The Exchange Rate and Foreign Exchange Reserves:
Japan and United States, 1974 to 2010
by
Zhenfei Tang
A dissertation submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Economics,
Master of Science
Auburn, Alabama
Augst 4th, 2012
Keywords: exchange rate, trade, foreign exchange reserves,
floating exchange rate model
Copyright 2012 by Zhenfei Tang
Approved by
Henry Thompson, Chair, Professor of Economics
John D. Jackson, Professor of Economics
Hyeongwoo Kim, Associate Professor of Economics
ii
Abstract
The exchange rate is very difficult to predict. In 1971, the fixed exchange rate
system transferred to a floating exchange rate system after the collapse of the Bretton
Woods System. The Bretton Woods system established the principle for commercial and
financial transactions among the major industrial countries after World War II. Japan,
United States, and Germany are the major three influential countries in international
commerce. The Japanese yen, US dollar, and German mark are the major currencies in
the exchange rate market. In a floating exchange rate regime, the exchange rate may
reflect the financial situation of countries. Central banks might allow one currency price
to float freely between upper and lower bond. Central banks can buy or sell foreign
exchange against their currency to affect the exchange rate. This is called official
intervention. This thesis examines two major currencies, Japanese yen and the US
dollars, in an exchange rate model depending on international trade, central bank foreign
exchange reserves, and interest rates. Unit root tests for stationarity and Bayesian
information criterion (BIC) are used in this thesis. Finally a lagged transformation model
tests the short term and long term adjustments.
iii
Acknowledgments
I would like to thank my parents, Xinming Tang and Yuru Zhao. Without their
financial support and emotional encourage, I would have not had the chance to come to
United States. I also want to thank Department of Economics and all my instructors in
Auburn University for giving me the opportunity to learn more about Economics. A
special thanks will be given to my committee, Dr. Thompson, Dr. Jackson and Dr. Kim
for their guidance and advice through my Graduate School career.
iv
Table of Contents
Abstract ............................................................................................................................................ ii
Acknowledgments........................................................................................................................... iii
List of Tables ................................................................................................................................... v
Chapter ? Introduction .................................................................................................................... 1
Chapter ? Literature Review ........................................................................................................... 3
Chapter ? Data Description and Variable Definations .................................................................. 16
Chapter ? The Model .................................................................................................................... 21
Chapter? Empirical Results .......................................................................................................... 39
Chapter? Conclusion ..................................................................................................................... 47
References ..................................................................................................................................... 50
Appendix ........................................................................................................................................ 52
v
List of Tables
Table1. SCAN ESACF Result Table ............................................................................... 60
Table3. Ordinary Least Square (OLS) Result ................................................................... 63
Table 4. Lagged transformation Model (LTM) Result ..................................................... 64
Table 5. Total Effect Table ............................................................................................... 65
1
Chapter ?
Introduction
The exchange rate is the rate one currency can be changed to the other in the
foreign exchange market, the price of one country?s currency in terms of the other
currency. A country can obtain foreign currency income through export in international
markets, making estimation of the exchange rate a critical objective of all international
investors. Greenspan (2002) remarked that interest rate differentials, productivity gain
differentials, and chronic external imbalances explain exchange rates. But none has been
found to be consistently useful in forecasting exchange rates.
In the history of global exchange rate market, 1971 is a land mark when the collapse
of the Bretton Woods System transferred the fixed exchange rate to a floating exchange
rate system. A fixed exchange rate is advantageous to both developed and emerging
economies because it acts as a credible constraint on the value of domestic money. Fixed
exchange rates can keep inflation under control and offer risk-averse countries, especially
emerging ones, a method to avoid undesired inflation. The analysis of exchange rate and
foreign exchange reserves in the floating exchange rate is a relevant topic.
Most papers focus on foreign exchange reserves. Some papers argue that official
intervention works in the exchange rate market. There are several papers focusing on the
volatility of exchange rates and official intervention. This thesis builds a model to link
foreign exchange reserves to the exchange rate market. This thesis explains the factors of
2
two countries, Japan and United States, on the exchange rate in a model depending on
international trade, central bank foreign exchange reserves, and interest rates.
There are four chapters in this thesis. Chapter ? is Introduction. Chapter ? is
literature review where some research ideas are described. Chapter ? , Chapter ? and
Chapter V are about test statistics, empirical results, and a conclusion. Chapter ? is the
conclusion of the thesis.
3
Chapter ?
Literature Review
This chapter presents literature related to exchange rate models, and overall
usefulness of foreign exchange reserve position from central banks. The volatility of
exchange rate movements and the importance of foreign exchange reserves and some
economic theory are discussed in this thesis.
Money is an intermediate medium of exchange that facilitates trade. People trade
with money in the form of checks, bank deposits, credit cards, cash, and so on. The
scarcity of money reflects scare resourced and the need for economic choice. The
exchange rate reflects the relative price between two currencies. The exchange rate also
shows the influence of the direction and level of international finance. If domestic
currency depreciates, foreign investors would like to buy cheaper home stocks and bonds.
Relatively high growth rate in money supply leads to inflation and depreciation. Money
supply differentials explain long term trends in exchange rate. Short term exchange rate
changes are very difficult to predict.
In international economics, demand for foreign exchange has a negative slope and
supply has a positive slope if import demand is elastic. Japan and United States are major
trade partners in the world. Japanese yen and US dollars are major transaction currencies
in the global trade market. The exchange market is clear in case that these two currencies
are floating. Some evidence suggests import demand is elastic over long time periods.
4
When domestic buyers want to buy foreign products, domestic currency is traded for
foreign currency on the foreign exchange market. Suppose a US importer purchases
manufactured goods from a Japanese firm. The importer earns in dollars while the
Japanese counterpart gets income in yen and transfer it to the bank account of the
Japanese exporter.
The exchange rate in fact is a relative price between two countries. In foreign
exchange rate market, exchange rate is determined by money supply and demand. Here
Japanese yen and US dollars can be an example to explain demand and supply of money
in foreign exchange rate market. There are participants who need US dollars in exchange
rate market. Japanese buy US goods or exports and investments. Others supply the US
dollars in foreign exchange rate market. Americans buy Japanese imported goods.
Americans invest in Japan. World investors or speculators can profit from expected
exchange rate movement, which may influence both demand and supply of money.
Various governments impact the exchange rate in the foreign exchange rate market.
Foreign exchange rate is determined by the interaction of supply and demand. Let the
interaction point is E1yen per dollar. See Figure2.1.
5
Figure2.1 Market equilibrium exchange rate
As we move up the vertical axis, the dollar appreciates. The demand for dollars
slopes down. If dollars appreciate against the yen, Japanese will buy fewer American
products. Because they are more expensive to them, the quantity demand for dollars will
fall. The supply curve will slope up because Americans will buy more Japanese goods as
the dollar appreciates. Consumers in United States will buy more Japanese goods for a
low price. The quality supplied of dollars will rise.
When exchange rate fluctuates, it is due to a shift in the supply and demand curve. If
US economy is growing faster than Japan economy, Americans buy more imported
Japanese products. The supply of dollars increases. The dollar depreciates. Here the
equilibrium exchange rate moves downward from E1 yen per dollar to E2 yen per dollar.
The yen appreciates and the dollar depreciates. See Figure 2.2.
Figure 2.2 Supply curve shift and exchange rate
6
Speculators can anticipate the movements in yen per dollar exchange rate, and they
will start to buy or sell dollars or yens. If speculators expect the dollar to appreciate, they
start buying it. The demand for dollars increases. Some productivity shocks will affect
the demand of money. An earthquake in Japan, or a flood in United States, will affect
exports and imports. An earthquake in Japan forces it to import more food from the U.S,
which increases the demand for the dollars, and the US dollars will appreciate. Here the
demand curve shifts rightward. The yen per dollar equilibrium move upward from E1 yen
per dollar to E3 yen per dollar. The yen depreciates. See Figure 2.3.
Figure2.3 Demand cure movement and exchange rate.
An unstable foreign exchange market occurs if exports are inelastic. The supply
curve has a negative slope. Suppose foreign exports are inelastic and supply slopes
downward as the graph A lower yen/$ rate leads to an increase the quantity of US dollars
along the supply curve. The supply of dollars might slope downward during the contact
period of the J curve.
7
The Bretton Woods fixed exchange rate system started from the end of World War
II until the oil price hikes in the 1970s. The US dollar was the dominant economy and
standard currency. The Bretton Woods system is similar to gold standard in the late
1800s or some other common standard or definition for currencies. The Bretton Woods
system was only successful because United States was the only dominant economy.
Europe and Japan had been destroyed by World War II. The system depends on
conservative US monetary policy to stable prices and reliable currency standard.
Meese and Rogoff (1983b) investigate the bad performance of exchange rate
models especially monetary model of exchange rates. They use vector autoregressions
(VAR) to identify the factors that influence the exchange rate in both short and long term
through the money supplies among US and other foreign currencies, relative outputs,
interest rate differentials and trade balance of US and foreign countries. The VAR results
show that innovation in exchange rate describe a large portion of the forecast error
variance at one month and three month forecast period. Innovations in the rest of
variables become more important for the period of one or three years. They suggest that
the failure of the exchange rate models is a result of volatility of time varying risk
premium, volatility of long run real exchange rates, and bad measurement of inflationary
expectations or money demand.
