Sales and Consumer Inventory

TL;DR: In this article, the authors explore whether the data support the hypothesis that temporary price reductions (sales) are common for many goods and naturally result in a large increase in the quantity sold.

Abstract: 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.

Summary

1. Introduction

• For many non-durable consumer products prices tend to be at a modal level with occasional short-lived price reductions, namely, sales.
• The authors discuss, in somewhat more detail, how their findings relate to this literature in Section 4 (as they present their results).
• The authors focus here on three product categories available in the data: laundry detergents, softdrinks and yogurt.
• In all three categories there is an interaction between size and both the frequency of a sale and 8 Such models, predict that accumulation should occur during sale periods, but during non-sale periods demand should be independent of duration since the previous sale.

3. The Model

• The authors present a simple inventory model, which they use to generate testable predictions about both observable household purchasing patterns and aggregate (store level) demand patterns.
• In order to derive analytic predictions, the model abstracts from important dimensions of the problem, like non-linear pricing and brand choice.
• In Hendel and Nevo (2002) the authors impose more structure in order to deal with the additional dimensions ignored here.

3.1 The Basic Setup

• Consumer i obtains the following flow utility in period t where is the quantity consumed, is a shock to utility and is the utility from consumption of the outside good.
• For simplicity the authors assume the shock is additive in consumption, , affecting the marginal utility from consumption.
• 13 A Markov process fits the observed prices reasonably well.
• Both these alternative assumptions, which have been made by previous work, are nested within their framework.
• Each of these products is assumed to be a minor component of the bundle, hence, need for these products does not generate a visit to the store.

3.2 Consumer Behavior

• The solution of the consumer’s inventory problem is characterized by the following Lagrangian where and are the Lagrange multipliers of the constraints in equation (1).
• Manipulating the first order conditions the authors get the main result.
• Moreover, the inventory level that triggers a purchase is which is decreasing in 14 If only discrete quantities are available or prices are non-linear in quantities then the target inventory S(@) becomes a function of and .
• Consumers behave according to an S-s rule, where the upper band, S, is a decreasing function of current price and the lower band, s, declines both on prices and the utility shock.

3.3 Testable Implications

• In this section the authors present the testable implications of the model.
• An immediate implication of Propositions 1 and 2, not predicted by the static model, is that Implication I1: Quantity purchased and the probability of purchase decline in inventories.
• Therefore, for most of the paper the authors resort to predictions on other aspects of consumer behavior, which indirectly testify on stockpiling.
• Duration until next purchase is longer during a sale, also known as Implication I2.
• Then consumer’s inventory would be higher today, relative to her inventory if the previous purchase was not during a sale.

4. Results

• In this section the authors test the implications derived in the previous section.
• Both these problems suggest that a correct definition of a sale will vary across households and across products.
• A broad product definition captures the fact that different brands are substitutes.
• For each household, the relevant category might not include all products but only those UPCs the household actually consumed.
• In that case the duration from last purchase, regardless of the brand, determine the current inventory (see details in Hendel and Nevo, 2002).

4.1 Aggregate data: the effect of duration from previous sales

• According to implication I5, aggregate demand should increase with the duration from the previous sale (i.e., as consumers run out of the inventory stockpiled during the last sale).
• Moreover, the effect of duration while stronger during sales, should also be present during non-sale periods.
• The authors already discussed demand accumulation in section 2.3.
• The numbers presented in Table 3 show duration effects are present at the aggregate level.
• In accordance with I5, duration matters during both non-sale and sale periods and the effect is more pronounced during the sale periods.

4.2 Household sales proneness

• In this section the authors study the factors that impact a household’s fraction of purchases on sale.
• For the 1,039 households the authors regress the fraction of times the household bought on sale, in any of the three categories they study, during the observed period on various household characteristics.
• These effects are just barely statistically significant, and some not significant, at standard significance levels.
• In fact dog ownership is uncorrelated with those proxies, moreover, the significance of the dog dummy variable is not affected by controlling for search proxies (see column (vi)).
• Column (v) shows that households who shop more frequently tend to buy more on sale.

