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K=1 ln AIt µI βk1I the natural logarithm of attraction becomes     βk21 . . βkI1  ln zk1t ε1t βk22 . . βkI2    ..   ..  +     .  ... ... 30) βk2I . . βkII K Bk ln zkt + εt . 29) implies that ln Mit = ln Ait − ln vector notation this gives   ln M1t I   ln Mt :=  ...  = ln At − iI ln Ajt , I j=1 Ajt . 31) j=1 ln MIt where iI denotes a (I × 1) unity vector. 31) cannot be estimated directly due to the nonlinear dependence of ln( Ij=1 Ajt ) on the model parameters, a reduced-form model should be considered.

The total number of brands in the market, after the introduction, will be denoted by I. So, before the introduction we have brands i = 2, 3, . . , I and after the introduction we have the brands i = 1, 2, . . , I. Following Cooper and Nakanishi (1988), the overall attraction of brand i = 2, . . , I at time t = 1, . . 3 Attraction Model 45 see also Chapter 2. As usual, xkjt denotes the k-th marketing instrument of brand j at time t, and the parameter associated with the effect of this instrument on brand i is denoted by βkji .

Vec[T Σ  .. 49) and ˜ −1 ) ˜ ∂vec(Σ ˜ −1 ) = −(Σ ˜ −1 ∂ Σ Σ ˜ −1 )2ii ei,I−1 = vec(−Σ ∂σi ∂σi   ηˆ1 ˜ 1 ∂ (Σ) .  η , . . , ηˆ )(Σ ˜ −1 )2 ei,I−1 ] ˜ Σ ˜ −1 )2 ei,I−1 +  = tr[−T Σ(  .. 50) where eik is a zero vector of size (k × 1) with the i-th element equal to 1. 51) ˆI2 . 48). The concentrated likelihood now has to be optimized over just one parameter, that is σI . 1 Introduction The introduction of a new brand in an existing market can have a large impact on the competitive structure, which concerns the market shares, the marketing instrument elasticities (as established by consumer behavior) and the use of marketing-mix instruments by brand managers.

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