The Global Journal of Finance and Economics, Vol. 10, No. 2, (2013) : 191-204
RATIONALITY OF EURO BOND RATE AND
LIBOR EXPECTATIONS
Fazlul Miah, Abdoul Wane and Baeyong Lee
ABSTRACT
This study investigates the rationality of a previously unexploited consensus survey data on
interest rates for three important interest rates, namely, three month and twelve month LIBOR
rates and ten year Euro bond rates. The forecast horizons are three, six and twelve months.
Data is collected from www.fx4casts.com for the period December, 2001 to September, 2009.
The study uses restricted cointegration test and FMOLS cointegration regression estimation
technique to assess the relationship between the actual and the expected interest rates. It also
performs Engle-Granger cointegration test to compare the results with the earlier two methods.
Consistent with earlier studies, the investigation shows that survey expectations are not rational
for all the rates and for all the horizons and that forecast error increases with the forecast
horizon. Although statistically insignificant, three month ahead expectations of 3 and 12 month
LIBOR rates came close to be rational.The study contributes to the on-going debate on financial
market efficiency. The findings have implication on term premium in financial assets and on the
famous forward discount puzzle in international finance.
Keywords: Rational Expectations Hypothesis, Consensus Survey Data, LIBOR Rates, Euro Bond
Rates, Cointegration.
INTRODUCTION
Forecasting of important economic and financial variables, like exchange rate, interest rate,
GDP growth rate, etc. has drawn considerable interest among professionals and academicians
in the recent past due to its importance in economic modelling and policy analysis. The debate
regarding the rationality of agents’ expectations in general, and the efficiency of financial markets
in particular continues to be an important area in financial economics literature.
Interest rate is an important macroeconomic variable, and economic agents use forecasted
interest rates data to make important financial decisions, for example, financial planners use
horizon analysis to make investment decisions, and horizon analysis depends on the forecast of
*
**
***
Assistant Professor Economics, College of Industrial Management, King Fahd University of Petroleum and
Minerals, Dhahran, Saudi Arabia, E-mail: fmiah@kfump.edu.sa
Associate Professor of Economics, School of Business and Economics, Fayetteville State University,
Fayetteville, NC 27301, E-mail: awane@uncfsu.edu
Associate Professor of Finance, School of Business and Economics, Fayetteville State University, Fayetteville,
NC 27301, E-mail: blee@uncfsu.edu
192
Fazlulu Miah, Abdoul Wane and Baeyong Lee
interest rates. According to European Central Bank (ECB), “Expectations of future official
interest-rate changes affect medium and long-term interest rates. In particular, longer-term interest
rates depend in part on market expectations about the future course of short-term rates.”(http:/
/www.ecb.europa.eu/mopo/intro/transmission/html/index.en.html).Researchers have used
forecasted data on interest rates to understand extent of term premiums in interest rates, which
has implications on the substitutability of financial assets of different maturities and across
different countries. The absence and presence of term premium provide important clues to
monetary authorities in formulating monetary policy. It has also implications on debt management
policy by financial institutions. Besides, interest rate is the primary determinant of the foreign
exchange rate, and thus, interest rate expectations have implication on the famous forward
discount puzzle in the forward exchange market.
There has been very little effort made in literature to investigate the rationality of interest
rate expectations of consensus survey data. Consensus survey data carries unique information
as it is the mean of expectations of experts. There are only a few sources available to obtain
consensus survey data. Previously, a number of studies investigated survey based expectations
on exchange rates and inflation rates. However, thereare very few studies that have investigated
the hypothesis of whether interest rate expectations are rational and whether agents use all
available information efficiently. There is a need for a comprehensive study on the issue of
rationality of interest rate expectations. This paper attempts to extend the limited work on interest
rate expectations to fill the gap by utilizing a data source previously unexploited by the
researchers.In this paper, we are particularly interested in studying Euro bond and LIBOR rates
as these are some of the most important interest rates in the global financial markets. The results
of this study will enhance our understanding of efficiency of financial markets, which will be
useful to both researchers and policy makers. The study will shed light on term premia, and also
help us understand the forward discount puzzle in the currency market.
