Export Subsidies, Balance of Payments and Growth
- The Case for Export Promotion Policies
Joy Mazumdar
Department of Economics
Emory University
Atlanta, GA 30322
USA
jmazumd@emory.edu
August 1999
Abstract
There seems to be general agreement that export promotion policies played an important role in the growth process of the newly industrializing countries (NICs) of
East Asia (especially Taiwan and S. Korea). This paper argues that export promotion polices like export subsidies help the growth process in developing countries by
increasing the rate of return to investment. Moreover, balance of payments considerations make export subsidies superior to other policies that increase the pro…tability
of investment (e.g. reduction in the import tari¤s on investment goods or investment
subsidies).
JEL Classi…cation: F43, F31, F13, O20
1
I. INTRODUCTION
The role of government policy in the extraordinary growth experience of the East
Asian economies - Taiwan, S. Korea, Hong Kong, Singapore and Japan is still a matter
of controversy. The neoclassical view is that government policies that interfered
with market forces played a small role in the growth process. There are others
(e.g. Amsden 1989 ,Wade 1990) who argue that government intervention was widely
prevalent in these countries and this phenomenal growth would not have been possible
without it.
There seems to be general agreement, however, that export promotion policies
played an important role in the growth process of at least some of these countries
.Export incentives of many kinds were widely prevalent in both Taiwan and Korea.
Export processing zones (EPZs) were set up so that …rms located inside these zones
could import intermediate inputs free of duties and taxes and administrative costs in
return for exporting all their production. Cheaper credit was made available by the
government to exporters. For example, the Bank of Taiwan started the Export Loan
Program in 1957 which extended short term loans to exporters at 0.99% per month
which was considerably less than the 1.65% per month that other borrowers had to
pay (Scott 1979). The Taiwanese government also encouraged domestic industries
to form export cartels to prevent excessive competition in the domestic markets. In
the late 50s and 60s cartels were formed in industries such as paper, textiles, canned
foodstu¤s, steel products among other. Their schemes amounted to levies on domestic
sales, export quotas in proportion to each members’ output (with penalties if exports
fell short).
Adherents to the neoclassical view argue that export promotion policies helped
because they corrected existing government induced distortions in the economy and
2
prevented the government from introducing large price distortions. The World Bank
(see the East Asian Miracle 1993 for the World Bank’s analysis of the East Asian
growth process), which attempts to strike a compromise between the neoclassical
view and what it calls the “revisionist” view (i.e., the one in favor of government
intervention), suggests that export oriented policies helped …rms in these economies
to catch up quickly to international best practices and therefore achieve high rates of
total factor productivity growth1 .
A view that argues against the export led explanation of East Asian growth comes
from Rodrik (1995). He draws a sharp distinction between government policies that
favored investment and export promotion policies that fostered exports. According to
the World Bank export promotion policies spurred the growth process while policies
that favored investment did not have a signi…cant e¤ect on growth. Rodrik, on
the other hand, argues that policies aimed at boosting investment led to the high
growth rates by solving a coordination problem and export promotion policies did
not signi…cantly alter the incentives to export. The increase in exports/gdp that
was observed was a result of the investment boom. I will argue in this paper that
such a sharp distinction between export promotion policies and investment boosting
policies need not be made. I will show in this paper that export promotion policies
e.g. export subsidies increase the rate of return to investment and therefore end up
increasing investment.
1
There are various reasons why export orientation may help productivity growth. Exporting
…rms are forced to be more e¢cient because they have to compete in the international market.
They may be able to acquire technology more easily if they are supplying intermediate goods to
a major producer in the industrialized world. In this case, the producer in the developed nation
is more willing to share know how especially if it is old knowledge with the exporting …rm in the
developing country. Export oriented economies are also more likely to attract export oriented direct
foreign investment that may have spillover bene…ts for the rest of the economy. Also countries that
export more earn the foreign exchange needed to import sophisticated machinery from abroad.
3
The link between export promotion polices and growth that has been emphasized
so far is productivity growth or technological change in …rms that have to compete in
global markets (see, e.g., Aw and Hwang 1995, Tybout and Westbrook 1995). However, there is evidence to suggest that the documented positive association between
exporting and e¢ciency arises not because exporting causes …rms to become more
productive but due to the self selection of more e¢cient …rms into the export market (Clerides, Lach and Tybout, 1998). Also it seems that the important sources of
growth for E Asian economies has been factor accumulation (physical capital, human
capital and labor participation rates ) and not technological change (Young, 1995).
This suggests that if we are to look for a link between export promotion and growth
we should look at the links between export oriented policies and factor accumulation.
Since capital accumulation played an important role in the growth process, in this
paper we will analyze the links between export subsidies and capital accumulation.
In this paper we will show that export oriented policies increased overall investment.
The intuition behind this is the following. The bulk of the machinery investment
in developing countries is imported since developing countries have a comparative
disadvantage in equipment production. The East Asian economies were no exception.
Their exports, at least in the early stages of their development, consisted mainly of
consumption goods while their imports were mainly raw materials and investment
goods. For example, machinery and transport equipment constituted only 0.3% of
Korea’s exports and 20% of her imports in the early 1960s. We will show that given
this trade pattern, export subsidies increase the rate of return to investment because
they increase the domestic price (that is, the price that producers receive) of the
consumption good relative to that of the investment good.
