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Incomplete market dynamics and cross-sectional distributions


The size distributions of many economic variables seem to obey the double power law, that is, the power law holds in both the upper and the lower tails. I explain this emergence of the double power law-which has important economic, econometric, and social implications-using a tractable dynamic stochastic general equilibrium model with heterogeneous agents subject to aggregate and idiosyncratic investment risks. I establish theoretical properties such as existence, uniqueness, and constrained efficiency of equilibrium, and provide a numerical algorithm that is guaranteed to converge. The model is widely applicable: it allows for arbitrary homothetic CRRA recursive preferences, an arbitrary Markov process governing aggregate shocks, and an arbitrary number of technologies and assets with arbitrary portfolio constraints.

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