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An Extreme Value Reference
Price Approach
Sanjoy Ghose and Oded Lowengart
January 19, 2005
1
Effect of Price on Choice
 Price
Only models
 Inclusion of Reference Price
2
Reference Price Categories
 External
Reference Price
 Internal Reference Price
3
Internal Reference Prices
 Many
different operationalizations
 Issue of appropriateness
4
Logic & Forms
 Decaying
memory of past occurrences
 Last Price paid (Winer, 1986; Mayhew
& Winer, 1992)
 Variation of past average prices
– Weighted log-mean average (Kalwani et
al., 1990)
– Exponentially weighted average
(Obermiller, 1990)
5
Event Recall
 Hastie’s
theory on memory
 Srull’s experiments
 Incongruence vs Congruence of
Information
 Effect on recall
6
Price & Information
Congruence
 Let Pexp
= Expected price of consumers
 Let price at time t = Pt
 If Pt is similar to Pexp then Pt is
congruent information

7
If Pt >> (or <<) than Pexp, then Pt is
incongruent information
Price & Information
Congruence
The greater the degree of deviation of Pt
from Pexp, the greater the incongruency of
information.
 The greatest incongruency should occur
with the maximum and minimum prices
faced by consumers from t=0 to t=t.

8
Price & Information
Congruence
Such maximum and minimum prices should
be most easily recalled
 We hypothesize that these prices would be
used as reference points in price
evaluations.

9
Other Related Literature
 Monroe
(1979)
 Range Theory (Volkmann, 1951)
– Applications to Pricing in the Mktg. lit.
 Experimental
studies
Janiszewski and Lichtenstein, 1999
 Niedrich, Sharma, and Wedell, 2001
– price attractiveness
 recommends that it was important for future
research to consider range in the operationalization
of reference prices in choice models.

10
Let V be the Utility
V  X   Y
(1)
where
X - gain
Y - loss
 and  - parameters,
Similar to Rajendran & Tellis (1994)..
11
X  PMax  PAct
(2)
Y  PAct  PMin
(3)
Substituting (2) and (3) into (1),
V   ( PMax  PAct )   ( PAct  PMin )
 PMax  PMin  (   ) PAct
V  1PMax  2 PMin  3 PAct
Where,
12
1  2  3
(4)
Extreme Values of Reference
Price
13

Consumers would utilize the maximum and
minimum prices they have paid in their
previous shopping trips as reference prices.

This should be reflected in superior
performance of a model based on the EVRP
approach.
Range Theory
A stimulus range is based on its
extreme points
Relative judgment and
anchoring effects
Human Association Memory
A new incongruent stimulus
leads to a larger associative
memory network
Different memory retrieval for
Incongruent information
Anchoring Points - Product Line
A new extreme stimulus is more
noticeable than other stimulus
Behavioral Theory
Individuals can be happy and
sad at the same time
Price Implications
A price range is related to the
extreme price levels
Price attractiveness is relative
to the extreme prices
New extreme prices change the
range
Price Implications
A new extreme (high/low) price
has more memory associations
than an expected new price
New extreme prices retrieved
better from memory than
regular prices
Price Implications
A new extreme
(maximum/minimum) price is
more noticeable
Price Implications
Both maximum and minimum
prices can be simultaneously
used in evaluating new prices
Internal Reference Price Conceptualization
Consumers use both high and low extreme points (price) in their evaluations of a new price at the same time
Consumers can recall better extreme values (price) as compared with regular prices (expected) they paid previously
Consumers use extreme points (price) to decide about the attractiveness of the offer
Consumers use maximum and minimum prices as anchoring
Choice/Purchase Quantity Implications: Focus of the Current Research
Consumers use two internal reference prices to evaluate current price - comparing current price against the two, simultaneously in a brand
choice/purchase quantity situation
A maximum paid price - high anchoring - creates gains
A minimum paid price - low anchoring - creates losses
Theoretical Framework
14
Hypotheses

15
1) For the aggregate sample, the EVRP
approach for modeling consumer choice can
serve as a better representation of internal
reference price as compared to a last price
paid formulation.
Hypotheses

