My master thesis on exchange rate modelling and imperfect knowledge. With a exchange rate model including risk, based on the Vector Auto Regressive (VAR) method.
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DET SAMFUNDSVIDENSKABELIGE FAKULTET
KØBENHAVNS UNIVERSITET
Kandidatspeciale
David Pedersen
Imperfect Knowledge Economics
A solution to the exchange rate disconnect puzzle?
Vejleder: Michael Bergman
Afleveret den: 21/04/08
2.
Summary
Traditional exchange rate models based on the monetary approach have had a rather hard time at
explaining the fluctuations of exchange rates over the last thirty years. Mainstream exchange rate
models assume that macroeconomic fundamentals determine the value of the exchange rate, at
least in the long run. But this sharp prediction has been rejected in several empirical studies,
showing that there is a rather weak connection between the variables. A surprising result which
has been labeled “the exchange rate disconnect puzzle”.
The theory of Imperfect Knowledge economics (IKE), suggested by Michael D. Goldberg and
Roman Frydman (2007), puts forth a proposal for solving the apparent puzzle: Agents are
assumed to be heterogeneous. Furthermore, it is assumed that the agents acknowledge that their
understanding of the true model of the economy is limited. Thus, by definition, the overall result
of the IKE model has to be different from that of the rational expectations outcome given by the
monetary approach to exchange rates.
The structure of the thesis
Overall, the thesis is divided into two parts: The theoretical part of IKE and the empirical test of
one of the assumptions of the theory, the importance of uncertainty in regards to exchange rate
determination. This is chapter 4 and 5 of the thesis, respectively. Before the discussion and test of
the IKE theory, chapter 2 and chapter 3 discuss the foreign exchange market and the economic
agents participating in the market (chapter 2), as well as the theory and empirical results of the
monetary approach (chapter 3).
Stylized facts – chapter 2
This chapter both discusses the time series properties of three of the most traded currencies, as
well as the agents and the market in which the currencies are traded. Several findings are
reported: Exchange rates are non-normal, has over-kurtosis; the market is decentralized and has a
rather low degree of transparency; and the agents are heterogeneous and use different methods
for the calculation of future exchange rates.
Exchange rates: models and puzzles – chapter 3
Chapter 4 discusses the mainstream approach to exchange rates, namely the monetary approach.
Two typical monetary models, the flexible price monetary model (FPMM) and the sticky price
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monetary model, are presented and discussed. This is followed by a short study of the empirical
achievements of the monetary approach. The overall conclusion of the monetary approach’
empirical success is not supportive; hence the exchange rate disconnect puzzle, the purchasing
power parity puzzle and the forward premium puzzle. Thus, it seems that a new approach to the
modeling of exchange rates seems warranted. One such approach is discussed in this chapter as
well, the microstructure approach. The microstructure approach relaxes some of the more critical
assumptions of the monetary approach: That private information can have a significant effect,
that agents are heterogeneous, and that the institutions and structure of the exchange rate market
matter for the determination of exchange rates. Assumptions which are in line with the findings
of chapter 2. Testing a simple microstructure model with order flow included shows that private
information can have a significant effect; a result supported by several articles. Thus, the sharp
assumptions of the monetary approach seem to impede useful information on exchange rates.
The theoretical part – chapter 4
The main theme of the IKE theory is the importance of imperfect knowledge; and the
assumption that the agents recognize that their (individual) knowledge is limited. Hence, the
agents act like scientists, testing various strategies over time. Furthermore, the agents do not only
use strict macroeconomic models for forecasting the future exchange rate, but make use of
technical trading, insights from the microstructure approach and their experience. The IKE
theory adds the findings from prospect theory to the description of the agents utility: The aspect
of loss aversion (i.e. the disutility from a loss exceeds the utility of gains of the same size),
reference dependence (utility is defined relative to a reference point), and diminishing sensitivity
(i.e. the marginal utility of both gains and losses decreases with their size). Furthermore it is
assumed that loss aversion increases with the position size, preventing agents from taking
unlimited positions in the foreign exchange market. When these assumptions are coupled with
the “gap effect” – the difference between the historical benchmark value of the exchange rate
and the expected value of the exchange rate have an effect on the expected utility of agents – and
conservative revisions of strategy – i.e. agents stick to their strategies and are slow to revise them
– the exchange rate disconnect puzzle can be explained: The exchange rate diverge from PPP (i.e.
the historical benchmark) because agents are heterogeneous and thus have different expectations
(bulls or bears). But the gap effect, i.e. increases of loss aversion, pulls back the exchange rate if it
is “too” misaligned. Therefore the exchange rate does not entirely abandon the fundamental
value.
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The empirical part – chapter 5
In the empirical part a VAR model is used when testing one of the main assumptions of the IKE
theory: The importance of uncertainty. Running a GARCH model on the macroeconomic
fundamentals provide a proxy for uncertainty, as the conditional variance changes according to
changes in the fundamentals. Adding the GARCH variables to a simple monetary model is tested
to be a stationary relation for Japan, pointing to the significance of uncertainty.
Main conclusion – chapter 6
The overall conclusion supports the IKE theory: From a theoretical point, the theory
incorporates several stylised facts, such as heterogeneous agents and the use of different methods
and models. From an empirical point, the test of the importance of private information as well as
the VAR model seems to support the IKE theory as well.
Thus, I cannot reject the hypothesis that the IKE theory can explain the exchange rate
disconnect puzzle.
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5.
Imperfect knowledge economics
- A solution to the exchange rate disconnect puzzle?
David Pedersen
April 2008
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6.
Preface
For this thesis I have been inspired by the course in International Monetary Economics as well as
the seminar Empirical International Finance.
First of all a special thanks to my advisor, Michael Bergman, for guidance, critical questions and
useful discussions as well as a high degree of patience.
Other persons have given valuable remarks as well, which I appreciate: Thanks to Michael D.
Goldberg for answering several questions regarding imperfect knowledge economics (IKE) and
thanks to Katarina Juselius for introducing me to the interesting ideas of IKE in the early spring
of 2007. Thanks to Lars Christensen, Chief Analyst at Emerging Market Research at Danske
Bank, and Teis Knuthsen, Head of FX Research at Danske Bank, for interesting discussions of
exchange rates, seen from a practical point of view.
Last but not least, thanks to Gitte and my beautiful daughter, Freja, for putting up with me over
the months, and making the process much more fun.
