Estimating trading risks in the presence of reporting bias

1. Luigi Reggi
Rockefeller College
University at Albany SUNY
PAD 703 – Economic and Financial Theory
1
Online feedback and reputation

2. Readings
2
Dellarocas, C., & Wood, C. A. (2008). The sound of silence in
online feedback: Estimating trading risks in the presence of
reporting bias. Management Science, 54(3), 460-476
Dellarocas, C. (2003). The digitization of word of mouth:
Promise and challenges of online feedback mechanisms.
Management science, 49(10), 1407-1424

3. Research Questions
Is eBay online feedback biased?
What determines this bias?
Main conclusions:
- Yes, our quantitative estimates of positive
transaction outcomes are lower than positive
feedback posted online
- Evidence of both positive and negative
reciprocation
3

4. Agenda
• Background
• Dataset and descriptive statistics
• Methodology and results of 2 models
• Discussion
• Conclusions
4

5. Background
• Online feedback
–elicits good behavior and cooperation
–facilitates transaction among strangers
–improve efficiency of online markets
• Internet Auctions accounts for 16% of all
consumer frauds
5

6. eBay feedback mechanism
• Voluntary self-reporting of the outcomes
of the transactions
–Public report of private outcomes:
OUTCOME ====> FEEDBACK
• Bi-directional
6

7. eBay feedback mechanism
7

8. Dataset
• 51,052 eBay rare coin auctions in 2002
–16,045 Buyers
–6,242 Sellers
• Info on: seller, buyer and feedback
posted (type, timing, etc.)
8

9. Feedback
9
Type of
feedback
Seller’s
feedback
Buyer’s
feedback
Positive (+) 99.3% 98.9%
Neutral (o) 0.1% 0.5%
Negative (-) 0.6% 0.5%
% of auctions where seller or buyer posted feedback:
% of auctions where seller posted feedback: 77.5%
% of auctions where buyer posted feedback: 67.8%

10. Type of feedback and relative order
25 combinations
10
Who
comments
first
Seller’s
feedback
Buyer’s
feedback
% of auctions
Seller Positive (+) Positive (+) 38.4%
Buyer Positive (+) Positive (+) 18.2%
Seller Positive (+) SILENCE 20.2%
Buyer SILENCE Positive (+) 10.4%
/ SILENCE SILENCE 11.8%
Subtotal 99.0%
All other 20 combinations 1.0%
Total (25 combinations) 100.0%

11. 1st model: simultaneous equations
11
Pr(jb, js) = SUM [ Pr(ib, is) * Pr(jb|ib) * Pr(js|is) ]
Prob of observing a
FEEDBACK PATTERN
(e.g. positive for buyer,
positive for seller)
j = feedback reported
i = outcomes of transaction
s = seller
b = buyer
Prob of given
OUTCOMES
of transaction
Prob that the buyer
reports feedback j
given oucome i
Prob that the seller
reports feedback j
given oucome i

12. 2 assumptions
• Assumption 1: one-to-one mapping
between outcomes and feedback types:
good outcome => positive feedback
mediocre outcome => neutral feedback
bad outcome => negative feedback
• Assumption 2: traders tell the truth
12

13. Estimation
• Maximum likelihood method
• Estimated probabilities of observing a given
outcome:
13
Seller’s
outcome
Buyer’s
outcome
Good 88.6% 81.3%
Mediocre 10.4% 17.4%
Bad 0.1% 1.1%

14. 2nd model: adding feedback timing
• Makes use of the 25 combination of type of
feedback and temporal ordering
• Estimated probabilities of observing a given
outcome:
14
Seller’s
outcome
Buyer’s
outcome
Good 85.6% 78.9%
Mediocre 13.7% 20.4%
Bad 0.6% 0.7%

15. 2nd model: adding feedback timing
2nd mover propensity to report given 1st mover
feedback
15
Second
mover
Oucome
experienced by
second mover
First mover’s feedback
Positive Neutral Negative
Seller
Good increase decrease
Mediocre decrease increase
Bad decrease increase increase
Buyer
Good increase decrease
Mediocre decrease
Bad increase

16. Conclusions
1. We derived quantitative estimates of
satisfaction => BIAS
2. We could extract information from silent
transactions
3. Reciprocity in people’s online reporting
behavior has an impact both on negative
and positive feedback
4. General methodology that can be applied to
a variety of bidirectional feedback
mechanisms
16

17. Add silent feedback!
17

18. II PART
Connections to PAD 703 materials
18

19. Bayes’ rule
• Pr(feedback type| experienced outcome)
• Pr(feedback type of 2nd mover | feedback
type of 1st mover)
19

20. Sequential games (1/2)
20
Seller
Buyer Buyer Buyer Buyer
positive
(+) neutral
(0)
silence
(s)
negative
(-)
+ 0 - s + 0 - s + 0 - s + 0 - s
+1
+1
0
+1
-1
+1
0
+1
+1
0
0
0
-1
0
0
0
+1
-1
0
-1
-1
-1
0
-1
+1
0
0
0
-1
0
0
0
p depends on the
outcome of transaction
p of reporting depends on
the outcome of transaction AND
on Seller first move
19,613
0
60
10,220
7
1
7
4
2
12
163
5,318
64
93
6,026
18
eBay
score
no. of
auctions

21. Sequential games (2/2)
21
Buyer
Seller Seller Seller Seller
positive
(+) neutral
(0)
silence
(s)
negative
(-)
+ 0 - s + 0 - s + 0 - s + 0 - s
+1
+1
0
+1
-1
+1
0
+1
+1
0
0
0
-1
0
0
0
+1
-1
0
-1
-1
-1
0
-1
+1
0
0
0
-1
0
0
0
9,303
0
12
5,318
0
31
93
4
2
31
93
10,220
163
93
6,026
4
eBay
score
no. of
auctions

22. Reputation
• Repeated play
• Incentive to “cooperate”
• Works in the long-run and rewards the
most patient player
22
P2
Cooperate Defect
P1
Cooperate 1, 1 -1, 2
Defect 2, -1 0,0

23. Reputation
• High promised future gains from
reputation => overcome short-term
temptation to cheat
• Supported by a trigger strategy
cheating => bad reputation!
• Not showing the whole history of
received feedback => Incentive to keep
on “cooperating”
23