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Introduction
The aim of this paper is to give an estimate of the future interest rate set by the central banks
of three different regions: United States, European Union, and the United Kingdom. Our
forecasts cover a period starting from the second quarter of 2004 until the last quarter of 2005.
In section 1, we start by explaining the data sources we use and which specific variables we
took into account. In section 2, we estimate Taylor rules for the three respective regions, in
order to discover the reaction function of their central banks. In section 3, in order to arrive at
forecasts of the interest rate, we combine these rules with estimations of expected economic
fundamentals.
Finally, we compare our forecasts with forecasts of Reuters, which can be considered as
consensus forecasts. Moreover, we will add in this comparison the forecasts based on the
original Taylor rule.
Data description
In order to estimate our Taylor rule which will be used to forecast the level of the American,
British and European interest rates, we obtained the data from IFS, AWM and Datastream. In
Table 1, for each country you will find the source from which we extracted the data and the
description of each variable as given in the data source we used. When the data came from
IFS or Datasream, we also included the series code.
Table 1: Description of variables considered in the Taylor rule
Europe
UK
USA
UK
Real output
YER
AWM
European
Consumer prices
GDP US
GDP
VOL,1995=100
VOL,1995=100
(11299BVRZF…)
(11199BVRZF…)
IFS
IFS
Expected British
Expected US
Expected
Inflation
Inflation
Inflation
(EMIFINFRR)
(UKIFINFRR)
(USIFINFRR)
Datastream
Datastream
Datastream
Nominal short-term STN
interest rate
AWM
UK T-bill rate 3m
Federal
Funds rate
(11160C..ZF…)
(11160C..ZF…)
IFS
IFS
We used quarterly data, starting in the first quarter of 1991 until the last quarter of 2003. We
justify this short sample period by the fact that expected inflation for the three regions has
only been available since the first quarter of 1991. In order to enlarge our sample size, we
could have used as expected inflation the ex-post realized inflation. However, if you want to
make forward looking forecasts, you have to consider the expected inflation as central banks
do, and not the ex-post realized one.
Concerning the end period of our sample, for some of the above variables, we did not have
data for the last year at our disposal. It is the case for the European real output data coming
from the Area Wide Model which ended on the last quarter of 2002. In order to be able to
forecast for years 2004 and 2005, we had to have data for 2003. So, we gathered European
real output growth for each quarter of 2003 and we multiplied these growth rates by the real
output level we had for the end of 2002. After having solved this problem, we needed to have
the output gap level to include it in the Taylor rule of each country. We made a regression
with the logarithm of real output as a regressand, including as independent variables a
constant, a time trend and a quadratic time trend. The residuals obtained by this regression are
considered to be the relative output gap.
Concerning the forecasting step, we had to find some reliable predicitions of real output and
consumer price index as inputs in our forecasting model and predicitions of interest rates in
order to compare them to our own forecasts. For consumer price index and real output, we
find forecasts coming from different institutions but the more homogeneous and complete
were the ones from Reuters agency. These forecasts were not always available till the end of
2005 depending on the country and on the variable. So, when for example we did not have
them for the last quarter of 2005, we considered it equal to the forecasts given for the previous
quarter. Moreover, especially concerning real output forecasts, for each of the three countries,
Reuters agency only provides year on year quarterly GDP growth rates. It means that to make
our own expectations, we have to multiply the real output level of the same quarter of the
previous year by one plus the growth rate.
Finally, concerning the interest rate we forecast, it is the refinancing rate of ECB for Europe,
the repo rate of the Bank of England for UK and the Federal Funds rate of Federal Reserve for
United States. However, we have to precise that the forecasted interest rates are not the same
than the ones used in our Taylor rule which could slightly bias the value of coefficients.
Methodology
In order to forecast monetary policy, we should have some guidance on the way the different
central banks react on changes in the economic climate. Taylor (1993) argues that the
reaction function of the central bankers can quite accurately be described in a rule in which
inflation and output (and their deviations from the target) are the key determinants of the
interest rate. He defends this proposal by showing that equation (1) gave a good picture of
interest rate movements in the U.S during the period 1987-1992.
it = r + Πt + α(Πt-Π*) + βyt
In which i stands for current nominal short term interest rate, Π represents inflation and y
measures the output gap. This original rule has some drawbacks however. First of all, it does
not take expectations into account. It is well documented that central banks are not targeting
current inflation, but are more concerned with expected inflation. The reason is of course that
prices are sluggish and do not respond immediately to changes in the economic conditions.
Therefore, equation (2) is often estimated:
it = r + Πt + α(E(Πt+n) -Π*) + βyt
This is a forward looking rule, which takes expected inflation in period t+n into account. The
determination of n cannot be done in a mechanical way. We set n equal to 2. A next
modification to this rule is to introduce lagged interest rate. This is done because it is
observed that interest rates are largely persistent. This is due to the tendency of central
bankers to smoothen the evolution of interest rate and change the rates only by 25 or 50 basis
points.
