***
-0.650***
(0.213)
(0.268)
(0.188)
0.178***
0.134***
0.172***
(0.053)
(0.049)
(0.048)
-0.020
-0.027
(0.020)
(0.018)
-
π
(4)
(1)
-
λ π2
+
π2
Dep. Variable: 1 if chose Deferred scheme, 0 if
chose Fully-Contingent scheme
(5) Practice
(6) Baseline productivity
0.013
(0.042)
(7) Gender
-0.338
(0.181)
(8) Constant
N
P-Value Wald Test rows (1) to (4) are
jointly 0
Pseudo R2
0.064
0.212
0.243
(0.270)
(0.408)
(0.571)
95
95
95
0.000
0.000
0.000
0.122
0.131
0.144
Notes. Probit estimates with standard errors clustered by high-education institution level, in parenthesis. Sample corresponds to
all subjects in the Decision condition. Null hypothesis from the model in column (1), estimates without controls in column (2),
additional controls in columns (3) and (4). Loss aversion, λ, corresponds to a continuous variable ranging from 1 to 5, where 1
denotes subjects who accepted all lotteries in the lottery task and 2 denotes subjects who rejected lotteries involving loosing half
or more of the possible gain (see the exact task description in Section 4.2). Probability of success, πi , corresponds to the difference
between the number of correct matrices needed for success in the Choice stage minus the number of correct matrices in the In-LabPractice stage for subjects in both the Practice and No-Practice treatments. Baseline productivity corresponds to the number of
correctly solved matrices in the Piece-Rate condition. Gender is a dummy variable taking the value of one if the subject is female.
Level of significance: ∗ p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01
41
A
Appendix Tables
Table A1: Scheme Choice in the Choice Stage by Treatment
No-Practice Treatment
Practice Treatment
Scheme Choice
Choice for
Another Worker
Scheme Choice
Choice for
Another Worker
(1)
(2)
(3)
(4)
Deferred Scheme
63.64%
52.73%
52.50%
48.72%
Fully-Contingent Scheme
36.36%
41.82%
47.50%
43.59%
Indifferent
0%
5.45%
0%
7.69%
N
55
55
40
39
27.28%
10.91%
5.00%
5.13%
P-Value H0: Difference=0 (Binomail test)
0.000
0.049
0.532
0.314
P-Value H0: Difference=0 (Proportion test)
0.000
0.041
0.527
0.266
Chosen Payment Scheme
Difference between Deferred and Fully-Contingent
Notes. Table A1 presents the share of subjects in the Decision condition who in the Choice stage chose the Deferred and the
Fully-Contingent schemes by treatment. Columns (1) and (2) show subjects’ scheme preference for subjects in the No-Practice
treatment where subejcts faced the task for the same time in the first period. Columns (3) and (4) show the same but for subjects
in the Practice treatment who practiced the task before the first period during . One subject in the Practice condition skipped the
question on motivating another worker and thus the total sample in column (4) is 94 rather than 95 subjects.
