A General Equilibrium Model of Supply Chain Interactions and Risk

Transcription

A General Equilibrium Model of Supply Chain
Interactions and Risk Propagation
John Birge and Jing Wu1
1
University of Chicago Booth School of Business
SCF Symposium, Madrid
John Birge and Jing Wu (Chicago Booth)
Equilibrium in Supply Chain Networks
June 20, 2016
1 / 29
S&P 500 Supply Chain Network
ACT
ACT
HP
HP
SXL
SXL
FLR
ADI
FLR
NEM
ADI
MMM
NEM
MMM
AN
CNP
ALV
CREE
KO
GAS
EIX
AN
BDX
LEA
CERN
AEP
BDX
LEA
CERN
EIX
CTSH
NXPI
EMR
CMI
BWP
CNP
ALV
CREE
KO
GAS
CTSH
NXPI
EMR
CMI
AEP
BWP
ESRX
ESRX
PRGO
PRGO
KR
CSX
MUR
KR
CSX
MUR
BWA
ADBE
CRM
DISCA
ITW
BWA
ADBE
CRM
DISCA
ITW
ABT
ABT
AMGN
AMGN
RAI
RAI
CBS
CBS
CTXS
GLW
CTXS
GLW
SNI
IEP
SNI
RAX
TSCO
IEP
RAX
TSCO
TW
PLL
TW
PLL
PLD
ROP
PLD
ROP
DLPH
DLPH
HTZ
HTZ
ETE
ETE
WM
PG
HSY
WM
DCI
VRSN
PG
HSY
C
WDC
SNDK
C
SNDK
URI
MSFT
LMT
EPD
HSIC
VAL
DD
COL
QCOM
XLNX
MNST
LMT
DD
COL
MNST
FFIV
MCK
IT
AKAM
FFIV
CCK
WLL
MCK
NEE
ASH
ATVI
MU
AKAM
TSN
ETP
CVX
S
PNW
ETP
INTC
MKC
PXD
MKC
PXD
SO
JCI
ACN
SO
PH
XEL
MOLX
JCI
PVH
OKS
CCK
NEE
SJM
CSCO
S
PNW
ASH
ATVI
MU
TSN
IT
WLL
CVX
SJM
CSCO
INTC
XEL
SCG
D
XYL
RTN
QCOM
XLNX
JBL
HD
ADSK
KMB
EMC
EPD
HSIC
VAL
NU
TRIP
SWKS
SCG
MSFT
RTN
TXN
IP
HON
MXIM
HD
ADSK
D
XYL
WDC
TRW
ADS
MXIM
KMB
EMC
CSC
AVGO
MWV
NU
TRIP
SWKS
BEAM
URI
JBL
TRW
HON
NTAP
TXN
IP
CSC
AVGO
MWV
DCI
VRSN
NTAP
BEAM
ADS
ACN
PH
MOLX
PVH
OKS
HRL
TMO
HRL
TMO
FLS
CL
FLS
CL
PCP
JNPR
TEL
PCP
K
JNPR
OGE
A
AXP
TEL
K
OGE
A
AXP
VMC
VMC
VFC
LUV
WAB
VFC
MSM
EXC
FL
NSC
DAL
FL
NSC
DAL
BBBY
HFC
NOC VRTX
ULTA
MON
RHT
XRX
CPA
UAL JOY
ULTA
RHT
XRX
ALTR
ALTR
AES
BX
INTU
EMN
HSP
KMI
AES
BX
GPS
EA
MAS
NUE
VRSK
MSM
EXC
AVP
TKR
VMW
CLX
BBBY
HFC
NOC VRTX
MON
CPA
UAL JOY
INTU
LUV
WAB
AVP
TKR
VMW
CLX
EMN
GPS
EA
MAS
NUE
VRSK
HSP
KMI
CAH
CAH
CHD
CHD
NUAN
NUAN
IPG
IPG
RL
PPG
CI
CHKP
RL
PPG
IHS
CVS
CI
GILD
CHKP
RJF
GGP
PXP
IHS
TYC
LINTA
UA
CVS
GILD
RJF
GGP
TYC
LINTA
PXP
SIG
OMC
UA
SIG
OMC
HRS
HRS
BMC
WINKORS
CHK
APH
BMC
BBY
OII
LOW
BTU
BMY
GIS
KRFT
LLY
FRX
EFX
BLL
