Bulletin of Monetary Economics and Banking, Vol. 22, No. 3 (2019), pp. 263 - 286
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
Keywords: G7 countries; asymmetry; Structural break; Exchange rate; Interest rate differential.
JEL Classification: E43; F21; F31.
Article history: |
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Received |
: March 18, 2019 |
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Revised |
: October 20, 2019 |
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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
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
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
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
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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
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
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
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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
(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
are computed as , , , , and . However, since, in the
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, respectively, the
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 |
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where |
is the linear error correction term, the parameter |
is the speed of |
adjustment, and the underlying
(3)
The
(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.,
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
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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.
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ER |
INTR |
MS |
IPI |
CPI |
ER |
INTR |
MS |
IPI |
CPI |
Description |
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Euro Area |
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Canada |
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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 |
0.25 |
0.41 |
0.79 |
0.38 |
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Kurtosis |
3.15 |
1.88 |
1.86 |
2.74 |
1.72 |
2.06 |
2.51 |
1.95 |
3.24 |
1.87 |
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Japan |
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UK |
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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 |
1.17 |
0.75 |
0.02 |
0.74 |
0.17 |
0.29 |
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 |
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Reference Country (US) |
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Mean |
- |
1.97 |
73.12 |
105.26 |
97.79 |
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Std. Dev. |
- |
1.98 |
23.94 |
5.68 |
11.16 |
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Skewness |
- |
0.97 |
0.40 |
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Kurtosis |
- |
2.65 |
1.91 |
2.16 |
1.75 |
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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
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
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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
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ER |
INTR_DIFF |
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Exchange Rate |
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2018 |
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Exchange Rate and Interest Rate in Canada, 2000M1 to 2018M12
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ER |
INTR_DIFF |
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Rate Interest |
Exchange Rate |
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Period |
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Figure 1.
Exchange Rate and Interest Rate Movements in G7 Countries (Continued)
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Exchange Rate and Interest Rate in Japan, 2000M1 to 2018M12 |
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Exchange Rate |
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Rate Interest |
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Exchange Rate and Interest Rate in UK, 2000M1 to 2018M12 |
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Exchange Rate |
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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
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Exchange Rate and Interest Rate Differential in Canada, 2000M1 to 2018M12
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Exchange Rate and Interest Rate Differential in G7 Economies |
