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Archives of Business Research – Vol. 11, No. 3
Publication Date: March 25, 2023
DOI:10.14738/abr.113.14223.
Kurihara, Y. (2023). How can Exchange Rates be Determined? Revisited from the Case of US-Yen Exchange Rate. Archives of
Business Research, 11(3). 53-61.
Services for Science and Education – United Kingdom
How can Exchange Rates be Determined?
Revisited from the Case of US-Yen Exchange Rate
Yutaka Kurihara
Department of Economics, Aichi University, Japan
Abstract
The issue ‘how can exchange rates be determined?’ has been discussed since the
mid-1970s when a floating exchange rate system was introduced in developed
economies. Many theories have been presented and have been examined
empirically. Despite the fact that some trends which are strongly related to
economic conditions all over the world have existed, several theories are now
supported by academic fields. There seems to be some consensus. On the other
hand, empirical studies have varied and they are not unified. This study focuses on
representative theories, namely purchasing power parity, monetary approach, and
interest rate parity, and these theories are examined empirically. The results show
that these three theories fit well with reality. Representative theories can be used
for the prediction of exchange rates when some limitations are permitted. However,
examining long-term periods introduce many factors that have an influence on
exchange rates. There are still many problems that interfere with exchange rate
prediction.
Keywords: exchange rate; monetary approach; Purchasing Power Parity; US dollar; yen.
INTRODUCTION
Developed countries introduced a floating exchange rate system early in the 1970s. According
to the introduction of this system, theories of exchange rate determination have been provided
from various academic fields. Despite the fact that some trends which are associated with
economic/political conditions all over the world have existed, however, several theories are
obtained as common acknowledgements. Empirical analyses based on these theories have been
presented, however, these results are varied and they are not yet unified.
This study focuses on representative theories, namely purchasing power parity, monetary
approach, and interest rate parity, and these theories are examined empirically. Purchasing
power parity has been used not only by academic fields but also business fields. It has been said
that this theorem does not fit well with the short-term, but fits well in the long-term in general.
The monetary approach has also been evaluated highly as long-term exchange rate
determination theory instead of short-term, and it has not received much attention for the time
being. However, most developed countries have employed monetary easing policy, so this
theory has again been noticed by academic fields. Finally, the interest rate parity theorem has
been used as short-term exchange rate determination theory. From the 1980s, capital
movements in the world have expanded rapidly under the globalization of the economy, and it
has been said that such movements are related with this arbitrage transaction.
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Archives of Business Research (ABR) Vol. 11, Issue 3, March-2023
Services for Science and Education – United Kingdom
This study empirically examines these theories for the case of US dollar-yen exchange rate. The
structure of this study is as follows. Section 1 is an introduction. Section 2 surveys related
previous studies. Representative theories of exchange rate determination are provided in
section 3 and these three representative theories are examined empirically in section 4. Finally,
section 5 provides a review of this study and raises some issues for the future.
RECENT EXISTING STUDIES RELATED WITH EXCHANGE RATE DETERMINATION
There has been a lot of discussion about how to determine exchange rates. Also, exchange rate
prediction is one of the most significant issues and concerns in international economics and
international finance. For the prediction, business persons are very interested in it, needless to
say.
Purchasing Power parity (PPP) has a long history (for example, [1]). Recently, [2] indicated the
validity of PPP, however, the regression analyses showed that the PPP does not want to be in
all exchange rate regimes where a nonlinearity relation among variables is contained in the
estimated equations. [3] revealed that the PPP relation alone determines the exchange rates for
the US, France, Germany, and Italy. On the other hand, a linear relationship of PPP and
uncovered interest rates parity determines exchange rates for Canada. [4] suggested that the
PPP does not hold for eurozone economies. [5] showed that the results for uncovered interest
rates parity are unfavorable in general. [6] examined the PPP in 27 emerging economies by
employing non-linear unit root test and reported that traditional unit root tests fit well with
PPP in approximately half of the currencies. Also, they found that non-linear quantile unit root
test fits much more with PPP. On the other hand, [7] revealed that the theory does not hold.
After that monetary approach had been provided, [8], [9], and others provided a flexible price
type monetary model. Also, a sticky price type monetary model was provided by [10], [11] and
others, with the common focus on important macroeconomic fundamentals. [12] found that
Taylor rule models fits better than the random walk model, monetary model, PPP model and
interest rate parity model in the short-term, and also showed that monetary models outperform
better in the long-term.
[13] listed a) factor model, b) factor along with Taylor rule model, c) factor along with monetary
model, and factor along with PPP model and examined them empirically. It showed that factor
with PPP model outperforms well.
Finally, covered-uncovered interest rate parity theory is employed especially for examining
short-term level. In the past, [14] proposed a portfolio balance approach. [15] showed the
predictive power of the Taylor rule, monetary model, PPP model, and uncovered interest rate
parity model is better than the random walk model for most countries. [16] found that a Taylor
rule with similar kinds of coefficients without smoothing of interest rate as well as PPP provides
a better performance of prediction over the random walk model. However, covered interest
rate theory has not been examined fully. The reason may be the data availability. This study
focuses on this issue. Compared with the uncovered interest rate parity, covered one has the
merit of avoiding exchange rate predictions which vary depending on people.
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Kurihara, Y. (2023). How can Exchange Rates be Determined? Revisited from the Case of US-Yen Exchange Rate. Archives of Business Research, 11(3).
53-61.
