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An Extreme Value Reference Price Approach
Sanjoy Ghose and Oded Lowengart
January 19, 2005
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Effect of Price on ChoiceEffect of Price on Choice
Price Only models Inclusion of Reference Price
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Reference Price CategoriesReference Price Categories
External Reference Price Internal Reference Price
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Internal Reference PricesInternal Reference Prices
Many different operationalizations Issue of appropriateness
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Logic & FormsLogic & 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)
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Event RecallEvent Recall
Hastie’s theory on memory Srull’s experiments Incongruence vs Congruence of
Information Effect on recall
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Price & Information Price & Information CongruenceCongruence
Let Pexp = Expected price of consumers
Let price at time t = Pt
If Pt is similar to Pexp then Pt is congruent information
If Pt >> (or <<) than Pexp, then Pt is incongruent information
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Price & Information Price & Information CongruenceCongruence
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.
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Price & Information Price & Information CongruenceCongruence
Such maximum and minimum prices should be most easily recalled
We hypothesize that these prices would be used as reference points in price evaluations.
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Other Related LiteratureOther 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.
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V X Y (1)
where
X - gain
Y - loss
and - parameters,
Let V be the Utility
Similar to Rajendran & Tellis (1994)..
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MinAct PPY
ActMax PPX (2)
(3)
Substituting (2) and (3) into (1),
)()( MinActActMax PPPPV (4)
ActMinMax PPP )(
ActMinMax PPPV 321
321 Where,
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Extreme Values of Reference Extreme Values of Reference PricePrice
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.
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Range TheoryA stimulus range is based on its extreme points Relative judgment and anchoring effects
Price ImplicationsA price range is related to the extreme price levelsPrice attractiveness is relative to the extreme pricesNew extreme prices change the range
Human Association MemoryA new incongruent stimulus leads to a larger associative memory network Different memory retrieval for Incongruent information
Price ImplicationsA new extreme (high/low) price has more memory associations than an expected new priceNew extreme prices retrieved better from memory than regular prices
Anchoring Points - Product LineA new extreme stimulus is more noticeable than other stimulus
Price ImplicationsA new extreme (maximum/minimum) price is more noticeable
Internal Reference Price ConceptualizationConsumers use both high and low extreme points (price) in their evaluations of a new price at the same timeConsumers can recall better extreme values (price) as compared with regular prices (expected) they paid previouslyConsumers use extreme points (price) to decide about the attractiveness of the offerConsumers use maximum and minimum prices as anchoring
Behavioral TheoryIndividuals can be happy and sad at the same time
Price ImplicationsBoth maximum and minimum prices can be simultaneously used in evaluating new prices
Choice/Purchase Quantity Implications: Focus of the Current ResearchConsumers use two internal reference prices to evaluate current price - comparing current price against the two, simultaneously in a brand choice/purchase quantity situationA maximum paid price - high anchoring - creates gainsA minimum paid price - low anchoring - creates losses
Theoretical Framework
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HypothesesHypotheses
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.
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HypothesesHypotheses
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.
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EVRP & SegmentsEVRP & Segments
Ratio of incongruent & congruent Info (Srull, 1981)
Number of price points faced by consumer
Purchase frequency
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HypothesesHypotheses
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.
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HypothesesHypotheses
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.
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HypothesesHypotheses
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.
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Gains & LossesGains & 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
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ModelModel
mj
j
U
U
ijtijt
ijt
P1
)(
)(
exp
exp
ijtijtijt VU
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ijtijtijtloss
ijtgain
ijtjijt LOYFEATDISPPPV 654min
3max
2
EVRP Model
)( minPPloss act
)( max actPPgain
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LPP Model
ijt
ijtijtlosslast
ijtgainlast
ijtjijt
LOY
FEATDISPPPV
6
542312
otherwise 0
0)( if 11
oijt
rijt Pp
otherwise 0
0)( if 12
oijt
rijt Pp
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APP Model
ijtijt
ijtlossaverage
ijtgainaverage
ijtjijt
LOYFEAT
DISPPPV
65
42312
otherwise 0
0)( if 11
oijt
rijt Pp
otherwise 0
0)( if 12
oijt
rijt Pp
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DataData
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.
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VariablesVariables
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
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Description of Conceptual Approach
Subject Node
Max....
5.95
4.01 3.95
Min...
