Nonparametric vs parametric binary choice models: An empirical investigation

The estimation of conditional probability distribution functions (PDFs) in a kernel nonparametric framework has recently received attention. As emphasized by Hall, Racine and Li (2004), these conditional PDFs are extremely useful for a range of tasks including modelling and predicting consumer choice. The aim of this paper is threefold. First, we implement nonparametric kernel estimation of PDF with a binary choice variable and both continuous and discrete explanatory variables. Second, we address the issue of the performances of this nonparametric estimator when compared to a classic on-the-shelf parametric estimator, namely a probit. We propose to evaluate these estimators in terms of their predictive performances, in the line of the recent "revealed performance" test proposed by Racine and Parmeter (2009). Third, we provide a detailed discussion of the results focusing on environmental insights provided by the two estimators, revealing some patterns that can only be detected using the nonparametric estimator.