42
Table A2: Average Productivity Across Stages for Subjects Choosing the Deferred Scheme and Those in the
Fixed-Payment Condition Who Are in the Same High-Education Institution
Choice
Stage
(1)
Second-Period
Stage
(2)
Piece-Rate
Stage
(3)
In-Lab Practice
Stage
(4)
7.43
7.75
6.05
5.38
6.23
6.55
6.65
5.15
Difference
1.20
1.20
-0.61
0.23
P-Value H0: Difference = 0 (Mann-Whitney)
0.483
0.399
0.337
0.804
Difference adjusted by baseline productivity
1.56
1.54
-0.75
0.60
P-Value H0: Difference adjusted by baseline productivity = 0
0.056
0.096
0.365
0.465
Deferred Scheme
(Subset of Choice condition (N=21))
Fixed-Payment Scheme
(Whole Fixed-Payment condition (N=26))
Notes. Table A2 displays the average productivity (number of correctly solved matrices in a four-minute task) of subjects in
the Decision condition who chose the Deferred scheme and those in the Fixed-Payment condition who belong to the same higheducation institution. Namely, the 21 subjects choosing the Deferred scheme correspond to subjects in the No-Practice treatment in
the Decision condition, who chose the Deferred scheme and belong to the same (and only) high-education institution of subjects in
the Fixed-Payment condition. Columns (1) and (2) compare the productivity across scheme choices in the Choice and second-period
stages. Column (3) compares the (baseline) productivity across scheme choices in the In-Lab-Practice stage. Column (4) compares
the (baseline) productivity across scheme choices in the Piece-Rate stage where subjects were paid around $0.6 cents for each
correct matrix. The p-value for the null hypothesis shows that the productivity difference between those paid by the Deferred and
the Fixed-Payment schemes is zero, which corresponds to that of a standard non-parametric Mann-Whitney test for differences in
means. The p-value adjusted by baseline productivity correspond to the t-test using clustered standard errors at the high-education
institution level in a regression of the number of correct matrices in the corresponding stage on a dummy variable taking value 1 if
the subject was paid with the Deferred scheme and 0 if the subject was paid with the Fixed-Payment scheme, correcting by baseline
productivity. In columns (1), (2) and (4) baseline productivity corresponds to the number of correct matrices in the Piece-Rate
stage, while in column (3) it corresponds to productivity in In-Lab-Practice stage.
43
Table A3: Determinants of the Probability of Success in the Choice Stage Including Scheme Choice
Dep. Variable: 1 if succeded in Choice
round, 0 if not
Overall
(1)
Deferred scheme
0.196
(0.280)
Threshold
-0.444***
(0.111)
Difficulty (decimals)
-0.149
(1.632)
Difficulty (position)
0.190***
(0.045)
Fast
-0.162
(0.133)
Productivity during practice
0.406***
(0.133)
Gender
0.291
(0.389)
Constant
-0.438
(0.703)
N
95
Pseudo R2
0.359
Notes. Probit estimates with standard errors clustered by high-education institution level, in parenthesis. Deferred scheme takes
the value of one if the subject chose the Deferred scheme, and zero otherwise. Threshold corresponds to the number of correct
matrices required to succeed in the Choice stage, defined as number of correct matrices in the Piece-Rate stage minus one if
productivity is higher than one, and one if productivity is equal to zero or one. Difficulty (decimals) is a proxy of the level of
difficulty of the task in the Decision condition, defined as the proportion of solved matrices where the two correct numbers have
two decimals (rather than zero or one). Difficulty (position) is a discrete proxy of the level of difficulty of the task in the Decision
condition ranging from one to three depending on the distance between the two correct numbers within the four by three matrix.
The higher the index, the closer to opposite borders of the matrix the two numbers are. Fast corresponds to the total number of
solved matrices in the Decision condition, irrespectively of whether they were correctly or incorrectly solved. Productivity during
practice corresponds to the number of correctly solved matrices during practice. For subjects in the No-Practice treatment, this
number is computed using the In-Lab-Practice stage, while for subjects in the Practice treatment it is computed as the average
number of correct matrices in the Practiced-From-Home stage. Gender takes the value of one if the subject is female.
Level of significance: ∗ p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01
44
Table A4: Model Estimates for Scheme Choice With Only Non-Switchers in the Loss Aversion Measure
H0
(1)
λπ
(2)
(3)
(2)
(3)
(4)
+
5.315***
5.915***
6.065***
(1.922)
(1.942)
(1.580)
-6.324***
-6.823***
-6.981***
(2.403)
(2.328)
(1.918)
-17.230***
-18.788***
-19.578***
(2.390)
(1.881)
(2.509)
18.053***
19.299***
18.151***
(2.711)
(2.469)
(2.432)
-0.026
-0.038*
(0.019)
(0.020)
-
π
(4)
(1)
-
λ π2
+
π2
Dep. Variable: 1 if chose Deferred scheme, 0 if
chose Fully-Contingent scheme
(5) Practice
(6) Baseline productivity
0.035
(0.053)
(7) Gender
-0.285
(0.336)
(8) Constant
N
P-Value Wald Test rows (1) to (4)
Pseudo R2
1.699*
1.913**
1.986***
(0.989)
(0.868)
(0.489)
71
71
71
0.000
0.000
0.000
0.102
0.117
0.131
Notes. Probit estimates with standard errors clustered by high-education institution level, in parenthesis. Sample corresponds
to the 71 subjects in the Decision condition who made consistent choices in the lotteries to estimate the loss aversion measure.