Monetary policy can affect international trade and finance. Inflation occurs when
the supply of currency grows faster than the production of money. Inflation can affect the
credit market and foreign exchange market. Stable growth in the money supply leads to
low or zero inflation. So inflation has little effect on exchange rate market if it is
correctly anticipated. Monetary policy has been proposed to control the money supply.
8
Inflation is predictable with monetary rules. Central Bank or monetary authorities may
help the economy adjust to external shocks. But monetary policy has its limits. Large
monetary contraction may lead to economic crisis.
Monetary policy affects inflation, the nominal interest rate, and the exchange rate.
Central banks actively trade in the exchange rate market in the floating exchange rate
system. Monetary policy is not an effective tool for influencing international trade and
finance. Steady growth of money supply leads to a steady interest rate and a reliable
exchange rate which is the foundation for business, traders, and investors to make better
plans.
Business cycles alternate periods of recessions and booms which are a natural part
of a dynamic economy. Foreign business cycles may affect domestic economics through
export. For example, a recession starts when firms sell inventories. As inventories decline,
firms begin to produce more products to build back the same inventories level as before.
Foreign firms can start to purchase overflowing inventories from domestic manufacturers.
A recession begins when foreign buyers stop buying domestic products or domestic firms
cut output.
In an open economy, the exchange rate is both a source of shocks and a mechanism
to transmit shocks, and monetary policy choices are dependent on exchange rate
dynamics. Central Banks manage the supply of money supply to intervene the business
cycle. Increasing the money supply will lower the interest rate and encourage investment.
Active monetary policy may not guide the economy from recession to expansion. In
theory, monetary policy should establish reliable money supply with zero inflation.
9
The treasury bill rates or government bond rates are treated as risk free rate in
economics, especially the long term treasury bill rate. The discount rate in business can
be this risk free rate plus suitable risk premium. Treasury bill rates include the inflation
expectation in one country. Consider the uncovered exchange rate between United States
and Japan. When the treasury bill rate in Japan increases, United States investors will
buy Japanese treasury bills more than United States treasury bills. In that case, the
exchange rate yen per dollar will rise.
In contrast to increase the Japanese Treasury bill rate, if the United States increases
its Treasury bill rate in the market, more Japanese traders purchase US Treasury bill. The
dollar will appreciate.
In business, interest rate or discount rate is more relevant than treasury bills rate. The
risk premium differs between industries. Treasury bills rate is consider the interest rate
without any risk premium. It can be used as simple interest rate to analyze the exchange
rate.
Rasmus, Fatum and Michael Hutchison (2005) investigate the effectiveness of
intervention in exchange rate market with recently published official daily Bank of Japan
intervention data. They explore the effectiveness of official Japanese intervention
operations in affecting the exchange rate, especially in a period of interest rate
inflexibility. Japan?s current zero interest rate environment has no room for monetary
policy stimulus to support foreign exchange operations. They use a non parametric sign
test for the median to show the directions of exchange rate change following intervention
events and a matched sample test to learn whether there is a significant shift in the
10
exchange rate change between the pre-event and post-event periods. They conclude that
intervention can be effective even if there is no supporting interest rate change. That
means that even if the Bank of Japan follows a zero interest rate policy it could depreciate
the exchange rate but the success rate is not as high as none zero interest policy.
According to their event study results, intervention is effective over a period of 2-5 days
with an extension of the framework up to two weeks.
Bonser-Neal (1996) discusses whether official intervention of central banks can
stabilize foreign exchange rates. She argues that there are mainly three reasons causing
volatile exchange rates: changes in market fundamentals, the degree of confidence with
market expectations, and speculative exchange rate movements unrelated to market
fundamentals. She builds a GARCH model to estimate the volatility related to central
bank intervention. She uses implied volatility of foreign exchange currency option prices
which is forward looking. She uses US macroeconomic data and other foreign variables
to ensure the volatility changes attributed to intervention do not affect some other
macroeconomic cause of volatility. The estimated model is
%?(yen/dollar volatility) = ?0 + ?1 Fed Intervention
+ ?2 Bank of Japan intervention + ?3 Macro & other variables + error
The results provide little support for the view that central bank intervention decreases
the volatility of exchange rate. From early 1985 till 1991, central bank intervention has
little effect on volatility and in some cases increased exchange rate volatility. Central
Banks can reduce exchange rate volatility if they resolve market uncertainty about future
fundamentals and policies.
11
Government central banks can buy and sell currencies in order to influence or
manage exchange rates. A depreciated or devalued currency implies more expensive
imports and cheaper export than before. In a flexible exchange rate system, official
international reserve can allow a central bank to purchase domestic currency which is a
liability for central banks. This action can stabilize domestic currency.
Supply and demand is the most important tool in economics. Prices of products in
the market are determined by goods and service traded in markets. According to Adam
Smith, price is the invisible hand in the market. Money between buyers and sellers
changes hands at promised prices in market transactions. International transactions can
occur when the buyer and seller are from different countries. The international
transaction involves exchange rate when the buyer?s currency is convert to seller?s
currency.
Imports are foreign products that domestic consumers can get without producing.
Exports are goods one country has to produce but cannot consume currently. One
country pays for import goods with the foreign currency it collects from export goods or
service. When goods are exported, the foreign importer must trade domestic currency for
foreign currency to pay for the exporter.
Amaya (1998) notes that Japan is one of the leading countries in world trade and
investment. Japan has very high relative savings rates to other countries. On the contrary,
United States has very low savings rates and foreign investment. The main reason is that
the shin-jinrui (young wealthy) in Japan spend more and save less, while baby boomers
in United States save money for retirement. Suppose there is no arbitrage in foreign
12
exchange rate market in both countries. In that case, foreign capital is supposed to move
to Japan. The exchange rate between these two countries will change. When foreign
countries increase investment in Japan, the dollar depreciates.
Each country chooses its inflation rate through political and economic process. So if
inflation rates are different from each other across countries, exchange rates will adjust.
Government or monetary authorities can change the supply of money.
Sarno, Taylor, and Frankel (2003) describe some economic models about the
exchange rate market. They offer exchange rate models using the latest econometric
techniques, which cover the main theories that explain the determination of exchange
rates and utilizes recent empirical data on exchange rate behavior. Their book is the
introduction of methodology to research in the exchange rate which is the economic
foundation on foreign exchange rate market.
Official intervention in the foreign currency exchange market happens when the
financial authorizes buy or sell foreign exchange against their native currency to affect
the exchange rate. When Bretton Woods adjustable peg exchange rate system collapsed
in the early 1970s, the economics profession favored pure float exchange rate system
with zero intervention. As the result of the realization of the speed which capital could
move among developed countries, an increasing number of economists and foreign
exchange market participants during the early 1980s appeared to favor intervention. The
main argument promoted a case for exchange rate system intervention is called the
?mistaken rate? issue: under a floating exchange rate system, an inefficient foreign
exchange market tends to generate the wrong rate which implies abnormal returns rather
13
than correct returns reflecting the economic fundamentals. Official intervention is a
useful tool to induce an appropriate rate, which is to say that the exchange rate moves
toward what the monetary authorities believe to be the correct rate.
Bayoumi and Eichengreen (1998) discussed the exchange rate volatility and
intervention with implications of the theory of optimum currency areas. They linked the
theory of optimum currency areas to the exchange rates of industrial countries. Those
countries with more stable rates suffer the greatest reduction in the transaction value of
domestic currency when their exchange rates changes because they have very small size
and dependence on trade. Countries with more variable exchange rates face more
asymmetric shocks than those with less volatile rates. Asymmetric shocks increase the
volatility of the exchange rate through magnifying exchange market pressure. Official
intervention could reduce the variability of exchange rate.
Kathryn Dominguez (1992) provides evidence that United States, Germany, Japan
central banks influence the value of a currency is interpreted as a signal of a change in
monetary policy. If central banks buy dollars in the foreign exchange market, central
banks attempt to support the dollar. In the long run, the value of dollars will rise due to
tight monetary policy. Fed Reserve will reduce the growth in the supply of dollars which
would lead to dollar appreciation. Participants in the market may view central bank's
activities as credible signal. The Fed, the German Bundesbank, and the Bank of Japan
publicized their plan to sell dollars through coordinated intervention following the Plaza
Agreement of September 1985. Participants in the foreign exchange market believed that
Fed agreed in principle to increase the growth of the U.S money supply. They expected
dollar depreciation in the future. They started to sell dollars. The Plaza Agreement
14
influenced the market expectation. German Bundesbank and Bank of Japan tried to resist
continued dollar depreciation with the Louvre Agreement in June 1987, but Fed did not
join in the buying of dollars at once. Market participants did not give central bank efforts
credibility and the dollar depreciation continued.
Schwartz (2000) discusses foreign exchange intervention as a policy tool.
Schwartz discusses central bank official intervention in the past and target zones for a
bilateral exchange rate that central banks will defend by intervening. Schwartz also
explained the exchange rate from national and international view points and observations
on the case of Bank of Japan. The conclusion of the paper shows that intervention by
monetary authorities has little effect on the exchange rate. The thesis presents the same
result as Schwartz discusses in the paper, that official intervention has little effect in the
foreign exchange rate market.
