Do Sunk Costs of Exporting
Matter for Net Export Dynamics?
George Alessandria
Horag Choi
FRB Philadelphia University of Auckland
Motivation
1. Net exports appear slow to respond to ∆RER.
– Lags attributed to sunk costs - Baldwin (88), Baldwin & Krugman
(89), Dixit (89a,b), & Backus, Kehoe and Kydland (94).
2. Evidence fixed entry/continuation cost matter for firm
level trade dynamics.
– Big, productive firms enter/exit foreign markets - Roberts & Tybout
(97), Bernard & Wagner (98), Aw, Chung & Roberts (98), Bernard
& Jensen (99), Das, Roberts & Tybout (01).
Do sunk costs matter for aggregate fluctuations?
Findings on Sunk Costs
1. NX & business cycle dynamics are nearly identical to
those in a model without sunk costs.
– With sunk costs the # of goods changes, so taste for variety matters.
· For reasonable parameter values, indifferent between lots from a few suppliers or a
little from lots of suppliers.
· Business cycle synchronization is decreasing in love of variety.
2. Exporter participation systematically varies over business
cycle.
– Exporting lags source GDP, leads destination GDP.
– This is consistent with evidence of US export to OECD countries.
Model
• t = 0, 1, 2, ...∞, st = (s0, · · · , st) history of events, including t
• 2 countries {h, f } , consume non-traded final good
• Continuum, unit mass differentiated h & f intermediates
– Each variety produced by 1 domestic owned firm, i ∈ [0, 1]
¡ t−1¢
¡ t−1¢
t
– Differ by techn. η (i, s ) , k i, s , export status m i, s
= 0, 1
• Fixed export costs
– hire τ 0 workers start & τ 1 to workers continue
– {E (st) , E ∗(st)} denotes set of h & f exporters
• Complete asset markets
Consumer’s Problem
max E0
ct,lt,Bt+1
Ptct +
X
st+1
• Pt, wt
∞
X
β tU (ct, lt) ,
t=0
Q(st+1|st)B(st+1) ≤ Ptwtlt + Bt + Πt + PtTt,
denote price level & real wage
• Πt
sum of home country profits
• Tt
lump sum gov’t transfers
Foreign problem with *, in foreign currency,
Competitive Final Goods Sector
R1
d
d (i) di,
max PtDt − 0 Ph,t (i) yh,t (i) di − 0 Pf,t (i) yf,t
subject to
R1
½ h
ρ
ρ ¾1
i
h
i
ρ
R
R1 d
θ
θ
1
θ
d
θ
Dt = a1 0 yh,t(i) di + (1 − a1) N ∗λ i∈E ∗ yf,t(i)
,
t
d (i) = 0
yf,t
i∈
/ Et∗
t
Nt∗ =# foreign exporters
d (i), y d (i)
Input Demand yh,t
f,t
⇒
Prices
Pt, Ph,t, Pf,t,
i ∈ Et∗,
Intermediate Goods Producers - firm i
• Individual state is (η, k, m),
iid
• Key assumption: η ∼ N(0, σ 2η ),
©
ª
0
0
