Imperfect Competition in Milk
Retailing
Vardges Hovhannisyan
Outline





Background
Demand and Supply Models
Data
Results
Future Work
Background

Increased need to better understand the milk demand
(E.Lopez, R. Lopez, 2009)

Do retailers exercise market power? (Capps, Sherwell,
2005)
- Increased retail concentration
- Introduction of private label products
Demand Model (BLP, 1995)





Market level data
Aggregate quantity and price
Accounts for price endogeneity
More realistic elasticity measures (vis-a-vis
logit, nested logit)
Characteristic based approach
- solves dimensionality problem
- allows for predicting demand for new products
BLP Demand Model

How to construct the demand functions?
- Aggregate demand for product j
q jt  i t1 E[1{i chooses j}]  i t1 Pr(i chooses j )
N
N
(1)
- Indirect utility function (i.e. assuming quasi-linear utility)
U ijt  x jt i  p jti   jt   ijt
(2)
BLP Demand Model
- Individual probabilities
Pijt 
e
1 
x jt i  p jti  jt
xikt i  p jti  jt
J
e
k 1
(3)
- Predicted market shares
s jt  
 ,
e
1 
x ' jt i  p jti  jt
x 'ikt i  p jti  jt
J
e
k 1
dF ( ,  )
(4)
BLP Demand Model
-
S ajt
-
Demand equations

s jtp

 ,
e
1 
x ' jt i  p jti  jt
x 'ikt i  p jti  jt
J
e
k 1
BLP aims at estimating F ( ,  )
dF ( ,  )
(5)
BLP Estimation

GMM (why?)
-
Construct the GMM objective function based on the moment
conditions E[ jt | z jt ]  0
(6)
-
Need to obtain the implied values of  jt via the BLP theorem

BLP theorem
J
For a given F ( ,  ) , a unique set { jt } j 1 , t  1,..., T
solves the demand equations
Estimation Details
 i   
         Di  vi , Di
 i  
•
Assume
•
Indirect utility is
PD ( D), vi
Pv (v)
(7)
U ijt  x jt   p jt   jt  [ p jt , x jt ]( Di  vi )   ijt (8)
 jt ( x , p , ; )
jt jt jt 1
•
ijt ( x , p , D ,v ; 2)
jt jt i i
Indirect utility from an outside good is
U iot  0   o Di   o vio   iot
Estimation Details

Integrate  ijt to obtain
Pijt 

e
1 k e
 kt  ikt
(9)
Simulate market shares
s jtp 

 jt  ijt
1
ns
Pijt

i

1
ns
(10)
Construct the demand equations
S ajt  s jtp
(11)
Estimation Details

Contraction mapping solves the share equations (11) for the mean
utility
 hjt1   hjt  log S ajt  log s jtp ( hjt , 2 )

a
a
Obtain the market shocks (for logit  jt  log S jt  log Sot )
 jt   jt  ( x jt   p jt )

(12)
(13)
Construct the moment conditions and the GMM objective function
min  ( ) Z  1Z T  ( )

(14)
Supply Scenarios

Simple linear pricing model
retailer margin: pt  ptw  ctr  (Tr *  rt )1 st ( p)
(17)
manufacturer margin: ptw  ctw  (Tw *  wt )1 st ( p)
(18)

Hybrid model
retailer margin as in (17)
manufacturer margin: ptw  ctr  ctw  (Twn *  wt )1 stn ( p) (19)
Supply scenarios

Non-linear pricing models
o
Manufacturer margin=0 with retailers as residual claimant
retailer margin given by(17), s.t. ptw  ctw
o
Retail markup=0
manuf.margin: pt  ctr  ctw  (Tw *  rt ) 1 st ( p) (20)

Manufacturer collusion
Manuf.margin given by(18),s.t.Tw  T1
Retailer margin given by(17)
Supply Scenarios

Retail collusion
retailer margin given by(17), s.t. Tr  T1
manufacturer margin given by(18)

Monopoly
total margin: pt  ctr  ctw  (T1 *  rt ) 1 st ( p)
with Tr  Tw  T1
Data

Weekly data from IRI on the amount of milk sold and
milk prices in 2001-06

Market level data, no consumer or household
purchase behavior observed

Products as brand-chain-fat content, focus on a
Midwestern city in the U.S.

