Structural Models for Customer Behavior under Nonlinear Pricing Schemes

1. Structural Models for Customer Behavior under Nonlinear Pricing Schemes Raghu Iyengar Columbia University

2. Scenario • Consider two wireless calling plans - • How do customers choose a plan and decide on usage? • Impact of access fee and marginal price on - • Customer behavior • Firm profitability

3. Pricing Scheme – Wireless Services p2 > p1 Plan A Access fee = $30 Free minutes = 200 Marginal price =$0.40 R2 p1 = 0 Cost of Consumption F overage underage qt1 qt2 Included Minutes Consumption • If consumption is qt1 then total cost = F (access fee) • If consumption is qt2 then R2 = F + (qt2 – Incl. Min.) p2

4. Issues • Marginal price depends on consumption • Choice and consumption are related • Customers can defect

5. Dissertation • Develop structural models for explaining: • Choice of calling plans within a service provider • Consumption of minutes • Defection decisions (churn) • Policy experiments (Firm decisions) • Myopic customers (Essay-1) • Forward-looking customers (Essay-2)

6. Presentation Outline • Past Research • Structural model (Essay-1) • Data description • Null models / estimation results • Policy experiments • Essay-2 (brief description)

7. Past Research • Marketing • Subset of decisions • Simpler pricing schemes – linear price, two-part tariffs • Economics • Labor supply • Nonlinear income taxes

8. Essay1 - Myopic Customers

9. Anticipated Consumption Plan Choice Defection Actual Usage Modeling – Choice and Consumption Process (beginning of month) (during the month)

10. Utility Specification For customer i , plan j and decision time t : • x1ijt : Minutes consumed • x2it : Outside good (numeraire) • zijt, wijt : Vectors containing covariates (past usage) • ij : Plan specific intercept • ijt : Choice errors

11. Utility Maximization – Budget Set Plan1 Plan2 Optimal Consumption Optimal Consumption F1 F2 p1 p2 p1 C1 p2 C2 C1 C2 A1 B A2 B • For customer i , plan j and time t :

12. Choice Decision • Value of a plan = Maximum utility that a consumer derives under that plan • Value = f (Optimal Consumption) • Customers choose plan with the highest value at the beginning of every time period

13. Actual Qty. Optimal Qty. Optimization error Actual Consumption • Actual Consumption = Optimal Consumption + Error • If Aj < Optimal Qty. < B

14. Economic Restrictions • Slutsky restrictions • Ensures quasiconcavity of utility function

15. Customer Heterogeneity • i – Set of all customer-specific parameters • Sicontains demographics for customer i •  and  are population-level parameters • Hierarchical Bayesian Model

16. Data • Wireless Service Provider • Monthly billing data : September, 2001- May, 2003 • New customers : August, 2001- December, 2001 • 300 customers • 5151 observations – each a monthly bill • Average 17 months per customer

17. Data • Four calling plans • 200, 300, 350 and 500 peak minutes • Access Fee - $30, $35, $40, $50 • Marginal Price - $0.40 per minute • 70% of the data covered by these four plan types • Summary statistics • 98 people churn • 5% observations have a plan change

18. Variables • State dependence • Effect of past choices on current decisions • Dummy variable that captures past choice • Past usage variables • Promotional events • Free roadside assistance, valentine’s day promotion • Dummy variable that captures a promotion

19. Null Models

20. Expected Consumption Plan Choice Defection Actual Usage Null Models • Biggest challenge – how to incorporate the entire pricing schedule • Two null models – they differ in how the expectation process is specified

21. Null Models • Null Model - 1 • Previous month’s usage as the expected consumption • Null Model – 2 • Expectation formation uses covariates • Both models incorporate customer heterogeneity

22. Model Comparison • Structural model is overwhelmingly supported by the data (Kass and Raftery, 1995)

23. Estimates – Structural Model • The subscripts z and w refer to the covariates in the vector zijt and wijt respectively

24. Estimates – Structural Model • Overage variables • Negative effect on choice and consumption • Upgrade plans or lower usage • Underage variables • Negative effect on utility of plans • Positive effect on consumption • Downgrade plans or increase usage

25. Managerial Questions • How do the different components of the pricing scheme affect customers’ decisions? • What is the relationship between pricing, customer responses and customer lifetime value?

26. Policy Experiments

27. Policy Experiments • Access price / marginal price • Price increase / price decrease • Temporary / permanent

28. Plan 3 – Price Increase Plan 3 – Price Decrease Plan 1 2 3 4 200 Minutes 300 500 350 Policy Experiments – Marginal Price Change Effect of 25% Permanent Change in Marginal Price for Plan 3 • Time varying elasticity • Adjacent plan effect • Asymmetric price effect

29. Plan 3 – Price Increase Plan 3 – Price Decrease Policy Experiments – Marginal Price Change Effect of 25% Temporary Change in Marginal Price for Plan 3 • Ripple effect

30. Plan 1 2 3 4 Minutes 200 300 350 500 $30 $35 $40 $50 Access Fee Policy Experiments – Customer Value 5% Decrease in the plan prices • Access price effect is higher than marginal price for most cases • Highest effect of access price on “low usage” users on Plan 1 • Highest effect of marginal price on “high usage” users on Plan 4

31. Conclusions • Developed a structural model • Adaptable to other service contexts • Used policy experiments for gauging the effect of changes in pricing schemes on • Customer behavior • Firm profitability

32. Essay-2 : Learning Models

33. Essay-2 : Learning Models • Myopic learning model • Consumers are uncertain about actual usage while choosing plans • They have prior beliefs about the distribution of actual usage • They observe their actual usage and update (learn) their beliefs

34. ; Essay-2 : Myopic Learning Model Belief specification Usage

35. Essay-2 : Forward-Looking Model • Assumptions • Mental hassle costs associated with plan changes • Customer and plan-specific variance • Customers’ beliefs • Priors on the different variances • Usage on a plan leads to an update of the belief parameters associated with only that plan

36. Essay-2 : Forward-Looking Model • Tradeoff • Stick with a plan : get more precise information about the variance associated with only that plan • Change plans : improve the knowledge of the variance under the chosen plan but pay mental hassle costs of switching • Dynamic Programming

37. Extensions • Competition • Rollover and other features • Roaming, long distance and other types of minutes