Bulletin of Monetary Economics and Banking, Vol. 22, No. 3 (2019), pp. 263 - 286

p-ISSN: 1410 8046, e-ISSN: 2460 9196

EXCHANGE RATE AND INTEREST RATE DIFFERENTIAL

IN G7 ECONOMIES*

Peter Golit**, Afees Salisu***, Akinwunmi Akintola****

Faustina Nsonwu*****, Itoro Umoren******

**Research Department, Central Bank of Nigeria, Abuja, Nigeria. Email: pdgolit@cbn.gov.nga

***Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam ; Faculty of Business Administration, Ton Duc Thang University, Ho Chi Minh City, Vietnam ; Centre for Econometric & Allied Research, University of Ibadan, Ibadan, Nigeria. Email : afees.adebare.salisu@tdtu.edu.vn

****Research Department, Central Bank of Nigeria, Abuja, Nigeria. Email: aaakintola@cbn.gov.ng

*****Research Department, Central Bank of Nigeria, Abuja, Nigeria. Email: nfnsonwu@cbn.gov.ng

******Research Department, Central Bank of Nigeria, Abuja, Nigeria. Email: ieumoren@cbn.gov.ng

ABSTRACT

We offer new insights on the dynamics of the exchange rate–interest rate differential for the case of G7 economies. We show that the nexus is better considered using an asymmetric model, as suggested by a host of previous studies. In addition, we find the role of accounting for structural breaks to be prominent. We also show differences in the nexus between euro and non-euro G7 countries, suggesting heterogeneous monetary policies. Thus, we document the strongest evidence for the sticky price hypothesis in Japan and lesser evidence in the euro countries and the United Kingdom, with Canada consistently revealing evidence for the flexible price hypothesis.

Keywords: G7 countries; asymmetry; Structural break; Exchange rate; Interest rate differential.

JEL Classification: E43; F21; F31.

Article history:

 

 

Received

: March 18, 2019

Revised

: October 20, 2019

Accepted

: October 25,

2019

Available online : October 28,

2019

https://doi.org/10.21098/bemp.v22i3.1147

*The authors wish to acknowledge the useful comments by the anonymous reviewers and the managing editor – Professor Paresh Kumar Narayan. The technical support received from the econometric workshops of the Central Bank of Nigeria is graciously acknowledged.

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I. INTRODUCTION

Models of the exchange rate–interest rate differential are not new in the literature, studies exploring the diverse theoretical models (e.g., Bautista, 2006; Hacker et al., 2013; Frankel, 2014; Moosa and Burns, 2014; Andries et al., 2017; Özmen and Yilmaz, 2017) are far from conclusive, and various assumptions of an open economy continue to lead to different conclusions. Amidst these diversities, the unstable nature of the linear econometric modeling of the exchange rate and its fundamentals is brought to the fore by the burgeoning of empirical studies incorporating nonlinearities into the nexus (e.g., Christodoulakis and Mamatzakis, 2013; Ding and Yang, 2017; Bahmani-Oskooee and Motavallizadeh-Ardakani, 2018; Cheikh and Zaied, 2019). These points inform the empirical motivation for this study to explore the asymmetric nature of the exchange rate–interest rate differential in the context of the G7 countries (Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States) as a case study.1

The theoretical motivation for this study is apparent from the multiple theoretical postulations. For instance, the juxtaposition of the predictions of the sticky price and flexible price hypotheses suggest potential asymmetries in the exchange rate–interest rate differential nexus (Frankel, 1979). While the sticky price, for example, predicts a short-run negative relation between the exchange rate and the interest rate differential, the flexible price, on the other hand, argues for a positive relation between them. In other words, the uncovered interest rate parity establishes a connection between the exchange rate and the interest rate differential, as long as the latter is not zero. As further presented by Auten (1963), the theory differentiates between the effects of the interest rate differential on the exchange rate when it favors the home country and when it favors the foreign country. If the positive interest rate differential favors the foreign country (i.e., the foreign interest rate exceeds the domestic interest rate), investment flows will seek a higher interest rate abroad and, hence, increase the exchange rate (i.e., a positive relation). On the other hand, because prices usually display downward rigidity, when the domestic interest rate exceeds the foreign interest rate, prices will not fall to the full extent of the contractionary monetary policy that raised the domestic interest rate in the first place. Thus, a negative relationship is expected between investment inflows and exchange rate under this scenario.

There are also technical motivations for this study that cannot be ignored. For instance, Meese and Rogoff (1983) argue that ignoring nonlinearities is one of the major reasons why macroeconomic fundamentals fail to predict exchange rates out of sample (Moosa, 2013). Ghartey (2018) also argues in support of asymmetry in the exchange rate dynamics that fits the data-generating process well and yields superior estimates, especially in the presence of structural breaks. Kilian and Taylor (2003) also argue that a nonlinear model better fits the exchange rate.

1The analysis is conducted for four units: the euro area as a unit (comprising France, Germany, and

Italy) and each of Canada, Japan, and the United Kingdom, which represent the non-euro area. The United States is implicitly featured as the reference country for which the exchange rates are described and the foreign country for which the interest rate differentials are defined. Hence, the interest rate differential is the difference between the U.S. interest rate and each of the other six country’s interest rates.

Exchange Rate and Interest Rate Differential in G7 Economies

265

 

 

Similarly, Rocha (2012) demonstrates that asymmetries are present even in the dynamics of the interest rate in terms of nonlinear interactions, impacting the financial channel of monetary policy. Overall, empirically, the nonlinear relation between interest rate and exchange rate is informed by the studies of Jackman et al. (2013), Li (2011), and Ozcelebi (2019). Notably, Christodoulakis and Mamatzakis (2013) indicate that asymmetry is an important consideration in determining the exchange rates of the G7 countries, which the present study explores.

