This paper investigates the (break) stationarity null hypothesis using data for 25 interest rates with different maturities and risk characteristics in Canada and the US. In contrast to a large part of the literature, this paper reports strong empirical evidence in favour of the null hypothesis of stationarity for the interest rate series.

Hyunsok Kim

Mario Cerrato

Ronald MacDonald

English

Research Papers in Economics

Nominal Interest Rates and Stationarity
Mario Cerrato*, Hyunsok Kim*1 and Ronald MacDonald*
University of Glasgow, Department of Economics, Adam Smith building.
May 25, 2010
1Hyunsok Kim University of Glasgow, Department of Economics, Adam Smith building
(E-mail: h.kim.3@research.gla.ac.uk); Mario Cerrato (E-mail: m.cerrato@lbss.gla.ac.uk)
and Ronald MacDonald (E-mail: r.macdonald@lbss.gla.ac.uk). We would like to thank
Karim Abadir for his helpful comments and suggestions.Abstract
This paper investigates the (break) stationarity null hypothesis using data for 25
interest rates with di⁄erent maturities and risk characteristics in Canada and the
US. In contrast to a large part of the literature, this paper reports strong empirical
evidence in favour of the null hypothesis of stationarity for the interest rate series.
11 Introduction
Nominal interest rates of di⁄erent interest rate maturities are often found to be non-
stationary, (Campbell and Clarida (1987); Newbold et al. (2001)), a result which
has important implications for investment decisions and asset pricing models. For
example, Gaussian interest rates models are very popular amongst practitioners and
they hypothesise that interest rates are mean reverting, which seems at odds with
the empirical evidence. However, most of the empirical papers that report non-
stationary interest rates use standard linear econometric methods1. Such methods
are questionable since these studies, generally, use very long time series in which
structural breaks may have occured. In this paper we use a battery of recently de-
veloped unit root tests for (multiple) structural breaks and a new dataset consisting
of twenty-￿ve short-long nominal interest rates for the US and Canada. We show
signi￿cant empirical evidence that interest rates (of di⁄erent maturities) are indeed
stationary around a structural break. Our ￿nding of stationary nominal interest
rates has important implications for testing, for example, the Fisher e⁄ect and term
structure relationships, since it invalidates the use of cointegration methods, the
approach generally used in this context, to test such relationships
2 Econometric Methodology
The transition functions St(￿) (with ￿ being a set of parameters to be estimated)
considered in previous structural break models are given in Table (1)where ￿ = 1 is
consistent with the logistic function2.
The structural change with logistic smooth transition (hereafter LSTR) is the one
considered in Leybourne et al. (1998), where the time of the transition is determined
by c, while its speed is determined by the parameter ￿.
Since the logistic function-based models are unable to capture more than one
1Newbold et al (2001) being one of the few exceptions.
2Refer to Cerrato et al. (2010) for a complete description of these transition functions and tests.
2Model Transition Function: St(￿) Parameter: ￿
LSTR [1 + expf￿￿ (t ￿ cT)g]
￿1 ￿;c
ESTR 1￿exp
￿
￿￿2 (t ￿ cT)
2￿
￿;c
Asym ESTR 1￿exp
￿
￿It￿2
1 (t ￿ cT)
2 ￿ (1 ￿ It)￿2
2 (t ￿ cT)
2￿
￿1;￿2;c
Sym K-STR
￿
1 + exp
￿
￿￿2 (t ￿ c1T)
2￿￿￿
1 ￿ exp
￿
￿￿2 (t ￿ c2T)
2￿￿
￿1 ￿;c1;c2
Asym K-STR
￿
1 + exp
￿
￿￿2
1 (t ￿ c1T)
2￿￿￿
1 ￿ exp
￿
￿￿2
2 (t ￿ c2T)
2￿￿
￿1 ￿1;￿2;c1;c2
Table 1: Functions for Structural Change
break, Sollis (2005) extends the model by considering an exponential smooth tran-
sition (hereafter ESTR) and asymmetric exponential smooth transition (hereafter
Asymmetric ESTR). This is asymmetric around the time of the transition cT. The
value of St(￿) depends on the value of the parameter ￿ and when t = cT, transition
