This paper applies some of the key insights of dynamic discrete choice models to continuous-time job search models. Our framework incorporates preference shocks into search models, resulting in a tight connection between value functions and conditional choice probabilities. In this environment, we establish constructive identification of the model parameters, including the wage offer distributions off- and on-the-job. Our framework makes it possible to estimate nonstationary search models in a simple and tractable way, without having to solve any differential equations. We apply our method using Hungarian administrative data. Longer unemployment durations are associated with lower offer arrival rates, resulting in accepted wages falling over time. Counterfactual simulations indicate that increasing unemployment benefits by 90 days results in a 14-day increase in expected unemployment duration.