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Q UANTITY P REMIA AND W ITHIN -S TORE S EARCH C OSTS In Kyung Kim Indiana University August 30, 2013 1 / 42 P RICES E XPECTATION WITHIN A S TORE When consumers are shopping in a store, they usually do not expect to pay more per unit for a

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SLIDE 1

QUANTITY PREMIA AND WITHIN-STORE SEARCH COSTS

In Kyung Kim

Indiana University

August 30, 2013

1 / 42

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SLIDE 2

PRICES EXPECTATION WITHIN A STORE

◮ When consumers are shopping in a store, they usually do

not expect to pay more per unit for a larger package than they do for a smaller package.

◮ Same unit price makes sense under the law of one price. ◮ Quantity discount also makes sense under the law of

diminishing marginal utility.

◮ It is hard to find any reason for consumers to purchase a

larger package with a higher unit price.

2 / 42

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SLIDE 3

AN EXAMPLE OF UNIT PRICE DISPERSION

AND QUANTITY SURCHARGE

3 / 42

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SLIDE 4

LITERATURE REVIEW

◮ Costly search

◮ Stigler (1961), Rothschild (1973), Reinganum (1979),

Burdett and Judd (1983)

◮ Information clearinghouse

◮ Rosenthal (1980), Varian (1980), Baye and Morgan (2001)

◮ Empirical work

◮ Hypothesis test ◮ Sorensen (2000), Brown and Goolsbee (2002), Baye,

Morgan, and Scholten (2004)

◮ Structural estimation ◮ Hong and Shum (2006), Moraga-González and

Wildenbeest (2008)

4 / 42

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SLIDE 5

CONTRIBUTION OF THIS PAPER

Explore within-store unit price dispersion and search costs.

◮ Provide an explanation of quantity premium based on

model with costly price information.

◮ Recover determinants of comparison costs. ◮ Investigate how location on shelves and aisles’ impact on

quantity discount, premia and unit price dispersion.

5 / 42

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SLIDE 6

THE MODEL

ASSUMPTION AND NOTATION

◮ Three players: retailer, heavy users, and light users ◮ A product is sold by the piece and a K pack of the same

product is also available.

◮ Light users’ demand for the product is

DL = 1 if PL ≤ VL,

  • therwise.

◮ Heavy user’s demand is

DH = K if P ∗

H ≤ VH,

  • therwise.

6 / 42

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SLIDE 7

THE MODEL

ASSUMPTION AND NOTATION

◮ Two types of light users:

◮ Type 1 light users have a higher reservation value than

heavy users. (V 1

L > VH)

◮ Type 2 light users have a lower reservation value than

heavy users. (V 2

L < VH) ◮ The proportion of the type 1, type 2 light users, and heavy

users: γ1, γ2, γ3(= 1 − γ1 − γ2).

◮ Neither type of light user has any incentive to purchase a

multi-pack: V 1

L ≤ KVH.

7 / 42

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SLIDE 8

THE MODEL

ASSUMPTION AND NOTATION

◮ Heavy users’ strategy set is {Compare Unit Prices, Do Not

Compare}.

◮ It incurs a constant positive comparison cost, C∗ > 0 for

heavy users to check the single unit price.

◮ Take product assortment and shelf space allocation as

given.

◮ Focus on the decision of single unit price and multi-pack

unit price.

8 / 42

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SLIDE 9

THE MODEL

ASSUMPTION AND NOTATION

◮ The retailer’s profit per unit is equal to the unit price it

charges minus the wholesale price per unit. π = P − W.

◮ The profit from the sale of one individual unit is either

π1

L = V 1 L − W 1 L or π2 L = V 2 L − W 2 L.

◮ The profit from the sale of one multi-pack is

KπH = K(VH − WH).

◮ Assume that when the multi-pack unit price is higher than

the single unit price (PH = VH, PL = V 2

L), the profit per unit

from the sale of one multi-pack is larger than the profit from the sale of one individual unit: πH > π2

L.

