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learning - Editorial Express
Tests for Consumer Learning by Experience in
Frequently Purchased Products
Matthew Osborne
U.S. Department of Justice
Antitrust Division
Overview
• Many situations where want to know, is
experiential learning present?
– Merger review
– Government provision of information
– New product introduction
• Are there simple ways to test for learning?
– Robust to inclusion of alternative dynamics?
• Switching costs, variety-seeking, inventory
behavior
Approach
• Dynamic model of learning
– Similar to those used in empirical literature
– Embed switching costs, variety-seeking,
stockpiling
• Derive implications of learning
– Numerical simulation
– Example: Application to scanner data
Simple Model
Established (Product 1):
0 + ηi 1{yi, t-1 = 1}
New (Product 2), expected:
γi0 + ηi 0
New, taste known:
γi + ηi 1{yi, t-1 = 2} + εit
+ εit
i.i.d. part of tastes.
• Permanent part of tastes (learning):
• Distribution before learning: N(γi0, σ2).
• True taste: γi
• Switching Costs/Variety-Seeking:
• ηi : allow dynamics even if σ2 = 0.
• yi, t-1 is product choice in t-1.
Simple Model
• Allow forward-looking consumers
– Discount factor: d.
– If d > 0: Benefit to experiment:
• Might like and repurchase.
• Option value of learning.
– Positive under no switching costs.
– Increasing in σ2.
– Cost of experiment:
• Expected taste less than favorite product utility.
Stockpiling
• Choose 2 sizes (1, 2 units)
– Can bundle small sizes
• Consumption requirement of 1 unit.
– Stockout cost
• Store visit cost.
• Consumer choice:
– Purchase, and product consumption
• Markov prices
Implication: Share Difference
• Maintained hypothesis:
– d > 0; h = 0
– prices fixed over time (or markov)
• First two periods after new product intro.
– Share who choose new, then do not, minus
– Share who do not choose new, then do.
• Difference is positive if s2 > 0, 0 otherwise.
– Static demand: can permute choices.
– Option value: choose sooner rather than later.
Implication: Rising Tenure
• Maintained hypothesis:
– Any d, any h.
– Prices fixed/Markov over time
• Among consumers whose previous purchase
was new product:
• s2 > 0: Share repurchasers rises over time.
– Initially, people who experiment
– Later, those who like product
• Does not tell us about option value
Implication: Small Size Choice
• Maintained hypothesis:
– d > 0, any h
– Prices Markov
• Among new product purchasers, share
choosing small size decreases over time.
• Risky to experiment with larger size.
Data Set: Laundry Detergent
• Household level repeated panel data from
Sioux Falls, SD.
• New product introductions:
12/28/85
Liquid Cheer Liquid Surf
5/86
9/86
Liquid Dash
5/87
8/20/88
Test Implementation
• Prices in data aren’t Markov
– Introductory pricing
• Procedure:
– estimate with flexible choice models.
– predict at constant prices.
Test Results
1. Share who choose new and then do not greater
than share who do not and then do.
 Support in Cheer and Dash.
2. Among previous purchasers, share of individuals
repurchasing product rises over time.
 Support in all products (Dash is weak).
3. Smaller size choice on initial purchase.
 Support in all products.
Simulations
• 3 products:
– 2nd has normally distributed taste.
• Expected tastes (gi0) normal.
• Base model: standard normal.
– Others (6) change means, variances.
• Logit error
• 500 simulated consumers, 100 periods.
– Each market is re-drawn 25 times.
Simulated Share Difference
No Inventories
Inventories
0.0
-0.028
Learning
0.106
0.060
Myopic Learning
0.013
-
h=1
No Learning
-0.070
-0.068
Learning
0.048
0.020
h = -1
No Learning
0.122
0.025
Learning
0.210
0.112
No Learning
h=0
Rising Tenure
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
No Learning
Period
59
57
55
53
51
49
47
45
43
41
39
37
35
Learning
33
31
Repurchase Probability
Eta = 0, Forward-Looking Learning
Increase in Repurchase Rate
No Inventories
0.0
-0.002
Learning
0.050
0.034
Myopic Learning
0.041
-
No Learning
-0.001
0.009
Learning
0.062
0.040
No Learning
-0.002
-0.001
Learning
0.039
0.025
No Learning
h=0
h=1
h = -1
Inventories
Small Size Choice
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
No Learning
Period
60
58
56
54
52
50
48
46
44
42
40
38
36
34
Learning
32
30
Share
Share of Small Size of New Product Purchases, h = 0
Change in Small Size Share
Change over 5 pds
h=0
h=1
h = -1
No Learning
0.003
Learning
-0.021
No Learning*
0.001
Learning*
-0.024
No Learning*
0.007
Learning*
-0.014
Product Space
Market Shares:
Type
Cheer Surf
Dash
Other
Era
Wisk
Tide
Solo
Total
Liquid
0.03
0.06
0.02
0.14
0.06
0.10
0.09
0.03
0.53
Powder
0.07
0.03
0.01
0.21
-
-
0.16
-
0.47
Procter & Gamble: Cheer, Dash, Era, Tide, Solo.
Unilever: Surf, Wisk.
Product Space
• Liquid Sizes
32 oz
64 oz
96 oz
128 oz
other
15.5
52.9
11.4
17.5
2.7
• Powder Sizes (oz)
17-20
34-49
65-84
144-157 other
8.8
33.5
32.3
20.5
4.9
Share Difference Model
• Random coefficients logit
– Multinomial logit as baseline
• Dummy variables for new products on
– First purchase after intro
– Second purchase after intro
– Second purchase, given previously chose
new
Share Difference Results
Product
Random
Coefficients
Multinomial
Logit
Cheer
0.061
-0.050
Surf
-0.019
-0.048
Dash
0.016
0.019
Rising Tenure
• Allow h to vary over time for new products
– Split into 3 periods, for each new product
introduction.
– h + ljk0 + ljk1ln(t)
– Expect ljk1 to be positive
Results
Small Size Choice
• Inventory model
– Reduced form
– Dummy variables to allow new size on first
purchase to differ
Small Size Results

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