LITERATURE REVIEW
To the best of our knowledge there are only a few studies (Friedman (1980), Froot (1989),
MacDonald and McMillan (1994), and Jongen and Verschoor (2008)) that investigated the
properties of survey data on interest rate expectations. A related area is the survey expectations
of exchange rates, and more studies are available in that area (See Jongen, Verschoor and Wolf
(2008). The general conclusion of these studies is that survey data is a biased predictor of future
change in interest rates, and that agents do not incorporate all available information in forming
their expectations. Friedman (1980) uses survey data published by Goldsmith Nagan Bond and
the Money Market Letter to study rationality of interest rate expectations. He performs
unbiasedness and efficiency tests for six US interest rates at the three and six month horizon
from 1969 to 1976 time period, and he concluded that survey respondents did not make unbiased
predictions and that they did not incorporate all available information contained in common
macroeconomic and macro-policy variables, like, unemployment rate, growth of industrial
production, inflation, growth in money stock, and federal government budget deficit. Froot
(1989) analysed data from three different sources and found that expectations hypothesis does
not hold for short term or long term interest rates. He uses both short and long term US, UK and
other international interest rates, and thus, it is a comprehensive study. The data period ranges
Rationality of Euro Bond Rate and LIBOR Expectations
193
from 1969 – 87. Moreover, he decomposed the error into two components: error due to term
premia and error due to failure of rational expectations. He found that both errors contribute to
the bias in the forecast. MacDonald and Macmillan (1994) conducted a similar analysis with
UK interest rate data (1989 – 1992), and found similar results in general. The data set allowed
them to investigate expectations of individual forecasters, and they found some evidence of
heterogeneous behaviour, in terms of the importance of term premia. Most recently, Jongen
and Verschoor (2008) used data from Consensus Economics of London for the period 1995 2004 to test the unbiasedness and orthogonality propositions of the interest rate expectations of
20 countries at the three and twelve month horizon, and they also found that interest rate forecasts
are not rational and that agents do not use all available information in making their predictions.
They also found that forecast errors on EMS interest rates are smaller and less volatile than
errors on non-EMS interest rates.
DATA AND METHODOLOGY
We perform cointegration tests and regression analysis to assess the relationship between the
actual and the expected series. First, we conduct restricted cointegration test as proposed by Liu
and Madala (1992), and FMOLS cointegration regression analysis as proposed by Phillips and
Hensen (1990). We also perform Engle-Granger (1987) cointegration test to compare our results
with the earlier two methods. A brief description of these tests and methods are given below.
In restricted conintegration test, we takethe difference between the actual and the expected
series after carefully matching the two series, and then test for thestationarity of the error series.
If the error series is stationary, then, the two series are said to be co-integrated. We use three
unit root tests to investigate stationarity of the level data and also the error series. Theunit root
tests used are ADF, DF-GLS, and KPSS. We avoid describing these tests here to save space and
the descriptions are easily available in any econometric text book. We perform these tests using
two options:constant only, and constant and linear trend only. However, for the expected interest
rates to be rational, we also require that the errorseries be a white noise process. We will use Qtest statistics to check for serial correlation in the error series.
Then, we useFully Modified Ordinary Least Square (FMOLS) method to investigate the
relation between the actual and the expected rates from regression perspective. The equation
we propose for estimation is as follows:
Yt = a + bXt + et where Yt and Xt are actual and expected inflation rates.
FMOLS method corrects for the asymptotic endogeneity and the autocorrelation problems,
and, thus, the estimator is asymptotically unbiased. We perform a simple t-test to check if the
slope coefficient is equal to 1. If we are able to accept the null hypothesis that the slope coefficient
is equal to 1, we conclude that the two series are cointegrated. For rationality, we require that
the errors must be serially uncorrelated. Again, we will use Q-statistics to check for the presence
of serial correlation in the data.
We also perform Engle-Granger residual based cointegration test to check for consistency
with the earlier two methods. Since we have a single equation with two variables, we avoided
more advanced system cointegration testing methodologies, like Johansen’s cointegration test.
194
Fazlulu Miah, Abdoul Wane and Baeyong Lee
In Engle-Granger test, two series of order I(1) are regressed and the residual series from the
regression is then used to check for its unit root. The test has two steps. Let us assume that the
two variables Yt and Xt are I(1). In the first stage, we perform an OLS regression on the following
equation:
Yt = a + bXt + et
Now we take the residual series and estimate an equation as follows:
�eˆt � a1eˆt �1 � � t
If we can reject the null hypothesis that a1 is equal to zero, we conclude that the residual
series contains no unit root, and hence, Yt and Xt are cointegrated.
