The Invariant Distribution of Wealth and Employment Status in a Small Open Economy with Precautionary Savings

Christian Bayer, Alan D. Rendall and Klaus Wälde

No 7397, CESifo Working Paper Series from CESifo

Abstract: We study optimal savings in continuous time with exogenous transitions between employment and unemployment as the only source of uncertainty in a small open economy. We prove the existence of an optimal consumption path. We exploit that the dynamics of consumption and wealth between jumps can be expressed as a Fuchsian system. We derive conditions under which an invariant joint distribution for the state variables, i.e., wealth and labour market status, exists and is unique. We also provide conditions under which the distribution of these variables converges to the invariant distribution. Our analysis relies on the notion of T-processes and applies results on the stability of Markovian processes from Meyn and Tweedie (1993a, b,c).

Keywords: uncertainty in continuous time; counting process; existence; uniqueness; stability (search for similar items in EconPapers)
JEL-codes: C62 D91 J63 (search for similar items in EconPapers)
Date: 2018
New Economics Papers: this item is included in nep-lma and nep-ltv
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Related works:
Journal Article: The invariant distribution of wealth and employment status in a small open economy with precautionary savings (2019)
Working Paper: The Invariant Distribution of Wealth and Employment Status in a Small Open Economy with Precautionary Savings (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:ces:ceswps:_7397

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