A symmet ric Info rmat ion, A dverse Select ion and Seller...

Asymmetric Information, Adverse Selection and Seller Revelation on eBay Motors

Asymmetric Information, AdverseSelection and Seller Revelation on

eBay Motors

Greg Lewis

University of Michigan

February 13, 2007


Motivation

eBay MotorsOnline used car market$1 billion in revenues in 2005Pundits predicted it wouldn’t work

Market for Lemons (Akerlof 1970)Quality heterogeneityAsymmetric information (condition, history, parts)No credible disclosure technology ! adverseselection

Empirical questions:How much information is disclosed on eBayMotors?Is such disclosure selective?


Line of Attack

Link price and informationObtain unique eBay datasetProvide quantitative measures of webpage contentRun hedonic regressionsFind large e!ect of amount of information on price

Analyze auction model with strategic sellerrevelation

Equilibrium with selective disclosureSellers reveal favorable private informationBidders view absence of information as bad signal


Line of Attack

Deduce model predictionsPrior mean valuation increasing in amount ofinformation disclosedInformation measures endogenous

Estimate model and test predictionsDevelop new common value auction estimatorRecover mean valuationsTest for endogeneity using semiparametric controlfunction

Quantify impact of disclosuresMagnitude of structural resultsCounterfactual simulation


Findings

1 Strong evidence of selective disclosure by sellers2 Disclosures reduce information asymmetries

and potential for adverse selection


Contribution

Adverse selection in used car marketsLittle empirical evidence (e.g. Bond (1982,1984),Genosove (1993))Quantify role of disclosure in limiting informationasymmetries

eBay LiteratureRole of reputation (Resnick/Zeckhauser (2002))Role of information dispersion (Pai-Ling Yin)Direct analysis of role of information on eBay

Empirical literature on disclosureJin (2005), Jin and Leslie (2003)


Contribution

Information disclosure in auctionsLinkage principle (Milgrom & Weber (1982))Costly revelation (Grossman (1981), Milgrom(1981), Jovanovic (1983))Provide measure of amount of disclosure, and showpositively correlated with value

New common values eBay estimatorBajari & Hortacsu (2003), Hong & Shum (2002)Robust to early and non-credible bidsComputationally lightControl function approach for endogeneity


Outline of Talk

1 eBay Motors

2 Theory

3 Estimation

4 Results

5 Simulation

6 Conclusions


eBay Motors

Outline

1 eBay Motors

2 Theory

3 Estimation

4 Results

5 Simulation

6 Conclusions


eBay Motors

How eBay Motors works

Seller posts an auction webpageAuction has fixed duration, bid at any time

People “snipe”, bidding at last momentOver 10% of bids on Corvettes in last 10 minutes(Adams et al)Late Bidding Model

Potential bidders can communicate with seller

Close of auction, pay second highest bidPick up car and pay after close of auction

Ex-post verifiability of information


eBay Motors

A Tale of Two Cars

Car 1 (good webpage)2 pages text, 28 photos37 bidsfinal price $6875, blue book = $5100

Car 2 (poor webpage)3 lines text, 3 photos4 bidsfinal price $1225, blue book = $4700


eBay Motors

What is Information?

Distinction between:Seller’s Private InformationBidder’s Private InformationPublic Information(seller chooses to post on webpage)

I refer to information as the content of auctionwebpages (public)I refer to the amount of information as aquantitative measure of that content

Bytes of text in descriptionNumber of photos


eBay Motors

Data

Collect bids, item, seller characteristics fromover 40000 auctions

Download eBay auction webpages over a 6 monthperiod ! unique panel datasetModels chosen include classic cars, reliable cars,pickupsUse text parsing program to obtain variables

Drop auctions with < 2 bids, re-listings,missing data, proprietary software


eBay Motors

Characteristics of Dropped Auctions

Table: Characteristics of Dropped Auctions

n " 2 n < 2Age 19.51 18.52Mileage 123050 107853Text 1680 1701Photos 12.1 10.8Starting Bid 2640 10071


eBay Motors

Trading Activity

Sellers listing exactly one car”Private Sellers” = 83.4% of sellersAccount for 54.3% of listings

Sellers listing more than one car”Dealers” = 16.6% of sellersAccount for 45.7% of listings