4.3 Sale vs. non-sale purchases

• In this section the authors discuss the main predictions of the model at the level of the individual.
• The next three columns display the averages during sale purchases minus the average during non-sale purchases.
• 18 Actually, their theory has predictions regarding both the within and between effects and therefore in some cases also regarding the total effect.
• This is true both when comparing between households (households that make a larger fraction of their purchases during sales tend to buy more quantity) and within a household over time (when buying during a sale a household will tend to buy more), as predicted by Proposition 2.
• Third, there might be consumption and stockpiling of several products.

4.4 Inventories, purchases and promotional activities

• Up to now the results focused on testing the implications of their model assuming the authors cannot observe inventories.
• In the second set of regressions, the dependent variable is the quantity purchased, measured in 16 ounce units.
• The authors divide this quantity by 104 weeks to get the average weekly consumption for each household.
• First, the inventory variable was constructed under the assumption of constant consumption, which might be right on average but will yield classical measurement error and will bias the coefficient towards zero.
• In reality, however, consumers might be using different brands for different tasks, which is also likely to bias the coefficient towards zero.

4.5 A cross-category comparison

• The last set of tests of their theory involve a comparison across products.
• Prices tend to change every 6-7 weeks and stay constant till the next change.
• Assuming that milk is not storable (and that the only reason for sales is to exploit consumer heterogeneity in storage costs), then according to their model there should be no sales for milk.
• Further evidence linking the relation between the easier-to-store size and sales is presented in the last column of Table 2, where the authors show the potential gains from stockpiling (defined in the Introduction) for the different sizes.
• Bigger savings are associated with the containers easier to store, namely larger sizes of detergents and soda, while small yogurt containers.

5. Implications for Demand Estimation: Short vs long run elasticities

• In this section the authors attempt to quantify the bias in demand elasticities that would arise from neglecting dynamics.
• Short run elasticity estimates are likely to overstate consumers’ long run price responses, which involve consumption responses but no stockpiling.
• The authors interpret higher quantity adjusted purchases during sales as evidence of consumption effects.
• The authors then divide this number by the consumption rate after a non-sale purchase: 4.79/43.75.
• Thus, neglecting dynamics would have lead us to conclude that demand is 74% more elastic that it really is.

6. Conclusions and Extensions

• The authors data consists of an aggregate detailed scanner data and a household-level data set.
• (3) When buying on sale households tend to buy more quantity (either by buying more units or by buying larger sizes), buy earlier and postpone their next purchase.
• Calculations based on their findings suggest that in the presence of stockpiling standard, static, demand estimation may be misleading.
• The authors are currently exploring extensions along several dimensions.
• The structural model provides interpretable estimates and enables us to perform counterfactual experiments.

Figures

Table 6 Purchase Conditional on Store Visit and Quantity Purchased Conditional on Purchase by Household as a Function of Price and Promotional Activities

Table 1 Percent of Weeks on Sale and Quantity Sold on Sale, by Category for Different Definitions of Sale

Table 2 Quantity Discounts and Sales

Table 5 Differences in Purchasing Patterns Between Sale and Non-Sale Purchases

Table 3 Demand as a Function of Duration from Previous Promotional Activity

Table 7 Consumption vs Stockpiling Effects

Table 4 Correlation Between Households Fraction of Purchases on Sale and Household Characteristics

Full text

NBER WORKING PAPER SERIES
SALES AND CONSUMER INVENTORY
Igal Hendel
Aviv Nevo
Working Paper 9048
http://www.nber.org/papers/w9048
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
July 2002
We wish to thank David Bell for the data, Iain Cockburn, Ken Hendricks, Chad Jones, John Kennan, Ariel
Pakes, Rob Porter, Joel Waldfogel and seminar participants in several seminars for comments and
suggestions. The second author wishes to thank the Center for the Study of Industrial Organization at
Northwestern University, for hospitality and support, and gratefully acknowledges support from the NSF
(SES-0093967). The views expressed herein are those of the authors and not necessarily those of the
National Bureau of Economic Research.
© 2002 by Igal Hendel and Aviv Nevo. All rights reserved. Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given
to the source.

