the changing relation between the canadian and u.s. yield curves

Journal of International Money and Finance 30 (2011) 965–981

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Journal of International Moneyand Finance

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The changing relation between the Canadianand U.S. yield curves

Edwin Wong 1, Kathlyn Lucia, Stephanie Price, Richard Startz*

Department of Economics, University of Washington, Box 353330, Savery 305, Seattle, WA 98195, USA

Keywords:Term structureStructural breakMonetary policyInflation

* Corresponding author. present address: DepartCA 93106-9210, USA. Tel.: þ1 805 893 2895; fax: þ

E-mail addresses: [email protected] (E. Wong), s

1 Present address: Department of Health Service

0261-5606/$ – see front matter � 2011 Elsevier Ltdoi:10.1016/j.jimonfin.2011.06.002

a b s t r a c t

The term structures of Canada and of the United States, twocountries with historically interdependent economic ties, havebeen closely linked. We investigate the link between Canadian andU.S. yield curves and show previously strong correlations betweenyield curve components dissipate after Canadian monetary policyreforms in the early 1990s. We attribute the separated ties to theadoption of explicit inflation targets in 1991 and the maintenanceof credibility in price stability as a central policy goal by the Bankof Canada. The effect is particularly evident in the diminishedcross-country correlations of the short term bond yields. Addi-tionally, there exists strong evidence of cointegration before thereforms, evidence which weakens after the policy change date.Lastly, the results on the term structure are shown using a vectorautoregression with an endogenously determined break date forCanadian and U.S. estimates of the three-factor Nelson and Siegel(1987) yield curve model.

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1. Introduction

Canada and the United States historically maintain close economic ties and maintain inter-relatedeconomic policies. This paper describes the link between the term structures of interest rates in theUnited States and Canada. We find strong correlation between U.S. and Canadian bond yields untila change in Canadian monetary policy induced a structural break in the determinants of the Canadian

ment of Economics, 2127 North Hall, University of California, Santa Barbara,1 805 893 [email protected] (R. Startz).

s, Box 357660, University of Washington, Seattle, WA 98195-7660, USA.

d. All rights reserved.

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http://dx.doi.org/10.1016/j.jimonfin.2011.06.002

E. Wong et al. / Journal of International Money and Finance 30 (2011) 965–981966

term structure. After this break date, the cross-border relationship breaks down as short term Canadianyields begin to follow a path independent of the U.S. We attribute the separated ties to the adoption ofexplicit inflation targets in 1991 and the maintenance of credibility in price stability as a central policygoal by the Bank of Canada

The approach adopted in this paper estimates yield curves for both countries at each period by usingthe three-factor Nelson and Siegel (1987) model. We then examine the evolution of these time varyingyield curve factors by estimating an unrestricted VAR(1) for each country. Testing for a structural breakin yield curve parameters suggests January 1993 as the break point, a date following closely on theheels of Canadian monetary policy reform. We find the relation between U.S. and Canadian yields isstrong before the structural break, but greatly diminishes afterwards for short term rates. For example,cointegration tests on yields for both countries find strong evidence of cointegration before thestructural break and weak evidence of cointegration after the structural break in long run yields.Allowing for uncertainty in the break date for the cointegrating relationship suggest a regime shift inthe mid 1990s in the determination of long run yields, attributed to credibility in Canadian monetarypolicy and a decline in long run inflation uncertainty. Overall, the results of these tests imply theequilibrium relationship between U.S. and Canadian bond yields breaks down after a change inCanadianmonetary policy. By accounting for a structural break in the determination of short termyieldcurve factors in Canada, the influence of U.S. determinants on the Canadian term structure becomessubstantially weakened. The implications of the monetary policy shift are present in the macro-economy as the Canadian short rate is more closely tied to inflation and less connected to theunemployment after the structural break. Evidence in this paper also shows that the greater emphasison inflation also induced a change in the connection between the yield curve and the Canada/U.S.exchange rate.

This paper continues as follows. In Section 2 we discuss the Nelson and Siegel (1987) model as wellas relevant literature. We describe the characteristics of data used in constructing term structures inSection 3. Section 4 discusses the specification of the VAR(1) model of Nelson-Siegel factor loadingsthat we estimate. Our results are reported in Section 5 and lastly Section 6 provides concludingremarks.

2. Background and literature review

The Canadian and U.S. economies are closely tied through trade and capital markets, as well aspolicy interactions. Simply because the U.S. economy is (roughly) ten times the size of the Canadianeconomy in terms of GDP, one expects U.S. activity to drive Canadian activity more than Canadianactivity drives U.S. activity. However, there is more room for independence in monetary policy thanthere is on the real side. For example, by estimating a joint U.S.-Canada unobserved component model,Fung and Remolona (1998) suggest that monetary policy carries across borders. They show thatinflation shocks affect each country independently, but real shocks affect both countries. They furthershow differences in inflation risk premium and expectations in each country explain yield and inflationspreads.

The interconnected economic ties between Canada and the United States not only result fromproximity, but a shared history emerging from the 1970s and into the 1980s. Facing similar episodes ofstagflation in the early 1970s and oil supply shocks in the late 1970s, both countries sought to controlinflation by targeting monetary aggregates. After abandoningmonetary targets in the early 1980s, bothcountries were faced with a brief period of recession, followed by recovery during the middle part ofthe decade. Inflation again became an increasing cause for concern toward the end of the 1980sresulting from expansionary fiscal policy and rising commodity prices. Both countries tookmeasures tocurb inflationary pressures, by manipulating the short rate to achieve policy goals. Throughout the1980s, the Bank of Canada’s failure to announce a clear and credible policy objective resulted insensitivity of Canadian interest rates to changes in interest rates in the United States, yet another factorin the interconnected term structures across countries.

Nelson and Siegel (1987) develop a parsimonious model of the yield curve that is flexible enough totake on the various shapes of the yield curve: monotonic, humped, and inverted. The Nelson-Siegelcurve is often written as in Equation (1).

