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Matching and Saving in Continuous Time: Theory

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  • Christian Bayer
  • Klaus Wälde

Abstract

We analyse optimal saving of risk-averse households when labour income stochastically jumps between two states. The generalized Keynes-Ramsey rule includes a precautionary savings term. A phase diagram analysis illustrates consumption and wealth dynamics within and between states. There is an endogenous lower and upper limit for wealth. We derive the Fokker-Planck equations for the densities of individual wealth and employment status. These equations also characterize the aggregate distribution of wealth and allow us to describe general equilibrium. An optimal consumption path exists and distributions converge to a unique limiting distribution.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 3026.

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Date of creation: 2010
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Handle: RePEc:ces:ceswps:_3026

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Keywords: matching model; optimal saving; incomplete markets; Poisson uncertainty; Fokker-Planck equations; general equilibrium;

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Cited by:
  1. Carlos Miguel Silva & Ana Paula Ribeiro, 2011. "The Impacts of Structural Changes in the Labor Market: a Comparative Statics Analysis Using Heterogeneous-agent Framework," CEF.UP Working Papers, Universidade do Porto, Faculdade de Economia do Porto 1104, Universidade do Porto, Faculdade de Economia do Porto.

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