This, however, raises the question why were export subsidies used to boost investment instead of other policies. Speci…cally, a reduction in the import tari¤ or
an investment subsidy would all increase the pro…tability of investment and would
4
therefore lead to capital accumulation. In this paper we will show that if the country
wants to maintain a …xed exchange rate for whatever reason then balance of payments
considerations make export subsidy the preferred policy. All the other policies lead
to foreign exchange reserve out‡ows. An export subsidy leads to a smaller reserve
out‡ows compared to the other policies and possibly no reserve out‡ows. This, in
our opinion, was the reason for the success of export oriented policies. We know
that export promotion policies were often started to ease the balance of payments
situation. For example, in Taiwan trade policy reform, which included increasing the
incentives to export, was introduced in the 1958-62 period, after the country had been
running current account de…cits for many years in the 50s and the United States had
signalled that aid to Taiwan, which …nanced a signi…cant portion of the current account de…cits, would be terminated. The export incentive schemes continued through
the 70s but were scaled back as foreign exchange reserves became substantial (Wade
1990).
The intuition behind why export promotion policies lead to smaller reserve out‡ows is the following. Demand for nominal money depends on the interest rate and
the nominal price of the consumption good. Higher is the nominal price of the consumption good, the higher is the amount of nominal money consumers are willing to
hold2 . Export subsidies increase the nominal price of the consumption good while the
other policies do not. When any policy that increases the return to investment (e.g.
an export subsidy or a reduction in the import tari¤ in our model or an investment
subsidy) is introduced, money demand falls since interest rates go up and households
change the composition of their assets in favor of capital. A …xed exchange rate
implies that this money has to ‡ow out of the economy and it takes the form of
2
The intuition is that if the nominal price of the consumption good rises then the utility derived
from spending a dollar on the consumption good falls and the consumer is more willing to hold that
dollar.
5
reserve out‡ows. Since money demand is higher under export subsidies than under
other investment enhancing policies they lead to smaller reserve out‡ows than other
policies.
The e¤ect of all export incentives would be to push the prices of the exportable
goods in the domestic market above their world prices. . Such an arrangement could
be sustained if the domestic market of these goods was protected. In fact there
is evidence to suggest that in Taiwan in the 1961-71 period among manufactured
goods, the highest rate of nominal protection was extended to export-competing
industries; the rates of protection for export-import competing, non import competing
and import competing sectors were lower (Kuo 1983). An interesting point to note is
that a situation in which the domestic price of the exportable is kept higher than the
world price with the help of import barriers would look suspiciously like “dumping”
to foreign competitors.
Export promotion policies, therefore, increase capital accumulation without leading
to an excessive loss of foreign exchange reserves unlike other investment boosting
policies. This, in our opinion, was the reason for their success. This interpretation
of export promotion policies is consistent with many of the stylized facts of the East
Asian growth experience - high saving and investment rates, high export/gdp ratio,
protected domestic markets (even with respect to the exportable good), the practice
of dumping and accumulation of foreign exchange reserves.
The paper is organized as follows. Section II describes the model. Section III
compares the various policies. Section IV concludes.
II. THE MODEL
Assume that there is a small economy with identical households that trades goods
with the rest of the world. There are two goods - a consumption good (X) and an
investment good (Y). We will assume that this economy has a comparative advantage
6
in the consumption good so that at world relative prices it exports the consumption
good and imports the investment good. We will assume that there is no international
borrowing or lending so that investment in the economy will have to equal its savings.
The consumptions-savings decision is carried out by the representative household
which optimizes over an in…nite horizon.
We will assume that trade is not completely free - there is an import tari¤ on the
investment good. The reason for this assumption is to see the e¤ects of di¤erent
policies in an economy in which policy induced distortions already exist. This is the
actual environment in which governments in developing countries operate and contemplate policy changes. We will see in the following sections that once an import
tari¤ is already in place, a reduction in the tari¤ will cause foreign exchange out‡ows (although it makes the economy more e¢cient). This is consistent with trade
liberalization experiences of many countries and may partly explain the resistance of
governments to reducing import tari¤s.
The government uses the following three policy instruments - import tari¤, export
subsidy and investment subsidy. The last of these is not a trade policy instrument.
However, as will be shown, since a reduction in the import tari¤ and an increase in
the export subsidy have the e¤ect of increasing the rate of return to investment, a
comparison of these policies with an investment subsidy seems natural.
The production side of the economy is as follows. The goods are produced with
three primary factors - labor (L), physical capital (K) and human capital (H). Labor
and physical capital are perfectly mobile across sectors. Human capital is sector
speci…c3 . Labor and human capital are …xed in supply. The amount of capital changes
3
The assumption of a sector speci…c third factor (in this case human capital) has been made so
that the country does not specialize in the production of one good. If there were only two factors
that were mobile then our assumption of equal factor intensities across sectors would imply that
the small open economy would end up specializing in the production of one good. Since that is
unrealistic, the presence of a third immobile factor has been assumed. Human capital does not play
7
when there is positive net investment. There is perfect competition in both goods
and factor markets and the factors are fully employed. The production technology is
Cobb-Douglas and is of the following form
Qj = Aj (Kj Lj )®=2 Hj1¡®
(1)
where, j = x; y .
We have assumed that the factor intensities are the same across sectors. This
a departure from the standard Heckscher-Ohlin model in which the di¤erent factor
intensities across sectors (and di¤erent endowments) gives rise to trade. In this model,
trade exists between this country and the rest of the world because of di¤erent As
or total factor productivity levels in this country in the two sectors that are di¤erent
from those of the rest of the world. This departure has been made for the following
reason. We are trying to model a developing country. This means that the capital
labor ratio of this country will be lower than that of the developed nations. Assuming
that the bulk of the trade of this country is with the advanced nations (which is the
case for most developing countries) the standard H-O model would imply that the
rate of return to investment would fall with free trade. This seems counter-intuitive.
Also, it makes the analysis simpler because the trade pattern does not change as
capital accumulates and per capita gross domestic product can be expressed as a
function of the per capita capital stock and has the same functional form as the
single good model (except for a multiplicative term).
