The Diffusion of Wal-Mart and Economies of Density. by Tom Holmes

The Diffusion of Wal-Mart and Economies of Density by Tom Holmes

Economies of Density: network of stores. Cost savings achieved by having a dense Logistics of deliveries Save on trucking costs Facilitates just-in-time inventory approach Distribution Center proximity (but note 85 deliveries a week across all sources) Management

Wal-Mart Big. Wants to get even bigger. Efforts to block this.

Idea Increasing density can lead to cannibalization of sales Tradeoff between diminishing returns from cannibalization and cost savings If economies of density don t matter Wal-Mart will try to keep stores far apart to prevent them from cannibalizing each others sales. Use a revealed-preference approach to infer economies of density.

How do I use the information in this choice behavior? Estimate a demand model for Wal-Mart stores Provide evidence of significant diminishing returns from cannibalization Put forth a dynamic model of Wal-Mart s site selection problem and use perturbation techiques to put a lower bound on a measure of density economies. Back it out as a residual. Other interpretations?

Model Discrete set of points B on a plain B wal B set with Wal-Mart. of locations with a Wal-Mart j B wal is store number.set B super B wal subset that sell groceries Besides geography, model has four key ingredients...

Ingredient 1: A Model of Sales Store-level revenue R j =R gen j +R groc j R gen j (B wal ) sales of general merchandise at store j given store configuation B wal R groc j (B super ) is is grocery revenue.

Ingredient 2: Density Economies Store density Proportioniate decay α =.02 Store Density at location is Density gen = X Density indexes d gen and d groc d gen =1 k B wal exp( αy k ) 1 Density gen Equals 0 for singleton store. Equals 1 for infinitely dense network.

Distribution Center d RDC = distance to closest RDC Density benefit for a supercenter at location is Density Benefit =φ gen d gen +φ groc d groc +φ RDC d RDC +φ FDC d FDC

Ingredient 3: Fixed coefficient Inputs for Variable Inputs

Ingredient 4: Fixed cost that varies by population density Motivation Form f j = γ 0 + ω 1 ln m j + ω 2 ³ ln mj 2

Wal-Mart s Problem 1. How many new Wal-Marts and how many new supercenters to open? 2. Where to put the new Wal-Marts and supercenters? (locatons are permanent, no exit) 3. How many new distribution centers to open? 4. Where to put the new distribution centers? My approach: Solve 2, conditioned upon 1,3,4.

Wal-Mart s Problem max a TX t=1 (ρ t β) t 1 P h gen j Bt wal π jt + P h j Bt super groc π jt for operating profit defined by f gen jt f groc jt + φ gen d gen jt + φ groc d groc jt + φ RDC d RDC i jt + φ FDC d FDC jt i. π k jt = ³ μ w jt ν Labor r jt ν Land Rk jt (θ) Approach: Assume measurement error on R k ij, w jt, r jt Strategy: (1) Estimate demand parameters θ (and technology) (2) Bound φ gen,φ groc, φ RDC,φ FDC, ω 1,ω 2 using a perturbation approach (moment inequalities)

Data Element 1: Store-Level Data for 2005 Source: TradeDimensions (ACNeilsen) Store Type N Mean Sales ($Millions/Year Employment Bldg Size (1,000 sq ft.) All 3,176 70.5 254.9 143.1 Regular 1,196 47.0 123.5 98.6 SuperCenter 1,980 84.7 333.8 186.9

Data Element 2: Facility opening states Various sources, including Wal-Mart Supercenters Regional Food Decade Distribution Disribution Open Wal-Marts Centers Centers 1960s 15 0 1 0 1970s 243 0 1 0 1980s 1,082 4 8 0 1990s 1,130 679 18 9 2000s 706 1,297 14 25 But Look at Pretty Pictures.