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Contents
CHAPTER 1: INTRODUCTION....................................................................................................9
1.1 INTRODUCTION ........................................................................................................................................9
1.2 DEFINITION: THE EXCHANGE RATE DISCONNECT PUZZLE ..........................................................11
1.3 DELIMITATION ........................................................................................................................................12
1.4 STRUCTURE OF THE THESIS ..................................................................................................................12
CHAPTER 2: STYLISED FACTS.................................................................................................. 15
2.1 INTRODUCTION ......................................................................................................................................15
2.2 THE FOREIGN EXCHANGE MARKET ...................................................................................................16
2.3 EXCHANGE RATE DATA.........................................................................................................................17
2.3.1 Descriptive statistics......................................................................................................................................17
2.3.2 Stylised facts of exchange rate data ................................................................................................................21
2.4 THE STRUCTURE OF THE FOREIGN EXCHANGE MARKET ...............................................................22
2.4.1 Features of the foreign exchange market ...................................................................................................22
2.4.2 Participants of the foreign exchange market..............................................................................................22
2.5 CONCLUSION ...........................................................................................................................................24
CHAPTER 3: EXCHANGE RATES: MODELS AND PUZZLES ...............................................26
3.1 INTRODUCING EXCHANGE RATE THEORY .............................................................................................26
3.2 THE MACROECONOMIC APPROACH TO EXCHANGE RATES ............................................................27
3.2.1 Purchasing power parity...........................................................................................................................27
3.2.2 The interest rate – Uncovered interest rate parity .....................................................................................29
3.2.3 The money supply....................................................................................................................................30
3.2.4 Summing up................................................................................................................................................31
3.3 THE MONETARY APPROACH ......................................................................................................................32
3.3.1 The flexible price monetary model..................................................................................................................33
3.3.2 The sticky price monetary model....................................................................................................................34
3.3.3 The monetary approach – summing up..........................................................................................................36
3.4 EMPIRICAL STUDIES OF EXCHANGE RATES ............................................................................................36
3.4.1 Empirical results of the seventies ...................................................................................................................36
3.4.2 Modern empirical results ...............................................................................................................................37
3.4.3 Exchange rate puzzles..................................................................................................................................38
3.4.4 Puzzles after all?..........................................................................................................................................40
3.4.5 Critique of the Rational Expectations Hypothesis.........................................................................................41
3.4.6 Different solutions to the exchange rate puzzles .............................................................................................42
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3.5 THE MARKET MICROSTRUCTURE APPROACH .........................................................................................43
3.5.1 Introducing market microstructure.................................................................................................................43
3.5.2 Order flow as an important factor for exchange rates .....................................................................................45
3.5.3 A microstructure model of exchange rates ......................................................................................................47
3.6 CONCLUSION ...........................................................................................................................................50
CHAPTER 4: IMPERFECT KNOWLEDGE ECONOMICS.......................................................53
4.1 INTRODUCING IMPERFECT KNOWLEDGE ECONOMICS ......................................................................53
4.2 IMPERFECT KNOWLEDGE AND UNCERTAINTY.....................................................................................55
4.2.1 Knightian uncertainty....................................................................................................................................55
4.2.2 Imperfect knowledge ......................................................................................................................................55
4.3 MODELLING PREFERENCES AND FORECASTING STRATEGIES ..........................................................57
4.3.1 The expected utility hypothesis.......................................................................................................................57
4.3.2 Critique of the expected utility hypothesis.......................................................................................................58
4.3.3 Prospect theory..............................................................................................................................................58
4.3.4 Prospect theory and the foreign exchange market – the IKE approach............................................................59
4.3.5 Equilibrium in the FX market under Prospect theory: UAIP ......................................................................63
4.3.6 Modelling forecasting strategies I: The Gap effect ...........................................................................................65
4.3.7 Modelling forecasting strategies II: Conservative revisions ...............................................................................67
4.3.8 Summing up.................................................................................................................................................68
4.4 IKE AND THE EXCHANGE RATE: A MONETARY MODEL ....................................................................69
4.4.1 A monetary model with IKE-expectations.....................................................................................................70
4.4.2 Money markets.............................................................................................................................................70
4.4.3 Goods markets .............................................................................................................................................71
4.4.4 Foreign exchange market ..............................................................................................................................71
4.4.5 The social context .......................................................................................................................................73
4.4.6 The solution to the model .............................................................................................................................74
4.4.7 The intuition of the result ..........................................................................................................................76
4.5 IKE AND THE EXCHANGE RATE DISCONNECT PUZZLE ......................................................................77
4.6 CRITIQUE OF IMPERFECT KNOWLEDGE ECONOMICS ........................................................................78
4.7 CONCLUSION ...........................................................................................................................................79
CHAPTER 5: EMPIRICAL TEST.................................................................................................82
5.1 INTRODUCING THE EMPIRICAL PART .......................................................................................................82
5.2 THE MODEL: MOTIVATION AND SET-UP............................................................................................83
5.3 THE MODEL: SPECIFICATION AND ESTIMATION ..............................................................................85
5.3.1 Introducing the empirical test .....................................................................................................................85
5.3.2 The data ...................................................................................................................................................85
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5.3.3 A brief discussion of multivariate cointegration...........................................................................................86
5.3.4 GARCH(p,q) estimation .........................................................................................................................87
5.3.5 Cointegration analysis .............................................................................................................................89
5.3.6 Lag length, residual analysis and dummy variables ..................................................................................93
5.3.7 Testing the models ...................................................................................................................................94
5.3.8 Conclusion ........................................................................................................................................... 103
5.4 THE RESULT FROM AN IKE PERSPECTIVE ...................................................................................... 103
5.5 CONCLUSION ........................................................................................................................................ 104
CHAPTER 6: CONCLUSION ..................................................................................................... 105
LITERATURE.............................................................................................................................. 107
APPENDIX A – FIGURES ...........................................................................................................114
APPENDIX B – MODELS............................................................................................................118
APPENDIX C – EMPIRICAL RESULTS ....................................................................................121
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Chapter 1
Introduction
“To repeat a central fact of life, there is remarkably little evidence that macroeconomic variables
have consistent strong effects on floating exchange rates, except during extraordinary
circumstances such as hyperinflations. Such negative findings have led the profession to a certain
degree of pessimism vis-à-vis exchange rate research”
Frankel and Rose (1995), p. 1709.
1.1 Introduction
For most modern economies the exchange rate is, in the words of Obstfeld and Rogoff (2000),
the single most important relative price, essential for a number of economic activities. Exchange
rate fluctuations are therefore carefully followed: By investors, as it affect the value of
international portfolios; by governments, as it affects prices on exports, imports and the value of
international debt; and by Central Banks, as it affects inflation objectives and the value of
international reserves. For the financial market in general, the fluctuations of exchange rates are
important as well: Directly, as the market for foreign exchange is the largest financial market in
the world; and indirectly, as currency fluctuations influence a range of other asset prices.
It is a puzzle, then, that exchange rate theories have had such a hard time explaining the currency
fluctuations since the free float in the 1970s, and that the link between macroeconomic variables
and the exchange rate appear almost non-existent. The empirical result of the weak relation
between exchange rates and macroeconomic variables, as reported by for example Meese and
Rogoff (1983), has since been dubbed the “exchange rate disconnect puzzle”. Meese and Rogoff
(1983) concluded that a simple random walk model would predict major-country exchange rates
as well as a range of exchange rate models. The assumption of mainstream exchange rate theories
that the value of a given currency is determined by macroeconomic fundamentals such as output,
money supply and interest rates therefore seems to be too simple. At least in the short to medium
run of six to twelve months. Looking at figure 1 below, depicting the value of the US real
effective exchange rate, it is evident that institutions such as the Central Banks also matter for the
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pricing of a currency. The Plaza Accord, for example, apparently had an impact on the value of
the dollar – which was not solely grounded in changes of macroeconomic fundamentals1.
Figure 1 – The US real effective exchange rate since 1970
12 0 1 20
In d e x
11 5 1 15
T h e P la z a A c c o rd
11 0 1 10
10 5 1 05
T h e L o u vre A c co rd
10 0 1 00
percent
percent
95 95
90 90
85 85
80 P a u l V o lc k e r a p p . c h a irm a n o f 80
th e F e d
75 75
7 0 72 74 76 7 8 80 82 84 86 88 90 9 2 94 9 6 98 00 02 0 4 0 6 08
.
Source: EcoWin database
In the foreign exchange market two rather large players, Central Banks and international
companies, do not solely have profit maximisation as their main objective but in addition
objectives such as price stability (Central Banks) or hedging their investments (companies). This,
obviously, affects the determination of exchange rates. Furthermore, the structure of the foreign
exchange market, which is both highly decentralised and has a quite low degree of transparency,
matters for the price setting as well. But most important for the exchange rate determination are
the economic agents in the market. Not only the aforementioned institutions and organisations,
but also the traders and investors who are buying and selling currency on a daily basis. In
traditional exchange rate theories, these agents are assumed to be homogenous and endowed
with rational expectations; i.e. they know the true model of the economy and do not
systematically over– or underestimate the value of the exchange rate. Furthermore, private
information is not deemed important in the pricing of currencies, as all agents have access to the
same relevant information, according to rational expectations.
The question, then, is whether the hypothesis of fully rational individuals is where the many
problems and puzzles of modern day exchange rate theory come from? The answer to that
1 The Plaza Accord was an agreement between USA, Germany, France, UK and Japan to intervene in the foreign
exchange market with the objective of a depreciation of the dollar.
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question is yes, according to the book “Imperfect knowledge economics: Exchange rates and
risk” by Roman Frydman and Michael D. Goldberg (2007). They consequently propose a new
theory for explaining the puzzles which are haunting exchange rates research: Imperfect
knowledge economics (IKE). The IKE theory instead suggests that agents are heterogeneous and
therefore have different expectations of the future price of a given currency. Furthermore, the
agents are fully aware that they do not know the true model of the economy. Hence, they use a
portfolio of models and methods, as well as experience and creativity, when forecasting the
future exchange rate. The result that exchange rates are not always perfectly correlated with
macroeconomic fundamentals, is therefore no surprise according to the IKE theory. Seemingly
the disconnect puzzle between fundamentals and the exchange rate is no longer a puzzle when
seen from the theoretical perspective of IKE.
From this introduction follows the purpose of the thesis: “Does Imperfect Knowledge Economics provide
a solution to the exchange rate disconnect puzzle?
1.2 Definition: The exchange rate disconnect puzzle
The hypothesis of this thesis is whether the imperfect knowledge economics theory gives a
reliable solution to the exchange rate disconnect puzzle. It is therefore necessary first to define
the exchange rate disconnect puzzle.
Definition of the exchange rate disconnect puzzle: The finding that the fundamentals and
the (nominal) exchange rate are only weakly correlated has been defined as the “exchange rate
disconnect puzzle” by Obstfeld and Rogoff (2000).