BIIB
N
NFLX
LLTC
MYL
AEE
FTI
HOG
OKE
ECL
SCCO
LNKD
Y
NWL
LKQ
CAG
FDX
SRCL
CPN
SLB
FBHS
PAA
RS
SE
WMB
WRB
CMCSA
EQT
L
STJ
EW
STZ
WAT
ROK
DOW
URBN
FDX
CPN
SWN
WFT
TIF
MTD
ED
BMRN
POM
XRAY
DTE
TRMB
DOX
LNKD
EQT
L
STJ
EW
EEPLNT
RIG
PAYX
HUM
RMD
ECL
SCCO
Y
SRCL
GRA
FAST
ENR
CCI
WDAY
HOG
OKE
SLB
KSU
CAM
NBR
BIIB
LLTC
AEE
FTI
SE
WMB
WRB
COH
ALB
DNR
MAT
BLL
NFLX
MYL
DOW
URBN
LKQ
NI
HAS
NKE
NBR
FAST
MTD
ED
BMRN
POM
XRAY
DTE
N
ROK
RIG
PAYX
HUM
RMD
NWL
CAG
UTX
MCHP
EPB
HRB
KSU
CAM
ENR
CCI
TRMB
DOX
FBHS
CHRW
VZ
CNA
CXO
COH
KRFT
WDAY
LOW
BTU
VMED
NOV
CCL
FISV
CPB
EFX
NI
HAS
ALB
DNR
MAT
BAX
IDXX
NE
SNA
UTX
MCHP
EPB
HRB
NKE
BBY
DFS
HOLX
TDG
VZ
CNA
CXO
CMCSA
APC
ONXX
ILMN
LULU
PNR
CHRW
NOV
CCL
FISV
CPB
STX
FRX
VMED
NE
SNA
GIS
IR
LLY
ILMN
LULU
PNR
TDG
APH
OII
BAX
IDXX
STX
WINKORS
CHK
DFS
HOLX
IR
BMY
APC
ONXX
GRA
SWN
WFT
STZ
WAT
EEPLNT
OXY
PAA
TIF
RS
OXY
DG
DG
ADP
ST
LUK
T
BEAV
DO
DO
SYMC
SYMC
PX
PEP
PX
LYB
DTV
BSX
FNF
MLM
MJN
OCN
KBR
WHR
BSX
FNF
MLM
MJN
OCN
HNZ
VLO
BRCM
DLTR
AMZN
ALXN
QGEN
VLO
LEN
FTR
KSS
MMP
GRMN
FLEX
WSM
EOG
GWW
WLK
SIAL
BPL
DPS
SWK
MO
TAP
LVLT
BCR
BHI
WHR
MRVL
MO
TAP
LVLT
MMP
GRMN
ORCL
IFF
ZMH
BCR
BHI
IFF
ZMH
WMT
MRVL
FOSL
WMT
FOSL
QEP
AAPL
DTV
AMZN
LEN
FTR
KSS
ORCL
JCP
BRCM
DLTR
ALXN
QGEN
SWK
MDLZ
LYB
FLEX
WSM
EOG
GWW
WLK
SIAL
BPL
DPS
PEP
UNP
JCP
KBR
HNZ
ADP
ST
LUK
T
BEAV
UNP
QEP
MDLZ
SHW
CHTR
AGCO
AAPL
SHW
CHTR
AGCO
CLF
JBHT
CLF
JBHT
LTD
NFG
KLAC
IRM
ISRG
SYY
SYK
LNG
FDO
SYY
SYK
LNG
TDC
LTD
NFG
M
FDO
PII
INGR
SHLD
DUK
ARE
EL
KLAC
IRM
ISRG
TDC
SHLD
DUK
ARE
EL
M
PII
INGR
DHR
RRC
DHR
RRC
TWX
TWX
SRE
SRE
APD
WAG
NVDA
VAR
APD
COV
WAG
NVDA
VAR
COV
GPC
GPC
COP
COP
BG
CMS
CLR
CF
AET
BG
CMS
CLR
SNPS
CF
AET
SNPS
JNJ
MA
UPS
JNJ
MA
ACMP
UPS
ACMP
NBL
NBL
CTL
CTL
ETR
DDR
SPLS
FMC
WPZ
RSG
DLR
ETR
DDR
SPLS
PETM
PPL
PETM
PPL
HES
DRC
APA
CVI
JPM
DVN
CELG
SBH
WPZ
HES
DRC
APA
CVI
JPM
DKS
VHI
FMC
RSG
DLR
DVN
CELG
SBH
NLSN
CQP
DOV
AMT
DKS
VHI
NLSN
AON
CCE
FE
TOL
CQP
DOV
AMT
AON
CCE
FE
TOL
AA
AA
SIRI
TGT
COST
SBAC
SIRI
XEC
TGT
COST
SBAC
MDT
LLL
MDT
LLL