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Figure 2.
Exchange Rate and Interest Rate Differentials in G7 Countries (Continued)
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Exchange Rate and Interest Rate Differential in Japan, 2000M1 to 2018M12 |
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|
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||
|
80 |
|
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|
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|
|
60 |
02 |
03 |
04 |
05 |
06 |
07 |
08 |
09 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
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Period |
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Exchange Rate and Interest Rate Differential in UK, 2000M1 to 2018M12 |
2 |
|
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1 |
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0 |
Differential Rate Interest |
Exchange Rate |
.9 |
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.8 |
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.7 |
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.6 |
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.5 |
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ER |
INTR_DIFF |
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.4 |
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2000 |
2002 |
2004 |
2006 |
2008 |
2010 |
2012 |
2014 |
2016 |
2018 |
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Period |
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274 |
Bulletin of Monetary Economics and Banking, Volume 22, Number 3, 2019 |
|
|
To test the stationarity of the series, we explore both the conventional augmented
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 |
||||||
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Series |
Statistics |
I(d) |
Statistics |
I(d) |
Break Date |
Statistics |
I(d) |
Break Date |
||
|
||||||||||
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|
Euro Area |
CPI |
I(1) |
I(1) |
2009 M10 |
I(1) |
2014M07 |
||||
|
IPI |
I(1) |
I(0) |
2008 M09 |
I(0) |
2008M05 |
||||
|
INTR |
I(1) |
I(0) |
2015 M04 |
I(0) |
2008M11, 2012M01 |
||||
|
MS |
I(2) |
I(0) |
2000 M11 |
I(1) |
2009M01, 2014M11 |
||||
|
ER |
I(1) |
I(1) |
2008 M10 |
I(1) |
2002M12 |
||||
|
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|
Canada |
CPI |
I(0) |
I(0) |
2002M01 |
I(0) |
- |
||||
|
IPI |
I(1) |
I(0) |
2000M11 |
I(0) |
2007M12 |
||||
|
INTR |
I(1) |
I(0) |
2008M09 |
I(0) |
2008M01 |
||||
|
MS |
I(1) |
I(1) |
2008M06 |
I(1) |
2003M09, 2008M12 |
||||
|
ER |
I(1) |
I(1) |
2008M10 |
I(1) |
2014M12 |
||||
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Japan |
CPI |
I(0) |
I(1) |
2014M04 |
I(1) |
2008M11, 2014M04 |
||||
|
IPI |
I(0) |
I(0) |
2003M08 |
I(0) |
2008M11, 2012M08 |
||||
|
INTR |
I(1) |
I(0) |
2006M02 |
I(1) |
2007M09, 2016M02 |
||||
|
MS |
I(1) |
I(1) |
2008M10 |
I(1) |
2005M12 |
||||
|
ER |
I(1) |
I(1) |
2016M12 |
I(1) |
2012M11 |
||||
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|
Exchange Rate and Interest Rate Differential in G7 Economies |
|
|
275 |
||||||||
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Table 2. |
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Unit Root Test Results (Continued) |
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|||||
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||||||||
Country |
ADF Unit Root Test |
ADF Test with Structural Break |
Narayan and Liu (2015) Unit Root Test |
||||||||
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||
Series |
Statistics |
I(d) |
Statistics |
I(d) |
Break Date |
Statistics |
I(d) |
Break Date |
|||
|
|||||||||||
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|
|
UK |
CPI |
(10)a^ |
I(2) |
I(1) |
2001M01 |
I(1) |
- |
||||
|
IPI |
I(1) |
I(0) |
2000M11 |
I(0) |
2008M11 |
|||||
|
INTR |
I(1) |
I(0) |
2008M10 |
I(1) |
2003M08, 2008M11 |
|||||
|
MS |
I(1) |
I(1) |
2010M02 |
I(1) |
2010M04, 2016M01 |
|||||
|
ER |
I(1) |
I(1) |
2008 M11 |
I(1) |
- |
|||||
|
|
|
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|
|
|
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|
|
|
US |
CPI |
(1)a# |
I(1) |
I(1) |
2008 M11 |
I(1) |
2008M08, 2014M10 |
||||
|
IPI |
(2)a^ |
I(1) |
I(0) |
2008 M09 |
I(0) |
2008M09, 2015M09 |
||||
|
INTR |
(0)a# |
I(1) |
I(1) |
2009 M01 |
I(1) |
2006M05, 2008M11 |
||||
|
MS |
I(1) |
I(1) |
2011 M08 |
I(1) |
2008M09 2011M04 |
|||||
|
|
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|
|
|
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
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
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
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.
