We investigate the sensitivity of consumer surplus estimates to parametric assumptions on individual preference heterogeneity in a discrete choice framework. We compare results from a parametric random coefficients logit model and a recently proposed nonparametric sieve estimator. In particular, we provide an assessment of the direct economic value of crossing the Alps for the European road freight sector. Using revealed preference data from a detailed survey on transalpine road freight traffic, we estimate the yearly cost of closing the Mont-Blanc Tunnel, which was closed for 3 years following a large accident in early 1999. Ultimately, our results permit the economic evaluation of security and transport policy measures affecting transalpine traffic. Our findings suggest that the way we model unobserved heterogeneity significantly affects our welfare results.