Fixedsearch Sequentialsearch Information clearinghouse

Pricedispersion and

search

Paul Schrimpf

Introduction

Models ofpricedispersionFixed search

Sequential search

Informationclearinghouse

Hong andShum (2006)

Additionalempiricalwork

Koulayev(2013)

References

Price dispersion and search

Paul Schrimpf

UBCEconomics 565

November 25, 2015

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

References

• Theory and overview of reduced form empirical work:Baye, Morgan, and Scholten (2006)

• Structural empirical papers:• Hong and Shum (2006), Moraga-González andWildenbeest (2008), De los Santos, Hortaçsu, andWildenbeest (2012), Wildenbeest (2011)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

1 Introduction

2 Models of price dispersionFixed searchSequential searchInformation clearinghouse

3 Hong and Shum (2006)

4 Additional empirical work

5 Koulayev (2013)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Section 1

Introduction

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

• Homogenous product and competitive market:• Theory ⇒ one price• Reality ⇒ price dispersion

• Explanations:• Unobserved product heterogeneity

• Likely part of explanation, but it is largely tautological• Imperfect information and search costs

• Stigler (1961)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Section 2

Models of price dispersion

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Models of price dispersion• Key point: relationship between price dispersion andprimitives (search cost, market size, number of firms,demand elasticity) depends on modeling assumptions

• Types:1 Search

1 Fixed : gather n prices, choose lowest price2 Sequential : sequentially gather prices, stop when price

low enough3 Information clearinghouse : some consumers loyal to

one firm, others buy from lowest price

2 Bounded rationality: small departure from Nashequilibrium in firms’ pricing game can give large pricedispersion

• Quantal response equilibrium, ε-equilibrium, mistakenbeliefs about price distribution

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search

• Stigler (1961)• Assumptions:

1 Distribution of prices on [p, p], non-degenerate CDF F(p),known by consumers

2 Each consumer wants to buy K units3 Search process: optimally choose fixed number of price

quotes, n; buy from firm with lowest price

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search - modelimplications

• Number of price quotes:(

E[p(1:n∗−1)] − E[p(1:n∗)])K ≥ c ≥

(E[p(1:n∗)] − E[p(1:n∗+1)]

)K

n∗ increasing in K• Firm expected demand:

Q(p) = µn∗K(1 − F(p))n∗−1

• Transaction costs decrease with price dispersion• If G is a mean preserving spread of F, then

EG[p(1:n)] < EF[p(1:n)] for n > 1

• Expected total costs are lower with greater pricedispersion

• If G is a mean preserving spread of F, thenEG[p(1:n∗

G)]K − cn∗G < EF[p(1:n∗

F)]K − cn∗F for n > 1

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search - critique I

• Rothschild (1973) critique:1 distribution of prices is not endogenous

2 fixed search may not be optimal for consumers

• For (2) need to be more specific about searchenvironment

• Fixed search optimal if e.g. waiting time to obtain eachprice quote

• Diamond (1971) in sequential or fixed search modelwith homogenous firms and consumers, there is anequilibrium where all firms charge the monopoly price

• Can obtain non-degenerate equilibrium distribution ofprices by introducing firm heterogeneity or consumersearch cost heterogeneity

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search - endogenous pricedispersion I

• Burdett and Judd (1983) : equilibrium price dispersionwith ex-ante identical consumers and firms

• Assumptions:1 Consumers: unit demand with reservation price v2 Fixed sample search3 Firms: constant marginal cost m, optimal monopoly

price p∗

4 Consumer utility given price p∗ and n = 1 is positive

• Equilibrium: price distribution, F(p), and searchdistribution, P(n = i) for i = 1, 2, ...

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search - endogenous pricedispersion I

• Implications:• If F(p) non-degenerate, then P(n = 1), P(n = 2) > 0 and

P(n > 2) = 0, let θ = P(n = 1), 1 − θ = P(n = 2)• Firm profits:

π(p) ={

(v − m)θ if p = v

(p − m)P(consumer purchases) if p < v

={

(v − m)θ if p = v

(p − m) [θ + (1 − θ)(1 − F(p))] if p < v

• Firms indifferent among prices implies:

F(p) = 1 − v − pp − m

θ1 − θ

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search - endogenous pricedispersion II

• Consumers indifferent between n = 1 and n = 2 pinsdown θ (generally two equilibria with θ ∈ (0, 1) (there’salso an equilibrium where firms charge monopoly priceand n = 1 for all consumers))

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Sequential search I

• Sequential search: consumer pays cost c to obtain pricep ∼ F; can either buy at price p (or any previous price)or search again