The wage of labor (wl ) and the rental price of capital (r) have to be the same
across sectors. Pro…t maximization and perfect competition imply that the marginal
revenue product of each factor equals its price. Therefore,
®
wl = pj Aj
2
Ã
Hj
Lj
!1¡® Ã
Kj
Lj
!®=2
(2)
any role in the growth process as in the endogenous growth models. In this model growth is medium
run and arises because of capital accumulation.
8
j = x; y:
®
r = pj Aj
2
Ã
Hj
Kj
!1¡® Ã
Lj
Kj
!®=2
(3)
j = x; y
where pj is the domestic price of the jth good.
Using equations (2) and (3), we get,
Ky
wl
Kx
=
=
r
Lx
Ly
(4)
Using equations (2) and (4) we get,
px
Ay
=
py
Ax
µ
Hy
Hx
¶1¡® Ã
Lx
Ly
!1¡®
(5)
For a small open economy such as this one, the domestic relative price is a function of the world relative price, import tari¤ and export subsidies, all of which are
exogenous. That is,
px
pw
x (1 + tx )
= w
py
py (1 + ty )
(6)
where w denotes world, ty is the (nominal) import tari¤ rate on the investment
good and tx is the (nominal) rate of export subsidy on the consumption good.
One can see from equation (5) that the ratio Lx =Ly is determined by the domestic
relative price of X. The ratio Lx =Ly is equal to the ratio Kx =Ky (equation 4). This
ratio along with the full employment conditions Lx + Ly = L and Kx + Ky = K
determine the quantities of labor and capital employed in the two sectors and therefore
the quantities of the two goods produced at any point in time.
One can see from equation (5) that since Hx and Hy are constant any increase in
the relative price of X will increase the quantity of X produced, since it will increase
Lx (and therefore Kx ), and reduce the production of Y.
We will de…ne R as follows.
R ´ r(1 + i)=py
9
(7)
where i is the rate of investment subsidy (paid as a per cent of the rental price r)
R is equal to the rental price that the owners of capital receive divided by the price
of the capital good. R minus the depreciation rate will equal the real interest rate in
this economy. We will assume for now that i is equal to 0.
Using the de…nition of R and the fact that the rental price of capital has to equal
the marginal revenue product of capital in the Y industry (equation 3) we get,
Ã
!®=2 Ã
Ly
®
R = Ay
2
Ky
Hy
Ky
!1¡®
(1 + i)
(8)
A. The Model Without Money
Let us assume for the moment that there is no money in this economy. Therefore,
there is only one asset in this economy i.e., capital. The representative consumer
derives utility from the consumption good only and solves the following optimization
problem.
Maximize
U=
Z
0
1
e¡¯t u(c)dt
subject to the constraint that at each instant
pk k_ = wl l + r(1 + i)k + wh ¡ px c ¡ pk ±k + T
where l, k and c are the per capita quantities of labor, capital and consumption,
respectively, pk is the price of 1 unit of capital stock, wh is the income from the human
capital endowment and T is import tari¤ revenue less taxes (to …nance the export
subsidies or investment subsidies). We will assume that both taxes and transfers are
lump sum. The government’s budget is always balanced.
I will assume that there are no adjustment costs associated with the installation of
the capital stock. Therefore, an existing unit of capital and a new unit produced are
perfectly substitutable so that pk = py .
10
The consumer’s optimization problem implies that in the steady state we will have
R =¯+±
(9)
Therefore, any government policy that raises R above the r.h.s. of the equation (9)
will lead to higher capital accumulation and growth4 .
The E¤ects of an Export Subsidy and Other Policies.—
An export subsidy will be a subsidy on the exports of the consumption good since
the country has a comparative advantage in it. The e¤ect of this subsidy will be to
increase the domestic relative price of good X since otherwise no producer will sell
in the domestic market (the higher domestic price of the X good will presumably be
supported by an import tari¤ on X).
Assume that the country is initially in the steady state, i.e., equation (9) holds. Let
us consider the e¤ects of an export subsidy on the return to capital, R and growth.
An increase in R will lead to capital accumulation (and therefore growth) and the
capital stock will grow till R is driven down to the steady state level. From equation
(6) we can see that the export subsidy will increase the relative price of X. This will
increase the labor and capital employed in the consumption goods sector and reduce
it in the investment goods sector (equation 5). Let us look at equation (8) in order
to analyze the e¤ects of this on R. At any point in time the capital labor ratio in
the Y industry is equal to the overall capital labor ratio since the these ratios have
to be the same across both industries (equation 4). Therefore, the term within the
…rst set of parentheses on the r.h.s. of equation (8) does not change as a result of
the export subsidy in the instant the policy is introduced. Both labor and capital in
the Y sector decrease by the same proportion leaving the ratio unchanged and equal
to the overall capital labor ratio. However, since Ky falls the term within the second
4
Di¤erent policies will be considered to have the same e¤ect on growth if the increase in the
steady state capital stock is the same. However, the rate of accumulation may di¤er.
11
set of parentheses in equation (8) or the ratio of Y speci…c human capital to capital
rises (since Hy is constant). This raises R. This leads to capital accumulation in the
economy which increases K and therefore Ky and brings down the rate of return to
capital.
In this model with no money, a reduction in the import tari¤ on the investment
good will have exactly the same e¤ect as an export subsidy. From equation (6) we can
see that it will reduce py =px which will lead to a decrease in Ky , an increase in R and
capital accumulation and growth. An investment subsidy, i.e., an increase in i, will
lead to an increase in R (see equation (7)) but it will leave py =px unchanged. Since
R will be pushed above the steady state level, this policy will also lead to capital
accumulation.