Fortified with the foregoing incentives, we proceed to adopt the nonlinear ARDL framework developed by Shin et al. (2014) to determine the asymmetric dynamics of the nexus in the presence of structural breaks. Thus, we also account for structural breaks based on the break dates revealed by Narayan and Liu’s (2015) unit root test.2 This is not trivial, but necessary to account for the shifts observed from the plot of the series (see Figures 1 and 2) and their influence on the nexus. There are also theoretical considerations for why structural breaks could matter for the nexus of concern. Considering the growing integration of the world economy and the special economic cooperation between the G7 economies, the example of the global financial crisis and its aftermath could fuel concerns regarding the sensitivity of the nexus to policy shifts in the area of study. To this end, we categorize the G7 countries into euro area and non-euro area countries and hypothesize that the significance, or otherwise, of asymmetries and structural break in the nexus can vary between the two categories. We expect this unevenness between the euro and non-euro area countries, given the spillover impacts of U.S. monetary policy (the reference country) to the euro area and the bond between the euro/dollar exchange rate are empirically reported to be strong (Hanisch, 2019; Heimonen, 2009), whereas the same cannot necessarily be said of the non-euro area.

The foregoing efforts produce interesting findings that have not yet been clarified in the literature. First, we show differences in the relation between the interest rate differential and the exchange rate for the G7 countries between the euro and non-euro areas. We demonstrate that the relation is best captured in the presence of asymmetries and structural breaks for the euro countries. On the hand, only structural breaks seem to matter in the nexus for the non-euro countries, individually. We find the strongest evidence for the sticky price hypothesis in Japan and lesser evidence in the euro area and the United Kingdom while the flexible price hypothesis is observed for Canada.

The remainder of the paper is structured as follows. Section II describes the methodology. Section III explains the data and offers preliminary results. Section IV presents the main empirical results and discusses the findings. Section V concludes the paper.

2The high frequency and trending nature of the series require us to adopt a unit root test that adequately captures the same. Among the competing tests of Narayan and Liu (2015) and Narayan and Popp (2010), preference is accorded to the former for a number of technical reasons that are described by Salisu, Adediran, Oloko, and Ohemeng (2019), Salisu and Adeleke (2016), and Salisu,

Ndako, and Oloko (2019). However, because the structural break test chosen is a series-based analysis that produces a break date(s) for each series, we incorporate the breaks found for the regressand (i.e., the exchange rate) into our predictive models for both linear and nonlinear ARDL.

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II. MODEL AND METHODOLOGY

Although a number of competent and alternative models of international economics exist in the literature, the flexible price monetary model of the exchange rate proposed by Frenkel (1976) and Bilson (1978) has continued to dominate the analysis of interest rate differentials and exchange rates.3 The model is particularly rooted in three key assumptions, namely, purchasing power parity, uncovered interest parity, and the existence of stable money demand functions for domestic and foreign economies (see also Bianco et al., 2012; Civcir, 2003). The fundamentals of exchange rate determination typically consist of growth of the money supply, output, and short-term interest rate for both the domestic and foreign countries of a bilateral exchange rate. The justifications for these variables in the determination of bilateral exchange rates are well documented in the seminal paper of Frankel (1979), and we do not intend to reproduce the derivations here to avoid repetition. However, the underlying theoretical expectations are reflected in this paper, as follows:4

(1)

where is the logarithm of the exchange rate (the ratio of domestic currency

to the U.S. dollar), mt is the logarithm of the domestic nominal money supply, is the inflation rate, it is the interest rate, with the corresponding foreign variables (using U.S. data) denoted by an asterisk, c is an arbitrary constant, and is a

disturbance term. The long-run parameters for the intercept and slope coefficients

are computed as , , , , and . However, since, in the

long-run, it is assumed that

,

 

,

 

,

 

,

 

 

 

, respectively, the short-run estimates are obtained as and . Equation (1) can be respecified to include an error correction term, as

follows:

(2)

3Notwithstanding variants with sticky prices by Dornbusch (1976) and with trade balances by Hooper

and Morton (1982).

4The choice of this model is underscored by the mixed order of integration evident in the unit root analyses for the relevant series

Exchange Rate and Interest Rate Differential in G7 Economies

267

 

 

 

where

is the linear error correction term, the parameter

is the speed of

adjustment, and the underlying long-run parameters are as previously defined.In terms of a theoretical a priori, an increase in the domestic interest rate lowers the demand for domestic currency and causes depreciation. In terms of equation (1), the coefficient of the nominal interest differential is hypothesized to be positive rather than negative. The inclusion of other variables in the specification is mainly to avoid an omitted variable bias. That said, it must be noted that the ARDL model(s) specified thus far only presumes the relation between the exchange rate and the interest rate differential to be linear (symmetric). Thus, the variant of the ARDL model that allows for our hypothesis of an asymmetric response of the exchange rate to the interest rate differential is expressed as follows:

(3)

The short-run asymmetric situation can be represented as

(4)

The computation of the asymmetric effect follows the approach of Shin et al.

(2014), where and are computed as the positive and negative partial sum decompositions of the interest differential, respectively, as follows:5

(5a)

(5b)

5Several studies have also adopted this approach to analyse the asymmetric response of exchange rates (e.g., Bahmani-Oskooee and Aftab, 2017a,b; Bahmani-Oskooee and Kanitpong, 2017; Salisu and

Ndako, 2018).

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We further extend both the linear and nonlinear ARDL models to include endogenous structural breaks. For the linear (ARDL) model, the specification is as follows:

(6)

The nonlinear ARDL (NARDL) is specified as

(7)

As shown in equations (6) and (7), the breaks are captured with the inclusion

of , where Brt is a dummy variable for each of the breaks, defined as Brt = 1

for , and otherwise Brt = 0. The period is represented by t ; TBr represents the

structural break dates, where denotes the number of breaks, and Dr is the coefficient of the break dummy. All the other parameters are as previously defined.

III. DATA AND PRELIMINARY ANALYSIS

The study employs common samples (monthly data) for the period from January 2000 to December 2018, except for Japan (April 2002 to December 2018), because the data were not readily available. Data used for the study were sourced from the International Monetary Fund, International Financial Statistics, and the Federal Reserve Database. The variables include the nominal exchange rate (ER) with the U.S. dollar as the reference currency and a nominal interest rate measure (INTR) as the three-month Treasury bill rate. Others are a money supply measure (MS) via an aggregate monetary index, output growth using industrial production index (IPI), and the Consumer Price Index (CPI) as a measure of inflation. Table 1 presents descriptive statistics of the series, namely, the mean, standard deviation, skewness, and kurtosis.

