FINANCIAL CRISES, NONLINEAR DYNAMICS
AND MACROECONOMIC ISSUES IN CURRENCY
MARKETS

By
Dooyeon Cho

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Economics
2011

Abstract
FINANCIAL CRISES, NONLINEAR DYNAMICS AND
MACROECONOMIC ISSUES IN CURRENCY MARKETS
By
Dooyeon Cho

This dissertation consists of three chapters on international ﬁnancial crises, nonlinear
dynamics and macroeconomic issues in currency markets. The ﬁrst chapter examines the
mechanisms behind output drops across a sample of 23 international ﬁnancial crises. While
three generations of models have studied the causes of ﬁnancial crises, less is known about the
mechanisms by which crises lead to output drops. One unresolved question is whether the
mechanisms behind output drops are similar across episodes. To address this question, we
apply the Business Cycle Accounting (BCA) methodology by Chari et al. (2007) to a sample
of crises. While the eﬃciency wedge is invariably the most important one, the relevance
of the labor and investment wedges varies depending on the size of the output drop and
the severity of banking problems–as measured by bank closures, nonperforming loans and
credit ﬂows. Typically, in cases with smaller output drops and milder banking crises, the
labor wedge tends to be more important than the investment wedge. The opposite is true in
cases, such as those in East Asia in 1997/98, with larger output drops and severe banking
problems.
The second chapter explores the interaction between exchange rate volatility and fun-

damentals by examining the role of trade intensity in the reversion of exchange rates to
long-run equilibrium values. While exchange rates remain mostly unpredictable, researchers
have been able to link currency ﬂuctuations to some fundamentals such as interest rates,
Taylor rule fundamentals, and relative PPP. In an eﬀort to add to this literature, in this
paper we present evidence of a link between trade intensity and exchange rate dynamics.
We ﬁrst establish a negative eﬀect of trade intensity on exchange rate volatility via panel
regressions using distance as an instrument to correct for endogeneity. We also run a nonlinear model of mean reversion to compute half-lives of deviations of bilateral exchange rates
from relative PPP, and ﬁnd these half-lives to be signiﬁcantly lower high trade intensity
currency pairs. This ﬁnding does not appear to be driven by Central Bank intervention. In
an application, we show that our ﬁndings can be used to improve the performance of currency trading strategies, by allowing the thresholds beyond which a currency is considered
overvalued to depend on trade intensity.
The last chapter provides an extensive analysis for both nonlinear and long memory characteristics as well as mean reverting behavior of real exchange rates. This paper estimates
a fractionally integrated, nonlinear autoregressive ESTAR (FI-NLAR-ESTAR) model for
strongly dependent processes developed by Baillie and Kapetanios (2008). While the linear
fractionally integrated model appears to fail to detect mean reversion in real exchange rates,
the nonlinear long memory model is found to be more supportive of signiﬁcant empirical
evidence for the presence of slow mean reversion in real exchange rates for all of the currencies considered in this study over the recent ﬂoat. The results suggest that a model that is
capable of representing both nonlinear and long memory characteristics may help identifying
mean reversion in real exchange rates.

ACKNOWLEDGMENTS
This dissertation would not have been possible without the guidance and the help of several
individuals who in one way or another contributed and extended their valuable assistance in
the preparation and completion of this study. First, my utmost gratitude goes to my main
advisor, Richard T. Baillie for his patience and steadfast encouragement to complete this
study. I am truly indebted and grateful to my another advisor, Antonio Doblas-Madrid,
whose encouragement, supervision and support from the preliminary to the concluding level
enabled me to develop the subjects. They have inspired me so that I could overcome all
the obstacles in the completion of this research work. I would like to express my deepest
gratitude to both advisors for guiding my research for the past several years, helping me to
develop my background in both Economics and Finance, and allowing me the opportunity
to write papers together for publication. I could never have reached the depths of this
dissertation without their insightful advice. Besides my advisors, I would like to sincerely
thank the faculty members, Raoul Minetti and Kirt C. Butler. Regarding my research work,
they helped me by generously providing their insights and suggestions.
I would like to thank my fellow graduate students for sharing their enthusiasm and comments for my work: Jieun Chang, Kang-Hung Chang, Sanders Chang, Guojun Chen, ByungCheol Kim, Jaesoo Kim, Sang-Hyun Kim, Do Won Kwak, Sanglim Lee, Gabriele Lepori,
Seunghwa Rho, Valentin Verdier, and Wei-Siang Wang.
Last but not least, I would like to express my gratitude to my parents and elder brother,
Sungyeon (Joe) Cho for their unwavering love and support through the good and bad times.

iv

Contents

List of Tables

vii

List of Figures

viii

1

2

Business Cycle Accounting for International Financial Crises: The Link
Between Banks and the Investment Wedge
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The model and business cycle accounting procedure . . . . . . . . . . . . . .
1.2.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 The business cycle accounting procedure . . . . . . . . . . . . . . . .
1.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Wedges and Observables . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Wedges with alternative speciﬁcation: Variable capital utilization . . . . . .
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
7
7
10
14
16
19
23
25

Trade Intensity, Carry Trades and Exchange Rate Volatility
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Evidence on the exchange rate volatility - trade intensity linkage
2.3.1 Measuring exchange rate volatility . . . . . . . . . . . .
2.3.2 Trade intensity . . . . . . . . . . . . . . . . . . . . . . .
2.4 Econometric Framework . . . . . . . . . . . . . . . . . . . . . .
2.4.1 The ESTAR model . . . . . . . . . . . . . . . . . . . . .
2.4.2 Estimation of half-lives of deviations from PPP . . . . .
2.5 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Preliminary Analysis . . . . . . . . . . . . . . . . . . . .
2.5.2 Estimation results from ESTAR models . . . . . . . . . .
2.5.3 Half-lives and government intervention . . . . . . . . . .
2.6 Application to carry trades . . . . . . . . . . . . . . . . . . . . .
2.6.1 Deﬁnition of carry trade returns . . . . . . . . . . . . . .
2.6.2 Portfolio Analysis . . . . . . . . . . . . . . . . . . . . . .
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56
56
62
63
63
64
67
67
70
73
73
75
77
79
79
80
83

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3

Nonlinear Long Memory Properties and Mean
change Rates in the Post-Bretton Woods Era
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
3.2 The FI -NLAR-ESTAR model . . . . . . . . . . . .
3.3 Data and Summary Statistics . . . . . . . . . . . .
3.4 Empirical Results . . . . . . . . . . . . . . . . . . .
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . .

vi

Reversion of Real Ex137
. . . . . . . . . . . . . . 137
. . . . . . . . . . . . . . 141
. . . . . . . . . . . . . . 144
. . . . . . . . . . . . . . 146
. . . . . . . . . . . . . . 149

List of Tables
1.1

Benchmark Model Parameter Values . . . . . . . . . . . . . . . . . . . . . .

27

1.2

Pre-crisis Year and Change (%) in per capita real GDP . . . . . . . . . . . .

28

1.3

Data Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

1.4

Change in Output, Labor, Investment . . . . . . . . . . . . . . . . . . . . . .

30

1.5

Contributions of wedges to output drops . . . . . . . . . . . . . . . . . . . .

31

1.6

Contributions of wedges during post-crisis years . . . . . . . . . . . . . . . .

32

1.7

Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

1.8

Summary of Banking crises

. . . . . . . . . . . . . . . . . . . . . . . . . . .

34

1.9

Contributions of wedges to output drops with alternative speciﬁcation . . . .

39

1.10 Contributions of wedges during post-crisis years with alternative speciﬁcation

40

1.11 Correlations with alternative speciﬁcation: Variable capital utilization . . . .

41

2.1

Trade intensity matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

2.2

Eﬀects of trade intensity on real exchange rate volatility - IV estimation . . .

88

2.3

Eﬀects of trade intensity on real exchange rate volatility - Robustness checks

89

2.4

Estimation results from ESTAR models . . . . . . . . . . . . . . . . . . . . .

93

2.5

Half-life estimates for real exchange rates . . . . . . . . . . . . . . . . . . . . 117

2.6

Volatility of selected indicators for diﬀerent exchange regimes . . . . . . . . . 118

2.7

Performance statistics for carry trade portfolios . . . . . . . . . . . . . . . . 119

3.1

Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

3.2

Estimated FI-NLAR-ESTAR models for monthly real exchange rates . . . . 152

3.3

Fractional integration analysis for ARFIMA models . . . . . . . . . . . . . . 154

3.4

Fractional integration analysis for FI-NLAR-ESTAR models . . . . . . . . . 155

vii

List of Figures

1.1

Output paths and three measured wedges . . . . . . . . . . . . . . . . . . . .

42

1.2

Data and predictions of the models with all wedges but one . . . . . . . . . .

44

1.3

Predicted paths of output using two diﬀerent models: A case of Korea . . . .

51

1.4

Scatter plots: Association between contribution of wedge and output drop (%) 52

1.5

Predicted paths of output using two diﬀerent models . . . . . . . . . . . . .

53

1.6

Output paths and three measured wedges using the models with VCU . . . .

54

2.1

Scatter plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

2.2

Generalized impulse response functions (GIs) . . . . . . . . . . . . . . . . . . 122

2.3

Sharpe ratios without and with a momentum trading strategy . . . . . . . . 134

2.4

Performance of portfolios without and with a momentum trading strategy . . 135

3.1

Logarithms of monthly real exchange rates vis-`-vis the US Dollar over time
a

3.2

Autocorrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

viii

156

Chapter 1
Business Cycle Accounting for
International Financial Crises: The
Link Between Banks and the
Investment Wedge

1.1

Introduction

Over the last three decades, international ﬁnancial crises have struck in countries as diverse
as Argentina, Korea, Turkey and Finland. Typical symptoms of crises have been large real
depreciations, current account reversals (or sudden stops), diﬃculties in the banking sector
and, in some cases, sovereign default. On the real side of the economy, crises have typically
led to dramatic declines in output and employment. It is precisely because of these severe

1

real eﬀects, that international ﬁnancial crises are a topic of perennial interest for academic
economists and policymakers alike.
Economists have developed an extensive literature examining the causes of crises, as recurrent waves of ﬁnancial disasters have led to the subsequent development of diﬀerent generations of models. Latin American crises in the 1970s and 1980s motivated ﬁrst generation
models (e.g., Krugman (1979), Flood and Garber (1984)), highlighting the incompatibility
of ﬁxed exchange rates with monetized ﬁscal deﬁcits. The European ERM crisis of 1992/93
and Mexico’s 1994/95 episode led to second generation theories (e.g., Obstfeld (1994), Cole
and Kehoe (1996), (2000)), emphasizing multiple equilibria and self-fulﬁlling prophecies.
And after the Asian crisis of 1997/98, third generation models (e.g., Burnside et al. (2001),
Schneider and Tornell (2004)) tended to stress the role of government guarantees and currency mismatches in private sector balance sheets. However, as Calvo (2000) noted, while
all three generations have provided valuable insights into how and when crises are possible,
they have had less to say about the mechanisms through which crises lead to output drops.
In all three generations, typically, the objective is to determine conditions under which markets can force governments to abandon currency pegs and/or default, assuming that the
abandonment/default has adverse real eﬀects. This assumption is often made because it is
diﬃcult to generate output drops endogenously. In fact, in many environments, crises may
raise output, as real depreciations improve net exports.
The literature seeking to identify mechanisms by which crises lead to output drops is
relatively more recent and less extensive. Regarding output drops in speciﬁc episodes, to
our knowledge, the cases that have been most extensively studied are Mexico in 1994/
95 and Korea in 1997/98. In the context of the “Tequila” crisis, Meza (2008) ﬁnds that
2

changes in ﬁscal policy account for about 20 percent of the output drop in Mexico in 1995,
while Kehoe and Ruhl (2009) ﬁnd that reallocation from nontradable to tradable sectors
explains the evolution of the real exchange rate and trade ﬂows, but not the drop in output
and total factor productivity (TFP). In the case of Korea’s 1997/98 crisis, Benjamin and
Meza (2009) develop a model of sectoral reallocation which takes into account the eﬀect of
high interest rates on ﬁrms’ working capital, and show that the model accounts for about
half of the decline in GDP and TFP.
In this paper, instead of studying the role of speciﬁc frictions in a given episode, our
approach is to perform an exploratory analysis of output drops throughout a sample of
crises. We employ the Business Cycle Accounting (BCA) methodology developed by Chari,
Kehoe and McGrattan (2007) (CKM henceforth). BCA decomposes output ﬂuctuations into
ﬂuctuations due to changes in an eﬃciency wedge, which captures changes in TFP, a labor
wedge, which captures labor-market distortions, an investment wedge, capturing investmentmarket distortions, and a government consumption wedge, capturing government purchases
plus net exports. After estimating the processes governing all wedges, we use simulations
where some wedges vary and others are held constant to discern which kinds of distortions
play the most important role accounting for observed ﬂuctuations. Thus, BCA provides a
priori guidance for economists seeking to explicitly model frictions. One important question
that this analysis will help us answer is to what extent crises are alike. That is, if a similar
combination of wedges accounts well for the data in all (or most) episodes, it may be possible
to develop one single model of output drops with general applicability. On the other hand, it
could be that diﬀerent crises, or clusters of crises, are driven by diﬀerent sets of distortions.
In that case, much like in the aforementioned three generations, it may be preferable to
3

develop multiple models, tailored to diﬀerent varieties of crises.
To construct our sample, we start from the list of episodes compiled by Kaminsky (2006).
After dropping some cases due to data limitations, we are left with the following 23 episodes,
involving 13 countries: Argentina (1981, 1985, 1989, 1994, 2001), Brazil (1987, 1991, 1999),
Chile (1982, 1994), Finland (1991), Indonesia (1997), Israel (1983), Korea (1997), Malaysia
(1997), Mexico (1982, 1994), Philippines (1983, 1997), Sweden (1992), Thailand (1997), and
Turkey (1994, 2000). Note that this sample oﬀers variation along several potentially interesting dimensions. First, the sample includes crises of the 1980s, which are generally explained
by ﬁrst-generation models, and crises of the 1990s and 2000s, which do not conform to ﬁrstgeneration crisis models. The sample also oﬀers wide variation along other dimensions, such
as the size of the output drop and speed of recovery, rates of inﬂation, the geographical
location of the crisis, and the severity of banking crises.
After applying the BCA methodology to all cases and examining the results, some patterns
emerge. Across the sample, the eﬃciency wedge plays the leading role in accounting for
the drop, often explaining well over half of it. The labor wedge follows, explaining on
average about 20 percent of the drop, and the investment wedge comes third, accounting on
average for circa 14 percent of the drop. Finally, the government consumption wedge plays
a negligible role. In light of previous studies, these average percentages are not surprising.
More novel is our ﬁnding that, behind these average percentages, there exist wide variations
between episodes. These variations are fairly systematic along some dimensions. First, the
percentages of the drop explained by the eﬃciency and investment wedges are positively
correlated with crisis severity (i.e., these wedges explain larger percentages of the drops in
crises with larger drops), whereas the percentage explained by the labor wedge is negatively
4

correlated with severity. On the other hand, in the three years after the crisis year—deﬁned
as the year of the biggest output drop—we ﬁnd that the eﬃciency wedge contributes most
to recoveries, while the labor wedge, and even more so the investment wedge, are typically
very persistent. That is, on average, the labor wedge contributes to the drop in output in the
crisis year, and barely contributes to growth in the following three years, while the investment
wedge tends to depress output not only in the crisis year, but also in the following three
years. Regarding correlations, the contributions of the eﬃciency and investment wedges
to the recoveries are markedly positively correlated with the size of the recovery, while
the contribution of the labor wedge to the recovery is essentially uncorrelated with the
size of the recovery. Perhaps the most salient stylized fact that holds in our sample is a
relationship between the investment wedge and several measures of banking crisis severity.
These measures include the fraction of banks closed relative to the total number of banks,
the share of nonperforming loans (NPLs) at the peak of the crisis, and the change in real
bank credit to the private sector. Finally, we also examine other factors, such as inﬂation,
and the time and geographical location of the crisis. We ﬁnd that the importance of the
investment wedge, the size of the output drop, and the severity of banking problems appear
to be particularly pronounced in East Asian crisis episodes when compared to Latin and
European crises. To a lesser extent (and due to considerable overlap), the same diﬀerences
arise when comparing crises of the 1980s to those after 1990. Finally, we ﬁnd no relationship
between the relative importance of diﬀerent wedges and other variables, such as inﬂation
rates.
As a robustness check, we re-run the BCA analysis in our sample allowing for variable
capital utilization, and ﬁnd that, relative to the baseline case, the importance of the eﬃciency
5

wedge falls and the importance of the labor and investment wedges increases, although the
eﬃciency wedge continues to explain the largest fraction of the drops, followed by the labor
and investment wedges. Overall, our results remain qualitatively unaltered. That is, the
correlations with crisis severity remain positive for the eﬃciency and investment wedges and
negative for the labor wedge, and the contribution of the investment wedge continues to be
correlated with our measures of banking crisis severity.
Regarding previous literature, our ﬁnding that the eﬃciency, labor, and investment wedges,
in this order, play the most important roles explaining output is consistent with the ﬁndings
of related studies. In fact, the roles of the eﬃciency and labor wedges have been highlighted
by CKM, Ahearne et al. (2006), Kersting (2008), Cociuba and Ueberfeldt (2008) and Lama
(2011), for, respectively, the United States, Ireland, the U.K., Canada, and six Latin American countries. On the other hand, our ﬁndings point to two arguments against dismissing
the investment wedge as a tertiary, relatively unimportant force. First, the investment wedge
tends to be persistent, in the sense that it typically continues to contribute to output drops
several years after the crisis. Second, the relevance of the investment wedge is greater in more
severe crises and in crises with deep banking problems. These characteristics are typical of
the wave of crises that hit East-Asia in 1997-98. Regarding our ﬁndings on the investment
wedge, the study that most relates to ours is Chakraborty (2009)’s BCA analysis of Japan
in the 1990s, which found the eﬃciency and investment wedges to be most relevant, with the
labor wedge playing a smaller role. Moreover, this study relates the investment wedge to a
well-known feature of Japan’s economy during this period, the lack of lending by so-called
‘zombie banks’.
In sum, our results suggest that researchers interested in modeling output drops in the
6

aftermath of crises may be well advised to use diﬀerent frictions, depending on the severity of
banking sector diﬃculties. In cases with relatively mild banking crises, frictions that translate
into the productivity and labor wedges are most likely to drive the bulk of the economic
activity. On the other hand, in episodes where banking crises—as measured by the share of
nonperforming loans and the prevalence of bank closures—are more severe, the eﬃciency and
investment wedges are likely to explain most of the movement in macroeconomic aggregates.
The rest of the paper is organized as follows. In Section 1.2, we introduce the model and
describe the measurement and accounting procedure. In Section 1.3, we describe our data.
In Section 1.4, we present and discuss results. In Section 1.5, we re-run our analysis allowing
for variable capital utilization, and in Section 1.6, we conclude.

1.2

The model and business cycle accounting procedure

1.2.1

The model

Following CKM, here, we sketch the model and accounting procedure. The model is a
standard neoclassical growth model. Every period t, the economy is hit by one of a ﬁnite
number of events st . The history of realized events up to period t is denoted by st =
(s0 , ..., st ) . The initial realization of the event s0 is exogenously given. As of period 0,
πt st denotes the probability of any particular history st . The economy has four stochastic
variables which depend on st : the eﬃciency wedge At st , which acts like time-varying
productivity; the labor wedge 1−τlt st , which is akin to a time-varying tax on labor income;

7

the investment wedge 1/ 1 + τxt st , which has the same eﬀect as a time-varying tax on
investment, and the government consumption wedge gt st , which resembles government
expenditure.1
The population Nt is assumed to grow at the constant rate γn . The representative
consumer chooses per capita consumption ct st and per capita labor lt st to maximize
∞

β t πt st U ct st , lt st

Nt ,

(1.1)

t=0 st

where β ∈ (0, 1) is a discount factor. Utility maximization is subject to the budget constraint
ct st + 1 + τxt st
=

1 − τlt st

(1 + γn ) kt+1 st − (1 − δ) kt st−1

(1.2)

wt st lt st + rt st kt st−1 + Tt st ,

where kt st−1 , (1 + γn ) kt+1 st − (1 − δ) kt st−1 , and Tt st are, respectively, per
capita capital, per capita investment and per capita lump-sum taxes/transfers. The wage
rate and rental rate on capital are denoted, respectively, by wt st and rt st , and δ is the
rate at which capital depreciates.
Every period t, ﬁrms choose per capita capital kt st−1 and per capita labor lt st to
maximize proﬁts
At st F kt st−1 , (1 + γ)t lt st

− rt st kt st−1 − wt st lt st ,

(1.3)

where γ denotes the constant rate of labor-augmenting technical progress.
1

Several modiﬁcations of the BCA model, which incorporate additional wedges, have
been developed, often with the objective of tailoring the procedure to developing economies.
Despite the merits of the extensions, we have chosen to stick to the baseline BCA model
because, in our judgment, it remains the most standard and commonly used version. By
employing the well-known original version, we hope that it will be easier to compare our
ﬁndings with those of existing and future studies. Moreover, some countries in our sample,
e.g., Finland, are developed countries.
8

Equilibrium in the economy is fully described by
ct st + (1 + γn ) kt+1 st − (1 − δ) kt st−1

+ gt st = y t st ,

yt st = At st F kt st−1 , (1 + γ)t lt st
−

,

Ult st
t
t
t
t ) = 1 − τlt (s ) At s (1 + γ) Flt ,
Uct (s

(1.4)
(1.5)
(1.6)

and
Uct st

1 + τxt st

πt st+1 st Uct+1 st+1

= β

(1.7)

st+1

× At+1 st+1 Fkt+1 st+1 + (1 − δ) 1 + τxt+1 st+1

,

where Uct and Ult denote the ﬁrst derivatives of the utility function with respect to consumption and labor and similarly, Flt and Fkt denote the ﬁrst derivatives of the production
function with respect to labor and capital. Equation (1.4) is the feasibility constraint of the
economy. Equation (1.5) is the production function. Equation (1.6) states that in equilibrium, the marginal rate of substitution between consumption and leisure equals the marginal
product of labor, distorted by τlt (st ). And ﬁnally, equation (1.7) is an intertemporal Euler
equation, distorted by τxt st and τxt+1 st+1 .
As CKM and Chakraborty (2009) emphasize, the wedges or frictions represent all possible distortions that can enter the ﬁrst order conditions. Taxes can be thought of as the
typical wedges. For example, the labor wedge can be any kind of friction that distorts the
relationship between the marginal product of labor and the marginal rate of substitution
between consumption and leisure. These frictions may arise from a variety of sources, such
as taxes, monopoly power by unions or ﬁrms, sticky wages or sticky prices. CKM generalize
these results by illustrating the mapping, and showing that explicitly modeled frictions amap
9

into wedges in this prototype economy.2 For example, input-ﬁnancing frictions map into efﬁciency wedges, investment-ﬁnancing frictions into investment wedges, and ﬂuctuations in
net exports in an open economy map into government consumption wedges. Also, sticky
wedges and monetary shocks map into labor wedges.
Consequently, by construction, the model exactly reproduces the data on output, labor,
investment, and consumption when all four wedges are jointly fed into the model.

1.2.2

The business cycle accounting procedure

How to measure the wedges
As in CKM, we assume that the mapping from the event st to all the wedges is one to one and
onto. The accounting procedure is to conduct experiments that isolate the marginal eﬀect
of each wedge as well as the marginal eﬀects of combinations of the wedges on aggregate
variables. For example, in conducting the experiment that isolates the marginal eﬀect of the
investment wedge, we hold all other wedges ﬁxed at some constant levels in all periods.
To implement the accounting procedure, we assume that the production function has the
Cobb-Douglas form
F (k, l) = k α l1−α ,

(1.8)

where α is the capital share and the utility function is of the form
U (c, l) = log c + ψ log(1 − l),
2

(1.9)

CKM demonstrate the mapping from detailed economies with frictions to prototype
economies with wedges. They also deal with the mapping of ﬁnancial frictions to investment
wedges. They focus on the ﬁnancial frictions in the Bernanke et al. (1999) model and abstract
from the monetary features of that model (For more details, see pages 828-834 in CKM).

