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Article Excerpt
1. Introduction
How does local competition influence a retailer's inventory holdings? Although an active theoretical literature has recently emerged to explore this question, the question has so far received no direct empirical investigation, which is the objective of this paper.
We focus on two mechanisms by which the degree of competition a retailer faces moderates the retailer's days-of-supply of inventory (i.e., the amount of inventory the retailer carries relative to its sales). First, competition has a sales effect--increased competition lowers a retailer's sales. Inventory theory (e.g., Zipkin 2000) is clear on the direction of the sales effect: lower sales leads to a higher days-of-supply because of economies of scale in inventory management. Second, competition has a service-level effect--increased competition influences the retailer's service level, which, roughly speaking, is the probability that the retailer has an item in stock when a customer requests it. Here, theory is ambiguous. On the one hand, more competition leads to more-intense price competition and lower margins, which suggests that a lower service level is optimal. On the other hand, more competition gives consumers more choices for where and what to purchase, which suggests that a higher service level is optimal so as to better retain demand. Therefore, two questions naturally emerge from this discussion: (1) Can we empirically resolve the direction of the service-level effect? (2) How large is the service-level effect relative to the sales effect? If the service-level effect is positive (i.e., more competition leads to higher service levels), then these two effects are additive with respect to increased competition, which certainly leads to a higher days-of-supply. If the service-level effect is negative, then these two effects moderate each other and the net impact of competition on days-of-supply may be small (if their strengths are comparable).
We explore these issues in the context of the automobile industry. In particular, we collected daily inventory and sales data over a six-month period from General Motors (GM) dealerships located in more than 200 markets within the United States. Our data, collected with a custom-built Web crawler, enables us to track individual vehicles (via each vehicle's unique identification number, or VIN) as they were added to or removed from a dealership's inventory because of a sale to a consumer or a transfer between dealerships. We focus on isolated markets so that we can clearly identify the number of competitors (i.e., dealerships) in the same market and the type of competitors within the same market (i.e., the number of GM dealerships and the number of non-GM dealerships), but we provide some evidence that the dealers in our sample are representative of the entire population of GM dealers.
Table 1 reports summary statistics from our data and illustrates the considerable heterogeneity in inventory holdings across brands and across dealerships within a brand. Our empirical strategy exploits this cross-sectional variation in the observed markets to identify the effects of interest. We use instrumental variables to control for the endogeneity of market entry decisions with respect to unobserved market characteristics. (For example, some markets could have more GM dealerships because GM is aware of certain market characteristics that make them favorable to GM dealerships, and those unobserved characteristics may also influence inventory holdings in those markets.) We focus on the auto industry because it is economically significant, and detailed data on local inventory holdings are available (via our Web crawler). Although our results are specific to this industry, our econometric methods could be applied to study inventory in other retail industries. Furthermore, some of our findings may apply broadly to other forms of retailing.
Table 1 Inventory Holdings of General Motor Brand Dealerships in Our
Data Sample (from August 15, 2006, to February 15, 2007)
Buick Cadillac Chevrolet GMC Pontiac Saturn All
Number of 134 109 170 101 134 6 654
dealers
Average 12 12 44 17 16 93 23
inventory per
dealer
Mean days-of 151 151 133 130 197 118 152
-supply
Std. deviation 80 83 43 59 91 32 76
of days-of
-supply
This research is related to the growing empirical literature on inventory. Wu et al. (2005) study the relationship between firm inventory holdings and financial performance, whereas Hendricks and Singhal (2005) study the impact of supply chain disruptions (including problems with inventory) on short-term financial and accounting measures. Gaur et al. (2005) find that as a retailer's margins decrease and capital intensity increases, it tends to carry less inventory relative to sales (i.e., days of supply). Rumyantsev and Netessine (2007) use aggregate inventory data to measure the relationship between demand uncertainty, lead times, gross margins, and firm size on inventory levels. Rajagopalan (2005) estimates the effect of product variety on inventory levels of publicly listed U.S. retailers. Amihud and Mendelson (1989) use public data on manufacturing firms to estimate the effect of market power (proxied by the firms' margins and market shares) on inventory levels and variability. They find that firms lower their inventory as market power decreases, i.e., as competition intensifies. Cachon and Olivares (2009) study inventory in the auto industry at the brand level (e.g., Honda, Chevrolet) and report a positive association between the number of dealerships and inventory, among other factors that influence inventory. Note that all of these studies use aggregated inventory at a brand, company or industry level, and either have no measure of competition or only an indirect measure of competition (e.g., observed margins or total number of dealerships). In contrast, this work has data on individual units of inventory and direct measures of the degree of competition in local markets.
In our work, a dealer's inventory service level is one measure of the quality of the service the dealer provides for its customers--customers prefer higher service levels, and a high service level is costly to the dealer. Therefore, our work is related to the considerable literature that empirically investigates the relationship between competition and the level of quality provided in a market. For example, Berry and Waldfogel (2003) compare two industries, local newspapers (where quality is measured by the amount of content and the number of reporters) and restaurants (where quality is measured through ratings). They find that competition decreases quality in the newspaper industry, but increases quality with restaurants. Cohen and Mazzeo (2004) study retail banking, where quality is measured in terms of the number of branches a bank operates. As with newspapers, they find that higher competition leads to lower quality. Others use product variety as a measure of quality, such as Berry and Waldfogel (2001) with radio broadcasting, Alexander (1997) with music recording, Ellickson (2007) with supermarkets and hair-cutting establishments (i.e., barber shops and salons), and Watson (2009) with eyeglass retailers. As in our paper, in each of those studies there exists competing theories regarding the relationship between competition and quality.
