Dynamics of Firms and Trade in General Equilibrium

Transcription

Dynamics of Firms and Trade in General
Equilibrium
Robert Dekle, Hyeok Jeong and Nobuhiro Kiyotaki
USC, Seoul National University and Princeton
Figure 1a. Aggregate exchange rate disconnect (levels)
128000
64000
10 -2
32000
16000
Aggregate Exports
Aggregate Imports
8000
1970
1975
1980
1985
1990
Corr(Exp, REER) = −0.40∗∗
1995
2000
2005
2010
2015
Corr(Imp, REER) = −0.42∗∗
(0.19)
(0.18)
Figure 1b. Aggregate exchange rate disconnect (HP filtered)
0.25
Aggregate Exports
Aggregate Imports
Real Ef. Exchange Rate
0.2
Log-deviation from HP trend
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
1970
1975
1980
1985
1990
Corr(Exp, REER) = 0.47 ∗∗∗
(0.11)
1995
2000
2005
2010
Corr(Imp, REER) = 0.19
(0.16)
2015
Real Effective Exchange Rate index (log scale)
Thousand million yen, constant prices (log scale)
0.015
Figure 1a. Aggregate exchange rate disconnect (levels)
128000
64000
10 -2
32000
16000
Aggregate Exports
Aggregate Imports
8000
1970
1975
1980
1985
1990
Corr(Exp, REER) = −0.40∗∗
1995
2000
2005
2010
2015
Corr(Imp, REER) = −0.42∗∗
(0.19)
(0.18)
Figure 1b. Aggregate exchange rate disconnect (HP filtered)
0.25
Aggregate Exports
Aggregate Imports
Real Ef. Exchange Rate
0.2
Log-deviation from HP trend
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
1970
1975
1980
1985
1990
Corr(Exp, REER) = 0.47 ∗∗∗
(0.11)
1995
2000
2005
2010
Corr(Imp, REER) = 0.19
(0.16)
2015
Real Effective Exchange Rate index (log scale)
Thousand million yen, constant prices (log scale)
0.015
TABLES FOR DJK WORKING PAPER
Table 1. Exports regression, Kaigin panel
(1)
(2)
(3)
(4)
(5)
(6)
(7)
All
Sample
High
Profitability
Low
Profitability
Big
Employment
Small
Employment
Big
Sales
Small
Sales
0.374
0.284
0.393
0.338
(0.049)*** (0.110)** (0.054)*** (0.061)***
0.398
0.315
0.417
0.305
log Y*
(0.055)*** (0.125)** (0.061)*** (0.072)***
log Agg TFP
0.378
1.537
0.106
0.389
(0.080)*** (0.181)***
-0.089
(0.104)***
2.112
2.158
2.091
2.721
log Firm TFP
(0.079)*** (0.169)*** (0.089)*** (0.121)***
6.289
7.744
5.963
10.412
Cons
(1.596)*** (3.611)** (1.771)*** (2.083)***
F-stat
325.8
118.6
228.2
250.2
0.042
0.122
0.029
0.171
Adj. R-sq.
# Obs.
9,997
2,034
7,963
3,549
0.406
(0.068)***
0.424
(0.076)***
0.301
(0.111)***
1.898
(0.101)***
4.803
(2.190)**
152.5
0.002
6,448
0.389
(0.063)***
0.594
(0.073)***
0.588
(0.105)***
1.726
(0.111)***
2.55
-2.109
171.7
0.126
3,089
0.369
(0.065)***
0.316
(0.073)***
0.3
(0.106)***
2.253
(0.102)***
7.79
(2.107)***
196.2
0.022
6,908
log RER
Size differentiation is done by 75th percentile. * p < 0.1; ** p < 0.05; *** p < 0.01.
Date: July 25, 2013.
R.A. Gabriel Tenorio, Princeton.