Repeat buyers are a small fraction (2.2%)


eBay Motors

Variation in Information Measures

Table: Variation in Information Measures

Private Sellers DealersText 1434 2248

(1479) (2765)Photos 11 13.8

(6.3) (7.1)


eBay Motors

Hedonic Regressions

Hedonic regression (OLS):

log(p) = Z! + " (1)

wherep is final auction priceZ is a vector of covariatesInclude title, transmission, year and model fixede!ects


eBay Motors

Table: Hedonic Regressions

(1) (2)Log Text Size 0.0775*** 0.0886***Photos 0.0212*** 0.0221***Number of Options 0.0239***Log Feedback -0.0193***% Negative Feedback -0.0029***Total Listings 0.0011Warranty 0.7979***Warranty*Logtext -0.0780***Warranty*Photos -0.0165***


eBay Motors

Table: Hedonics by Subsample

Full Private Dealers DealersLog Text Size 0.0804*** 0.0998*** 0.0330*** 0.1584***Photos 0.0221*** 0.0223*** 0.0195*** 0.0219***Model FE yes yes yes yesYear FE yes yes yes yesSeller FE no no no yes


eBay Motors

Table: Hedonics for 1984-2006 Mustangs

Estimated Coe"cientLog Text Size 0.0907***Photos 0.0179***Year FE yes


eBay Motors

Text coe!cients by year

5 10 15 20Age

!0.05

0.05

0.1

0.15

0.2

Estimated Coefficient


eBay Motors

Photo coe!cients by year

5 10 15 20Age

0.01

0.02

0.03

Estimated Coefficient


eBay Motors

Potential Explanations

Seller E!ectFixed e!ects results suggest no

Advertising E!ectWarranty result suggests genuine informationTest later

Strategic E!ect (Winner’s Curse)

Selective Disclosure

Auction model with disclosure nests last three


Theory

Outline

1 eBay Motors

2 Theory

3 Estimation

4 Results

5 Simulation

6 Conclusions


Theory

Modeling Choices

Symmetric pure common value auction modelJustified by tests (Athey/Haile)Consistent with strategic Winner’s Curse storyParticipants in an auction have similar preferences

Multidimensional private information for sellersMeasure amount of information revealed

Credible but costly revelationCredibility from institutional featuresOpportunity cost of posting text, photos

Bajari & Hortacsu (2003) late bidding model


Theory

Formalism

N bidders, realization n common knowledge

Common Value V # FBidder signals X1 · · ·Xn c.i.i.d # G |v

Private communications

Seller signals S1 · · · Sm c.i.i.d. # H |vCar features, history, conditionSignals may be of di!erential importance

V , X1 · · ·XN , S1 · · · Sm a"liated


Theory

Formalism

Seller can reveal signal Si publicly at cost ci

Amount of information I = # signals revealedEach revelation must be written up / displayedEqual weighting of signals

Model extremely generalMultidimensional real-valued signalsArbitrary revelation costsNecessitates strong assumption later

Two-stage gameSeller makes disclosuresBidders participate in auction


Theory

Late Bidding Model

eBay format is English auction with re-entry

Sniping ! late observation of bids impossibleTwo Bidding Rounds:

Early-bidding, [0, # $ $), bidders observe eachothers bids, exit non-bindingLate-bidding, [# $ $, # ], sealed-bid auction

Late bids unrecorded if pt > bt

bidder i ’s true valuation unrecordedmay misinterpret earlier bid by i as valuation

Can show bid zero in early stage, play secondstage as sealed bid auction


Theory

Modeling Disclosure

Seller chooses which signals to revealSeller’s private information realization sReporting policy R(s) : Rm ! {0, 1}m

Reported Signals sRDefine expected value with public signals

w(x , y , s; n) = E [V |X = x , Y = y , S = s, N = n] (2)

Make additivity assumption

w(x , y , s; n) =m!

j=1

fj(sj) + g(x , y , n) (3)


Theory

Proposition (Costly Revelation)

For c > 0, there exists a sequential equilibrium in which

1 The reporting policy R is characterized by cuto!st = t1 · · · tm % R &' such that:

R(si ) =

"1 if si " ti0 otherwise

where ti = inf {t : E [!i (t, t !; n)|t ! < t] " ci}.2 Bidders bid zero during the first stage of the auction, and bid

vR(x , x , sR ; n) = E [w(x , x , sR ; n)|{si < ti}i"U ]

during the second stage, where sR is the vector of reported signalsand U = {i : R(si ) = 0} is the set of unreported signals.

3 The final auction price p! = vR(x (n#1:n), x (n#1:n), sR ; n).


Theory

Key Result

Proposition (Expected Monotonicity)

The interim prior mean E [V |I ] is strictly increasing in theamount of information I .

New theory resultProof shows that equilibrium strategies inducea"liation between I and VHinges on additivity and conditional independenceof signalsImplies that if seller’s private information is“separable” in some sense then amount ofdisclosure is positively correlated with value


Theory

Predictions

Theory predicts:1 Interim prior mean E [V |I ] increasing in I2 Endogeneity of information measure I


Estimation

Outline

1 eBay Motors

2 Theory

3 Estimation

4 Results

5 Simulation

6 Conclusions


Estimation

Motivation

Why do I need a structural econometric model?

