Correcting for endogeneity due to omitted attributes in discrete-choice models: the multiple indicator solution

Various transportation discrete-choice models suffer from endogeneity due to the omission of attributes that are relevant for the decision maker, but cannot be measured by the researcher. The control function (CF) method can be used to address this model flaw in discrete-choice models in which the problem occurs at the level of each alternative. However, the CF requires instrumental variables, which are difficult to obtain in various practical cases. In comparison, the multiple indicator solution (MIS) method does not require instruments, but indicators, which may be easier to gather in various circumstances. The MIS method has only been described so far for linear models. In this article, we show that MIS can be extended to discrete-choice modelling under mild assumptions. We also discuss the conditions under which it could be applied in practical transportation models estimated with revealed preference (RP) and stated preferences (SP) data where the source of endogeneity can be identified explicitly. We then use Monte Carlo experiments to illustrate the finite sample properties of MIS and CF. Results seem to suggest that MIS is robust to mild violations of modelling assumptions. We finally illustrate the application of the MIS method to an SP experiment of dwelling choice, showing that the MIS seems to have addressed successfully the omission of quality inferred from a picture.