10

where ψ denotes the time allocation parameter. We borrow parameter values from the
business cycle literature. Concretely, in Table 1.1, we describe our sources and numerical
values for each country. We then use these values together with the data to derive the steady
state value of the wedges.
To measure the wedges, note that the eﬃciency wedge At and the labor wedge τlt can
be directly calculated from equations (1.5) and (1.6) without computing the equilibrium
of the model. Also, following CKM, we measure the government wedge gt directly from
the data as the sum of government spending and net exports.3 Measuring the investment
wedge τxt is not as straightforward. Since the Euler equation (1.7) involves expectations
over time, and agents’ optimal decision rules depend on the stochastic process driving the
wedges, measuring this wedge requires that we compute the equilibrium of the model.
To estimate the stochastic process for the state, we follow CKM and specify a VAR(1)
process for the four dimensional state st = (log At , τlt , τxt , log gt ). The process has the form
st+1 = P0 + P st + Qεt+1 ,

(1.10)

where the shock is independent and identically distributed over time and is distributed
normally with mean zero and covariance matrix V . The estimate of V is positive semideﬁnite, because we estimate the lower triangular matrix Q, where V = QQ . The matrix
Q has no structural interpretation. We use a standard maximum likelihood procedure to
estimate the parameters P0 , P and V of the VAR(1) process for the wedges.4 To do so, we
3 Meza

(2008) adds net exports to investment rather than government spending since he
analyzes the role of actual ﬁscal policy.
4 As the yearly-data analysis in CKM, we impose the additional restriction that the
covariance between the shocks to the government consumption wedge and those to all other
wedges is zero. In other words, we assume that the government consumption wedge is
uncorrelated with all other wedges for the structure of the matrix.
11

use the log-linear decision rules of the prototype economy along with data on output, labor,
investment, and the sum of government spending and net exports. Speciﬁcally, we use the
log-linear method when we derive estimates of the process for the wedges and for computing
equilibria.
We assume that the economy is in the steady state in pre-crisis year t, where the crisis
year t + 1 is deﬁned as the year with the greatest output drop. We solve the model using
log-linearization and the method of undetermined coeﬃcients. The model is expressed in
state-space form as follows

Xt+1 = AXt + B t+1

(1.11)

Yt = CXt + wt ,
ˆ
where Xt = [log kt , log zt , τlt , τxt , log gt , 1] , zt = At /(1+γ)t , Yt = [log yt , log xt , log lt , log gt ] ,
ˆ
ˆ
ˆ
ˆ
and wt = Dwt−1 + ηt . The matrix A summarizes coeﬃcients linking Xt to Xt+1 , including
the coeﬃcients in matrices P and P0 from the above process and the coeﬃcients linking Xt to
ˆ
kt+1 (found via log-linearization and the method of undetermined coeﬃcients). The matrix
B summarizes variance-covariance parameters, including Q from the VAR(1) process above.
Finally, C summarizes the coeﬃcients linking Xt to Yt (found via log-linearization and the
method of undetermined coeﬃcients), and elements of D are the parameters governing serial
correlation of the measurement error. We assume that E ηt ηt = 04x4 and E

t ηs

= 0 for

all periods t and s.
The log-likelihood function to be maximized is given by
T −1

log |Ωt | + trace Ω−1 ut ut − log |∂f (Zt , Θ) /∂Zt | ,
t

L (Θ) =
t=0

12

(1.12)

where the parameters to be estimated are in vector Θ, ut is the innovation vector, and Ωt
is its covariance. The last term in (1.12) is nonzero if the elements of Y are not the raw
series but depend on the raw series Z plus the parameter vector. Following CKM, for the
results reported, we ﬁx parameters of preferences, production, and growth and estimate the
processes for the wedges. The parameters to be estimated are elements of P0 , P and Q.
The log-likelihood function above is obtained using the Kalman ﬁlter, which generates oneperiod-ahead predictions compared to the actual data. The diﬀerences between the actual
data and the predictions generated by the ﬁlter enter into the log-likelihood function. Once
we have estimated P0 , P and V , we can ﬁnd the realized values of the wedges. (For more
technical details, see Appendices of Chari et al. (2006).)

Evaluating the contribution of each wedge
Having measured realized values for the four wedges, we now implement the simulations
that allow us to determine the extent to which output ﬂuctuations can be attributed to
each wedge. For each episode, we let t and t + 1 denote, respectively, the pre-crisis and the
crisis year. To determine the relevance of a given wedge, we simulate the model letting that
wedge vary only up to the pre-crisis year t, and holding that wedge ﬁxed at its pre-crisis
level from time t + 1 onwards, so as to nullify the eﬀect of changes in that speciﬁc wedge.5
For instance, to compute the share of the drop due to the eﬃciency wedge, we conduct a
simulation in which we feed into the model the full series for the labor, investment, and
government consumption wedges, together with a truncated eﬃciency wedge, which equals
5

Meza (2008) constructs counterfactual wedges that eliminate the eﬀect of changes in
ﬁscal policy. He solves the ﬁscal policy model to ﬁnd the relation between wedges and ﬁscal
policy variables.

13

the realized wedge for years up to the pre-crisis year t but is held constant at its year-t level
from the crisis year t + 1 onwards. Using the same method, we evaluate the importance of
the labor, investment, and government consumption wedges, accordingly.
We feed the truncated wedge along with the other wedges into the model. The greater the
diﬀerence between the actual and the predicted output drop, the greater the importance of
the truncated wedge. For brevity, we will not report results with the truncated government
consumption wedge since, in our sample, as well as in previous studies, there is virtually no
diﬀerence between the output path in the data and the output path predicted by the model
that ignores changes in this wedge from the crisis year onward.

1.3

Data

To build our sample, we begin with the list of crises compiled by Kaminsky (2006). After
dropping cases due to data limitations, 13 countries and 23 crisis episodes remained in
our sample. The countries, pre-crisis years, and output drops observed in these crises are
displayed in Table 1.2. The crises occurred mostly during the 1980s and 1990s, and some
in the early 2000s, and involved the following countries: Argentina, Brazil, Chile, Finland,
Indonesia, Israel, Korea, Malaysia, Mexico, Philippines, Sweden, Thailand, and Turkey. The
crises were on average quite severe. In fact, the average output drop between the pre-crisis
year t and the crisis year t + 1 is approximately 8 percent. In Table 1.4, we show, along
with the percentage drops in output, the percentage drops in employment and investment,
for each crisis in the sample. The average drop in employment, at 3.2%, is smaller than
the drop in output. Investment, on the other hand, is much more volatile than output, and

14

registers an average drop of about 25%.
Most of our data are from the International Financial Statistics (IFS ). The only series
that are not from this source are working age population (i.e., population aged 15-64), total
employment, and hours worked, which are collected from the International Labour Oﬃce
(ILO) LABORSTA database. The years for which we have found data are shown in Table
1.3. With the exception of Turkey, for which data start in 1988, for all other countries, the
ﬁrst year is 1980. The last year diﬀers by country, varying between 2005 and 2007.
The series for per capita output (y), per capita investment (x), per capita labor input (l),
per capita government consumption (g) and per capita consumption (c) are constructed as
follows. Per capita output (y) is the sum of nominal GDP, deﬂated using the GDP deﬂator
and dividing by population aged 15-64. In the case of Mexico, we added services from, and
depreciation of, consumer durables to GDP. We were not able to ﬁnd this information for
other countries. We also omitted sales taxes, since they are small and unavailable for most
countries. The series for per capita investment (x) is given by gross ﬁxed investment (plus
personal consumption expenditures on durables in the case of Mexico), deﬂated and divided
by population aged 15-64. Using both the law of motion for capital and the perpetual
inventory method, we calculate the series for per capita capital stock (k). To construct the
series for the per capita labor input (l) , we multiply annual hours worked per employed
person by total employment, and divide the result by population aged 15-64. Since the value
obtained is total hours worked per year, we divide it by the number of weeks per year (50)
and the endowment of total hours per week (100). As mentioned earlier, the series for per
capita government consumption (g) is the sum of government spending and net exports of
goods and services, which, again, is deﬂated and divided by working-age population. By
15

equation (1.4), the series for per capita consumption (c) is simply obtained by subtracting
per capita investment (x) and per capita government consumption (g) from per capita output
(y).
Regarding data on banking crises, our sources are the following. Data on percentages
of banks closed and shares of nonperforming loans over total loans come from Laeven and
Valencia (2008) and Reinhart and Rogoﬀ (2009). We gathered data on credit extended
from the World Bank’s series “Domestic Credit Provided by Banking Sector (% of GDP)”.
We multiplied this series by nominal GDP (from IFS ) to obtain nominal domestic credit
provided by the banking sector, and deﬂated this series using the CPI series (also from IFS )
to ﬁnally obtain real domestic credit.

1.4

Results

The output paths and realized values for the eﬃciency, labor, and investment wedges for all
countries are depicted in Figure 1.1. Already at ﬁrst glance, it quickly becomes apparent that
there is a much stronger association between output and the eﬃciency wedge than between
output and the labor or investment wedge. This holds not only in crisis years—most of
which stand out visually due to the large output drops—but typically through the sample
period. In Figure 1.2, we show the paths of output, investment, and labor for all countries.
Every graph shows the data together with the results from three simulations, each including
all wedges except for respectively, the eﬃciency, labor, and investment wedge. Clearly, some
wedges play a much more important role in some episodes than in others, with the labor
wedge, for example, playing an important role in Argentina in 2001, and the investment

16

wedge playing a key role, for example, in Malaysia in 1997.
To quantify the importance of a given wedge for a given episode, our primary measure is the
percentage contribution to the output drop in the crisis year. We compute this percentage by
performing the following calculations, which are similar to the calculations in Meza (2008).
Let yi,t and yi,t+1 denote country i’s real (detrended) per capita output in, respectively, the
pre-crisis year t and the crisis year t+1, and let di,t = (yi,t −yi,t+1 )/yi,t be the corresponding
percentage output drop. Next, for each wedge w ∈ {Eﬃciency, Labor, Investment}, we take
output values from a simulation where we feed into the model realized values of wedges other
than w, and let w vary only up to pre-crisis year t, holding it ﬁxed at its year-t level in later
years. We let yi,t+1 (w) denote the year-t + 1 (detrended) per-capita output generated by
this simulation, and di,t (w) = (yi,t − yi,t+1 (w))/yi,t denote the simulated percentage drop.
Finally, we deﬁne Φi,t (w), the contribution of wedge w to the output drop in country i
between years t and t + 1 as
Φi,t (w) =

di,t − di,t (w)
.
di,t

(1.13)

To interpret this measure, it is useful to look at Figure 1.3. As we can see in the top
panel, when the eﬃciency wedge is held constant, output falls by about 7 percentage points,
whereas in the data, it falls by about 12 points. The diﬀerence of approximately 5 points,
about 40%, is the amount attributable to the eﬃciency wedge. Doing this for all wedges
and crises, we obtain the contributions shown in Table 1.5. Not surprisingly, the eﬃciency
wedge is usually largest, whereas the contributions of the labor and investment wedges vary
widely between episodes. On average, the eﬃciency wedge accounts for 62.2% of the decline
of output, the labor wedge, 21.7%, and the investment wedge for 14%.6
6 It

is worth noting that there is a high correlation (0.58 for labor and 0.47 for investment)
17

Three remarks are in order. First, although the average contribution of the investment
wedge—as measured by Φi,t (w)—is lower than that of the labor wedge, we must keep in mind
that this is an unweighted average, which assigns the same weight to each episode regardless
of severity. As we will see shortly, since the importance of the labor and investment wedges is
respectively, negatively and positively correlated with the size of the output drop, a severityweighted average would lower the average importance of the labor wedge and raise that of
the investment wedge. Second, there are instances where the contribution of a given wedge
is negative (e.g., the labor wedge in Indonesia in 1997). In these cases, the wedge completely
misses the evolution of output, leading to an expansion instead of a contraction. The third
remark is that, by construction, the sum of the fractions explained by diﬀerent wedges need
not equal one.
We also examine the eﬀect of the wedges in the post-crisis years t + 1 to t + 4. Given that,
over these three years, output recovers in some cases and falls or stagnates in others, we
cannot use an analog version of Φi,t (w) to measure the wedge’s contributions. This would
be problematic given the diﬃculty in interpreting signs, and the fact that in several cases,
output at t + 1 is very similar to output at t + 4, which would make the denominator close
to zero. In these cases, wedge contributions would be very large numbers, which would skew
averages. To avoid these issues, we deﬁne an alternative measure as follows. For country i
and wedge w ∈ { Eﬃciency, Labor, Investment} the contribution to the recovery is given by
κi,t+1 (w) = [yi,t+1 (w) − yi,t+1 ] − [yi,t+4 (w) − yi,t+4 ].

(1.14)

between the contributions of the labor and investment wedges, given in Table 1.5, and the
drops in labor and ivestment given in Table 1.4. Thus, although the reported measures
of contributions focus on output, the importance of the labor and investment wedges are
informative about the evolution of labor and investment.

18

This measure simply captures whether the gap between the predicted and actual outputs
shrinks over the course of the post-crisis years t + 1 to t + 4. Once more, Figure 1.3 is helpful
to interpret the measure. In the top panel, we can see that the gap between simulated and
actual outputs does not shrink, but instead grows slightly, over the course of the years t+1 to
t + 4. Hence, the contribution of the eﬃciency wedge to recovery would be slightly negative.
Calculating κi,t+1 (w) in this fashion for all episodes and wedges, we obtain Table 1.6. As we
can see, the eﬃciency wedge contributes most to recoveries, on average about 3.4 percentage
points, whereas the labor wedge’s average contribution to recoveries is positive, but close to
zero, and the investment wedge’s contribution averages minus 0.4 points.

1.4.1

Wedges and Observables

Our sample includes crisis episodes that are heterogeneous along a number of observable
dimensions, including the severity of the crisis, the degree of problems in the banking sector,
the time and geographical location of the crisis, inﬂation rates, and so on. This variability
may be useful in order to uncover associations between particular observables and the contributions of the three wedges. In turn, these associations could provide hints as to what
mechanisms or frictions underlie the distortions measured by the wedges.
In this section, we report the most salient associations between the relative contributions of
diﬀerent wedges and other observable variables. First, we discuss the correlations between the
contributions of wedges and the size of the output drop. Second, we document a correlation
between the importance of the investment wedge and several measures of banking crisis
severity. This association is arguably the most intriguing, since it points to speciﬁc frictions

19

that may be related to the wedges. Finally, we discuss other correlates, such as rates of
inﬂation, the geographical location of the crisis, and the time of the crisis.

Size of the Output Drop The association between crisis severity and the contribution
of each wedge is depicted in Figure 1.4. Clearly, there is a positive relationship between the
size of the output drop and the contribution of the eﬃciency and investment wedges, and a
negative relationship between the output drop and the contribution of the labor wedge. Table
1.7 (a), which shows correlations between output drop and the contribution of each wedge,
conveys the same message. The eﬃciency and investment wedges play more important roles
in more severe crises, while the relative importance of the labor wedge is negatively correlated
with severity.
A similar picture emerges when we consider the contributions of diﬀerent wedges to recoveries (or stagnations) in post-crisis years. The contributions of the wedges—as deﬁned
by κi,t+1 (w)—correlate with the size of the recovery, measured as yi,t+4 − yi,t+1 as follows.
The eﬃciency and investment wedges display strong positive correlations (0.73 and 0.67,
respectively), while the labor wedge has a small negative correlation coeﬃcient -0.05. That
is, the contributions of the eﬃciency and investment wedges to the recoveries tend to be
greater for episodes with better post-crisis performance.

Severity of Banking Crises Perhaps the most striking association between our ﬁndings
and observables is the existence of a correlation between the percentage contribution of the
investment wedge to output drops and various measures of banking crisis severity. Using
the database compiled by Laeven and Valencia (2008), and supplementing with information

20

from Reinhart and Rogoﬀ (2009), we compiled information, for each crisis, on the fraction
of all banks closed, as well as on the fraction of nonperforming loans (NPLs) at the peak of
the crisis. This information, along with some qualitative comments, is summarized in Table
1.8.
To illustrate the relationship between banking and the investment wedge, in Figure 1.5,
we compare Brazil in 1987, a crisis with relatively mild banking problems to Indonesia in
1997, a crisis with more serious banking problems. In the graph, it is clear that the contribution of the investment wedge is greater in the latter. While we deliberately chose these
two crises for illustrative purposes, the message from the comparison holds more generally.
As can be seen in Table 1.7, panel (b), the ratio of banks closed to the total number of banks
correlates positively with investment wedge’s contribution to the output drop. The ratio is
essentially uncorrelated with the contribution of the eﬃciency wedge, and somewhat negatively correlated with the contribution of the labor wedge. This measure of banking crisis
severity, however, does not adjust for the size of the closed institutions, and may therefore
misrepresent the aggregate signiﬁcance of the crisis. To address this issue, we also examine
a diﬀerent measure of severity, the share of nonperforming loans throughout the banking
sector at the peak of the crisis. As displayed in Table 1.7, panel (b), using this measure
yields a similar pattern of correlations. The correlation with the eﬃciency wedge turns negative, but remains very small, the correlation with the investment wedge remains positive,
and increases, and the correlation with the labor wedge remains negative.
Finally, we examine the ﬂow of bank credit to the private sector in the crisis year, as well
as in the three following years. While the series from the World Bank (see the Data Section
above) is available as a percentage of GDP, multiplying the series by nominal GDP, and
21

deﬂating using the CPI, we construct a series for the ﬂow of real credit from the banking
system to the private sector. As displayed in Table 1.7, panel (b), the percentage drop in real
credit is positively correlated with the contribution of the investment wedge to the output
drop. The sign is positive, regardless of whether we consider the drop of credit between years
t and t + 1, t and t + 2, t and t + 3, or t and t + 4.
In sum, a variety of measures consistently point to a relationship, which seems plausible
intuitively, between banking crisis severity and the investment wedge.

Other Correlates: Inﬂation, Time, Geographical Location We also explored several
additional variables and experimented with various subsampling criteria in search of patterns.
Speciﬁcally, we considered inﬂation, geography, and whether the crisis took place before or
after 1990.
We found no signiﬁcant correlation between the rate of inﬂation during the crisis year and
the contributions of diﬀerent wedges to the output drop. Despite the often-heard argument
that inﬂation distorts investment decisions by increasing the uncertainty faced by lenders,
we actually ﬁnd a small negative correlation between the inﬂation rate and the contribution
of the investment wedge to the output drop. Associations with the contributions of the
eﬃciency and labor wedges are also very weak.
A much stronger pattern emerges when one examines results depending on the geographical
location of the crisis. In Asian crises (meaning, for our purposes, Korea, Indonesia, Malaysia,
the Philippines, and Thailand), the eﬃciency wedge accounts for 51.6% of the decline in
output, the labor wedge for 14.5%, and the investment wedge for 39.2%, on average. For the
remaining crises, i.e., in Latin American and European crises (including Turkey as European),

22

the eﬃciency wedge accounts for 66% of the decline of output, the labor wedge for 24.2%, and
the investment wedge, on average, for 6.6%. The importance of the investment wedge is not
only higher on average for Asian countries, but also very strongly correlated with severity.
Table 1.7 (c) displays correlations between the percentage output drop and each wedge’s
contribution for both subsamples. In Asian crises, the contribution of the eﬃciency and
investment wedges is highly correlated with severity, while the contribution of the labor wedge
correlates negatively with severity. In European and Latin American crises, the contributions
of the eﬃciency and labor wedges are mildly positively correlated with severity, and the
contribution of the investment wedge is mildly negatively correlated with severity. Although
these ﬁndings regarding the geographical location of the crisis are rather pronounced, they
are more diﬃcult to interpret than our ﬁndings on banking crisis severity.
Finally, we compared crises of the 1980s to crises of the 1990s and 2000s. Due to our
sample size, however, this exercise overlaps to a substantial degree with breaking up the
sample between Asian and non-Asian crises. Thus, we ﬁnd a more important role for the
investment wedge in post-1990 crises and a more important role for the labor wedge in the
crises of the 1980s.

1.5

Wedges with alternative speciﬁcation:

Variable

capital utilization
In this section, following CKM, we consider an alternative speciﬁcation of the technology
allowing for variable instead of ﬁxed capital utilization. This speciﬁcation of the technology

23

is due to Kydland and Prescott (1988) and Hornstein and Prescott (1993). We assume that
the production function is now
y = A (kh)α (nh)1−α ,

(1.15)

where n is the number of workers employed and h is the length (or hours) of the workweek.
Labor input is given by l = nh.
We assume that the number of workers n is constant and that all the variation in labor is
from the workweek h. Under the assumption of variable capital utilization, the services of
capital kh are proportional to the product of the stock k and the labor input l. So, variations
in the labor input induce variations in the ﬂow of capital services. The capital utilization
rate is proportional to the labor input l, and the eﬃciency wedge is proportional to y/k α .
This change of speciﬁcation results in nontrivial changes in measured wedges. The output
paths and realized values for the eﬃciency, labor, and investment wedges with variable
capital utilization for all countries are depicted in Figure 1.6. Not surprisingly, relative to
the baseline case, the importance of the eﬃciency wedge falls and the contributions of the
labor and investment wedges increase. Nevertheless, the eﬃciency wedge continues to explain
the largest fraction of the drops. Moreover, variable capital utilization does not qualitatively
alter our overall ﬁndings. In Tables 1.9 and 1.10, we report the contributions to output drops
and recoveries, respectively, while Table 1.11 is an analog of Table 1.7, and thus displays
correlations between wedge contributions and observables. The wedges shown in Table 1.9
correlate with the size of the output drop in the same way as the wedges in Table 1.5, that
is, positively for eﬃciency and investment, and negatively for labor. Similarly, the messages
from Tables 1.10 and 1.11 coincide with those from Tables 1.6 and 1.7, respectively. In

24

particular, in Table 1.11, (panel (b)) the contribution of the investment wedge to the output
drop continues to be correlated with our measures of banking crisis severity.

1.6

Conclusion

Using the ‘Business Cycle Accounting’ methodology developed by Chari, Kehoe and McGrattan (2007), we study output drops across a sample of 23 international ﬁnancial crises.
Throughout the sample, the eﬃciency wedge is consistently the most important wedge in
terms of its ability to explain the output drop, followed by the labor and investment wedges.
We also ﬁnd that the importance of diﬀerent wedges varies widely across episodes. The importance of the eﬃciency and investment wedges correlates positively with severity, as well
as with bank closures. By contrast, the labor wedge is relatively more relevant in less severe
crises, and in crises with milder banking problems. Moreover, the investment wedge tends
to be persistent, in the sense that it tends to cause output to decline for several years after
the crisis.
By uncovering some stylized facts, this study points to some directions for future research.
Our main ﬁndings regarding banking crises and the investment wedge suggest a need for crisis
models that explicitly incorporate a banking sector as a crucial intermediary for investment.
Another direction for future research is to investigate whether there are institutional or
other diﬀerences (beyond banking crisis severity) that may account for the diﬀerent results
obtained for Asian versus non-Asian countries. Perhaps some hints may be found in Cargill
and Parker (2002), who argue that, when compared to their Western counterparts, East
Asian ﬁnancial systems are more heavily intermediated by banks, place more emphasis on

25

state-bank-ﬁrm relationships, and are extremely reluctant to impose bankruptcy, especially
on large borrowers.

26

Table 1.1. Benchmark Model Parameter Values
Country
Technology
progress
rate (γz )
Argentina
0
Brazil
0
Chile
0.020
Finland
0.024
Indonesia
0.024
Israel
0.015
Korea
0.053
Malaysia
0.034
Mexico
0
Philippines
0
Sweden
0.020
Thailand
0.038
Turkey
0.012

Population
growth
rate (γn )
0.016
0.020
0.015
0
0.023
0.025
0.015
0.028
0.032
0.025
0
0.021
0.024

Parameter Values
Discount
Dep.
factor
rate of
(β)
capital (δ)
0.920
0.050
0.900
0.070
0.980
0.050
0.980
0.050
0.960
0.050
0.950
0.050
0.980
0.047
0.960
0.050
0.962
0.050
0.964
0.050
0.950
0.050
0.917
0.100
0.900
0.050

Time
Capital
allocation
share
parameter (ψ)
(α)
2.33
0.400
3.93
0.400
3.36
0.300
2.24
0.350
2.24
0.350
2.24
0.350
3.46
0.297
2.24
0.350
2.24
0.350
2.24
0.350
2.24
0.350
2.24
0.350
2.24
0.350

Note. The benchmark model parameter values have been obtained from the business
cycle literature: Argentina - Kydland and Zarazaga (2002), Brazil - Lama (2011),
Chile - Bergoeing et al. (2002) and Simonovska and Soderling (2008), Korea - Otsu
(2008), and Mexico - Meza (2008). For the remaining 8 countries, parameter values
were obtained by calibration for the corresponding data.

27

Table 1.2. Pre-crisis Year and Change (%) in per capita real GDP
Country
Argentina

Brazil

Chile
Finland
Indonesia
Israel
Korea
Malaysia
Mexico
Philippines
Sweden
Thailand
Turkey

Pre-crisis Year
1980
1984
1988
1994
2001
1987
1991
1998
1981
1998
1990
1997
1983
1997
1997
1981
1994
1983
1997
1991
1997
1993
2000

Change (%) in per capita real GDP
-6.84
-6.81
-8.26
-4.07
-13.17
-2.37
-2.77
-1.91
-15.45
-4.08
-8.98
-19.54
-1.66
-11.59
-13.20
-4.17
-8.41
-8.66
-2.75
-3.48
-15.08
-10.63
-10.73
-8.03

Average

Note. A change (%) in per capita real GDP is calculated between the pre-crisis year
and the following year for each episode.

28

Table 1.3. Data Availability
Country
Argentina
Brazil
Chile
Finland
Indonesia
Israel
Korea
Malaysia
Mexico
Philippines
Sweden
Thailand
Turkey

Period
1980 - 2005
1980 - 2006
1980 - 2007
1980 - 2006
1980 - 2006
1980 - 2007
1980 - 2006
1980 - 2006
1980 - 2005
1980 - 2005
1980 - 2007
1980 - 2006
1988 - 2005

Note. For Turkey, the data set runs from 1988 instead of 1980.