1
In Kaigin data, the average total sales of exporters is twice as
large as non-exporters ! Consistent with Melitz (2003)
But
Correlation between …rm size and export dummy is weak 0:09
Correlation between …rm size and export share of exporters is
even weaker 0:03
Many …rms have negative pro…t, 8% in total and 11% among
exporters
! We consider heterogeneous productivity of each product
and each …rm produces multiple products
40
Figure 1. Decomposition of shipment change
(%)
4
30
20
1
2
8
10
1
15
5
0
4
1
1
16
10
13
-17
-15
5
1
0
3
1
0
3
1
1
3
2
4
1
2
1
13
1
0
5
18
17
13
21
19
19
2
1
11
0
-10
-20
-19
-3
-14
-2
-3
-3
-4
-4
-13
-14
-4
-3
-3
-3
-11
-12
-4
-4
-3
-3
-13
-15
-14
-23
-3
-3
-5
-7
0
-30
-4
-6
-9
-1
-40
98-99
99-00
00-01
01-02
02-03
03-04
04-05
05-06
06-07
continuing products increase
continuing products decrease
extensive margins entry
extensive margins exit
intensive margins add
intensive margins drop
n.e.c
total change
07-08
08-09
Small Open Economy Model
A continuum of home …rm h 2 Ht: Firm h produces Iht number of di¤erentiated products for home and export market
1
0
H
l
B hit C
H
qhit
= ahitZt @
F
qhit
L
20
1
F
6B hit C
6
A
t 4@
= ahitZ
A
l
L
0
L
1
1
H
m
hit C
B
L
0
@
1
L
; for i = 1; 2; ::; Iht
A
11
F
m
hit C
B
@
A
1
L
L
3
L
7
7
5
; for i = 1; 2; ::Iht
Home output for home and export markets are produced as
QH
t =
QFt =
2
Z
6
4
h2Ht
2
Z
6
4
h2Ht
0
Iht
BX
@
0
i=1
Iht
BX
@
i=1
H
qhit
F
qhit
1
1
1
1
3
C
A
7
5
dh
C
A
dh75
3
1
1
A new entrant who pays a sunk cost Et at date t draws an
opportunity of producing a new products from date t+1 with
probability E . The productivity of the new product is distributed as
Prob (ahit
where
> 1 and
a) = F (a) = 1
>
a
; for a 2 [1; 1)
1:
A …rm must pay the …xed maintenance cost for each product
in order to produce and maintain its productivity
ahit+1
8
>
>
<
ahit; with probability 1
=>
>
:
0; with probability
In addition, each maintained product yields an opportunity to
produce another new product with probability
< with the
same Pareto distribution.
Each …rm can produce many products. Each product multiplies
and dies like "amoeba."
Home …nal goods market
QH
t = Ct +
EtNEt
+ Nt
NEt is measure of entering …rms, Nt is measure of di¤erentiated products maintained, and
0
1
NEt A
@
; >0
(1)
Et = E
NE
The representative household supplies labor Lt; consumes …nal
goods Ct and holds home and foreign real bonds Dt and Dt
to maximize its expected utility
U0 = E0
1
X
t=0
0
tB
B
@
1+1=
ln Ct
Lt
0
1 + 1=
+
t
C
C
tA
ln D
subject to the budget constraint
Ct + E NEt + Nt + Dt + tDt
= wLtLt + t + Rt 1Dt 1 + tRt 1Dt
t
: utility (liquidity) shock to foreign bond holding
1
1
Foreigners do not hold home bond ! Dt = 0
Foreign bond holding of home household
Dt = Rt 1Dt
F F
+
p
1
t Qt
Mt H
where Mt H is total import of intermediate input
Foreign aggregate demand for home exports are given by
QFt = (pFt )
'
Yt
where Yt is an exogenous foreign demand
Competitive Equilibrium
All …rms choose to pay the …xed maintenance cost
Nt+1 = (1
+
) Nt +
E NEt
(2)
Price of di¤erentiated goods is a mark-up over the unit cost
and the price index of home …nal goods at home is
1=
pH
t
=
wt = (wLt)
L
2
Z
6
4
h2Ht
1
t
L
0
Iht
BX
@
i=1
; a
1
1
pH
hit
Z 1
1
C
A
a
3
7
5
1
=
dh
1
wt
1
-1 aN
1
dF (a)
1
(3)
1
t
0
=@
1
Zt
+1
Only products with higher than at productivity is exported.