Data Element 3: Demographic Information by Block Group Source: Census 1980, 1990, 2000 1980 1990 2000 N 269,738 222,764 206,960 Mean population (1,000) 0.83 1.11 1.35 Mean Density (1,000 in 5 mile radius) 165.3 198.44 219.48 Mean Per Capita Income (Thousands of 2000 dollars) 14.73 18.56 21.27 Share old (65 and up) 0.12 0.14 0.13 Share yound (21 and below) 0.35 0.31 0.31 Share Black 0.13 0.13 0.13

Data Element 4: Wages and Rents Wages: County Business Patterns, 1977-2004 o Take average retail wage by county(exclude eating and drinking) o A few missing values for some years. Interpolate Rents o Measure of rent in vicinity of store (block groups in 2 mile radius) o Rent Index = (Value of owner-occupied homes + 100 monthly rent)/land o Sample of 56 Wal-Marts in Iowa and Minnesota with information about assessed value. Correlation of assessed value of land (per unit sales) with index is.77

Data Element 5: Annual Reports Aggregate sales (to backcast demand model) Information about cannibalization from management s report As we continue to add new stores in the United States, we do so with an understanding that additional stores may take sales away from existing units. We estimate that comparative store sales in fiscal year 2004, 2003, 2002 were negatively impacted by the opening of new stores by approximately 1%

Particulars of Demand: Consumers distributed across discrete locations (blockgroups) Total spending λ gen t and λ groc t. Logit model to allocate spending across.. outside good is composite of retail alternatives (that gets better with higher population density) inside goods are all Wal-Marts within 25 miles. Keep track of distance between blockgroup and the Wal-Mart (as crow flies)

Specification of utilities for consumer k at u k 0 = o(m )+z ω + ζ k 0 +(1 σ)ε k 0. u k j = τ (m ) y j + x j γ + ζ k1 +(1 σ) ε k j. m population density (population within 5 mile radius). x j store characteristics o(m) = γ 0 + γ 1 ln(m)+γ 2 (ln(m)) 2 τ(m) = τ 0 + τ 1 ln(m)

Demand model predicts sales of each block group to each Wal-Mart For each store add up block group sales to get store-level sales b R gen j is predicted sales of Wal-Mart regular stores b R gen j + b R groc j is predicted sales of supercenters Measurement error where ε measure j ε gen j =ln( R gen j ) ln(r gen (θ)). is normally distributed j Two Models: MLE and Constrained MLE to fit cannibalization rate of 1% for 2006

Estimates of Demand Model Implied cannibalization rates σ 2 =.06, fit is good. λ gen =1.7 andλ groc =1.7 ($1,000 per person per year) Implied comparative statics sensible Effect of population density Effect of disance to closest Wal-Mart

Cannibalization Rates (Percent Existing Firms Sales Lost to New Stores) Cannibalization Percent Fiscal Year Wal-Mart s Report Unconstrained Model Constrained Model 1999 no report.69.44 2000 no report.95.65 2001 no report.61.37 2002 1.00.73.49 2003 1.00 1.41.93 2004 1.00 1.48 1.06 2005 1.00 1.55 1.10 2006 1.00 1.35 1.00*

Within- State Age Evidence on Diminishing Returns Incremental Operating Profits on General Merchandise Incremental Sales ($million) Incremental Operating Profit ($million) Standalone Operating Profit ($million) Incremental Store Density Index Incremental Distribution Center Density (miles) N 1-2 288 38.35 3.55 3.62 0.82 343.26 3-5 614 39.98 3.55 3.70 0.96 202.04 6-10 939 38.04 3.39 3.64 0.98 160.68 11-15 642 36.75 2.95 3.36 0.99 142.10 16-20 383 33.48 2.86 3.47 1.00 113.66 21 and above 310 29.95 2.44 3.56 1.00 90.19

