Therefore, this paper’s proposition is to test for the existence of transaction costs to motivate the inclusion of an intercept term in a cointegration equation of real interest rates

TRANSACTION COSTS, STRUCTURAL CHANGE, AND THE INTEGRATION OF INTERNATIONAL FINANCIAL MARKETS: AN ANALYSIS OF INTEREST RATES IN TEN

OECD COUNTRIES, 1980-2000.

GHALI, Khalifa H.^* EID, Musaed Ben Abstract

This paper argues that conventional tests of financial market integration may be misleading because they neglect to consider two important issues: (i) testing the existence of transaction costs and (ii) testing the existence of structural change. While the existence of transaction costs may inhibit the one-to-one correspondence between changes in real interest rates in different countries, it could also be misleading to assume the existence of such costs while they do not. Therefore, this paper’s proposition is to test for the existence of transaction costs to motivate the inclusion of an intercept term in a cointegration equation of real interest rates. It is shown that this is possible using the Johansen (1994) procedure to test for the inclusion of deterministic components in the cointegration space. It is also noted that the empirical literature has neglected the problem of stability of financial markets and, hence, its consequences on financial integration tests. To solve these two issues, this paper proposes a model of financial market integration that allows for the existence of transaction costs and for the possibility of structural change. This alternative model generates much stronger support for interest parity than is found in the existing literature.

JEL classifications: F21, F31, F32, F36

Keywords: Financial Market Integration; Transaction Costs; Structural Change; Vector Error-Correction; Real Interest Rate Parity.

1. Introduction

The integration of international financial markets has been the subject of a long debate in the literature. While casual observation suggests that global capital markets are becoming increasingly integrated, the empirical literature suggests that international financial market integration remains incomplete and may not be increasing over time. This lack of empirical evidence led some economists to question the relevance of the market integration hypothesis. However, for some others, the casual evidence is correct but the empirical tests have been misleading. For a long time, financial integration has been interpreted to mean equal real interest rates among countries. Among the first who have used this approach are Mishkin (1984a, b), Cumby and Mishkin (1986), and Merrick and Saunders (1986). Their results, however, failed to support the real interest rate equalization hypothesis. Even when Mark (1985) adjusted the interest rates to differences in national tax rates, the results were unfavorable to real interest rate equalization. More recently, Goodwin and Grennes (1994) have argued that these empirical tests are misleading in the sense that the equalization of real interest rates may not be the appropriate criterion for testing financial market integration. In this respect, they

* Khalifa H. Ghali and Musaed Ben Eid Department of Economics, College of Business Administration, Kuwait UniversityP.O. Box 5486. Safat, code: 13055. The State of Kuwait,

e-mail: [email protected]

advanced two reasons not to expect equal real interest rates, even in a well-integrated and efficient international credit market. These reasons are: (1) the existence of non-traded goods; and (2) the existence of transaction costs. The existence of non-traded goods implies that their prices will not be equalized. Hence, since nominal interest rates are deflated by price indices that include non-traded goods, they may not be equalized.

Therefore, equalization of real interest rates should not be expected to hold in this case, even if markets are well integrated. Moreover, in the presence of transaction costs, real interest rates in an efficient and integrated market should differ by an amount that will not exceed transaction costs. Within a band determined by these costs, national real interest rates will, hence, fluctuate independently of one another in response to local changes in domestic supply and demand conditions. Conventional procedures of testing the financial integration hypothesis have often assumed that the differential between the real interest rates of two countries (r_tⁱandr_t^j) is such that r_tⁱ −r_t^j =c, where c represents transaction costs. However, the empirical applications have typically abstracted from transaction costs by testing the equality of real interest rates to test for market integration. In this respect, it has become a common practice to test whether a linear relationship between two interest rates yields a unitary slope and a zero intercept. However, in the presence of transaction costs, one should not expect these hypotheses to hold. To the contrary, if we explicitly allow for the presence of transaction costs, any values of the slope and intercept could be consistent with well –integrated financial markets.The objective of this paper is to improve upon the conventional procedures for testing financial market integration in at least three different ways. First, we propose to test financial market integration by explicitly recognizing the existence of transaction costs. In particular, we propose to test whether the existence of transaction costs is supported by the data and that by testing the relevance of including an intercept in a regression of interest rates. For this, we develop a vector error-correction (VEC) model within which we formally test for the inclusion of an intercept in the cointegration space using the tests developed by Johansen (1994). As shown by Johansen (1992, 1994), the choice to include an intercept in a long-run relationship should be consistent with the data because it has serious implications on the results of the cointegration tests. When Johansen (1988) first derived the Likelihood- based cointegration test, he derived it for a model that does not include an intercept term.

He extended his procedure to a model with an intercept in his (1991) paper. It turns out, as he shows, that the asymptotic distributions of the cointegration test depend on whether an intercept is included in the deterministic part of the model. The importance of transaction costs to interest rate arbitrage has been discussed by Frankel and Levich (1975), Bahmani-Oskooee and Das (1985), and Clinton (1988), among others. Although these costs may be small in international financial markets, their existence may inhibit the one-to-one correspondence between real interest rates as conventionally presumed in the literature. Therefore, if the data support the existence of an intercept term in the cointegration space, this would indicate the importance of transaction costs in the investigated markets. Otherwise, cointegration can be tested in the absence of an intercept term, meaning that transaction costs are absent or minimal.Second, the issue of the stability of financial markets and its implications on testing financial market integration has never been discussed in the literature. Since structural changes may have taken place during the period of estimation, it is plausible to allow for the possibility of structural

