Online Appendix
Appendix 1. Definitions of job creation and destruction
The magnitude of JC in firm i in year t is represented as
𝑆
𝐶
𝐽𝐶𝑖,𝑡 = ∑ ∆𝑁𝑖,𝑑,𝑡,
𝑑=1
𝐶where 𝑑 is the index of division and ∆𝑁𝑖,𝑑,𝑡
is the change change in the number of workers in

job creating divisions:𝐶∆𝑁𝑖,𝑑,𝑡= 𝑁𝑖,𝑑,𝑡 − 𝑁𝑖,𝑑,𝑡−1 ,conditional on
𝑁𝑖,𝑑,𝑡 − 𝑁𝑖,𝑑,𝑡−1 > 0.
In the above equations, S is the number of divisions in firm i, 𝑁𝑖,𝑑,𝑡 is the number of workers
employed in division d in firm i in year t. Similarly, The magnitude of JD in firm i in year t isrepresented as𝑆
𝐷
𝐽𝐷𝑖,𝑡 = ∑ ∆𝑁𝑖,𝑑,𝑡,
𝑑=1
𝐷where ∆𝑁𝑖,𝑑,𝑡
is the change in the number of workers in job destroying divisions:𝐷∆𝑁𝑖,𝑑,𝑡= −(𝑁𝑖,𝑑,𝑡 − 𝑁𝑖,𝑑,𝑡−1 ),conditional on
𝑁𝑖,𝑑,𝑡 − 𝑁𝑖,𝑑,𝑡−1 < 0.
We note that newly established and closed firms are excluded because they are beyond the scopeof this study’s objectives. The reason is that such JC/JD instances significantly differ from thosein existing firms.

1Appendix 2. Additional figures and tables
Figure A1

Average employment change for Japanese FDI/non-FDI firms

80 (Persons)
60
40
20

0
-20
-40
-60
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016

-80

labor change in non-FDI firmlabor change in FDI firm

Source: Authors’ calculation based on BSJBSA.

2

Table A1 Robustness check: industry-average affiliates as IV
(1)

(2)

(3)

(4)

(5)

(6)

Dependent variable

JC

JC

JD

JD

Net

Net

Asia_affiliate

185.5**

144.1**−9.466−14.01

197.1***

154.1**(73.31)(72.90)(74.02)(74.03)(73.67)(74.04)–339.2***−301.6**−241.5*−239.3*−71.84–32.92(130.0)(128.2)(131.3)(130.2)(117.7)(116.4)–49.02***−43.71***

14.52***

18.66***–71.70*** −70.59***(3.305)(3.776)(3.337)(3.834)(3.302)(3.777)−1.332

16.93

30.04

28.73

–35.23–9.651(20.34)(20.37)(20.54)(20.69)(22.66)(22.77)−0.0964*** −0.0998*** −0.123*** −0.125*** −0.0403−0.0366(0.0233)(0.0233)(0.0235)(0.0237)(0.0280)(0.0279)–0.00544–0.00511

0.000261

9.79e–05−0.00832 −0.00701(0.0155)(0.0154)(0.0156)(0.0156)(0.0227)

EU_NA_affiliate

Capital_intensity

R&D share

Foreign_capital_share

Firm_age

TFP_LP−1.94842.37***−53.81***(7.816)(7.891)(8.075)ln_Revenue(0.0226)35.48***

39.12***−7.736(8.079)(8.204)(8.465)

Firm FE

Yes

Yes

Yes

Yes

Yes

Yes

Year FE

Yes

Yes

Yes

Yes

Yes

Yes

Observations

147,152

147,152

147,152

147,152

124,758

124,758

Number of firms

18,793

18,793

18,793

18,793

16,574

16,574

Cragg-Donald Wald F statistic

76.68

78.00

76.68

78.00

73.57

74.38

Notes: Standard errors are in parentheses. *** Significant at 1%. ** Significant at 5%. * Significant
at 10%. We use mean_Asia_affiliate and mean_EU_NA_affiliate as instrumental variables.