In Obstfeld and Rogoff (2000: 373) the puzzle is defined as follows: “The weak relationship between
the exchange rate and virtually any macroeconomic aggregates”. The definition of Sarno (2005: 674):
“Fundamentals appear to be unable to explain both the actual level of exchange rates – not only on daily, but even
monthly, quarterly and annually – and their volatility”. Other authors (e.g. Lyons, 2001: 172) label it the
“exchange rate determination puzzle”, but this identical to the exchange rate disconnect puzzle.
The conclusion of a weak relationship between exchange rates and macroeconomic fundamentals
(e.g. output, money supply) dates back to the aforementioned influential article of Meese and
Rogoff (1983), which will be discussed further in the empirical survey in chapter 3.
Although often discussed apart from each other, the exchange rate disconnect puzzle and the
purchasing power parity (PPP) puzzle – mentioned in chapter 3 – are very much linked together.
The first puzzles’ subject is the disconnect between fundamentals and the exchange rate, whereas
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the PPP puzzles’ subject is the long half-life when the exchange rates move towards the
fundamental value (given by PPP); half-lifes that reach as much as 3 or 4 years (Obstfeld and
Rogoff, 2000: 373; Rogoff, 1996). When looking at the disconnect puzzle, one can therefore not
go without discussing the PPP puzzle as well.
1.3 Delimitation
First of all I have chosen to focus solely on the monetary approach and let the imperfect
knowledge economics theory be a critique thereof. I have not included discussions of, for
example, the new open economy macroeconomics (NOEM) or the portfolio balance models
approaches to exchange rates. Regarding the former, the NOEM approach has not produced
empirical exchange rate equations that alter the Meese and Rogoff (1983) result (cf. Lyons, 2001:
294). The monetary approach, on the other hand, has been the dominating theory of exchange
rate research since the 1970s, despite its empirical shortcomings discussed in chapter 3. Nor do I
discuss the results of behavioural economics, interesting as it may be. This could be a focus of
another thesis.
Secondly, this thesis try to answer whether the imperfect knowledge economics theory put forth
a constructive solution to the disconnect puzzle. Other solutions to the puzzle outside of the
realm of the imperfect knowledge theory (e.g. transport costs, bubbles, behavioural economics
result etc.) will therefore only be touched upon briefly, relevant as they might be for the
disconnect puzzle itself.
1.4 Structure of the thesis
The thesis is structured as follows:
Chapter 2 – Stylised facts: This chapter examines the foreign exchange market from three
angles: The exchange rates and the time series property thereof; the structure of the foreign
exchange market; and the economic agents in the market with focus on the traders. This insight is
used in the following chapters, especially in regards to the IKE theory in chapter 4 which builds
on several of the stylised facts from chapter 2.
Chapter 3 – Exchange rates: Models and puzzles: The focus of this chapter is the monetary
approach and the empirical results of this theory. The main idea of the monetary approach is
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presented by two often used models, the flexible price monetary model (FPMM) and the sticky
price monetary model. The empirical study following the models demonstrate the shortcomings
of the monetary approach, one of them the exchange rate disconnect puzzle. The rational
expectations hypothesis, the backbone of the monetary approach, is discussed and criticised.
Then follows a discussion of the microstructure approach to exchange rate which serves to: i)
introduce a micro foundation to exchange rate research missing from the monetary approach,
and ii) be an introduction to the ideas of imperfect knowledge in the following chapter, which
builds on several of the insights from microstructure theory.
Chapter 4 – Imperfect Knowledge Economics: This chapter discuss the imperfect knowledge
economics (IKE) theory with the main focus on the book “Imperfect knowledge economics:
Exchange rates and risk” by Frydman and Goldberg (2007). A theoretical model based on the
IKE theory is set up, and it is discussed why this provides a theoretical solution to the exchange
rate disconnect puzzle.
Chapter 5 – Empirical test: The empirical chapter tests a monetary model with the addition of
uncertainty. The IKE theory assumes that uncertainty plays an important part in the price setting
of exchange rates, and this hypothesis is tested using the Johansen method in a multivariate VAR
model on Norway and Japan against USA. Furthermore I test a simple monetary model for both
countries which supports the general result of the shortcoming of the monetary approach seen in
chapter 3. The tests of the models with uncertainty result in some support for the importance of
the uncertainty variables in the determination of exchange rates, at least for Japan. Furthermore,
the GARCH variables, proxying uncertainty, seem to be significant for the models.
One has to be aware, though, that some of the assumptions of the VAR model are violated.
Chapter 6 – Conclusion: This chapter presents the overall conclusion of the thesis, and answers
the question put forth in the introduction: Does the Imperfect Knowledge Economics theory
provide a solution to the exchange rate disconnect puzzle? The result of the thesis, and hence the
answer to this question, is based on two foundations: i) The theoretical foundation of IKE, which
appears quite strong as it is based on the stylised facts discussed in chapter 2 and chapter 3 as
well as the robust results of prospect theory and the microstructure approach; ii) The empirical
foundation from testing the IKE assumptions, which show that both private information (chapter
3 on microstructure) as well as uncertainty (the empirical test of chapter 5) play a role in regards
to exchange rate determination.
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Based on this, I cannot reject the hypothesis that IKE could be a solution to the exchange rate
disconnect puzzle.
I have split the appendix in three parts: A) With figures; B) with models and calculations thereof;
and C) with results from various estimations and tests.
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Chapter 2
Stylised facts
“One of the most fascinating thing about the foreign exchange market is the huge sums of
money that are exchanged on a daily basis”
Keith Pilbeam, (2006), p. 4
2.1 Introduction
A necessary condition for understanding the movements and the predictability of assets and asset
returns, in this case exchange rates, is understanding the financial data as well as the market in
which these prices are set. As a starting point for the analysis later in the thesis, it is therefore
relevant to look into the regularities and composition of the foreign exchange market. This
chapter does exactly that.
The results from the latest survey of the Bank of International Settlements (BIS, 2007) show the
size and trading structures of the foreign exchange markets. The statistical properties of time
series data of exchange rates, on the other hand, are important for an initial understanding of the
exchange rate movements. The statistical properties of exchange rates, and financial data as a
whole, are often referred to as “stylised facts”, i.e. a broad generalisation of empirical findings.
The descriptive statistics of exchange rates, as we shall see, very much follows that from other
financial time series data of bonds and equities; i.e. heavy tails, over-kurtosis, (left-) skewness and
rejection of the normality assumption (see for example Campbell et al, 1997: 19ff or Pagan,
1996).
This chapter is structured as follows: First a short look at the latest BIS (2007) survey of the
foreign exchange market. Then the descriptive statistics of three different exchange rates will be
discussed. Finally a discussion of the structure and agents of the exchange rate market, based on
the survey by Cheung and Chinn of American (2001) and English traders (Cheung et al, 2004).
The insights from this chapter is build upon in chapter 3, where the monetary and microstructure
approach to exchange rates are discussed, as well as in chapter 4 of the imperfect knowledge
economics.
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2.2 The foreign exchange market
The Bank of International Settlements (BIS, 2007a) triennial survey analyses the turnover of the
foreign exchange markets. According to Sarno and Taylor (2002: 271) it represents “the most
reliable source of information of foreign exchange market activity”. Table 1 below shows the result from the
survey. As can be seen, the daily turnover of the traditional (i.e. spot, forwards and swaps) foreign
exchange markets reached $3.2 trillion, an increase of almost 71 % from 2004. This increase is,
according to BIS (2007a: 1), driven by both increased activity of investor groups (e.g. hedge
funds) and technical trading. This is further supported by the second BIS report (2007b: 65),
which also points out that the foreign exchange market has been relatively attractive to leveraged
investors with short-term horizons, as well as investors with longer investment horizons trying to
diversify their portfolio.
Table 1 – Foreign exchange turnover from the BIS survey, 2007
Source: BIS Triennial Survey (2007)
The dollar is the main currency although with a small downward trend since 2004 (BIS, 2007a: 7).
The Japanese Yen (JPY) and the Norwegian krone (NOK), used in the empirical test of chapter
5, are the third and tenth most traded currencies, respectively. The United Kingdom is the
geographical centre for foreign exchange trading followed by the United States and Japan (ibid.:
9). The most traded currency cross is the USD/EUR, amounting more than a quarter (27%) of
the total market turnover. Then follows USD/Other (19%), USD/JPY (13%) and USD/GBP
(12%). The largest part of the trades is between dealers (43%), followed by deals with other
financial institutions (40%) and non-financial customers (17%) (cf. BIS 2007a: 6).
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Overall the volume of the foreign exchange market is enormous, and it dwarfs any other financial
instrument (Lyons, 2001: 41).
2.3 Exchange rate data
2.3.1 Descriptive statistics
This section serves to give a general description of the time series properties of exchange rates.