XEC
MSI
EXPE
HAL
ORLY
ESV
CE
MSI
AAP
EXPE
HAL
CNH
ARG
ORLY
ESV
CE
AAP
CNH
ARG
OC
OC
AZO
TSO
AZO
TSO
VIAB
REGN
VIAB
REGN
LBTYA
LBTYA
WFM
DISH
WFM
CA
DISH
CA
AMP
KMP
AMP
KMP
LIFE
CFN
IBM
LIFE
GM
AGN
CFN
IBM
DE
GM
AGN
DE
GD
GD
PFE
MRK
EQIX
PFE
CNX
MRK
EQIX
CNX
FCX
WLP
RKT
YHOO
WGP
EBAY
MOS
NVE
FCX
WLP
FB
RKT
YHOO
WGP
TJX
CAT
MWE
EBAY
MOS
NVE
FB
TJX
CAT
MWE
MPC
GOOG
JEC
MPC
XOM
MHK
ABC
GOOG
JEC
PCAR
XOM
MHK
ABC
ANSS
PCAR
ANSS
TXT
TXT
F
F
TWC
AMAT
BA
DELL
PWR
TWC
AMAT
BA
DELL
PWR
NRG
HPQ
NRG
PM
HPQ
WU
PM
WU
AVT
AVT
GE
GE
CBI
CBI
Figure: Who are my customers (left) and suppliers (right)
Green: Manufacturing, Blue: Transportation Warehousing, Red: Wholesale Retail
June 20, 2016
2 / 29
Outline
Empirical Observations: Propagation of risk on two levels (direct and
indirect)
1st-order effects (direct propagation)
2nd-order effects (systematic risk)
Equilibrium Network Model
Implications of the Model
Conclusions and Future Directions
June 20, 2016
3 / 29
Empirical Observations
Pricing and Risk Basics
Model of share price at time t:
pt =
∞
X
e −(rs +δs )s ds
s=0
Expected dividends ds
Depends on supply chain partners (first-order).
Changes may be delayed due to inattention or invisibility.
Risk premium, δs
Depends on multiplicity of connections to transmit risk (second-order).
Reliability issues may create nonlinear effects on the risk of network position.
June 20, 2016
4 / 29
Literature
Literature
1st-order effects
Industry level: Menzly & Ozbas (2007), Shahrur, Becker, & Rosenfeld (2010),
Fruin, Osiol, & Wang (2012).
Firm level: Hendricks & Singhal (2003), Cohen & Frazzini (2008), Atalay,
Hortacsu, & Syverson (2013, working).
2nd-order effects
Asset pricing: Sharpe (1964), Lintner (1965), Fama & French (1993).
Network risk: Acemoglu, Carvalho, Ozdaglar, & Tahbaz-Salehi (2012),
Anupindi & Akella (1993), Cachon, Randall, & Schmidt (2007), Ahern (2012),
Carvalho and Gabaix (2013), Kelly, Lustig, & Nieuwerburgh (2013, working),
Herskovic (2014, working).