3

Table A2 Robustness check: export controlled; exchange rate as IV
(1)

(2)

(3)

(4)

(5)

(6)

Dependent variable

JC

JC

JD

JD

Net

Net

Asia_affiliate

15.33**

11.23*-12.32** -12.49** 24.49*** 20.39***(5.962)(5.977)(6.141)

EU_NA_affiliate

Capital_intensity

R&D share

Foreign_capital_share(5.223)(5.238)-33.88*** -36.44*** -43.04*** -43.36*** 6.522

4.183(7.613)(6.677)(7.619)(7.841)(6.158)(7.848)(6.668)-63.88*** -59.48*** 5.742

7.641** -70.28*** -67.53***(3.471)(3.535)(3.575)(3.641)(3.040)(3.098)-18.28

3.755

6.282

3.321

-19.296.426(24.69)(24.64)(25.43)(25.38)(21.62)(21.59)-0.0512* -0.0493-0.0124-0.0134-0.0482* -0.0453*(0.0311) (0.0311) (0.0320) (0.0320) (0.0272) (0.0272)
Firm_age

0.03140.03180.03560.0357-0.00124 -0.000869(0.0266) (0.0266) (0.0274) (0.0274) (0.0233) (0.0233)
TFP_LP-12.15**24.96***-36.43***(5.499)(5.664)(4.817)ln_Revenue

Export intensity

27.60***

19.74***

9.824**(4.875)(5.022)(4.273)

25.66

17.63

-21.66-21.1948.56*** 39.77***(15.87)(15.87)(16.35)(16.35)(13.90)(13.91)

Firm FE

Yes

Yes

Yes

Yes

Yes

Yes

Year FE

Yes

Yes

Yes

Yes

Yes

Yes

Observations

118,859

118,859 118,859 118,859 118,859 118,859

R-squared

0.005

0.005

0.005

0.004

0.008

0.008

Number of firms

15,535

15,535

15,535

15,535

15,535

15,535

Cragg-Donald Wald F statistic

30598

30601

30598

30601

30598

30601

Sargan statistic

0.330

0.252

0.197

0.168

1.093

0.848

Sargan test p-value

0.566

0.616

0.657

0.682

0.296

0.357

Notes: Standard errors are in parentheses. *** Significant at 1%. ** Significant at 5%. * Significant
at 10%. Instrumental variables are real effective exchange rates of Japan against Asian countries,
RER_Asia; regional real effective exchange rates of Japan against EU and North American countries,
RER_EU/NA; the number of Asian affiliates in the previous year, Lag_Asia_affiliate; and the numberof EU and North American affiliates in the previous year, Lag_EU/NA_affiliate.

4

Table A3 Robustness check: export controlled; industry-average affiliates as IV
(1)

(2)

(3)

(4)

(5)

(6)

Dependent variable

JC

JC

JD

JD

Net

Net

Asia_affiliate

185.4**

144.1**-8.845-13.61

196.5*** 153.9**(72.91)(72.65)(73.70)(73.85)(73.29)(73.89)-337.1*** -300.7**-253.0* -251.0* -57.24-20.06(129.4)(130.8)(115.4)

EU_NA_affiliate

Capital_intensity

R&D share

Foreign_capital_share

Firm_age

TFP_LP(129.7)(116.7)-49.03*** -43.72*** 14.57*** 18.77*** -71.74***-70.68***(3.326)(3.832)(3.362)(3.895)(3.313)(3.825)-1.428

16.87

30.57

29.37

-36.31-10.75(20.48)(20.55)(20.71)(20.89)(22.93)(23.11)-0.0961***-0.0997***-0.124***-0.126***-0.0379 -0.0345(0.0239)(0.0239)(0.0241) (0.0243) (0.0283) (0.0283)-0.00547-0.00512

0.000433 0.000277 -0.00882 -0.00747(0.0155)(0.0154)(0.0156) (0.0156) (0.0227) (0.0226)-1.98742.58***-54.03***(7.979)(8.066)(8.230)ln_Revenue

Export intensity(127.6)35.44***

39.53***-8.171(8.390)(8.528)(8.823)-4.008-1.850

22.34

23.09

-28.46-25.58(25.93)(25.93)(26.21)(26.36)(28.48)(28.72)

Firm FE

Yes

Yes

Yes

Yes

Yes

Yes

Year FE

Yes

Yes

Yes

Yes

Yes

Yes

Observations

118,859

118,859

118,859 118,859 118,859 118,859

R-squared

0.005

0.005

0.005

0.004

0.008

0.008

Number of firms

15,535

15,535

15,535

15,535

15,535

15,535

Cragg-Donald Wald F statistic

30598

30601

30598

30601

30598

30601

Notes: Standard errors are in parentheses. *** Significant at 1%. ** Significant at 5%. * Significant
at 10%. We use mean_Asia_affiliate and mean_EU_NA_affiliate as instrumental variables.

