# Bubbly Markov equilibria

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## Abstract

Bubbly Markov equilibria (BME) are recursive equilibria on the natural state space which admit a non-trivial bubble. The present paper studies the existence and properties of BME in a general class of overlapping generations economies with capital accumulation and stochastic production shocks. Using monotone methods, we develop a general approach to construct Markov equilibria and provide necessary and sufficient conditions for these equilibria to be bubbly. Our main result shows that a BME exists whenever the bubbleless equilibrium is Pareto inefficient due to either overaccumulation of capital or inefficient risk sharing between generations.

## Keywords

Asset bubbles Stochastic OLG Production Markov equilibria Pareto optimality## JEL Classification

C62 D51 E32## Notes

### Acknowledgements

We would like to thank Tim Deeken, Tomoo Kikuchi, Herakles Polemarchakis, Clemens Puppe, Kevin Reffett, Caren Söhner, John Stachurski, and Klaus Wälde for helpful suggestions and discussions and two anonymous referees for their valuable and very constructive comments. We also thank seminar participants at various conferences including the 2013 SAET Conference in Paris, the 2013 Annual Meeting of the Verein für Socialpolitik in Düsseldorf, the 2014 CEF Conference in Oslo, and the 2017 SAET conference in Faro.

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