• Choose ph,t, l, m , k ,
o
n
V (η, k, m, s) = max V 0 (η, k, m, s) , V 1 (η, k, m, s)
Intermediate Goods Producers - value of not exporting
¡
¢R
V 0 (η, k, m, s) = maxph,k0 Πh (η, k, s)+EQ s0|s
£
¡ 0 0
¢ ¡ 0¢
0
V η , k , 0, s dφ η ,
Πh (η, k, s) = phyhd (ph) − P wl + k0 − (1 − δ) k
yhd = ez eη kαl1−α
0
F OC s :
ph (η, k) =
(1−α) yh
θ l
¡ 0 ¢R ¡ 0 0
¢ ¡ 0¢
0
EQ s |s V2 η , k , 0, s ∂φ η = P
⇒ k0 = K 0 does not depend on η
¤
Intermediate Goods Producers - value of exporting
¡
¢R
V 1 (η, k, m, s) = max Πh + Π∗h + EQ s0|s
£
Πh = phyhd − P wl + k0 − (1 − δ) k
¤
¡ 0 0
¢ ¡ 0¢
0
V η , k , 1, s ∂φ η ,
Π∗h = ep∗hyh∗d − w [τ 0 + m (τ 1 − τ 0)] ,
yhd(i) + yh∗d(i) = ez eη kαl1−α
0
F OC s :
(1−α) yh+yh∗
ph = θ
¡ 0 ¢R l ¡ 0 0
¢ ¡ 0¢
0
EQ s |s V2 η , k , 1, s ∂φ η = P
⇒ k0 = K 1 (s) > K 0 (s) does not depend on η
Aggregate Decision Rules
Remark: If τ 0 − τ 1 not too large, ∃η1 (s) , η0 (s):
¡
¢
¡
¢
V 1 η 1, K 1, 1, s = V 0 η 1, K 1, 1, s
¡
¢
¡
¢
V 1 η 0, K 0, 0, s = V 0 η 0, K 0, 0, s ,
(Marginal Stopper)
(Marginal Starter)
Figure I
Value of Firms
Values
Exporting Firm
(after Costs 1 )
MB
B
Exporting Firm
(before Costs)
B
B
B
Non-exporting Firm
?
6
Exporting Firm
(after Costs 0 )
t
1 (s )
t
0 (s )
56
(st )
Aggregate Decision Rules
n1(s) = Pr (mt = 1|mt−1 = 1) = Pr[η > η 1(s)],
n0(s) = Pr (mt = 1|mt−1 = 0) = Pr[η > η 0(s)].
Exporter Ratio = N(s) =
R1
0 m(i, s)di
N(s0) = n1(s)N (s) + n0(s)[1 − N(s)]
%
Last Period's Non-exporters
Starters
Productivity (η)
η0?(s)
%
Last Period's Exporters
Stoppers
η1(s)
Productivity (η)
N(s’)=Pr(η>η1(s))*N(s)+(1-N(s))Pr(η>η 0(s))
Equilibrium
Is a sequence of decision rules, allocations and prices
satisfying
• Consumer maximization
• Final good producers’ profit maximization
• Intermediate good producers’ profit max
• Market clearing
• Government budget constraint.
Market Clearing
D(s) = c(s) +
Z
x(i, s)di
Z
D∗(s) = c∗(s) + x∗(i, s)di
Z 1
l(s) =
l(i, s)di
Z0 1
l∗(i, s)di.
l∗(s) =
0
yhd(i, s) + yh∗d(i, s) = yh(i, s)
yfd (i, s) + yfd∗(i, s) = yf∗ (i, s)
B(s) + B ∗(s) = 0
i ∈ [0, 1] ,
i ∈ [0, 1] ,
Calibration
[cγ (1−l)1−γ ]1−σ
U(c, l) =
,
1−σ
½ h
ρ
ρ ¾1
i
h
i
R1 d θ θ ρ
R1 d θ θ
1
D = a1 0 yh(i) di + (1 − a1) N ∗λ 0 yf (i) di
y (z, η, k, l) = ez eη kαl1−α
Z(st) = MZ(st−1) + ν(st),
iid
η ∼ N(0, σ 2η ),
iid
ν(st) ∼ N(0, Ω),
Calibration
Markups
Labor share
Time working
Scale
Depreciation
Discount
IES
Elasticity of subst.
