Balance of Payments and Foreign Exchange
Dynamics
—SD Macroeconomic Modeling (4) —
Kaoru Yamaguchi, Ph.D. *
Doshisha Business School
Doshisha University
Kyoto 602-8580, Japan
E-mail: kaoyamag@mail.doshis
Abstract
This paper tries to model a dynamic determination of foreign ex-
change rate in an open macroeconomy in which goods and services are
freely traded and financial capital flows efficiently for highest returns. For
this purpose it becomes necessary to employ a new method contrary to
standard methods of dealing with a foreign sector as adjunct to macroe-
conomy; that is, an introduction of another macroeconomy as a foreign
sector. Within this new framework of open macroeconomy, transactions
among domestic and foreign sectors are handled according to the prin-
ciple of accounting system dynamics developed by the author, and the
balance of payments is attained. For the sake of simplicity of analyzing
foreign exchange dynamics, macro variables such as GDP, its price level
and interest rate are treated as outside parameters. Then, eight scenarios
are produced and examined to see how exchange rate, trade balance and
financial investment, etc. respond to such outside parameters. To our
surprise, expectations of foreign exchange rate turn out to play a crucial
role for destabilizing trade balance and financial investment. The impact
of official intervention on foreign exchange and a path to default is also
scussed.
“This paper is submitted to the 25th International Conference of the System Dynami
Society, Boston, USA, July 29 - August 2, 2007. In September 2006, I made a visit to the
following colleagues: Mr. David Wright, Senior Lecturer, Univ. of Bergen, Norway, and
Dr. Burkhard Schade, Dr. Wolfgang Schade and his research group at Fraunhofer Institute,
Karlsroohe, Germany. I’m very thankful for the dialogues with them and advices offered
. which gave me very valuable
to me on the subject of this macroeconomic modeling, seri
opportunities to reconsider my present on-going research for further improvements. ‘Thi
research is partly supported by by the grant awarded by the Japan Society for the Promotion
of Science.
1 Open Macroeconomy as a Mirror Image
This is the fourth paper of a series of macroeconomic modeling that tries to
model macroeconomic dynamics. In the first paper [5], money supply and cre-
ation processes of deposits were modeled. Analytical method employed in the
model is the principle of accounting system dynamics developed by the author
[4]. In the second paper [6], dynamic determination processes of GDP, interest
rate and price level were modeled on the basis of the same principle, and four
sectors of macroeconomy were introduced such as producers, consumers, banks
and government. The third paper [7] tried to integrate real and monetary
tors that had been analyzed separately in the previous two models; that is
adding the central bank, five sectors of the macroeconomy were fully integrated
together with a labor market. Figure 1 illustrates an overview of our macroc-
conomi
stem and shows how the five macroeconomic sectors, still excluding
foreign sector, interact with one another and exchange goods and servi
money.
for
|
|
5
Figure 1: Macroeconomic System Overview
As a natural step of the research, we are now in a position to open our
macroeconomy to a foreign sector so that goods and s are freely traded
and financial assets are efficiently invested for higher returns. The analytical
method employed here is the same as the previous papers; that is, the one based
on the principle of accounting system dynami
The method requires to manipulate all transactions among macroeconomic
sectors, and when applied to a foreign sector, it turns out to be necessary to in-
troduce another macroeconomy as a reflective image of domestic macroeconomy.
Contrary to a method employed in standard international economics textbooks
such as [1] and [2], a foreign sector is no longer treated as an additional macroe-
ctor adjunct to a domestic macroecono:
To understand this, for instance, consider a transaction of importing goods.
They add to the inventory of importers (a red disk numbered 1 in Figure 3 be-
low), while the same amount is reduced from the inventory of foreign exporters
(a red disk numbered 4 in Figure 4 below). To pay for the imported goods, im-
porters withdraw their deposits from their bank and purchase foreign exchange,
(red disks numbered 2 and 3 in Figures 3 and 6 below), which is then sent to the
deposit account of foreign exporters’ bank that will notify the receipts of export
payments to exporters (red disks numbered 3 and 4 in Figures 7 and 4 below).
In this way, a mirror image of domestic macroeconomy is needed for a foreign
country as well to describe even domestic transaction processes of goods and
Similar manipulations are also needed for the transactions of foreign
and financial investment. Figure 2 expresses our image of modeling open
macroeconomy by the principle of accounting system dynamics.
service:
direct
Figure 2: Foreign Sector as a Mirror Image of Domestic Macroeconomy
2 Open Macroeconomic Transactions
Modeling open macroeconomy was hitherto considered to be easily completed
by merely adding a foreign sector, and this paper is supposed to be the last one
in our SD macroeconomic modeling series as stated in [7] : “our next and final
paper in this series of macroeconomic modeling will be to open the integrated
model to foreign sector.” The introduction of a foreign country as a mirror
image of domestic macroeconomy makes our analysis rather complicated.
To overcome the complexity, we are forced, in this paper, to focus only on a
mechanism of the transactions of trade and foreign investment in terms of the
balance of payments and dynamics of foreign exchange rate. For this purpose,
transactions among five domestic sectors and their counterparts in a foreign
country are simplified as follows.
Producers
Major transactions of producers are, as illustrated in Figure 3, summarized as
follows
e GDP (Gross Domestic Product) is assumed to be determined outside the
economy, and grows at a growth rate of 2% annually.
e Produces are allowed to make direct investment abroad as well as finan-
cial investment out of their finan bonds
investment abroad.
and cash!, and receive investment income from the
Meanwhile, they are also required to pay foreign investment income (re.
turns) to foreign investors according to their foreign financial liabilities
and equity .
