# A numerical estimation method for discrete choice models with non-linear externalities

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A numerical estimation method for discrete choice models with non-linear externalities
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numerical estimation method for discrete choice modelswith non-linear externalities. Ugo Gragnolati, Giulio Bottazzi and Fabio Vann i Scuola Superiore Sant'Anna di Pisa   IWcee14 International Workshop on Computational Economics and Econometrics The Socio-Economics of Networks: Theory and Applications  Rome , June 26th 2014  2 OUTLINE Numerical estimation of parameters and development of algorithms and computational calculations (M  TL B  oriented codes with a toolbox under development) : ● ( Topics ) Stochastic discrete choice model where individual choices are determined by intrinsic features of the object of choice and by the choices of other individual (externalities). ● ( Model ) Introduction of a framework to carry out inferential analysis on the parameters. Detect the presence of non-linear externalities. ● ( Methods ) Numerical study for the estimation of the parameter and evaluation of their statistical significance. Limits and advantages of some computational methods. ● ( Applications ) The inferential analysis are applied to the case of firm localization detect whether the localization of firms across commuting zones shows non-linear externalities.  3 The Discrete Choice Model and a Non-Linear Extension  4 General Overview   ● A variety of individual choices are determined by intrinsic features of the object as well as by choice of other individuals. ● Examples: Consumers buy a product on the basis of qualities of the product and as a function of the number of other consumer possessing the product. ● Social medias with consumers preferences ● Firm choosing a place for localization on the base of geographic characteristics also taking in account of the presence of other firms in the area. ● In general – interdependencies in the decisions of agents: the number of agents making a certain choice contributes to determining how many other agents will make the same choice.  5 Discrete Choice Model ● The interdpenendencies can be captured by treating individual utility as a function of the other agents' choices. ● The probability that an agent chooses a certain alternative will be a function of the fraction of agents that have already chosen that same alternative together with its intrinsic features. ● Class of stochastic models within the “generalized” Polya Urn Schemes in particular modified version of a Markov process known in physics as Ehrenfest-Brillouin mdodel ( G. Bottazzi and A. Secchi. LEM-WP September 2007, Bottazzi et. Al 2008 ). ● Description in terms of time evolution of the process, with a equilibrium distribution.

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