Standard deviations in parenthesis below point estimates. (b) Loss aversion, λ, corresponds to a continuous variable ranging from 1
to 5, where 1 denotes subjects who accepted all lotteries in the lottery task and 2 denotes subjects who rejected lotteries involving
loosing half or more of the possible gain (see the exact task description in Section 4.2). Null hypothesis from the model in column
(1), estimates without controls in column (2), and additional controls in columns (3) and (4). Probability of success, π corresponds
to the estimated probability of success in Table 9. Practice takes a value zero for subjects in the No-Practice treatment, and the
number of Practice-from-Home tasks for subjects in the Practice condition. Baseline productivity corresponds to the number of
correctly solved matrices in the Piece-Rate condition. Gender is a dummy variable taking the value of one if the subject is female.
Level of significance: ∗ p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01
45
Table A5: Model Estimates for Scheme Choice With Only Non-Switchers in the Loss Aversion Measure and
With Alternative Specification for the Probability of Success
H0
(1)
λπ
(2)
λ π2
(3)
π
(4)
π2
Dep. Variable: 1 if chose Deferred scheme, 0 if
chose Fully-Contingent scheme
(1)
(2)
(3)
(4)
+
0.294***
0.286***
0.312***
(0.108)
(0.089)
(0.108)
-0.055***
-0.052***
-0.055***
(0.017)
(0.018)
(0.019)
-0.572**
-0.562**
-0.607**
(0.292)
(0.268)
(0.281)
0.143***
0.134***
0.145***
(0.047)
(0.049)
(0.052)
-0.020
-0.026
(0.020)
(0.017)
+
(5) Practice
(6) Baseline productivity
0.017
(0.046)
(7) Gender
-0.405
(0.289)
(8) Constant
N
P-Value Wald Test rows (1) to (4) are
jointly 0
Pseudo R2
0.115
0.212
0.322
(1.108)
(0.408)
(0.785)
71
71
71
0.000
0.000
0.000
0.101
0.110
0.128
Notes. Probit estimates with standard errors clustered by high-education institution level, in parenthesis. Sample corresponds
to the 71 subjects in the Decision condition who made consistent choices in the lotteries to estimate the loss aversion measure.
Standard deviations in parenthesis below point estimates. (b) Loss aversion, λ, corresponds to a continuous variable ranging from 1
to 5, where 1 denotes subjects who accepted all lotteries in the lottery task and 2 denotes subjects who rejected lotteries involving
loosing half or more of the possible gain (see the exact task description in Section 4.2). Null hypothesis from the model in column
(1), estimates without controls in column (2), and additional controls in columns (3) and (4). Probability of success, πi , corresponds
to the difference between the number of correct matrices needed for success in the Choice stage minus the number of correct matrices
in the In-Lab-Practice stage for subjects in both the Practice and No-Practice treatments. Practice takes a value zero for subjects in
the No-Practice treatment, and the number of Practice-from-Home tasks for subjects in the Practice condition. Baseline productivity
corresponds to the number of correctly solved matrices in the Piece-Rate condition. Gender is a dummy variable taking the value
of one if the subject is female.
Level of significance: ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01
46
B
B.1
Appendix: The Laboratory Experiment
Invitation Email
Hello [NAME],
Thank you for your interest in participating in this study!
This is a simple scientific study, which has one objective: to better understand the
productivity of people.
By participating in this study you can earn money. The amount of money you will
earn depends on your involvement, but we assure you that you will be able to earn
at least $7,000. If your participation is good, you'll have the opportunity to earn
more.
