An experimental investigation of moral hazard in costly investments.
Deck, Cary A. ; Reyes, Javier
1. Introduction
Frequently, parties make sequential decisions regarding investments
for which the probability of success or failure is dependent on the
amount of total investment. Depending on the circumstances, the second
investment could function as a complement, enabling an endeavor to be
successful that otherwise would not be. However, the investments could
function as substitutes if the first investor, anticipating the actions
of the second investor, invests less. For example, a private sector firm
that provides financing and construction management for highways and
other infrastructure may invest less money and effort knowing that the
public sector acting as a debt guarantor will provide what is needed to
complete the project or cover the costs of default in case the project
fails. A boss may put less effort into a report, knowing that an
underling will catch any errors. When parents allow an adult son or
daughter to move back into their home, this can enable the son or
daughter to regroup before returning to a self-reliant life, but it can
also weaken the incentive for the son or daughter to regroup. In the
academic realm, coauthorship can enable researchers to realize synergies
in their work, but one coauthor might exert less effort with the
expectation that her coauthor will pick up the slack.
The macroeconomic literature on catalytic finance provides another
example of this investment problem. Recently a number of emerging
economies have experienced crises requiring significant structural
domestic adjustments to reestablish steady economic growth. The rescue
packages led by the IMF (1) have been heavily criticized. (2) If the
IMF's stamp of approval (i.e., bailout/support) enhances
investors' perception about a good outcome in a crisis country and
increases the probability of the successful implementation of reforms,
that is, it has a catalytic effect, then the troubled economy will
quickly regain access to international capital markets and will be
allowed to refinance its short-term debt. However, IMF support to crisis
or crisis-prone countries introduces moral hazard. A debtor country that
can avoid or alleviate a crisis by implementing costly (political or
economic) reforms may decide not to do so as long as they can be
substituted by readily available IMF support packages.
This paper reports a series of laboratory experiments that
investigate behavior in what we term a costly investment game. This game
is similar to the ultimatum game in that, in equilibrium, a first mover can take advantage of her position to earn a higher share of the profit.
However, the games differ in some key respects. As with the examples
given above, the payoffs remain uncertain even after both investments
have been made. Further, costly investments by the first mover cannot be
recouped if the second mover effectively "rejects" an offer by
not providing sufficient additional investment. The next section of the
paper describes the game, which closely follows the catalytic finance
model of Morris and Shin (2006). Separate sections provide the design
and results of the experiments. A final section contains concluding
remarks.
2. Costly Investment Game
Morris and Shin (2006) develop a model in which investors make
sequential investment decisions. Specifically, in Morris and Shin
(2006), a debtor country is faced with a solvency problem. Knowing the
economic fundamentals, the debtor can engage in costly reforms after
which the IMF can decide whether or not to extend support. Based on
these decisions there is some probability that the country will be
solvent, which is beneficial to both parties. (3) While Morris and Shin
(2006) focus exclusively on the issue of catalytic finance, as described
above, this appealing model can be applied to other settings as well.
For example, consider two coauthors editing a paper. While both authors
benefit from the paper being published, both may prefer to let the other
shoulder the burden.
Our objective is to compare the theoretical predictions of Morris
and Shin (2006) for the interaction of the first and second investors,
which we term the costly investment game, with what we observe in the
laboratory. (4) Thus, we present a brief description of their model,
extracting only the essential conditions needed for our experimental
analysis, and refer the reader to the original paper for details.
Structure of the Costly Investment Game
Two investors want to see a project succeed, meaning that it
surpasses some threshold that could differ by investor. In the catalytic
finance story this amounts to the economy being solvent, as determined
by the demands of its creditors, and fundamentally sound. For the
coauthors, this means that the paper is publishable perhaps by different
level journals as determined by an editor. Both investors observe the
initial state of the project, denoted by [phi]. For the catalytic
finance story this represents the economic fundamentals of economy and
for coauthors it represents the quality of the idea or the manuscript in
its current state. The first investor can exert costly effort, e, to
improve the project (reforms by the debtor country or other forgone
research by the coauthor) at a cost of c(e) = [e.sup.2].
Based on the first investor's decision, the initial quality of
the project, [theta], is drawn from a normal distribution with mean
[phi] + e and variance l/[alpha]. With a normalization, the economy is
considered to be sound or the paper publishable if [theta] [greater than
or equal to] = 0. After observing both [theta] and e, but not the
realization of [theta], the second investor can provide additional
support, m at a cost of c(m) = bm. (5) This represents the IMF providing
additional support or the second author revising the paper. For the
economy to be solvent or the paper publishable at a better journal, it
must be that [theta] + m exceeds a level 7. This threshold is a function
of the opportunity cost of a third party given by L and their private
signals of the true quality [theta]. (6) In the catalytic finance story,
[gamma] is the percentage of creditors who roll over their debt, which
is a function of their alternative investment opportunities and private
information. In the coauthor story, [gamma] is the likelihood an editor
will accept a paper, which is a function of the marginal paper at the
journal and the private signals given by the reviewers. These private
signals are assumed to be unbiased and normally distributed with a
variance of 1/[beta].
Following Morris and Shin (2006), the payoffs to the first and
second investors are given by Equations 1 and 2, respectively.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
Morris and Shin (2006) show that if [alpha]/[beta] [less than or
equal to] [square root of 2 [pi]] then there is a unique critical
realization of [theta], denoted by [[theta].sup.*], below which the
project will not be successful. When [alpha] and [beta] [right arrow]
[infinity] (i.e., there is very good information), it is possible to
show that the optimal amount of second-investor support is dependent on
the opportunity cost, [lambda], of the third party, which ultimately
defines the threshold for success. Optimal support is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)
That is, the second investor does not want to contribute additional
resources if the project is hopeless or is already of sufficient
quality. But the second investor will contribute just enough to take the
project over the threshold if it is sound.
Given the optimal response of the second investor, the effort that
maximizes the first investor's payoff is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)
This means that the first investor wants to exert just enough
effort to induce the second investor to complete the task. From Equation
3 the second investor will expend enough resources to meet the
opportunity cost of the third party, who ultimately determines success.
As [lambda] increases so does m. Based on Equation 4 as [phi] increases,
meaning the project's initial state is greater, then the effort of
the first investor is reduced since not as much effort is needed to
induce the second investor to contribute.
