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Article Excerpt
Retailers and manufacturers believe that the mere presence of certain items in a retail assortment increases the sales volume of the whole assortment. This paper provides an empirical study of the role of every item in an assortment. Our results show that many items affect category sales over and above their own sales volume. After deconstructing the role of a stockout of individual items into three effects--lost own sales, substitution to other items, and the category sales impact--we find that the category impact has the largest magnitude. Interestingly, the disproportionate impact of individual items on category sales is not restricted to top-selling items, for almost every single individual item affects category sales. It seems that variety is indeed the price of entry in retailing. Our results support recent findings that more frequently purchased categories are less adversely affected by reductions in assortment. We also find that the assortment appears to gain attractiveness when certain items are out of stock, a result that is consistent with the discussion in the literature concerning category clutter.
Key words: apparel retailing; retail assortment; category management; out-of-stocks; substitution; key items; hierarchical Bayes; COM-Poisson
1. Introduction
In retailing, one of the most important decisions is the selection of items to inventory. Items not only generate profits directly by their own sales, but items also are interrelated within categories and indirectly contribute to category volume. For instance, individual items can serve as buffer inventory (purchased as substitutes when preferred items are temporarily out of stock) or as alternatives for variety seekers, and the collection of inventoried items helps craft the visual presentation of the retailer and affects the store image (e.g., a wide assortment category killer). Therefore, retail inventory decisions involve more than sales projections of individual items.
Considering the contribution of an item to category sales volume, the presence or absence of any individual item in a category can contribute in one of three ways. First, an item contributes its own sales volume to the category. Second, the absence of an item can affect sales of other items, in that remaining in-stock items can serve as alternatives when a more preferred item is temporarily out of stock (A. C. Nielsen 2005, Anupindi et al. 1998). Third, the presence of an individual item may impact sales of the entire category over and above the sales of the item itself, possibly by drawing attention to the category, improving the presentation, and stimulating the category sales overall (Berlyne 1960, Koopmans 1964, Kahn and Lehmann 1991, Kahn 1995).
The contribution of this research is a model that deconstructs every item's category contribution, using out-of-stocks in an apparel category. In apparel categories, items within a collection are typically from the same manufacturer and are priced identically within a time period. The lack of price variation prohibits use of typical utility models, because these models mine variation in prices to infer consumer preferences. However, out-of-stocks induce variation in the assortment, and the model that we develop utilizes the variation in product assortment to infer consumer preferences. The out-of-stocks can be viewed as natural experiments, and they can (1) result in lost sales, (2) lead to substitution to other items, and (3) impact the sales of the entire category due to a temporary change in the available selection. A key contribution of this research is the simultaneous modeling of all three effects for every item at the store level, using data with assortment variation but no price variation. The state space of out-of-stocks can be complex, and our model provides a parsimonious approach compared to utility-theoretic approaches (Kim et al. 2002, Kalyanam and Putler 1997).
One of our major findings is that out-of-stocks of many items, in addition to affecting own sales, significantly affect the sales of the entire set of remaining items in the category. A few important items such as navy-large have large impacts on category sales. Additionally, items with relatively large category impacts are not necessarily top sellers. The item tan-extra large ranks as one of the top five items in terms of overall category impact, but it only ranks a 10 in terms of sales. Our findings suggest that retailers should look beyond marketing tactics such as category advertising (Bass et al. 2005) to the role of key items in stimulating category demand.
A simulation analysis based on our model estimates shows that although a few key items have a very high impact on category sales, the out-of-stocks of many other items also depress category sales. It seems that after all, as speculated upon by others (Hoch et al. 1999), variety is indeed the price of entry in retailing despite the fact that only a few items are best sellers. A second set of findings is with regard to substitution. Although substitution proportional to share is a common assumption in the literature, our results show that substitution is not widespread, is limited to only a few colors, and can be asymmetric. Consistent with intuition, there is very little substitution across sizes.