The task at hand is quite simple, but the specific details will be introduced at the
time of the study.
The study will last about 25 minutes (or less) and will be held on [DATE] in the
Computer Room of the School of Economics and Management on the San Joaquín
campus at the Universidad Católica de Chlie. A second stage of the study will take
place approximately one month after this initial stage, on [DATE].
You can choose to participate from any of the 3 following time slots: 11:00 AM,
12:00 PM or 1:00 PM.
You won’t need to bring anything to participate.
To register, you can reply to this email with your first and last name, institution,
major and the time slot that works for you for the study on [DATE].
Thank you very much for your interest!
The research team
School of Economics and Management
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B.2
First-period Laboratory Program
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Please, identify yourself with your UC email address.
Log In
UC Email address
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Thanks for coming!
This is an individual study.
Please, remain SILENT at all times to avoid
distracting other participants.
The study will begin as soon as all
other participants arrive.
The person in charge of the room will
announce out loud when you can start.
Start
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You will now proceed to the "consent form" of this study.
The consent form is a small description of the study and its objectives. Reading and
accepting a consent form is a standard practice required by the Human-Subjects
Comitee of the University, which regulates research studies involving people.
Read the consent form
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Consent Form
(The standard consent form has been omited for space purposes. Available upon request.)
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This study has two stages
The first stage of the study will take place during the next 25 minutes. The second stage will take
place in approximately one month. We will inform you of the details of the second stage as this
first stage evolves.
Each stage has its own payments. Payments in each stage will depend on your performance.
However, in each stage we ensure you a minimum payment of $2.000 and a maximum payment
of $25.000. Therefore, the minimum you can earn is $4.000 and the maximum is $50.000.
Payment in this first-stage will be paid in cash at the end of the session (that is, today before leaving
the computer laboratory).
Payments in the second stage will be paid at the end of teh second stage in approximately one
month.
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Before starting the first stage, we invite you to participate in a brief activity.This
activity will help us to better understand your performance.
In this activity you will have the chance of earning $5.000.
Continue
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Lottery Activity
To the right there is a table with 11 lotteries.
In each lottery you can win $5.000
or lose an amount that increases progresively.
In each lottery is equality likely to win or lose.
We will now ask you to state, for each of the 11
loteries, whether you would like play it or not.
Win $5000 or lose:
$0
$500
$1.000
$1.500
$2.000
$2.500
$3.000
$3.500
$4.000
$4.500
$5.000
Example 1: If We offer you the lottery "Win $5.000 or lose $500", would you rather
play it or not?
If you rather play it, then will randomly chose whether you win $5.000 or if you lose $500.
If you rather not play it, then nothing will be chosen and you will not win nor lose.
Example 2: If We offer you the lottery "Win $5.000 or lose $4.500", would you
rather play it or not?
If you rather play it, then will randomly chose whether you win $5.000 or if you lose $4.500.
If you rather not play it, then nothing will be chosen and you will not win nor lose.
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Lotteries activity payments
After you decide whether you rather accept or reject each lottery, we will randomly
chose one of the 11 lotteries and implement your decision of whether play or not
that chosen lottery.
If your decision was to play the randomly chosen lottery and you win, then $5.000
pesos will be added to today's payments.
If your decision was to play the randomly chosen lottery and you loose, then the lost
amount pesos will be substracted from today's payments.
If your decision was not to play, then you will not win nor lose anything. Therefore,
nothing will be added nor substracted to today's payments because the lottery will not
be played.
Continue to see an example of the lotteries activity
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Lotteries Example
Before making your actual lottery choices, you will work through the activity, but
without a payment.
The objective is that you can familiarize with the activity before the paid activity
takes place. After this example is over, you will make your actual paid choices.
Please, in the table below, let us know whether you would be willing to play
each of the lotteries.
Remeber, to choose whether you want play each lottery, your must answer:
"If this lottery is randomly chosen, would I rather play it (and thus risk winning or
losing), or I rather not play it (and thus not risk winning nor losing)?