URL: http://dx.doi.org/10.14738/abr.113.14223
THEORETICAL ANALYSIS
Before this section, this study reviewed past studies about exchange rate determination. For
the middle/long-term theory of exchange rate, monetary approach and PPP have been
recognized widely and used. PPP was provided a long time ago and has been employed and
debated not only in the academic field, but also in the business field. Big Mac index employing
this PPP is widely known and has been used not only in academic fields but also in business.
The PPP may be most well-known for exchange rate determination theory.
However, from the early 1970s, exchange rates have been said to change with asset prices. Huge
capital movements over GDP began to occur globally. Until that time, exchange rates had been
said to change with international commodity movements, but the situation has changed forms
significantly. The exchange rates have shifted movements from following international trade to
following assets.
Purchasing Power Parity (PPP)
This theory states that exchange rate is determined by purchasing power of different
currencies. If the different prices were available on the same product, traders would buy at the
cheap price in one place and sell them at the higher price in another place. So, the different
prices would be equalized. This is called ‘law of one price’. PPP is based on this issue. If the law
of one price is held, this equation (1) is held.
P = S・P*
(1)
P:domestic price (yen) P*:foreign price (US dollar) S:spot exchange rate (yen/US
dollar)
This is called absolute PPP. This is far from the reality, so exchange rate is employed and this is
called relative PPP.
ds
s
=
dp
p -
dp∗
p∗
(2)
Except for fresh food, energy prices and so on, it takes time for prices to change. Compared with
exchange rates, interest rates stock prices and so on, prices are in general sticky, so PPP holds
in the long-term instead of short-term.
Mainly in the business world, Big Mac Index is used to calculate exchange rates. Currently, the
exchange rate calculated by this index is almost \75/US dollar (February, 2023). It does not fit
well in reality. On the other hand, yen appreciation was ongoing in 2010, so the exchange rate
calculated from Big Mac Index fits well in reality.
Monetary Approach
Monetary approach uses supply and demand for money in markets. This model depends on a
condition that money demand is stable and expresses as the equation (3) (of Japan):
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Archives of Business Research (ABR) Vol. 11, Issue 3, March-2023
Services for Science and Education – United Kingdom
M/P = L (Y, i) (3)
where M denotes money stock, P denotes the price level, L denotes the money demand, Y
denotes income, and i denotes interest rate.
This is the case of the US.
M*/P*=L*(Y*,i*) (4)
This model is based on an assumption that the PPP holds:
s =p/p* (5)
where s means spot exchange rate, p means domestic price (Japan), and p* means foreign price
(US).
In this equation (3), L=(Y,i)= Y
Φe
−λi. Φ is and λ are (semi-) elastic. The exchange rate can
be expressed by using the log linearized form, and it can be formed as the differences of money
stock, incomes, and interest rates. The hypothesis that money stock and income elasticity are
the same in both markets is employed. The following equation can be set:
s = α + β(m-m*) -γ(y-y*) + η(i-i*) (6)
α is constant. β, and γ, and η are (semi-) elastic.
This study focuses on these theories from the view of middle- or long-run.
Covered Interest Rate Parity
It can be said that both PPP and monetary approach focus on real markets, however, asset
markets should be taken into account.
If 1yen is invested by yen and interest rate applied to this investment is i×100%, total principle
and interest is (1+i). Moreover, if 1yen is invested by US dollar, contracts forward transaction,
the total principle and interest is changed into yen, it can be f
s
(1 + i
∗
)yen. In this case, s
denotes spot exchange rate and f denotes forward exchange rate.
The two of principle and interest should be the same, so the equation (7) holds.
(1+i)=
f
s
(1 + i
∗
) (7)
It can be obtained (8).
f − s
s
=
i − i ∗
1 + i ∗
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Kurihara, Y. (2023). How can Exchange Rates be Determined? Revisited from the Case of US-Yen Exchange Rate. Archives of Business Research, 11(3).
53-61.
URL: http://dx.doi.org/10.14738/abr.113.14223
This is called covered interest rate parity. Moreover, for the case of uncovered interest rate
parity, f becomes the expected exchange rate. However, the ways of how to obtain the expected
exchange rate are quite different. So, this study uses covered interest rate parity instead of
uncovered interest rate parity. This theory is considered to be suitable for short-term exchange
rate determination.
EMPIRICAL ANALYSES
Exchange rates have moved from the past. Figure 1 shows the yen/US dollar exchange rate
movements from the 1990s.
Figure 1. US dollar/yen from the 1990s.
After the bubble economy burst in the early 1990s, the movement of selling foreign assets and
changing foreign currencies into yen occurred. Yen had appreciated. In 1995, however, yen’s
appreciation peaked. After that, Japanese economy fell into recession and a rise in oil prices
occurred, which led to depreciation of the yen. When the financial crisis from 2007 to 2008 and
Great East Japan Earthquake in 2011 occurred, yen appreciated drastically. In 2011, yen hit the
75-yen level. After that, during ‘Abenomics’ (Abe is the past prime minister’s name) era (from
2013), large monetary expansion was conducted and depreciation of the yen promoted;
however, the yen weakened with the birth of the Trump administration. In 2022, due to the
expanding of the interest rate difference, yen depreciated and it hit the 150-yen level.
In section 2, preliminary analyses were performed to conduct empirical examinations. Three
representative theories of exchange rate determination are checked empirically.
First, PPP is checked by this estimated equation (8).
ds
s
=α+β(dp
p -
dp∗
p∗
)+ε (8)
0.00
20.00
40.00
60.00
80.00
100.00
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160.00
180.00
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