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The author extends the Diamond (1965) model of national debt in two directions. She first introduces technological uncertainty and then she allows the stock of debt to vary. The author studies the dynamical equilibria of the resulting stochastic system and she establishes conditions for the existence of stationary states that are expressed in terms of invariant distributions. Since conditions that ensure the existence of a stochastic stationary state with positive debt are very restrictive, in this model financial instability is a pervasive phenomenon and allocations are in general dynamically inefficient.
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Graziella Bertocchi (1994) studied this question.
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