« Produces now add net investment income (investment income received
paid) to their GDP revenues (the added amount is called GNP (Gross Na
tional Product)), and deduct capital depreciation (the remaining amount
is called NNP (Net National Product)).
¢ NNP thus obtained is completely paid out to consumers, consisting of
workers and shareholders, as wages to workers and dividend to sharehold-
ers.
e Produc
are thus constantly in a state of cash flow deficits. To make
new investment, therefore, they have to borrow money from banks, but
for simplicity no interest is assumed to be paid to the banks.
¢ Producers imports goods and services according to their economic activi-
ties, the amount of which is assumed to be 10% of GDP in this paper.
ities of a
Similarly, their exports are determined by the economic act
uuntry, the amount of which is also assumed to be 10% of foreign
Foreign producers are assumed to behave similarly as a mirror image of
domestic producers as illustrated in Figure 4.
1In this paper, financial assets are not broken down in detail and simply treated as financial
assets. Hence, returns from financial investment are uniformly evaluated in terms of deposit
returns.
1 rem |“@
ay
rosy, ain
cers:
Figure 3: Transactions of Produc
"ers
ctions of Foreign Produc
Figure 4: Trans:
[erie
‘Seer
Consumers and Government
Transactions of consumers and government are illustrated in Figure 5, some of
which are summarized as follows.
e Consumers receive the amount of NNP as income, out of which 20% is
levied by the government as income tax. The remaining amount becomes
their disposable income.
¢ Consumers spend 60% of their disposable income and save the remaining
as deposits with banks.
spends the amount it receives as income tax, and its
¢ Government only
budget is assumed to be in balance.
couse $$)
Figure 5: Transactions of Consumers and Government
Banks
Transactions of banks are illustrated in Figure 6, some of which are summarized
as follows.
¢ Banks receive deposits from consumers and make loans to producers.
¢ Banks are obliged to deposit a portion of the depo required reserve
with the central bank, but such activities are not considered in this paper.
¢ Banks buy and sell foreign exchange at the request of producers and the
central bank.
e Their foreign exchange are held as bank reserves and evaluated in terms
of book value. In other words, foreign exchange reserves are not deposited
with foreign banks. Thus net gains realized by the changes in foreign
exchange rate become part of their retained earnings (or losses
e Foreign currency is assumed to play a role of key currency or vehicle
currency. Accordingly foreign banks need not set up foreign exchange
account. This is a point where a mirror image of open macroeconomic
symmetry breaks, as illustrated in Figure 7.
Central Bank
In the integrated model [7], the central bank pla
viding a means of transactions and store of value;
a
an important role of pro-
that is, currency, and its
sued were assumed to be gold and
sources of as which currency i
government Tr
simplified, as illustrated in Figure 8, so long as nec
purpose in this paper.
stions of the central bank here are exceptionally
ary for the analytical
The central bank can control the amount of money supply through mon-
etary policies such as the manipulation of required reserve ratio and open
market operations. However, such a role of money supply by the central
bank is not considered here.
The central bank is allowed to intervene foreign exchange market; that
is, it can buy and sell foreign exchange to keep a foreign exchange ratio
stable. These transactions are manipulated with commercial banks, which
inescapably change the amount of currency outstanding and, hence, money
supply. In this paper, however, such an effect of money supply on interest
rate is assumed to be out of consideration.
in
ssumed to be de-
Foreign exchange reserves held by the central bank i
posited with foreign banks so that it receives interest payments.
The central bank of foreign country is excluded simply because forcign
currency is assumed to be a vehicle currency, and it needs not to hold
foreign reserves (that is, its own currency) to stabilize its own exchange
rate in this simplified open macroeconomy.
3 The Balance of Payments
All transactions with a foreign country such as foreign trade and foreign inv
ment (that is, payments and receipts of foreign exchange) are booked according
toa double entry bookkeeping rule, and such a bookkeeping record is called the
balance of payments. According to [1] in page 295, all payment ded in
the debit side with a minus sign, while all receipts are recorded in the credit side
with plus sign. Hence, by definition, the balance of payments are kept in bal-
all the time. It cor of current account, capital and financial account,
and net official re
are rec
ance
orve a
Lom
Figure 6: Transactions of Banks
Figure 7: Transactions of Foreign Banks
10
7 baths Re
ctions of the Central Bank
Figure
Current account consists of trade balance of goods and services and net
tment income. Capital account i transfer of fund by the gov-
ernment that is excluded from our analysis here. Financial account consists
of direct and financial foreign investment. Figure 9 illustrates all transactions
which enter into the balance of payments account.
Figure 10, obtained from one of our simulation runs, displays relative pd
ccount, capital and financial account, and net official reserv
in reserve assets). A numerical value of the balance of pay
all the time; that is a zero value.
tions of current a
assets (or changes
hown in the figure as being in balance
ment:
ll
eps spy
1 tama.
