Corporate Governance Spillovers ppendix E Ing-Ha Cheng y Princeton niversity JO MRKET PPER November 7, 008 bstract This ppendix outlines an alternative model to that of the main paper, "Corporate Governance Spillovers," here manipulation is a strategic substitute in. Keyords: corporate governance, relative performance evaluation, CEO turnover, peer e ects, governance spillovers, competitive pressure, earnings manipulation For helpful comments and encouragement, I thank Wei Xiong, Markus runnermeier, Hyun Shin, Harrison Hong, Jonathan Parker, Motohiro Yogo, Darius Palia, Jakub Jurek, Zhiguo He, Martin Oehmke, Konstantin Milbradt, dam Zaadoski, lice Hsia, as ell as seminar participants at the Civitas Foundation Finance Seminar at the endheim Center for Finance, Princeton niversity. I also thank Jonathan Parker for generous funding during this research, and Motohiro Yogo for access to data froudit nalytics. ll errors and omissions are my on. y endheim Center for Finance, Princeton niversity, 6 Prospect ve., Princeton, NJ 085, e-mail: icheng@princeton.edu, http://.princeton.edu/icheng/.
The model in Cheng (008) supposes that, if one manager is caught manipulating earnings (ith instantaneous probability i m i ), the second manager receives = as compensation. I interpret this as meaning that a scandal freezes the relative performance evaluation mechanism, so that the opposing manager receives = as a consequence. This assumption is clearly limiting, since its realism is in doubt. another, perhaps more realistic, possibility. either rm, the SEC conducts an investigation of the hole industry. This ppendix addresses Suppose that, once manipulation is discovered at Speci cally, assume that an industry-ide investigation occurs ith instantaneous probability ( + m ). From the results of this investigation, managers ho are "clean" (ere not manipulating at the moment detection occurred at either rm) keep their jobs and receive =, and managers ho are "dirty" get red and receive zero. The investigation, hoever, is not perfect, so that a "dirty" manager to escapes detection by the SEC ith probability ( F (m i )), here F is some cumulative distribution function. nother interpretation of this imperfect investigation mechanism is that a "dirty" manager may plead his case before the SEC based on the severity of his manipulation and escape ith some probability. This model is not exactly a generalization of the model in the paper, but rather is a di erent model. In the model of the paper, manipulation is a strategic complement in : for a xed ;, high manipulation by one manager is associated ith high manipulation by the other manager. in. The detection structure in this ppendix creates the possibility of strategic substitutes Intuitively, hen one manager is manipulating more, the other manager has an incentive to manipulate less, since this increases his chances of obtaining =, conditional on an industry investigation occurring. In the model of the paper, because detection at one rm does not lead to an investigation at the other rm, the manipulation strategy is dependent primarily on the relative performance payo s, creating the strategic complementary. as complementary to the model in the paper. Thus, this model should be vieed In this ppendix, I sho that governance spillovers - that is, that manipulation is still a strategic complement in - still occur even hen manipulation is a strategic substitute in. That is, lo values of i increase the manipulation pro le of m i, even though m i and m i may be strategic substitutes in. Thus, the strategic complementarity in does not drive the governance spillover result. Furthermore, the "-shape" pattern predicted in the model only occurs for su ciently high H. That is, managers only manipulate hen ahead hen the payo for inning is su ciently high. This makes sense in the context of mergers and acquisitions, since the payo s from successfully acquiring a target are very high for the acquiring CEO. Note that I am still assuming that detection only occurs as a function of current manipulation, hich is still a limitation. The direct generalization (in a solvable form) is much less interesting than this case. dditionally, the probability of detection is no longer convex in manipulation, hich also moves the model toards strategic substitutability in.
Model and Equilibrium. max max m The HJ for the game described above is 00 + ( m ) 0 + ( + m ) ( F ()) 00 + ( m ) 0 + ( + m ) ( F (m )) + + = 0 = 0 The FOC for manager is 0 + ( + m ) f () + ( F ()) = 0 0 + ( + m ) + ( ) = 0 0 m + = 0 0 + m = and similarly for manager here I use the uniform distribution F (m) = m. conditions are then = m = 0 + m The to rst order Substituting, = = = = 0 + 0 + 0 + 0 + " 0 + 0 + 0 + + # 5
Panel : Manipulation Panel : alue Functions 0.8 8 0.6 0. 0. 7 6 0 5 0. 0. 0.6 0.8 m 0. 0. 0 0. 0. 0. 0. 0 0. 0. Figure : Equilibrium Manipulation. No suppose manipulation is constrained ithin [0; m]. 8 8 < < = max : min 0 + : 8 8 < < m = max : min 0 + : h Then h 0 + i 9 9 = = 5 ; m ; ; 0 ; i 9 9 = = 5 ; m ; ; 0 ; Implications. I compute the equilibrium for the same parameters as in the paper (in particular, H = ), except I rst use = 5 and = 500 as a benchmark case, e ectively making manipulation extraordinarily costly for, both in a relative and absolute sense. I furthermore suppose m = to justify the use of the uniform CDF F. This case is represented by the solid lines in Figure.I then compute the equilibrium for = 5 and = 5 as the "governance spillover" case, hich is represented by the dashed lines. Governance spillovers still occur in the sense that eakening governance at rm increases the incentive for r to manipulate. Intuitively, manager anticipates that manager can "keep himself alive" for longer (relative to the benchmark case) and thus must react by boosting his manipulation, thus keeping himself alive longer as ell. The main di erence ith the model in the paper is that managers no longer manipulate hen they are ahead. In other ords, manipulation is a strategic substitute, so that the prediction of manipulation as a -shaped in relative performance breaks don. Hoever, this is because I have
Panel : Manipulation Panel : alue Functions 0.8 0.6 0. 0 0. 8 0 0. 6 0. 0.6 0.8 m 0. 0. 0 0. 0. 0. 0. 0. 0 0. 0. 0. Figure : Equilibrium Manipulation hen H = :5. assumed H =, so that the outperformance incentive is a guarantee of the manager s current age. s the gure illustrates, this is no longer strong enough to sustain the -shaped pattern. For higher values of H, hoever, the -shaped pro le returns (in a slightly altered form), since the explicit payo of outperforming the competing manager is increased. gain, this is perhaps more appropriate to the setting of mergers and acquisitions, here the payo s for acquiring CEOs are high (see citations in paper). Figure plots the equilibrium manipulation hen H = :5. Each manager manipulates only hen they are extremely far ahead and thus likely to in the game. This is also an artifact of the linear detection probabilities. convex detection probability ould likely smooth out the manipulation by one manager hen he is ahead, at a cost of reduction in level. Hoever, this introduces a non-linearity in and m that cannot be readily solved even using numerical methods.