Generalized compensation principle

Abstract

We generalize the classic concept of compensating variation and the welfare compensation principle to a general equilibrium environment with distortionary taxes. We derive in closed-form the solution to the problem of designing a tax reform that compensates the welfare gains and losses induced by an arbitrary economic disruption. In partial equilibrium, average taxes simply increase or decrease to counteract the revenue gains or losses caused by the disruption. In general equilibrium, the compensation features three elements that depart from this benchmark and respectively account for (i) the incidence of the initial exogenous shock, and the fact that the tax reform itself induces indirect welfare effects caused by (ii) the non-constant marginal product of labor and (iii) the skill complementarities in production. This leads to a progressive compensating tax reform, with average tax rates increasing at a rate given by the ratio of the elasticity of labor demand and the elasticity of labor supply net of the rate of progressivity of the pre-existing tax code. We also derive a closed form formula for the fiscal surplus of the wage disruption and the compensation, thus generalizing the traditional Kaldor-Hicks criterion. Finally, we apply our formula to the compensation of automation: in the U.S., one additional robot per thousand workers requires a reduction (resp., increase) in the average tax rate at the 10th (resp., 90th) percentile of the income distribution equal to 2 percentage points (resp., 0.5 pp).