Markets defined as city*(a 4-week period)
Product
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Manufacturer
Retail Chain
Bareman's Dairy
2
Bareman's Dairy
2
Bareman's Dairy
2
Bareman's Dairy
2
Dean Foods Co
1
Dean Foods Co
3
Dean Foods Co
1
Dean Foods Co
3
Dean Foods Co
1
Dean Foods Co
3
Dean Foods Co
1
Dean Foods Co
3
Johnson & Johnson
1
Johnson & Johnson
3
Johnson & Johnson
1
Johnson & Johnson
3
Johnson & Johnson
1
Johnson & Johnson
3
Johnson & Johnson
1
Johnson & Johnson
3
Private Label
1
Private Label
2
Private Label
3
Private Label
1
Private Label
3
Private Label
1
Private Label
2
Private Label
3
Private Label
1
Private Label
2
Private Label
3
Organic Valley
1
Organic Valley
3
Organic Valley
1
Organic Valley
1
Organic Valley
3
Organic Valley
1
Fat Content
Skim
Low
Reduced
Whole
Skim
Skim
Low
Low
Reduced
Reduced
Whole
Whole
Skim
Skim
Low
Low
Reduced
Reduced
Whole
Whole
Skim
Skim
Skim
Low
Low
Reduced
Reduced
Reduced
Whole
Whole
Whole
Skim
Skim
Low
Reduced
Reduced
Whole
# of 4-Weeks
78
78
78
78
78
78
78
34
78
78
78
78
78
78
41
31
78
78
66
78
71
25
78
71
78
71
25
78
71
25
78
66
17
64
66
16
66
Not in 4-weeks
1-17,21,28-52,78
18-19,42-51,54-78
32-78
2-11,15,17
1-7,
1-35,61-78
1-7,
1-7,
1-35,61-78
1-7,
1-35,61-78
1-5, 71-78
1-60,78
1-7, 71-78
1-5, 71-78
1-60,77,78
1-5, 71-78
Manufacturer
Bareman's Dairy
Bareman's Dairy
Bareman's Dairy
Bareman's Dairy
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Median Price ($/pint)
0.316
0.312
0.312
0.313
0.321
0.334
0.343
0.344
0.359
0.378
0.386
0.397
0.412
0.437
0.455
0.473
0.524
0.794
0.879
0.898
0.882
0.877
0.789
0.558
0.479
0.434
0.423
0.396
0.386
0.383
0.369
0.381
0.384
0.396
0.427
0.441
0.506
0.565
Mean Price ($/pint)
0.321
0.312
0.312
0.314
0.337
0.418
0.414
0.411
0.411
0.454
0.449
0.483
0.536
0.576
0.600
0.615
0.653
0.680
0.701
0.723
0.698
0.690
0.667
0.647
0.628
0.611
0.606
0.590
0.576
0.573
0.559
0.578
0.581
0.599
0.615
0.618
0.634
0.636
Min Price ($/pint)
0.246
0.244
0.243
0.243
0.243
0.243
0.243
0.243
0.243
0.244
0.244
0.245
0.245
0.245
0.245
0.245
0.245
0.245
0.245
0.245
0.230
0.230
0.230
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
0.227
Max Price ($/pint)
0.498
0.498
0.498
0.522
0.637
1.074
1.074
1.074
1.074
1.074
1.074
1.074
1.074
1.074
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
1.150
St. Dev.
0.046
0.041
0.040
0.042
0.067
0.192
0.179
0.174
0.164
0.203
0.192
0.213
0.257
0.272
0.282
0.285
0.295
0.293
0.295
0.289
0.298
0.301
0.307
0.311
0.313
0.313
0.314
0.313
0.312
0.312
0.311
0.316
0.316
0.320
0.322
0.321
0.323
0.322
Ave. Market Share (%)
0.015
0.015
0.037
0.047
0.180
0.158
0.225
0.211
0.335
0.309
0.348
0.322
0.296
0.278
0.268
0.262
0.244
0.231
0.218
0.205
0.277
0.268
0.633
0.662
0.924
1.003
0.974
1.374
1.369
1.336
1.564
1.509
1.491
1.438
1.392
1.377
1.332
1.317
Milk Price ($/pint) and Combined Market Share (%) by Manufacturer
Manufacturer
Bareman's Dairy
Dean Foods Co
Johnson & Johnson
Private Label
Organic Valley
Median
Mean Price
Market Share
0.313
0.315
0.115
0.351
0.422
2.088
0.499
0.636
2.003
0.434
0.622
10.383
0.427
0.609
9.856
Variable
Results from Logit Demand
OLS
Price
-0.617*
Preliminary(0.041)
Results
Product Fixed Effects
