I present an explicitly solved equilibrium model for the distribution of wealth and income in an incomplete-markets economy. I first propose a self-insurance model with an inter-temporally dependent preference [Uzawa, H. 1968. Time preference, the consumption function, and optimal asset holdings. In: Wolfe, J.N. (Ed.), Value, Capital, and Growth: Papers in Honour of Sir John Hicks. Edinburgh University Press, Edinburgh, pp. 485–504]. I then derive an analytical consumption rule which captures stochastic precautionary saving motive and generates stationary wealth accumulation. Finally, I provide a complete characterization for the equilibrium cross-sectional distribution of wealth and income in closed form by developing a recursive formulation for the moments of the distribution of wealth and income. Using this recursive formulation, I show that income persistence and the degree of wealth mean reversion are the main determinants of wealth-income correlation and relative dispersions of wealth to income, such as skewness and kurtosis ratios between wealth and income.
Wang, Neng. "An Equilibrium Model of Wealth Distribution." Journal of Monetary Economics 54, no. 7 (2007): 1882-1904.
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