If there were no second investor the optimal investment would be
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)
That is, the first investor would exert enough resources to reach
the threshold on their own if it were possible to do so. As noted by
Morris and Shin (2006), Equations 4 and 5 are the basis for the moral
hazard problem since it is not possible to unambiguously rank the
optimal levels of effort under these two different scenarios. If the
fundamentals are such that -1 [less than or equal to] [phi] < - (1
[lambda]), then the second investor serves as a strategic complement
enabling the project to be completed successfully. But when - (1 -
[lambda] [less than or equal to] [phi] < [lambda], the second
investor is a substitute for the first. In the first scenario the first
investor cannot be successful alone, but in the second scenario she
could be.
More generally, when there is not perfect information, the
situation changes in two important ways. First, the probability of
success differs for the first and second investors. Second, both parties
will optimally expend more effort than under certainty, the magnitude of
which depends on [alpha] and [beta]. Unfortunately, there is no closed
form solution. Therefore, at this point we introduce the parameter values we consider in the experiments described below: [alpha] = 10,
[beta] = 100. First we note that our values of [alpha] and [beta], while
somewhat arbitrary, satisfy the sufficient condition for uniqueness of
[[theta].sup.*]. The optimal amount (7) for the first investor is given
in Equation 6,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)
and the optimal amount for the second investor is given by Equation
7,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)
Therefore, one would expect to see the first overrespond to the
underlying fundamentals of the project, leaving the second investor to
worry about reaching the third party's threshold.
The experiment that follows evaluates how observed investments
change as [phi] and [lambda] vary. Specifically we use values of [phi]
[member of] {-0.05, -0.55} and [lambda] [member of] {0.6, 0.7}. Table 1
presents the theoretical predictions for each case. We introduce the
notation C and S for strategic complements and substitutes,
respectively, and use a subscript or a superscript [lambda] to denote its relative value. Appendix A contains the probability table for each
investor associated with each condition.
Comparison of Investment and Ultimatum Games
The crux of the model is that the first investor will do just
enough so that the second investor will opt to see the project to
fruition. The equilibrium concept assumes that the investors are not
concerned about how the gains from success are shared between the
parties or that the investments are done in the most efficient way.
However, previous experimental evidence has shown that decision makers
do worry about things other than their own monetary payoff. One of the
most studied games in the experimental literature is the ultimatum game.
(8) Cox and Deck (2005) conduct experiments with a mini-ultimatum game
in which the first mover can propose to keep $8, leaving $2 for the
second mover, or the first mover can propose to split the money equally
so that each would receive $5. The second mover could then decide to
accept the proposal or reject it, in which case both people received $0.
Standard self-interested theory as assumed by the model of Morris and
Shin (2006) would suggest that the first mover keep $8, and that the
second mover would accept it. Yet, Cox and Deck (2005) found that
approximately 20% of unequal offers were rejected by second movers and
36% of first movers proposed the equal split.
The robustness of previous experimental results would seem to call
into question the applicability of the equilibrium predictions of Morris
and Shin (2006), but this game differs from a standard ultimatum game in
several key ways. (9) In the costly investment game, there is a gain
only when the two parties invest sufficiently. This is like framing the
ultimatum game as a situation in which each party is given $10 if
together they invest a total of $10. As an example, the first mover
agrees to pay $2 and the second mover agrees to invest $8, then the
payoffs to the first and second movers, respectively, would be $8 and
$2. In the costly investment game, the first investor incurs the
investment cost regardless of the decision of the second investor. In
the example above, this would be equivalent to the first mover having to
pay $2 regardless of whether or not the second mover subsequently
invests $8. Another difference in the ultimatum and costly investment
game is that while both parties receive the same nominal benefit from
success, the distribution of income is determined by the relative costs
of the investments, which differ by role. Counting the example, this
would be a $X investment costing the first investor $[X.sup.2]/10 and a
$Y investment costing the second mover $ Y/2.
The introduction of uncertainty also represents a divergence from
the standard ultimatum game. In the costly investment game, the more
that is invested, the (perhaps weakly) greater is the likelihood of the
good outcome occurring. Finishing the example, this would be similar to
each party receiving $10 with probability (X + Y)/20. Previous
experimental evidence on risk attitudes suggests that behavior might not
match the risk-neutral predictions of the model. While there is
disagreement as to the level of risk aversion that people exhibit,
studies typically find that most people are risk averse. (10) In
general, the effect of risk attitude is unclear in this model. Increased
risk aversion may make an investor less likely to invest, thus avoiding
the risk altogether, or it might cause overinvesting so as to increase
the likelihood of success. However, given the parameter values discussed
in the preceding subsection and the discrete nature of the experiment
discussed in the next section, moderate levels of risk aversion or
risk-seeking behavior would not impact the optimal level of investments.
3. Experimental Design
To examine how the investments depend on the underlying parameters
of the model, we conducted a series of laboratory experiments in a
within-subjects 2 x 2 x 2 design. As described in the previous section,
the first dimension is the level of the underlying fundamentals of the
project, [phi], and the second dimension is the threshold, [lambda]. The
third dimension is the existence of the second investor.
First we summarize the parameter choices discussed previously:
[alpha] = 10, [beta] = 100, [phi] [member of] {-0.05, -0.55}, [lambda]
[member of] {0.6, 0.7}, and, as suggested in Morris and Shin (2006),
c(e) = [e.sup.2]. The other parameter of the model is the per-unit cost
to the second investor, b, which we set equal to 0.5.
In the experiments, a success corresponded to receiving $10, and
the bad outcome was receiving $0. This is a simple scaling of the
payoffs and costs in Equations 1 and 2 by a factor of 10, and it also
keeps the gains similar to those in the standard ultimatum game.
Information on the probability of the good outcome was presented to both
subjects through a pair of tables. (11) The column headings were the
first investor's cost, row headings were the cost to the second
investor, and each cell showed the probability of success. In the
experiment, the first investor selected an investment level by clicking
on the appropriate column in the upper table. This action highlighted
the selected column in both tables and asked the subject to confirm the
selection. Once the first investor confirmed the choice, it was revealed
to the second investor, who could then select a level of support by
clicking on a row in the lower table. Again, the selection was
highlighted in both tables and the subject was asked to confirm the
choice. At this point the first investor was informed of the second
investor's decision, and the probabilities of success for each
party were common information. In situations where there was no second
investor, the investor observed only one table, which contained a single
row. Still the column headings were the investment cost, the table
entries were the probabilities associated with the good outcome, and
subjects had to confirm their selection after making a decision.