29

Table 1.4. Change in Output, Labor, Investment

Country
Argentina

Brazil

Chile
Finland
Indonesia
Israel
Korea
Malaysia
Mexico
Philippines
Sweden
Thailand
Turkey
Average

Pre-crisis Year
1980
1984
1988
1994
2001
1987
1991
1998
1981
1998
1990
1997
1983
1997
1997
1981
1994
1983
1997
1991
1997
1993
2000

Output
-6.84
-6.81
-8.26
-4.07
-13.17
-2.37
-2.77
-1.91
-15.45
-4.08
-8.98
-19.54
-1.66
-11.59
-13.20
-4.17
-8.41
-8.66
-2.75
-3.48
-15.08
-10.63
-10.73
-8.03

Change (%)
Labor
Investment
-2.38
-16.32
-0.41
-17.90
-0.24
-23.64
-5.75
-13.70
-7.20
-26.75
-0.32
-0.28
-4.02
-8.21
-1.20
-5.65
-12.32
-33.41
-3.24
-23.50
-5.81
-22.46
-4.27
-57.49
-0.54
-13.51
-8.28
-39.45
-3.37
-46.12
0.62
-19.61
-0.04
-18.63
-2.94
-37.21
-6.02
-20.18
-4.87
-15.44
-0.50
-48.42
-0.01
-30.49
-0.46
-39.50
-3.20
-25.12

Note. Output and investment are real values per person aged 15-64.

30

Table 1.5. Contributions of wedges to output drops
Contribution (%) of each wedge
Country
Pre-crisis Year Eﬃciency Labor Investment
Argentina
1980
74.93
16.17
5.19
1984
77.34
12.12
11.28
1988
76.03
5.70
16.99
1994
20.98
112.78
-6.12
2001
48.88
58.48
-2.54
Brazil
1987
155.39
43.00
-74.67
1991
40.12
54.99
-7.53
1998
59.06
15.24
7.96
Chile
1981
31.11
56.65
-3.77
1998
51.52
16.75
55.69
Finland
1990
50.27
18.08
15.29
Indonesia
1997
72.36
-15.98
37.88
Israel
1983
84.68
-27.21
77.00
Korea
1997
41.61
22.43
33.46
Malaysia
1997
75.02
-15.26
43.01
Mexico
1981
78.48
-18.21
29.91
1994
64.10
2.82
-34.42
Philippines
1983
74.29
8.92
29.52
1997
-26.33
121.09
15.67
Sweden
1991
11.98
50.98
20.46
Thailand
1997
72.43
-33.93
51.87
Turkey
1993
105.36
-1.66
-7.46
2000
91.02
-5.61
8.31
Average
62.20
21.67
14.04

31

Table 1.6. Contributions of wedges during post-crisis years
Contribution (%) of each wedge
Country
Pre-crisis Year Eﬃciency Labor Investment
Argentina
1980
-1.50
-1.75
-0.19
1984
1.72
2.23
-0.27
1988
10.94
4.79
-2.12
1994
6.82
3.97
0.35
2001
19.12
-2.74
5.19
Brazil
1987
-5.16
0.41
0.87
1991
5.56
-0.97
0.05
1998
-3.04
3.81
-0.29
Chile
1981
-8.70
5.67
-1.69
1998
0.19
-0.65
0.81
Finland
1990
2.99
-2.81
-5.43
Indonesia
1997
3.96
-2.51
2.07
Israel
1983
8.01
1.59
-2.13
Korea
1997
-1.85
3.76
0.30
Malaysia
1997
1.25
0.96
-2.71
Mexico
1981
-3.78
2.33
-5.29
1994
4.63
-0.29
1.16
Philippines
1983
-6.26
3.75
-2.89
1997
1.33
5.05
-0.66
Sweden
1991
7.07
-4.49
-1.63
Thailand
1997
12.08
-9.19
-0.11
Turkey
1993
10.60
-4.94
1.15
2000
11.72
-6.30
3.35
Average
3.38
0.07
-0.44
Note. Size of recovery is measured as (yi,t+4 −y i,t+1 ).

32

Size of recovery
-1.63
2.72
9.89
11.82
21.24
-1.43
7.51
2.30
-6.95
0.45
-8.49
-1.75
8.52
1.61
-3.11
-7.31
7.50
-6.60
6.33
0.70
-3.92
9.23
9.14
2.51

Table 1.7. Correlations
(a) Correlations between output drop (%) and the contribution of the wedge:
Overall
Contribution of the
Eﬃciency wedge
Labor wedge
Investment wedge

Correlation with the output drop (%)
0.087
-0.338
0.157

(b) Correlations between contributions of wedges and measures of banking
crisis severity

Contribution of the
Eﬃciency wedge
Labor wedge
Investment wedge

Correlation with measures of banking crisis severity
Share of
Credit drop from t to
bank closed NPLs t + 1 t + 2 t + 3
t+4
-0.046
0.033
-0.117
-0.190
0.149
0.198 0.049 0.182 0.266 0.200

(c) Correlations between output drop (%) and the contribution of the wedge:
Asian crises versus European and Latin crises
Contribution of the
Eﬃciency wedge
Labor wedge
Investment wedge

Correlation with the output drop (%)
Asia
Europe and Latin America
0.778
-0.102
-0.864
0.048
0.794
-0.176

33

Table 1.8. Summary of Banking crises
Country

Crisis
Year
Argentina 1980

Share of NPLs
Banks
at peak (%)
closed (%)
9
9.8

1985

30

N/A

1989

27

15.8

1995

17

2.4

2001

20.1

0

Brief summary
The failure of a large private bank (Banco de Intercambio
Regional) led to runs on three other banks. Eventually, more
than 70 institutions - 16% of commercial bank assets and
35% of ﬁnance company assets - were liquidated or subjected
to central bank intervention.
In early May, the government closed a large bank, leading to
large runs, which led the government to freeze dollar deposits
on May 19.
Nonperforming assets accounted for 27% of aggregate portfolios and 37% of state banks’ portfolios. Failed banks held
40% of ﬁnancial system assets.
The Mexican devaluation led to a run on the banks, which
resulted in an 18% decline in deposits between December
and March. 8 banks suspended operations, and 3 banks
collapsed. Through the end of 1997, 63 of 205 banking
institutions were closed or merged.
In March 2001, a bank run started due to a lack of public
conﬁdence in government policy actions. In late November
2001, many banks were on the verge of collapsing, and
partial withdrawal restrictions were imposed (corralito)
and ﬁxed term deposits (CDs) were reprogrammed to stop
to outﬂows from banks (corralon). In December 2002, the
corralito was lifted. In January 2003, one bank was closed,
3 banks were nationalized, and many others were reduced in
size.

34

Table 1.8. Summary of Banking crises (continued)
Country

Crisis
Year
1985

Share of NPLs
at peak (%)
N/A

1990

16

1994-1996

15

1980

35.6

Finland

1998
1991-1994

1.44
13

Indonesia

1997-2002

35.5

Brazil

Chile

Banks
Brief summary
closed (%)
0
3 large banks (Comind, Maison Nave, and Auxiliar) were
taken over by the government.
0
Deposits were converted to bonds. Liquidity assistance to
public ﬁnancial institutions.
N/A
In 1994, 17 small banks were liquidated, 3 private banks
were intervened, and 8 state banks were placed under
administration. The Central Bank intervened in or put
under temporary administration 43 ﬁnancial institutions,
and banking system nonperforming loans reached 15% by
the end of 1997. Private banks returned to proﬁtability in
1998, but public banks did not begin to recover until 1999.
13.1
3 banks began to lose deposits; interventions began 2 month later. Interventions occurred in 4 banks and 4 nonbank ﬁnancial institutions, accounting for 33% of outstanding loans.
In 1983, there were 7 more bank Interventions and one ﬁnanciera, accounting for 45% of ﬁnancial system assets. By the
end of 1983, 19% of loans were nonperforming.
0
N/A
0
A large bank (Skopbank) collapsed on September 19 and
was intervened. Savings banks were badly aﬀected; The
government took control of 3 banks that together accounted
for 31% of system deposits.
27.7
Through May 2002, Bank Indonesia closed 70 banks and
nationalized 13 out of 237. Nonperforming loans were 65-

35

Table 1.8. Summary of Banking crises (continued)
Country

Crisis
Year

Share of NPLs
at peak (%)

Banks
closed (%)

Israel

1983

N/A

0

Korea

1997

35

37.3

Malaysia

1997

30

0

1981-1982

N/A

0

1994-1997

18.9

0

Mexico

Brief summary
75% of total loans at the peak of the crisis and fell to about
12% in February 2002.
Stocks of the 4 largest banks collapsed and were nationalized by the state.
Through May 2002, 5 banks were forced to exit the market
through a “purchase and assumption formula,” 303 ﬁnancial
institutions (215 of them credit unions) shut down, and 4
banks were nationalized. Banking system nonperforming
loans peaked between 30 and 40% and fell to about 3%
by March 2002.
The ﬁnance company sector was restructured, and the
number of ﬁnance institutions was reduced from 39 to 10
through mergers. 2 ﬁnance companies were taken over by
the Central Bank, including the largest independent ﬁnance
company. 2 banks - accounting for 14% of ﬁnance system
assets were deemed insolvent and were to be merged with
other banks. Nonperforming loans peaked between 25 and
35% of banking system assets but fell to 10.8% by March
2002.
There was capital ﬂight. The government responded by nationalizing the private banking system.
In 1994, 9 banks were intervened and 11 participated in the
loan/purchase programs of 34 commercial banks. The 9 banks

36

Table 1.8. Summary of Banking crises (continued)
Country

Philippines

Crisis
Year

Share of NPLs
at peak (%)

Banks
closed (%)

Thailand

19

0

1997-1998

Sweden

1981-1987

20

2.6

1991-1994

13

0

1996

33

2.4

Brief summary
accounted for 19% of ﬁnancial system assets and were deemed
insolvent. 1% of bank assets were owned by foreigners,
and by 1998, 18% of bank assets were held by foreign banks.
The commercial paper market collapsed, triggering bank runs
and the failure of nonbank ﬁnancial institutions and thrift banks. There were problems in two public banks accounting for
50% of banking system assets, 6 private banks accounting for
12% of banking system assets, 32 thrifts accounting for 53%
of thrifts banking assets, and 128 rural banks.
1 commercial bank, 7 of 88 thrifts, and 40 of 750 rural banks
were placed under receivership. Banking system nonperforming loans reached 12% by November 1998 and were expected
to reach 20% in 1999.
The Swedish government rescued Nordbanken, the second
largest bank. Nordbanken and Gota bank, with 22% of banking system assets, were insolvent. Sparbanken Foresta, accounting for 24% of banking system assets, intervened. 5 of the 6
largest banks, accounting for over 70% banking system assets,
experienced diﬃculties.
As of May 2002, the Bank of Thailand shut down 59 of 91
ﬁnancial companies (13% of ﬁnancial system assets and 72%
of ﬁnance company assets) and 1 of 15 domestic banks, and
nationalized 4 banks. A publicly owned assets management

37

Table 1.8. Summary of Banking crises (continued)
Country

Turkey

Crisis
Year

1994
2000

Share of NPLs
Banks
at peak (%)
closed (%)

4.1
27.6

0
15

Brief summary
company held 29.7% of ﬁnancial system assets as of March
2002. Nonperforming loans peaked at 33% of total loans and
were reduced to 10.3% of total loans in February 2002.
3 banks failed in April.
2 banks closed, 19 banks have been taken over by the Savings
Deposit Insurance Fund.

Sources: Laeven and Valencia (2008) and Reinhart and Rogoﬀ (2009)

38

Table 1.9. Contributions of wedges to output drops with alternative speciﬁcation
Contribution (%) of each wedge
Country
Pre-crisis Year Eﬃciency Labor Investment
Argentina
1980
55.90
22.54
3.65
1984
67.74
11.38
16.54
1988
68.75
3.00
23.84
1994
-25.03
153.26
-4.98
2001
30.00
74.94
-2.21
Brazil
1987
148.71
66.37
-124.39
1991
-3.34
88.71
-23.73
1998
38.24
28.21
6.50
Chile
1981
12.58
78.02
-9.33
1998
31.04
29.44
68.42
Finland
1990
29.93
30.51
16.64
Indonesia
1997
59.47
-29.02
76.20
Israel
1983
19.47
117.47
134.49
Korea
1997
23.89
34.16
41.80
Malaysia
1997
64.46
-16.34
57.79
Mexico
1981
69.21
-37.49
179.16
1994
57.13
-1.97
-39.83
Philippines
1983
59.40
10.06
41.37
1997
-90.88
170.99
25.35
Sweden
1991
-29.76
82.86
22.39
Thailand
1997
66.39
-34.98
75.59
Turkey
1993
101.73
-2.06
-8.52
2000
86.64
-6.56
13.24
Average
40.94
37.98
25.65

39

Table 1.10. Contributions of wedges during post-crisis years with alternative speciﬁcation
Contribution (%) of each wedge
Country
Pre-crisis Year Eﬃciency Labor Investment
Argentina
1980
-0.16
-2.02
-1.11
1984
1.66
2.81
-0.97
1988
10.89
5.15
-3.81
1994
5.59
5.18
-0.15
2001
18.50
-4.83
6.11
Brazil
1987
-5.05
0.42
2.02
1991
5.53
-1.62
0.82
1998
-5.94
5.78
-0.66
Chile
1981
-11.49
8.17
-3.31
1998
0.21
-0.82
1.15
Finland
1990
6.19
-5.22
-6.82
Indonesia
1997
3.80
-3.80
4.68
Israel
1983
8.43
5.52
-4.54
Korea
1997
-3.55
5.28
0.04
Malaysia
1997
1.26
1.15
-3.77
Mexico
1981
-3.19
2.85
-16.44
1994
2.97
-0.22
1.58
Philippines
1983
-7.35
5.47
-4.39
1997
-1.07
7.64
-1.80
Sweden
1991
9.29
-7.09
-1.96
Thailand
1997
14.74
-12.55
2.61
Turkey
1993
13.20
-7.66
1.93
2000
13.18
-8.92
4.72
Average
3.38
0.03
-1.05
Note. Size of recovery is measured as (yi,t+4 −y i,t+1 ).

40

Size of recovery
-1.63
2.72
9.89
11.82
21.24
-1.43
7.51
2.30
-6.95
0.45
-8.49
-1.75
8.52
1.61
-3.11
-7.31
7.50
-6.60
6.33
0.70
-3.92
9.23
9.14
2.51

Table 1.11. Correlations with alternative speciﬁcation: Variable capital utilization
(a) Correlations between output drop (%) and the contribution of the wedge:
Overall
Contribution of the
Eﬃciency wedge
Labor wedge
Investment wedge

Correlation with the output drop (%)
0.262
-0.509
0.084

(b) Correlations between contributions of wedges and measures of banking
crisis severity

Contribution of the
Eﬃciency wedge
Labor wedge
Investment wedge

Correlation with measures of banking crisis severity
Share of
Credit drop from t to
bank closed NPLs t + 1 t + 2 t + 3
t+4
0.046
0.113
-0.210
-0.214
0.076
0.275 0.173 0.298 0.356 0.300

(c) Correlations between output drop (%) and the contribution of the wedge:
Asian crises versus European and Latin crises
Contribution of the
Eﬃciency wedge
Labor wedge
Investment wedge

Correlation with the output drop (%)
Asia
Europe and Latin America
0.793
0.113
-0.880
-0.240
0.936
-0.190

41

Figure 1.1. Output paths and three measured wedges
Argentina

Brazil

Chile

Finland

Indonesia

Israel

Note. All values are normalized to equal 100 in 1980. For Turkey, in 1988. The
solid line denotes the output path. The dashed, circle marker, and dash-dotted
lines denote the measured eﬃciency, labor, and investment wedges, respectively.

42

Figure 1.1. Output paths and three measured wedges (continued)
Korea

Malaysia

Mexico

Philippines

Sweden

Thailand

Turkey

43

Figure 1.2. Data and predictions of the models with all wedges but one
Argentina

Note. The top, middle, and bottom panels are output, labor, and investment,
respectively. The solid line denotes the data. The dashed, circle marker, and
dash-dotted lines denote the predictions of the model with no eﬃciency wedge,
of the model with no labor wedge, and of the model with no investment wedge,
respectively.

44

Figure 1.2. Data and predictions of the models with all wedges but one (continued)
Brazil

Chile

45

Figure 1.2. Data and predictions of the models with all wedges but one (continued)
Finland

Indonesia

46

Figure 1.2. Data and predictions of the models with all wedges but one (continued)
Israel

Korea

47

Figure 1.2. Data and predictions of the models with all wedges but one (continued)
Malaysia

Mexico

48

Figure 1.2. Data and predictions of the models with all wedges but one (continued)
Philippines

Sweden

49

Figure 1.2. Data and predictions of the models with all wedges but one (continued)
Thailand

Turkey

50

Figure 1.3. Predicted paths of output using two diﬀerent models: A case of Korea
(a) Eﬃciency wedge

(b) Labor wedge

(c) Investment wedge

Note. Time t denotes the pre-crisis year for the Korean crisis episode. The solid
line is the actual output path, and the line with square markers denotes the constructed output path.

51

Figure 1.4. Scatter plots: Association between contribution of wedge and output drop (%)
(a) Eﬃciency wedge
(b) Labor wedge

(c) Investment wedge

Note. The x-axis is the output drop (%), and the y-axis is the contribution
of each wedge (%). The depicted straight line is the OLS regression line.

52

Figure 1.5. Predicted paths of output using two diﬀerent models
(1) Less severe banking crisis: Brazil 1987
(1a) Eﬃciency wedge

(1b) Labor wedge

(1c) Investment wedge

(2) More severe banking crisis: Indonesia 1997
(1a) Eﬃciency wedge

(1b) Labor wedge

(1c) Investment wedge

Note. Time t denotes the pre-crisis year for each crisis episode. The solid line
is the actual output path, and the line with square markers denotes the constructed output path.

53

Figure 1.6. Output paths and three measured wedges using the models with VCU
Argentina

Brazil

Chile

Finland

Indonesia

Israel

Note. As for Figure 1.1.

54

Figure 1.6. Output paths and three measured wedges using the models with variable
capital utilization (continued)
Korea

Malaysia

Mexico

Philippines

Sweden

Thailand

Turkey

55

Chapter 2
Trade Intensity, Carry Trades and
Exchange Rate Volatility

2.1

Introduction

For international economists, exchange rate determination is both a topic of perennial interest
and a formidable challenge. While some models—e.g., Taylor et al. (2001), Molodtsova and
Papell (2009), Mark (1995), and others—have been shown to outperform the random walk
famously proposed by Meese and Rogoﬀ (1983), the fraction of exchange rate movement
that can be accounted for, let alone predicted, remains very low.1 Moreover, some of the
empirical regularities that have been found are at odds with theory. Most strikingly, a
large literature (e.g., Hansen and Hodrick (1980), Fama (1984), Hodrick (1987, 1989), Froot
and Thaler (1990), Engel (1996), Mark and Wu (1997), among others) has established the
1 In

a recent interview with The Region—a magazine published by the Minneapolis Fed—
Kenneth Rogoﬀ summarizes his view on the state of the literature by stating that, when it
comes to understanding exchange rates, “the glass is 95 percent empty”.

56

empirical failure of uncovered interest parity (UIP), a building block of many well-known
international ﬁnance models (e.g., Dornbusch (1976), Flood and Garber (1984), and many
others). In fact, the carry trade—an investment strategy that exploits the failure of UIP
by borrowing low-interest currencies to invest in high-interest rate currencies—has attracted
growing attention from investors and economists alike (see Brunnermeier et al. (2008), and
Bhansali (2007), among others). Another empirical ﬁnding that is at odds with theory is the
proﬁtability of momentum strategies. As documented, for example, by Asness et al. (2009),
trading strategies that exploit the persistence of exchange rate trends are popular among
market participants and are on average proﬁtable. Given that momentum and carry trading
strategies are essentially blind to fundamentals, some authors, notably Brunnermeier et al.
(2008) have remarked that these strategies are likely to give rise to exchange rate bubbles,
temporarily driving exchange rates to unsustainable levels. Fortunately, however, other wellknown models of exchange rate determination fare better than UIP when confronted with
data. In particular, there is ample evidence that relative purchasing power parity (PPP)
does have some traction in the medium/long run. While real exchange rates are notoriously
volatile, they consistently tend to revert back to long-run equilibrium levels. Moreover,
although linear models yield puzzlingly long half-lives of deviations from PPP (see, e.g.,
Rogoﬀ (1996)), estimates from nonlinear models—where the speed at which deviations vanish
is an increasing function of the size of the deviations—are more supportive of relative PPP
(see, e.g., Taylor et al. (2001)). Combining the failure of UIP with the predictive power of
fundamentals, Jord` and Taylor (2009) show that the crash risk, or negative skewness, of
a
the carry trade can be greatly reduced using fundamentals-augmented carry trade strategies
that take into account not only interest rate diﬀerentials, but also measures of fair value
57

implied by fundamentals, such as relative PPP.
In this paper, we seek to further examine the mechanism by which exchange rates revert
to PPP by considering the role of trade intensity. The theory behind this link is simply
that PPP is based on the Law of One Price, which in turn hinges on goods arbitrage. As
real exchange rate deviations from PPP widen, the number of tradable goods for which
price diﬀerences exceed transaction costs also rises. After the usual J-curve lag, agents
begin to take advantage of these opportunities for goods arbitrage, buying cheap currencies
and selling expensive ones in the process. Our main hypothesis is that this reequilibration
process should be stronger and faster the higher the trade intensity between countries.2 In
other words, our hypothesis is that trade intensity can help us understand and predict the
dynamics of bilateral real exchange rate.
We consider a sample of 91 currency pairs involving 14 countries over the period 1980-2005.
Following Betts and Kehoe (2008), we deﬁne trade intensity (maximum) between countries
A and B as the greater of two fractions. The ﬁrst is the fraction of country A’s exports plus
imports to country B divided by country A’s total exports plus imports. The second is the
fraction of country B’s exports plus imports bound for country A divided by country B’s
total exports plus imports. We also deﬁne trade intensity (average), which is the average of
the two aforementioned fractions, as an alternative measure to trade intensity (maximum).
Not surprisingly, trade intensity and exchange rate volatility are negatively correlated in our
2

Although turnover in foreign exchange markets far exceeds the value of world exports
and imports, a commonly held view among foreign exchange practitioners is that goods
trade nevertheless inﬂuences exchange rates in a non-negligible way. The reason for this is
that, while day traders account for the bulk of speculative trades, they open and close their
positions very frequently. By contrast, a goods-trade related foreign exchange transaction
opens a position that is, so to speak, never closed. Therefore, export/import driven foreign
exchange transactions typically exert pressure on a currency in a much more consistent
direction than speculative trades.
58

sample. This correlation is likely a product of causality in both directions. As mentioned
above, trade intensity may reduce volatility through goods arbitrage, which exerts pressure
to reduce deviations from PPP. In the other direction, there is the argument—often brought
up in defense of ﬁxed exchange rates—that lower exchange rate volatility may increase
trade intensity between countries by reducing uncertainty and hedging costs associated with
trade between the two countries. Since we are primarily interested in the ﬁrst direction
of causality, we begin the analysis by implementing panel regressions with exchange rate
volatility as a dependent variable and trade intensity as one of our independent variables,
using the distance between two countries as an instrument. This approach is similar to that
of Broda and Romalis (2009). Coeﬃcient estimates from these regressions across various
speciﬁcations repeatedly show a negative eﬀect of trade intensity between two countries on
their bilateral real exchange rate. We also ﬁnd that, consistent with the literature on carry
trades (see, for instance, Bhansali (2007)) exchange rate volatility increases with the absolute
value of interest rate diﬀerentials. These results are robust to the use of diﬀerent measures
of exchange rate volatility and trade intensity, and to considering only major currency pairs,
versus minor/exotic pairs. Finally, the results are qualitatively preserved when we restrict
attention to just the ﬁrst, or second half, of the 1980-2005 period.
In order to quantify how the size and persistence of deviations from PPP diﬀer between
high and low trade intensity currency pairs, we estimate a nonlinear model of exchange
rate reversion. Speciﬁcally, we estimate a Smooth Transition Autoregressive (STAR) model,
which allows the speed at which exchange rates converge to their long-run equilibrium values to depend on the size of the deviations. This is consistent with Taylor et al. (2001),
who provide evidence of nonlinear mean reversion in a number of major real exchange rates.
59

The model thus allows for the possibility that real exchange rates may behave like unit
root processes when close to their long-run equilibrium levels, while becoming increasingly
mean-reverting the further they move away from equilibrium. Nonlinear models help explain so-called PPP puzzle—see Rogoﬀ (1996)—which is the fact that estimates from linear
models of half-lives of deviations from PPP seem implausibly long. For our comparison, we
restrict attention to 35 highest and 35 lowest currency pairs, as ordered by trade intensity.
We make this choice to ensure that the diﬀerence in trade intensities between the two sets of
currency pairs is so large and stable that variations of trade intensity over time are negligible
in comparison to the diﬀerences in trade intensities between the two sets of pairs. After estimating the ESTAR models, we investigate the dynamic adjustment in response to the shock
to real exchange rates of the estimated ESTAR model by computing the generalized impulse
response functions (GIs) using the Monte Carlo integration method introduced by Gallant
et al. (1993). We ﬁnd that, as hypothesized, the estimates of the half-lives of deviations from
PPP for a given currency pair are higher the less intense the trade relationship between two
countries. For currency pairs in the high trade intensity group, the average half-life of deviations from PPP is given by 21.57 months, whereas for low trade intensity pairs, it is 28.34
months. Moreover, this ﬁnding is statistically signiﬁcant. We also verify that our result is
not driven by Central Bank intervention. That is, a possible concern when interpreting our
results is that, if Central Banks exhibit more fear of ﬂoating in response to exchange rate
ﬂuctuations against important trading partners, the observed diﬀerences in volatility may
primarily be due to oﬃcial reserve transactions, rather than trade. To address this concern,
we consider various proxies for intervention—speciﬁcally the volatility of reserves and interest rates, following Calvo and Reinhart (2002). To judge by these measures, government
60

intervention is unlikely to be the cause of the faster convergence of exchange rates in high
trade intensity cases, since the degree of currency intervention is typically lower for currency
pairs in the high trade intensity group.
Our ﬁndings on trade intensity and exchange rate dynamics may be used to improve the
performance of trading strategies, such as the carry trade. To illustrate how to apply our
ﬁndings, we carry out a simple exercise, similar in spirit to Jord` and Taylor (2009). In our
a
exercise, we simulate a PPP-augmented carry trade strategy, which gives a buy signal only
if there is a positive interest rate diﬀerential and the high interest currency is undervalued
according to relative PPP. The criterion to decide whether a currency is over- or undervalued
according to relative PPP is simply whether the (9 month lagged) real exchange rate is above
or below its historical average by a percentage τ . Our ﬁndings resemble those of Jord`
a
and Taylor (2009), since we ﬁnd that the PPP-augmented strategy yields a higher Sharpe
ratio and lower negative skew than the naive carry trade strategy, which simply buys high
interest rate currencies regardless of any fundamental valuation measures. Trade intensity
is useful to ﬁne-tune this strategy by letting the threshold τ depend on trade intensity. For
high trade intensity currency pairs, the best performing strategies become active starting
at relatively small deviations from the long run real exchange rate. Speciﬁcally, the best
performing strategies have τ equal to 30 or 70 percent, depending on whether the strategy
includes momentum or not. On the other hand, we ﬁnd that, for low trade intensity currency
pairs, it is best to bet on mean reversion only once the deviations have become quite large.
Speciﬁcally, the best performing strategy leans against a deviation from PPP only once this
deviation is τ = 130% or greater (both with and without momentum).
The rest of the paper is organized as follows. In Section 2.2, we describe our data. In
61

Section 2.3, we provide preliminary evidence of a linkage between trade intensity and exchange rate volatility. In Section 2.4, we introduce the ESTAR model, and describe how to
estimate half-lives of deviations from PPP. In Section 2.5, we present and discuss empirical
results from ESTAR models along with robustness checks conducted for results from panel
regressions. Further, we investigate whether our half-life estimates are mainly driven by
government intervention. In Section 2.6, we deﬁne carry trade returns, and the performance
statistics for carry trade strategies is presented. In Section 2.7, we conclude.

