Mele, Antonio
(2011):
*Repeated moral hazard and recursive Lagrangeans.*

Preview |
PDF
MPRA_paper_30310.pdf Download (864kB) | Preview |

## Abstract

This paper shows how to solve dynamic agency models by extending recursive Lagrangean techniques à la Marcet and Marimon (2011) to problems with hidden actions. The method has many advantages with respect to promised utilities approach (Abreu, Pearce and Stacchetti (1990)): it is a significant improvement in terms of simplicity, tractability and computational speed. Solutions can be easily computed for hidden actions models with several endogenous state variables and several agents, while the promised utilities approach becomes extremely difficult and computationally intensive even with just one state variable or two agents. Several numerical examples illustrate how this methodology outperforms the standard approach.

Item Type: | MPRA Paper |
---|---|

Original Title: | Repeated moral hazard and recursive Lagrangeans |

Language: | English |

Keywords: | repeated moral hazard; collocation method; dynamic models with private information; recursive contracts |

Subjects: | D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D86 - Economics of Contract: Theory C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis |

Item ID: | 30310 |

Depositing User: | Antonio Mele |

Date Deposited: | 21 Apr 2011 21:09 |

Last Modified: | 28 Sep 2019 02:46 |

References: | [1] Ábrahám, Á., Koehne, S. and N. Pavoni (forthcoming), "On the First Order Approach in Principal-Agent Models with Hidden Borrowing and Lending", Journal of Economic Theory [2] Ábrahám, Á. and N. Pavoni (2008), "Principal-Agent Relationships with Hidden Borrowing and Lending: The First-Order Approach in Two Periods", mimeo, UCL [3] Ábrahám, Á. and N. Pavoni (2009), " Efficient allocations with moral hazard and hidden borrowing and lending: A recursive formulation, Review of Economic Dynamics, Volume 11, Issue 4, October 2008, Pages 781-803 [4] Abreu, D., Pearce, D. and E. Stacchetti (1990) “Toward a Theory of Discounted Repeated Games With Imperfect Monitoring,” Econometrica, vol. 58(5), pp. 1041-1063. [5] Atkeson, A. and H. Cole (2008), “A Dynamic Theory of Optimal Capital Structure and Executive Compensation,” mimeo, UCLA [6] Chien, Y. and H. Lustig (Forthcoming) "The Market Price of Aggregate Risk and the Wealth Distribution" Review of Financial Studies [7] Clementi, G. L., Cooley,T. and C. Wang (2006), "Stock Grants as a Commitment Device", Journal of Economic Dynamics and Control 30(11): 2191-2216 [8] Clementi, G. L., Cooley, T. and S. Di Giannatale (2008a), "Total executive compensation", mimeo [9] Clementi, G. L., Cooley, T. and S. Di Giannatale (2008b), "A theory of firm decline", mimeo [10] Fernandes, A. and C. Phelan (2000), "A Recursive Formulation for Repeated Agency with History Dependence", Journal of Economic Theory 91(2): 223-247 [11] Friedman, E. (1998), "Risk sharing and the dynamics of inequality", mimeo, Northwestern University [12] Hopenhayn, H. A. and Nicolini, J. P. (1997), "Optimal Unemployment Insurance", Journal of Political Economy 105(2): 412-438 [13] Jewitt, I. (1988) "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-90, September. [14] Judd K. (1998), "Numerical Methods in Economics", MIT Press, Cambridge (MA) [15] Judd K., J. Conklin and Sevin Yeltekin (2003) "Computing Supergame Equilibria", Econometrica, 2003 71(4): 1239-1255. [16] Ke, R. (2010), "A Fixed-Point Method for Validating the First-Order Approach: Necessary and Sufficient Condition and its Implications", mimeo [17] Kocherlakota, N. (2004), "Figuring out the Impact of Hidden Savings on Optimal Unemployment Insurance," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(3), pages 541-554, July. [18] Koehne, S. (2009), "The First-Order Approach to Moral Hazard Problems with Hidden Saving", mimeo, University of Mannheim [19] Lehnert A., Ligon E. and R. M. Townsend (1999), "Liquidity Constraints and Incentive Contracts", Macroeconomic Dynamics 3: 1-47. [20] Lucas, R. E. (1990), "Why doesn’t Capital Flow from Rich to Poor Countries?", American Economic Review 80, 92-96 [21] Luenberger D. G. (1969), "Optimization by vector space methods", Wiley and Sons, New York [22] Marcet, A. and R. Marimon (2011), "Recursive contracts", mimeo, EUI and LSE [23] Marimon, R., Messner, M. and N. Pavoni (2011), "Solving recursive contracts with non-unique solutions", mimeo, [24] Mele, A. (2009), "Dynamic risk sharing and moral hazard", work in progress [25] Messner, M. and N. Pavoni (2004). "On the Recursive Saddle Point Method: A Note", IGIER Working Paper n. 255 [26] Mirrlees, J. A. (1975), "The Theory of Moral Hazard and Unobservable Behaviour: Part I", published in: The Review of Economic Studies, Vol. 66, No. 1, Special Issue: Contracts (Jan., 1999), pp. 3-21 [27] Paulson, A. L., Karaivanov, A. and Townsend R. M. (2006), "Distinguishing Limited Liability fromMoral Hazard in aModel of Entrepreneurship", Journal of Political Economy 144(1): 100-144 [28] Pavoni, N. (2007), "On optimal unemployment compensation", Journal of Monetary Economics 54(6): 1612-1630 [29] Pavoni, N. (forthcoming), "Optimal Unemployment Insurance with Human Capital Depreciation and Duration Dependence", International Economic Review [30] Phelan, C. and R. M. Townsend (1991), "Computing Multi-Period, Information Constrained Equilibria", Review of Economic Studies 58(5): 853-881 [31] Quadrini,V. (2004), "Investment and liquidation in renegotiation-proof contracts with moral hazard", Journal of Monetary Economics, 51(4): 713-751 [32] Rogerson, W. (1985a), "Repeated Moral Hazard", Econometrica, 53: 69-76 [33] Rogerson, W. (1985b), "The First-Order Approach to Principal-Agent Problems", Econometrica, 53 (6): 1357-1368 [34] Sleet C. and S. Yeltekin (2003), “On the Approximation of Value Correspondences”, mimeo, Carnegie Mellon University [35] Sleet C. and S. Yeltekin (2006), “Credibility and Endogenous Societal Discounting”, Review of Economic Dynamics 9, 2006; 410-437. [36] Sleet C. and S. Yeltekin (2008a), “Solving private information models”, mimeo, Carnegie Mellon University [37] Sleet C. and S. Yeltekin (2008b), “Politically Credible Social Insurance”, Journal of Monetary Economics 55, 2008; 129-151 [38] Shimer, R. and I. Werning (forthcoming), "Liquidity and insurance for the unemployed", American Economic Review [39] Spear, S. and S. Srivastava (1987), "On Repeated Moral Hazard with Discounting", Review of Economic Studies 54(4): 599-617 [40] Thomas, J. and T.Worrall (1990) "Income fluctuations and asymmetric information: An example of a repeated principal-agent problem", Journal of Economic Theory 51: 367-390 [41] Werning, I. (2001), "Repeated Moral-Hazard with Unmonitored Wealth: A Recursive First-Order Approach", mimeo, MIT [42] Werning, I. (2002), "Optimal Unemployment Insurance with Unobservable Savings", mimeo, MIT [43] Zhao, R. (2007), “Dynamic risk-sharing with two-sided moral hazard”, Journal of Economic Theory 136: 601-640. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/30310 |