• Optimal strategy = reservation price p∗ = min{p, z∗}where

c =∫ z∗

p(z∗ − p)f(p)dp =

∫ z∗

pF(p)dp

• With homogeneous firms and consumers uniqueequilibrium is for firms to charge the monopoly price

• Equilibrium price dispersion with:• Heterogeneous firm marginal cost and elastic demand(i.e. not unit demand); or

• Heterogeneous search costs (and assumptions aboutdistribution of search costs)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Information clearinghouse

• Finite number n > 1 of homogeneous firms• Constant marginal cost c• Clearinghouse charges ϕ ≥ 0 to firms to list their prices

• Consumers with unit demand and reservation price v• S > 0 “shoppers” consult clearinghouse, buy at lowestprice if < v, else visits one other firm buys if price < v,else does not buy

• L > 0 “loyal” consumers visit firm i, buy if pi < v

• Equilibrium with price dispersion if L > 0 or ϕ > 0• Non-clearinghouse prices all = v• Distribution of clearinghouse prices ≤ v

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Section 3

Hong and Shum (2006)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Hong and Shum (2006): “Usingprice distributions to estimate

search costs”

• Goal: estimate consumer search costs• Environment: online booksellers

• Homogeneous product• Homogeneous firm costs

• Data: distribution of prices

• Method: use distribution of prices + assumption aboutform of search to estimate distribution of consumercosts

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search I

• Firm marginal cost r, continuum of firms withequilibrium price distribution Fp

• Consumer search cost ci ∼ Fc• Number of searches

(E[p(1:n(ci)−1)] − E[p(1:n(ci))]

)K ≥ ci ≥

(E[p(1:n(ci))] − E[p(1:n(ci)+1)]

)K

• Define ∆n = E[p(1:n−1)] − E[p(1:n)]; FP observed, so ∆n

identified• Let qn = Fc(∆n−1) − Fc(∆n) = portion of consumers whoobtain n prices

• qn not observed• Assume Fc such that qn = 0 for all n > K (could berelaxed, but complicates econometrics)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Fixed search II

• Firms indifferent among prices p ∈ [p, p], so

(p − r)q1 = (p − r)[

K∑

k=1

qkk(1 − Fp(p)

)k−1

]

• Observed prices pj, j = 1, ..., nf

(p − r)q1 = (p − r)[

K∑

k=1

qkk(1 − Fp(pj)

)k−1

]

identifies q1, ..., qK and r

• Knowing q1, ..., qK can solve for Fc(∆1), ..., Fc(∆K)• Estimate using empirical likelihood (≈ efficientlyweighted GMM)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

• Estimates forBillingsleyusing 20prices, K = 3,and 5moments

• q1 = 0.633,q2 = 0.309,q3 = 0.058

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Sequential search I• Consumer search cost ci ∼ Fc• Reservation price, p∗

i = p(ci) = min{z(ci), p} where

ci =∫ z(ci)

p(z(ci) − p)f(p)dp =

∫ z(ci)

pF(p)dp

Let G(p) = CDF of p∗i

• Firm indifference:

(p − r) (1 − G(p)) = (p − r) (1 − G(p))

• Data: nf prices, but nf − 1 indifference conditions, soneed some restriction

• Parametric assumption about Fc• (in fixed search model, assumption about K played asimilar role)

• Or fix r and estimate Fc nonparametrically

• Estimate by MLE

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Results

• For text books: Stokey-Lucas, Lazear, Billingsley, Duffie• Fixed search model:

• Median search cost ≈ $2.50 (quantiles above mediannot identified)

• 25%tile $0.68 - $2.50• Selling cost r ≈ 65% of median price

• Sequential search model:• Median search cost $9.22-$29.40• Search cost such that z(ci) = p, $4.56 − $19.19• Selling cost r ≈ 40% of median price

• Check whether parametric assumption drivingsequential results: fix r and estimate nonparametrically

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Section 4

Additional empirical work

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Additional empirical work I

• Moraga-González and Wildenbeest (2008):• Oligopoly version of Hong and Shum (2006) fixed searchmodel

• MLE instead of nonparametric EL

• Chen, Hong, and Shum (2007):• Model selection test to choose between fixed andsequential search

• Test is inconclusive

• Moraga-González, Sándor, and Wildenbeest (2012)• Hong and Shum (2006)/Moraga-González andWildenbeest (2008) fixed search model with multiplemarkets

• Data: multiple markets with common search costdistribution, but different reservation prices, firm costs,and/or number of firms

• Semi-nonparametric estimator• Application: memory chips

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Additional empirical work II• De los Santos, Hortaçsu, and Wildenbeest (2012)

