Causal Linkages Between US and Eurodollar Interest Rates: Further Evidence Jian Yang* Department of Accounting, Finance & MIS Prairie View A&M University Jaeun Shin Department of Economics Texas A&M University Moosa Khan Department of Accounting, Finance & MIS Prairie View A&M University
Abstract This study examines causal linkages between US and Eurodollar interest rates during 1983-2002. Recursive cointegration analysis shows that a stable cointegration relationship between the two interest rates emerges only since the early 1990s, when the Fed used federal funds rate targeting and eliminated the reserve requirement on Eurocurrency deposits. The study further reveals that bi-directional causality exists between the two rates over the period of 1993-2002 while unidirectional causality from Eurodollar rate to the US rate is found to exist over the period of 1983-1991. These findings consistently support increased interest rate linkages especially since the early 1990s. Key Words: interest rates; recursive cointegration analysis; causality
*Correspondence: Jian Yang, Department of Accounting, Finance & MIS, P.O. Box 638, Prairie View A & M University, Prairie View, Texas 77446, USA. Tel.: +1-9368574011; Fax: +1-936-8572797; Email address:
[email protected]
Causal Linkages Between US and Eurodollar Interest Rates: Further Evidence
1. Introduction The international linkage of short-term interest rates is a fundamental issue to financial market participants and national monetary authorities. Numerous researchers have investigated the lead-lag relationship between (offshore) Eurocurrency and domestic money market interest rates. Knowledge of this relationship is necessary to understand the degree and the extent of the international financial market integration. It is also highly relevant to the ability of national governments to successfully implement monetary and fiscal policies (Swanson, 1987).
Although the issue has been examined
in the context of some other countries such as UK and Japan (e.g., Kaen and Hachy, 1983; Lo, Fung and Morse, 1995), most studies have focused on the US due to the dollar’s role as the primary international currency during the last four decades. Previous studies have produced conflicting conclusions on the causal relationship between the Eurodollar and US money market interest rates.1 Early works (e.g., Hendershott, 1967) supported the position that Eurodollar rates followed US domestic interest rates in the 1960s when US capital controls were in place. By contrast, during the post-US capital control era of the 1970s and 1980s, Swanson (1987) demonstrated that the main direction of causality ran from the offshore Eurodollar interest rate to the US domestic rate while a feedback was often observed. On the other hand, Fung and Isberg (1992) found unidirectional causality running from the US domestic interest rate to
1
the offshore market rate during 1981-1983, which was reversed during the later period of 1984-1988. More recent literature (e.g., Mougoue and Wagster, 1997; Clinebell, Kahl, and Stevens, 2000) argued that US Federal Reserve monetary policy changes might have influenced the observed direction of causality between the two variables. Mougoue and Wagster (1997) found bidirectional causality between the US and Eurodollar interest rates during 1973-1979, unidirectional causality from the Eurodollar rate to the US domestic rate during 1979-1982, and reverse unidirectional causality from the US domestic rate to the Eurodollar rate during 1982-1992. Similarly, Clinebell, Kahl, and Stevens (2000) found unidirectional causality running from the US interest rate to the offshore LIBOR rate under the regime of borrowed reserves targeting. Further, both Mougoue and Wagster (1997) and Clinebell, Kahl, and Stevens (2000) argued that the evidence of unidirectional causality running from the US interest rate to the offshore rate did not support the argument of increasing financial market integration over time. The conflicting conclusions on the direction of causality between the two variables may be attributed to the differences in the empirical techniques employed. Recognizing nonstationarity of interest rates, more recent studies (Fung and Isberg, 1992; Mougoue and Wagster, 1997) exploited the notion of cointegration and the closely related error correction models (ECM) to conduct causality analysis. Such a consideration is important, as existence of cointegration and the significance of error correction term(s) is important to sound causal inference (Granger, 1988). This study examines causal linkages between US domestic and offshore (Eurodollar) interest rates during 1983-2002. It contributes to the literature in several
2