E. Wong et al. / Journal of International Money and Finance 30 (2011) 965–981 967

ytðsÞ ¼ Lt þ St

1� e�ls

ls

!þ Ct

1� e�ls

ls� e�ls

!(1)

yt(s) is the time t yield on a s-period bond. L, S, and C, estimated each period, are interpreted as the levelfactor (y(N)), the slope factor (y(0) – y(N)), and a curvature factor. Diebold and Li (2006) and Dieboldet al. (2006) extract latent factors from estimates of Nelson Siegel yield curves and use VARs to studythe driving forces of these latent factors. We use similar methodology to study the cross-border drivingrelations between Canadian and U.S. yield curves.

The central finding of this paper is the existence of structural change in the determination of Canadianyieldcurve components, particularly in the slope factor. The structural change stems fromexplicit inflationtargeting during the early 1990s. Other studies have established analogous changes in Canada, but typi-cally from a closed economy perspective. For example, Bolder et al. (2004) identifies December 1996 asa point of structural change. They apply a principal componentsmodel similar to this paper and show theimportance of the slope factor in explaining the yields increases after the structural break. Using databetween1967and1996, Schich (2002)finds the slope componentof theyield curve is a strongpredictoroffuture inflation. However, he is unable to identify any structural changes prior to 1996. Studies have alsolinked theU.S. economywith theCanadianyield curve. Forexample, Lange (2005) applies a structuralVARmodel showing that U.S. monetary policy has a large, significant and persistent effect on the 10-year-and-over Government of Canada bond yield. Consistent with our findings, Boothe (1991) shows that bondyields in the United States and Canada are cointegrated across maturities between 1972 and 1989.

3. Data

The term structure in either country consists of a set of zero-coupon yields for bonds maturing speriods away. Our choice of data is based on convenience of availability and comparability with otherstudies. We consider bonds with maturity lengths of 3, 6, 9, 12, 15, 18, 21, 24, 30, 36, 48, 60, 72, 84, 96,108 and 120 months. The sampling period is 216 monthly observations from January 1986 throughDecember 2003.

There exist several methods for decouponing bonds in order to obtain zero-coupon yields. For theU.S. we use yields computed by the unsmoothed Fama and Bliss (1987) method (see also Bliss, 1996).2

The Fama-Bliss method uses forward prices to interpolate end-of-month bond prices with maturitiesbetween one and five years. Zero-coupon yields for Canada are obtained from the Bank of Canada andare generated using Merrill Lynch Exponential Splines, a technique outlined by Bolder and Gusba(2002) and extended by Bolder et al. (2004). The latter introduced a comprehensive database ofconstant maturity zero-coupon yield curves for the Government of Canada bond market, which is keptcurrent and publicly available on the Bank of Canada’s website.

We beginwith descriptive statistics and thenmove tomore formal modeling. Univariate descriptivestatistics for bonds with s months to maturity from both countries are in Table 1. Observing thedescriptive statistics, the mean yield curve is upward sloping and concave for both countries. However,the average Canadian yield is greater than American yields at all maturities. Furthermore, Canadianyields generally exhibit higher variance and persistence.

Fig. 1 plots Canadian and U.S. yields for selected maturities, illustrating two important points. Firstthe U.S. and Canadian zero-coupon yields are strongly correlated during the early years of the sample.During this earlier period, Canadian yields are above the corresponding U.S. yields. According to Clinton(1998), higher Canadian yields are a result of a less-liquid market, a perception of greater risks anda frequent expectation the Canadian dollar will decline in value. In addition, the Canadian yields appearto peak in the first half of the 1990s. Clinton (1998) attributes this fact to increasingly unsustainablegrowth in public debt, historical problems with inflation and structural problems in the public andprivate sectors. Second, there appears to be a structural break in Canadian data that occurs in the early1990s. After this point, the Canadian yields for the various maturities fall below those of the U.S., where

2 We are grateful to Robert Bliss for providing U.S. yield data.

Table 1Descriptive Statistics for respective Canada and U.S. Yield Curves: 1986–2003.

Maturity Mean Std. Dev. Min Max rð1Þ rð12Þ rð30ÞCanada3 6.436 2.979 1.979 13.484 0.978 0.730 0.3736 6.454 2.853 1.939 13.073 0.978 0.736 0.3769 6.504 2.747 2.035 12.979 0.977 0.738 0.37712 6.561 2.653 2.223 12.858 0.976 0.738 0.37915 6.617 2.569 2.429 12.786 0.975 0.737 0.38218 6.672 2.494 2.574 12.715 0.974 0.736 0.38721 6.723 2.429 2.730 12.628 0.973 0.735 0.39324 6.771 2.371 2.887 12.534 0.973 0.734 0.39930 6.858 2.277 3.100 12.352 0.972 0.736 0.41436 6.935 2.204 3.249 12.199 0.972 0.738 0.42748 7.070 2.098 3.532 11.992 0.972 0.746 0.45360 7.187 2.022 3.813 11.861 0.972 0.755 0.47772 7.287 1.964 4.043 11.729 0.973 0.763 0.49984 7.370 1.919 4.223 11.563 0.973 0.770 0.51996 7.439 1.886 4.358 11.376 0.974 0.777 0.534108 7.496 1.864 4.459 11.205 0.975 0.782 0.545120 7.549 1.851 4.542 11.087 0.976 0.787 0.552

United States3 4.911 1.916 0.876 9.131 0.978 0.599 �0.0296 5.039 1.932 0.958 9.324 0.978 0.603 �0.0079 5.145 1.943 0.979 9.343 0.977 0.610 0.01812 5.290 1.963 1.040 9.641 0.975 0.613 0.02715 5.431 1.966 1.066 9.698 0.975 0.616 0.05218 5.516 1.936 1.144 9.660 0.974 0.614 0.07421 5.588 1.902 1.219 9.544 0.973 0.613 0.09524 5.626 1.858 1.299 9.524 0.972 0.610 0.11330 5.785 1.808 1.447 9.510 0.971 0.610 0.15536 5.899 1.747 1.618 9.461 0.969 0.611 0.18848 6.111 1.660 1.999 9.348 0.966 0.620 0.26260 6.234 1.595 2.351 9.293 0.965 0.627 0.31372 6.390 1.549 2.663 9.286 0.965 0.646 0.36684 6.487 1.495 3.003 9.395 0.966 0.656 0.39996 6.590 1.471 3.221 9.521 0.967 0.672 0.435108 6.641 1.459 3.389 9.594 0.966 0.681 0.461120 6.638 1.437 3.483 9.527 0.965 0.688 0.485


previously they were above the U.S. yields by a fairly consistent 2–3%. In addition to falling below theU.S. yields, the Canadian yields now follow their own path, independent of the U.S. This independentrelationship weakens as the maturity date lengthens implying a structural break in the determinationof the Canadian short run rates.