If we take lagged interest rates into account, we should estimate the following equation (3)
it = (1-ρ)(r + Πt + α(E(Πt+n) -Π*)+ βyt) + ρ it-1
ρ stands for the adjustment factor. It measures the importance of past interest.
Now we move to the issue of estimation these rules. The original Taylor rule (equation (1))
can easily be estimated by OLS. However, this is no longer the case for the second equation.
On the one hand, we assume that the current interest rate is influenced by the expected
inflation. On the other hand, predictions on expected inflation include the current stance of
the monetary policy. In other words, we face an endogeneity problem. This problem can be
tackled by using GMM estimation techniques. As instrumental variables, we then use lagged
values of our independent variables.
In the next section, we report the results of our estimations. We estimated two different
models, both equation (2) and (3). Since our measure of expected inflation only starts in
1991, we have to restrict our sample to the first quarter of 1991 as starting point and the last
quarter of 2003 as ending point. When interpreting the results, we should bear in mind that
the coefficient estimates on inflation and output gap should be adjusted for the adjustment
factor.
The results from estimating a Taylor Rule
Europe
As stated earlier, the regressors we used for estimating a Taylor rule are a constant, the
relative current output gap, the expected inflation in 2 quarters and the lagged interest rate, a
regressor included to capture the smoothing effect which is well documented in the monetary
litterature, while the instrument list contains the one period lagged relative output gap, the
expected inflation for the next quarter and the two period lagged interest rate. Table 2 reports
the estimated coefficients for this equation.
Table 2 – Estimated Taylor rule for Europe including interest rate smoothing
Variable
C
GAP*100
EXPINF(2)
STN(-1)
R-squared
Adjusted R-squared
S.E. of regression
Durbin-Watson stat
Coefficient Std. Error
-0.625125
0.085507
0.654974
0.799645
0.979843
0.978403
0.39044
1.156538
t-Statistic
Prob.
0.209632 -2.982014
0.090825
0.94145
0.200962 3.259195
0.071883 11.12421
Mean dependent var
S.D. dependent var
Sum squared resid
J-statistic
0.0048
0.3519
0.0022
0
5.846115
2.656778
6.402624
1.30E-26
As we can see from this table, the expected inflation and the lagged interest rate are highly
significant and their coefficients have a positive sign. The fact that the relative current output
gap is not significant could be due to two reasons. First of all, we could argue that this is due
to our small sample which biases our t-statistics and thus providing no relevant information
on the significance of the coefficients. A second argument could be that the European Central
Bank simply does not take the output gap into account while setting the interest rate. This
second argument can be validated by the fact that the ECB explicitly mentions that its main
objective is controlling the price level. If we divide the coefficient of the expected inflation by
one minus the coefficient of the interest rate smoothing component, we see that this is bigger
than one. If this would not be the case, a rise in inflation of e.g. 1% would make the ECB
adapt its interest rate by less than 1% which would decrease the real interest rate which in turn
would stimulate the economy even more and thus accelerating inflation.
We also redid the Taylor rule estimation exercise without taking interest rate smoothing into
account. The results from this estimation can be found in Table 3.
Table 3 – Estimated Taylor rule for Europe without interest rate smoothing
Variable
C
GAP*100
EXPINF(2)
R-squared
Adjusted R-squared
S.E. of regression
Durbin-Watson stat
Coefficient Std. Error
-2.435991
-0.400734
3.261658
0.857282
0.850644
1.026754
0.474986
t-Statistic
0.958963 -2.540236
0.161025 -2.488649
0.364624 8.945263
Mean dependent var
S.D. dependent var
Sum squared resid
J-statistic
Prob.
0.0148
0.0168
0
5.846115
2.656778
45.3316
4.32E-29
This means that we removed the one period lagged interest rate from the regressors list and
the two period lagged interest rate from the instrument list. All coefficients are significantly
different from zero. Once again the positive sign of the coefficient for the expected inflation is
intuitive. If we compare the Durbin-Watson statistics for both estimations, we see that when
we exlude the lagged interest rate from the estimation there is much more positive
autocorrelation in the residuals than when we include an interest rate smoothing component.
Also the R² favours the estimation including an interest rate smoothing component.
The accuracy of the Taylor rule can be tested by examining the fit between the actual interest
rate series and the interest rate series fitted by the model. Appendix 1 shows this fit for
Europe, when using the model including lagged interest rates. We see that the fit is quite
good. However, at the beginning and at the end of our estimation period, the fit deteriorates.
Recently, there seems to be a positive spread between the fitted curve and the actual curve.
