Nested logit and GEV models

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Nested logit and GEV models

• Example Demand for Pharmaceuticals,
  anti-inflammatory drugs

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Anti-inflammatory drugs

• Level1AEddiksyrederivater
• Level AkConfortid, Indocid,,,,,
• Level 1B Oksikamer
• Level BkBrexidol,,,,
• Level 1C Propionsyrederivater
• Level Ck Iboprofen,Naproxen,,,
• Level 1DKoksiber
• Level Dk Celebra,,,

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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

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Other examples

• Travels public or private
• Given public train, bus or airplane
• Given private own car or rental car

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Other examples

• Wine from Spain or Italy
• Given Spain what brand
• Given Italy what brand

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Why nested logit

• A natural tree decision structure
• Within one branch, correlation across
  alternatives (with drugs, sideffect may be
  correlated)
• No correlation across branches

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Software programs

• Stata, not so good,
• SAS seems ok
• Gauss, of course
• TSP also good
• LIMDEP, perhaps

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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

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Then if
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• 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

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Example 1

• Multinomial Logit

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Example 2

• A nested structure
• Two branches,
• In branch 1, one alternative
• In branch 2, two alternatives, with correlations
  in the tasteshifters

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Choice probailities

• The GEV model

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Derivaties and elasticities

• The nested- or rather the corrlation structure-
  has a strong impact on the price elasticities

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Nested logit.

• Ujkvjk?jk
• j indicates upper level (Level 1 Groups of
  pharmaceutical, Lj)
• k indicates drugs at lower level
• k?Lj
• We will use the GEV structure

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Two stage version of nested logit
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The Likelihood
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