breaks in the data. This is an important issue to investigate. The recent developments in time series techniques prove that ignoring structural breaks in the data may result in serious misspecifications and lead to erroneous inferences. In particular, ignoring structural breaks may lead to misspecification of the integration properties of interest rates. In this respect, the existing literature has always argued for difference-stationary real interest rates (i.e I(1)) by using classical unit root tests, while it could be that interest rates are trend-stationary (i.e. I(0)) under the trend-break hypothesis. Therefore, the results of no cointegration found in bivariate cases could be the consequence of misspecification of the order of integration of interest rates. Moreover, ignoring structural breaks in the data may have serious consequences on the formulation of the model and the results of cointegration. The existence of structural breaks in the data calls for a particular treatment of the deterministic components of the model such as the inclusion of shift dummies, which if ignored lead to misleading results. We herein deal with the issue of stability of financial markets by adopting unit root tests that allow for the existence of breaks in the data. In particular, we test for unit roots under the trend-break hypothesis with three different characterizations of the break under the alternative, as developed by Perron (1997). With this, we are able to identify the possible breaks in the data and, whenever breaks exist, we include shift dummies in the deterministic part of the model to ensure the stability of the cointegration space and the long-run parameters. Finally, since financial market integration is defined here to mean the existence of common stochastic trends between real interest rates and is, consequently, tested by testing for cointegration, we also investigate the influence that financial markets exert on each other, and that by testing for long-run Granger-causality between real interest rates. This is also an important question to investigate because the finding of financial integration does not provide information on how financial markets interact with each other nor does it allow gauging the influence that one financial market has on the others. These implications can be obtained by identifying the direction of the flow of causality between financial markets. We apply our methodology to data on real interest rates from ten countries, namely Belgium, Canada, France, Germany, Italy, Japan, Norway, Switzerland, UK and USA over the period 1980:1-2000:7. The empirical evidence presented here shows that conventional tests of the interest parity suffer from substantial biases due to overlooking these issues and, hence, leads to question the validity of their results. In particular, it is shown that, when these issues are properly dealt with, there is a stronger support for international financial market integration than is reported in the literature. The remaining of the paper is organized as follows. Section 2 describes the econometric methodology, section 3 reports the empirical results, and section 4 concludes.

2. The econometric methodology

2.1 A vector error-correction model of financial market integration.To model the intertemporal interaction between real interest rates, we start by representing their short- run dynamics by a vector autoregressive (VAR) model where all variables are allowed to be endogenous. Then, the idea that some or all of them share common stochastic trends (i.e cointegrated) can be tested and exploited to model their interaction within a vector error-correction (VEC) model, which captures both the short-run as well as the long-run dynamics of real interest rates. This methodology can be used to model the relationship between interest rates either in the bi-variate case or in the multivariate case. For the general case, consider a VAR(k) model of the form:

Xt = Φ1 Xt-1 + Φ2 Xt-2 + ... + Φk Xt-k + µ + δDt + ηt, t=1, ..., T, (1)

where Xt is a p x 1 vector containing the real interest rates of p different countries. µ is an intercept term and D_t is a matrix containing deterministic variables such as trend and dummies. D_t can also include stochastic variables that are weakly exogenous and excluded from the cointegration space. Suppose for the time being that some or all the real interest rates in X_t are I(1). If we exploit the idea that there may exist co-movements of these interest rates and possibilities that they will trend together towards a long-run equilibrium state, then by the Granger representation theorem, we may posit the following testing relationships that constitute a vector error-correction (VEC) model:

∆Xt =Γ1 ∆Xt - 1+Γ2 ∆Xt - 2+. . .+Γk - 1 ∆Xt - k + 1+ΠXt -1+µ+δDt+ηt, t = 1,…,T (2) where ∆ is the first difference operator, Γ’s are estimable parameters, ηt is a vector of impulses which represent the unanticipated movements in Xt, with ηt ~ niid(0, ∑), and Π is the long-run parameter matrix. With r cointegrating vectors (1 ≤ r ≤ p-1), Π has rank r and can be decomposed as Π = αβ´, with α and β both p x r matrices; β are the parameters in the cointegrating relationships and α are the adjustment coefficients which measure the strength of the cointegrating vectors in the VEC model. With this, the model can be written as:

∆Xt =

∑

^{− + µ + δD}

=¹Γ∆ − + ′ −

1

1 k

i

t i

t

i X

α β

X t + ηt, t = 1,...,T (3) Hence, the cointegration methodology illustrates well the conflict that exists between the

equilibrium framework and the disequilibrium environment from which the data are collected. As formulated in the VEC model in (3), this conflict can be easily resolved by extending the equilibrium framework into one that accounts for disequilibrium and that by including the equilibrium error measured by (β´X_{t -1}). Once the equilibrium conditions are imposed, the model is now describing how in each short-term period real interest rates are adjusting towards their long-run equilibrium state. In this respect, each cointegrating vector is indicating an independent direction where a stable long-run equilibrium exists and, the adjustment coefficients α measure the speed of adjustment of each interest rate to the long-run equilibrium state. Following Toda and Phillips (1993, 1994), Hall and Milne (1994), and Giles and Mirza (1999), imposing a zero restriction on the adjustment coefficients in (3) can be interpreted as a test of long-run Granger-causality. Johansen and Juselius (1992) term this test as a test of weak exogeneity. A variable is weakly exogenous if its adjustment coefficient is zero, implying that it is not adjusting to the long-run equilibrium relationships. This also means that the long-run movement of the variables in the cointegration space does not have any influence on its short-run behavior.