Exchange Rate and Interest Rate Differential in G7 Economies

269

 

 

Table 1.

Summary Statistics

This table provides basic descriptive statistics of the data. The variables ER, INTR, MS, IPI, and CPI represent Exchange Rate, Interest Rate, Money Supply, Industrial Production Index and Consumer Price Index, respectively.

 

ER

INTR

MS

IPI

CPI

ER

INTR

MS

IPI

CPI

Description

 

 

Euro Area

 

 

 

Canada

 

 

Mean

0.84

1.89

80.58

99.11

91.11

1.23

2.27

70.22

109.02

98.58

Std. Dev.

0.13

1.64

20.66

4.68

8.75

0.19

1.52

27.18

6.79

9.69

Skewness

0.95

0.51

-0.22

0.25

-0.26

0.41

0.79

0.38

-0.35

-0.10

Kurtosis

3.15

1.88

1.86

2.74

1.72

2.06

2.51

1.95

3.24

1.87

 

 

 

Japan

 

 

 

 

UK

 

 

Mean

105.1

0.28

91.36

101.34

101.49

0.63

2.72

80.46

103.37

98.38

Std. Dev.

13.46

0.24

8.60

8.69

1.69

0.08

2.24

26.44

6.98

11.80

Skewness

-0.63

1.17

0.75

0.02

0.74

0.17

0.29

-0.28

0.30

0.08

Kurtosis

2.36

3.30

2.20

3.40

2.22

2.59

1.36

1.61

2.65

1.57

 

 

Reference Country (US)

 

 

 

 

 

 

Mean

-

1.97

73.12

105.26

97.79

 

 

 

 

 

Std. Dev.

-

1.98

23.94

5.68

11.16

 

 

 

 

 

Skewness

-

0.97

0.40

-0.17

-0.20

 

 

 

 

 

Kurtosis

-

2.65

1.91

2.16

1.75

 

 

 

 

 

Starting with the mean, the Japanese yen/U.S. dollar exchange rate with a mean value of 105 reveals Japan as the economy with the weakest currency relative to the U.S. dollar, when compared to the exchange rates of the other G7 countries. The average interest rate for the period under consideration is 2% for Canada and the United Kingdom, which is the highest, and Japan is the country with the lowest interest rates. The inference from the standard deviation also is that Japan is the country with the most volatile exchange rate, while the United Kingdom has the least volatile exchange rate. However, as expected of developed economies, the standard deviation for the interest rate seems to be reasonable for both the euro and non-euro G7 countries. With respect to the distributions, we find evidence of non-zero skewness for all the series and across all the G7 countries. The kurtosis statistic is, however, mostly platykurtic in a number of countries, except in a few instances in the case of Japan, Canada, and the euro area. These differences could support our assumption of different responses of exchange rates to changes in the interest rate differential across countries.

Figures 1 and 2 are graphical illustrations of comovements between the exchange rate and the interest rate, as well as between the exchange rate and the interest rate differential, respectively. A cursory look at Figure 1 shows that comovements between the exchange rate and interest have mainly been in the opposite direction, with the likely exception of the euro area. That is, unlike the non-euro G7 countries, there are few instances, particularly in the early period of the sample, where the exchange rate and interest rate appear to be moving in the same direction in the euro area. Similarly, the plots of the exchange rate and the interest rate differential in Figure 2 mostly move equally in the opposite direction, but the movement is mixed in the case of the euro area.

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Figure 1.

Exchange Rate and Interest Rate Movements in G7 Countries

The first to fourth quadrant represent figures for Euro area, Canada, Japan, and UK respectively.

Exchange Rate and Interest Rate in Euro Area, 2000M1 to 2018M12

 

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

ER

INTR_DIFF

5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4

 

Exchange Rate

1,2

 

 

 

 

 

 

 

 

 

3

Rate Interest

 

 

 

 

 

 

 

 

 

2

1,1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

1,0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0

0,9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,8

 

 

 

 

 

 

 

 

 

 

 

 

0,7

 

 

 

 

 

 

 

 

 

 

 

 

0,6

 

 

 

 

 

 

 

 

 

 

 

 

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

 

 

 

 

 

 

 

Period

 

 

 

 

 

 

 

Exchange Rate and Interest Rate in Canada, 2000M1 to 2018M12

 

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

ER

INTR_DIFF

5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4

 

 

1,8

 

 

 

 

 

 

 

 

 

3

Rate Interest

Exchange Rate

 

 

 

 

 

 

 

 

 

 

1,6

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

1,4

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

1,2

 

 

 

 

 

 

 

 

 

 

 

 

1,0

 

 

 

 

 

 

 

 

 

 

 

 

0,8

 

 

 

 

 

 

 

 

 

 

 

 

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

 

 

 

 

 

 

 

Period

 

 

 

 

 

 

 

Exchange Rate and Interest Rate Differential in G7 Economies

271

 

 

Figure 1.

Exchange Rate and Interest Rate Movements in G7 Countries (Continued)

 

 

 

 

Exchange Rate and Interest Rate in Japan, 2000M1 to 2018M12

 

 

1,0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ER

 

INTR_DIFF

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,6

 

Exchange Rate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,4

 

140

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,2

Rate Interest

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

120

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

18

 

 

 

 

 

 

 

 

 

 

 

Period

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Exchange Rate and Interest Rate in UK, 2000M1 to 2018M12

 

8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ER

INTR_DIFF

 

 

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

 

 

 

4

 

Exchange Rate

.9

 

 

 

 

 

 

 

 

 

2

Rate Interest

 

 

 

 

 

 

 

 

 

 

.8

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

.7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.6

 

 

 

 

 

 

 

 

 

 

 

 

.5

 

 

 

 

 

 

 

 

 

 

 

 

.4

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

 

 

 

 

 

 

 

Period

 

 

 

 

 

 

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Figure 2.