Sales and Consumer Inventory
Igal Hendel and Aviv Nevo
NBER Working Paper No. 9048
July 2002
JEL No. L0, L4, D1, D4
ABSTRACT
Temporary price reductions (sales) are common for many goods and naturally result in large
increase in the quantity sold. We explore whether the data support the hypothesis that these increases are,
at least partly, due to dynamic consumer behavior: at low prices consumers stockpile for future
consumption. This effect, if present, renders standard static demand estimates misleading, which has
broad economic implications. We construct a dynamic model of consumer choice, use it to derive testable
predictions and test these predictions using two years of scanner data on the purchasing behavior of a
panel of households. The results support the existence of household stockpiling behavior and suggest that
static demand estimates, which neglect dynamics, may overestimate price sensitiveness by up to a factor
of 2 to 6.
Igal Hendel Aviv Nevo
Department of Economics Department of Economics
Social Science Building University of California
University of Wisconsin 549 Evans Hall #3880
1180 Observatory Drive Berkeley, CA 94720-3880
Madison, WI 53706-1393 and NBER
and NBER nevo@econ.berkeley.edu
igal@ssc.wisc.edu

2
1. Introduction
For many non-durable consumer products prices tend to be at a modal level with occasional
short-lived price reductions, namely, sales. Unsurprisingly, during sales the quantity sold is higher.
Price reductions may have two effects on quantity bought: first, a consumption effect if consumption
is price sensitive, second, a stockpiling effect if dynamic considerations lead consumers to
accumulate inventory for future consumption. For example, in our sample the quantity of laundry
detergents sold is 4.7 times higher during sales than during non-sale periods (provided there was no
sale the previous week). Instead if there was a sale in the previous week, then 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. These effects, which have been documented in the economics
and marketing literature (see Section 1.1), are consistent with stockpiling. We want to analyze what
is behind these patterns of demand. Do consumers stockpile? Does stockpiling explain the observed
demand accumulation ? Is the observed behavior consistent with dynamic forward looking behavior?
In order to address these questions we derive and test the implications of a consumer inventory
model.
There are several reasons to study and quantify consumers’ stockpiling behavior. First,
suppose the data available for demand estimation presents frequent price reductions (as is the case
with scanner data). In principle, the presence of frequent sales is a blessing for demand estimation,
as they provide price variability needed to identify price sensitivities. However, when the good in
question is storable, there is a distinction between the short run and long run reactions to a price
change. Standard static demand estimation would capture 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.
Second, detailed data, such as the household-level sample we describe below, present an
opportunity to study whether a dynamic model of forward looking agents fits household behavior.
The pronounced price changes, observed in some of the products we study, create incentives for

2
This is for the 24 products we have in our data set. For the households we observe these products account
for 22 percent of their total grocery expenditure.
3
In ongoing work we study the behavior of a storable good monopolist. Most of the literature on sales is based
on the Sobel (1984, 1991) model, which is a model of durable goods. Preliminary results show the main forces at play
are quite different when the good is instead storable.
3
consumers to stockpile. Our analysis will focus on grocery products, in particular, laundry detergents,
yogurt and soft-drinks. From our data we can compute the potential gains from dynamic behavior.
One such measure is given by comparing the actual amount paid by the household to what they
would have paid if the price was drawn at random from the distribution of prices for the same
product at the same location over time. This is a lower bound on the potential gross gains from
optimizing behavior. In our data the average household pays 12.7 percent less than if they were to
buy the exact same bundle at the average price for each product.
2
Some households save little, i.e.,
they are essentially drawing prices at random, while others save more (the 90
th
percentile save 23
percent). Assuming savings in these 24 categories represent saving in groceries in general, the total
amount saved by the average household, over two years in the stores we observe, is 500 dollars (with
10
th
and 90
th
percentiles of 150 and 860 dollars, respectively). Hence, the price movements provide
incentives for storage and dynamic behavior.
Third, consumer stockpiling has implications for how sales should be treated in the consumer
price index. If consumers stockpile, then 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, 2001).
A final motivation to study stockpiling behavior, is to understand sellers' incentives when
products are storable. Although this paper does not answer this question, our findings provide some
guidance on how to model the problem.
3
If we observed the consumers’ inventories then determining whether consumers stockpile
in response to price movements would be straightforward. For instance, we could test if after a sale
end-of-period inventories are higher. However, consumption and therefore inventory, is
unobservable. We could make an assumption about consumption, for example, that it is constant.

