matching - faculty of artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · matching...
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![Page 1: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/1.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Matching
Paul Schrimpf
UBCEconomics 565
November 24, 2014
![Page 2: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/2.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
References
• Brief review: Fox (2009)
• Longer review: Graham (2011)
• Extensive notes: Galichon (2011)
• Identification: Fox (2010b), Galichon and Salanié (2010),and many of the papers below
• Applications• Marriage: Choo and Siow (2006) , Galichon and Salanié(2010)
• Mergers: Uetake and Watanabe (2012), Park (2012),Oktay Akkus and Hortaçsu (2012)
• Venture capital: Sørensen (2007)• Downstream - upstream firms: Fox (2010a)• Medical residents: Agarwal (2012)
![Page 3: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/3.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
1 Introduction
2 Sørensen (2007)
3 Fox (2010a)
4 Fox and Bajari (2013)
![Page 4: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/4.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Section 1
Introduction
![Page 5: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/5.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Introduction
• Matching: payoffs depend on who matches with whom• Examples:
• Firm mergers• Firm upstream/downstream relationships• Workers and firms• Houses for consumers• Marriage
• Model primitive: payoffs of all potential matches
• Equilibrium: pairwise stability - no couple would preferto deviate
![Page 6: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/6.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Introduction
• Structural empirical matching models:• Data on observed matches and their characteristics• Goal: estimate payoff function
![Page 7: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/7.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Types of matching• Transferable vs non transferable utility
Matching
One-to-one
UnilateralPreferences(housing)
BilateralPreferences(marriage)
Many-to-one(workers to firms)
Many-to-many(players into teams)
![Page 8: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/8.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Matching – theory
• Much more developed than empirical work
• Optimal transportation theory – results imply existenceand (in some cases) uniqueness of optimal matching;and existence, uniqueness, and efficiency of equilibrium
• See Galichon (2011) and references therein
![Page 9: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/9.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Section 2
Sørensen (2007)
![Page 10: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/10.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Sørensen (2007) “How Smart IsSmart Money? A Two-SidedMatching Model of Venture
Capital”
• Fact: companies invested in by more experiencedventure capitalists are more likely to go public
![Page 11: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/11.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
![Page 12: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/12.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Sørensen (2007) “How Smart IsSmart Money? A Two-SidedMatching Model of Venture
Capital”
• Question: is this because experiences VCs invest inbetter companies or because experienced VCs’influence adds value to companies?
• Matching model used to distinguish these explanations
![Page 13: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/13.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Why matching?
• VCs affect company value by:• Monitoring, management• Providing contacts• Signaling value to other investors
• Prior evidence that companies care about identity ofinvestors; do not simply take best financial offer
![Page 14: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/14.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Model I
• Set of investors I, set of companies J
• One-to-many: company has one investor; investormany companies
• Valuation of match Vij• Match correspondence µ• Payoffs: non transferable
• Investor: πi(µ(i)) = λ∑
j∈µ(i) Vij
• Company: πj = (1 − λ)Vµ(j)j
• Equilibrium: pairwise-stability• Opportunity cost of deviating for a pair that is notmatched in µ
Vij ≡ Vµ(j)j ∨ minj′∈µ(i)
Vij′
![Page 15: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/15.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Model II
• Opportunity cost of remaining in match
Vij ≡ maxi′∈I:Vi′ j>minj′∈µ(i′ ) Vi′ j′
Vi′j ∨ minj′∈J:Vij′ >Vµj′ j′
Vij′
• µ is stable ⇔ Vij < Vij∀ij ∈ µ ⇔ Vij > Vij∀ij ∈ µ• Define Γµ as set of all valuations such that µ is stable
![Page 16: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/16.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Empirical model
• Observe µ, investor and company characteristics Wij,Xij, outcomes IPOij
• Vij = W′ijα + ηij
• Likelihood of matches: P(µ ∈ Γµ − Wα)• Outcome: IPOij = 1{Xijβ + εij > 0}• Assume (ε, η) ∼ N
• Estimate using MCMC
![Page 17: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/17.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
![Page 18: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/18.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Conclusions
• This paper: use a matching model to correct forselection
• Focus is not necessarily matching by itself
• Does not look at efficiency of matching or anycounterfactuals related to matching
• Related work:• Park (2012): mutual fund mergers, very similar approach• Uetake and Watanabe (2012): bank mergers followingderegulation, moment inequalities based on matchstability
![Page 19: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/19.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Section 3
Fox (2010a)
![Page 20: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/20.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Fox (2010a) “Estimatingmatching games with transfers”
• Context: Car parts suppliers and automotive assemblers
• Goal: estimate revenues from producing differentportfolios of parts
• Motivating examples:• GM considered divesting Opel – potential loss tosuppliers who would not gain as much from specializing
• Asian assembly plants enter North America – howbeneficial to North American parts suppliers?
