Domestic vs. International Correlations of Interest Rate Maturities

Abstract

The association between long and short interest rates is traditionally envisaged from a purely domestic perspective, where it is believed an empirical regularity. Hence, the weakening of this relationship in the first half of the 2000s has represented a conundrum, calling for a reassessment of the term structure and the conduct of monetary policy. Some commentators have called for investigations into the international dimension of this puzzle. Hence, in this paper we employ recent advances in panel data econometrics to investigate the co-movement of interest rate maturities both at the domestic and international levels for a sample of industrial countries. Specifically, we use the Ng (2006) spacings correlations approach to examine interest rates correlations between and within countries. Compared to alternatives, this method does not just estimate bivariate correlations, but also assesses the degree of panel correlation without being restricted by the assumption of either zero or complete panel correlation. We find very small correlations between the different maturities of domestic rates and much higher correlations of international rates. Moreover, international correlations between long rates are significantly higher than those between short rates. These findings suggest a scenario for national monetary policy, where financial globalization may have changed the transmission mechanism, advocating searches for the “missing†yield curve in its international dimension.

Full text

  



Volume 30, Issue 2

Domestic vs. International Correlations of Interest Rate Maturities

Joseph P Byrne
University of Glasgow
Giorgio Fazio
University of Palermo, University of Glasgow Norbert Fiess
World Bank
Abstract
The association between long and short interest rates is traditionally envisaged from a purely domestic perspective,
where it is believed an empirical regularity. Hence, the weakening of this relationship in the first half of the 2000s has
represented a conundrum, calling for a reassessment of the term structure and the conduct of monetary policy. Some
commentators have called for investigations into the international dimension of this puzzle. Hence, in this paper we
employ recent advances in panel data econometrics to investigate the co-movement of interest rate maturities both at
the domestic and international levels for a sample of industrial countries. Specifically, we use the Ng (2006) spacings
correlations approach to examine interest rates correlations between and within countries. Compared to alternatives,
this method does not just estimate bivariate correlations, but also assesses the degree of panel correlation without being
restricted by the assumption of either zero or complete panel correlation. We find very small correlations between the
different maturities of domestic rates and much higher correlations of international rates. Moreover, international
correlations between long rates are significantly higher than those between short rates. These findings suggest a
scenario for national monetary policy, where financial globalization may have changed the transmission mechanism,
advocating searches for the “missing”yield curve in its international dimension.
The authors would like to thank, without implicating, the editor and an anonymous referee for useful comments on the paper, Serena Ng for
making available her Matlab code. Giorgio Fazio would like to acknowledge financial assistance from MIUR grant PRIN#2007F2fy95_004
Citation: Joseph P Byrne and Giorgio Fazio and Norbert Fiess, (2010) ''Domestic vs. International Correlations of Interest Rate Maturities'',
Economics Bulletin, Vol. 30 no.2 pp. 1082-1090.
Submitted:Apr082010. Published: April 22, 2010.

  

1. Introduction
The empirical literature has traditionally investigated the term structure of interest
rates from a purely domestic perspective and the co-movement between long rates and short
rates is considered a “broad empirical regularity”, as noticed by Rudebusch et al. (2006).
However, more recently, and in particular from the end of 1990s and through the 2000s,
changes in domestic short term interest rates seem to have become less potent at influencing
the long end of the yield curve. This conundrum, as notably first defined by Greenspan
(2005), has sparked an intensive debate in research and policy circles (see Rudebusch et al.
2006, and Atkenson and Kehoe, 2009) both on the relationship between short and long rates
and on the implications for the conduct of monetary policy. According to Bernanke (2007)
this phenomenon requires further investigation from an international perspective. Indeed,
increasing international financial integration (see Lane and Milesi-Ferretti 2007, 2008) seems
to have redefined the operating environment of domestic monetary policy, as also discussed
by Rogoff (2007), Borio and Filardo (2007) and Spiegel (2008).
Hence, in this paper we employ recent advances in panel data econometrics to
investigate the relationship between short and long term interest rates not only from the
domestic, but also from the international perspective for four industrialized countries. In
particular, we exploit the concordance between the null hypothesis of no correlation and
uniformity of the probability integral transformations of the ordered correlations, following
the spacings approach of Ng (2006). This approach was originally developed to overcome
some of the limitations of traditional methods in testing the extent of cross-sectional
correlation in panel data sets and represents a natural means for examining international and
domestic interest rates correlations. Compared to other alternatives, this methodology not
only does estimate bivariate correlations, but exploits the panel dimension of the data to
provide an assessment of the overall panel cross-sectional correlation. Further, this approach
does not assume that there is either no correlation or complete correlation in the panel,
utilizing a break point test to identify which correlations are relatively large and which are
small.
Our approach allows us to identify fresh empirical evidence on the domestic and
international correlations between interest rates of different maturities, corroborating the view
that further investigation is needed on the international dimension of the domestic
conundrum.
The paper is set out as follows: section 2 presents our methodology. Section 3
presents the results. Section 4 concludes.
2. Empirical Strategy
We are interested in the domestic and international correlation structure of interest
rates at different maturities. Specifically, we have investigated interest rate series of three
maturities (3 months, 1 year and 10 years) and for four countries (United States, Germany,
Canada and the United Kingdom). Three month T-Bills ( M
tj
i3
,) are from IMF International
Financial Statistics, and one year ( Y
tj
i1
,) and 10 year yields on zero-coupon bonds ( Y
tj
i10
,) are
provided by national central banks. Hence, there are twelve time series (N=12) and 66
potential correlations (n = N·(N-1)/2). Data is monthly from 1999M1 to 2006M7.
In order to investigate the correlation between domestic and international interest
rates, we employ a methodology that allows us to capture the overall correlation structure of
the data. First, we perform the panel test for cross-sectional correlation proposed by Ng