I rather play the lottery
Win $5000 or lose:
I rather not play the lottery
$0
$500
$1000
$1500
$2000
$2500
$3000
$3500
$4000
$4500
$5000
Continue with the example
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Lotteries Example
Suppose the lottery "Win $5.000 or lose $0" is randomly chosen. According to
your previous choices:
You rather play/ not play this lottery
What does your choice imply?
Now it will be randomly chosen whether I won $5.000 or I lost $0.
Not it will be randomly chosen whether I won $5.000 or I lost $1.000.
I will not win nor lose because the lottery will not be played.
Now it will be randomly chosen how much I lost.
Continue with the example
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Lotteries Example
Suppose the lottery "Win $5.000 or lose $4.500" is randomly chosen. According to
your previous choices:
You rather play/not play this lottery
What does your choice imply?
Now it will be randomly chosen whether I won $5.000 or lose $2.000.
Now it will be randomly chosen whether I won $5.000 or lose $4.500.
I will not win nor lose because the lottery will not be played.
Now it will be randomly chosen how much I lost.
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Now your will make your lottery choices for a payment.
Please, chose between the two choices below.
I understand the activity and wnat to make my actual choices.
I rather read the instructions and go through the examples one more time.
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Please,make your choice for each of the lotteries in the table below.
Win $5000 or lose:
I rather play the lottery
I rather not play the lottery
$0
$500
$1000
$1500
$2000
$2500
$3000
$3500
$4000
$4500
$5000
Continue
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Lottery results
The randomly chosen lottery was:
Win $5000 or lose $X
I you chose to play this lottery, them we will let you know whether you won or lose
before finishing the study.
Continue
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We will now describe the study.
As we metioned before, this study has two stages.The first stage taks place today,
and a second stage will take place in a approximately a month.
In both stages you will perform a task that we will described in detail next.
In both stages you will receive a payment to perform the task.
Such payment will depend on your performance on the task.
Please, read the description of the task carefully. There is no time restriction to read
this description.
Read the task description
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Task description
You will have to find the two numbers that add up to 10 in a table containing 12
numbers. You can click here see an example of the table.
Once you know which are the two numbers that add up to 10, you will have to click
on both numbers to mark your choice.
After you click on a number, it will change its color. You will not be able to
change your choice after you have clicked on a given number.
If the two chosen numbers were correct, a counter placed at the top of the
page will increase in one. If your answer was incorrect, the couter will not change.
After you click on your two chosen numbers, you will have to click on the "next"
button to move to the next table.
Tables can have one or two decimal numbers. The number of decimals in each
table is randomly chosen, and therefore how hard it is to solve a given table also
changes randomly.
You will have 4 minutes to solve as many tables as possible, with a maximum of 20
tables (sum among correct and incorrect tables).
Besides the counter of correct tables, on top of the page there will be a cronometer
indicating how much time of the 4 minutes has elapsed.
Continue with the descrption of the study
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Practice round
Before the study begins, you will have a practice round. During this practice round
we will not count the number of correct tables. You will not receive a monetary
compensation for this practice either. The only objective of this practice round is
that you familiarize yourself with task.
Study and payments
Once the practice round is over, the first stage of the study will be begin.
This first stage has two parts. In each part you will have to solve the same task
that you solved during the practice round.
The only difference with the practice round is that in both of these parts you
will receive a monetary compensation based on your performance.
In each part we will describe in detail the monetary compensation associated
to each part.
During both parts of this first stage of the study the counter of correct matrices
will be active.
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Whenever your are ready, please choose whether you want to start with the
practice round or you rather read the task and payment description again.
Start practice
I want to read the task and payment description agin before stating the practice round.
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Table 1 out of 20
00:11
5.44
2.06
0.63
0.89
9.50
8.79
7.56
7.67
1.2
2.44
5.69
5.23
Next table
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You have finished the practice round
We will now describe the first part and its payments.
Please, read this description carefully.
There is no time restriction to read this description.