Exchange Rate and Interest Rate Differentials in G7 Countries

The first to fourth quadrant represent figures for Euro area, Canada, Japan, and UK respectively.

Exchange Rate and Interest Rate Differential in Euro Area, 2000M1 to 2018M12

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

0

 

 

1,2

 

 

 

 

 

 

 

 

-1

Differential Rate Interest

Exchange Rate

 

 

 

 

 

 

 

 

 

1,1

 

 

 

 

 

 

 

 

-2

 

 

 

 

 

 

 

 

 

1,0

 

 

 

 

 

 

 

 

-3

 

 

 

 

 

 

 

 

 

0,9

 

 

 

 

 

 

 

 

-4

 

 

 

 

 

 

 

 

 

0,8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,7

 

 

 

 

 

 

 

 

 

 

 

0,6

 

 

 

 

 

 

 

 

 

 

 

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

 

 

 

 

 

 

Period

 

 

 

 

 

 

Exchange Rate and Interest Rate Differential in Canada, 2000M1 to 2018M12

 

 

 

 

 

 

 

 

 

 

2,4

 

 

 

ER

INTR_DIFF

 

 

 

 

 

2,0

 

 

 

 

 

 

 

 

 

 

 

1,6

 

 

 

 

 

 

 

 

 

 

 

1,2

Differential Rate Interest

Exchange Rate

 

 

 

 

 

 

 

 

 

0,8

1,8

 

 

 

 

 

 

 

 

0,4

1,6

 

 

 

 

 

 

 

 

0,0

 

 

 

 

 

 

 

 

-0,4

1,4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1,2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1,0

 

 

 

 

 

 

 

 

 

 

 

0,8

 

 

 

 

 

 

 

 

 

 

 

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

 

 

 

 

 

 

Period

 

 

 

 

 

Exchange Rate and Interest Rate Differential in G7 Economies

273

 

 

Figure 2.

Exchange Rate and Interest Rate Differentials in G7 Countries (Continued)

 

 

 

 

Exchange Rate and Interest Rate Differential in Japan, 2000M1 to 2018M12

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ER

 

 

INTR_DIFF

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-2

Differential Rate Interest

Exchange Rate

140

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

120

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-5

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

18

 

 

 

 

 

 

 

 

 

 

 

Period

 

 

 

 

 

 

 

 

 

 

 

Exchange Rate and Interest Rate Differential in UK, 2000M1 to 2018M12

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

0

Differential Rate Interest

Exchange Rate

.9

 

 

 

 

 

 

 

 

-1

 

 

 

 

 

 

 

 

 

.8

 

 

 

 

 

 

 

 

 

.7

 

 

 

 

 

 

 

 

-2

 

 

 

 

 

 

 

 

 

.6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.5

 

 

 

 

 

 

ER

INTR_DIFF

 

 

 

 

 

 

 

 

 

 

 

.4

 

 

 

 

 

 

 

 

 

 

 

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

 

 

 

 

 

 

Period

 

 

 

 

 

 

274

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To test the stationarity of the series, we explore both the conventional augmented Dickey–Fuller (ADF) test, as well as the version that accounts for structural breaks. The unit root test results are documented in Table 2, where the order of integration tends to hover around I(0) and I(1). The fact that this evidence of mixed order of integration reported in the table holds for ADF tests both with and without structural breaks thus reaffirms our choice of estimation technique, namely, the linear and nonlinear ARDL models. The ARDL framework allows for the combination of the series with a mixed order of cointegration. For more reliability, we apply the Narayan–Liu (2015) unit root test (for motivation, see Salisu and Adeleke, 2016; Salisu, Adediran, Oloko, and Ohemeng, 2019; Salisu, Ndako and Oloko, 2019) to confirm the order of integration of the series and to obtain break dates for the regressand to be carried forward to estimate the model.

Table 2.

Unit Root Test Results

This table presents results of unit root tests. Three tests are used: namely, ADF, ADF with a break and the Narayan and Liu break tests. Here, a, b and c represent, 1%, 5% and 10% levels of significance, respectively. The superscripts ^ and # represent unit root test equations with ‘constant only’ and ‘constant and trend’, respectively. The accompanying values in round brackets are the optimal lags. I(d) represent the order of integration indicated by the test.

Country

ADF Unit Root Test

 

ADF Test with Structural Break

Narayan and Liu (2015) Unit Root Test

 

 

 

 

 

 

 

 

 

Series

Statistics

I(d)

Statistics

I(d)

Break Date

Statistics

I(d)

Break Date

 

 

 

 

 

 

 

 

 

 

 

Euro Area

CPI

-3.367 (13)b#

I(1)

-14.358 (0)a#

I(1)

2009 M10

-14.109a#

I(1)

2014M07

 

IPI

-5.554 (2)a^

I(1)

-6.185 (3)a^

I(0)

2008 M09

-3.421a#

I(0)

2008M05

 

INTR

-10.995 (0)a^

I(1)

-5.860 (3)a^

I(0)

2015 M04

-8.984a#

I(0)

2008M11, 2012M01

 

MS

-10.283 (9)a^

I(2)

-6.256 (0)a^

I(0)

2000 M11

-7.465a#

I(1)

2009M01, 2014M11

 

ER

-11.064 (0)a#

I(1)

-11.562 (0)a#

I(1)

2008 M10

-10.342a#

I(1)

2002M12

 

 

 

 

 

 

 

 

 

 

Canada

CPI

-3.676 (1)b#

I(0)

-5.026 (1)b#

I(0)

2002M01

-5.667a#

I(0)

-

 

IPI

-3.844 (14)b#

I(1)

-5.622 (0)a#

I(0)

2000M11

-7.907a#

I(0)

2007M12

 

INTR

-5.571 (1)a#

I(1)

-5.386 (2)a#

I(0)

2008M09

-31.708a#

I(0)

2008M01

 

MS

-12.987 (0)a^

I(1)

-13.747 (0)a^

I(1)