Data on interest rate expectations are collected from www.Fx4casts.com for this study. The
time period is December 2001 – September 2009. The journal provides monthly consensus
forecasts of interest rates (of various maturities) at the three, six and twelve month ahead for
many countries. Data on spot interest rates are also provided in the journal.
EMPIRICAL TESTS AND RESULTS
Table 1 provides the descriptive statistics of all the series: actual, expected and the forecast
errors. Forecast errors are defined as the difference between the actual observed interest rates
and its forecasted rates. For example, if a forecast is done today for three months ahead interest
rate, forecast error will be the difference between the interest rate observed three months later
and the forecasted rate that is made today. Table 1 reveals that all the three, six and twelve
month-ahead forecasts closely follow the actual rates as the mean, the standard deviations, and
the sums of actual and expected series are close to one another. A simple test of equality of
means between actual and expected series shows that there is no statistical difference between
the two means. A visual inspection of the actual and the expected series is depicted in Figure 1
and in Figure 2. Figure 1 shows that the actual and the expected rates closely follow each other.
Forecast errors thorizons in Figure 2 also follow each other. We also notice both in tables 1, and
3 that the forecast errors become larger as the forecast horizon increases, which is visible in the
mean and in the sum of the observations of each series. We also notice that three month ahead
forecast means are below the actual averages for all the horizons, six month ahead forecasts are
close to the actual averages and twelve month ahead forecasts are above the actual averages.
However, the sums of the errors in table 3 clearly show that the sums of the errors become
larger as the forecast horizons become longer. Jarque-Bera statistics in table 3 show that the
distribution is not normal in almost all the error series, except in six and twelve month ahead
forecast error of 10 year bond. We do get a feeling that the forecasters did a good job following
the actual rates. Although actual and forecasted series follow each other closely and the means
of the two are statistically indifferent as shown in table 2, test of rationality requires that the
relationships be tested formally using cointegration methods or regression analysis.
Following our methodology we performed unit root tests on the actual and expected inflation
rates at all the different horizons. Table 4 reports the results of three unit root tests, namely
ADF, DFGLS, and KPSS. We are only reporting the summary of the results of the tests without
Rationality of Euro Bond Rate and LIBOR Expectations
195
Table 1
Descriptive Statistics of Actual and Forecasted Series
A12
ML
F312
ML
F612 F1212
ML
ML
Mean
3.2256
Median
3.0700
Maximum 5.4500
Minimum 1.3700
Std. Dev. 1.0744
Skewness 0.4064
Kurtosis
1.9553
Jarque-Bera 6.8622
Probability 0.0323
Sum
303.21
Sum
107.36
Sq. Dev.
Obser94
vations
3.0785
2.9500
5.1500
0.9500
1.1064
0.1191
1.8941
5.0123
0.0815
289.38
113.85
3.1976
2.8550
5.5000
1.2200
1.1309
0.2331
1.7922
6.5645
0.0375
300.58
118.95
94
94
A10
YB
F310
YB
F610
YB
F12
10YB
A3
ML
F33
ML
F63
ML
F123
ML
3.3567
3.2800
4.9500
1.7500
0.9224
0.0996
1.7494
6.2810
0.0432
315.53
79.141
3.9972
4.0300
5.2800
2.9900
0.5137
0.1719
2.8388
0.5649
0.7539
375.74
24.549
3.8686
4.0900
5.4200
1.0200
0.9649
-1.4239
5.0674
48.506
0.0000
363.65
86.587
4.0197
4.2000
5.8100
1.3000
0.9336
-1.1032
4.3442
26.145
0.0000
377.86
81.064
4.1741
4.2500
6.2300
1.9200
0.7326
-0.5122
4.3918
11.699
0.0028
392.37
49.915
3.0393
2.8650
5.0500
0.8900
1.0614
0.3794
2.0894
5.5033
0.0638
285.70
104.77
2.9929
2.8300
5.1800
0.8800
1.0789
0.3166
2.0752
4.9198
0.0854
281.34
108.26
3.0805
2.8550