Table 2 presents the cross-country correlations between bond yields at each maturity. The right-mostcolumn shows correlations for the full sample. All correlations are high, and increasingwithmaturity from0.81 to 0.95. The left two columns give correlations for our two sub-periods. The evident change is that thecorrelation of short maturities falls in the second sub-period. For example, the correlation in the 3-monthmaturity falls from 0.91 to 0.66. We attribute this effect to a fundamental change in the determination ofshorter term bond yields by the Bank of Canada, which we describe in detail in Section 5.1.

If yields are nonstationary, correlations computed on levels may be spurious. VAR estimation needsto account for nonstationarity if it exists. Table 3 presents unit root tests running augmented Dickey–Fuller tests on all available maturities with the null hypothesis that yields are I(1) without drift. Theresults reported in Table 3 provide no significant evidence against a unit root for either country.

4. Model

We estimate separate Nelson-Siegel term structure models for Canada and for the United Statesduring each period in our sample. As in Diebold and Li (2006), l is taken to be 0.0609, the value

Fig. 1. Yearly average zero-coupon yields for Canada and the U.S. between 1986–2003.


Table 2Correlation Coefficients between U.S. and Canada Bond Yields.

Maturity Correlation

1986–1993 1993–2003 1986–2003

3 0.908 0.659 0.8136 0.907 0.701 0.8249 0.899 0.726 0.83412 0.894 0.736 0.83915 0.896 0.743 0.84818 0.897 0.752 0.85721 0.896 0.760 0.86424 0.894 0.767 0.86930 0.891 0.777 0.88336 0.889 0.788 0.89348 0.884 0.804 0.91260 0.887 0.812 0.92372 0.883 0.810 0.93184 0.874 0.816 0.93596 0.865 0.833 0.942108 0.859 0.853 0.947120 0.847 0.877 0.953


maximizing the medium term loading at 30 months. Equation (1) states the yield at time t for a newlyissued bond maturing s periods in the future is a function of a long term level loading, short term slopeloading, and medium term curvature loading.

Given the time series for three factors for each country, and because of the presence of unit roots inlevel and slope factor loadings for both countries, we estimate an unrestricted VAR(1) for the first-differences of the six estimated factors (see Diebold et al., 2006). Specifically,

DBt ¼ GDB0t�1 þ et (2)

Table 3Unit root tests on yields for the sample 1986–2003. The ADF critical values are calculated fromMacKinnon et al. (1999). The ADFlags are defined according to the Schwarz Info Criterion.

Maturity (months) ADF P-value ADF P-value

U.S. Canada

3 �0.631 0.860 �1.310 0.6256 �0.601 0.866 �1.216 0.6689 �0.680 0.848 �1.162 0.69112 �0.701 0.843 �1.149 0.69715 �0.752 0.830 �1.155 0.69418 �0.820 0.811 �1.170 0.68821 �0.875 0.795 �1.188 0.68024 �1.004 0.752 �1.207 0.67230 �1.092 0.719 �1.238 0.65836 �1.145 0.698 �1.260 0.64848 �1.244 0.655 �1.282 0.63860 �1.353 0.605 �1.293 0.63372 �1.426 0.569 �1.298 0.63184 �1.420 0.572 �1.287 0.63696 �1.410 0.577 �1.258 0.649108 �1.535 0.514 �1.216 0.668120 �1.673 0.443 �1.167 0.689


26 L

37

26gUS

1;1 gUS1;2 gUS1;3 gC1;1 gC1;2 gC

1;3

37

Bt ¼

666666666664

US

SUSCUSLCANSCANCCAN

777777777775; G ¼

666666666664

gUS2;1 gUS2;2 gUS2;3 gC

2;1 gC2;2 gC2;3


3;1 gC3;2 gC3;3


4;1 gC4;2 gC4;3


5;1 gC5;2 gC5;3


6;1 gC6;2 gC6;3

777777777775where Bt is the 6 � 1 vector estimated factors from the U.S. and Canada; G is a 6 � 6 matrix of factorloading coefficients; and E(ete0t) ¼ U allowing for correlation of errors across equations.

5. Results

5.1. Structural breaks and sub-samples

The historical events pertaining to Canadian monetary policy reform provide a basis for investi-gating the existence of a structural break in bond yield determination. To determine whethera structural break exists in the Canadian slope factor loading, the Andrews (1993) test is employed. TheAndrews test allows for any criterion test statistic. We construct a Wald statistic based on the nullhypothesis that coefficients in the Canadian slope equation are equal before and after the structuralbreak. While historical events suggest a range of possible break dates, the exact date is not knownwithcertainty. In fact, there exists the possibility that no break occurred, hence we let the data speak foritself. Table 4 presents test statistics of the Andrews test with the break point search range betweenJanuary 1990 and December 1993. The maximized test statistic value of 18.565 corresponding to theperiod January 1993 allows for rejection of the null hypothesis of no structural change at the 5% level.3

We attribute the change in the relationship between term structures between the United States andCanada to a fundamental change in the conduct of monetary policy, specifically the treatment ofinflation. The timing is consistent with the expectation that the structural break coincide with thechange in monetary policy in Canada during the period 1989–1993, but is likely to occur at the latterpart of this period at the completion of all monetary reforms. Similar tests of a structural break in theCanadian level equation produce an estimated break date of April 1997, although the maximized teststatistic of 11.433 is not significant.