2008M06

-15.106a#

I(1)

2003M09, 2008M12

 

ER

-10.817 (0)a#

I(1)

-11.852 (0)a#

I(1)

2008M10

-9.294a#

I(1)

2014M12

 

 

 

 

 

 

 

 

 

 

Japan

CPI

-11.364 (0)a#

I(0)

-13.186 (0)a#

I(1)

2014M04

-11.384a#

I(1)

2008M11, 2014M04

 

IPI

-3.117 (12)b^

I(0)

-7.343 (0)a^

I(0)

2003M08

-16.271a#

I(0)

2008M11, 2012M08

 

INTR

-13.280 (0)a#

I(1)

-5.640 (0)a#

I(0)

2006M02

-69.975a#

I(1)

2007M09, 2016M02

 

MS

-10.520 (0)a#

I(1)

-11.945 (0)a#

I(1)

2008M10

-9.732a#

I(1)

2005M12

 

ER

-11.088 (0)a#

I(1)

-11.490 (0)a#

I(1)

2016M12

-9.283a#

I(1)

2012M11

 

 

 

 

 

 

 

 

 

 

Exchange Rate and Interest Rate Differential in G7 Economies

 

 

275

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2.

 

 

 

 

 

 

 

Unit Root Test Results (Continued)

 

 

 

 

 

 

Country

ADF Unit Root Test

ADF Test with Structural Break

Narayan and Liu (2015) Unit Root Test

 

 

 

 

 

 

 

 

 

 

Series

Statistics

I(d)

Statistics

I(d)

Break Date

Statistics

I(d)

Break Date

 

 

 

 

 

 

 

 

 

 

 

 

UK

CPI

-14.031

(10)a^

I(2)

-16.208 (0)a^

I(1)

2001M01

-18.066a#

I(1)

-

 

IPI

-2.950 (13)b^

I(1)

-11.585 (0)a^

I(0)

2000M11

-18.278a#

I(0)

2008M11

 

INTR

-5.148 (2)a#

I(1)

-7.174 (3)a#

I(0)

2008M10

-15.136a#

I(1)

2003M08, 2008M11

 

MS

-4.767 (4)a#

I(1)

-8.914 (3)a#

I(1)

2010M02

-8.9254a#

I(1)

2010M04, 2016M01

 

ER

-11.494 (0)a#

I(1)

-12.362 (0)a#

I(1)

2008 M11

-11.112a#

I(1)

-

 

 

 

 

 

 

 

 

 

 

 

US

CPI

-9.852

(1)a#

I(1)

-10.998 (1)a#

I(1)

2008 M11

-7.565a#

I(1)

2008M08, 2014M10

 

IPI

-5.554

(2)a^

I(1)

-6.185 (3)a^

I(0)

2008 M09

-7.397a#

I(0)

2008M09, 2015M09

 

INTR

-9.514

(0)a#

I(1)

-10.283 (0)a#

I(1)

2009 M01

-15.260a#

I(1)

2006M05, 2008M11

 

MS

-12.145 (0)a#

I(1)

-13.323 (0)a#

I(1)

2011 M08

-11.602a#

I(1)

2008M09 2011M04

 

 

 

 

 

 

 

 

 

 

 

IV. RESULTS AND DISCUSSION

A. Main Results

The theoretical perspective informing the a priori expectation of the exchange rate and interest rate differential relation, states that an increase in the interest rate differential favoring the domestic economy will lead to more foreign currency chasing the domestic currency, thereby leading to foreign capital inflows that will ultimately lead to appreciation of the domestic currency. This effect indicates a negative relation between the exchange rate and the interest rate differential. However, an increase in the domestic interest rate, holding the foreign rate (the U.S. interest rate) constant, will not necessarily lead to more foreign capital inflows into the domestic economy. Due to the level of economic instability, it will lead to depreciation of the domestic currency, thereby indicating a positive relation with interest rate differential. In an attempt to draw a meaningful inference on the extent to which these assertions define the movement of the exchange rate along with the interest rate differential in the G7 countries, we consider both the linear and nonlinear ARDL models, accounting for structural breaks in the data. The estimated results are reported in Tables 3 to 6.

The results using the euro as a unit are shown in Table 3, and those for Canada, Japan, and the United Kingdom (the non-euro area) are shown in Tables 4 to 6, respectively. Four variants of the ARDL model are presented in the tables: the linear ARDL models with and without structural breaks in the data and their nonlinear counterparts (i.e., nonlinear ARDL models without and with structural breaks). However, not all the models perform equally well across the samples in terms of diagnostics, model performance criteria, and the existence of cointegration (long- run relation). In all countries, the effect of structural breaks on the results is highly influential. This is evident in the bounds cointegration test results, which improved

276

Bulletin of Monetary Economics and Banking, Volume 22, Number 3, 2019

 

 

after we accounted for structural breaks on either the linear or asymmetric ARDL model Although not as pronounced as the effect of structural breaks on cointegration, the results also raise a strong case for accounting for asymmetry. We report differing impacts of positive and negative interest rate differentials on the exchange rates across the four samples, supporting previous studies (e.g., Li, 2011; Jackman et al., 2013; Ozcelebi, 2019).

Based on the objective of the study, which is focused on the relation between the interest rate differential and the exchange rate, we dwell more on the results that produce better estimates of cointegration between the variables and better diagnostics. In line with one of the focuses of the study, which is to compare the results for the euro and non-euro G7 countries, we highlight that the best model for the former is the nonlinear ARDL with structural breaks, while the latter, the linear ARDL with structural breaks, gives better estimates. This is not an absolute, however, since some evidence of asymmetry reported for the non-euro area cannot be ignored. We find a negative relation between the variables prominent in the euro area, whether linear or nonlinear. Even when positive and negative asymmetries give rise to positive and negative effects, respectively, it is the negative effect that is found to be statistically significant. Conversely, in the non-euro area, a positive effect is more pronounced in Canada in both the short and long-run, even when positive and negative asymmetries also lead to positive and negative changes on the exchange rate, respectively. Japan also records different results from the euro area, in that positive and negative asymmetries produce negative and positive impacts on the exchange rate, respectively. However, Japan and the United Kingdom record predominantly negative impacts, as for the euro area.