1 To recover the relationship between latentvalues and covariates

Object of demand estimation2 To carefully test prediction

Prediction is E [V |I ] increasing in I , not E [p|I ]Winner’s Curse - better informed bidders bid moreSo E [p|I ] could be increasing for strategic reasons

3 To perform the counterfactual simulation


Estimation

Parameterization

Parameterize interim priorBidders observe covariates z , have interim prior F |zLet interim prior F |z be Log Normal (µ, %)Let conditional signals G |v be Log Normal (v , r)Let µ = &z , % = #(!z)Model parameters ' = (&, !, r)

Include number of photos and bytes of text asregressors


Estimation

Estimation Strategy

Inherent Di"cultiesLatent v and bidder signals x1 · · · xn

Bid function depends non-linearly on latentvariables

Approach the problem by pseudo-maximumlikelihood (PML)

Dependent variable is price

p = v(x (n!1:n), x (n!1:n), n)

Posit log-normal distribution for p with mean andvariance E [log p|zj , '; n] and $[log p|zj , '; n]Maximize pseudo-likelihood function over '


Estimation

PML Asymptotics

Estimator consistent and asymptotically normal(Gourieroux, Monfort and Trognon (1984))

Idea is:Pseudo-likelihood from quadratic exponentialfamily + moments correctly specified( Limiting PL maximized at '0

Standard M-estimation conditions to get '̂n ! '0

Global identification required - numerical checks


Estimation

Computation

Moments complicated, for example:

v(x , x , n;µ,!, r) =

#eq"((x $ q)/r)2"((x $ q)/r)n#1"((q $ µ)/!)dq#"((x $ q)/r)2"((x $ q)/r)n#1"((q $ µ)/!)dq

Standard tricksPre-compute moments on gridUse scale properties of log normal distribution

New trick exploits PML approachScale properties ! $&(!, r) computable by WLSNested loop, inner loop &, outer loop (!, r)Avoids curse of dimensionality


Estimation

Advantages of Estimator

Previous approachesBajari/Hortacsu (2003) - Bayesian MCMCHong/Shum (2002) - Quantile Estimation

Advantages:Robust estimation (only use second highest bid)Much less computationally intensive in highdimensions (minutes vs days)Can use non-linear control function for endogeneity


Estimation

Endogeneity of Information

May be concerned about endogeneity ofinformation

Omitted quality index (µ = &z + (, % = !z "

Information measure I correlated with (

Does this cause an endogeneity problem?Depends on true moment specificationNo advertising e!ect ( I redundant given (Control function approach to test for advertisinge!ect


Estimation

Control Function Approach

Suppose I have an instrument W

Specify policy function: I = g(z ), W ) + h(()

Kernel Estimation of residualsm = I $ E [I |z ), W ]

h monotone, so * control function f (m)

Idea: Blundell/Powell(2003), Pinkse (2000),Newey et al (1999)

Asymptotics: Andrews (1994a, 1994b)


Estimation

Control Function Asymptotics

M-estimation with plugged-in $mSpecification correct( maximizer of limiting PL function = '0

Need stochastic equicontinuity of criterionfunction

Infinite-dimensional first stage nuisance parameterNeed criterion function “smooth” in function space

Kernel estimationBandwidth by cross validation (no oversmoothing)“Smooth” Trimming (underweight low density obs)


Estimation

Instrument

Exploit panel data

Instrument W = amount of information It$1

for previous car sold

Find It$1 and I strongly correlated in dataNeed It$1 independent of (t

Need ( randomly assigned over time within sellersUnobserved car characteristics idiosyncraticIt!1 related to (t!1, independent of (t


Results

Outline

1 eBay Motors

2 Theory

3 Estimation

4 Results

5 Simulation

6 Conclusions


Results

Table: Structural Demand Estimation

(1) (2)µLog Text 0.0537*** 0.0592***Photos 0.0185*** 0.0179***Log Feedback -0.0195***Percentage Negative Feedback -0.0027**%Age 0.0127*** 0.0126***Log of Text Size -0.0070 -0.0081Photos -0.0178*** -0.0182***Mean % 0.8472*** 0.8442***r 1.2099* 1.2095*


Results

Structural Results I

Model prediction µ = E [V |I ] + I confirmedWinner’s Curse e!ect

Estimates show 1 unit increase in % ( 10% , pText insignificant, photos do decrease uncertaintyEach photo adds about $7 by decreasing Winner’sCurse

Sources of informationForming posterior, bidder weights private signaland public signalWeighting depends roughly on r/(r + %)Estimate 59% public signal, 41% private signal


Results

Table: Structural Demand Estimation by Car Group

Classic Cars Reliable Cars PickupsµLog of Text Size 0.1157*** 0.0395*** 0.0596***Photos 0.202*** 0.0062*** 0.0172***%Log of Text Size -0.0107 -0.0047 -0.0021Photos -0.0052*** -0.0034 -0.0072Mean % 0.8512 0.6567 0.8065r 1.1996 1.0918 1.2658