Productivity
0.11 θ = 0.9
0.64 α = 0.36
0.25 γ = 0.294
λ = 0, λ = {θ − 1, 1 − θ, 1}
δ = 0.025
β = 0.99
σ=2
1.5 ρ = 1/3
"
#
0.95 0
M=
0 0.95
V ar( ) = V ar( ∗) = σ 2 = 0.0072,
Corr( , ∗) = 0.25
Exporter Characteristics/Dynamics - Census’ LRD 84-92
Bernard & Jensen (95, 99, 01) find:
1. Not all firms export
– Less than 50% of U.S. plants in LRD, 20 percent in Census of Mfrs
2. Exporters are:
– Bigger − 100% more shipments, 90% more employees
– More Productive − 12 to 18% higher TFP
– Larger exporter premia in Census of Mfrs (Bernard, et al. 02)
3. Change identity, annually
– 14% of non-exporters STARTED exporting
– 13% of exporters STOPPED exporting
¢
¡
Calibration - trade costs τ 0, τ 1, ση , a
Variables
Import share
Starters (n0)
Stoppers (1 − n1)
X
ln A
A
ln
ln
N
YX
YN
LX
LN
• New exporter:
BJ (99, 01)
Model
0.15
0.036
0.032
0.12 to 0.18
0.15
0.035
0.035
0.154
0.952 to 1.139 0.902
0.776 to 0.952 0.902
entry costs ≈ 16.5% of sales
• Continuing exporter:
trade cost ≈ 1.7% of sales
• Total trade costs ≈ 1.3% of GDP
Evaluating the Model
Consider 3 models
1. No costs, 2. Sunk Cost, 3. Fixed Exit
Sensitivity
1. Exporter Persistence, 2. Taste for Variety, 3. Markup
Table 1. Business Cycle Properties
Variations on Benchmark Economy
Fixed
IID
Love
Hate
High
Persistence
Exit
Expo Variety Variety
No
Costs
Sunk
Cost
1.42
0.46
1.29
0.16
1.31
0.17
1.30
0.16
2.81
0.33
0.32
0.32
-0.38
0.16
0.07
-0.52
0.56
-0.49
-0.52
0.56
-0.50
-0.52
0.57
-0.49
0.90
0.81
0.69
0.79
0.71
0.79
0.70
0.79
0.21
0.52
0.01
0.18
0.20
0.52
-0.01
0.17
0.20
0.53
0.00
0.18
Data
Std. dev (in percent)
Y
NX/Y
Std dev (rel to Y)
RER
Domestic corr. w/Y
NX/Y
RER
Q,NX/Y
Persistence
NX/Y
RER
International correlation
Y
C
I
L
0.51
0.32
0.29
0.43
Table 1. Business Cycle Properties
Variations on Benchmark Economy
IID
Love
Hate
Fixed
High
Persistence
Expo Variety Variety
Exit
No
Costs
Sunk
Cost
1.42
0.46
1.29
0.16
1.31
0.17
1.30
0.16
1.31
0.16
1.30
0.16
2.81
0.33
0.32
0.32
0.32
0.32
-0.38
0.16
0.07
-0.52
0.56
-0.49
-0.52
0.56
-0.50
-0.52
0.57
-0.49
-0.52
0.57
-0.50
-0.52
0.56
-0.49
0.90
0.81
0.69
0.79
0.71
0.79
0.70
0.79
0.72
0.79
0.69
0.79
0.21
0.52
0.01
0.18
0.20
0.52
-0.01
0.17
0.20
0.53
0.00
0.18
0.20
0.52
-0.01
0.18
0.21
0.52
0.00
0.18
Data
Std. dev (in percent)
Y
NX/Y
Std dev (rel to Y)
RER
Domestic corr. w/Y
NX/Y
RER
Q,NX/Y
Persistence
NX/Y
RER
International correlation
Y
C
I
L
0.51
0.32
0.29
0.43
Table 1. Business Cycle Properties