June 20, 2016
5 / 29
Data
Empirical Observations: Data
Scope is limited to U.S. public listed firms
Stock data: CRSP (monthly returns over July 2011 - June 2013)
Supply chain sales data (SPLC)
Compustat: SEC public filings (10% rule).
Bloomberg terminal (320k units): conference call transcripts, capital market
presentations, firm press releases, product catalogs, firm websites.
Both are public information.
SEC’s Statement of Financial Accounting Standards No. 14 (SFAS 14)
“if 10% or more of the revenue of an enterprise is derived from sales to any single
customer, that fact and the amount of revenue from each such customer shall be
disclosed” in interim financial reports issued to shareholders
June 20, 2016
6 / 29
Data
First-order Effects
Example Relationship
Customer to Supplier
Calloway Golf/Coastcast (Cohen and Frazzini (2008))
Calloway misses earning forecase by half ($0.36 from $0.70).
Calloway’s stock price drops 30%.
Coastcast share price (50% of sales to Calloway) unchanged for one month.
June 20, 2016
7 / 29
Data
First-order Effects
Example Relationship
Supplier to Customer
Philips/Sony/Ericsson v. Nokia
Fire in Philips plant, key chip supplier for Nokia and Ericsson, in March 2000.
Philips states 1-week shutdown, then revises to 6 weeks.
Nokia (multi-sourcing) reacts quickly.
Ericsson (single sourcing) reacts slowly, lost $2.34B, acquired by Sony.
June 20, 2016
8 / 29
Data
First-order Effects
First-order Effects
wijin denotes the supplier weight of j as a fraction of i’s procurement.
wijout denotes the customer weight of j as a fraction of i’s sales.
wijin =
salesji
salesji
salesij
salesij
= PN
, wijout =
= PN
.
Procurement i
Sales
i
k=1 saleski
k=1 salesik
ri,t is the return of firm i in month t.
The following specification is tested:
X
X
ri,t = α + β1 ri,t−1 + β2
wijin rj,t−1 + β3
wijout rj,t−1
j
+β4
X
j
wijin rj,t + β5
j
X
wijout rj,t + i,t
(1)
j
Hypothesis:
Suppliers’ and customers’ concurrent performance relates to the firm.
Supplier momentum (one-month lag) may be related to firm performance
(following Cohen and Frazzini (2008)).
June 20, 2016
9 / 29
Data
First-order Effects
First-order Effects
Results
Table: Fama-Macbeth Regression of Concurrent Returns and Momentum.
α
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
Ave. Coef
(T-Stat)
-0.001
(-0.96)
0.009***
(10.38)
0.009***
(10.53)
0.008***
(11.09)
0.008***
(10.92)
0.003***
(3.61)
-0.002**
(-2.26)
0.004***
(4.51)
-0.002*
(-1.92)
-0.001*
(-1.80)
ri,t−1
-0.088***
(-11.06)
-0.090***
(-9.08)
-0.047***
(-6.96)
P
in
j wij rj,t−1
0.036**
(2.17)
0.057***
(2.96)
P
out
j wij rj,t−1
0.024
(0.95)
0.004
(0.09)
P
in
j wij rj,t
0.399***
(20.90)
P
out
j wij rj,t
0.755***
(3.12)
0.022**
(1.83)
-0.040
(-0.66)
0.619***
(37.25)
0.992***
(4.54)
0.018*
(1.57)
0.625***
(36.44)
0.001
(0.0274)
0.393***
(22.48)
1.001***
(4.51)
0.744***
(3.20)
*p-value<10%, **p-value<5%, ***p-value<1%
Controls: MKT, SMB, HML, MOM, cross-firm effect, industry effect.
June 20, 2016
10 / 29
Data
Second-order Effects
Assumption
Acemoglu, Carvalho, Ozdaglar, & Tahbaz-Salehi (2012) (and the extension later)
finds that microeconomic idiosyncratic shocks lead to aggregate flucturations,
which means
A firm’s systematic risk is formed from the aggregation of idiosyncratic shocks.