The data in the following section covers the euro/dollar (EUR/USD), dollar/Japanese Yen
(USD/JPY) and dollar/British pound (USD/GBP). The three crosses have been chosen as they
are the three most traded currencies (BIS, 2007a: 8).
The data is obtained from the EcoWin database. The frequency is on a daily, weekly and monthly
basis, and covers the period from the 1st of July 1974 to 31st October 2007. Figure 2, 3 and 4
below show the realisations of the exchange rates over the period.
Figure 2 – Daily observations for EUR/USD from July 1974
1,5
1,4
1,3
1,2
1,1
1
0,9
0,8
0,7
0,6
1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Source: EcoWin
For the euro/dollar exchange rate, figure 2 above, the maximum value (i.e. weak dollar) over the
period is 1.45 (September 8th 1992) and minimum value 0.63 (February 26th 1985). For the
dollar/yen, figure 3 below, the maximum (here: strong dollar) is 306.8 (December 8th 1975) and
minimum 80.6 (April 18th 1995). For the dollar/pound in figure 4 below, the maximum is 0.95
(January 11th 1985) and minimum value 0.401 (October 8th 1980).
From figures 2 and 4 (EUR/USD and USD/GBP) it is evident that the US dollar reached a local
maximum (i.e. strong dollar) in the mid 1980s.
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Figure 3 – Daily observations for USD/JPY from July 1974
285
255
225
195
165
135
105
75
1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Source: EcoWin
Figure 4 – Daily observations for USD/GBP from July 1974
1
0,9
0,8
0,7
0,6
0,5
0,4
1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Source: EcoWin
In the following the data for the three currencies is transformed into log-returns, given by
equation (2.2) below, which is defined as the natural logarithm of the gross return, equation (2.1).
(Campbell et al, 1997: 9-11).
Pt
(2.1) Rt = −1
Pt −1
Pt
(2.2) rt ≡ log (1 + Rt ) = log = pt − pt −1
Pt −1
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Now the distribution of the log returns of the exchange rates can be computed. Figure 5 below
shows the plot of daily log returns. Simple “eyeball econometrics” shows a high degree of
volatility, some serial correlation and some volatility clustering (cf. Campbell et al, 1997: 482).
The graphical log return of weekly and monthly observations, respectively, are found in appendix
A, figure 1 and 2. Table 2 below shows the descriptive statistics of the log-returns for daily,
weekly and monthly observations.
Figure 5 – Daily log returns for USD/GBP, EUR/USD and USD/JPY
Table 2 – Descriptive statistics for daily, weekly and monthly observations of log returns
EUR/USD USD/JPY USD/GBP
Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly
Mean 0,00002 0,0001 -0,0005 -0,0001 -0,0005 -0,0024 0,0000 0,0000 -0,0003
Maximum 0,0615 0,0707 0,1243 0,0415 0,0317 -0,1566 0,0382 0,1282 0,1282
Minimum -0,0648 -0,0718 -0,0931 -0,0695 -0,0423 0,1153 -0,0343 0,2816 -0,1250
Std. Dev 0,0063 0,0135 0,0292 0,0065 0,0077 0,0324 0,0049 0,0071 0,0299
Skewness 0,0805 -0,0351 0,1464 -0,5952 -0,4731 -0,4869 0,7187 0,2816 -0,2079
Kurtosis 5,0232 2,0099 1,0591 6,5260 2,1249 1,6655 9,2880 2,2127 1,5944
Normality test 3528.7 ** 184.29 ** 16.899 ** 3965.5 ** 155.02 ** 28.259 ** 1253.2 ** 194.10 ** 31.495 **
From table 2 the means are (slightly) different from zero, indicating that the euro has (on
average) depreciated against the dollar on a monthly basis, whereas the dollar has appreciated
against the yen and the British pound over the period. But note that none of the means are
19
21.
significantly different from zero, given the standard deviations. The skewness and kurtosis in
table 2 are given by (Campbell et al, 1997: 16-17):
ˆ ≡ E ⎢ (ε − μ ) ⎥
⎡ 3
⎤
Skewness : S
⎢ σ
3
⎣ ⎥
⎦
(2.3)
⎡ ( ε − μ )4 ⎤
Kurtosis : K ≡ E ⎢
ˆ ⎥
⎢ σ
4
⎣ ⎥
⎦
Where ε is a random variable with mean of μ and variance of σ2. The skewness, S, measures the
asymmetry of the distribution, with the normal distribution having a skewness of 0. The
distribution of USD/JPY in table 2 thus has more negative than positive returns for all three
frequencies. For the other currency crosses, EUR/USD and USD/GBP, the skewness measure
changes sign over the frequencies. The kurtosis, K, in table 1 is the “excess” kurtosis, i.e. above
the normal distribution which has kurtosis of 3. According to the relatively large and positive
kurtosis of table 2, the returns of exchange rates have more mass in the tails than predicted by
the normal distribution. The excess kurtosis declines over all three currency crosses as the
interval increases. Both the kurtosis and the skewness figures for the daily frequencies in table 2
are highly statistically significant, as the standard error2 for the kurtosis is 0.052 ( 24 ) and for
T
the skewness 0.026 ( 6 ).The skewness turns insignificant for the EUR/USD at weekly and
T
monthly basis, and for the USD/GBP at the monthly frequency, whereas the kurtosis stays
significant over the frequencies. Finally, the normality (or Jarque-Bera) test jointly measures
whether the skewness and kurtosis equals that of the normal distribution (i.e., 0 and 3
respectively). This is soundly rejected for all three currencies.
The results above are in line with the results of Boothe and Glassman (1987: 303-304) for
exchange rate returns. They find clear signs of excess kurtosis, which declines as the interval
increases, a strong rejection of normality and some signs of skewness.
Another way to describe the distributions of the exchange rate returns is by using quantile-
quantile (QQ) plots. Then, the quintiles of a given sample are matched with the theoretical
quintiles. Figure 6 below shows the QQ-plots of the distributions against the normal distribution.
As is evident from the three plots, there are too many observations in the tails of the distribution
(red line) compared with the normal distribution (black line). Hence the returns are not normally
2 ˆ ˆ
Following Campbell et al (1997: 17) the variances of the S and K estimators are 6/T and 24/T, respectively.
20
22.
distributed, which is also the result of the normality test in table 2. The negative skewness from
table 2 of the USD/JPY, for example, is quite obvious from figure 6 (bottom chart).
Figure 6 – QQ plots for the three currency crosses
2.3.2 Stylised facts of exchange rate data
From the results above the following properties emerge:
• Exchange rates appear to be extremely volatile
• The distributions of exchange rate returns are non-normal
• Fat tails compared with the standard normal distribution. That is, large returns occur more often than
expected (kurtosis significantly larger than 3)
• The distributions are skewed, i.e. the distribution is not symmetric. The direction of the skewness is not
unequivocal, though, and turns insignificant – for some currency crosses - as frequencies decrease.
The stylised facts presented above are in line with the general result of exchange rates, see for
example Boothe and Glassman (1987), and for financial assets in general, see for example
Campbell et al (1997: 21, 67).
21
23.
2.4 The structure of the foreign exchange market
In the following section the foreign exchange market is, in the words of Sager and Taylor (2006),
put “under the microscope”. As discussed in the introduction, and further elaborated on in
chapter 3, the link between macroeconomic fundamentals and the exchange rate is mixed, to say
the least. To understand why this is so, looking at the market and the participants therein can give
useful information.
This section first looks at the features of the foreign exchange market, then the participants of
the market.
2.4.1 Features of the foreign exchange market
One important thing to notice regarding the foreign exchange market is the low level of
transparency (see for example Lyons, 2001: 41; Sager and Taylor, 2006; Sarno and Taylor, 2002:
266). Where equity and bond trades has to be disclosed within minutes in most markets, trades in
the foreign exchange market has no requirement of disclosure and hence the trades in the market
is generally not observable. Furthermore, as noted by Sager and Taylor (2006: 82), the foreign
exchange market is highly decentralized, which (further) implies some degree of lack of
transparency. As noted (ibid.: 82): “ It [the foreign exchange market] is opaque – or lacks transparency – in
the sense that the absence of a physical marketplace makes the process of price-information difficult to observe and
understand”. As mentioned by Sarno and Taylor (2002: 266), this decentralisation increases
inefficiency compared with more centralised markets such as the equity market. The high degree
of decentralisation furthermore implies that there is some degree of fragmentation; that is,
transactions may occur at the same time at different prices (ibid.: 267). The aspect of lacking
transparency, and its effect on exchange rate determination, will be discussed further in chapter 3,
and is an important part of understanding the foreign exchange market.