Results

Table: Structural Demand Estimation with Controls

No Control With ControlµLog of Text Size 0.0623*** 0.0444***Control 0.0508***Control Squared -0.0179*%Log of Text Size -0.0450*** -0.0447***Mean % 0.8324 0.8319r 1.2162 1.2160Log Likelihood -1591.6473 -1581.7041


Results

Structural Results II

Coe"cient on text size falls when control addedEvidence of endogeneity

Use likelihood ratio testLR test statistic - 19.88Chi-squared statistic )2

2,0.999 = 13.81Reject null of no endogeneity


Results

Table: Demand Estimation by Car Group with Control

Classic Cars Reliable Cars PickupsµLog of Text Size 0.0660*** -0.0216 0.0108Control 0.0749*** 0.1157*** 0.0641**Control Squared -0.0293* -0.0180 -0.0003%Log of Text Size -0.0322 -0.0423 -0.0548**Mean % 0.8753 0.6064 0.7784r 1.2241 1.2379 1.3442


Results

Results Summary

Validate model predictionsE [V |I ] increasing in information measures II endogenous

Selective disclosure accounts for most of theobserved relationship between price and I

Little evidence of an advertising e!ect

Value of information highest for classic cars,then pickups, then reliable cars


Simulation

Outline

1 eBay Motors

2 Theory

3 Estimation

4 Results

5 Simulation

6 Conclusions


Simulation

Simulation Idea

Counterfactual where sellers can’t discloseinformation on webpage

Get at importance of public disclosures for marketBidders now have “coarse priors”(e.g. E [log V |z ] vs E [log V |z , I ])Prior underestimates value of “peaches” ;overestimate “lemons”Still receive unbiased private signals

For random sample of 1000 datapoints:Structural estimates + !E [I |z ] ! coarse priorsCompute expected counterfactual prices pc

Compute baseline prices pb, for a car of “averagequality”


Simulation

Simulation results

!15 !10 !5 5 10 15

Rel. Value !%"

!15

!10

!5

5

10

15

Rel. Price !%"


Simulation

Simulation results

Fit straight lines:Actual slope = 1.01 (mechanically true)Counterfactual slope = 0.61Implies for an $11000 peach with characteristicsworth $10000, get about $400 less undercounterfactual ! adverse selection

Can also simulate value/price ratio - 1.17Kelly blue book retail/private party price between1.15 and 1.25Think of retail price as value ! correct ballpark


Conclusions

Outline

1 eBay Motors

2 Theory

3 Estimation

4 Results

5 Simulation

6 Conclusions


Conclusions

Conclusions and Future Research

ConclusionsStrong evidence of selective disclosure by sellersDisclosures reduce information asymmetries andpotential for adverse selection

ExtensionsE"ciency implications?Examine fraction of non-traded cars in data and incounterfactual


Conclusions

Test for Common Values

Implement Athey/Haile (2002) test ofsymmetric PV vs CV environmentPV + Exchangeability implies:

2

nPr(B(n#2:n) < b)+

n $ 2

nPr(B(n#1:n) < b) = Pr(B(n#2:n#1) < b)

Test equality of distributions using modifiedKolmogorov-Smirnov statistic and subsampling

Haile/Hong/Shum (working paper)


Conclusions

Table: Test for Common Values

Critical ValuesSample Size S0.9 S0.95 S0.99

30 % 48.592 50.184 52.59540 % 49.41 50.393 53.07Test Statistic 51.664

Reject private values framework at 5% level


Conclusions

Robustness: Starting Bids

Table: Full Data vs Reserves < 20% of final price

Full Low ReserveµLog Text 0.0537*** 0.0546***Photos 0.0185*** 0.0183***%Age 0.0127*** 0.0123***Log of Text Size -0.0070 -0.0038Photos -0.0178*** -0.0057*Mean % 0.8472*** 0.8235***r 1.2099* 1.2212


Conclusions

Robustness: Estimation Technique

Table: PML vs NLS

PML NLSµLog Text 0.0537*** 0.0485***Photos 0.0185*** 0.0154***%Age 0.0127*** 0.0071***Log of Text Size -0.0070 -0.0111*Photos -0.0178*** -0.0202***Mean % 0.8472*** 0.6480r 1.2099* 1.3503


Conclusions

Goodness of Fit Tests

Table: Full vs Restricted Model

Full Model No Covariates for %µLog Text 0.0537*** 0.0807***Photos 0.0185*** 0.0255***%Age 0.0127***Log of Text Size -0.0070Photos -0.0178***Mean % 0.8472*** 0.8592***r 1.2099* 1.1069***Log Likelihood -2478.5 -3857.3

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