Effects of connections may be nonlinear due to interactions - risk
diversification or aggregation?
Firm level shocks may be exogenously correlated due to geographical
proximity and sector proximity.
A manufacturer (e.g., Nokia) may have diversification incentives to add an
independent supplier to increase reliability (reduce systematic risk exposure
with greater centrality).
A distributor (e.g., a beverage distributor) may have concentration incentives
to add similar suppliers (e.g., French wineries) to build on existing capabilities
(increase systematic risk exposure with greater centrality).
June 20, 2016
11 / 29
Data
Second-Order Results: Manufacturing
Table: Factor Sensitivities by Eigenvector Centrality for Manufacturing Firms.
N3
Portfolio
1(High)
2
3
4
5(Low)
High-Low
α (%)
0.235
(1.50)
0.114
(0.49)
0.295*
(1.78)
0.277
(1.34)
0.328
(1.33)
0.482*
(1.86)
0.356
(0.89)
0.571
(1.36)
0.507
(1.55)
0.934*
(1.95)
-0.272*
(-1.72)
-0.820*
(-1.96)
Factor Loadings
Rmt − Rft
SMB
HML
0.888***
(15.47)
0.894***
-0.347*
0.018
(12.23)
(-2.07)
(0.119)
0.773***
(13.79)
0.938***
-0.184
-0.453***
(14.28)
(-1.22)
(-3.29)
1.060***
(17.60)
0.953***
0.363*
-0.005
(11.63)
(1.93)
(-0.03)
1.256***
(12.97)
1.087***
0.446
0.130
(8.22)
(1.47)
(0.47)
1.410***
(11.96)
1.157***
0.780**
-0.257
(7.63)
(2.24)
(-0.80)
-0.522
(-3.92)
-0.263
-1.127**
0.275
(-1.28)
(-2.40)
(0.64)
*p-value¡10%, **p-value¡5%, ***p-value¡1%
MOM
0.084
(1.025)
Adj. R 2 (%)
90.85
90.01
88.74
-0.061
(-0.83)
93.77
-0.008
(-0.09)
93.04
-0.142
(-0.96)
87.82
92.78
87.45
85.54
-0.132
(-0.78)
87.53
0.216
(0.94)
Controls: MKT, SMB, HML, MOM, cross-industry concentration.
June 20, 2016
12 / 29
Data
Second-Order Results: Logistics
Table: Factor Sensitivities by Eigenvector Centrality Centrality for Logistics Firms.
N4
Portfolio
1(High)
2
3
4
5(Low)
High-Low
Alpha(%)
1.314***
(3.26)
1.428***
(3.44)
0.894***
(3.78)
0.916***
(2.41)
0.812**
(2.23)
0.801**
(3.36)
0.708**
(2.50)
0.669**
(2.14)
0.759
(1.44)
0.485
(0.84)
0.556
(1.53)
0.975*
(1.93)
Factor Loadings
Rmt − Rft
SMB
HML
0.747***
(7.62)
0.768***
0.006
-0.589
(5.85)
(0.02)
(-2.14)
0.671***
(11.67)
0.976***
0.034
-0.502
(8.13)
(0.13)
(-1.99)
0.964***
(10.89)
0.758***
-0.140
-0.152
(10.03)
(-0.81)
(-0.96)
0.857***
(12.40)
0.916***
-0.171
-0.190
(9.26)
(-0.75)
(-0.92)
0.776***
(6.03)
0.942***
-0.548
0.141
(5.17)
(-1.31)
(0.37)
-0.029
(-0.20)
-0.175
0.553
-0.730
(-0.90)
(1.24)
(-1.69)
MOM
Adj. R 2 (%)
84.93
0.024
(-0.16)
86.43
0.031
(0.23)
72.32
0.164
(1.93)
83.75
0.019
(0.17)
85.49
70.41
83.05
86.41
69.60
0.048
(0.23)
67.70
-0.024
(-0.11)
Controls: MKT, SMB, HML, MOM, cross-industry concentration.
June 20, 2016
13 / 29
Data
Second-Order Results: Mining, Utilities, and Construction
Table: Factor Sensitivities by Eigenvector Centrality for NAICS 2 Industries.