2.4.2 Participants of the foreign exchange market
Cheung and Chinn (2001) analyse the composition of foreign exchange traders in the US using
survey data. According to the result, traders in the US foreign exchange market can roughly be
divided into four groups (ibid.: 453)3: technical trading (29.5%), customer order (23.4%),
fundamental analysis (24.9%) and “jobbing” (21.1%). Jobbing refers to a trader continuously
3 The specific question in the survey is: The best way to describe your spot FX trading is: “Technical trading rules”,
“fundamental analysis”, “customer orders driven”, “jobbing approach”, “other”. Note that the sum of the categories
does not equal 1 as there, in some cases, are multiple responses or incomplete replies (Cheung and Chinn, 2001: 453)
22
24.
buying and selling to take many (small) profits (cf. Cheung and Chinn, 2001: 454). Apparently,
only about a quarter of the respondents (state that they) use fundamental analysis as their
foremost strategy when forecasting exchange rate movements. This could, to some extent,
explain elements of the “exchange rate disconnect puzzle”, as the largest part of the traders seem
to base their strategy on other issues than the fundamental value. One should note, though, that
the number of respondents in the survey is only 142, and therefore not necessarily descriptive of
the US foreign exchange market as a whole. Furthermore the respondents in the survey, for a
large part, have rather small positions to manage.
But the overall conclusion of investor heterogeneity is supported by others. Frankel and Froot
(1990: 184), for example, concludes that the largest part of foreign exchange forecasting firms in
the years 1983-88 described themselves relying exclusively on technical trading. They state that
“shifts over time in the weight that is given to different forecasting techniques are a source of changes in the demand
for dollars, and that large exchange rate movements may take place with little basis in macroeconomic
fundamentals” (ibid.: 184). This apparent heterogeneity of traders is also supported by Frankel and
Rose (1995: 1712), De Bondt and Thaler (1994) and Sager and Taylor (2006: 91), and it seems to
be a robust finding. Menkhoff and Taylor (2007: 940) study the research on technical trading and
conclude: “Almost all foreign exchange professionals use technical analysis as a tool in decision making, at least
to some degree”.
The traders in the survey of Cheung and Chinn (2001: 459) assess that the fundamentals have
little to no effect on the shorter horizon, here intraday and medium run (up to six months). But a
large part (88.4%) of the respondents do believe that macroeconomic fundamentals influence the
exchange rate in the long run – here defined as longer than six months. This is, somewhat, in line
with the empirical results of exchange rate research, as mentioned in the introduction and
discussed further in chapter 3. As to why the exchange rate value differs from the fundamental
value, the respondent’s point to excess speculation (74%) and hedge fund/institutional
manipulation (68%). Around 40% of the traders in the survey believe that central bank
intervention cause the deviations from fundamental value, whereas 52% believe that this has no
effect on the exchange rates. As the most important macroeconomic fundamental the traders in
the survey point to unemployment (33.0%) and the interest rate (30.9%), whereas inflation
(18.3%) and money supply (1.6%) seem less important. A rather surprising result compared with
the mainstream view of macroeconomic variables and the exchange rate. Cheung and Chinn
(2001: 457) furthermore point out that the importance of different macroeconomic variables
shifts over time; but with interest rates always remaining important. Finally a large part (63%) of
the traders interprets the PPP model, discussed in chapter 3 below, as “merely academic jargon”
23
25.
(Cheung and Chinn, 2001: 465). Furthermore, only 13% would sell dollars if the PPP model
indicated a dollar overvaluation. As with the macroeconomic fundamentals, the trader’s views of
the relevance of the PPP model change with the horizon: at the long horizon, 40% of the
respondents find that PPP in fact has some influence.
The main results of Cheung and Chinn (2001) are more or less reproduced in a survey by Cheung
et al (2004) of UK-based foreign exchange dealers. Cheung et al (2004) also find that the agents
are heterogeneous. Furthermore, the dealers in the survey think that over-reaction as well as
speculative and band-wagon effects are very important for exchange rate determination. The UK
dealers, on the other hand, find that fundamentals have significant effect at rather short time
horizons of around six months. But only 27% of the respondents would sell dollars if the PPP
model showed that it was overvalued (ibid.: 297), in line with the result from Cheung and Chinn
(2001).
2.4.3 Stylised fact of the foreign exchange market:
• The foreign exchange market is characterised by a rather low level of transparency
• The foreign exchange market is highly decentralised
• The agents in the market have heterogeneous expectations and employ different methods
• The agents assessment of the importance of different macroeconomic variables change over time
• The agents believe that macroeconomic fundamentals matter in the “long-run”, but have little to no effect
at shorter horizons.
• The agents believe that the PPP model is only valid in the long run.
2.5 Conclusion
In this chapter the foreign exchange rate, the foreign exchange market, and the participants of the
market has been examined.
The foreign exchange market is, by far, the largest financial market in the world, and its size
(measured by turnover) has increased markedly (70%) over the last three years. The descriptive
statistics of exchange rate returns follow that of most other financial assets; i.e. the distribution of
returns is non-normal, skewed and fat-tailed. This change as the frequencies decreases, with less
extreme observations at monthly basis compared with the weekly and daily basis for all three
currencies.
24
26.
The exchange rate market is characterised as being less transparent than other financial asset
markets, clouding the price information and further exacerbating the effect of the heterogeneous
agents as well as the tendency of asymmetric information.
Looking at the participants of the exchange rate market, the primary conclusion is that the traders
dealing with exchange rates are heterogeneous. Some use fundamental analysis as their primary
tool when forecasting exchange rates and deciding strategies; but a large part of the traders seem
to primarily use other methods which do not depend on fundamental values (e.g. technical
trading). Traders do believe that fundamentals have some importance, though. But which types
of fundamentals are important can differ over time, and it seems that the macroeconomic
fundamentals are only reckoned to be important in the long run.
25
27.
Chapter 3
Exchange rates: models and puzzles
“The clear conclusion is that exchange rates are moved largely by other factors than the obvious,
observable, macroeconomic fundamentals. Econometrically, most of the “action” is in the error
term.”
Rudiger Dornbusch and Jeffrey Frankel, (1987), p. 10
“Exchange rate economics is characterized by a number of anomalies, or puzzles, which we
struggle to explain on the basis of either sound economic theory or practical thinking… the
international finance profession has not yet been able to produce theories and, as a consequence,
empirical models that allow us to explain the behavior of exchange rates with a reasonable degree
of accuracy.”
Lucio Sarno, (2005), p. 674
3.1 Introducing exchange rate theory
Before the free floating of exchange rates in the 1970s, and the following expansion of theoretical
exchange rate models, the approach to exchange rate determination was primarily based on the
goods market (Lyons, 2001: 2). That is, demand for foreign exchange was assumed to come
primarily from the sales (and purchases) of goods across borders; an increase in exports is
followed by an increase in the demand for domestic currency to pay for the goods. This
approach, at first, sounded plausible. But the trade balances turned out to be uncorrelated with
the exchange rate movements. Furthermore, trade in goods and services accounts for a very small
fraction of the daily foreign exchange trading, around 5 % (ibid.: 2). As a consequence of this the
asset market – or monetary – approach emerged in the 1970s, and this has since been the
dominant approach for exchange rate research (Sarno and Taylor, 2002: 46). In this chapter the
focus is on the monetary approach of exchange rate modelling and its empirical results. As an
alternative to the monetary models the market microstructure approach is discussed as well.
The chapter is structured as follows: First an introduction to the macroeconomic approach to
exchange rates. Then follows a discussion of the monetary approach to exchange rates, with
focus on the two most used models, the flexible price monetary model and the sticky price (or
26
28.
overshooting) model. Then a survey of the empirical results of exchange rate studies. This leads
to a discussion of the exchange rate puzzles emerging from the empirical results. Then follows a
discussion of the rational expectations hypothesis (REH), a central part of exchange rate
modelling. Finally the microstructure approach is discussed, an alternative method of determining
exchange rate movements and a good starting point for understanding the IKE theory in chapter
4.
3.2 The macroeconomic approach to exchange rates
As mentioned in the introduction to chapter 1 macroeconomic fundamentals are, from an
academic viewpoint, seen as important when evaluating the determinants of exchange rates. In
the following, two of the building blocks for the exchange rate models presented in section 3.3
will be discussed: the purchasing power parity and the uncovered interest rate parity.
3.2.1 Purchasing power parity
A first approximation of what determines the exchange rate is the purchasing power parity (PPP).