While export subsidies increase the rate of return to investment, there are other
policies that achieve the same result. For example, an import subsidy (or a reduction
in import tari¤) or an investment subsidy would have the same e¤ect. The question
is why export subsidies were used instead of these other policies. A possible reason
could be that export subsidies have a favorable e¤ect on the foreign exchange reserve
position of a country while the other policies do not. This seems plausible especially
because export subsidies were often used in response to a deteriorating balance of
payments position. In order to show the e¤ects of export subsidies vis a vis other
policies we have to analyze a model with money.
B. The Model With Money
We will assume the same production technology as before. We will, however,
introduce money in the utility function. The consumer’s problem now is as follows
Maximize
U=
Z
0
1
¡¯t
e
!
Ã
M
dt
u c;
µpx + (1 ¡ µ)py
12
subject to the constraint
py k_ + M_ = wl l + rk + wh ¡ px c ¡ pk ±k + T
where M is nominal money.
The consumer, therefore, derives utility from real money balances. Since we have
two nominal prices in this model, the average price level the consumer takes into
consideration is a weighted average of the two nominal prices. We have assumed that
the weights are …xed5 .
We will assume that the exchange rate is …xed at s in this economy. Therefore,
domestic nominal prices will depend on world prices and the tari¤ rates. Therefore,
we will have,
pj = spw
j (1 + tj )
(10)
for j = x; y .
The superscript w denotes world and t is the tari¤ (or subsidy in case x) rate.
I will assume for now that the government does not interfere with the money supply.
The central bank’s assets are government bonds and foreign currency reserves. It’s
liabilities consist of the money in circulation M. Assets of the central bank equal its
liabilities so that
M =B+C
(11)
where B is government bonds (which households do not hold) and C is foreign
currency reserves.
Since the exchange rate is …xed and the government does not attempt to change
the money supply (i.e., it does not change B ), any change in the holdings of nominal
5
This is an ad hoc assumption and has been made for the sake of simplicity. Ideally, the price
index should be derived from an optimization problem of the consumer. The functional form of the
price index will not have any signi…cance for the …nal results because it will drop out of the dynamic
equations.
13
money will have to involve foreign exchange reserve ‡ows or changes in C. For
example if agents wanted to hold less money than is available, they would spend it on
goods. In a model with ‡exible exchange rates this would merely increase the price
level in the economy (inducing people to hold the amount of nominal money available
in the economy) and the exchange rate would adjust accordingly. This cannot happen
in this model with …xed exchange rates. The price level is tied down by the …xed
exchange rate. Any excess money would ‡ow out of the economy leading to a reserve
out‡ow.
The consumer’s optimization problem leads to the following three equations.
¸=
and
uc
px
(12)
¸_
=¯+±¡R
¸
(13)
¸_
um px
=¯¡
¸
uc [µpx + (1 ¡ µ)py ]
(14)
where, ¸ is the multiplier associated with the consumer’s budget constraint and
is equal to the marginal utility from one unit of domestic currency spent on the
consumption good. uc and um are the partial derivatives of the instantaneous utility
function with respect to the …rst and second arguments, respectively (I have omitted
the arguments for the sake of clarity).
We will assume that the instantaneous utility function has the following form
u(c; m) = ½ ln(c) + (1 ¡ ½) ln(m)
where m =
M
µpx +(1¡µ)py
(15)
or real money balances.
This function along with equations (12), (13) and (14) imply
c=
½
¸px
14
(16)
and
M=
1¡½
¸(R ¡ ±)
(17)
Taking logs and di¤erentiating both sides of equation (17), we get,
M_
¸_
R0 k_
=¡ ¡
M
¸ R¡±
(18)
Using the fact that (wl l + rk + wh) is equal to per capita national income and
therefore the (nominal) value of goods produced in the economy at domestic prices
and taking into account the import tari¤s, export subsidies etc., the budget constraint
of the consumer can be expressed as
_
pw
yk+
pw
x
_
M
s
pw
y
=g ¡ w
±k ¡ c
px
w
(19)
where g w is per capita income in terms of the consumption good valued at the
world relative price.
It will be useful to derive an expression for per capita national income g w (the
total value of goods produced in the economy) in terms of the consumption good
valued at world relative prices. Using equations (1) and (5) and the fact the capital
labor ratios will be the same in both sectors, we get the following expression for g w
(h and k are per capita quantities of human and physical capital, respectively and
the superscript w denotes world).
®=2
g w = Ax h1¡®
x k
where
¹´
1 + ¹f
(1 + f )®
(20)
pw
py
y
¥
w
px
px
(21)
and
µ
Ay
f´
Ax
¶1=1¡®
hy
hx
Ã
py
px
!1=1¡®
µ
Ay
=
Ax
15
¶1=1¡®
hy
hx
Ã
pw
y
pw
x
!1=1¡®
¹1=(®¡1)
(22)
The expression
py
px
>
pw
y
.
pw
x
1+¹f
(1+f )®
increases with
py
px
when
py
px
<
pw
y
pw
x
and decreases with
py
px
when
That is, smaller is the distortion between world prices and domestic prices,
higher is the value of national income at world prices.
We can use equations (3), (5), (20) and the de…nition of R and ¹ to derive an
expression for the ratio between g w and R which will be useful for later analysis.
gw
2 py 1 + ¹f
=
k
R
® px (1 + f )
(23)
Both ¹ and f depend on py =px or the domestic relative price of the investment good.
If the domestic relative price of the investment good is higher than the world price
then both g w and R increase as py =px decreases (due to a reduction in the import
f 1¡¹
has
tari¤ or an export subsidy). It can be shown that the inequality 1 >
1+f 1¡®
to hold for g w =R to decrease as py =px decreases keeping k constant (see Appendix
A.1). This condition will hold if f is small. We will have a small f if hy =hx or Ay =Ax
is small (see equation 22). That is, if the Y (or the investment goods) sector is small
due to very low productivity in this sector or scarcity of the Y speci…c factor. Then
the increase in g w as a result of better reallocation of resources is small because the
f 1¡¹
from
Y sector is not very large to begin with. We will assume that 1 >
1+f 1¡®
now on.
