Measuring Intentional Manipulation: A Structural Approach

The following post comes to us from Anastasia Zakolyukina of the University of Chicago Booth School of Business.

In the paper, Measuring Intentional Manipulation: A Structural Approach, which was recently made publicly available on SSRN, I suggest a structural model of a manager’s manipulation decision that allows me to estimate his costs of manipulation and to infer the amount of undetected intentional manipulation for each executive in my sample. The model follows the economic approach to crime (Becker, 1968) and incorporates the costs and benefits of manipulation decisions. The model is a dynamic finite-horizon problem in which the risk-averse manager maximizes his terminal wealth. The manager’s total wealth depends on his equity holdings in the firm and his cash wealth. The model yields three predictions. First, according to the wealth effect, managers having greater wealth manipulate less. Second, according to the valuation effect, the current-period bias in net assets increases in the existing bias. Third, the manager’s risk aversion, the linearity of his terminal wealth in reported earnings, and the stochastic evolution of the firm’s intrinsic value produce income smoothing. Furthermore, the structural approach allows partial observability of manipulation decisions in the data; hence, I am able to estimate the probability of detection as well as the loss in the manager’s wealth using the data on detected misstatements (i.e., financial restatements).

I contribute to the literature by providing estimates of the manager’s manipulation costs and the extent of undetected intentional manipulation. I find that the costs of manipulation are low: the probability of detection is 9%, and the marginal loss in wealth for inflating the stock price by 1% is 0.51% for non-technical restatements. These costs result in high estimates of the incidence of undetected manipulation. Specifically, the model predicts that about 66% of executives manipulate at least once with a value-weighted bias in the stock price of 15.5%. At the same time, the unconditional rate of manipulation is lower: CEOs bias their earnings reports in 45% of CEO-years, and a value-weighted bias in the stock price is 6% across all CEO-years. Finally, I find that the model-implied measure of manipulation performs significantly better than the commonly used measures of discretionary accruals out-of-sample. Therefore, researchers should exercise caution in relying on such measures as proxies for earnings management and, instead, should carefully consider the costs and benefits of manipulation that are relevant to their particular setting.

These findings can be useful for investors, boards of directors, regulators and researchers. The estimated cost of manipulation parameters can be utilized in calculating the cost to a CEO of misreporting earnings by 1% or by a given amount. The only data that this calculation requires is the firm’s price-to-earnings multiple and the hypothetical level of bias per share, scaled by the stock price before a CEO joins a firm. In addition, the model can be applied to the time-series of stock prices and the time-series of executive compensation to infer the extent of undetected manipulation.

The structural approach can be used to analyze counterfactuals. For instance, one can evaluate how an increase in the probability of detection changes the extent of manipulation. However, to make sensible counterfactual predictions, one has to consider how investors would react to a change in the policy parameters. For instance, if the costs of manipulation increase, fewer managers would find it optimal to manipulate; in equilibrium, investors may place greater weight on reported earnings; thus, price-to-earnings multiples would increase, which, in turn, increase the manager’s incentives to manipulate. These issues can be addressed by explicitly modeling an equilibrium interaction between the manager’s reporting choices and investors’ inferences about manipulation.

An analysis of counterfactuals can also be useful in helping regulators decide about the resources that should be invested in detection and the punishment for misreporting. For instance, similar expected costs of manipulation can be achieved by adjusting the probability of detection or the punishment for misreporting. However, the relative sensitivities of the manipulation decision to the probability of detection and punishment can differ depending on whether an executive is risk-averse or risk-loving. If an executive is risk-averse, then the increase in the punishment for manipulation would have a greater effect on reducing misstatements than an equivalent change in the probability of detection, whereas if an executive is risk-loving, an increase in the probability of detection would have a greater effect than an equivalent change in the punishment for manipulation (Becker, 1968).

A structural approach involves trade-offs between restrictive assumptions that make estimation feasible and sufficient flexibility to capture the patterns observed in the data. In my analysis, I make a variety of important assumptions; these choices represent limitations to my results. First, I do not model a rational expectations equilibrium that involves the market anticipating the manager’s reporting choices. Second, I do not incorporate the strategic decision of the board regarding the optimal compensation contract. In doing so, I avoid solving a difficult multi-period problem that lies beyond the scope of this paper. Another limitation of this paper and a potential area for future research in structural estimation relates to my assumption that only executives’ equity holdings provide an incentive to misreport earnings. Other incentives to misreport include career concerns, bonuses, and debt covenants. Consequently, the measure of intentional manipulation suggested here may be biased to the extent that other incentives to misreport are also important.

The full paper is available for download here.


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