DBJ Discussion Paper Series, No.1204

A Macroeconomic Consequence of Foreign Direct Investment
under a Flexible Exchange Rate:
The Welfare Economics of Industrial Hollowing

Masayuki Otaki(Institute of Social Science, University of Tokyo)

July

2012

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings, conclusions
or recommendations expressed in these papers are those of the authors and do not reflect
the views of the Institute.

A Macroeconomic Consequence of Foreign Direct Investment
under a Flexible Exchange Rate: The Welfare Economics of Industrial Hollowing
Masayuki Otaki
Institute of Social Science, University of Tokyo
ohtaki@iss.u-tokyo.ac.jp
Abstract
This article considers macro and welfare economic implications concerning foreign
direct investment under a flexible exchange rate system. There are serious conflicts
between foreign-invested firms and their home country as a whole. Although lower
wages incentivize firms to obtain foreign direct investment, such a movement harms thewelfare of the home-country’s economy in the following ways.
First, an increase in unemployment in the home country worsens the economy’s
welfare as proved by Otaki [1]. Second, an appreciation in the real exchange rate, whichis induced by the transfer of earned profits in foreign countries to the home country,
reduces the value of profits in terms of domestic goods. We prove that such an
appreciation entirely cancels the benefit from the cost reduction that originates fromthe foreign direct investment in lower-wage countries.
In the end, only the downturn in employment circumstance remains. In this sense,
the glut of foreign direct investment is harmful and, some coordination is required
between firms and the government of the home country.
Keywords: Macroeconomics of foreign direct investment, Industrial hollowing,
Exchange rate appreciation, Leakage of effective demand11. Introduction
Although, according to the neoclassical trade theory that deals with a barter
economy, it seems natural and efficient for a higher-wage and capital-abundant
country to export her real capital, such conventional wisdom cannot apply to amonetary economy in which idle resources (specifically labor forces) are prevalent evenif every price adjusts flexibly, as proved by Otaki [2], [1], [3]. Based on Otaki [4], thisarticle analyzes the macro and welfare economic consequences of foreign direct
investment of a small and monetary economy under a flexible exchange rate system.
Foreign direct investment causes serious conflicts between capital-exporting firms
and their home country. It directly deprives the home country of employment
opportunities and reduces the effective demand in the home country. Such a process iscumulative and self-enforcing. 1
In addition, lower-wage countries, ceteris paribus, attracts foreign direct investment
seeking more profits. However, under the flexible exchange rate system, the transfer of
earned profits to the home country appreciates the real exchange rate, as long as
savings in the home country are insensitive to the real exchange rate. Thus, theadditional profits that are sent from the lower-wage country are entirely absorbed bysuch an appreciation.
This phenomenon is a type of fallacy of composition. That is, although the realexchange rate is an exogenous variable for each firm, it is endogenous for the homecountry as a whole, and it is realigned by the synchronized profits transfer of foreign
direct invested firms. Accordingly, as long as domestic savings are insensitive to thereal exchange rate, the social benefits of foreign direct investment are absorbed by theappreciation of the exchange rate.
In sum, the stagnant and cumulative effect of foreign direct investment remains onlyin the home country. Such investment increases unemployment and results in a
reduction of the effective demand, among other effects. We shall prove that sucheconomic consequences worsen the resource allocation of the home country in the senseof Pareto. That is, differing from the classical barter economy, industrial hollowing is aserious problem in the monetary economy.
The structure of this paper is as follows. In Section 2, we construct a macroeconomic
model of a small open country in which the international movement of real capital isperfect (without any restriction). Section 3 addresses the welfare implication of foreign
Kahn [5] carefully distinguishes the home investment from the foreign direct
investment, when he calculates the employment multiplier. His discussion clearly
indicates that an opposite effect to the home economy’s employment exists in these twocapital investments.
12