5.5200
1.3400
1.1030
0.4412
2.0987
6.2313
0.0443
289.57
113.145
3.2053
3.1300
4.9200
1.6400
0.8757
0.2003
1.9047
5.3271
0.0697
301.30
71.324
94
94
94
94
94
94
94
94
94
A3ML, A12ML, A10YB: Actual 3 and 12 month LIBOR rates, and Actual 10 year bond rate respectively
F33ML, F63ML, F123ML: Forecast of 3 month LIBOR rate 3, 6, and 12 month ahead respectively
F312ML, F612ML, F1212ML: Forecast of 12 month LIBOR rate 3, 6 and 12 month ahead respectively
F310YB, F610YB, F1210YB: Forecast of 10 year bond rate 3, 6, and 12 month ahead respectively
Table 2
Test of Equality (t-test) of Means between Actual and Expected Series
Series
Value
Probability
Accept /Reject
A10YB and F1210YB
A10YB and F310YB
A10YB and F610YB
A3ML and F33ML
A3ML and F63ML
A3ML and F123ML
A12ML and F312ML
A12ML and F612ML
A12ML and F1212ML
-1.917
1.14
-0.205
0.297
-0.261
-1.169
0.925
0.174
-0.897
0.059
0.253
0.838
0.767
0.797
0.144
0.356
0.862
0.370
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Accept
Table 3
Descriptive Statistics of Forecast Error Series
FE33ML FE63ML FE123ML FE310YB FE610YB FE1210YB FE312ML FE612ML FE1212ML
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
Sum
Sum Sq. Dev.
Observations
0.026813
0.000000
2.010000
-0.980000
0.369946
2.248458
13.63774
505.7470
0.000000
2.440000
12.31738
91
0.169886
0.010000
2.990000
-1.380000
0.745831
1.693276
6.375564
83.83160
0.000000
14.95000
48.39490
88
0.234878
-0.065000
3.510000
-1.150000
1.037299
1.498583
4.720469
40.80533
0.000000
19.26000
87.15505
82
-0.011099
0.110000
1.100000
-2.560000
0.624995
-1.810354
7.835864
138.3773
0.000000
-1.010000
35.15569
91
0.259432 0.485366 -0.073956 0.121477 0.258780
0.250000 0.480000 -0.030000 0.020000 -0.055000
1.890000 1.950000 1.630000 2.800000 3.080000
-1.560000 -0.660000 -1.220000 -1.850000 -1.160000
0.667203 0.635729 0.419229 0.758991 1.041049
-0.165635 0.256886 0.003907 0.917248 1.162834
3.350987 2.275892 5.771862 5.533394 3.436225
0.854082 2.693339 29.13244 35.87270 19.13001
0.652437 0.260105 0.000000 0.000000 0.000070
22.83000 39.80000 -6.730000 10.69000 21.22000
38.72887 32.73624 15.81778 50.11791 87.78648
88
82
91
88
82
196
Fazlulu Miah, Abdoul Wane and Baeyong Lee
Figure 1: Graph of Actual and Expected Series for three and Twelve Month
LIBOR and 10 year Bond rates at 3, 6, and 12 month forecas
Rationality of Euro Bond Rate and LIBOR Expectations
Figure 2: Graph of Forecast Errors for three and Twelve Month LIBOR and 10 year
Bond rates at 3, 6, and 12 month forecast horizons
197
198
Fazlulu Miah, Abdoul Wane and Baeyong Lee
Rationality of Euro Bond Rate and LIBOR Expectations
199
reporting the actual statistics to save space. These tests were performed on the actual as well as
on the expected series using two options: a constant only, and a constant and atrend. ADF and
DFGLS tests show that both the actual and the expected series are nonstationary for all the
expected and also all the actual series. Interest rates are shown to be nonstationary in numerous
other studies. Since expected rates follow the actual rates closely it is not surprising that all of
the expected rates are also nonstarionary. This signifies that forecasters have predicted the
direction of changes correctly on average. However, KPSS test shows that actual and expected
series are stationary. This is a good example which shows that different unit root tests can
Table 4
Unit Root Tests on Actual and Forecasted (Expected) Series
F121
0YB
ADF
F121
2ML
F123
ML
F310
YB
F312
ML
F33
ML
F610
YB
F612
ML
F63
ML
A10
YB
A3
ML
A12
ML
Constant
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
Constant,
Trend
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
Constant
S
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
Constant,
Trend
S
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
DF-GLS Constant
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
KPSS
Constant,
Trend