The ultimate success of the project was determined by rolling two
10-sided dice. Each die had the integers from 0 to 9. The first die
rolled determined the first digit and the second die determined the
second digit. If the number rolled was less than the selected entry in
the appropriate table, then the good outcome (payoff equals $10 minus
cost) was realized, otherwise the bad outcome (payoff equals $0 minus
cost) was realized. Rolling dice served two purposes. First, it is an
easily understandable way to generate a random number, helping to ensure
subject comprehension. Second, it provided credibility to the subjects,
since the dice were rolled on a document camera in their presence with
the live image projected on a large screen at the front of the lab. (12)
To ensure that subjects could pay the cost associated with their actions
even if the bad outcome was realized, each subject was endowed with $10.
(13)
Six subjects participated in each session. After entering the lab,
all subjects read a set of written directions explaining the decision
task faced by both investors as well as the decision task faced by a
single investor. (14) Each session included 20 investment games, some
involving two investors and some involving a single investor. All six
subjects made decisions in the solo investment games, but the same three
randomly chosen subjects were second movers in every game with two
investors. To control for reputation and repeated play effects,
counterparts were randomly assigned before each game with two investors.
To control for possible wealth effects over the course of the
experiment, at the end of each session a volunteer was solicited from
among the subjects. (15) This volunteer rolled a 20-sided die to
determine which period's decision would actually count for the
payoff. Subjects were informed of this procedure before the experiment
began. At the conclusion of the experiment, subjects were paid privately
by the experimenters and dismissed.
Subjects in each of the eight sessions played the same 20 costly
investment games, but the order was different in an attempt to control
sequencing effects. Table 2 gives the game order for each session. The
first four games in each session involved single-player games against
nature, thus giving the subjects experience with the interface and
providing us with information regarding their degree of risk aversion.
Games five through eight involved simple two-investor games and were
designed to give the subjects experience in their respective roles as
the first decision maker or the second decision maker prior to making
decisions in the games of interest. (16) The last 12 games involved the
games of interest, along with two other games based on different
parameter values of [alpha], [beta], [phi], and [lambda], which were
included so that that the exact treatment effects would not be
transparent to subjects. The subjects played these six games twice; once
as a game with two investors and once as a game with a single investor.
(17) Since a subject was not allowed to participate in multiple
sessions, a total of 48 subjects completed the one hour experiment. The
subjects were recruited from undergraduate business classes at the
University of Arkansas. For many this was their first experiment, but
some had previously participated in other unrelated experiments. In
addition to salient payment, which averaged $12.54, subjects received a
$5 show-up fee. Subjects received this $5 before beginning the
experiment so that it was transparent to the subjects that the $10
endowment in the experiment did not include the show-up fee.
[FIGURE 1 OMITTED]
4. Behavioral Results
The results are presented as a series of findings. The first
finding investigates the impact of the existence of a second investor on
the decision of the initial investor.
FINDING 1. The change in initial investments due to the presence of
a second investor is consistent with the predictions of Morris and Shin
(2006).
EVIDENCE: Figure 1 plots the within-subject difference in
investment when there is and when there is not a second investor. (18)
In games [S.sup.[lambda]] and [S.sub.[lambda]], the first investor is
predicted to invest less when there is the possibility of a subsequent
investment by someone else, and that is what we clearly observe. For
games [C.sup.[lambda]] and [C.sub.[lambda]], the second investor is
predicted to serve as a strategic complement to the first investor, and
again we observe the predicted outcome. For quantitative support we rely
on a nonparametric sign test, with the unit of observation being the
eight-session level average within-subject differences. This controls
for the fact that the decisions from subjects in the same session are
not independent. The null hypothesis of no second-investor effect can be
rejected in favor of the one-sided alternative suggested by the theory
at the 95% confidence level for [S.sup.[lambda]] (p = 0.0352), for
[S.sub.[lambda]] (p = 0.0039), and for [C.sub.[lambda]] (p = 0.0039).
(19)
[FIGURE 2 OMITTED]
The games in which investments are strategic substitutes are such
that a sole investor's optimal choice is on the interior of the
action space. However, this is not the case for complements. In part
this is a feature of the base model. For the investments to be
complementary, it has to be the case that an investor cannot be
successful on her own and thus the investor prefers to not invest if
there is no possibility of subsequent support. It is fair to ask whether
this behavior is an artifact of the extreme nature of being complements.
Without going into the details of the games, based on behavior observed
in games five through eight with other probabilities tables, the answer
appears to be no.
Having established that the general behavioral patterns conform to the model, the analysis now turns to the model's specific
predictions. In all games in which there was a second investor, 12.5% of
the pairs reached the equilibrium predictions. Forty-seven percent of
behavior in the single-investor games was consistent with the
equilibrium prediction. It is worth noting that there were 112 possible
outcomes in the two-investor games as compared with only 11 possible
outcomes in the single-investor game.
Figures 2 through 5 plot the frequency of the outcomes by subject
pairs in the games of interest. The gray shaded areas indicate regions
where theoretically the first investor invested an insufficient amount
to make it worthwhile for the second investor to invest anything. Black
shaded areas indicate that the first investor has invested sufficiently
so that there is no reason for the second investor to contribute
anything. The outlined cells indicate the best response (optimal
reaction) curve of the second investor to an initial investment in the
intermediate range. The bolded outline indicates the subgame perfect
Nash equilibrium of the game. Recall from Equation 7 that the optimal
response for the second investor is [lambda] - ([phi] + e - 0.15) in the
case that e [greater than or equal to] -[phi] + 0.15. That is,
additional investment by the first player is exactly offset by a
reduction in the investment of the second player. But, when 0 < [phi]
+ e < 0.15, the optimal level for the second investor is to just
reach the threshold value, [lambda].
