Hand in the cookie jar: an experimental investigation of equity-based compensation and managerial fraud.

• Author: Bruner, David

1. Introduction

   It has long been recognized that the managers and owners of a firm have different incentives. The owner seeks to maximize the value of the firm, while the manager may derive utility from additional factors, such as the firm's market share, total output, and total employment. Equity-based compensation has been an increasingly popular means by which to align the incentives of top management with those of the shareholders. By providing a share in the ownership of the firm, equity provides the manager with a greater incentive to maximize the value of the firm. However, recent theoretical and empirical work indicates that the use of equity-based compensation has the (unintended, presumably) consequence of creating an incentive to commit fraud. Management's ability to manipulate information regarding the firm's actual performance raises the possibility that reported output (profits) will be overstated. This paper provides behavioral evidence (gleaned from a laboratory experiment) that increasing the level of equity causes both the level of effort and the amount of fraud to increase.

   Several recent empirical studies have cited the increasing use of equity-based compensation for top-level executives (Anderson, Banker, and Ravindran 2000; Hall and Murphy 2002; Hall 2003; Itner, Lambert, and Larcker 2003; Murphy 2003). In 1984, for example, stocks and options comprised less than 1% of total CEO compensation for the median firm for U.S. publicly traded corporations. By 2001 stocks and options accounted for nearly two thirds of total executive compensation for the median firm. This phenomenon is even more pronounced in "new economy" firms, defined as companies in the computer, software, Internet, telecommunications, and networking industries. Fama (1980) alludes to this phenomenon by arguing that it is the market for executive labor that demands the use of performance-based compensation. It is ironic that the very market creating the incentive to use equity-based pay may be a victim of the incentive equity-based pay creates to improve accounting and financial statements, fraudulently if necessary. Denis, Hanouna, and Sarin (2006); Erickson, Hanlon, and Maydew (2006); and Johnson, Ryan, and Tian (2006) find that executives in firms accused of corporate malfeasance relied significantly more on equity-based compensation than did those in firms that had not been accused of fraud. Furthermore, Chert et al. (2006) find evidence that weaker corporate governance, as measured by board characteristics, is associated with a higher incidence of fraud. (1)

   Recent theoretical models emphasize management's ability to manipulate the reported earnings of the firm. Goldman and Slezak (2006) and Robison and Santore (2006) derive agency models in which a key element is the agent's ability to provide false information to the principal concerning the outcome of the agent's effort. While these models differ in the details, equity compensation provides the incentive for all agents to overstate the value of the firms they manage. Thus, increasing equity compensation is predicted to increase managerial effort as well as fraudulent reporting; although, this latter effect will be dampened by increased auditing (enforcement) and sanctions for fraudulent activity. The purpose of this paper is to empirically test these theoretical predictions using behavioral evidence from a laboratory experiment.

   There are obvious limitations to the use of laboratory investigations of managerial malfeasance. (2) Despite the many insights of the empirical literature utilizing field data, there are several issues that are difficult to address with such data. While the component of executive compensation that is based on the equity value of the firm is public knowledge, the effective enforcement (audit) effort is not. Further, absent an explicit policy intervention, the field data typically do not contain specific changes in the enforcement levels. The theoretical predictions of management behavior are often predicated on the fact that the managers are fully aware of the probability of an audit by a regulatory agency and of the effectiveness of such audits, but, as we have noted, there is often considerable uncertainty, and the analyst working with field data must make inferences regarding management's perceptions of the regulatory processes. Of course, with field data, by necessity one can only measure detected fraud. Finally, the reactions to changes in equity compensation levels and to the probability of fraud being detected depend on individual risk attitudes, which are not easily observed in the field. (3)

   The laboratory offers the researchers considerable control via the construction of the institution and the use of induced values (Smith 1982). This control affords us an opportunity to test the predictions of the recent theoretical models of managerial malfeasance through varying parameters predicted to affect the level of such malfeasance. In the controlled environment of the lab we are able to collect data on the actual effort and fraud choices of human subjects and to observe how these choices are affected by a change in the level of equity-based compensation and in the likelihood of fraud detection. While not the case with the field data, the laboratory allows us to observe the amount of fraud committed when it goes undetected. Also, by manipulating a single variable and holding all other factors constant, we are able to observe causation rather than simply correlation. (4) Our design introduces orthogonal variation to equity-based compensation and the probability that fraud will be detected. Further, our design allows us to control for risk attitudes, since we are able to elicit individual risk attitudes over the domain of the payoffs provided in the effort and fraud decision setting.