aspects. First, we extend previous studies by investigating an additional 10-year sample period beyond the early 1990s. The study periods covered in recent studies (Mougoue and Wagster, 1997; Clinebell, Kahl, and Stevens, 2000) typically end by the early 1990s when borrowed reserve targeting of the US Fed monetary policy prevailed. An extended analysis is warranted as the US Fed changed its operating procedure to federal funds rate targeting and eliminated the reserve requirement on Eurocurrency liabilities in the early 1990s (Urich and Wachtel, 2001; Cyree, Griffiths and Winters, 2003). As discussed below, such regulatory changes should result in a closer tie between the US domestic and Eurocurrency interest rates, which may be reflected on their long-run relationship and dynamic causal linkages. Second, extending the work of Mougoue and Wagster (1997), we employ a relatively new technique of Hansen and Johansen (1999) to detect possible multiple structural breaks in the cointegration relationship. While Mougoue and Wagster (1997) demonstrated the importance of detecting structural breaks on causal linkage of interest rates, they applied a switching regression model to test parameter constancy of an ECM model which implicitly assumes stability of the long-run cointegration relationship. However, if the underlying long-run relationship is not stable, conclusions might be questionable. Third, we conduct impulse response analysis to provide additional insight into the causal linkage pattern. It is well known that Granger causality tests only allow for the statistical significance of the causal relationship. According to Sims (1980), impulse response analysis may produce insight into the strength of the causal relationship between economic variables in addition to the direction of causality. Phylaktis (1999) is
3
probably the only noticeable exception that has applied the impulse response analysis as a useful indicator of the degree of interest rate linkages. The rest of this paper is organized as follows. Section 2 discusses the methodology used, Section 3 presents empirical findings, and Section 4 concludes the paper.
2. Methodology 2.1. Recursive Cointegration Tests When modeling multiple nonstationary economic time series, it has become a standard practice to start with cointegration analysis.
This is due to the fact that
nonstationarity of time series can give rise to spurious correlations among these variables. The cointegration technique is suitable for retrieving the long-run relationship, if any, among nonstationary variables, while allowing for flexible short-run dynamic specification. ⎛X ⎞ Let X t = ⎜⎜ 1t ⎟⎟ , where X 1t represents the US interest rate measured by the yield ⎝ X 2t ⎠
on certificates of deposits (CD), while X 2 t represents the Eurodollar rate in London. The two interest rate series can be modeled by the following ECM model: k
∆X t = ΠX t −1 + ∑ Γi ∆X t −i + µ + ε t (t = 1,..., T )
(1)
i =1
⎛Π where Π = ⎜⎜ 11 ⎝ Π 21
Π 12 ⎞ ⎛Γ ⎟⎟ and Γi = ⎜⎜ 11 Π 22 ⎠ ⎝ Γ21
Γ12 ⎞ ⎟ are 2x2 coefficient matrixes and the rank Γ22 ⎟⎠ i
of Π = αβ ' determines the number of cointegrating vectors (r). The Johansen (1991)’s trace test statistics can be employed to test the number of cointegrating vectors.
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Unlike previous studies, this study applies the recursive cointegration technique (Hansen and Johansen, 1999) to test constancy of cointegration rank, which can shed light on the stability of the cointegration relationship. Some recent studies (e.g., Yang, 2003) have employed this method to serve a similar purpose. The rank constancy test can be done under two VAR representations of equation (1). In the “Z-representation” all the parameters of the ECM are reestimated using the recursive estimations, while under the “R-representation” the short-run parameters Γi are fixed to their full sample values and only the long-run parameters in the equation (1) are reestimated. According to Hansen and Johansen (1999), the result from the “R-representation” would be more relevant in recursive cointegration analysis. Mathematically, the “Rrepresentation” can be derived as shown below (see Hansen and Johansen (1999) for more details). Let Z 0t = ∆X t , Z 1t = X t −1 , Z 2t = (∆X t'−1 ,..., ∆X t'− k +1 ) . For the ease of the
presentation, we can also ignore deterministic terms such as µ in equation (1). Equation (1) can thus be formulated as Z 0t = αβ ' Z 1t + ΓZ 2t + ε t
(t = 1,..., T )
(2)
Maximum likelihood estimation of equation (3) based on all data consists of a reduced rank regression of Z 0t on Z 1t conditional on Z 2t . Define R0(Tt ) and R1(tT ) as residuals from the regressions of Z 0t and Z 1t on Z 2t , respectively (where the superscript T denotes that estimation is based on full sample data). That is,
[
]
Z 2t
[
]
Z 2t
(T ) R0(Tt ) = Z 0t − M 02(T ) M 22
(T ) R0(Tt ) = Z 1t − M 12(T ) M 22
−1
−1
where
5
t
M ijt = ∑ Z it Z 'jt (i, j =0,1,2) s =1