[FIGURE 3 OMITTED]
The most striking feature of these figures is the degree to which
the second-investor behavior conforms to the theoretical predictions of
Morris and Shin (2006). In every single case where the first
investor's decision is predicted to induce zero investment by the
second player (the gray and black shaded areas), that is exactly what we
observe. Further, in only three instances where the second investor is
predicted to invest did we observe investment levels differing from the
predicted levels by more than one unit. Finding 2 evaluates the
consistency of the second investor's behavior with the theoretical
prediction.
FINDING 2. Statistically, second-investor choices increase one for
one with increases in threshold level for success. Further, the second
investor provides the optimal amount of additional support, exactly
absorbing excess initial investment.
EVIDENCE: Support for this finding is based on estimating the
mixed-effects model [m.sub.ijg] = [[beta].sub.0] + [[beta].sub.1] x
[Lambda.sub.g] + [[beta].sub.2] X [Net.sub.g] + [[beta].sub.3] X
[NetP.sub.g] + [[epsilon].sub.i] + [[zeta].sub.ij] + [u.sub.ijg], where
[[epsilon].sub.i] ~ N(0, [sigma]21), [zeta] [i.sub.ij] ~N(0, [sigma]22),
[u.sub.ijg] ~ N(0, [sigma]23). This repeated measures model estimates a
fixed effect for each treatment game g while allowing each session i and
each subject j within a session to have a random effect. Lambda is a
dummy variable that takes the value of 1 if [lambda] = 0.7 and 0 if
[lambda] = 0.6 for the observation. Net is the value of [phi] + e -
0.15, to which the second investor is responding. NetP is a dummy
variable that takes on the value of 1 if [phi] + e < 0.15 and 0
otherwise; that is, it indicates that the initial investment was below
the optimal level. The estimation is restricted to the subset of data in
which the optimal response of the second investor is to provide positive
support for the project. Note that second investors always provided zero
support when it was optimal to do so, as shown in Figures 2-5. Table 3
provides the estimation results, which, for brevity, do not include the
random effects. The coefficient on the dummy variable Lambda is 0.07715,
which is not significantly different than 0.1 (p = 0.4235 in the
two-tailed test). Thus, [lambda] increasing by 0.1 leads to a 0.1
increase in support as predicted. That is, the second investor increases
her investment to match increases in the success threshold. The baseline case, where the threshold, [lambda], is equal to 0.6 and the initial
investment is set to e = -[phi] + 0.15 so that NetP = 0 and therefore
the optimal second investment is m = 0.6, yields the hypothesis
[[beta].sub.0] = 0.6, which cannot be rejected at standard levels of
significance (p = 0.3622 in two-tailed test). When the first investor
overinvests, e > -[phi] + 0.15, the second investor responds by
decreasing her own investment, m, one for one as predicted.
[FIGURE 4 OMITTED]
This is evidenced by the fact that [[beta].sub.2] = - 1 (p = 0.4097
in the two-tailed test). In the case that initial investment is too low,
the second investment should equal [lambda]. Given the discrete nature
of the game, the only possible effort in this category is e = -[phi] +
0.05, which is 0.1 below the optimal. The estimated change in the second
investment in this position is [[beta].sub.2] x (-0.1) + [[beta].sub.3].
Assuming that [[beta].sub.2] = - 1, [[beta].sub.3] should equal -0.1.
This null hypothesis cannot be rejected (p = 0.8630 in the two-tailed
test).
The observed behavior of the second investor differs from what is
typically found in ultimatum games. (20) In the strategic substitutes
games shown in Figures 4 and 5, investments of $1.60 or less by the
first investor force the second investor to invest at least $2.00 for
the good payoff to be achieved. This is analogous to the decision of a
first mover in a mini-ultimatum game to opt for the $8-$2 split instead
of the $5-$5 split. Cox and Deck (2005) find that 20% of such
"greedy" proposals are rejected, but we find that 0 of 15
greedy choices are rejected in one case and only 1 of 8 greedy choices
is rejected in the other. One explanation given for the typical
ultimatum game behavior is a desire for equality motivated by
"fairness" and, therefore, it is worth noting what a
comparable behavior would be in the costly investment game. Consider the
situation in which costs are borne (nearly) equally by both investors.
Graphically, such outcomes form a downward sloping path, from the top
left to the bottom right, in Figures 2 through 5. Casual inspection of
these figures suggests that this is not how second movers are
responding. An alternative consideration could be efficiency, which
would mean maximizing the total expected payout of the investors. Second
movers motivated by efficiency would respond in the same way as the
theoretical predictions presented above for initial investments at or
above the optimal level. However, second investors motivated in this way
would increase their investments even as the first mover underinvested.
Graphically this would be a downward continuation of the diagonal path,
from top left to bottom right, in Figures 2-5, which is not consistent
with the pattern we observe.
Even though the second investor responds optimally, the first
investors do not seem to anticipate this behavior. Based on the
theoretical model, the first investor should choose to invest e = -[phi]
+ 0.15. However, from the 11 instances in Figures 2 and 3 where no
investment is undertaken when investments are complements, it is
apparent that many first players do not trust that the second player
will provide sufficient help to warrant investing. But, from Figures 4
and 5, it is apparent that first investors tend to overinvest in the
case of strategic substitutes. Finding 3 compares first-investor
behavior with the theoretical predictions.
[FIGURE 5 OMITTED]
FINDING 3. As the underlying fundamentals, [phi], increase, the
first investors respond by investing less. This shift is in the
direction predicted, but the magnitude is smaller than expected. In
contrast with the theoretical predictions, the success threshold,
[lambda], does affect the behavior of the first investors.
SUPPORT: The quantitative evidence is based on the estimation of a
mixed-effects model, [e.sub.ijg] = [[gamma].sub.0] + [[gamma].sub.1] X
[Phi.sub.g] + [[gamma].sub.2] x [Lambda.sub.g] + [[gamma].sub.3] X [(Phi
X Lambda).sub.g] + [[epsilon].sub.i] + [[zeta].sub.ij] [u.sub.ijg],
where Phi is a dummy variable that takes the value of 1 if [phi] = -0.05
and 0 if [phi] = -0.55 for the observation, Phi X Lambda is an
interaction between Lambda and Phi, and the other terms are as before.