: oN] oe o =o
ay LEER, =
a swaps a
a
an
E
<0
gaiew
2 AG 190g
ae
rs an ae ais
Ga.) (wh a btn)
mo ee antes causke
“ae Mu SONU] LD
(oan eg 10) (790299 102
one pea ID
road a) sitrooey aa)
(8 9009 w 9004 +) LIPID Covaeieg iss04 =) 1188 (8 990 4) p99 (osauceg =) 11920,
Figure 9: The Balance of Payments
12
Bal ance of Paynents
Dol | ar/ Year
°
0 6 +2 I 24 30 36 42 48 54 60
Tine (Year)
Current Account : run
"Capital & Financial Account" : run
Change in Reserve Assets : run
Balance of Paynents : run
Figure 10: A Simulation of Balance of Payments
4 Determinants of Trade
Let M and X be real imports and exports, and Y and P be real GDP and its
price level, respectively. Counterpart variables for a foreign country is denoted
with a subscript f. A foreign exchange rate E is defined as a price of foreign
currency (which has a unit of FE here) in terms of domestic dollar currency; for
instance, 1.2 dollars per FE. Then, a price of imports is calculated as Pyy = PyE.
Imports are here simply assumed to be a function of real GDP and price of
imports such that
aM aM
M = M(Y, Pyr), where and —— <0. 1
(¥, Pu), where 5 > 0 and se <0 (1)
This implies that imports increases as
GFagh Loskup = Inports: Tenand Carve domestic economic activities, hence GDP,
5 | expand, and decreases as price of imports
rises as a standard downward-sloping de-
mand curve conjectures. Figure 11 illus-
trates one of such demand curves employed
in this paper in which demand is normalized
between a scale of zero and five on a verti-
cal axis against a price level of between zero
and two on a horizontal axis.
o i From these simple assumptions, we can
Figure 11: Normalized Demand
Curve 2B
derive the following relations:
M=M(Y,Pm)=M(Y,P/B), (2)
_ aM
~ OPu
aM 0M @Py OM
alain = P, 4
OE ~ OPy, OE ~ OPy,*! <°
These relations imply that imports de
<0 (3)
ase as foreign price of imports increases
and/or foreign exchange rate appreciates.
In our model, imports function is further simplified as a product of imports
determined by the size of GDP and a normalized demand curve such that
M = M(Y, Py) = M(Y)D(Pyr) = mY D(P;E) (5)
where m is a constant coefficient of imports on GDP.
Exports are nothing but imports of a foreign country, and similarly deter-
mined as a mirror image of domestic imports function such that
ax ax
X =X(¥j, Pus), where and
(Yr Parp), where = > 0 and 55 <
(6)
This implies that exports increase as foreign economic activities, hence foreign
GDP, expand, and decreases as price of imports in a foreign country rises as a
standard downward-sloping demand curve conjectures.
calculated by a domestic price and
foreign exchange rate such that Pyy,y = P/E. Hence, we obtain the following
relations:
Price of imports in a foreign country is
X = X(Vj, Pa.s) = X (Vp, P/E), (7)
OX OX OPwy OX 1
OP OPyy OP OPuyE
OX _ OX OPuy __OX ez
OE OPyy OE OPuy\ EP
Thus, exports decrease as a domestic price ri
(8)
)>0. (9)
. Meanwhile, whenever foreign
exchange appreciates, our products become cheaper in a foreign county and
exports incr
Exports are similarly broken down as a product of foreign imports and nor-
malized demand curve of foreign country, which is assumed to be exactly the
same as domestic demand curve for imports.
X = X(¥j, Pass) = X(¥p)D(Pas,p) = mY D(P/E) (10)
where my is a constant import coefficient of a foreign country.
4
Let us define trade balance as
TB(E:Y,Y;,P, Ps) = X(E:Y;, P) — M(E:Y, Py) (a1)
Then we have
aTB_ aM __. aTB_ ax
Or 7 ay <° By 7 ay?” (12)
OTB aX oTB aM
77 =e or _ >0. (13)
=— <0, aE,
OP @aP OP; OP;
OTB _0X 0M
dE OE OE
es that a trade balance is an incr
>0. (14)
The last relation indic: easing function of
foreign exchange rate. The relation is also confirmed in our model as illustrated
in the two diagrams of Figure 12 in which upward-sloping blue curves are ob-
tained from our simulation runs. As an mirror image, foreign trade balance
is shown to be a decreasing function of foreign exchange rate, as indicated by
downward-sloping red curves.
‘Trade Balance vs E Trade Balance vs E
& Dal Lar/Year Dal Lar! Year
8 FEDYear 8 FE/Year
4 Dal Lar/ Year 4 Dal Lar! Year
4 FEYear 4 FE/Year
© Dat Lar/ Year © Dal Lar! Year
0. FEVYeae 0 FE/Year
<4) Dal Lar/ Year <4, Dal Lar/ Year
U4 FEVYear “4 BEVYear
<8 Dal Lar/ Year <8 Dal Lar) Year |
Ty FE/Year "8 FE/Year
0.9% 0,950 0.900 0970 oR) 0.990 r 1030 Too 7000
Frei gn Exchange Rate Focci gn Exchange Rate
Trade Balance : run Dllar/Year ‘Trade Bal ance run, —————— altar Year
Forei gn Trade Bal ance (FE)" : run ————FE/Year_"Porei gn Trade Balance (FE)” : run FE Year
Figure 12: Trade Balance vs Foreign Exchange Rate
National Income Identity
Let us now brie’
follows:
ly summarize our model in terms of national income account as
Y=OW -T)+14+G4+TB(B) (15)
That is to say, GDP is the sum of consumption spending, investment, govern-
ment expenditure and trade balance. In our model of foreign trade, investment
is calculated to make this equation an identity all the time.