Using (23), (20) and the de…nition of ¹, we get the following expression for R
w
®
1¡® (®=2¡1) px
R = Ax hx k
¹(1 + f)1¡®
w
2
py
(24)
That is, R is a function of k and ¹, besides the other parameters of the model. R
is an increasing function of ¹;as was explained before and a decreasing function of k.
Let us de…ne a new variable V such that
V ´
pw
yk+
pw
x
M
s
(25)
The variable V is the total value of assets held by domestic agents in terms of the
consumption good at world prices.
16
Using equations (25) and (17), we get,
pw
yk+
V ´
1¡½
s¸(R ¡ ±)
pw
x
(26)
Equations (26) and (24) de…ne k as a function of V , ¸ and ¹:We have, therefore,
k = F (V; ¸; ¹)
(27)
An examination of equation (26) will reveal that k is an increasing function of all
three variables.
The Equations of Motion.—
Using the de…nition of V_ , equations (19), (20), (16) and (27) we get,
½
1 + ¹f ®=2 pw
F
¡ yw ±F ¡
V_ = Ax hx1¡®
®
(1 + f )
px
¸px
(28)
Using equations (24) and (27) we can rewrite equation (13) as,
w
¸_
(®=2¡1) px
= ¯ + ± ¡ Ax h1¡®
F
¹(1 + f )1¡®
x
¸
pw
y
(29)
The third term on the right hand side of equation (29) is just R.
Equations (28) and (29) are two di¤erential equations in V and ¸ (since F is a
function of these variables) that describe the dynamics of the system
In the steady state, we will have the following
V_ = ¸_ = 0
(30)
The phase diagram of the system is shown in Figure 1. The V_ = 0 locus is
negatively sloped because along this line the following has to hold (see equation (28))
½
1 + ¹f ®=2 pw
= Ax h1¡®
F
¡ yw ±F
x
¸px
(1 + f )®
px
17
(31)
As V increases the right hand side of the equation increases since F (which is k) is
an increasing function of V and k is less than the “golden rule” capital stock at which
the di¤erence between output and depreciation expenditure is maximized (if ¹ were
equal to 1 then this would occur at the capital stock at which R = ±; for ¹ < 1 this
occurs where R < ±. Since we know R > ¯ + ± when the economy is out of steady
state we know that the capital stock is less than the “golden rule”). Therefore, ¸ has
to decrease to raise the left hand side and reduce the right hand side of the equation
(F is an increasing function of ¸).
The ¸_ = 0 locus is negatively sloped also since the following has to hold
Axhx1¡® F (®=2¡1)
pw
x
¹(1 + f )1¡® = ¯ + ±
pw
y
(32)
The left hand side is just R. An increase in V will increase F (or k) and therefore
reduce R. As a result, ¸ will have to decrease to reduce F and raise R.
It can also be shown that the ¸_ = 0 locus is steeper than the V_ = 0 locus. Totally
di¤erentiating (31) and manipulating the resulting expression we get the following
expression for the slope of the V_ = 0 locus.
d¸
=¡
dV
FV
F¸
"
·
® 1+¹f (®=2¡1)
Ax h1¡®
F
x
(1+f )®
Ax h1¡®
x
2
® 1+¹f (®=2¡1)
¡
®F
2 (1+f )
¡
pw
y
±
pw
x
pw
y
±
pw
x
¸
½
+ 2
¸ px F¸
#
(33)
where FV and F¸ are the partial derivatives of F with respect to the two variables
and are both positive, as was explained before. The expression within brackets in
the numerator is positive because k is less than the “golden rule” k. Therefore,
the expression within brackets in denominator is positive and is greater than the
corresponding expression in the numerator since the …rst two terms are the same and
the last terms is positive (F¸ is positive). Therefore, the absolute value of the slope
of this locus is less than FV =F¸ .
Totally di¤erentiating (32) and manipulating the resulting expression we get the
18
following expression for the slope of the ¸_ = 0 locus.
d¸
FV
=¡
dV
F¸
(34)
Therefore, the slope of the ¸_ = 0 locus is steeper than that of the V_ = 0 locus. The
system exhibits the saddlepoint property, as we can see in Figure 1, so that there is an
unique path leading to the steady state. The jump variable is ¸. The predetermined
variable is the total value of assets, V . Therefore, At any instant in time both k and
w
M can jump but the sum (pw
y k +M=s)=px cannot jump. At any instant, a decrease in
M , therefore, will be accompanied by an increase in k. Any adjustment to the total
wealth, V , will have to take place through ‡ows which can occur only over time.
If there is a positive shock to R it is clear from equation (29) that F (or k) will have
to increase for the system to be in equilibrium again since R will have to decrease
to the steady state value and it depends negatively on k. The e¤ects of an increase
in ¹ (or a decline in the domestic relative price of the investment good), which will
increase R, on the steady state are shown in Figure 2. The V_ = 0 locus shifts down
because an increase in ¹ increases F and also the expression (1 + ¹f )=(1 + f )® (as
was explained before) in equation (31). Since k or F is less then the “golden rule”
this will increase the right hand side of the equation. This will mean that at the
same ¸, V will have to be lower (to decrease F ) for the equation to hold. The ¸_ = 0
locus should shift up when ¹ increases. This may not be obvious at …rst because an
increase in ¹ seems to have an ambiguous e¤ect on the left hand side of equation
(32) since while ¹ and f go up, F increases also. However, the e¤ect of an increase
in F will be less than the e¤ect of the other two variables. This is because the left
hand side of this equation is just R and an increase in ¹, keeping the other variables
a¤ecting F the same (namely., V and ¸), cannot increase F so much that R stays
constant or actually falls. If R were to stay constant or actually fall as a result of an
increase in ¹ then from equation (26) it is clear that at the same ¸, V (or ¸) would
19
have to rise. That is, we would not be able maintain our assumption that V and
¸ are the same. An increase in ¹ with a corresponding rise in F is consistent with
constant V and ¸ only if R increases. Therefore, the left hand side of equation (32)
will have to increase as a result of an increase in ¹. This will mean that at the same
level of ¸, V will have to be higher to increase F so that the equation holds. The
implication of the shifts in these two loci is that the V will be higher and ¸ will be
lower in the new steady state. That is, consumers will have more assets and a higher
level of consumption in the new steady state.