McKinnon (1999) asserts that Japan was in a liquidity trap with short term interest
rate and the monetary base over expanded in the late 1990s. Japan?s dilemma is the result
of market expectations from 1971 that yen is likely to be higher in the long run. The Bank
of Japan cannot by itself affect the exchange rate no matter its intervention is sterilized or
not. The upward pressure on yen reflects mercantile pressure from the United States. The
appreciation pressure on the yen is associated with trade disputes between Japan and
United States. The current unwillingness of Japanese financial institutions adds to the
shock of dollar claims that invests the US current account deficit. Only Japan and United
States joint program of long run yen stabilization will bring yen to international levels.
The expectation of inflation in the United States has led to lower the interest rate in
United States which has pushed Japanese interest rate four percentage points lower by the
15
expectation of the appreciation of the yen. McKinnon contends that Bank of Japan by
itself can do little to escape from the liquidity trap. Monetary base may contract to keep
exchange rate steady. So the recommendation of raising monetary base would make
adjustment more difficult than before.
16
Chapter ?
Data Description and Variable Definations
This chapter describes the data sources in the thesis, and reports statistical results.
The dataset comprises quarterly time series spanning from January 1974 to December
2010 for United States and Japan. All the data are from International Monetary Fund
International Statistics resource CD. The database resource CD starts from 1945 to 2010,
published in June 2011. In 1971, the Bretton Woods system collapsed. Japanese yen was
permitted to float above its fluctuation ceiling 357.30 yen per dollar on August 28th, 1971.
On February 14th, 1973, the theoretical official rate was set at 277.20 yen per dollar based
on Japanese yen stable gold content. At the same time, the effective exchange rate is set
to float upward and no margins were maintained in exchange rate transaction. In this
thesis, the research period started from the first quarter in 1974 to the last quarter in 2010
which is the floating exchange rate period. The exchange rate system changed from fixed
exchange rate system to floating exchange rate system. The dataset shows the time series
economic data in the floating exchange rate system.
The exchange rate is Japanese yen per dollars. Exports and imports are in domestic
currency for each country. United States foreign exchange reserve, Japan foreign
exchange reserve, are in millions units of currency. There are 156 observations for each
variable.
The dependent variable is exchange rate (EXR) from International Monetary Fund
International Statistics Database. The dependent variable measures the relative price of
17
two currencies in foreign exchange market. It is also regarded as the value of one
country?s currency in terms of the other currency. The exchange rate in this model is the
nominal exchange rate, yen per dollar. The dependent variable measured as Japanese yen
per dollar that means one US dollar can get the number of yen according to the exchange
rate in the foreign exchange market.
There are eight independent variables in this thesis. According to the characteristics
of the variables, there are four major groups of independent variables.
The first group is export value for Japan and United States. Export is the income of
one country if the country sells domestic products to foreign countries. Export in
international financial statistical database is counted in domestic currency. When a
country sells more products to the other, it will earn more money from the foreign
country. If Japan increases its export to the United States, the demand of yen will
increase. The demand of Japanese yen should shift rightward. The same thing happens if
United States buyers demand more Japanese products.
The changes of export will affect the equilibrium exchange rate in both countries. If
the United States increases export to Japan, the United States exporter will earn more
Japanese yen. The demand for yen should increase. If the United States decreases export
to Japan, the United States exporter will obtain less Japanese yen. The demand for yen
will decline. Exports are calculated in their own domestic currency for both countries in
quarterly time series data based on the international trade balance sheet. Export data can
be treated as income of one country from international trade through selling products to
the other countries. Export is also the foreign currency income for United States and
18
Japan under goods and service account in international trade. Japanese export is
described as JPEXP which is the variable name in the model and United States export is
described as USEXP.
The second group is import value for United States and Japan which is the foreign
consumption for each country. Import in international financial database is freight on
board. American consumers purchase Japanese products and Japanese consumers
purchase American products. In the early 1900s, there was an international trade theory
called proportions theory of two Swedish economists, Eli Hechscher and Bertil Ohlin.
This theory is called Heckscher- Ohlin theory. Heckscher-Ohlin theory states that a
country should specialize in production and exports with the factors that are most
abundant. Leontief (1953) notes the empirical problems with H-O model, known as
Leontief paradox that United States tended to export labor intensive goods despite have a
capital abundance. He found out that the US?s exports less capital intensive than import.
Samuelson (2001) emphasized gains from trade of intermediate goods are considerable in
the international trade. Japan and United States are two developed countries. The
technology of these two countries is the same across the countries. Japanese buyers can
import more agricultural products which are the main export products in the United
States. American consumers would like to buy more digital products from Japanese
manufacturers, which are the well-known products in the world. Imports activities will
affect the supply and demand of money to affect the exchange rate. If American buyers
purchase Japanese products, the supply of US dollars declines. The exchange rate
between Japan and United States rises. If Japanese consumers buy American export
19
products, the supply of Japanese yen decline. The yen appreciates. USIMP reflects the
import value of United States quarterly. JPIMP shows the import value of Japan quarterly.
The third group of independent variables is interest rates. The interest rate is the
nominal interest rate. The interest rate reflects the monetary policy. When one country
changes the supply of currencies, the interest rate will change. If Federal Reserve
increases the supply of US dollars in the market, the interest rate declines. If Bank of
Japan decrease the supply of Japanese yen in the market, the interest rate of Japanese yen
decline. Here in the model the interest is lending rate for both countries, the lending rate
bank offered on loan to prime customers such as corporations, financial institution. The
lending rate is the interest rate in most economic or financial models with the
consideration of inflation. In the International Financial Statistics database, there are
lending rates for United States. For Japan, the lending rate data comes from Bank of
Japan time series database. In this case, United States lending rate and Japan lending rate
are chosen.
The fourth group is foreign exchange reserve. Foreign exchange reserve is the
foreign money or bonds held by central banks and monetary authorities which are
accounted in US dollars for these two countries. The Central Bank can intervene to
influence the exchange rate through changing foreign exchange reserve. Foreign
exchange reserve is the effective instrument when central bank clears the excess demand
or excess supply through purchasing or selling foreign currencies. The foreign exchange
reserve in this database for Japan and United States is in US dollars because US dollars
are the most popular currency in international commerce.
20
The two available instruments are monetary policy and direct intervention in
foreign exchange market. Dominguez and Frankel (1993) argue that monetary policy and
official intervention are not effective tools separately. These two instruments are
combined. Official intervention is not stable to intervene in the foreign exchange rate
market. Interventions can also have a signal effect which means that they can provide
information for monetary policy in the future. Here foreign exchange reserves show the
liability of central bank which can reflect the official intervention in the foreign exchange
market.
In this model, USFOREV shows United States foreign exchange reserve and
JPFOREV stands for Japanese foreign exchange reserve. Japan is by far the larger
participant in the foreign exchange market. The Bank of Japan can still influence the
exchange rate market by its foreign exchange reserve. United States is one of the free
economic countries without much government intervention in the exchange market.
When the Bank of Japan increases its foreign exchange reserve, the dollar appreciates.
21
Chapter ?
The Model
This chapter presents a general model of independent variables that affects the
exchange rate between Japan and United States. The exchange rate is posited to be a
function of 1) Japanese export and United States export 2) Japanese import and United
States import 3) Japanese foreign exchange reserve and United States foreign exchange
reserve. 4) the Japanese treasury bill rate and the United States treasury bill rate. The
exchange rate can be expressed as a function of eight variables,
e = f (XJP , XUS, MJP, MUS, RJP, RUS) (1)
where e= EXR, XJP = JPEXP, XUS = USEXP, MJP = JPIMP, MUS = USIMP, RJP =
JPFOREV, RUS = USFOREV.
The equilibrium exchange rate is the intersection point when the demand cure of yen
and supply curve of US dollars intersects. The market equilibrium exchange rate can be
endogenous variable in the demand and supply system.
The equilibrium exchange rate is determined by the supply and demand of two
currencies. The equilibrium exchange rate is defined when the supply of Japanese yen
equals the demand of Japanese yen. The demand for yen is determined by United States
imports, Japanese exports, United States foreign exchange reserve. The supply curve
function is described:
QD= QD (e, XJP, Mus, Rus) (2)
22
The coefficients of implicit demand function are all positive in theory which means
that Japanese export, US import and US foreign exchange reserve have positive
relationship with the supply of the US dollars. If US imports decline, the supply curve of
US dollars shifts leftward. The equilibrium exchange rate decreases. Japan can earn US
dollars if export goods and services to United States. When Japan increases export to the
United States, Japan can earn more US dollars. The rising supply of US dollars will shift
the supply cure rightwards. The equilibrium exchange rate declines. When United States
Federal Reserve would like to intervene in the foreign exchange market, they will
increase foreign exchange reserve. When the United States Federal Reserve increases
foreign exchange reserves, the supply curve of US dollars moves right. That will result
in a decrease in the equilibrium exchange rate. So in this thesis, a positive sign marks the
positive relationship among exchange rate and independent variables in the demand
function.
