Kuhn, Moritz (2008): Recursive equilibria in an Aiyagari style economy with permanent income shocks.
Download (279kB) | Preview
In this paper, we prove the existence of a recursive competitive equilibrium (RCE) for an Aiyagari style economy with permanent income shocks and perpetual youth structure. We show that there exist equilibria where borrowing constraints are never binding. This allows us to establish a non-trivial lower bound on the equilibrium interest rate. To solve the individual’s problem, we present a new approach that uses lattices of consumption functions to deal with the non-compact state space and the unbounded utility function. The approach uses only the first order conditions of the problem (Euler equations). The proof is constructive and it serves as a theoretical foundation for the convergence of a policy function iteration procedure.
|Item Type:||MPRA Paper|
|Original Title:||Recursive equilibria in an Aiyagari style economy with permanent income shocks|
|Keywords:||Permanent income shocks; incomplete markets; dynamic general equilibrium; heterogeneous agents|
|Subjects:||D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D52 - Incomplete Markets
D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies
E - Macroeconomics and Monetary Economics > E2 - Macroeconomics: Consumption, Saving, Production, Employment, and Investment > E21 - Consumption; Saving; Wealth
|Depositing User:||Moritz Kuhn|
|Date Deposited:||19. Jul 2011 12:50|
|Last Modified:||13. Feb 2013 14:53|
S. Rao Aiyagari. Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics, 109(3):659 – 684, 1994.
Richard Blundell, Luigi Pistaferri, and Ian Preston. Consumption inequality and partial insurance. American Economic Review (forthcoming).
Christopher D. Carroll. Buffer-stock saving and the life cycle / permanent income hypothesis. Quarterly Journal of Economics, 112(1):1–55, 1997.
Christopher D. Carroll. Theoretical foundations of buffer stock saving. NBER Working Paper No. 10867, Nov. 2004, 2004.
Christopher D. Carroll and Miles S. Kimball. On the concavity of the consumption function. Econometrica, 64(4):981 – 992, 1996.
Christopher D. Carroll and Andrew A. Samwick. The nature of precautionary wealth. Journal of Monetary Economics, 40(1):41 – 72, 1997.
Wilbur John Coleman II. Equilibrium in a production economy with an income tax. Econometrica, 59(4):1091–1104, 1991.
George M. Constantinides and Darrell Duffie. Asset pricing with heterogeneous consumers. Journal of Political Economy, 104(2):219 – 240, 1996.
Patrick Cousot and Radhia Cousot. Constructive versions of tarski’s fixed point theorems. Pacific Journal of Mathematics, 82(1), 1979.
Angus Deaton. Saving and liquidity constraints. Econometrica, 59(5):1221–1248, 1991.
Angus Deaton and Guy Laroque. On the behavior of commodity prices. Review of Economic Studies, 59:123, 1992.
Darrell Duffie, John Geanakoplos, Andreu Mas-Colell, and Andy McLennan. Stationary markov equilibria. Econometrica, 62:745 – 782, 1994.
Edward J. Green. Individual level randomness in a nonatomic population. Working paper, 1994, 1994.
Jonathan Heathcote, Kjetil Storesletten, and Giovanni L. Violante. Consumption and labor supply with partial insurance: An analytical framework. June 2009.
Mark Huggett. The risk-free rate in heterogeneous-agent incomplete-insurance economies. Journal of Economic Dynamics and Control, 17(5-6):953–969, 1993.
Mark Huggett and Sandra Ospina. Aggregate precautionary savings: when is the third derivative irrelevant? Journal of Monetary Economics, 48:373 – 396, 2001.
Stephen C. Kleene. Introduction to Metamathematics. North-Holland, Amsterdam, 1952.
Tom Krebs. Non-existence of recursive equilibria on compact state spaces when markets are incomplete. Journal of Economic Theory, 115:134 – 150, 2004.
Tom Krebs. Job displacement risk and the cost of business cycles. American Economic Review, 97(3):664 – 686, 2007.
Sadatoshi Kumagai. An implicit function theorem: Comment. Journal of Optimization Theory and Applications, 31(2), 1980.
Cuong Le Van and John Stachurski. Parametric continuity of stationary distributions. Economic Theory, 33(2):333 – 348, 2007.
Lars Ljunggqvist and Thomas J. Sargent. Recursive Macroeconomic Theory. MIT Press, 2000.
Costas Meghir and Luigi Pistaferri. Income variance dynamics and heterogeneity. Econometrica, 72(1):1–32, 2004.
Sean Meyn and Richard Tweedie. Markov Chains and Stochastic Stability. Springer London, 1993.
Jianjun Miao. Competitive equilibria of economies with a continuum of consumers and aggregate shocks. Journal of Economic Theory, 126:274 – 298, 2006.
Guillaume Rabault. When do borrowing constraints bind? some new results on the income fluctualtion problem. Journal of Economic Dynamics and Control, 26:217–245, 2002.
Pontus Rendahl. Inequality constraints in recursive economies. EUIWorking Paper 2006/6.
Nancy L. Stokey and Robert E. Lucas with Edward C. Prescott. Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge, 1989.
Alfred Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics, 5:285–309, 1955.
Chris I. Telmer. Asset pricing puzzles and incomplete markets. The Journal of Finance, 48(5):1803 – 1832, 1993.
Eberhard Zeidler. Nonlinear Functional Analysis and its Applications I, Fixed-Point Theorems. Springer, 1986.