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A nested logit model of strategic promotion

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Abstract

This paper presents a test of the nature of the pricing and promotion game played by supermarket retailers in a large, U.S. market. Using a nested-logit modeling approach, the results show that retailers set discount depth and promotional frequency in a manner that is less competitive than Bertrand. We also find that the elasticity of substitution among competing stores is lower than among products within each store, but not equal to zero. Therefore, sales do cannibalize existing products, but can also build a significant amount of store-traffic. Relative to strategic factors, price promotions have their greatest impact on store-conditional product demand.

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Notes

  1. Zhou (2001) offers another dynamic explanation for sales that regards regular price reductions as necessary to restore brand loyalty given its tendency to degrade slowly over time.

  2. Pauwels et al. (2002) outline a number of other ways in which promotion increases demand independent of the price effect. Impulse buying, stockpiling, purchase acceleration, learning and reinforcement are all ways in which promotions can increase demand independent of the pure price effect. In this study, we focus on the static effects of price promotion on product demand and firm rivalry in both promotional depth and breadth. Although price promotion has dynamic effects (Erdem et al., 2003) for most consumer products, because fresh produce is highly perishable, consumers are not likely to stockpile or accelerate purchases. Moreover, incorporating dynamic rivalry in a theoretically consistent way is beyond the scope of this paper. Pakes and McGuire (1994) provide a theoretical framework for specifying and estimating dynamic models for differentiated product oligopolies.

  3. A reviewer questions our choice of a nested logit model on the argument that consumers buy many different types of fruit on each shopping occasion. However, based on our analysis of a 2,718 household sample of AC Nielsen HomeScan panel data, households tend to buy a single product (UPC coded fruit) 71.9% of the time and one or two products 95.5% of the time. While this does not suggest that purchases are strictly discrete, fresh fruit is a nearer approximation at the household level than the beer data described by Slade (2004) yogurt data in Draganska and Jain (2005), both of which are estimated with discrete choice models. Villas Boas and Zhao (2005) discuss the bias that results when multiple purchases do, in fact, occur within a nested logit framework (p. 86).

  4. Aggregating promotion decisions in this way also represents an alternative approach to estimating discrete games (Bresnahan and Reiss, 1991). Estimating separate equations for each binary discount variable would not only be intractable for reasons of dimensionality, but would require a large-scale simultaneous probit model. Sequential methods could potentially be used to estimate such a system, but as Bresnahan and Reiss (1991) point out, consistent estimates of retailer conduct could not be recovered by imposing cross-equation parameter restrictions implied by the general Nash solution. McAfee (1995) also looks at multi-product retailer price dispersion this way—each retailer chooses a probability of sale rather than a particular product to promote each week.

  5. Note that the solution for ∇ n makes use of the fact that n j =E[d ij ] so the derivative of mean utility in the number of sale products is: \( \partial {\delta_j}/\partial{n_j} = \partial {\delta_j}/\partial{E(d(_{ij})=\alpha_1 + \alpha_2 p_{ij}}\).

  6. The random utility model includes three promotion-related effects: (1) an increase in utility from paying a lower price, as measured by the price elasticity, (2) a shift in demand from the “announcement effect” of a promotion, and (3) a rotation of the demand curve, estimated through an interaction term between the sale indicator and price variables. All three are implicitly assumed to be endogenous in the instrumental variables estimation technique described below.

  7. While the cross-price elasticities also consist of product, store and category components, we simplify the response-estimation procedure by using the partial cross-elasticity. Little additional information is gained by estimating responses to each cross-elasticity component.

  8. We define the GMM weighting matrix as White's (1980) consistent heteroskedastic matrix wherein the weights are variances calculated from a first-stage instrumental-variable regression.

  9. Theil's U statistic is calculated as: \({ U = \sqrt{\frac{(1/n)\sum_i(y_i-\hat{y}_i)^2}{(1/n)\sum_i y^2_i}} }\), where y i is the variable of interest and n is the number of observations in the validation data set.

  10. In the marketing literature, researchers have documented many other possible effects of price promotion. While the store-level scanner data used here is not conducive to estimating the direct effect of promotions on cross-category purchases (Ainslie and Rossi, 1998) or the cherry picking behavior documented by Fox and Hoch (2005), the nested logit model accounts for this type of behavior in an indirect way. Although the IAA property means that price changes for a particular product induce equal-proportionate responses among all other products in the same store, the nested logit scaling parameter picks up the effect of extremely price-sensitive consumers (cherry pickers) going from store to store to find the lowest price for specific products. Without household level data, however, we cannot comment on how individual behavior differs based on the opportunity to take advantage of a price promotion.

  11. Note, of course, that the cross-price elasticities with respect to all other products in the same store are identical. This is a consequence of the IIA property of the nested logit model discussed above. To the extent that these elasticities are driven by market share and not by behavioral responses, these elasticities are somewhat less interesting as estimation “results” than elasticities estimated with models that do not have the IIA property.

  12. Finding a high cross-price elasticity is not inconsistent with our assumption that produce managers set prices on a category-wide basis. In fact, we expect to find wide disparities in own- and cross-price elasticities for products that are not priced optimally on an individual basis. For example, given our empirical results, produce managers should reduce banana prices significantly in order to both raise banana revenue and attract shoppers from other stores. Doing so, however, would lower the estimated demand elasticity until it is approximately equal to that of the other products.

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Acknowledgments

The author gratefully acknowledge the financial support of the National Institute for Commodity Promotion Research and Evaluation at Cornell University and the Food Systems Research Group and at the University of Wisconsin at Madison.

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Correspondence to Timothy J. Richards.

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JEL classifications L13 · L66 · L81 · M31 · C35

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Richards, T.J. A nested logit model of strategic promotion. Quant Market Econ 5, 63–91 (2007). https://doi.org/10.1007/s11129-006-9013-1

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