|
|
|
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|
ARDL |
|
|
|
NARDL |
|
||||
|
|
|
|
|
|
|
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|
|
|
(2,0,0,0,0) |
|
|
(2,0,0,0,0) |
|
(2,0,0,0,0,0) |
|
(2,0,0,0,0,0) |
|
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- |
|
- |
|
|||
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(0.002) |
|
|
(0.002) |
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|||
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|||||
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0.0058 |
|
0.002 |
|
|||
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- |
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- |
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(0.004) |
|
(0.003) |
|
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|||||
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|||
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- |
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- |
|
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|
||||
|
|
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|
|
(0.003) |
|
(0.003) |
|
|||
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|||||
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|||
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
ECTt |
|
|
|
|
|
|
||||||||||||
|
|
|
(0.0166) |
|
|
(0.026) |
|
(0.023) |
|
(0.031) |
|
|||||||||
|
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- |
|
- |
|
|||
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|
|
(0.033) |
|
|
(0.014) |
|
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|||
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|||||
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|
0.058 |
|
0.012 |
|
|||
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- |
|
|
- |
|
|
|
||||
|
|
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|
|
(0.036) |
|
(0.022) |
|
||||
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||||||
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||||
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- |
|
|
- |
|
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|||
|
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|
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|
|
|
(0.021) |
|
(0.011) |
|
|||
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|||||
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|
|
|
|
|
|
|
|||
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
Panel A: Cointegration Test Result |
|
|
|
|
|
||||
Level of Significance |
|
ARDL |
|
|
|
NARDL |
|
|
|
|||||||||||
I(0) |
I(1) |
I(0) |
I(1) |
I(0) |
I(1) |
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 |
|
|
NARDL |
|
|
||||
|
|
Adj. R2 |
|
0.977 |
|
|
0.978 |
|
0.977 |
|
0.978 |
|
||||||||
|
|
|
1370.991*** |
|
1261.138*** |
|
1218.725*** |
|
1142.425*** |
|
||||||||||
Post Estimation Results |
|
SIC |
|
|
|
|
|
|
||||||||||||
|
|
6.361 |
|
|
6.264 |
|
5.756 |
|
7.431 |
|
||||||||||
|
|
|
|
|
|
|
|
|||||||||||||
|
|
21.203 |
|
|
14.916 |
|
16.56* |
|
12.170 |
|
||||||||||
|
|
|
4.194** |
|
|
2.935** |
|
3.817*** |
|
2.775** |
|
|||||||||
|
|
|
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.
|
|
|
|
|
|
|
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|
|
|
ARDL |
|
|
|
NARDL |
|
||||
|
|
|
|
|
|
|
|
|
|
|
(2,1,1,0,0) |
|
|
(2,1,1,0,0) |
|
(2,0,1,1,1,0) |
|
(2,0,1,1,0,0) |
|
|
|
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|
0.003 |
|
|
0.004** |
|
- |
|
- |
|
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(0.002) |
|
|
(0.002) |
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|||
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|||||
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|
0.0049** |
|
0.005** |
|
|||
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- |
|
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- |
|
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|||
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|
(0.002) |
|
(0.003) |
|
|||
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|||||
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|||
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- |
|
|
- |
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|
||||
|
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|
|
|
|
(0.003) |
|
(0.003) |
|
|||
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|||||
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|
|
|
|
|||
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
ECTt |
|
0.009*** |
|
|
|
|
|
|||||||||||
|
|
|
(0.002) |
|
|
(0.036) |
|
(0.001) |
|
(0.008) |
|
|||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
0.320 |
|
- |
|
- |
|
||
|
|
|
|
|
|
|
|
|
|
|
(0.518) |
|
|
(0.048) |
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.654 |
|
0.142 |
|
|||
|
|
|
|
|
|
|
|
|
|
- |
|
|
- |
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
(1.628) |
|
(0.103) |
|
||||
|
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||||||
|
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|
||||
|
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|
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|
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- |
|
|
- |
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(0.434) |
|
(0.092) |
|
|||
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|||||
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|
|
|
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|
|||
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
Panel A: Cointegration Test Result |
|
|
|
|
|
||||
Level of Significance |
|
ARDL |
|
|
|
NARDL |
|
|
|
|||||||||||
I(0) |
I(1) |
I(0) |
I(1) |
I(0) |
I(1) |
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 |
|
|
NARDL |
|
|
||||
|
|
Adj. R2 |
|
0.986 |
|
|
0.987 |
|
0.987 |
|
0.986 |
|
||||||||
Post Estimation |
|
|
1883.470*** |
|
1714.088*** |
|
1560.943*** |
|
1547.368*** |
|
||||||||||
|
SIC |
|
|
|
|
|
|
|||||||||||||
Results |
|
|
9.346 |
|
|
8.650 |
|
6.211 |
|
4.963 |
|
|||||||||
|
|
15.172 |
|
|
12.313 |
|
17.722* |
|
20.965** |
|
||||||||||
|
|
|
0.425 |
|
|
0.547 |
|
0.472 |
|
0.808 |
|
|||||||||
|
|
|
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.
