TY - GEN
T1 - Approximate versus exact equilibria in dynamic economies
AU - Kubler, Felix
AU - Schmedders, Karl
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
KW - Approximate equilibria
KW - Backward error analysis
KW - Computational economics
KW - Dynamic stochastic general equilibrium
KW - Perturbed economy
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U2 - 10.1007/978-3-540-76591-2_10
DO - 10.1007/978-3-540-76591-2_10
M3 - Conference contribution
AN - SCOPUS:53749084623
SN - 9783540765905
T3 - Lecture Notes in Economics and Mathematical Systems
SP - 135
EP - 163
BT - Computational Aspects of General Equilibrium Theory
ER -