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An Extreme Value Reference Price Approach

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An Extreme Value Reference

Price Approach

Sanjoy Ghose and Oded Lowengart

January 19, 2005

- Price Only models
- Inclusion of Reference Price

- External Reference Price
- Internal Reference Price

- Many different operationalizations
- Issue of appropriateness

- 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)

- Hastie’s theory on memory
- Srull’s experiments
- Incongruence vs Congruence of Information
- Effect on recall

- 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

- 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.

- Such maximum and minimum prices should be most easily recalled
- We hypothesize that these prices would be used as reference points in price evaluations.

- 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.

- Applications to Pricing in the Mktg. lit.

Let V be the Utility

Similar to Rajendran & Tellis (1994)..

(2)

(3)

Substituting (2) and (3) into (1),

(4)

Where,

- 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

Both maximum and minimum prices can be simultaneously used in evaluating new prices

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

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

- 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.

- 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.

- Ratio of incongruent & congruent Info (Srull, 1981)
- Number of price points faced by consumer
- Purchase frequency

- 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.

- 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.

- 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.

- Consumers evaluate losses & gains differently (Kahneman & Tversky, 1979)
- We believe: On any given purchase occasion, a consumer is always evaluating a loss as well asa gain

EVRP Model

LPP Model

APP Model

- 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.

- 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

Price

Subject Node

5.95

5.95 ... Max

Max....

5.12

4.56

4.50

4.12

3.95

4.01

3.95

3.24

Min...

3.12

3.12 ... Min

t=1

t=2

t=4

t=5

t=6

t=7

t=8

t=10

Time

t=3

t=9

- 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

- EVRP model provides superior fit based on the four different measures in Table 2
- Supporting hypotheses 1 and 2

- 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

- To test hypotheses 3 to 5
- High & low frequency of purchase
- Checked segmentation scheme
- LL test (Gensch, 1985)

- 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.

- 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

- 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

Table 9: Regression Results – Aggregate Level

Table 10: Regression Results – High Frequency Purchasing Segment

Table 11: Regression Results – Low Frequency Purchasing Segment

- 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

- 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

- 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

- Niedrich et al (2001) say it is important to consider range in the operationalization of choice models
- EVRP --- a first step in that direction

- 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

- 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

- 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.