an extreme value reference price approach

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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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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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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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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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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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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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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


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


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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Table 10: Regression Results – High Frequency Purchasing Segment

Estimated Parameter

P-value


Feature -3.722 0.5231

Gain 0.196 0.0000

Loss -0.250 0.0000

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Table 11: Regression Results – Low Frequency Purchasing Segment

Estimated Parameter

P-value


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.

an extreme value reference price approach

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