5

Table A4

Results of GMM estimation
(1)

(2)

(3)

(4)

(5)

(6)

Dependent variable

JC

JC

JD

JD

Net

Net

Asia_affiliate

83.90

85.13

-208.0**-209.7**233.4***

238.3***(96.99)(97.11)(95.38)(95.45)(86.21)(86.51)-195.1*-196.6*-321.1**-318.7**297.7**

296.0**(107.8)(107.9)(125.5)(125.7)(117.4)(117.9)-154.6***-159.3***117.7***

126.1***-269.6***-282.9***(22.57)(22.72)(24.70)(25.15)(27.28)(28.86)-26.78***-27.03***43.40***

43.77***-62.01***-62.31***(9.354)(9.431)(13.53)(13.46)(17.55)(17.67)0.01920.0193-0.134***-0.134***0.09180.0916(0.0423)(0.0423)(0.0398)(0.0398)(0.0569)(0.0570)0.02640.02640.03190.0319-0.00871-0.00924(0.0256)(0.0256)(0.0233)(0.0233)(0.0103)(0.0105)

EU/NA_affiliate

Capital_intensity

R&D share

Foreign_capital_share

Firm_age

TFP_LP-38.19***67.89***-111.1***(7.938)(12.41)(17.61)

ln_Revenue-38.69***68.56***-111.9***(8.080)(12.60)(17.90)Year FE

Yes

Yes

Yes

Yes

Yes

Yes

Observations

112,234

112,234

112,234

112,234

96,32696,326

Number of firms

17,737

17,737

17,737

17,737

15,654

15,654

Sargan statistic

834.4

832.4

437.4

438.1

303.7

301.2

Hansen statistic

52.42

52.33

49.25

49.34

54.49

54.36

Notes: Robust standard errors are in parentheses.
*** Significant at 1%. ** Significant at 5%. * Significant at 10%.
The results do not change when “Export_intensity” is included.

6

Appendix 3. Real effective exchange rate
The regional real exchange rate is constructed as follows. The bilateral real exchange rate of Japanagainst country 𝑐 in year 𝑡 is
𝑅𝐸𝑅𝑐,𝑡 =𝑁𝐸𝑅𝑐,𝑡 × 𝐶𝑃𝐼𝑐,𝑡,
𝑁𝐸𝑅𝐽𝑃𝑁,𝑡 × 𝐶𝑃𝐼𝐽𝑃𝑁,𝑡

𝑁𝐸𝑅𝑐 : US dollar per country 𝑐´s currency,
𝐶𝑃𝐼𝑐 : Consumer price index in country 𝑐,where 𝑁𝐸𝑅𝑐 and 𝐶𝑃𝐼𝑐 are obtained from IMF International Financial Statistics. Supposing 𝑐
is in Asia, its real exchange rate weighted by FDI stock is
𝐴𝑠𝑖𝑎
𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑_𝑅𝐸𝑅𝑐,𝑡=

𝐹𝐷𝐼𝑐,𝑡× 𝑅𝐸𝑅𝑐,𝑡 ,∑𝑘∈𝐴𝑠𝑖𝑎 𝐹 𝐷𝐼𝑘,𝑡

𝐹𝐷𝐼𝑐 : Japanese outward FDI stock to country 𝑐,where FDI stock data are obtained from JETRO. The regional real exchange rate of Japan against
Asian countries is then
𝑅𝐸𝑅𝑡𝐴𝑠𝑖𝑎 = 100 ×𝐴𝑠𝑖𝑎∑𝑘∈𝐴𝑠𝑖𝑎 𝑤 𝑒𝑖𝑔ℎ𝑡𝑒𝑑_𝑅𝐸𝑅𝑘,𝑡𝐴𝑠𝑖𝑎∑𝑘∈𝐴𝑠𝑖𝑎 𝑤 𝑒𝑖𝑔ℎ𝑡𝑒𝑑_𝑅𝐸𝑅𝑘,1996.

We normalise the 1996 level to 100. The regional real exchange rate of Japan against European
and North American countries is obtained in similar calculations.

7Appendix 4. Theory
1

Setting

We provide the full analysis of the theoretical part of the paper. Some explanations are overlappedwith those in the text. The base model is a search-and-matching model with heterogeneous jobs
developed by Wasmer (1999). Firms have two types of jobs in domestic activities: skilled andunskilled. We assume that an exogenous increase in FDI raises labor demand in a way that makes
the separation (or destruction) of both types of domestic jobs less likely.1 The expansion of foreign activities requires the support of headquarters and home branches through administration,customization, production for exports, and so forth. How much demand for a skilled job increases
relative to the other, however, depends on the destination of FDI. This differential impact of FDI
on demand for heterogeneous jobs is the key to our theoretical mechanism.
The economy consists of a continuum of risk-neutral, infinitely lived workers of size L and acontinuum of risk-neutral, infinitely lived firms of size one. The representative firm produces output
Y from capital stock K and employment N . The production function, Y = G(K, N ), is specified asa constant-returns-to-scale for both factors.2 The employment N consists of two types of workers:
N = Nh + Nl , where Nj is the mass of type-j ∈ {h, l} workers. The firm posts Vj of vacancies for j
job type at a cost cj . The matching process between firms and workers is costly in that unemployedworkers and vacancies meet each other randomly. The existing match of type j job breaks with anexogenous Poisson separation (destruction) rate sj . The two types of jobs differ in the following
way: the firm finds it costlier to search for high-skilled workers than low-skilled workers: ch > cl but
tends to continue the match with high-skilled workers longer than that with low-skilled workers:
sh < sl . The higher hiring cost for the high-skilled worker pays off in the longer continuation ofmatch, while the lower hiring cost for the low-skilled worker comes at the expense of the shorter
continuation.
The matching process is governed by a constant-returns-to-scale matching function, m(U, V ) =U η V 1−η , where U is the mass of unemployed workers, V= Vh + Vl is the mass of vacancies andη ∈ (0, 1) the matching elasticity. m(·) is the Poisson arrival rate so that there are on averagem∆t matches during a short time interval ∆t. We assume that the matching is formed sequentially.
First, m(U V ) matches are formed on average per unit of time between ex ante identical unemployedworkers and total vacancies. Then, m(U, Vh ) matched workers out of m(U, V ) get employed in thehigh-skilled job, while the remaining m (U, V ) − m(U, Vh ) matched workers in the low-skilled job.
The Poisson arrival rate of matching for a vacancy j ∈ {h, l} with an unemployed worker, denoted
1

This assumption is in line with the fact that outward FDI by Japanese multinationals is complementary to exports
of intermediate goods from home, which is likely to raise the demand for workers in home (Nishitateno, 2013).
2
Because all firms are symmetric and the mass of firms is one, variables for individual firms are also aggregate
ones. Thus, we omit the index of firms.

8

by qj , is thus:
qh ≡
ql ≡

m(U, V ) m(U, Vh )·= (θvh )−η ,Vhm(U, V )m(U, V ) m(U, V ) − m(U, Vh )q − v h qh·==Vlm(U, V )1 − vhθ−η 1 − vh1−η
1 − vh,where θ ≡ V /U ; vj ≡ Vj /V ; and q ≡ m (U, V ) /V = m(1/θ, 1) = θ−η . Given the vacancy-unemployment
share θ, both arrival rates decrease with the share of high-skilled vacancy vh . Higher vh makes eachhigh-skilled vacancy more difficult to match with an unemployed worker (lower qh ). It also raises themass of high-skilled match (higher m(U, Vh )/V = vh qh ) and, thus, crowds out low-skilled matches(lower ql ). The Poisson arrival rate of matching for an unemployed worker with a vacancy j isdefined similarly.
Job creation is measured by the mass of vacancies that match with unemployed workers. Aggregate job creation and high/low-skilled job creations (per unit of time) are given by:
JC = q · V = θ−η V = θ1−η U,
JCh = qh · Vh = θ−η vh1−η V = θ1−η vh1−η U,JCl = JC − JCh = θ−η 1 − vh1−η V = θ1−η 1 − vh1−η U.
Similarly, job destruction is measured by the mass of newly separated matches. Aggregate job
destruction and high/low-skilled job destructions (per unit of time) are given by:
JD =X

sj · Nj ,j=h,lJDj = sj · Nj .

2

Firm’s problem

The representative firm chooses the infinite-time schedule of capital investment I, capital stock K,
the mass of each type of vacancy Vj , and each type of employment Nj , to maximize the discounted
sum of the stream of future profits:
Z ∞max{I(t),K(t),Vh (t),Vl (t),Nh (t),Nl (t)} 0e−rt G(K(t), N (t)) −

X
j=h,l

9

{wj (t)Nj (t) + cj Vj (t)} − I(t) dt,

subject to the law of motion capital and the evolution of employment j ∈ {h, l}:K̇(t) = I(t) − δK(t),Ṅj (t) = qj (t)Vj (t) − sj Nj (t),where the dot represents the time derivative: ẋ ≡ dx/dt. The notations are defined as follows:r : interest rate,
XN=
Nj : total employment,
j=h,lwj : wage of type-j labor,
cj : vacancy cost for type-j job,qh = (θvh )−η : rate of a high-skilled vacancy matching with a unemployed worker,
ql = θ−η (1 − vh−η )/(1 − vh ) : rate of an low-skilled vacancy matching with a unemployed worker,
vh = Vh /V = Vh /(Vh + Vl ) : share of high-skilled vacancy,
sj : separation rate of type-j match.
Set the Hamiltonian as
H = G(K, N ) −X(wj Nj + cj Vj ) − I +

j=h,l

X

λj (qj Vj − sj Nj ) + µ(I − δK),

j=h,lwhere λj and µ are associated co-state variables. The necessary conditions are∂H= −cj + λj qj = 0,∂Vj∂Hrλj = λ̇j += λ̇j + GN − wj − λj sj ,∂Nj
→ λ̇j = (r + sj )λj − (GN − wj ),∂H= −1 + µ = 0,∂I
∂Hrµ = µ̇ += µ̇ + GK − µδ,∂K→ µ̇ = (r + δ)µ − GK ,lim e−rt λj (t)Nj (t) = 0,

t→∞

(A1)

(A2)
(A3)

(A4)

lim e−rt µ(t)K(t) = 0,t→∞where GK and GN respectively represent the derivative of G(·, ·) with respect to its first and second
argument. In what follows, we will focus on steady states where λ̇h = λ̇l = µ̇ = 0 and suppress the10

time index unless otherwise noted. From (A1) and (A2), we have
GN = wj + (r + sj )cj /qj ,(A5)which means that the marginal product of a worker must be equal to the wage plus the expected
recruitment cost. As we will see later, we assume that FDI changes the separation rate of each job
type sj differently depending on its destination, Asia or Europe/North America.
From (A3) and (A4), we have
GK = r + δ,(A6)which pins down the capital-labor ratio: k ≡ K/N . Letting g(k) ≡ G(K/N, 1), the property of
constant-returns-to-scale implies that GK = g 0 (k) and GN = g(k) − kg 0 (k). Once k is pinned downby (A6), GN is also determined.

3

Wage bargaining

Let Jj be a marginal value to the firm from hiring one type-j ∈ {h, l} worker. This must be equal
to the discounted sum of the flow profit and the expected future profits, Letting ∆t be a small timeinterval, the following must hold:1[(GN − wj )∆t + (1 − sj ∆t) · Jj + sj ∆t · 0],
1 + r∆t
G N − wj.
→ Jj =
r + sjJj =(A7)On the other hand, the marginal value to the firm from posting a vacancy for type-j worker is zero
because all vacancy opportunities are exhausted by many atomistic firms.
The value to the type-j worker Wj and the value of an unemployed worker WU are respectivelyrWj = wj + sj (WU − Wj ),X
rWU = z +θj qj (Wj − WU ),

(A8)
(A9)

j=h,l

where z is an unemployment benefit. Once matched, the firm and the worker engage in the generalized Nash bargaining, resulting in the following sharing rule:
Wj − WU : Jj − 0 = β : 1 − β,→ Wj − WU =

11

βJj
,
1−β

(A10)

where β ∈ (0, 1) represents the worker’s bargaining power and as noted earlier the value of themarginal vacancy is zero.
From (A5) and (A7) to (A10), we have(r + sj )(Wj − WU ) = wj − rWU ,→ (r + sj ) ·∵ (A8)

β G N − wj
= wj − rWU ,1 − β r + sj

→ β(GN − wj ) = (1 − β)(wj − rWU ),X→ wj = βGN + (1 − β) · z +
θj qj (Wj − WU )

∵ (A7)&(A10)∵ (A9)

j=h,l


G
−
w
β
j
N
→ wj = βGN + (1 − β) · z +
θ j qj ·1 − β r + sj
j=h,l

X
(r + sj )cj /qj→ wj = βGN + (1 − β)z + βθ j qj ·,r + sjj=h,lX→ wj = βGN + (1 − β)z + β
θj cj = w.
X

∵ (A7)&(A10)∵ (A5)
(A11)

j=h,l

The wage turns out to be common between the two types of workers. This result comes from thefacts that both types of job have the same productivity and that they are perfect substitute inproduction.
As we will see later, FDI affects the two types of job vacancies differently depending on its
destination, Asia or Europe/North America. This heterogeneous impact changes the average searchPPcost per unemployed worker, j θj cj = j cj Vj /U , and then affects the bargaining position between
the matched firm and workers.

4

Coexistence of the two types of jobs

4.1

Steady-state equilibrium

From (A5), we have
wh = GN − ch (r + sh )(θvh )η ,(A12)

wl = GN − cl (r + sl )θη (1 − vh )/(1 − vh1−η ).

(A13)

We see that the wage of each type of job, wj , decreases with the share of vacancy for the job, vj ,implying that these two equations can be thought of as the labor demand curves for each type of

12

job.3 The wage-setting curves are given by (A11):
wh = βGN + (1 − β)z + βθX

vj cj ,

(A14)

vj cj .

(A15)

j=h,l

wl = βGN + (1 − β)z + βθ

X
j=h,l

Equations through (A12) to (A15) determine the steady-state values of (wh , wl , θ, vh ).
We use (A12) and (A13) to obtainch (r + sh )(θvh )η − cl (r + sl )θη (1 − vh )/(1 − vh1−η ) = 0,
→ ch (r + sh )vhη (1 − vh1−η ) − cl (r + sl )(1 − vh ) = 0,
→ ch (r + sh )vhη + [cl (r + sl ) − ch (r + sh )]vh − cl (r + sl ) = 0,
→ vhη + (ec − 1)vh − ec = 0,(A16)

where ec ≡ cl (r + sl )/ch (r + sh ),which determines vh . We impose restrictions on parameters to ensure that both types of jobs coexistc − 1)evh − ec. From the facts
at the steady states. Let us define a function such that H(evh ) = vehη + (ethat H(evh = 0) = −ec < 0 and H(evh = 1) = 0, the condition for H(evh ) = 0 to have a solution forve ∈ (0, 1) is that an infection point of H(evh ) must be in [0, 1]. The unique infection point is derivedas
0 = H 0 (evh ) = ηevhη−1 + ec − 1,

 1
1−η
η
#
→v =
.
1−e
c
v # is in (0, 1) if η + e
c < 1, in which case G(ṽh ) = 0 has a unique solution such that vh ∈ (0, v # ).
The condition will be assumed in the following analysis.

4.2

Stability

We will check that (a) vh , the unique solution of (A16), constitutes a unique stable steady state
and that (b) the corner solutions, vh ∈ {0, 1}, are unstable. From (A1) and (A2), we have the lawsof motion for qh :q̇h /qh = (GN − wh )qh−η /ch − (r + sh ),It can be checked that ∂wh /∂vh = −ηch (r + sh )θη vhη−1 < 0; ∂wl /∂vl = −∂wl /∂vh = −cl (r + sl )θη vhη (1 − η −ec)(1 − vh )/(vh − vhη )2 , noting that vhη + (ec − 1)vh − ec = 0 and 1 − η − ec > 0, as we will see shortly.
3

13

where qh is a function of vh such that qh = (θvh )−η . Since (A12) implies GN > wh , q̇h /qh decreases
with qh , which ensures the stability of the steady state at which q̇h /qh = 0.
Next, we consider two endpoints. At vh → 0, we have
lim q̇h /qh = ∞ > (GN − wl )θ−η − (r + sl ) = q̇l /ql ,vh →0in which case the firm posts more vacancies for high-skilled job so that vh ' 0 is unstable. The
result is rather intuitive because very few vacancies increases their filling rate significantly due tofewer rivals, resulting in more job postings in the future. Similarly, we can check that vh ' 1 isunstable. We thus conclude that vh satisfying (A16) is the unique stable steady state.

5Effect of FDI

We model FDI as a decrease in the separation rate: ∂sj /∂F DI < 0. We consider the effect of FDI
in the short run where only jump variables, i.e., vacancies Vj , wages wj , respond to changes in FDI.
Given Nj , FDI decreases job destruction of both types of jobs:
∂sj
∂JDj
=
Nj < 0,∂F DI∂F DI
which immediately implies that FDI also decreases aggregate job destruction:
X ∂sj
∂JD
=
Nj < 0.
∂F DI
∂F DI
j=h,l

To see the effect of FDI on job creation, we need to know how FDI affects the share of highskilled vacancy, vh , and the vacancy-unemployment ratio, θ. Applying the implicit function theoremto (A16), we obtainvh0 =ec0 (1 − vh ),
ηvhη−1 + ec−1
1 − vhr + sh s0h s0l cl (r + sl )=− 0
2
r + slsl ch (r + sh ) ηe
c/vh − (1 − η)(1 − e
c)
{z
}
|
{z
}|

(A17)

<0

R0


< 0 if s0 /s0 < S b ≡ (r + sh )/(r + sl )h l=,≥ 0 if s0 /s0 ≥ S b
h l
where

vh0 ≡

∂vh
,
∂F DI

s0j ≡

∂sj
< 0,
∂F DI

s0 cl (r + sl )
∂e
c
e
c ≡
= l
∂F DI
ch (r + sh )20

r + sh s0h− 0
r + slsl

The sign of vh0 is determined by whether s0h /s0l is greater than S b ≡ (r + sh )/(r + sl ).

14


.

From (A12) and (A14), we havech (r + sh )(θvh )η + βθ[ch vh + cl (1 − vh )] − (1 − β)(GN − z) = 0.
Differentiating both sides with respect to F DI gives
ch s0h (θvh )η + ηch (r + sh )(θvh )η−1 (θvh0 + vh θ0 ) + βθ0 [ch vh + cl (1 − vh )] + βθvh0 (ch − cl ) = 0,
where θ0 ≡

∂θ
.
∂F DI

This is simplified to[ηvh0 /vh + s0h /(r + sh )][(1 − β)(GN − z) − βθg] + βθvh0 (ch − cl ),(1 − β)(GN − z)η/θ + βf (1 − η)
Θ1 s0h − Θ2 s0l=,ch (r + sh )2 [(1 − β)(GN − z)η/θ + βf (1 − η)][ηec − vh (1 − η)(1 − ec)]> 0 if s0 /s0 < S d ≡ Θ2 /Θ1h l,=≤ 0 if s0 /s0 ≥ S d

θ0 = −hwhere f ≡

X

(A18)

l

vj cj ,x ≡ (1 − β)(GN − z) − βθf > 0,j=h,l

Θ1 ≡ vh ch (r + sh )[βθ(1 − vh )ec(ch − cl ) + x(1 − η − ec)] > 0,
Θ2 ≡ cl (r + sh )(1 − vh )[ηx + βθvh (ch − cl )] > 0,
and where we used the following relation:ch (r + sh )(θvh )η = (1 − β)(GN − z) − βθf > 0.

∵ (A12)&(A14)

Job creation, defined as JC = θq(θ)U = θ1−η U , is an increasing function of θ given U and thus
decreases (or increases) with F DI if s0h /s0l < S d (or s0h /s0l > S d ).
With these in hand, we can see the effect of FDI on job creation of the two types of jobs. It can15be checked that JCh = (θvh )1−η U always increases with F DI:∂[(1 − η)(θvh )−η (vh θ0 + θvh0 )U ]∂JCh=,∂F DI 
∂F DI

∂JCh
= sign{θ0 /θ + vh0 /vh },→ sign
∂F DI




0
0
2
= sign (Γ2 sl − Γ1 sh )/ [ch (r + sh ) (ηx + βθf ){ηec − vh (1 − η)(1 − e
c)}]
|
{z
}

>0


= sign Γ2 s0l − Γ1 s0h


> 0
≤ 0

if s0h /s0l > S a ≡ Γ2 /Γ1,

if s0h /s0l ≤ S a

where Γ1 ≡ ch (r + sh )[x{ηec − vh (1 − η)(1 − ec)} + βθcl ec(1 − vh )] > 0,
Γ2 ≡ βθc2l (r + sh )(1 − vh ),Sb − Sa =xch (r + sh )2 [ηec − vh (1 − η)(1 − ec)]r + sh Γ2−=> 0.
r + slΓ1Γ1 (r + sl )JCh increases (or decreases) with F DI if s0h /s0l > S a (or s0h /s0l < S a ).
On the other hand, JCl = JC − JCh = θ1−η (1 − vh1−η )U may increase or decrease with F DI
depending on s0h /s0l :∂[(1 − η)θ−η {(1 − vh1−η )θ0 − θvh−η vh0 }U ]∂JCl=,
∂F DI 
∂F DI

∂JCl
→ sign= sign{ec(1 − vh )θ0 − θvh0 }
∂F DI







3
−1
2
0
0
c − vh (1 − η)(1 − ec)}= sign (Ω1 sh − Ω2 sl )/ {cl (1 − vh )} · vh ch (r + sh ) (ηx + βθf ){ηe

|
{z
}


>0


> 0 if s0 /s0 < S c ≡ Ω2 /Ω1

h l
0
0
,
= sign Ω1 s1 − Ω2 s2
≤ 0 if s0 /s0 ≥ S c
h l



r + slwhere Ω1 ≡ vh ch (r + sh )(r + sl ) (1 − ec){x + βθvh (ch − cl )} + βθcl 1 +
−e
c
> 0,
r + shr + sl22Ω2 ≡ ch (r + sh ) βθ(ch − cl )(1 − ec)vh + ηx(1 − ec) + βθcl 1 +−ecvh + ηxec > 0,
r + shxvh c2h (r + sh )3 (ηx + βθf )[ηec − vh (1 − η)(1 − e
c)]
Θ2 Ω2
Sd − Sc =
−
=
> 0.
Θ1 Ω1
Θ1 Ω1
We summarize the results in the following proposition.

Proposition.

Assume that (i) an exogenous increase in FDI decreases the job-separation rate16

sj ; (ii) the relative cost of high-skilled vacancy is sufficiently high, i.e., η + e
c < 1 or ch /cl >(r + sl )/[(1 − η)(r + sh )]; and (iii) the marginal product of labor is sufficiently high, i.e., x > 0 orP
GN > z + β j vj cj /(1 − β). Depending on the magnitude of the effect of FDI on sh relative to thaton sl , i.e., s0h /s0l , we obtain the following comparative-statics results.

s0h
∂sh
∂sl
≡
0
sl
∂F DI ∂F DI[0, S a )

∂JC
∂F DI
+

∂JCh
∂F DI
−

∂JCl
∂F DI
+

∂vh
∂F DI
−

[S a , S b )

+

+

+

−

(ii)

[S b , S c )

+

+

+

+

(iii)

[S c , S d )

+

+

−

+

(iv)

[S d , ∞)

−

+

−

+

(v)

Case
(i)

We note that the effects of FDI on aggregate job destruction, high-skilled job destruction, and lowskilled job destruction are always negative.

We suppose that FDI to Asia decreases sl much significantly than sh , corresponding to case (i).
Then it leads to an expansion of total job creation and low-skilled job creation, and an contractionof high-skilled job creation. On the other hand, we suppose that FDI to Europe or North America
has an exactly opposite effect of job separations rates, corresponding to case (v). It results in an
opposite effect on total job creation, and high/low-skilled job creations.

References
Nishitateno, S. (2013). Global production sharing and the FDI–trade nexus: New evidence from theJapanese automobile industry. Journal of the Japanese and International Economies, 27:64–80.
Wasmer, E. (1999). Competition for jobs in a growing economy and the emergence of dualism.
Economic Journal, 109(457):349–371.

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