On Choosing a Flat-Rate Income Tax Schedule

This paper applies a numerical optimization technique using microunit tax data to the problem of choosing the parameters of a flat-rate tax system, should one be desired. Our approach is to first formulate explicit objectives that a flat-rate tax might reasonably be designed to meet, such as minimizing the extent of changes in households' tax burdens and minimizing the efficiency cost of the tax system. The next step uses an optimization algorithm to calculate the flat-rate schedule which comes closest to meeting the objectives,subject to the constraint that it raise the same revenue as the current incometax system. The calculations are carried out using a sample of 947 tax returns randomly drawn from the Treasury Tax File for 1977 which are updated to repro-duce the pattern of tax returns that would be filed in 1982.The analysis shows that the flat-rate system which minimizes the sum of the absolute deviations in tax liabilities features a marginal tax rate between 0.204 and 0.254, though a different definition of tax burden changes which puts more emphasis on reproducing the tax burdens of high-income households has an optimal marginal tax rate of 0.382. We also derive the optimal flat-rate schedules when another objective is to minimize the efficiency cost of the tax system.