function S(yt￿d;￿) takes converges to zero. Cerrato et al (2010) propose an alterna-
tive transition function which they call K-STR. This transition function is able to
capture structural changes taking place around long-run equilibrium path.
The transition functions are compared in Figure (1). The LSTR function only
considers a single break whereas the ESTR function considers multiple breaks. The
asymmetric ESTR suggested by Sollis (2005) has similar properties as the ESTR
but it allows asymmetric scale parameters, ￿1 and ￿2 where It = 1 if (t ￿ cT) ￿ 0
and 0 otherwise. The transition function St(￿) is also bounded from 0 to 1 when
the ￿1and ￿2 are su¢ ciently large values and if ￿1 6= ￿2 the speed of transition is
asymmetric either side of the mid-point cT:
-0.5 0.0 0.5
0.5
1.0
LSTR
-0.5 0.0 0.5
0.5
1.0
ESTR
Figure 1: Simulation for the LSTR and ESTR
33 Empirical Results
The dataset used in this study is unique, consisting of 25 monthly Canadian and US
interest rates of di⁄erent maturity and risk spanning the period 1985:01 to 2004:04.
For the Canadian rates, it consists of T-bill rates of di⁄erent maturities, government
bonds and Scotia indices for yields on corporate bonds. The US rates consist of
T-bills with di⁄erent maturities, government bond yields, commercial paper and
yields on corporate AAA and BAA rated bonds. The data are taken from Moon
and Perron (2007). Since the 1980s, the perception of the output-in￿ ation trade-
o⁄ changed. For example, the Federal reserve with Alan Greenspan at the helm,
devoted more attention to keeping a low in￿ ation level than in the past since such
a policy, combined with the larger predictability of monetary policy, contributed to
making the economic environment more stable. Indeed, large parts of the literature
claim that monetary policy in the US had not experienced any sort of permanent
structural break since the late 1970s3. Is this, however, borne out by the evidence?
We apply the econometric methodologies presented above. Furthermore, we also
use the K-STR test suggested in Cerrato et al. (2010). The empirical results are
reported in the table below. There is a very strong evidence of stationarity when
the ESTR is used. The test shows that both short and long term interest rates
in Canada are stationary. Furthermore, signi￿cant evidence of stationarity is also
detected in the case of short and long term interest rates in the US. The US short
term interest rates is stationary regardless of the econometric methodology used.
This result is consistent with Newbold et al. (2001) which ￿nds short-term interest
rates in the US during the period 1890-1934 as stationary.
The table below shows the break dates for the interest rate series which were
found stationary using the Sollis test4. In some cases the break date was estimated
3That is policy rue has not changed much since the post WWII experience (see Bernanke and
Mihov, 1998 amongst the others). Furthermore, the Canadian policy of shift towards zero in￿ ation
in Februart 1988 may have also caused structural breaks.
4We have selected the Sollis test since it is the test which shows more evidence of stationarity.
4Monthly (1985 - 2004)
LSTR ESTR Sym K-STR Asym K-STR
Country k tLSTR k tESTR k tA
S k tA
AS
Canadian rates
1 month 11 -3.5969 12 -4.2597￿￿ 12 -1.4024 9 -2.5257
3 month 11 -3.5535 12 -3.7338 9 -2.1828 9 -2.4727
6 month 10 -3.5755 2 -3.6740 11 -1.0917 10 -3.1454
1 year 10 -3.4225 2 -4.1913￿￿ 10 -2.2062 10 -3.0509
2 years 2 -3.4747 2 -4.7004￿￿ 1 -1.1062 2 -3.1862
3 years 1 -3.6427 2 -4.6089￿￿ 1 -1.3187 1 -3.3684
5 years 1 -3.5240 3 -4.6285￿￿ 3 -2.0708 3 -2.9268
7 years 0 -3.6022 0 -4.7385￿￿ 12 -1.8826 0 -2.7829
10 years 12 -3.8180 1 -4.8208￿￿￿ 12 -2.0279 0 -2.3533
1-m com.paper 11 -3.7381 12 -3.9020￿ 9 -2.1829 11 -2.8551
3-m com.paper 11 -3.6322 11 -4.8361￿￿￿ 9 -2.2129 9 -2.8768
1-m bank.acc. 11 -3.7054 11 -5.0982￿￿￿ 9 -2.1644 9 -2.6649