Read the first-part description and its payments
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In this first part you will perform the same task your performed during the practice round. This
time, however, you will receive a monetary payment. This payment will be added to your total
earnings in this first stage.
The monetary payment for this first part corresponds to:
$400 pesos per correct table
For instance, if you solve 2 tables correctly, you will earn $400*2=$800 pesos. If you solve 14
tables correctly you will earn $400*14=$5600 pesos.
Incorrect tables do not discount money from your correct tables.
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When you are ready to start this first part, press the following button.
Start the first part
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This is table 1 out of 20
Number of tables correctly solved: 0
00:10
3.64
2.86
9.7
0.25
3.63
4.92
8.59
8.67
4.78
9.45
2.56
7.44
Next
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You have finished the first part.
In this first part, you correctly solved 1 table
We will now describe the payments associated to the second part. Please, read
carefully the description of payments associated to the second part.
There is no time restriction to read this description.
Read the second-part description and its payments
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Next, the second part of this first stage of the study will begin.
This second part will be connected to the second stage of the study, as we will explain you now.
As we told you before, in this second part you will perform the same task as in the first part
and in the practice. The major difference is this time you will be performing two rounds of the
task rather than one.
1)
Round one will begin right after you finished reading the instructions about this second
part.
2)
Round two will begin in a month, when you will be asked to come participate in the second
stage of the study
Next, we will describe the payments associated to this second part.
Remember to read carefully the payments associated to this second part. There is no time
restriction to read it.
Continue the payment description
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Second Part Payments
Besides performing the task two times (the first round now and the second one within a month),
in this second part you get to choose the payment scheme.
That means that, unlike the fist part in which the payment scheme was $400 for each table
correcly solved, now you get to choose the payment scheme between two options. Both options
state a payment for round one and another one for round two.
Once you chose your preferred payment scheme between the options, you will perform the
first round of the task and will be paid accordingly to your choice.
The payment of this first round will be added to your lottery payments and the first part payments
which paid $400 for each table correctly solved. Remember that you will receive today the total
payment of this first stage (lottery + $400 each table + first round) in cash before you exit the lab...
You will receive second round's payment once the second stage of the study is over, in a
month.
Continue payment description
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Second Part Payments
Now, we will show you the two available payments schemes
As we told you before, both options state a payment for round one and another one for round two.
That means that the payment scheme that you choose today will define your payments
for both the round your about to perform now and the one that is in a month.
Once you have chosen your preferred payment scheme you won't be able to ever change it (not
now, not in the second round), under any circumstances.
Now we will describe you the two payment scheme options available.
Remember to read carefully the options. There is no time restriction t read it.
Continue to payment scheme options
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Payment Scheme 1
Payment Scheme 2
Success = To solve correctly 1 or more tables
First Round Payment
It only depends on how many tables were correctly solved in round one.
The first round payment will be received in cash today as you exit the lab.
$13.000 if successful in the first round.
$10.000 independently of
whether successful in the first round.
$3.000 if not successful in the first round.
Second Round Payment
It depends on how many tables were correctly solved in round one and two.
The second round payment will be received once the second stage of the study is over.
$18.000 if successful in the first
and second round.
$21.000 if successful in the first
and second round.
$14.000 if successful in the first but not
in the second round.
$17.000 if successful in the first but not
in the second round.
$14.000 if successful in the second but
not in the first round.
$7.000 if successful in the second but
not in the first round.
$9.000 if not successful in either stage.
$2.000 if not successful in either stage.
I choose Payment Scheme 1
I choose Payment Scheme 2
I am indifferent: Please, make a random choice for me
Before making a decision, I want to read over the instructions
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Payment Scheme 2
Success = To solve correctly 1 or more tables
First round payment
(To be receieved today in cash)
$10.000 independently of whether successful in the first round.
Second round payment
(To be received in a month)
$21.000 if successful in the first and second round.
$17.000 if successful in the first but not in the second round.
$7.000 if successful in the second but not in the first round.