Variations on Benchmark Economy
Fixed
IID
Love
Hate
High
Persistence
Exit
Expo Variety Variety
No
Costs
Sunk
Cost
1.42
0.46
1.29
0.16
1.31
0.17
1.30
0.16
1.31
0.16
1.30
0.16
1.32
0.19
1.21
0.09
2.81
0.33
0.32
0.32
0.32
0.32
0.31
0.37
-0.38
0.16
0.07
-0.52
0.56
-0.49
-0.52
0.56
-0.50
-0.52
0.57
-0.49
-0.52
0.57
-0.50
-0.52
0.56
-0.49
-0.53
0.57
-0.50
-0.48
0.55
-0.49
0.90
0.81
0.69
0.79
0.71
0.79
0.70
0.79
0.72
0.79
0.69
0.79
0.73
0.80
0.63
0.77
0.21
0.52
0.01
0.18
0.20
0.52
-0.01
0.17
0.20
0.53
0.00
0.18
0.20
0.52
-0.01
0.18
0.21
0.52
0.00
0.18
0.19
0.53
-0.05
0.15
0.27
0.47
0.15
0.26
Data
Std. dev (in percent)
Y
NX/Y
Std dev (rel to Y)
RER
Domestic corr. w/Y
NX/Y
RER
Q,NX/Y
Persistence
NX/Y
RER
International correlation
Y
C
I
L
0.51
0.32
0.29
0.43
Table 2: Sensitivity
High Markup
Data
Sunk Cost No Cost Sunk Cost
CRS
Std. dev (in percent)
1.42
0.46
1.31
0.17
1.24
0.10
1.31
0.16
1.25
0.11
2.81
0.32
0.41
0.37
0.40
-0.38
0.16
0.07
-0.52
0.56
-0.50
-0.39
0.60
-0.31
-0.44
0.61
-0.40
-0.40
0.60
-0.33
0.90
0.81
0.71
0.79
0.75
0.77
0.81
0.78
0.78
0.77
0.51
0.32
0.29
0.43
0.20
0.52
-0.01
0.17
0.19
0.58
0.03
0.12
0.15
0.60
-0.10
0.05
0.19
0.59
0.02
0.11
Y
NX/Y
Std dev (rel to Y)
RER
Domestic corr. w/Y
NX/Y
RER
Q,NX/Y
Persistence
NX/Y
RER
International correlation
Y
C
I
L
Role of Entry for Propagation?
• Key
to Hysteresis literature was that aggregate dynamics
following entry different than without entry
• Explore
this idea by considering shock away from steady
state (i.e. when number of exporters differs).
• Consider
positive productivity shock at home followed 10
periods later by positive shock abroad
Figure IV
Response to a Home Productivity Shock Followed by a Foreign Productivity Shock
a. Productivity
b. Exporters
0.8
0.8
0.6
P e rc e n t c h a n g e
P e rc e n t c h a n g e
0.6
0.4
0.2
0
0.4
0.2
0
-0.2
Home
Home
Foreign
Foreign
-0.2
-0.4
0
20
40
60
80
100
0
20
40
Period
c. Net Exports
80
100
d. Real Exchange Rate
0.10
0.2
0.05
0.1
P e rc e n t c h a n g e
P e r c e n t o f o u tp u t
60
Period
0.00
-0.05
-0.10
-0.15
0.0
-0.1
-0.2
-0.3
No Costs
No Costs
Sunk Cost
Sunk Cost
-0.4
-0.20
0
20
40
60
80
100
Period
0
20
40
60
Period
59
80
100
Export Participation and Business Cycle
• Recalibrate annual version of model
• Annual
data on US exporters and exports to 13 OECD
countries from 1995 to 2003.
Conclusions
1. Sunk costs of exporting matter for firm-level dynamics,
but have little effect on aggregate fluctuations.