direct investment. Section 4 contains brief concluding remarks.
2.The Model
2.1

The Structure of the Model

We consider a small open economy under a flexible exchange rate system based on astandard two-periods overlapping generations (OLG) model. The world economy
consists of two economies: the home country and the foreign country. The home country
is very small relative to the foreign country and the behavior of the home-country’s
industries never affects its counterpart’s economic conditions, such as the real GNP.
The home country has two industries: the mobile and tradable industry (industry a )which can freely change its location and the immobile and non-tradable industry(industry b ). Each industry consists of differentiated goods within the interval[0,1] .Each firm monopolistically produces its differentiated good. The technology isidentical for all firms regardless of the country or industry to which each belongs. A unit
labor produces a unit good. That is, the labor productivity is assumed to be unity for all
firms. Furthermore, individuals can participate with work only when he/she is young.
There is an asymmetry in the nominal wage determination. In the home country, thenominal wage is determined by the following two-step game developed by Otaki [1]. In
the first stage, each employer decides its pricing strategy and employment policy tomaximize its profits. The second stage determines the nominal wage in accordance withthe asymmetric Nash bargaining solution between the employer and his ensured
employees.
In the foreign country, there is no bargaining power for employees, and the nominal
wage keeps to the minimum reservation level. Thus, seeking more profit, all firms
belonging to the mobile and tradable industry (industry a ) move their factories to theforeign country as soon as international capital movement is permitted. This is thedefinition of industrial hollowing in our model. Furthermore, for simplicity, we assume
that the foreign country is unable to produce good a . In addition, since every good isdifferentiated, a firm can segregate the domestic and foreign markets, and thus, a pricediscrimination policy is possible. This fact implies that the purchasing power parity
theory never holds concerning exchange rate determination.
Finally, for simplicity, both governments keep the real money supply constant.
Seigniorage is consumed by both industries (a and b) in the same proportion as in theprivate sectors.

3

2.2 Optimization Problems of Economic Agents
2.2.1 Individuals
We assume that every individual has the following utility function.

u (c1 , c2 ) ≡ [ c1 ] [ c2 ]
c

1− c

1
2

1
2

1

1−η
1−η −1− δα , ci ≡ [ cai ] [ cbi ] , cki ≡  ∫10 [ cki ( z ) ]
dz 
,


−1

1 > c > 0,η > 1,

(1)

where ci denotes the aggregate consumption during the i-th stage of life, cki is theaggregate consumption of industry k‘s goods during the i-th stage of life, and cki(z) is theconsumption of good z that belongs to industry k . αis the disutility of labor, andδ is adefinition function that takes the value unity when employed and zero whenunemployed.
To solve this optimization problem, we need three steps. First, given the expenditureof k industry’s goods yki (k=a or b), we maximize cki with respect to cki (z). As the second
step, since cki becomes a function of yki , we need to maximize
11

ci ≡ [ cai ( yai ) ] 2 [ cbi ( ybi ) ] 2
with respect to yki under the given total real spending during period i ,yi.
The final step is the maximization of[c1 ( y1 )] [c2 ( y2 )]c

1− cwith respect to yi under the lifetime budget constraint.
The first step leads us the following demand function: p ( z) =cki ( z )  ki  Pki 

−η

1
Y
1
1−η
1−η


yki , Pki ≡  ∫ 0 [ pki ( z )] d  z , yki ≡ ki , (2)Pkiwhere Yki is the nominal expenditure for goods k. Since the equilibrium is symmetric,
without the loss of generality, we can set

Pi ≡ Pai = Pbi ,∀i.
Hence, the second step of the maximization becomes1

1

max yki [ yai ] 2 [ ybi ] 2 , s.t. yi =yai + ybi , yi ≡

4

Yi
.
Pi

The solution is

y=
y=
ai
bi

yi
.
2

(3)

By using (3), the final maximization is expressed by

max Yi [ y1 ] [ y2 ]c

1− c

, s.t. y1 + ρ y2 = y, y ≡

Y
P1

(4)

W here Y is the nominal income earned when the employee is young, and ρ is the
inflation rate. Equation (4) leads us to the Keynes’ type aggregate consumption of theyoung generation. That is,(5)

y1 = c ⋅ y.

Substituting Equation (5) and the lifetime budget constraint into Equation (4), we
obtain the following indirect utility function concerning the consumption stream:

AY l
IU ( P , P , Y ) ≡ =A[ ρl ]−[1−c ] y l , A ≡ c c [1 − c]1−c . (6)l cl 1− c[ P1 ] [ P2 ]The superscript l (l = h, f ) denotes the home and foreign country. From Equation (6),
l
1

l
2

l

we obtain the nominal reservation wage Wt during period t asRl

Wt Rl = A−1 Pt l [ ρ ]1−c α .

