Characterizing the impact of discrete indicators to correct for endogeneity in discrete choice models

Endogeneity is a common problem in econometric modelling that may lead to estimating inconsistent parameters. In the scientific literature, the Multiple Indicator Solutions (MIS) method is used to correct for endogeneity. This approach uses indicators that, in practice, tend to be collected as discrete using Likert scales; however, theoretically, the MIS method is derived considering continuous indicators. To close this research gap, this paper focuses on characterizing the impact of discrete indicators when correcting for endogeneity using the MIS method in the case of discrete choice models (DCM). Our findings show that (i) under some conditions, using discrete indicators instead of continuous ones seems not to be a problem, however, (ii) there is also evidence that indicates that the correction could fail under not unusual circumstances.