Forecasting with strategic transport models corrected for endogeneity

Abstract

The correction of endogeneity is a problem in strategic transport modelling; the question remains on how to make appropriate forecasts in this case. We propose a variation of the classical Control Function (CF) method, called Control Function Updated (CFU), which considers updating the endogeneity correction using information from the future equilibria. The proposed method is assessed using Monte Carlo simulation for a strategic transport model affected by three endogeneity sources, examining the equilibrium results for various future scenarios. We compare the CFU method by doing nothing and with the classical CF approach. The forecasts are evaluated in terms of recovering the true (simulated) travel times and two indices of fit. Results show that the endogenous (do nothing) model produces large biases in simulated travel times and poor goodness-of-fit measures that steeply worsen with time in future scenarios. The corrected models perform much better and, in particular, the new CFU approach shows statistically significant improvements over the classical approach in all scenarios tested.

KEYWORDS:

• Endogeneity
• discrete choice models
• forecasting
• control function
• strategic transport models

Acknowledgements

We wish to acknowledge the insightful comments of the Editor and four unknown referees, which helped us to improve the paper considerably. Of course, any remaining errors are our fault.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 ESTRAUS is a simultaneous equilibrium model designed to analyse and evaluate multimodal urban transport systems with multiple user classes, which has been extensively applied in Santiago and other Chilean cities.

2 We made a sensitivity analysis considering changes in the tolerance (0.1, 0.01 and 0.0001). The results showed no significant differences with the tolerance initially contemplated.

3 The t-test statistic has the form $t=\frac{\overline{X}-\mu }{sd/\sqrt{n}}$ where $\overline{X}$ is the sample mean from a sample X₁, X₂, … , X_n, of size n, sd is the estimate of the standard deviation of the population, and μ is the population mean.

4 When the sign of the parameter is known a one-sided test should be applied; the critical value of t is 1.64 for a one-sided test at the 95% confidence level.

5 Boxplots were introduced by Tukey (1977). They consist of a rectangle with bottom and topside at the 1^st and 3^rd quartile (i.e. 25^th and 75^th percentiles). The distance between the 1^st and 3^rd quartiles is known as the interquartile range (IQR). It allows getting an idea of the dispersion (accumulation) of the values drawn. Usually, they have a horizontal line added at the median (2^nd quartile or 50^th percentile), and other lines known as whiskers. They have a length 1.5 times the IQR added at the top and bottom. Observations outside of the whiskers are plotted and considered as outliers.

6 Note that the TTE reached with endogenous and corrected models could be ‘theoretically' higher or smaller than the true TTE. All this depends on the simulation conditions considered.

7 We are grateful to an anonymous reviewer for having made us look deeper into this finding.

8 AIC is a measure of the relative quality of a statistical model. It provides a trade-off between the goodness of fit of the model and its complexity (Akaike 1974).

9 We simulated a case with endogeneity only in travel time due to the equilibrium conditions (i.e., no endogeneity due to measurement error and omitted variables), so the cost was not endogenous. We found that the effect was similar but smaller than in the case with three endogeneity sources, an expected result; as there is less bias, the TTE will tend to be closer to those in the true model. So, there appears to be an additive effect regarding endogeneity sources; that is, if the endogeneity sources increase, the bias also does.

10 For the other scenarios and years, the performance is similar. We highlighted in bold the values from Table 5 used to apply the LR test.

11 Again, these values are highlighted in bold in Table 6.

Additional information

Funding

This research was partially funded by Agencia Nacional de Investigación y Desarrollo (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.