Abstract
In this paper, I investigate the geographic location decisions of supermarkets to infer their tradeoffs between locating close to favorable demand conditions and differentiating themselves geographically from rivals. The model is based on a discrete-choice game between two types of supermarkets, and incorporates firm uncertainty arising from firm- and location-level private information as well as researcher uncertainty arising from location-level common information. Thus the model addresses the concern that firms’ actions may be based on factors that are unobservable to the researcher, thus correlated conditional on observables. The estimates reflect a significant level of common information. Importantly, I find that ignoring unobserved location heterogeneity results in biased estimates of both the competitive effects and the effects of location-specific observables on profits. Counterfactual predictions are therefore misleading if unobserved location heterogeneity is unaccounted for.
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Notes
The work by Datta and Sudhir (2012), also in this issue, introduces data on zoning restrictions and documents the resulting bias corrections.
Absent any unobserved location heterogeneity, for α = 0, p u1 = .90, p u2 = .04 , p u3 = .06, whereas p v1 = .21, p v2 = .29 , p v3 = .50 and for α = − 1, p u1 = .81, p u2 = .07 , p u3 = .12 and p v1 = .24, p v2 = .31, p v3 = .46
When σ 2 = 0, I calculate the co-location probability as \(p^{*2}_{u1}+ p^{*2}_{u2}+p^{*2}_{u3}\) in Market U and similarly for Market V, where \(p^*_l\) is the solution to the set of equalities of the form \(p_l=\frac{exp(x_l \beta+p_l\alpha)}{\sum^3_{j=1} exp(x_j \beta+p_j\alpha)}\). When σ 2 > 0, I calculate this probability by averaging over 500 co-location probabilities based on the solutions to the set of equalities of the form \(p_l=\frac{exp(\epsilon_l+x_l \beta+p_l\alpha)}{\sum^3_{j=1} exp(\epsilon_j+x_j \beta+p_j\alpha)}\).
Census block groups are the smallest geographic unit for which the U.S. Census supplies comprehensive demographic data. The Census Bureau defines census block groups as meeting an optimum size of 1,500 people. The first quartile of all census block groups in the United States has 827 people, whereas the third quartile has 1,604. On average, census block groups span 1.7 square miles.
Geocorr is a geographic correspondence engine for the Census 2000 hosted by the Missouri Census Data Center. It is available at http://mcdc.missouri.edu/websas/geocorr2k.html.
Because the complete list of census block groups that intersect the market may span a much larger geography, I check to make sure the boundaries of this geography still satisfy the geographic isolation requirements for the market.
Alabama, Arkansas, Arizona, California, Colorado, Kentucky, Mississippi, Nebraska, New Hampshire, Tennessee, Washington, West Virginia and Wyoming.
Consumers are not likely to travel more than 10 miles one way for grocery shopping. This is the maximum distance the literature on food deserts considers for rural areas. However, the edges of a market may encompass a much larger area to enclose all competitors in that market. This range will give the necessary scope for spatial differentiation opportunity.
Note that allowing for type heterogeneity uncovers a significant effect of race. The health policy literature also finds that the disparities related to healthy food access and consumption are associated with racial segregation and low incomes (Ford and Dzewaltowski 2008; Zenk et al. 2005b; Gallagher 2006; Morland et al. 2002). For example, African Americans on average travel the farthest to grocery stores in Chicago compared to other ethnic groups. Unfortunately, the data does not allow me to determine the reason behind supermarkets’ preferences. These negative impacts may be due to higher costs or unfavorable demand conditions associated with these demographics.
This distance metric is calculated based on the probability of location outcomes. The probability of observing at least one firm in location L is \(2p_L+pr_L^2\), the probability of the nearest supermarket being in location M is \(p_M^2+2p_M p_R\) and the probability of both supermarkets locating in R is \(p_R^2\). Thus the expected minimum distance from L is \(E(\min(d_L))=10 (p_M^2+2p_M p_R)+ 20p_R^2\).
Even in the extreme case where all the population in location L are African Americans and none in location R, the probability that a high type supermarket chooses location L is 0.37 under Model 1A. Therefore, the inclusion of location unobservables leads to more clustering in this market in all the cases we consider. More generally, however, location unobservables are less likely to increase firm clustering in markets with higher variance in location attractiveness. In fact, as the example in Section 2.4 demonstrated, common information may decrease firm clustering. Therefore, although its impact is mostly positive in this counterfactual, the prediction difference between Models 1 and 1A decreases with the variance in location attractiveness and may reverse in other applications. In that case, we expect Models 1 and 1A predictions to cross.
For an example of controlling for location-specific unobservables and the resulting endogeneity in estimating spatial demand, see the recent work by Pancras et al. (2012).
The release of the initiative read “Residents of these communities, which are sometimes called ’food deserts’ and are often found in economically distressed areas, are typically served by fast food restaurants and convenience stores that offer little or no fresh produce. Lack of healthy, affordable food options can lead to higher levels of obesity and other diet-related diseases, such as diabetes, heart disease, and cancer. Through this new multi-year Healthy Food Financing Initiative and by engaging with the private sector, the Obama Administration will work to eliminate food deserts across the country within seven years.”
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Acknowledgements
I thank the Trade Dimensions for providing the data for research purposes. This paper is based on a chapter of my dissertation. I am indebted to Miguel Villas-Boas and Richard Gilbert for early guidance on this project. This paper has greatly benefitted from the comments of two anonymous referees, Daniel Ackerberg, Ying Fan, Jeremy Fox, Kostis Hatzitaskos, Puneet Manchanda, Pinar Karaca-Mandic, Peter Reiss, Peter Rossi, S. Sriram and Ting Zhu. I am grateful Tom Marini for data assistance. The usual disclaimer applies.
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Orhun, A.Y. Spatial differentiation in the supermarket industry: The role of common information. Quant Mark Econ 11, 3–37 (2013). https://doi.org/10.1007/s11129-012-9123-x
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DOI: https://doi.org/10.1007/s11129-012-9123-x