(7)2.2.2 Employers
It is clear from Equations (2) and (3) that every firm belonging to industry a faces theidentical demand function−η pth ( z )  yth f
 ptf ( z ) =c ( z ) =
c
z
,
(
)


at
h 
f
 Pt  2
 Pt 
h
at

−η

ytf
2

(8)

where cat (l = h, f ) is the demand for good a within the home and foreign country,lrespectively. yt (l = h, f ) denotes the real effective demand of country l during periodlt . In addition, let us define the real exchange rate et byEt Pt fet ≡ d ,pt
where Et is the nominal exchange rate.
We regard the production-wage determination as the following two-stage gamedeveloped by Otaki [1]. First, an employer determines the employment and price levelso as to maximize its profits. Second, an employer and a certain member of individuals,
5who have been ensured employment, negotiate the nominal equilibrium wage inaccordance with the asymmetric Nash bargaining solution of which the threaten point
is( 0,W ) .
R

Since the production function is linear, we can separate a firm’s profit maximization
into the domestic and foreign markets. Since these problems are essentially identical,
for avoiding the duplication of elementary calculation, we confine ourselves to thedomestic market problem.
Let us denote asθthe bargaining power of an employer. Then the equilibrium
nominal wage of industry a in the domestic labor market is determined as
(9)

h*
W=
θWt Rh + [1 − θ ] path ( z ) . 2
at

By following Equation (9), the profit function of each firm within industry a isrepresented by=
π ath ( z ) θ [ patd ( z ) − Wt Rh ]cath ( z ) .

(10)

Maximizing (10) with respect to pai ( z ) , we obtain the following optimal-pricing rulehconcerning the domestic market regardless of the strength of the bargaining power θ ,=path* ( z )Wt Rh, ∀t , z.
[1 − η −1 ](11)Thus, every firm offers the same price regardless of the industry to which it belongs.
In the foreign country market, we obtain the optimal-pricing rule via the sameprocedure as

Wt Rf=, ∀t , z.
p ( z)[1 − η −1 ]
f*
at

(12)

Combining Equations (11) and (12) with (7), we obtain the world-common
equilibrium inflation rate ρ * as1 [1 − η −1 ] A  1−cρ* = 

α

 .

(13)

Substituting Equations (11) and (12) into (10), the equilibrium aggregate profit
function

2

π at*
Pt h*

is obtained as

For the precise procedure for solving this bargaining problem, see Otaki [1].
6

π at*

=
Pt h*

η −1

θ yth + et ytf  .
2

(14)

It is apparent from Equation (14) that all factories belonging to the mobile industry amove from the home country where 1 > θ > 0 , to the foreign country where θ = 1 . We

define such an international capital movement as industrial hollowing.
2.3 Market Equilibrium
2.3.1 The Foreign Exchange Market

From the property of the OLG model without bequest motive, the domestic savings forforeign currency should be always equal to the sum of the expenditure of the foreign
old generation and the government toward industry a plus the wage payments toforeign employees who work in industry a.
Thus, the equilibrium condition for the foreign exchange in the stationary state is

1 − c h [1 − c]e f EiWi R a=yy + a* y .
pi
2
2

(15)

The left-hand side of Equation (15), is the foreign currency savings of the young
generation in the home country. The first term of the right-hand side of this equation is
the sum of the consumption of the old generation in the foreign country of good a andits government expenditure. The second term is the total wage payments to foreign
employees; y a is expressed asya =y h + ey f
.
2

(16)

In addition, from Equation (11), we obtain

EiWi R= [1 − η −1 ].
pia

(17)

Substituting Equations (16) and (17) into (15) and rearranging the terms, we finallyobtain the following equation concerning the equilibrium condition for the foreignexchange market:η −1 − c  h  c + η −1  f
 2  y = 1 − 2  ey .





(18)

To let the above equation have economic meaning, we assume that η −1 > c .
Equation (18) can be reinterpreted as follows. The total demand for the domestic
currency (the left-hand side of (18)) is the profits earned in the foreign country

7

η −1
2

yh

minus the young-generation’s consumption of good a ,c hy . This subtraction is2

necessary because the consumption of good a economizes the demand for the domestic
currency.
The right-hand side of (18) represents the supply for the domestic currency. It consists

1− c f]ey ,2of the expenditure of the older generation in terms of the domestic currency [1 − η −1]ey f . This addition is necessary
2plus the total wage payments of industry a , [because the wage payments to employees in the foreign country demand much foreign
currency.
2.3.2 The Aggregate Goods Market
Next we examine the aggregate goods market. The equilibrium condition is defined as1 − c h EiWi R a 1 − c f 
EW R hy=c  y h − i ai y a  + m + y −y −ey  ,
pi
pia
2


 2


(19)

where y h (≡ y a + y b ) is the home country’s real GNP (not GDP) in terms of the price ofa (mobile) industry’s goods. The terms in the first bracket of the RHS of the above
equation express the total consumption of the younger generation in the home country.

