By Marek Kapicka
I quantify the welfare gains from introducing history dependent income tax in an incomplete markets framework where individuals face uninsurable random walk idiosyncratic shocks. I assume that the income tax paid is a function of a geometrical weighted average of past incomes, and solve for the optimal weights. I find that the optimal weights on past incomes decline geometrically at a rate equal to the discount rate. The welfare gains from history dependence are large, about 1.77 percent of consumption. I decompose the total effect into an efficiency effect that increases labor supply, and an insurance effect that reduces volatility of consumption and find that, quantitatively, the insurance effect dominates the efficiency effect. The optimal tax increases consumption insurance by trading higher tax progressivity with repect to past incomes for a reduced tax progressivity with respect to the current income.
Interesting result. It clearly makes sense that taxes should not only depend on income in the current snapshot in time. The paper shows that even a rigid formula on past taxes easily enhances welfare. Imagine if the formula were more flexible than a weighted average.