![Page 21: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/21.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Fox (2010a) “Estimatingmatching games with transfers”
• Data: part suppliers and assembler matches• No observed prices
• Approach: use equilibrium conditions of matchingmodel to identify revenue function
![Page 22: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/22.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Model I
• Two-sided, many-to-manyUpstream Downstream
Example Parts AssemblersCharacteristics u ∈ U d ∈ DTransfer t −t
• Full match: ⟨u, d, t⟩• Physical matches M = {⟨u1, d1⟩, ..., ⟨rn, dn⟩}
• Mu = set of d matched with u• Md = set of u matched with d
• Revenue functions rup(Mu), rdown(Md)• Equilibrium: pairwise stability ⇒
rup(Mu1) + tu1,d1 ≥ rup (Mu1 \ ⟨u1, d1⟩ ∪ ⟨u1, d2⟩) + tu1,d2
![Page 23: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/23.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Estimator I
• Add pairwise stability conditions to eliminate transfers:
rup(Mu1) + rdown(Md1) + rup(Mu1) + rdown(Md1) ≥≥rup (Mu1 \ ⟨u1, d1⟩ ∪ ⟨u1, d2⟩) +
+ rdown (Md1 \ ⟨u1, d1⟩ ∪ ⟨u2, d1⟩
)+
+ rup (Mu2 \ ⟨u2, d2⟩ ∪ ⟨u2, d1⟩) ++ rdown (
Md2 \ ⟨u2, d2⟩ ∪ ⟨u1, d2⟩)
• Use to form maximum score estimator• Assume r(M) = Z(M)′β• Then inequalities ⇔ X′
u1,u2,d1,d2β ≥ 0• Objective:
QH(β) = 1H
∑
h∈H
∑
u,d
1{X′u1,u2,d1,d2β ≥ 0}
![Page 24: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/24.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Empirical specification I
• Data from SupplierBusiness on 1252 suppliers, 14assemblers with 52 brads, 392 models, and 52492 partsin 187 component categories
• Data includes mainly North American and Europeanfirms
• Observation:⟨ u︸︷︷︸
part supplierFederal-Mogul
, d︸︷︷︸car model
Fiat
, l︸︷︷︸part
front pads
⟩ in market
h︸︷︷︸componentdisk brakes
• Revenue function:• rup(M) = Zup(M)′βup
![Page 25: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/25.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Empirical specification II
• Zup(M) = measure of specialization of supplier in itsmatches, specifically HHI of parts across
• Assemblers, brands, models, continents
•
• rdown(M) = Zdown(M)′βdown
• Zdown(M) = measure of specialization of parts in itsmatches, specifically HHI of suppliers across
• Assemblers, brands, models
![Page 26: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/26.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Results
![Page 27: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/27.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Results
![Page 28: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/28.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Results
![Page 29: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/29.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Other applications andextensions I
• Identification: Fox (2010b)
• Unobserved heterogeneity: Fox and Yang (2012)• Matching maximum score estimator of Fox (2010a) usedin
• Fox and Bajari (2013): FCC spectrum auction – no tradesafter auction implies pairwise stability
• Oktay Akkus and Hortaçsu (2012): bank mergers,matching with observed transfers
• Levine (2009): pharmaceutical marketing firms anddrugs
![Page 30: Matching - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/09-matching.pdf · Matching PaulSchrimpf Introduction Sørensen (2007) Fox(2010a) FoxandBajari (2013) References Matching](https://reader034.vdocuments.us/reader034/viewer/2022050210/5f5c85625c596564e22fdf55/html5/thumbnails/30.jpg)
Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Section 4
Fox and Bajari (2013)
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Fox and Bajari (2013)“Measuring the Efficiency of an
FCC Spectrum Auction”
• Estimates an auction model using pairwise stability• C block FCC spectrum auctions 1995-1996
• Simultaneous ascending auctions for 480 geographicareas
• Theory & evidence from other FCC auctions suggestscollusion
• Goal: estimate distribution of valuations & andallocative efficiency
• Identifying assumption: allocation of licenses ispairwise stable in matches, that is, an exchange of twolicenses by winning bidders must not raise the sum ofthe valuations of the two bidders
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Background
• C block 1900 MHz spectrum used for mobile phones• Auction format:
• Multiple rounds• Each round, simultaneously submit bids (or not) on all480 regions
• Auction ends when no more bids placed on any item ina round
• Lasted 185 days
• Only new carriers participated (small business discount)
• 255 bidders, 85 winners, most either went bankrupt ormerged with incumbent carriers
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Suggestive evidence ofintimidatory collusion
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Valuations
• a = 1, ..,N bidders, j = 1, .., L licenses• Profit of bidder a from J ⊂ L
πa(J) −∑
j∈J
pj
• Parameterization:
πa(J) = πβ(wa, xJ)︸ ︷︷ ︸±1·eliga·(
∑jinJ popj)+β′complemj
+∑
j∈J
ξj +∑
j∈J
εa,j
• π(w, x) and ξj common knowledge of bidders, ξjunobserved by econometrician
• ε i.i.d., private for bidders, unobserved byeconometrician
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Measuring complementarities
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
• Each bidder makes a payment before the auction beginsfor initial eligibility. A bidder’s eligibility is expressed inunits of total population. A bidder cannot bid on apackage of licenses that exceeds the bidder’s eligibility.
