Nested logit and GEV models

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

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

3. 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,,,

4. 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

5. Other examples • Travels; public or private • Given public; train, bus or airplane • Given private; own car or rental car

6. Other examples • Wine; from Spain or Italy • Given Spain; what brand • Given Italy; what brand

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

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

9. 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

10. Then if

11. 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

13. Example 1 • Multinomial Logit

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

21. Choice probailities • The GEV model

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

26. 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:

29. Two stage version of nested logit

32. The Likelihood