Johansen (1988) developed the estimation of the VEC model using a maximum likelihood procedure which tests the cointegrating rank r and estimates the parameters β and α. The recent literature has demonstrated that the Johansen cointegrating approach performs in general better than a range of other procedures for estimating the cointegrating vectors (Gozalo 1994; Hargreaves 1994; Toda 1995; Haug 1996, among others). For example, Gonzalo (1994) reports, from simulation experiments, that Johansen’s estimator has superior finite sample performance compared to many other methods for estimating the parameters of the cointegrating vectors. Toda (1995) reports that, for samples containing at least one hundred data points, the asymptotic distributions of Johansen’s statistics are good approximations to the exact distributions when the null hypothesis is true.

2.2 Specification of the deterministic components. It is important to notice that the two test statistics proposed by Johansen to test for cointegration, the Trace test and λmax

(maximum eigenvalue) test, have asymptotic distributions that are not invariant to the assumptions regarding the presence of deterministic components in the model (intercept, trend, and dummies). Johansen (1991, 1994) has proved that the asymptotic distributions of the tests for cointegration change depending on what assumptions are made regarding these terms. This means that misspecification of the deterministic components leads to incorrect cointegration tests and, thus, to misleading inferences. In fact, Johansen (1988) derived the cointegration test based on a VAR model without a constant term; he extended this test to a model that includes an intercept term in his 1991 paper. It turns out also that the asymptotic distributions of the tests for cointegration change depending on whether the deterministic part of the model contains a time trend and dummies. Despite the serious implications of the misspecification of the deterministic part of the model on the results of cointegration, the survey conducted by Giles and Mirza (1999) indicates that this issue was neglected in the applied research that uses the Johansen cointegration procedure. To illustrate how the specification of the deterministic components of the model has implications on the cointegration space, we start by specifying the unrestricted model and that by setting D_t = t in (3) in order to allow for a linear trend in the model in addition to the intercept. With this, both the intercept and the deterministic time component are present in VAR and, the model in (3) can be rewritten as:

Xt

∆ =

∑

⁻ t = 1, …, T (4)

=¹Γ∆ − + ′ − + + +

1

1 ,

k

i

t t

i t

i X

α β

X

µ δ

t

η

At this stage, we do not include dummy variables in the deterministic part of the model for ease of exposition. Since dummy variables are exogenously determined, they can be included in the deterministic part of the model at the final stage of model specification. In our case, the decision to include dummies will be based on the existence of breaks and, therefore, will be used to account for structural change.Now to see how different assumptions about the intercept and the time components lead to different model specifications, with different implications concerning the data generating processes and the cointegration space, we further decompose δ and µ in (4) as follows:

δ = αδ1 + α⊥δ2 µ = αµ1 + α⊥µ₂

where: δ2 = α⊥(α⊥′α⊥)^-1α⊥′δ is a (p - r)-dimensional vector of quadratic trend coefficients in the data, δ1 = α(α′α)^-1α′δ is an r-demensional vector of linear trend coefficients in the cointegrating relations, µ₂ = α⊥(α⊥′α⊥)^-1α⊥′µ is a (p – r) dimensional vector of linear trend slopes in the data, andµ₁ = α(α′α)^-1α′µ is an r-dimensional vector of intercepts in the cointegration relations. Using this decomposition, the unrestricted model in (4) can be rewritten as:

∆Xt =

∑

⁻ ∆X

= 1Γ

1 k

i

i t -i+ α ^′

⎟⎟

⎟

⎠

⎞

⎜⎜

⎜

⎝

⎛

1 1

δ µ β

1

~

−

Xt +α⊥µ2 + α⊥δ2t + ηt , t = 1, …, T (5)

in which ~ ₁

−

Xt = (X^’t-1 1 t) ^’. Now, depending on the restrictions imposed on these deterministic components, we can distinguish between the following five different model specifications (see Johansen and Juselius 1990, Johansen 1992, and Johansen 1994).

Model 1: The unrestricted model where no restrictions are imposed on δ and/or µ. In this case, the cointegration space contains an intercept as well as a time trend component.

This model is consistent with the existence of quadratic trends in the data and, hence, linear trends in the differenced series. This specification is more appropriate in cases of quadratic growth in the interest rates. Model 2: δ₂ = 0, δ₁, µ₁, µ₂ unrestricted. In this case the model excludes quadratic trends but allows the cointegration space to contain a linear trend since δ₂ ≠ 0. This is the case where real interest rates are allowed to be trend stationary and, this trend stationarity is allowed for the series as well as for the cointegrating relationships. Model 3: δ = 0, and µ₁, µ₂ are unrestricted. In this case since µ2 ≠ 0 the model allows for linear trends in the data through µ2 but no trends in the cointegrating relations. Given that µ1 ≠ 0 the cointegrating relations have a non-zero intercept. Model 4: δ = 0, and µ2 = 0, but µ1 unrestricted. In this case the model does not allow for linear trends in the data. The only deterministic component present in the model is the intercept in the cointegrating relationships. Model 5: δ = 0, and µ = 0. In this case there are no deterministic components in the data, and all intercepts in the cointegration relations are zero. This is an extreme case where no intercepts are allowed at least to account for data measurement. Thus, since different assumptions about the deterministic components lead to different specifications of the model and the cointegration space, which in turn yield different distributions of the Johansen cointegration tests, Johansen (1994) suggested testing and identifying the relevant components to include in the model before testing for cointegration. In this respect, Johansen (1994) suggested using a general-to-specific modeling strategy whereby, starting with the unrestricted model, restrictions on the deterministic components are gradually imposed in order to identify those that should be retained in the model. Following Johansen (1994) and making use of the λ²-test based on the so-called Pantula principle (Pantula, 1989), we herein use a sequential procedure that allows to simultaneously select the model (Model 1, …, Model 5) and the cointegrating rank r. The procedure is as follows. Let Crm denote the combination of the rank and the model, where r is the rank (r = 1, 2, 3, p-1) and m is the model (m = Model 1, …, Model 5). Since Model 1 is the unrestricted model, we start by selecting between Model 1 and Model 2. Then, in the second phase, the retained model will be tested against Model 3. We continue this procedure until model 5. In each one of these phases we select jointly the model and the cointegrating rank r. To sequentially select between two competing combinations we start by fixing the rank starting with r = 1. Then we select the model for which the trace statistic passes the critical value, and that starting with the most restrictive model. If neither model is selected, we change the rank to the higher order and repeat the procedure until one of the two models is selected. For example, for the models Model 1 and Model 2, we sequentially test and choose between Cr1 and Cr2, for r = 1, …,p-1. Starting with the most restrictive combination C02, we compare the trace test statistic of this model to the corresponding critical value. If the model is rejected we keep the rank assumption (r = 1) and change to model 2 (i.e C01). If this model is also rejected, we change the rank to r = 2 and repeat the same procedure. So we keep changing the rank and model until the first time the joint hypothesis concerning the rank and model specification is accepted. Once a model is selected (either Model 1 or Model 2), the selected model will be tested against Model 3 using the same procedure and, the process continues until a particular specification is selected with a specific rank.

