two-sided matching in international markets 2018.pdf · 2018. 6. 7. · objectives enduring issues:...

Two-Sided Matching in International Markets

J. Eatona,b , D. Jinkinsc , J. Tybouta,b , D. Xud ,b

aPenn State U., bNBER, cCopenhagen Business School, dDuke U.

May 25, 2018

Disclaimer

This research was supported by the National ScienceFoundation (Grant No. SES-1426645). All results havebeen reviewed by the U.S. Census Bureau to ensure thatno condential information is disclosed. Any opinions,ndings, conclusions and recommendations expressedherein are those of the authors and do not necessarilyrepresent the views of the NSF or the U.S. CensusBureau.

Objectives

� Enduring issues: nature, severity, and welfare implications oftrade frictions.

� Imperfect approaches: xed costs, beachhead costs, icebergcosts.

� This paper: dynamic search model with buyer-sellermatching in international markets.

� retailers intermediate between exporters and consumers� endogenous search and matching e¤ort on both sides of themarket.

� many-to-many matching with discrete numbers of businesspartners.

� characterize market equilibria in steady state and transition.

Applications

� Measure the value of international business relationships

� Measure international search/matching costs, assess theirrole in inhibiting trade

� Measure incidence of search/matching costs across rmtypes and states.

� Characterize welfare and market structure e¤ects ofglobalization shocks.� e¤ects of changes in the global population of sellers (the"China shock")

� e¤ects of reductions in search/matching costs (the "internetshock")

� Assess impact of key players on equilibria (granularity)

Applications




� Characterize welfare and market structure e¤ects ofglobalization shocks.

� e¤ects of changes in the global population of sellers (the"China shock")



Applications




� Characterize welfare and market structure e¤ects ofglobalization shocks.� e¤ects of changes in the global population of sellers (the"China shock")



Some related papers

� Firm dynamics with customer accumulation (Albornoz etal., 2012; Drozd and Nosal, 2012; Eaton et al., 2015;Piveteau, 2015; Fitzgerald et al., 2016; Arkolakis, 2016)

� Trade with search and matching frictions in productmarkets (Rauch and Watson, 2003; Rauch and Watson,2004; Drozd and Nosal, 2012; Antras and Costinot, 2011;Fernandez, 2012; Eaton et al. 2015)

� Intermediated trade models (Rauch and Watson, 2004;Antras and Costinot, 2011; Fernandez-Blanco, 2012; Bernardand Dhingra, 2015)

� Models of rm-to-rm trade (Antras and Shor, 2012;Bernard, Moxnes, and Saito, 2015; Sugita, Teshima, andSiera, 2014; Carballo, Ottaviano, and Volpe-Martincus, 2016;Bernard, Moxnes, and Ullveit-Moe, 2016)

� Dynamic models of trading networks (Chaney, 2014; Lim,2016)

Data

� Fit to customs records on U.S. apparel imports.� shipment values, dates, and HS10 codes� identies buyers (importing retailers/wholesalers) and sellers(foreign exporters)

� Why U.S. apparel?� retailing is a relatively simple technology.� buyers are mostly retailers and local distributors, while sellersare mostly foreign rms

� natural experiment: major new players in the market andMultibre Arrangement phase-out

U.S. apparel consumption and imports

4060

8010

012

0bi

llion

s of

$

1990 1995 2000 2005 2010 2015Year

consumption_b imports_b

Number of apparel exporters to U.S.

8090

100

110

120

130

Num

. of S

elle

rs (1

,000

)

1996 1998 2000 2002 2004 2006 2008 2010year

Number of apparel exporters to U.S., by country

020

4060

Num

. of S

elle

rs (1

,000

)

1996 1998 2000 2002 2004 2006 2008 2010year

Mexico El Salvador HondurasIndia Pakistan BangladeshVietnam Cambobia IndonesiaChina

Value of U.S. apparel imports, by country

02

46

Impo

rt va

lue

($ B

illio

n)

1996 1998 2000 2002 2004 2006 2008 2010year

Mexico El Salvador Honduras IndiaPakistan Bangladesh Vietnam CambobiaIndonesia China

Degree distribution: sellers per buyer, 2000

05

10lo

g(#

buye

rs w

ith a

t lea

st x

sel

lers

)