• geomcomplemJ =∑
i∈J popi
∑j∈J\{i}
popipopj
distδi,j∑
j∈L\{i}popipopj
distδi,j
• travelcomplemJ =∑
i∈J popi∑
j∈J\{i} trips(origin i, destination j)∑j∈L\{i} trips(origin i, destination j)
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Pairwise stability
• Pairwise stable in matches:
πa(Ja)+πb(Jb) ≥ πa ((Ja \ {ia}) ∪ {ib})+πb ((Jb \ {ib}) ∪ {ia})
• Evidence for:• Often satisfied in experimental data• Swaps did not occur after auction• Holds in theoretical models of ascending auctions withcollusion: Brusco & Lopomo (2002) andEngelbrecht-Wiggans & Kahn (2005) and Milgrom (200)
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Estimation
• Similar to Fox (2010a), but without transfers
• Objective function = sum of indicators for pairwisestability inequalities
• Fixed effects drop out of pairwise stability conditionsfrom differencing
• Inference through subsampling
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Interpretation
• SD of elig · (∑
pop) 0.029, SD of geocomplem is 0.024
• βgeo = 0.32, so geocomplem 32% as important aspopulation
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
• 6.7 and 9.8 are implausibly large — imply increasingcomplementarity is worth as much as having 6 timesthe population in the area
• Model with prices implies value of nationwide license is$360 billion, but total bids where $10 billion, annualrevenues in 2006 were $113 billion
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Agarwal, Nikhil. 2012. “An Empirical Model of the MedicalMatch.” URL http://www.people.fas.harvard.edu/~agarwal3/papers/AgarwalJMP.pdf.
Choo, Eugene and Aloysius Siow. 2006. “Who Marries Whomand Why.” Journal of Political Economy 114 (1):pp. 175–201.URL http://www.jstor.org/stable/10.1086/498585.
Fox, Jeremy T. 2009. “Matching models: empirics.” In TheNew Palgrave Dictionary of Economics, edited by Steven N.Durlauf and Lawrence E. Blume. Basingstoke: PalgraveMacmillan. URL http://www.dictionaryofeconomics.com/article?id=pde2009_M000426.
———. 2010a. “Estimating Matching Games with Transfers.”Working paper, University of Michigan. URLhttp://www-personal.umich.edu/~jtfox/working-papers/matching_fox.pdf.
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
———. 2010b. “Identification in matching games.”Quantitative Economics 1 (2):203–254. URLhttp://dx.doi.org/10.3982/QE3.
Fox, Jeremy T. and Patrick Bajari. 2013. “Measuring theEfficiency of an FCC Spectrum Auction.” AmericanEconomic Journal: Microeconomics 5 (1):100–146. URLhttp://www.aeaweb.org/articles.php?doi=10.1257/mic.5.1.100.
Fox, Jeremy T. and Chenyu Yang. 2012. “UnobservedHeterogeneity in Matching Games.” Working Paper 18168,National Bureau of Economic Research. URLhttp://www.nber.org/papers/w18168.
Galichon, Alfred. 2011. “Theoretical and Empirical Aspects ofMatching Markets.” URLhttp://alfredgalichon.com/wp-content/uploads/2012/10/MatchingnotesColumbia.pdf.
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Galichon, Alfred and Bernard Salanié. 2010. “Matching withtrade-offs: revealed preferences over competingcharacteristics.” URL http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1640380.
Graham, B. 2011. “Econometric methods for the analysis ofassignment problems in the presence of complementarityand social spillovers.” Handbook of social economics1:965–1052. URL http://128.32.105.3/~bgraham/Published/HandbookOfSocialEconomics_1B_2011/BSG_HandbookOfSocialEconomics_1B_2011.pdf.
Levine, Anna A. 2009. “Licensing and scale economies in thebiotechnology pharmaceutical industry.” URLhttp://apps.olin.wustl.edu/workingpapers/pdf/2010-11-004.pdf.
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Matching
Paul Schrimpf
Introduction
Sørensen(2007)
Fox (2010a)
Fox and Bajari(2013)
References
Oktay Akkus, J. Anthony Cookson and Ali Hortaçsu. 2012.“The Determinants of Bank Mergers: A RevealedPreference Analysis.” URLhttps://docs.google.com/uc?export=download&id=0B9xl-vM6JOoDMjVtVXhiNWt5bjA.
Park, Minjung. 2012. “Understanding Merger Incentives andOutcomes in the US Mutual Fund Industry.” URL http://faculty.haas.berkeley.edu/mpark/MergerPaper.pdf.
Sørensen, Morten. 2007. “How Smart Is Smart Money? ATwo-Sided Matching Model of Venture Capital.” TheJournal of Finance 62 (6):pp. 2725–2762. URLhttp://www.jstor.org/stable/4622352.
Uetake, Kosuke and Yasutora Watanabe. 2012. “Entry byMerger: Estimates from.” URLhttp://www.kellogg.northwestern.edu/faculty/watanabe/htm/EntryByMerger.pdf.