Reputation Signals and Market Outcomes · 2018. 8. 31. · Reputation Signals and Market Outcomes Hugo Hopenhayn UCLA Maryam Saeedi CMU September2,2017 Hugo Hopenhayn UCLA , Maryam

Reputation Signals and Market Outcomes

Hugo HopenhaynUCLA

Maryam SaeediCMU

September 2, 2017

Hugo Hopenhayn UCLA , Maryam Saeedi CMU Reputation Signals and Market Outcomes -p. 1

Introduction

• Certification widely used in markets for goods and services◦ Examples: Ebay: Top Rated Sellers, Airbnb: Superhost, Yelp:

stars.• Valued by Consumers

◦ Ebay: Consumers willing to pay 15% and 10% more forbadged sellers in auctions and buy-it-now.◦ Yelp’s grading leads to a 5–9% increase in revenue.◦ Consumers tend to be more responsive to changes in these

quality signals than to other information on performance.

• Question: Impact of certification technology on marketoutcomes (prices, market shares, welfare)• Optimal Design


Certification

• Firms differ in qualities z• Certification technology two parts: z → σ and some

threshold(s) σ∗.◦ Quality of signal◦ Threshold for certification

• Part 1: Consider impact of threshold change◦ For simplicity: perfect signal (σ = z, σ∗ = z∗)

• Part 2: Impact of better information (higher correlationbetween qualities and signals)


Basic Model: Supply

• Competitive Equilibrium (part Cournot in paper)• Continuum of firms mass one• Distribution of qualities F (z)

• Each firm supply function S (p)

◦ Simplification: assume same technology independent of quality◦ In paper extensive and intensive margins


Basic Model: Demand

• Discrete choice - unit demand• Utility: U (z, θ) = θ1z + θ0 − p• z can be interpreted as expected quality• Joint distribution G (θ0, θ1)

• Outside good normalized to zero• Special cases:◦ Additive quality premium: θ1 same for all (parallel demand

functions)◦ Vertical differentiation model


Quality Partition

• Threshold z∗

• zH , zL: the average quality for firms above and below thethreshold• Supply

SH (p) = (1− F (z∗))S (p)

SL (p) = F (z∗)S (p)

• Can be interpreted as intensive+extensive margin changes• Equilibrium: pL and pH such that

DL (z∗, pL, pH) = SL (pL)

DH (z∗, pL, pH) = SH (pH)

• Equilibrium is unique• Illustrate AQP


Demand


Demand


Demand


Equilibrium


Equilibrium


Equilibrium


Changing the Threshold

How are prices affected by an increase in the threshold?• Share of firms in low and high quality groups changes• Expected quality of both groups increases• Effect on zH − zL ambiguous• Goods may become more or less substitutable

PropositionIf z∗ increases at least one of the prices pH or pL must increase.

If zH − zL increases too, then pH must increase.

• Specialize to AQP case


Changing the Threshold

How are prices affected by an increase in the threshold?• Share of firms in low and high quality groups changes• Expected quality of both groups increases• Effect on zH − zL ambiguous• Goods may become more or less substitutable

PropositionIf z∗ increases at least one of the prices pH or pL must increase.If zH − zL increases too, then pH must increase.

• Specialize to AQP case


Example 1: pL decreases


















Example 2: pH decreases


















Increase Threshold: Results

• If zH − zL increases then pH increases• If zH − zL decreases then pL increases• p′L < pH

• Sufficient conditions:1. If S is convex, then pH increases2. If S is concave, then pL increases


Increase Threshold: Results

• If zH − zL increases then pH increases• If zH − zL decreases then pL increases• p′L < pH• Sufficient conditions:

1. If S is convex, then pH increases2. If S is concave, then pL increases


Linear Supply Case

pL = P (Q) + zL, pH = P (Q) + zH , p̄ = P (Q) + z̄

• For fixed Q, p̄ is independent of z̄• Aggregate supply is linear in p̄• Q is independent of z∗

1. Both prices increase & price decreases for HL firms◦ Share of firms LL and HH firms increase◦ Share of HL firms decreases◦ Extensive margin: Possible entry in LL and HH and exit inHL.

2. Consumer Surplus does not change!


Linear Supply Case






Linear Supply Case






Results from Empirical Paper

• “Natural” experiment in 2009 eBay increased requirements forbadge• Findings in paper (Hui, Saeedi, Spagnolo, Tadelis):

◦ Classified firms in HH, LL, HL, LH• Findings

◦ p decreases for HL◦ sales increase for all but the HL group◦ More entry at the tails of the quality distribution

• Consistent with AQP with linear supply or Cournot.


Optimal Partition: Linear Case

• Optimal z∗: maximizes welfare.• Restrict analysis to linear supply case (apply also in a

Cournot model)• Max welfare same as maximizing profits/revenues

• πL ∝ p2L and πH ∝ p2H=⇒max Ep2 (z∗)

• p2L = a+ bzL + z2L =⇒max bEz + Ez2 (z∗)

• Optimal z∗ maximizes variance between =⇒ minimizesvariance within• same as k-mean criterion for clustering




Cournot model)• Max welfare same as maximizing profits/revenues• πL ∝ p2L and πH ∝ p2H=⇒max Ep2 (z∗)



















PropositionThe optimal threshold satisfies

z∗ =zL (z∗) + zH (z∗)

2

CorollaryIf F is symmetric (mean=median) then z∗ is equal to the median.


Improved information

• Better classification system results in mean preserving spreadof zL and zH• Better information always leads to higher pH• What about pL?

◦ Example: pL could go up (intuition: opening markets, gainsfrom better sorting)◦ In the above case or pure vertical differentiation, pL decreases

• Welfare increases


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Reputation Signals and Market Outcomes · 2018. 8. 31. · Reputation Signals and Market Outcomes Hugo Hopenhayn UCLA Maryam Saeedi CMU September2,2017 Hugo Hopenhayn UCLA , Maryam