The sticky price hypothesis that specifies a negative relation, especially in the short run, between the interest rate differential and the exchange rate appears to be supported by evidence in Japan; however, the situation is less clear in the euro area and in the United Kingdom, where the negative relation between the exchange rate and the interest rate differential extends to the long-run. On the other hand, evidence obtained for Canada appears to validate the flexible price hypothesis, with a positive nexus between the exchange rate and the interest rate differential in the short and long-run.

Table 3.

Empirical Results for Euro Area

This table reports the main results. Here, ***, ** and * represent 1%, 5% and 10% levels of significance, respectively. The term NA implies not applicable or not available, CV denotes control variable, NARDL stands for nonlinear ARDL, and SB indicates structural break. Values in parenthesis are the standard errors of the associated statistics.

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

 

 

 

 

 

 

 

 

(2,0,0,0,0)

 

 

(2,0,0,0,0)

 

(2,0,0,0,0,0)

 

(2,0,0,0,0,0)

 

 

 

 

 

 

 

 

 

 

 

 

-0.001

 

 

-0.005**

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.002)

 

 

(0.002)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0058

 

0.002

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.004)

 

(0.003)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Short-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

-0.004*

 

-0.008***

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.003)

 

(0.003)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

ECTt

 

-0.061***

 

 

-0.136***

 

-0.099***

 

-0.177***

 

 

 

 

(0.0166)

 

 

(0.026)

 

(0.023)

 

(0.031)

 

 

 

 

 

 

 

 

 

 

 

 

-0.016

 

 

-0.036**

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.033)

 

 

(0.014)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.058

 

0.012

 

Long-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.036)

 

(0.022)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

-0.046**

 

-0.049***

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.021)

 

(0.011)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

 

 

 

 

 

 

 

 

 

Panel A: Cointegration Test Result

 

 

 

 

 

Level of Significance

 

ARDL

 

ARDL-SB

 

 

NARDL

 

 

NARDL-SB

 

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

 

10%

2.67

3.03

 

 

4.06

5.12

3.03

4.06

2.99

2.75

3.79

5.19

2.75

3.79

5%

 

3.47

 

 

4.57

 

3.47

4.57

 

3.12

4.25

 

3.12

4.25

1%

 

4.4

 

 

 

5.72

 

4.4

5.72

 

3.93

5.23

 

3.93

5.23

 

 

 

 

 

 

 

 

 

 

Panel B: Diagnostic Test/Post Estimation Result

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

Adj. R2

 

0.977

 

 

0.978

 

0.977

 

0.978

 

 

 

F-statistic

 

1370.991***

 

1261.138***

 

1218.725***

 

1142.425***

 

Post Estimation Results

 

SIC

 

-4.633

 

 

-4.662

 

-4.628

 

-4.661

 

 

Q-statistics (10)

 

6.361

 

 

6.264

 

5.756

 

7.431

 

 

 

 

 

 

 

 

 

 

Q2-statistics (10)

 

21.203

 

 

14.916

 

16.56*

 

12.170

 

 

 

ARCH-LM (5)

 

4.194**

 

 

2.935**

 

3.817***

 

2.775**

 

 

 

ARCH-LM (10)

 

2.279**

 

 

1.720*

 

2.135**

 

1.752*

 

Economies G7 in Differential Rate Interest and Rate Exchange

277

Table 4.

Empirical Results for Canada

This table reports empirical results for Canada. Here, ***, ** and * represent 1%, 5% and 10% levels of significance, respectively. The term NA implies not applicable or not available, CV denotes control variable, NARDL stands for nonlinear ARDL, and SB indicates structural break. Values in parenthesis are the standard errors of the associated statistics.

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

 

 

 

 

 

 

 

 

(2,1,1,0,0)

 

 

(2,1,1,0,0)

 

(2,0,1,1,1,0)

 

(2,0,1,1,0,0)

 

 

 

 

 

 

 

 

 

 

 

 

0.003

 

 

0.004**

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.002)

 

 

(0.002)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0049**

 

0.005**

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.002)

 

(0.003)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Short-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

-0.0016

 

-0.0009

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.003)

 

(0.003)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

ECTt

 

0.009***

 

 

-0.014***

 

-0.0076***

 

-0.036***

 

 

 

 

(0.002)

 

 

(0.036)

 

(0.001)

 

(0.008)

 

 

 

 

 

 

 

 

 

 

 

 

-0.350

 

 

0.320

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.518)

 

 

(0.048)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.654

 

0.142

 

Long-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(1.628)

 

(0.103)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

-0.215

 

-0.026

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.434)

 

(0.092)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

 

 

 

 

 

 

 

 

 

Panel A: Cointegration Test Result

 

 

 

 

 

Level of Significance

 

ARDL

 

ARDL-SB

 

 

NARDL

 

 

NARDL-SB

 

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

 

10%

2.58

3.03

 

 

4.06

3.07

3.03

4.06

2.60

2.75

3.79

3.04

2.75

3.79

5%

 

3.47

 

 

4.57

 

3.47

4.57

 

3.12

4.25

 

3.12

4.25

1%

 

4.4

 

 

 

5.72

 

4.4

5.72

 

3.93

5.23

 

3.93

5.23

 

 

 

 

 

 

 

 

 

 

 

Panel B: Diagnostic Test/Post Estimation Result

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

Adj. R2

 

0.986

 

 

0.987

 

0.987

 

0.986

 

Post Estimation

 

F-statistic

 

1883.470***

 

1714.088***

 

1560.943***

 

1547.368***

 

 

SIC

 

-5.111

 

 

-5.102

 

-5.085

 

-5.076

 

Results

 

Q-statistics (10)

 

9.346

 

 

8.650

 

6.211

 

4.963

 

 

Q2-statistics (10)

 

15.172

 

 

12.313

 

17.722*

 

20.965**

 

 

 

ARCH-LM (5)

 

0.425

 

 

0.547

 

0.472

 

0.808

 

 

 

ARCH-LM (10)

 

1.541

 

 

1.198

 

1.837*

 

2.158**

 

278

2019 3, Number 22, Volume Banking, and Economics Monetary of Bulletin

Table 5.