The supply cure of Japanese yen is determined by United States exports, Japanese
imports, and Japanese foreign exchange reserve. The demand function is specified as:
QS = QS (e, XUS, MJP, RJP) (3)
The coefficients in the implicit supply function are positive which show that the
positive relationship between US exports, Japanese imports, and Japanese foreign
exchange reserve. If United States exports more products to Japan, the supply of Japanese
yen decreases and shifts the supply curve leftward. The market equilibrium exchange rate
declines. If Japan increases imports, the supply curve of Japanese yen shifts leftward. The
market equilibrium exchange rate rises. When Bank of Japan increases foreign exchange
23
reserve to influence and stabilize the exchange rate market, the demand curve of Japanese
yen move to the right hand side. If firms in United States increase export foods and
service to earn Japanese yen in international market, there will be more US dollars in the
US market. Increase in United States export will shift supply curve leftward. The
equilibrium exchange rate will rise. The positive signs in supply function below show
the positive relationship among exchange rate and independent variables.
The solution of supply curve and demand curve functions together is the market
equilibrium exchange rate. In this thesis, the supply and demand functions transform to
log transformed linear regression functions. Log transformed linear regression
coefficients are point estimates of elasticity. The aim is to interpret theory in terms of the
estimated elasticities c1 = , c2 = , c3= , which are the coefficients in the
market equilibrium exchange rate equation. The implicit demand and implicit supply
function can be solved in the following equation. Equation supply (2) and demand
function (3) together, solve for emkt:
emkt (?/$) = c0 + c1X + c2M + c3R + u (4)
Here, emkt = lne, X= ln XJP - ln XUS, M= lnMJP - ln MUS, R = ln RJP - ln RUS.
Market equilibrium exchange rate is a log transformed regression model. The log
transformed ratio is the same as the difference between two variables. After log
transformed this model, the dependent variables on the right hand become the difference
of log transformed variables.
24
In market equilibrium exchange rate equation, X, M, R, are the difference of log
transformed variable. It can be treated as ratio of log transformed independent variables
from the demand function and supply function. The market equilibrium exchange rate
equation is defined as lne. The negative signs of ln XUS, lnMUS, ln RUS reflects the
negative relationship among lne and independent variables. In market equilibrium
exchange rate equation, the changing of independent variables and the moving of
dependent variable is in the same direction.
Interest rates change when the monetary authorities or central banks increase or
decrease the supply of money. The interest rates are exogenous variables in the
equilibrium exchange rate equation. The interest rate is a percentage, not log transformed.
The interest rate can reflect the monetary policy in both two countries. Interest rate
difference, exogenous variable in the equation, is similar to log transformed independent
variables. In this model, interest rate difference (I) , I = ?i = iJP ? iUS, which is the
difference between Japanese lending rate and United States lending rate, reflects the
interest rate effect or monetary policy effect. The market equilibrium exchange rate
model function becomes:
lne = c0 - c1X + c2M + c3R + c4I + u (5)
The coefficients in the market equilibrium exchange rate equation show the
relationship between each independent variable and dependent variable. The coefficients
of export difference (X) can be negative. If Japanese consumers purchase US export
products, the demand of quantity of US dollars in the foreign exchange rate market
decreases. The demand of quantity of US dollars declines which means that participants
25
in the market sell yens to get dollars. The equilibrium market exchange rate declines.
The coefficient of import difference (M) can be positive. If the supply of dollars increases
in the foreign exchange rate market, there are more participants buying dollars to get yens.
The market equilibrium exchange rate rises. The coefficient of foreign exchange reserve
difference (R) can be positive. If Bank of Japan would like to buy yens in the market, the
demand of quantity of dollars rises. The market equilibrium exchange rate increases.
There is positive relationship among M and R market equilibrium exchange rate. The
coefficient of interest rate difference (I) can be negative. The increase of interest rate in
one country will depreciate the domestic currency against others. There is negative
relationship between interest rate difference and market equilibrium exchange rate.
The first step for this new model is unit root test to test for stationarity. Stationarity is
a tool in time series. Raw data may be transformed to a stationary process. This thesis
utilizes the augmented Dickey?Fuller test (ADF test). The ADF test is an augmented
version of the Dickey-Fuller test. The results of ADF test is in Appendices Table 1. An
ARCH model is built to test the residual heteroskedasticity.
The second step for this new model is log transformed linear regression. Durbin-
Watson test is done after the regression model. The test statistics results show the model
has a high and residual correlation by the Durbin-Watson test. The model is built on
difference stationary variables I(1) and stationary variables I(0). See Table 3. ARCH
model is also built here to test for the residual heteroskedasticity.
Finally lagged transformed model is built in this thesis. Lagged transformed model
shows that the contemporaneous effect and lagged effect in the model. In the long run,
26
the variables in the thesis show the strong relationship among dependent variable and
independent variables. The lagged transformed model is compared with other significant
model in in this thesis.
There are a lot of statistical software packages to deal with time series data. In this
thesis, SAS 9.2 is used to do the ADF test. Mohamed (2003) describes the ADF test of
quarterly data time series model in SAS 9.2.
The raw data in this thesis is quarterly data, sequential equal time increments. The
dependent variables and independent variables are both non stationary random walk
process as integrated order 1. Regressing the dependent and independent variables will
generate a spurious regression. The time plot of variables moving during the time period
shows the relationship between dependent variable exchange rate and each independent
variable in the model (See Appendix Figure 6). Granger and Newbold (1974) introduced
the spurious regression that produces apparently significant statistics results between
series that contain trends and are otherwise random. If both mean and variance are
constant over time, then the series follows a stationary process. Otherwise, the series is
described as a non stationary process, but may be a random walk with unit root.
To transform a non stationary to stationary series subtract each variable in the series
from its predecessor. Differencing a series produces other sets of observations as the first
differenced values, the second differenced values, and so on.
x level xt
x 1st differenced value (?xt ) xt - xt-1
Suppose there is a very simple and model:
27
yt = ? + ?xt +?t (6)
If a series is stationary without differencing, it can be designed as I(0), or integrated
of order 0. A series is stationary with first differences is designed as I(1), or integrated of
order 1. Stationarity is important for its influence in behavior. For example, if there is a
shock in this simple model, the shock will die away soon for a stationary process. That
means a shock in period t will produce a smaller effect in period t+1, a much smaller
effect in period t+2, and so on. Every independent variable needs to test stationarity
before Ordinary Least Square (OLS) regression analysis. The data is quarterly and
stationarity test will include at least five lagged periods. The quarterly data may have
seasonality problems. For example, the first quarterly data in one year may affect the next
first quarterly data in the next year. The seasonality problem often appears in agricultural
products. The spring and fall may have quite different results of agricultural products.
Here Jenkins, Reinsel (1994) and Choi (1992) provide method to decide how many
lags should include in the model. They uses SCAN method. In this thesis, both methods
are use to decide the numbers of lags in the unit root test.
Given a stationary or non-stationary time series {xt : 1? t ? n} by using mean
corrected form yt = xt - ? with autoregressive order of p+d and with a true moving-
average order of q. SCAN method can be used to analyze eigenvalues of the ARMA
process.
For autoregressive test order h = pmin ?, p max and moving- average test order j =
qmin, ?, q max. Moving average test order l = qmin ,?, q max performs the following step.
1. Let Yh, t = (xt, xt-1, ?, x t-h)? . Computing the following (h+1)?(h+1) matrix
? (h, l+1) = (? -1 (? , t ? l - 1Y?h, l) (7)
28
?*(h, l+1) = (? h,t Y?h,t)-1(? (8)
A* (h, l) = ? * (h, l+1) ? (m, l+1) (9)
, where t ranges from h + l +2 to n.
2. Find the smallest eigenvalue, ? * ( h, l), A* (h, l) and its corresponding
normalized eigen-vector ?h, l = (1, -?1(h, l) , -?2(h,l), ?., -?h(h,l) ). The squared
typical correlation estimate is ? * (h, l).
3. With the ?h,l as AR (h) coefficients, obtain the residuals for t= h+l +1 to n, by
following the formula:
wt (h, l) = yt ? ?1(h, l)yt-1 ? ?2(h, l) yt-2 - ? -?h(h, l)yt-m. (10)
4. From the autocorrelations of the residuals, rk(w), the standard error of the squared
correlation estimate by
var ( ? * (h, l) ?) ? ? ? (11)
, where d (h, l) = (1+ 2? rk(w(h, l))).
The test statistics uses in the method as an identification criterion is
C (h, l) = (n ? h ? l) ln( 1 ? ?*(h, l) / d (h, l)) (12)
which is chi square ?2 distribution if h = p +d and l ? q or if h ? p + d and l = q. If h > p
and l < q, there is more than one zero correlation between Yh, t and Yh, t ? l -1. Since ?*(h, l)
is the smallest correlations for each (h, l), the percentiles of c (h, l) are less than those of
?2. For h < p and l < q, no conclusions about the distribution of c(h, l) are made.
Bayesian information criterion (BIC) is a statistical method to provide the standard to
select the best model. The Bayesian information criterion (BIC) is an asymptotic result
derived under the assumptions that the data distribution is the one of the exponential
families. Here is the equation as follows:
29
BIC = -2ln (L) + kln(n) (13)
Here in the equation above, n is the size of the sample. k is the number of free
parameters to be estimated in the model. L is the maximum value of the likelihood
function for the estimated model. Under the assumption that the model errors or
disturbances are normally distributed, BIC equation becomes as follows,
BIC = nln ( ) + kln(n) (14)
The residual sum of square (RSS) is the residual sum of squares from the estimated
model. Here in the thesis, RSS comes from the Augmented Dickey Fuller (ADF) test on
the selected lags in ADF test model.