2. A Model of Managerial Behavior

   Goldman and Slezak (2006) and Robison and Santore (2006) provide the basis for the following theoretical discussion of the effects of equity-based pay and monitoring on the amount of fraud that is committed. In these models, the manager is compensated via a two-part contract, (w, [alpha]), where w denotes the manager's salary income and [alpha] denotes the percentage of total firm equity given to the manager. For her part, the manager must make two decisions: the level of effort and the value of the firm to report to the market.

   More precisely, the manager first must choose an effort level, L, which adds value to the firm. There are diminishing marginal returns to effort such that the value of the firm, g(L), is a strictly concave function of the amount of effort the manager contributes [i.e., g'(L) > 0, g"(L)

   After the manager chooses effort, she must choose the value of the firm to report to the shareholders. Any value in excess of the true value reported by the manager is considered fraud. Thus, the reported value of the firm is the true value of the firm plus any additional value the manager chooses to report, g(L) + F, where F is the amount of fraud committed by the manager. (5) The potential to commit fraud is sufficient to generate a reaction from the market. The market rationally expects some level of fraud, [F.sup.e]. (6) It is not costless for the manager to defraud the shareholders. There is a known probability, p, that the manager will be caught committing fraud and that sanctions, s(F), will be imposed on the manager. The sanctions function is increasing and strictly convex in the amount of fraud [i.e., s'(F) > 0 and s"(F) > 0].

   The manager's preferences over potentially random distributions of wealth are given by the mean-variance utility function shown in Equation 1:

   [EU.sub.M] = E([W.sub.M]) - [r.sub.M][[sigma].sup.2.sub.wm], (1)

   where [W.sub.M] is the manager's wealth; [[sigma].sup.2.sub.wm] is the variance of the manager's wealth; and [r.sub.M] [greater than or equal to] 0 is a risk aversion parameter. It is straightforward to calculate the variance of s(F), which equals the variance in the manager's wealth: (7)

   [[sigma].sup.2.sub.s](F) = p[[s - ps].sup.2] + (1 - p)[[0 - ps].sup.2] = p(1 - p)[s.sup.2].

   Recalling that s"(F) > 0, it follows that

   d[[sigma].sup.2.sub.s](F) / dF = 2p(1 -p)s(F)s'(F) > 0,

   [d.sup.2][[sigma].sup.2.sub.s](F) / [dF.sup.2] = 2p(1 -p)(s(F)s"(F) + [[s'(F)].sup.2]) > 0.

   Choosing a greater value of fraud increases the variance of the manager's wealth. So the cost of choosing greater fraud has two costs for the risk-averse manager: the increase in the expected sanction and the increase in risk.

   We solve for the manager's optimal choices backwards since a rational manager will anticipate her future choice of fraud when she chooses effort. Once effort has been chosen, the manager must choose a level of fraud. The manager's objective function is given by the following:

   Max [alpha](g(L) + F - [F.sup.e]) - L - ps(F) - [r.sub.M][[sigma].sup.2.sub.s](F). (2)

   At an interior solution to Equation 2, the first-order condition with respect to F is

   [alpha] - ps'(F) - [r.sub.M] d[[sigma].sup.2.sub.s](F) / dF = 0. (3)

   Given that s(F) is convex, the sufficient second-order condition is satisfied thus:

   -ps"(F) - [r.sub.M] [d.sup.2][[sigma].sup.2.sub.s](F;[t.sub.F] / [dF.sup.2]

   Equation 3 implicitly defines the optimal level of fraud, [F.sup.*] = F([alpha], p), which is independent of the level of effort. In choosing the optimal level of effort, the manager anticipates her future choice of fraud, thus:

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

   At an interior solution, the first-order condition with respect to L is

   [alpha]g'(L) - 1 = 0. (4)

   Equation 4 implicitly defines the optimal level of effort, [L.sup.*] = L([alpha]). The only parameter that enters the manager's choice of effort is [alpha], the percentage of equity.

   As Equation 5 shows, effort is increasing in [alpha]:

   [dL.sup.*] / d[alpha] = -g'([L.sup.*]) / [alpha]g"([L.sup.*]) > 0. (5)

   The optimal level of fraud is increasing in...