IV
-0.763*
(0.042)
Time Fixed Effects
Measure of fit (R sq)
Pints-capita-year
25
50
75
100
0.934
0.934
Estimated price coefficient sensitivity to market definition
-1.669*
-2.434*
(0.114)
(0.114)
-0.759*
-0.947*
(0.050)
-0.499*
(0.050)
-0.612*
(0.033)
-0.373*
(0.025)
(0.033)
-0.454*
(0.025)
Estimation Results from the Mixed Logit Demand Specification
Mean utility Income
Constant
Price
Fat
Retail chain 1
Retail chain2
Income_sq
Age
Child
Unobserved
0.106
6.099*
-12.966*
-30.393*
3.738
-5.488*
0.487
0.118
0.015
1.544
2.391
0.952
-1.946*
5.119*
-2.298
10.510*
-0.352
-1.251*
(0.418)
(0.020)
(7.132)
(1.483)
(4.338)
(0.003)
-5.324*
4.590*
3.560*
4.355*
2.168*
0.504*
(0.232)
(0.261)
(0.068)
(2.562)
(1.024)
(0.001)
3.626*
-0.812*
1.480
4.785*
12.245*
-9.977*
(0.008)
(0.282)
(1.427)
(0.081)
(2.548)
(4.893)
22.102*
10.691
-65.046
-23.327
-4.601
5.993
(0.067)
(8.236)
(35.785)
(22.013)
(9.614)
(3.500)
Product
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Manufacturer
Bareman's Dairy
Bareman's Dairy
Bareman's Dairy
Bareman's Dairy
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Retail Chain
2
2
2
2
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
2
3
1
3
1
2
3
1
2
3
1
3
1
1
3
1
Fat Content
Skim
Low
Reduced
Whole
Skim
Skim
Low
Low
Reduced
Reduced
Whole
Whole
Skim
Skim
Low
Low
Reduced
Reduced
Whole
Whole
Skim
Skim
Skim
Low
Low
Reduced
Reduced
Reduced
Whole
Whole
Whole
Skim
Skim
Low
Reduced
Reduced
Whole
Logit Own-Price Elasticity Mixed Logit Own PriceElasticity
-0.92
-1.13
-0.88
-1.09
-0.90
-1.11
-0.92
-1.13
-1.17
-1.44
-2.44
-3.01
-1.08
-1.32
-1.04
-1.27
-1.12
-1.38
-2.47
-3.04
-1.15
-1.42
-2.47
-3.03
-2.93
-3.60
-2.76
-3.39
-2.89
-3.56
-2.74
-3.37
-2.94
-3.62
-2.76
-3.40
-2.89
-3.55
-2.74
-3.37
-0.87
-1.07
-0.79
-0.97
-0.78
-0.96
-0.85
-1.05
-0.79
-0.97
-0.86
-1.05
-0.80
-0.98
-0.79
-0.97
-0.87
-1.07
-0.81
-0.99
-0.78
-0.96
-2.74
-3.37
-2.52
-3.10
-2.74
-3.37
-2.74
-3.37
-2.52
-3.10
-2.74
-3.37
Product
Manufacturer
Retail Chain
Fat Content
Lerner Index (%)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Bareman's Dairy
Bareman's Dairy
Bareman's Dairy
Bareman's Dairy
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Dean Foods Co
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Johnson & Johnson
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Private Label
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Organic Valley
Organic Valley
2
2
2
2
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
2
3
1
3
1
2
3
1
2
3
1
3
1
1
3
1
Skim
Low
Reduced
Whole
Skim
Skim
Low
Low
Reduced
Reduced
Whole
Whole
Skim
Skim
Low
Low
Reduced
Reduced
Whole
Whole
Skim
Skim
Skim
Low
Low
Reduced
Reduced
Reduced
Whole
Whole
Whole
Skim
Skim
Low
Reduced
Reduced
Whole
0.640
0.639
0.639
0.639
0.645
0.656
0.666
0.675
0.693
0.709
0.711
0.723
0.731
0.752
0.754
0.763
0.765
0.789
0.785
0.813
0.787
0.783
0.805
0.785
0.809
0.789
0.785
0.807
0.788
0.784
0.807
0.804
0.806
0.803
0.800
0.801
0.800
Retail Market Power (Lerner Index)
Future Work




Box-Cox Mixed Logit Model
Supply scenarios implied by dynamic
interactions among the retailers
Structural change by the entry of Wall-Mart in
2003
Variable marginal costs
Questions ? ?