Given any two estimated models, the model with the lower value of BIC is the one to
be preferred. The BIC is an increasing function of RSS and also an rising function of k,
the number of free parameters to be estimated in the model. That means, unexplained
variation in the dependent variable and the number of explanatory variables increase the
value of the BIC.
In the thesis, the numerical values of the dependent variable which are the
differences of the variables in the model are identical for all the estimates being
compared. The BIC can be used to compare estimated models only when the numerical
values of the dependent variable are identical for all the estimates being compared.
In the thesis, the extended sample autocorrelation function (ESACF) provides the
method to identify the orders of a stationary and non-stationary ARMA process based on
iterated least square estimates of the autoregressive parameters. Tsay and Tiao (1984)
provide the technique of the ESACF method. Choi (1992) provides the useful
descriptions of the algorithms.
30
Here in the thesis, given stationary or non-stationary time series {zt : 1? t ? n} with
mean corrected form ?t = zt - ?z with autoregressive order p + d and with moving average
order of q. In this thesis, the ESACF method is used to estimate the unknown order p + d
and q through analyzing the autocorrelation functions with filtered series of the form:
wt(m, j) = ?(m, j) (?) ?t = ?t - ? ?i(m, j) ?t ? i (15)
where ? is the backshift operator, m = pmin, . . . , pmax are autoregressive test orders, where
j = qmin + 1, . . . , qmax + 1 are moving average test orders, and where ?i(m, j) are
autoregressive estimators under the assumption that the series is an ARMA ( m, j )
process.
The SCAN method and ESACF method provide the autoregressive orders and BIC
test statistics result. The BIC results define the autoregressive orders for Augmented
Dickey-Fuller (ADF) test. The number of the lagged differences in the thesis model can
derive from the lowest BIC test statistics results. The autoregressive orders of the log
transformed exchange rate ADF autoregressive order is one. The autoregressive orders
of log transformed export difference in the ADF model are five. The autoregressive
orders of the log transformed import difference in the ADF model are five. The
autoregressive orders of the log transformed foreign exchange reserve difference in the
ADF model are four. The autoregressive orders of the log transformed interest rate
difference in the ADF model are thirteen.
The stationarity test will take the Augmented Dickey-Fuller (ADF) technique (Dickey
and Fuller, 1981) which actually is auto-regression model in the following regression
equation (Dickey and Fuller, 1981). The ADF test formula is as follows,
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?xj,t = ? ?j,k xj,t-k + ki x j, t-1 + ? k,t (16)
where ?xj,t is the 1st differenced value of xt, ki xj,t-1 is the 1st lagged value of xt,
? ?j,k ?xi, t-k are the 1st, 2nd, 3rd,4th,& tth lagged value of the 1st differenced value of x,
and ?k,t is the error term.
The model hypothesis tests are: The Model is
H0: Non stationary
H1: Stationary
There is no trend in the ADF test. The graph of log transformed data shows that
there is no significant trend for the dependent variable and independent variable. See
Appendices Figure1. Scatter plot matrices of variables moving during the period in the
model. In the thesis, the same methodology and technique is used for the ADF test. In
the thesis, the dependent variable is y in the previous simple model. All the four
independent variables substitute for x in above model.
The ADF test models in this thesis can use the same equation as equation (16) with
the same method. ki (i= 1,2,3,4,5, . . ., n) shows the coefficient of lag term which is one
lag before the current term. The coefficient of one lag term ki before current term is the
mark in ADF test. Four ADF test models of independent variables in this thesis will be:
?Xj,t = k1Xt-1 + ? ?j,k ?Xj,t-k + ?k,t (17)
?Mj,t = k2Yt-1 + ? ?j,k ?Yj,t-k + ?k,t (18)
?Rj,t = k3Rt-1 + ? ?j,k ?Rj,t-k + ?k,t (19)
?Ij,t = k4It-1 + ? ?j,k?Ij,t-k + ?k,t (20)
There are totally seven T test statistics values in each equation. The second
coefficients k1, k2, k3, k4, which are the coefficient of first lag of independent variables
32
are the most important in the test. The T test statistics results of first lag value of
independent variables are compared with the critical value in Augmented Dickey-Fuller
test. The dataset in this thesis is quarterly series so stationary tests have to be conducted
at level up to 5 lagged periods. The sixth independent variable in the ADF test is fourth
lagged of the first difference which can show four quarters or one year ago the same
quarter. When critical value is larger than test statistics results, the model fails to reject
ADF hypothesis test. When the test statistics results are larger than critical values, the
model rejects the null hypothesis. The ADF test statistics test results table is in Table 2.
The test statistics critical value with constant for 5% confidence interval is -2.79, for
1% confidence interval is -3.96, and for 10% interval is -2.57. The test statistics critical
value with constant and time trend for 5% level is -3.41, for 1% level is -3.96 and for 10%
level is -3.12.The test statistic value for X, M, R, I with constant are -0.68, -1.67, -3.80, -
2.31. Here 5% level is chosen as confidence interval. The test statistical value of X,-0.68,
is larger than -2.79 at level 5% which fails to reject the null hypothesis of unit root or non
stationarity. Export difference (X) follows a non-stationary process. The test statistical
value of import difference is ? 1.67 which is larger than -2.79 at level 5%. This result
fails to reject the null hypothesis of non-stationarity of import difference (M) so there are
no unit roots in import difference and export difference series. Import and export
difference (X, M) follows non stationary process. The results of foreign exchange reserve
difference (R) and interest rate difference rejects the null hypothesis. The test statistical
value of foreign exchange reserve difference is -3.80 which is smaller than critical value,
-2.79, at level 5%. The result rejects the null hypothesis of non stationarity. The test
statistical value of interest rate difference (I) is -2.31 which is larger than critical value, -
33
2.79, at level 5%. The result fails to reject the null hypothesis of non stationarity. The
conclusion is that foreign exchange reserve difference (R) follows stationary process at 5%
level. In this case, there are unit roots for foreign exchange reserve difference. The
export difference, the import difference and the interest rate difference follow non
stationary process.
The test statistics critical value with constant and time trend for 5% confidence
interval is -3.41, for 1% confidence interval is -3.96, and for 10% interval is -3.12. The
test statistic value for X, M, R, I with constant are -3.22, -1.94, -3.73, -2.21. Here 5%
level is chosen as confidence interval. The test statistical value of X,-3.22, is larger than -
3.12 at level 10% which rejects the null hypothesis of unit root or non stationarity. Export
difference (X) follows a stationary process. The test statistical value of import difference
is ? 1.94 which is larger than -3.41 at level 5%. This result fails to reject the null
hypothesis of non-stationarity of import difference (M) so there are no unit roots in
import difference and export difference series. Import and export difference (I, M)
follows non stationary process. The results of foreign exchange reserve difference (R)
and export difference rejects the null hypothesis. The test statistical value of foreign
exchange reserve difference is -3.73 which is smaller than critical value, -3.41, at level
5%. The result rejects the null hypothesis of non stationarity. The test statistical value of
interest rate difference (I) is -2.21 which is larger than critical value, -3.41, at level 5%.
The result fails to reject the null hypothesis of non-stationarity. The conclusion is that
foreign exchange reserve difference (R) follows a stationary process at 5% level. The
export difference (X) follows a stationary process at 10% level. In this case, there are
34
unit roots for foreign exchange reserve difference at 5% level. The import difference and
the interest rate difference follow non stationary process.
The test statistics critical value with constant, lags of the difference and time trend for
5% confidence interval is -3.41, for 1% confidence interval is -3.96, and for 10% interval
is -3.12. The test statistic value for X, M, R, I with constant are -2.97, -3.00, -3.84, -4.36.
Here 5% level is chosen as confidence interval. The test statistical value of X,-2.97, is
larger than -3.41 at level 10% which fails to reject the null hypothesis of unit root or non
stationarity. Export difference (X) follows a stationary process. The test statistical value
of import difference is ? 3.00 which is larger than -3.41 at level 5%. This result fails to
reject the null hypothesis of non-stationarity of import difference (M) so there are no unit
roots in import difference and export difference series. Import and export difference (X,
M) follows non stationary process. The results of foreign exchange reserve difference (R)
and export difference rejects the null hypothesis. The test statistical value of foreign
exchange reserve difference is -3.84 which is smaller than critical value, -3.41, at level
5%. The result rejects the null hypothesis of non stationarity. The test statistical value of
interest rate difference (I) is -4.36 which is larger than critical value, -3.41, at level 5%.
The result fails to reject the null hypothesis of non stationarity. The conclusion is that
foreign exchange reserve difference (R) follows a stationary process at 5% level. The
interest rate difference (I) follows a stationary process at 1% level. In this case, there are
unit roots for foreign exchange reserve difference at 5% level. The import difference and
the interest rate difference follow non stationary process.
35
The dependent variable, exchange rate is also a time series variable. There may be
a unit root in exchange rate lne series. Under the same hypothesis as independent
variables, another ADF test is to test stationarity of dependent variable.