Table 4 provides the estimation results. As predicted, an increase in
fundamentals, [phi], leads to lower initial investments, but not at the
one-for-one rate predicted as [[gamma].sub.1] [not equal] 0.5 (p <
0.001 in the two-tailed test). It is important to keep in mind that this
model examines the average effect. For many of the subjects, those that
did not invest at all in the case of strategic complements where [phi]
is low, investments actually increased with [phi]. This counteracts the
investment reduction for subjects who behaved according to the theory
and trusted the second investor to contribute in the substitutes games.
Given the large number of subjects who did not invest in the complements
scenario, it is not surprising that the average investment in the
baseline case, [phi] = -0.55 and [lambda] = 0.6, is below the
theoretical prediction. Note that in the baseline case, investment
should be -[phi] + 0.15 = 0.7. Thus the null hypothesis is that
[[gamma].sub.0] = 0.7, which can be rejected at standard significance
levels (p < 0.001 in the two-tailed test). The fact that the first
investors respond to [gamma] is evidenced by the fact that
[[gamma].sub.2] [not equal to] 0 (p = 0.0482 in a two-tailed test). In
fact, it appears that increasing [lambda] by 0.1 leads to a 0.1 increase
in initial investments. This is also consistent with the first investor
not being willing to rely on the second investor. The lack of an
interaction effect, [[gamma].sub.3] = 0 (p = 0.1845 in a two-tailed
test), is consistent with the theory.
First-investor overinvestment in the case of strategic substitutes
is not too surprising given previous ultimatum game results.
Thirty-seven percent of first movers invested more than $1.60 in
[S.sub.[lambda]]. This is similar to the 36% of first movers making an
equal split proposal in the mini-ultimatum game of Cox and Deck (2005).
As the threshold [lambda] increases between [S.sub.[lambda]] and
[S.sup.[lambda]], meaning that the second investor should invest more
conditional on e, fewer of the first investors exploit their first mover
advantage, meaning they bear part of the additional burden. What is
surprising is how many (38%) of the first movers actually opted to
undertake the majority of the investment themselves. It is tempting to
speculate that this pattern suggests that first movers are likely to
take responsibility for their own situation, but given the neutral
framing of the decision task it seems more reasonable that this is
further evidence of a lack of trust in second-mover responses. (21)
Throughout this paper, theoretical predictions are based on an
assumption of risk neutrality. It is reasonable to ask how sensitive
these predictions are to issues of risk aversion. Given the parameters
selected and the discrete nature of the experiment, people with risk
attitudes similar to what has been reported previously (see Holt and
Laury 2002; Deck, Lee, and Reyes, in press; and references therein)
would make similar choices. (22) However, we do note that we find
substantial risk-loving behavior. (23) In the fourth game of the
experiment, subjects had to choose between paying $5 of their $10
endowment for a 49% chance of winning $10 and simply keeping the $10
endowment. Twenty-seven of the 48 subjects (56%) opted for the risky
option, indicating at least a modest degree of risk-loving behavior.
This could be further evidence that the mechanism for measuring risk
attitudes can affect the observed level of risk aversion (see Isaac and
James 2000; Berg, Dickhaut, and McCabe 2005). In our experiments, we did
not observe any extreme risk aversion. No subject was consistent with a
constant relative risk aversion parameter greater (more risk averse)
than 0.38, and only one subject was consistent with a risk parameter
greater than 0.28.
5. Conclusions
In many situations, the investments of multiple parties impact the
probability of a successful outcome. This enables success in cases in
which a single investor could not be successful alone but can also lead
to moral hazard problems if the first mover can rely on a subsequent
investor to bail her out. A key challenge for second movers in setting
policies, either the IMF providing support to a debtor country or a
coauthor deciding to exert effort in a research project, is trying to
determine into which category a problem falls. The model of Morris and
Shin (2006) provides a straightforward theoretical framework for this
problem. Our paper reports a series of experiments largely confirming
their theoretical predictions. The existence of a second investor
influences the first investor in the direction predicted. In general we
find that second investors are best responding to the first investors,
but first investors deviate from the theoretical predictions in
intuitive ways.
The case of strategic substitutes is similar to the standard
ultimatum game. In the ultimatum game a first mover proposes an
allocation of a fixed amount of money, which a second mover can accept
or reject. Typically, only a small percentage of first movers propose an
allocation that is overwhelmingly in their own favor in an attempt to
keep (nearly) everything. This is similar to what we observed in the
costly investment game. In the ultimatum game it is not uncommon to see
such unequal offers rejected by second movers in favor of both parties
receiving nothing. But we see very few "rejections" by second
investors. To be fair, there are some key differences between the two
games, any of which could explain the difference. For example, perhaps
the fact that investors have to forgo investment costs irrespective of the ultimate success of the project causes first investors to invest
less given the uncertainty of how second investors will react and second
investors understand this and therefore are more willing to accept low
initial investments. Regardless of the cause of this difference, our
work joins Salmon and Wilson (2006) in calling into question the degree
to which ultimatum game behavior is robust to different institutional
settings. (24)
The ability of the model to categorize behavior suggests some
policy implications. For example, as it is currently implemented, the
support of the IMF can serve as an alternative to costly reforms/efforts
that the debtor should undertake. The behavioral observations suggest
that the burden could be shifted to the first investor by laying out the
specific conditions under which the second investor would provide
support. But for such a policy to work it would have to be the case that
the IMF could credibly commit to it and therefore allow a country to
default. Of course, in the case of coauthors it is not necessarily clear
who "should be" responsible for the investments. Returning to
the parent and adult child example of the introduction, this policy
would require the parent to lay out specific conditions under which
support would be provided. Short of enacting such policies, second
investors will continue to be taken advantage of when their support is
not catalytic.
As with any empirical study, one must be careful in extrapolating
to the more general problem of interest. For example, one criticism
often raised in laboratory experiments is that the subjects in the lab
are not as "sophisticated" as the population of interest.
However, it is difficult to imagine any group's behavior in the
second-investor role (including the IMF or PhD researchers) being more
consistent with the theoretical predications. But more sophisticated
first investors who believed that the second investor would provide
support might have been more willing to push responsibility onto the
second investors. The implications of this would presumably be even
greater coordination when the two parties are in complementary roles
since more initial investors would be willing to take the risk and even
less initial investment when the second investor provides a strategic
substitute.