The transition into the 1990s marked the independence of the conduct of monetary policy.Specifically, Bank of Canada Governor John Chow’s announcement of price stability as the Bank’sprimary objective in 1988 established credibility. Nevertheless, the most significant change was theundertaking of explicit inflation targets in the February of 1991, as a response to inflationary pressuresobserved in the late 1980s. The identification of structural change in the determination of the short ratein our model coincides with timing of these measures. Inflation targets included reducing 12 monthconsumer price inflation to 3% by 1992 and to 2% by 1995. The Bank of Canada implemented theseinflation targets by setting the short term interest rate. Bond yields had a lagged response to this policytool. Consistent with Clinton (1998) and Bhuiyan and Lucas (2007), a structural break should exist inthe determination of Canadian short run rates. Such a change, which we estimate resulted roughlya third of the way into our sample represented a significant change from the monetary policy adoptedin the 1980s. Adoption and implementation of these targets resulted in immediate effects in the realeconomy, specifically a deep contraction of the Canadian economy shown by falling economic growthand increasing unemployment through 1999 as outlined in Curtis (2005). Nevertheless, the new policyachieved the desired effects with regard to inflation, which are well documented in Longworth (2002).Most importantly, the level and variance of inflation both decline when compared to measures in theprevious two decades, robust across a variety of inflation measures.

3 Extending the search range to January 2000 yields the same break date.

Table 4Wald statistics from the Andrews–Zivot test for structural change in the Canadian slope equation between January 1990 andDecember 1993.

Date Wald stat Date Wald stat

Jan-90 6.594 Jan-92 5.392Feb-90 7.032 Feb-92 6.097Mar-90 6.078 Mar-92 5.864Apr-90 6.820 Apr-92 6.128May-90 7.497 May-92 6.630Jun-90 5.509 Jun-92 6.525Jul-90 5.525 Jul-92 7.202Aug-90 5.128 Aug-92 7.356Sep-90 4.411 Sep-92 7.304Oct-90 6.820 Oct-92 16.000Nov-90 7.069 Nov-92 14.816Dec-90 7.352 Dec-92 12.235Jan-91 7.397 Jan-93 18.565Feb-91 5.097 Feb-93 15.708Mar-91 4.772 Mar-93 18.317Apr-91 4.783 Apr-93 13.004May-91 5.229 May-93 12.815Jun-91 5.085 Jun-93 12.613Jul-91 4.698 Jul-93 12.270Aug-91 4.611 Aug-93 12.144Sep-91 4.521 Sep-93 13.446Oct-91 4.916 Oct-93 14.035Nov-91 4.937 Nov-93 14.366Dec-91 4.952 Dec-93 12.877


Canada also looked to foster smooth adjustments in short term interest rates. The goal was toprevent uncertainty about future monetary policy. Bolder et al. (2004) deems the Canadian bondmarket a less risky place during the mid-to-late 1990s as the level of volatility in the various Canadianyield curve measures fall significantly during this time. In fact, in 1991 we observe a dramatic increasein the volume of open market operations conducted by the Bank of Canada. Racette and Raynauld(1994) analyzes the Canadian monetary policy during 1989–1993 and find monetary policy inCanada primarily emphasized severe reductions in inflation in the early 1990s.

Canada’s policy was in sharp contrast to U.S. monetary policy at the time, which emphasizeda balanced approach to controlling inflation, real output growth and unemployment, resulting ina boom in the U.S. economy during the same period.While the United States was able to achieve similardecreases in inflation level and uncertainty during the decade of the 1990s relative to the previous twodecades, the effect was achieved without the explicit targets employed by Canada. Mankiw (2001)attributes the results to fortunate economic circumstances and maintaining a “covert” inflationtarget of about 3%. The anecdotal evidence suggests a structural break in policy occurred sometimeduring this four year period and is most likely to be evidenced in the dynamics of short rates.

5.2. VAR estimation results

Consider the estimation of model (2) using three samples. First, we estimate the joint U.S.-CanadaVAR model using the entire sample. We proceed by dividing observations into two distinct sub-samples representing pre and post monetary policy shift. Because the relationship between theshort term and long term aspects of the term structure are of interest, and the fact the curvaturecomponent of the Nelson-Siegel model is not well identified, interpretation of results focuses on theslope and level components. Distinguishing effects between two distinct periods of Canadianmonetarypolicy plausibly support the observation that the correlation between U.S. and Canadian short termbond yields once existed, but cease after our estimated structural change date. Differing effectsresulting from dichotomizing the full sample exist only for the Canadian short rate. In each of the threesamples, all estimated coefficients in the Canadian level equation are insignificant. We also find the U.S.slope factor is a major determinant of the U.S. term structure throughout the sample.


The top panel of Table 5 presents coefficient estimates from the full sample from February 1986 toDecember 2003. The most important results involve the effects of the U.S. level and slope factors. Bothterms are strongly significant in the equations for short term factors in both countries with the effectmore pronounced in Canada. For example, the coefficient for lagged change in the U.S. slope factor is0.761 in the Canadian slope equation and 0.368 in the U.S. slope equation. The result in itself is notable,albeit perhaps unsurprising when evaluating the behavior of short term rates in Canada, suggestinga larger influence from U.S. than Canadian monetary policy. The remaining two significant coefficientestimates involve the lagged U.S. slope factor in the U.S. level equation and the lagged U.S. level factor inthe U.S. curvature equation with both marginally significant at the 5% level.

Accounting forastructuralbreak in termstructuredynamicsyields fardifferent results. Thesecondpanelof Table 5 summarizes results for the unrestricted VAR(1) model using the first sub-sample from January1986 to January 1993. The primary observation from the first sub-sample is the significant effect of termstructure components from both countries on the Canadian slope component. In the Canadian slope

Table 5Joint VAR estimates for Nelson-Siegel factors by sample. Significance at the 10%, 5% and 1% levels are indicated by one, two andthree asterisks, respectively.

