Control Function Approach for Addressing Endogeneity in Transport Models: A Case Study on the London–Amsterdam Route

Endogeneity is a key empirical challenge in transportation modeling, which may lead to inconsistent estimates and biased policy decisions. This paper investigates the sources of endogeneity and focuses on tackling this issue for a discrete choice model analyzing the multimodal London–Amsterdam route, where air transport and high-speed rail (HSR) compete. Contrary to previous literature, we found no evidence of endogeneity in service frequency for the London–Amsterdam market. This could be attributed to market-specific features, such as feeding considerations, slot retention dynamics, and the congestion of the HSR network, which constrains capacity expansion opportunities. Conversely, we observed that fare introduced endogeneity into the model. To address this issue, we applied the control function approach and proposed two novel instruments: the fare for similar markets and the price of power sources. These instruments proved to be effective in correcting for endogeneity by increasing model performance. We also discuss the adverse impact of neglecting endogeneity and estimate price and frequency elasticities, ultimately demonstrating the significance of dealing with endogeneity in ensuring the reliability of results in transportation studies and appropriately informing policy decisions.