This paper establishes global stability for a class of stochastic increasing returns accumulation models. The nature of the unique stochastic steady state is investigated. It is found that the models generate highly path dependent time series over long horizons. The findings demonstrate that the standard stability concept used in stochastic growth theory is satisfied by models which contradict our intuitive association of globally stability with unique, history-independent outcomes for each set of economic fundamentals. At the same time, the analysis provides a principled theoretical framework for integrating increasing returns models more closely with the cross-country income data.
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