Continuous Markov Equilibria with Quasi-Geometric Discounting

48 Pages Posted: 7 Mar 2014

See all articles by Satyajit Chatterjee

Satyajit Chatterjee

Federal Reserve Bank of Philadelphia

Burcu Eyigungor

Federal Reserve Bank of Philadelphia

Date Written: Februrary 27, 2014

Abstract

We prove that the standard quasi-geometric discounting model used in dynamic consumer theory and political economics does not possess continuous Markov perfect equilibria (MPE) if there is a strictly positive lower bound on wealth. We also show that, at points of discontinuity, the decision maker strictly prefers lotteries over the next period's assets. We then extend the standard model to have lotteries and establish the existence of an MPE with continuous decision rules. The models with and without lotteries are numerically compared, and it is shown that the model with lotteries behaves more in accord with economic intuition.

Keywords: Quasi-geometric, Quasi-hyperbolic, Time consistency, Markov Perfect Equilibrium, Debt Limit, Continuous Solutions, Lotteries

JEL Classification: C73, D11, D90, E21, H63, P16

Suggested Citation

Chatterjee, Satyajit and Eyigungor, Burcu, Continuous Markov Equilibria with Quasi-Geometric Discounting (Februrary 27, 2014). FRB of Philadelphia Working Paper No. 14-6. Available at SSRN: https://ssrn.com/abstract=2405099 or http://dx.doi.org/10.2139/ssrn.2405099

Satyajit Chatterjee (Contact Author)

Federal Reserve Bank of Philadelphia ( email )

Ten Independence Mall
Philadelphia, PA 19106-1574
United States
215-574-3861 (Phone)
215-574-4364 (Fax)

HOME PAGE: http://sites.google.com/site/chatterjeesatyajit/home

Burcu Eyigungor

Federal Reserve Bank of Philadelphia ( email )

Ten Independence Mall
Philadelphia, PA 19106-1574
United States

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