at =
2
6
6
6
6
4
(
1) aZtNt
'
+1
t Yt
3
17
7
7
7
5
1
A
1
( -1)+( +1- )(1-')
(4)
1
1
The input composite market equilibrium is
Xt =
0
B
@
1
L
Lt C
L
0
B
@
A
Mt
1
=
11
H
L
XtH
L
C
A
=
1
L(
0 Ct )
+1
+1
+
at
0
1
B wt
B
@ (1
t
L+
1
C
C
A
L )(1+ )
Nt
1
L
(5)
(6)
Free entry condition is
Et
=
E Et ( t;t+1V t+1)
: free entry
(7)
where the value function of the average product
Vt =
where
t;t+1
t
+ (1
+
)Et (
t;t+1V t+1)
(8)
3
(9)
= Ct=Ct+1 and
t
=w
2
6
t4
(
Xt
1)Nt
1
at
7
5
The …nal goods market clearing implies
1
Ct +
H
1
N
+
N
=
aN
Z
X
t
t t
Et Et
t
(10)
Net foreign assets evolve as
tDt =
tRt 1Dt
( +1- )(1-')
1
1 + at
'
t Yt
(1
L)wtXt
(11)
Home demand for home bond and foreign bond imply
1 = RtEt(
t
Rt Et (
t;t+1
t;t+1)
Ct
t+1) = t
Dt
(12)
(13)
(1 13) determine wt; at; Xt; XtH ; Ct; t; Rt; V t; t, Et; NEt,
Nt+1 and Dt as a function of the state variables Mt =
(Nt; Dt 1; Zt; t ,Yt ; Rt )
2
Table 2a. Baseline parameterization
β
θ
ψ
ψ0
γL
α
ϕ
φ
κ
κE
η
δ
λ
λE
σ
Z
Y∗
G/C
ξ∗
R∗
Discount factor
0.92
Elasticity of substitution between products
4.19
Frisch elasticity of labor supply
6.02
Labor disutility
12.84
Labor share
0.85
Productivity distribution shape parameter
3.64
Elasticity of foreign demand
0.75
Export cost
3.14
Maintenance cost
16.57
Entry cost
89.26
Elasticity of entry cost
0.1
Probability of losing product
0.12
Probability of drawing new product for incumbent 0.49
Probability of producing new product for entrant
0.41
Std. dev. of noise for sales
1.67
Steady state aggregate productivity
1
Steady state foreign demand
106
Steady state govt. expenditure / cons.
0.28
Steady state liquidity shock
0.01
Steady state foreign interest rate
1.05
Table 2b. Steady state moments (aggregate and cross-sectional)
Data Model
C/Y
0.56
0.66
D∗ /Y
0.20
0.19
Exp/Y
0.12
0.12
NE /N
0.10
0.15
Mean log Rev
17.77 17.77
SD log Rev
1.42
1.84
Mean log Dom
17.65 17.66
SD log Dom
1.41
1.84
Mean log Exp
16.03 15.58
SD log Exp
2.09
1.85
Mean P R
0.03
0.15
SD P R
0.06
0.15
#Exp/N
0.39
1.00
Corr P R, log Rev 0.07
0.71
Corr ES, log Rev 0.17
0.32
2
Table 2a. Baseline parameterization
β
θ
ψ
ψ0
γL
α
ϕ
φ
κ
κE
η
δ
λ
λE
σ
Z
Y∗
G/C
ξ∗
R∗
Discount factor
0.92
Elasticity of substitution between products
4.19
Frisch elasticity of labor supply
6.02
Labor disutility
12.84
Labor share
0.85
Productivity distribution shape parameter
3.64
Elasticity of foreign demand
0.75
Export cost
3.14
Maintenance cost
16.57
Entry cost
89.26
Elasticity of entry cost
0.1
Probability of losing product
0.12
Probability of drawing new product for incumbent 0.49
Probability of producing new product for entrant
0.41
Std. dev. of noise for sales
1.67
Steady state aggregate productivity
1
Steady state foreign demand
106
Steady state govt. expenditure / cons.