N2
Portfolio
1(High)
2
3
4
5(Low)
High-Low
α (%)
-1.153*
(-1.74)
-1.179
(-1.52)
-0.897
(-1.25)
-1.023
(-1.21)
-0.346
(-0.62)
-0.680
(-1.09)
-0.374
(-0.58)
-0.598
(-0.83)
-0.479
(-0.72)
-0.626
(-0.82)
-0.674*
(-1.95)
-0.553
(-1.51)
Rmt − Rft
1.399***
(9.09)
1.458***
(5.80)
1.512***
(9.06)
1.583***
(5.76)
0.762***
(5.93)
0.935***
(4.63)
1.129***
(7.58)
1.213***
(5.20)
1.339***
(8.74)
1.456***
(5.90)
0.060
(1.25)
0.002
(0.02)
Factor Loadings
SMB
HML
-0.091
(-0.15)
-0.330
(-0.68)
MOM
0.114
(0.45)
Adj. R 2 (%)
79.54
76.83
79.42
-0.329
(-0.48)
0.092
(0.17)
-0.103
(-0.37)
76.28
61.90
-0.458
(-0.92)
0.262
(0.67)
0.155
(0.76)
59.96
72.88
-0.071
(-0.12)
-0.376
(-0.84)
0.261
(1.11)
71.72
78.22
-0.201
(-0.33)
-0.215
(-0.45)
0.221
(0.89)
0.110
(0.51)
-0.115
(-0.68)
-0.107
(-1.20)
75.94
June 20, 2016
14 / 29
Data
Centrality Implications to Different Industries
Both shock correlation and network topology matter for systematic risk.
Methodology:
Expected returns should be explained by all systematic risk factors.
Split firms into quintiles based on centrality measures.
If ∆α 6= 0 for two extreme quintile portfolios, supply chain network leads to
”anomalies” in systematic risk.
Positions in the supply chain affects a firm’s exposure to the systematic risk
besides the network topology.
Upstream firms in manufacturing have diversification incentive to form
supplier connections to operationally hedge risk.
Downstream firms in logistics have concentration incentive to form supplier
connections to leverage economy of scale thus aggregate risk.
June 20, 2016
15 / 29
Simple Investment Model
Suppose an economy with 2 regions (A and B) and 3 potential future states below
with equal probability (Prob (S = Si ) = 13 , ∀i ∈ {1, 2, 3}):
S1 : both A and B function;
S2 : A cannot produce and B can;
S3 : B cannot produce and A can.
Next, suppose 4 firms: 3 manufacturers and 1 distributor.
Manufacturers: limited capacity and payoff of 1 as long as one input region
functions.
Sources:
Firm 1 only from region A
Firm 2 only from region B
Firm 3 from both
Firm 4 is the distributor and connects to both A and B with a fixed cost of 1 in all
states.
Payoffs:
Π1 = {1, 0, 1}, Π2 = {1, 1, 0}, Π3 = {1, 1, 1}, Π4 = {1, 0, 0}.
June 20, 2016
16 / 29
Investment Model Solution
Let Ω denote the covariance matrix for the firms’ payoffs.
 1

− 16 0 16
3
1
 −1
0 16 
6
3

Ω=
 0
0 0 0 
1
1
0 13
6
6
Suppose we have a representative mean-variance investor, and let
µ = [µ1 , µ2 , µ3 , µ4 ] denote firms expected return.
Then for any feasible returns µ̃ the investor targets, the investor find the portfolio
weights w = [w1 , w2 , w3 , w4 ] by solving
0
0
0
min{w Ωw |w µ = µ̃; w 1 = 10 }
w
,
June 20, 2016
17 / 29
Simple Investment Results
The result of the equilibrium of investment is:



 1
1
µ1
6 w1 + 6 w4
1
 µ2 

 1

 = 1  6 w1 + 6 w4  + λ 2
 µ3  λ1 
 λ1
0
1
1
µ4
w
+
w
3 1
3 4
Therefore,
µ3 < µ1 = µ2 < µ4
i.e. the manufacturers have lower risk than the distributor, and the dual sourcing
manufacturer is less risky than the single sourcing manufacturer.