2.2

Data

We collect monthly nominal exchange rates vis-`-vis the US Dollar (USD) from January 1980
a
through December 2008 for the following 13 currencies: Australian Dollar (AUD), Canadian
Dollar (CAD), Danish Krone (DKK), Great Britain Pound (GBP), Japanese Yen (JPY),
Korean Won (KRW), Mexican Peso (MXN), New Zealand Dollar (NZD), Norwegian Krone
(NOK), Singapore Dollar (SGD), Swedish Krona (SEK), Swiss Franc (CHF), and Turkish
Lira (TRY). We also collect monthly interest rates for 14 countries. The consumer price index
(CPI) is used to measure the price level, and then the real exchange rate is constructed using
Equation (2.1). The foreign exchange reserves are also collected to investigate whether halflife estimates are driven by government intervention, instead of trade. The data are mainly
drawn from the International Financial Statistics (IFS ), and the data for annual exports
used to measure trade intensity are taken from Betts and Kehoe (2008).3 When we conduct
3

The data along with a data appendix for annual exports to measure
trade intensity in this paper are publicly available at Timothy Kehoe’s webpage,
http://www.econ.umn.edu/˜tkehoe/research.html.

62

a preliminary analysis, we use the data ending in December 2005 due to data limitation for
trade intensity. There are a number of combinations that can be made from currencies listed
above, which result in 91 currency pairs. In what follows, we consider these 91 currency
pairs, involving 14 countries to analyze a linkage between trade intensity and exchange rate
volatility. When two currencies are paired, they are listed based on the alphabetical order
of the base currency.

2.3

Evidence on the exchange rate volatility - trade
intensity linkage

We study the link between trade intensity and exchange rate volatility. We conjecture that
the more intense the trade relationship between two countries, the less volatile their bilateral
real exchange rate. To investigate the link between them, we ﬁrst document how to measure
exchange rate volatility, and deﬁne trade intensity in the following two subsections.

2.3.1

Measuring exchange rate volatility

The real exchange rate, qt , is deﬁned in logarithmic form as
q t ≡ st − pt + p∗
t

(2.1)

where st is the logarithm of the nominal exchange rate which is measured as the price of
the domestic currency in terms of the foreign currency, and pt and p∗ denote the logarithm
t
of the domestic and foreign price levels, respectively. As noted in particular by Taylor et al.
(2001), the real exchange rate may be interpreted as a measure of the deviation from PPP.
63

To measure exchange rate volatility between countries i and j, we calculate the standard
deviation of the monthly logarithm of the bilateral real exchange rates over the one-year
period for each currency pair. To consider a longer term than the one-year window, we
implement panel regressions using diﬀerent time windows such as the three-year window and
six-year window for robustness checks, and results for diﬀerent time windows are reported
in Table 2.3 (c). Some other papers use the ﬁrst-diﬀerence of the monthly logarithm of the
bilateral real exchange rates (denoted by ∆qt ) as a measure of exchange rate volatility.4 (See,
e.g. Brodsky (1984), Kenen and Rodrik (1986), Frankel and Wei (1993), Dell’Ariccia (1999),
Rose (2000), and Clark et al. (2004)) As noted by Clark et al. (2004), this volatility measure
has the property that it will be equal to zero if the exchange rate follows a constant trend,
which could be expected and therefore would not be a source of uncertainty any more. More
speciﬁcally, for monthly real exchange rates between countries i and j, we deﬁne exchange
rate volatility as the standard deviation of the bilateral real exchange rate as

V olatilityij = 

1
T −1

1
2

T

qij,t − q ij

2

(2.2)

t=1

where qij,t is the monthly logarithm of the bilateral real exchange rate between countries i
and j, and q ij is the mean value of qij,t over time period T .

2.3.2

Trade intensity

We consider trade intensity which is deﬁned as relative importance of the trade relationship
between two countries. Following Betts and Kehoe (2008), we deﬁne trade intensity between
4 When

we use the ﬁrst-diﬀerence of the monthly logarithm of the real exchange rates as
a measure of exchange rate volatility rather than the level of the monthly logarithm of the
real exchange rates, we obtain similar results with much higher statistical power to reject a
null hypothesis.
64

any two countries, X and Y as the greater of two fractions which are given as follows
 

 
export

+export

X,Y,t
Y,X,t 
 
,

exportX,i,t + exporti,X,t
 all
all


tradeintmax = max 
X,Y,t

 



exportX,Y,t +exportY,X,t
 

all

exportY,i,t +

all

exporti,Y,t













(2.3)

where exportX,Y,t is measured as free on board (f.o.b.) merchandise exports from country
X to country Y at year t , measured in year t US dollars. We denote this by tradeintmax
X,Y,t
avg

to distinguish tradeintX,Y,t which is an alternative measure to (2.3), and is deﬁned as (2.4)
below. In this deﬁnition of trade intensity, Betts and Kehoe (2008) implicitly assume that
trade intensity need only be high for one of the two countries in any bilateral trade relationship for the same strong relation between the relative price of goods and the real exchange
rate to be observed. For example, the Chile-US relationship is a high trade intensity relationship, even though Chile accounts for only 0.4 percent of US trade, because the United
States accounts for 20.5 percent of Chilean trade. In Betts and Kehoe (2008), a bilateral
trade relationship with country X or country Y is deﬁned as “high intensity” if tradeintmax
X,Y
is greater than or equal to 15 percent and “low intensity” otherwise. Chile, for example, has
a high intensity trade relationship with the United States, because trade with the United
States accounts for 20.5 percent of Chile’s total trade over 1980–2005, on average. In this
paper, as a comparison, we deﬁne the alternative measure of trade intensity between any
two countries, X and Y as

65

 

 
export

+export

X,Y,t
Y,X,t 
 
,

exportX,i,t + exporti,X,t
 all
all


avg
tradeintX,Y,t = avg 

 



exportX,Y,t +exportY,X,t
 

all

exportY,i,t +

all

exporti,Y,t













(2.4)

This deﬁnition uses the average of two fractions in any bilateral trade relationship. If we
apply the deﬁnition in (2.4) to the Chile-US example given above, we obtain 10.5 percent
instead of 20.5 percent between Chile and the United States. In what follows, we employ
both measures, the maximum and the average of two aforementioned fractions. Tables 2.1
(a) and (b) illustrate trade intensity matrices based on the average over the entire sample
period, 1980-2005 for both measures, respectively.
We ﬁrst illustrate Figures 2.1 (a) and (b) showing scatter plots of exchange rate volatility
against trade intensity (maximum) and trade intensity (average), respectively, for 91 currency pairs involving 14 countries over the period 1980-2005. It can be clearly seen that there
is a negative relationship between exchange rate volatility and trade intensity. As a preliminary analysis, we implement panel regressions with a dependent variable being exchange
rate volatility, and results from panel regressions are reported in Table 2.2. To investigate
nonlinear mean reversion to PPP, we focus on 35 highest and 35 lowest trade intensity currency pairs based on trade intensity (average).5 Using 70 currency pairs selected by a rank
order of trade intensity (average), we estimate the ESTAR models, and then calculate halflives of deviations from PPP by generating generalized impulse response functions (GIs). In
5

When we use trade intensity (maximum) instead of trade intensity (average) in determining 35 highest and 35 lowest trade intensity currency pairs, there is little diﬀerence in
rank orders, and this implies that results do not depend mainly on how we measure trade
intensity.

66

the next two sections, we introduce the ESTAR model, and demonstrate how to measure
half-lives of deviations from PPP.

2.4
2.4.1

Econometric Framework
The ESTAR model

In this section, we consider one of the regime-switching models which is known as the smooth
transition autoregressive (STAR) model (Granger and Ter¨svirta (1993) and Ter¨svirta
a
a
(1994)). In this model, adjustment takes place in every period but the speed of adjustment varies with the extent of the deviation from equilibrium. Speciﬁcally, we estimate the
Exponential Smooth Transition Autoregressive (ESTAR) model which allows for regimeswitching or state-dependent behavior to study a nonlinear mean reversion of real exchange
rates (Taylor et al. (2001)). The STAR model allows for smooth rather than discrete adjustment in explaining nonlinear adjustment. The STAR model for the real exchange rate,
qt deﬁned in (2.1) may be written as
p

(qt − µ) =





p

∗
θj qt−j − µ  Φ (qt−d − µ; γ, c) + εt

θj qt−j − µ + 
j=1

(2.5)

j=1

where {qt } is a stationary and ergodic process, εt ∼ iid 0, σ 2 , and Φ (·) is the transition
function that determines the degree of mean reversion and itself governed by the parameter
γ, which determines the speed of mean reversion to PPP. The parameter µ is the equilibrium
level of {qt }, and d > 0 is the delay parameter which is an integer.

67

The STAR model (2.5) may also be written, reparameterized in a ﬁrst diﬀerence form as


p−1

p−1

βj ∆qt−j + α∗ + ρ∗ qt−1 +

∆qt = α + ρqt−1 +
j=1

∗
βj ∆qt−j  Φ (qt−d ; γ, c) + εt (2.6)
j=1

where ∆qt−j = qt−j − qt−j−1 . A transition function suggested by Granger and Ter¨svirta
a
(1993) is the exponential function
Φ (qt−d ; γ, c) = 1 − exp −γ (qt−d − c)2 /σqt−d

with γ > 0

(2.7)

where qt−d is a transition variable, σqt−d is the standard deviation of qt−d , γ is a slope
parameter, and c is a location parameter. The restriction on the parameter (γ > 0) is an
identifying restriction. When the transition function is given by Equation (2.7), Equation
(2.6) is called the exponential STAR (ESTAR) model. The exponential function in Equation (2.7) is bounded between 0 and 1, and depends on the transition variable qt−d . The
exponential function also has the properties that Φ (qt−d ; γ, c) → 1 both as qt−d → −∞ and
qt−d → ∞ whereas Φ (qt−d ; γ, c) = 0 for qt−d = c, and is symmetrically inverse-bell shaped
around zero. For either γ → 0 or γ → ∞, the exponential function given by Equation (2.7)
approaches a constant which is equal to 0 and 1, respectively. Thus, the model reduces to
a linear model in both cases, and the ESTAR model does not nest a Self-Exciting Threshold Autoregressive (SETAR) model as a special case. The exponent in Equation (2.7) is
normalized by dividing by σqt−d which is the standard deviation of qt−d , and it allows the
parameter γ to be approximately scale-free, and is useful for the initial estimates for the
nonlinear least squares estimation algorithm. The values taken by the transition variable
qt−d and the transition parameter γ together will determine the speed of mean reversion to
PPP. For any given value of qt−d , the transition parameter γ determines the slope of the

68

transition function, and thus the speed of transition between two extreme regimes, with low
values of the transition parameter γ implying slower transitions.
In the STAR model given in the ﬁrst diﬀerence form as in Equation (2.6), the pivotal
parameters for the stability of qt are ρ and ρ∗ in the linear and nonlinear parts, respectively.
Taylor et al. (2001) discuss that the inﬂuence of transactions costs suggests that the larger
the deviation from PPP, the stronger the tendency to move back to long-run equilibrium.
This implies that in Equation (2.6), while ρ ≥ 0 is admissible, one must have ρ∗ < 0 and
(ρ + ρ∗ ) < 0 for qt to be mean reverting. In other words, for small deviations, the real
exchange rate, qt may be characterized by unit root or explosive behavior, but for large
deviations it is mean reverting.
The ESTAR model is reasonable to use for our study since it allows for symmetric and
nonlinear adjustments between two extreme regimes, with the rate of which in turn depends
on the state of speciﬁed transition variables. The ESTAR model has been applied to real
(eﬀective) exchange rates with a transition variable being qt−d . (e.g. Michael et al. (1997),
Sarantis (1999), and Taylor et al. (2001)). The ESTAR model has also been applied to various
macroeconomic issues such as debt and inﬂation. Among others, Sarno (2001) provides
strong empirical evidence of nonlinear mean reversion in the US debt-GDP ratio using the
ESTAR model. Gregoriou and Kontonikas (2009) test nonlinearities in inﬂation deviations
from the target by estimating the ESTAR model, and ﬁnd that the model is capable of
capturing the nonlinear behavior of inﬂation misalignments.
For empirical applications, Granger and Ter¨svirta (1993) and Ter¨svirta (1994) suggest
a
a
choosing the order of the autoregression, p, through inspection of the partial autocorrelation
function (PACF). The PACF is preferred to the use of an information criterion such as
69

the Akaike information criterion (AIC), Bayesian information criterion (BIC) or Schwarz
information criterion (SIC) because the information criterion may bias the chosen order of
the autocorrelation toward low values and any remaining correlation may have an inﬂuence
on the power of subsequent linearity tests. Therefore, a lag order of p for each currency pair
is selected by the PACF of the real exchange rate, qt . Following van Dijk et al. (2002b),
we set the maximum value of the delay parameter, d equal to 6. We consider the lags of
the real exchange rate as the transition variable, that is, qt−d for d = 1, 2, ..., 6. Then, the
delay parameter d is selected after we compare p-values of the Lagrange Multiplier (LM) test
statistics for linearity applied to the time series for qt . The p-values of the LM tests indicate
that linearity can be rejected at a certain signiﬁcance level when qt−d (d ∈ {1, 2, ..., 6}) is
used as the transition variable. Based on the p-values for the LM statistics, an appropriate
d is selected as the delay parameter. In Table 2.4, the values selected for the lag order p and
delay parameter d are reported in the second and third rows, respectively. Then, the ESTAR
model of the form (2.6) is estimated by nonlinear least squares (NLS) with the selected lag
order p and delay parameter d which are suggested by the PACF and the linearity tests
results, respectively, for 35 highest and 35 lowest trade intensity currency pairs.

2.4.2

Estimation of half-lives of deviations from PPP

Having estimated the ESTAR model, we consider the nonlinear mean-reverting properties
exhibited by real exchange rates. To be more speciﬁc, we investigate the dynamic adjustment
in response to the shock of the estimated ESTAR model by computing generalized impulse
response functions (GIs). The Generalized Impulse Response Function (GI), proposed by

70

Koop et al. (1996) is designed to solve the problem of the treatment of the future that is
dealt with by using the expectation operator conditioned only on the history and on the
shock. In other words, the problem of dealing with shocks that occur in intermediate time
periods is solved by averaging them out. Therefore, the response to be constructed is an
average of what might occur given the present and past. The GI generalizes the concept of
impulse response, and is known to be applicable to nonlinear models. The GI for a speciﬁc
current shock εt = δ and history ωt−1 is deﬁned as
GIq (h, δ, ωt−1 ) = E [qt+h | εt = δ, ωt−1 ] − E [qt+h | ωt−1 ]

(2.8)

for h = 0, 1, 2, .... In Equation (2.8), the expectation of qt+h given that the speciﬁc current
shock δ occurs at time t is conditioned only on the history and on this shock. Given the
construction of the GI above, the natural baseline for the impulse response function is then
deﬁned as the expectations of qt+h conditional only on the history of the process ωt−1 , and
the current shock is also averaged out.
As pointed out by Koop et al. (1996), the GI is a function of both the shock δ and history
ωt−1 , and we may treat them as realizations from the same stochastic process that generates
the realizations of {qt }. Thus, the GI deﬁned above may be considered as the realization of
a random variable deﬁned as
GIq (h, εt , Ωt−1 ) = E [qt+h | εt , Ωt−1 ] − E [qt+h | Ωt−1 ]

(2.9)

Equation (2.9) is the diﬀerence between two conditional expectations being themselves random variables. Thus, GIq (h, εt , ωt−1 ) represents a realization of this random variable. With
nonlinear models, the shape of the GI is not independent of on the history of the time the
shock occurs, the size of the shock, or the distribution of future exogenous innovations. We
71

generate the GIs, both conditional on the history and conditional on the shock using the
Monte Carlo integration method introduced by Gallant et al. (1993).6 More speciﬁcally,
we compute history- and shock-speciﬁc GIs as deﬁned in (2.8) for all observations in the
estimation sample and value of the initial shock. For the history and the initial shock, we
compute GI∆q (h, δ, ωt−1 ) for horizons h = 0, 1, 2, ..., 100. The conditional expectations in
Equation (2.8) are estimated as the means over 2000 realizations of ∆qt+h , accomplished by
iterating on the ESTAR model, with and without using the selected initial shock to obtain
∆qt and using randomly sampled residuals of the estimated ESTAR model elsewhere. Impulse responses for the level of the real exchange rate, qt are obtained by accumulating the
impulse responses for the ﬁrst diﬀerences as
h

GIq (h, δ, ωt−1 ) =

GI∆q (i, δ, ωt−1 )

(2.10)

i=1

The estimated GIs for both high and low trade intensity currency pairs are depicted in
Figures 2.2 (a) and (b), respectively. The initial shock is normalized to 1, and the generated
GIs clearly show the nonlinear adjustment dynamics of real exchange rates to the shock.
The half-lives of real exchange rates to the shock are calculated by measuring the discrete
number of months taken until the shock to the level of the real exchange rate has fallen
below a half. That is, we estimate half-lives considering how much the shock is persistent
until the GI falls below 50 percent.
6

Kili¸ (2009b) suggests half-life measures conditional on various regimes to examine
c
persistence in the PPP relations using nonlinear ESTAR(1) models. He computes regimedependent half-lives for the point estimates by standard asymptotic normal methods and
simulations. However, as noted by Baillie and Kapetanios (2010), the usual closed form
ln(0.5)
solution for half-life, h, given by h = ln(ˆ) , where ρ denotes the estimated AR coeﬃcient
ˆ
ρ
of an AR(1) model, is only valid for AR(1) models, and there is no closed form solution for
general AR(p) models.

72

2.5

Empirical Results

2.5.1

Preliminary Analysis

Results from instrumental variable (IV) estimation using panel data
We consider how trade intensity between two countries aﬀects exchange rate volatility. Before
analyzing results from instrumental variable (IV) estimation using panel data, we ﬁrst look
at scatter plots for a quick overview of the data. Figure 2.1 depicts scatter plots for real
exchange rate volatility against trade intensity (maximum) and trade intensity (average),
respectively for 91 currency pairs involving 14 countries over the periods 1980-2005. The
straight line is depicted by the Ordinary Least Squares (OLS) regression. As evidenced by
the OLS estimates reported, which are signiﬁcant at the 1 percent level for both measures,
a negative relationship between real exchange rate volatility and trade intensity begins to
emerge.
In case there is the issue of endogeneity, the ordinary least squares (OLS) regression
generally produces biased and inconsistent estimates. In order to control for the potential
endogeneity, we use the instrumental variable (IV) estimation approach. Speciﬁcally, we
use the distance between two countries as an instrument for trade intensity. The distance
between two countries is exogenous and not determined by exchange rate volatility, but it
is also an appropriate proxy variable for trade intensity. Table 2.2 presents a preliminary
instrumental variable (IV) estimation using panel data for the eﬀects of trade intensity on
real exchange rate volatility. Although preliminary, the negative association between trade
intensity and exchange rate volatility continues to appear. Both measures of trade intensity,

73

maximum and average, are negatively related with real exchange rate volatility. Besides this
main ﬁnding, we also ﬁnd that exchange rate volatility increases with the absolute value of
interest rate diﬀerentials, which is consistent with the view that carry trades—known for
their negative skewness or crash risk—lead to an increase in volatility of the exchange rates
between investment and funding currencies.

Robustness checks
In Table 2.3, we conduct a number of robustness checks for results from instrumental variable
(IV) estimation using panel data: (a) outliers truncated for the real exchange rate volatility
variable, (b) by subperiods: 1980-1992 and 1993-2005, (c) by Major vs. Minor, or “Exotic”,
currency pairs, and (d) by diﬀerent time windows: 3 year-window and 6 year-window. First,
in Table 2.3 (a), we truncate outliers of the dependent variable, which is real exchange rate
volatility by excluding all observations that are more than about two standard deviations
from the mean in any period t. This has little impact on the results, suggesting that they
are not primarily driven by outlier observations. Second, we divide the entire sample period
into two subperiods: 1980-1992 (a ﬁrst half of the entire sample period) and 1993-2005 (a
second half of the entire sample period). This division of the period makes no diﬀerence
to the main results, as reported in Table 2.3 (b). Third, we investigate whether our results
are diﬀerent for Major currency crosses, which add up to 42 out of our total of 91, and
Exotic currency crosses, which include the remaining 49 out of 91.7 This robustness test is
7

The most traded currency pairs in the foreign exchange market are called the Major
currency pairs. They involve the currencies such as Australian Dollar (AUD), Canadian
Dollar (CAD), Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Franc
(CHF), and US Dollar (USD). On the other hand, the Exotic currency pairs are deﬁned as
those pairs that are emerging economies rather than developed countries.

74

driven by potential concerns about volatility diﬀerences being driven by market liquidity,
which is greater for Major currency pairs. As can be seen from Table 2.3 (c), the results in
both subsamples are almost exactly equal to each other and to the overall results reported
in Table 2.2. Finally, we check to make sure our results are robust to a longer term than
1 year-window which is considered in the base case, 3 year-window and 6 year-window. As
evidenced by Table 2.3 (d), these diﬀerent time-windows do not at all aﬀect the coeﬃcients
on any of the other variables of interest. Overall, the negative relationship between trade
intensity and exchange rate volatility holds up well across the diﬀerent robustness tests.

2.5.2

Estimation results from ESTAR models

While the preliminary analyses have the advantage of simplicity, they fail to capture the
nonlinearity of exchange rates. In Table 2.4, we report estimation results from ESTAR
models as given by (2.6). Following Ter¨svirta (1994), the ESTAR models are estimated by
a
nonlinear least squares (NLS), with the starting values obtained from a grid search over γ and
c. The estimations are also implemented with the selected lag order p and delay parameter d
which are suggested by the PACF and the linearity tests results, respectively, for both high
and low trade intensity currency pairs. As explained above, regression results are consistent
with discussion by Taylor et al. (2001) which states that in Equation (2.6), while ρ ≥ 0 is
admissible, meaning that random walk or explosive dynamics are possible when deviations
from PPP are small, one must have ρ∗ < 0 and (ρ + ρ∗ ) < 0 for qt to be overall mean
reverting. The theory behind nonlinear mean reversion is related to transactions costs. As
deviations from PPP grow, an increasing number of trade ventures become proﬁtable in

75

spite of transaction costs. Trade-driven currency transactions intensify, and exert stronger
pressure steering the exchange rate back to the PPP level.
Details of residual diagnostic tests applied to the model are also reported in the last panel of
Table 2.4. LM test results show that the ESTAR model appears to capture all of the residual
autocorrelation for most currency pairs considered in this paper. The residual standard
deviations, denoted by σε and the sum of squared residuals (SSR) from the regression are
ˆ
also reported. The results for the test of no remaining nonlinearity in the residuals suggest
that the model selected is adequate as there is no evidence for remaining nonlinearity in the
residuals. Also, AIC, BIC and the sample size T are reported in the last three rows in Table
2.4.
Having estimated ESTAR models,8 we ﬁrst generate generalized impulse response functions
(GIs) as described above. Then, using the GIs, we calculate half-lives of deviations from PPP
to investigate the persistence of the shock to real exchange rates. In Table 2.5, the estimated
half-lives for real exchange rates (measured in months) are reported for high and low trade
intensity currency pairs, respectively. Typically, our estimates of the half-lives of deviations
from PPP for a given currency pair are higher the less intense the trade relationship between
two countries. More speciﬁcally, the average of half-lives for high trade intensity currency
pairs is greater than that for low trade intensity currency pairs by about 6.8 months, as
can be seen in Table 2.5. The t -statistic for the diﬀerence in means test is 2.11, and this
results in a rejection of the null hypothesis of no diﬀerence in means.9 Thus, the half-lives
8 The

estimated transition functions, plotted against time for high and low trade intensity
currency pairs are available from the authors.
9 Although trade is endogenous to the real exchange rate, the diﬀerences in trade intensity
between these two sets of country pairs very large and stable. In spite of dramatic movement
in real exchange rates throughout the sample period, trade intensity for all low-intensity

76

of deviations from PPP based on the estimations of the ESTAR models and the generated
GIs suggest that deviations from PPP are corrected faster for country pairs with relatively
more intense trade relationships.

