The Stationary Distribution of Wealth with Random Shocks

January 2002 Abstract. A convergence model with wealth accumulation subject to i.i.d. random shocks is examined. The transfer function shows what kt+1 wealth at t + 1 would be, given kt, with no shock. It has a positive slope, but its concavity/convexity is indeterminate. The stationary distribution of wealth satis...es 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 ̄-convergence. “Twin peaks” in the stationary distribution cannot be excluded.