Instability and concentration in the distribution of wealth

We consider a setup in which infinitely lived households face idiosyncratic investment risk and show that in this case the equilibrium distribution of wealth becomes increasingly right-skewed over time until wealth concentrates entirely at the top. The households in our setup are identical in terms of their patience and their abilities, and we assume that there are no redistributive mechanisms—neither explicit in the form of government tax or fiscal policies, nor implicit in the form of limited intergenerational transfers. Our results demonstrate that the presence of such redistributive mechanisms alone ensures the stability of the distribution of wealth over time.