Demand for nondurable goods: a shortcut to estimating long‐run price elasticities

• DOI: http://doi.org/10.1111/1756-2171.12194
• Published date: 01 August 2017
• Date: 01 August 2017
• Author: Helena Perrone

RAND Journal of Economics

Vol.48, No. 3, Fall 2017

pp. 856–873

Demand for nondurable goods: a shortcut

to estimating long-run price elasticities

Helena Perrone∗

When consumers stockpile, static demand models overestimate long-term price responses. This

article presents a dynamic model of demand with consumer inventories and proposes a shortcut

to estimate the long-run price elasticities without having to solve the dynamic program. Using

French data on food purchases, I find elasticities consistent with those that result from the

full-blown estimations found in the literature.

1. Introduction

Standard demand models assume that consumers, purchase choices are static (see, e.g.,

Berry, Levinsohn, and Pakes, 1995; and Nevo, 2001; among many others). However, there is

substantial empirical evidence that in a number of products, consumers stockpile (e.g., Boizot,

Robin, and Visser, 2001; Hendel and Nevo, 2006a). When this is the case, ignoring dynamics

may lead to upward-biased estimates of long-run demand price elasticities, because a static

model captures not only the effect of prices on consumption but also the short-term variation in

inventories (Hendel and Nevo, 2006a, 2006b).

To deal with these issues, we need to estimate a dynamic model, but this can be costly

because estimation of a dynamic demand model usually requires solving a dynamic programming

problem, which is a computer time-consuming numerical exercise. However, because for most

policy purposes, for example, competition policy, we require long-run elasticities, it is important

to develop techniques to estimate long-run effects without completely solving the dynamic

programming problem. This article contributes to the literature by proposing a simple procedure

to estimate long-run own-price elasticities that does not require solving the value function. My

method, although simple, is flexible with respect to consumer heterogeneity, price processes, and

consumers’ future price expectations. Note that the model in its current format does not address

brand differentiation, hence, I can estimate long-run own-price elasticities, but not cross-price

elasticities.

In the model, consumers maximize their discounted utility flow by choosing, in each period,

how much to purchase, how much to consume, and how much to leave as inventory of a single

∗Universitat Pompeu Fabraand Barcelona GSE; helena.perrone@upf.edu.

I would like to thank Larbi Alaoui, Steven Berry,Christian Brownlees, Jan Eeckhout, Juanjo Ganuza, Christian Michel,

Aviv Nevo, Vincent Requillart, and Michael Waterson for helpful comments. I would also like to thank anonymous

referees whose comments and suggestions greatly improved the article. I am especially grateful to Pierre Dubois for

his encouragement, guidance, and support throughout this work. Research support by CAPES and INRA is kindly

acknowledged. All errors are mine.

856 C2017, The RAND Corporation.

PERRONE / 857

homogeneous product. Future prices are uncertain. In the model, when prices are high relative to

expected future prices, consumers only purchase to cover current consumption, not to stockpile.

Consumers purchase and store at discounted prices, using stocks to avoid having to purchase

at high prices. If storage were costless and there was no discounting, they would buy their

lifetime consumption when the price is at its lowest. However,storage is costly. Thus, consumers

hold limited stocks that they supplement when prices are low and deplete when prices are high,

purchasing at nonsale prices only if there is not enough of the product in storage to cover current

consumption. Therefore, in periods of high prices, the purchase decision depends on how much

of the product consumers already have in stock and on consumption at current prices.

I propose to use these properties of the model to simplify estimation. In particular, the

key to the simplicity of the method is twofold. First, I estimate parameters when choices are

not affected by future expected variables that require solving the value function. Second, I only

require current observable variables and the beginning-of-the-period inventory level, which I

am able to construct from the panel data. Note that restricting the estimation sample does not

create a selection problem under the standard assumption that the marginal utility of income is

independent of the price level.

The empirical implementation requires an assumption concerning how consumers form fu-

ture price expectations, a utility function specification, and an assumption regarding consumption

out of stock. However, the methodology is quite flexibleand allows for various alternative assump-

tions. In the application, I consider a constant absolute risk aversion (CARA) utility specification

and three alternative price expectation formation hypotheses. The first assumes that consumers

always expect prices to return to their regular (mean) level, whereas the second and third price

expectation formation hypotheses assume different first-order Markov processes.

With respect to consumption out of stock (consumption in periods when the consumer

does not purchase the product but still consumes it), I assume that it depends on the expected

replacement costs, which I proxy by the average price paid for each unit in stock. I empirically

check the sensitivity of the results to this assumption by estimating the model in subsamples with

increasingly shorter interpurchase periods. The shorter the interpurchase periods, the less I have

to assume the out-of-stock level of consumption. Furthermore, I also estimate parameters in a

subsample that includes only purchases made at high prices following periods of purchases at

high prices. This means that in this subsample, inventories are always zero (at the beginning and

end of each period) and consumption equals purchases in each period. Parameter identification

therefore does not require the use of the out-of-stock consumption assumption because, according

to the model, consumers never consume from stock in this subsample.

The model is estimated using French homescan data on food products overthree years (1999,

2000, 2001). In the data, each observation is a purchase occasion, and I observe exactly what

was purchased, when it was purchased, and the price paid. The empirical analysis is performed

considering five different product categories: butter, coffee, milk, pasta, and yogurt. Note that in

contrast to the United States, the most common type of milk in France is shelf-stable ultrapasteur-

ized (UHT) milk. It represents more than 97% of French milk consumption (Institut Professionnel

du Lait de Consommation, www.iplc.fr). It can be stored on shelves for a long time whileclosed

and for approximately one week in a refrigerated area once opened. This is the type of milk I

consider in the sample, not fresh milk.

Consistent with previous results in the literature, the estimation results show that the price

elasticities yielded by a static model that ignores inventories consistently overestimate long-run

responses. The bias ranges from 20% up to more than 100%. The magnitudes of my long-run price

elasticity estimates are also consistent with previous literature estimates obtained by solving the

complete dynamic programming model, which is further evidence supporting my method (see,

e.g., Sun, Neslin, and Srinivasan, 2003; Sun, 2005; Hartmann and Nair, 2009; Hendel and Nevo,

2006b, 2013). (Note that these articles focus on different products and, as expected, numbers are

similar but not identical.) The results are robust to the assumption on consumption out of stock,

to the estimation method, and to the price expectation hypothesis (although the results are more

C

The RAND Corporation 2017.