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# March 2008 - page 11 / 39

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Patients are assumed to be administered one regimen at a given time, which maximizes their utility. This implicitly defines a region of the unobserved term for which alternative j yields a higher utility than any other alternative k

Ajt = {εit|uijt

u

i k t k =6

j}

The market shares for each regimen j can be obtained by aggregating the individual preferences over the region Ajt

σ j t = Z A t d P ( ε )

If ε is assumed to be drawn from the extreme value distribution, the integral can be computed analytically:

σjt =

1+

exp(

J k=1 t

p j t + β x j t + ξ j +

ξ j )

exp(

p k t + β x k t + ξ k

+

ξ k )

W e d e fi n e t h e m e a n u t i l i t y l e v e l δ j t =

p j t + β x j t + ξ j +

ξ j , a n d t h e r e f o r e ,

t h e m a r k e t s h a r e s c a n b e w r i t t e n a s t h e f u n c t i o n σ j t ( δ t ) , w i t h of mean utilities at time t. δ t

being the vector

T h e m a r k e t s h a r e s p r e d i c t e d b y t h e m o d e l σ j t ( δ t ) a r e t h e n m a t c h e d w i t h t h e o b s e r v e d m a r k e t s h a r e s s j t . B e r r y ( 1 9 9 4 ) s h o w s t h a t δ j c a n b e u n i q u e l y i d e n t i fi e d b y i n v e r t i n g t h e m a r k e t s h a r e f u n c t i o n σ 1 ( s t ) = δ t . F o r t h e l o g i t m o d e l , inversion yields t h e

ln sjt

ln s0t =

p j t + β x j t + ξ j

+

ξ j

Because the unobserved drug regimen characteristics are likely to be correlated with price, the estimation of the equation above requires the use of instrumental variables. We obtain our instruments by using the supply side market equilib- rium conditions. Because price is a function of marginal cost and markups, any exogenous variable that shifts marginal costs or markups is a good instrument. We follow Bresnahan et al. (1997) and use the number of products in the market

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