The remaining analysis can be based on the following regression equation where the parameter Γ has been filtered out: R0(Tt ) = αβ ' R1(tT ) + Rε(tT )
(t = 1,..., T )
(3)
Equation (3) is termed the “R-representation”, and cointegration rank (as determined by the rank of Π = αβ ' ) can be obtained recursively by increasing t by one data point each time until it reaches the full sample size, T. Noteworthy, the “R-representation” is constructed in such a way that any rejection of stability is due to changes in the long-run relationship, rather than due to shifts in short-run dynamics. 2.2. Granger causality tests
Given the identified break(s) in the cointegration relationship, we can divide the sample into different subperiods. If there is no cointegration over a certain subperiod, Equation (1) is reduced to a first differenced VAR model, as the lagged level of X t −1 (i.e., the error correction term) does not exist. Hence, we can jointly model two interest rate series in a first differenced VAR model in the case of no cointegration, or an ECM model in the case of cointegration during a particular subperiod. As an illustration, in the case of an ECM, conducting the Granger causality test from X 2t (Eurodollar rate) to X 1t (US domestic interest rate) is equivalent to testing the following coefficient restrictions in Equitation (1): Π 12 = (Γ12 )1 = (Γ12 )2 = ... = (Γ12 )k = 0
(4)
In the case of a first differenced VAR, the coefficient restriction on Π 12 does not apply and thus can be excluded.
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As pointed out in the literature (Lo, Fung and Morse, 1995; Mougoue and Wagster, 1997), the issue regarding time zone differences of trading hours between the two daily interest rates should be addressed in the causality test, as the end-of-day interest rate quotes are not simultaneous in both markets. The US market closes after the London market, and as a result, cannot affect the London market on the same day. On the other hand, the daily closing quotes of the US cannot affect the same-day London Eurodollar quotes. Thus, following Lo, Fung and Morse (1995) and Mougoue and Wagster (1997), we use the same-day quotes to analyze the effect of the Eurodollar market on the US market. However, when we analyze the impact of the US domestic rate on the Eurodollar rate, we align the data so that the Eurodollar rate on day t is matched to the US CD rate on day t-1. 2.3 Impulse Response Analysis
In addition to the Granger causality tests widely used in previous studies, impulse response analysis is conducted as a robustness check on the causal relationship between the two variables under investigation. Many researchers (e.g., Sims, 1980, p.20) argue that Granger causality tests only allow for statistical significance of economic variables in explaining a dependent variable, and such tests could yield misleading inferences. Specifically, some variables may not be statistically significant in explaining a dependent variable for various reasons (e.g., instability) but may be economically significant (which may be captured by the magnitudes of coefficient estimates). These variables, which may be statistically insignificant but economically significant, should not be ignored in the model specification. According to Sims (1980), impulse response analysis allows for the economic significance of the variables in explaining a dependent variable.
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Also, instead of conducting the traditional orthogonalized impulse response analysis (Sims, 1980), this study employs generalized impulse response analysis as developed in Pesaran and Shin (1998). As is well known, the traditional orthogonalized impulse response analysis based on the Choleski factorization is sensitive to the ordering of variables when the residual covariance matrix is non-diagonal. By contrast, generalized impulse response analysis results in a unique solution and circumvents the problem of sensitivity of impulse response functions to the ordering of variables. The method has not been commonly applied in financial research, with a few recent exceptions (e.g., Ewing, 2003). Specifically, from model (1), we can write ∆X t as an infinite moving average process: ∞ , t=1, 2, …, T ∆X = ∑ C ε t i t −i i=0
(5)
The (scaled) generalized impulse response function which measures the effect on ∆X t + n of the shock to the jth equation in model (1) is given by Pesaran and Shin (1998) as ψ ( n ) = σ − 1 / 2 C Σe j , j
where
jj
n
n = 0, 1, 2,…
(6)
σ jj is jj th element of the variance-covariance matrix Σ and e j is a m x 1 vector
with unity at the jth row and zeros elsewhere. The generalized impulse response function can provide insight into how significantly innovations in a particular market in the system may affect other markets through dynamic interactions among them.