|
|
|
|
|
|
|
|
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ARDL |
|
|
|
NARDL |
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
(2,0,0,0,1) |
|
|
(1,0,0,0,1) |
|
(2,0,0,0,0,1) |
|
(2,0,0,0,0,1) |
|
|
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|
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|
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|
|
|
|
- |
|
- |
|
|||
|
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|
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(0.001) |
|
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(0.001) |
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|||
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|||||
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|||||
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- |
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|
- |
|
|
|
|||
|
|
|
|
|
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|
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|
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|
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(0.004) |
|
(0.004) |
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|||
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|||||
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|||
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- |
|
|
- |
|
0.009* |
|
0.009* |
|
||
|
|
|
|
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|
|
|
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|
|
|
(0.005) |
|
(0.005) |
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|||
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|||||
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|||
|
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CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
ECTt |
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
(0.008) |
|
|
(0.012) |
|
(0.001) |
|
(0.0021) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
- |
|
- |
|
|||
|
|
|
|
|
|
|
|
|
|
|
(0.100) |
|
|
(0.034) |
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|||
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|
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|||||
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|||||
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- |
|
|
- |
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
(0.051) |
|
(0.028) |
|
||||
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||||||
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||||
|
|
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|
|
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|
|
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|
|
- |
|
|
- |
|
0.137** |
|
0.080*** |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(0.063) |
|
(0.038) |
|
|||
|
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|||||
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|
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|
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|
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|
|
|
|
|
|
|
|
|||
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
Panel A: Cointegration Test Result |
|
|
|
|
|
||||
Level of Significance |
|
ARDL |
|
|
|
NARDL |
|
|
|
|||||||||||
I(0) |
I(1) |
I(0) |
I(1) |
I(0) |
I(1) |
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 |
|
|
NARDL |
|
|
||||
|
|
Adj. R2 |
|
0.973 |
|
|
0.975 |
|
0.974 |
|
0.976 |
|
||||||||
Post Estimation |
|
|
926.900*** |
|
978.600*** |
|
842.387*** |
|
819.856*** |
|
||||||||||
|
SIC |
|
|
|
|
|
|
|||||||||||||
Results |
|
|
11.181 |
|
20.695** |
|
11.468 |
|
10.931 |
|
||||||||||
|
|
6.372 |
|
|
5.5081 |
|
6.289 |
|
5.412 |
|
||||||||||
|
|
|
0.747 |
|
|
0.369 |
|
0.900 |
|
0.505 |
|
|||||||||
|
|
|
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 |
|
|
|
NARDL |
|
||||
|
|
|
|
|
|
|
|
|
|
|
(2,1,0,0,1) |
|
|
(2,1,0,0,1) |
|
(2,0,0,1,0,1) |
|
(2,0,1,0,0,1) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
- |
|
- |
|
|||
|
|
|
|
|
|
|
|
|
|
|
(0.002) |
|
|
(0.003) |
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.0045 |
|
0.0033 |
|
|||
|
|
|
|
|
|
|
|
|
|
|
- |
|
|
- |
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(0.006) |
|
(0.007) |
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
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|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
- |
|
|
- |
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(0.004) |
