arXiv subjects

Mogens Fosgerau

Publications and source records attributed to Mogens Fosgerau.

10 recordsLinked to original sources

arXiv2026

Estimating the perturbed utility route choice model with trip-level data

We provide an estimator for the perturbed utility route choice (PURC) model that works with data at the level of individual trips. The estimator is a nested fixed-point algorithm that combines an upper bias-corrected linear regression problem with a lower individual-level perturbed utility maximization problem. We establish the statistical properties of the microPURC estimator and confirm these results with an experiment using simulated data. Finally, we demonstrate the estimator in practice using a large real-world dataset.

stat.ME↗

arXiv2026

Convex Duality in Perturbed Utility Route Choice

This paper develops a highly general convex duality framework for the perturbed utility route choice (PURC) model. We show that the traveler's constrained, potentially non-smooth utility maximization problem admits a dual formulation: an unconstrained concave maximization problem with a differentiable objective. The unique optimal flow can be recovered link-by-link from any dual solution via the convex conjugates of link perturbation functions. These properties enable efficient gradient-based optimization for large-scale networks and fast computation for sensitivity analysis. Finally, the framework reveals a structural analogy between PURC and current flow in electrical circuits.

econ.TH↗

arXiv2024

Sensitivity analysis of the perturbed utility stochastic traffic equilibrium

This paper develops a sensitivity analysis framework for the perturbed utility route choice (PURC) model and the accompanying stochastic traffic equilibrium model. We derive analytical sensitivity expressions for the Jacobian of the individual optimal PURC flow and equilibrium link flows with respect to link cost parameters under general assumptions. This allows us to determine the marginal change in link flows following a marginal change in link costs across the network. We show how to implement these results while exploiting the sparsity generated by the PURC model. Numerical examples illustrate the use of our method for estimating equilibrium link flows after link cost shifts, identifying critical design parameters, and quantifying uncertainty in performance predictions. Finally, we demonstrate the method in a large-scale example. The findings have implications for network design, pricing strategies, and policy analysis in transportation planning and economics, providing a bridge between theoretical models and real-world applications.

econ.EM↗

arXiv2023

Perturbed utility stochastic traffic assignment

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We formulate the PURC equilibrium assignment problem as a convex minimization problem and find a closed-form stochastic network loading expression that allows us to formulate the Lagrangian dual of the assignment problem as an unconstrained optimization problem. To solve this dual problem, we formulate a quasi-Newton accelerated gradient descent algorithm (qN-AGD*). Our numerical evidence shows that qN-AGD* clearly outperforms a conventional primal algorithm as well as a plain accelerated gradient descent algorithm. qN-AGD* is fast with a runtime that scales about linearly with the problem size, indicating that solving the perturbed utility assignment problem is feasible also with very large networks.

math.OC↗

arXiv2023

Nontransitive Preferences and Stochastic Rationalizability: A Behavioral Equivalence

Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper shows that behavior from nontransitive preferences under a monotonicity assumption is equivalent to a transitive stochastic choice model. In particular, nontransitive preferences are regularly interpreted as a strength of preference, so we assume alternatives are chosen proportionally to the nontransitive preference. One implication of this result is that one cannot distinguish ``complementarity in attention" and ``complementarity in demand."

econ.TH↗

arXiv2022

Bikeability and the induced demand for cycling

To what extent is the volume of urban bicycle traffic affected by the provision of bicycle infrastructure? In this study, we exploit a large dataset of observed bicycle trajectories in combination with a fine-grained representation of the Copenhagen bicycle-relevant network. We apply a novel model for bicyclists' choice of route from origin to destination that takes the complete network into account. This enables us to determine bicyclists' preferences for a range of infrastructure and land-use types. We use the estimated preferences to compute a subjective cost of bicycle travel, which we correlate with the number of bicycle trips across a large number of origin-destination pairs. Simulations suggest that the extensive Copenhagen bicycle lane network has caused the number of bicycle trips and the bicycle kilometers traveled to increase by 60% and 90%, respectively, compared with a counterfactual without the bicycle lane network. This translates into an annual benefit of EUR 0.4M per km of bicycle lane owing to changes in subjective travel cost, health, and accidents. Our results thus strongly support the provision of bicycle infrastructure.

econ.EM↗

arXiv2021

A perturbed utility route choice model

We propose a route choice model in which traveler behavior is represented as a utility maximizing assignment of flow across an entire network under a flow conservation constraint}. Substitution between routes depends on how much they overlap. {\tr The model is estimated considering the full set of route alternatives, and no choice set generation is required. Nevertheless, estimation requires only linear regression and is very fast. Predictions from the model can be computed using convex optimization, and computation is straightforward even for large networks. We estimate and validate the model using a large dataset comprising 1,337,096 GPS traces of trips in the Greater Copenhagen road network.

econ.EM↗

arXiv2020

Identification of a class of index models: A topological approach

We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions characterizing the model compared to existing strategies; in particular, it does not require any large support conditions on the regressors of our model. We apply the general identification result to additive random utility and competing risk models.

econ.EM↗

arXiv2017

Discrete Choice and Rational Inattention: a General Equivalence Result

This paper establishes a general equivalence between discrete choice and rational inattention models. Matejka and McKay (2015, AER) showed that when information costs are modelled using the Shannon entropy function, the resulting choice probabilities in the rational inattention model take the multinomial logit form. By exploiting convex-analytic properties of the discrete choice model, we show that when information costs are modelled using a class of generalized entropy functions, the choice probabilities in any rational inattention model are observationally equivalent to some additive random utility discrete choice model and vice versa. Thus any additive random utility model can be given an interpretation in terms of boundedly rational behavior. This includes empirically relevant specifications such as the probit and nested logit models.

econ.EM↗

arXiv2016

Modeling the relation between income and commuting distance

We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK, and the US, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent $γ\approx 3$ and (ii) an average growing slowly as a power law with an exponent less than one that depends on the country considered. The classical theory for job search is based on the idea that workers evaluate the wage of potential jobs as they arrive sequentially through time, and extending this model with space, we obtain predictions that are strongly contradicted by our empirical findings. We propose an alternative model that is based on the idea that workers evaluate potential jobs based on a quality aspect and that workers search for jobs sequentially across space. We also assume that the density of potential jobs depends on the skills of the worker and decreases with the wage. The predicted distribution of commuting distances decays as $1/r^{3}$ and is independent of the distribution of the quality of jobs. We find our alternative model to be in agreement with our data. This type of approach opens new perspectives for the modeling of mobility.

physics.soc-ph↗