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
Constant
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
Constant,
Trend
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
NS
Constant
S
S
S
S
S
S
S
S
S
S
S
S
Constant,
Trend
S
S
S
S
S
S
S
S
S
S
S
S
Constant
S
S
S
S
S
S
S
S
S
S
S
S
Constant,
Trend
S
S
S
S
S
S
S
S
S
S
S
S
S: Stationary; NS: Non Stationary
Table 5a
Unit Root Tests on the Forecast Error Series
FE1210 FE123 FE1212 FE310 FE312
YB
ML
ML
YB
ML
ADF
Constant
NS
Constant, Trend
DF-GLS
Constant
Constant, Trend
KPSS
Constant
Constant, Trend
FE33 FE610 FE612
ML
YB
ML
S
S
S
FE63
ML
NS
NS
NS
S
NS
NS
NS
NS
NS
S
S
S
S
NS
S
NS
NS
S
S
S
S
S
NS
NS
NS
NS
NS
S
S
S
S
NS
S
S
S
S
S
S
S
S
S
NS
NS
NS
S
S
S
S
S
NS
200
Fazlulu Miah, Abdoul Wane and Baeyong Lee
Table 5b
Q Tests on the Error Series
Series
FE312ML
FE33ML
FE610YB
FE612ML
4
8
12
24
36
17.368 (0.0000)
59.860 (0.0000)
67.391 (0.0000)
105.28 (0.0000)
34.907 ().0000)
61.452 (0.0000)
102.94 (0.0000)
123.43 (0.0000)
43.879 (0.0000)
75.537 (0.0000)
111.41 (0.0000)
140.20 (0.0000)
56.167 (0.0000)
79.556 (0.0000)
134.27 (0.0000)
143.71 (0.0000)
69.575 (0.0000)
81.611 (0.0000)
167.28 (0.0000)
166.82 (0.0000)
provide conflicting results. Although KPSS test results differ from the other two unit root tests,
KPSS does provide consistent results for all the actual and the expected series at all the horizons.
We also repeated the same tests on the log of all the series and there is no significant change in
the results. These results are reported below the unit root test in the level data. In order to check
for the order of integration, we repeated the unit root tests on all the level series using first
difference, and found out that all the series are stationary at the first difference, except for
A3ML, which required the 2nd difference. Thus, all our series are I(1), except for A3ML, which
is I(2). Thus, we can perform formal cointegration tests, which require the same order of
integration of the series. We did not report all these test results in the paper in order to save
space.
Results of the restricted cointegration test are reported in tables 5a, and 5b. In the first
stage of this test, we performed unit root tests on the forecast error series. As mentioned earlier,
forecast errors are defined as the difference between the actual observed rate and the forecasted
rate. We carefully calculated the forecast error series and performed three unit root tests, namely
ADF, DFGLS, and KPSS. In the second stage of the restricted cointegration test, we performed
Q-test on the error series and the results are reported in Table 4b. All the three tests show that
four of the nine forecast error series are stationary, and thus, there is cointegration between the
two series. These error series are for the three and the six month ahead forecast of 12 month
LIBOR rates, and the three months ahead forecast of three month LIBOR rates and the six
month ahead forecast of 10 year bond rates. Almost all the unit root tests have given us consistent
results. KPSS test further showed that three month forecast of 10 year bond is also stationary,
and thus,cointegrated. Since the other two tests showed that the error series is nonstationary, we
concluded that the three month ahead forecast of 10 year bond is nonstationary. Now we check
the results of the Q-test. We performed Q-test only on those four error series, which were
stationary in table 3 since all other error series came out to be nonstationary, and thus, no
cointegration in the level series. The tests clearly showed the presence of serial correlation in
the error series as the test statistics are high and the null of no serial correlation is rejected at all
levels of lags. The chosen lags are 4, 8, 12, 24 and 36. Based on our criteria, we concluded that
none of the forecasts passed the test of rationality using restricted cointegration method.
