Skip to main content
SpringerLink
Log in

Addressing endogeneity in strategic urban mode choice models

Transportation volume 48, pages 2081–2102 (2021)Cite this article

Abstract

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3

Notes

  1. 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).

  2. SECTRA is the Chilean governmental agency for transport planning and policy formulation.

  3. 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.

  4. 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).

References

  • Amemiya, T.: The estimation of a simultaneous equation generalized probit model. Econometrica 46, 1193–1205 (1978)

    Article  Google Scholar 

  • Anderson, J., Hernandez, S.: Roadway classifications and the accident injury severities of heavy-vehicle drivers. Anal. Methods Accid. Res. 15, 17–28 (2017)

    Google Scholar 

  • Bass, F.: A simultaneous equation regression study of advertising and sales of cigarettes. J. Mark. Res. 6, 291–300 (1969)

    Article  Google Scholar 

  • Bass, P., Donoso, P., Munizaga, M.: A model to assess public transport demand stability. Transp. Res. Part A Policy Pract. 45, 755–764 (2011)

    Article  Google Scholar 

  • Ben-Akiva, M.E., Lerman, S.R.: Discrete Choice Analysis: Theory and Application to Travel Demand. The MIT Press, Cambridge (1985)

    Google Scholar 

  • Berry, S., Levinsohn, J., Pakes, A.: Automobile prices in market equilibrium. Econometrica 63, 841–890 (1995)

    Article  Google Scholar 

  • Bresnahan, T.F.: The apple–cinnamon cheerios war: valuing new goods, identifying market power, and economic measurement. In: Bresnahan, T.F., Gordon, R.J. (eds.) The Economics of New Goods. NBER Studies in Income and Wealth Number, vol. 58. The University of Chicago Press, Chicago (1997)

    Chapter  Google Scholar 

  • Bun, M.J., Harrison, T.D.: OLS and IV estimation of regression models including endogenous interaction terms. Econ. Rev. 38, 814–827 (2018)

    Article  Google Scholar 

  • Casey, B.: Early retirement: the problems of “instrument substitution” and “cost shifting” and their implications for restructuring the process of retirement. In: Schmähl, W. (ed.) Redefining the Process of Retirement. Springer, Berlin (1989)

    Google Scholar 

  • Chou, C., Chen, P.: Preferences and willingness to pay for green hotel attributes in tourist choice behaviour: the case of Taiwan. J. Travel Tour. Mark. 31, 937–957 (2014)

    Article  Google Scholar 

  • Citilabs: Discover Cube 6.4 Tutorial. Citilabs, Inc., Sacramento (2016)

    Google Scholar 

  • Davison, A.C., Hinkley, D.V.: Bootstrap Methods and Their Application, vol. 1. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  • De Cea, J., Fernández, J.E., Dekock, V., Soto, A.: Solving network equilibrium problems on multimodal urban transportation networks with multiple user classes. Transp. Rev. 35, 293–317 (2005)

    Article  Google Scholar 

  • Domencich, T., McFadden, D.: Urban Travel Demand: A Behavioural Analysis. North Holland, Amsterdam (1975)

    Google Scholar 

  • Fernández-Antolín, A., Guevara, C.A., De Lapparent, M., Bierlaire, M.: Correcting for endogeneity due to omitted attitudes: empirical assessment of a modified MIS method using RP mode choice data. J. Choice Model. 20, 1–15 (2016)

    Article  Google Scholar 

  • Gaudry, M.J., Jara-Diaz, S.R., Ortúzar, J. de D.: Value of time sensitivity to model specification. Transp. Res. Part B Methodol. 23, 151–158 (1989)

    Article  Google Scholar 

  • Granados, N., Gupta, A., Kauffman, R.J.: Online and offline demand and price elasticities: evidence from the air travel industry. Inf. Syst. Res. 23, 164–181 (2012)

    Article  Google Scholar 

  • Guevara, C.A.: Endogeneity and sampling of alternatives in spatial choice models. Ph. D. Thesis, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology (2010)

  • Guevara, C.A.: Critical assessment of five methods to correct for endogeneity in discrete-choice models. Transp. Res. Part A Policy Pract. 82, 240–254 (2015)

    Article  Google Scholar 

  • Guevara, C.A.: Overidentification tests for the exogeneity of instruments in discrete choice models. Transp. Res. Part B Methodol. 114, 241–253 (2018)

    Article  Google Scholar 

  • Guevara, C.A., Ben-Akiva, M.E.: Endogeneity in residential location choice models. Transp. Res. Rec. 1977, 60–66 (2006)

    Article  Google Scholar 

  • Guevara, C.A., Ben-Akiva, M.E.: Addressing endogeneity in discrete choice models: assessing control-function and latent-variable methods. In: Hess, S., Daly, A. (eds.) Choice Modelling: The State-of-the-Art and The State-of-Practice. Edward Elgar publishers, Cheltenham (2010)

    Google Scholar 

  • Guevara, C.A., Ben-Akiva, M.E.: Change of scale and forecasting with the control-function method in logit models. Transp. Sci. 46, 425–437 (2012)

