1 Estimating Heterogeneous Price Thresholds Nobuhiko Terui* and Wirawan Dony Dahana Graduate School of Economics and Management Tohoku University Sendai , Japan *Voice & Fax: International Conference at ISM

2 General nonlinear stochastic utility function ： Domain of relevant threshold variable : Disjoint sub-domains ： Threshold points

3 3 Regimes Model Nonlinear Random Utility Function - Asymmetric Market Response -

4 Consumer Behavior Theory 1. Reference Price (RP) and its conceptualizations Adaptation-Level Theory 2. Asymmetric response around RP Prospect Theory 3. The Existence of Price Threshold Assimilation-Contrast Theory

5 The Object of This Research => Propose “Threshold Probit Model “in the form of incorporating these concepts together   Estimate Price Thresholds Latitude of Price Acceptance ” at Household level.   Search for an Efficient Pricing through Customization Strategy

6 Tools ・ Threshold Probit Model ・ Hierarchical Bayes Modeling ・ MCMC =>Gibbs Sampling for Response Parameters =>Metropolis-Hastings Sampling for Threshold Parameters

7 The Meaning of Model: 3 Regimes Model

8 Threshold Probit Model and Hierarchical Bayes Modeling ● Choice Probability

9 ● Within Subject Model

10 ● Likelihood for consumer h ● Total likelihood

11 ● Between Subjects Model (1)Market Response (2)Price Threshold

12 ● Price Threshold Models Note: Model 3 does not assume a priori insensitivity and it can be interpreted as price threshold model a posteriori as price threshold model a posteriori when we observe the insignificant estimate of when we observe the insignificant estimate of or in weaker form or in weaker form when the relation and is confirmed. when the relation and is confirmed.

13 Household “ h’ ” homogeneity ● HB(Hierarchical Bayes) Model (2)Homogeneous parameter: (1)Heterogeneous parameter ： homogeneity

14 ● Conditional Posterior Density for MCMC

15 VI. ＝＞ Metropolis Sampling with Random Walk MCMC: Matrix notation: HB model for household h: I. ～ V. ＝＞ Gibbs Sampling by Full Conditional Densities (Rossi, McCulloch and Allenby(1996)) (Rossi, McCulloch and Allenby(1996))

16 Empirical Application

17 ● Marketing Mix Variables X = [Constant, Price, Display, Feature,Brand loyalty ] X = [Constant, Price, Display, Feature,Brand loyalty ] ( Display, Feature: 1 or 0) ( Display, Feature: 1 or 0) Price : log(price) Price : log(price) Display and Feature: binary, Display and Feature: binary, Brand loyalty: smoothing variable over past purchases Brand loyalty: smoothing variable over past purchases proposed by Guadagni and Little(1983) proposed by Guadagni and Little(1983) Empirical Results ● Reference Price ; Brand Specific RP (Breisch et al. (1997))

18 ● Household Specific Variables = [Constant, Hsize, Expend, Pfreq] = [Constant, Hsize, Expend, Pfreq] Hsize: 1-6(Number of Family), Hsize: 1-6(Number of Family), Expend: 9 categories (Shopping Expenditure / Month), Expend: 9 categories (Shopping Expenditure / Month), Pfreq: 3 categories (Shopping Frequency), Pfreq: 3 categories (Shopping Frequency), = [Constant, Hsize, Expend, Pfreq, Dprone, RP, BL] = [Constant, Hsize, Expend, Pfreq, Dprone, RP, BL] Dprone: deal proneness (Bucklin and Gupta(1992)) Dprone: deal proneness (Bucklin and Gupta(1992)) RP: reference price level (Kalyanaram and Little(1994)) RP: reference price level (Kalyanaram and Little(1994)) BL: brand loyalty level (Kalyanaram and Little(1994)) BL: brand loyalty level (Kalyanaram and Little(1994)) ・ ・ Proportion of purchase (of any the five brands) made on promotion; ;

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22 ● Distribution of Price Thresholds

23 ● LPA v.s. Household Characteristics “Hsize” increases => LPA is getting Narrower “Expend” increases “Expend” increases =>LPA is getting Wider

24 ● LPA v.s. Household Characteristics “Dprone” increases => LPA is getting Narrower “Pfreq” increases => LPA is getting Wider

25 ● LPA v.s. Household Characteristics “RP” increases => LPA is getting Wider “BL” increases => LPA is getting Wider

26 ● Effectiveness of Marketing Mix: Beta coefficients

27 ○ Price Gain (Regime 1) & Price Loss (Regime 3): : “Price” > “Display” > (”Brand Loyalty”) “Feature”, ○ LPA (Regime 2): “Display” > (”Brand Loyalty”>) “Feature”. ● Marketing Mix Effectiveness

28 Figure 2: Expected Incremental Sales and Profits ● Customized Pricing

29 [1] Customized Discounting (2)Expected Incremental Profit : (M: margin 0.3 assumption) (1)Expected Incremental Sales (Discount Promotion) I. α % discount from individual (lower) price threshold Conditional on

30 Unconditional Estimates

31 [2] Customized Price Hike Strategy II. α % price hike from individual (upper) price threshold (1)Expected Incremental Sales (2)Expected Incremental Profit : (M: margin 0.3 assumption) Conditional on

32 Unconditional Estimates

33 ● Large Difference of Sales ・ Between (LPA and LOSS) ・ Between (LPA and GAIN)

34 ● Maximal Profits happen at ・ r 1h (Discounting) ・ r 1h (Discounting) ・ r 2h (Hike) ・ r 2h (Hike)

35 Non-customized Pricing (flat pricing) Manager does not now know the price thresholds Manager does not now know the price thresholds ＝＞ has to try possible levels f pricing. ＝＞ has to try possible levels f pricing. ＝＞ d* = 0,±1, ±2, …, ±15% ＝＞ d* = 0,±1, ±2, …, ±15% Compare their incremental profits with those of optimal Compare their incremental profits with those of optimal customized pricing at r 1h and r 2h customized pricing at r 1h and r 2h

36 [3] Difference from non-customized pricing depends on the regime determined by depends on the regime determined by discount level discount level Conditional on Unconditional (ii) Price Hike (i) Discounting

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38 A. Customized Discount Strategy (customized couponing) Sales: (1)For every brand, there is a great difference of sales increase between price gain regime and (negative) increase between price gain regime and (negative) LPA at LPA at (2) The sales of most expensive brand E change most. Profit: (1)Optimal discount levels happen at the lower price threshold for every brand. threshold for every brand. ● Empirical Implications

39 B. Customized Price Hike Strategy Sales: (1)Large difference between inside and outside of the upper price threshold for every brand. upper price threshold for every brand.Profit: (2) The price hike at the level of makes the incremental profits most. the incremental profits most.

40 Summary 1. 1.Modeling (i) Non-linear(piecewise linear) Random Utility Price Threshold, => Latitude of Price Acceptance Asymmetric Market Response (ii) Continuous Mixture Model (HB to Threshold Probit Model) => Heterogeneous Consumers (iii)

41 ２． Empirical Findings and Implications (i) Price threshold models dominates Linear model =>Existence of Heterogeneous Price Threshold (ii) Marketing Mix Effectiveness ○ Price Gain &Loss Regimes: “Price” > “Display” > (”Brand Loyalty”) “Feature” ○ LPA Regime: “Display” > (”Brand Loyalty”) “Feature” (iii) Estimated “Heterogeneous Price Thresholds” => Incremental Profit r 1h => Discounting(Target Couponing) r 2h => Price Hike r 2h => Price Hike => Important information for customization strategy of => Important information for customization strategy of pricing. pricing.