Estimating Cannibalization

Cannibalization of own assortment is a general concern to many retailers when introducing new products. The focus of this study is estimating the cannibalization effect in terms of change in discrete choice probability pre- and post-introduction. We use an MCMC Gibbs sampler to estimate individual-specific brand preference and sensitivity to marketing decision variables specified by the Multinomial Probit (MNP) model. Estimates for these parameters are then used to simulate choice probabilities by means of the GHK simulator. Given that the MNP model notoriously suffers from identification issues, we compare two different iden­tifying model specifications, each placing a different restriction on the covariance matrix of errors. The element-restricted model fixes just one parameter of the diagonal of this matrix, while the trace-restricted model fixes the trace of the matrix. We evaluate both methods in a simulation study and conclude that trace-restricted model outperforms the element-restricted model in overall model-fit, although the element-restricted model has slightly better predic­tive accuracy. We then apply the trace-restricted model to empirical sales data containing a new product introduction in the laundry detergent category. This approach allows one to observe changes in competitive structure as well as changes in sensitivities to marketing decision variables in the face of new product introductions.