Incomplete market dynamics and cross-sectional distributions

• Published in: Journal of economic theory Vol. 154; pp. 310 - 348
• Main Author: Toda, Alexis Akira
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.11.2014; Elsevier Science Publishing Company, Inc
• Subjects: Agency theory; Aggregates; Algorithms; Applied general equilibrium analysis; Arbitrariness; Dynamics; Econometrics; Economic theory; Economics; Emergence; Equilibrium; General economic equilibrium; Inequality; Markets; Markov analysis; Mathematical models; Power; Power law; Probability distribution; Risk; Robustness; Stochastic models; Studies; Technology; Uniqueness; D52; D31; E21; D58; G11; Emergence; Robustness; Power law; Applied general equilibrium analysis; Inequality
• ISSN: 0022-0531; 1095-7235
• DOI: 10.1016/j.jet.2014.09.015

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.