|
(0.004) |
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
ECTt |
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
(0.022) |
|
|
(0.015) |
|
(0.024) |
|
(0.018) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
- |
|
- |
|
|||
|
|
|
|
|
|
|
|
|
|
|
(0.028) |
|
|
(0.054) |
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.059 |
|
0.050 |
|
|||
|
|
|
|
|
|
|
|
|
|
- |
|
|
- |
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
(0.088) |
|
(0.112) |
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||
|
|
|
|
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|
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|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
- |
|
|
- |
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(0.045) |
|
(0.052) |
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
Panel A: Cointegration Test Result |
|
|
|
|
|
||||
Level of Significance |
|
ARDL |
|
|
|
NARDL |
|
|
|
|||||||||||
I(0) |
I(1) |
I(0) |
I(1) |
I(0) |
I(1) |
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 |
|
|
NARDL |
|
|
||||
|
|
Adj. R2 |
|
0.973 |
|
|
0.973 |
|
0.973 |
|
0.973 |
|
||||||||
Post Estimation |
|
|
925.340*** |
|
835.041*** |
|
834.374*** |
|
759.622*** |
|
||||||||||
|
SIC |
|
|
|
|
|
|
|||||||||||||
Results |
|
|
10.877 |
|
|
9.856 |
|
7.310 |
|
10.786 |
|
|||||||||
|
|
|
18.121 |
|
|
15.037 |
|
14.376 |
|
14.273 |
|
|||||||||
|
|
|
3.778 |
|
|
3.079** |
|
2.696** |
|
2.957** |
|
|||||||||
|
|
|
2.166** |
|
|
1.691* |
|
1.445 |
|
1.619 |
|
|||||||||
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
|
|
280
2019 3, Number 22, Volume Banking, and Economics Monetary of Bulletin
Exchange Rate and Interest Rate Differential in G7 Economies |
281 |
|
|
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
V. CONCLUSION
Using the cases of the euro and
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* |
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
(0.006) |
|
(0.003) |
|
(0.008) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
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|
|
0.0092 |
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
- |
|
- |
|
- |
|
|
|
|
|
|
|
|
|
|
|
|
(0.014) |
|
|
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|||
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||||
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|
|
- |
|
- |
|
- |
|
||
|
|
|
|
|
|
|
|
|
|
(0.008) |
|
|
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|
|||
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||||
|
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|
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|
|
|
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|
|
|
|
|
|
|
|
|
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||
|
|
ECTt |
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|
|
(0.063) |
|
|
(0.019) |
|
(0.022) |
|
(0.078) |
|
|
|
|
|
|
|
|
|
|
|
- |
|
|
0.120 |
|
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|
||
|
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|
|
|
|
|
(0.110) |
|
(0.031) |
|
(0.014) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
0.0203 |
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
- |
|
- |
|
- |
|
||
|
|
|
|
|
|
|
|
|
(0.031) |
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
- |
|
- |
|
- |
|
|
|
|
|
|
|
|
|
|
|
|
(0.013) |
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
CV |
|
Yes |
|
|
Yes |
|
Yes |
|
Yes |
|
||||||
|
|
|
|
|
|
|
|
|
|
Panel A: Cointegration Test Result |
|
|
|
|
|
|||
Level of Significance |
|
Euro Area |
|
Canada |
|
|
Japan |
|
|
UK |
|
|||||||
|
|
|
|
|
|
|||||||||||||
|
I(0) |
I(1) |
I(0) |
I(1) |
I(0) |
I(1) |
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 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
Adj. R2 |
|
0.952 |
|
|
0.966 |
|
0.944 |
|
0.953 |
|
||||||
Post Estimation |
|
|
148.543*** |
|
238.289*** |
|
108.511*** |
|
123.006*** |
|
||||||||
|
SIC |
|
|
|
|
|
|
|||||||||||
Results |
|
|
|
|
|
|
|
|||||||||||
|
|
20.382** |
|
|
16.314* |
|
13.497 |
|
8.890 |
|
||||||||
|
|
|
|
|
|
|
|
|||||||||||
|
|
7.665 |
|
|
10.936 |
|
7.989 |
|
7.973 |
|
||||||||
|
|
|
0.502 |
|
|
1.354 |
|
0.352 |
|
0.4110 |
|
|||||||
|
|
|
0.538 |
|
|
0.852 |
|
0.862 |
|
0.7703 |
|
282
2019 3, Number 22, Volume Banking, and Economics Monetary of Bulletin
Exchange Rate and Interest Rate Differential in G7 Economies |
283 |
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