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Applying Negishi’s method to stochastic models with overlapping generations


Brumm, Johannes; Kübler, Felix (2013). Applying Negishi’s method to stochastic models with overlapping generations. NCCR FINRISK Working Paper Series 851, University of Zurich.

Abstract

In this paper we develop a Negishi approach to characterize recursive equilibria in stochastic models with overlapping generations. When competitive equilibria are Pareto-optimal, using Negishi-weights as a co-state variable has three major computational advantages over the standard approach of using the natural state: First, the endogenous state space is a unit simplex and thus easy to handle. Second, the number of unknown functions characterizing equilibrium dynamics is orders of magnitude smaller. Third, approximation errors have a compelling economic interpretation. Our main contribution is to show that the Negishi approach extends naturally to models with borrowing-constraints and incomplete financial markets where the welfare theorems fail. Many of the computational advantages carry over to this setting. We derive sufficient conditions for the existence of Markov equilibria in the complete markets model as well as for models with incomplete markets and borrowing constraints.

Abstract

In this paper we develop a Negishi approach to characterize recursive equilibria in stochastic models with overlapping generations. When competitive equilibria are Pareto-optimal, using Negishi-weights as a co-state variable has three major computational advantages over the standard approach of using the natural state: First, the endogenous state space is a unit simplex and thus easy to handle. Second, the number of unknown functions characterizing equilibrium dynamics is orders of magnitude smaller. Third, approximation errors have a compelling economic interpretation. Our main contribution is to show that the Negishi approach extends naturally to models with borrowing-constraints and incomplete financial markets where the welfare theorems fail. Many of the computational advantages carry over to this setting. We derive sufficient conditions for the existence of Markov equilibria in the complete markets model as well as for models with incomplete markets and borrowing constraints.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:1 March 2013
Deposited On:03 Mar 2014 09:43
Last Modified:16 Feb 2018 19:55
Series Name:NCCR FINRISK Working Paper Series
OA Status:Green
Official URL:https://www.zora.uzh.ch/93707/
Related URLs:http://www.nccr-finrisk.uzh.ch/wps.php?action=query&id=851
Other Identification Number:merlin-id:9271

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