2. Any effect depends on the taste for variety matters
Table I
Parameter Values
Benchmark Model
Preferences
= 0:99,
= 2,
Production
= 0:36,
= 0:025, a1 = 0:757,
Productivity
Trade costs
= 0:9,
= 1=3,
= 0:303
=0
M11 = M22 = 0:95, M12 = M12 = 0,
V ar( ) = V ar( ) = 2 = 0:0072
Corr( ; ) = 0:25,
= 0:50
0
= 0:048,
1
= 0:010
V ariations
No Cost
= 0:308, a1 = 0:761,
0
=
1
=0
Fixed Exit
a1 = 0:757,
0
= 0:168,
1
= 0,
Pr (exit shock) = 0:047
Permanent Exporters
a1 = 0:756,
0
= 0:181,
1
= 0:012
IID Exporters
= 0:306, a1 = 0:759,
0
=
Love Variety
=
0
= 0:048,
Hate Variety
= 1 , a1 = 0:801,
High Markup
No Cost
Sunk
CRS
= 2=3
= 0:393, a1 = 0:761
= 0:368, a1 = 0:742,
0 = 0:144,
= 1=3,
= 0:368, a1 = 0:763,
0:1, a1 = 0:752,
High Armington
No Cost
Sunk-CRS
= = 2=3
a1 = 0:641
= 1=3, a1 = 0:647,
Annual
M11 = M22 = 0:954 ,
= 0:304,
= 0:10,
54
0
= 0:005
= 0:048,
0
2
1
= 0:16,
= 0:02422 ,
0 = 0:021,
1
1
= 0:01
= 0:01
0
= 0:047
= 0:144,
1
= 0:052
1
1
= 0:25,
= 0:01
1
= 0:047
= 0:96,
Table II
Business Cycle Statistics
55
Sunk Fixed
High
IID
Data No Costs Cost
Exit
Persistence Exporters
Standard deviation (in percent)
Y
1.42
1.27
1.28
1.28
1.29
1.28
nx
0.46
0.16
0.16
0.16
0.16
0.16
Standard deviation (relative to output)
C
0.79
0.36
0.36
0.36
0.36
0.36
I
3.25
3.36
3.37
3.36
3.36
3.36
L
0.85
0.47
0.47
0.47
0.46
0.47
q
2.81
0.33
0.32
0.32
0.32
0.33
Domestic correlation with output
C
0.83
0.95
0.95
0.95
0.95
0.95
I
0.93
0.98
0.98
0.98
0.98
0.98
L
0.85
0.99
0.99
0.99
0.99
0.99
nx
-0.38
-0.49
-0.50
-0.50
-0.50
-0.49
q
0.16
0.56
0.56
0.56
0.57
0.56
q; nx
0.07
-0.50
-0.51
-0.50
-0.51
-0.50
Persistence
Y
0.87
0.69
0.69
0.69
0.69
0.69
C
0.91
0.73
0.73
0.73
0.74
0.73
I
0.84
0.67
0.68
0.67
0.68
0.67
L
0.95
0.68
0.68
0.68
0.68
0.68
nx
0.90
0.69
0.71
0.70
0.72
0.69
q
0.81
0.79
0.79
0.79
0.79
0.79
International correlation
Y
0.51
0.22
0.22
0.21
0.21
0.22
C
0.32
0.54
0.54
0.55
0.54
0.54
I
0.29
0.02
0.00
0.00
0.01
0.01
L
0.43
0.19
0.19
0.18
0.19
0.19
* International correlations are from Kehoe and Perri (2000).
