Deconvoluting preferences and errors: a model for binomial panel data

Let U be an unobserved random variable with compact support and let e_t be unobserved i.i.d. random errors also with compact support. Observe the random variables V_t, X_t, and Y_t = 1{U +d X_t+e_t < V_t}, t <= T, where d is an unknown parameter. This type of model is relevant for many stated choice experiments. It is shown that under weak assumptions on the support of U +e_t, the distributions of U and e_t as well as the unknown parameter d can be consistently estimated using a sieved maximum likelihood estimation procedure. The model is applied to simulated data and to actual data designed for assessing the willingness-to-pay for travel time savings.