"The Stationary Distribution of Wealth with Random Shocks"
Christopher Bliss
Nuffield College, Oxford University, Oxford OX2 6LE, UK.
Abstract: A convergence model with wealth accumulation subject to i.i.d. random
shocks is examined. The transfer function shows what k_{t+1} - wealth at t+1 - would be,
given k_t, with no shock: It has a positive slope, but its concavity/convexity is
indeterminate. The stationary distribution of wealth satisfies a Fredholm integral equation.
This distribution can be examined by direct analysis of the wealth-accumulation stochastic
process and via the Fredholm equation. The analysis resembles some econometric theory
of time series. Economic theory forces consideration of a broad range of cases,
including some which violate B-convergence. "Twin peaks" in the stationary distribution
cannot be excluded.
Keywords: Convergence, stochastic process, wealth distribution