LUS,t–1 SUS,t–1 CUS,t–1 LCAN,t–1 SCAN,t–1 CCAN,t–1 R2 F-Stat

Full sampleLUS,t �0.242* �0.171** 0.030 0.075 �0.049 �0.012 0.053 2.322

(0.125) (0.080) (0.029) (0.093) (0.041) (0.021)SUS,t 0.453*** 0.368*** 0.006 �0.002 0.095* 0.014 0.115 5.387

(0.151) (0.097) (0.035) (0.113) (0.050) (0.025)CUS,t 0.723** 0.291 �0.018 �0.125 �0.022 0.062 0.047 2.031

(0.349) (0.224) (0.080) (0.260) (0.260) (0.059)

LCAN,t 0.042 �0.081 0.034 �0.167 0.011 �0.004 0.022 0.947(0.148) (0.095) (0.034) (0.110) (0.049) (0.025)

SCAN,t 1.186*** 0.761*** 0.011 �0.309* �0.113 �0.015 0.162 8.071(0.223) (0.143) (0.051) (0.166) (0.073) (0.037)

CCAN,t �0.356 �0.174 0.082 0.398 �0.221 �0.014 0.028 1.203(0.534) (0.343) (0.122) (0.398) (0.175) (0.090)

First sub-sample: January 1986–January 1993LUS,t �0.301 �0.271** 0.015 0.091 �0.027 0.002 0.077 1.288

(0.188) (0.121) (0.046) (0.139) (0.057) (0.029)SUS,t 0.304 0.340*** 0.002 0.060 0.053 �0.003 0.118 2.062

(0.197) (0.127) (0.048) (0.146) (0.059) (0.031)CUS,t 0.520 0.116 0.046 �0.159 0.133 0.143* 0.114 1.978

(0.497) (0.321) (0.121) (0.368) (0.150) (0.077)

LCAN,t 0.114 �0.171 0.028 �0.178 0.004 0.018 0.061 0.999(0.246) (0.159) (0.060) (0.182) (0.074) (0.038)

SCAN,t 1.441*** 0.946*** �0.048 �0.583** �0.258** �0.024 0.299 6.561(0.344) (0.222) (0.084) (0.255) (0.104) (0.054)

CCAN,t �0.993 �0.647 0.113 0.395 �0.194 �0.059 0.038 0.609(0.922) (0.595) (0.225) (0.683) (0.278) (0.143)

Second sub-sample: February 1993–December 2003LUS,t �0.113 �0.040 0.058 0.053 �0.083 �0.038 0.056 1.470

(0.183) (0.121) (0.039) (0.141) (0.066) (0.032)SUS,t 0.542** 0.396** �0.007 0.026 0.140 0.044 0.128 3.682

(0.239) (0.158) (0.051) (0.184) (0.086) (0.042)CUS,t 1.370*** 0.723** 0.021 �0.323 �0.253 �0.076 0.073 1.973

(0.514) (0.341) (0.109) (0.396) (0.186) (0.090)

LCAN,t �0.027 �0.049 0.056 �0.149 0.035 �0.038 0.036 0.920(0.195) (0.129) (0.042) (0.150) (0.070) (0.034)

SCAN,t 0.795*** 0.596*** 0.027 0.264 0.185* 0.017 0.140 4.081(0.302) (0.200) (0.064) (0.232) (0.109) (0.053)

CCAN,t 0.579 0.572 0.080 0.610 �0.276 0.032 0.072 1.940(0.677) (0.449) (0.144) (0.521) (0.244) (0.118)


equation, the estimated coefficient for the Canadian level factor is �0.583 and the coefficient for theCanadian slope factor is �0.258. The full sample fails to capture the significant effects of lagged Canadianlevel and laggedCanadianslope inthefirst sub-sample. Inaddition, coefficients forU.S. level andslope in theCanadian slope equation remain significant, andhave a larger effect relative to the full sample. TheU.S. levelcoefficient is 1.441 compared to 1.186 for the full sample and the U.S. slope coefficient is 0.946 compared to0.761 for the full sample. The implication is U.S. determinantsmore strongly influence Canadian short ratesbefore monetary policy reforms. Public uncertainty of Canadian monetary policy goals is likely anothercontributing factor of the U.S. effect. The importance of the U.S. slope component also extends to the U.S.termstructure. TheU.S. slopecomponentdrives the termstructure as laggedchanges inU.S. slopepositivelyaffect changes in U.S. slope with a coefficient estimate of 0.340 and negatively affects changes in U.S. levelwith a coefficient estimate of �0.271. In contrast, Canadian factors have little effect on U.S. rates.

The bottom panel of Table 5 presents results of the unrestricted VAR(1) model for the secondsample period January 1993 to December 2003. The results further emphasize the changing dynamicsof the Canadian short rate after monetary reform. First, observe changes in U.S. term structure coef-ficients in the Canadian slope equation. Specifically, the decrease in the magnitude from 1.441 to 0.795in the level component and 0.946 to 0.596 in the slope component between sub-samples show anattenuation of U.S. monetary policy on the Canadian short rate. Second, the significance of the laggedU.S. slope factor continues to strongly affect contemporaneous U.S. slope. The estimate of 0.542 for g2,1

US

suggests an increasing importance of the level factor in determining U.S. short rates after 1993.Canadian factors generally have a small effect on the term structure in both countries, regardless of

the sample period. Specifically, U.S. factors remain unaffected by lagged Canadian factors throughoutthe sample. The notable exception is the negative effect on the Canadian short rate exhibited in the firstsub-sample. After the estimated break date, this negative effect ceases. The shift in signs for g5, 1C andg5,2C coefficient estimates suggests new Canadian policies for determining short rate. Coefficient esti-

mates in the Canadian slope equation are not significant at the 5% level; however gC5;2 is significant atthe 10% level. Finally, separating the data set into two samples introduces significance in determinantsof the medium-term factor for the U.S. However, shifts in significance before and after the break datefail to follow any meaningful pattern.