?lnet,j = k5lnet-1 + ? ?j,k?lnej,t-k + ?k,t (21)
The test statistics value with constant is -0.99 which is also greater than critical value
-2.79 at level 5%. The test statistics value with constant and time trend is -2.12 which is
larger than critical value at any level. The BIC help the ADF to pick eleven lags. The test
statistics result with constant, time trend and lags is -2.76. The market equilibrium
exchange rate is following a non-stationary process so there is no unit root in market
equilibrium exchange rate. The test statistics result table in Table 2.
The residual plots of ADF test show that in some periods these independent
variables are riskier than others because the variance in some periods is larger than others.
In this case, the expected values of error terms are greater than others. There may be
heteroskedasticity in the error variance. The independent variables in this thesis have
very large error variance. The residual plot of shows the amplitude of the returns varies
over time which is described as ?volatility clustering?. See Appendix Figure 11, Figure
12, Figure 13, Figure 14, and Figure 15.
The variables in the model are non stationary process. The residual is non stationary.
The standard ordinary least square regression result does not hold. The standard ordinary
least square regression gives spurious results. The exchange rate and import difference
are following a difference stationary which is also called I (1). The foreign exchange
reserve difference, export difference and interest rate difference are following stationary
process, which are called I(0).
36
The ordinary least square (OLS) regression can give best linear unbiased estimation
(BLUE) when all the variables in the model are stationary. In the thesis, exchange rate,
export difference, import difference are difference stationary, I (1). Foreign exchange
reserve difference and interest rate difference are stationary, I (0). The model can use
exchange rate difference (?e), difference of export difference (?X), difference of import
difference (?M), foreign exchange reserve difference (R), and interest rate difference (I).
?e = f (?X, ?M, R, I) (22)
?e = -0.021* + 0.055?X + 0.27?M** + 0.00083R ? 0.0038I **+ ?t (23)
(0.013) (0.059) (0.081) (0.0033) (0.0019)
The regression result shows that import difference has the strongest positive effect in
the model. The coefficient of the difference of the foreign exchange reserve difference is
very small. If there is one percent change in foreign exchange reserve, exchange rate
difference will only move 0.083 percent. Trade variables have strong linear relationship
with dependent variable. If there is an increase in import difference about 1 percent,
exchange rate will increase 27 percent. The sign of interest rate difference should be
positive in the model. The unexpected inflation will have negative effect on exchange
rate. If there is one percent increase in interest rate, the exchange rate will decrease 0.38
percent which shows very tiny effect on exchange rate.
The residuals of each variable in the model may have the autocorrelation. The most
common test for autocorrelation is Durbin-Watson test. The assumption of Durbin-
Watson test is that the noise or disturb terms are stationary and normally distributed with
mean zero.
H0: ? = 0
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Ha: ? ? 0
The residual correlation in the regression is ?. The null hypothesis is that the errors or
noise terms are uncorrelated. The alternative hypothesis is that error terms have
correlation following AR(1) process. To test H0 against Ha, get the least square estimator
? and residuals e1, e2, e3, . . . , en. The test statistics is as follows:
d = ? (et ? et-1)2 / ? et2 (24)
where ei = yi ? ?i and yi is the observed values of the response variable for individual i.
?i is the predicted values of the response variable for individual i. d decrease as the serial
correlations increase. Upper and lower critical values, dU and dL have been tabulated for
different value of k which is the number of explanatory variables in the model and n.
Durbin Watson test result in the model is 2.16. The critical value for the lower is 1.68,
and the critical value of the upper is 1.80. In the model, d = 2.16 is larger than the upper
critical value, 1.80. The test statistics result fails to reject the null hypothesis. So there is
no serial correlation in the model.
The residuals may have heteroskedasticiy in the model. The ARCH model can be
used to test heteroskedasticity. The ARCH model which is autoregressive conditional
heteroskedasticity is designed to deal with this heteroskedasticity.
The model in this thesis explain ARCH(1) model for dependent variable lne and
independent variables X, M, R, I .The model explains ?y? which represents means of lne,
X, M, R, I, mean equation using AR(1) model.
yt = c + ? yt-1 + ut (25)
Var(ut | ?t-1 ) = ht (26)
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Var(ut | ?t-1 ) is the conditional variance of ut, where ?t-1 is the information set
available at t -1.
The model explains the conditional variance:
ht = ? + ?1ut-12 + ? + ?qut-q2 (27)
These two equations (25) and (26) can consist of AR (1)-ARCH(Q) model which is
AR(1) Mean and ARCH(Q) Variance equations.
So ARCH (1) model is as follows:
ht = ? + ?1ut-12 (28)
The ARCH (1) model in this thesis is test the heteroskedasicity of the residuals in
every ADF test model. The error term can be expressed in this thesis by the past values of
lagged residuals:
?t2 = a0 + a1?k,t-12 (29)
The hypothesis test of ARCH model is as follows:
H0: a0 = a1 = 0
H1: a0 ?0 or a1 ? 0
Here in the thesis T test and F test statistics test the ARCH effect of the residual. In
the thesis, ARCH (1) model is built to test the heteroskedasticity. The lag order for
ARCH model is one. The F test critical value of the model is 3.90. F test statistics result
is 0.54 which is greater than critical value (F1,150 = 3.90). The test result fails to reject the
null hypothesis of no ARCH effect. The T test results of variance one lag before is -0.73
which is larger than critical value 1.65. The test result fails to reject the null hypothesis
of no ARCH effect. There are no ARCH effects of the residual in the model. See Table 3.
39
Chapter?
Empirical Results
The regression model is this thesis is based on the factors affect the exchange rate
market. Durbin Watson test result is 2.16 which is larger than upper critical value 1.80.
There is no serial correlation if Durbin Watson test result is between 1.80 and 2.20. Here
in the thesis, the Durbin Watson test result of the OLS regression is in the interval. The
test statistics result fails to reject the null hypothesis of no serial correlation in the
residuals. So error terms have no serial correlation. There is no stationarity of e, X and
M which means that these three variables in this regression model are not following
stationary process. The exchange rate, the export difference, and import difference are
following difference stationary process. The regression model with all stationary
variables which are three difference variables and two level variables is based on
stationary variable. The regression model is:
?e = -0.021* + 0.055?X + 0.27?M** + 0.00083R ? 0.0038I** + ?t (30)
(0.013) (0.059) (0.081) (0.0033) (0.0019)
The statistics result shows that is 84%. There is very significant linear relationship
according to the goodness and fitness test. The explanatory variables in the model can
explain 84% of the dependent variable which is the exchange rate difference. The test
statistical result shows that two of the coefficients of independent variables are very
significant. Only the difference of the export difference which is the difference of
Japanese export and US export difference and the difference of the foreign exchange
reserve are less significant than other variables. The results show that foreign exchange
reserve is not the effective method to intervene the foreign exchange market. The t test
40
result of the intercept provides the evidence to reject the null hypothesis of zero intercept.
The small intercept of the regression model show that there are not much unexplained
information in the model. The linear regression results are very significant in test
statistics.
This thesis use Bayesian information criterion (BIC) to derive the number of the lags
of the first difference of variables in ADF test model to test stationarity of variables in the
model. The technique in SAS programming to run ADF test provides ?best fit?
mathematic equation. The dependent variable is the first difference of every variable in
the thesis model and independent variables are the number of previous lagged value of
the first difference defined by BIC method in the model. Here every variable in the model
includes the dependent variable, e, independent variables such as X, M, R, and I. The test
results prove non-stationary process for exchange rate, import difference and export
difference. The test statistics provide a path to fail to reject the null hypothesis for 5%
level -3.41. The test statistics values of export difference and import difference are -2.97,
-3.00 which are larger than critical value of 5% level, so export difference (X) and import
difference (M) are following non-stationary process. The test statistical value of foreign
reserve difference (R) and interest rate difference (I) are -3.84,-4.36 which are larger than
critical value -3.41 at level 5%, so foreign exchange reserve difference and interest rate
difference are stationary process for rejection of the null hypothesis. There are unit roots
of foreign exchange reserve difference and interest rate difference in ADF test model.
There is linear relationship among trade variables and dependent variable, exchange
rate. Export and import are two main effective variables in foreign exchange rate market
for the higher coefficients than other independent variables. Japan and United States can
41
get counterpart currencies from exports and imports. If one country imports or exports
products in international commerce, the market equilibrium will move upward or
downward for the changes of money supply and demand. The exchange rate will
appreciate or depreciate. The rise of US imports and Japanese exports will increase the
demand of the quantity of Japanese yens in the foreign exchange rate market. When one
percent of import changes in the market, 27% change in the market equilibrium exchange
rate. If the US exports and Japanese imports rise, the supply of quantity of Japanese yens
will increase the supply of quantity of US dollars. The rising one unit of export in the
market, the market equilibrium exchange rate increases by 5.5%. Comparing with export
difference, import difference plays a more important role on market equilibrium
exchange rate.
The foreign exchange reserve is not an effective tool to stabilize the exchange rate.
Compared with monetary policy, official intervention is less effective than monetary
policy on the exchange rate. That is the reason why some European countries set the
upper and lower band for the exchange rate. Now the Central bank of European Union set
the upper and lower band of the euro. Central banks sell their domestic currencies when
the currency is appreciate or overvalued and buy their currencies when the currency is
undervalued. One percent increases in foreign exchange reserve, the market equilibrium
exchange rate might only move upward 0.083%. In fact, there is no significant effect.