Private saving is defined as $, = Y —T — C. Government saving is defined
as Sy =T—G. Then national saving is obtained as a sum of these savings such
that
S=S,+5)=Y-C-G, (16)
15
which reduces to
S-—I=TB(E). (17)
Saving less investment is called net foreign investment, which is equal to trade
balance. This becomes another way of describing the above national income
identity in terms of net foreign investment and trade balance.
5 Determinants of Foreign Investment
Foreign investment consists of direct investment and financial im
. In this paper finan
stocks, bonds and cash, which constitute financial a
sts are not specified without losing generality
footnote above. Foreign investments are here assumed to be determined on a
principle of foreign exchange market efficiency under the uncovered interest rate
parity (UIP) condition as explained in standard textbooks such as [1] and [3].
Let i and R be interest rate and a rate of return from financial investment,
and E® be an expected foreign exchange rate. A rate of return from a bank
deposit is the same as the interest rate:
a already mentioned in the
Rai (18)
‘An expected return from a deposit with a foreign bank is calculated as
Be
=(1+i;)—-1 19
Ry = (+i (19)
Thus we obtain
OEE? Q (20)
aR, _ (1 +iy)
a
ial investment de
ange rate
This implies that a rate of return from foreign finan
foreign exchange rate appreciates, but it increas
is expected to appreciate.
Let us define an expected return arbitrage as
when forei
ign excl
A(E, E'
ip) = Ry(E, Eis) — Rl) (22)
and net capital flow(NCF) as
NCF = Foreign Investment Abroad — Investment Abroad (23)
This is the amount of capital we receive from foreign country’s investment le
the amount we invest abroad. Under the assumption of an efficient financial
market, if expected returns are greater in a foreign country and an expected
return arbitrage becomes positive, then financial capital contimues to outflow
until the arbitrage ceases to exist. Ina similar fashion, if expected returns are
greater in a domestic market and an expected return arbitrage becomes negative,
16
then financial capital continues to inflow until the arbitrage disappears. Hence,
so long as a foreign exchange market is efficient, the relation between net capital
flow and an expected return arbitrage become as follows:
{ NCF <0 ifA>0
NCF>0 ifA<0 (24)
It is unrealistic, however, to assume an indefinite outflow of capital even if
A > 0, or an indefinite inflow of capital even if A < 0. So it is assumed here
that the maximum amount of direct and financial investment made available per
year is a finite portion of domestic investment and financial assets. Yet, actual
amount of financial investment is further assumed to be dependent on a level of
an expected return arbitrage by its factor. Figure 13 illustrates table functions
of investment levels that are assumed in our model in terms of expected return
arbitrate.
Geaph Lookup - Direct Investnent Index Table Geaph Lookup - Financial Investnent Index Table
iB Ll
-0.4 -Ld
-0.2 0.2 -0.2 0.2
Figure 13: Direct and Financial Investment Indices
Specifically, left-hand diagram shows
which assumes that between the arbitrage range of -0.01 and 0.01 direct in-
vestment is not made. Right-hand diagram shows a table function of financial
investment, which assumes that between the arbitrage range of -0.01 and 0.01
ial capital flows slowly between a portion of -0.02 and 0.02. These as-
sumptions are made to reflects a realistic situation in which direct investment
itive to the arbitrage values compared with financial investment.
apital flow could be described as a function of an expected
ach that
a table function of direct investment,
finan
is not so
In this way net
return arbitrage
NCF = NCF(A(B,E*)), where 2NCF <9 (25)
OA
It is important to note, however, that this functional relation holds only in the
neighborhood of equilibrium, so do the following relations as well.
ONCE OR,
0A OE OA OE
>0 (26)
17
ONCF _ONCF 0A _ ONCF OR;
OE® — «OA_-~OE® ~—SOOA_COOE®
Whenever a foreign exchange rate begins to appreciate, an expected return
arbitrage declines, and capital begins to inflow, causing a positive net capital
flow. When foreign exchange rate is expected to appreciate, an expected return
arbitrage increases and capital begins to outflow, causing a negative net capital
flow. In this way, changes in a foreign exchange rate and its expectations play
a crucial role for financial investment.
It is examined in our model that these relations only hold in the neighbor-
hood of equilibrium. In Figure 14, net capital flow is shown to be an increasing
<0 (27)
NCF vs E
NCF vs E
e ‘
}
_ f as
5 \ .
3-2 53
a a
3 Ls
4 °
0.500.950 0.0.9 0.980 0.990 a a CT
Foreign Exchange Rate Torcln Bxchuge Rate
Net Capital Laws ru capital ttn: rn
Figure 14: Net Capital Inflow vs Foreign Exchange Rate
function only when a foreign exchange rate is around the equilibrium; that is,
between 0.983 and 1.018. TI ate a limitation of the above mathe-
matical method of economic analy:
textbooks. In other words, mutually interdependent economic behaviours can-
not be fully captured unless they are simulated in a system dynamics model
such as the one in this paper.
which has been dominantly used in many
6 Dynamics of Foreign Exchange Rates
How are the foreign exchange rate and its expectations determined, then? For-
cign exchange rate is here simply assumed to be determined by the excess de-
mand for foreign exchange; that is, a standard logic of price mechanism in
economic theory. From the left-hand diagram of Figure 9, demand for foreign
is shown to stem from the need for payments due to imports, direct
stment abroad, and foreign investment income, as well as for-
eign exchange purchase by the central bank. Supply of foreign exchange r
from the receipts from foreign country due to exports, foreign direct and finan-
stment abroad, and investment income from abroad, as well as foreign
ntral bank.
sults
cial inv
exchange sale by the
18
alculated as follows:
Hence, excess demand for foreign exchange is
Excess Demand for Foreign Exchange
= Imports - Exports
+ Investment Abroad - Foreign Investment Abroad
+ Foreign Investment Income - Investment Income
+ Foreign Exchange Purchas
= — Trade Balance (TB)
— Net Capital Flow (NCF)
— Net Investment Income (NIT)
+ Net Exchange Reserves (NER)
- Foreign Exchange Sale
(28)
Net investment income is derived from the financial assets invested abroad
and here assumed to be dependent only on domestic and foreign interest rates.
