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Poverty traps in Markov models of theevolution of wealth

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  • Blume, Lawrence E.
  • Durlauf, Steven N.
  • Lukina, Aleksandra

Abstract

Poverty trap models are dynamical systems with more than one attractor. Similar dynamical systems arise in optimal growth and macroeconomic models. These systems are often studied empirically by ad hoc methods relying on intuition from deterministic systems, such as looking for multiple peaks in the stationary distribution of states. We develop Markov wealth processes in which parents' investments in children stochastically determine children's wealth, and consequently their own investment choices. We show that, relative to a zero-shock process, some of the multiple attractors are less fragile than are others, and that their presence dominates the stationary behavior of the wealth distribution. Typically, mass accumulates around attractors. An only slightly stochastically perturbed deterministic system will have an invariant distribution which puts close to probability 1 on a single steady state rather than having significant mass distributed among several attractors. We also examine how policy effects the shape of the invariant distribution.

Suggested Citation

  • Blume, Lawrence E. & Durlauf, Steven N. & Lukina, Aleksandra, 2020. "Poverty traps in Markov models of theevolution of wealth," Discussion Papers, Research Unit: Economics of Change SP II 2020-303, WZB Berlin Social Science Center.
  • Handle: RePEc:zbw:wzbeoc:spii2020303
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    References listed on IDEAS

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    1. Becker, Gary S & Tomes, Nigel, 1979. "An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1153-1189, December.
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    More about this item

    Keywords

    Poverty traps; wealth distribution; wealth mobility;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D3 - Microeconomics - - Distribution

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