(1)

9 / 42

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SLIDE 10

THE MODEL

ASSUMPTION AND NOTATION

◮ If heavy users never compare the two unit prices,

PH = VH and PL = V 1

L

if B > A, V 2

L

if B < A, where A ≡ (γ1 + γ2)π2

L + Kγ3πH and B ≡ γ1π1 L + Kγ3πH. ◮ If heavy users always compare the two unit prices,

PH = VH and PL = V 1

L

if B > D, V 2

L

if B < D, where B ≡ γ1π1

L + Kγ3πH and D ≡ (γ1 + γ2 + Kγ3)π2 L. ◮ Therefore, the retailer’s strategy set is {Quantity Discount,

Quantity Premium}.

10 / 42

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SLIDE 11

THE MODEL

STRATEGIES

◮ The retailer’s strategy is

◮ Quantity Discount with probability α. ◮ Quantity Premium with probability (1 − α).

◮ The heavy user’s strategy is

◮ Compare Unit Prices with probability β. ◮ Do Not Compare with probability (1 − β). 11 / 42

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SLIDE 12

THE MODEL

PAYOFF MATRIX

Heavy User Compare Do Not Compare Store Quantity Discount (B, − C∗) (B, 0) Quantity Premium (D, K(VH − V 2

L) − C∗)

(A, 0)

◮ K(VH − V 2 L) can be defined as a potential search benefit.

12 / 42

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SLIDE 13

THE MODEL

EQUILIBRIA

◮ Under the assumption (1), D < A. ◮ Three separate cases, D < B < A, D < A < B, and

B < D < A, lead to different equilibria.

◮ For instance, when D < B < A and C∗ < K(VH − V 2

L), we

have a mixed strategy equilibrium with α = 1 − C∗ K(VH − V 2

L),

and β = (γ1 + γ2)π2

L − γ1π1 L

Kγ3(πH − π2

L)

. (2)

◮ The higher the comparison cost or the smaller the potential

benefit of search, the higher the probability of quantity premium.

13 / 42

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SLIDE 14

THE MODEL

AN EXAMPLE OF MIXED STRATEGY EQUILIBRIUM

Heavy User Compare Do Not Compare Store Quantity Discount (10, −1) (10, 0) Quantity Premium ( 5, 2) (15, 0)

◮ The retailer charges a premium on multi-packs one out of

three times. (α = 2/3)

◮ Heavy users compare unit prices one out of two times.

(β = 1/2)

14 / 42

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SLIDE 15

THE MODEL

AN EXAMPLE OF PURE STRATEGY EQUILIBRIUM

Heavy User Compare Do Not Compare Store Quantity Discount (15, −2) (15, 0) Quantity Premium ( 5, −1) (10, 0)

◮ Quantity Discount with probability 1 is the retailer’s

dominant strategy.

◮ Do Not Compare with probability 1 is the heavy user’s

dominant strategy.

15 / 42

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SLIDE 16

TABLE: Equilibria

Condition Cost of Comparison Equilibrium V 1

L > VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/QD, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QP , Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L = VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/ND, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QP , Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L > VH = V 2 L

B < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

16 / 42

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SLIDE 17

TABLE: Equilibria

Condition Cost of Comparison Equilibrium V 1

L > VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/QD, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QP , Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L = VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/ND, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QP , Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L > VH = V 2 L

B < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

16 / 42

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SLIDE 18

TABLE: Equilibria

Condition Cost of Comparison Equilibrium V 1

L > VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/QD, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L = VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/ND, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L > VH = V 2 L

B < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

17 / 42

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SLIDE 19

TABLE: Equilibria

Condition Cost of Comparison Equilibrium V 1

L > VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/QD, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L = VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/ND, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L > VH = V 2 L

B < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

17 / 42

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SLIDE 20

TABLE: Equilibria

Condition Cost of Comparison Equilibrium V 1

L > VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/QD, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L = VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/ND, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L > VH = V 2 L

B < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

17 / 42

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SLIDE 21

TABLE: Equilibria

Condition Cost of Comparison Equilibrium V 1

L > VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/QD, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L = VH > V 2 L

D < B < A C∗ < K(VH − V 2

L)

Mixed Strategy Equilibrium (QP/ND, Check/No Check) C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) D < A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