Empirical Results for Japan

This table reports empirical results for Japan. Here, ***, ** and * represent 1%, 5% and 10% levels of significance, respectively. The term NA implies not applicable or not available, CV denotes control variable, NARDL stands for nonlinear ARDL, and SB indicates structural break. Values in parenthesis are the standard errors of the associated statistics.

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

 

 

 

 

 

 

 

 

 

(2,0,0,0,1)

 

 

(1,0,0,0,1)

 

(2,0,0,0,0,1)

 

(2,0,0,0,0,1)

 

 

 

 

 

 

 

 

 

 

 

 

-0.0023

 

 

-0.004**

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.001)

 

 

(0.001)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-0.012**

 

-0.015***

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.004)

 

(0.004)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Short-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

0.009*

 

0.009*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.005)

 

(0.005)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

ECTt

 

-0.023***

 

 

-0.059***

 

-0.067***

 

-0.112***

 

 

 

 

 

 

 

 

 

 

 

 

(0.008)

 

 

(0.012)

 

(0.001)

 

(0.0021)

 

 

 

 

 

 

 

 

 

 

 

 

-0.099

 

 

-0.0719

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.100)

 

 

(0.034)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-0.182***

 

-0.133***

 

Long-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.051)

 

(0.028)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

0.137**

 

0.080***

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.063)

 

(0.038)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

 

 

 

 

 

 

 

 

 

Panel A: Cointegration Test Result

 

 

 

 

 

Level of Significance

 

ARDL

 

ARDL-SB

 

 

NARDL

 

 

NARDL-SB

 

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

 

10%

1.36

3.03

 

 

4.06

4.57

3.03

4.06

2.01

2.75

3.79

4.47

2.75

3.79

5%

 

3.47

 

 

4.57

 

3.47

4.57

 

3.12

4.25

 

3.12

4.25

1%

 

4.4

 

 

 

5.72

 

4.4

5.72

 

3.93

5.23

 

3.93

5.23

 

 

 

 

 

 

 

 

 

 

 

Panel B: Diagnostic Test/Post Estimation Result

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

Adj. R2

 

0.973

 

 

0.975

 

0.974

 

0.976

 

Post Estimation

 

F-statistic

 

926.900***

 

978.600***

 

842.387***

 

819.856***

 

 

SIC

 

-4.631

 

 

-4.674

 

-4.631

 

-4.686

 

Results

 

Q-statistics (10)

 

11.181

 

20.695**

 

11.468

 

10.931

 

 

Q2-statistics (10)

 

6.372

 

 

5.5081

 

6.289

 

5.412

 

 

 

ARCH-LM (5)

 

0.747

 

 

0.369

 

0.900

 

0.505

 

 

 

ARCH-LM (10)

 

0.622

 

 

0.521

 

0.550

 

0.456

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Economies G7 in Differential Rate Interest and Rate Exchange

279

Table 6.

Empirical Results for UK

This table reports results for the UK. Here, ***, ** and * represent 1%, 5% and 10% levels of significance, respectively. The term NA implies not applicable or not available, CV denotes control variable, NARDL stands for nonlinear ARDL, and SB indicates structural break. Values in parenthesis are the standard errors of the associated statistics.

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

 

 

 

 

 

 

 

 

(2,1,0,0,1)

 

 

(2,1,0,0,1)

 

(2,0,0,1,0,1)

 

(2,0,1,0,0,1)

 

 

 

 

 

 

 

 

 

 

 

 

-0.0034

 

 

-0.0009

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.002)

 

 

(0.003)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0045

 

0.0033

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.006)

 

(0.007)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Short-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

-0.007*

 

-0.004

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.004)

 

(0.004)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

ECTt

 

-0.070***

 

 

-0.051***

 

-0.076***

 

-0.066***

 

 

 

 

 

 

 

 

 

 

 

 

(0.022)

 

 

(0.015)

 

(0.024)

 

(0.018)

 

 

 

 

 

 

 

 

 

 

 

 

-0.048*

 

 

-0.019

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

 

(0.028)

 

 

(0.054)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.059

 

0.050

 

Long-run

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.088)

 

(0.112)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-

 

 

-

 

-0.097**

 

-0.066

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.045)

 

(0.052)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

 

 

 

 

 

 

 

 

 

Panel A: Cointegration Test Result

 

 

 

 

 

Level of Significance

 

ARDL

 

ARDL-SB

 

 

NARDL

 

 

NARDL-SB

 

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

 

10%

1.99

3.03

 

 

4.06

2.30

3.03

4.06

1.54

2.75

3.79

2.08

2.75

3.79

5%

 

3.47

 

 

4.57

 

3.47

4.57

 

3.12

4.25

 

3.12

4.25

1%

 

4.4

 

 

 

5.72

 

4.4

5.72

 

3.93

5.23

 

3.93

5.23

 

 

 

 

 

 

 

 

 

 

Panel B: Diagnostic Test/Post Estimation Result

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARDL

 

ARDL-SB

 

NARDL

 

NARDL-SB

 

 

 

Adj. R2

 

0.973

 

 

0.973

 

0.973

 

0.973

 

Post Estimation

 

F-statistic

 

925.340***

 

835.041***

 

834.374***

 

759.622***

 

 

SIC

 

-4.786

 

 

-4.770

 

-4.769

 

-4.751

 

Results

 

Q-statistics (10)

 

10.877

 

 

9.856

 

7.310

 

10.786

 

 

 

Q2-statistics (10)

 

18.121

 

 

15.037

 

14.376

 

14.273

 

 

 

ARCH-LM (5)

 

3.778

 

 

3.079**

 

2.696**

 

2.957**

 

 

 

ARCH-LM (10)

 

2.166**

 

 

1.691*

 

1.445

 

1.619

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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B. Robustness