0 2 4 6 8 10log(# sellers)

lnFreq_upsum Fitted values

y ear 2011

� Client counts are roughly Pareto-distributed across buyers

Degree distribution: buyers per seller, 2000

05

1015

log(#

sell

ers

with

at l

east

x b

uyer

s)

0 1 2 3 4log(# buyers)

lnFreq_upsum Fitted values

y ear 2011

� Client counts are nearly Pareto-distributed across sellers to regressions

Imports per seller and buyer connections

� Buyers with many suppliers import less per supplier

Network dynamics: relationship duration

46

810

1214

log

Fre

quen

cy

0 5 10 15duration

� Match durations are nearly a Poisson process

Transition dynamics: partner counts

Transition of Number of Sellers for each Buyer

tnt + 1 0 1 2 3 4 51 0.34 0.24 0.19 0.10 0.05 0.032 0.25 0.16 0.18 0.14 0.09 0.063 0.21 0.11 0.14 0.14 0.13 0.114 0.19 0.07 0.10 0.12 0.12 0.115 0.17 0.06 0.08 0.09 0.11 0.10

Transition dynamics: partner counts

Transition of Number of Buyers for each Seller

tnt + 1 0 1 2 3 4 51 0.32 0.31 0.21 0.09 0.09 0.022 0.19 0.22 0.23 0.17 0.17 0.053 0.13 0.15 0.18 0.18 0.18 0.094 0.10 0.10 0.13 0.16 0.16 0.125 0.08 0.07 0.10 0.13 0.14 0.13

Buyer and seller life cycles

Age and Partner Counts(relative to entry year)

Buyer SellerAge # Sellers Cumulative # # Buyers Cumulative #2 0.59 1.59 0.21 1.223 0.79 2.77 0.29 2.414 1.23 4.89 0.45 4.48

� Buyers and sellers sample many business partners over theirlife cycles

� Average duration of relationships 1.24 years

Micro features of the apparel market: types of agents

� Manufacturers: use labor, materials and other inputs to makeapparel

� Wholesalers and retailers: acquire apparel from manufacturers orsourcing rms

� Consumers: purchase apparel from retailers throughbrick-and-mortar stores and web sites

Our modeling abstractions

� We wont distinguish commercial apparel importers (buyers) bytype: wholesalers, retailers, sourcing rms, and other.

� Many major importers are both wholesalers andretailers. types of buyers

� Most wholesale/retailers have their own sourcing divisions(McFarland et al., 2012; Lu, 2016).

� We will assume buyers do not own their suppliersproductionfacilities.

� With a few exceptions (e.g., Hanes), this is a goodapproximation to the data. related party trade .

� We will not distinguish between web and brick-and-mortar outlets.� Wholesale/retailers often outsource brick-and-mortar retailing(e.g., Macys carries Polo line)

� Most branded merchandise sells for the the same price (givenbarcode), in both types of outlets (Cavallo, 2016)

Model structure

Preferences

� As a group, domestic consumers spend a xed amount E onproduct category of interest (apparel).

� Measure-MB continuum of buyers (retailers), indexed by b, o¤ervarious, possibly overlapping, menus of varieties.

� Sellers (exporters), indexed by x , each supply a distinct variety to anite number of stores.

� Consumer demand represented by nested CES utility function

C =�Zb2MB

(µbCb)η�1

η

� ηη�1, Cb =

"∑x2Jb

�ξxC

bx

� α�1α

# αα�1

Revenue ow

� Exogenous marginal cost of a buyer-seller pair: cxb� Optimal mark-up (Hottman et al., 2015, Atkeson and Burstein2008):

pxb � cxbpxb

=1η

� Share of variety x in sales of retailer b:

hx jb =c̃1�αxb

∑x2Jb c̃1�αxb

wherec̃xb =

cxbξx

Revenue ow

� Bargaining (Stole and Zweibel, 1996; Brugemann et al.,2016)� Surplus from match divided up according to Nash bargaininggame

� buyer bargains continuously with all sellers, treating each asmarginal supplier

� xed share of surplus (β) for each seller implies same xedshare of prot ow

� Implied payment ow from buyer b to seller x : Details

ln r xbt =�

α� ηα� 1

�ln hx jb,t+ ln

�µbc̃xb

�η�1+d t

=

�α� ηα� 1

�ln hx jb,t+(η � 1) ln µb � (η � 1) ln

�cxbξx

�| {z }

υxb

+d t

� When α > η, diminishing returns to adding clients.

