Investigating the Properties of the Eskin/Kalwani & Silk
Model of Repeat Buying for New Products

Peter S. Fader
Bruce G.S. Hardie

Lutz Hildebrandt, Dirk Annacker, and Daniel Klapper (eds.)
Marketing and Competition in the Information Age
Proceedings of the 28th EMAC Conference
May 11-14, 1999
Berlin: Humboldt University


A key component of any new product sales forecasting model is that which captures the number of repeat purchases made by each household over time. When modeling repeat sales, it is very common to use the so-called "depth-of-repeat" formulation which decomposes repeat sales into the number of consumers that have made at least 1, 2, 3, ... repeat purchases. Perhaps the best known depth-of-repeat model is a remarkably parsimonious framework proposed by Eskin (1973) -- and further developed by Kalwani and Silk (1980) -- that has been used in various academic and commercial settings.

Despite the historical popularity of the Eskin/Kalwani & Silk (E/KS) model, very little is know about its properties. This paper provides validation evidence for the model, using a simulation-based approach to examine its capabilities across a wide variety of realistic market situations.

After briefly reviewing the E/KS model, we first examine its ability to provide insights into the structure of the repeat buying process. In a series of simulations for a simple stationary market, we show that the model fares very poorly in this regard. In sharp contrast, we show that the forecasting performance of the model, even under data conditions that include different types of nonstationarity, is quite impressive. We systematically vary three factors (length of calibration period, purchase cycle (fast vs. slow), and degree of consumer heterogeneity), and find that the week 52 E/KS forecasts are remarkably robust. As expected, forecast accuracy improves significantly as more data are available to fit the model, but variations in the other two factors lead to relatively modest differences, as measured by the absolute percentage error in the year-end sales estimates as well as a measure of forecast bias.

We close with a brief examination of the simulated markets with the worst forecasts, observing that they tend to be associated with highly unsuccessful products (i.e., those with the strongest degree of consumer rejection). Other conclusions and future research directions are summarized as well.