A positive shock to R would mean that ¸_ will be negative as the economy moves
to the new steady state. Equation (18) then implies that M_ will be positive as the
economy moves to the new steady state (since R0 < 0 and k_ > 0). That is the economy
will accumulate money (and foreign exchange reserves) as the economy moves to the
new equilibrium. However, the immediate e¤ect of a policy shock that raises R could
be a decrease in money demand. In other words, right at the instant the economy is
hit by the shock, demand for nominal money can jump down. Since this will mean an
excess of money in the economy, there will be an excess of expenditure over income
and an out‡ow of foreign exchange reserves in the instant the economy is it by the
shock.
III. COMPARISON OF VARIOUS POLICIES IN THE MODEL WITH
MONEY
A. Export Subsidy vs. Tari¤ Reduction
In the presence of an import tari¤ on the investment good both the export subsidy
and the import tari¤ reduction move the domestic relative price closer to the world
relative price and therefore reduce the distortion. This has the e¤ect of raising national income at world relative prices, g w . Also, they both increase the rate of return
20
to investment R ¡ ± through their e¤ect on R (see equations 5 and 8) . The di¤erence
between the two policies is that while the export subsidy increases the nominal price
of the consumption good, the import tari¤ reduces the nominal price of investment
good (see equation 10). This will have implications for money demand and reserve
out‡ows in the period the policy is introduced.
Result 1
The immediate e¤ect of an increase in R as result of a reduction in import tari¤s
will be an excess of money and therefore a reserve out‡ow6
Proof:
The e¤ect of an import tari¤ will be a reduction in py or the nominal price of the
investment good. This will increase the relative price of the consumption good and
therefore R.
We have to show that in the period the policy is introduced, money demand is less
than the money supply (or the money demand in the original steady state).
According to the consumer’s budget constraint the following will have to hold for
all periods including the period the policy is introduced
pw
y
w
_
±k ¡ c
V =g ¡ w
px
(35)
Since V_ have to be positive in all periods7 , the following will have to hold in the
6
This e¤ect is similar to the e¤ects of foreign exchange liberalization on reserve ‡ows when
exchange rates are …xed (Park 1994)
7
This is because of the following reason. Suppose V_ were negative in any period. This means
that V would be lower in the next period. The dynamic equation governing ¸ implies that it would
be lower in the next period too since R > ¯ + ±. This implies that in the next period that F (or k)
is lower in the next period since it depends positively on V and ¸. Since F is lower and ¸ is lower
in the next period, the dynamic equation governing V implies that V_ will gain be negative so that
in the period after that V will be still lower. This logic will carry over to all subsequent periods
21
period the policy is introduced
pw
y
±k ¡ c > 0
g ¡ w
px
w
(36)
The inequality above and equations (16) and (17) imply
gw ¡
pw
½ M
y
(R ¡ ±) > 0
±k
¡
pw
1 ¡ ½ px
x
(37)
Dividing both sides of the inequality by (R ¡ ±) we get
gw ¡
pw
y
±k0
pw
x
R¡±
¡
½ M
>0
1 ¡ ½ px
(38)
In the original steady state since consumption was equal to income minus depreciation expenditure we had (the subscript 0 denotes the original steady state)
g0w ¡
pw
y
±k0
pw
x
R0 ¡ ±
¡
½ M0
=0
1 ¡ ½ px0
(39)
Since the inequality (38) will have to hold in the period the policy is implemented
the following will have to be true in this period
gw ¡
pw
y
±k
pw
x
R¡±
pw
g0w ¡ pyw ±k0
½ M
½ M0
x
¡
¡
>
1 ¡ ½ px
R0 ¡ ±
1 ¡ ½ px0
(40)
The question we have to answer is whether in the period the policy is introduced
k and M will be equal to their values in the original steady state. If that is the case,
since the inequality above has to hold, then the following will have to be true
gw ¡
pw
y
±k0
pw
x
R¡±
pw
g0w ¡ pyw ±k0
½ M0
½ M0
x
¡
>
¡
1 ¡ ½ px0
R0 ¡ ±
1 ¡ ½ px0
(41)
The reduction of the tari¤ increases R as well as g w at the original capital stock k0 .
The domestic price of the consumption good px stays the same in the case in which
so that V will keep on decreasing and will move away from the new steady state V which is higher
than the one in the old steady state. Since this cannot happen, V_ will have to be positive always.
22
pw
the import tari¤ is reduced. It can be shown that (g w ¡ pyw ±k0 )=(R ¡ ±) falls when
x
f 1¡¹
py =px falls as long as 1 >
(see appendix A.2). Therefore, the …rst term
1+f 1¡®
on the l.h.s. of the inequality (40) will be less than the …rst term on the r.h.s. in
the period the policy is implemented. So, the inequality above cannot hold. The
inequality (40) will hold in the period the policy is introduced only if k > k0 since
the …rst term increases with k (the numerator is an increasing function of k and the
denominator is a decreasing function of k). This implies that M < M0 since aggregate
w
wealth (pw
y k + M=s)=px in the period the policy is introduced is the same as in the
steady state since it cannot jump. Any increase in k will therefore mean a reduction
in M .