Matching hazards

� buyer (seller) visibility levels

σB , σS

� chosen continuously by each agent to maximize expectedpresent value of market participation. Details

� visibility choices depend upon� own type: µb 2 fµigi=1,I , ξx 2 fξjgj=1,J� current portfolio of business relationships: s = (s1, s2, .., sJ )for buyers, n for sellers

� market tightness: match arrival rate per unit of visibility(θB , θS ). Details

� costs of visibility (search costs)

� match arrival hazards

σBi (s)θB , σSj (n)θ

S

Search (visibility) costs

� Buyerssearch costs depend on chosen visibility σB and numberof business partners, s :

kB�

σB , s�=kB0�σB�νB

(s + 1)γB

� Sellerssearch costs,depend on chosen visibility σS and numberof business partners, n

kS�

σS , n�=kS0�σS�νS

(n+ 1)γS

� Things to note� convexity: νB , νS > 1� network e¤ects: γB ,γS > 0

Steady states and transition dynamics

� Given σBi (s) and σSj (n), a matching function, and the exogenous

match separation hazard, δ, equations of motion for the meaures ofeach type of agent (MBi (s), M

Sj (n)) are implied. Details

� Imposing stationary (ṀBi (s) = ṀSj (n) = 0 ) determines

equilibrium network structure.

� Can solve for transition between steady states using techniques fromAcemoglu and Hawkins (2015)

Transfer function estimates

1st Stage IV-FE 2nd stage IV-FE(dep. var.: ln hx jb,t ) (dep. var.: ln rxbt )

(1) (2) (3) (4)

ln ĥx jb,t 0.194(0.008)

0.073(0.011)

ln r c�x j�b,t�0.239(0.002)

ln r̄ c�bj�x �0.381(0.004)

instrument ln r c�x j�b,t ln r̄c�bj�x

match e¤ects yes yes yes yesyear e¤ects yes yes yes yesR2 0.8896 0.9045 0.8615 0.8314obs. 771,200 1,256,000 771,200 1,256,000

ln rxbt =�

α�ηα�1

�ln hx jb,t + υxb + dt + εxbt

Transfer function and preference parameters

� Fix ρ = 0.05 and β = 0.5

� Assume α = 4.35 (Hottman, et al., 2015).

� Infer η = 3.70 from α�ηα�1 = 0.193

� Infer from match e¤ects and estimate of η thatvar(ln µx ) = 0.71 and var(ln ξb) � 0.24

� Discretize distributions following Kennan (2006).

Calibrating remaining parameters

� Calibrate seach cost parameters to minimize sum of Euclideandistances (model versus data) for:

� Buyer and seller degree distributions

� Buyer and seller sizes (partner counts) over their life cycles

� Within-buyer share of largest seller versus number of sellers

� Partner transition matrices

Remaining parameter estimates

� Imposing symmetry on cost function convexity parametersνB = νS = 3.099

� Imposing symmetry on cost function network parametersγB = γS = 2.870

� Cost function scalars: kB0 = 2.578, and kS0 = 0.465� separation hazard inferred from separation rate that best matchesmatch duration distribution, imposing Poisson process: 0.81

� Adjusting for buyer and seller deaths,δ = 0.81� 0.07� 0.15 = 0.59.

Matching moments: client distributions

� Target is estimated quadratic approximation to clientdistributions. graphs

ln(1� F (c)) = β0 + β1 ln c + β2 (ln c)2 + e

buyers per seller selllers per buyerdata model data model

β1 -1.898 -1.765 -1.208 -0.975β2 -0.200 0.000 0.0106 -0.001R2 0.997 0.989 0.987 0.998

Matching moments: buyer and seller life cycles

Sellers per buyer (relative to birth year)age Data Model2 1.68 1.293 2.08 1.614 2.27 1.93Buyers per seller (relative to birth year)age Data Model2 1.36 1.253 1.61 1.494 1.83 1.64

Matching moments: within buyer share of largest seller

# partners Data Model1 1.000 1.0002 0.763 0.6623 0.660 0.5694 0.600 0.5145 0.553 0.467

Matching moments: sellers per buyer transition probs.

simulated dataprobs: sellers per buyer probs: sellers per buyern! n! n! n! n! n!

