Simultaneous equation modeling of freeway accident duration and lanes blocked

• To avoid endogeneity bias, accident duration and lanes blocked are simultaneously estimated.
• Duration is modeled by the accelerated failure time models with frailty parameter distributions.
• Number of lanes blocked is modeled by the ordered response models.
• A case study of Taiwan freeway crashes shows that the simultaneous equation model outperforms.
• The existence of endogeneity has been successfully significantly tested.

Unbiased estimates are crucial to providing correct information that is required in accident management. Whereas earlier studies have proposed various approaches to reduce the adverse effects of unobserved heterogeneity, this study proposes accelerated failure time (AFT) models of accident duration with flexible distributions of the error term and the frailty parameter. A two-stage residual inclusion (2SRI) method for identifying the effects of endogenous variable in the nonlinear AFT models is adopted. The Taiwanese freeway accident databases were used to evaluate the applicability of the proposed approach. The results reveal that AFT models with a non-monotone Log-logistic error term distribution and a gamma frailty parameter distribution outperformed those with other assumed distributions. Number of lanes blocked was found as a significant endogenous variable to accident duration; the endogenous variable effect, if not accounted for or accounted by traditional two-stage least squares estimators, would underestimate the effect of the number of lanes blocked on accident duration.