Endogeneity and Price Sensitivity in Customized Pricing

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Endogeneity and Price Sensitivity in

Customized Pricing

Choice Based Revenue Management Workshop Georgia Tech University

May 22, 2012

Robert Phillips

A. Serdar Simsek

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Columbia Business School 2

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Columbia Business School

What is the Issue?

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• In Customized Pricing, the seller knows the identity and needs of the buyer and can use this information in setting prices.

• Information is available on customers who did not purchase as well as those who do purchase.

• Price-sensitivity in Customized Pricing is often estimated by applying Bernoulli regression to the record of wins and losses . • However, if unrecorded customer characteristics correlated with

price-sensitivity are used in setting price, then straightforward Bernoulli regression may lead to price-sensitivity being

underestimated. This is a problem of endogeneity.

• We show that this is indeed the case using two unique auto-lending databases – one on-line and one indirect.

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An Industry/University Collaboration

This project was a collaboration among:

– Columbia University Researchers

– Nomis Solutions (Provided data)

– A major auto lending company (Provided data, insight into the auto-lending process and data, analytic guidance).

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Agenda

1. Customized Pricing and Auto Lending

2. The Problem of Endogeneity

3. Numerical Studies

4. Conclusions and Discussion

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Customized Pricing

•

Buyer approaches potential seller(s) with

a need.

• Seller knows identity and expressed need

of buyer and can “customize” offer price

accordingly.

• This often involves a “Request for

Proposal” (RFP) or a “Request for Quote”

(RFQ).

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Customized Pricing: A customer-pull process

... ... ... ...

Potential customers approach one-at-a-time and express their individual needs. "Fallout" "Buyers" Prices quoted to both buyers and to "fallout" (shoppers who did not buy) are known. An individual (customized) price is quoted to each potential customer.

$

$ $$

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Auto Lending: Sources and Channels

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Channels

_Sources

Banks and Credit Unions Indirect (Dealer)

On-line

Manufacturers (e.g. GMAC)

Direct

Specialist Lenders (e.g. Americredit)

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Columbia Business School 0 0.5 1 $9.00 $9.25 $9.50 $9.75 $10.00 Price W in/ Lo s s

Estimating Price Sensitivity for Customized Pricing

Fit a standard response curve (e.g. probit, logit)

using binary regression (Phillips 2005, 2012; Agarwal

and Ferguson 2009).

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Agenda

1. Customized Pricing and Auto Lending

2. The Problem of Endogeneity

3. Numerical Studies

4. Conclusions and Discussion

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Endogeneity and Pricing

Several studies have looked at the influence of endogeneity in list pricing

situations:

– Villas-Boas and Winer (1999), Kuksov and Villas-Boas (2008), Petrin and Train (2010)

– Survey: Louviere et al. (2005)

In a meta-study of price-elasticity studies, Bijmolt et al. (2005) found that treatment of endogeneity is the strongest determinant of price-elasticity differences among estimates of price-elasticity in the same industry by different researchers.

Our study is, to our knowledge, the first to address the issue of endogeneity in customized pricing.

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Endogeneity and Customized Pricing

Endogeneity will be present in customized pricing if there are unrecorded

variables that are correlated both with both customer price-sensitivity and rate offered.

Auto lending examples might include: – Willingness to bargain

– Expressed eagerness to purchase – Appearance, home address, …

We anticipate that endogeneity of this type will be strongly present in situations in which there is face-to-face interaction between lender and borrower, but not present in situations where there is no such interaction.

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A Causality-Based View

13 Price Response (Take/No Take) Price Willingness-to-pay Observed Variables Unobserved Variables

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Agenda

1. Customized Pricing and Auto Lending

2. The Problem of Endogeneity

3. Numerical Studies

4. Conclusions and Discussion

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Control Function Approach

We use a two-step approach to endogeneity correction (Rivers and Vuong, 1988)

1. Regress key variable (APR) on

• Exogenous variables (customer, loan, and market characteristics),

• Additional instruments (relevant to APR, exogenous) to obtain the residuals.

2. Regress outcome variable (take/not take) on: • Exogenous variables

• Endogenous variable (APR), • Residuals

Significance of the residuals in Step 2 is a test for endogeneity.

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Instrumental Variables

We use as instruments the mean interest rates that are offered for similar loans in other regions during the same month. These instruments:

– Share the same marginal cost characteristics

– Are uncorrelated with unobserved characteristics of current customer.

– Average out national demand shocks.

Time of the loan offer:

– Captures possible seasonal effects on offered APR’s – Plausibly uncorrelated with unobserved customer type

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Data Sources

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Online Lender: ~ 150,000 observations over 30 months (2002-2004).