3. Empirical results Following earlier studies (e.g., Swanson, 1987; Mougoue and Wagster, 1997), we
8
use daily closing quotes on the three-month US CD rate and the three-month Eurodollar deposit rate from January 3, 1983 to December 31, 2002.2 These two rates are more comparable than any other rates in the US and Eurodollar markets. The sample period chosen covers a period of borrowed reserves targeting in the U.S. (from 1983 to the end of the 1980s), in order to see whether inferences based on this targeting system in earlier studies are still valid. The data are obtained from Datastream. Consistent with the literature, both interest rate series are found to have a unit root. 3 To test for possible structural breaks in the long-run relationship between US and Eurodollar interest rates, the recursive cointegration technique is applied. The optimal lag is selected by applying Akaike Information Criterion (AIC) based on the whole sample period. As noted previously, the results of the recursive cointegration technique are expected to be more informative than the standard Johansen cointegration technique, because the former reveals the stability (or lack thereof) of the cointegration relationship. In Figure 1, we show normalized trace tests calculated at each trading day over the period January 1, 1984 through December 31, 2002. The one-year period in 1983 is used as the base period. Statistics in the figure are normalized by the 5% critical values (figure entries greater than 1.0 indicate that the null hypothesis can be rejected at that data point at the 5% level). From Figure 1, it is evident that no cointegration exists over the 19841991 period under both Z- and R-representations, except for a short “window” in 1984 under Z representation. By contrast, one cointegrating vector appears to exist after 1992. The standard Johansen cointegration test results (Table 1) based on the division of two sample subperiods, 1983-1991 and 1993-2002, confirm that no cointegration exists before 1992 and one cointegrating vector exists since 1993.
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Interestingly, the break in the long-run relationship coincides well with the recent monetary policy target change and elimination of Eurocurrency liabilities in the early 1990s (Urich and Wachtel, 2001; Cyree, Griffiths and Winters, 2003). As discussed in Urich and Wachtel (2001) and Mougoue and Wagster (1997), the use of the federal funds rate target was developed in the 1960s and was used throughout the 1970s until October 1979. After its brief use of nonborrowed reserves targeting from 1979-1982, the Fed introduced borrowed reserves targeting since 1982. However, the demand for discount window borrowing became less stable and less predictable, and the Fed gradually moved back to federal funds rate targeting in the early 1990s. Moreover, the Fed removed both the secrecy that long surrounded the monetary policy targets and the delays in policy announcements which obviously helped strengthen the impact of monetary policy changes on financial market movements. As the federal funds rate became the benchmark US domestic interest rate since early 1990s, the three (3) percent reserve requirement on US banks’ Eurocurrency liabilities was eliminated in December 1990. Consequently, reserve deposits borrowed in the Eurocurrency market for settlement purposes became essentially equivalent to deposits borrowed in the federal funds market (Cyree, Griffiths and Winters, 2003). Hence, the law of one price should apply and drive the rates in both Eurodollar and federal funds markets together. By contrast, the three (3) percent reserve requirement on Eurocurrency liabilities over 1980-1990 might have prevented the Eurodollar rate from being tied closely enough with the US domestic rate to form a long-run relationship. As pointed out by Cyree, Griffiths and Winters (2003), when Eurocurrency liabilities are subject to the reserve requirement, Eurocurrency liabilities may not be a viable
10
alternative funding source for banks in managing their reserve accounts. Instead, banks use other funding sources for that purpose. Based on the finding of no cointegration in the first subperiod and cointegration in the second subperiod, we model the interest rate series using a first differenced VAR for the first subperiod and an ECM for the second subperiod. Table 2 reports the Granger causality test result for the two subperiods, with the time zone adjustment as suggested in Mougoue and Wagster (1997) and Lo, Fung and Morse (1995).4 During the period of 1983-1991 under the regime of borrowed reserves targeting, it is found that unidirectional causality runs from the Eurodollar market to the domestic market. This contradicts the finding of Mougoue and Wagster (1997) for the comparable period but supports that of Fung and Isberg (1992). In the period of 1993-2002 under the regime of federal funds rate targeting, bidirectional causality is found to exist between US and Eurodollar interest rates. Overall, the results indicate that the Eurodollar interest rates exerted causal influence on the domestic interest rates in both subperiods and that the causality from the domestic market to the Eurodollar market became significant only in the second subperiod of 1993-2002. The causal influence of the Eurodollar rate on the US rate may be a reflection of the fact that interest rate determination in the Eurodollar market is relatively free from regulatory constraints and thus more sensitive than that in the US market to changes in US domestic credit conditions. The causal inference of the US rate on the Eurodollar rate in the second period but not in the first period corresponds well to the finding of Cyree, Griffith and Winters (2003). In particular, they find that during the post-1991 period with no reserve requirement on Eurocurrency liabilities, US banks
