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Approximate versus exact equilibria in dynamic economies


Kubler, F; Schmedders, K (2008). Approximate versus exact equilibria in dynamic economies. In: Brown, D; Kubler, F. Computational aspects of general equilibrium theory: refutable theories of value. Berlin: Springer, 135-164.

Abstract

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents
and incomplete financial markets. While there are several algorithms that compute prices and allocations for which agents’ first-order conditions are approximately satisfied
(“approximate equilibria”), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. We give a simple example to illustrate that approximate equilibria might be very far from exact equilibria. We then interpret approximate equilibria as equilibria for close-by economies; that is, for economies with close-by individual endowments and preferences.

We present an error analysis for two models that are commonly used in applications, an overlapping generations (OLG) model with stochastic production and an asset pricing
model with infinitely lived agents.We provide sufficient conditions that ensure that approximate equilibria are close to exact equilibria of close-by economies. Numerical
examples illustrate the analysis.

Abstract

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents
and incomplete financial markets. While there are several algorithms that compute prices and allocations for which agents’ first-order conditions are approximately satisfied
(“approximate equilibria”), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. We give a simple example to illustrate that approximate equilibria might be very far from exact equilibria. We then interpret approximate equilibria as equilibria for close-by economies; that is, for economies with close-by individual endowments and preferences.

We present an error analysis for two models that are commonly used in applications, an overlapping generations (OLG) model with stochastic production and an asset pricing
model with infinitely lived agents.We provide sufficient conditions that ensure that approximate equilibria are close to exact equilibria of close-by economies. Numerical
examples illustrate the analysis.

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Additional indexing

Item Type:Book Section, refereed, further contribution
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2008
Deposited On:09 Jan 2009 09:30
Last Modified:06 Dec 2017 16:41
Publisher:Springer
Series Name:Lecture Notes in Economics and Mathematical Systems
Number:604
ISBN:978-3-540-76590-5
Additional Information:This article first was published in Econometrica 73(4):1205–1235, July 2005 (you see that version in the added pdf).
Official URL:http://www.springer.com/economics/economic+theory/book/978-3-540-76590-5
Related URLs:http://opac.nebis.ch/F/?local_base=NEBIS&con_lng=GER&func=find-b&find_code=SYS&request=005522033

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