Optimal Life-cycle Capital Taxation under Self-Control Problems

We study optimal taxation of savings in an economy where agents face self-control problems and are allowed to be partially naive. We assume that the severity of self-control problems changes over the life-cycle. We focus on quasihyperbolic discounting with constant elasticity of intertemporal substitution utility functions and linear Markov equilibria. We derive explicit formulas for optimal taxes that implement the efficient allocation. We show that if agents' ability to self-control increases concavely with age, then savings should be subsidized and the subsidy should decrease with age. We also show that allowing for age-dependent self-control problems creates large effects on the level of optimal subsidies, while optimal taxes are not very sensitive to the level of sophistication.