Net exchange reserves depend on the official foreign exchange intervention.
Therefore, NII and NER are not dependent on foreign exchange rate and its
expectations.
With these relations taken into consideration, dynamics of foreign exchange
sd as a function of excess demand for foreign
s a function of E and E® as follows:
rate is mathematically express
exchange, which in turn becom
dB
G7 (TBE) -
CF(E, E*) —
II + NER) = W(E, E°) (29)
On the other hand, a formation of expected foreign exchange rates is difficult
to formalize. Here it is simply assumed that actual expectations of foreign
exchange rate fluctuates randomly around the current exchange rate by the
factor of random normal distribution of Nrandom(m, sd) where (m, sd) denotes
mean and standard deviation, and accordingly an expected foreign exchange
rate is obtained as an adaptive expectation against the actual expectation of
random normal distribution.
Mathematically, dynami
is described as
s of the expected foreign exchange rate thus defined
andom(m, 8d) E — E®) = ©(E, E®) (30)
‘tual trends
od foreign exchange rate can be e
of various
adjusted to th
situations by refining values in mean and
standard deviation. Figure 15 illustrates how foreign exchange rate and its
economi
expectation are modeled in our economy.
Now dynamic modeling of foreign exchange rate in our open macroeconomy
is complete. It consists of three equations: (15), (29), and (30), out of which
three variables E, E® and TB are determined, given parameters outside such as
Exchange
45 3s
& Par
it a 53
Wed >
Vy
ae
5 i
é
2 4
2 | 2 5 \
5a a | zee - |
Ze * | Bee Bot
a 2
Excess Denand for
Exchange Rate
5 Foreign Exchan
Foreign
Exchange Rate
J met
Change in
Forei gn Exchange
Figure 15: Determination of Foreign Exchange
GDP, its price level and interest rate, as well as random normal distribution of
expected foreign exchange rate. Schematically, it is written as
(Y,Y;, P, Py, i,i7, Nrandom) => (E, E*, TB) (31)
Figure 16 draws a theoretical gist of our open macroeconomic framework as a
simplified causal loop diagram of the dynamics of foreign exchange rate in our
open macroeconomy.
20
arricial
a
ee Rate (i)
—_- ance ae
YA Expected
Forel gh
Exchange
cr a. ae °F
a (vr)
Rate
Random Norval en
Distribution
Figure 16: Causal Loop Diagram of the Foreign Exchange Dynamics
7 Behaviors of Current Account
An Equilibrium State (S)
We are now in a position to examine how our open macroeconomy behaves.
Let us start with an equilibrium state of trade and foreign exchange. Domestic
and foreign GDPs are assumed to grow at an annual rate of 2%. Random
normal distribution for the expected foreign exchange rate is assumed to have
a zero mean value and 0.1 value of standard deviation. Figure 17 illustrates
such
stment, government expenditures, exports and
the equilibrium state under such circumstances. Macroeconomic figures
as consumption spending, inve
imports are shown to be growing, while trade balance is in equilibrium at a zero
value in the left-hand diagram. On the other hand, a constant foreign exchange
rate at one dollar per FE and its fluctuating expected rates are shown in the
right-hand diagram.
Nati onal Incone Spending
Forei gn Exchange Rate
1 AA br Ay | pra At
i PUA W A
09
o 6 2 W mM 3 a6 4 4 S50
Tine (Year)
Conte apie es" g,
Givetment Expenditure "Ege litefam oe is 243036 aa
Exot a Tine (Year)
Figure 17: Equilibrium State of Trade and Foreign Exchange Rate (S)
In this state of equilibrium, financial investment is not yet considered. Hence,
21
%
in spite of non-zero expected return arbitrate, caused by the fluctuations of
estimated foreign exchange rates, capital flows are not provoked, and accordingly
trade balance stays undisturbed.
Change in real GDP (S1)
enarios can be considered that lead economic behaviors out of the
above equilibrium s Let us start with two simple cas apital
flows are allowed; that is, our dynamic system of foreign exchange rate is now
simply described as
beh
‘s in which no ¢:
ate.
aE W(-TB(E)) (32)
dt
As a first scenario, suppose a foreign real GDP decreases by 60 (billion)
dollars at the year 7 due to a recession in a foreign country. The effect of this
ession appears first of all as a sudden drop in our exports which are wholy
dependent on foreign economic activities. This sudden plunge in expor
a trade deficit. This will begin to increase demand for foreign exchange, be
imports become relatively larger than exports, which in turn will cause foreign
exchange rate to appreciate. The appreciation of foreign exchange rate makes
imported goods more expensive, and eventually curbs the imports and trade
balance will be gradually restored. In due course a new equilibrium state of
foreign exchange rate will be attained at 1.056 dollars per FE (an appreciation
rate of 5.6%)
In this way a flexible foreign exchange rate play ve role of restoring
trade imbalance as illustrated in Figure 18. Trade balance in a foreign country
moves exactly into the opposite direction, so that a perfect mirror image of
trade balance is created as reflected in the right-hand diagram.
