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

ABSTRACT

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.

KEYWORDS:

• Instrumental variables
• indicators
• control function
• Monte Carlo
• stated preferences

Acknowledgments

We would like to acknowledge the valuable comments provided by three anonymous referees and by the attendants of the conferences CCHIT2013, ICMC2013 and PANAM2014, where preliminary versions of this research were presented. Of course, all potential errors remain ours. Research assistantship of Franco Pinto is also acknowledged in the development of preliminary version of the SP survey described in Section 5. All Monte Carlo experiments were generated and/or estimated using the open-source software R (R Development Core Team 2008). The final version of this article was prepared when the leading author was a Visiting Academic at the Choice Modelling Centre of the Institute for Transport Studies of the University of Leeds, UK.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

C. Angelo Guevara http://orcid.org/0000-0001-9307-804X

Notes

1. Instead, for a case of endogeneity occurring at an aggregate level, the BLP method (Berry, Levinsohn, and Pakes 1995) should be preferred in general, since it should be easier to apply and would require fewer assumptions.

2. Net monthly family income in Chilean pesos of 2014.

3. The standard errors for the MIS method were estimated by bootstraping (Petrin and Train 2002).

4. The analysis in this paragraph was suggested by one of the anonymous referees that reviewed a preliminary version of this article. Off course, all potential errors remain ours.

Additional information

Funding

This work was funded in part by CONICYT, FONDECYT [grant number 1150590], Complex Engineering Systems Institute, Chile [grant numbers ICM P-05-004-F and CONICYT FBO16], Leverhulme's Visiting Professorship [grant number VP1-2015-054] and the Spanish Ministry of Economy and Competitiveness [grant number ECO2014-52587-R].