EiWi R a
Note that we must deduct the real wage payments
y to the foreign countrypiafrom the real GNP y k to calculate the real disposable income.
The second term is the sum of the government’s and the older generation’s
expenditures in terms of the home currency.

3

The terms in the second bracket

correspond to the home-country’s current account surplus.
the home-country firms (the surplus of trade balance). −income account. −1− c hy is the real export of2

EiWi R ay is the surplus of thepia

1− c fey represents the surplus of the capital account.
2

Since there is no asset-accumulation motive in this model, the terms inside the second
bracket takes value zero, as indicated by Equation (15). Accordingly, combining with(16), the aggregate goods market is cleared when
We here assume that domestic money is credible in the sense of Otaki [4], and that thecurrent prices are not affected by a change in the nominal money supply.
3

8

h
y=
c  y h − [1 − η −1 ] y a  + m .

(20)

By using Equation (15), (20) can be rewritten as1 + η −1  h 1 − η −1 f
y h + ey f =+=
y h c [ y h − [1 − η −1 ]mc
 2  y − 2 ey + m. (21)
2





(

To summarize, we have two endogenous variables y h , e() and two structural)

equations (14) and (20) with two exogenous variables m, y f . Thus, the model is closed.

3. Welfare Implications of Foreign Direct Investment
In this section, we analyze the positive and normative implications of foreign direct
investment by the comparative statics of the model. First, we begin with the case for an
increase in the foreign country’s real disposable income y f .
From the maximization condition of a firm that belongs to industry a , the output for
the foreign country proportionately increases with f . However, we must note that theforeign country’s disposable income y f always appears as the product with the realexchange rate e in market equilibrium conditions (18) and (21).
Accordingly, it is apparent that, regardless of the level of the foreign disposable
income y f , as long as the real exchange rate properly adjusts so that the product ey f is
kept constant, there is no substantial effect on the domestic economy. This property
implies that even if the foreign country upturns and provides the foreign-invested firmwith additional business opportunities, such a possibility immediately disappears
because of the appreciation of the real exchange rate. This appreciation is caused by
the simultaneous moves of firms to transfer would-be profits to the home country. Thus,
foreign direct investment never cultivates new business opportunities per se.
However, as seen in the second term of Equation (21), which never appears without
foreign direct investment, we can ascertain that there is a negative effect on thedomestic effective demand. This is because foreign direct investment deprives thehome country of the domestic employment opportunities and because a part of theeffective demand flows to the foreign country as wage payments to foreign employees.
. Thus, there emerges the coexistence of higher unemployment and continuous
appreciation of the real exchange rate in an industrially hollowed country together
with its surrounding economies’ growth. Although such a tendency is observed in many9

advanced countries, it is especially prominent in Japan.
Next, let us analyze the welfare-economic implication of foreign direct investment.
Since, from Equations (6) and (13), the net welfare gain is proportionate to the real
total sales after deducting the real reservation wage payment, the total indirect utility
is proportionate to the domestic real GNP y . (Note that the distribution ratio betweenhthe real reservation wage to residuals is η −1 :1 − η −1 .)Accordingly, it is apparent from Equation (21) that the equilibrium real GNP isalways higher in the case without industrial hollowing. This is because, as previously
discussed, a leak of the domestic effective demand, which comes from wage payments
to the foreign country, exists. Thus, the industrial hollowing brings about a negative
welfare effect for the home country. This tendency becomes more prominent as themonopolistic power of the tradable and mobile industry (industry a) declines, and η−1takes a lower value since such decline results in higher wage payments to foreigncountries.
Hence, foreign direct investment under a flexible exchange rate system harms the
economic welfare of the home country as a whole, although it is a rational behavior forindividual firms. As such, an economic conflict emerges between the home country andinternationalized individual firms.
Second, let us consider the effectiveness concerning the domestic fiscal-monetary
policy. From Equation (21), it is clear that the multiplier of our fiscal-monetary policy
is smaller than in the case of a closed economy without foreign direct investment. That
is,