In the case where only two variables are involved, the test is easier to conduct since the comparison between models will be only for r = 1.

2.3 Testing for unit roots with structural breaks. The issue of whether macroeconomic time series should be modeled as difference stationary processes or as trend stationary processes has received considerable attention during the past two decades. Since the publication of the study by Nelson and Plosser (1982) who found evidence of difference stationarity in US macroeconomic variables, almost all applied research using the Dickey-Fuller (1979) unit root test confirmed the conclusion that most macroeconomic time series contain unit roots. However, Perron (1989) proved that the Dickey-Fuller test is biased against rejecting the null hypothesis of a unit root when the true data generating process is in fact trend stationary with a break in the intercept or the slope of the trend function. Consequently, Perron (1989) proposed to test the unit root null using a modified Dickey-Fuller test which specifies the alternative under the following three characterizations of the trend-break: 1) The Crash Model: This model allows for a change in the intercept under the null and alternative hypotheses. In addition, this change is assumed to occur gradually and in a way that depends on the correlation structure of the noise function. This model was termed the “innovational outlier model” in the terminology of Perron (1989) and will be denoted later by model IO1. The null hypothesis of a unit root is tested using the t-statistic for testing α = 1 in (6):

∑

= −

− + ∆ +

+ +

+ +

= ^k

i

t t i t

b t

t DU t D T y c y e

y

1

1

) 1

(

α δ

β θ

µ

(6)

where Tb is the time of the break, DUt = 1(t > Tb) and D(Tb)t = 1(t = Tb + 1) with 1(.) being the indicator function.

2) The Mixed Model: This model allows for a break to occur simultaneously in both the intercept and the slope at time Tb. This model is also an innovational outlier model where the change occurs gradually in both the intercept and the slope. This model will be denoted by model IO2. In this model the unit root test is performed using the t-statistic for the null hypothesis that α = 1 in the following regression

(7) DT

∑

= −

− + ∆ +

+ +

+ + +

= ^k

i

t i t i t

b t

t

t DU t DT D T y c y e

y

1

) 1

(

α δ

γ β θ

µ

t = 1(t > Tb)t

3) The Changing Growth Model: In this model only a change in the slope is allowed with both segments of the trend function are joined at the time of the break Tb. Moreover, the change here is supposed to occur rapidly and corresponds to the “additive outlier model”

in the terminology of Perron (1989). This model will be denoted by model AO. To test the unit root hypothesis, Perron (1989) uses a two-step procedure. First, the series is detrended using the following regression where DT = 1(t > Tb)(t – Tb)

y_t =

µ

+

β

t+

γ

DT_t *+~y_t. (8) Then the test is performed using the t-statistic for α = 1 in the regression:

∑

(9)

= −

− + +

= ^k

i

t i t i t

t y c y e

y

1

1 ~ .

~

~

α

In order to device unit root tests that have power against the trend break stationary alternative, Perron (1989) first specifies the location of the break-date Tb. Then, given the break-date, he estimates a regression that nests the random walk null and the trend-break stationary alternative of choice. The assumption that the break date is known a priori was,

however, criticized because the choice of Tb is correlated with data, which makes Perron (1989) test reject the unit root null too often (see for example Christiano 1992; Banerjee, Lumsdaine and Stock 1992; Zivot and Andrews (1992), and Perron and Vogelsang 1992).

In order to avoid this bias, some studies have proposed extensions of Perron’s (1989) unit root tests where the break-date is endogenously determined: Zivot and Andrews (1992), Banerjee et. al. (1992), Perron and Vogelsand (1992), Perron (1997), and Vogelsand and Perron (1998), among others. These studies have proposed to apply Perron’s (1989) methodology for each possible break date in the sample, which yields a sequence of t- statistics. Then, using this sequence, a minimum t-statistic can be constructed that maximizes evidence against the null hypothesis. Therefore, the availability of the minimum t-statistics avoids the need for the a priori knowledge of the break-date.

Although the issue of break-date determination has been resolved, the issue that still remains is how to choose between the three alternatives of the unit root test. That is, how to characterize the form of the break. In this respect, Sen (2003) argues that the selection of the form of the break is also correlated with the data and, therefore, misspecification of the alternative may induce power distortions. He assessed the performance of the minimum t-statistics when the form of the break is misspecified. The simulation results of Sen (2003) indicate that the loss of power is minimized when the mixed model specification is used to characterize the form of the break. Therefore, he suggests that practitioners should use the form of the break specified under the mixed model IO2, which is the most general characterization under the alternative, unless prior information suggests using either the crash model IO1 or the changing growth model AO.