4.124.50
3.95 3.243.12
4.56
3.12 ... Min
5.95 ... Max
t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9 t=10 Time
5.12
Price
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Table 1: MNL Results: Calibration Sample – Aggregate Level
Variable EVRP Last Price Average PriceCoefficient P-value Coefficient P-value Coefficient P-value
Display 1.5604 0.0000 1.3764 0.0000 1.4731 0.0000Feature 1.3903 0.0000 1.4759 0.0000 1.3164 0.0001Brand Specific 1 -1.2466 0.0166 0.0314 0.9266 -0.2640 0.4860Brand Specific 2 0.0585 0.8742 0.9091 0.0024 0.6785 0.0307Brand Specific 3 0.2505 0.4101 0.5174 0.0842 0.3885 0.2009Brand Specific 4 -0.0421 0.9197 -0.1910 0.6461 -0.1359 0.7432Brand Specific 5 -1.3287 0.0073 -0.2411 0.5401 -0.4777 0.2361Brand Specific 6 -0.4006 0.2438 0.1857 0.5331 0.1411 0.6352Loyalty 3.6325 0.0000 3.7921 0.0000 3.7359 0.0000Gain 0.0071 0.0088 0.0039 0.0900 0.0104 0.0035Loss -0.0116 0.0000 0.0041 0.1042 -0.0042 0.2857
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ResultsResults
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
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Table 2: Goodness-of-Fit Measurements - Aggregate Level - Calibration Sample
Goodness of-fit Measures EVRP Last Price Average PriceLog Likelihood -299.747 -304.631 -304.744BIC 657.211 666.979 667.205AIC 632.494 642.262 642.488CAIC 668.211 677.979 678.205
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ResultsResults
EVRP model provides superior fit based on the four different measures in Table 2
Supporting hypotheses 1 and 2
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Table 3: Accuracy of Model Prediction -Aggregate Level - Hold-Out Sample
Prediction EVRP Last Price Average PriceHit-rate 60% 57% 57%
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ResultsResults
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
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SegmentationSegmentation
To test hypotheses 3 to 5 High & low frequency of purchase Checked segmentation scheme
– LL test (Gensch, 1985)
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Table 4: Log-Likelihood Tests – Calibration Segmented Sample
EVRP Last Price Average PriceLL - Aggregate Model -299.747 -304.631 -304.744LL - High Frequency Segment -154.921 -156.354 -157.266LL - Low Frequency Segment -132.357 -134.949 -133.9332LL 24.938 26.656 27.09
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Table 5: MNL Results: High Frequency Purchasing Segment – Calibration Sample
Variable EVRP Last Price Average PriceCoefficient P-value Coefficient P-value Coefficient P-value
Display 1.9515 0.0000 1.6565 0.0001 1.8172 0.0000Feature 0.5902 0.2342 0.7056 0.1564 0.5543 0.2618Brand Specific 1 -1.9329 0.0251 -0.3585 0.4614 -0.4456 0.3994Brand Specific 2 -0.2606 0.6540 0.7627 0.0680 0.6521 0.1395Brand Specific 3 -0.2882 0.5201 0.0152 0.9725 -0.0766 0.8641Brand Specific 4 -0.4890 0.4335 -0.7288 0.2417 -0.6676 0.2842Brand Specific 5 -2.6480 0.0075 -1.2865 0.1104 -1.4208 0.0797Brand Specific 6 -1.1091 0.0528 -0.2956 0.5137 -0.3252 0.4748Loyalty 4.3960 0.0000 4.5246 0.0000 4.5814 0.0000Gain 0.0082 0.0627 0.0023 0.4919 0.0074 0.1340Loss -0.0124 0.0080 0.0065 0.0826 0.0013 0.8041
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Table 6: MNL Results: Low Frequency Purchasing Segment – Calibration Sample
Variable EVRP Last Price Average PriceCoefficient P-value Coefficient P-value Coefficient P-value
Display 1.4134 0.0042 1.3351 0.0061 1.3637 0.0057Feature 2.0136 0.0000 2.0959 0.0000 1.9276 0.0001Brand Specific 1 -1.1673 0.0915 -0.2675 0.6090 -0.6461 0.2693Brand Specific 2 -0.5750 0.2896 0.0464 0.9252 -0.1801 0.7185Brand Specific 3 0.2544 0.5588 0.5032 0.2348 0.3764 0.3796Brand Specific 4 0.0724 0.8934 0.0407 0.9398 0.0671 0.9014Brand Specific 5 -0.7790 0.1800 -0.0570 0.9064 -0.2988 0.5530Brand Specific 6 -0.2420 0.5705 0.1104 0.7849 0.0731 0.8560Loyalty 2.8825 0.0000 3.0463 0.0000 2.9667 0.0000Gain 0.0063 0.0990 0.0064 0.0596 -0.0078 0.2266Loss -0.0108 0.0029 0.0005 0.8956 0.0142 0.0107
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Segment level findings: Segment level findings: Tables 5 and 6Tables 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.
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Table 7: Goodness-of-Fit Measurements - Disaggregate Level - Calibration Period
Goodness of-fit Measures EVRP Last Price Average PriceHigh Frequency SegmentLL -154.921 -156.354 -157.266BIC 366.779 369.645 371.469AIC 342.842 345.708 347.532CAIC 377.779 380.645 382.469Low Frequency Segment LL -132.357 -134.949 -133.933BIC 316.908 322.092 320.060AIC 297.714 302.898 300.866CAIC 327.908 333.092 331.060
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Table 8: Accuracy of Model Predictions – Hold-Out Segmented Sample
EVRP Last Price Average PriceHigh Frequency SegmentHit-rate 65% 62% 61%Low Frequency SegmentHit Rate 56% 51% 52%
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Segment level findingsSegment 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
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ResultsResults 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
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Quantity AnalysisQuantity Analysis
Table 9: Regression Results – Aggregate Level
Estimated Parameter
P-value
Special display 7.645 0.0290
Feature 0.094 0.9781
Gain 0.287 0.0000
Loss -0.262 0.0000
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Quantity AnalysisQuantity Analysis
Table 10: Regression Results – High Frequency Purchasing Segment
Estimated Parameter
P-value
Special display 6.122 0.2518
Feature -3.722 0.5231
Gain 0.196 0.0000
Loss -0.250 0.0000
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Quantity AnalysisQuantity Analysis
Table 11: Regression Results – Low Frequency Purchasing Segment
Estimated Parameter
P-value
Special display 8.844 0.0657
Feature 2.315 0.6096
Gain 0.327 0.0000
Loss -0.261 0.0000
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ResultsResults
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
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SummarySummary
Reference Price based choice models have always done better than price-only models
Internal Reference Price models have been mainly driven by the decaying memory concept
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SummarySummary
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
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SummarySummary
Niedrich et al (2001) say it is important to consider range in the operationalization of choice models
EVRP --- a first step in that direction
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SummarySummary
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
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Managerial ImplicationsManagerial 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 Managers may want to consider non-price forms
for promotion if the goal is to increase short-term sales
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Managerial ImplicationsManagerial 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.
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