1
>
1− c

1
.
1 + η −1 
1− c 
 2 

Such a decline in the effectiveness of aggregate management policies also comes fromthe fact that there is a leakage of the domestic effective demand via wage payment to
the foreign country. Together with a weakening monopolistic power (lower value of η −1 ),the decline in the power of fiscal-monetary policy becomes more serious. This is also
because higher wage payments are required.
4. Concluding Remarks
This article analyzed macroeconomic effects concerning foreign direct investment in asmall open country under a flexible exchange rate system with a rigorous dynamic
microeconomic foundation. Obtained economic consequences are not so optimistic forindustrial hollowing.
10

First, industrial hollowing occurs whenever wage is cheaper than in the home country.
Foreign direct investment is beneficial for each firm as long as the macroeconomic
circumstances are kept intact despite of such a collective movement, which we callindustrial hollowing. However, industrial hollowing under a flexible exchange rate isharmful to the home-country’s economy. Massive transfer of earnings to the homecountry appreciates the real exchange rate enough to cancel out the spurious benefits
from foreign direct investment.
There remains only the contraction of employment opportunities in the home country.
The unemployment caused by industrial hollowing reduces the real effective demand
and real disposable income via the multiplier effect. Thus, the economic welfare isdeteriorated by industrial hollowing, as proved by Otaki [1]. In other words, there is aserious political conflict between a nation state and internationalized firms.
Second, the effectiveness of the fiscal-monetary policy, which is defined by the value ofthe fiscal multiplier, is weakened by industrial hollowing. Such a difficulty comes fromthe leakage of the effective demand that accompanies industrial hollowing. That is, thedomestic effective demand leaks to the foreign country via the wage payments. It
results in lowering the value of the fiscal multiplier. The decline in the power of theaggregate demand management should be taken into serious consideration whenever
we think of the current severe constraint concerning fiscal discipline, although such a
discussion is partly beyond the scope of this paper.
To summarize, libertarianism concerning foreign direct investment is neverpreferable. Some regulations based on common sense and coordination between themonetary authority and internationalized firms are urgently required.

References[1] M. Otaki, “A Welfare Economic Foundation for the Full-Employment Policy,” Economics
Letters, Vol. 102, No. 1, 2009, pp. 1-3. doi:10.1016/j.econlet.2008.08.003[2] M. Otaki, “The Dynamically Extended Keynesian Cross and the Welfare-Improving Fiscal
Policy,” Economics Letters, Vol. 96, No. 1, 2007, pp. 23-29. doi:10.1016/j.econlet.2006.12.005[3] M. Otaki, “A Pure Theory of Aggregate Price Determination,” Theoretical Economics Letters,Vol. 1, No. 3, 2011, pp. 122-128. doi:10.4236/tel.2011.13026

11

[4] M. Otaki, “A Keynesian Model of a Small Open Economy under a Flexible Exchange Rate
System,’’ Theoretical Economics Letters, forthcoming.

[5] R.F. Kahn, ``The Relation of Home Invest to Unemployment,’’ Economic Journal, Vol. 41, 1931,
pp. 173-198.

12

Errata

1. Replace Equation (15) on page 6 with
E W   1ey f
1[1  c]  y h  i a*i  
2
2
pi 

2. Delete sentence from the second line of the bottom of page 6 to the eighth line of page4.
3. Replace Equation (18) on page 6 with [1  c] 1  h  [1  c]  c 1  fy  ey .
22

4. Replace Equation (19) on page 7 with

1



EW
E W   1ey f 
y h  c  y h  i a* i y a   m   [1  c]  y h  i a* i  
.
pi
p
2
2
i






5. In the second paragraph of 2.3.2, there is a sentence that begins with ``


EW 
1
1 c hy with [1  c]  y h  i a*i  .
2
pi 
2


real export of the home-country firms.’’ Replace

6. Following the above sentence, there are sentences ``account. 1 c hy is the2

EiWi
is the surplus of incomepia*1 c fey represents the surplus of the capital account. ”
2These sentences should be modified as `` 1ey f2

represents the surplus of the capital

account.’’
7. To the end of 2.3.2, add the following sentences.
``Substituting (18) into (21) and solving on y , we obtain
h

yh 

m
1
[1  c][1   1 ] 
1
1   c[1   ] 2
1  c  c 1 (22).

From (18) and (22), we can also ascertainde 0. ’’
dm
8. The inequality that appears on page 9 should be modified as

1

1 c

1
1
[1  c][1   1 ] 
1
1  c[1   ] 2
1  c  c 1 .