Using a four-month panel of revised Current Population Survey data from September-December 1993, we extend the class of semiparametric hazard models of the type first studied by Prentice and Gloeckler (1978), and brought to the attention of economists by Meyer (1988, 1990), to incorporate inequality restrictions on the shape of the hazard. This extension enables us to test hypotheses regarding the shape of the hazard implied by search theory using duration data alone. These tests provide another link between the empirical and theoretical literatures on unemployment duration and job search. The GHK probability simulator makes it straightforward to generate approximate hypothesis test results, as simulation estimates of the probability under the null hypothesis are generated using the asymptotic normal approximation to the distribution of the hazard parameters obtained from maximum likelihood estimation. Importance sampling is used to conduct inference under the null and obtain exact finite sample estimates of the probability the null is satisfied. A new algorithm for maintaining stability of the importance weights is also developed.