We test the sensitivity of our estimates to gain confidence in the results. A number of processes exist for this, including the prominent adoption of different proxies for one or more variables in the model or alternative data frequencies, for example. We embrace the second option, banking on previous clues that the predictability models of financial series such as those assessed here could be sensitive to the choice of data frequency (e.g., Narayan and Liu, 2015; Narayan and Sharma, 2015; Salisu and Adeleke, 2016; Narayan et al., 2018; Salisu, Ndako, and Oloko, 2019). Hence, having employed monthly observations in the main analysis, we thought it revealing to determine the sensitivity of the results using a quarterly data frequency. The effort proved instructive (see Table 7). For brevity, we implement it for the best models for each case identified in the main analysis, that is, the nonlinear ARDL with structural breaks for the euro area unit and the linear ARDL with structural breaks for each of the non-euro countries. As in the main analysis, the positive and negative interest rate differential asymmetries produce positive and negative effects on the exchange rate, respectively. Additionally, the results for Canada support the flexible price hypothesis, whereas those for Japan and the United Kingdom provide weak evidence showing affinity to the sticky price hypothesis, as for the main results. In passing, we reject across the board the null of no cointegration between the variables, supporting the earlier choice of the underlying models when we considered a monthly data frequency.

V. CONCLUSION

Using the cases of the euro and non-euro G7 countries, we explore both the conventional and augmented versions of ARDL models to simultaneously capture the need for asymmetry and structural breaks in the exchange rate–interest rate differential nexus. We advanced theoretical, empirical, and technical reasons for considering asymmetry and structural breaks in the relation. Further, we were theoretically motivated by the possibility of testing the validity, or otherwise, of the flexible/sticky price hypotheses in the countries. Consequently, we find that the consideration of structural breaks matters in the nexus and is more prominent than asymmetry. When we compare the results for the euro and non-euro G7 countries, we highlight that the nonlinear ARDL with structural breaks is the best model for the former, while the linear ARDL with structural breaks gives the better estimates in the latter. We inform policymakers of the need to note differences in the empirical results, with the strongest evidence of the sticky price hypothesis found for Japan and lesser evidence for the euro area and the United Kingdom, and strong evidence of the flexible price hypothesis for Canada. In sum, we demonstrate the credibility of our results for an alternative data frequency, as revealed through monthly observations.

Table 7.

Empirical Results for Alternative Data Frequency

This table reports results based on a different data frequency. Here, ***, ** and * represent 1%, 5% and 10% levels of significance, respectively. The term NA implies not applicable or not available, CV denotes control variable, NARDL stands for nonlinear ARDL, and SB indicates structural break. Values in parenthesis are the standard errors of the associated statistics.

 

 

 

 

 

 

 

 

 

 

Euro Area

 

 

Canada

 

Japan

 

UK

 

 

 

 

 

 

 

 

 

 

 

NARDL (1,0,0,2,0,0)

ARDL (1,1,1,0,0)

 

ARDL (3,2,0,0,0)

 

ARDL (2,0,3,1,0)

 

 

 

 

 

 

 

 

 

 

-

 

 

0.012*

 

-0.007*

 

-0.017*

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.006)

 

(0.003)

 

(0.008)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0092

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

(0.014)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Short-run

 

 

 

 

 

 

 

 

 

-0.028***

 

 

-

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

(0.008)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

ECTt

 

-0.452***

 

 

-0.1000***

 

-0.129***

 

-0.456***

 

 

 

 

 

 

 

 

 

 

 

(0.063)

 

 

(0.019)

 

(0.022)

 

(0.078)

 

 

 

 

 

 

 

 

 

 

 

-

 

 

0.120

 

-0.057*

 

-0.038**

 

 

 

 

 

 

 

 

 

 

 

 

 

(0.110)

 

(0.031)

 

(0.014)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0203

 

 

 

 

 

Long-run

 

 

 

 

 

 

 

 

 

 

 

-

 

-

 

-

 

 

 

 

 

 

 

 

 

 

(0.031)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-0.062***

 

 

-

 

-

 

-

 

 

 

 

 

 

 

 

 

 

 

(0.013)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CV

 

Yes

 

 

Yes

 

Yes

 

Yes

 

 

 

 

 

 

 

 

 

 

 

Panel A: Cointegration Test Result

 

 

 

 

 

Level of Significance

 

Euro Area

 

Canada

 

 

Japan

 

 

UK

 

 

NARDL-SB

 

ARDL-SB

 

 

ARDL-SB

 

ARDL-SB

 

 

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

F-stat

I(0)

I(1)

10%

7.799

2.75

 

 

3.79

4.890

3.03

4.06

5.253

2.2

3.09

6.379

3.03

4.06

5%

 

3.12

 

 

4.25

 

3.47

4.57

 

2.56

3.49

 

3.47

4.57

1%

 

3.93

 

 

5.23

 

4.4

5.72

 

3.29

4.37

 

4.4

5.72

 

 

 

 

 

 

 

 

 

 

Panel B: Diagnostic Test/Post Estimation Result

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Euro Area

 

Canada

 

Japan

 

UK

 

 

 

 

 

 

 

 

 

 

 

NARDL-SB

 

ARDL-SB

 

ARDL-SB

 

ARDL-SB

 

 

 

Adj. R2

 

0.952

 

 

0.966

 

0.944

 

0.953

 

Post Estimation

 

F-statistic

 

148.543***

 

238.289***

 

108.511***

 

123.006***

 

 

SIC

 

-3.629

 

 

-3.936

 

-3.563

 

-3.818

 

Results

 

 

 

 

 

 

 

 

Q-statistics (10)

 

20.382**

 

 

16.314*

 

13.497

 

8.890

 

 

 

 

 

 

 

 

 

 

Q2-statistics (10)

 

7.665

 

 

10.936

 

7.989

 

7.973

 

 

 

ARCH-LM (5)

 

0.502

 

 

1.354

 

0.352

 

0.4110

 

 

 

ARCH-LM (10)

 

0.538

 

 

0.852

 

0.862

 

0.7703

 

282

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