An experimental investigation of moral hazard in costly investments.

• Author: Deck, Cary A.
• Position: Author abstract

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]

   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]...