Appendix A: Probability Tables by Treatment
The following are screenshots. In each pair, the top table is for
the first investor and the lower table is for the second investor.
[ILLUSTRATIONS OMITTED]
Appendix B: Experiment Directions
You are participating in a research experiment through Interactive
Decision Experiments at Arkansas (IDEA). At the end of the experiment
you will be paid your earnings in cash. Therefore, it is important that
you understand the directions completely before beginning the
experiment. If at any point you have a question, please raise your hand
and a lab monitor will approach you. Otherwise, you should not
communicate with others (please turn off all cel phones pagers, etc.).
In today's experiment you will start with an initial $10 (in
addition to your $5 show-up fee) and you will have to make a series of
decisions. You will have to make one decision each round. You do not
know how many decision rounds there will be, but at the end of the
experiment one decision round will be randomly selected and your
earnings in that round will be added to your initial $10. What happens
in one round does not have any impact on what happens in another round.
In some rounds you will make the only decision that affects your payoff
and your decision will not affect anyone else's payoff. In some
rounds you will be randomly assigned a counterpart from the other
participants in the experiment. In this case your payoff and your
counterpart's payoff will depend on the decision made by you and
the decision made by your counterpart.
So what kind of decision are you going to have to make? Each period
there is a chance that you will earn an additional $10. The probability
of earning the $10 depends on your action (and your counterpart's
action, if applicable). However, each action has a cost associated with
it. This cost must be paid regardless of whether or not you earn the
additional $10.
Let's look at an example. Here are the screens for two
randomly assigned counterparts. The dollar amounts on the top row are
the costs associated with each of the first decision maker's
choices. The costs in the first column are the costs associated with
each of the second decision maker's choices. The entries in the
table are probabilities of earning the additional $10. Notice that the
top table on both screens gives the probability of the first decision
maker earning the $10 and the bottom table gives the probability of the
second decision maker earning the $10. Also notice that the
probabilities can differ between the two tables.
[ILLUSTRATIONS OMITTED]
In this case the person on the left will make a decision first.
This person has three choices (columns in the table): the first costing
$3, the second costing $6, and the third costing $9. To make a choice
this person simply clicks the mouse on a column in the top table.
Once the first decision maker selects a column, that column is
highlighted in blue and a button appears that says "Send
Decision." A decision is not final until this button is pressed. So
at this point the decision maker can change the selected action by
clicking on another column. Once this button is pressed the decision
cannot be changed.
[ILLUSTRATION OMITTED]
After the first decision maker presses "Send Decision,"
the second decision maker can make one of two choices (one costing $2
and the other costing $7) by clicking on a row in the lower table.
Notice that the first decision maker's choice is highlighted in
yellow on the second decision maker's screen. Again, a decision is
not final until the "Send Decision" button is pressed. So at
this point the decision maker can change the selected action by clicking
on another row. Once this button is pressed the decision cannot be
changed.
[ILLUSTRATION OMITTED]
Now that both people have made a choice, the probability that each
participant gains $10 can be determined. It is the probability in the
table for the selected column and row. In this example, the first
decision maker selected the $6 column and the second decision maker
selected the $7 row. Therefore, the probability that the first decision
maker gains $10 is 0.5 and the probability that the second decision
maker gains $10 is 0.4.
So do they get the additional $10 or not? To determine this, two
10-sided dice will be rolled. You are free to inspect each die and will
be able to watch the dice being rolled. The roll of the dice could be
anything from 0.00, 0.01, 0.02, to 0.98, 0.99, with every number equally
likely. Thus, there are 100 equally likely outcomes. The first die
rolled will give the first digit and the second die will give the second
digit. If the probability from your table is greater than the number
rolled, you will earn the additional $10. Otherwise, you will not earn
the additional $10.
In our example, decision maker 1 will earn the additional $10 if
the number rolled is 0.00, 0.01, 0.02, ..... 0.48, 0.49. Notice that out
of the total 100 outcomes there are 50 outcomes for which decision maker
1 will earn the $10. Decision maker 2 will earn the additional $10 if
the number rolled is 0.00, 0.01, 0.01,....,0.38 0.39. Out of the total
100 outcomes there are 40 outcomes for which decision maker 2 will earn
the $10.
In our example, decision maker 1 expects to receive $5. If we were
to roll the dice many, many times, sometimes decision maker 1 would earn
$10 and sometimes decision maker 1 would earn $0, but if we took the
average earnings across all of the rolls it would be $5. This can be
calculated as the probability, which is 0.5 x $10 = $5. Similarly,
decision maker 2 expects to receive 0.4 x 10 = $4.
Suppose the first die rolled landed on 4 while the second die
landed on 5. The rolled number would be 0.45. This is less than 0.5, so
the first decision maker would earn the additional $10. However, the
rolled number is greater than 0.4, so the second decision maker would
not earn the additional $10. In this case the screens of the two
decision makers would look like the following.
[ILLUSTRATIONS OMITTED]
Notice that the period earnings are recorded at the bottom of the
screen and that each person has to pay the cost associated with their
action, regardless of the outcome. The period earnings do not include
the initial $10. If this round is randomly selected at the end of the
experiment, the first decision maker would be paid the initial $10 plus
an additional $10 minus the cost of $6 ($10 + $10 - $6) = $14 in
addition to the $5 show-up fee. The second decision maker would be paid
the initial $10 minus the cost of $7 ($10 - $7) = $3 in addition to the
$5 show-up fee.
It is not always the case that one decision maker earns the
additional $10 and the other does not. It is possible for both decision
makers to earn an additional $10 each. It is also possible for neither
decision maker to earn the additional $10. Had the number rolled been
less than 0.4 in the example, then each decision maker would have earned
the additional $10. Had the number rolled been greater than (or equal
to) 0.5 in the example, neither decision maker would have earned the
additional $10.
Remember that only one round will be randomly selected at the end
of the experiment to calculate your actual cash payoff.
The previous example involved two randomly assigned counterparts.
In some rounds you will not have a randomly selected counterpart. In
this case the probability that you earn the additional $10 will only
depend on your own action and your action will not impact anyone
else's probability of earning the additional $10. The following
example shows such a case.