B < D < A C∗ > K(VH − V 2

L)

Pure Strategy Equilibrium (QP , No Check) V 1

L > VH = V 2 L

B < A C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (ND, No Check) C∗ > K(VH − V 2

L)

A < B C∗ < K(VH − V 2

L)

Pure Strategy Equilibrium (QD, No Check) C∗ > K(VH − V 2

L)

17 / 42

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SLIDE 22

EMPIRICAL ANALYSIS

OUTLINE

The empirical part of the paper conducts the followings one by

  • ne.
  • 1. Derivation of the empirical framework.
  • 2. Data explanation.
  • 3. Graphical analysis.
  • 4. Estimation of the regression model.

18 / 42

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SLIDE 23

EMPIRICAL ANALYSIS

DERIVATION OF THE EMPIRICAL FRAMEWORK

◮ When there is a pure strategy equilibrium with quantity

premium, C∗ is larger than K(VH − V 2

L). ◮ When there is a mixed strategy equilibrium, then C∗ takes

the value of (1 − α)K(VH − V 2

L). ◮ When there is a pure strategy equilibrium with quantity

discount or no price discrimination, C∗ can be either greater or less than K(VH − V 2

L).

19 / 42

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SLIDE 24

EMPIRICAL ANALYSIS

DERIVATION OF THE EMPIRICAL FRAMEWORK

◮ When there is a pure strategy equilibrium with quantity

premium, C∗ is larger than K(VH − V 2

L). ◮ When there is a mixed strategy equilibrium, then C∗ takes

the value of (1 − α)K(VH − V 2

L).

19 / 42

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SLIDE 25

EMPIRICAL ANALYSIS

DERIVATION OF THE EMPIRICAL FRAMEWORK

◮ When there is a pure strategy equilibrium with quantity

premium, C∗ is larger than K(VH − V 2

L). ◮ When there is a mixed strategy equilibrium, then C∗ takes

the value of (1 − α)K(VH − V 2

L). ◮ The probability of quantity premium, 1 − α, is defined as

follows. 1 − α =

  • 1

if

C∗ K(VH−V 2

L) ≥ 1,

C∗ K(VH−V 2

L)

if

C∗ K(VH−V 2

L) < 1.

(3)

19 / 42

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SLIDE 26

DERIVATION OF THE EMPIRICAL FRAMEWORK

For the empirical work, take natural logarithms of (3).

ln(1 − αij) = ln C∗

ij − ln Ki − ln(VHij − V 2 Lij)

if ln C∗

ij − ln Ki − ln(VHij − V 2 Lij) < 0,

if ln C∗

ij − ln Ki − ln(VHij − V 2 Lij) ≥ 0.

(4)

The quantity premium, VHij − V 2

Lij, is observed with an error

term. VHij − V 2

Lij = ∆Pij exp(ε1ij).

⇒ ln

  • VHij − V 2

Lij

  • = ln ∆Pij + ε1ij,

(5) where ∆Pij ≡ N

t PHijt−PLijt N

.

20 / 42

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SLIDE 27

DERIVATION OF THE EMPIRICAL FRAMEWORK

An Example of calculating ∆P.

21 / 42

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SLIDE 28

DERIVATION OF THE EMPIRICAL FRAMEWORK

Assume comparison costs are given by: ln C∗

ij = β0+β1HDij +β2V Dij +β3BSij +β4SBij +

  • j

αjDr

j +ε2ij.

(6)

◮ HDij is the horizontal distance. ◮ V Dij represents the vertical distance. ◮ BSij is a bottom shelf dummy. ◮ SBij is number of products sharing the same brand

adjusted to the store size.

◮ Also include retailer dummies.

22 / 42

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SLIDE 29

DERIVATION OF THE EMPIRICAL FRAMEWORK

◮ By plugging equations (5) and (6) into (4), obtain the

following Tobit model. yij = y∗

ij

if y∗

ij < 0,

if y∗

ij ≥ 0,

(7) where yij = ln(1 − αij). The latent variable, y∗

ij, is linear in

regressors. y∗

ij = β0 + β1HDij + β2V Dij + β3BSij + β4SBij +

  • j

αjDr

j+

+ δ1 ln Ki + δ2 ln (∆Pij) + εij.

