Abstract:

We consider taxation in heterogeneous agents economies in the spirit of Aiyagari (1994). We allow arbitrary, potentially non-linear and joint, taxes on earnings and capital income. We show that responses of earnings and savings to any tax perturbation can be characterized in terms of certain linear operators. These operators generalize notions of Slutsky matrices and income effects to dynamic stochastic settings, and are easy to construct from equilibrium allocations. Using these operators, one can characterize effects of arbitrary tax reforms on tax revenues, welfare, and the joint distribution of earnings and wealth in the economy. We derive formulas that characterize optimal taxes. These formulas resemble the classical ABC formulas familiar from static models such as Saez (2001) but have additional dynamic adjustments. We develop computational techniques that allow one to use these formulas to compute optimal taxes. We find that optimal taxes in a calibrated incomplete markets dynamic economy substantially differ from their static counterpart because of the impact that such taxes have on the joint distribution of earnings and wealth.