There are theoretical foundations for why the absence of any item can increase or decrease the demand for the entire category over and above the item's own sales. First, each individual item might contribute to the variety within the assortment (Hoch et al. 1999), and a loss of variety would reduce the desirability of the assortment for consumers with uncertain preferences (Koopmans 1964, Reibstein et al. 1975, Kreps 1979, Kahn and Lehmann 1991) and for those who tend to seek variety (Berlyne 1960, Helson 1964, McAlister and Pessemier 1982, Kahn 1995). Second, retailers work to maintain aesthetically pleasing displays of categories in order to attract consumers; out-of-stocks may erode the aesthetic value of the category presentation, which is the so-called "broken assortment" effect (Smith and Achabal 1997). Both of these reasons support the conclusion that out-of-stocks of an item would lessen category demand over and above own sales.
There is also a theoretical foundation for a result in which some out-of-stocks would increase category demand. Reasons why purchase amounts would increase after deletion of nonfavorite items include the elimination of clutter (Boatwright and Nunes 2001, Borle et al. 2005). In addition, Iyengar and Lepper (2000) demonstrated that choosing among too many items is demotivating and can reduce sales. In light of the relationship of individual items and category sales, retailing textbooks (Levy and Weitz 2004, p. 420) advise readers to take into account the impact of an item on the overall assortment, although these texts do not provide any guidance on the magnitude of these effects or how they should be identified.
The empirical study of out-of-stock data requires careful attention to model specification. In retail sales data, concurrent stockouts of multiple items can occur in periods of high demand. The simultaneity of stockouts and periods of high demand can lead to a positive stockout coefficient implying that a stockout can actually increase sales of the item! We control for demand shocks and concurrent stockouts using a simultaneous equations approach, estimating the joint distribution of sales and stockouts in a hierarchical Bayes model. Manchanda et al. (2005) present a similar modeling approach in a different context. We find that a naive model, one that does not account for this joint distribution, yields coefficients with the wrong signs on the stockout variable.
Another characteristic of retail sales data for apparel categories is that unit sales for each item at the store level are sparse. For example, in our data set, 3.6 units of each item were sold per store in each time period. In addition, stockouts occur in any time period with probability less than 0.03, leaving little information at the store level to estimate item- and store-specific parameters. We therefore utilize a hierarchical model that shares information across stores. Additionally, our model allows for over- or underdispersion relative to the common Poisson sales model. We also model substitution in a flexible manner, without imposing the independence of irrelevant alternatives (IIA) restriction of switching proportional to share.
Our research contributes to the existing research on the effects of out-of-stocks. Anupindi et al. (1998) developed a model that used Information on stockouts to infer item demand and substitution patterns; they found significant differences between demand rates and observed sales of products even for items that were rarely out of stock. We extend their work by estimating not only substitution and lost sales, but by also estimating which items, if any, affect sales of the entire category. Anupindi et al. (1998) contains a thorough discussion of prior models that incorporate stockouts, which did not measure substitution effects or quantify the impact of individual items on category sales.
Our paper also contributes to the growing research on how consumers make choices within assortments and respond to changes in assortments. Lattin and Roberts (1992) measured how the structure of a category affects product selection. We consider the opposite directional effect, how the presence of individual products affects purchase in the category. Kim et al. (2002) use price variation to infer item utilities and substitution, whereas we use the variation in the in-stock items to deconstruct each item's absence into own sales, substitution, and a category effect.
Borle et al. (2005) assessed the impact of a large-scale reduction in assortment on store sales, and found a decline in store sales. Prior work had found the sales impact of assortment reductions to be small (Dreze et al. 1994, Broniarczyk et al. 1998, Boatwright and Nunes 2001). These previous studies all measured the impact of permanent and simultaneous elimination of multiple items from frequently purchased grocery categories, using experimental data or household data. Our paper examines these effects in the context of an infrequently purchased and discretionary apparel category. We use store-level data with out-of-stock information, a type of data that is more readily accessible to retailers.
Our research also builds on and contributes to the literature on measuring the variety of an assortment. Category assortment is known to affect store visits (Borle et al. 2005), an issue even more critical to supermarkets in light of the growth of Walmart (Singh et al. 2006). Hoch et al. (1999) used the information structure of a category to provide models of perceived variety. We empirically infer the contribution of each item on the attractiveness of an assortment, showing how the temporary absence of even small-share products disproportionately affects category sales. We formulate an assortment attractiveness index that changes when individual items are out of stock. The assortment attractiveness index allows us to study the differential effects of colors and sizes on the attractiveness of the assortment using actual sales, as opposed to perceptions of variety.
The rest of this paper is organized as follows: In the next section ([section] 2) we describe the data, in...
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