Measurement of own-and cross-price e ff ects

The accurate measurement of ownand cross-price effects is difficult when there exists a moderate to large number of offerings (e.g., greater than fi ve) in a product category because the number of cross-effects increases geometrically. We discuss approaches that reduce the number of uniquely estimated effects through the use of economic theory, and approaches that increase the information contained in the data through data pooling and the use of informative prior distributions in a Bayesian analysis. We also discuss new developments in the use of supply-side models to aid in the accurate measurement of pricing effects. Introduction The measurement of price effects is difficult in marketing because of the many competitive offerings present in most product categories. For J brands, there are J2 possible effects that characterize the relationship between prices and sales. The number of competitive brands in many product categories is large, taxing the ability of the data to provide reliable estimates of ownand cross-price effects. A recent study by Fennell et al. (2003), for example, reports the median number of brands in 50 grocery store product categories to be 15. This translates into 225 ownand cross-effects that require measurement in the demand system. Structure-imposing assumptions are therefore required to successfully estimate price effects. At one end of the spectrum, a pricing analyst could simply identify subsets of brands that are thought to compete with each other, and ‘zero-out’ the cross-effects for brands that are assumed not to compete. While this provides a simple solution to the task of reducing the dimensionality of the measurement problem, it requires strong beliefs about the structure of demand in the marketplace. Moreover, this approach does not allow the data to express contrary evidence. Alternatively, one might attempt to measure directly all J2 ownand cross-price effects. However, it is quickly apparent that using a general rule of thumb that one should have n data points for each effect-size measured rules out the use of most commercially available data. Using weekly sales scanning data and the rule that n 5 5 results in the need for 20 years of data in food product categories such as orange juice or brownies. One could also engage in the generation of data through experimental means, using surveys or fi eld experiments. The data requirements, however, remain formidable. We discuss approaches to measuring price effects that rely on modeling assumptions to (i) reduce the number of the effects being measured; and/or (ii) increase the information available for measurement. We begin with a brief review of economic theory relevant to price effects, and then discuss the use of economic models to measure them. We then turn our attention to approaches that increase the available information. These approaches are Bayesian in nature, with information being available either through prior information or from data pooled from other sources. We provide a brief review of modern Bayesian 62 Handbook of pricing research in marketing methods for pooling data, including the use of hierarchical models, and models that incorporate the price-setting behavior of fi rms (i.e. supply-side models). We conclude with a discussion of measuring price effects in the presence of dynamic effects and other forms of interactions. 1. Economic models for pricing According to economic theory, own-price effects should be negative and cross-price effects should be positive for competitive goods. As the price of a brand increases, its own sales should decline. As the price of a competitive brand increases, sales should increase. A commonly encountered problem in the use of regression models for measuring price effects is that cross-effects are often estimated to have the wrong algebraic sign – i.e. they are estimated to be negative when they should be positive. Similarly, but less often, ownprice effects are estimated to be positive when they should be negative. When price effects estimates have erroneous signs and large standard errors, a pricing analyst may be tempted to zero them out and re-estimate the remaining effects as described above. However, doing so imposes strong assumptions about the competitive nature of demand – it means that price of one brand has no effect on another brand, for any price, including zero. While approaches such as Bayesian variable selection (George and McCulloch, 1993) help quantify uncertainty in specifi cation searches (Leamer, 1978) such as this, they require the strong assumptions that some of the effect-sizes have a prior probability of being zero. The assumption of a zero effect is often untenable, especially when deriving estimates from aggregate sales data where at least some customers will react to the price change. So, while the practice of setting coefficients to zero solves the problem of incorrectly signed estimates, it does so by imposing somewhat unbelievable assumptions about the structure of demand. An alternative approach is to employ economic theory to avoid the direct estimation of the J2 price effects. As with any theory, the use of an economic model reduces the dimensionality of the effects through model parameters. Economic models of behavior are based on the idea of constrained utility maximization: Max x U(x1,. . ., xJ ) 5 a J