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This document explores the application of Nested Logit and Generalized Extreme Value (GEV) models in analyzing the demand for pharmaceuticals, particularly anti-inflammatory drugs. It discusses various drug categories (Level 1A to Level 1D) and illustrates how these models account for correlation within alternatives while maintaining independence across branches. Additionally, it provides insights into the implications for choice probabilities, elasticities, and relevant software for modeling. The analysis includes examples of consumer choices in different scenarios to highlight the practical utility of these models.
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Nested logit and GEV models Example: Demand for Pharmaceuticals, anti-inflammatory drugs
Group 2 Group 1 Drug 11 Drug 12 Drug 13 Drug21 Drug22
Anti-inflammatory drugs • Level1A:Eddiksyrederivater: • Level Ak:Confortid, Indocid,,,,, • Level 1B: Oksikamer • Level Bk:Brexidol,,,, • Level 1C: Propionsyrederivater • Level Ck: Iboprofen,Naproxen,,, • Level 1D:Koksiber • Level Dk: Celebra,,,
Other examples • To evade taxes or not • Given evasion, how many hours of work in regular and irregular jobs • Given no tax evasion, how many hours of work in regular jobs
Other examples • Travels; public or private • Given public; train, bus or airplane • Given private; own car or rental car
Other examples • Wine; from Spain or Italy • Given Spain; what brand • Given Italy; what brand
Why nested logit • A natural tree decision structure • Within one branch, correlation across alternatives (with drugs, sideffect may be correlated) • No correlation across branches
Software programs • Stata, not so good, • SAS seems ok • Gauss, of course • TSP also good • LIMDEP, perhaps
The generalized extreme value model: GEV • G is homogenous of degree 1 • The kth partial derivative of the G-function exist, is continuous, non-negative if k is odd, and non-positive if k is even, and
is a multivariate distribution function, the choice probabilities that result from the maximization of the random utilities for which the multivariate distribution function is given by F(.) are equal to
Example 1 • Multinomial Logit
Example 2 • A nested structure • Two branches, • In branch 1, one alternative • In branch 2, two alternatives, with correlations in the tasteshifters
Choice probailities • The GEV model
Derivaties and elasticities • The nested- or rather the corrlation structure- has a strong impact on the price elasticities
Nested logit. • Ujk=vjk+jk • j: indicates upper level (Level 1: Groups of pharmaceutical, Lj) • k: indicates drugs at lower level • kLj • We will use the GEV structure:
