IMES DISCUSSION PAPER SERIES

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Perspective Broad-Perspective Review Series
Review

Role of Foreign Direct Investment as a Long-term
Capital Flow Channel
Naohisa Hirakata and Mitsuru Katagiri
Discussion Paper No. 2024-E-5

INSTITUTE FOR MONETARY AND ECONOMIC STUDIESBANK OF JAPAN
2-1-1 NIHONBASHI-HONGOKUCHOCHUO-KU, TOKYO 103-8660
JAPAN

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IMES Discussion Paper Series 2024-E-5
June 2024

Role of Foreign Direct Investment as a Long-term
Capital Flow Channel

Naohisa Hirakata* and Mitsuru Katagiri**
Abstract
This paper investigates the role of foreign direct investment (FDI) in accounting forthe long-term trend of capital flows under demographic changes. For this purpose,
we incorporate horizontal FDI under the proximity-concentration trade-off into a
two-country DSGE model and conduct a quantitative analysis using long-term
Japanese data for capital flows since the 1960s. The quantitative analysis finds thatthe transition dynamics solely driven by demographic changes well account for the
long-term trend of capital flows and that multinational firms’ endogenous decisionon FDI in response to population aging is key to explaining the long-term trend.

Keywords: Capital flows; Demographic changes; Foreign direct investment (FDI)
JEL classification: F12, F23, F32*General Manager, Niigata Branch, Bank of Japan (E-mail: haohisa.hirakata@boj.or.jp)**Associate Professor, Faculty of Business Administration, Hosei University (E-mail:mitsuru.katagiri@hosei.ac.jp)
We would like to thank Kosuke Aoki, Gianluca Benigno, Hirokazu Ishise (discussant), Takashi
Kano (discussant), and Kiminori Matsuyama for their helpful suggestions and comments. We
also appreciate the comments of seminar participants at the Bank of Japan, Hosei University,
Waseda University, GRIPS, the 23rd Japanese Macroeconomic Conference, and the 2022
Australasia Meeting of the Econometric Society. Views expressed in this paper are those of theauthors and do not necessarily reflect the official views of the Bank of Japan. This work was
supported by the Japan Society for the Promotion of Science (KAKENHI, Grant No.22K01509).

1

Introduction

Foreign direct investment (FDI) is characterized by two distinct but closely related aspects.
First, FDI is a main channel of international capital flows, along with foreign portfolio investment (FPI). Particularly, FDI accounts for a substantial share of the long-term trendof capital flows in many countries. Second, on the production side, FDI is a main tool
for multinational firms to capture foreign demands. These two aspects of FDI can beinterpreted as two sides of the same coin, as capital flows associated with FDI aim at
financing multinational firms’ production in foreign countries. Hence, modeling multinational firms’ decisions on FDI is key to understanding the long-term trend of international
capital flows, as well as the resultant sectoral savings in the Flow of Funds.
In this paper, we investigate the role of FDI as a capital flow channel by incorporating
horizontal FDI under the proximity-concentration trade-off à la Helpman et al. (2004) intoa two-country DSGE model. Although the importance of FDI in accounting for capital
flows has been long recognized in the empirical literature, quantitative analysis focusing
on the role of FDI as a capital flow channel is novel. In the open economy macroeconomics
literature, on the one hand, most previous studies do not distinguish FDI from other capital
flows and discuss the dynamics of capital flows by assuming only one type of aggregate
capital. On the other hand, in the international trade literature, most previous studies
do not refer to FDI as a capital flow channel but investigate FDI only as multinational
production. Hence, this paper’s theoretical contribution is to bridge the gap between
them by modeling the dual aspect of FDI, i.e., capital flows and multinational production,
in a unified framework. Namely, in our model, households and firms accumulate domestic
and foreign capital as in a standard open-economy macroeconomic model; however, incontrast to previous studies, the model assumes that there exist two forms of foreign
assets, FPI (riskless bonds) and FDI, and that heterogeneous firms with respect to theirproductivity choose between exports and FDI under the proximity-concentration trade-off.
Our motivation to investigate the role of FDI as a capital flow channel is based on
the Japanese experiences for the last six decades. The left panel in figure 1 shows thesubstantial changes in the Japanese current account and its composition, i.e., trade andincome balance, since the 1960s. It indicates that the income balance surplus (the green linewith x-marks) has significantly increased recently, along with the decline in trade balance1Figure 1: Current account in Japan
6

3
2.5

4

Income from FDI
OthersIncome balance

2
2

1.5
1

0

0.5
Current accountTrade balance
Income balance

-2

-4
1960

0
-0.5

1970

1980

1990

2000

2010

2020

2000

2005

2010

2015

2020

Note: The left panel shows the Japanese current account and its composition, i.e., trade and income balance,since the 1960s. The right panel shows changes in the ratios of income balance surplus to nominal GDP
since 1996. The income from FPI includes those from all types of investment other than FDI. The share of
the income from FDI and FPI is available only from 1996 because their definitions differ between before andafter 1996.
Sources: Balance of payments statistics, Bank of Japansurplus (the red dashed line). Furthermore, as shown in the right panel in figure 1, thisrecent rise in income balance surplus is mostly explained by increased income from FDI.
As a result, FDI also plays a vital role in accounting for sectoral savings in the Flow ofFunds. Figure 2 shows that corporate savings have been increasing since around 1990 (thered line with x-marks in the left panel) and that more than half of corporate savings since2010 is accounted for by an increase in outward FDI (the black bars in the right panel).
Specifically, corporate savings in Japan are around zero when excluding FDI from firms’
financial assets.
In the quantitative analysis, we compute transition dynamics based on past and future
projections of demographics in Japan and examine the role of FDI through a counterfactual
simulation for FDI openness. Based on previous studies, we choose demographic changes
as the sole driver for international capital flows in our quantitative analysis. The previous
studies demonstrate that the long-run trend of international capital flows is primarily
accounted for by demographic changes, rather than other factors such as productivity

2

Figure 2: Sectoral saving in Japan
10

Household
Corporate
Overseas
Government

10

5

5
0
0
-5
-5

-10
1980

Cash and Deposit
FDI
Loan (-)
OthersCorporate Savings
Corporate Savings (excl. FDI)

-10

1990

2000

2010

-15
1980

2020

1990

2000

2010

2020

Note: The left panel shows sectoral savings in the Flow of Funds in Japan since 1980. The right panel
decomposes the corporate savings into FDI (the black bars) and other major components.
Source: Flow of Funds, Bank of Japan

growth or fiscal policy, and emphasize that the share of the working-age population has
particularly crucial effects on capital flows through labor supply. While Japan is a leading
example of such rapid demographic changes, population aging is becoming one of themost important long-term economic challenges in many advanced and Asian emerging
market economies, particularly China. Hence, the Japanese experience with the effects ofdemographic changes on capital flows should have implications for those other countries
that are expected to face such challenges in the future.
The main results of the quantitative analysis are summarized as follows. First, thelong-run trend of the current account, including its composition, i.e., trade and income
balance, and the composition of sectoral savings, can be fairly well accounted for solely bydemographic changes. The consumption and savings behavior of households to smoothconsumption is key to understanding these results. Specifically, in anticipation of population aging, households accumulate a part of their capital as foreign assets, resulting in thelarge trade surplus and the high household savings rate observed in Japan until the 1990s.
Nevertheless, once the working-age population started to decrease in around 2000, they
saved less and relied more on the returns on foreign assets, making the model consistent3with the recent decrease and increase in trade and income balance surplus, as well as thedecline in the household savings rate. The forecasting path based on population projection
indicates that those trends will continue and that trade and income balance surplus willreach around -5% and 5% of GDP in 2050, respectively. Interestingly, those simulation results for the past and future developments in capital flows in Japan are consistent with thewell-known “stages-of-the-balance-of-payments hypothesis,” implying that demographic
changes may be one of the driving forces to explain the hypothesis.
Second, we find that multinational firms’ endogenous decisions on FDI play a crucialrole in explaining the dynamics of the current account, particularly its composition, underdemographic changes. In our model, a decline in the working-age population raises domestic labor costs, thus encouraging productive firms to produce more in foreign countries
through FDI rather than export. Thus, due to the endogenous choice between exports and
FDI, the trade balance surplus has substantially declined, while the income balance has
increased. Quantitatively, the baseline simulation driven only by demographics accounts
for around half of the recent rise in outward FDI in Japan. On the other hand, when we
do not incorporate such an endogenous choice between exports and FDI as in a standard
international trade model, productive firms would do their business abroad only throughexports, even in the face of the decline in the working-age population; therefore, the model
without FDI cannot replicate the rise in income balance surplus observed in Japan.
Literature Review

In the previous literature, while the difference between FDI and FPI

has been intensively examined in light of, for instance, information asymmetricity or
institutions (e.g., Albuquerque, 2003; Goldstein and Razin, 2006; Daude and Fratzscher,2008), most studies in the open economy macroeconomics literature ignore the difference
between them. Notable exceptions are McGrattan and Prescott (2009, 2010) and McGrattan(2012), which distinguish FDI from other types of capital to investigate the welfare gainfrom FDI openness or the effects of intangible assets on FDI returns of the U.S. multinationalfirms. Also, Russ (2004) incorporates FDI into a two-country DSGE model with money
to investigate the relationship between FDI and exchange rate volatility. Those studies,
however, do not take into account the recent advances in the international trade literature,including the proximity-concentration trade-off between export and horizontal FDI as
investigated in, for example, Brainard (1997), Markusen and Venables (2000) and Helpman4

et al. (2004). To the best of our knowledge, our paper is the first study to introduce thechoice between exports and horizontal FDI by heterogeneous firms under the proximityconcentration trade-off into a DSGE model. In so doing, our paper is highly indebted to themethodology for aggregation proposed by Ghironi and Melitz (2005), which incorporates
the entry decision to export markets by heterogeneous firms into a DSGE model. Our
paper also contributes to the literature on the relationship between demographics andcapital flows. While our quantitative result is not new but in line with previous studies
emphasizing the importance of demographics, such as Domeij and Floden (2006), Krueger
and Ludwig (2007), Ferrero (2010), Backus et al. (2014) and Sposi (2019), none of theprevious studies focus on the role of FDI. Finally, our paper sheds new light on theliterature about the rise in global corporate savings (e.g., Chen et al., 2017). While theliterature points out numerous factors contributing to the recent rise in corporate savings,
our quantitative exercise implies that an increase in foreign asset accumulation by nonfinancial firms through FDI can be added to the list of those factors, at least in Japan.
The rest of the paper is organized as follows. In Section 2, we formulate our model.
Section 3 conducts a quantitative analysis focusing on the Japanese economy. Concluding
remarks are given in Section 4.

2

Model

The economy consists of two countries, home and foreign. An asterisk denotes foreign
variables. The model structure is a kind of mixture of standard models in open-economy
macroeconomics and international trade. Namely, households accumulate domestic andforeign capital as in a standard open-economy macroeconomic model; however, in contrast to previous studies, the model assumes that there exist two forms of foreign assets,
FPI (riskless bonds) and FDI, and that heterogeneous firms concerning their productivity
choose between exports and FDI under the proximity-concentration trade-off as in Helpman et al. (2004). In what follows, we first describe optimization in both a final goods
firm and an intermediate goods firm and then characterize the household’s behavior andaggregate dynamics.

5

2.1

Final Goods Firm

The representative final goods firm in the home country produces the final good, Yt , byaggregating the intermediate goods, yt (ω), using the CES aggregator:
Z
Yt =

ω∈Ωt

yt (ω)

θ−1
θ

θ
! θ−1

dω

,

where θ is the elasticity of substitution and Ωt is the set of available intermediate goods inthe home country in period t. Let pt (ω) be the price of each intermediate good. The priceindex in the home country, Pt , is defined as:
Z
Pt =

ω∈Ωt

1
! 1−θ
,
pt (ω)1−θ dωand the demand for each intermediate good is derived as a result of profit maximizationof the representative final goods firm:pt (ω)yt (ω) =
Pt

!−θ
Yt .

(1)

The price index and the demand for each intermediate good in the foreign country, P∗t andy∗t (ω), are defined similarly. Note, however, that the set of available intermediate goods inthe home and foreign country are not necessarily the same, i.e., Ωt , Ω∗t .

2.2

Intermediate Goods Firm in Domestic Market

There is a continuum of intermediate goods firms in each country. They are different
with respect to the intermediate goods they produce, ω ∈ Ω, and their productivity, z(ω).
In the home country, the intermediate goods firms produce using labor, l, and capital, k,according to the following Cobb–Douglas technology:yt (ω) = z(ω)kt (ω)α lt (ω)1−α ,(2)where α is the capital share. We assume that the firms’ idiosyncratic productivity, z, isconstant over time as in Melitz (2003). The maximization problem for the intermediate6

goods firms is:max

pt (ω)yt (ω) − wt lt (ω) − rk,t kt (ω),Pt

(3)

subject to (1) and (2). wt and rk,t are the real wage rate and the real rental rate of capitalin the home country at period t. Hereafter, each firm’s optimized policy is characterized
as a function of idiosyncratic productivity z because the intermediate goods firms areheterogeneous with respect only to z and symmetric for all other aspects.
As a consequence of the above optimization problem, the intermediate goods firms
charge a price that includes a proportional markup, θ/(θ − 1), over their effective marginalcost. Let pt (z) be the price charged by the intermediate goods firms with productivity z.
Then, the intermediate goods price relative to the price index is given by:
ρt (z) ≡pt (z)
θ λt
,
=
Pt
θ−1 z

where λt is the marginal cost of production, which is defined by:λt ≡rαk,t w1−αtαα (1 − α)1−α.

Furthermore, the demand for capital and labor is given by:
kt (z) =
and



1
α
1−
ρt (z)1−θ Yt
rk,t
θ



1−α
1
lt (z) =1−
ρt (z)1−θ Yt .
wtθFinally, the profit of the intermediate goods firms becomes:
dt (z) =1
ρt (z)1−θ Yt .
θThe profit of the intermediate goods firms is distributed to the stockholders.
In the foreign country, we can describe the behavior of intermediate goods firms in thesame manner. We can similarly derive their price, ρ∗t (z), demand for capital and labor, kt∗ (z)and l∗t (z), and profit, d∗t (z).

7

2.3

Export and Foreign Direct Investment

The intermediate goods firms can do business in the other country in addition to theirown country. In so doing, there are two ways: export or FDI. The intermediate goods
firms would be involved in exporting (or FDI) if the expected profit from export (or FDI)
is positive. In what follows, we will describe the entry decision for the exporting and FDI
market. While we mainly focus on the decisions by intermediate goods firms in the homecountry, those in the foreign country are described similarly.
Export and FDI are different in terms of cost structure and hiring. When the intermediate goods firms export, they need to pay a fixed cost, fX . The fixed cost is measured
by effective labor in their own country, wt fX , in real terms. In addition, exporting theirproducts to the other country requires an iceberg-type trade cost, τ. When the intermediate goods firms conduct FDI, on the other hand, they only need to pay a fixed cost fI .
While they do not need to pay any variable costs to carry out FDI, the fixed cost for FDI
is assumed to be larger than that for exporting (i.e., fX < fI ) as in Helpman et al. (2004)
to capture the proximity-concentration trade-off. In addition to the difference in the cost
structure, export and FDI are different in terms of labor cost. The exporting firms in thehome country hire their workers in the home country, while the FDI firms in the homecountry hire their workers in the other country. Therefore, the FDI firms’ production
function is characterized by yt (ω) = zktα l∗1−α, and their labor cost as well as the fixed costt
are measured by the wage rate in the foreign country, w∗t .
Under these assumptions, we can derive prices, labor demand, capital demand, andprofits for the exporting and FDI firms. Hereafter, variables for the exporting and FDI
firms are denoted by the subscripts X and I, respectively. Let pX,t (z) and pI,t (z) be the prices
charged by the exporting and FDI firms with productivity z. Then, the prices charged by
the exporting and FDI firms relative to the price index in the other country, P∗t , are givenby:ρX,t (z) ≡pX,t (z)τ θ λX,t=∗
Pt
Qt θ − 1 zandρI,t (z) ≡pI,t (z)θ λI,t
=
,
∗
Pt
θ−1 z

where Qt is the real exchange rate based on the price indices. While the marginal cost forexporting firms is the same as that of the domestic firms (i.e., λX,t = λt ), the marginal costof FDI firms is different from that for domestic and exporting firms because they have tohire their workers in the foreign country and because the return from FDI should consider
8exchange rate changes. That is, the marginal cost for the FDI firm in the home country isdefined by:
λI,t ≡

rαk,I,t w∗1−αtαα (1 − α)1−α,where rk,I,t is the rental rate of capital for FDI firms. The capital demand of exporting and
FDI firms is:
kX,t (z) =



Qt α
1
1−
ρX,t (z)1−θ Yt∗
rk,t
θ

and

kI,t (z) =αrk,I,t1−1
ρI,t (z)1−θ Yt∗ .
θ

Note that the capital demand is driven by the aggregate demand in the foreign country,
Yt∗ , rather than that in the home country. As for the labor demand of exporting and FDI
firms, they must hire labor for production as well as for operational fixed costs. Thus, thelabor demand for exporting and FDI firms is given by:
lX,t (z) =andQt (1 − α)11−ρX,t (z)1−θ Yt∗ + fX
wt
θ



1−α
1
lI,t (z) =1−
ρI,t (z)1−θ Yt∗ + fI .
∗wt
θNote that the FDI firms pay their labor cost based on the foreign country’s wage rate, w∗t .
Finally, the profit of the exporting and FDI firm becomes:
dX,t (z) =Qt
ρX,t (z)1−θ Yt∗ − wt fXθ

anddI,t (z) =1
ρI,t (z)1−θ Yt∗ − w∗t fI .
θ

As mentioned before, the intermediate goods firms would enter the exporting market or
the FDI market if their profit was positive. That is, the intermediate goods firms would
enter: (i) the exporting market if dX,t > 0 and dX,t > Qt dI,t , (ii) the FDI market if Qt dI,t > 0
and Qt dI,t > dX,t , and (iii) neither the exporting nor FDI market otherwise.
Because of the scale economy caused by fixed costs, fX and fI , only productive andlarge firms do business in the other country through export or FDI. Moreover, because of
the assumption of fI > fX , the FDI firms are more productive and larger than the exporting
firms, as in Helpman et al. (2004). Let zX,t and zI,t be the thresholds for exporting and FDI.
That is, dX (zX,t ) = 0 and dI (zI,t ) = 0. Then, the intermediate firms’ decision is summarized9

as follows.
Only domestic market
if z ≤ zXDomestic and exporting market if zX < z ≤ zI





 Domestic and FDI market
if z > zI

2.4

Aggregation

The aggregation of the firm sector is not trivial because intermediate goods firms areheterogeneous with respect to their productivity z. Here, to make the model tractableenough to conduct a quantitative exercise, we follow Ghironi and Melitz (2005) to aggregate
the firm sector. First, the productivity distribution of the intermediate goods firms isassumed to be Pareto distributed with lower bound zmin and shape parameter κ > θ − 1,
i.e., G(z) = 1 − (zmin /z)κ . Let the total mass of intermediate goods firms be Nt . Then, thefraction of intermediate firms that enter the exporting market and FDI market is:
!κ


NX,t
zmin
zmin κ
−
=
Nt
zX
zI,t

and

NI,t
zmin
=
Nt
zI,t

!κ
,

where NX and NI are the mass of exporting and FDI firms, respectively. Next, we define akind of average productivity, z̃ as follows:
"Z ∞
z̃ ≡

θ−1

z

#1/(θ−1)dG(z)= νzmin ,zmin

where ν ≡ [κ/(κ − θ + 1)]1/(θ−1) . Similarly, we define the average productivity for theexporting and FDI firms in period t as follows:1!κ !−1!κ !−1  θ−1
 θ−1

zI,t
zX,t

z̃X,t ≡ ν zI,t 1 −+ zθ−1
X,t 1 −
zX,t
zI,t

and

z̃I,t ≡ νzI,t .

As in Melitz (2003) and Ghironi and Melitz (2005), the average productivity is sufficient
statistics that summarize all information regarding the productivity distribution. Hence,the economy can be aggregated as if there exist Nt intermediate goods firms with productivity z̃. Furthermore, the exporting and FDI markets can be considered as if there exist
NX firms with productivity z̃X in the exporting market and NI firms with productivity z̃I10

in the FDI market, respectively. Hereafter, we denote the average for any variables, x, as
follows:x̃t ≡ xt (z̃), x̃X,t ≡ xX,t (z̃X,t ) and x̃I,t ≡ xI,t (z̃I,t ).
For example, the average prices are defined by: p̃t ≡ pt (z̃), p̃X,t ≡ pX (z̃X,t ) and p̃I,t ≡ pI (z̃I,t ).
Given these average productivities, the price index is redefined. It is easily shown thati1/(1−θ)h∗∗, which is equivalent to:(p̃∗I,t )1−θ(p̃∗X,t )1−θ + NI,t
Pt = Nt (p̃t )1−θ + NX,t∗∗Nt (ρ̃t )1−θ + NX,t(ρ̃∗X,t )1−θ + NI,t(ρ̃∗I,t )1−θ = 1.

(4)

Note that the price index in the foreign country, P∗t , can be redefined in the same manner,and the equation corresponding to (4) holds.
Finally, the average dividend, Dt , is defined using these average productivities as:
NX,t ˜
NI,t ˜
Dt = d˜t +dX,t +Qt dI,t .
Nt
Nt

(5)

In the following subsection, the average dividend will be used for computing the firm
value and for deciding whether new entrants enter the economy or not.

2.5

Entry and Exit

The intermediate goods firms actively enter and exit in every period. For their exits, we
assume that an exogenous exit shock hits the intermediate goods firms with probability δin every period. When the exit shock hits them, they let all employees go and sell all capital.
For their entry, on the other hand, we assume that the potential entrants endogenously
choose to enter the economy if and only if their value is larger than the entry cost. They are
assumed to be identical prior to entry, and their initial productivity follows the cumulative
distribution function, G(z), which is the same distribution as the productivity distributionof incumbent firms. Thus, the value of new entrants, Vt , is:
Vt =

∞
X

[β(1 − δ)]s−t

s=t+1

Λs
Ds ,
Λt

(6)

where Ds is the average dividend in period s, which is defined in (5), and Λt is theaggregate marginal utility of consumption. Note that the value of these entrants is equal11to the average value of the incumbent firms because we assume that the productivity ofeach incumbent firm is constant after the entry. We assume that the new entrants must
pay a fixed entry cost, fE , to enter the economy. As the entry cost is also measured by aneffective labor unit, the entrant must pay wt fE in real terms to enter the economy. Thus,
the new entrants enter the economy if:
Vt ≥ wt fE .
We assume that new entry continues until this condition is satisfied with equality.
Let NE,t be the mass of entrants. Then, the law of motion for the mass of intermediate
goods firms is:
Nt = (1 − δ)(Nt−1 + NE,t−1 ),where (1 − δ) is the survival rate. As the law of motion indicates, we assume that the exit
shock hits the intermediate goods firms after the new entrants enter the economy.

2.6

HouseholdWe assume a representative household in each of the home and foreign countries. While
we will mainly describe the household decision in the home country, the same applies tothat in the foreign country.
We assume a representative household that consists of Mt members. The representative household inelastically supplies Lt labor units and obtains labor income, wt Lt . In ourquantitative simulation, Mt and Lt correspond to the total population and working-age
population, respectively. The household can invest in intermediate goods firms in thefollowing three ways. First, the household rents the capital to firms that produce domestically (i.e., domestic or exporting firms), Kt , with a return of (1 + rk,t − δK ), where δK is
the depreciation rate of capital. Second, the household rents the capital to FDI firms, KI,t ,with a return of (1 + rk,I,t − δK ). Investment in capital incurs an investment adjustment
cost, Φ(Kt , Kt−1 ) ≡ ϕKt−1 (Kt /Kt−1 − 1)2 . Third, the household invests in intermediate goods
firms by financing its setup and obtaining its share, Xt , whose value is Vt defined in (6).
As this share of the firm gives an average dividend, Dt , in every period, the representative
household obtains Xt Dt dividends in every period.

12The household also saves as a form of riskless bonds denominated in the home andforeign currency, Bt and B∗,t . Then, the representative household’s budget constraint is:η
Xt
Vt + Bt + Qt B∗,t + Qt (B∗,t )21−δ
2= wt Lt + (1 + rk,t − δk )Kt−1 − Φ(Kt , Kt−1 ) + (1 + rk,I,t − δk )Qt KI,t−1 − Qt Φ(KI,t , KI,t−1 )Mt Ct + Kt + Qt KI,t ++Xt−1 (Dt + Vt ) + (1 + rt−1 )Bt−1 + (1 + r∗t−1 )Qt B∗,t−1(7)where rt and r∗t are the risk-free rates in the home and foreign countries, respectively, and
Qt is the real exchange rate. We assume that the household needs to pay a tiny cost, η, forholding the riskless foreign bonds as in Ghironi and Melitz (2005). The bond holding costhelps avoid indeterminacy for bond holdings in the steady state and captures the homebias in the household’s investment behavior. We will discuss the role of home bias in moredetail later.
The household maximizes the discounted sum of utility from consumption subject tothe budget constraint. That is, the household’s optimization problem is:

max

∞
X

1−γ

C
β Mt t ,
1−γ
t=0
t

(8)

subject to (7). As a result of this optimization problem, we obtain five Euler equations,each of which is with respect to Bt , B∗t , Kt , KI,t and Xt :Bt : 1 = β(1 + rt )

Λt+1
Λt

(9)

Λt+1 Qt+1
Λt Qt
Λt+1
: 1 + Φ1 (Kt , Kt−1 ) = β[1 + rk,t+1 − δK − Φ2 (Kt , Kt−1 )]Λt
Λt+1 Qt+1: 1 + Φ1 (KI,t , KI,t−1 ) = β[1 + rk,I,t+1 − δK − Φ2 (KI,t , KI,t−1 )]Λ t QtΛt+1: Vt = β(1 − δ)
(Vt+1 + Dt+1 ) ,Λt

B∗,t : 1 + ηB∗,t = β(1 + r∗t )

(10)

Kt

(11)

KI,t
Xt

(12)
(13)

−γ

where Λt ≡ Ct is the marginal utility of consumption in period t. Note that population,
Mt , does not show up in the Euler equations because we assume that the representative
household maximizes the lifetime utility of the whole family rather than per capita lifetime
13

utility, as indicated by the household preference in (8).1

2.7

Market Clearing Conditions

In each country, there are four markets to be cleared in the equilibrium: labor, domestic
capital, FDI, and share. The market clearing conditions for these markets are:∗ ∗Labor : Lt = Nt l̃t + NX,t l̃X,t + NI,tl̃I,t + NE,t fE

Domestic capital : Kt−1 = Nt k̃t + NX,t k̃X,t
FDI : KI,t−1 = NI,t k̃I,tShare : Xt = (1 − δ)(Nt + Nt,E )

(14)
(15)
(16)
(17)

These equations’ left-hand sides and right-hand sides are the supply and demand for labor,
domestic capital, FDI, and share, respectively. Note that the labor demand for FDI firms
is that of foreign FDI firms.
The net supply of riskless bonds in the international bond market must be zero in theequilibrium for both currencies:
Bt + B∗t = 0

andB∗,t + B∗∗,t = 0,(18)where Bt and B∗t are the home bonds held by the home and foreign households, while B∗,tand B∗∗,t are the foreign bonds held by the home and foreign households.
Note that the capital stock in the home country, K̂t−1 , which is defined by∗ ∗K̂t−1 = Nt k̃t + NX,t k̃X,t + NI,tk̃I,tis not equal to the capital owned by the household in the home country, i.e., K̂t−1 ,Kt−1 + Qt KI,t−1 . This is because the household rents the capital to the FDI firms that operate
in the foreign country, and the FDI firm’s capital is counted as the host country’s capitalstock. The goods market-clearing condition (i.e., GDP = GDE) is therefore characterized1

As is well known, no substantial changes exist between those two assumptions, and the latter assumption
just requires some adjustments in algebra.

14

by using the capital stock, K̂t ,Yt = Ct + K̂t − (1 − δk )K̂t−1 .
In equilibrium, the goods market-clearing condition is satisfied by Walras’ Law, given thefour market-clearing conditions from (14) to (17) and the balance of payments identity
below.

2.8

Current Account

The current account in this model CAt is defined as the sum of trade balance TBt andincome balance IBt :CAt ≡ TBt + IBt .

(19)

The trade balance, TBt , in this model is equal to exports minus imports:∗
TBt ≡ Qt NX,t (ρ̃X,t )1−θ Yt∗ − NX,t(ρ̃∗X,t )1−θ Yt .

(20)

The income balance, IBt , consists of the net FDI return (= return on the outward FDI minus
return on the inward FDI) and the net bond return:
Qt r∗t−1 B∗,t−1 − rt−1 B∗t−1
|
{z
}

IBt ≡

Net income from foreign bond investment

+

i
i h
∗ ∗
∗
d˜I,t Qt NI,t + (rk,I,t − δK )Qt NI,t k̃I,t − d˜∗I,t NI,t+ (r∗k,I,t − δK )NI,t
k̃I,t
{z
}
|
{z
} |
h

(21)

Return on inward FDI

Return on outward FDI

In equilibrium, changes in net foreign assets must be equal to current account. Let ∆FDIt
and ∆FDI∗t be the outward and inward FDI flow for the home country. As they are definedin the model by:∆FDIt ≡ Qt KI,t − Qt KI,t−1

and

15

∗
∗
∆FDI∗t ≡ KI,t
− KI,t−1,the balance of payments identity, i.e., changes in net foreign assets equal current accountCAt , is formulated by:
CAt = (∆FDIt − ∆FDI∗t ) + [Qt (B∗,t − B∗,t−1 ) − (B∗t − B∗t−1 )],(22)

where the right-hand side represents the change in net foreign assets and the left-handside is the current account for the home country.

2.9

Sectoral saving

The current account dynamics are intrinsically associated with households and firms’
consumption and saving behavior. Since the current account is the net accumulation offoreign assets, the current account CAt is equal to changes in overseas savings, −∆SOt .
Furthermore, market clearing in the savings market implies that −∆SOt should be financedCby household savings SH
t or corporate savings St :CAt = −∆SO
t
C
= ∆SH
t + ∆St .

(23)

There are no government savings since we do not incorporate the public sector in ourmodel. We will discuss how we map the quantitative results in our model to data in moredetail in the next section.
Household saving The household in the home country saves in the form of foreign assets
including FDI in addition to domestic assets. As the budget constraint (7) indicates, thehousehold savings ∆SHt can be expressed as the sum of domestic capital investment, FDI
investment, and net foreign bond investment:
∆SH
=
t


 

Kt + (Nt + NE,t )Vt − Kt−1 + (Nt−1 + NE,t−1 )Vt−1|{z}
Domestic capital investment+ Qt (KI,t − KI,t−1 ) + Qt (B∗,t − B∗,t−1 ) − (B∗t − B∗t−1 ),
|
{z
} |
{z
}
Net
foreignbondinvestment∆FDI t16(24)

which implies that the household accumulates external assets not only through foreign
bond investment but also through outward FDI. Therefore, given the home bias in foreign
investment by the household, the outward FDI is an important channel to accumulate
external assets.
Corporate saving

The corporate saving SCt is defined by firms’ financial assets minus theirfinancial liabilities. The equations (22), (23), and (24) indicate that changes in corporatesaving equal changes in domestic capital investment:
h
i h
i
∗
∗
∆SCt = − Kt + (Nt + NE,t )Vt + KI,t
+ Kt−1 + (Nt−1 + NE,t−1 )Vt−1 + KI,t−1.

(25)

Even though FDI is part of corporate financial assets, this result implies that FDI flows
do not show up as part of corporate savings. In our model, all financial assets of firms
are FDI stocks, and all assets, including FDI stocks, are financed by financial liabilities.
Hence, all changes in FDI must be associated with the same amount of changes in financial
liabilities, thus making FDI flows neutral to corporate savings. On the other hand, changes
in domestic capital investment influence corporate savings because they change financial
liabilities without changing financial assets. However, the equation (25) does not mean thatfirms’ FDI motive is irrelevant to corporate savings. Rather, for instance, when firms shift
their foreign businesses through export to those through FDI, the equation (25) implies
that corporate savings increase.

3

Quantitative Analysis: Case in Japan

This section applies our model to study long-run capital flows and sectoral savings inJapan under demographic changes. In our quantitative analysis, we compute transition
dynamics based on the past, and future projections of, demographic changes in Japan andexamine the role of FDI in accounting for the transition dynamics of capital flows andsectoral savings. In the transition dynamics, households and firms are assumed to makeall decisions under perfect foresight, as future demographic changes are foreseeable tosome extent. In the first period, all agents in the model foresee demographic changes anddecide the future path of consumption and savings. Therefore, even before population

17

Figure 3: Total and Working-age Population in Japan (1947=1.0)
1.09
Total population
Working age population

1.08
1.07
1.06
1.05
1.04
1.03
1.02
1.01
1
1950

1960

1970

1980

1990

2000

2010

2020

2030

2040

2050

2060

Note: The figure shows Japan’s total and working-age population from 1947 to the present and theirprojection up to 2060. The projection is based on the 2019 projection by the National Institute of Populationand Social Security Research.

aging occurs, households and firms save or borrow to smooth consumption in anticipationof population aging in the future.
When computing the transition dynamics, we refer to Japan as a home country in themodel and use the working-age population as a critical variable reflecting the dramatic
demographic changes in Japan. Figure 3 shows Japan’s total and working-age populationfrom 1950 to the present and their projection up to 2060. The figure indicates that Japan
has faced, and will face, a considerable decrease in the working-age population relative
to the total population: The number of the working-age population in Japan significantly
increased and reached a level close to 10% higher than the 1950s at the peak in the 1990s,
but after peaking out in the 1990s, it has been declining at an unprecedentedly rapid paceand is expected to decline until 2060. In 2060, its level is expected to return to the levelin the 1950s. The total population, on the other hand, also shows similar hump-shaped
dynamics. Still, the magnitude of its changes is much more moderate than that of theworking-age population, implying that the working-age population ratio has considerablychanged (and will change) in Japan.
In the quantitative analysis, we input the past, and future projection of, the number
18

of working-age population into the model as an exogenous path of labor endowment Lt
and compute the transition dynamics under the perfect foresight assumption. We choose
demographics as the sole driver of capital flows in our quantitative exercise because
several previous studies that we mention in the introduction demonstrate that the longrun trend of international capital flows is primarily accounted for by demographics rather
than other factors, including productivity growth or fiscal policy. In particular, Krueger
and Ludwig (2007) uses an overlapping generations model and shows that changes in
the working-age population, rather than the total population, strongly influence capital
flows through the effects on labor supply.2 Hence, in our baseline quantitative analysis,
we use the working-age population in Japan as a sole driver of capital flows and keep
other possibly relevant variables constant throughout the sample periods.3 Given that it
is not feasible for our model to take into account the whole age structure due in part to thecomplicated model structure with firm heterogeneity, our quantitative approach using theworking-age population as an exogenous change in labor endowment is a parsimonious
way to capture the essential economic consequences of population aging.
In the following quantitative exercise, we investigate whether the model quantitatively
accounts for capital flows in Japan and what the model predicts about the future path ofcapital flows based on the current projection of population aging. To examine the role of
FDI, we compare the simulation results using a baseline model with FDI to those using amodel without FDI as in a standard open-macroeconomics model. Finally, we touch on themodel prediction about sectoral savings in Japan. In what follows, we first calibrate themodel parameters and then compute the transition dynamics of capital flows in the faceof demographic changes in Japan.

19

Table 1: Calibration by standard values
Parameter

3.1

Value

Discount factor

β

0.96

Elasticity of intertemporal substitutionγ

2.0

Capital share for production

α

0.36

Depreciation rate for capital

δk

0.1

Exit rateδ

0.1

Degree of substitution for goodsθ

4.0

Shape of productivity distribution

κ

4.25

Iceberg cost for exportsτ

1.3

Calibration

For quantitative analysis, we first calibrate the model parameters. First, we calibrate mostparameter values to standard ones. One period in the model is assumed to equal one year,
and the discount rate β is then set to 0.96. The parameter for the elasticity of intertemporal
substitution γ is set to 2.0. The capital share, the depreciation rate for capital, and the entry
rate are set to standard values, α = 0.36, δk = 0.1, and δ = 0.1, respectively. The parameters
for the degree of substitution and the shape of productivity distribution, θ and κ, are set to
4.0 and 4.25 according to Melitz and Redding (2013). As for the trade costs, the iceberg costfor exports is assumed and set to 30%, i.e., τ = 1.3, as in other studies in the international
trade literature. Finally, given that the equilibrium does not depend on the values of fixed
costs for exports and FDI but on the ratios of those fixed costs to the entry cost, the entry
cost, fE and fE∗ , is normalized to one. Those calibration results are summarized in table 1.
Second, we use indirect inference to calibrate the remaining five parameters, namely,
the cost for bond holdings, η, the fixed cost for export in the home and the foreign country,
fX and fX∗ , and the fixed cost for FDI in the home and the foreign country, fI and fI∗ .
Specifically, first, we assume the trade cost is the same in the home and foreign countries,
2

Imrohoroglu et al. (2006) argue that demographics have little effect on the Japanese savings rate, basedon their analysis using a neoclassical growth model. However, given that they incorporate changes in the
total population rather than the working-age population, their analysis ignores the age structure and theeffects of population aging on labor supply.
3

In a robustness check in Appendix A, we use total population in Japan and total and working-age
population in the U.S. as a proxy for exogenous changes in Mt , L∗t and M∗t in the model, and obtain similar
results to the baseline case.

20

Table 2: Calibration by indirect inferenceWith FDI

Parameter

w/o FDI

Fixed cost for outward FDI

fI

18.8

N.A.

Fixed cost for inward FDI

fI∗

324.8

N.A.

Fixed cost for exports

fX , fX∗

.636

2.428

Adjustment cost for FPI

η

.0474

.0599

i.e., fX = fX∗ . Then, those key parameters are calibrated to minimize the loss function
based on the absolute distance between data and the model-implied values for the current
account, trade balance, income balance, and outward and inward FDI stocks relative to
GDP in Japan. The loss function for estimation is defined as,
2020
X X|Xdata − Xmodel |t

Xt t=1955

t
data
|Xt |

)
FDIt FDIt∗
where Xt ∈ CAt , TBt , IBt ,
,
,
Yt
Yt
(

(26)

and we compute fX , fI , fI∗ , and η to minimize the loss function in the model with andwithout FDI. In so doing, we repeatedly compute the model-implied values and minimize
the loss function using a standard hill-climbing algorithm.
Table 2 shows that the loss function is minimized by fX = .636, fI = 18.8, fI∗ = 324.8 andη = .0474 for the model with FDI, and fX = 2.428 and η = .0599 for the model without FDI.
There are some notable features. First, the fixed cost for FDI fI is almost thirty times larger
than for exports fX . While they seem too different at first glance, it is not surprising giventhat FDI needs tremendous costs for operating businesses in foreign countries. Second,the cost for inward FDI fI∗ is more than ten times larger than that for outward FDI fI . Thevery high cost of inward FDI reflects the extremely low level of inward FDI in Japan, as
shown later. Third, there is a nontrivial cost for foreign bond holdings η, which implies
the existence of home bias in financial investment by households. Moreover, the cost forbond holdings and the fixed cost for export are higher in the model without FDI, as bondinvestment and export are the only ways to accumulate external assets and do foreignbusiness in the model without FDI, respectively. Even with FDI, since FDI is a restrictive
channel for capital flows, the value of η substantially affects the shape of the current
account and its components. In particular, as η becomes larger, the economy approaches
21financial autarky with balanced trade.

4

Simulation Results

This section gives the simulation results of the quantitative exercise. As discussed in
more detail below, we obtain the following two takeaways. First, the simulation paths
in response to demographic changes can reasonably account for the long-run trend ofcurrent account dynamics and its composition, as well as FDI dynamics, in Japan. Second,
FDI plays a crucial role in explaining the long-run trend of the current account in Japan,
particularly the dynamics of its composition. In what follows, we show our quantitative
results in more detail and discuss economic intuitions behind the above two main results.

4.1

Long-run Trend of Capital Flows and FDI

Figure 4 displays the simulation results for the current account and its composition (theblue bold lines), along with data in Japan (the thin red lines). The simulation results imply
that demographics alone can reasonably account for the long-run trend of the Japanesecurrent account and its composition.4 In particular, the baseline simulation is consistent
with the significant decrease in trade balance surplus along with the increase in income
balance surplus, which we have observed in Japan in the last several decades.
The household’s consumption and savings behavior for consumption smoothing is
key to replicating the long-term current account dynamics in Japan. Until the 1970s, theJapanese working-age population was expected to grow in the future, resulting in a current account deficit and an increase in external debt, as seen in most emerging market
economies. From the 1970s to around 2000, as the working-age population increased, thecurrent account recorded a surplus due to a large trade balance surplus. The substantial
trade balance surplus until around 2000 can be interpreted as a consequence of consumption smoothing. That is, since households knew that the working-age population would
decrease in the future, they saved in part as a form of external assets. Finally, as theworking-age population started to decline in the 2000s, the trade balance surplus began
4
It is not surprising that the model simulation replicates the average level of current account surplus andits compositions, as we use those data as calibration targets in the loss function (26). However, it is obviously
impossible to match their dynamics by only adjusting parameters in indirect inference.

22

Figure 4: Data and model generated path: Current account in Japan
6

Current Account

4

2

0
Data
Baseline
Time-varying FDI cost
Without FDI-2-4
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050
6
Data
Baseline
Time-varying FDI cost
Without FDI

Trade Balance

4

2

0

-2

-4
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050
6

Income Balance4

Data
Baseline
Time-varying FDI cost
Without FDI

2

0

-2

-4
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050

Note: The figure displays the simulated path by the model versus the data on the current account, tradebalance, and income balance. In each panel of the figure, the thin red line and the bold blue line show thedata and the transition dynamics of the baseline simulation. Also, the light blue dotted line and the green
dashed line represent the simulation results for the hypothetical case where FDI is unavailable and thosewith a time-varying FDI cost, respectively.

23

to decrease as well. On the other hand, the income balance started to run a surplus due toincome from external assets accumulated through the past trade balance surplus.
The model-generated paths can also account for the long-run trend of FDI dynamics.
The first two panels in Figure 5 show the model-generated paths for outward and inward
FDI stocks relative to GDP (the blue bold lines), along with the data (the red thin lines).
The figure highlights two notable features. First, inward FDI has been very low comparedto outward FDI. As discussed in calibration, the exceptionally low level of inward FDI inJapan leads to an asymmetrically high cost for inward FDI in our calibration (See Table 2).
Second, and more importantly, outward FDI stocks have been dramatically increasing andhave almost quadrupled since 2000 in the data. While the model-generated path, driven
only by demographics, cannot completely track such a dramatic increase in outward FDI, it
replicates the increasing trend since around 2000. More specifically, the outward FDI ratio
in the model has almost doubled since 2000, implying that demographics can account foraround half of the recent rise in outward FDI in Japan. As discussed below, the increase in
FDI stocks driven by factor price changes under demographic changes is key to replicating
the dynamics of the current account and its composition.

4.2

Role of FDI as a Capital Flow Channel

In this subsection, we examine the role of FDI in accounting for capital flows in Japan. As
discussed below, we find that FDI plays a crucial role in explaining the dynamics of thecurrent account, particularly the developments in income balance. In what follows, wefirst examine the role of FDI by comparing the baseline simulation with the counterfactual
simulation without FDI. Then, we introduce a time-varying FDI cost to improve the model
fit, further indicating the importance of FDI in explaining capital flows.
4.2.1

Counterfactual Simulation without FDI

To examine the role of FDI in accounting for the trend of current account in Japan, we
conduct a counterfactual simulation where FDI is unavailable. The model without FDI
differs from the baseline model with FDI mainly in the following two aspects, whichreflect the dual aspects of FDI in our model. First, since firms cannot produce and sell
their products in foreign countries through FDI, they can access foreign markets only24

Figure 5: Data and model generated path: FDI stocks in Japan

Outward FDI stock to GDP ratio
80

Inward FDI stock to GDP ratio
80

Fixed cost for outward FDI
25
Baseline
Time-varying FDI cost

Data
Baseline

60

60

20

FDI cost change

15
40

40
10

20

20

0
1980

2000

2020

2040

5
0

0
1980

2000

2020

2040

1980

2000

2020

2040

Note: The first two panels show the data and the model-generated paths for outward and inward FDI
stocks relative to GDP. The thin red lines show data, while the thick blue lines and the green dashed lines
show model outputs with a constant and time-varying FDI cost, respectively. The last panel shows the fixed
operational cost for FDI in the baseline and the simulation with a time-varying cost of FDI.

through exports. Second, since firms cannot accumulate foreign assets through FDI,
households’ investment in riskless bonds (FPI) would be the only channel to accumulate
external assets.5 Those two differences imply that the model without FDI is close to a
standard open-economy macroeconomic model with heterogeneous firms such as Ghironi
and Melitz (2005).
In each panel of figure 4, the light-blue dotted line labeled “without FDI” shows thetransition dynamics in the hypothetical case where FDI is unavailable. The figure indicatesthat the model without FDI cannot well account for the long-run trend of the current
account, particularly its composition. More specifically, the counterfactual simulation
where FDI is unavailable displays: (i) the income balance (the bottom panel) is almost
zero even in the face of population aging and thus cannot replicate its dramatic increasesince the 1990s, and (ii) the decrease in trade balance surplus (the middle panel) is much
more moderate than the baseline case and data.
5

While we assume that households cannot hold equity of foreign firms directly, this assumption has little
effect on our quantitative results because foreign households can borrow from abroad by riskless bonds andinvest in equity.

25

Figure 6: Real Interest Rate and Terms of Labor

Note: The figure shows the developments in real interest rates (the left panel) and the terms of labor (theright panel). In both panels, the bold blue lines and the dashed light blue lines represent the simulation
results for the case with and without FDI, while the thin red lines show actual data. The real interest rate in
the data is calculated by subtracting the inflation rate from the short-term interbank market rate. The termsof labor are calculated by relative wages across the two countries adjusted by real exchange rates, wt /(Qt w∗t ),as in Ghironi and Melitz (2005), while those in data use the PPP-adjusted wages in Japan relative to the U.S.
Sources: Ministry of Health, Labour and Welfare; Ministry of Internal Affairs and Communication; Bank ofJapan; FRED; World Bank.

The developments in factor prices are crucial to understanding the role of FDI, as firms
endogenously choose between exports and FDI in response to their changes. Figure 6
illustrates the developments in real interest rates (the left panel) and the terms of labor (theright panel). In both panels, the bold blue lines and the dashed light blue lines represent
the simulation results for the case with and without FDI, while the thin red lines show
actual data.6 The figure indicates that the model-implied real interest rates and terms oflabor are quantitatively consistent with actual data in Japan, even though they are nottargeted in calibration at all. Specifically, the model simulation implies that (i) real interest
rates have declined since the 1980s and are expected to decline further, and (ii) the termsof labor had increased until around 2010 and started to decrease. Given that any dynamics
in our simulation are driven only by demographics, the figure implies that the decline
in the working-age population since the 1990s, as well as the rise in household savingsin anticipating population aging, makes the labor force scarce relative to capital, thus
6

The terms of labor in the model are calculated by relative wages across the two countries adjusted by realexchange rates, wt /(Qt w∗t ), according to Ghironi and Melitz (2005), while those in the data use PPP-adjusted
wages in Japan relative to the U.S.

26

increasing labor costs and decreasing capital costs in Japan.
While the factor price changes in Figure 6 are almost identical in the economy with andwithout FDI, the endogenous response by firms to those changes is in contrast between
them, resulting in significantly different current account dynamics. In the economy with
FDI, i.e., the baseline simulation, the rise in labor costs and the decline in capital costs
encourage productive firms in Japan to produce more in foreign countries through FDI
rather than produce in Japan and export. Thus, due to the endogenous choice between
exports and FDI, the trade balance surplus has declined since the 1990s, while the income
balance has increased since then. On the other hand, when we do not incorporate FDI as ina standard international finance or trade model, productive firms would do their businessabroad only through exports, even in the face of the decline in the working-age population.
Therefore, the model without FDI predicts a milder decline in the trade balance surplus
and a smaller increase in the income balance surplus, making the model unable to replicate
the current account dynamics in Japan, particularly since the 1990s.
While such international relocation through FDI is often considered negative for domestic workers, the model simulation implies that households benefit from it by obtaining
higher returns on FDI as stockholders. According to the relationship in (24), households
indirectly hold external assets through FDI when Japanese firms invest abroad throughFDI. Of course, in reality, households who lose their jobs due to the increase in outward
FDI may not be the same as those who benefit from it as stockholders of multinationalfirms. While the representative household assumption in our model is too simple to analyze such an issue associated with heterogeneity among households, it is an interesting
issue to be explored in future work.
4.2.2

Time Varying FDI Cost

While our quantitative exercise indicates that FDI plays an important role in accounting
for the trend of capital flows, figure 5 shows that the baseline simulation (the blue boldlines) obviously underestimates the recent rise in FDI stocks. Specifically, (i) outward FDI
has doubled since the 2000s in the simulation while it has become more than quadrupledin data, and (ii) inward FDI has remained at a very low level while it has increased sincethe 2000s in data. In fact, the underestimation of the increase in FDI stocks leads tothe underestimation of the recent rise in income balance surplus in figure 4. While our27simulation assumes a constant FDI cost, fI and fI∗ , throughout the simulation periods, theunderestimation of FDI stocks implies that the FDI cost has probably decreased underglobalization in the last half-century.
In this subsection, we conduct an additional simulation assuming a time-varying anddeclining cost of FDI to account for Japan’s recent rise in FDI stocks. Specifically, we
assume that the fixed operational cost for outward and inward FDI has proportionallydropped until 2020 from 100 fI to g fI and from 100 fI∗ to g∗ fI∗ , where fI and fI∗ are thebaseline calibration values. To fit the data of FDI stocks, we pick g = 0.07 and g∗ = 0.01,
respectively. That is, we assume that the fixed cost of FDI has become less than 0.1%
during the last half century, as shown in the right panel in figure 5.
The green dashed lines in figures 4 and 5 show the simulation results with the timevarying FDI cost. First, with the time-varying FDI cost, the model can account for thedramatic rise in FDI stocks since the 2000s (figure 5). This result is mechanical because wepick the values of g and g∗ to fit the data of FDI stocks. Second and more importantly, withthe rise in FDI stocks, the model replicates a dramatic increase in income balance surplus
in data. The bottom panel of figure 4 shows that the income balance surplus has increased
since the 2000s more substantially than the baseline and consequently fits the Japanesedata better. Furthermore, the model fit for the current account and trade balance is almost
the same or slightly better than the baseline simulation.
Overall, assuming the time-varying and decreasing FDI cost significantly improves themodel fit, particularly for income balance. Hence, while the quantitative exercise here
takes the decline in the FDI cost as exogenously given, it further endorses the importanceof FDI in explaining the current account dynamics. Exploring what drives the decline in
the FDI cost in Japan should be a fruitful future research agenda.

4.3

Model Forecasts and the Stages of the Balance of Payments

What does the model predict about the current account in the future? Since demographics
are foreseeable to some extent, our simulation should provide reasonable forecasting paths
for the current account and its composition in the next several decades under the ongoing
trend of population aging.
Figure 4 shows the forecasting path of the Japanese current account and its composition
until 2050. The baseline simulation (the blue bold lines) indicates that (i) the current
28

account surplus will continue to decrease and will be around zero in 2050, (ii) the tradebalance surplus will continue to decrease and reach around -2 percent of GDP in 2050,
and (iii) the income balance surplus will continue to increase. While the model with timevarying FDI cost (the green dashed lines) gives a similar prediction, it predicts a more
substantial decrease and increase in a trade and income balance surplus, respectively,
than the baseline (-5 and 5 percent of GDP in 2050). The declining FDI cost leads to amore significant decrease in trade balance surplus, as well as a more substantial increasein an income balance surplus, because it accelerates the Japanese firms’ transition fromexports to FDI under population aging. Thus, the model forecasts imply that the Japanese
economy will face a more significant decrease and increase in trade and income surplus
in the future if the current declining trend in FDI costs continues.
Interestingly, those simulation results for the past and future developments in capital
flows in Japan are consistent with the well-known “stages-of-the-balance-of-payments
hypothesis” by Geoffrey Crowther.7 According to this hypothesis, a typical classification
defines four stages: (i) a young and growing debtor (trade and income balance deficit), (ii)a mature debtor (trade balance surplus and income balance deficit), (iii) a young creditor(trade and income balance surplus), and (iv) a mature creditor (trade balance deficit andincome balance surplus). According to this classification, the current account deficit fromthe 1960s to the 1980s implies that Japan was at stages (i) and (ii). Since the 1990s, as
trade and income balance ran a surplus, Japan has been at the stage of (iii). Since themid-2000s, however, the trade balance surplus has decreased while the income balance
surplus has increased. The forecasting path suggests that in line with the hypothesis, Japanis transiting to a “mature creditor,” i.e., stage (iv), characterized by a trade balance deficit
and income balance surplus. Since our exercise uses demographics as the sole driver ofcurrent account dynamics, the quantitative result implies that demographic changes may
be a driving force to explain the hypothesis.

4.4

Sectoral Savings in Japan

In this subsection, we investigate the dynamics of sectoral savings under demographic
changes in Japan. The sectoral composition of savings in Japan has dramatically shifted
7

For more details about this hypothesis, see, for example, Fischer and Frenkel (1974) and Lane andMilesi-Ferretti (2002).

29

Figure 7: Data and model generated path: Sectoral saving in Japan

Householddata
data (with gov. savings)
Model (baseline)

10
5
0
-5
-10
1980

1990

2000

2010

2020

2030

2040

2050

2030

2040

2050

2030

2040

2050

Oversea
10
5
0
-5
-10
1980

1990

2000

2010

2020

Corporate
10
5
0
-5
-10
1980

1990

2000

2010

2020

Note: The figure illustrates the model’s simulation path and the sectoral savings data in Japan. There are
two data sequences, namely, (i) the data where the government savings are divided in half and added to thehousehold and corporate savings (the pink dashed lines), and (ii) the data ignoring the government savings(the red lines).

30

in the last three decades, as shown in figure 2 in the introduction. In particular, the figure
indicates that corporate savings have increased since around 1990, as household savings
have decreased. Since we can define sectoral savings in the model as consistent with data,
it is worthwhile to examine whether the transition dynamics under demographic changes
in our model account for the recent developments in sectoral savings and what drives the
dynamics of sectoral savings.
Figure 7 illustrates the model-generated paths and the data of sectoral savings in Japan.
The figure demonstrates that the model (the blue bold lines) can fairly well account for the
long-run trend of sectoral savings in Japan (the thin red lines) since the 1980s. Specifically,
the simulated path explains: (i) the household saving rate has been decreasing sincearound 1990, (ii) the corporate saving rate has been increasing since around 1990, and (iii)the financial surplus of the overseas sector continues to record deficit. According to themodel prediction, such a shift in sectoral savings in Japan will continue due to the decreasein the working-age population.
Population aging has generated a shift in sectoral savings through the following two
mechanisms. First, the decline in the working-age population has decreased the householdsavings rate since the 1990s as a result of the household’s consumption smoothing. At
the same time, given that most household savings take the form of domestic physicalinvestment, the decline in household savings has decreased the financial liabilities in thecorporate sector and thus raised corporate savings. Second, population aging has further
increased corporate savings by encouraging large firms to shift from exports to FDI, as
explained in the previous subsection. Hence, since the 1990s, corporate savings haveincreased in exchange for declining overseas savings. The second mechanism is consistent
with the fact that more than half of corporate savings since 2010 can be accounted for by
an increase in outward FDI in Japan (the right panel in figure 2).
While the model dynamics under demographic changes can account for the long-term
trend in Japanese sectoral savings, they are subject to some caveats. First, since our model
does not have a public sector, government savings do not exist in the model. The pinkdashed lines in figure 7 show the case where government savings are divided in half
and added to the household and corporate savings to maintain consistency with data.
Compared with the data ignoring government savings (the red lines), while those twodata sequences exhibit some gaps by construction, these gaps do not substantially affect31

our quantitative assessment. Second, our simulation results underestimate the rise incorporate savings in around 2000. However, this is unsurprising because we do not modelother relevant factors contributing to the increase in corporate savings, including the firm’s
precautionary motive for cash holdings.
In sum, our quantitative exercise shows that demographic changes can broadly accountfor a long-run trend of sectoral savings in Japan, including the recent rise in corporatesavings. Note that our quantitative exercise does not argue that an increase in FDI by nonfinancial firms under population aging is the main factor of corporate savings. Rather,while the previous literature points out numerous factors contributing to the recent surge
in global corporate savings, our exercise implies that outward FDI under population aging
can be added to the list of those factors at least in Japan. Hence, while the recent increase incorporate savings in Japan is driven by many factors including the lack of Japanese firms’
risk-taking or strengthening corporate governance, there is also a secular trend driven by
population aging.

5

Concluding Remarks and Policy Implications

This paper investigates the role of FDI in accounting for the long-term trend of capital
flows under demographic changes. For this purpose, we incorporate horizontal FDI
under the proximity-concentration trade-off à la Helpman, Melitz, and Yeaple (2004) intoa two-country DSGE model and conduct a quantitative analysis using long-term Japanesedata since the 1960s. The quantitative analysis finds that the trend of the current account,
including its composition and dynamics of sectoral savings in Japan, can be well accounted
for solely by demographic changes. Our simulation implies that multinational firms’
endogenous choice between exports and FDI in the face of factor price changes driven bydemographics is key to explaining those trends.
The quantitative analysis has some policy implications for the Japanese economy. First,
the simulation exercise implies that the recent decline in a trade balance surplus and therecent increase in corporate savings in Japan can be accounted for by demographic changes
at least in the long run. In other words, they do not necessarily reflect, for instance, a lossof competitiveness of Japanese firms or a passive risk-taking attitude of Japanese firms.
Second, the simulation results indicate that the decreasing trend of trade balance surplus
32

and the increasing trend of corporate savings will continue for the next several decades, as
population aging continues. Furthermore, given the crucial role of FDI in accounting forthe long-run trend of capital flows, greater FDI openness in the future, if any, will reinforce
those trends. Hence, Japanese policymakers should take into account those trends as given
when they develop their policies and strategies for international finance.

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Appendix A. Robustness Checks
In the appendix, we conduct the following four additional simulation exercises as robustness checks. First, we take into account changes in the total population in addition to theworking-age population (the blue dotted lines in figure 3) as exogenous changes in Mt .
Second, we take into account not only the total population and working-age population in
Japan but also demographics in foreign countries. As a proxy for demographics in foreigncountries, we use changes in the U.S. working-age population as exogenous changes in L∗t ,given that the U.S. has been the most important counterpart for Japan in trade and FDI.
Third, we take into account the fact that some older people continue to work in Japan.
Based on the latest male and female labor force participation rate for 65 or older people,
we use the sum of the working-age population and old workers as a proxy for the labor
supply, Lt . Fourth, we use the number of labor forces rather than the working-age population as a proxy for Lt to consider the recent rise in labor participation rate particularly
among female workers.8
Figure 8 shows the simulation results for the first and second robustness checks. First,
the simulation paths, which take into account the total population (the green dashed lines),
are very close to the baseline case. The small effect of the total population is consistent withthe previous papers such as Imrohoroglu et al. (2006), and implies that considering thedevelopments in the working-age population rather than the total population is necessary
to capture the effects of demographics on capital flows. Second, the simulation paths thattake into account the U.S. demographics (the dotted light blue lines) are also close to thebaseline case, while they fluctuate more than the baseline due to demographic changes in
the U.S. Similarly, figure 9 shows the simulation results for the third and fourth robustness
checks. In both robustness checks, the current account surplus is somewhat smaller thanin the baseline case. This is because households have less incentive to save than thebaseline, as the adverse effects of population aging are mitigated by working in old age.
Nonetheless, the simulation paths are close to the baseline and do not substantially change
the quantitative assessments.
8

In this exercise, the future path of labor forces is assumed to be constant at the level in 2020.

35

Figure 8: Data and model generated path: Current account in Japan
6

Current Account

4

2

0

-2

Data
Baseline
With total pop
With total pop + U.S. pop-41960 1970 1980 1990 2000 2010 2020 2030 2040 2050
6
Data
Baseline
With total pop
With total pop + U.S. pop

Trade Balance

4

2

0

-2

-4
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050
6

Income Balance4

Data
Baseline
With total pop
With total pop + U.S. pop

2

0

-2

-4
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050

Note: The figure displays the simulated path by the model on the current account, trade balance, and income
balance. In each panel of the figure, the thin red line and the bold blue line show the data and the transition
dynamics of the baseline simulation. Also, the green dashed line represents the simulation results whichtake into account total population changes, and the light blue line represents those which take into accountchanges in both the total population in Japan and the U.S. population.

36

Figure 9: Data and model generated path: Current account in Japan
6

Current Account

4

2

0
Data
Baseline
With old workers
Labor force-2-41960 1970 1980 1990 2000 2010 2020 2030 2040 2050
6
Data
Baseline
With old workers
Labor force

Trade Balance

4

2

0

-2

-4
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050
6

Income Balance4

Data
Baseline
With old workers
Labor force

2

0

-2

-4
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050

Note: The figure displays the simulated path by the model on the current account, trade balance, and income
balance. In each panel of the figure, the thin red line and the bold blue line show the data and the transition
dynamics of the baseline simulation. Also, the green dashed line represents the simulation results, which
consider workers over 65 years old, and the light blue line represents those that use the labor force insteadof the working-age population as a measure of labor endowment, Lt .

37