PPP states that arbitrage will, when goods are measured in the same currency, lead to equalisation
of goods prices internationally (Pilbeam, 2006: 126 or Sarno and Taylor, 2002: 51). That is, the
purchasing power of a US dollar, say, should be the same in both the Euro-zone and USA. PPP
is defined as follows by Sarno and Taylor (2002: 51): “.. The PPP exchange rate is the exchange rate
between two currencies which would equate the two relevant national price levels if expressed in a common currency
at that rate, so that the purchasing power of a unit of one currency would be the same in both countries”. If the
exchange rate is misaligned (i.e. either over- or undervalued according to PPP), arbitrage would
secure that the currency reaches the parity as investors seek to take profit. As with the uncovered
interest parity presented below, the PPP builds on the notion of market efficiency. The definition
of an informational efficient market is (Campbell et al, 1997: 20-21): “Price changes must be
unforecastable if they are properly anticipated, i.e. if they fully incorporate the expectations and information of all
market participants”. Or, in the words of Malkiel (1992): “A capital market is said to be efficient if it fully
and correctly reflects all relevant information in determining security prices. Efficiency with respect to an information
set … implies that it is impossible to make economic profits by trading on the basis of [that information set]”.
That is, a market in which the prices fully reflect the (available) information is efficient. For a
more thorough discussion of the efficient market hypothesis, see Campbell et al (1997) or Sarno
and Taylor (2002).
The absolute PPP condition states that:
(3.1) st = pt − pt*
27
29.
Where s is the (log) exchange rate, p is the (log) price level and an asterisk denotes a foreign
variable. In the following, s denotes domestic price of foreign currency, and hence an increase
(decrease) in s is seen as depreciation (appreciation). From the PPP condition, the real exchange
rate, q, can be obtained, which can be seen as a measure of deviation from PPP:
(3.2) qt ≡ st − pt + pt*
Figure 7 and 8 below plots the USD/JPY and EUR/USD against the (computed) exchange rate
as given by the PPP condition in equation (3.1).
Figure 7 - USD/JPY and the PPP model, 1980 to 2007
300 300
275 275
250 250
225 225
200 200
percent
percent
175 175
P P P m odel
150 150
125 125
U S D / JP Y
100 100
75 75
80 82 84 86 88 90 92 94 96 98 00 02 04 06 08
.
Source: EcoWin
Figure 8 – EUR/USD and the PPP model, 1988 to 2007
1,6 1,6
1,5 1,5
1,4 1,4
1,3 EUR/U SD 1,3
percent
percent
1,2 1,2
1,1 1,1
1,0 1,0
PPP m odel
0,9 0,9
0,8 0,8
88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07
.
Source: EcoWin
28
30.
As can be seen from both figures 7 and 8 above there are large deviations between the factual
exchange rate (red dotted line) and the value given by the PPP model (blue line). Furthermore,
the swings away from parity appear to be relatively persistent, for example from 1999 to 2003 for
EUR/USD or 1991 to 1997 for USD/JPY.
For the USD/JPY cross, the fundamental value given by PPP somewhat trends the nominal
exchange rate over the period. For the EUR/USD, on the other hand, the PPP value appears
more stationary around a value of 1.1, and the spot exchange rate then “cycles” around this. The
primary conclusion based on visual inspection of the two charts follows the general conclusion
on the outcome of PPP against the spot exchange rate, see for example Pilbeam (2006: 131ff).
One important thing to notice from the two charts is that the exchange rate does not fully
abandon the relationship with the PPP value, although the swings away from it can take several
years. Instead, the PPP value seems to act like an anchor around which the exchange rate gyrates.
If the nominal exchange rate appears “too” misaligned, it is pulled back towards the fundamental
value of PPP.
The apparent disconnect in the figures 7 and 8 between the PPP value and the exchange rate is
part of the “disconnect puzzle”. That is, the exchange rate seems to be, at least in the short-to
medium term, disconnected from the fundamental value (here given by PPP). But the moves
away from PPP seem to be bounded to some extent. Furthermore the slow return towards the
PPP value (i.e. the high half-lifes of the return to the fundamental value) has been dubbed the
“PPP puzzle”, following Rogoff (1996). Both puzzles will be discussed further in section 3.4.3
below on exchange rate puzzles.
The imperfect knowledge economics theory, presented in chapter 4, tries to take into account the
empirical regularities from the charts above. Hence, two of the questions which the imperfect
knowledge economics theory seeks to answer are: i) Why is the exchange rate “disconnected”
from the fundamental value? And ii) why does the exchange rate return to parity?
3.2.2 The interest rate – Uncovered interest rate parity
Another macroeconomic fundamental looked at when discussing exchange rate movements is the
interest rate. Bacchetta and Wincoop (2007: 346) point out that “… FX changes are predictable by
interest rate differentials”. This leans on another cornerstone of foreign exchange rates: the
uncovered interest rate parity (UIP). As with the PPP condition above, the UIP is an arbitrage
condition, securing that no excess return can be earned in an efficient market (Sarno and Taylor,
2002: 5). The UIP is given in equation (3.3) below. It states that changes in the interest rate
differential are set off by equal changes in the (expected) exchange rate, securing equality between
foreign and domestic asset return.
29
31.
(3.3) Δste+1 = it − it*
The domestic investor faces a choice of a secure domestic investment – with the payoff it in
period t+1 – or investing abroad with payoff it* plus the gain/loss from movements in the
currency. In an efficient market, defined as in section 3.2.1 above, the profit from the two
choices has to be equal.
The empirics on the UIP relationship are also mixed; a finding which has been dubbed the
“forward bias puzzle” or UIP puzzle (cf. Lewis, 1995) – another exchange rate puzzle that will be
discussed in section 3.4.3.
Figure 9 below shows the EUR/USD plotted against the 10 year bond differential between USA
and Euroland. There seems to be some connection between the two variables at some periods in
time, especially from 2002 until the beginning of 2005. But there is not a clear correlation over
the time span.
Figure 9 – EUR/USD plotted against the US/EUR 10 year interest rate differential, 2000-2008
1,6 1,50
1,5 1,25
U SD 10 yrs. - E U R 10 yrs. > > 1,00
1,4
0,75
1,3 0,50
percent
percent
1,2 0,25
1,1 0,00
-0,25
1,0
< < E U R /U SD -0,50
0,9 -0,75
0,8 -1,00
00 01 02 03 04 05 06 07 08
.
Source: EcoWin
3.2.3 The money supply
A third important fundamental when analysing exchange rates is the money supply. As the
money supply is, in the long run, assumed to correlate with the prices, this is just another side of
the argument from the PPP condition above.
Figure 10 below plots the relative money supplies against the exchange rate. There seems to be a
close relation between relative money supply and the exchange rate for a long period, around
1988 to the beginning of 1996. But this very close relationship clearly breaks down completely in
the middle of 2002 until 2007. Again, this does not coincide with the monetary models presented
30
32.
in the next section. Why do macroeconomic fundamentals appear closely related to the exchange
rate for some period of time, but unrelated for other time periods? The imperfect knowledge
theory does have an explanation for this question as well.
Figure 10 – USD/JPY plotted against the relative monetary base of USA and Japan, 1988-2007
80 115
90 110
<< USD/JPY
100 105
100
110
95
percent
percent
120
90
130
85
140 80
150 75
US monetary base/Japan monetary base (2000 = 100)>>
160 70
88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07
.
Source: EcoWin
3.2.4 Summing up
Overall, the macroeconomic glance at the exchange rate seems less than clear cut at describing
the exchange rate movements. As the figures above suggest the conclusions regarding the
relationship between the macroeconomic fundamentals and the exchange rate are mixed. Sarno
and Taylor (2002: 264) conclude: “…there seem to be substantial and often persistent movements in exchange
rates which are largely unexplained by macroeconomic fundamentals”. Part of this could stem from the
survey of the traders in chapter 2: Only around a quarter of the traders (predominantly) use
fundamental analysis when assessing future exchange rate values. The traders also believe that the
relationship between fundamentals and the exchange rate is rather small at short to medium
horizons, but larger when looking beyond six months. Finally, the structure of the market itself –
e.g. the lack of transparency – could have an effect on the exchange rate determination.
In the next section, the two parity conditions from above – PPP and UIP – is the basis for the
monetary approach to the exchange rates. The empirical survey following the theoretical models
underlines the initial result from visual inspection of the charts above – the puzzling result that
31
33.
fundamentals and exchange rates seem disconnected, at least for (longer) periods of time. A
result in sharp contrast with the conclusion of the two models, which we turn to now.
3.3 The monetary approach
The monetary approach encompasses the flexible and the sticky price model, as well as several
other exchange rate models not discussed in this thesis.
The two models both starts from defining the exchange rate as the relative price of two countries
moneys (Sarno and Taylor, 2002: 108), and assume that the (relative) supply and demand for
money is the key determinant of exchange rates (Pilbeam, 2006: 152). Furthermore, the approach
assumes that there are no barriers (transaction costs) in the capital market (Frankel, 1995: 97).
Domestic and foreign assets are assumed to be perfect substitutes, i.e. the assets are equally risky.
