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# Modeling the relation between income and commuting distance

## Author

Listed:
• Giulia Carra

(IPHT - Institut de Physique Théorique - UMR CNRS 3681 - CNRS - Centre National de la Recherche Scientifique - Université Paris-Saclay - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

• Ismir Mulalic

(DTU - Technical University of Denmark [Lyngby])

• Mogens Fosgerau

(DTU - Technical University of Denmark [Lyngby])

• Marc Barthelemy

(CAMS - Centre d'analyse et de mathématique sociale - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, IPHT - Institut de Physique Théorique - UMR CNRS 3681 - CNRS - Centre National de la Recherche Scientifique - Université Paris-Saclay - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

## Abstract

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 $\gamma \approx 3$ 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.

## Suggested Citation

• Giulia Carra & Ismir Mulalic & Mogens Fosgerau & Marc Barthelemy, 2017. "Modeling the relation between income and commuting distance," Post-Print cea-01568435, HAL.
• Handle: RePEc:hal:journl:cea-01568435
DOI: 10.1098/rsif.2016.0306
Note: View the original document on HAL open archive server: https://hal-cea.archives-ouvertes.fr/cea-01568435
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File URL: https://hal-cea.archives-ouvertes.fr/cea-01568435/document

## Citations

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Cited by:

1. Eliasson, Jonas & Fosgerau, Mogens, 2017. "Cost-benefit analysis of transport improvements in the presence of spillovers, matching and an income tax," Working papers in Transport Economics 2017:3, CTS - Centre for Transport Studies Stockholm (KTH and VTI).

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