$2.000 if not successful in either stage.
I confirm I have chosen Payment Scheme 2
Before making a decision, I want to read over the instructions
8&6WXG\
%HIRUHWKHVHFRQGSDUWEHJLQVDQG\RXSHUIRUPWKHWDVNSOHDVHDQVZHUWKHIROORZLQJTXHVWLRQ
+RZGLG\RXFKRRVHEHZHHQSD\PHQWVFKHPHVRQHDQGWZR"
:HPHDQZKDWZDV\RXUGHFLVLRQEDVHGRQ"
Please, be as detailed as possible.
Continue
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When you are ready to start the second part, press the following button.
Remember that you'll be paid following the payment scheme 2, as you chose.
Start the second part
This is table 1 out of 20
Number of tables correctly solved: 0
00:09
4.26
3.64
5.60
7.8
1.71
9.4
7.29
6.28
7.3
1.7
5.62
2.71
Next
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You have finished round one.
Remember that round 2 will be performed in the second stage of the study in a month.
Round two's payment will be paid accordingly to the payment scheme you chose today.
Continue
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Before showing you your results from round one and your payments, we ask
you to answer the following question.
Imagine you have to pay a person to make him or her solve correctly as many tables
as he or she can in the second part of this study (rounds 1 and 2). This person decided
not to play in the lottery game, meaning that he or she doesn't like to run risk.
Also, imagine that you would get $1000 for each correctly solved table that person gets.
What payment scheme would you choose to pay him or her with?
Once the study is over, we will choose randomly a participant and ask other (one of
those who chose not to play any lottery) to repeat this study with the payment scheme
that the participant chose in this question. The randomly chosen participant (who may
be you!) will get $1000 for each correctly solved table in rounds one and two.
(If you want to look at the payment scheme table again, press HERE)
With Payment Scheme 1
With Payment Scheme 2
I'm indifferent
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How did you make a decision to motivate the other participant with payment scheme 1 or 2?
That is to say, what was your decision based on?
If you were indifferent, why were you indifferent?
Please, be as detailed as possible.
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Your results and payments
1) The randomly chosen lottery was: Win $5000 or lose $2000 and you chose to play
the lottery.
2) Given that you chose to play, your lottery result is: You lose $2000 pesos.
3) In the first part of this first stage of the study, you correctly solved 1 table.
Under payment of $400 pesos each table, you earn $400 pesos.
4) ,QWKHVHFRQGSDUWRIWKLVILUVWVWDJHRIWKHVWXG\\RX correctly solved 0 tables.
Under payment scheme 1, you earn $3000 pesos.
The addition of these 3 payments is your total payment in the study. It corresponds to:
$-2000 + $400 + $3000 = $1400 pesos.
In both stages of the study we guarantee a minimum payment of $2000 pesos.
If your total payment is less thant that, then you'll earn $2000 pesos.
Continue
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Your total payment from this first stage will be paid when all participants in the lab
have finished the study.
Once it happens, the person in charge of the lab will call you by your name and
ask you to tell him how much your total payment is.
Remember taking the receipt we gave you at the beginning of the study because
you must sign it.
The second stage of the study will be performed in a month, during the week of
September the 21st. In the ocasion, you'll be performing the remaining second round
and will get paid accordingly to the payment scheme chosen today.
We'll send you an e-mail with details about the second stage of the study during the
week of September the 14th.
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If you have any comment, please write it down in the following box.
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Please, raise your hand to show you have finished the study.
Once everybody has finished the study, you will be allowed to leave the lab. In
the meanwhile, please remain silent during the remaining time so you will not
disrrupt other participants.
The person in charge on the room will announce out loud when you can leave.
Your total payment was:
$2000
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B.3
Calibration of the Deferred Contract
Following the model in Section 4.1, the parameters were calibrated as follows,
Parameter
πh
πl
c
µ(c)
λ
η
U
U2
Number
0.7
0.001
$3,500 CLP
$3,500 CLP
2.5
0.01
$18,000 CLP
$5,000 CLP
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