3. Empirical results

Taking into account the issues discussed above, our empirical investigations of the interest parity hypothesis will be conducted according to the following steps. First, we test for unit roots in the real interest rates allowing for the existence of structural change and that by using the Perron (1997) procedure described above. The results of this step will serve two purposes: (i) the determination of the appropriate order of integration of the interest rates; and (ii) the identification of structural-break-dates. Knowledge about the break dates will allow the inclusion of shift dummies in the deterministic part of the VEC model in order to account for structural change as discussed earlier, while knowledge of the order of integration of the interest rates has implications on the feasibility of conducting the cointegration tests. In the second step we test for cointegration between real interest rates both in the bivariate and the multivariate cases.

Before doing so, we use the sequential testing procedure described above to identify the deterministic components that should be included in the model. Once these are specified, we proceed to test for cointegration, estimate the cointegrating vectors and the adjustment coefficients, and identify the direction of long-run Granger-causality between real interest rates.

3.1 The data. The data consist of domestic money market interest rates and consumer price indices for ten countries, namely Belgium, Canada, France, Germany, Italy, Japan, Norway, Switzerland, UK, and USA. Monthly data were collected over the period 1980:1 – 2000:7 from the IMF publication International Financial Statistics. Inflation rates are measured by changes in the consumer price indices. The money market rates used are the same as defined by the IMF. In particular, the money market rates for Japan and Norway are the call money rates. For Belgium, Italy, France, and Switzerland, these are the money

market interest rates. For Canada it is the overnight money market rate. For the UK it is the overnight interbank rate, and for the US it is the federal funds rate. The real interest rates were obtained by taking the difference between the nominal money market rates and the corresponding inflation rates. Table 1 presents a summary of data.

Table 1: Average interest rates and consumer prices, 1980:1 to 2000:7

Average CPI Interest Rate

Country Average CPI

Interest Rate Country

91.160 2.570

Japan 80.171

7.374 Belgium

73.685 7.550

Norway 78.062

6.180 Canada

82.454 3.970

Switzerland 80.528

8.848 France

70.842 7.650

UK 92.993

5.510 Germany

74.635 5.200

USA 67.792

8.850 Italy

Source: IMF International Financial Statistics

3.2 Test results for unit roots. This section presents the results of testing for the existence of unit roots in the real interest rates of the ten countries in the sample using the procedure described above. Since the form of the break is unknown, we follow the recommendation of Sen (2003) and use the mixed model IO2 in (7) as the alternative. The choice of the appropriate break date (Tb) and order of the lag-truncation parameter (k) are determined endogenously following Perron (1997), with k-max = 12. In particular, the break-date Tb is selected as the value which minimizes the t-statistic for testing α = 1. The truncation lag parameter k is selected using a general-to-specific recursive procedure based on the t-statistic on the coefficient associated with the last lag in the estimated autoregression. That is, the procedure selects the value of k such that the coefficient on the last lag in an autoregression is significant, up to a maximum order k-max. For each one of the real interest rates, table 2 reports the estimated truncation lag k, the estimated break date (Tb), and the t-statistics of the parameters in equation (7).

Table 2. Test results for unit roots

k Tb

θ^ˆ

t t_βˆ t_γˆ t_δˆ

α

ˆ t_αˆ ^5%

Belgium 1 1990:9 3.24 1.20 -3.38 -1.57 0.875 -4.47 -4.91 Canada 9 1990:9 1.29 2.21 -2.38 -0.37 0.733 -4.97 -4.91 France 3 1989:12 3.60 3.11 -3.74 -1.62 0.872 -4.61 -4.91 Germany 12 1983:4 -2.46 -3.11 3.04 0.56 0.934 -2.67 -4.91 Italy 11 1986:3 3.28 3.15 -3.38 -2.19 0.836 -4.53 -4.91 Japan 12 1997:2 -2.33 -3.59 2.35 0.42 0.887 -3.00 -4.91 Norway 3 1986:5 -0.28 5.78 -2.00 5.17 0.674 -7.24 -4.91 Switzerland 12 1989:10 4.14 4.28 -4.35 -1.88 0.682 -5.00 -4.91 UK 10 1985:4 2.68 2.51 -2.71 -1.14 0.837 -3.97 -4.91 USA 12 1990:6 -4.31 -3.31 4.09 0.75 0.853 -4.43 -4.91 Note:Tb is the break date, k is the value of the lag-truncation parameter chosen according to the Perron (1997) procedure with k-max = 12. Mixed-model regression:

∑

= −

− + ∆ +

+ +

+ + +

= ^k

i

t i t i t b t t

t DU t DT DT y c y e

y

1

1 .

)

( α

δ γ β θ µ

Concerning the existence of structural change and the stability of financial markets, the results of table 2 indicate the existence of structural breaks in the real interest rates of the ten countries. In particular, we can see that, for each country, the existence of structural change has affected either the slope or the intercept, or both, of the trend function of the real interest rates. Looking att_γˆ, we

can see that the slope of the trend function of each interest rate was affected by the existence of structural change. Moreover, looking at , we can see that, except for Canada and Norway, structural change has affected the intercept of the trend function of real interest rates. Therefore, it is important to take into account the effects of structural breaks on real interest rates when conduction tests of the interest rate parity. Ignoring the effects of structural change, as is always the case in the literature, leads to question the stability and, hence, the validity of the results of these tests.

θ^ˆ

t

The last two columns report the unit root test statistics and critical values. The results in this table indicate that the null of unit root cannot be rejected for seven countries, which are Belgium, France, Germany, Italy, Japan, UK, and the US. However, the unit root hypothesis is rejected for three countries, which are Canada, Norway, and Switzerland.

