The Di ff usion of Wal-Mart and Economies of Density by Tom Holmes - - PowerPoint PPT Presentation

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

Economies of Density: Cost savings achieved by having a dense network of stores.

• 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 oth- ers’ sales.

• Use a revealed-preference approach to infer economies of den-

sity.

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 can-

nibalization

• Put forth a dynamic model of Wal-Mart’s site selection prob-

lem 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
• Bwal ⊆ B set with Wal-Mart.

j ∈ Bwal is store number.set

• f locations with a Wal-Mart
• Bsuper ⊆ Bwal subset that sell groceries

Besides geography, model has four key ingredients....

Ingredient 1: A Model of Sales

• Store-level revenue Rj =Rgen

j

+Rgroc

j

— Rgen

j

(Bwal) sales of general merchandise at store j given store configuation Bwal — Rgroc

j

(Bsuper) is is grocery revenue.

Ingredient 2: Density Economies

• Store density

— Proportioniate decay α = .02 — Store Density at location is Densitygen

• =

X

k∈Bwal

exp(−αyk) — Density indexes dgen

• and dgroc
• dgen
• = 1 −

1 Densitygen

• — Equals 0 for singleton store.

Equals 1 for infinitely dense network.

• Distribution Center

dRDC

• = −distance to closest RDC
• Density benefit for a supercenter at location is

Density Benefit = φgendgen

• +φgrocdgroc
• +φRDCdRDC
• +φFDCdFDC

Ingredient 3: Fixed coefficient Inputs for Variable Inputs

Ingredient 4: Fixed cost that varies by population density

• Motivation
• Form

fj = γ0 + ω1 ln mj + ω2

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 T

X

t=1

(ρtβ)t−1

⎡ ⎢ ⎣ P

j∈Bwal

t

h

πgen

jt

− fgen

jt

+ φgendgen

jt

+ φRDCdRDC

jt

i

+ P

j∈Bsuper

t

h

πgroc

jt

− fgroc

jt

+ φgrocdgroc

jt

+ φFDCdFDC

jt

i ⎤ ⎥ ⎦ .

for operating profit defined by πk

jt =

³

μ − wjtνLabor − rjtνLand

´

Rk

jt(θ)

Approach: Assume measurement error on ˜ Rk

ij, ˜

wjt, ˜ rjt Strategy: (1) Estimate demand parameters θ (and technology) (2) Bound φgen, φgroc, φRDC, φFDC, ω1, ω2 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 Decade Open Wal-Marts Supercenters Regional Distribution Centers Food Disribution Centers 1960s 15 1 1970s 243 1 1980s 1,082 4 8 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
• Take average retail wage by county(exclude eating and

drinking)

• A few missing values for some years. Interpolate
• Rents
• Measure of rent in vicinity of store (block groups in 2 mile

radius)

• Rent Index = (Value of owner-occupied homes +

100×monthly rent)/land

• 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 λgen

t

and λgroc

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

uk0 = o(m) + zω + ζk0 + (1 − σ)εk0. ukj = −τ (m) yj + xjγ + ζk1 + (1 − σ) εkj. m population density (population within 5 mile radius). xj store characteristics

• (m) = γ0 + γ1 ln(m) + γ2 (ln(m))2

τ(m) = τ0 + τ1 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 Rgen

j

is predicted sales of Wal-Mart regular stores — b Rgen

j

+ b Rgroc

j

is predicted sales of supercenters

• Measurement error

˜ εgen

j

= ln( ˜ Rgen

j

) − ln(Rgen

j

(θ)). where εmeasure

j

is normally distributed

• Two Models: MLE and Constrained MLE to fit cannibalization

rate of 1% for 2006

Estimates of Demand Model

• Implied cannibalization rates
• σ2 = .06, fit is good.

λgen = 1.7 and λgroc = 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*

Evidence on Diminishing Returns Incremental Operating Profits on General Merchandise

Within- State Age N Incremental Sales ($million) Incremental Operating Profit ($million) Stand- alone Operating Profit ($million) Incremental Store Density Index Incremental Distribution Center Density (miles) 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

Incremental Profits on Groceries

Within- State Age N Incremental Sales ($million) Incremental Operating Profit ($million) Stand- alone Operating Profit ($million) Incremental Supercenter Density Index Incremental Distribution Center Distance (miles) 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) = Πgen(a) + φgendgen(a) + φRDCdRDC(a) − ω1F1(a) − ω2F2(a) +similar terms for groceries

• a0 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(a0, θ) ≥ v(a, θ), for all a 6= a0 Or ∆v(a, θ) ≥ 0, for ∆v(a, θ) = v(a0, θ) − v(a, θ).

• Given an alternative policy a and a parameter vector θ, we
• bserve

∆˜ v(a, θ) = ∆v(a, θ) + εa,

• Measurement error from wage and rent estimate for each store

location.

∆v(a, θ) = ∆Πgen

a

+ φgen∆dgen

a

− ω1∆Fa,1 − ω2∆Fa,2 ≥ 0,

• Follow recent literature and take a moment inequality ap-

proach — Take subsets of A in which measurement error averages

• ut, so above holds in expecation.
• I define 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)

Present Value Differences Farther Sooner Deviations Number of Deviations Sample Size ΔΠgen

($million) Δdgen

ΔdRDC

(100s of

year miles) ΔF1

gen

ΔF2

gen

239,698 15,000

• 1.28

0.82 5.90

• 0.74
• 4.63

Estimates of Lower Bound on φgen

Moments Period φRDC 0.00 .02 .05 .10 .20 Farther Sooner Deviation and ω1 = 0 and ω2 = 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:

φgroc ≤ φgen (binding) φFDC φRDC = φgroc φgen ω1 ≥ 0 (coefficient on ln(m)) ω2 ≤ 0 (coefficient on ln(m)2) ζgroc

ω

≤ 1 (fixed cost for groc relative to gen) (binding)

• Fix φRDC and solve problem of minimizing φgen subject to

above

Estimates of Lower Bound on φgen

Moments Period φRDC 0.00 .02 .05 .10 .20 Farther Sooner Deviation and ω1 = 0 and ω2 = 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

— Store openings and conversions — Above gives 10 groups of peturbations

• Instruments: Need to be positive

— Vector of ones (Basic Moments) — Interactions: z+

a

= c+ + ∆dgen

a

≥ 0 z−

a

= c− − ∆dgen

a

≥ 0 — Same with other ∆dk

a, ∆F k a,1, ∆F k a,2.

• Together get 272 inequalities

Estimates of Lower Bound on φgen

Moments Period φRDC 0.00 .02 .05 .10 .20 Farther Sooner Deviation and ω1 = 0 and ω2 = 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

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 compa-

nies 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 Location Number of Stores Mean Store Density Index To current density from half density To Most Dense State (NJ) 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 Location Number of Stores Mean Store Density Index To current density from half density To Most Dense State (NJ) 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