Scale effects in dynamic contracting
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Scale effects in dynamic contracting Shirley Bromberg-Silverstein1 · Santiago Moreno-Bromberg2 · Guillaume Roger3 Received: 31 May 2019 / Accepted: 19 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We study a continuous-time contracting problem in which project scale plays a role. The agent may speculate to enhance the drift of a cash-flow process; doing so exposes the principal to large, infrequent losses. The optimal contract includes scale as an instrument: downsizing along the equilibrium path is necessary to preserve incentive compatibility. We characterize the optimal contract, and specifically the downsizing process, and prove there is an optimal liquidation scale that is reached in finite time. We also analyze some finer properties of the state variables of the contract and the resulting value function of the principal. The optimal contract is implemented using standard financial securities plus debt covenants; holding equity is essential to curb risk taking. Conflicts emerge between classes of security holders and explain phenomena like priority of claims at liquidation. Keywords Downsizing · Dynamic contracts · Moral hazard · Risk taking JEL Classification D82 · D86 · G28 · L43
We thank Andrea Barth, Cosimo Munari, Oleg Reichmann, Jean-Charles Rochet, Mario Šiki´c and Quynh Anh Vo for their helpful comments and suggestions, as well as participants at the 2015 Stanford Institute for Theoretical Economics (Segment IV) for stimulating discussion and seminar participants at Berkeley Haas, Melbourne, Monash, Stanford GSB, Sydney, UNSW, USC, UTS, UZH, the FIRN Corporate Finance conference and the FIRN Financial Stability conference. The research leading to these results has received funding from the ERC (Grant Agreement 249415-RMAC) from NCCR FinRisk (project “Banking and Regulation”) and from the Swiss Finance Institute (project “Systemic Risk and Dynamic Contract Theory”), and it is gratefully acknowledged.
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Santiago Moreno-Bromberg [email protected] Shirley Bromberg-Silverstein [email protected] Guillaume Roger [email protected]
1
Mathematics Department, Metropolitan Autonomous University (Iztapalapa), Mexico City, Mexico
2
Department of Banking and Finance, University of Zurich, Plattensstrasse 14, 8032 Zurich, Switzerland
3
Monash University, Clayton, Australia
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Mathematics and Financial Economics
Introduction This paper is concerned with a stylized, dynamic-contracting problem in which the scale of a project (for example, the size of a firm) plays an essential role in shaping incentives for both the principal (she) and the agent (he). Control over size is, therefore, an essential contracting variable. It is necessary to provide the agent with the correct incentives; for the principal it endogenously determines the termination hurdle. More specifically, preserving incentive compatibility requires at times downsizing the project. Eventually, scale reaches a level below which the principal optimally terminates the contract and liquidates
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