[ILLUSTRATION OMITTED]
Notice that there is only one table and that it has only one row
that does not have a cost associated with it. In this example, the
decision maker has six choices (columns). The selected column is again
highlighted in blue. Recall that a decision is not final until the
"Send Decision" button is pressed. So at this point the
decision maker can change the selected action by clicking on another
column. Once this button is pressed the decision cannot be changed.
Suppose that this decision maker presses "Send Decision"
and then a 0.40 is rolled on the two dice. Since 0.40 is not less than
0.40, this decision maker does not earn the additional $10. The period
earnings are thus $0 minus the $5 cost = -$5, the amount that shows up
at the bottom of the screen for the second period.
If the second period was randomly selected at the end of the
experiment, this person would be paid the initial $10 plus the period
earnings of -$5 = $5 in addition to the $5 show-up fee.
If you have any questions, please raise your hand and a lab monitor
will approach you. Otherwise, please wait quietly for further directions
from the experimenter. The experiment will not begin until everyone
participating in the experiment has completed the directions, so please
wait patiently.
Decision Maker's Screen
[ILLUSTRATION OMITTED]
Received July 2006; accepted January 2007.
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(1) Including those for Argentina, Brazil, Ecuador, Indonesia,
Korea, Mexico, Russia, and Thailand, among others.
(2) See Rodrik (1995); Haldane (1999); Bird, Mori, and Rowlands
(2000); and Bulir et al. (2002).
(3) They use the framework of global games to solve the endogeneity
problem present between the decisions of debtor countries, the IMF, and
private creditors. Based on experimental evidence, Heinemann, Nagel, and
Ockenfels (2004) conclude that "the global game solution is an
important reference point and provides correct predictions for
comparative statics" (p. 1584). Therefore, our costly investment
game assumes the resulting equilibrium behavior of the creditors to
derive the probability of success. The interested reader is directed to
Carlsson and van Damme (1993); Frankel, Morris, and Pauzner (2003); and
Morris and Shin (2003) for a more general discussion of global games.
(4) While Morris and Shin (2006) include the role of a third party,
the creditors, our focus is on the moral hazard present between the
first and second investors.
(5) The cost structure was designed for the catalytic finance story
where reforms might be increasingly difficult politically for the home
government. The same could be true of two coauthors if, for example, one
was about to go up for tenure whereas the other held a chaired position.
(6) The third party is assumed to receive a payoff of 1 >
[lambda] if the project is successful and 0 if it is not, but success
ultimately depends on a cumulative decision of independent third parties
(creditors in catalytic finance and referees in coauthorship).
(7) The optimal investments in Equations 6 and 7 also incorporate
the discrete nature of the decision task faced by the subjects as
described later in the paper.
(8) See Camerer and Thaler (1995) and Kagel and Roth (1995) for a
review of the literature on ultimatum games.
(9) A priori we did not expect these differences to matter, but, as
will be shown in the results, behavior does differ between the costly
investment game and the ultimatum game.
l0 See, for example, Isaac and James (2000); Holt and Laury (2002);
and Deck, Lee, and Reyes (in press). However, this is not always true;
see, for example, Berg, Dickhaut, and Rietz (2005).
(11) As discussed in the Structure of the Costly Investment Game
section, given that [alpha] < [infinity], the probability of success
differed by role. Subjects had complete information regarding the
probability tables for both roles while making decisions. Appendix A
contains the probability tables for the four treatments of interest.
(12) Subjects were given the opportunity to inspect the dice before
the experiment began to ensure credibility.
(13) Since it is not possible to force subjects to pay losses out
of their own pockets, the experimenter loses control of the
subject's motivation if earnings are negative.
(14) The experiments used neutral language so as not to bias
subjects. A copy of the directions is included in Appendix B.
(15) Wealth effects refer to the possibility that behavior could be
dependent on current wealth. A person who has just earned $10 may be
willing to take a risk that she would not be willing to take if she had
lost $10.
(16) The probability tables for investment games not shown in
Appendix A are available from the authors on request. Two of these games
were examples of strategic complements and strategic substitutes; to
satisfy intellectual curiosity, the other two were sequential public
goods games with marginal per capita (probability) returns of 0.06 and
0.08. In these games a dollar spent increased the probability of earning
$10 by either 0.06 or 0.08, up to a maximum of one. Consistent with
previous results, the higher per capita return increased investment by
the first movers, but interestingly we only observed two instances of
complete free riding by second movers.
(17) For the single-investor version of [C.sup.[lambda]], the
probability table would contain only zeros. In its place we substituted
the single-investor version of the complements/substitutes game from
periods 5-8. In a pilot study several subjects expressed frustration
with the all-zeros game. It is worth noting that all of the subjects in
the pilot chose to make zero investment in that game as predicted.
(18) The sole investment decisions made in the games of interest by
subjects who were in the role of the second investor in the two-investor
games are omitted from this discussion.
(19) As noted in footnote 17, there was no one-player version of
[C.sup.[lambda]] in the actual experiments since subjects in a pilot
experiment overwhelmingly expressed frustration at making a decision
when every probability entry was zero. Assuming that these subjects
would have behaved identically to those in the pilot and exerted zero
effort in the one-player version of [C.sup.[lambda]], the sign test
would result in p = 0.0039.
(20) Ultimatum game experiments are typically one shot, meaning
that the subjects do not have the opportunity to learn over the course
of the experiment. We do not see any improvements in second-investor
behavior in the sense of converging to the theoretical predictions over
the course of the games of interest. However, learning may be a factor
due to experience in the first eight games.
(21) In another series of experiments reported in Cox and Deck
(2005), approximately half of the subjects are found to exhibit trust.
(22) Holt and Laury (2002) estimate risk attitudes in the
laboratory, while Deck, Lee, and Reyes (in press) use naturally
occurring data from a game show. The lack of responsiveness claim is
based on the assumption of constant relative risk aversion and is due in
part to the large changes in probability in the model associated with
0.1 increment changes in e and m about their optimal levels. Our choice
of increments was designed to keep the number of table entries
manageable and simultaneously allow us to present subjects with the same
cost choices in all four treatments. Games 5-8 exhibit far more gradual
changes in probability, but the general pattern was similar to what is
reported here, though there was somewhat greater variation, which could
be due to the probabilities or subject experience.