An assumption that also covers the goods market. From this follows that the PPP condition
holds, and exchange rates are then given by the price difference between two countries. The price
level of a country is given by the demand and supply for money.
Another hypothesis shared by the two models is that of rational expectations on the part of the
agents, a key building block of most modern economic models (e.g. Frydman and Goldberg,
2007: 11; De Grauwe and Grimaldi, 2006a: 1). Rational expectation is given by the following
equation (Pilbeam, 2006: 226):
(3.4) Est +1|t = st +1 + ut +1
That is, the agents do not, on average, systematically over- or underestimate the future exchange
rate. The rational expectations hypothesis (REH) first took its form in the influential article by
Muth (1961: 316), who concluded that: “expectations… are necessarily the same as the predictions of the
relevant economic theory”. The agents in the market therefore utilise the same model as the
economist, and this is furthermore the true model of the economy. Thus, the agents know the
true model of exchange rate movements as well as the information which affects it. Hence,
private information does not matter for the determination of, in this case, exchange rates.
Furthermore information is assumed to be used effectively, cf. Muth (1961: 316). Markets are
therefore assumed to be efficient, following the discussion in section 3.2.1. Hence, the price of a
currency reflects the (relevant) information of the fundamental variables available to the agents. If
new information is revealed, this is (immediately) incorporated in the valuation of the asset. If the
agents did not use the new (relevant) information, they would pass up on profit opportunities –
which rational agents would not do.
The hypothesis of rational expectations has been criticised from several sides. The general
critique of the rational expectations hypothesis will be discussed further in section 3.3.4, as it is an
32
34.
important component of understanding the imperfect knowledge economics theory presented in
chapter 4.
3.3.1 The flexible price monetary model
For the flexible price monetary model (FPMM), prices are assumed to be fully flexible. That is,
the prices react instantly to (for example) excess demand. Versions of the model were first
presented by Frenkel (1976) and Mussa (1976). The three equations below sum up the model
(following Pilbeam (2006: 152-153) and McNown and Wallace (1994: 397)):
(3.5) st = pt − pt*
Equation (3.5) is the PPP condition discussed above. An asterisk denotes a foreign variable and
all variables are in logarithms.
(3.6) mt = pt + β1 yt − β 2it
(3.7) m* = p* + β 1* y* − β 2*it*
t t t
Equation (3.6) and (3.7) is the domestic and foreign money demand, respectively. M is the level
of the money supply, y the income and i the interest rates. As the money market is assumed to be
in equilibrium, money supply equal money demand. Solving for st in equation (3.5), using (3.6)
and (3.7), yields the so-called generic monetary approach to the exchange rate (cf. Sarno and
Taylor, 2002: 109):
(3.8) ( ) (
st = ( mt − mt* ) − β1 yt − β 1* y * + β 2it − β 2*it*
t
)
According to equation (3.8), an increase (decrease) in domestic money supply, relative to the
foreign money supply, should lead to depreciation (appreciation)4. A rise (fall) in domestic output,
on the other hand, induces an appreciation (depreciation) of the currency. And finally, an increase
(decrease) in the domestic interest rate induces depreciation (appreciation) of the domestic
currency.
Inserting the UIP condition ( E ( Δst +1 ) = it − it* ) into equation (3.8) and assuming that β1 = β1* and
β 2 = β 2* yields the following equation (cf. Sarno and Taylor, 2002: 109):
(3.9) ( )
st = ( mt − mt* ) − β1 yt − y* + β 2 E ( Δst +1 )
t
Rearranging equation (3.9) yields:
4 Note, once again, that st is defined as units of domestic currency per foreign currency. Hence, an increase in st
denotes a depreciation
33
35.
β β
(3.10) st =
1
1 + β2
( )
( mt − mt* ) − 1 + 1β yt − y*t + 1 + 2β E ( st +1 )
2 2
Forward iteration then yields the rational expectations solution to equation (3.10):
i
∞
⎛ β ⎞
(3.11) st =
1
1 + β2 i =0 ⎝
⎣ ( )
∑ ⎜ 1 + 2β ⎟ Et ⎡( mt +i − mt*+i ) − β1 yt +i − y*t+i ⎤
⎦
2 ⎠
Since the rational expectations result of equation (3.11) yields a (potentially) infinite set of
solutions (cf. Sarno and Taylor, 2002: 110), the general exchange rate given by this equation –
denoted st – has numerous solutions:
%
(3.12) st = st + Bt
%
Where Bt is a bubble term given by:
1
(3.13) Et ( Bt +1 ) = (1 + β 2 ) Bt
β2
In the absence of rational bubbles, the exchange rate is thus given by equation (3.9) (and (3.11) as
well) above. Hence the flexible price monetary model delivers a sharp prediction of the
connection between the macroeconomic fundamentals (here: money supply and output) and the
exchange rate between two countries. In section 3.4 below, the empirical results of the model will
be discussed. But first the sticky price version of the monetary approach is put forth as a slightly
different approach to exchange rate determination.
3.3.2 The sticky price monetary model
The domestic country in the sticky price monetary model is assumed to be a small participant in
the capital market, and thus faces a given interest rate (Dornbusch, 1988: 62). Assets are still
assumed to be perfect substitutes, “given a proper premium to offset anticipated exchange rate changes”
(ibid.: 62), and perfect capital mobility is assumed. This is given by the uncovered interest rate
parity, discussed in section 3.2.2: If the domestic exchange rate is expected to depreciate, the
interest rate on domestic assets will rise to offset this depreciation. The UIP condition is
reproduced in equation (3.14) below.
(3.14) i = i* + Es
&
The expectation of the exchange rate is formed as the difference between the long-run exchange
rate (given by PPP) and the current exchange rate; it is assumed that the current exchange rate
will converge towards the long-run value at a constant rate.
(3.15) Es = θ ( s − s )
&
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The current exchange rate value is denoted by s, the long-run value by s and θ is the coefficient
of adjustment (cf. Dornbusch, 1988: 63). The expected rate of depreciation is therefore
determined by the gap between the current exchange rate and the long run fundamental value
(which is assumed to be known by the agents), as well as the speed of adjustment given by the
parameter θ.
As in the flexible price model above, the demand for holding money in the domestic country is
given by:
(3.16) mt − pt = β1 yt − β 2it
Combining the three equations above yields the following relationship between the current spot
exchange rate, its long-run fundamental value and the price level:
(3.17) pt − mt = β 2it* + β 2θ ( s − s ) − β1 yt
As noted by Dornbusch (1986: 63), assuming a stationary money supply implies equality of the
interest rates in equation (3.14) as well as equality between the expected value of the exchange
rate and the current exchange rate in equation (3.15). This leads to the following equation for the
long-run equilibrium price level:
(3.18) pt = mt + ( β 2it* − β1 yt )
Inserting equation (3.18) into (3.17) yields the following relationship between the exchange rate
and the price level:
1
(3.19) s=s− ( p − p)
β 2θ
Given the long-run values of the exchange rate and the price, the spot exchange rate is
determined by this equation. In the short run, an increase in the money supply m, with prices
fixed at p, is only held if interest rates drop (following equation (3.16)). Following the UIP
condition in equation (3.15) the lower domestic interest rate leads investors to require an
appreciation of the currency. This is achieved by an initial depreciation (i.e. overshooting) of the
currency, s larger than s , which is then followed by an appreciation to satisfy the UIP condition.
The increase in the money supply leads to a higher price level in the long run, from equation
(3.18) and the assumption of long-run neutrality of money, and a depreciated currency –
according to the PPP condition. But to uphold the UIP condition (expected appreciation of the
currency to offset the lower interest rate) the currency in the short-run overshoots the long-run
value, and then appreciates towards the new (albeit lower) long-run value. This is, in a short
version, the exchange rate “overshooting” model. In appendix B, a slightly more sophisticated
version of the model is shown (based on Sarno and Taylor, 2002: 104-7). From this can be seen
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that equation (3.19) above is the saddle path of the model. For any given price level the exchange
rate adjusts accordingly (instantly) to clear the asset market, following the money market
equilibrium (equation (3.16)) and the UIP condition (equation (3.14)). As the exchange rate (in
the example above) is higher than its long run equilibrium (and thus cheap), domestic prices
slowly increase to restore equilibrium, pressured by the excess demand for domestic goods
(Dornbusch, 1988: 65).
3.3.3 The monetary approach – summing up
As mentioned in the introduction, the monetary approach – either in the flexible or in the sticky
price version – has been the dominant method of modelling exchange rate movements since the
mid-seventies. Although the two models have differences – most notably whether prices are
assumed sticky or fully flexible in the short run – the models reach the same conclusion: The
value of the exchange rate – and its movements – are guided by macroeconomic fundamentals.