cause
a det
Foreign Exchange Rate Trade Balance
Lt nar Ma
Sree soo
os see
a a ata — —
Time (Year)
Time (Year
Figure 18: Foreign GDP Plunge and Restoring Trade Bal
($1)
Change in Price (S2)
scond scenario, let us consider an opposite situation in which a foreign
by 10% due to an economic boom in a foreign country. The inflation
22
makes imported goods more expensive and imports are suddenly suppres:
causing a surplus trade balance. Trade surplus will bring in more foreign e
change, causing a foreign exchange rate to depreciate. The depreciated foreign
exchange rate now makes imported goods relatively cheaper and stimulates im-
ports again. In this way trade balance will be restored and a new level of
exchange rate is attained in due course at 0.97 dollars per FE (a depreciation
rate of 3 %) as illustrated in Figure 19.
Foreign Exchange Rate Trade Bal ance
A
1 Poth
a Ta
a0 36
i (Year aa
——E—eeE tim (Yea)
Figure 19: Foreign Inflation and Restoring Trade Balance ($2)
8 Behaviors of Financial Account
Expectations and Foreign Investment (S3)
In the above equilibrium state, standard deviation of random normal distribu-
tion is assumed to be 0.1, and expected foreign exchange rates are allowed to
move randomly. Accordingly, non-zero return arbitrage caused by such fluctua-
tions of foreign exchange rate could have triggered capital inflows and outflows
under the assumption of efficient financial market. Yet, in order to sce the effect
of activities and price levels on trade balance and exchange rate, fi-
is excluded from the analysis. In this sense, the equilibrium
d above is not a real equilibrium state under free capital flows.
From now on Ict us consider three cases in which free capital flows are allowed
for higher returns. In other words, behaviors of three variables E, E® and TB
are fully analyzed under the three equations: (15), (29), and (30).
As a scenario 3, let us consider the original equilibrium state again and see
what will happen if free capital flows are additionally allowed for higher returns.
As a source of financial investment, 20 % of domestic investment is assigned to
direct investment abroad, and 30 % of financial s are allowed for financial
stment. The actual financial investment, however, depends on the scale of
illustrated in Figure 13 above.
Figure 20 illustrates a revised equilibrium state under free flows of capi-
tal. Top-right figure shows the existence of the expected return arbitrage under
state d
23
the fluctuations of expected foreign exchange rates. The emergence of the arbi-
trage undoubtedly trigger capital flows of financial investment for higher returns,
breaking down the original equilibrium state of trade balance, as shown in the
bottom two diagrams. In this way, the original equilibrium state of trade
easily thrown out of balance by merely introducing random expectations of for-
cign exchange rate under an efficient capital market. In other words, random
expectations among financial investors are shown to be a cause of trade turbu-
lence, and hence economic fluctuations of boom and bust in international trade.
What surprised me is that a flexible foreign exchange rate can no longer restore
a trade balance. This is an unexpected simulation result in this research.
Foreign Exchange Rate Interest Arbitrage
12 0.02
oe -0.01
Export s- I nports
200 Dollar) Year
au 10 Dollar’ Year
130 Dol ar/Year
S Dillar/ Year
100 Dol ar/ Year
0 Dillar/ Year
50) Dol lar/ Year
2S. Dollar’ Year
0 Dillar/Year
10 Dollar! Year
a
0 Tine ( Year)
a 485460 Exports : Expectation, ——————— ilar! Year
Time (Year) Inports | Expectation Dollar’ Year
Trade Bal ance Expectation Dollar’ Year
Figure 20: Random Expectations and Foreign Investment ($3)
Change in Interest Rate (S4)
Under the cenario 3, let us additionally suppos
nario 4, that a domestic interest rate suddenly plummets by 2% and becomes 1%
from the original 3% at the year 7. This drop may be caused by an inc
money supply. The lowered interest rate surely drives capital outflows abroad.
This in turn will increase the demand for foreign exchange, and a foreign ex-
change rate will begin to appreciate. The appreciation of foreign exchange rate
makes exports price relatively cheaper, and trade balance turns out to become
surplus. Figure 21 illustrat
ituation of the abov
ase in
how a plummet of interest rate appreciates foreign
24
exchange rate and improve a trade balance.
Foreign Exchange Rate Interest Arbitrage
12 0.08
| PAO PAR AAP _ LAT a
wae :
Daa YM 4
2 30 6
Time (Year).
Trade Bal ance Exports-I nport s
200 Dal lar/Year
a 40 Dal lar Year
AN] 150° Dall ar/ Year
1» YON AS 38 BENS!
Y N90 Datta Yee Be
5 L mar ae
ms ™ iQ) Raa Your TTY
20 TPN PD Val [
0 6 2 ® 2 30 3 4 ae SF 60
Dal lar Year
0 Dallar/Year
-2 Dollar! Year
Tine (Year)
6 2 We 230 36 4 S460 Exports : Lnterest Plunge § ——————— Lar! Year
Time (Year) Inmoets : Interest Plummet —————— Dal lar’ Year
rede at ance Toterest Plummet, Dal Lar’ Year
Figure 21: Interest Plummet under Random Expectations ($4)
Left-hand diagram of Figure 22 illustrates the balance of payments under
the original equilibrium state (scenario 3). Current account is shown to be
in deficit all the time, and in order to finance it financial account has to be
in surplus. Under the same situation, a domestic interest rate is additionally
lowered (scenario 4). Right-hand diagram indicates how lowered interest rate
stimulates the economy and improves a deficit state of the balance of payments.