Within- State Age Incremental Sales ($million) Incremental Profits on Groceries Incremental Operating Profit ($million) Standalone Operating Profit ($million) Incremental Supercenter Density Index Incremental Distribution Center Distance (miles) N 1-2 202 42.30 3.86 3.93 0.73 252.90 3-5 484 42.71 3.97 4.13 0.93 171.17 6-10 775 41.00 3.63 3.97 0.99 113.52 11-15 452 36.70 3.19 3.84 1.00 95.32 16-20 67 29.69 2.71 3.42 1.00 93.95

Estimating Bounds on Parameters using pairwise deviations v(a, θ) =Π gen (a)+φ gen d gen (a)+φ RDC d RDC (a) ω 1 F 1 (a) ω 2 F 2 (a) +similar terms for groceries a 0 rollout pattern that Wal-Mart actually did a pairwise deviation that flips opening dates of two stores e.g. store #1 in 1964, #2 in 1962

Revealed preference implies v(a 0,θ) v(a, θ), for all a 6= a 0 Or v(a, θ) 0, for v(a, θ) =v(a 0,θ) v(a, θ). Given an alternative policy a and a parameter vector θ, we observe ṽ(a, θ) = v(a, θ)+ε a, Measurement error from wage and rent estimate for each store location.

v(a, θ) = Π gen a + φ gen d gen a ω 1 F a,1 ω 2 F a,2 0, Follow recent literature and take a moment inequality approach Take subsets of A in which measurement error averages out, so above holds in expecation. Idefine subsets based on: Opening date of store relative to first store in state (switch early stores with late stores) (2 moment inequalities) Stores in same state located in different population density locations(3 moment inequalities)

Number of Deviations Sample Size Present Value Differences Farther Sooner Deviations ΔΠ gen ($million) Δd gen Δd RDC ( 100s of year miles) ΔF 1 gen ΔF 2 gen 239,698 15,000-1.28 0.82 5.90-0.74-4.63

Estimates of Lower Bound on φ gen Moments Period φ RDC 0.00.02.05.10.20 Farther Sooner Deviation and ω 1 = 0 and ω 2 = 0 All Years 1.56 1.42 1.20.84.12 Basic All.59.46.25.00.00 1988-2006.79.66.46.12.00 Basic plus Interactions All.66.66.67.68 3.16 1988-2006.85.86.86.87 3.17

Linear Programming Problem Constraints in addition to moment inequalities: φ groc φ gen (binding) φ FDC φgroc = RDC φ φ gen ω 1 0(coefficient on ln(m)) ω 2 0(coefficient on ln(m) 2 ) ζ groc ω 1(fixed cost for groc relative to gen) (binding) Fix φ RDC and solve problem of minimizing φ gen subject to above

Store openings and conversions Above gives 10 groups of peturbations Instruments: Need to be positive Vector of ones (Basic Moments) Interactions: z a + = c + + d gen a 0 za = c d gen a 0 Same with other d k a, F k a,1, F k a,2. Together get 272 inequalities

A Sense of Magnitudes What happens if we change density, but keep sales the same E.g., suppose we split Wal-Mart into two separate companies and eliminate density benefits across companies. But consumers still doing same things, so sales at each store the same. Use bounds to get an estimates in the change in density economies. Take ratio to 1.3 percent of sales (Walmart s distribution costs as a percent of sales)

Lower Bound on Savings from Increased Density (Expressed as a percentage of.013*sales) General Merchandise Bound Number of Mean Store Density To current density from half To Most Dense State (NJ) Location Stores Index density U.S. 3,176.948 6.4 4.9 ND 8.505 25.3 78.9 CA 159.945 5.4 4.0 NJ 41.980 2.4 0.0

Lower Bound on Savings from Increased Density (Expressed as a percentage of.013*sales) Groceries Bound Number of Mean Store Density To current density from half To Most Dense State (NJ) Location Stores Index density U.S. 1,980.923 9.1 6.2 ND 1.525 19.9 51.7 CA 13.665 19.6 36.6 GA 101.963 5.3 0.0