Periodic Reporting for period 4 - GEM (Generalised Entropy Models for Spatial Choices)
Reporting period: 2022-03-01 to 2023-06-30
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, the currently used 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.
This project will develop 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.
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.
This project will develop 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.
The first main contribution so far is a model and related estimation procedures that can be used to predict the demand for differentiated products, the Inverse Product Differentiation Logit (IPDL) model. A "product" can be many different things. The main feature is that the researcher needs access to market share data and that products can be segmented along a number of dimensions. In that case, the IPDL model is available. It is estimable using simple methods, it is very fast and can handle very large models. It facilitates dealing with endogeneity or reverse causality, as occurs for example when prices are responsive to demand.
The second main contribution is the discovery that rational inattention discrete choice models can be based on generalised entropy and that generalised entropies exist such that the predicted demand of the rational inattention model may have the form of any additive random utility discrete choice model. This is important in several ways. First, the result opens for the reinterpretation of existing discrete choice models. The conventional discrete choice model treats consumers as perfectly utility maximising and having perfect information regarding all choice alternatives. These assumptions are unreasonable but needed to make progress. Now we can relax the assumptions while still using the same models. Second, we now have also the possibility of using new models that take into account the effects of inattention. This can be important for describing phenomena that are difficult to describe using conventional models. In particular, we can now better think about consideration sets in different settings and explain how these may emerge within the framework of the model.
The third main contribution is a generalised entropy model for network route choice, which can be based on very large transport networks and use travel data aggregated to the level of origin-destination pairs. It allows data to be used with very high resolution, the model can be estimated with plain linear regression in short time, it allows that most of the network is unused for any specific origin-destination pair, and it predicts substitution patterns directly generated by the network structure. These points in conjunction make it fair to consider the new route choice model a major breakthrough in the area of route choice modelling.
The second main contribution is the discovery that rational inattention discrete choice models can be based on generalised entropy and that generalised entropies exist such that the predicted demand of the rational inattention model may have the form of any additive random utility discrete choice model. This is important in several ways. First, the result opens for the reinterpretation of existing discrete choice models. The conventional discrete choice model treats consumers as perfectly utility maximising and having perfect information regarding all choice alternatives. These assumptions are unreasonable but needed to make progress. Now we can relax the assumptions while still using the same models. Second, we now have also the possibility of using new models that take into account the effects of inattention. This can be important for describing phenomena that are difficult to describe using conventional models. In particular, we can now better think about consideration sets in different settings and explain how these may emerge within the framework of the model.
The third main contribution is a generalised entropy model for network route choice, which can be based on very large transport networks and use travel data aggregated to the level of origin-destination pairs. It allows data to be used with very high resolution, the model can be estimated with plain linear regression in short time, it allows that most of the network is unused for any specific origin-destination pair, and it predicts substitution patterns directly generated by the network structure. These points in conjunction make it fair to consider the new route choice model a major breakthrough in the area of route choice modelling.
The project is on track to deliver a new kind of models that will have application for the description and prediction of consumer demand in a wide range of settings. The models will be able to describe demand in which the substitution between products is governed by similarity, expressed in terms of distance in a space of characteristics. A range of methods for estimating these models will be available.
The project will furthermore contribute to understanding the role of inattention in forming behaviour. This relates not only to consumer choices but also to wider issues such as stereotyping and discrimination.
The project will furthermore contribute to understanding the role of inattention in forming behaviour. This relates not only to consumer choices but also to wider issues such as stereotyping and discrimination.