On the existence and uniqueness of stationary equilibrium in Bewley economies with production

I prove existence of stationary recursive competitive equilibrium in Bewley economies with production under specifications in which (i) utility function is allowed to be unbounded, and (ii) the underlying discrete idiosyncratic productivity process can take any form, aside from mild restrictions. Some of the intermediate results provide theoretical basis for assumptions often made in the quantitative macroeconomics literature. By providing an example, I illustrate that equilibrium is not necessarily unique, even under typical specifications of the model, and discuss the underlying reasons for multiplicity.

[1]  C. Carroll.  The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence , 1992 .

[2]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[3]  Albert Marcet,et al.  Incomplete Markets, Labor Supply and Capital Accumulation , 2002 .

[4]  Wilbur John Coleman.  Solving the Stochastic Growth Model by Policy-Function Iteration , 1990 .

[5]  A. Deaton.  Saving and Liquidity Constraints , 1989 .

[6]  Distributional Comparative Statics with Heterogeneous Agents , 2016 .

[7]  When do borrowing constraints bind? Some new results on the income fluctuation problem , 2002 .

[8]  Richard Clarida.  Consumption, Liquidity Constraints and Asset Accumulation in the Presence of Random Income Fluctuations , 1987 .

[9]  Marilda Sotomayor.  On income fluctuations and capital gains , 1984 .

[10]  R. Jagannathan,et al.  Uninsured Idiosyncratic Risk and Aggregate Saving , 1994 .

[11]  Jack Schechtman,et al.  Some results on “an income fluctuation problem” , 1977 .

[12]  Donald M. Topkis,et al.  Minimizing a Submodular Function on a Lattice , 1978, Oper. Res..

[13]  Adam Szeidl.  Stable Invariant Distribution in Buer-Stock Saving and Stochastic Growth Models , 2013 .

[14]  Charles A. Wilson,et al.  Optimal Intertemporal Consumption under Uncertainty , 2000 .

[15]  S. Zeldes,et al.  Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence , 1989 .

[16]  D. Gale,et al.  Optimal growth under factor augmenting progress , 1969 .

[17]  Makoto Nirei.  Liquidity Constraints and Precautionary Savings : A Quantitative Analysis , 2004 .

[18]  Jess Benhabib,et al.  The wealth distribution in Bewley economies with capital income risk , 2015, J. Econ. Theory.

[19]  D. Acemoglu,et al.  Robust Comparative Statics in Large Dynamic Economies , 2015, Journal of Political Economy.

[20]  John Stachurski,et al.  Economic Dynamics: Theory and Computation , 2009 .

[21]  Jianjun Miao.  STATIONARY EQUILIBRIA OF ECONOMIES WITH A CONTINUUM OF HETEROGENEOUS CONSUMERS , 2002 .