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Erschienen in: Quantitative Marketing and Economics 1/2009

01.03.2009

Spatial competition with endogenous location choices: An application to discount retailing

verfasst von: Ting Zhu, Vishal Singh

Erschienen in: Quantitative Marketing and Economics | Ausgabe 1/2009

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Abstract

This paper examines the importance of geographical differentiation in store location decisions of firms in the retail discount industry. Using a novel data set that includes the store locations and accompanying market conditions for all stores belonging to the Wal-Mart, Kmart, and Target chains, we study the factors that influence the entry and location decisions of these firms. The model involves an incomplete information game between the three players where each firm has private information about its own profitability. A key feature of our modeling approach is that it permits asymmetries across firms in the impact of exogenous market characteristics and competitive interaction effects. Variations in the exogenous firm specific characteristics, such as the distances from the market to firms’ headquarters and the nearest distribution centers, serve as exclusion restrictions and provide the source for model identification. Parameter estimates of the payoff functions are used to predict the equilibrium market structure under a variety of market conditions that provide insights into the competitive landscape of the industry. Results show that all firms exert a strong negative impact on competitors when they are in close proximity, but the effect decreases with distance to rivals suggesting strong returns to spatial differentiation in this industry. Target stores fare well under competition except when these competitors are in close proximity. Wal-Mart’s supercenter format is found to be the most formidable player as it substantially impacts competitors even at a large distance. We also find significant asymmetries across players in their response to market conditions and competition interactions.

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Fußnoten
1
Kyle (2006) makes similar arguments in the context of entry in pharmaceutical drugs.
 
2
In principle, the unobserved market characteristics can impact firms differently. In the empirical application we allowed for this possibility by estimating an additional model which allows for the unobserved market factor to vary across firms and found no substantial differences in results.
 
3
As discussed below in the context of format choices, it is also possible for the parameters to be contingent on the actions taken by firms.
 
4
The marketwide random component is ignored as it does not provide any additional insight into the importance of asymmetric effects.
 
5
The scenarios and parameter values are partly motivated by our empirical results.
 
6
For a detailed background on these firms, interested readers are referred to Zhu et al. (2008) and three recent books on each firm: The Wal-Mart Decade: How a New Generation of Leaders Turned Sam Walton’s Legacy into the World’s #1 Company (Robert Slater) Portfolio Hardcover (2003); On Target: How the World’s Hottest Retailer Hit a Bullseye ( Laura Rowley) Wiley (2003); Kmart’s Ten Deadly Sins: How Incompetence Tainted an American Icon, (Marcia Layton Turner) John Wiley & Sons (July 18, 2003).
 
7
For very large urban counties (for example LA county), we use the first three digits of the tract number to create sub-markets. The complete census tract ID is defined as follows: SS-CCC-TTTTTT, where the first two digits “SS” represents State FIPS code, the next three digits “CCC” represents County FIPS Code, and the last six digits “TTTTTT” is the census tract number. This definition defines a market as the tracts within a county with the same first three digits in their tract numbers and all six digit codes as locations.
 
8
We assume that firms are located at the centroid of the location, i.e., census tract. We calculate the distance between locations using the Haversine Formula. Based on latitude-longitude coordinate data, the distance between two points, a and b, is given by
$$ d_{a,b}\!=\!2R\arcsin\left[\!\min\left\{\! \left( \left( \sin\left( 0.5\left( lat_{b}\!-\!lat_{a}\right) \right) \right) ^{2}\!+\!\cos\left( lat_{a}\right) \cos\left( lat_{b}\right) \left( \sin\left( 0.5\left( lon_{b} \!-\!lon_{a}\right) \right) \right) ^{2}\right) ^{0.5},1\!\right\} \!\right] $$
where R = 3961 miles denotes the radius of the earth.
 
9
One problem of the likelihood approach is that there might be multiple equilibria in the incomplete information game. Although we solved for the fixed point by using different starting values, uniqueness of the solution is not guaranteed. However, as long as the strength of competition effect is moderate, the equilibrium can be solved uniquely. We show analytical and simulation results in the Appendix.
 
10
A concern in our modeling framework is potential cannibalization across markets since each market is treated independently. This is less likely to be an issue in the non-MSA markets where the distance between the adjacent stores is quite large. Note however that the travel time in MSA markets is likely to larger potentially mitigating cannibalization. Jia (2008) makes contribution to the literature by incorporating the “spill over” effects across market within a firm. However the implicit assumption in her approach is the externality between two close-by stores within the same chain is positive.
 
11
According to an independent study by McKinsey & Co., Wal-Mart’s efficiency gains were the source of 25% of the entire U.S. economy’s productivity improvement from 1995 to 1999. “Can Wal-Mart get any bigger” Time Magazine (Vol. 161, issue 2, 2003).
 
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Metadaten
Titel
Spatial competition with endogenous location choices: An application to discount retailing
verfasst von
Ting Zhu
Vishal Singh
Publikationsdatum
01.03.2009
Verlag
Springer US
Erschienen in
Quantitative Marketing and Economics / Ausgabe 1/2009
Print ISSN: 1570-7156
Elektronische ISSN: 1573-711X
DOI
https://doi.org/10.1007/s11129-008-9048-6

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Acknowledgments

2008 QME participants