Nested logit and GEV models Example: Demand for Pharmaceuticals, anti- inflammatory drugs

Drug 11 Drug 12 Drug 13 Drug21 Drug22 Group 1 Group 2

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

Then if

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 k  Lj We will use the GEV structure:

Two stage version of nested logit

The Likelihood