Long corporate 12 -3.5923 0 -3.8644￿ 12 -1.7123 12 -0.9741
Mid corporate 1 -3.3048 0 -4.0469￿ 9 -1.5129 1 -0.8860
US rates
3 month 11 -4.3153￿￿ 11 -4.3153￿￿ 11 -4.3115￿￿ 11 -4.2667￿￿
6 month 10 -4.0584￿ 11 -4.0098￿ 10 -3.2293 1 -1.4697
1 year 12 -2.8722 12 -1.9203 12 -2.7608 12 -2.7446
2 years 9 -2.9590 10 -2.4653 9 -3.2371 9 -3.2224
3 years 11 -4.9474￿￿￿ 8 -5.1829￿￿￿ 11 -4.5891￿￿ 11 -4.6484￿￿
5 years 1 -3.1292 9 -3.3262 9 -3.2367 9 -3.2205
7 years 9 -3.6300 9 -3.7416 9 -3.3787 9 -3.3539
10 years 9 -2.8731 12 -2.6786 9 -2.5094 9 -2.4978
1-m com.paper 9 -4.2350￿￿ 12 -4.5695￿￿ 9 -3.7990 9 -3.7666
AAA 9 -3.0351 0 -2.7621 9 -3.0389 9 -3.0338
BAA 9 -4.4186￿￿ 11 -4.2611￿￿ 9 -4.0263￿ 9 -3.9854￿
Table 2: Estimated Results for monthly Canadian and US interest rates
5Monthly (1985 - 2004)
ESTR
Canadian rates US rates
break date break date
1 month 1986.10 3 month 2002.06
1 year 1988.10 6 month
2 years 3 years 1990.02
3 years 1988.04 1-m com.paper
5 years BAA
7 years 1999.06
10 years 1989.07
1-m com.paper 1989.04
3-m com.paper
1-m bank.acc. 1987.04
Long corporate
Mid corporate 1988.12
Table 3: Break date of ESTR estimates
as taking place outside the sample data used, and therefore not computed5. The
Canadian economy was hit hard by the recession of the early 1980s, with interest
rates, unemployment and in￿ ation being higher than in the United States. During
the middle of the 1980s, the economy recoved sharply and Canada￿ s economic growth
was the highest of any OECD country. The break dates for Canada between 1986-
1989 may be driven by this economic event. On the other hand the 2002 break data
for 3-months US T-Bill rates may capture the e⁄ect of the recession which started
in 2001.The recovery was hesitant until the end of the war in Iraq.
4 Conclusion.
In this paper we apply the latest structural break econometrics to identify the pres-
ence of structural breaks in 25 interest rates series of di⁄erent maturity and risk.
We show strong evidence of structural breaks for the majority of time series consid-
ered. We also report the approximate break dates using the exponential transition
function. Our analysis suggests that Canadian interest rates were highly a⁄ected by
5Note that, in this case, the transition function is exponential and not logistic.
6the recession of the early 1980s, while there is clear evidence that short term Trea-
sury rates were a⁄ected by the 2001 recession in the US. The presence of structural
breaks in the short term rates in Canada and the US are new results which have not
yet been reported in the literature, and they suggest that care should be taken when
applying contegration based relationships to various interest parity conditions, such
as term structure conditions and the Fisher e⁄ect.
7References
Bernanke, B. S. and I. Mihov (1998). Measuring monetary policy. The Quarterly
Journal of Economics 113, 869￿ 902.
Campbell, J. Y. and R. H. Clarida (1987). The term structure of euromarket
interest rates. Journal of Monetary Economics 19, 25￿ 44.
Cerrato, M., H. Kim, and R. MacDonald (2010). Equilibrium exchange rate de-
termination and multiple structural changes. University of Glasgow Dept. of
Economics Discussion Papers 2010-14.
Leybourne, S. J., P. Newbold, and D. Vougas (1998). Unit roots and smooth
transitions. Journal of Time Series Analysis 19, 83￿ 97.
Moon, H. R. and B. Perron (2007). An empirical analysis of nonstationarity in
a panel of interest rates with factors. Journal of Applied Econometrics 22,
383￿ 400.
Newbold, P., S. Leybourne, R. Sollis, and M. E. Wohar (2001). US and UK interest
rates 1890-1934 new evidence on structural breaks. Journal of Money Credit
and Banking 33, 235￿ 250.
Sollis, R. (2005). Evidence on purchasing power parity from univeriate models:
The case of smooth transition trend-stationarity. Journal of Applied Econo-
metrics 20, 79￿ 98.
8

Nominal interest rates and stationarity

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