Variance decompositions provide additional evidence of the diminishing connection in yield curvesafter the implementation of Canadian inflation targets. Fig. 2 displays decompositions for the first dif-ferenced Canadian slope factor before and after the regime shift. The Cholesky ordering assumes theslope factor, dictated by monetary policy, is the most exogenous. We also assume the level factor,determined bymarket forces, is themost endogenous. The percentage of forecast variance inDSCAN, t dueto the U.S. level and slope decreases after the structural break at all horizons, particularly in the former.Conversely, the percentage of variance due to changes in Canadian yield curve components increasesafter January 1993. However, variance decompositions in Fig. 2 are not robust to the Cholesky ordering.

Table 6 summarizes results of F-tests for hypotheses of joint significance in U.S. and Canadian VARcoefficients, respectively, in the Canadian slope equation. This test identifies collective country effectson the Canadian short rate. Test statistics with and without the curvature factor are included. Theresults coincidewith VAR results. Before the estimated break date, both the U.S. and Canadian effect aresignificant at the 1% level. After the structural break, the U.S. effect remains significant, however, theeffect weakens. For example, the F-statistic including U.S. level and slope is now only significant at the5% level. Furthermore, the Canadian effect is no longer significant.

5.3. Macro factors

To investigate the implications of structural change in the determination of the yield curve, we addfirst differenced macroeconomic variables to the vector DBt in expression (2), analogous to Dieboldet al. (2006). We include the Canada/U.S. exchange rate and for both countries, the unemploymentrate, the overnight rate and the deviation of price inflation from the target 2% level.4 Annual price

4 U.S. macro data obtained from the Federal Reserve Bank of Saint Louis. Canadian macro data obtained from StatisticsCanada.

Fig. 2. Variance decomposition for the Canadian slope factor.


inflation is measured as the twelve month percentage change in the Consumer Price Index. While thecorrelation in yield curve components degrades after the early part of 1993, variables related to themacroeconomy remain linked. Figs. 3 and 4 show the connected relationship for unemployment andinflation. Between 1992 and 1993, Canada experienced a discrete drop in the inflation rate from levelsabove 5% to the targeted 2% level. After the 1993 break date, inflation in the United States also exhibiteda downward trend toward the 2% level, although the change was gradual.

Table 6Results for joint F-test that coefficients in the slope equation are equal before and after the estimated break. Significance at the10%, 5% and 1% levels are indicated by one, two and three asterisks, respectively.

Full sample 1986–1993 1993–2003

U.S. 12.349*** 8.605*** 3.290**(0.000) (0.000) (0.023)

Canada 1.769 4.187*** 1.058(0.154) (0.008) (0.370)

U.S without curvature 17.757*** 11.873*** 4.746***(0.000) (0.000) (0.010)

Canada without curvature 2.4281* 5.797*** 1.541(0.091) (0.005) (0.218)

2

4

6

8

10

12

14

1986 1988 1990 1992 1994 1996 1998 2000 2002

Unemployment (Canada)Unemployment (U.S.)

Year

Une

mp.

Rat

e

Fig. 3. Unemployment rates for Canada and the United States.


Results for the Canadian level and slope factors from the VAR analysis with the inclusion of macrovariables are in Table 7. The unemployment rate, along with the slope and level factors in the U.S. arestrong determinants of the Canadian slope factor before the break. The effect of each of thesecomponents dissipates, particularly with regard to unemployment. The coefficient estimate is �1.249,significant at the 5% level before the break and not significant after the break. The lagged change in U.S.inflation was also a strong predictor of the Canadian level factor prior to 1993, but dissipates after thebreak.

The preceding VAR analysis includes macro variables lagged one period. However, monetary policymay reflect lagged data beyond one month. To examine this possibility, we compute correlationsbetween the Canadian slope factor and macro variables lagged one, six, nine and twelve months,respectively. Before the estimated structural break, the Canada short rate exhibits a strong negativecorrelation with lagged unemployment in both countries. This relationship dissipates after January1993. For example, the correlation between the Canadian slope factor and twelve month laggedunemployment in Canada was �0.805 before the break and �0.182 after. The Canadian slope factor isalso positively correlated with lagged inflation deviations from 2% after the estimated break date.Consistent with the goal to fight inflation, large deviations from the target level are associated with

-1

0

1

2

3

4

5

6

7

1986 1988 1990 1992 1994 1996 1998 2000 2002

Inflation (Canada)Inflation (U.S.)

Year

Infl.

Rat

e

Fig. 4. Annual inflation rates for Canada and the United States.


increases in the Canadian short rate. Finally, while the correlation between the Canadian slope and U.S.yield curve components diminishes, the correlation with U.S. macro factors, particularly inflation,remains present as macro components in both countries are themselves correlated.

The exchange rate is also a channel throughwhich the Bank of Canada conducts its monetary policy.Under uncovered interest parity, increases in the interest rate are associated with an appreciation ofa country’s currency as the return on investment increases. However, exchange rate movementsdepend on short rate changes in Canada relative to corresponding changes in the United States. Theoryalso predicts the inflation rate in Canada relative to the United States affects the exchange rate. Prior tothe estimated structural break, the correlation between the Canada/U.S. exchange rate and the slopefactor spread is negative. In other words, increases in the Canada short rate, relative to the U.S. shortrate are associated with the appreciation of the Canadian dollar. However, this correlation is positiveand smaller in magnitude after the 1993 structural break. Instead, the inflation spread becomes a moreimportant determinant of the exchange rate. After the implementation inflation targets, increases inthe inflation rate in Canada relative to the United States are more strongly associated with a depreci-ation of the Canadian dollar.

