Before 1979, unemployment insurance (UK) benefits were not treated as taxable income in the United States. Several economists criticized this policy on the ground that not taxing UK benefits while taxing earned income allegedly encourages unemployed persons to conduct longer than socially optimal job searches. Since 1979, however, UK benefits received by persons in higher-income families have been subject to income tax. This paper investigates whether the introduction of benefit taxation has had the predicted effect of reducing unemployment duration. The study uses data on a sample of persons that filed for UK in 1978 or 1979 to examine whether high-income claimants collected benefits for shorter periods after the tax change than they did before benefits became taxable. As part of the empirical analysis, the paper develops a generalization of the Weibull distribution and applies a limited-dependent-variable technique for this distribution similar to the Tobit technique for the normal distribution. Despite some variation in the results from different model specifications, the analysis presents persuasive evidence of a tax effect on unemployment duration. The 1979 policy change is estimated to have reduced average compensated unemployment duration among the sampled high-income claimants by about one week.