11
actively used the London interbank loan market to manage their domestic reserve accounts and thus their settlement behavior with the US Fed had an impact on the London interbank rate. By contrast, there was no such impact on the Eurodollar market in the pre-1991 period. In sum, the Granger causality test result is consistent with the cointegration test result, and both suggest increasing international money market integration since the early 1990s. The Granger causality test is also conducted using the same-day observations without the time zone adjustment. There is significant two-way causality between the
Eurodollar market and the domestic market interest rates in both subperiods (Table 3). Compared to Table 2, the result illustrates the importance of making appropriate time zone adjustment in Granger causality tests as proposed in the literature (Mougoue and Wagster, 1997; Lo, Fung and Morse, 1995). Extending the previous studies, impulse response analysis with the time zone adjustment is further conducted to shed light on the strength of the causal relationship. Both median impulse responses and the associated 95% confidence bands are plotted in Figure 2. The overall finding from the impulse response analysis is consistent with the Granger causality test result with the time zone adjustment (Table 2). In the first subperiod of 1983-1991, over the 10-day horizon, the response of the Eurodollar rate to a shock in the US CD rate was statistically indifferent from zero. By contrast, the response of the US CD rate to a shock in the Eurodollar rate is statistically significant at least up to 4 days after the shock. The evidence is thus consistent with the finding of unidirectional causality from Eurodollar to the US over the same period.
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In the second subperiod of 1993-2002, the response of the Eurodollar rate to a shock in the US CD rate is statistically significant for approximately up to 4 days and dies away afterwards. However, the response of the US CD rate to a shock in the Eurodollar rate is statistically significant throughout the 10-day horizon and is much more persistent. Again, the finding of the impulse response analysis is consistent with that of the bi-directional causality based on the Granger causality test result in Table 2. This analysis further shows that the strength of causality from the Eurodollar rate to the US CD rate is more conspicuous than the other way around in the period of 1993-2002. Finally, the impulse response analysis is also conducted without the time zone adjustment. As might be expected, the overall finding from the impulse response analysis is consistent with bi-directional Granger causality in both periods, as reported in Table 3. In the first subperiod, the response of the Eurodollar rate to a shock in the US CD rate is statistically significant, albeit only as short as two days. In the second subperiod, the response of the Eurodollar rate to the shock in the US CD rate is as significant and persistent as the other way around. Therefore, we cannot infer that the strength of causality from the Eurodollar rate to the US CD rate is more conspicuous, or vice versa. A comparison of Figures 2 and 3 reinforces the importance of making appropriate time zone adjustment in conducting impulse response analysis (and perhaps the closely related forecast error variance decomposition).
4. Conclusions This study examines causal linkages between the US and Eurodollar interest rates during the period of 1983-2002. Using recursive cointegration analysis, we found that no cointegration exists between the interest rates before 1992, while a clear and stable
13
pattern of long-run relationship emerges after 1992, approximately when the Fed moved from borrowed reserves targeting to federal funds rate targeting in monetary policy operations and the reserve requirement on Eurocurrency deposits was eliminated. Further analysis reveals that there exists bi-directional causality between the two rates over the period of 1993-2002 while unidirectional causality from Eurodollar rate to the US rate over the period of 1983-1991. These findings consistently lend support to the argument of increasing financial market integration since the early 1990s, which, however, contradicts some recent studies (Mougoue and Wagster, 1997; Clinebell, Kahl, and Stevens, 2000) but supports earlier ones (Swanson, 1987; Fung and Isberg, 1992). The findings of this study carry important implications. In particular, the US monetary authority cannot conduct its monetary policy independent of external market considerations and must factor in feedback from these markets, notably the Eurodollar market. Equally important, the finding also suggests that better short-term interest rate forecast can be obtained by combining information from both US and Eurodollar markets.