◮ Model implies

δ1 = −1, δ2 = −1 (8) which allows for direct test of the model’s fitness for the data.

23 / 42

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SLIDE 30

DATA

MAIN DATA SET

◮ Weekly retail prices collected from 169 stores by the Korea

Consumer Agency (KCA) since December of 2009.

◮ 25 products for which both multi-pack and single unit prices

are available.

◮ They are simultaneously available only at several stores for

different number of weeks.

◮ Exclude cases where both prices are simultaneously

reported for less than 8 weeks.

◮ 942 product/store combinations.

24 / 42

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SLIDE 31

TABLE: Summary Statistics of the Data

Description Mean

  • Std. Dev.

Min Max Weeks 52.05 31.25 8.00 113.00 Prob of Q.P . 0.24 0.38 0.00 1.00 Potential Search Benefit 1.03 0.92 0.01 8.45

◮ “Weeks” represents the number of weeks when both unit

prices of a product in a store are available.

◮ The probability of quantity premium, 1 − α, is calibrated as

the ratio of the number of weeks at which the multi-pack unit price is higher than the single unit price to “Weeks”.

25 / 42

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SLIDE 32

DATA

TYPE OF EQUILIBRIUM

◮ Upon the size of the quantity premium probability, 1 − α,

they are sorted into three types of equilibrium:

◮ 353 combinations with 1 − α ∈ (0, 1) into the mixed strategy

equilibrium.

◮ 120 combinations with 1 − α = 1 into the pure strategy

equilibrium with quantity premium.

◮ 469 combinations with 1 − α = 0 into the pure strategy

equilibrium with quantity discount or no price discrimination.

26 / 42

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SLIDE 33

DATA

ADDITIONAL DATA SET

◮ Horizontal and vertical distances between the price tag of

multi-pack and single item.

◮ Manually collected only at stores located in Seoul

Metropolitan Area on two separate occasions, first in December of 2012 and second in July of 2013.

◮ 181 observations from 54 stores.

27 / 42

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SLIDE 34

DATA

ADDITIONAL DATA SET: GEOGRAPHIC LOCATION OF STORES

28 / 42

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SLIDE 35

GRAPHICAL ANALYSIS

◮ The Tobit model (7) predicts a negative relationship

between the potential search benefit and probability of quantity premium holding the comparison cost constant.

◮ A positive relationship between distances and comparison

cost is also expected in the model.

◮ We graphically present above relationships before the

estimation of our Tobit model.

29 / 42

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SLIDE 36

GRAPHICAL ANALYSIS

RECOVERY OF COMPARISON COSTS

◮ If the quantity premium, VHij − V 2 Lij, can be observed with

no error term, VHij − V 2

Lij = ∆Pij.

then, we can recover comparison costs directly from our main price data.

◮ By rearranging (4), we can define Cij as follows.

Cij = C∗

ij

if C∗

ij < Ki∆Pij,

Ki∆Pij if C∗

ij ≥ Ki∆Pij,

(9) where C∗

ij ≡ (1 − αij)Ki∆Pij. ◮ Using the equation (9), we recover 353 comparison costs

and 120 censoring points.

30 / 42

slide-37
SLIDE 37

GRAPHICAL ANALYSIS

DISTRIBUTION OF COMPARISON COSTS AND CENSORED VALUES

31 / 42

slide-38
SLIDE 38

GRAPHICAL ANALYSIS

PROBABILITY OF QUANTITY PREMIUM DECREASES AS POTENTIAL BENEFITS OF SEARCH GROW

32 / 42

slide-39
SLIDE 39

GRAPHICAL ANALYSIS

THE AVERAGE DISTANCE INCREASES AS THE SIZE OF COMPARISON COST GETS LARGER.

33 / 42

slide-40
SLIDE 40

GRAPHICAL ANALYSIS

PRICE DISPERSION AND COMPARISON COST

◮ Another interesting empirical question is the impact of

search cost on the price dispersion level.