Indirect Lender: ~2,300,000 observations over 38 months (2009 – 2011). Data was from all approved loan offers for each lender over the period. Both data sets included:

• Customer characteristics (risk, region)

• Loan characteristics (term, amount, size-of-loan) • Outcome (Customer Take/Not Take)

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Data Elements

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Element

Name Comment Online Indirect

Term Term of the loan (months) Y Y

Type New or Used Y Y

Prime Rate Rate at time of approval. Y Y

Amount Size of loan ($) Y Y

∆ Rate APR – Prime Rate Y Y

Tier Risk-based classification of borrowers. 4 tiers for on-line, 6 tiers for off-line

Y Y

Customer Cash Cash incentive provided by supplier via indirect channel

NA Y

Subvention Was the rate offered a promotion? (Y/N)

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Model Estimate Result - Online

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Variable

Class Variable Estimate

Term 48 60 > 66 .24*** .66*** 1.43*** Vehicle Type Used 1.30***

Prime Rate Log(Amount) -1.39*** 8.02*** ∆ Rate Tier 1 Tier 2 Tier 3 Tier 4 -76.02*** -54.34*** -41.55*** -38.08*** Rate Residual N/A Variable Class Variable Estimate Uncorrected Corrected Term 48 60 > 66 .24*** .66*** 1.43*** .27*** .60*** 1.50*** Vehicle Type Used 1.30*** 1.42***

Prime Rate Log(Amount) -1.39*** 8.02*** -1.39*** 8.02*** ∆ Rate Tier 1 Tier 2 Tier 3 Tier 4 -76.02*** -54.34*** -41.55*** -38.08*** -79.86*** -58.02*** -45.23*** -41.76***

Rate Residual N/A 4.01

Not Significant

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Online Results

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For the on-line data:

• All variables in both the uncorrected and corrected models enter with high confidence (p < .001).

• The rate residual does not enter with high confidence (p > .1). • Adjusting the coefficients for endogeneity does not change

their values significantly.

Endogeneity does not appear to significantly effect the estimation of price-sensitivity for the on-line data.

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Model Results - Indirect

21 Variable Class Variable Uncorrected Estimate Term 48 60 > 66 -.30*** -.48*** -.61*** Vehicle Type Subvention? Used No 1.21*** -1.48*** Prime Rate Log(Amount) Customer Cash ($1,000) -33.72*** .05*** .93*** ∆ Rate Tier 1 Tier 2 Tier 3 Tier 4 Tier 5 Tier 6 -8.65*** -5.82*** -4.88* -7.93*** -6.93*** -15.94*** Rate Residual N/A Variable Class Variable Estimate Uncorrected Corrected Term 48 60 > 66 -.30*** -.48*** -.61*** -.27*** -.46*** -.51*** Vehicle Type Subvention? Used No 1.21*** -1.48*** 1.46*** -1.13*** Prime Rate Log(Amount) Customer Cash ($1,000) -33.72*** .05*** .93*** -20.25*** -.07*** 1.05*** ∆ Rate Tier 1 Tier 2 Tier 3 Tier 4 Tier 5 Tier 6 -8.65*** -5.82*** -4.88* -7.93*** -6.93*** -15.94*** -16.84*** -14.29*** -13.65* -17.02*** -15.42*** -24.80*** Rate Residual N/A 9.03***

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Indirect Model Results

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• Endogeneity is present and highly significant.

• Correcting for endogeneity leads to significant changes in

the rate coefficient in the models – the uncorrected model

was systematically and significantly

underestimating

price

sensitivity.

• Log(amount) coefficient changed sign from positive to

negative.

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Agenda

1. Customized Pricing and Auto Lending

2. The Problem of Endogeneity

3. Numerical Studies

4. Conclusions and Discussion

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Conclusions

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• Endogeneity does not appear to have a strong influence on price-sensitivity estimates for the on-line channel.

• Endogeneity has a major effect on price-sensitivity estimates for the indirect (face-to-face) channel.

• Even corrected for endogeneity, indirect auto lending demonstrates much less price-sensitivity than on-line lending. We attribute this to a channel effect.

• Our approach provides a workable test for the presence of endogeneity in customized pricing data as well as a

procedure of adjusting price-response estimates to account for endogeneity.

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QUESTIONS?

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List Pricing: The Most Common Consumer Pricing

Approach

The seller sets and publicizes a price.

A (usually unknown) population of potential buyers observes the price.

Some subset of potential buyers actually purchases.

This is generally unobservable

This is observable demand