0.28
Steady state liquidity shock
0.01
Steady state foreign interest rate
1.05
Table 2b. Steady state moments (aggregate and cross-sectional)
Data Model
C/Y
0.56
0.66
D∗ /Y
0.20
0.19
Exp/Y
0.12
0.12
NE /N
0.10
0.15
Mean log Rev
17.77 17.77
SD log Rev
1.42
1.84
Mean log Dom
17.65 17.66
SD log Dom
1.41
1.84
Mean log Exp
16.03 15.58
SD log Exp
2.09
1.85
Mean P R
0.03
0.15
SD P R
0.06
0.15
#Exp/N
0.39
1.00
Corr P R, log Rev 0.07
0.71
Corr ES, log Rev 0.17
0.32
3
0.30
Figure 3a. Cross sectional distribution of total sales by export status: Kaigin data
0.20
0.15
0.00
0.05
0.10
Density
0.25
Exporter
Non−exporter
12
14
16
18
20
22
24
Total sales (log)
0.2
0.1
0.0
Density
0.3
0.4
Figure 3b. Cross sectional distribution of total sales by export status: Model
10
12
14
16
18
Total sales (log)
20
22
24
3
0.30
Figure 3a. Cross sectional distribution of total sales by export status: Kaigin data
0.20
0.15
0.00
0.05
0.10
Density
0.25
Exporter
Non−exporter
12
14
16
18
20
22
24
Total sales (log)
0.2
0.1
0.0
Density
0.3
0.4
Figure 3b. Cross sectional distribution of total sales by export status: Model
10
12
14
16
18
Total sales (log)
20
22
24
3
Table 3a. Calibration of stochastic processes
Efficient Subjective
Standard deviation
σZ (%)
0.87
0.59
∗
σY (%)
1.35
5.46
σG (%)
0.83
0.61
σξ∗ (%)
22.05
79.16
Autocorrelation
ρZ
0.55
0.73
ρY ∗
0.94
0.84
ρG
0.95
0.95
ρξ∗
0.95
0.27
4
Table 3b. Sample and simulated moments
Data
Standard deviation
SD GDP (%)
0.88
(0.10)
SD Gov / SD GDP 0.63
(0.11)
SD Inv / SD GDP 3.13
(0.13)
SD Exp / SD GDP 4.63
(0.70)
SD RER (%)
3.52
(0.31)
Autocorrelation
AC(1) GDP
0.55
(0.15)
AC(1) Gov
0.65
(0.07)
AC(1) Inv
0.58
(0.13)
AC(1) Exp
0.36
(0.18)
AC(1) RER
0.49
(0.06)
Correlation with GDP
Corr Gov, GDP
0.08
(0.19)
Corr Inv, GDP
0.96
(0.01)
Corr Exp, GDP
0.55
(0.19)
Corr RER, GDP
0.42
(0.16)
Efficient Subjective
0.93
0.96
0.83
0.59
2.80
2.47
2.41
4.24
3.07
3.57
0.34
0.40
0.49
0.49
0.30
0.23
0.45
0.37
0.46
0.28
0.12
0.08
0.97
0.85
0.08
0.53
-0.04
-0.59
Data and output from the model are HP filtered.
HAC robust standard errors are shown in parenthesis.