2
(2006) and then we implement simple tests to investigate statistical differences between
coefficients.
2.1 Ng (2006) Spacings
Most tests for cross-sectional correlation in panels of dimension N×T are based on the
null of no correlation and an alternative of greater than zero correlation for some units.
Unfortunately, such tests provide little guidance about the nature and pervasiveness of cross-
sectional correlation in panels, making it unclear whether rejection or acceptance of the null
is due to a large or small number of uncorrelated units. To investigate this issue, Ng (2006)
introduces a panel test for cross-sectional correlation when some, but not necessarily all, units
are correlated. The suggested uniform spacing methodology facilitates the estimation of the
number of correlated pairs; the evaluation of the magnitude of the correlations; and the
identification of the underlying series, which produce small or large correlations.
The panel cross-section correlation test of Ng (2006) is based on a probability integral
transformation of ordered correlations. Transformed correlations are first ordered by size and
then partitioned by means of a breakpoint analysis into two subsamples of small (S) and large
(L) correlations, where the proportion of low correlations is represented by the
parameter
θ
ˆ∈[0,1]. The variance ratio of the two subsamples is then evaluated. The spacings
variance ratio (svr) test proposed by Ng is asymptotically standard normal in large samples
and can be applied to the full set of correlations as well as subsets. As an example, if the
hypothesis of no correlation is rejected for the L sample, but not the S sample, the fraction
θ
ˆ
of correlation coefficients is not statistically different from 0. A q-q plot of the probability
integral of the transformed ordered correlations, j
φ
, can also be used to uncover the extent of
cross-sectional correlation in the data. Homogeneity in correlations implies that the q-q plot is
flat over a subset. The test proposed by Ng allows us to test the overall significance of
correlations in the sample. However, we are also interested to investigate the statistical
difference between correlation coefficients.
2.2 Fisher’s z Transformation
Given that correlation coefficients are constrained in the [-1, 1] space, in order to test
hypotheses about specific values, we transform the Pearson’s correlation coefficients, rij, into
Fisher’s z correlations, rij(z):
)1(
)1(
ln
2
1
)(
ij
ij
ij r
r
zr −
+
=, (1)
where ⎟
⎠
⎞
⎜
⎝
⎛
−
≈3
1
,0)( T
Nzrij , where T is the sample size, if the null hypothesis of zero
correlation is true. Tests of equality of correlation coefficients for independent samples, N1
and N2, follow the test statistic:
)3(
1
)3(
1
)()(
21
2,1,
−
+
−
−
=
NN
zrzr
zijij , (2)
which is distributed as N(0,1) under the null.

3
Table 1. Spacings Variance Ratio Test Statistics
θ
ˆ Number of small
correlation pairings Small svr Large svr
1999-2006 0.333 22 out of 66 -0.633 5.067*
Notes:
θ
ˆ is the proportion of correlations that are small. svr is the Ng (2006) Spacings Variance Ratio test and
gives an indication of whether correlation is significantly different from zero, distributed as standard normal,
therefore the critical value is 1.65 (significant at 5% marked with asterisk). First order serial correlation is
removed following Ng (2006). Since N = 12, there are n = N·(N-1)/2 = 66 correlations.
3. Results
As mentioned above, the svr test partitions the series of correlations into subsets of
small (S) and large (L) correlations, where the proportion of low correlations in the first set is
given by
θ
ˆ. For our panel of interest rates we find
θ
ˆ=0.333, i.e. 22 out of 66 correlations are
small. The q-q plot of j
φ
in Figure 1 deviates substantially from the 45% line, indicating
highly heterogeneous correlations. The svr test statistics for the S and L samples are -0.633
and 5.067, respectively, indicating no evidence of correlated pairs in the S sample, but
substantial correlations in the L sample. Table 2 presents a lower diagonal matrix of
correlations.
010 20 30 40 50 60 70
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Figure 1. j
φ
: 3M, 1Y and 10Y Interest Rates in 4 Countries