Further analysis using first differences of the real interest rates of the first group reveals that these are I(1) rather than I(2). Therefore, we conclude that the real interest rates of the first group of countries are I(1), while the real interest rates of the second group are I(0). These findings have important implications on the cointegration tests of the interest rate parity hypothesis. First, the real interest rates of Canada, Norway, and Switzerland cannot be included in any bivariate cointegration tests of interest parity, as usually done in the literature using classical unit root tests. This is because, in the bivariate case, both interest rates have to be nonstationary. Second, when conducting multivariate cointegration tests of interest parity, the I(0) real interest rates should be included in the model as weakly exogenous variables.

3.3 Test results for cointegration. Based on the results of the unit root tests conducted above, we herein present the cointegration test results of interest parity in two cases; the bivariate case and the multivariate case. In each case we choose between the alternative models (model 1 – model 5) using the sequential procedure described above in order to choose the deterministic components that should be included in VEC. In addition, we include shift dummies in the deterministic part of the VEC model in order to account for structural change. The dummy variables included take two values: 0 before the break date and 1 after the break date. In the bivariate case, we start by investigating the hypothesis of interest rate parity between the US real interest rate and each one of the interest rates of the remaining countries. Table 2a reports the Johansen cointegration test results of interest parity in comparison with the US real interest rate. In particular, Table 2a reports the maximum eigenvalue (λmax) and trace statistics, the 10% critical values, and indicates the selected model for cointegration. In this case, the real interest rates of Canada, Norway, and Switzerland were dropped from the analysis because of their stationarity status. According to the results of table 2a, the real interest rate of the US cointegrates with the real interest rates of six out of the seven countries included in the analysis. The only country whose interest rate does not cointegrate with the US interest rate is Italy.

This finding, thus, lends strong support to the interest rate parity hypothesis. Next, while it has been a common approach in the literature to look only at the results of cointegration, it is also important to investigate how interest rates interact with each other, both in the short-run as well as the long-run. In this respect, we extend the cointegration analysis to investigate two important issues: (i) the speed of adjustment of interest rates to the long-run equilibrium; and (ii) the direction of long-run Granger-causality. The first issue is related to the question of whether, in the short-run, interest rates are adjusting in order to reach the equilibrium state and, if they are adjusting, it is important to know how

fast interest rates are adjusting to reach this equilibrium. Answers to these questions would provide even stronger evidence on financial market integration. This is because cointegration means the existence of a long-run equilibrium, but it also means that, in the short-run, there is disequilibrium. Therefore it is important to know whether, and how fast, interest rates are moving to this equilibrium. If interest rates reveal to be adjusting, with “reasonable” speed of adjustment, to the long-run equilibrium, then international financial markets should be expected to be more and more integrated in the future.

Table 2a. Interest parity cointegration test results: comparison with US interest rates λmax Hypothesis Test statistic 10% Trace Hypothesis Test statistic 10%

Belgium (intercept in cointegration space, intercept and shift dummies in VEC)

r = 0 14.83 10.29 r = 0 17.87 17.79

r = 1 3.05 7.50 r ≤ 1 3.05 7.50

France (intercept in cointegration space, intercept and shift dummies in VEC)

r = 0 29.16 10.29 r = 0 34.30 17.79

r = 1 5.14 7.50 r ≤ 1 5.14 7.50

Germany (intercept in cointegration space, intercept and shift dummies in VEC)

r = 0 15.88 10.29 r = 0 22.61 17.79

r = 1 6.74 7.50 r ≤ 1 6.74 7.50

Italy (no intercept in cointegration space, intercept and shift dummies in VEC)

r = 0 12.51 10.60 r = 0 22.15 13.31

r = 1 9.63 2.71 r ≤ 1 9.63 2.71

Japan (intercept in cointegration space, intercept and shift dummies in VEC)

r = 0 20.52 10.29 r = 0 22.39 17.79

r = 1 1.87 7.50 r ≤ 1 1.87 7.50

UK (intercept in cointegration space, intercept and shift dummies in VEC)

r = 0 17.54 10.29 r = 0 25.26 17.79

r = 1 5.72 7.50 r ≤ 1 5.72 7.72

Concerning the second issue, it is important to know that cointegration is the result of the existence of a common stochastic trend, with continuous feedbacks between the real interest rates. Therefore, it is important to know whether these feedbacks are going in both directions or in only one direction. This would provide information on the relative influence that real interest rates have on each other.Table 2b provides information on the estimated long-run relationships and the speed of adjustment of each interest rate for the countries whose interest rates cointegrate with the US real interest rate. The cointegrating vectors in this table are normalized on the US real interest rate. The results of this table can be summarized as follows: (i) In all cases the intercept term in the cointegrating equation is statistically significant. This result indicates the importance of allowing for transaction costs and, hence, the inappropriateness of testing the equality of real interest rates to test financial market integration. As for the slope coefficients, we can see that they are different, implying that different interest rates have different effects on the US interest rate. (iii) Concerning the adjustment of real interest rates to their respective long-run equilibrium with US real interest rates, the results are mixed. In the cases of Belgium, France, and Germany, only the US interest rate is adjusting to the long-run equilibrium with a monthly speed of adjustment between 6.6% and 8%. In the cases of Japan and UK, all interest rates are adjusting to the long-run equilibrium. In particular, in the case of Japan both the US and Japanese interest rates are adjusting with similar speed of adjustment of about 5.6%. However, in the case of UK, while both interest rates are adjusting, UK interest rates have higher speed of adjustment (8.4%) compared to the US

interest rate (2.6%). These results indicate that, in the cases of Belgium, France, and Germany, it is the US interest rate that is catching-up to reach a long-run equilibrium with the other rates. However, in the case of Japan (and UK), both rates are adjusting to reach the long-run equilibrium. (vi) It should be noted that the findings in (iii) above are related to the direction of the flow of long-run causality between real interest rates. In this respect, we can see that, in the cases of Belgium, France, and Germany, there is a one- way causal flow running from these three countries’ interest rates to the US interest rate.