5.4. Cointegration of bond yields

As an additional test of the connection of term structures between the Canada and the United States,we perform cointegration tests across countries for each smonth bond yield. Evidence of cointegrationwould provide additional evidence of an equilibrium relationship between term structures. Following

Table 7Joint VAR estimates for the Canadian level and slope factors with the inclusion of macro variables in the United States andCanada. Significance at the 10%, 5% and 1% levels are indicated by one, two and three asterisks, respectively.

Full sample First sub-sample Second sub-sample

LCAN,t SCAN,t LCAN,t SCAN,t LCAN,t SCAN,t

U.S variablesLUS,t–1 0.022 1.079*** �0.043 1.255*** �0.073 0.705**

(0.164) (0.247) (0.278) (0.369) (0.215) (0.334)SUS,t–1 �0.162 0.543*** �0.196 0.616** �0.105 0.492*

(0.121) (0.182) (0.204) (0.271) (0.167) (0.259)CUS,t–1 0.032 �0.010 0.006 �0.065 0.050 0.025

(0.035) (0.053) (0.061) (0.082) (0.045) (0.069)Umemp. Rate �0.131 �0.584** �0.108 �1.249** 0.181 �0.114

(0.195) (0.293) (0.369) (0.492) (0.234) (0.363)Overnight Rate 0.050 0.048 �0.022 0.003 0.114 0.151

(0.131) (0.197) (0.194) (0.258) (0.200) (0.311)Inflation �0.147 0.026 �0.246* 0.062 0.009 0.094

(0.096) (0.144) (0.147) (0.196) (0.146) (0.227)

Canada variablesLCAN,t–1 �0.213* �0.437** �0.112 �0.718*** �0.157 0.171

(0.115) (0.172) (0.191) (0.254) (0.160) (0.249)SCAN,t–1 0.001 �0.228*** �0.008 �0.381*** 0.005 0.104

(0.053) (0.079) (0.079) (0.105) (0.084) (0.130)CCAN,t–1 �0.007 �0.013 0.027 �0.009 �0.032 0.003

(0.026) (0.039) (0.040) (0.054) (0.037) (0.057)Unemp. rate �0.083 �0.076 �0.346 0.407 0.013 �0.274

(0.128) (0.191) (0.241) (0.321) (0.152) (0.237)Overnight rate 0.034 0.224*** 0.010 0.285*** 0.115 0.085

(0.052) (0.078) (0.074) (0.099) (0.094) (0.146)Inflation 0.120* 0.009 0.133 0.051 0.042 �0.008

(0.062) (0.094) (0.110) (0.147) (0.084) (0.130)

Exchange rate �0.006 2.554 0.368 4.465 �0.985 0.976(1.684) (2.526) (3.823) (5.087) (1.524) (2.365)

R-squared 0.062 0.221 0.149 0.429 0.067 0.162F-statistic 1.058 4.541 1.024 4.375 0.701 1.897

Table 8Residual based cointegration test between U.S. and Canada yields. The augmented Engle Granger (AEG) test statistics arecalculated using test regressions that include a constant. Regression 1 tests for cointegrating taking U.S. yields as the dependentvariable in the estimating equation. Similarly, regression 2 takes Canada yields as the dependent variable. Significance at the 10%,5% and 1% levels are indicated by one, two and three asterisks, respectively.

Maturity Regression 1 Regression 2

Full sample 1986–1993 1993–2003 Full sample 1986–1993 1993–2003

3 �1.797 �2.150 �2.060 �1.069 �1.665 �1.2046 �1.621 �1.915 �2.072 �0.988 �1.454 �1.8679 �1.63 �1.917 �2.630* �1.144 �1.458 �2.02712 �1.651 �1.952 �2.669* �1.230 �1.505 �2.11515 �1.777 �2.133 �2.630* �1.686 �1.658 �2.08118 �1.859 �2.248 �2.675* �1.806 �1.762 �2.09621 �1.919 �2.335 �2.631* �1.888 �1.819 �2.12624 �2.208 �3.128** �2.607* �1.927 �1.852 �2.14130 �2.354 �3.249** �2.517 �2.134 �1.988 �2.07336 �2.432 �3.310** �2.399 �2.263 �2.023 �1.97848 �2.663* �3.409** �2.128 �2.599* �3.079** �1.79260 �2.739* �3.360** �1.962 �2.754* �3.085** �1.75472 �2.863* �3.436** �1.74 �2.931** �3.240** �1.65584 �2.842* �3.112** �1.715 �2.911** �2.825* �1.72496 �2.942** �3.127** �1.719 �3.016** �2.847* �1.805108 �3.076** �3.122** �1.772 �3.229** �1.947 �1.889120 �3.340** �3.172** �2.001 �3.569*** �3.201** �2.161


a two-step procedure described by Engle and Granger (1987) and outlined by Boothe (1991), we test fora cointegrating relationship between the Canadian and U.S. yields at the different maturities. The firststep is to run two de-meaned cointegrating regressions: 1) regress the Canadian yields on a constantand the U.S. yields for eachmaturity and 2) regress the U.S. yields on a constant and the Canadian yieldsfor each maturity. The second step is to perform a unit root test on the residuals of these OLSregressions, where the null hypothesis states the residuals are distributed I(1). Columns 2 and 5 ofTable 8 report results for the cointegration of yields between countries during the full sample period.Observe the Augmented Engle-Granger (AEG) test statistics from the full sample approach the Phillips-Ouliaris (PO) critical value as the length of maturity increases.5 Therefore, there is stronger statisticalevidence of cointegration between the two countries as the maturity period lengthens. Specifically,significant evidence of cointegration begins to emerge starting at bond maturities of 48 months inlength. Furthermore, evidence of cointegration is robust across the two cointegrating specifications.

Table 8 also reports results for the two sub-samples that are before and after our estimated breakdate of January 1993. In regards to the sub-sample results, there is strong evidence of cointegrationbetween Canadian and U.S. yields of varyingmaturity before the structural break and weak evidence ofcointegration after the structural break in shorter term maturities. This implies the Canadian and U.S.yields are strongly correlated before the structural break, but no longer share a long term trend afterthe fact. The change in the cointegrating relationship between countries is not captured by our analysisof Nelson-Siegel factors, and suggests a fundamental change occurs even in long term yields.

