Forecasting market shares from models for sales
Introduction
Market researchers often focus on modeling and forecasting marketing performance measures, such as brand choice and interpurchase times at the individual household level and sales and market shares at the aggregated level (see e.g. Leeflang, Wittink, Wedel and Naert (2000) and Franses and Paap (2001) for recent surveys). Household-specific data usually concerns cross sections or panels, while aggregated data often concerns weekly or monthly time series observations. Cross-sectional or panel data have the advantage that the effects of marketing instruments can be observed at the individual level, while a potential disadvantage is that often one needs to account for unobserved heterogeneity across households. In contrast, time series observations do not suffer from such heterogeneity, but there it is only possible to draw inference at the aggregate level and one has to take account of possibly complicated dynamic patterns.
Here the focus is on forecasting market shares at the brand level. Indeed, market shares can be of particular interest, as shares automatically imply that a manager can evaluate the sales performance relative to the performance of the product category. Also, market shares are less sensitive to the impact of growth and seasonal fluctuations. One obvious question is whether one should construct a quantitative model for market shares using, for example, the familiar attraction model (see Brodie & Kluyver, 1987; Kumar, 1994), or that one should construct a model for sales using for example the scan∗pro model (see Wittink, 1987; Wittink, Addona, Hawkes & Porter, 1988; Foekens, Leeflang & Wittink, 1994; Van Heerde, Leeflang & Wittink, 2000). In the latter case one can then use these models to generate sales forecasts and, given these, forecasts of market shares.
In this note we will confine ourselves to the question how one can generate forecasts for shares given models for sales, as this turns out not to be a trivial exercise. We will indicate that simply dividing brand sales forecasts by category sales forecasts, which seems to be common practice, yields biased forecasts for market shares. Hence, one needs to resort to an alternative method. We propose a simulation-based method to obtain unbiased forecasts. Simulation-based methods have become increasingly more common in models for marketing performance measures such as brand choice and interpurchase times (see e.g. Allenby & Rossi, 1999; Bronnenberg, Mahajan & Vanhonacker, 2000).
The outline of this paper is as follows. In Section 2, we discuss two methods for forecasting market shares given models for sales. The first method is the above-mentioned division of forecasts, which will be called the naive method, and the second is the more appropriate simulation based method, denoted by SB. In Section 3, we illustrate the practical relevance of the SB method for an example concerning five brands of tuna fish. In Section 4, we conclude with some remarks.
Section snippets
Forecasting market shares
Suppose that there are I brands in a certain product category, and suppose the availability of weekly scanner data on sales and various explanatory variables. One possible form of a sales model assumes a multiplicative specification to relate explanatory variables such as promotion and price to current sales (see, for example, Wittink et al., 1988), although other forms are of course also possible (see Leeflang et al., 2000). The sales of brand i, i=1,…,I at time t, t=1,…,T, denoted by Si,t,
Illustration
The two forecasting methods discussed in the previous section are illustrated using a multiple-equation model for the sales of five brands of tuna fish1. The data involve 52 weekly observations, concerning sales and actually paid prices, amongst other variables. Since our interest does not necessarily lie in the most adequate model for these variables, we
Some concluding remarks
In this paper we proposed a simulation-based method to generate forecasts for market shares in case one is interested in using econometric models to correlate sales with explanatory variables. The method has various advantages over the naive forecasting method that transforms forecasted sales to market share forecasts. First it yields unbiased forecasts. Second it facilitates the calculation of, logically consistent, possibly asymmetric, confidence regions around the forecasts. Finally, the
Acknowledgements
A computer program, which was used for all calculations in this note, can be obtained from the corresponding author. More detailed estimation results appear in the companion working paper, which is distributed as report ERS-2000-03-MKT of the Erasmus Research Institute of Management (www.erim.eur.nl). We thank the Editor, an anonymous Associate Editor and two anonymous referees for helpful suggestions.
Biography: Philip Hans FRANSES is Professor of Applied Econometrics and Director of the Rotterdam Institute of Business Economics, both at the Erasmus University Rotterdam. His research interests include modeling time series, with a specific focus on seasonality, outliers, and forecasting.
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Biography: Philip Hans FRANSES is Professor of Applied Econometrics and Director of the Rotterdam Institute of Business Economics, both at the Erasmus University Rotterdam. His research interests include modeling time series, with a specific focus on seasonality, outliers, and forecasting.