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In: The economic journal: the journal of the Royal Economic Society, Band 116, Heft 515, S. F480-F498
ISSN: 1468-0297
In: American economic review, Band 95, Heft 2, S. 118-121
ISSN: 1944-7981
In: The new Palgrave economics collection
In: Journal of political economy, Band 123, Heft 4, S. 749-777
ISSN: 1537-534X
In: The economic journal: the journal of the Royal Economic Society, Band 125, Heft 583, S. 350-377
ISSN: 1468-0297
In: Journal of political economy, Band 123, Heft 2, S. 444-496
ISSN: 1537-534X
SSRN
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.