First and foremost the money supply (and demand) but also prices, output and interest rates.
Furthermore, both models employ the UIP and PPP condition.
In the following section the empirical results of the models are discussed, leading to a discussion
of the exchange rate disconnect puzzle. As shown in the beginning of this chapter, exchange
rates seem to be disconnected, at least in the short to medium run, from the fundamental value –
in contrast with the hypothesis of the two monetary models. Rudiger Dornbusch – the originator
of the sticky price model presented above – concluded in the late 1980s: “By now there are, I believe,
no more serious claims for the empirical relevance [of the simple monetary model]” (cited in Frankel, 1995:
139).
But not all empirical studies reach the same conclusion regarding the problems of the monetary
approach to exchange rate determination. Following the discussion of the exchange rate puzzles,
four different papers will be presented which show that the monetary approach actually has
important insights regarding exchange rate behaviour.
3.4 Empirical studies of exchange rates
3.4.1 Empirical results of the seventies
The macroeconomic overview in the beginning of this chapter hinted at potential problems when
explaining exchange rates from a purely macroeconomic standpoint. The PPP charts, for
example, show persistent discrepancies between the fundamental value and the nominal exchange
rate. The question, then, is how the monetary models of the exchange rate have performed
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empirically since the free floating of the 1970s. The short answer to that question would be: Not
very good.
Initially, the result of Frenkel (1976) strongly supported the flexible price monetary model when
looking at the German exchange rate vis-à-vis the American dollar during the hyperinflation in
the 1920s. Frenkel found that the coefficient of the money stock estimate (in equation (3.8)) was
near unity, in line with theory. But, as pointed out by for example Sarno and Taylor (2002: 123),
he overlooked the fact that the time-series in his regression could have been non-stationary.
Following Frenkels supportive result of the flexible price monetary model, the model “ceases to
provide a good explanation of variations in the exchange rate data” (Sarno and Taylor, 2002: 124). The
seminal article by Meese and Rogoff (1983) concluded that a random walk model performs at
least as well as three different monetary models – including the flexible as well as the sticky price
monetary model – when forecasting 1-12 months ahead. A ground-breaking result, which has
been rather robust to different tests since then. And a result that has “had an enduring effect on the
profession … [leading] Frankel and Rose to advocate a move away from fundamentals based models”
(MacDonald, 1999: 675). Besides the poor out of sample forecast, the coefficient estimates of
models like equation (3.8) as well as the empirical fit thereof were only good in periods of
hyperinflations – as the result of Frenkel (1976) for example shows (Frankel and Rose, 1995:
1693). The article by Meese and Rogoff (1983) initiated the so-called “exchange rate disconnect
puzzle” (cf. Obstfeld and Rogoff, 2000), i.e. the finding that macroeconomic fundamentals and
the (nominal) exchange rate are only weakly correlated.
In the next section, the more recent empirical results of exchange rate research is presented and
discussed.
3.4.2 Modern empirical results
With the introduction of more advanced econometric methods for testing, the monetary models
have been examined numerous times over the last two decades.
McNown and Wallace (1994) test the flexible price model, using multivariate cointegration, on
three high-inflation countries and find strong support for long-run cointegration. But when
tested on industrialised countries, this relationship disappears. A result in line with the conclusion
from the previous section that the monetary models are most successful in periods with
hyperinflation. MacDonald and Taylor (1994) use multivariate cointegration tests as well, and find
some support for the monetary model. But the coefficients are of the wrong sign, compared with
equation (3.8) above. Groen (2000) uses panel-data set, thereby trying to reduce the small sample
bias. Using a panel of the G7 countries, he cannot reject the null-hypothesis of no-cointegration.
Cushman et al (1996) reach a less pessimistic result than Meese and Rogoff (1983), as they find
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that the exchange rate seems to be related to fundamentals (Cushman et al, 1996: 358). But, on
the other hand, they conclude that the pure monetary model seems inadequate at explaining
exchange rates over the floating period. Furthermore, one should note that they chose the seven
countries which experienced the highest inflation rate during the current float. Mark (1995) finds
that fundamentals may be able to predict the exchange rate, but only at long horizons (three-to-
four years). Frankel (1995) tests a general monetary equation of exchange rate determination
(combining long-run monetary equilibrium path with short-run overshooting) on five currencies.
He finds wrong signs on most coefficients and low significance levels; only for France are all four
coefficients in line with the hypothesis. Finally, Cheung et al (2005) test a range of exchange rate
models, including the PPP and UIP. They reach the mixed conclusion that “the results do not point
to any given model/specification combination as being very successful. On the other hand, some models do well at
certain horizons, for certain criteria. And indeed, it may be that one model will do well for one exchange rate, and
not for another” (Cheung et al, 2005: 1171).
The overall conclusion drawn from the results mentioned above is summed up by Sarno and
Taylor (2002: 136): “Empirical work on exchange rates has still not produced models that are sufficiently
statistically satisfactory to be considered reliable and robust, either in-sample or in out-of-sample forecasting”. This
conclusion is further supported by the empirical test in chapter 5, on the Japanese Yen and the
Norwegian krone against the US dollar, where a generic version of the monetary approach is
tested and firmly rejected. Thus, the problems of the monetary models when describing the
exchange rate movements seem to be a rather robust finding.
3.4.3 Exchange rate puzzles
The conclusion from the brief survey of exchange rate studies in section 3.3.1 and 3.3.2 above
emphasizes the definition of the exchange rate disconnect puzzle from the introduction in
chapter 1: The finding that macroeconomic fundamentals and the (nominal) exchange rate are
only weakly correlated (Obstfeld and Rogoff, 2000). Furthermore that the correlation is almost
zero in the short to medium run but increases somewhat in the longer run. Thus at three to four
years the fundamentals can predict (some of) the trend in exchange rate movement.
The influential result of Meese and Rogoff (1983: 17) that “the [monetary models] do not perform
significantly better than the random walk model” underlines the disconnect puzzle: Models based on
fundamentals fare no better than a simple random walk at predicting the exchange rate. This is
also evident from the PPP charts above (figures 7 and 8), as the nominal exchange rate
overshoots (or undershoots) its fundamental value for longer periods of time – up to several
years. This could lend some support to the conclusion of the Dornbusch (1976) overshooting
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model presented above – i.e. the exchange rate overshoots the long-run value – but studies rule
out this solution (see for example Eichenbaum and Evans, 1995).
As categorized by Obstfeld and Rogoff (2000: 380) the exchange rate disconnect puzzle is the
term for a broader class of puzzles regarding the weak link between the economy and the
exchange rate. Thus, the PPP puzzle (Rogoff, 1996) is a special case of the disconnect puzzle.
The PPP puzzle is best described by the question of Rogoff (1996: 647): “How can one reconcile the
enormous short-term volatility of real exchange rates with the extremely slow rate at which shocks appear to damp
out?”. The rather large half-lifes of the deviations from PPP is evident from figures 7 and 8 as
well. According to the result of Rogoff (1996), the PPP deviations die out at approximately 15
percent per year; implying half-lifes of roughly 3-4 years. Others (for example Murray and Papell,
2005) find even higher half-lifes than Rogoff. This finding further emphasizes the overall
disconnect puzzle of exchange rates.
Another puzzle of exchange rate research – though less related to the disconnect puzzle – is the
forward premium puzzle based on the result of Eugene Fama (1984). Fama estimated a
regression on the uncovered interest rate parity (equation (3.14) above) like the following:
(3.20) Δst +1 = β 0 + β1 ( ft − st ) + ut
With ft being the forward rate, ut the disturbance (error) term and st the spot exchange rate. Given
that the agents are risk neutral and have rational expectations, the slope parameter should equal 1
and the disturbance term should be uncorrelated with information available at time t, following
the notion of efficient markets (Taylor, 1995: 15). But studies on regression equations resembling
equation (3.20) find that the β-parameter is closer to minus unity than 1 (see Lewis, 1995; Taylor,
1996; Frydman and Goldberg, 2007: 141ff.). Excess returns are apparently non-zero, i.e. they are
predictable given current information (the forward rate, ft). Furthermore, the variances of the
returns are relatively large given the expected exchange rate changes (Lewis, 1995: 1922). The
theoretical prediction of equalisation between the expected returns of two countries has thus
been rejected by the empirics. As concluded by Lewis (1995: 1914): “The behaviour of domestic relative
to foreign returns has decisively rejected this assumption [i.e. UIP] over the floating period”.
The two building blocks – PPP and UIP – of the monetary approach apparently have several
problems when tested empirically. This obviously feed into the overall empirical performance of
models based on these two parity conditions, such as the two monetary models.
In the next section, the view of the exchange rate puzzles and the empirical results of this and the
former section will be challenged.
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