initial n n� 1 n n+ 1 n� 1 n n+ 12 0.348 0.466 0.185 0.449 0.358 0.1933 0.340 0.461 0.198 0.430 0.348 0.2214 0.378 0.405 0.217 0.405 0.360 0.2355 0.338 0.422 0.239 0.395 0.361 0.244

probs: buyers per seller probs: buyers per sellern! n! n! n! n! n!

initial n n� 1 n n+ 1 n� 1 n n+ 12 0.344 0.465 0.189 0.516 0.343 0.1423 0.317 0.439 0.243 0.467 0.348 0.1864 0.333 0.399 0.267 0.434 0.345 0.2215 0.273 0.434 0.292 0.432 0.335 0.234

Preliminary model implicationsbased on Colombian footwear imports

� Cost of search

� Value of business relationships

� Welfare e¤ects of scaling down search costs by 30 percent

Search costs by type of buyer

� Large buyers spend disproportionately more on matching. To staylarge, they must replace suppliers at a rapid rate.

� Overall, search costs are 7.8% of export revenuescould account fora substantial fraction of unexplained trade frictions.

Buyer versus seller search costs

� Sellers bear most of the matching costs, especially at large rms.

Value of international business connections

0 10 20 30 40 500

50

100

150

200

250

300

350

400

number of suppliers

inta

ngib

le c

apita

l

Intangible capital by firm type and number of sellers

low mumed. muhigh mu

� For a high-µ retailer with 30 suppliers, value of portfolio, withreplacement: $540, 000; without replacement: $2, 300, 000.

Counterfactual: 30% reduction in ko

0 10 20 30 40 50-15

-10

-5

0

5

10

number of suppliers

chan

ge in

val

ue

Change in intangible capital with 30% search cost reduction

low mumed. muhigh mu

� Reductions in search cost reduce value of customer connections, buthelp high-µ, small s retailers.


� Takes 6-7 years to transit to new steady state.


� Most adjustment comes in the right-hand taillarge rms searchrelatively more intensively, crowding out small rms.

Observed change in degree distribution2006-09 versus 2010-12

In progress

� Redo experiments in previous slides for U.S. apparel

� Explore the role of luck in determining buyer and sellersuccess.

� Posssible decomposition of changes in network structure� choose change in search cost (k0) to match trade expansionand shift in degree dist., given assumptions about mass ofsellers (MS ).

� how much is due to changes in e¢ ciency of search/matchingk0 versus MS ?

Payment ows

πTi (s) =EPη

�P(s)1�η

P�η

�µ

η�1i

=E

ηP1�η

"J

∑jsj

�η

η � 1

�1�αc̃1�αji

# η�1α�1

µη�1i

∂πTi (s)∂sj

=1

α� 1

�η

η � 1

��η EP1�η

"J

∑jsj c̃1�αji

# α�η1�α

c̃1�αji µη�1i

= (hj ji )α�ηα�1

EP1�η

�η

η � 1

��η �µic̃ji

�η�1 � 1α� 1

�So, assuming sellers incur some fraction λ of their matchs marginalcosts and get share β of the rent ow:

rTi (s) = (hj ji )α�ηα�1

EP1�η

�η

η � 1

��η �µic̃ji

�η�1 � βα� 1 + λ

�

Value functions

Flow value of a type-i buyer currently in state s :

ρV Bi (s)

= πBi (s)� kBs (σBi (s)) + σBi (s)J

∑j

θBPSjhV Bi (s+ `j )� V Bi (s)

i+δ

J

∑jsjhV Bi (s� `j )� V Bi (s)

iFlow value to a type-j seller of match with a type-i buyer in state s :

ρV Sji (s) = τji (s) + σBi (s)

J

∑k

θBPSkhV Sji (s+ `k )� V Sji (s)

i+δ

J

∑k=1

(sk � 1k=j )hV Sji (s� `k )� V Sji (s)

iwhere θB is arrival hazard of sellers per unit of buyer visibility andremaining denitions appear on the next slide.

First order conditions

� Denitions� PBi (s) = H

Bi (s)/H

B : relative visibility of type-i buyers instate s

� PSj = HSj /H

S : relative visibility of type-j sellers

� `j : 1� J vector of zeros except for j th element, which is 1.� First-order conditions:

∂kB�σBi , s

�∂σBi

= ∑j

θBPSjhV Bi (s+ `j )� V Bi (s)

i∂kS

�σSj , n

�∂σSj

= ∑i

∑s2S

θSPBi (s)VSji (s+ `j ).