2.5.3

Half-lives and government intervention

We also investigate whether these diﬀerences in volatility may be due to Central Bank
intervention in currency markets, or fear of ﬂoating, instead of trade. To investigate this, we
construct measures of oﬃcial intervention using volatility of reserves and interest rates as
proxies for intervention, as in Calvo and Reinhart (2002). We then examine whether there
is an association between the half-lives of deviations from PPP and government intervention
which is measured by two indicators. The bilateral exchange rates are reported with respect
to the US Dollar (USD), and with respect to the Euro (EUR) for the US Dollar (USD).10 We
denote the absolute value of the percent change in the exchange rate and foreign exchange
reserves by , ∆F/F , respectively. The absolute value of the change in interest rate is given by
∆i (= it − it−1 ). We denote some critical threshold by xc , and then estimate the probability
that the variable x falls within some prespeciﬁed bounds. We set xc at 2.5 percent, as in
Calvo and Reinhart (2002). The probability that the monthly exchange rate change falls
within the 2.5 percent band should be greater for currencies that are more intervened, or
less ﬂoating. The opposite should apply to changes in foreign exchange reserves, as the most
common form of intervention is precisely to buy or sell reserves. Similarly, volatile interest
rates are taken as evidence that monetary authorities use interest rate policy as a means
country pairs remain far below any high-intensity pair at all times.
10 The European currency unit (ECU) which was the precursor of the new single European
currency, the Euro (EUR) is used before the introduction of the Euro on January 1, 1999.

77

of stabilizing the exchange rate. Thus, the probability that interest rates change by 400
basis points (4 percent) or more on any given month should be greater for more intervened
currencies.
Table 2.6 presents evidence on the frequency distribution of monthly percent changes in
the exchange rate, foreign exchange reserves, and nominal money market interest rates for
diﬀerent exchange regimes. For example, as can be seen in the second column of Table 2.6,
for the United States, there is about 63.5 percent probability that the monthly USD/EUR
exchange rate change would fall within a 2.5 percent band. For USD/JPY, the probability
is slightly lower at 59.48 percent. To quantify a degree of government intervention, we use
a rank order for reserves and interest rates which is assigned 1 for most ﬂoating exchange
regimes, and 14 for least ﬂoating exchange regimes. We use an average value of two rank
orders assigned for each country, and when currency pairs are considered, we average the
ranks out.
When we compute intervention rankings for high versus low trade intensity currency pairs,
we obtain an average of 5.66 for high trade intensity currency pairs, and 8.91 for low trade
intensity pairs.11 This suggests that our half-life estimates are not mainly driven by government intervention. In other words, Central Bank intervention is unlikely to be the cause of
the faster convergence of exchange rates to their long run levels, since the degree of currency
intervention is typically lower for currency pairs in our high trade intensity group.

11 When

we use percents instead of rank orders, there is little diﬀerence between high and
low trade intensity currency pairs. The use of percents does not change our main results on
government intervention.
78

2.6
2.6.1

Application to carry trades
Deﬁnition of carry trade returns

Following Brunnermeier et al. (2008), we denote the excess return to a carry trade strategy
of an investment in the target currency ﬁnanced by borrowing in the funding currency by
ERt+h = (it − i∗ ) − ∆st+h
t

(2.11)

where the period h is the point where the investor shorts the investment currency, it is the
interest rate at time t for the investment currency, i∗ is the interest rate at time t for the
t
funding currency, st is the logarithm of the nominal exchange rate which is measured as the
price of the domestic currency in terms of the foreign currency, and the second term on the
left hand side, ∆st+h is a depreciation or an appreciation of the investment currency. Under
the assumption that uncovered interest rate parity (UIP) condition holds, there should be
no excess return to the carry trade strategy on average

Et (ERt+h ) = 0

(2.12)

Et (∆st+h ) = (it − i∗ )
t

(2.13)

or

where Et is the conditional expectations operator on a sigma ﬁeld of all relevant information
up to and including time t.
It implies that the interest rate diﬀerential should, on average, be equal to the future
expected exchange rate change. To oﬀset the positive interest rate diﬀerential, the nominal
exchange rate at time t+h, st+h should increase so that the investment currency depreciates,
79

or equivalently the funding currency appreciates. However, empirically UIP does not hold in
the sense that the investment currency appreciates, or the investment currency depreciates
less than the interest rate diﬀerential. In either case, it makes the carry trade strategy
proﬁtable, on average.

2.6.2

Portfolio Analysis

Conditioning carry trade strategies on trade intensity
In recent years, the strategy known as the carry trade has received growing attention, both
from investors and academic researchers. In its simplest, or na¨ form, the carry trade
ıve
consists of borrowing low interest rate currencies to invest in high interest rate currencies.
This carry trade is called na¨ because it is blind to fundamentals other than the interest
ıve
rate. It has been well documented that the carry trade is proﬁtable on average, given the
empirical failure of uncovered interest parity (UIP). However, the carry trade has also been
known to be subject to large crash risk, or negative skewness of returns. To mitigate this
risk, some authors have proposed diversiﬁcation (Burnside et al. (2007)), the use of options
(Burnside et al. (2011)), and conditioning on fundamentals. The latter strategy has been
proposed by Jord` and Taylor (2009), who show that the crash risk of the carry trade can be
a
substantially reduced by taking macroeconomic fundamentals into account, i.e., by following
a fundamentals-augmented carry trade strategy.
In the spirit of Jord` and Taylor (2009), we examine the usefulness of our ﬁndings on
a
trade intensity for carry trades. For the currencies in our sample over the period, January
1980 - December 2008, we implement a PPP-augmented carry trade strategy as follows. For

80

each currency cross, we compare a 15-year moving average of the real exchange rate to the
current real exchange rate, lagged by 9 months.12 The PPP-augmented carry trade strategy purchases currency A against currency B only if the interest rate diﬀerential between
currency A and currency B exceeds the diﬀerence between a median and minimum of all
the interest rates in our data set (also with currency A’s interest rate being greater than
currency B’s interest rate), and currency A is undervalued vis-`-vis currency B, according
a
to PPP (with the aforementioned 9 month lag). If one of these two conditions fails, currency A is not purchased against currency B. We use trade intensity to decide at what point
we consider a currency to be suﬃciently over- or undervalued. We take the ratio of the
9-month-lagged real exchange rate to the 15-year moving average of the real exchange rate,
and consider a currency overvalued if this ratio is greater than 1 + τ , where τ ranges from 0
to 2, in increments of 0.1. We also experiment with the inclusion/exclusion of a third condition, momentum, which speciﬁes that currency A is to be purchased only if it appreciated
against currency B in the previous month. Although momentum strategies have little or no
theoretical underpinnings, they are quite popular among traders.
In Table 2.7 (a) and (b), we report performance statistics for carry trade portfolios without
and with a momentum trading strategy, respectively over the entire sample period. In Table
2.7 (a) which has been implemented without a momentum trading strategy, for high trade
intensity currency pairs, the na¨ carry trade strategy yields an annualized return of -1.6
ıve
percent, with a standard deviation of 0.011, resulting in a Sharpe ratio equal to -0.121,
on a monthly basis. When we implement the PPP-augmented carry trade strategy with a
12 When

we use a 10-year moving average of the real exchange rate instead of a 15-year
moving average, the main results do not change substantially.

81

threshold τ of 0 percent, the Sharpe ratio increases up to 0.018 with the annualized return
and standard deviation being 0.4 percent and 0.020, respectively. This annualized return
refers only to months in which the strategy is active. For any given currency pair, there
are months in which the PPP-augmented strategy is inactive, because the high-interest rate
currency is not undervalued. A similar improvement is also observed for low trade intensity
currency pairs, as the Sharpe ratio increases from 0.031 for the na¨ strategy to 0.061 for
ıve
the PPP-augmented strategy. Likewise, in Table 2.7 (b) which has been implemented with
the addition of a momentum requirement, for high trade intensity currency pairs, the na¨
ıve
carry trade strategy yields an annualized return of 0.9 percent, with a standard deviation of
0.020, resulting in a Sharpe ratio equal to 0.039, on a monthly basis. When we implement
the PPP-augmented carry trade strategy with a threshold τ of 0 percent, the Sharpe ratio
increases up to 0.055 with the annualized return and standard deviation being 1.9 percent
and 0.029, respectively. A similar improvement is also observed for low trade intensity
currency pairs, as the Sharpe ratio increases from 0.110 for the na¨ strategy to 0.141 for
ıve
the PPP-augmented strategy. These gains in performance achieved when taking PPP into
account are consistent with Jord` and Taylor (2009).
a
Trade intensity begins to play a role as we raise the threshold τ . Figure 2.3, panels (a)
and (b), show how Sharpe ratios change as we increase the thresholds without and with
a momentum trading strategy, respectively. When we implement the strategy without a
momentum condition, for both high and low trade intensity currency pairs, the Sharpe ratio
is hump-shaped, peaking when τ equals 0.7 and 1.3, respectively and falling for higher levels
of τ . Similarly, when we implement the strategy with a momentum trading, the Sharpe
ratio peaks when τ equals 0.3 and 1.3, respectively and falling for higher levels of τ . For
82

high trade intensity currency pairs, as τ rises above 0.7 or 0.3 for each case, the number of
active months falls drastically, and the standard deviation rises, as the strategies are almost
never active. On the other hand, for low trade intensity currency pairs, deviations from PPP
above 70 or 30 percent are not rare, and Sharpe ratios continue to rise as τ rises above 0.7
or 0.3, and are highest when τ equals 130 percent. Figure 2.4, panels (a) and (b), show the
cumulative performance of fundamentals-augmented carry trade portfolios without and with
a momentum trading strategy, respectively over time, for various thresholds. Each line shows
the evolution of one dollar for a diﬀerent ‘overvaluation’ threshold over the entire sample
period. As the graphs show, returns accrue in a relatively smooth fashion. Although there
are some periods in which the strategies yield losses, the crashes that are typical of the na¨
ıve
carry trade are notoriously absent. That is, as in Jord` and Taylor (2009), the inclusion of
a
PPP fundamentals is eﬀective in reducing the negative skewness, or ‘Peso problem’ of the
simple carry trade.
Overall, these results suggest that conditioning on trade intensity may be a useful way
to ﬁne-tune fundamentals-augmented carry trade strategies. In particular, for high trade
intensity currency pairs, it is best to set the threshold for over/undervaluation at a lower
level than for low trade intensity pairs. These results ﬁt squarely with our main ﬁnding that
deviations from PPP have shorter half-lives for high trade intensity currency pairs.

2.7

Conclusion

In recent years, researchers interested in exchange rate volatility have devoted growing
amounts of attention to trading strategies that are unrelated to fundamentals, such as the

83

carry trades and momentum trades. This represents an important addition to the literature on exchange rates, which previously focused mostly on macroeconomic fundamentals.
The view that emerges from combining old with new insights is that, while fundamentals
drive exchange rates in the long run, short run speculative trading strategies may give rise
to substantial but temporary deviations of exchange rates from their long run fundamental
values.
This paper explores further the interaction between volatility and fundamentals by examining the role of trade intensity in the reversion of exchange rates to long-run equilibrium
values. Following recent literature on nonlinearity, we estimate an ESTAR model, which
allows the speed at which exchange rates converge to their long-run equilibrium to depend
on the size of these deviations. We ﬁnd estimates of the half-lives of deviations from PPP to
be higher the less intense the trade relationship between two countries. These results continue to hold as we perform a series of robustness tests. Moreover, exchange rate volatility
increases with the absolute value of interest rate diﬀerentials, which is consistent with the
notion that carry trades tend to increase volatility. We also verify that the faster convergence
to equilibrium values observed for high trade intensity pairs does not appear to be driven by
Central Bank intervention. Finally, we show that taking trade intensity into account may be
useful to ﬁne tune carry trade strategies that are sophisticated in the sense that they take
fundamentals into account, purchasing currencies only if they are undervalued according to
PPP. Speciﬁcally, the performance of these strategies improves if the threshold used to deﬁne
overvaluation or undervaluation is allowed to depend on trade intensity.
Several avenues for future work are worth pursuing. One is to provide further support for
the ﬁndings of this paper by providing more detailed evidence on the exchange rate impact
84

of trade-related currency transactions. Another avenue, on the theoretical front, would be to
build a model of exchange rate determination that combines speculative and trade-related
currency transactions.

85

Table 2.1. Trade intensity matrices
(a) Trade intensity (maximum) matrix
Aus.
Aus.
Can.
Den.
G.B.
Jap.
Kor.
Mex.
N.Z.
Nor.
Sin.
Swe.
Swi.
Tur.
U.S

0.028
0.011
0.091
0.346
0.077
0.003
0.339
0.004
0.072
0.019
0.022
0.016
0.254

Can.
0.028
0.015
0.051
0.052
0.033
0.020
0.024
0.044
0.012
0.023
0.032
0.025
0.877

Den. G.B.
0.011 0.091
0.015 0.051
0.268
0.268
0.084 0.113
0.018 0.041
0.004 0.014
0.005 0.107
0.155 0.361
0.011 0.070
0.232 0.257
0.051 0.241
0.021 0.242
0.140 0.401

Jap. Kor. Mex.
0.346 0.077 0.003
0.052 0.033 0.020
0.084 0.018 0.004
0.113 0.041 0.014
0.353 0.051
0.353
0.011
0.051 0.011
0.214 0.039 0.008
0.049 0.017 0.002
0.315 0.077 0.005
0.067 0.016 0.008
0.134 0.027 0.016
0.099 0.045 0.003
0.560 0.421 0.889

N.Z.
0.339
0.024
0.005
0.107
0.214
0.039
0.008
0.002
0.037
0.009
0.008
0.003
0.206

Nor.
0.004
0.044
0.155
0.361
0.049
0.017
0.002
0.002

Sin.
0.072
0.012
0.011
0.070
0.315
0.077
0.005
0.037
0.010

Swe.
0.019
0.023
0.232
0.257
0.067
0.016
0.008
0.009
0.265
0.011

Swi.
0.022
0.032
0.051
0.241
0.134
0.027
0.016
0.008
0.017
0.027
0.061

0.010
0.265 0.011
0.017 0.027 0.061
0.014 0.015 0.045 0.099
0.109 0.402 0.199 0.355

Tur.
0.016
0.025
0.021
0.242
0.099
0.045
0.003
0.003
0.014
0.015
0.045
0.099

U.S.
0.254
0.877
0.140
0.401
0.560
0.421
0.889
0.206
0.109
0.402
0.199
0.355
0.373

0.373

Note. Trade intensity (maximum) is calculated as an average value over the sample period, 1980-2005, using
Equation (2.3). Betts and Kehoe (2008) use this measure of trade intensity in the paper.

86

Table 2.1. Trade intensity matrices (continued)
(b) Trade intensity (average) matrix
Aus.
Aus.
Can.
Den.
G.B.
Jap.
Kor.
Mex.
N.Z.
Nor.
Sin.
Swe.
Swi.
Tur.
U.S

0.017
0.008
0.064
0.209
0.061
0.002
0.214
0.004
0.071
0.017
0.018
0.010
0.138

Can.
0.017
0.008
0.039
0.051
0.022
0.014
0.013
0.025
0.007
0.013
0.018
0.013
0.620

Den. G.B.
0.008 0.064
0.008 0.039
0.160
0.160
0.046 0.085
0.012 0.034
0.002 0.012
0.004 0.059
0.136 0.228
0.008 0.050
0.184 0.172
0.045 0.152
0.015 0.131
0.073 0.243

Jap. Kor. Mex.
0.209 0.062 0.002
0.051 0.022 0.014
0.046 0.012 0.002
0.085 0.034 0.012
0.236 0.034
0.236
0.010
0.034 0.010
0.113 0.022 0.005
0.028 0.012 0.001
0.191 0.064 0.004
0.039 0.012 0.006
0.076 0.019 0.011
0.051 0.025 0.002
0.398 0.239 0.518

N.Z.
0.214
0.013
0.004
0.059
0.113
0.022
0.005
0.001
0.024
0.006
0.006
0.003
0.105

Nor.
0.004
0.025
0.136
0.228
0.028
0.012
0.001
0.001

Sin.
0.071
0.007
0.008
0.050
0.191
0.064
0.004
0.024
0.008

Swe.
0.017
0.013
0.184
0.172
0.039
0.012
0.006
0.006
0.235
0.010

Swi.
0.018
0.018
0.045
0.152
0.076
0.019
0.011
0.006
0.017
0.021
0.054

0.008
0.235 0.010
0.017 0.021 0.054
0.009 0.009 0.028 0.063
0.058 0.219 0.107 0.187

Tur.
0.010
0.013
0.015
0.131
0.051
0.025
0.002
0.003
0.009
0.009
0.028
0.063

U.S.
0.138
0.620
0.073
0.243
0.398
0.239
0.518
0.105
0.058
0.219
0.107
0.187
0.190

0.190

Note. Trade intensity (average) is calculated as an average value over the sample period, 1980-2005, using
Equation (2.4). This is an alternative measure to Trade intensity (maximum) in Betts and Kehoe (2008).

87

Table 2.2. Eﬀects of trade intensity on real exchange rate volatility - IV estimation
[1]

[2]

Real exchange rate volatility at time t-1

Trade intensity (maximum)

-0.054
(0.007)

Trade intensity (average)

[3]
0.123
(0.021)

[4]
0.123
(0.021)

-0.049
(0.007)
-0.077
(0.010)

-0.070
(0.006)

Interest rate diﬀerential in an absolute value

0.033
(0.004)

0.033
(0.004)

0.034
(0.005)

0.033
(0.005)

Intercept

0.045
(0.003)

0.045
(0.003)

0.039
(0.003)

0.039
(0.003)

2366

2366

2275

2275

No. of observations

Note. Results from instrumental variable estimation using panel data with country
ﬁxed eﬀects are reported. The distance between two countries (in logs) is used as an
instrument to estimate the relationship between trade intensity and real exchange
rate volatility. The sample period is from January 1980 to December 2005, and all of
91 currency pairs involving 14 countries are included. The dependent variable is real
exchange rate volatility. Standard errors are reported in parentheses below the corresponding coeﬃcients.

88

Table 2.3. Eﬀects of trade intensity on real exchange rate volatility - Robustness checks
(a) By truncating outliers
[1]

[2]

Real exchange rate volatility at time t-1

Trade intensity (maximum)

-0.058
(0.005)

Trade intensity (average)

[3]
0.140
(0.022)

[4]
0.141
(0.022)

-0.052
(0.005)
-0.084
(0.007)

-0.075
(0.007)

Interest rate diﬀerential in an absolute value

0.014
(0.003)

0.014
(0.003)

0.019
(0.003)

0.019
(0.003)

Intercept

0.038
(0.002)

0.039
(0.002)

0.052
(0.003)

0.052
(0.003)

2156

2156

2065

2065

No. of observations

Note. Results from instrumental variable estimation using panel data with country
ﬁxed eﬀects are reported. The distance between two countries (in logs) is used as an
instrument to estimate the relationship between trade intensity and real exchange
rate volatility. The sample period is from January 1980 to December 2005, and all of
91 currency pairs involving 14 countries are included. We truncate outliers of the real
exchange rate volatility variable. The dependent variable is real exchange rate volatility. Standard errors are reported in parentheses below the corresponding coeﬃcients.

89

Table 2.3. Eﬀects of trade intensity on real exchange rate volatility - Robustness checks (continued)
(b) By subperiods

Real exchange rate volatility at time t-1

Trade intensity (maximum)

Robustness checks
Subperiod for 1980-1992
[1]
[2]
[3]
[4]
0.113
0.114
(0.032) (0.032)
-0.062
(0.010)

Trade intensity (average)

-0.059
(0.011)
-0.092
(0.015)

Subperiod for 1993-2005
[1]
[2]
[3]
[4]
0.103
0.103
(0.030) (0.030)
-0.045
(0.009)

-0.088
(0.017)

-0.038
(0.009)
-0.063
(0.012)

-0.054
(0.013)

Interest rate diﬀerential in an abs. value

0.017
(0.007)

0.016
(0.007)

0.011
(0.008)

0.010
(0.008)

0.044
(0.006)

0.044
(0.006)

0.044
(0.006)

0.043
(0.006)

Intercept

0.041
(0.005)

0.042
(0.005)

0.054
(0.005)

0.054
(0.005)

0.037
(0.004)

0.037
(0.004)

0.033
(0.004)

0.033
(0.004)

1183

1183

1092

1092

1183

1183

1092

1092

No. of observations

Note. Results from instrumental variable estimation using panel data with country ﬁxed eﬀects are reported. The
distance between two countries (in logs) is used as an instrument to estimate the relationship between trade intensity and real exchange rate volatility. The sample period is from January 1980 to December 2005, and all of 91 currency pairs involving 14 countries are included. The entire sample period is divided into two subperiods: 1980-1992
(a ﬁrst half) and 1993-2005 (a second half). The dependent variable is real exchange rate volatility. Standard errors
are reported in parentheses below the corresponding coeﬃcients.
90

Table 2.3. Eﬀects of trade intensity on real exchange rate volatility - Robustness checks (continued)
(c) By Major vs. Exotic currency pairs

Real exchange rate volatility at time t-1

Trade intensity (maximum)

Robustness checks
42 Major currency pairs
[1]
[2]
[3]
[4]
0.120
0.117
(0.031) (0.032)
-0.049
(0.006)

Trade intensity (average)

-0.043
(0.007)
-0.068
(0.009)

49 Exotic currency pairs
[1]
[2]
[3]
[4]
0.093
0.093
(0.029) (0.028)
-0.048
(0.013)

-0.060
(0.009)

-0.047
(0.013)
-0.075
(0.020)

-0.073
(0.020)

Interest rate diﬀerential in an abs. value

0.190
(0.022)

0.190
(0.022)

0.176
(0.024)

0.175
(0.024)

0.030
(0.005)

0.030
(0.005)

0.032
(0.005)

0.031
(0.005)

Intercept

0.046
(0.003)

0.045
(0.003)

0.041
(0.004)

0.040
(0.004)

0.051
(0.007)

0.052
(0.007)

0.065
(0.009)

0.065
(0.009)

1092

1092

1050

1050

1274

1274

1225

1225

No. of observations

Note. Results from instrumental variable estimation using panel data with country ﬁxed eﬀects are reported. The
distance between two countries (in logs) is used as an instrument to estimate the relationship between trade intensity and real exchange rate volatility. The sample period is from January 1980 to December 2005, and 91 currency
pairs are divided into 42 Majors and 49 Exotics. The dependent variable is real exchange rate volatility. Standard
errors are reported in parentheses below the corresponding coeﬃcients.

91

Table 2.3. Eﬀects of trade intensity on real exchange rate volatility - Robustness checks (continued)
(d) By diﬀerent time windows

Real exchange rate volatility at time t-1

Trade intensity (maximum)

Robustness checks
3-year window
[1]
[2]
[3]
0.017
(0.039)
-0.107
(0.014)

Trade intensity (average)

[4]
0.017
(0.039)

-0.098
(0.016)
-0.154
(0.021)

[1]

6-year window
[2]
[3]
0.072
(0.060)

-0.098
(0.020)
-0.141
(0.023)

[4]
0.069
(0.060)

-0.070
(0.022)
-0.140
(0.029)

-0.101
(0.032)

Interest rate diﬀerential in an abs. value

0.062
(0.010)

0.061
(0.010)

0.073
(0.011)

0.072
(0.011)

0.108
(0.017)

0.106
(0.016)

0.113
(0.016)

0.112
(0.016)

Intercept

0.072
(0.007)

0.072
(0.007)

0.076
(0.009)

0.078
(0.008)

0.070
(0.009)

0.071
(0.009)

0.052
(0.010)

0.053
(0.010)

819

819

728

728

455

455

364

364

No. of observations

Note. Results from instrumental variable estimation using panel data with country ﬁxed eﬀects are reported. The
distance between two countries (in logs) is used as an instrument to estimate the relationship between trade intensity and real exchange rate volatility. The sample period is from January 1980 to December 2005, and diﬀerent time
windows are considered to investigate a longer term: 3-year window and 6-year window. The dependent variable is
real exchange rate volatility. Standard errors are reported in parentheses below the corresponding coeﬃcients.

