Marginal deadweight loss when the income tax is nonlinear

Almost all theoretical work on how to calculate the marginal deadweight loss has been done for linear taxes and for variations in linear budget constraints. This is quite surprising since most income tax systems are nonlinear, generating nonlinear budget constraints. Instead of developing the proper procedure to calculate the marginal deadweight loss for variations in nonlinear income taxes a common procedure has been to linearize the nonlinear budget constraint and apply methods that are correct for variations in a linear income tax. Such a procedure leads to incorrect results. The main purpose of this paper is to show how to correctly calculate the marginal deadweight loss when the income tax is nonlinear. A second purpose is to evaluate the bias in results that obtains when the traditional linearization procedure is used. We perform calculations based on the 2006 US tax system and find that the relative deadweight loss caused by increasing existing tax rates is large but less than half of Feldstein's (1999) estimates for the 1994 tax system.