Endogeneity is a potential anomaly in econometric models, which may cause inconsistent parameter estimates. Transport models are prone to this problem and applications that properly correct for it are scarce. This paper focuses on how to address this issue in the case of strategic urban mode choice models (i.e., the third stage of classic strategic transport models), possibly the main tool for the assessment of costly transport projects. To address this problem, we propose and validate, for the first time, adequate instruments that may be obtained from data that is already available in this context. The proposed method is implemented using the Control Function approach, which we use to detect and correct for endogeneity in a case study in Valparaiso, Chile. The effects arising from the neglected endogeneity in this case study reflect on an overestimation between 26–49% of the subjective value of time and an underestimation of 33–75% of modal elasticities.
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The size distortion corresponds to the difference between the nominal significance of the tests, and the empirical size for the Type I error under the null hypothesis. This type of measure is a standard tool for the assessment of the statistical tests (Guevara 2018).
SECTRA is the Chilean governmental agency for transport planning and policy formulation.
An additional issue that did not come out in this application, but may be relevant for other cases, is what to do when the endogenous variable interacts with exogenous variables, such as level of income or gender. Bun and Harrison (2018) formally show that, under such circumstances, the endogeneity bias will reduce to zero for the ordinary least squares estimator, as far as the interaction term is concerned. The same holds for the Control Function method in discrete choices, something that has been implicitly used, among others, by Petrin and Train (2010) and Guevara and Ben-Akiva (2006). We thank an anonymous reviewer for having asked this question.
Following Rivers and Vuong (1988), note that when using a two-step procedure, the test for the presence of endogeneity does not require correcting the standard errors with bootstrap. This holds because the test is evaluated under the null hypothesis that there is no endogeneity. Therefore, the population coefficient of the residuals is zero. This logic holds for Wald, Lagrange Multiplier and LR tests, when used to evaluate the presence of endogeneity, which is what we use in this section (see, for example, the discussion in Guevara 2010, Ch. 2).
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The authors would like to thank SECTRA (Secretaría de Planificación de Transporte de Chile) and, in particular Alan Thomas, for the provision of the real data used in the study. Preliminary work for this research was presented at the 6th International Choice Modelling Conference, Kobe, Japan. This research was partially funded by ANID, FONDECYT 1191104 and by the Instituto Sistemas Complejos de Ingeniería (ISCI), through the Grant ANID PIA/BASAL AFB180003. We are also grateful for the support received from the BRT+Centre of Excellence (www.brt.cl), financed by the Volvo Research and Educational Foundations. Finally, we wish to acknowledge the relevant and insightful comments of three unknown referees, which helped us to improve the paper considerably. Of course, any remaining errors are our fault.
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Guerrero, T.E., Guevara, C.A., Cherchi, E. et al. Addressing endogeneity in strategic urban mode choice models. Transportation 48, 2081–2102 (2021). https://doi.org/10.1007/s11116-020-10122-y