(23) Previous studies on risk attitudes often find evidence that at
least some of the subjects are risk seeking. See, for example, Holt and
Laury (2002); Berg, Dickhaut, and Rietz (2005); and Deck, Lee, and Reyes
(in press), among others.
(24) Salmon and Wilson (2006) consider an auction environment with
second chance offers where the seller can make a take it or leave it
offer to the party losing the auction. They find that the sellers'
attempt to capture most of the surplus in this secondary market and the
bidders are agreeable to this allocation.
Cary A. Deck * and Javier Reyes ([dagger])
* University of Arkansas, Department of Economics, Sam M. Walton
College of Business, WCOB 402, Fayetteville, AR 72701, USA; E-mail
[email protected].
([dagger]) University of Arkansas, Department of Economics, Sam M.
Walton College of Business, WCOB 402, Fayetteville, AR 72701, USA;
E-mail
[email protected]; corresponding author.
For helpful comments we thank Christopher P. Ball, Fabio Mendez,
three anonymous referees, and participants at the Missouri Economic
Conference. Remaining errors are our own. We gratefully acknowledge
support from the National Science Foundation (SES 0350709).
Table 1. Theoretical Predictions for Given Parameter Values
Optimal e with
No Second
Condition [phi] [lambda] Investor
[S.sub.[lambda]] -0.05 0.6 0.7
[S.sup.[lambda]] -0.05 0.7 0.8
[C.sub.[lambda]] -0.55 0.6 0.0
[C.sup.[lambda]] -0.55 0.7 0.0
Optimal e
with Second Relationship
Condition Investor of e and m Optimal m
[S.sub.[lambda]] 0.2 Substitutes 0.8 - e
[S.sup.[lambda]] 0.2 Substitutes 0.9 - e
[C.sub.[lambda]] 0.7 Complements 1.3 - e
[C.sup.[lambda]] 0.7 Complements 1.4 - e
Optimal second investment, m, is conditional on assumption that the
first investor is providing a level of at least -[phi] + 0.15, but
not so much as to complete the project alone.
Table 2. Sequence of Games by Session
Games 1-4, Games 5-8,
Session One Investor Two Investors
1 [R.sub.1], [R.sub.2], [PG.sub.8], C,
[R.sub.3], [R.sub.4] [PG.sub.6], S
2 [R.sub.1], [R.sub.2], [PG.sub.8], C,
[R.sub.3], [R.sub.4] [PG.sub.6], S
3 [R.sub.1], [R.sub.2], S, [PG.sub.6],
[R.sub.3], [R.sub.4] C, [PG.sub.8]
4 [R.sub.1], [R.sub.2], S, [PG.sub.6],
[R.sub.3], [R.sub.4] C, [PG.sub.8]
5 [R.sub.1], [R.sub.2], S, [PG.sub.6],
[R.sub.3], [R.sub.4] C, [PG.sub.8]
6 [R.sub.1], [R.sub.2], S, [PG.sub.6],
[R.sub.3], [R.sub.4] C, [PG.sub.8]
7 [R.sub.1], [R.sub.2], [PG.sub.8], C,
[R.sub.3], [R.sub.4] [PG.sub.6], S
8 [R.sub.1], [R.sub.2], [PG.sub.8], C,
[R.sub.3], [R.sub.4] [PG.sub.6], S
Games with
Two
Session Games 9-14and 15-20 Investors
1 [S.sup.[lambda]], [C.sup.[lambda]], [D.sub.1], Games 15-20
[D.sub.2], [S.sub.[lambda]], [C.sup.[lambda]]
2 [C.sub.[lambda]], [S.sup.[lambda]], [D.sub.1], Games 15-20
[D.sub.2], [C.sup.[lambda]], [S.sup.[lambda]]
3 [S.sub.[lambda]], [C.sub.[lambda]], [D.sub.2], Games 15-20
[D.sub.1], [S.sup.[lambda]], [C.sup.[lambda]]
4 [C.sup.[lambda]], [S.sup.[lambda]], [D.sub.2], Games 15-20
[D.sub.1], [C.sub.[lambda]], [S.sub.[lambda]]
5 [S.sup.[lambda]], [C.sup.[lambda]], [D.sub.1], Games 9-14
[D.sub.2], [S.sub.[lambda]], [C.sub.[lambda]]
6 [C.sub.[lambda]], [S.sub.[lambda]], [D.sub.1], Games 9-14
[D.sub.2], [C.sup.[lambda]], [S.sup.[lambda]]
7 [S.sub.[lambda]], [C.sub.[lambda]], [D.sub.2], Games 9-14
[D.sub.1], [S.sup.[lambda]], [C.sup.[lambda]]
8 [C.sup.[lambda]], [S.sup.[lambda]], [D.sub.2], Games 9-14
[D.sub.1], [C.sub.[lambda]], [S.sub.[lambda]]
[R.sub.1], [R.sub.2], [R.sub.3], and [R.sub.4] denote single-investor
games used to assess risk attitudes. [PG.sub.8] and [PG.sub.6] denote
sequential public goods games with marginal per capita (probability)
returns of 0.08 and 0.06, respectively. C and S refer to complement
and substitute games, and [D.sub.1] and [D.sub.2] refer to games
derived from other parameter values in the model of Morris and Shin
(2006). The single-investor version of C/S was substituted for the
single-investor version of [C.sup.[lambda]], as described in footnote
17.
Table 3. Mixed-Effects Estimation for Second Investor
Standard
Value Error d.f. t p
[[beta].sub.0] 0.57498 0.0272 48 21.123 -0.0001
[[beta].sub.1] 0.07715 0.0283 48 2.725 0.0089
[[beta].sub.2] -0.93157 0.0823 48 -11.317 -0.0001
[[beta].sub.3] -0.09195 0.0464 48 -1.982 0.0532
Table 4. Mixed-Effects Estimation for First Investor
Standard
Value Error d.f. t p
[[gamma].sub.0] 0.5388 0.0437 69 12.337 <0.0001
[[gamma].sub.1] -0.1335 0.0448 69 -2.982 0.0040
[[gamma].sub.2] 0.0900 0.0448 69 2.011 0.0482
[[gamma].sub.3] -0.0849 0.0633 69 -1.341 0.1845
