The Temporal Stability of the NBD-Dirichlet Model Parameters

Abstract

We report on the temporal stability of the parameters of the NBD-Dirichlet model, a well-known stochastic theory of buying behaviour. This model is widely used and recommended as a stationary market benchmark against which the dynamic effects of marketing interventions can be assessed. Yet there is little work assessing how sensitive the model parameters are to minor fluctuations present in most markets most of the time, and the model’s assumption of stationarity is sometimes criticized. Using six sets of panel data from Fast Moving Consumer Goods (FMCG) markets in the UK, we assess the stability of the model’s three parameters (M, K and Phi) by generating monthly time-series of the parameters’ values, calculating coefficients of variation and fitting trend lines to the time-series. In the 18 time-series examined, we find three cases of minor non-stationarity (on the order of a 1% change per month), and one case of a moderate (rather than low) coefficient of variation. We conclude that the Dirichlet’s assumptions of stationarity in FMCG markets are largely justified.

Keywords: Dirichlet model, parameters, temporal stability, stochastic models

JEL Classification: M31, C23