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References Clinebell, J. M., D. R. Kahl, and J. L. Stevens (2000). Integration of LIBOR and Treasury bill yields over different monetary regimes. Global Finance Journal, 11, 17-30. Cyree, K. B., M.D. Griffiths, and D. B. Winters (2003). On the Pervasive effects of Federal Reserve Settlement Regulations. The Federal Reserve Bank of St. Louis Review, (March/April) 27-46.
Ewing, B. T. (2003). The response of the default risk premium to macroeconomic shocks. Quarterly Review of Economics and Finance, 43, 261-272. Fung, H.G., and S. Isberg (1992). The international transmission of Eurodollar and US interest rates: A cointegration analysis, Journal of Banking and Finance, 16, 757769. Granger, C.W.J. (1988). Some recent developments in a concept of causality. Journal of Econometrics, 39, 199-211.
Hansen, H., Johansen, S., 1999. Some tests for parameter constancy in cointegrated VAR models. Econometrics Journal, 2, 306-333. Hendershott, P.H. (1967). The structure of international interest rates: The US treasury bill rate and the Eurodollar deposit rate, Journal of Finance, 22, 455-465. Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59, 1551-1580. Kaen, F. R., and G. A. Hachy (1983). Eurocurrency and national money market interest rates: an empirical investigation of causality. Journal of Money, Credit and Banking, 15, 327-338.
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Lo, W.C., H.G. Fung, and J.N. Morse (1995). A note on Euroyen and domestic yen interest rates, Journal of Banking and Finance, 19, 1309-1321. Mougoue, M., and J. Wagster (1997). The causality effects of the Federal Reserve’s monetary policy on US and Eurodollar interest rates, Financial Review, 32, 821845. Pesaran, M.H., Shin, Y. (1998). Generalized impulse response analysis in linear multivariate models. Economics Letters, 58, 17-29. Phylaktis, K. (1999). Capital market integration in the Pacific Basin region: an impulse response analysis. Journal of International Money and Finance, 18, 267-287. Sims, C., (1980). Macroeconomics and reality. Econometrica, 48, 1- 48. Swanson, P. E. (1987). Capital market integration over the past decade: the case of the US dollar, Journal of International Money and Finance, 6, 216-225. Urich, T., and Wachtel, P. (2001) Financial market responses to monetary policy changes in the 1990s, Contemporary Economic Policy, 19, 254-267. Yang, J. (2003). Market segmentation and information asymmetry in Chinese stock markets: a VAR analysis. Financial Review, 38, 591-609.
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Table 1 Cointegration Tests on US and Eurodollar Interest Rates
Without Linear Trend T
C (5%)
Decision
With Linear Trend Ho = r
T
C (5%)
Decision
----------------------- Whole Sample (01/03/83-12/31/02) -------------------37.57
20.17
R
0
33.43
15.20
R
1.63
9.09
F#
1
0.01
3.96
F
---------------------- First Sub-period (01/03/83-12/31/91) ------------------18.79
20.17
F#
0
16.58
15.20
R
2.16
9.09
F
1
0.23
3.96
F
----------------------- Second Sub-period (01/01/93-12/31/02) --------------32.84
20.17
R
0
30.86
15.20
R
1.37
9.09
F#
1
0.22
3.96
F
Notes: r is the number of cointegrating vectors; T is the trace test statistics and, C is the trace test critical values. R indicates that we reject the null hypothesis that the number of cointegrating vectors is less than or equal to r (when T is greater that C (5%)) while F indicates that we fail to reject the null hypothesis. Starting at the top of the table and moving sequentially across from left to right and from top to the bottom, we should stop testing at the first “F” (failure to reject). The symbol (#) indicates the stopping point.