Bal ance of Paynents Balance of Paynents
» r ®
WW
til i
" Mert iad hl * Leh
‘ Teli aa
eM tee CAN tia
cia any Mh \ I Yo
-~
ae a oe a a
fim {ean fier vee!
Figure 22: Comparison of the Balance of Payments between $3 and S4
25
Change in GDP and Free Capital Flow (S5)
Let us revisit the scenario 3. Then as a scenario 5, let us additionally assume a
decrease in foreign GDP by 60 (billion) dollars at the year 7 due to a recession
in a foreign country as in the scenario 1. Furthermore, the central bank is
now assumed to hold foreign exchange reserves of 100 (billion) dollars that are
deposited with foreign banks.
As already discussions in the scenario 1, foreign exchange rate continues to
appreciate, yet trade balance is no longer attained and trade deficits continues
for a foresceable future due to the disturbance caused by free capital flows as
explored in the scenario 3. Top diagrams of Figure 23 illustrate these situa-
tions. Bottom-left diagram indicates current account deficits in the balance of
payments, which has to be offset by the net inflow of capital.
Foreign Exchange Rate Trade Bal ance
vy
os
a
Tim en)
Bal ance of Paynents Forei gn Exchange Reserves
Py 7 on
Hana it! \
i Ly Mik wn, Hila
MW i
i, Wt AM
Fi CC] 7 i it i i E400
VII Lal Th \ MV
ao \
TUG 2
men Ny Nl } ”
am o 6 12 1 4 WW 36 42 48 54 60 0
Tie (Yea %
Figure 23: Foreign GDP Plunge and Foreign Investment ($5)
Bottom-right diagram shows that foreign exchange reserves by the central
bank continues to grow at a rate of the foreign interest rate of 3 %. From a
well-known principle of a doubling time of exponential growth, the reserves keep
doubling approximately every 23 years.
26
9 Foreign Exchange Intervention
Official Intervention and Default (S6)
In the
nario 5 above, our macroeconomy continues to suffer from a continual
depreciation of domestic currency (or an appreciation of foreign exchange rate),
and deficits in trade and accordingly in current account. Surely, s
macroeconomic situation in a competitive international economic environment
cannot be left uncontrolled. To prevent such an economic cris
as scenario 6, an official intervention to the foreign exchange market; specifically,
the central bank (and government) begins to sell foreign exchange in order to
reduce foreign exchange rate, say, to 1.02 dollars per FE; that is, by 2 % of the
original equilibrium exchange rate.
As Figure 24 illustrates, even under such circumstances trade and current
continue to persist. Gradually, the foreign exchange reserves
begins to decline due to the official intervention, and becomes lower than the
original reserve level of 100 (billion) dollars around the year 40 and completely
gets depleted around the year 50, as indicated in the bottom right-hand diagram.
This implies the government is forced to declare financial default, that i
economic destruction, unless successfully eliciting an emergent loan from the
international institutions such as the IMF.
is let us introduce
account deficit
Forei gn Exchange Rate Trade Bal ance
FAT SEES TT NA
‘ f | at Ot AA OAY 2
i L 5S ok
L ate ‘
ws 0 IN rai “KL LIT
iss
a 20
Bal ance of Paynents Forei gn Exchange Reser ves
Ps |e
[we
1 att
* viayy ‘00
Ahi \
: Aaa
Tine (Year)
Figure 24: Official Intervention and Default ($6)
27
Zero Interest Rate and Default (S7)
To avoid such financial default, now suppose, as scenario 7, money supply is
increased to stimulate the economy and a domestic interest rate is lowered by
introduced from the original 3%. This poli
of zero interest rate surely improves trade balance and the balance of payments
3%; that is, a zero interest rate i
as Figure 25 indicates. Yet, under the official intervention of keeping a foreign
exchange rate below 1.02 dollars per FE, the central bank (and the government)
erves”. The original 100 (billion)
rves will be completely depleted around the year
12 as the bottom right-hand diagram indicates. Therefore, this zero interest
the government can successfully borrow foreign
exchange from the international institutions such as the IMF.
is forced to keep selling foreign exchange res
dollars of foreign exchange
policy does not work unle
Foreign Exchange Rate Trade Bal ance
1.2 @
09
oe 2 ® 4 0 4% 2 SF wo
Time ( Year) oo 2 8
Bal ance of Paynents Forei gn Exchange Reserves
200 800 =
100 400
» LU .
il +1, 600
=100
-2,800
-200
o 6 2 WM 3 36 A WS HO 4 G09
Time (Year) rr a)
M6
Time (Year)
Figure 25: Zero Interest Rate and Default (S7)
No Official Intervention (S8)
Let us further suppose that the central bank (and the government) give
sup
clling foreign exchange to avoid a depletion of
scenario 8 surely brings about a further appreciation
official intervention and stop:
its foreign reserves. This
it ing the rate below this level, the central bank (and the gov-
ernment) has to keep selling 60 (billion) dollars of foreign exchange annually instead of 20
(billion) dollars in the previous scenario
28
of foreign exchange rate. But to our surprise, after attaining a highest value of
1.212 dollars at the year 41, it begins to depreciate as the top left-hand diagram
of Figure 26 illustrates. Moreover, trade balance and the balance of payments
are getting improved, and foreign exchange reserves keeps growing according to
the same figure. This is another counter-intuitive result in a sense that official
intervention to foreign exchange market won't work to save the economic c
In this way, so long as the working of our domestic macroec
erned, combined policies of zero interest rate and no official intervention seem
to work. Yet, from a foreign country’s point of view, the same polici
its economy as a mirror image of our economy. Hence, a so-called trade war
becomes unavoidable in the international macroeconomic framework. Our sim-
fully exposed one of the fundamental
causes of economic conflicts among nations.
