This paper presents a model of compensating differentials in which firms' costs of providing amenities may depend on unobserved worker productivity. Estimating the model requires measures of workers' willingness to pay for job amenities at the individual level. We measure workers' preferences using a Bayesian Adaptive Choice Experiment (BACE), a dynamic preference elicitation method that we introduce. The estimated model matches key patterns in the data, and we use the estimates to explore the welfare consequences of workers facing different amenity prices.