4
Domestic correlations of short and long rates
We first turn our attention to the correlation between rates at different maturities
within the same country, i.e. the domestic term structure. Interestingly, all within country
correlations between 10 year bonds and three month rates are in the Small sample, denoted by
superscript S, and, according to the svr test statistic and p-values, they are not significantly
different from zero. For the US such low correlation of 10 year and three month rates (-0.097)
is consistent with the Greenspan conundrum that long rates have recently failed to respond to
policy-driven changes in the short term interest rate. Our findings suggest, however, that the
conundrum is not just US-specific, but an international phenomenon, since in Germany, the
UK and Canada the correlations between short and long interest rates are also low (-0.041,
-0.062 and -0.085) and insignificantly different from zero. Furthermore, we find weak
statistical correlation between three month rates and one year bond yields for the UK and
Germany, but less so for Canada and the US, indicating that the Greenspan conundrum may
apply more readily to the European countries even at short-end maturities. For the US and
Canada the term structure seems to survive only between the 3 moths and 1 year rates.

5
Table 2. Correlations in Interest Rates for Four Industrial Countries
MtUK
i3
, MtUS
i3
, MtCN
i3
, MtGE
i3
, YtUK
i1
, YtUS
i1
, YtCN
i1
, YtGE
i1
, YtUK
i10
, YtUS
i10
, YtCN
i10
, YtGE
i10
,
MtUK
i3
, 1.000
MtUS
i3
, 0.448
L
,* 1.000
MtCN
i3
, 0.345
L
,* 0.676
L
,* 1.000
MtGE
i3
, 0.317
L
,* 0.371
L
,* 0.432
L
,* 1.000
YtUK
i1
, 0.098S 0.093S 0.018S 0.206L 1.000
YtUS
i1
, 0.293
L
,* 0.359
L
,* 0.206L 0.092S 0.575
L
,* 1.000
YtCN
i1
, 0.257
L
,* 0.260
L
,* 0.278
L
,* 0.119S 0.524
L
,* 0.746
L
,* 1.000
YtGE
i1
, 0.244
L
,* 0.162S 0.127S 0.208L 0.550
L
,* 0.663
L
,* 0.672
L
,* 1.000
YtUK
i10
, -0.062S -0.052S -0.047S -0.019S 0.643
L
,* 0.314
L
,* 0.307
L
,* 0.435
L
,* 1.000
YtUS
i10
, -0.047S -0.097S -0.085S -0.166S 0.519
L
,* 0.549
L
,* 0.421
L
,* 0.565
L
,* 0.659
L
,* 1.000
YtCN
i10
, -0.012S -0.157S -0.085S -0.218
L
,* 0.503
L
,* 0.431
L
,* 0.532
L
,* 0.505
L
,* 0.689
L
,* 0.818
L
,* 1.000
YtGE
i10
, -0.055S -0.074S -0.037S -0.041S 0.510
L
,* 0.348
L
,* 0.380
L
,* 0.592
L
,* 0.807
L
,* 0.735
L
,* 0.743
L
,* 1.000
Notes: This table presents bivariate Pearson’s correlation statistics for three month ( M
tj
i3
,), one year ( Y
tj
i1
,) and 10 year rates ( Y
tj
i10
,) for the UK, the US, Germany and Canada
based on monthly data between 1999M1 and 2006M7. Correlation in the small group according Ng (2006) are denoted by superscript S. Large by superscript L. Correlations
that are significantly different from zero are marked with an asterisk (*).

