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# lecture3 - Econ 103C-Lecture 3 Applications of Moral Hazard...

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Econ 103C-Lecture 3 Applications of Moral Hazard David Sraer U.C. Berkeley February 11, 2008 David Sraer (U.C. Berkeley) Econ 103C-Lecture 3 February 11, 2008 1 / 28

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Lessons from previous lectures General model have not a lot of general predictions. . . Need to work with a simpler framework adapted to the economic situation to obtain clear predictions! However one clear message stems from “informativeness principle”: an optimal contract should not be based on uninformative signals. If there is one type of worker for which optimal contract theory should apply, it is CEOs ! Unfortunately, it seems CEO compensation do not respect “informativeness principle”. . . How can we establish such a fact using real world data? = Bertrand &Mullainathan (2001) David Sraer (U.C. Berkeley) Econ 103C-Lecture 3 February 11, 2008 2 / 28
A brief refresher: CEO compensation with 2 shocks Consider a model of CEO compensation where ﬁrm output is p = e + o + u . o and u are pure random shocks, such that o N (0 , σ 2 O ), u N (0 , σ 2 u ) and cov ( o , u ) = 0. o is observable and veriﬁable by the principal (the shareholder) while u is not observable. The shareholder is risk neutral while the CEO is risk averse with CARA utility, with r his risk-aversion parameter. Let u be the CEO reserve utility and c ( e ) = e 2 2 his cost of eﬀort. To be realistic, let us consider only linear contracts (base pay+stocks): s ( p , o ) = w + α p + β o CEO expected utility u = - exp - r ± w + α p + β o - e 2 2 - r 2 ( α 2 σ 2 u +( α + β ) 2 σ 2 o ) ² CEO selects eﬀort: e ? = α David Sraer (U.C. Berkeley) Econ 103C-Lecture 3 February 11, 2008 3 / 28

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Solving for the optimal contract Plugging the (IC) constraint, the shareholder program becomes: max α,β, w (1 - α )( α + o + u ) - β o - w w + α 2 2 - r 2 ± α 2 σ 2 u + ( α + β ) 2 σ 2 o ² u FOC in w ( λ Lagrange multiplier): λ = 1 > 0, so (IR) is binding. FOC in β : - o + λ ( o - γ ( β + α ) σ 2 o ) = 0 = α = - β Optimal CEO compensation must “ﬁlter out” o from optimal compensation as o is not informative of CEO eﬀort (Informativeness principle) FOC in α provides optimal stock grant: α ? = 1 1+ r ( σ 2 o + σ 2 u ) Optimal compensation: s ( p , o ) = w ? + α ? ( p - o ) The CEO should be rewarded only for “extra-performance” relative to lucky shocks o ! David Sraer (U.C. Berkeley) Econ 103C-Lecture 3 February 11, 2008 4 / 28
The empirical approach Bertrand&Mullainathan exhibits shocks to performance that are unrelated to CEO’s eﬀort: oil prices for CEO of oil-related companies! Let’s ﬁrst be convinced that oil-related companies have their proﬁt dependent on oil prices Here are oil prices over long period: David Sraer (U.C. Berkeley) Econ 103C-Lecture 3 February 11, 2008 5 / 28

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Empirical Speciﬁcation Here are average rate of accounting returns of U.S. oil related company; Little doubt that when oil prices go up, ROA of oil-related company go up!
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## This note was uploaded on 08/01/2008 for the course ECON 103C taught by Professor Sraer during the Spring '08 term at Berkeley.

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lecture3 - Econ 103C-Lecture 3 Applications of Moral Hazard...

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