16
2) For the aggregate sample, the EVRP
approach for modeling consumer choice can
serve as a better representation of internal
reference price as compared to an average
price paid formulation.
EVRP & Segments
 Ratio
of incongruent & congruent Info
(Srull, 1981)
 Number of price points faced by
consumer
 Purchase frequency
17
Hypotheses
 3) The EVRP approach for modeling
consumer choice can serve as a better
representation of internal reference price in
the high frequency segment than in the low
frequency segment.
18
Hypotheses
 4) For each of the two buyer frequency
segments, the EVRP approach for modeling
consumer choice can serve as a better
representation of internal reference price as
compared to a last price paid formulation.
19
Hypotheses

20
5) For each of the two buyer frequency
segments, the EVRP approach for modeling
consumers’ choice can serve as a better
representation of internal reference price as
compared to an average price paid
formulation.
Gains & Losses
 Consumers
evaluate losses & gains
differently (Kahneman & Tversky,
1979)
 We believe: On any given purchase
occasion, a consumer is always evaluating a
loss as well as a gain
21
Model
Pijt 
exp

j m
j 1
(U ijt )
exp
(U ijt )
U ijt  Vijt   ijt
22
gain  ( Pmax  Pact )
loss  ( Pact  Pmin )
EVRP Model
Vijt   j   2 Pijtmax  gain  3 Pijtmin loss   4 DISPijt  5 FEATijt  6 LOYijt
23
LPP Model
Vijt   j   2 Pijtlast gain1   3 Pijtlastloss 2   4 DISPijt   5 FEATijt
  6 LOYijt
1 if ( pijtr  Pijto )  0
1  
 0 otherwise
1 if ( pijtr  Pijto )  0
2  
 0 otherwise
24
APP Model
Vijt   j   P
  P
average gain
2 ijt
1
 5 FEATijt   6 LOYijt
1 if ( pijtr  Pijto )  0
1  
 0 otherwise
1 if ( pijtr  Pijto )  0
2  
 0 otherwise
25
 2   4 DISPijt 
averageloss
3 ijt
Data
A.C. Nielsen company scanner panel data
set of laundry detergents: Sioux Falls
market
 Seven leading brands of liquid detergents
 Tide 128 oz, Tide 96 oz, Tide 64 oz, Wisk
64 oz, Wisk 32 oz, Surf 64 oz, and Surf 32
oz.

26
Variables
Minimum Price - the lowest price paid or
observed by consumer i for choice
alternative j in previous purchase occasions
 Maximum Price - the highest price paid or
observed by consumer i for choice
alternative j in previous purchase occasions