Since M in the period the policy is introduced will have to be less than M0 there
will be a reserve out‡ow the instant the policy is introduced.
The intuition behind the previous result is the following. In the period the policy is
introduced, aggregate wealth V cannot jump. However consumers are able to change
the composition of their asset holdings. Since now k yields a higher return, agents will
reduce their holdings of M and increase their holdings of k. This additional amount
of k is obtained through imports paid for by money (i.e., foreign exchange reserves).
In order to show that an export subsidy will actually lead to a smaller reserve
out‡ow than a reduction in the import tari¤ for the same increase in R, we have to
look at the phase diagram of this system under the two policies (Figure 3). The …gure
shows the new steady states under the two policies.
Equation (32), which de…nes the ¸_ = 0 locus, has been reproduced here for convenience.
w
1¡® (®=2¡1) px
¹(1
Ax hx F
pw
y
+ f )1¡® = ¯ + ±
(42)
As one can see from equation (42), the ¸_ = 0 locus will be the same under the two
23
policies if the ¹ is the same under the two policies (that is, the relative price of the
investment good is the same under both policies).
However, the V_ = 0 locus for the export subsidy will be below that of the tari¤
reduction case. This will be clear if one examines equation (31), which de…nes the
V_ = 0 locus and is reproduced below.
pw
½
1¡® 1 + ¹f
®=2
= Ax hx
F
¡ yw ±F
®
¸px
(1 + f )
px
(43)
An export subsidy will lead to a higher px than the tari¤ reduction case (see equation
10) although the relative price between the two good will be the same. This implies
that ¸ will have to be lower to keep V_ = 0 at the same value of V .
One can see that the saddlepoint path of the export subsidy case (XX) lies below
that of tari¤ reduction case (MM). In the neighborhood of the steady state point,
the saddlepoint path of the export subsidy case has to lie below the tari¤ reduction
case since steady state of the former policy below that of the latter. The reason the
saddlepoint path of the export subsidy case always lies below that of tari¤ reduction
case is the following. Suppose over a certain range XX was above MM. Since it would
eventually have to end up below MM (because the steady state ¸ corresponding to
the export subsidy is lower than that of the tari¤ case), XX would have to intersect
MM at some point and at that point of intersection, the absolute value of the slope of
XX would have to be higher than that of MM. We will show that this is not possible.
That is, at the same ¸ and V (which will have to be true at the point of intersection
of XX and MM), the slope of XX will always be less than the slope of MM. The slopes
_ V_ . If one looks at the system consisting of equations
of these lines are equal to ¸=
(28) and (29) then one can see that at the same V and ¸, ¸_ will be the same under
both systems. However, V_ will be higher in the case of the export subsidy since px
will be higher. That is, the slope of XX will be lower at that point. Therefore XX
will always have to lie below MM.
24
Since the initial V has to be the same under the two policies, the initial ¸ (i.e., the
one at the point of introduction of the policy) will be lower for the export subsidy.
This leads to following result.
Result 2
The reserve out‡ow in the export subsidy case will be lower than in the case in
which the import tari¤ is reduced for the same increase in initial R.
Proof
In order to see this, we have to show that money demand in the period the policy
is introduced is higher in the export subsidy case compared to the tari¤ reduction
case.
Since ¸ is lower in the export subsidy case, money demand will be higher in this
case compared to the tari¤ reduction case if R were the same (see equation 17). The
only way money demand would be lower (or the same) in the export subsidy case as
the tari¤ reduction case is if initial R were higher. This can happen only if initial k
(this is not the same as the old steady state k since in this model a discrete increase
in k is possible by spending money balances) were lower. Since initial V is the same
under the two policies this would be possible only if less money was spent in the
export subsidy case to acquire capital. But that would be possible only if money
demand were higher in the export subsidy case. This is a contradiction. Therefore,
the only possibility is that money demand is higher in the export subsidy case.
R will be higher. But this is still consistent with a higher money demand because
¸ will be lower in the subsidy case.
The intuition behind this result is the following. An increase in the real interest rate
induces consumers to invest more and therefore consume less of both the consumption
good as well as M . However, the consumer can be induced to hold more M and
25
therefore consume less of the consumption good if the relative price between the
consumption good and nominal money, which is the nominal price of the consumption
good, px , increases. This is what the export subsidy achieves. A higher nominal price
of the consumption good means that the marginal utility derived from spending a
unit of currency on the consumption good decreases. Therefore, agents are willing to
hold more money.
B. Export Subsidy vs. Investment Subsidy
Let us now assume that instead of the export subsidy, a subsidy is paid to the
owners of capital so that the rental price that they receive increases to r(1 + i). Let
i be such that the increase in R is the same as that in the export subsidy case.
Result 3
The immediate e¤ect of an investment subsidy will be a reserve out‡ow.
Proof
Again, since V_ have to be positive the inequality (40) has to hold in the period the
policy is introduced. I have reproduced it here for convenience.
gw ¡
pw
y
±k
pw
x
R¡±
pw
g0w ¡ pyw ±k0
½ M
½ M0
x
¡
¡
>
1 ¡ ½ px
R0 ¡ ±
1 ¡ ½ px0
In case of the investment subsidy R increases but g w does not since the product
price distortion is still as high as before. Therefore, if the initial capital stock is equal
to k0 (and nominal money is equal to M0 ) then the …rst terms on the l.h.s. of the
inequality above will be less than the …rst term on the r.h.s. The the inequality above
can hold only if k is higher than k0 and M is lower than M0 . That is, there will have
to be a reserve out‡ow.