6
Table 3. Test of Equality of Correlation Coefficients
Country Pairings M
tj
i3
, Y
tj
i10
, Z
Corr( tUK
i,,tUS
i,) 0.448 0.659 -2.051
Corr( tUK
i,,tCN
i,) 0.345 0.689 -3.219
Corr( tUK
i,,tGE
i,) 0.317 0.807 -5.251
Corr( tUS
i,,tCN
i,) 0.676 0.818 -2.179
Corr( tUS
i,,tGE
i,) 0.371 0.735 -3.649
Corr( tCN
i,,tGE
i,) 0.432 0.743 -3.279
Joint test of: ∑shortij,
r
1
n -∑longij,
r
1
m=0 -3.253
Notes: This table presents Pearson’s correlation statistics for three month ( M
tj
i3
,) and 10 year rates ( Y
tj
i10
,) for
the UK, the US, Germany and Canada. Z is the test statistic according to equation (2) which is based on the
Fisher’s z transformation. The two tailed 95% critical values are
±
1.96.
International correlations of short and long rates
A more refined picture emerges once we split cross-country correlations by maturity
(3 month versus 10 year rate). International correlations between short interest rates are
considerably larger than the domestic term structure correlations and range between
corr( MtUK
i3
,,MtGE
i3
,) = 0.317 and corr( MtUS
i3
,,MtCN
i3
,) = 0.676. This results is interesting, since the short
rate can be considered mainly a policy variable, and these correlations seem to indicate that
although monetary policies should be independent, they do exhibit some degree of
international correlation.
Correlations are even more sizeable for long interest rates, ranging from
corr( YtUK
i10
,,YtUS
i10
,) = 0.659 to corr( YtUK
i10
,,YtCN
i10
,) = 0.818 (see Table 3). Further, individual and
group tests of coefficients’ equality are clearly rejected, indicating that long rates are indeed
significantly more correlated than short rates.1
These results show that increasing financial integration is impacting long interest rates
more than short interest rates. The finding of lower cross sectional correlation in short rates
relative to long rates may depend on the fact that short rates should be more susceptible to
idiosyncratic shocks and domestic policy actions. While on one side this could be the
outcome of the attempt to pursue independent monetary policies on the part of domestic
authorities, on the other it may suggest that due to international financial integration the long
end of the maturity spectrum has become more tied to its international dimension, as
suggested by Bernanke (2007), and less responsive to its domestic dimension.
1 There is also evidence of a statistically significant difference in average correlation between three month and
one year interest rates at 10% but less evidence of a statistical difference between one year and 10 year bond
yields. These results are available upon request.

7
4. Conclusions
The relationship between short and long interest rates is typically envisaged from a
purely domestic standpoint. Prompted by the recent increase in financial globalization, and its
potential consequences for national economies, in this paper we have added an international
dimension to the conventional analysis. In particular, we have investigated both the domestic
and international relationships between interest rates at different maturities. Some important
stylized facts have emerged. Within countries, long interest rates are not correlated with short
interest rates. We take this as evidence that the term structure has “gone missing” in the
period analyzed, not just in the US, where the problem was first highlighted by former Fed
Chairman Greenspan, but also in the other three countries in our sample: Canada, Germany
and the UK. Furthermore, there seems to be evidence of international cross-country
correlations between short term rate, indicating some degree of monetary policy
interdependence. However, and notably, these correlations are significantly smaller than the
international correlations between long rates. We take this as evidence of financial
globalization at the long end of the yield curve. Finally, this seems to suggest that searches
for the “missing” yield curve could benefit from a deeper investigation into the international
dimension of the term structure.

8
References
Atkenson, A. and P.J. Kehoe (2009) “On the Need for a New Approach to Analyzing
Monetary Policy” NBER Macroeconomics Annual, 23, 389-426
Borio, C.E.V. and A.J. Filardo (2007) “Globalisation and inflation: New cross country
evidence on the global determinants of global inflation” BIS working paper number 227.
Bernanke, B.S. (2007) “Globalization and Monetary Policy”, speech at the Fourth Economic
Summit, Stanford Institute for Economic Policy Research, Stanford, California, March 2,
2007.
Greenspan, A. (2005) Statement to the Senate Committee on Banking, Housing, and Urban
Affairs, presenting the Federal Reserve Board’s Monetary Policy Report to the Congress.
16th February, www.federalreserve.gov/boarddocs/hh/2005/february/testimony.htm.
Lane, P.R. and G.M. Milesi-Ferretti (2007) “The external wealth of nations mark II: Revised
and extended estimates of foreign assets and liabilities, 1970-2004” Journal of International
Economics, 73, p. 223-250.
Lane, P.R. and G.M. Milesi-Ferretti (2008) “The Drivers of Financial Globalization”
American Economic Review: Papers & Proceedings, 98, p. 327-332.
Ng, S. (2006) “Testing Cross-Section Correlation in Panel Data using Spacings” Journal of
Business and Economics Statistics, 24, p. 12-23.
Rogoff, K.S. (2007) “Impact of Globalization on Monetary Policy” in The New Economic
Geography: Effects and Policy Implications, Federal Reserve Bank of Kansas City.
Rudebusch, G. D., E.T. Swanson and T. Wu. (2006) “The Bond Yield “Conundrum
from a macro finance perspective” Monetary and Economic Studies, 24, p. 83-109.
Spiegel, M. (2008) “Financial Globalization and Monetary Policy Discipline: Survey with
New Evidence from Financial Remoteness” FRBSF Pacific Basin working paper number
WP10.