Error and Generalization in Discrete Choice Under Risk

I compare the generalization ability, or out-of-sample predictive success, of four probabilistic models of binary discrete choice under risk. One model is the conventional homoscedastic latent index model—the simple logit—that is common in applied econometrics: This model is “context-free” in the sense that its error part is homoscedastic with respect to decision sets. The other three models are also latent index models but their error part is heteroscedastic with respect to decision sets: In that sense they are “context-dependent” models. Context-dependent models of choice under risk arise from several different theoretical perspectives. Here I consider my own “contextual utility” model (Wilcox 2011), the “decision field theory” model of Busemeyer and Townsend (1993) and the “Blavatskyy-Fishburn” model (Fishburn 1978; Blavatskyy 2014). In a new experiment, all three context-dependent models outperform the context-free model in prediction, and significantly outperform a linear probability model (suggested by contemporary applied practice a la Angrist and Pischke 2009) when the latent preference structure is rank-dependent utility (Quiggin 1982). All of this holds true for function-free estimations of outcome utilities and probability weights as well as parametric estimations. Preoccupation with theories of the deterministic structure of choice under risk, to the exclusion of theories of error, is a mistake.