Market tightness

� Visibility of type j sellers who are matched with n buyers:HSj (n) = σ

Sj (n)M

Sj (n)

� Overall visibility of sellers to buyers:

HS =J

∑j=1

nmax

∑n=0

HSj (n)

� Visibility of type i buyers who are matched with s sellers:HBi (s) = σ

Bi (s)M

Bi (s)

� Overall visibility of buyers to sellers:

HB =I

∑i=1

smax

∑s=0

HBi (s)

� exogenous: MBi =smax∑s=1

MBi (s), MSj =

nmax∑n=1

MSj (n)

Market tightness, continued

� Measure of match ow per unit time (Petrongolo and Pissarides,2001):

X = f (HS ,HB ) = HB�1� (1� 1

HB)H

S�� HB

h1� e�HS/HB

i� Match ow per unit of buyer visibility, seller visibility:

θB =f (HS ,HB )

HB, θS =

f (HS ,HB )HS

� Share of matches involving buyers of type i with s sellers, sellers oftype j with n buyers:

PBi (s) = HBi (s)/H

B , PSj (n) = HSj (n)/H

S

Equations of motion

� Suppressing the state vector s, the measure of type�i buyers withsj type�j sellers evolves according to:

ṀBi (sj ) = σBi (sj � 1)θBMBi (sj � 1) + δ(sj + 1)MBi (sj + 1)��

σBi (sj )θBMBi (sj ) + δsM

Bi (sj )

�.

s = 1, ..., smax; i = 1, ..., I

ṀBi (0) = δMBi (1)� σBi (0)θBMBi (0) i = 1, ..., I

� For measures of sellers, replace B with S , i with j , and s with n(number of buyers).

Dealing with clustering

� Some retailers specialize in plastic/rubber top sports shoes;others mens leather shoes. Ditto for suppliers.

� Remedy: type-i buyer and type-j seller are compatible withprobability

dij 2 [0, 1]� Expected success rates for type-i buyer; type-j seller

aBi =∑j ∑

∞n=0 dijσ

Sj (n)P

Sj (n)

∑j ∑∞n=0 σ

Sj (n)P

Sj (n)

aSj =∑i ∑

∞s=0 dijσ

Bi (s)P

Bi (s)

∑i ∑∞s=0 σ

Bi (s)P

Bi (s)

Dealing with clustering, continued

� For type-i buyer with s suppliers, hazard of nding anothercompatible seller is

σBi (s)aBi θ

B

� For a type-j seller with n buyers, the hazard of nding anothercompatible buyer is

σSj (n)aSj θS

� Complication: aBi and aSj depend on dij , which cannot be

directly observed.


� Probability that a randomly matching seller encounters atype-i buyer; randomly matching buyer encounters a type-jseller:

φBi =∑∞s=0 σBi (s)P

Bi (s)

∑i 0 ∑∞s=0 σ

Bi 0 (s)P

Bi 0 (s)

,

φSj =∑∞n=0 σSj (n)P

Sb (j)

∑j 0 ∑∞n=0 σ

Sj 0(n)P

Sj 0 (n)

� Letting fij be the observed joint distribution of matches,

fij = φBi φSj dij

dij =fij

φBi φSj


� Substituting this dij expression back into the success ratefunctions yields:

aBi =∑j ∑

∞n=0 dijσ

Sj (n)P

Sj (n)

∑j 0 ∑∞n=0 σ

Sj 0(n)P

Sj 0 (n)

=∑j fijφBi

and

aSj =∑i ∑

∞s=0 dijσ

Bi (s)P

Bi (s)

∑i 0 ∑∞s=0 σ

Bi 0 (s)P

Bi 0 (s)

=∑i fijφSj

� Implication: aBi and aSj are additional objects to update, but

given fij , there are no additional parameters involved.

010

2030

Impo

rt va

lue

($ b

illio

n)

2003 2004 2005 2006 2007 2008 2009 2010 2011year

Wholesaler (W) Retailer (R) Both W and RNeither W nor R Unmatched

020

4060

Impo

rt va

lue

($ B

illio

n)

1996 1998 2000 2002 2004 2006 2008 2010year

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two-sided matching in international markets 2018.pdf · 2018. 6. 7. · objectives enduring issues:...

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