Table 6a and 6b provide the results of the FMOLS cointegration regression. It is performed
using onlya constant option and a constant and a trend option. Table 5a also shows the coefficient
tests with associated probabilities. We testedthe null hypothesis that the slope coefficient b = 0
and 1. Cointegration requires that the slope coefficient is equal to 1 residuals are serially
uncorrelated. In only two cases, we find that the slope coefficients were very close to one. They
are the three month ahead forecast of three month LIBOR (A3ML and F33ML), and the three
Rationality of Euro Bond Rate and LIBOR Expectations
201
Table 6a
FMOLS Regression Results
Rt+k= � + � Ret, t+k+ �t
Rt+k
Ret, t+k
��(P: a = 0)
Constant
� (P: a = 0)
Constant and
trend
� (P: � = 0)
(P: � = 1)
Constant
�
(P: b = 0)
(P: b = 1)
Constant and Trend
A10YB
F310YB
A10YB
F610YB
A10YB
F1210YB
A3ML
F33ML
2.3500
(0.0000)
2.7761
(0.0000)
3.3853
(0.0000)
0.0530
(0.7010)
2.4835
(0.0000)
3.0829
(0.0000)
3.7400
(0.0000)
0.0664
(0.6489)
A3ML
F63ML
0.4794
(0.1850)
0.5029
(0.1763)
A3ML
F123ML
A12ML
F312ML
0.8346
(0.2662)
0.0714
(0.7026)
0.8809
(0.2232)
0.0067
(0.9699)
A12ML
F612ML
0.4004
(0.3271)
0.4073
(0.3125)
A12ML
F1212ML
0.8179
(0.3014)
0.8451
(0.2488)
0.4112
(0.0000)
0.2772
(0.0094)
0.1107
(0.4773)
0.9805
(0.0000)
(0.6486)
0.7994
(0.0000)
(0.0636)
0.6651
(0.0036)
1.0009
(0.0000)
(0.9988)
0.8434
(0.0000)
(0.1823)
0.6856
(0.0026)
0.3901
(0.0000)
0.2336
(0.0363)
0.0577
(0.7354)
1.0125
(0.0000)
(0.8035)
0.8399
(0.0000)
(0.2618)
0.4458
(0.1004)
0.9501
(0.0000)
(0.3627)
0.7572
(0.0000)
(0.0742)
0.4117
(0.0947)
Note:
FMOLS regression is on the level data and actual and expected data are matched carefully with the forecast
horizon. For example, three month ahead current forecast data is paired with actual data observed three months
later. In Engel-Granger cointegration test, we only report the decisions to save space.
Table 6b
Q tests on the Residual Series
Series
4
8
12
24
36
Constant only
Constant only
Constant only
Constant only
Constant only
Constant and trend Constant and trend Constant and trend Constant and trend Constant and trend
A3ML
and
F33ML
A12ML
and
F312ML
A3ML
and
F63ML
A12ML
and
F612ML
36.254 (0.0000)
33.434 (0.0000)
62.699 (0.0000)
53.361 (0.0000)
77.245 (0.0000)
67.601(0.0000)
82.962 (0.0000)
71.730 (0.0000)
84.73 (0.0000)
74.117 (0.0000)
25.363 (0.0000)
23.471 (0.0000)
29.810 (0.0000)
32.470 (0.0000)
37.794 (0.0000)
47.946 (0.0000)
49.789 (0.0000)
60.926 (0.0000)
63.366 (0.0000)
73.259 (0.0000)
176.16 (0.0000)
174.45 (0.0000)
185.81 (0.0000)
183.61 (0.0000)
194.44 (0.0000)
191.47 (0.0000)
213.42 (0.0000)
206.69 (0.0000)
232.16 (0.0000)
224.33 (0.0000)
126.11 (0.0000)
131.20 (0.0000)
135.77 (0.0000)
141.76 (0.0000)
148.70 (0.0000)
159.86 (0.0000)
152.65 (0.0000)
167.04 (0.0000)
170.76 (0.0000)
181.51 (0.0000)
202
Fazlulu Miah, Abdoul Wane and Baeyong Lee
month ahead forecast of twelve month LIBOR (A12ML and F312ML) rates. We could not
reject the null hypothesis of b = 1. We also found that six month ahead forecast of the three
month LIBOR (A3ML and F63ML), and the six month forecast of twelve month LIBOR (A12ML
and F612ML) rates have slope coefficients close to one. We also tested the hypothesis that the
slope coefficient is equal to 1, and we were unable to reject the null hypothesis as well. We do
not discuss the estimation results from other regressions using different other series as the slope
coefficients in those estimations are far from one.