This is because only the US interest rate is adjusting to the long-run equilibrium.

Therefore, the US real interest rate is influenced and, thus, is adjusting to the interest rates of these countries. However, in the cases of Japan and UK, interest rates are all adjusting and therefore, the flow of Granger-causality is running in both ways, between the interest rates of US and Japan and between the interest rates of US and UK.

Table 2b. Cointegrating equations and speed of adjustment Speed of Adjustment

Country

US ( . )

Intercept Slope Belgium -0.066 (-3.784) -0.006 (-0.387) -4.202 (-3.166) 0.817 (4.017)

France -0.080 (-5.555) -0.005 (-0.393) -7.141 (-7.899) 0.870 (4.439) Germany -0.067 (-4.020) -0.009 (-0.609) -5.364 (-4.113) 0.523 (3.304) Japan -0.056 (-3.180) 0.057 (3.312) -2.484 (-3.498) -0.456 (-3.957) UK -0.026 (-1.983) 0.084 (3.874) 2.083 (3.449) -1.223 (-3.798) Notes: Figures between brackets are t-statistics.

While the comparison of real interest rates with the US interest rate provided insightful information on market integration and on the intertemporal interaction between them, an international comparison between all the real interest rates in a bivariate context would provide information on how each financial market is integrated with the others. To obtain this information, we redo the same exercise using all possible couples of real interest rates among the seven countries. Table 3a provides information on the cointegration results of testing the interest rate parity hypothesis between couples of countries. Figures in this table are the Johansen max-eigenvalue statistics for the null hypothesis of no cointegration. From the results of this table we can notice the widespread integration of real interest rates among the seven countries. The only cases of no-cointegration are between the US and Italy real interest rates and between the UK and Italy interest rates.

Since it is also important to know how all these interest rates are interrelated, we next test for the bivariate long-run Granger-causality and the direction of causal flows between all interest rates in a similar manner as done before.

Table 3a. Interest parity cointegrating test results: international comparison US Belgium France Germany Italy Japan UK

US ---

Belgium 14.83* ---

France 29.16* 15.19* ---

Germany 15.88* 17.35* 14.75* ---

Italy 12.51* 16.64* 13.45* 14.93* ---

Japan 20.52* 14.93* 12.55* 10.75* 17.46* --- UK 17.54* 22.85* 17.64* 19.65* 7.37 23.57* ---- Notes: Figures in the table are the max-eigenvalue statistics of the Johansen cointegration test. The 10% critical value is 10.29. The trace statistics lead to the same conclusions.

Table 3b provides information on the results of testing for long-run causality between the interest rates of each couple of countries. Figures in this table are the adjustment coefficients (and their t-statistics) of the real interest rates of the countries in the first row to the real interest rates of the countries in the first column. Hence, the direction of the flow of causality in this table is from the countries in the first column to the countries in the first row.

Table 3b. Long-run Granger-causality between real interest rates

US Belgium France Germany Italy Japan UK

US --- -0.006

(-0.38) -0.005

(-0.39) -0.009

(-0.60) --- 0.057 (3.31) 0.084

(3.87) Belgium -0.066

(-3.78) --- 0.056 (3.502) 0.074

(3.75) 0.055

(3.61) 0.033

(1.30) 0.068 (4.51) France -0.80

(-5.55)

-0.012 (-0.74)

--- 0.023 (1.83)

0.078 (3.61)

0.018 (1.16)

0.055 (4.26) Germany -0.067

(-4.02) -0.024

(-1.12) -0.036

(-2.67) --- 0.062 (2.94) 0.007

(0.59) 0.101 (4.13) Italy --- -0.014

(-1.16) -0.018

(-0.98) -0.036

(-2.39) --- 0.029 (0.99) --- Japan -0.056

(-3.18) -0.065

(-2.88) -0.047

(-3.26) -0.080

(-3.10) -0.054

(-4.11) --- 0.098 (4.76) UK -0.020

(-1.98) -0.007

(-0.99) -0.003

(-0.43) -0.018

(-1.65) --- -0.015 (-1.39) ---

Notes: Figures in the table are the adjustment coefficients and their t-statistics. The flow of long-run causality is from the countries in the first column to the countries in the first row.

As can be seen in the table, all real interest rates are influencing each other, either directly or indirectly. In this context, we should notice the existence of direct as well as indirect causal links between the interest rates. For example, the US interest rate does not have a direct causal effect on the interest rates of Belgium, France, and Germany, but has an indirect influence on them through its effects on Japan interest rates. This can be seen from the fact that the US rate affects Japan rate, which in turn affects Belgium, France, and Germany interest rates. This means that the effect of US interest rate on those of Belgium, France, and Germany is an indirect one. It is also interesting to note that, although the interest rates of US and Italy are not cointegrated, they are indirectly influencing each other through their influence on other markets. The same note applies to the relationship between the interest rates of UK and Italy. In the multivariate case, we extend our investigations to test for cointegration between the seven I(1) real interest rates. We also estimate the long-run relationship between them and test for the existence and direction of long-run Granger-causality. Although the I(0) real interest rates of Canada, Norway, and Switzerland can be included in the analysis as weakly exogenous variables, we choose not to do so because of the large number of interest rates involved.