4
Indeed we will see in Section 4 that the consumption effect is important for some products.
4
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, therefore, take an alternative route. We propose a dynamic model of consumer choice
and use it to derive implications about the variables we observe. For example, as we show below the
model predicts that when purchasing on sale the duration to next purchase should increase (relative
to non-sale purchases by the same household). Furthermore, if there is a consumption effect this
increase should be less than the increase in quantity purchased. Therefore, using household purchase
data we test the link between current prices and duration to next purchase, instead of testing the
(negative) relation between end-of-period inventories and current price. This is just one example of
how the model helps us circumvent the problem of not observing inventories, by providing
implications about behavior we do observe.
We concentrate on those predictions of the model that stem exclusively from the stockpiling
effect, but would not be expected under static behavior (i.e., when only the consumption effect is
present). In our model the consumer maximizes the discounted expected stream of utility by
choosing in each period how much to buy and how much to consume. She faces uncertain future
prices and in any period decides how much to purchase for inventory and current consumption.
Optimal behavior follows a (conditional) s-S type behavior: if inventory is low enough the consumer
buys and fills her inventory to a target level.
In order to test the model we use store and household-level data. The data were collected
using scanning devices in nine supermarkets, belonging to different chains, in two sub-markets of
a large mid-west city. The store level data includes weekly prices, quantities, and promotional
activities. The household-level data set 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, how much was paid and whether a coupon was

Frequently asked questions

Q1. What are the contributions in this paper?

In this paper, Hendel et al. studied the effect of temporary price reductions on consumer behavior and found that consumers tend to stockpile goods for future consumption. 

Q2. How do the authors find that static demand estimates may overestimate own-price elasticities?

The authors find that static demand estimates, which neglect dynamics, may overestimate own-price elasticities by up to a factor of 2 to 6. 

Q3. What are the characteristics of the household that are less likely to buy on sale?

Households with higher per person income are less likely to buy on sale, and so are households with a female with post high school education. 

Q4. What is the effect of short run elasticity estimates?

Short run elasticity estimates are likely to overstate consumers’ long run price responses, which involve consumption responses but no stockpiling. 

Q5. What are the implications of ignoring the dynamic effects?

Preliminary results, using data from the laundry detergents category, suggest that ignoring the dynamic effects can substantially bias the estimates of own- and cross-price elasticities and have profound effects on their31implications. 

Q6. What is the main alternative hypothesis the authors consider?

The main alternative hypothesis the authors consider is that consumers behave in a static fashion, buying more during sales, purely for consumption reasons. 

Q7. How much of the variation is explained by the observed demographics?

Overall observed demographics explain less than 3 percent of the variation, across households, in the fraction of purchases on sale. 

Q8. What is the significance of the coefficients in Table 6?

Simulations based on the preliminary results in Hendel and Nevo (2002), where the authors model the discreteness of purchases and non-linear prices, suggest that the magnitude of the coefficients presented in Table 6 is consistent with stockpiling behavior that is economically significant. 

Q9. What is the effect of the duration of a sale on the household?

Both these effects are predicted by the model since the longer the duration from the previous sale, on average, the lower the inventory each household currently has, making purchase more likely. 

Q10. How do the authors calculate the consumption rate after a sale?

For detergents, the authors compute the consumption rate after a sale by dividing the quantity sold during sales, 4.79+1.14, by duration after sales, 43.75+1.95.24