Section 3 describes the data and the specification of the model. Section 4 shows our main results, and [section]5 provides a sensitivity analysis and further empirical evidence. Section 6 measures the relative magnitude of the effects we identify and discusses the implication for adding and subtracting dealerships to local markets. We conclude and discuss our findings in [section]7.
2. An Empirical Model of Retail Inventory
In this section, we use a basic inventory model to motivate a general empirical framework for the relationship between retail inventory and competition. In the subsequent sections we apply this framework to our analysis of inventory of vehicles at automobile dealerships.
Orders are received at the beginning of each period with zero lead time. Let D be i.i.d. normal demand in each period with mean [mu] and standard deviation [sigma]. Some fraction of the demand that is not fulfilled from in-stock inventory is backordered; the remaining demand is lost. Each period inventory is ordered so that there are Q units on hand before demand occurs. In this model the service level is the probability that all demand within a period is satisfied from inventory. The service level is increasing in z = (Q - [mu])/[sigma], so for convenience we refer to z as the service level, with the understanding that it is really a proxy for the service level. The expected inventory at the end of each period, I, is then
I = [sigma](z + L(z)), (1)
where L(z) is the standard normal loss function (see Zipkin 2000 for additional details).
It is empirically inconvenient to work with (1) directly because demand is not observable. However, (I) can be written as
I = [[sigma].sub.s]K(z) (2)
(see the appendix for details), where [[sigma].sub.s] is the standard deviation of sales (min{Q, D}) and K(z) is an increasing function. As in van Ryzin and Mahajan (1999), we use
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
to approximate the standard deviation of sales, where S is observed sales over a sample period, and A and [[beta].sub.s] are coefficients. The [[beta].sub.s] coefficient reflects the degree to which there are economies of scale in inventory management with respect to sales. (1) If [[beta].sub.s] = 1, then days-of-supply (inventory divided by daily demand rate) is independent of expected sales, whereas if [[beta].sub.s] < 1, then higher-sales retailers carry a lower days-of-supply for the same service level.2 Combining (2) and (3) and taking logarithms yields
log I = constant + [[beta].sub.s] log S + log K (z). (4)
The above equation suggests that a firm's inventory level can be decomposed into two separate components: a sales component, [[beta].sub.s] logS, and a service-level component, log K(z).
According to (4), competition can influence a firm's inventory through its sales, through its service level, or through both. The meaning of competition can depend on the particular retail industry considered, but to provide concreteness to this discussion, we use the term "competition" to refer to the number and type of retailers in a market. For example, in the context of our data analysis, competition depends on the number of dealerships in a market and which dealerships are in a market (e.g., GM versus non-GM). Given this interpretation, if a market's sales potential sales is reasonably fixed, then it is intuitive that entry (i.e., more competition) could reduce each firm's sales (the fixed market potential is allocated among more firms). However, entry could increase a retailer's sales either because price competition is sufficiently severe to increase total sales (i.e., total potential demand increases) or via a retail agglomeration effect--consumers may be more likely to search a retailer located near other retailers rather than an isolated retailer because the consumer wishes to economize on search costs. (3) We are not directly concerned with the specific mechanism by which competition influences sales because we conjecture that these mechanisms influence inventory only through their effect on sales.
A retailer's service-level choice depends on the retailer's estimates of the cost of stocking too much inventory (the overage costs) relative to the cost of stocking too little inventory (the underage cost). The overage cost is composed of the opportunity cost of capital, storage costs, and depreciation. The underage cost depends on the behavior of consumers when they do not find their preferred product (which may depend, in part, on consumer characteristics like brand preferences, income, etc.). In such a situation a consumer could purchase some other product at the retailer (substitute), defer purchase of the most preferred product to a later time (backorder), or leave the retailer without making a purchase (the no-purchase option). The retailer's optimal service level depends on the ratio of these costs: as the underage cost increases relative to the overage cost, the retailer's optimal service level increases.
With this understanding of how a retailer chooses a service level, we conjecture that there are three mechanisms by which competition influences the service-level component of (4): a margin mechanism, a demand-retention mechanism, and a demand-attraction mechanism. The margin mechanism is simply that additional competitors increases the intensity of price competition, which lower margins, thereby decreasing the underage cost; i.e., a smaller margin reduces the consequence of losing a customer because of a stockout, thereby lowering the incentive to hold inventory. The demand-retention mechanism influences underage costs via consumer behavior once the consumer has chosen to shop at a retailer. As more competitors enter a market, consumers are more likely to choose the "no-purchase" option relative to the "substitute" or "backorder" option, thereby leading to higher underage costs. Therefore, the margin and demand-retention mechanisms counteract each other. The demand-attraction mechanism states that a higher service level may attract more demand to a retailer (i.e., influence their choice of where to shop), because, all else being equal, a consumer prefers to shop at a retailer with a higher service level. (See Dana and Petruzzi 2001 and Gerchak and Wang 1994 for single-firm models in which service level is used to attract demand.) According to the demand-attraction mechanism, more competition causes firms to increase their service level to build their market share.
There is theoretical support for these three mechanisms that link competition to service level. Deneckere and Peck (1995) consider a...
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