27
Description of Conceptual Approach
Price
Subject Node
5.95
Max....
5.12
4.56
4.50
t=1
28
4.12
3.95
Min...
t=2
5.95 ... Max
t=3
3.24
t=4
3.95
4.01
t=5
3.12
t=6
t=7
3.12 ... Min
t=8
t=9
t=10
Time
Table 1: MNL Results: Calibration Sample – Aggregate Level
Variable
Display
Feature
Brand Specific 1
Brand Specific 2
Brand Specific 3
Brand Specific 4
Brand Specific 5
Brand Specific 6
Loyalty
Gain
Loss
29
Average Price
Last Price
EVRP
Coefficient P-value Coefficient P-value Coefficient P-value
0.0000
1.4731
0.0000
1.3764
0.0000
1.5604
0.0001
1.3164
0.0000
1.4759
0.0000
1.3903
0.9266 -0.2640 0.4860
0.0314
-1.2466 0.0166
0.0307
0.6785
0.0024
0.9091
0.8742
0.0585
0.2009
0.3885
0.0842
0.5174
0.4101
0.2505
-0.0421 0.9197 -0.1910 0.6461 -0.1359 0.7432
-1.3287 0.0073 -0.2411 0.5401 -0.4777 0.2361
0.6352
0.1411
0.5331
0.1857
-0.4006 0.2438
0.0000
3.7359
0.0000
3.7921
0.0000
3.6325
0.0035
0.0104
0.0900
0.0039
0.0088
0.0071
0.1042 -0.0042 0.2857
0.0041
-0.0116 0.0000
Results
 EVRP model:
Significant gain and loss
parameters
 Losses loom larger than gains;
consistent with Prospect Theory
 Less face validity for LPP and APP
models especially for loss parameters
30
Table 2: Goodness-of-Fit Measurements - Aggregate Level - Calibration Sample
Goodness of-fit Measures
Log Likelihood
BIC
AIC
CAIC
31
EVRP
-299.747
657.211
632.494
668.211
Last Price Average Price
-304.631
-304.744
666.979
667.205
642.262
642.488
677.979
678.205
Results
 EVRP model
provides superior fit
based on the four different measures in
Table 2
 Supporting hypotheses 1 and 2
32
Table 3: Accuracy of Model Prediction -Aggregate Level - Hold-Out Sample
Prediction
Hit-rate
33
EVRP
60%
Last Price
57%
Average Price
57%
Results
 EVRP gave
better hit rate predictions
than LPP or APP
 Superiority similar to other works in
marketing literature (e.g., Manchanda
et al, 1999 Mktg Sci; Heilman et al.,
2000 JMR)
 Further support to hypotheses 1 & 2
34
Segmentation
 To
test hypotheses 3 to 5
 High & low frequency of purchase
 Checked segmentation scheme
– LL test (Gensch, 1985)
35
Table 4: Log-Likelihood Tests – Calibration Segmented Sample
LL - Aggregate Model
LL - High Frequency Segment
LL - Low Frequency Segment
2LL
36
EVRP
-299.747
-154.921
-132.357
24.938
Last Price
-304.631
-156.354
-134.949
26.656
Average Price
-304.744
-157.266
-133.933
27.09
Table 5: MNL Results: High Frequency Purchasing Segment – Calibration Sample
Variable
Display
Feature
Brand Specific 1
Brand Specific 2
Brand Specific 3
Brand Specific 4
Brand Specific 5
Brand Specific 6
Loyalty
Gain
Loss
37
EVRP
Last Price
Average Price
Coefficient P-value Coefficient P-value Coefficient P-value
1.9515
0.0000
1.6565
0.0001
1.8172
0.0000
0.5902
0.2342
0.7056
0.1564
0.5543
0.2618
-1.9329 0.0251 -0.3585 0.4614 -0.4456 0.3994
-0.2606 0.6540
0.7627
0.0680
0.6521
0.1395
-0.2882 0.5201
0.0152
0.9725 -0.0766 0.8641
-0.4890 0.4335 -0.7288 0.2417 -0.6676 0.2842
-2.6480 0.0075 -1.2865 0.1104 -1.4208 0.0797
-1.1091 0.0528 -0.2956 0.5137 -0.3252 0.4748
4.3960
0.0000
4.5246
0.0000
4.5814
0.0000
0.0082
0.0627
0.0023
0.4919
0.0074
0.1340
-0.0124 0.0080
0.0065
0.0826
0.0013
0.8041
Table 6: MNL Results: Low Frequency Purchasing Segment – Calibration Sample
Variable
Display
Feature
Brand Specific 1
Brand Specific 2
Brand Specific 3
Brand Specific 4
Brand Specific 5
Brand Specific 6
Loyalty
Gain
Loss
38
EVRP
Last Price
Average Price
Coefficient P-value Coefficient P-value Coefficient P-value
1.4134
0.0042
1.3351
0.0061
1.3637
0.0057
2.0136
0.0000
2.0959
0.0000
1.9276
0.0001
-1.1673 0.0915 -0.2675 0.6090 -0.6461 0.2693
-0.5750 0.2896
0.0464
0.9252 -0.1801 0.7185
0.2544
0.5588
0.5032
0.2348
0.3764
0.3796
0.0724
0.8934
0.0407
0.9398
0.0671
0.9014
-0.7790 0.1800 -0.0570 0.9064 -0.2988 0.5530
-0.2420 0.5705
0.1104
0.7849
0.0731
0.8560