In order to compare the investment subsidy with the export subsidy we have to
26
look at the phase diagrams of the two systems, as shown in Figure 4. The V_ = 0
line for the investment subsidy case lies above one for the export subsidy case. Again
since R is the same under the two policies ¸_ = 0 locus is the same for both. The
V_ = 0 line for the investment subsidy case lies above that of the export subsidy case
for the following reason. Let us look at equation (43) which de…nes the V_ = 0 locus.
In the export subsidy case for any V , ¸ will be lower for two reasons. Firstly, because
px is higher and secondly because ¹ will be higher since the export subsidy reduces
the relative price of the investment good while the investment subsidy does not. A
higher ¹ increases the right hand side of the equation directly as well as indirectly by
raising F .
Using the same reasoning as before we can show that the saddlepoint path for the
investment subsidy case will lie above that of the export subsidy case. Therefore,
proceeding in the same way as we did in the tari¤ reduction case, we can show that
the reserve out‡ow will be less in the export subsidy case. This leads to the following
result
Result 4
The reserve out‡ow in the export subsidy case will be lower than that in the
investment subsidy case.
Proof
Same as the one for Result 2.
IV. CONCLUSION
One of the main concerns of developing country policy makers is how to achieve high
investment and growth without incurring large foreign exchange reserve out‡ows since
developing countries have to import investment goods. This paper presented a model
in which export subsidies both increased investment as well as led to smaller reserve
27
out‡ows than other policies that were intended to boost investment. Export subsidies
can boost investment in an economy that exports consumption goods and imports
investment goods by reducing the relative price of the latter. They also reduce foreign
exchange reserve out‡ows because by increasing the price of consumption goods and
therefore taxing consumption they increase the demand for money. This, in our
opinion, was the reason for their success in the fast growing East Asian economies.
APPENDIX
A.1 To show g w =R falls as py =px decreases holding k constant if 1 >
f 1¡¹
.
1+f 1¡®
We have the following expression for g w =R
gw
2 py 1 + ¹f
=
k
R
® px (1 + f)
(44)
Using the de…nition of ¹ we have the following equation
gw
2 pW
1 + ¹f
y
=
k
W
R
® px ¹(1 + f )
(45)
¹ = ¹(py =px ); ¹0 < 0
(46)
f = f(py =px ); f 0 > 0
(47)
Now,
and,
Therefore, we have to show that
1+¹f
¹(1+f )
falls as py =px falls since we are holding k
constant. That is, we have to show that the derivative of
1+¹f
¹(1+f )
with respect to py =px
is positive. Now,
1+¹f
d ¹(1+f
)
d(py =px )
=
(¹0 f + f 0 ¹)(¹ ¡ 1) ¡ ¹0 (1 + f )
¹2 (1 + f )2
28
(48)
The right hand side of the equation above will be positive if the following is true
¡
¹0
f0
>
(1 ¡ ¹)
¹
1+f
(49)
Using the expression for f we get the following expression for f 0
¹0 1
f =¡
f
¹ 1¡®
0
(50)
Therefore, the inequality (49) can be written as the following
1>
A.2 To show (g w ¡
constant if 1 >
pW
y
pW
x
f 1¡¹
.
1+f 1¡®
pW
y
pW
x
(51)
±k0 )=(R ¡ ±) falls when py =px is reduced, keeping k
The derivative of (g w ¡
d[(g w ¡
f 1¡¹
1+f 1¡®
pW
y
pW
x
±k0 )=(R ¡ ±) with respect to py =px is the following
±k0 )=(R ¡ ±)]
=
d[py =px ]
(R ¡ ±)g w ¡ (g w ¡
(R ¡ ±)2
pW
y
pW
x
±k0 )R0
>0
(52)
The derivative will be positive if the following holds
gw
gw ¡
pW
y
pW
x
±k0
>
R0
R¡±
(53)
The inequality above can be written as
¡
gw
g w (1 ¡
pW
y ±k0
w )
pW
x g
<¡
R0
R(1 ¡ R± )
(54)
We know ¡g w =g w < ¡R0 =R since g w =R falls as py =px falls (g w and R both rise
as py =px falls) . So a su¢cient condition for inequality (54) to hold is the following
pW
1
y k0
<
W
w
px g
R
29
(55)
Or,
g w pW
x
>1
Rk0 pW
y
(56)
Using the expression for g w =R from equation (23) and the de…nition of ¹, the
inequality above can be written as the following
2 1 + ¹f
>1
® ¹(1 + f)
(57)
Since ® and ¹ are both less than 1 by assumption, the inequality (57) will always
hold.
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[5] Kuo, S., The Taiwan Economy in Transition, Westview Press, 1983.
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[7] Park, D., “Foreign Exchange Liberalization and the Viability of a Fixed Exchange
Rate Regime, Journal of International Economics, February 1994.
30
[8] Rodrik, D., “Getting Interventions Right: How South Korea and Taiwan Grew Rich,”
Economic Policy, April 1995.
[9] Scott, M., “Foreign Trade,” in W. Galenson (ed.), Economic Growth and Structural
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Cornell University Press, 1979.
[10] Tybout and Westbrook, “Trade Liberalization and Dimensions of E¢ciency Change
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[11] Wade, R., Governing the Market, Princeton University Press, 1990.
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31
λ
.
λ=0
.
V=0
V
Fig. 1.
32
λ
.
λ=0
µ
.
V=0
V
Fig. 2.
33
λ
.
λ=0
M
X
tariff
ex. sub.
.
V=0
M
X
.
V=0
V
Fig. 3.
34
λ
.
λ=0
I
X
inv. sub.
ex. sub.
.
V=0
I
X
.
V=0
V
Fig. 4.
35