Bunching and Taxing Multidimensional Skills

We characterize optimal policy in a multidimensional nonlinear taxation model with bunching. We develop an empirically relevant model with cognitive and manual skills, firm heterogeneity, and labor market sorting. We first derive two conditions for the optimality of taxes that take into account bunching. The first condition $-$ a stochastic dominance optimal tax condition $-$ shows that at the optimum the schedule of benefits dominates the schedule of distortions in terms of second-order stochastic dominance. The second condition $-$ a global optimal tax formula $-$ provides a representation that balances the local costs and benefits of optimal taxation while explicitly accounting for global incentive constraints. Second, we use Legendre transformations to represent our problem as a linear program. This linearization allows us to solve the model quantitatively and to precisely characterize bunching. At an optimum, 10 percent of workers is bunched. We introduce two notions of bunching $-$ blunt bunching and targeted bunching. Blunt bunching constitutes 30 percent of all bunching, occurs at the lowest regions of cognitive and manual skills, and lumps the allocations of these workers resulting in a significant distortion. Targeted bunching constitutes 70 percent of all bunching and recognizes the workers' comparative advantage. The planner separates workers on their dominant skill and bunches them on their weaker skill, thus mitigating distortions along the dominant skill dimension.