• Data on web browsing and purchases to test sequentialvs fixed search

• Key difference: behavior in sequential model dependson prices observed so far; in fixed model it does not

• Context: online book stores• Results: favor fixed search model; also evidence ofunobserved product heterogeneity (store loyalty)

• Hortaçsu and Syverson (2004)• Context: mutual funds• Model with search frictions and product heterogeneity• Results:

• Investors value observable nonportfolio productattributes

• Small search costs can rationalize price dispersion

• Wildenbeest (2011)• Vertical product differentiation and search frictions

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Additional empirical work III

• Fixed search model• ML estimation• Context: grocery items• Results: supermarket heterogeneity more importantthan search frictions

• Honka (2014): search & switching costs in autoinsurance

• Fixed search model• Consumer knows price of current insurer, and prices ofk others

• Pays switching cost if change insurer• Finds search costs more important than switching costsfor customer retention & consumer welfare

• Search with learning: De los Santos, Hortacsu, andWildenbeest (2012), Koulayev (2013)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Section 5

Koulayev (2013)

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Koulayev (2013)

• Search model with unknown distribution

• Model based on Rothschild (1974)

• Applied to S&P 500 mutual funds

• Highlights differences with search model with knownprice distribution

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Model I

• N products with utilities SN = {u1, ..., uN}, whereu1 > u2 > · · · > uN

• Consumer believes possible utilities SG = {u1, ..., uG}with SN ⊆ SG

• Search technology: each search independent and ugdrawn with probability pg

• Consumer does not know pg, has Dirichlet prior withparameters α1, ..., αG,

f(p1, ..., pg) =Γ(

∑αg)∏

γ(αg)∏

pαg−1g

which implies

E[pj] =αj∑αg

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Model II

• Bayesian updating: after seeing ug, ng times,

f(p|n) ∝f(n|p)f(p)

∝(∑

ng)!∏ng!

∏pngg

Γ(∑

αg)∏γ(αg)

∏p

αg−1g

∝Γ(

∑αg + ng)∏

γ(αg + ng)∏

pαg+ng−1g

soE[pj|n1, ..., ng] =

αj + nj∑αg + ng

• Sequential search and at end buy best good found

• Search cost c, best good found so far ur∗

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Model III

• Continue searching if

E[max{u, ur∗}|n] − ur∗ > c∑

ug>ur∗

(ug − ur∗)E[pg|n] > c

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Market shares I

• Observe: market shares, product characteristics

• Consumers have different search costs ci ∼ F(c)• Challenge: many search histories can lead to the samechoice; need to integrate over all search histories tocompute market shares

• Define kr = longest a consumer with best draw ur willcontinue searching

kr = max

1,

1c

∑

ug>ur∗

(ug − ur∗ )αg −∑

g

αg

• Show that market shares can be written as a function ofjust the k1, ...., kN

• kr is integer valued and decreasing in c

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Example

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Example

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

• Paper has simulations comparing price elasticity insearch with learning versus search without learningmodels

• Simulations also show that ignoring learning can leadto bias

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Application: S&P 500 mutualfunds

• ug = −price (fixed fee per $10,000 invested)

• log ci ∼ N(µ0 + µ1t, δ0 + δ1t)• Search probabilities depend on fund age:

ρjt =Aγjt∑Aγkt

• Rational prior: αjt = ρjtN0

• Consumers’ prior not identified from market share dataalone

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References


Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References


Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References


Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References


Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Baye, Michael R., John Morgan, and Patrick Scholten. 2006.“Information, Search, and Price Dispersion.” WorkingPapers 2006-11, Indiana University, Kelley School ofBusiness, Department of Business Economics and PublicPolicy. URL http://EconPapers.repec.org/RePEc:iuk:wpaper:2006-11.

Burdett, Kenneth and Kenneth L. Judd. 1983. “EquilibriumPrice Dispersion.” Econometrica 51 (4):pp. 955–969. URLhttp://www.jstor.org/stable/1912045.

Chen, Xiaohong, Han Hong, and Matthew Shum. 2007.“Nonparametric likelihood ratio model selection testsbetween parametric likelihood and moment conditionmodels.” Journal of Econometrics 141 (1):109 – 140. URLhttp://www.sciencedirect.com/science/article/pii/S0304407607000103. <ce:title>Semiparametricmethods in econometrics</ce:title>.

http://EconPapers.repec.org/RePEc:iuk:wpaper:2006-11

http://EconPapers.repec.org/RePEc:iuk:wpaper:2006-11

http://www.jstor.org/stable/1912045

http://www.sciencedirect.com/science/article/pii/S0304407607000103

http://www.sciencedirect.com/science/article/pii/S0304407607000103

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

De los Santos, Babur, Ali Hortacsu, and Matthijs RWildenbeest. 2012. “Search with Learning.” Tech. rep.URL http://www.bus.indiana.edu/riharbau/RePEc/iuk/wpaper/bepp2012-03-DelosSantos-Hortacsu-Wildenbeest.pdf.