    Article  Google Scholar 

  • Guevara, C.A., Navarro, P.: Detection of weak instruments when correcting for endogeneity in binary logit models. In: Proceedings 14th International Conference on Travel Behaviour Research (IATBR), Windsor, UK, July 19–23 (2015)

  • Guevara, C.A., Polanco, D.: Correcting for endogeneity due to omitted attributes in discrete-choice models: the multiple indicator solution. Transp. A Transp. Sci. 12, 458–478 (2016)

    Google Scholar 

  • Guevara, C.A., Tirachini, A., Hurtubia, R., Dekker, T.: Correcting for endogeneity due to omitted crowding in public transport choice using the Multiple Indicator Solution (MIS) method. Transp. Res. Part A Policy Pract. (2018). https://doi.org/10.1016/j.tra.2018.10.030

    Article  Google Scholar 

  • Hausman, J.A.: Specification tests in econometrics. Econometrica 46, 1251–1271 (1978)

    Article  Google Scholar 

  • Hausman, J.A.: Valuation of new goods under perfect and imperfect competition. In: Bresnahan, T.F., Gordon, R.J. (eds.) The Economics of New Goods. NBER Studies in Income and Wealth Number, vol. 58. The University of Chicago Press, Chicago (1996)

    Google Scholar 

  • Hausman, J.A., Leonard, G., Zona, J.D.: Competitive analysis with differentiated products. Ann. Econ. Stat. 34, 159–180 (1994)

    Google Scholar 

  • Hess, S., Beharry-Borg, N.: Accounting for latent attitudes in willingness-to-pay studies: the case of coastal water quality improvements in Tobago. Environ. Resour. Econ. 52, 109–131 (2012)

    Article  Google Scholar 

  • Hsiao, C.Y.: Passenger demand for air transportation in a hub-and-spoke network. PhD Thesis, Department of Civil and Environmental Engineering, University of California at Berkeley (2008)

  • Hurtubia, R., Bierlaire, M.: Estimation of bid functions for location choice and price modelling with a latent variable approach. Netw. Spat. Econ. 14, 47–65 (2014)

    Article  Google Scholar 

  • INRO: EMME/2 User’s Manual. INRO Inc., Montreal (1996)

    Google Scholar 

  • Instituto Nacional de Estadísticas: Chile proyecciones y estimaciones de población (2013). http://www.ine.cl/canales/chile_estadistico/demografia_y_vitales/demografia/demografia.php. Accessed 24 July 2019 (in Spanish)

  • Jensen, A.F., Cherchi, E., Mabit, S.L.: On the stability of preferences and attitudes before and after experiencing an electric vehicle. Transp. Res. Part D Transp. Environ. 25, 24–32 (2013)

    Article  Google Scholar 

  • Karaca-Mandic, P., Train, K.: Standard error correction in two-stage estimation with nested samples. Econom. J. 6, 401–407 (2003)

    Article  Google Scholar 

  • Lam, S.K., Ahearne, M., Hu, Y., Schillewaert, N.: Resistance to brand switching when a radically new brand is introduced: a social identity theory perspective. J. Mark. 74, 128–146 (2010)

    Article  Google Scholar 

  • Lee, L.: Amemiya’s generalized least squares and tests of overidentification in simultaneous equation models with qualitative or limited dependent variables. Econ. Rev. 11, 319–328 (1992)

    Article  Google Scholar 

  • Mariel, P., Hoyos, D., Artabe, A., Guevara, C.A.: A multiple indicator solution approach to endogeneity in discrete-choice models for environmental valuation. Sci. Total Environ. 633, 967–980 (2018)

    Article  Google Scholar 

  • Mumbower, S., Garrow, L.A., Higgins, M.J.: Estimating flight-level price elasticities using online airline data: a first step toward integrating pricing, demand, and revenue optimization. Transp. Res. Part A Policy Pract. 66, 196–212 (2014)

    Article  Google Scholar 

  • Nevo, A.: Measuring market power in the ready-to-eat cereal industry. Econometrica 69, 307–342 (2001)

    Article  Google Scholar 

  • Newey, W.: Efficient estimation of limited dependent variable models with endogenous explanatory variables. J. Econ. 36, 231–250 (1987)

    Article  Google Scholar 

  • Ortúzar, J. de D., Willumsen, L.G.: Modelling Transport, 4th edn. Wiley, Chichester (2011)

    Book  Google Scholar 

  • Orozco-Fontalvo, M., Arévalo-Támara, A., Guerrero-Barbosa, T., Gutiérrez-Torres, M.: Bicycle choice modelling: a study of university trips in a small Colombian city. J. Transp. Health 9, 264–274 (2018)

    Article  Google Scholar 

  • Petrin, A., Train, K.: Omitted product attributes in discrete choice models. Working Paper, Department of Economics, University of California, Berkeley (2002)

  • Petrin, A., Train, K.: A control function approach to endogeneity in consumer choice models. J. Mark. Res. 47, 3–13 (2010)

