Tax reform as a constrained optimization problem: a piecewise-linear framework and software implementation

Abstract

In many countries, income tax codes have grown into a complex tangle of interacting brackets, benefits, and deductions. Despite widespread calls for systematic reform, successful attempts at reform are rare. Part of the problem is the difficulty of designing viable reform proposals. Politically viable reform must offer hard guarantees on income effects, marginal rates, and budgetary cost. Existing microsimulation tools can evaluate a reform proposal but cannot generate one by themselves. We develop a framework that casts tax reform as a constrained optimization problem. We show that any statutory tax code satisfying four mild assumptions reduces to a finite-dimensional piecewise-linear function for each taxpayer group, so reform becomes a linear or mixed-integer linear program whose decision variables are legislatable parameters: rates, bracket cutoffs, and lump-sum transfers. We are able to recover current tax systems and generate provably optimal reform candidates within the modeled space, or a certificate that no reform satisfying certain policy design constraints exists. Behavioral effects can also be incorporated, producing a nonconvex mixed-integer formulation. We demonstrate the framework through a near-complete reconstruction of the Dutch income tax code, generating reforms that smooth marginal-rate spikes, cap household income losses, and roughly halve the number of active rules through a lexicographic procedure. Developed in close collaboration with the Dutch Ministry of Finance, the methodology is currently in active use there. An open-source software implementation is available as \texttt{TaxSolver}.