Binary discrete choice under asymmetric restrictions

A crucial assumption of discrete choice models requires that observed individual behavior is a direct function of unobserved individual utility maximization. There are situations, however, where observed behavior is ambiguous with respect to maximum utility. This is the case, when individual utility maximization is hampered by global restrictions of action. Typically, such restrictions are tied to particular decision alternatives, which causes an asymmetric influencing on individual behavior. The existence of global asymmetric restrictions upon individual behavior can be treated as a second unobserved variable. This leads to two separate models, which have to be estimated simultaneously: a decision model on the one hand and a restriction model on the other. The standard decision model arises as a special case with a zero restriction probability. McKelvey/Zavoina's PseudoR ² can be employed as a straightforward evaluation of the goodness-of-fit. Neglecting the presence of asymmetric restrictions or considering them as symmetric effects leads to biased estimators. This is discussed in a formal manner and demonstrated by means of a simulation study. The bias may occur in either direction. It is not only restricted to the model parameters themselves, but also to their standard errors. To avoid such bias, it seems advisable to use the extended model if ever possible and test for a zero restriction probability. I wish to thank Reinhard Hujer, Jo Grammig, Matthias Lob, Notburga Ott, Reinhold Schnabel and an anonymous referee for helpful comments on earlier drafts of this paper.