Semiparametric estimation of the random utility model with rank-ordered choice data

Abstract

We propose two semiparametric methods for estimating the random utility model using rank-ordered choice data. The framework is “semiparametric” in that the utility index includes finite dimensional preference parameters but the error term follows an unspecified distribution. Our methods allow for a flexible form of heteroskedasticity across individuals. With complete preference rankings, our methods also allow for heteroskedastic and correlated errors across alternatives, as well as a variety of random coefficients distributions. The baseline method we develop is the generalized maximum score (GMS) estimator, which is strongly consistent but follows a non-standard asymptotic distribution. To facilitate statistical inferences, we make extra regularity assumptions and develop the smoothed GMS estimator, which is asymptotically normal. Monte Carlo experiments show that our estimators perform favorably against popular parametric estimators under a variety of stochastic specifications.