92

Table 2.4. Estimation results from ESTAR models
(a) 35 highest TI currency pairs
USD/CAD
p
8
d
1
Linear part
ρ
0.002
(0.129)
β1
0.368
(0.173)
β2
0.367
(0.186)
β3
-0.132
(0.096)
β4
0.670
(0.198)
β5
0.005
(0.154)
β6
-0.288
(0.189)
β7
0.846
(0.216)
β8
β9
β10
Nonlinear part
ρ
-0.018
(0.128)
∗
β1
-0.362
(0.186)
∗
β2
-0.384
(0.199)
∗
β3
0.133
(0.125)
∗
β4
-0.708
(0.215)

USD/MXN
11
3

USD/JPY
2
5

USD/GBP
1
5

USD/KRW
10
2

KRW/JPY
4
3

0.080
(0.547)
-1.196
(0.674)
-0.548
(0.612)
-0.237
(0.274)
-0.332
(0.228)
-0.147
(0.185)
-0.296
(0.240)
-0.190
(0.293)
-0.010
(0.253)
0.447
(0.247)
0.918
(0.069)

0.139
(0.132)
-0.222
(0.250)

-0.027
(0.047)

0.062
(0.048)
1.353
(0.250)
-0.094
(0.175)
0.488
(0.196)
-0.510
(0.205)
0.495
(0.235)
-0.577
(0.246)
0.015
(0.175)
0.201
(0.258)
0.574
(0.232)

0.096
(0.086)
0.435
(0.203)
0.181
(0.186)
0.137
(0.155)

-0.125
(0.550)
1.201
(0.671)
0.554
(0.612)
0.309
(0.288)
0.252
(0.256)

-0.166
(0.132)
0.355
(0.263)

-0.011
(0.054)

-0.113
(0.065)
-1.830
(0.293)
0.110
(0.206)
-0.591
(0.220)
0.320
(0.264)

-0.131
(0.089)
-0.525
(0.254)
-0.139
(0.225)
-0.347
(0.202)

93

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs

∗
β5
∗
β6
∗
β7

USD/CAD
-0.029
(0.175)
0.242
(0.216)
-0.845
(0.243)

∗
β8
∗
β9
∗
β10

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

41.509
(1.073)
-0.735
(0.002)
0.017
1.043
(0.385)
3.424
(0.001)
0.632
0.098
-8.032
-7.807
348

USD/MXN
0.180
(0.189)
0.255
(0.250)
0.188
(0.297)
0.017
(0.257)
-0.393
(0.256)
-0.845
(0.089)
500.000
(3.058)
-3.075
(0.0001)
0.045
0.852
(0.493)
0.680
(0.709)
0.152
0.686
-6.039
-5.743
348

USD/JPY

USD/GBP

USD/KRW
-0.539
(0.253)
0.755
(0.267)
-0.161
(0.227)
-0.224
(0.329)
-0.484
(0.272)

KRW/JPY

20.795
(1.379)
-5.545
(0.009)
0.032
1.043
(0.385)
0.937
(0.486)
0.767
0.358
-6.813
-6.723
348

10.444
(1.256)
-0.166
(0.016)
0.030
2.332
(0.056)
1.665
(0.106)
0.183
0.313
-6.959
-6.892
348

8.534
(0.177)
-7.449
(0.005)
0.022
8.674
(0.001)
5.985
(0.001)
0.194
0.163
-7.490
-7.218
348

10.753
(0.634)
2.038
(0.015)
0.040
4.493
(0.002)
2.757
(0.006)
0.427
0.546
-6.367
-6.232
348

Note. Currency pairs are listed based on trade intensity. Heteroscedasticity-consistent standard errors are reported in parentheses below the corresponding coeﬃcient.
σε denotes the residual standard deviation. LM(4) and LM(8) denote the F variant
ˆ
of the LM test of no remaining autocorrelation in the residuals up to and including
lag 4 and lag 8, respectively. The p-values are reported in parentheses below the
corresponding values of the test statistics. pRNL is the p-value for the test of no
remaining nonlinearity in the residuals. SSR is the sum of squared residuals of the
regression from the estimated ESTAR models. AIC and BIC are the Akaike and
Bayesian information criteria, respectively. T refers to the sample size.

94

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
SEK/NOK
p
1
d
2
Linear part
ρ
0.239
(0.141)
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
Nonlinear part
ρ
-0.267
(0.141)
∗
β1
∗
β2

GBP/NOK
12
3

USD/SGD
1
6

NZD/AUD
4
6

JPY/AUD
12
2

SGD/JPY
1
6

-0.028
(0.043)
0.052
(0.100)
0.127
(0.105)
-0.057
(0.104)
-0.029
(0.080)
-0.151
(0.100)
-0.066
(0.091)
0.025
(0.092)
0.073
(0.078)
-0.031
(0.086)
0.072
(0.096)
0.112
(0.089)

0.360
(0.083)

-0.062
(0.093)
-0.010
(0.200)
-0.040
(0.165)
0.223
(0.187)

-0.042
(0.027)
0.211
(0.091)
-0.055
(0.078)
0.117
(0.073)
-0.194
(0.093)
0.226
(0.097)
-0.128
(0.090)
-0.015
(0.076)
0.022
(0.082)
-0.050
(0.080)
-0.015
(0.081)
0.206
(0.092)

0.119
(0.096)

-0.048
(0.086)
-0.275
(0.245)
-0.527
(0.257)

-0.372
(0.084)

-0.057
(0.111)
0.004
(0.243)
0.182
(0.204)

-0.003
(0.043)
-0.194
(0.236)
0.073
(0.210)

-0.149
(0.097)

95

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
SEK/NOK
∗
β3
∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10
∗
β11

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

50.519
(1.302)
0.057
(0.002)
0.019
0.503
(0.733)
0.657
(0.729)
0.701
0.123
-7.895
-7.827
348

GBP/NOK
-0.036
(0.252)
-0.011
(0.241)
0.484
(0.276)
0.255
(0.252)
0.280
(0.225)
-0.085
(0.194)
-0.092
(0.212)
-0.263
(0.230)
-0.018
(0.220)
4.166
(0.221)
-2.369
(0.021)
0.023
0.322
(0.863)
0.452
(0.889)
0.854
0.179
-7.367
-7.049
348

USD/SGD

NZD/AUD
-0.133
(0.214)

371.426
(25.787)
-0.898
(0.001)
0.015
5.320
(0.001)
2.694
(0.007)
0.519
0.079
-8.337
-8.270
348

6.369
(1.046)
-1.484
(0.036)
0.027
2.080
(0.083)
1.110
(0.356)
0.771
0.241
-7.183
-7.048
348

96

JPY/AUD
0.086
(0.158)
0.272
(0.200)
-0.654
(0.240)
0.283
(0.218)
0.002
(0.193)
0.339
(0.197)
0.275
(0.212)
0.025
(0.204)
-0.273
(0.239)
1.195
(0.363)
5.102
(0.116)
0.045
0.345
(0.847)
0.540
(0.826)
0.840
0.682
-6.030
-5.711
348

SGD/JPY

13.220
(1.149)
-4.488
(0.013)
0.029
1.063
(0.375)
1.211
(0.292)
0.995
0.281
-7.068
-7.000
348

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
USD/TRY
p
4
d
4
Linear part
ρ
0.208
(0.199)
β1
0.355
(0.296)
β2
-0.095
(0.274)
β3
-0.069
(0.204)
β4
β5
β6
β7
β8
β9
β10
β11
Nonlinear part
ρ
-0.229
(0.200)
∗
β1
-0.348
(0.324)
∗
β2
0.057
(0.302)

SEK/DKK
12
1

USD/CHF
12
2

GBP/SEK
1
5

GBP/DKK
4
6

GBP/CHF
1
4

0.004
(0.015)
0.001
(0.080)
0.120
(0.070)
0.016
(0.111)
-0.031
(0.083)
-0.105
(0.097)
-0.050
(0.064)
0.003
(0.063)
0.090
(0.093)
0.074
(0.117)
-0.011
(0.068)
-0.005
(0.079)

0.109
(0.088)
-0.112
(0.130)
0.069
(0.096)
-0.141
(0.119)
-0.043
(0.093)
0.098
(0.099)
-0.105
(0.097)
0.196
(0.094)
-0.047
(0.099)
0.051
(0.094)
0.028
(0.083)
0.248
(0.091)

-0.053
(0.049)

0.050
(0.119)
-0.875
(0.301)
-0.278
(0.250)
-0.590
(0.441)

0.162
(0.246)

-0.282
(4.097)
5.365
(77.248)
-5.339
(80.042)

-0.150
(0.091)
0.299
(0.158)
-0.155
(0.143)

-0.075
(0.081)

-0.068
(0.120)
1.093
(0.307)
0.310
(0.263)

-0.185
(0.248)

97

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs

∗
β3

USD/TRY
0.012
(0.212)

∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10
∗
β11

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

39.991
(0.939)
-1.212
(0.004)
0.040
1.945
(0.103)
1.626
(0.117)
0.751
0.558
-6.345
-6.210
348

SEK/DKK
2.995
(43.880)
-3.506
(48.676)
3.513
(52.839)
2.994
(43.558)
-1.375
(20.813)
-5.227
(75.456)
-6.763
(97.367)
3.328
(48.932)
-2.714
(41.236)
0.135
(0.185)
0.104
(18.662)
0.020
8.488
(0.001)
6.634
(0.001)
0.874
0.128
-7.704
-7.385
348

USD/CHF
0.336
(0.153)
0.031
(0.164)
-0.127
(0.148)
0.128
(0.162)
-0.174
(0.157)
0.044
(0.153)
0.091
(0.151)
-0.138
(0.146)
-0.184
(0.145)
13.537
(0.635)
-0.971
(0.007)
0.032
0.892
(0.469)
0.749
(0.648)
0.962
0.342
-6.719
-6.401
348

98

GBP/SEK

GBP/DKK
0.721
(0.446)

GBP/CHF

3.507
(0.438)
-2.285
(0.034)
0.026
0.620
(0.649)
0.594
(0.783)
0.975
0.224
-7.294
-7.227
348

500.000
(4.587)
-2.414
(0.0001)
0.024
2.992
(0.019)
1.787
(0.079)
0.401
0.189
-7.430
-7.295
348

500.000
(9.712)
-0.782
(0.0004)
0.028
1.725
(0.144)
1.852
(0.067)
0.096
0.269
-7.111
-7.043
348

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
USD/AUD
p
1
d
2
Linear part
ρ
0.144
(0.101)
β1

NOK/DKK
1
4

GBP/TRY
1
2

NZD/JPY
1
5

USD/SEK
8
5

USD/NZD
8
5

0.073
(0.041)

0.856
(0.477)

0.173
(0.123)

-0.033
(0.028)
-0.026
(0.114)
0.010
(0.082)
0.040
(0.100)
0.157
(0.112)
0.144
(0.083)
0.045
(0.076)
0.082
(0.071)

-0.033
(0.060)
0.047
(0.113)
0.102
(0.110)
0.073
(0.104)
-0.167
(0.110)
-0.181
(0.152)
0.187
(0.124)
0.187
(0.111)

-0.138
(0.041)

-0.901
(0.477)

-0.207
(0.122)

-0.054
(0.093)
0.561
(0.471)
-0.195
(0.187)
0.329
(0.280)
-0.442
(0.381)
-0.185
(0.306)
-0.332
(0.344)

-0.058
(0.077)
0.024
(0.168)
-0.131
(0.167)
0.219
(0.172)
0.273
(0.156)
0.396
(0.189)
-0.179
(0.177)

β2
β3
β4
β5
β6
β7
Nonlinear part
ρ
-0.182
(0.100)
∗
β1
∗
β2
∗
β3
∗
β4
∗
β5
∗
β6

99

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
USD/AUD

NOK/DKK

GBP/TRY

NZD/JPY

23.338
(1.692)
-0.624
(0.006)
0.032
0.998
(0.409)
1.060
(0.391)
0.758
0.339
-6.880
-6.812
348

5.658
(0.730)
0.038
(0.016)
0.017
1.227
(0.299)
1.388
(0.201)
0.957
0.098
-8.116
-8.049
348

500.000
(5.087)
-1.089
(0.0003)
0.046
2.027
(0.090)
1.345
(0.220)
0.638
0.732
-6.109
-6.042
348

277.480
(3.862)
-6.581
(0.001)
0.040
1.329
(0.259)
1.606
(0.122)
0.674
0.553
-6.388
-6.321
348

∗
β7

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

100

USD/SEK
0.047
(0.202)
0.997
(0.823)
-2.808
(0.262)
0.031
1.573
(0.181)
1.507
(0.154)
0.717
0.319
-6.852
-6.626
348

USD/NZD
-0.077
(0.158)
4.140
(0.330)
0.828
(0.026)
0.033
0.444
(0.777)
2.214
(0.026)
0.815
0.365
-6.717
-6.491
348

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
GBP/JPY
p
2
d
3
Linear part
ρ
0.461
(0.155)
β1
-0.236
(0.363)
β2

CHF/JPY
1
2

USD/DKK
4
6

SGD/AUD
1
2

SGD/KRW
10
2

GBP/AUD
1
2

0.335
(0.141)

0.038
(0.054)
-0.212
(0.167)
0.214
(0.184)
0.010
(0.142)

0.078
(0.075)

0.029
(0.038)
0.710
(0.307)
0.015
(0.148)
-0.130
(0.118)
-0.190
(0.111)
0.187
(0.091)
-0.124
(0.117)
0.133
(0.096)
-0.079
(0.110)
0.247
(0.101)

0.537
(0.302)

-0.378
(0.142)

-0.080
(0.052)
0.385
(0.181)
-0.191
(0.203)
0.056
(0.170)

-0.171
(0.068)

-0.273
(0.089)
-1.690
(0.432)
0.088
(0.324)
0.450
(0.181)
0.200
(0.171)

-0.570
(0.301)

β3
β4
β5
β6
β7
β8
β9
Nonlinear part
ρ
-0.489
(0.155)
∗
β1
0.369
(0.369)
∗
β2
∗
β3
∗
β4

101

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
GBP/JPY

CHF/JPY

USD/DKK

SGD/AUD

120.424
(3.370)
-5.347
(0.001)
0.034
1.239
(0.294)
0.880
(0.534)
0.423
0.397
-6.709
-6.619
348

62.657
(1.524)
-4.265
(0.001)
0.031
1.238
(0.295)
0.951
(0.474)
0.574
0.320
-6.936
-6.869
348

8.003
(0.795)
-2.788
(0.020)
0.031
0.869
(0.483)
0.813
(0.591)
0.818
0.318
-6.908
-6.773
348

4.715
(1.068)
0.473
(0.032)
0.029
1.230
(0.298)
0.776
(0.625)
0.975
0.295
-7.018
-6.950
348

∗
β5
∗
β6
∗
β7
∗
β8
∗
β9

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

102

SGD/KRW
-0.278
(0.172)
0.544
(0.138)
-0.323
(0.158)
0.290
(0.150)
-0.490
(0.177)
2.066
(0.084)
-6.434
(0.036)
0.024
8.436
(0.001)
6.443
(0.001)
0.375
0.195
-7.314
-7.042
348

GBP/AUD

121.028
(2.097)
-0.499
(0.001)
0.036
0.594
(0.667)
0.814
(0.591)
0.999
0.443
-6.612
-6.544
348

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
TRY/CHF
p
1
d
3
Linear part
ρ
0.297
(0.162)
β1
β2
β3
β4
β5
β6
β7
β8
β9
Nonlinear part
ρ
-0.328
(0.161)
∗
β1
∗
β2
∗
β3
∗
β4

KRW/AUD
10
2

GBP/NZD
1
1

USD/NOK
1
1

CHF/SEK
1
4

0.073
(0.105)
0.559
(0.378)
-0.095
(0.120)
-0.169
(0.119)
0.085
(0.135)
-0.161
(0.126)
-0.030
(0.114)
0.010
(0.105)
0.006
(0.105)
0.161
(0.134)

0.133
(0.257)

0.253
(0.344)

0.093
(0.051)

-0.196
(0.121)
-0.737
(0.402)
0.263
(0.165)
0.184
(0.202)
-0.254
(0.193)

-0.198
(0.254)

-0.285
(0.343)

-0.140
(0.051)

103

Table 2.4. Estimation results from ESTAR models (continued)
(a) 35 highest TI currency pairs
TRY/CHF
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

58.695
(2.022)
0.287
(0.003)
0.048
1.310
(0.266)
1.349
(0.218)
0.412
0.793
-6.028
-5.961
348

KRW/AUD
0.222
(0.156)
0.149
(0.161)
-0.142
(0.205)
-0.015
(0.180)
-0.051
(0.184)
13.780
(0.372)
6.776
(0.005)
0.034
4.248
(0.002)
2.187
(0.028)
0.121
0.401
-6.592
-6.320
348

GBP/NZD

USD/NOK

CHF/SEK

21.151
(2.140)
1.137
(0.010)
0.036
0.641
(0.634)
0.598
(0.780)
0.912
0.436
-6.627
-6.560
348

33.520
(1.540)
-2.730
(0.005)
0.030
1.825
(0.124)
1.393
(0.198)
0.629
0.308
-6.974
-6.906
348

8.679
(0.721)
-1.650
(0.011)
0.025
1.422
(0.226)
1.405
(0.193)
0.132
0.208
-7.368
-7.300
348

104

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
CHF/NOK
p
12
d
5
Linear part
ρ
0.362
(0.850)
β1
-0.257
(0.875)
β2
0.153
(0.925)
β3
-0.146
(0.820)
β4
-0.450
(0.806)
β5
-1.367
(0.406)
β6
0.149
(0.367)
β7
0.284
(0.457)
β8
-0.173
(0.247)
β9
0.392
(0.282)
β10
-0.585
(0.401)
β11
0.681
(0.207)
Nonlinear part
ρ
-0.398
(0.851)
∗
β1
0.261
(0.878)
∗
β2
-0.147
(0.859)

CAD/AUD
1
3

TRY/DKK
1
4

MXN/CAD
11
2

SEK/CAD
1
5

TRY/CAD
1
4

0.383
(0.255)

0.517
(0.149)

0.129
(0.912)
-0.390
(1.032)
0.940
(0.317)
-0.681
(0.340)
-0.293
(0.317)
-0.396
(0.268)
0.696
(0.312)
-0.164
(0.346)
0.389
(0.239)
-0.633
(0.346)
1.217
(0.093)

-0.031
(0.068)

0.522
(0.292)

-0.456
(0.255)

-0.553
(0.150)

-0.158
(0.913)
0.364
(1.034)
-0.942
(0.317)

-0.020
(0.071)

-0.542
(0.292)

105

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs

∗
β3
∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10
∗
β11

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

CHF/NOK
0.160
(0.795)
0.449
(0.812)
1.301
(0.409)
-0.199
(0.372)
-0.283
(0.468)
0.145
(0.258)
-0.376
(0.292)
0.647
(0.400)
-0.656
(0.219)
500.000
(1.462)
-1.563
(0.0001)
0.020
1.280
(0.278)
1.256
(0.266)
0.650
0.132
-7.674
-7.355
348

CAD/AUD

TRY/DKK

MXN/CAD
0.775
(0.351)
0.235
(0.338)
0.428
(0.269)
-0.731
(0.318)
0.160
(0.349)
-0.348
(0.243)
0.700
(0.347)
-1.187
(0.103)

SEK/CAD

TRY/CAD

500.000
(3.892)
0.237
(0.0002)
0.027
2.255
(0.063)
1.897
(0.060)
0.080
0.248
-7.193
-7.125
348

238.526
(3.674)
-1.191
(0.001)
0.043
3.309
(0.011)
2.575
(0.010)
0.654
0.620
-6.275
-6.207
348

500.000
(3.204)
2.203
(0.0002)
0.046
1.182
(0.319)
0.861
(0.550)
0.403
0.696
-6.024
-5.729
348

26.375
(2.196)
1.606
(0.008)
0.031
2.168
(0.072)
2.362
(0.018)
0.484
0.336
-6.886
-6.819
348

348.676
(3.892)
0.364
(0.0004)
0.040
2.073
(0.084)
1.549
(0.140)
0.836
0.553
-6.388
-6.321
348

Note. As for Table 2.4 (a).

106

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
NZD/CAD
p
4
d
6
Linear part
ρ
0.012
(0.156)
β1
0.577
(0.408)
β2
-0.048
(0.203)
β3
-0.332
(0.370)
β4
β5
β6
β7
β8
β9

SEK/KRW
10
2

NOK/KRW
10
6

GBP/MXN
11
3

KRW/DKK
1
2

CHF/MXN
11
4

0.050
(0.152)
-0.422
(0.230)
-0.097
(0.152)
0.264
(0.187)
-0.293
(0.137)
0.220
(0.165)
0.059
(0.176)
0.129
(0.146)
-0.160
(0.205)
0.189
(0.136)

0.057
(0.729)
0.914
(0.789)
0.209
(0.762)
0.728
(0.804)
-0.056
(0.658)
-0.550
(0.742)
-0.640
(0.316)
-0.891
(0.228)
-0.997
(0.413)
0.303
(0.268)

0.045
(0.567)
-0.618
(0.806)
-0.193
(0.566)
1.437
(0.456)
0.690
(0.361)
-0.183
(0.240)
0.144
(0.251)
-0.386
(0.427)
0.210
(0.378)
0.154
(0.412)
1.307
(0.143)

0.520
(0.292)

0.214
(1.147)
-0.909
(1.165)
-1.365
(1.681)
-0.384
(1.108)
0.354
(0.340)
0.874
(0.477)
0.496
(0.456)
-0.642
(0.600)
1.193
(1.001)
2.427
(0.630)
1.752
(0.342)

-0.740
(0.766)
-0.152
(0.153)
0.707
(0.278)
0.311
(0.197)

-0.144
(0.732)
-0.981
(0.797)
-0.086
(0.775)
-0.804
(0.803)

-0.091
(0.570)
0.726
(0.819)
0.214
(0.573)
-1.380
(0.462)

0.535
(0.290)

-0.264
(1.152)
0.984
(1.157)
1.392
(1.685)
0.494
(1.118)

β10
Nonlinear part
ρ
-0.034
(0.157)
∗
β1
-0.637
(0.408)
∗
β2
0.076
(0.240)
∗
β3
0.479
(0.376)

107

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
NZD/CAD
∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

165.502
(3.233)
-1.887
(0.001)
0.032
0.857
(0.490)
1.048
(0.400)
0.901
0.356
-6.794
-6.659
348

SEK/KRW
-0.247
(0.223)
0.362
(0.159)
-0.218
(0.196)
-0.035
(0.212)
-0.211
(0.188)
0.342
(0.224)
-0.150
(0.167)
26.083
(0.677)
-5.006
(0.002)
0.039
0.823
(0.511)
1.030
(0.413)
0.099
0.506
-6.360
-6.088
348

NOK/KRW
-0.023
(0.659)
0.633
(0.748)
0.730
(0.330)
0.852
(0.241)
1.010
(0.416)
-0.111
(0.282)

286.582
(2.334)
-4.757
(0.0002)
0.035
3.911
(0.004)
2.634
(0.008)
0.295
0.402
-6.590
-6.317
348

108

GBP/MXN
-0.697
(0.374)
0.220
(0.244)
-0.251
(0.258)
0.394
(0.433)
-0.190
(0.381)
-0.100
(0.419)
-1.320
(0.149)
56.800
(1.139)
-2.772
(0.001)
0.052
0.881
(0.475)
0.756
(0.642)
0.640
0.917
-5.749
-5.454
348

KRW/DKK

32.866
(0.879)
4.768
(0.003)
0.043
1.216
(0.304)
0.648
(0.737)
0.559
0.642
-6.240
-6.173
348

CHF/MXN
-0.371
(0.354)
-0.828
(0.481)
-0.523
(0.456)
0.679
(0.605)
-1.188
(1.004)
-2.300
(0.632)
-1.733
(0.341)
216.122
(1.968)
-1.947
(0.001)
0.059
0.542
(0.705)
0.491
(0.863)
0.729
1.163
-5.512
-5.216
348

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
SEK/SGD
p
1
d
2
Linear part
ρ
0.062
(0.074)
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
Nonlinear part
ρ
-0.118
(0.067)
∗
β1
∗
β2
∗
β3

MXN/KRW
11
3

TRY/AUD
6
1

TRY/NOK
9
1

TRY/SGD
1
1

DKK/AUD
10
3

0.176
(0.435)
-0.337
(0.695)
-0.157
(0.385)
0.271
(0.300)
0.588
(0.357)
0.480
(0.401)
0.135
(0.437)
0.010
(0.384)
-0.472
(0.742)
0.269
(0.254)
2.528
(1.913)

0.201
(0.227)
0.663
(0.306)
-0.340
(0.199)
0.264
(0.258)
0.193
(0.225)
0.209
(0.171)

0.189
(0.191)
0.183
(0.116)
0.659
(0.269)
-0.048
(0.143)
-0.003
(0.188)
-0.304
(0.189)
0.067
(0.208)
0.159
(0.204)
0.026
(0.151)

0.341
(0.277)

0.212
(0.115)
-0.440
(0.187)
0.076
(0.176)
0.077
(0.171)
-0.069
(0.128)
0.037
(0.179)
0.075
(0.152)
0.389
(0.200)
0.229
(0.162)
-0.035
(0.163)

-0.208
(0.437)
0.249
(0.699)
0.174
(0.390)
-0.272
(0.314)

-0.212
(0.227)
-0.651
(0.316)
0.450
(0.214)
-0.327
(0.276)

-0.202
(0.194)
-0.121
(0.187)
-0.755
(0.277)
0.022
(0.193)

-0.365
(0.276)

-0.253
(0.119)
0.538
(0.204)
-0.228
(0.217)
-0.005
(0.213)

109

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
SEK/SGD
∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

15.383
(2.314)
1.376
(0.015)
0.028
2.721
(0.030)
2.112
(0.034)
0.377
0.271
-7.101
-7.033
348

MXN/KRW
-0.698
(0.363)
-0.469
(0.402)
-0.165
(0.441)
-0.051
(0.399)
0.493
(0.749)
-0.214
(0.254)
-2.496
(1.909)
51.056
(0.886)
-4.274
(0.004)
0.052
1.298
(0.271)
1.053
(0.396)
0.795
0.917
-5.749
-5.454
348