Questions:
Does this result generalize to a broader classs of networks and what are other
empirical implications?
Are the output representations consistent with an equilibrium model of
production?
June 20, 2016
18 / 29
Equilibrium Network Model and Relationship to Literature
Previous literature focus on the sector level only.
Lucas (1977) argues that microeconomic shocks would average out at the
aggregated level proportional to √1n .
Acemoglu et al. (2012) suggests Lucas (1977) only holds under symmetric
network structure, and microeconomic shocks may lead to aggregated
fluctuations in asymmetric networks.
The change in the density of firm level connections is not captured.
We build a supply chain network model using two-level nested production
function capturing both the firm-level and sector-level connections.
June 20, 2016
19 / 29
Model Setup
An extension of Acemoglu et al. 2012
n industry sectors (S1 , S2 , ..., and Sn ).
Firms in the same sector have the same Cobb-Douglas CRS production
function to produce perfectly substitutable products.
Supply chain relationships are established ex-ante.
xijkl : output from firm l in sector j that inputs to firm k in sector i.
P
xi = k∈Si xik : output from firm k in sector i.
P
P
xij = k∈Si l∈Sj xijkl : the production from sector j to sector i.
P
xi = k∈Si xik : sector i’s total production.
k
A unit
P labor kallocating
Pn to to each firm (li ) in each sector (li ), i.e.
li = k∈Si li and i=1 li = 1.
P
Consumption from by firm k in sector i is cik , and ci = k∈Si cik .
Total consumption / GDP / labor wage is h.
June 20, 2016
20 / 29
Competitive Equilibrium
A competitive equilibrium of economy
We define a competitive equilibrium of economy with nPsectors consisting of
prices
(pi , i ∈ {1, ..., n}), wage h, consumption bundle ci = k∈Si cik , ∀i, k ∈ Si , and
quantities lik , xik , xijkl , ∀i, j, k, l such that
1
2
3
the representative consumer maximizes her utility;
the firms in each sector maximizes their profits (0 in expectation);
the labor and good markets clear at both levels, i.e. for any firm k in any
sector i, and for any sector i,
xik
=
cik
+
n X
X
xjilk ,
j=1 l∈Sj
xi = c i +
n
X
j=1
X
lik = li
k∈Si
xji ,
n
X
li = 1
i=1
June 20, 2016
21 / 29
Household and Firm Problems
The customer has Cobb-Douglas preferences over distinct goods from n
sectors subject to budget constraint, that is
1
max u (c1 , c2 , ..., cn ) = AΠni=1 (ci ) n , s.t.
n
X
pi ci ≤ h
i=1
Firm problem solves the following maximization problem
maxΠki
=
pi xik
−
hlik
−
n
X
j=1
xik = zik
X
xijkl
l∈Sj

(1−α)wij
n
X
Y
α

xijkl 
lik
j=1
pj
l∈Sj
June 20, 2016
22 / 29
From Firm Connections to Sector Connections
Since firms face the same input prices and own the same production
technology, they will choose the same proportions of inputs:
X
xijkl = γik xij , lik = γik li
l∈Sj
P
where γik =
l∈Sj
xijkl
xij
=
lik
li
is the firm’s sector share.
Firm-level networks determine the shape of the sector shock distribution.
The Origin of Sector Shock
α Qn
(1−α)wij
In sector i’s output, i.e. xi = zi (li )
, the sector productivity
j=1 (xij )
shock is a sum of firm level shocks, weighted by each firm’s sector share.
X
zi =
γik zik
k∈Si
June 20, 2016
23 / 29
From Firm Connetions to Sector Connetions
Firm-level connections affect the sector shock through the distribution of the
firm’s sector share γik .
0
Define the influencePvector as v =
n
vi = Pnpi xpi i xi thus i=1 vi = 1.