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Table 2 Granger Causality Tests (with time zone adjustment) Dependent
Causal Variable
Variable
H0: Cross-market variables do not cause dependent variable
Optimal lag length
Whole Period (1/3/1983-12/31/2002) Eurodollar
US
24.12(0.063)
15
US
Eurodollar
1710.5(0.000)
15
First Sub-period (1/3/1983-12/31/1991) Eurodollar
US
15.73(0.330)
14
US
Eurodollar
900.60(0.000)
14
Second Sub-period (1/1/1993-12/31/2002) Eurodollar
US
49.57(0.000)
12
US
Eurodollar
438.30(0.000)
12
Notes: The causality from the Eurodollar rate to the US rate is examined between the Eurodollar rate at time t and US CD rates at time t-1. Such an adjustment is made to address the time zone difference that the Eurodollar market (in the UK) is closed earlier than the U.S. market on the same calendar day. Column 3 reports F-statistics with pvalues in parenthesis. The optimal lag for each VAR equation is determined by the minimization of the Akaike information criterion.
18
Table 3 Granger Causality Test Results (without time zone adjustment) Dependent Variable
Causal Variable
H0: Cross-market variables do not cause dependent variable Whole Period (1/3/1983-12/31/2002)
Optimal Lag Length
Eurodollar
US
88.46(0.000)
14
US
Eurodollar
637.49(0.000)
14
First Sub-period (1/3/1983-12/31/1991) Eurodollar
US
26.73(0.014)
13
US
Eurodollar
370.35(0.000)
13
Second Sub-period (1/1/1993-12/31/2002) Eurodollar
US
167.40(0.000)
10
US
Eurodollar
152.07(0.000)
10
Notes: Column 3 reports F-statistics with p-values in parenthesis. The optimal lag for each VAR equation is determined by the minimization of the Akaike information criterion.
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The Trace tests Z(t)
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
1994
1996
1998
2000
2002
R(t)
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
1984
1986
1988
1990
1992
1 is the 10% significance level
Figure 1 Plots of Trace Test Statistics at Each Date during 1/1/1984 –12/31/2002
(The one-year period of 01/03/83-12/31/84 is used as a base period for initial estimation. Recursive estimates of test statistics under both Z-representation and R-representation are reported. Test statistics are normalized by the critical values at the 5% level; test statistics of the upper plot (corresponding to the null hypothesis r=0) exceeding 1.0 indicate rejection of the null hypothesis of no cointegration.)
20
Panel A. Period 1 (1/3/1983-12/31/1991) Response of US to EURO
Response of EURO to US 1.2
1.2 1.0
0.8
0.8 0.6
0.4 0.4 0.2
0.0
0.0 -0.4
-0.2 1
2
3
4
5
6
7
8
9
1
10
2
3
4
5
6
7
8
9
10
9
10
Panel B. Period 2 (1/1/1993-12/31/2002) Response of EURO to US
Response of US to EURO
1.2
1.0
1.0 0.8 0.8 0.6
0.6 0.4
0.4
0.2 0.2 0.0 -0.2
0.0 1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
Figure 2 Response to a One Unit Shock (with time zone adjustment)
21
6
7
8
Panel A. Period 1 (1/3/1983-12/31/1991) Response of EURO to US
Response of US to EURO
1.2
1.2
1.0 0.8
0.8 0.6
0.4 0.4 0.2
0.0
0.0 -0.2
-0.4 1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
9
10
Panel B. Period 2 (1/1/1993-12/31/2002) Response of US to EURO
Response of EURO to US 1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0 1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
Figure 3 Response to a One Unit Shock (without time zone adjustment)
22
7
8
Footnotes 1
A similar controversy exists in some studies involving non-US markets. In particular, Kaen and Hachy (1983) documented unidirectional causality from domestic to external markets in UK. Lo, Fung and Morse (1995) showed evidence of a strong causality running from Euroyen to Japanese interest rate with a weak feedback from the latter to the former.
2
Though it might be more desirable, intraday interest rate data have not been used in this line of research using cash market rates, probably due to their unavailability to most researchers. Also note that the use of daily data would ensure this study to be comparable with most of previous studies, where much controversy exists. 3
Results of several conventional unit root tests are available on request.
4
The estimation with the appropriate heteroscedasticity and autocorrelation-consistent covariance matrix was also applied to address any possible conditional heteroscedasticity and autocorrelation problems. The appropriate χ 2 statistic was used (instead of the F statistic) to test the above null hypothesis and the conclusion remained qualitatively the same.
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