Generalized entropy models

Objective

This project will create a new category of models that can be used for describing a wide range of spatial choice problems in the social sciences. Spatial settings often have a very large number of choice alternatives. Discrete choice models are used extensively to make counterfactual predictions based on observations of individual choices. Despite forty years of research, current spatial choice models still have two major generic short-comings that seriously limit their ability to make counterfactual predictions. The new category of models will address these two short-comings.

The first issue is that substitution patterns between choice alternatives are very complex. The new models will allow substitution patterns to be specified in a general and transparent way. The second issue is that so-called endogeneity issues are pervasive, which violates the underlying statistical assumptions of common models and leads to inconsistent results. The new models will enable endogeneity issues to be dealt with in a simple way.

The new models rely on a concept of generalised entropy and are related via duality to classical discrete choice models. A generalised entropy model, or just GEM, will be specified in terms of a transformation from choice probabilities to utilities. This idea is completely new. It is the exact opposite of classical discrete choice models and makes available a whole universe of new models. Early results suggest that GEM will enable the short-comings of the standard models to be overcome.

The project develops GEM in three prototypical spatial contexts: equilibrium sorting of households, travel demand modelling, and network route choice.

Classical discrete choice models are extensively used for policy analysis and planning. Replacing these by GEM will therefore influence a multitude of decisions across a range of sectors of great societal importance with environmental, economic and welfare consequences that reach far into the future.

Official page on cordis

Since I wrote the application, it has turned out there is a very nice connection to rational inattention. The generalized entropies can be used to construct a family of information cost functions that lead to choice models in the same way as the Shannon entropy corresponds to the multinomial logit model. With generalized entropy it is possible for the information cost to reflect that choice alternatives may be more or less similar, and similarity may be multi-dimensional.

Published papers

1. Fosgerau, M., Lindberg, P.O., Mattsson, L-G. Weibull, J. (2018) A note on the invariance of the distribution of the maximum. Journal of Mathematical Economics, Issue 74, 2018, Page(s) 56-61, ISSN 0304-4068. DOI: 10.1016/j.jmateco.2017.10.005

2. Jiang, G., Fosgerau, M., Lo, H.K. (2020) Route choice, travel time variability, and rational inattention. Transportation Research Part B: Methodological. https://doi.org/10.1016/j.trb.2019.05.020. https://www.sciencedirect.com/science/article/pii/S0191261518311433 

3. Fosgerau, M., Kristensen, D. (2021) Identification of a class of index models: A topological approach. The Econometrics Journal. Vol. 24 (1), pp. Pages 121–133.  (Open Access)

4. Fosgerau, M., Melo, E., de Palma, A., Shum, M. (2020) Discrete Choice and Rational Inattention: A General Equivalence Result. International Economic Review.  (Open access)

5. Matveenko, A. (2020) Logit, CES, and Rational Inattention. Economics Letters  (Open access)

6. Fosgerau, Sethi, Weibull. (2023) Equilibrium Screening and Categorical Inequality. American Economic Journal: Microeconomics, 2023, 15 (3), pp. 201–242.

7. Fosgerau, M., Paulsen, M., Rasmussen, T.K.. (2022) A perturbed utility route choice model. Transportation Research Part C. Vol. 136, 103514. (Open Access).  

8. Sørensen, J., Fosgerau, M.. (2022) How McFadden Met Rockafellar and Learned to Do More With Less. Journal of Mathematical Economics.  (Open access)

9.  Fosgerau, M., Melo, E., Shum, M., Sørensen, J.. (2021) Some Remarks on CCP-based Estimators of Dynamic Models. Economics Letters, Vol. 204 . (Open access) Jesper made the code available on his website.

10. Matveenko, A., Mikhalishchev, S.. (2021).  Attentional Role of Quota Implementation. Journal of Economic Theory, Vol. 198. (Open access)

11. Kristensen, D., Mogensen, P., Moon, J.M, Schjerning, B. (2021) Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods. Journal of Econometrics, Vol. 223, Issue 2, pp. 328-360.  (WP,Journal). 

12. Matveenko, A., Valei, A., Vorobyev, D. (2022). Participation quorum when voting is costly. European Journal of Political Economy, Vol. 73, 102126. (Open access).

13. Kim, D., Lee, Y-J. (2022). Vaccination Strategies and Transmission of COVID-19: Evidence across Advanced Countries, Journal of Health Economics, in press (Open access).

14. Fosgerau, M., Lukawska, M., Paulsen, M., Rasmussen, T.K. (2023) Bikeability and the induced demand for cycling. Proceedings of the National Academy of Sciences, 120 (16) e2220515120 (Open access).

15. Matveenko, A., Starkov, E. (2023). Sparking Curiosity or Tipping the Scales? Targeted Advertising with Consumer Learning. Forthcoming Journal of Economic Behavior and Organization. 

16. The Inverse Product Differentiation Logit Model. Fosgerau, Monardo, de Palma. (WP)  Conditional accept, American Economic Journal: Microeconomics.

Working papers

1. Iterative CCP estimation beyond the linear logit model. Nielsen.

2. Nontransitive Preferences and Stochastic Rationalizability: A Behavioral Equivalence. Fosgerau, Rehbeck

3. A Theory of the Perturbed Consumer with General Budgets. Fosgerau, McFadden. (WP)

4. Similarity, discrete choice and rational inattention. Fosgerau, Nielsen.  

5. Estimation of perturbed utility models using demand inversion. Nielsen, Fosgerau, Kristensen. 

6. Multidimensional Matching and Labor Market Complementarity. Andersen, Lee. (WP) 

7. A dynamic spatial equilibrium model for the housing and labor market. Andersen. 

8. A perturbed spatial equilibrium model. Andersen. 

9. The status quo and belief polarization of inattentive agents. (WP) Novak, Matveenko, Ravaioli. 

10. Optimally biased expertise. (WP) Ilinov, Matveenko, Senkov, Starkov.

Papers by other people

1. Julien Monardo explores the Flexible Inverse Logit Model. It is an instance of the IPDL. Analogue to Paired Combinatorial Logit, but estimable with regression.

2. Estimating Nesting Structures, by Ali Hortacsu, Jonas Lieber, Julien Monardo and Aureo de Paula. Uses lasso-type estimator to pick out IPDL nesting structure from a very large number of nests. In that way it deals with the  problem that the researcher has to specify the IPDL nesting structure.

3. Joonhwi Joo uses generalized entropy in a rational inattention model, where he tackles the fundamental issue that the consumer's subjective prior is unobserved. 

4. Jinghai Huo, Rubal Dua, and Prateek Bansal show that the IPDL outperforms the random coefficient logit model in an application to Chinese province level car sales data. Inverse Product Differentiation Logit Model: Holy Grail or Not?

Participants

• Jesper Riis-Vestergaard-Sørensen, UCPH

• Young-Jun Lee, UCPH

• Andrei Matveenko, UCPH

• Nikolaj Nielsen, UCPH

• Esben Scriver Andersen, UCPH

• Dennis Kristensen, UCL

• Mads Paulsen, DTU

• Thomas Kjær Rasmussen, DTU

• Stefan Mabit, DTU

Co-authors

• John Rehbeck, Ohio State

• Matt Shum, CalTech

• Emerson Melo, Indiana State

• André de Palma , ENS

• Julien Monardo, ENS Paris-Saclay and CREST

• Jörgen Weibull, SSE and TSE

• Dan McFadden, UC Berkeley 

• Per Olov Lindberg

• Lars-Göran Mattsson

• Gege Jiang

• Hong K. Lo, HKUST 

• Rajiv Sethi, Columbia University, and the Santa Fe Institute