Variations on Benchmark Economy
High Markup
Love
Hate
Sunk
Variety Variety No Costs Cost CRS
=
No Costs
SunkCRS
Measure
1.30
0.19
1.19
0.08
1.22
0.10
1.29
0.15
1.22
0.09
1.30
0.20
1.29
0.17
1.28
0.16
0.36
3.43
0.47
0.32
0.37
3.18
0.46
0.38
0.41
3.91
0.42
0.41
0.40
4.07
0.42
0.38
0.41
3.87
0.40
0.42
0.37
4.32
0.49
0.24
0.38
4.16
0.45
0.27
0.35
3.36
0.47
0.32
0.95
0.97
0.98
-0.50
0.57
-0.51
0.96
0.99
0.99
-0.45
0.55
-0.49
0.95
0.98
0.98
-0.36
0.59
-0.32
0.95
0.96
0.98
-0.41
0.61
-0.40
0.96
0.98
0.98
-0.35
0.59
-0.31
0.90
0.95
0.98
-0.07
0.59
0.38
0.91
0.96
0.98
0.02
0.60
0.46
0.95
0.98
0.99
-0.50
0.55
-0.46
0.69
0.74
0.69
0.69
0.73
0.80
0.68
0.73
0.66
0.66
0.63
0.77
0.69
0.73
0.67
0.68
0.75
0.77
0.70
0.73
0.70
0.70
0.81
0.78
0.69
0.73
0.68
0.68
0.78
0.77
0.70
0.73
0.67
0.68
0.87
0.85
0.70
0.73
0.68
0.68
0.93
0.83
0.69
0.73
0.68
0.68
0.71
0.80
0.21
0.55
-0.04
0.17
0.29
0.48
0.17
0.28
0.21
0.60
0.04
0.13
0.17
0.61
-0.07
0.11
0.21
0.58
0.07
0.19
0.07
0.74
-0.24
-0.24
0.08
0.71
-0.17
-0.12
0.22
0.53
0.00
0.19
Figure V
Correlation of nxt+k and qt
0.8
0.6
Correlation
0.4
0.2
0.0
-0.2
No Costs
-0.4
Sunk Cost
Fixed Exit
-0.6
-12
-8
-4
0
k
60
4
8
12
Figure VI
Exporter Dynamics: Impulse-Response
0.4
Percent change
0.2
0
Home
Foreign
-0.2
-0.4
0
5
10
15
Period
61
20
25
Figure VII
Exporter Dynamics - Data and Model
b. Source GDP t+k
1.0
0.5
0.5
C o r r e la tio n
C o r r e la ti o n
a. Trade t+k
1.0
0.0
-0.5
0.0
-0.5
Sunk Cost
Sunk Cost
Data
Data
-1.0
-1.0
-1
0
1
-1
k
1
k
c. RER t+k
d. Destination GDP t+k
1.0
1.0
0.5
0.5
C o r r e la t io n
C o r r e la t io n
0
0.0
-0.5
0.0
-0.5
Sunk Cost
Sunk Cost
Data
Data
-1.0
-1.0
-1
0
1
k
-1
0
k
62
1
Figure II
Exporter Characteristics and Hysteresis
a. Technology, Output and Labor
2.0
Log Exporter Premia
1.5
1.0
0.5
Z
Y&L
0.0
0
0.1
0.2
0.3
0.4
0.5
0.4
0.5
Probability of Exiting Export Market
b. Capital
Log Exporter Premia
0.3
0.2
0.1
0.0
0
0.1
0.2
0.3
Probability of Exiting Export Market
57
Figure III
Response to a Home Aggregate Productivity Shock
b. Exporters
a. Productivity
0.8
0.4
0.6
P e rc e n t c h a n g e
P e rc e n t c h a n g e
0.2
0.4
0.2
0
Home (Sunk Cost)
-0.2
Foreign (Sunk Cost)
0
Home (Fixed Exit)
Home
Foreign
Foreign (Fixed Exit)
-0.4
-0.2
0
5
10
15
20
0
25
5
10
Period
15
20
25
Period
c. Net Exports
d. Real Exchange Rate
0.10
0.4
0.05
P e rce n t c h a n g e
P e r c e n t o f o u tp u t
0.3
0.00
-0.05
0.1
No Costs
-0.10
0.2
No Costs
Sunk Cost
Sunk Cost
Fixed Exit
Fixed Exit
-0.15
0
0
5
10
15
20
25
Period
0
5
10
15
Period
58
20
25