TRY/AUD
-0.360
(0.244)
-0.390
(0.196)

TRY/NOK
-0.161
(0.221)
0.289
(0.201)
-0.039
(0.219)
-0.122
(0.226)
-0.109
(0.171)

TRY/SGD

DKK/AUD
0.053
(0.163)
-0.132
(0.210)
-0.043
(0.183)
-0.421
(0.230)
-0.317
(0.196)
0.209
(0.184)

51.563
(0.880)
0.891
(0.002)
0.043
0.998
(0.409)
1.258
(0.265)
0.485
0.618
-6.220
-6.040
348

53.757
(1.664)
-1.311
(0.002)
0.043
1.852
(0.119)
1.456
(0.173)
0.836
0.621
-6.169
-5.920
348

13.029
(0.652)
-0.024
(0.011)
0.041
2.206
(0.068)
1.382
(0.204)
0.584
0.585
-6.334
-6.266
348

6.832
(0.290)
2.044
(0.011)
0.035
0.877
(0.478)
1.033
(0.411)
0.984
0.408
-6.573
-6.301
348

110

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
SGD/NOK
p
1
d
3
Linear part
ρ
0.157
(0.166)
β1

DKK/CAD
1
6

SGD/DKK
10
3

SGD/CAD
1
3

SEK/MXN
11
1

SEK/NZD
1
4

0.077
(0.104)

0.010
(0.159)
-0.459
(0.351)
0.405
(0.344)
-0.110
(0.305)
-0.372
(0.339)
0.046
(0.328)
0.712
(0.291)
0.525
(0.352)
0.037
(0.264)
0.053
(0.275)

0.301
(0.133)

0.192
(0.378)
-0.480
(0.365)
-1.926
(0.896)
0.284
(0.754)
0.682
(0.547)
-0.793
(0.729)
0.240
(0.458)
0.459
(0.370)
0.433
(0.647)
-0.524
(0.205)
1.113
(0.547)

0.054
(0.223)

-0.104
(0.101)

-0.023
(0.161)
0.499
(0.357)
-0.422
(0.349)
0.193
(0.327)

-0.313
(0.133)

-0.215
(0.377)
0.530
(0.372)
1.979
(0.898)
-0.187
(0.765)

-0.091
(0.224)

β2
β3
β4
β5
β6
β7
β8
β9
β10
Nonlinear part
ρ
-0.187
(0.164)
∗
β1
∗
β2
∗
β3

111

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
SGD/NOK

DKK/CAD

SGD/DKK
0.410
(0.360)
-0.033
(0.343)
-0.712
(0.302)
-0.456
(0.365)
-0.0001
(0.278)
0.101
(0.292)

SGD/CAD

30.028
(1.072)
-1.491
(0.005)
0.026
0.682
(0.605)
0.924
(0.497)
0.703
0.239
-7.227
-7.159
348

13.847
(1.644)
1.913
(0.020)
0.032
1.474
(0.210)
1.370
(0.209)
0.803
0.356
-6.829
-6.761
348

26.892
(0.642)
-1.645
(0.003)
0.026
1.333
(0.258)
1.353
(0.217)
0.280
0.227
-7.162
-6.890
348

297.821
(3.632)
0.159
(0.0003)
0.021
0.253
(0.908)
0.393
(0.924)
0.939
0.151
-7.690
-7.623
348

∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

112

SEK/MXN
-0.721
(0.558)
0.856
(0.730)
-0.291
(0.464)
-0.420
(0.374)
-0.460
(0.655)
0.682
(0.216)
-1.032
(0.556)
45.770
(0.737)
-0.248
(0.002)
0.055
2.736
(0.029)
1.439
(0.180)
0.165
1.030
-5.633
-5.338
348

SEK/NZD

500.000
(6.104)
3.649
(0.0003)
0.036
1.347
(0.252)
1.264
(0.262)
0.933
0.444
-6.608
-6.541
348

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
CHF/NZD
p
1
d
4
Linear part
ρ
0.047
(0.090)
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
Nonlinear part
ρ
-0.157
(0.087)
∗
β1
∗
β2
∗
β3

NZD/MXN
11
4

NZD/DKK
1
3

SGD/MXN
11
4

NOK/AUD
1
2

TRY/NZD
1
1

0.226
(0.166)
-0.184
(0.169)
-0.258
(0.197)
-0.689
(0.413)
-0.072
(0.350)
0.797
(0.389)
-0.292
(0.313)
0.336
(0.355)
0.102
(0.344)
-0.199
(0.260)
1.186
(0.270)

0.749
(0.283)

0.423
(0.280)
-0.356
(0.251)
0.060
(0.331)
-0.239
(0.305)
0.555
(0.427)
-0.545
(0.424)
-0.394
(0.698)
0.530
(0.387)
-0.0002
(0.491)
-0.224
(0.421)
1.475
(0.156)

0.125
(0.140)

0.071
(0.172)

-0.266
(0.166)
0.228
(0.184)
0.245
(0.214)
0.837
(0.424)

-0.798
(0.284)

-0.459
(0.282)
0.334
(0.270)
-0.048
(0.333)
0.275
(0.309)

-0.241
(0.134)

-0.145
(0.149)

113

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
CHF/NZD
∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

14.142
(1.374)
2.029
(0.012)
0.038
0.707
(0.587)
0.731
(0.664)
0.519
0.495
-6.501
-6.433
348

NZD/MXN
0.027
(0.370)
-0.806
(0.391)
0.308
(0.320)
-0.294
(0.357)
-0.047
(0.345)
0.238
(0.262)
-1.071
(0.276)
34.497
(1.386)
-4.063
(0.006)
0.056
1.897
(0.111)
1.179
(0.311)
0.462
1.037
-5.626
-5.331
348

NZD/DKK

500.000
(3.892)
-3.693
(0.0002)
0.036
0.640
(0.634)
0.831
(0.576)
0.970
0.431
-6.639
-6.572
348

114

SGD/MXN
-0.629
(0.436)
0.585
(0.428)
0.357
(0.700)
-0.551
(0.390)
0.027
(0.495)
0.290
(0.417)
-1.437
(0.160)
68.666
(1.133)
-2.082
(0.002)
0.046
0.831
(0.506)
0.503
(0.854)
0.855
0.717
-5.995
-5.699
348

NOK/AUD

TRY/NZD

13.971
(0.686)
2.134
(0.010)
0.034
0.465
(0.761)
0.824
(0.582)
0.656
0.406
-6.699
-6.632
348

10.587
(3.254)
2.589
(0.031)
0.049
2.918
(0.021)
2.664
(0.008)
0.439
0.748
-6.086
-6.019
348

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs
MXN/DKK
p
11
d
6
Linear part
ρ
0.365
(0.655)
β1
-0.279
(0.638)
β2
-2.142
(0.946)
β3
0.088
(0.845)
β4
-1.299
(0.683)
β5
0.157
(0.549)
β6
0.226
(0.242)
β7
0.760
(0.234)
β8
1.027
(0.239)
β9
0.033
(0.416)
β10
1.074
(0.121)
β11
Nonlinear part
ρ
-0.403
(0.658)
∗
β1
0.322
(0.641)
∗
β2
2.206
(0.948)

MXN/AUD
12
5

TRY/MXN
11
2

NOK/NZD
1
3

NOK/MXN
11
4

0.623
(0.698)
0.631
(1.086)
-0.567
(0.932)
-0.989
(0.810)
-1.249
(1.151)
-0.617
(0.490)
-1.332
(1.262)
-0.636
(0.453)
-0.590
(0.287)
-0.170
(0.171)
1.113
(0.185)
0.366
(0.156)

0.053
(0.883)
-0.236
(0.744)
0.312
(1.003)
1.080
(0.458)
0.538
(0.847)
-1.656
(0.958)
-1.085
(0.801)
1.616
(0.916)
-2.321
(1.512)
-1.640
(1.281)
1.608
(0.660)

-0.094
(0.069)

0.138
(0.366)
-0.302
(0.469)
-0.327
(0.703)
-0.155
(0.512)
-1.532
(1.175)
-0.028
(0.493)
-0.032
(0.280)
0.177
(0.275)
0.125
(0.177)
-0.016
(0.217)

-0.662
(0.699)
-0.635
(1.092)
0.567
(0.934)

-0.089
(0.880)
0.334
(0.763)
-0.292
(1.007)

-0.026
(0.085)

-0.172
(0.368)
0.389
(0.476)
0.366
(0.737)

115

Table 2.4. Estimation results from ESTAR models (continued)
(b) 35 lowest TI currency pairs

∗
β3
∗
β4
∗
β5
∗
β6
∗
β7
∗
β8
∗
β9
∗
β10

MXN/DKK
0.018
(0.848)
1.245
(0.694)
-0.112
(0.553)
-0.258
(0.265)
-0.756
(0.240)
-1.031
(0.242)
0.110
(0.422)
-1.028
(0.134)

∗
β11

γ
c
σε
ˆ
LM(4)
LM(8)
pRNL
SSR
AIC
BIC
T

120.667
(1.149)
0.442
(0.001)
0.055
2.858
(0.024)
1.565
(0.135)
0.864
1.009
-5.654
-5.358
348

MXN/AUD
0.984
(0.821)
1.192
(1.176)
0.636
(0.498)
1.330
(1.271)
0.697
(0.466)
0.670
(0.298)
0.237
(0.185)
-1.029
(0.199)
-0.301
(0.188)
293.130
(1.594)
2.701
(0.0002)
0.052
1.803
(0.128)
1.225
(0.284)
0.807
0.907
-5.744
-5.425
348

TRY/MXN
-1.030
(0.460)
-0.592
(0.861)
1.686
(0.958)
1.088
(0.802)
-1.564
(0.917)
2.315
(1.513)
1.671
(1.285)
-1.524
(0.660)

NOK/NZD

NOK/MXN
0.251
(0.523)
1.571
(1.178)
0.067
(0.499)
-0.010
(0.290)
-0.153
(0.283)
-0.140
(0.185)
0.120
(0.231)

52.107
(0.660)
-1.617
(0.002)
0.055
2.403
(0.050)
1.946
(0.053)
0.612
1.003
-5.659
-5.364
348

7.836
(1.384)
3.593
(0.020)
0.034
1.053
(0.380)
0.715
(0.679)
0.736
0.404
-6.702
-6.635
348

77.307
(0.924)
-0.597
(0.002)
0.060
0.903
(0.463)
0.646
(0.738)
0.667
1.208
-5.488
-5.216
348

116

Table 2.5. Half-life estimates for real exchange rates
High trade intensity currency pairs
Half-life
USD/CAD
32
USD/MXN
16
USD/JPY
31
USD/GBP
14
USD/KRW
7
KRW/JPY
13
SEK/NOK
36
GBP/NOK
3
USD/SGD
56
NZD/AUD
35
JPY/AUD
22
SGD/JPY
25
USD/TRY
39
SEK/DKK
8
USD/CHF
18
GBP/SEK
12
GBP/DKK
38
GBP/CHF
27
USD/AUD
17
NOK/DKK
18
GBP/TRY
17
NZD/JPY
24
USD/SEK
18
USD/NZD
19
GBP/JPY
31
CHF/JPY
19
USD/DKK
26
SGD/AUD
16
SGD/KRW
1
GBP/AUD
21
TRY/CHF
21
KRW/AUD
4
GBP/NZD
12
USD/NOK
23
CHF/SEK
36
Average
21.57

Low trade intensity currency pairs
Half-life
CHF/NOK
23
CAD/AUD
11
TRY/DKK
19
MXN/CAD
28
SEK/CAD
21
TRY/CAD
33
NZD/CAD
35
SEK/KRW
12
NOK/KRW
7
GBP/MXN
17
KRW/DKK
43
CHF/MXN
21
SEK/SGD
19
MXN/KRW
22
TRY/AUD
39
TRY/NOK
41
TRY/SGD
32
DKK/AUD
62
SGD/NOK
28
DKK/CAD
64
SGD/DKK
45
SGD/CAD
53
SEK/MXN
49
SEK/NZD
23
CHF/NZD
6
NZD/MXN
24
NZD/DKK
14
SGD/MXN
26
NOK/AUD
16
TRY/NZD
27
MXN/DKK
24
MXN/AUD
27
TRY/MXN
27
NOK/NZD
6
NOK/MXN
48
28.34

Note. The half-lives are measured as the discrete number of months taken
until the shock to the level of the real exchange rate has fallen below a half.
117

Table 2.6. Volatility of selected indicators for diﬀerent exchange regimes

Country
Australia
Canada
Denmark
Great Britain
Japan
Korea
Mexico
New Zealand
Norway
Singapore
Sweden
Switzerland
Turkey
United States

Probability that the monthly change is
Greater than ±4 percent
Within a ±2.5 percent band:
(400 basis points):
Exchange rate
Reserves
Nominal interest rate
68.10
39.37
0.00
87.36
43.97
1.72
62.36
36.63
2.30
65.52
60.63
0.00
59.48
81.03
0.00
86.21
49.14
0.57
70.40
41.38
14.66
66.38
23.85
2.01
66.09
38.22
0.29
91.38
78.74
0.00
61.49
38.79
1.44
54.02
45.40
0.29
49.09
30.46
29.89
63.51
68.39
0.29

Note. The frequency distribution of monthly percent changes in the exchange rate, foreign exchange reserves, and nominal money market interest rates is reported for diﬀerent exchange rate regimes. The sample
period is from January 1980 to December 2008.

118

Table 2.7. Performance statistics for carry trade portfolios
(a) Without momentum trading

Strategy
Na¨ carry
ıve
PPP - τ = 0
PPP - τ = 0.1
PPP - τ = 0.2
PPP - τ = 0.3
PPP - τ = 0.4
PPP - τ = 0.5
PPP - τ = 0.6
PPP - τ = 0.7
PPP - τ = 0.8
PPP - τ = 0.9
PPP - τ = 1.0
PPP - τ = 1.1
PPP - τ = 1.2
PPP - τ = 1.3
PPP - τ = 1.4
PPP - τ = 1.5
PPP - τ = 1.6
PPP - τ = 1.7
PPP - τ = 1.8
PPP - τ = 1.9
PPP - τ = 2.0

High TI currency pairs
Return
Std. Dev. Sharpe
-0.016
0.011
-0.121
0.004
0.020
0.018
0.019
0.034
0.048
0.043
0.046
0.079
0.047
0.040
0.097
0.059
0.041
0.118
0.054
0.035
0.128
0.039
0.031
0.105
0.060
0.028
0.176
0.038
0.020
0.160
0.021
0.015
0.117
0.014
0.012
0.100
0.009
0.011
0.069
0.006
0.011
0.048
0.006
0.011
0.048
0.004
0.010
0.032
0.005
0.007
0.061
0.005
0.007
0.061
0.005
0.007
0.061
0.005
0.007
0.061
.
.
.
.
.
.

Low TI currency pairs
Return Std. Dev. Sharpe
0.006
0.016
0.031
0.015
0.021
0.061
0.011
0.027
0.032
0.035
0.035
0.084
0.053
0.048
0.092
0.067
0.039
0.141
0.062
0.036
0.144
0.072
0.032
0.184
0.074
0.033
0.186
0.067
0.028
0.200
0.052
0.027
0.160
0.053
0.024
0.181
0.057
0.025
0.189
0.060
0.022
0.231
0.062
0.022
0.238
0.058
0.021
0.230
0.052
0.020
0.214
0.054
0.020
0.228
0.052
0.019
0.224
0.041
0.018
0.189
0.027
0.016
0.140
0.022
0.016
0.120

Note. We report performance statistics for carry trade portfolios with strategies (15year moving average, interest rate diﬀerential (greater than (med-min)), and no momentum trading) over the sample period, January 1980 - December 2008: annualized
return, standard deviation, and Sharpe ratio on a monthly basis. “PPP - τ = 0” means
that we use PPP-augmented carry trade strategy with a threshold of τ = 0 percent.
Monthly returns are given only for months in which strategies are active. For na¨
ıve
carry trades, all months are active, for PPP-augmented carry trades, the number of
active months falls as the threshold increases.

119

Table 2.7. Performance statistics for carry trade portfolios (continued)
(b) With momentum trading

Strategy
Na¨ carry
ıve
PPP - τ = 0
PPP - τ = 0.1
PPP - τ = 0.2
PPP - τ = 0.3
PPP - τ = 0.4
PPP - τ = 0.5
PPP - τ = 0.6
PPP - τ = 0.7
PPP - τ = 0.8
PPP - τ = 0.9
PPP - τ = 1.0
PPP - τ = 1.1
PPP - τ = 1.2
PPP - τ = 1.3
PPP - τ = 1.4
PPP - τ = 1.5
PPP - τ = 1.6
PPP - τ = 1.7
PPP - τ = 1.8
PPP - τ = 1.9
PPP - τ = 2.0

High TI currency pairs
Return
Std. Dev. Sharpe
0.009
0.020
0.039
0.019
0.029
0.055
0.039
0.042
0.076
0.086
0.044
0.163
0.082
0.039
0.172
0.045
0.033
0.114
0.048
0.032
0.125
0.034
0.028
0.101
0.040
0.025
0.134
0.025
0.017
0.119
0.012
0.013
0.081
0.006
0.009
0.057
0.001
0.008
0.008
-0.002
0.007
-0.027
-0.002
0.007
-0.027
-0.005
0.006
-0.061
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

Low TI currency pairs
Return Std. Dev. Sharpe
0.029
0.022
0.110
0.053
0.031
0.141
0.076
0.045
0.141
0.076
0.048
0.132
0.073
0.039
0.158
0.077
0.040
0.160
0.069
0.036
0.159
0.059
0.032
0.155
0.069
0.032
0.180
0.056
0.025
0.188
0.042
0.023
0.152
0.048
0.021
0.193
0.052
0.021
0.208
0.054
0.020
0.228
0.054
0.018
0.243
0.050
0.018
0.229
0.042
0.017
0.204
0.045
0.017
0.226
0.042
0.016
0.214
0.027
0.014
0.162
0.014
0.011
0.103
0.010
0.010
0.077

Note. We report performance statistics for carry trade portfolios with strategies (15year moving average, interest rate diﬀerential (greater than (med-min)), and momentum trading) over the sample period, January 1980 - December 2008: annualized return, standard deviation, and Sharpe ratio on a monthly basis. “PPP - τ = 0” means
that we use PPP-augmented carry trade strategy with a threshold of τ = 0 percent.
Monthly returns are given only for months in which strategies are active. For na¨
ıve
carry trades, all months are active, for PPP-augmented carry trades, the number of
active months falls as the threshold increases.

120

Figure 2.1. Scatter plots
(a) Scatter plot of exchange rate volatility against trade intensity (maximum)

(b) Scatter plot of exchange rate volatility against trade intensity (average)

Note. The x-axis is trade intensity (maximum) and trade intensity (average) for (a)
and (b), respectively. The y-axis is real exchange rate volatility. Scatter plots are for
91 currency pairs involving 14 countries over the period 1980-2005. The straight line
is depicted by running the Ordinary Least Squares (OLS) regression.
121

Figure 2.2. Generalized impulse response functions (GIs)
(a) 35 highest TI currency pairs
(i) USD/CAD, (ii) USD/MXN, (iii) USD/JPY

(i) USD/GBP, (ii) USD/KRW, (iii) KRW/JPY

Note. The GIs for the currency pairs in order are plotted with the solid,
dashed, and dotted lines, respectively.
122

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(a) 35 highest TI currency pairs
(i) SEK/NOK, (ii) GBP/NOK, (iii) USD/SGD

(i) NZD/AUD, (ii) JPY/AUD, (iii) SGD/JPY

123

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(a) 35 highest TI currency pairs
(i) USD/TRY, (ii) USD/CHF, (iii) SEK/DKK

(i) GBP/SEK, (ii) GBP/DKK, (iii) GBP/CHF

124

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(a) 35 highest TI currency pairs
(i) USD/AUD, (ii) NOK/DKK, (iii) GBP/TRY

(i) NZD/JPY, (ii) USD/SEK, (iii) USD/NZD

125

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(a) 35 highest TI currency pairs
(i) GBP/JPY, (ii) CHF/JPY, (iii) USD/DKK

(i) SGD/AUD, (ii) SGD/KRW, (iii) GBP/AUD

126

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(a) 35 highest TI currency pairs
(i) TRY/CHF, (ii) KRW/AUD, (iii) GBP/NZD

(i) USD/NOK, (ii) CHF/SEK

127

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(b) 35 lowest TI currency pairs
(i) CHF/NOK, (ii) CAD/AUD, (iii) TRY/DKK

(i) MXN/CAD, (ii) SEK/CAD, (iii) TRY/CAD

128

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(b) 35 lowest TI currency pairs
(i) NZD/CAD, (ii) SEK/KRW, (iii) NOK/KRW

(i) GBP/MXN, (ii) KRW/DKK, (iii) CHF/MXN

129

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(b) 35 lowest TI currency pairs
(i) SEK/SGD, (ii) MXN/KRW, (iii) TRY/AUD

(i) TRY/NOK, (ii) TRY/SGD, (iii) DKK/AUD

130

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(b) 35 lowest TI currency pairs
(i) SGD/NOK, (ii) DKK/CAD, (iii) SGD/DKK

(i) SGD/CAD, (ii) SEK/MXN, (iii) SEK/NZD

131

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(b) 35 lowest TI currency pairs
(i) CHF/NZD, (ii) NZD/MXN, (iii) NZD/DKK

(i) SGD/MXN, (ii) NOK/AUD, (iii) TRY/NZD

132

Figure 2.2. Generalized impulse response functions (GIs) (continued)
(b) 35 lowest TI currency pairs
(i) MXN/DKK, (ii) MXN/AUD, (iii) TRY/MXN

(i) NOK/NZD, (ii) NOK/MXN

133

Figure 2.3. Sharpe ratios without and with a momentum trading strategy
(a) Sharpe ratios without a momentum trading strategy

(b) Sharpe ratios with a momentum trading strategy

Note. The x-axis refers to a threshold, and the y-axis refers to a Sharpe ratio.
“N” refers to the na¨ carry trade strategy. The solid line denotes high trade
ıve
intensity pairs, and the dashed line denotes low trade intensity pairs.

134

Figure 2.4. Performance of portfolios without and with a momentum trading strategy
(a) Performance of portfolios without a momentum trading strategy: High TI (top)
vs. Low TI (bottom)

Note. The x-axis refers to time, and the y-axis refers to an amount of dollars. The
short-dashed, solid, and circle-marker lines denote the na¨ carry trade strategy,
ıve
the PPP-augmented carry trade strategy with a threshold of 0 percent, and of 30
percent, respectively. Also, the dash-dotted, dotted, and long-dashed lines denote
the PPP-augmented carry trade strategy with a threshold of 50 percent, of 70 percent, and of 130 percent, respectively.
135

Figure 2.4. Performance of portfolios without and with a momentum trading strategy
(continued)
(b) Performance of portfolios with a momentum trading strategy: High TI (top)
vs. Low TI (bottom)

Note. As for Figure 2.4 (a).

