An Extreme Value Reference Price Approach

1. An Extreme Value Reference Price Approach Sanjoy Ghose and Oded Lowengart January 19, 2005

2. Effect of Price on Choice • Price Only models • Inclusion of Reference Price

3. Reference Price Categories • External Reference Price • Internal Reference Price

4. Internal Reference Prices • Many different operationalizations • Issue of appropriateness

5. 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)

6. Event Recall • Hastie’s theory on memory • Srull’s experiments • Incongruence vs Congruence of Information • Effect on recall

7. 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 • If Pt >> (or <<) than Pexp, then Pt is incongruent information

8. 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.

9. 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.

10. 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.

11. Let V be the Utility Similar to Rajendran & Tellis (1994)..

12. (2) (3) Substituting (2) and (3) into (1), (4) Where,

13. Extreme Values of Reference Price • 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.

14. 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

15. Hypotheses • 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.

16. Hypotheses • 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.

17. EVRP & Segments • Ratio of incongruent & congruent Info (Srull, 1981) • Number of price points faced by consumer • Purchase frequency

18. 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.

19. 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.

20. Hypotheses • 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.

21. 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 asa gain

22. Model

23. EVRP Model

24. LPP Model

25. APP Model

26. 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.

27. 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

28. Description of Conceptual Approach 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

30. 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

32. Results • EVRP model provides superior fit based on the four different measures in Table 2 • Supporting hypotheses 1 and 2

34. 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

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

39. 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.

42. 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

43. 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

44. Quantity Analysis Table 9: Regression Results – Aggregate Level

45. Quantity Analysis Table 10: Regression Results – High Frequency Purchasing Segment

46. Quantity Analysis Table 11: Regression Results – Low Frequency Purchasing Segment

47. 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

48. Summary • 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

49. 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

50. 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