◮ Brynjolfsson and Smith (2000), Brown and Goolsbee

(2002), Scholten and Smith (2002), Ancarani and Shankar (2004).

◮ Use the recovered comparison costs to see their

relationship within a store.

◮ Define the average standardized deviation of single unit

price from multi-pack unit price as our measure of dispersion. Dij =

N

  • t

|PLij − PHij| (PLij + PHij)/2 for a product i sold at a store j.

34 / 42

slide-41
SLIDE 41

GRAPHICAL ANALYSIS

THE LEVEL OF PRICE DISPERSION RISES AS COMPARISON COST INCREASES

35 / 42

slide-42
SLIDE 42

ESTIMATION

SAMPLE SELECTION PROBLEM

◮ Now, estimate the Tobit model (7). ◮ Potential sample selection problem from dropping those

  • bservations with 1 − α = 0.

◮ Suppose the population model is:

y∗

ij = xijβ + εij, ◮ Let s be the selection indicator. From table 2, we can

formulate: sij = 1 iff B′

ij < A′ ij

and VHij > V 2

Lij,

iff A′

ij < B′ ij

  • r

VHij = V 2

Lij, ◮ A sufficient condition for no sample selection problem is

that s is independent of y∗ and x.

36 / 42

slide-43
SLIDE 43

ESTIMATION

TABLE: Tobit Estimation

Exclude Separated Include Separated I Include Separated II Regressor Coeff.

  • Std. Err.

Coeff.

  • Std. Err.

Coeff.

  • Std. Err.

Horizontal Distance 0.608 (0.172)*** 0.056 (0.007)*** 0.615 (0.173)*** Vertical Distance 0.767 (0.255)*** 0.662 (0.262)** 0.724 (0.236)*** Bottom 1.935 (0.598)*** 1.860 (0.643)*** 1.928 (0.589)*** Same Brand 0.842 (0.572) 0.439 (0.718) 0.777 (0.571) Separated 3.056 (0.210)*** Retailer Nong-Hyup 1.793 (0.860)** 0.691 (0.585) 1.821 (0.855)** Lottemart 0.381 (0.850)

  • 0.683

(0.638) 0.250 (0.834) Lotte Department Store 1.380 (1.057) 0.404 (0.908) 1.305 (1.036) Lotte Supermarket 1.028 (0.842) 0.005 (0.557) 0.987 (0.832) Hyundai Department Store 0.910 (0.872) 0.246 (0.664) 0.866 (0.860) Homeplus

  • 0.349

(0.941)

  • 1.590

(0.726)**

  • 0.403

(0.931) Homeplus Express 2.074 (0.935)** 1.019 (0.715) 2.027 (0.916)** ln K

  • 1.284

(0.363)***

  • 1.275

(0.423)***

  • 1.243

(0.350)*** ln ∆P

  • 0.762

(0.187)***

  • 0.749

(0.193)***

  • 0.737

(0.176)*** Constant 1.745 (1.245) 3.002 (1.077)*** 1.620 (1.189) Observations 125 136 136 P seudoR2 0.287 0.278 0.325

Note: Log of quantity premium probability is the dependent variable in all three specifications. Heteroskedasticity robust standard errors are in parenthesis. *** indicates significant at 1% level, ** at 5% level, * at 10% level.

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slide-44
SLIDE 44

ESTIMATION

TABLE: Marginal Effects on the Probability of Quantity Premium at the Means

Exclude Separated Include Separated I Include Separated II Regressor M.E.

  • Std. Err.

M.E.

  • Std. Err.

M.E.

  • Std. Err.

