Taxing capital is a good idea: the role of idiosyncratic risk in an OLG model

We investigate an overlapping generations (OLG) model in which agents who live for two periods receive idiosyncratic productivity shocks when they are old. We show that, around zero tax equilibria, we can always construct a combination of a small capital tax and a lump-sum transfer that are Pareto-improving. As Dávila et al. (Econometrica (2012)) show, a capital reduction in one period raises the welfare level of agents who are old in that period, but lowers that of the young agents, because it reduces their wages. We show that the government can compensate for these wage losses by additionally taxing the old agents, such that their welfare gains remain positive. Our result is unchanged when earnings are uncertain at young age.