Mele, Antonio (2010): Repeated moral hazard and recursive Lagrangeans.
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This paper shows how to solve dynamic agency models by extending recursive Lagrangean techniques a la Marcet and Marimon (2009) 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|
|Keywords:||repeated moral hazard; recursive Lagrangean; collocation method|
|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
D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information; Mechanism Design
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
|Depositing User:||Antonio Mele|
|Date Deposited:||31. Mar 2010 05:52|
|Last Modified:||11. Jan 2014 10:05|
Abraham, A. and N. Pavoni (2008), "Principal-Agent Relationships with Hidden Borrowing and Lending: The First-Order Approach in Two Periods", mimeo, UCL
Abraham, A. 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
Abreu, D., Pearce, D. and E. Stacchetti (1990) \textquotedblleft Toward a Theory of Discounted Repeated Games With Imperfect Monitoring,\textquotedblright\ Econometrica, vol. 58(5), pp. 1041-1063.
Atkeson, A. and H. Cole (2008), \textquotedblleft A Dynamic Theory of Optimal Capital Structure and Executive Compensation,\textquotedblright\ mimeo, UCLA
Chien, Y. and H. Lustig (Forthcoming) "The Market Price of Aggregate Risk and the Wealth Distribution" Review of Financial Studies
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
Clementi, G. L., Cooley, T. and S. Di Giannatale (2008a), "Total executive compensation", mimeo
Clementi, G. L., Cooley, T. and S. Di Giannatale (2008b), "A theory of firm decline", mimeo
Fernandes, A. and C. Phelan (2000), "A Recursive Formulation for Repeated Agency with History Dependence", Journal of Economic Theory 91(2): 223-247
Friedman, E. (1998), "Risk sharing and the dynamics of inequality", mimeo, Northwestern University
Hopenhayn, H. A. and Nicolini, J. P. (1997), "Optimal Unemployment Insurance", Journal of Political Economy 105(2): 412-438
Jewitt, I. (1988) "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-90, September.
Judd K. (1998), "Numerical Methods in Economics", MIT\ Press, Cambridge (MA)
Judd K., J. Conklin and Sevin Yeltekin (2003) "Computing Supergame Equilibria", Econometrica, 2003 71(4): 1239- 1255.
Ke, R. (2010), "A Fixed-Point Method for Validating the First-Order Approach: Necessary and Sufficient Condition and its Implications", mimeo
Koehne, S. (2009), "The First-Order Approach to Moral Hazard Problems with Hidden Saving", mimeo, University of Mannheim
Lehnert A., Ligon E. and R. M. Townsend (1999), "Liquidity Constraints and Incentive Contracts", Macroeconomic Dynamics 3: 1-47.
Luenberger D. G. (1969), "Optimization by vector space methods", Wiley and Sons, New York
Marcet, A. and R. Marimon (2009), "Recursive contracts", mimeo, IAE
Mele, A. (2009), "Dynamic risk sharing and moral hazard", work in progress
Messner, M. and N. Pavoni (2004). "On the Recursive Saddle Point Method: A Note", IGIER\ Working Paper n. 255
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
Paulson, A. L., Karaivanov, A. and Townsend R. M. (2006), "Distinguishing Limited Liability from Moral Hazard in a Model of Entrepreneurship", Journal of Political Economy 144(1): 100-144
Pavoni, N. (2007),\ "On optimal unemployment compensation", Journal of Monetary Economics 54(6): 1612-1630
Pavoni, N. (forthcoming),\ "Optimal Unemployment Insurance with Human Capital Depreciation and Duration Dependence", International Economic Review
Phelan, C. and R. M. Townsend (1991), "Computing Multi-Period, Information Constrained Equilibria", Review of Economic Studies 58(5): 853-881
Quadrini,V. (2004), "Investment and liquidation in renegotiation-proof contracts with moral hazard", Journal of Monetary Economics, 51(4): 713-751
Rogerson, W. (1985a), "Repeated Moral Hazard", Econometrica, 53: 69-76
Rogerson, W. (1985b), "The First-Order Approach to Principal-Agent Problems", Econometrica, 53 (6): 1357-1368
Sleet C. and S. Yeltekin (2003), \textquotedblleft On the Approximation of Value Correspondences\textquotedblright , mimeo, Carnegie Mellon University
Sleet C. and S. Yeltekin (2006), \textquotedblleft Credibility and Endogenous Societal Discounting\textquotedblright , Review of Economic Dynamics 9, 2006; 410-437.
Sleet C. and S. Yeltekin (2008a), \textquotedblleft Solving private information models\textquotedblright , mimeo, Carnegie Mellon University
Sleet C. and S. Yeltekin (2008b), \textquotedblleft Politically Credible Social Insurance\textquotedblright , Journal of Monetary Economics 55, 2008; 129-151
Shimer, R. and I. Werning (forthcoming), "Liquidity and insurance for the unemployed", American Economic Review
Spear, S. and S. Srivastava (1987), "On Repeated Moral Hazard with Discounting", Review of Economic Studies 54(4): 599-617
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
Werning, I. (2001), "Repeated Moral-Hazard with Unmonitored Wealth: A Recursive First-Order Approach", mimeo, MIT
Werning, I. (2002), "Optimal Unemployment Insurance with Unobservable Savings", mimeo, MIT
Zhao, R. (2007), \textquotedblleft Dynamic risk-sharing with two-sided moral hazard\textquotedblright , Journal of Economic Theory 136: 601-640.