Horizontal Distance 0.587 (0.167)*** 0.051 (0.007)*** 0.587 (0.166)*** Vertical Distance 0.740 (0.249)*** 0.613 (0.245)** 0.691 (0.228)*** Bottom 1.869 (0.564)*** 1.724 (0.576)*** 1.841 (0.546)*** Same Brand 0.813 (0.547) 0.406 (0.665) 0.742 (0.540) Separated 2.918 (0.210)*** Retailer Nong-Hyup 1.732 (0.827)** 0.64 (0.537) 1.739 (0.812)** Lottemart 0.368 (0.821)

  • 0.633

(0.595) 0.239 (0.797) Lotte Department Store 1.333 (1.014) 0.374 (0.838) 1.246 (0.981) Lotte Supermarket 0.993 (0.812) 0.005 (0.516) 0.943 (0.794) Hyundai Department Store 0.879 (0.839) 0.228 (0.615) 0.827 (0.818) Homeplus

  • 0.337

(0.908)

  • 1.474

(0.664)**

  • 0.385

(0.888) Homeplus Express 2.004 (0.895)** 0.944 (0.655) 1.936 (0.865)** ln K

  • 1.240

(0.353)***

  • 1.181

(0.401)***

  • 1.187

(0.338)*** ln ∆P

  • 0.736

(0.175)***

  • 0.694

(0.174)***

  • 0.703

(0.162)***

Note: The table presents marginal effects on the right truncated mean for Tobit where log of quantity premium probability is the dependent variable. *** indicates significant at 1% level, ** at 5% level, * at 10% level.

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slide-45
SLIDE 45

DIAGNOSTICS

Non-normality or heteroskedasticity leads to an inconsistent estimator.

◮ The normality hypothesis can not be rejected. ◮ The model diagnostics show a strong rejection of the

homoskedasticity hypothesis.

◮ Apply the censored least absolute deviations estimation

suggested by Powell (1984).

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slide-46
SLIDE 46

ESTIMATION

TABLE: CLAD

Exclude Separated Include Separated II Variable Observed

  • Std. Err.

95% C.I. Observed

  • Std. Err.

95% C.I. Horizontal Distance 0.787 0.359 0.124 1.841 0.711 0.357

  • 0.002

1.155 Vertical Distance 0.718 0.207 0.341 0.977 0.641 0.201

  • 0.035

0.806 Bottom 0.751 0.995

  • 0.125

2.733 0.850 1.020

  • 0.598

4.382 Same Brand 0.237 0.450 0.000 1.678 0.320 0.420 0.155 3.011 Separated 3.155 0.321 2.529 3.588 Retailer Nong-Hyup 0.332 0.946

  • 0.625

2.735 0.549 0.850

  • 0.044

4.552 Lottemart

  • 0.263

0.750

  • 0.902

2.372

  • 0.215

0.761

  • 0.865

3.143 Lotte Dept. Store

  • 0.463

1.182

  • 1.505

0.992

  • 0.344

1.061

  • 1.715

1.603 Lotte Supermarket

  • 0.174

0.697

  • 0.655

0.362 0.127 0.758

  • 0.383

3.186 Hyundai Dept. Store

  • 0.599

1.295

  • 2.848

1.045

  • 0.282

1.091

  • 1.554

4.700 Homeplus Homeplus Express 0.806 1.151

  • 0.772

4.004 0.910 1.102

  • 0.308

4.411 ln K

  • 2.237

0.842

  • 4.342
  • 0.932
  • 1.896

0.647

  • 3.253
  • 0.622

ln ∆P

  • 0.743

0.352

  • 1.494
  • 0.194
  • 0.608

0.275

  • 1.147
  • 0.003

Constant 3.828 3.158

  • 0.829

11.663 2.504 2.343

  • 3.273

7.770 Observations 116 128 P seudo R2 0.580 0.634

Note: Log of quantity premium probability is the dependent variable in both specifications. *** indicates significant at 1% level, ** at 5% level, * at 10% level.

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slide-47
SLIDE 47

ROBUSTNESS

◮ Remember that we exclude cases where both prices are

simultaneously reported for less than 8 weeks.

◮ As a robustness check, we use different minimum number

  • f weeks: 20 and 30 weeks.

◮ They generate similar results.

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slide-48
SLIDE 48

CONCLUSION

◮ Showed that there exist 1) mixed strategy equilibria where

the retailers charges quantity premia with positive probabilities and 2) pure strategy equilibria where we always observe a quantity premium.

◮ Used a structural model to recover determinants of

comparison costs.

◮ Found that the greater the horizontal or vertical distance

between multi-packs and single units is, the more likely quantity premia is observed and the greater the unit price dispersion is.

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