2.8825
0.0000
3.0463
0.0000
2.9667
0.0000
0.0063
0.0990
0.0064
0.0596 -0.0078 0.2266
-0.0108 0.0029
0.0005
0.8956
0.0142
0.0107
Segment level findings: Tables
5 and 6
 EVRP:
parameter signs are generally
consistent with expectations
– losses loom larger than gains
– model has face validity
 signs
& significances of gain & loss
parameters show less face validity for
LPP and APP models.
39
Table 7: Goodness-of-Fit Measurements - Disaggregate Level - Calibration Period
Goodness of-fit Measures
High Frequency Segment
LL
BIC
AIC
CAIC
Low Frequency Segment
LL
BIC
AIC
CAIC
40
EVRP
Last Price
Average Price
-154.921
366.779
342.842
377.779
-156.354
369.645
345.708
380.645
-157.266
371.469
347.532
382.469
-132.357
316.908
297.714
327.908
-134.949
322.092
302.898
333.092
-133.933
320.060
300.866
331.060
Table 8: Accuracy of Model Predictions – Hold-Out Segmented Sample
High Frequency Segment
Hit-rate
Low Frequency Segment
Hit Rate
41
EVRP
Last Price
Average Price
65%
62%
61%
56%
51%
52%
Segment level findings
 EVRP has
the best fit (Table 7)
 Also has the best holdout sample
predictive accuracy (Table 8)
 True for both high purchase frequency
and low purchase frequency segments
 Supports hypotheses 4 and 5
42
Results
 EVRP (High
Freq. Segment):
McFadden’s R-sq. = .550 and Hit Rate
= 65%
 EVRP (Low Freq. Segment):
McFadden’s R-sq. = .408 and Hit Rate
= 56%
 EVRP provides better data
representation for high vs low freq
segment; Supports Hypothesis 3
43
Quantity Analysis
Table 9: Regression Results – Aggregate Level
Special display
Feature
Gain
Loss
44
Estimated
Parameter
7.645
0.094
0.287
-0.262
P-value
0.0290
0.9781
0.0000
0.0000
Quantity Analysis
Table 10: Regression Results – High Frequency Purchasing Segment
Special display
Feature
Gain
Loss
45
Estimated
Parameter
6.122
-3.722
0.196
-0.250
P-value
0.2518
0.5231
0.0000
0.0000
Quantity Analysis
Table 11: Regression Results – Low Frequency Purchasing Segment
Special display
Feature
Gain
Loss
46
Estimated
Parameter
8.844
2.315
0.327
-0.261
P-value
0.0657
0.6096
0.0000
0.0000
Results
Extreme value points model consistent with
expectations  both gains and losses are
statistically significant
 A larger effect for gains than losses for the
low frequency segment
 The high frequency segment show a larger
effect for losses than gains

47
Summary
 Reference
Price based choice models
have always done better than priceonly models
 Internal Reference Price models have
been mainly driven by the decaying
memory concept
48
Summary
 Instead,
incorporating the
incongruency of information approach
together with the range theory concept
 Recent work (2001) suggest the
attractiveness of range theory approach
for price attractiveness judgments
49
Summary
 Niedrich
et al (2001) say it is important
to consider range in the
operationalization of choice models
 EVRP --- a first step in that direction
50
Summary
 Past
studies on Internal reference price
--- either a gain or a loss on a given
purchase occasion
 Our concept: consumers maybe
experiencing a gain and a loss on each
purchase occasion
51
Managerial Implications

While a price promotion strategy might
have a short-run positive impact on sales,
the lowered price may result in the
installation of a new lower minimum price
in consumers' memories
– may lead to a negative effect on market shares
in the medium and long terms

52
Managers may want to consider non-price
forms for promotion if the goal is to
increase short-term sales
Managerial Implications
While a price increase may have an
immediate adverse effect on sales, the
possible higher maximum price level can
help future market share values in the form
of positive effect of gains
 Similar logic for choice of skimming vs.
penetration strategies for new product
introductions.

53
54