4
Figure 4. Impulse response to TFP shock Z
GDP
−3
Consumption (C)
0.01
0.01
1
Labor (L)
x 10
0.5
0.005
0.005
0
−0.5
0
0
5
10
15
20
0
0
F F
Export and import value (ε P Q , ε M)
5
−3
0.01
0
Exports
Imports
x 10
10
15
20
−1
0
5
Extensive margin (aexp)−α
10
15
20
Real exchange rate (ε)
0.01
−1
−2
0.005
0.005
−3
−4
0
0
5
15
20
−5
Net foreign assets (D*)
−3
0
10
x 10
0
5
−3
5
−0.5
4
−1
3
−1.5
2
−2
1
10
15
20
0
0
5
Intangible capital (N)
x 10
10
15
Shocks
0.01
Z
*
Y
G
ξ*
0.005
−2.5
0
5
10
15
20
0
0
20
5
10
15
20
0
0
5
10
15
20
Figure 5. Impulse response to foreign demand shock Y ∗
−3
2
−3
GDP
x 10
2
1.5
1.5
1
1
0.5
0.5
0
0
5
10
15
20
0
−3
x 10 Export and import value (ε P Q , ε M)
Exports
Imports
6
Labor (L)
x 10
0
0
5
−3
8
10
5
F F
8
−4
Consumption (C)
x 10
x 10
10
15
20
−5
0
5
10
15
20
0
6
4
4
2
2
0
0
−0.005
−2
0
5
10
15
20
−2
0
5
−3
0.02
1.5
0.015
10
15
20
−0.01
0
5
x 10
10
15
Shocks
0.015
1
0.01
0.5
0.005
Z
*
Y
G
ξ*
0.01
0.005
0
0
5
10
15
20
0
0
20
5
10
15
20
0
0
5
10
15
20
5
Figure 7. Impulse response to liquidity shock ξ ∗
−3
1
−3
GDP
x 10
4
0
−3
Consumption (C)
x 10
3
2
2
0
1
Labor (L)
x 10
−1
−2
−3
0
5
10
15
20
−2
0
−4
−1
−6
0
5
10
15
20
−2
0
5
F F
Export and import value (ε P Q , ε M)
0.03
10
15
20
0.03
Exports
Imports
0.02
0.02
0.02
0.01
0.01
0
0
0
−0.01
0
5
10
15
20
−0.01
0
5
−3
0.1
0
10
15
20
−0.02
0
5
x 10
10
15
Shocks
Z
*
Y
G
ξ*
0.2
−1
0.15
0.05
20
−2
0.1
−3
0
0
5
10
15
20
−4
0.05
0
5
10
15
20
0
0
5
10
15
20
7
6
Table 6. Panel regression on simulated data: Profitability interaction
Data
log RER
0.527
(0.065)***
-1.604
log RER × PR
(0.954)*
log Y*
0.383
(0.055)***
log Y* × PR
-0.357
(0.155)**
log Agg TFP
-0.678
(0.103)***
log Agg TFP × PR
21.09
(1.436)***
log Firm TFP
2.295
(0.084)***
Cons
7.573
(1.626)***
# Obs.
9,994
Model
(2)
(3)
(4)
1.95
2.00
1.65
(-0.02, 3.8) (0.11, 3.84) (1.18, 2.21)
-0.25
-1.81
-0.58
(-0.3, -0.23) (-4.11, 0.56) (-1.39, 0.27)
2.19
2.28
2.36
2.17
(-17.9, 23.33) (-2.06, 6.61) (-1.88, 6.69)
(0.9, 3.29)
-2.32
-0.83
(-5.72, 1.25) (-2.03, 0.43)
-0.83
-2.32
-2.64
-1.16
(-29.32, 24.36) (-8.62, 2.99) (-8.89, 2.21) (-2.77, -0.17)
7.76
1.16
(0.24, 16.04) (-1.26, 3.96)
0.98
(0.97, 0.99)
(1)
1.95
(-7.4, 11.07)
26,752
(10536, 38688)
For the model, 95% bootstrap confidence intervals (with 1,000 simulations) are shown in parenthesis.
8
Figure 8. Response of exports to the exchange rate at extensive and intensive margins

Dynamics of Firms and Trade in General Equilibrium

Transcription

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