Fig. 1 also demonstrates the divergence of yields in the mid 1990s. Graphs of the Canadian and U.S.yields appear to follow a similar trend until after the early 1990s. This further strengthens the theory ofa structural break in Canadian monetary policy. After Canada changed its approach to monetary policyand the structure of financial markets, the correlation between U.S. and Canadian yields appears todiminish.6

5 Augmented Dickey Fuller unit root tests applied to estimated cointegrating residuals do not follow the usual Dickey–Fullerdistribution under the null hypothesis. Instead Phillips and Ouliaris (1990) find the unit root tests follow asymptotic distri-butions which are functions of Wiener processes. The Phillips-Ouliaris critical values are reported in Phillips and Ouliaris(1990).

6 As a robustness check we also ran a Cointegrating Regression Durbin Watson (CRDW) test as outlined by Engle and Granger(1987). The results of this test also find increasing evidence of cointegration as the maturity period lengthens and evidence ofcointegration in the first sub-sample, but none in the second sub-sample.

Table 9Results for residual based cointegration tests with an unknown break. Reported are AEG statistics of the null hypothesis of nostructural change in the intercept and slope coefficients of the cointegrating equation. Significance at the 10%, 5% and 1% levelsare indicated by one, two and three asterisks, respectively.

Month Min AEG Break date AEG before AEG after

3 month �1.307 Mar-95 – –

6 month �1.472 May-95 – –

9 month �1.497 Jul-95 – –

12 month �1.710 Aug-95 – –

15 month �1.909 Nov-95 – –

18 month �2.245 Nov-95 – –

21 month �2.521 May-96 – –

24 month �2.803 May-96 – –

30 month �3.854 May-96 – –

36 month �4.885* May-95 �3.599*** �1.95848 month �6.965*** Jun-96 �5.418*** �2.915*60 month �8.766*** Aug-96 �5.509*** �4.366***72 month �9.337*** Aug-96 �6.604*** �3.785***84 month �7.964*** Jul-96 �6.568*** �3.812***96 month �7.269*** Jul-96 �5.721*** �3.033*108 month �6.540*** Aug-96 �5.494*** �2.485120 month �7.070*** Aug-96 �6.017*** �3.301**


Table 9 presents results of tests for the null hypothesis of no cointegration against the alternative ofa shift in both the constant and slope terms in the cointegrating equation assuming an unknownstructural break date. Specifically, we estimate

yUS;t ¼ a1 þ a2ftr þ b1yCAN;t þ b2yCAN;tftr þ et (3)

where fts is an indicator variable for an observation after the proposed break date. Tests of changes inthe cointegrating relationship associated with Equation (3) are performed for each maturity. Column 2presents the minimum AEG test statistics7 for the search range of January 1990 to January 2000. Acrossthe yield curve, there exists evidence of structural change in the cointegrating relationship for longterm yields with an estimated break date in the middle of 1996. These results coincide with theestimated break in long term yields in Section 5.1. Standard tests of cointegration before and after theestimated break are presented in Columns 4 and 5. For each maturity where there exists structuralchange in the cointegrating relationship, there also exists strong evidence of cointegration in the pre-break sample. In comparison, evidence of cointegration is weaker in the post-break sample, specificallyestimated AEG statistics are all smaller in absolute value.

Although the estimated VAR model fails to identify evidence of a structural change in long runNelson-Siegel factors, there nevertheless exists historical evidence to support the structural changeidentified in the cointegration analysis. With inflation exhibiting a lower persistence, and the Bank ofCanada establishing credibility to fighting inflationwhile maintaining established targets, the level anduncertainty of long term inflation expectations also drastically decrease during the second half of the1990s. The resulting decline in Canadian long rates and U.S.-Canada spreads are a direct consequence ofthis long run inflation control. This is in contrast to the United States, whereWatson (1999) documentsthe variance in changes of U.S. long term rates has risen during the second half of the 1990s.

6. Conclusion

This paper shows there is a correlated relationship between U.S. and Canadian term structures. Dueto increased risk perceptions, historically high inflation and weak confidence in the Canadian dollar,the Canadian yields for all maturities lie above those in the U.S. until a shift in monetary policy causeda structural break in the Canadian yields. Specifically, we attribute the changing relationship in term

7 Critical values for tests of changes in cointegrating relationships are from Gregory and Hansen (1996).


structures to the imposition of explicit inflation targets by Canada during the early 1990s, and thecredibility of the Bank of Canada to control inflation as a central policy goal. The result of this structuralbreak was a termination in the correlated relationship between the term structures in the twocountries.

The changing relationship between the U.S. and Canadian term structure is displayed through ourempirical results. The VAR estimation shows U.S. determinants strongly influence Canadian short ratesbefore the structural break. Specifically the Canadian short term rate is largely determined by the U.S.level and slope factors prior to this break. After the structural break the correlation between U.S. andCanadian bond yields breaks down as new Canadian monetary policy takes effect. In addition, tests forcointegration between the yields of the two countries display strong evidence of cointegration inmedium and long run rates before the structural break and no evidence of cointegration after thestructural break. The general conclusion of the cointegration tests imply the long–run equilibriumrelationship between U.S. and Canadian bond yields degrades after the shift in Canadian monetarypolicy.

According to the above results changes inmonetary policy can have strong effects on the integrationof neighboring countries. Canada, a country historically influenced by the U.S. economy, asserts itsindependence in the bondmarket by changingmonetary policy to place a hard target on inflation rates.Further analyses of shifts in the determinants of the term structure over other time periods couldpotentially shed light on the successes or failures in meeting policy goals in both countries. In addition,it would be interesting to see if the degeneration of a correlated term structure in response to changingmonetary policy exists for other integrated countries.

Acknowledgments

The authors thank the two anonymous referees for their valuable suggestions and acknowledgesupport from the Cecil and Jane Castor Professorship.

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the changing relation between the canadian and u.s. yield curves

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