Change of Scale and Forecasting with the Control-Function Method in Logit Models

The control-function method is the most suitable tool to address endogeneity for several discrete choice models that are relevant in transportation research. The estimators obtained with the control-function method are consistent only up to a scale. In this paper we first depict the determinants of this change of scale by adapting an existing result for omitted orthogonal attributes in Logit models. Then, we study the problem of forecasting under these circumstances. We show that a procedure proposed in previous literature may lead to significant biases, and we suggest novel alternatives to be used with synthetic populations. We also discuss potential extensions of these results to other non-Logit discrete choice models. We use Monte Carlo experimentation and real data on residential location choice to demonstrate these results. The paper finishes summarizing the findings of this research and suggesting future lines of research in this area.