Sales and consumer inventory.

Temporary price reductions (sales) are common for many goods and naturally result in a large increase in the quantity sold. We explore whether the data support the hypothesis that these increases are, at least partly, due to demand anticipation: at low prices, consumers store for future consumption. This effect, if present, has broad economic implications. We test the predictions of an inventory model using scanner data with two years of household purchases. The results are consistent with an inventory model and suggest that static demand estimates may overestimate price sensitivity.

1. Introduction

For many nondurable consumer products, prices tend to be at a modal level with occasional short-lived price reductions: sales. During sales, the quantity sold is, unsurprisingly, higher than during nonsale periods. Quantity purchased may increase due to a consumption effect if consumption is price sensitive, and a demand-anticipation effect when consumers can hold inventories for future consumption. (1) In our sample, for example, the quantity of laundry detergents sold is 4.7 times higher during sales than during nonsale weeks, provided there was no sale the previous week. If there was a sale in the previous week, the quantity sold is only 2.0 times higher. This pattern suggests not only that demand increases during sales, but that demand accumulates between sales. Demand accumulation has been documented by Pesendorfer (2002) using store-level data on ketchup purchases (see also Blatteberg and Neslin, 1990). Our goal is to study what forces are behind the demand accumulation documented by Pesendorfer. We derive and test the implications of a consumer inventory model.

There are several reasons to study and quantify consumers' inventory behavior. First, most of the work in industrial organization, from theoretical models to demand estimation, assumes away demand dynamics. In contrast, the purchase of most products involves some sort of intertemporal substitutability. The substitutability may arise because the product is durable or storable, or because consumption is intertemporally substitutable (like a vacation or a golf game). Scanner data present the opportunity to document potential dynamic household behavior in storable products. A first look at the data suggests that price fluctuations can translate into nontrivial savings from storing at low prices for future consumption. (2)

The second reason to look at intertemporal demand substitution is to quantify the implications of the frequent price reductions (present in typical scanner data) for demand estimation. In principle, sales provide the price variability needed to identify price sensitivities. However, when the good is storable, there is a distinction between the short-run and long-run reactions to a price change. Standard static demand estimation could capture (if the proper controls, like inventories, are included) short-run reactions to prices, which reflect both the consumption and stockpiling effects. In contrast, for most demand applications (e.g., merger analysis or computation of welfare gains from introduction of new goods) we want to measure long-run responses.

Third, product storability has implications for how sales should be treated in the consumer price index. Ignoring the fact that consumers can substitute over time will yield a bias similar to the bias generated by ignoring substitution between goods as relative prices change (Feenstra and Shapiro, 2003).

A final motivation for studying consumer inventory behavior is to gain some understanding of the forces that determine sellers' incentives when products are storable. Although this article does not address the question of optimal seller behavior, our estimates of households' response to sales are suggestive of the sources of gains from sales. (3)

Assessing whether consumers stockpile in response to price movements would be straightforward if we observed consumers' inventories. For instance, we could test whether end-of-period inventories are higher after sales. However, consumption, and therefore inventory, is unobservable. We could assume a consumption rate that jointly with observed purchases would enable us to infer inventories. While this approach might be reasonable for some products (those with no consumption effects), it would not help disentangle long-run from short-run effects for those products for which the distinction really matters. (4)

We take an alternative route. We present an inventory model and use it to derive implications about the variables we observe. For example, using household purchase data we test the link between prices and interpurchase durations, instead of testing the (negative) relation between end-of-period inventories and price.

We concentrate on those predictions of the model that stem from storing but would not be expected under static behavior. In the model, the consumer, who faces uncertain future prices, maximizes the discounted expected stream of utility by choosing in each period how much to purchase for inventory and current consumption. Optimal behavior is characterized by a trigger and target level of inventory, which depend on current prices.

To test the predictions of the model, we use store-level and household-level data. The data were collected using scanning devices in nine supermarkets, belonging to five different chains, in two submarkets of a large Midwestern city. The store-level data include weekly prices, quantities, and promotional activities. The household-level dataset follows the purchases of about 1,000 households over two years. We know when each household visited a supermarket, how much was spent in each visit, which product was bought, where it was bought, and how much was paid.

Since the model deals with a single homogeneous product purchased in a single store, whereas the data include multiple varieties purchased in several stores, we need a practical way to link model and data. Under the maintained assumption that visits to the different stores are exogenous to the needs of the goods in question, the multiplicity of stores presents no problem. Each visit, regardless of the store, is just a draw from the price distribution prevailing at the frequented stores. The multiplicity of products is more delicate. It requires a definition of what is a product. We take a broad product definition (unless otherwise stated), treating whole categories as a single product. How close substitutes different brands (or Universal Product Code (UPC)), are is an empirical matter beyond the scope of this paper. As we discuss in Section 4, a broad product definition seems natural for our descriptive purposes. The cost of treating different varieties as a single product is that it imposes duration dependence within categories, while there might not be such a link.

We test the implications of the model regarding both household and aggregate behavior, and find the following. First, using the aggregate data, we find that duration since previous sale has a positive effect on the aggregate quantity purchased, during both sale and nonsale periods. Both effects are predicted by the model, since (on average) the longer the duration from the previous sale the lower the inventory each household currently holds, making purchase more likely. Second, we find that indirect measures of storage costs are negatively correlated with households' tendency to buy on sale. Third, both for a given household over time and across households, we find a significant difference between sale and nonsale purchases, in both duration from previous purchase and duration to next purchase. The duration effects are a consequence of the dependence of the trigger and target inventory levels on current prices. To take advantage of the low price, during a sale a household will buy at higher levels of current inventory. Furthermore, during a sale a household will buy more; therefore, on average, it will take more time until the next time the inventory crosses the threshold for purchase. Fourth, even though we do not observe the household inventory, by assuming constant consumption over time we construct a measure of implied inventory. We find that this measure of inventory is negatively correlated with the quantity purchased and with the probability of buying. Finally, we find that the pattern of sales and purchases during sales across different product categories is consistent with the variation in storage costs across these categories.

There are several models of consumption that potentially explain why demand increases during sales. It is hard to rule all of them out (especially since consumption is unobserved). The main alternative hypothesis we consider is that consumers behave in a static fashion, buying more during sales, purely for consumption. Another alternative hypothesis is that price-sensitive consumers accumulate in the market until they find a sale (as in Sobel, 1984). Although some of the patterns in the data are consistent with Sobel-type models, others are not. In particular, household-level behavior is inconsistent with that model (see the next section).