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

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 PlanAccess Fee, Free MinutesMarginal Price A$30, 200 minutes$0.40 B$40, 350 minutes$0.35

Pricing Scheme – Wireless Services Cost of Consumption Consumption Included Minutes F q t2 q t1 R2R2 p 1 = 0 p 2 > p 1 underage overage  If consumption is q t1 then total cost = F (access fee)  If consumption is q t2 then R 2 = F + (q t2 – Incl. Min.) p 2 Plan A Access fee = $30 Free minutes = 200 Marginal price =$0.40

Issues  Marginal price depends on consumption  Choice and consumption are related  Customers can defect

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)

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

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

Essay1 - Myopic Customers

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

Utility Specification For customer i, plan j and decision time t :  x 1ijt : Minutes consumed  x 2it : Outside good (numeraire)  z ijt, w ijt : Vectors containing covariates (past usage)   ij : Plan specific intercept   ijt : Choice errors

Utility Maximization – Budget Set  For customer i, plan j and time t : F1F1 A1A1 B p1p1 p2p2 C1 C2 Optimal Consumption F2F2 A2A2 B p1p1 p2p2 C1 C2 Optimal Consumption Plan1 Plan2

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

Actual Consumption  Actual Consumption = Optimal Consumption + Error  If A j < Optimal Qty. < B Optimization error Optimal Qty.Actual Qty.

Economic Restrictions  Slutsky restrictions  Ensures quasiconcavity of utility function

Customer Heterogeneity   i – Set of all customer-specific parameters  S i contains demographics for customer i   and  are population-level parameters  Hierarchical Bayesian Model

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

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

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

Null Models

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

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

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

Estimates – Structural Model  The subscripts z and w refer to the covariates in the vector z ijt and w ijt respectively

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

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?

Policy Experiments

 Access price / marginal price  Price increase / price decrease  Temporary / permanent

Policy Experiments – Marginal Price Change Plan 3 – Price IncreasePlan 3 – Price Decrease Effect of 25% Permanent Change in Marginal Price for Plan 3  Time varying elasticity  Adjacent plan effect  Asymmetric price effect Plan Minutes

Policy Experiments – Marginal Price Change Effect of 25% Temporary Change in Marginal Price for Plan 3  Ripple effect Plan 3 – Price IncreasePlan 3 – Price Decrease

Policy Experiments – Customer Value  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 5% Decrease in the plan prices Minutes $35$40$50$30 Access Fee 2341 Plan

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

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

Essay-2 : Myopic Learning Model ; Belief specification Usage

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

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

Extensions  Competition  Rollover and other features  Roaming, long distance and other types of minutes