This result is consistent with the opinion that official intervention will not affect a
floating exchange rate.
Interest rate difference has negative relationship with the dependent variable, market
equilibrium exchange rate. When one country increases its discount rate, the stronger
42
currency will bring lower exchange rate for indirect exchange rate. In this model, when
Japanese economics becomes stronger and better than before what it was, the exchange
rate yen per dollar depreciates. Stronger yen lower the exchange rate yen per dollar.
Interest rate can be changed when central banks increase or decrease money supply in the
financial market. In the long term, monetary policy is not an effective tool in exchange
rate market. If the countries are under uncovered exchange rate system, the increase in
domestic interest rate will decrease the exchange rate. When interest rate is increasing,
more and more foreign capital moves to the country. The exchange rate will decrease. In
floating exchange rate market, the domestic will appreciate. These shocks in exchange
rate market will not hold for a long time. In the long run, the exchange rate will reach its
own equilibrium which reflects countries? economic fundamentals. The coefficient of
interest rate difference is 0.38% which means that one percent change in the interest rate
difference will change the market equilibrium exchange rate 0.38%. That is why some
economists agreed that interest rate movement or monetary policy will not change the
exchange rate that much. The exogenous variable, interest rate difference, is not
significant in the result.
Lagged transformation function is a transfer function with the effects of the
independent variables processes transferred onto an AR(1) process of the endogenous
variable, the dependent variable in the model, which is et in the thesis. The second order
LTM is
?et = f (?et-1, ?Xt, ?Xt-1, ?Mt, ?Mt-1, Rt, Rt-1, It, It-1) (31)
Estimated results are
?et = -0.022* - 0.20?et-1 ** + 0.11?Xt ? 0.12?Xt-1** + 0.36?Mt *** - 0.094?Mt-1
(0.013) (0.10) (0.067) (0.059) (0.086) (0.088)
43
-0.0011Rt + 0.0021?Rt-1 ? 0.0082It* + 0.0042It-1 +?t (32)
(0.0072) (0.0071) (0.0048) (0.0049)
The lagged transformation function combines the contemporaneous independent effect
from ?Xt, ?Mt, Rt, It and the lagged effects of ?Xt-1, ?Mt-1, Rt-1, It-1. The total effect ?Xt
on ?et over two periods is -0.01. The total effect ?Mt on ?et over two periods is 0.27. The
total effect Rt on ?et over two periods is 0.0010. The total effect It on ?et over two periods
is -0.0040.
The residual in the lagged transformed model should be white noise given the
difference variables. Durbin-Watson test is only applicable to the first order
autoregressive systems. Durbin-h test is applicable when there are endogenous lagged
variables in the model.
When there is one or more lagged dependent variables in the model, the Durbin-
Watson test statistics will be biased toward 2 which mean that even if the test result is 2
there may be serial correlation. This test for serial correlation when there is a lagged
independent variable in the equation based on h test.
Suppose there is an estimated model with OLS:
1t t t tY X Y? ? ? ??? ? ? ? (33)
The Durbin h statistics is defined as:
? ?1 [ ( )]
Th T Var? ?? ?
(34)
where T is the number of observations, where ?? is the estimated correlation coefficient
of the residuals, that is the autocorrelation coefficient of the residuals, and where The
?()Var? is the variance of the coefficient on the lagged dependent variable.
44
Solve for?? , substitute, and write the h statistics as:
1
?2 1 [ ( ) ]D W Th T V a r ??????? ???
(35)
Durbin has shown that the h statistics is approximately normally distributed with a
unit variance, hence the test for first order serial correlation can be done with the standard
normal distribution. It should be noted, however, that if ?[ ( )]TVar ? is greater than one,
then the ratio with the square root becomes negative and this test cannot be applied. So
the test is normal distribution Z test and the null hypothesis is that ? = 0.
If the Durbin h test result is within the interval (-1.96, 1.96), there is no serial
correlation in the residual. Durbin h test result of the lagged transformation function is -
0.75 which in the interval. The test result fails to reject the null hypothesis. There is no
serial correlation in the residual.
The total effect of export difference ?Xt = 0.11 ? 0.12 = -0.01.The total effect of
import difference ?Mt = 0.36 -0.094 = 0.35. The total effect of foreign exchange reserve
difference ?Rt = -0.0011+ 0.0021 = 0.0010. The total effect of interest rate difference It =
-0.0082 + 0.0042 = -0.0040.
The standard deviation of the total effect model with rules of error propagation is
derived by the following equation. Assume ? is the coefficient of the total effect model
? = ? ? ? ? ?? = (??2 + ??2).5
? = ?? or ? = ?/? ? ?? = ?((??/?)2 + (??/?)2).5 (36)
The standard deviation for each variable in the equation (32) and equation (36) can
be derived from standard error times the squared root of the number of the observations.
45
The standard error of the variables in the total effect model can be calculated by using
equation (36).
The standard error (SE) of the export difference ?Xt in the total effect model is 0.089.
The standard error (SE) of the import difference ?Mt in the total effect model is 0.12. The
standard error (SE) of the foreign exchange reserve difference Rt in the total effect model
is 0.010. The standard error (SE) of the interest rate difference It in the total effect model
is 0.0069.
The total effect model is as follows:
?et = -0.022* - 0.01?Xt + 0.27?Mt **+ 0.0010Rt - 0.0040It + et (37)
(0.013) (0.089) (0.12) (0.010) (0.0069)
The total effect model provides the strong evidence in the economic theory. The total
effect model shows that the coefficient of foreign exchange reserve ratio is 0.0010 which
is approximately zero. In the difference total effect model, the result shows that the
foreign exchange reserve has no effect in foreign exchange rate market. The activity of
central banks or monetary authorities which try to adjust the foreign exchange reserve
will not influence the exchange rate in the long run. The export difference and import
difference are the two main factors in the market equilibrium exchange rate equation. The
movement of exports and imports will affect the market equilibrium exchange rate in the
long run. Interest rate is the exogenous variable in the model. Interest rate shows the
negative effect on the market equilibrium exchange rate. If there is inflation in Japan, yen
will depreciate in the exchange rate market. Inflation will increase the nominal interest
rate. The intercept in the total effect is still insignificant that the result fails to reject the
46
null hypothesis of no intercept. The total effect model can explain all the differenced
variables in the model.
47
Chapter?
Conclusion
This thesis analyzes the exchange rate between Japan and United States. The
model reflects the influence of exports, foreign exchange reserves, and interest rates on
the exchange rate. These independent variables have direct or indirect effects on
exchange rate. The exchange rate is very volatile and difficult to determine. This thesis
builds the general outline of an empirical floating exchange rate model.
The thesis addresses the main factors in the exchange rate market. Export and import
are main two economic factors influencing the exchange rate. The import difference is
the most effective factor of all variables in the model. Export provides the foreign income
in international trade for goods and services. The United States as a buyer and Japan as a
buyer purchase from each other. The supply and demand of foreign exchange moves the
market equilibrium exchange rate upward or downward due to the import and export
activities. The coefficient of export shows the positive effect in the exchange rate model.
In theory the coefficient should be negative. In the total effect model, the negative
coefficient shows the negative relationship between export difference and exchange rate.
When Japanese firms sell products to buyers in United States, Japanese firms earn US
dollars in exchange rate market.
Central banks would like to stabilize the exchange rate. They increase or decrease
the money supply of their own currency. This is an indirect tool to affect exchange rate
because the money supply will bring inflation to economic systems. There are many
48
papers on the issue of whether monetary policy has little effect on exchange rate. In the
present results, the coefficient of the foreign exchange reserve is zero.
The negative coefficient of interest rate difference means that the increase in the
interest rate difference will decrease in the market equilibrium exchange rate. The
increase in the interest rate will lead to a reduction in the demand for money. Domestic
money supply increases will lead to a fall in the equilibrium interest rate. The monetary
policy shock should cause a depreciation of the domestic currency. The interest rate is the
exogenous variable in the market equilibrium exchange rate equation. The thesis
subtracts the interest difference as the monetary policy variable in the model. The low
coefficient of interest rate difference in the model shows that monetary policy is not the
method to control the volatility of exchange rate.
Central banks can buy or sell domestic currency or government bonds to stabilize the
exchange rate. The volatility of exchange rate is risky to export or import in international
trade. The appreciation of exchange rate will let export firms lose sales. On the contrary,
the depreciation of exchange rate will make export companies obtain more sales.
Some economists argue that floating exchange rate system is better than fixed
exchange rate. The flexible exchange rate system can automatically adjust and enable
countries to dampen the impact of shocks and foreign business cycle. It will also reduce
the crisis of balance of payment. When appreciation or depreciation occurs, central bank
and monetary authorities intervene to manage the float. In the model, the coefficient is
very low which shows that foreign exchange reserves are not an effective tool to control
the exchange rate.
49
Finally the analysis in this thesis model proves the total effect of the model in the
long run. Independent variables such as exchange rate, export difference, and import
difference are individually non stationary. Foreign exchange reserve difference and the
interest rate difference are stationary. The model is based on difference stationary
variables which are exchange rate, export difference, and import difference. Level
stationary variables are foreign exchange reserves and interest rate difference. The
coefficient in the lagged transformation function shows adjustment to the equilibrium in
the long run.