    Article  Google Scholar 

  • Rivers, D., Vuong, Q.: Limited information estimators and exogeneity tests for simultaneous probit models. J. Econ. 39, 347–366 (1988)

    Article  Google Scholar 

  • Rizzi, L.I., Ortúzar, J. de D.: Road safety valuation under a stated choice framework. J. Transp. Econ. Policy 40, 69–94 (2006)

    Google Scholar 

  • Sargan, J.: The estimation of economic relationships using instrumental variables. Econometrica 26, 393–415 (1958)

    Article  Google Scholar 

  • SECTRA: Actualización Diagnóstico del S.T.U. del Gran Valparaíso. Etapa I-SECTRA, Valparaiso (2014a) (in Spanish)

    Google Scholar 

  • SECTRA: Actualización y Recolección de Información del Sistema de Transporte Urbano, IX Etapa: Encuesta Origen Destino Santiago 2012. SECTRA, Santiago (2014b) (in Spanish)

    Google Scholar 

  • Staiger, D., Stock, J.H.: Instrumental variables regression with weak instruments. Econometrica 65, 557–586 (1997)

    Article  Google Scholar 

  • Stern, S.: Market definition and the returns to innovation: substitution patterns in pharmaceutical markets. Working Paper, Sloan School of Management, MIT (1996)

  • Stock, J.H., Yogo, M.: Testing for weak instruments in linear IV regression. In: Andrews, D.W., Stock, J.H. (eds.) Identification and Inference for Econometric Models, Essays in Honour of Thomas Rothenberg. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  • Tirachini, A., Hensher, D.A., Rose, J.M.: Crowding in public transport systems: effects on users, operation and implications for the estimation of demand. Transp. Res. Part A Policy Pract. 53, 36–52 (2013)

    Article  Google Scholar 

  • Torres, I., Greene, M., Ortúzar, J. de D.: Valuation of housing and neighbourhood attributes for city centre location: a case study in Santiago. Habit. Int. 39, 62–74 (2013)

    Article  Google Scholar 

  • Train, K.E.: Discrete Choice Methods with Simulation, 2nd edn. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  • Varela, J.M., Börjesson, M., Daly, A.: Quantifying errors in travel time and cost by latent variables. Transp. Res. Part B Methodol. 117, 520–541 (2018)

    Article  Google Scholar 

  • Varotto, S.F., Glerum, A., Stathopoulos, A., Bierlaire, M., Longo, G.: Mitigating the impact of errors in travel time reporting on mode choice modelling. J. Transp. Geogr. 62, 236–246 (2017)

    Article  Google Scholar 

  • Villas-Boas, J.M., Winer, R.S.: Endogeneity in brand choice models. Manag. Sci. 45, 1324–1338 (1999)

    Article  Google Scholar 

  • Walker, J.L.: (2001) Extended discrete choice models: integrated framework, flexible error structures, and latent variables. Doctoral dissertation, Massachusetts Institute of Technology

  • Williams, H.C.W.L.: On the formation of travel demand models and economic evaluation measures of user benefit. Environ. Plan. 9A, 285–344 (1977)

    Article  Google Scholar 

  • Wooldridge, J.: Econometric Analysis of Cross-Section and Panel Data, 2nd edn. The MIT Press, Cambridge (2010)

    Google Scholar 

  • Wooldridge, J.: Control function methods in applied econometrics. J. Hum. Resour. 50, 420–445 (2015)

    Article  Google Scholar 

  • Yáñez, M.F., Raveau, S., Ortúzar, J. de D.: Inclusion of latent variables in mixed logit models: modelling and forecasting. Transp. Res. Part A Policy Pract. 44, 744–753 (2010)

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Universidad Francisco de Paula Santander Ocaña, Sede el Algodonal Ocaña, Colombia

    Thomas E. Guerrero

  2. Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna, 4860, Macul, Santiago, Chile

    Thomas E. Guerrero

  3. School of Engineering, Future Mobility Group, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom

    Thomas E. Guerrero & Elisabetta Cherchi

  4. Department of Civil Engineering, Instituto Sistemas Complejos de Ingeniería (ISCI), Universidad de Chile, Blanco Encalada, 2002, Santiago, Chile

    C. Angelo Guevara

  5. Department of Transport Engineering and Logistics, Instituto Sistemas Complejos de Ingeniería (ISCI), BRT+ Centre of Excellence, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860, Macul, Santiago, Chile

    Juan de Dios Ortúzar

Authors
  1. Thomas E. Guerrero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Angelo Guevara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elisabetta Cherchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Juan de Dios Ortúzar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The authors confirm contributions to the paper as follows: study conception and design: TEG, CÁG and JDO; analysis and interpretation of results: TEG, CÁG, JDO and EC; draft manuscript preparation: TEG, CÁG, JDO and EC. All authors reviewed the results and approved the final version of the manuscript.

Corresponding author

Correspondence to Thomas E. Guerrero.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11116-020-10122-y

Keywords

search

Navigation