isis
nomy is con-
worsen
ple open macroeconomic model has su
Foreign Exchange Rate Trade Bal ance
LATA,
Lars Lea | » eal en
co LLL a
0,928
-40
a a |
‘hime (Year
Balance of Paynents Forei gn Exchange Reser ves
20 s00
AM
100 AN Woo
Beene
foe ae ja
ey
100 Aah) 200
iW
200 é
oe ae oa ew
os 2 W 2 3 3 2 a Sw
Tine (Year) Tine (Year)
Figure 26: No Offi
al Intervention ($8)
10 Missing Feedback Loops
We have now presented eight different scenarios of international trade and finan-
cial investment, which indicates capability of our open macroeconomic modeling.
Yet, our generic model is far from a complete open macroeconomy, because sig-
nificant economic variables such as GDP, its price level and interest rate are
treated as outside parameters, and no feedback loops exist in the sense that
29
they are affected by the endogenous variables such as a foreign exchange rate
and its expectations. Schematically, one-way direction of decision-making in the
equation (31) has to be made two-way such that
(YY), P, Pp isis,
andom) =» (E, E°, TB) (33)
Mundell-Fleming Model
Compared with our model, one of the repeatedly used open macroeconomic
model in standard international economics textbooks is the Mundell-Fleming
model that is described, according to [2], as
Y = OV-T7)+I())+G+TB(E) (34)
~ = L,Y) (35)
i= i (36)
This macroeconomic model indeed determines Y, E and i. In other words, sig-
nificant economic variables such as GDP and interest rate are simultaneously
determined in the model. In comparison, our model consisting of the three
equations: (15), (29), and (30), determines only three variables E, B® and TB,
and fails to determine Y and i.
Hence, Mundel-Fleming model could be said to be a better presentation of
open macroeconomy. Yet, it lacks a mechanism of determining money supply
M® and a price level P. In this sense, it is still far from a complete open
> model.
macroeconom!
Missing Loops
It is now clear from the above arguments that for a complete open macroeco-
nomic model some missing feedback loops have to be supplemented. They could
constitute the following in our model:
e Imports and exports are
tivities of GDPs, which are in turn affected by the size of trade balance.
Yet, they are missing.
ssumed to be determined by the economic ac-
¢ Foreign exchange intervention by the central bank (and the government)
such as the purchase or sale of foreign exchange surely changes the amount
of currency outstanding and money supply, which in turn must affect an
interest rate and a price level. Yet, they are being fixed.
A change in interest rates affec
the level of GDP. Yet, investment is not playing such a role.
investment, which in turn determines
¢ A change in price level must also affect consumption spending and hence
real GDP. Yet, these loops are missing.
30
imations on for-
© Official intervention must influence speculations and
eign exchange and investment returns among international financial in-
vestors. Yet, these fluctuations are only given by outside random normal
distribution.
Let us add these missing feedback loops to the causal loop diagram of the
foreign exchange dynamics in Figure 16. Then we obtain a complete feedback
loop diagram as illustrated in Figure 27.
<7 Mey. Supply
Nat Exchange
Reserves ¥\
Crticial )
Price (Pry aver vention
Randoen Norra wt
Distribution
Interest
Ryte (i)
Rate (i)
/
Figure 27: Missing Feedback Loops Added to the Foreign Exchange Dynamics
Obviously, our open macroeconomic model is not complete until these mis
ing loops are incorporated in the model. Specifically, the third paper [7] has
presented a model which determines GDP, money supply, a price level, invest-
ment and interest rate, to name but a few. Therefore, our next challenge is to
integrate the model with our present foreign exchange model by crating a whole
image of domestic macroeconomy as its foreign sector macroeconomy. I hope the
integration will complete our research for this macroeconomic modeling ser
11 Conclusion
This is the fourth paper in our series of system dynamics macroeconomic mod-
cling, and supposed to be the last one for presenting a generic macroeconomic
model. It turns out, unfortunately, that our open macroeconomic modeling
needed another model of the balance of payments and dynamics of foreign
exchange rate. Consequently, the approach in this paper led by the logic of
31
accounting system dynamics became an entirely new one in the field of interna-
tional economic:
Under the framework, a double-booking accounting of the balance of p
ments
stment are analytically examined together with an introduction of differe
tial equations of foreign exchange rate and its expected rate.
Upon a completion of the model, eight scenarios are are produced and ex-
amined by running various simulations to obtain some behaviors observed in
actual international trade and financial investment. It is a surprise to see how
an equilibrium state of trade balance is easily disturbed by merely introducing
random expec ors under the assumption of effi-
cient finai pability of our model furthermore,
the impact of official intervention on foreign exchange and a path to default is
discussed.
Finally, several missing feedback loops in our model are pointed out for
making it a complete open macroeconomic model. This task of completion will
inevitably lead to our next and hopefully last research in this system dynamics
macroeconomic modeling series in our next paper.
ay-
modeled. Then determinants of trade and foreign direct and financial
inv
To indicate the
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