Then we analysed the Q-test results for all the series whose coefficients are close to 1.
Table 5b clearly shows that residuals from all the four estimations have serial correlations. The
correlation problems are high in the six month ahead forecasts of the three and the twelve
month LIBOR rates than the three month ahead forecast of the same two LIBOR rates. It is
expected that the longer horizon forecasts will be more correlated than shorter horizons. Because
forecasters probably use more information from the past forecasts, the longer horizon forecasts
seems to be more correlated than the shorter horizons. Besides, actual rates are available in a
short period for shorter horizon forecasts than the actual rates for the longer horizons forecasts.
We require that the residuals be serially uncorrelated for the forecasts to be rational. Thus, we
concluded that none of the forecasts are rational. Three month ahead forecasts were close to
being rational, but because of serial correlation problems in the residual series, we concluded
that they were also not rational.
Some researchers argue that rationality tests are more appropriate if it is conducted using
the first difference (rate of change) of the series, not using the level series. The level regression
shows mere association. In order to satisfy that argument, we also performed FMOLS regression
of the equation using log data and also differenced data. However, given our data, the basic
results did not change significantly, and thus, we did not attempt to report those results in the
paper.
Table 6b: Q tests on the residual series Below in table 7, we report the results of EngleGranger cointegration test. We decided to perform Engle-Granger cointegration test in order to
compare our earlier test results from restricted cointegration test and FMOLS cointegration
regression with the Engle-Granger cointegration test results.
Table 7
Engle-Granger Cointegration Test Result
Actual Series
Engel-Granger Cointegration Test
Expected Series
Constant only
Constant and Trend
A10YB
A10YB
A10YB
A3ML
A3ML
A3ML
A12ML
A12ML
A12ML
F310YB
F610YB
F1210YB
F33ML
F63ML
F123ML
F312ML
F612ML
F1212ML
NC
NC
NC
C
NC
NC
C
NC
NC
C
NC
NC
C
NC
NC
C
NC
NC
Rationality of Euro Bond Rate and LIBOR Expectations
203
The test result in table 7 shows that three month ahead forecasts of the three months and
twelve months LIBOR rates were cointegrated. Besides, three month ahead forecast of the ten
year bond rates may also be cointegrated as the constant option of three month ahead forecasts
of ten year bond shows cointegration. These results are consistent with the earlier results.
However, we cannot decide about the rationality based on this result, because we cannot say
anything about the presence of autocorrelation in the residuals. In fact, Engle-Granger
cointegration test performs an OLS regression in its first stage. By following that procedure we
performed Q-tests on the three cointegrated series after conducting OLS regressions on actual
and expected series, and the Q-test shows significant presence of autocorrelation. Thus, it is fair
to say that cointegration of two variables may not constitute rationality. Cointegration signifies
long run relation among variables of interest. However, rationality requires not only cointegration
but also no serial correlation among the residuals.
SUMMARY AND CONCLUSION
We investigated the rationality of interest rate expectations of three month and twelve month
LIBOR rates, and ten year Euro bond rates in this research paper. We used almost eight years
(December 2001 – September 2009) of monthly survey data on interest rates collected from
www.Fx4casts.com. Two different methods are used to test the rationality of expectations. These
are restricted cointegration test and the regression method using FMOLS cointegrating regression.
We also performed Engle-Granger cointegration test to check for the consistency of the results
from the earlier two methods of investigation.
We are unable to confirm rationality of expectations using both the methods given the
requirements of rationality. We do observe that the three month ahead forecasts of three and
twelve month LIBOR rates are very close to the actual rates. Forecasters in general have done
a good job in forecasting these rates. Our observation is supported by the mean, standard deviation
and sum of actual and expected three month ahead forecasts of LIBOR rates, and the error
series reported in the descriptive statistics. These statistics are very close to the same statistics
of the actual rates.
The period of study considered for this research characterized by many uncertainties,
especially, the financial crisis period of 2007 - 2009. It is possible that our results are impacted
by the uncertainty of this period. However, we did not attempt to separate the period for an
independent investigation considering that the number of observations will be very small for
any meaningful study. However, our findings are consistent with the earlier studies on the
rationality of interest rate expectations.
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Fazlulu Miah, Abdoul Wane and Baeyong Lee
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