A Regime-Switching Model of Cyclical Category Buying

In many categories consumers display cyclical buying: they repeatedly purchase in the category for several periods, followed by several periods of not buying. We believe that the cyclicality is a manifestation of cross-category substitution by the consumer, caused by "variety-seeking" tendencies as well as by the firm's marketing activities in all relevant categories. We propose a Markov regime-switching random coefficient logit model to represent these behaviors as stochastic switching between high and low category purchase tendencies. The main feature of the proposed model is that it divides the stream of purchase decisions of a consumer into distinct regimes with different parameter values that characterize high versus low purchase tendencies. In an empirical application of the model to purchases of yogurt-buying households, we find that as many as 38.3% households display cyclicality between high and low yogurt-purchasing tendencies. Predictions from our proposed model track observed yogurt purchases of households over time closely, and the model also fits better than two benchmark models. Alternating between high and low purchase tendencies may correspond with changing levels of consumer inventory in a substitute category. If one ignores this phenomenon, a correlation between yogurt inventory and the error term in utility arises, leading to biased estimates. Also, we show that cyclicality in buying has a key implication for a firm's price promotion strategies: a price reduction that is offered to a household during its high purchasing tendency period will result in greater increases in sales than one that is offered during its low purchasing period. This opens up a new dimension for enhancing the effectiveness of promotions--customized timing of price reductions.