α 0
n1
−1
[I − (1 − α) W ]
satisfying
i=1
Supply Chain Network Systematic Risk
The aggregate output is a influence vector weighted sum of sector-specific
productivity shocks below.
0
y = lnh = v P
k k
where is a column vector with i = lnzi = ln
k∈Si zi γi . The volatility of the
aggregate output (the systematic risk) is
h 0 i
Var [y ] = Var v John Birge and Jing Wu (Chicago Booth)
June 20, 2016
24 / 29
Sparse v.s. Dense Supply Chain Networks
Sector A
Sector A
Sector B
Sector B
The firm’s sector share γik in the left case would have higher variance on the
distribution than the right case.
Similar to Proposition 4 inh Acemoglu
et al. (2015), the expected total output
i
0
E [y ] decreases when Var v increases, i.e.
1. Supply Chain Network and Sector Performance
For concave production functions, a sparse firm-level supply chain network results
in less total sector output than a dense network.
June 20, 2016
25 / 29
Simulation
Step 1 (Relationship-formation): Each firm chooses a set of suppliers.
Ex-ante the market is perfectly competitive.
Step 2 (Input-acquisition): Each firm draws i.i.d. production shock. Input
quantity depends on the supplier actual production.
The dense network has a low sector weight variance (std 0.0001 v.s. 0.0023).
2. Supply Chain Network and Firm Volatility
A sparse network results in more volatile firm production than a dense network.
1400
1200
1200
1000
1000
800
800
600
600
400
400
200
200
0
8.8
9
9.2
9.4
9.6
9.8
10
10.2
10.4
10.6
−3
0
0
0.005
0.01
x 10
0.015
0.02
0.025
0.03
0.035
Figure: Sector Weight γik Distribution (Left: 80% of Suppliers, Right: 2% of Suppliers).
June 20, 2016
26 / 29
Simulation (cont.)
Both cases exhibit sizable and systematic deviations from the normal
distribution (2%: heavy left tail, 80%: heavy right tail).
Only the sector weight with modest connection density is normal distributed.
Sufficient Statistics for Firm Production Variation
With firm-level supply chain connection variation, there is no guarantee that the
firm-level production is normally distributed.
−3
10.8
QQ Plot of Sample Data versus Standard Normal
x 10
QQ Plot of Sample Data versus Standard Normal
0.025
10.6
0.02
Quantiles of Input Sample
Quantiles of Input Sample
10.4
10.2
10
9.8
9.6
9.4
0.015
0.01
0.005
9.2
9
−4
−3
−2
−1
0
1
Standard Normal Quantiles
2
3
4
0
−4
−3
−2
−1
0
1
Standard Normal Quantiles
2
3
4
Figure: Q-Q Plot of the Sector Weight γik Distribution (Left: 80% of Suppliers, Right:
2% of Suppliers).
June 20, 2016
27 / 29
More Concentrated Economic Activities during Crisis.
Core: most (eigenvector) central firms; Periphery: least central firms.
Force-directed layout algorithm (Fruchterman and Reingold 1991).
Left: network in July 2007; Right: network in June 2009.
Economic activities for June 2009 supply chain network are more
concentrated than July 2007.
June 20, 2016
28 / 29
Conclusions & Future Directions
Conclusions and Future Directions
Evidence of concurrent supplier and customer effects plus supplier
momentum effects on returns.
Investors’ limited attention to supplier firms relative to customer firms.
Gradual diffusion of supply chain information downstream as opposed to
upstream.
Evidence of decreasing returns to centrality in manufacturing and increasing
returns to centrality in logistics.
Supply chain structure is an ex-ante determined and ex-post identifiable source
for systematic risk.
Upper-stream utility, mining, and construction firms behave similarly as
manufacturing.
Equilibrium model of firms connecting across sectors
Natural hedging decisions from manufacturers
Lower volatility effect for manufacturers implies conditions for increasing
conections to cause lower risk for upstream and higher risk for downstream
Future Directions
Additional empirical tests (including default propagation)
Incorporate of investment into the model formulation
June 20, 2016
29 / 29

A General Equilibrium Model of Supply Chain Interactions and Risk

Transcription

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