136

Chapter 3
Nonlinear Long Memory Properties
and Mean Reversion of Real Exchange
Rates in the Post-Bretton Woods Era

3.1

Introduction

While real exchange rates are known to be remarkably volatile, they consistently tend to
revert back to long-run equilibrium levels. Although deviations from Purchasing Power
Parity (PPP) in the short run are broadly observed, researchers believe that some form of
PPP holds at least as a long-run relationship (see, e.g., Rogoﬀ (1996) and Taylor et al.
(2001)). The mean reverting behavior of real exchange rates is well documented in many
previous studies. A considerable amount of literature (see, e.g., Abuaf and Jorion (1990)
[1973-1987], Frankel and Rose (1996a) [1948-1992], Diebold et al. (1991) [1832-1913], Froot
and Rogoﬀ (1995) [1913-1988], Lothian and Taylor (1996) [1791-1990], Papell (1997) [1973137

1994], Rogoﬀ (1996) [1972-1995], Taylor and Sarno (1998) [1973-1996], and Wu (1996) [19741993], among others. The sample period is also reported in brackets.) has examined whether
real exchange rates exhibit mean reversion, and whether there is evidence of PPP in the
long run under the recent ﬂoat. The results have generally been mixed with less evidence
of stationarity in the post-Bretton Woods period. Lothian and Taylor (1996) found strong
evidence of signiﬁcant mean reverting behavior of real exchange rates using the annual data
spanning two centuries. The authors argued that the slow adjustment and the low power of
conventional unit root tests do account for the widespread failure of such tests to reject the
null hypothesis of a unit root in the data for the recent ﬂoating rate period alone. Abuaf and
Jorion (1990), Murray and Papell (2005), and Rossi (2005) have used the data for exchange
rates in the post-Bretton Woods Era since 1973. However, Froot and Rogoﬀ (1995), Rogoﬀ
(1996) and many others found that it is notably much harder to detect mean reversion in
real exchange rates during the post-Bretton Woods period. Many other studies including
the aforementioned articles have mainly attempted to explain the puzzling inability to reject
the null hypothesis of nonstationarity using standard unit root tests.
There has also been a large amount of literature to study mean reversion in real exchange
rates by employing nonlinear models. Taylor et al. (2001) estimate a smooth transition
autoregressive (STAR) model, which allows the speed at which exchange rates converge
to their long-run equilibrium values to depend on the size of the deviations, and provide
evidence of nonlinear mean reversion in a number of major real exchange rates. The model
thus allows for the possibility that real exchange rates may behave like unit root processes
when close to their long-run equilibrium levels, while becoming increasingly mean-reverting
the further they move away from equilibrium. Cheung and Lai (2000) examine dollar-based
138

real exchange rates using fractional integration analysis which estimates a standard ARFIMA
model, and present evidence of mean reversion for many series. Furthermore, Cheung and
Lai (2001) show that the puzzling behavior of yen-based real exchange rates may stem from
long memory dynamics undermining unit root tests in their ability to identify mean reversion.
Recent evidence reveals that many univariate economic and ﬁnancial time series possess
both nonlinear and long memory properties. Motivated by this recent evidence, Baillie and
Kapetanios (2008) developed a general nonlinear, smooth transition regime autoregression
which is embedded within a strongly dependent, long memory process. The authors also
found that a fractionally integrated, nonlinear autoregressive ESTAR (FI-NLAR-ESTAR)
model is quite successful in representing the nonlinear structures and strong dependencies
within six monthly forward premia for the periods, December 1978 through December 1998
or January 2002 depending on whether the currency is included in the Eurozone, and the
historical yearly USD/GBP real exchange rate for the periods, 1791 through 1994. In their
paper, it has been shown that the time domain MLE is generally superior to the two step
estimator which is an alternative procedure of ﬁrst estimating the long memory parameter
by using the Local Whittle estimator to obtain a fractionally integrated ﬁltered series, before
estimating the remaining parameters. Also, van Dijk et al. (2002a) proposed a fractionally
integrated smooth transition autoregressive (FI-STAR) model to jointly capture both long
memory and nonlinear features, and found evidence of both long memory and nonlinear
behavior for three decades of monthly US unemployment. Hence, the article by Baillie and
Kapetanios (2008) aims to jointly model both nonlinearity and long memory for economic
and ﬁnancial time series which include forward premia, real exchange rates, and many others.
This paper examines nonlinear and long memory properties and mean reverting dynamics
139

of real exchange rates. The purpose of this paper is to ﬁnd evidence which is supportive
of mean reversion in real exchange rates by estimating the FI-NLAR-ESTAR model that is
capable of representing both nonlinear and long memory features for the various economic
and ﬁnancial time series. It has been found that the FI-NLAR-ESTAR model is quite successful in detecting the mean reverting dynamics of real exchange rates. While the nonlinear
long memory model has been found to be more supportive of strong empirical evidence for
the presence of slow mean reversion in real exchange rates, the linear fractionally integrated
model has not for all of the currencies considered in this study over the recent ﬂoat.
The contribution of this paper to the existing literature is that a model that is capable
of capturing both nonlinear and long memory characteristics may help identifying mean
reversion in real exchange rates. In particular, the fractional integration analysis reveals
that the null hypothesis of the presence of a unit root is rejected at least at the 5 percent
signiﬁcance level for all of the currencies considered in this study. This implies that a
linear fractionally integrated model such as ARFIMA can be improved by adding nonlinear
properties in terms of its ability to detect mean reversion to the long run equilibrium level
in real exchange rates.
The rest of the paper is organized as follows: Section 3.2 introduces the time series model
representing both nonlinearity and long memory. Section 3.3 presents empirical results from
the estimation of the model. Section 3.4 describes the data, and provides some summary
statistics. Section 3.5 concludes.

140

3.2

The FI -NLAR-ESTAR model

A univariate time series process with fractional integration in its conditional mean is represented by
(1 − L)d yt = ut ,

t = 1, 2, ..., T

(3.1)

where L is the lag operator, d is the long memory parameter and ut is a short memory
I(0) process. The time series yt is said to be a fractionally integrated process of order d, or
I(d) (see Granger and Joyeux (1980), Granger (1980) and Hosking (1981)). Long memory,
fractionally integrated processes are associated with hyperbolically decaying autocorrelations
and impulse response weights. Baillie (1996) provides detailed surveys of these models
and discussions of the applications to economics and ﬁnance. The parameter d is possibly
noninteger, and represents the degree of “long memory” behavior or persistence in the series.
For noninteger d, the operator (1 − L)d in equation (1) is through the binomial expansion
(1 − L)d = 1 − dL +

d (d − 1) 2 d (d − 1) (d − 2) 3
L −
L + ··· .
2!
3!

(3.2)

For d = 1, (1 − L)d is the usual ﬁrst-diﬀerencing operator. For −0.5 < d < 0.5, the process
is covariance stationary and invertible. For 0 < d < 0.5, the process possesses long memory,
and its autocorrelations are all positive and decay at a hyperbolic rate. For −0.5 < d < 0,
the sum of absolute values of the processes autocorrelations tends to a constant so that it
has short memory. For 0.5 ≤ d < 1, the process does not have a ﬁnite variance, but still
has a cumulative impulse response function with a ﬁnite sum, which implies that shocks to
the level of the series are mean reverting. The mean reverting property depends on whether
d < 1. For d = 1, the time series is a unit root process which implies the eﬀect of a shock does
not die out. However, a fractionally integrated process with d < 1 exhibits shock-dissipating
141

behavior. If the short memory process ut is represented as an ARMA(p,q ) process, equation
(1) becomes the ARFIMA(p,d,q) model
Φ (L) (1 − L)d yt = Θ (L) t ,

(3.3)

where Φ (L) = 1 − φ1 L − · · · − φp Lp , Θ (L) = 1 + θ1 L + · · · + θq Lq , and all roots of Φ (L)
and Θ (L) lie outside the unit circle.
A model that is capable of capturing both nonlinear and long memory features is the FINLAR-ESTAR model developed by Baillie and Kapetanios (2008). In the paper, the authors
consider a general nonlinear, smooth transition regime autoregression which is embedded
within a strongly dependent, long memory process. They consider situations where the
short memory process ut is allowed to be a nonlinear process, rather than a pure ARMA
process. To be more speciﬁc, by allowing for general nonlinear processes and from equation
(3.1)
ut = F ut−1 , · · · , ut−p + t ,

(3.4)

so that the short memory component of the process is a possibly nonlinear autoregression
involving the last p lags of the variable, ut . The strong dependent component is represented
by a fractionally integrated process as in equation (3.1), and the stationary I(0) component
is composed of an autoregression with a linear part of order p and a nonlinear part of order
k where the nonlinearity involves the use of a smooth transition function. The FI (d )NLAR(p,k ) -ESTAR model is represented as
(1 − L)d yt = ut ,

(3.5)

ut = α (L) ut−1 + β (L) ut−1 φ (ut−D ) + t ,

142

where the polynomials in the lag operator are α (L) = α0 +
k−1
i
i=0 βi L ,

p−1
i
i=0 αi L ,

β (L) = β0 +

φ (ut−D ) is the smooth transition autoregression function, D is a delay parame-

ter, and t is a white noise process. The most widely used nonlinear model is the Exponential
Smooth Transition Autoregressive (ESTAR) model introduced by Granger and Ter¨svirta
a
(1993) and Ter¨svirta (1994). A transition function suggested by Granger and Ter¨svirta
a
a
(1993) is the exponential function
φ (ut−D ) = 1 − exp −γ (ut−D − c)2

with γ > 0,

(3.6)

where ut−D is a transition variable, γ is a slope parameter, and c is a location parameter.
The restriction on the parameter (γ > 0) is an identifying restriction. Thus, the NLAR(p,k )
-ESTAR part is represented as
ut = α0 + β0 1 − exp −γ (ut−D − c)2
p

+

k

βi ut−i 1 − exp −γ (ut−D − c)2

αi ut−i +
i=1

(3.7)
+ t,

i=1

and this is the form of the model that is used for the empirical analysis of real exchange
rates in this study. The estimation of the model is implemented through the use of a time
domain MLE for a stationary, fractionally integrated, nonlinear autoregression with smooth
transition regimes.1 The model can be estimated by approximate MLE in the time domain.
Baillie and Kapetanios (2008) show that an alternative procedure of ﬁrst estimating the long
memory parameter by using the Local Whittle estimator to obtain a fractionally ﬁltered
series, before estimating the remaining parameters, is generally found to be inferior to the
1Baillie

and Kapetanios (2008) show that the use of a time domain MLE for stationary,
fractionally integrated, nonlinear autoregression with smooth transition regimes has desirable
asymptotic properties and possesses T 1/2 consistent parameter estimates with a limiting
Normal distribution.
143

full MLE.
Several previous studies including Diebold et al. (1991), Cheung (1993) and Cheung and
Lai (2000, 2001) have considered fractionally integrated, or long memory behavior of real
exchange rates. However, a recent paper by Baillie and Kapetanios (2007) constructs the
application of the tests based on logistic approximations and Artiﬁcial Neural Networks
(ANN ), and suggests the widespread presence of both nonlinear and long memory components in many economic and ﬁnancial time series such as the rate of inﬂation and real
exchange rates. For example, as mentioned earlier, van Dijk et al. (2002a) propose a time
series model to describe long memory and nonlinearity at the same time, and ﬁnd evidence
of both nonlinear and long memory properties for US unemployment. Hence, Baillie and
Kapetanios (2008) aim to jointly model both nonlinear and long memory characteristics for
strongly dependent processes, and include some applications of the methodology and estimation of a fractionally integrated, nonlinear autoregressive ESTAR model to forward premia
for six diﬀerent currencies and the yearly USD/GBP real exchange rate. They ﬁnd that
the estimated FI (d )-NLAR(p,k )-ESTAR models appear to be successful in representing the
nonlinear structures and strong dependencies.

3.3

Data and Summary Statistics

This study uses monthly price levels measured by consumer price indices (CPI), and monthly
spot exchange rates for the Swiss Franc (CHF), Great British Pound (GBP), Japanese Yen
(JPY), Norwegian Krone (NOK) and Swedish Krona (SEK) vis-`-vis the US Dollar. The
a
data used in this empirical study are collected from the International Financial Statistics

144

(IFS ) and spot exchange rates are measured as mid rates at the end of the month, from
January 1970 through October 2010, comprising a total of 490 monthly observations for each
currency.
The real exchange rate, qt , is deﬁned in logarithmic form as
q t ≡ st − pt + p∗
t

(3.8)

where st is the logarithm of the nominal exchange rate which is measured as the price of
the domestic currency in terms of the foreign currency, and pt and p∗ denote the logarithms
t
of the domestic and foreign price levels, respectively. If PPP held continuously, qt would
be a constant that reﬂects diﬀerences in units of measurement. As noted in particular
by Taylor et al. (2001), the real exchange rate may be interpreted as a measure of the
deviation from PPP. Since the real exchange rate is the nominal exchange rate which is
adjusted for relative price levels between two countries, variations in the real exchange rate
may represent deviations from PPP. Lothian and Taylor (1996) also noted that failure to
reject the hypothesis of nonstationarity in the real exchange rate has been evidence against
long-run PPP.
Figure 3.1 shows the logarithms of monthly real exchange rates over the periods, January
1970 through October 2010. Most of the sample periods fall into the post-Bretton Woods
ﬂoating exchange rate system. In all cases, it is observed that real exchange rates exhibit
large appreciations and depreciations against the US Dollar over the entire sample periods.
Table 1 presents some preliminary summary statistics for the time series data of real exchange
rates. The ﬁrst two rows show the mean and standard deviation of real exchange rates as
deﬁned in equation (3.8). It is interesting to note that the Swiss Franc (CHF) and Japanese

145

Yen (JPY)–two currencies that are most widely used as funding currencies for carry trades–
appear to exhibit higher exchange rate volatility than other three currencies, as indicated
by standard deviations of 0.21 and 0.25, respectively. In Table 3.1, ACF1 through ACF
6 denote autocorrelation functions up to lag 6. It is clearly indicated that real exchange
rates are strongly dependent processes. Many economic and ﬁnancial time series including
real exchange rates and forward premia are strongly persistent, and display slowly decaying
hyperbolic autocorrelations. The Ljung-Box test statistics for autocorrelations up to 20
lags also reveal that there is signiﬁcant evidence that there is autocorrelation between the
series for each currency. In Figure 3.2 (a), the ﬁrst 120 autocorrelations of the logarithms of
real exchange rates are plotted. Also, the autocorrelations of ﬁrst-diﬀerenced real exchange
rates are displayed in Figure 3.2 (b). The autocorrelations of real exchange rates show a
slow decay associated with fractionally integrated processes. The autocorrelations of ﬁrstdiﬀerenced real exchange rates display some negative values at low lags, which strongly
suggests overdiﬀerencing.

3.4

Empirical Results

The results from estimating FI-NLAR-ESTAR models for diﬀerent currencies are reported
in Table 3.2. The tests for nonlinearity denoted by TLG (proposed by Ter¨svirta et al.
a
(1993)) and ANN (proposed by Lee et al. (1993)), respectively indicate the necessity of
the nonlinear long memory model. The p-values for these nonlinearity tests are reported
in Table 3.2, and provide signiﬁcant evidence for nonlinearity. The chosen orders, p and k
of the models that optimized the information criteria are diﬀerent across the currencies. In

146

most cases, the lag orders selected by each information criterion were the same. Otherwise,
following Baillie and Kapetanios (2008), the choice from the Akaike criterion was used. The
most appropriate order of the linear autoregressive part varies between 8 for JPY and SEK,
and 12 for GBP, while the optimum order for the nonlinear autoregressive part is one for all
currencies. The long memory parameter d from MLE is relatively close to the Local Whittle
estimate for most currencies.2 It is in the range between 0.5 and 1 for most currencies which
implies nonstationarity of the process, but nevertheless existence of a cumulative impulse
response function with a ﬁnite sum, which implies that shocks to the level of the series are
mean reverting. It is in the range between 0 and 0.5 for GBP and SEK, which implies
covariance stationarity of the process. As noted by Baillie and Kapetanios (2008), two
of the estimated models have the ﬁrst nonlinear autoregressive coeﬃcient β1 being small
and not signiﬁcantly diﬀerent from zero. However, the eﬀect of nonlinearity enters through
the statistically signiﬁcant constant term β0 . Since the estimated long memory parameter
exceeds 0.5 in most cases, the models were also estimated after having ﬁrst-diﬀerenced the
data. It appeared that this did not change the results after having added unity to the
estimate of the long memory parameter. In the last three rows of Table 3.2, the estimation
results from Autoregressive Fractionally Integrated Moving Average (ARFIMA) models are
reported. The long memory parameter, d along with the chosen order, p of the model is
displayed.
Following Cheung and Lai (2000, 2001), the fractional integration analysis is implemented.
The results from ARFIMA models and FI-NLAR-ESTAR models are displayed in Tables 3.3
2 It

was not possible to ﬁnd an appropriate model for the Canadian Dollar (CAD), since
the estimate of γ was very large, and both the Local Whittle and MLE methods were not
able to reject the hypothesis of d = 1.

147

and 3.4, respectively. In each Table, the MLE of the long memory parameter d along with its
corresponding standard error is reported. The t-statistics for each hypothesis testing is also
reported. In Table 3.3, the results from ARFIMA models indicate that the null hypothesis
of d = 0 is rejected in favor of the alternative hypothesis of d > 0 at the 5 percent signiﬁcance
level for CHF and SEK, and at 1 percent signiﬁcance level for other currencies. However,
the null hypothesis of d = 1 (a unit root) cannot be rejected in favor of the alternative
hypothesis of d < 1 (mean reversion) at the any signiﬁcance level for CHF, JPY, and NOK,
while it is rejected at the 10 percent signiﬁcance level for GBP, and at 1 percent level for
SEK. For the ARFIMA model, these results provide no evidence of mean reversion at all
for three out of ﬁve currencies. In Table 3.4, the results from FI-NLAR-ESTAR models
indicate that all the currencies have an integration order of neither zero nor unity. The null
hypothesis of d = 0 is rejected in favor of the alternative hypothesis of d > 0 at the 1 percent
signiﬁcance level for all the currencies. Furthermore, the null hypothesis of d = 1 (a unit
root) is also rejected in favor of the alternative hypothesis of d < 1 (mean reversion) at the
5 percent signiﬁcance level only for NOK, and at the 1 percent level for all other currencies.
This ﬁnding is consistent with the result in Baillie and Kapetanios (2008). The authors
considered the historical series of the annual USD/GBP real exchange rate for the periods
spanning from 1791 through 1994, and found that the estimated nonlinear and long memory
model provides evidence of slow mean reversion of the historical series. Overall, the results
from FI-NLAR-ESTAR models suggest signiﬁcant empirical evidence of slow mean reversion
in real exchange rates for all the currencies in this study.
An investigation of the fractional integration analysis for two models clearly reveals the fact
that the model that is capable of capturing both nonlinear and long memory characteristics
148

outperforms the linear fractionally integrated model. That is, the FI-NLAR-ESTAR model
works better in terms of its ability to identify mean reversion to the long run equilibrium level
in real exchange rates. The need for the nonlinear model for strongly persistent processes is
apparently indicated by the fractional integration analysis which strongly supports the mean
reverting process of real exchange rates.

3.5

Conclusion

Although deviations from Purchasing Power Parity (PPP) in the short run are broadly observed, researchers believe that some form of PPP holds at least as a long-run relationship.
Several previous studies have examined whether real exchange rates exhibit mean reversion,
and whether there is evidence of PPP in the long run. This paper investigates both nonlinear
and long memory characteristics and mean reverting behavior of real exchange rates. The paper estimates a fractionally integrated, nonlinear autoregressive ESTAR (FI-NLAR-ESTAR)
model for strongly dependent processes developed by Baillie and Kapetanios (2008). It has
been found that the FI-NLAR-ESTAR model is quite successful in identifying the mean
reverting dynamics of real exchange rates. While the nonlinear long memory model has
been found to be more supportive of strong empirical evidence for the presence of slow mean
reversion in real exchange rates, the linear fractionally integrated model has not for all of
the currencies considered in this study over the recent ﬂoat. Overall, the results suggest that
the model that is capable of representing both nonlinear and long memory characteristics
may help identifying mean reversion in real exchange rates. That is, the FI-NLAR-ESTAR
model works better than the linear fractionally integrated model such as ARFIMA in terms

149

of its ability to detect mean reversion to the long run equilibrium level in real exchange rates.
The need for the nonlinear model for strongly persistent processes is apparently indicated by
the fractional integration analysis which is strongly supportive of the mean reverting process
of real exchange rates. In general, this study illustrates that the puzzling behavior of real
exchange rates may be due to both nonlinear and long memory dynamics, which weaken the
ability of standard unit root tests to detect mean reversion to the long run equilibrium level.

150

Table 3.1. Summary statistics

Currency
Mean
Standard dev.
ACF1
ACF2
ACF3
ACF4
ACF5
ACF6
LB
T

Real exchange rate
CHF
GBP
0.3187 -0.4267
0.2092 0.1484
0.9768 0.9757
0.9524 0.9474
0.9280 0.9182
0.9028 0.8889
0.8789 0.8591
0.8549 0.8291
5733.92 5461.51
490
490

JPY
4.7431
0.2518
0.9843
0.9672
0.9493
0.9306
0.9125
0.8950
6736.65
490

NOK
1.9121
0.1413
0.9724
0.9433
0.9123
0.8811
0.8524
0.8228
5292.47
490

SEK
1.8851
0.1873
0.9853
0.9688
0.9521
0.9338
0.9143
0.8944
6703.80
490

Note. Real exchange rates are in logs. ACF1-ACF6 denote autocorrelation functions up to lag 6. LB denotes the Ljung-Box test
statistic for autocorrelations up to 20 lags. T denotes the sample
size.

151

Table 3.2. Estimated FI-NLAR-ESTAR models for monthly real exchange rates
Real exchange rate
Currency
CHF
GBP
JPY
LW
0.9075
0.8757
0.6165
Nonlinearity tests
TLG
0.002
0.026
0.137
ANN
0.001
0.037
0.110
Estimation of FI-NLAR-ESTAR model
p
9
12
8
k
1
1
1
Linear AR parameters
α0
0.9356
-0.1033 -1.0460
(0.5044) (0.1319) (0.0442)
α1
-0.1081
0.8497
-1.6554
(0.2741) (0.3548) (0.2921)
α2
0.0823
0.0842
0.1162
(0.0572) (0.0552) (0.4743)
α3
0.0867
0.0385
0.0875
(0.0566) (0.0552) (0.3395)
α4
-0.0027
0.0388
-0.0444
(0.0690) (0.0551) (0.5132)
α5
0.0455
0.0152
0.0116
(0.0666) (0.0556) (0.1902)
α6
-0.0665 -0.0661 -0.0611
(0.0657) (0.0537) (0.6066)
α7
0.0848
0.0043
0.0413
(0.0691) (0.0508) (0.4822)
α8
-0.0171
0.0416
0.1279
(0.0987) (0.0538) (0.5507)
α9
0.1002
0.0450
(0.0594) (0.0556)
α10
-0.0739
(0.0557)
α11
0.1457
(0.0555)
α12
-0.0787
(0.0467)

152

NOK
0.6244

SEK
0.6592

0.000
0.000

0.009
0.012

10
1

8
1

-0.1208
(0.2618)
1.4066
(0.0578)
-0.2432
(0.1600)
-0.1522
(0.0940)
-0.0208
(0.1023)
0.0759
(0.0829)
-0.1280
(0.0817)
0.1338
(0.0882)
-0.0936
(0.0820)
0.0774
(0.0923)
-0.0705
(0.0511)

-0.1715
(0.3652)
0.6528
(0.5183)
0.0605
(0.1194)
0.1011
(0.1166)
0.0084
(0.1289)
0.0145
(0.1241)
-0.1231
(0.1137)
0.0785
(0.1158)
0.0676
(0.0983)

Table 3.2. Estimated FI-NLAR-ESTAR models for monthly real exchange rates
(continued)
Real exchange rate
Currency
CHF
GBP
Nonlinear AR parameters
β0
-1.9401
0.2132
(0.4007) (0.1489)
β1
-0.0105 -0.2141
(0.3192) (0.3443)
θ
0.2382
0.3091
(0.1571) (0.9293)
c
1.7175
0.1865
(0.0747) (0.3622)
d
0.6729
0.4182
(0.0763) (0.0207)
LBR
10.56
13.45
Results from ARFIMA models
p
9
9
d
0.9243
0.6485
(0.4141) (0.2550)

JPY

NOK

SEK

2.0330
(0.2350)
0.0633
(1.2233)
1.7287
(0.0237)
-0.6452
(0.0528)
0.6414
(0.0244)
6.09

0.1577
(0.2311)
-0.0008
(0.1223)
0.6007
(1.2970)
-2.5684
(0.2799)
0.5907
(0.1860)
8.76

2.5712
(0.4284)
-0.6328
(0.5509)
0.0439
(0.0216)
-0.8524
(0.0544)
0.4635
(0.0361)
11.07

10
0.7685
(0.2770)

11
0.9008
(0.2450)

8
0.2952
(0.1618)

Note. LW denotes the Local Whittle estimate. TLG and ANN
denote the tests for nonlinearity developed by Ter¨svirta et al.
a
(1993) and Lee et al. (1993), respectively. LBR denotes the
Ljung-Box statistic for residual autocorrelation.

153

Table 3.3. Fractional integration analysis for ARFIMA models
Results from ARFIMA models
Currency
d
Standard error
CHF
GBP
JPY
NOK
SEK

0.9243
0.6485
0.7685
0.9008
0.2952

0.4141
0.2550
0.2770
0.2450
0.1618

Testing H0 :d = 0
against H1 :d > 0
2.2321∗∗
2.5431∗∗∗
2.7744∗∗∗
3.6767∗∗∗
1.8245∗∗

Testing H0 :d = 1
against H1 :d < 1
-0.1828
-1.3784∗
-0.8357
-0.4049
-4.3560∗∗∗

Note. d denotes the MLE of the long memory parameter. The t-statistics
for each hypothesis testing are reported. ∗ , ∗∗ , and ∗∗∗ indicate statistical
signiﬁcance at the 10, 5, and 1 percent levels, respectively.

154

Table 3.4. Fractional integration analysis for FI-NLAR-ESTAR models
Results from FI-NLAR-ESTAR models
Currency
d
Standard error Testing H0 :d = 0
against H1 :d > 0
CHF
0.6729
0.0763
8.8191∗∗∗
GBP
0.4182
0.0207
20.2029∗∗∗
JPY
0.6414
0.0244
26.2869∗∗∗
NOK
0.5907
0.1860
3.1758∗∗∗
SEK
0.4635
0.0361
12.8393∗∗∗
Note. As for Table 3.3.

155

Testing H0 :d = 1
against H1 :d < 1
-4.2870∗∗∗
-28.1063∗∗∗
-14.6967∗∗∗
-2.2005∗∗
-14.8615∗∗∗

Figure 3.1. Logarithms of monthly real exchange rates vis-`-vis the US Dollar over time
a
CHF

GBP

JPY

NOK

SEK

Note. The sample period is from January 1970 through October 2010.

156

Figure 3.2. Autocorrelations
(a) CHF

(b) CHF

Note. (a) Autocorrelations of the logarithms of real exchange rates. The
horizontal axis represents the ﬁrst 120 lags of the autocorrelations of
monthly real exchange rates. (b) Autocorrelations of diﬀerenced real
exchange rates. The horizontal line represents the ﬁrst 120 lags of the
autocorrelations of the ﬁrst diﬀerences of monthly real exchange rates.
The dashed lines indicate the Bartlett 95 percent conﬁdence intervals.

157

Figure 3.2. Autocorrelations (continued)
(a) GBP

(b) GBP

158

Figure 3.2. Autocorrelations (continued)
(a) JPY

(b) JPY

159

Figure 3.2. Autocorrelations (continued)
(a) NOK

(b) NOK

160

Figure 3.2. Autocorrelations (continued)
(a) SEK

(b) SEK

161

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