De los Santos, Babur, Ali Hortaçsu, and Matthijs R.Wildenbeest. 2012. “Testing models of consumer searchusing data on web browsing and purchasing behavior.”The American Economic Review 102 (6):pp. 2955–80. URLhttp://www.aeaweb.org/articles.php?f=s&doi=10.1257/aer.102.6.2955.

Diamond, Peter A. 1971. “A model of price adjustment.”Journal of Economic Theory 3 (2):156 – 168. URLhttp://www.sciencedirect.com/science/article/pii/0022053171900135.

http://www.bus.indiana.edu/riharbau/RePEc/iuk/wpaper/bepp2012-03-DelosSantos-Hortacsu-Wildenbeest.pdf




http://www.aeaweb.org/articles.php?f=s&doi=10.1257/aer.102.6.2955

http://www.aeaweb.org/articles.php?f=s&doi=10.1257/aer.102.6.2955

http://www.sciencedirect.com/science/article/pii/0022053171900135

http://www.sciencedirect.com/science/article/pii/0022053171900135

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Hong, Han and Matthew Shum. 2006. “Using PriceDistributions to Estimate Search Costs.” The RAND Journalof Economics 37 (2):pp. 257–275. URLhttp://www.jstor.org/stable/25046241.

Honka, Elisabeth. 2014. “Quantifying search and switchingcosts in the US auto insurance industry.” The RANDJournal of Economics 45 (4):847–884. URLhttp://dx.doi.org/10.1111/1756-2171.12073.

Hortaçsu, Ali and Chad Syverson. 2004. “ProductDifferentiation, Search Costs, and Competition in theMutual Fund Industry: A Case Study of S&P 500 IndexFunds.” The Quarterly Journal of Economics 119 (2):403–456.URL http://qje.oxfordjournals.org/content/119/2/403.abstract.


http://dx.doi.org/10.1111/1756-2171.12073

http://qje.oxfordjournals.org/content/119/2/403.abstract

http://qje.oxfordjournals.org/content/119/2/403.abstract

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Koulayev, Sergei. 2013. “Search With Dirichlet Priors:Estimation and Implications for Consumer Demand.”Journal of Business & Economic Statistics 31 (2):226–239.URLhttp://dx.doi.org/10.1080/07350015.2013.764696.

Moraga-González, José Luis and Matthijs R. Wildenbeest.2008. “Maximum likelihood estimation of search costs.”European Economic Review 52 (5):820 – 848. URLhttp://www.sciencedirect.com/science/article/pii/S001429210700102X.

Moraga-González, José Luis, Zsolt Sándor, and Matthijs R.Wildenbeest. 2012. “SEMI-NONPARAMETRIC ESTIMATIONOF CONSUMER SEARCH COSTS.” Journal of AppliedEconometrics :n/a–n/aURLhttp://dx.doi.org/10.1002/jae.2290.

http://dx.doi.org/10.1080/07350015.2013.764696

http://www.sciencedirect.com/science/article/pii/S001429210700102X

http://www.sciencedirect.com/science/article/pii/S001429210700102X

http://dx.doi.org/10.1002/jae.2290

Pricedispersion and

search

Paul Schrimpf

Introduction


Sequential search


Hong andShum (2006)


Koulayev(2013)

References

Rothschild, Michael. 1973. “Models of Market Organizationwith Imperfect Information: A Survey.” Journal of PoliticalEconomy 81 (6):pp. 1283–1308. URLhttp://www.jstor.org/stable/1830741.

———. 1974. “Searching for the Lowest Price When theDistribution of Prices Is Unknown.” Journal of PoliticalEconomy 82 (4):689–711. URLhttp://www.jstor.org/stable/1837141.

Stigler, George J. 1961. “The Economics of Information.”Journal of Political Economy 69 (3):pp. 213–225. URLhttp://www.jstor.org/stable/1829263.

Wildenbeest, Matthijs R. 2011. “An empirical model ofsearch with vertically differentiated products.” The RANDJournal of Economics 42 (4):729–757. URL http://dx.doi.org/10.1111/j.1756-2171.2011.00152.x.




http://dx.doi.org/10.1111/j.1756-2171.2011.00152.x

http://dx.doi.org/10.1111/j.1756-2171.2011.00152.x

Documents

Fixedsearch Sequentialsearch Information clearinghouse