The coefficient of the foreign exchange reserve difference in lagged transformation
function model is negative. The coefficient of the foreign exchange reserve difference in
the total effect model is positive, the same as the result in the regression model. The very
low coefficient of the foreign exchange reserve difference is insignificant. This shows
that foreign exchange reserves in the exchange rate market fail to influence the exchange
rate in the present sample.
50
References
Amaya, Naohiro. "The Japanese Economy in Transition: Optimistic about the Short Term,
Pessimistic about Long Term." Japan and the World Economy (1988) page: 102-109.
Bayoumi, Tamim and Barry Eichengreen. "Exchange Rate Volatiltiy and Intervention:
Implications of the Thoery of Optimum Currency Areas." Journal of International
Economics 45 (1998) 191-209.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994), Time Series Analysis:
Forecasting and Control, Third Edition, Englewood Cliffs, NJ: Prentice Hall, 197?199.
Choi, ByoungSeon (1992), ?ARMA Model Identification?, New York: Springer-Verlag,
129?132.
Devereux, Michael B., and Charles Engel. "Fixed VS.Floating Exchange Rates:How
Price Setting Affects the Optimal Choice of Exchange Rate Regime." NBER Working
Paper Series (1998). Print. JEL NO.F3, F4
Dickey, D., and W. Fuller. "Distribution of the Estimators for Autoregressive Time Series
with a Unit Root." Journal of the American Statistical Association 74 (1979): 427-31.
Dickey, David A., and Wayne A. Fuller. "Likelihood Ratio Statistics for Autoregressive
Time Series with a Unit Root." Econometrica 49 (1981): 1057-072.
Dominguez, Kathryn., ?The role of internationl organizations in the Bretton Woods
system.? Working Paper NO.3951, National Bureau of Economic Research (1992).
"Durbin-Watson Critical Values." Statistics Table for Economists. University of
Warwick. Web. 23 Sept. 2011.
Fatum, Ramus, and Michael Hutchison. "Effectiveness of Official Daily Foreign
Exchange Market Intervention Operations in Japan." Journal of International Money and
Finance 25 (2006): 199-219.
Hodrick, Robert J. "The Empirical Evidence on the Efficiency of Forward and Future
Foreign Exchange Markets." Fundamentals of Pure and Applied Economics 24 (1987).
International Financial Statistics. International Monetary Fund, July 2011. CD. 21 Sept.
2011.
"Mackinnon's Critical Values." Statistics Table for Economists. University of Warwick.
Web. 23 Sept. 2011.
51
Leontief, W. W. "Domestic Production and Foreign Trade: The American Capital
Position Re-examined". Proceedings American Philosophical Society 97 (1953): 332?349.
McKinnon, Ronald I. "Annual Monetary Conference." Proc. of Cao Institute Annual
Monetary Conference. 1999.
McKinnon, Ronald I. ?The Foreign Exchange Origins of Japan?s Liquidity Trap,? Cato
Institute 17th Annual Monetary Conference, 1999.
Meese, R. and Rogoff, K. (1983 b) ?The out-of-sample failure of empirical exchange rate
models: Sampling error or misspecification?? Exchange Rates and International
Macroeconomics. Chicago, IL: The University of Chicago Press.67-112
Mohamed, Ismail, and Theresa R. DiVenti. "Using SAS? for Cointegration and Error
Correction Mechanism Approaches:Estimating a Capital Asset Pricing Model(CAPM)
for House Price Index Returns."
Mohamed, Ismail E. "Time Series Analysis Using SAS? Part IThe Augmented Dickey-
Fuller (ADF) Test.".
Neal, Catherine Bonser. "Does Central Bank Intervention Stablize Foreign Exchange
Rates?" Economic Review (1996).
Newbold, P., and Clive W.J Granger. "Experience with Forecasting Univariate Time
Series and the Combinationa of Forecasts." Journal of the Royal Statistical Society A
137.NO.2 (1974): 131-65.
Samuelson, Paul. "A Ricardo-Sraffa Paradigm Comparing the Gains from Trade in Inputs
and Finished Goods". Journal of Economic Literature (2001) 39 (4): 1204?1214
Schwartz, Anna J. "The Rise and Fall of Foreign Exchange Market Intervention." NBER
Working Paper Series E5, F3 JEL (2000).
Taylor, Mark P., and Jeffery A. Frankel. "Foreign Exchange Intervention." The
Economics of Exchange Rates. By Lucio Sarno. 1st ed. Cambridge UP.
Tsay, R. S. and Tiao, G. C. (1984), ?Consistent Estimates of Autoregressive Parameters
and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA
Models,? Journal of the American Statistical Association, 79 (385), 84?96.
52
Appendix
Figure 1. Exchange rate time plot from 1974 to 2010
Figure 2. Export time plot from 1974 to 2010
53
Figure 3. Import time plot from 1974 to 2010
Figure 4. Foreign Exchange time plot from 1974 to 2010
54
Figure 5. Lending rate time plot from 1974 to 2010
Figure 6. Export difference time plot from 1974 to 2010
55
Figure 7. Import difference time plot from 1974 to 2010
Figure 8. Foreign Exchange Reserve difference time plot from 1974 to 2010
56
Figure 9. Lending rate Difference time plot from 1974 to 2010
Figure 11. Market equilibrium exchange rate residual plot
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Lending Rate Difference
Lending Rate
Difference
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Exchange Rate Residual
Residual
57
Figure 12. Export difference residual plot
Figure 13. Import difference residual plot
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Export Difference Residual
Residual
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Import Difference Residual
Residual
58
Figure 14. Foreign reserve difference residual plot
Figure 15. Interest rate difference residual plot
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Foreign Exchange Reserve
Difference Residual
Residual
-6
-4
-2
0
2
4
6
Interest Rate Difference Residual
Residual
59
Figure 16. Ordinary Least Square(OLS) residual plot
-0.15
-0.1
-0.05
0
0.05
0.1
OLS Residual
Residual
60
Table1. SCAN ESACF Result Table
Variable SCAN BIC ESACF BIC
Exchange rate
(e)
p +d
1
4
3
1
q
3
0
2
0
-5.58
-5.58
-5.49
-5.60
p+d
4
1
2
3
5
q
2
3
3
3
2
-5.53
-5.58
-5.55
-5.53
-5.50
Export Difference
(X)
p+d
5
4
q
0
3
-5.51
-5.40
p+d
3
4
5
q
4
4
4
-5.45
-5.43
-5.52
Import Difference
(M)
p + d
3
1
q
0
4
-5.57
-5.56
p + d
1
3
Q
0
1
-5.59
-5.53
Foreign exchange
reserve
(R)
p + d
2
4
q
0
0
-1.41
-1.43
p + d
3
q
2
-1.37
61
Interest rate
(I)
p + d
2
3
1
q
0
4
5
-0.11
0.0060
-0.016
p + d
5
1
2
3
q
4
5
5
5
-0.011
-0.016
-0.014
0.014
62
Table 2. Augmented Dickey- Fuller Test Results
Variable ADFc ADFc,t ADFc, t, lag
Exchange rate (e) -0.99 -2.12 -2.76
Export difference(X) -0.68 -3.22* -2.97
Import Difference (M) -1.67 -1.94 -3.0
Foreign Exchange Reserve (R) -3.80*** -3.73** -3.84**
Interest Rate ( I) -2.31 -2.21 -4.36***
Note: In the thesis, ADF tests for each variable are single mean, constant with time
trend. SAS output provides the test statistical results with trend and constant.
Critical values with constant and time trend are 10% level -3.12, 5%level -3.41,
1%level -3.96. Critical values with constant only are 10% -2.57, 5% level -2.86, 1%
level -3.43.
63
Table3. Ordinary Least Square (OLS) Result
Intercept -0.021
(0.013)
?X 0.055
(0.059)
?M 0.27**
(0.081)
R 0.00083
(0.0033)
I -0.0017**
(0.00081)
R2 0.85
ARCH (1) ARCHF test: 0.53
ARCHt test: -0.73
Durbin Watson test 2.16
* Significant at the 10% level
** Significant at the 5% level
***Significant at the level 1% level
64
Table 4. Lagged transformation Model (LTM) Result
Variable
Coefficient
Intercept -0.022*
(0.013)
?et-1 -0.20**
(0.10)
?Xt 0.11
(0.067)
?Xt-1 -0.12
(0.059)
?Mt 0.36***
(0.086)
?Mt-1 -0.94
(0.088)
Rt -0.0010
(0.0072)
Rt-1 0.0021
(0.0071)
It-1 -0.0082
(0.0048)
It-1 0.0042
(0.0049)
R2
0.81
Durbin h test
-0.75
ARCH ARCHF0.32
ARCHT -0.57
* Significant at the 10% level
** Significant at the 5% level
***Significant at the level 1% level
65
Table 5. Total Effect Table
Variable
Coefficient
Intercept -0.022
(0.013)
X 0.010
(0.089)
M 0.27**
(0.12)
R 0.0010
(0.01)
I -0.0040
(0.0069)
* Significant at the 10% level
** Significant at the 5% level
***Significant at the level 1% level