Table 4a reports the results of testing for cointegration between the seven I(1) interest rates using the Johansen procedure. The table includes the λmax and trace statistics as well as their 10% critical values. These results were obtained after selecting between model 1 – model 5 in order to test for the appropriate deterministic components that should be included in the VEC mode. The final specification chosen is the one that includes an intercept term in the cointegration space. In addition, shift dummies were included in the deterministic part of the model to account for structural break. The results of table 4a indicate that real interest rates are cointegrated with one cointegrating vector driving

these series. This means that real interest rates are converging to a unique long-run equilibrium state. It is important to note that the existence of a unique equilibrium state provides stronger evidence on financial market integration than the multiple equilibria previously found in the literature. This is because when the equilibrium is unique, real interest rates are all moving in one direction, which is the one indicated by the cointegrating vector. While, when multiple equilibria exist, real interest rates are moving in different directions towards different equilibrium states. Moreover, when the equilibrium is unique, real interest rates share six common stochastic trends, while if there are more cointegrating vectors, the number of common stochastic trends will be less. Therefore, the results of multivariate cointegration provide even stronger support to the real interest parity than found previously in the literature.

Table 4a. Multivariate cointegration test results of real interest rates

λmax Trace

Hypothesis Statistic 10% Hypothesis Statistic 10%

H0: r = 0 48.79 29.54 H0: r = 0 135.29 126.71

H0: r = 1 18.98 25.51 H0: r ≤ 1 96.50 97.17

H0: r = 2 16.87 21.74 H0: r ≤ 2 67.52 71.66

H0: r = 3 12.88 18.03 H0: r ≤ 3 40.64 49.92

H0: r = 4 10.43 14.09 H0: r ≤ 4 20.76 31.88

H0: r = 5 4.61 10.29 H0: r ≤ 5 7.34 17.79

H0: r = 6 2.73 7.50 H0: r ≤ 6 2.73 7.50

Table 4b provides information on the cointegrating vector as well as on the adjustment coefficient of each one of the real interest rates. In this respect, we can see that all six interest rates enter significantly the cointegration space. Moreover, we can see that all the interest rates are adjusting to this long-run equilibrium, but with different speed of adjustment. In particular, we can see that UK has the highest speed of adjustment, followed by the US, then Germany, Japan, Italy, Belgium and France. Therefore, given that all interest rates are significant in the cointegrating equation, we can conclude that there is a long-run causality running in both directions between the seven real interest rates.

Table 4b. Cointegrating vector and adjustment coefficients

US Belgium France Germany Italy Japan UK βo

Coeff. 1 -1.498 (-2.49) 1.975

(3.37) 0.519

(2.78) -0.499

(-2.06) -1.072

(-2.28) -1.801

(-3.69) -10.347 (-5.56) Adjust.

Coeff.

-0.032 (-5.18)

0.010 (2.67)

-0.006 (-2.08)

-0.020 (-2.37)

0.015 (2.92)

0.015 (2.37)

0.045 (3.63) 4. Conclusion

This paper argued that the conventional tests of interest parity may have resulted in misleading results because they ignored two important issues: (i) testing for the existence of transaction costs; and (ii) testing for the existence of structural change. Specifically, the decision to include or to abstract from transaction costs may be in contradiction with the properties of the data generating processes and leads to incorrect cointegration test results if these were not formally tested for. In particular, the Johansen cointegration tests are very sensitive to whether an intercept is included in the cointegration space and, therefore, conventional tests which have assumed the existence or absence of transaction costs without pre-testing may have resulted in incorrect inferences. Moreover,

conventional tests have ignored the problem of structural change, which may induce breaks in the trend function of real interest rates and, consequently, result in the misspecification of their integration properties and lead to incorrect inferences. In light of these issues, this paper attempted to provide an in-depth empirical analysis of interest parity after allowing for the existence of transaction costs and structural change. In this context, we based our approach on a vector error-correction model capable of dealing with both issues. In particular, the question of whether an intercept term should be included in a cointegration equation of real interest rates to reflect the existence of transaction costs was investigated in the general context of the specification of the deterministic components of the model. In this respect, we have shown that different assumptions about these components result in five different specifications of the model and the cointegration space and, therefore, lead to different cointegration results.

Therefore, we proposed to use the sequential testing procedure proposed by Johansen (1994) in order to select the deterministic components in accordance with the data.

Concerning the existence of structural change and its implications on the results of the interest parity tests, we proposed to use a unit root testing procedure that accounts for the possibility of breaks in the data on real interest rates. In light of the recent advances in time-series techniques, this procedure should allow more appropriate estimation of the integration order of real interest rates. In addition, the information on the break-dates can be incorporated in the model in order to account for the effects of structural change on the parameter estimates and the cointegration space. Finally, we extended the conventional testing procedure of interest parity to an in-depth analysis of the intertemporal interaction of real interest rates and that by investigating their long-run causal relationships and their adjustment to equilibrium. We applied our approach to data on real interest rates from ten countries, namely Belgium, Canada, France, Germany, Italy, Japan, Norway, Switzerland, UK, and the US. The results of testing for the existence of unit roots under the trend-break hypothesis revealed the existence of a structural change either in the slope, the intercept, or both, of the trend function of the real interest rates of all countries.

It turns out also that three of the countries considered, namely Canada, Norway, and Switzerland have trend-stationary rather than difference-stationary real interest rates. In light of the results of the unit root tests, we conducted bivariate as well as multivariate cointegration tests of the interest parity using those real interest rates that contain unit roots. In each case, the choice of the deterministic components in the model was based on the Johansen (1994) sequential testing procedure. The results of this test indicated the significance of the intercept term in the cointegrating equations, and thus the importance of transaction costs in all financial markets considered. In all cases, the results provided strong evidence in support of the international financial markets integration and suggest a much stronger link among financial markets than is implied by the existing literature.

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