Despite this, we think that this Taylor rule can be considered as a reliable tool to forecast the
interest rate.
United Kingdom
The estimated Taylor rule for the United Kingdom essentially contains the same variables as
the one for Europe. The estimation output can be found in Table 4.
Table 4 - Estimated Taylor rule for the United Kingdom including interest rate smoothing
Variable
Coefficient Std. Error
C
GAPOK*100
EXPINF(2)
UKINTEREST(-1)
0.243083
0.16895
0.531788
0.68226
R-squared
Adjusted R-squared
S.E. of regression
Durbin-Watson stat
0.930271
0.925623
0.485051
1.196232
t-Statistic
0.448236
0.112673
0.431447
0.160247
Mean dependent var
S.D. dependent var
Sum squared resid
J-statistic
0.542309
1.499467
1.232568
4.257558
Prob.
0.5903
0.1407
0.2241
0.0001
6.016878
1.778552
10.58734
7.72E-28
Although, except for the lagged interest rate capturing the interest rate smoothing, non of the
coefficients seem to be significant, we need to be careful in interpreting the values for the tstatistics. The signs of all the coefficients are intuitive and the R²-statistic indicates that the
model fits the data pretty well. The coefficient of the expected inflation divided by one minus
the coefficient of the interest rate smoothing term yields a number which is bigger than one.
As we did for Europe, we re-estimated the Taylor rule without including the lagged interest
rate. The results for this estimation can be found in Table 5.
Table 5 – Estimated Taylor rule for the United Kingdom excluding interest rate smoothing
Variable
C
GAPOK*100
EXPINF(2)
R-squared
Adjusted R-squared
S.E. of regression
Durbin-Watson stat
Coefficient Std. Error
-0.718058
0.401247
2.290676
0.807279
0.7989
0.797577
0.926247
t-Statistic
Prob.
0.807849 -0.888851
0.14854 2.701274
0.284822 8.042483
Mean dependent var
S.D. dependent var
Sum squared resid
J-statistic
0.3787
0.0096
0
6.016878
1.778552
29.26193
3.79E-28
We see that expected inflation and the relative current output gap are significant and that the
signs of their coefficients are easily understood. But comparing the Durbin-Watson statistic of
Table 4 and Table 5, we see that the model excluding the interest rate smoothing term has
much more positive autocorrelation in the estimated residuals. The R²-statistic shows that the
model including an interest rate smoothing term fits the data better than the model without the
lagged interest rate.
Again, we examine the in sample fit of our model. In appendix 2, we observe that the fit is
good. In the most recent period, it seems that our prediction lags the actual period by one
observation.
United States
The estimated Taylor rule is the same for the US as it was for the UK and Europe. The results
of the estimation including lagged interest rates can be found in Table 5.
Table 6 - Estimated Taylor rule for the United States including interest rate smoothing
Variable
Coefficient Std. Error
C
GAP*100
EXPINF(2)
FED(-1)
0.067413
0.080511
0.166799
0.861154
R-squared
Adjusted R-squared
S.E. of regression
Durbin-Watson stat
0.918735
0.913655
0.481514
0.518902
t-Statistic
0.495968
0.075549
0.235933
0.065778
Mean dependent var
S.D. dependent var
Sum squared resid
J-statistic
0.135921
1.065673
0.706977
13.09191
Prob.
0.8925
0.2919
0.483
0
4.328404
1.638669
11.12906
9.69E-28
We can see that the estimation results for the federal funds rate are quite similar to the ones
for the United Kingdom interest rate, concerning their significance. Every variable, except the
lagged interest rate, seems to be statistically insignificant. Caution in interpreting the tstatistics is however required, due to the small sample used for estimating the results. The
signs of the coefficients are all positive, as one would expect. Dividing the coefficient of
expected inflation by one minus the coefficient of the lagged federal funds rate gives a value
which is bigger than one, as expected.
Once again the same exercise is done, excluding the interest rate smoothing term. These
results are reported in Table 7.
Table 7 – Estimated Taylor rule for the United States excluding interest rate smoothing
Variable
C
GAP*100
EXPINF(2)
R-squared
Adjusted R-squared
S.E. of regression
Durbin-Watson stat
Coefficient Std. Error
-0.496458
0.603558
1.854101
0.335666
0.308551
1.36261
0.237117
t-Statistic
1.682711 -0.295035
0.173139 3.485974
0.54158
3.4235
Mean dependent var
S.D. dependent var
Sum squared resid
J-statistic
Prob.
0.7692
0.001
0.0013
4.328404
1.638669
90.97854
1.27E-29
The coefficients of the output gap and the expected inflation are significant and their signs are
very intuitive. But once again, if we compare the Durbin-Watson statistic, concerning the
autocorrelation, and the R²-statistic, concerning the fit of the model, we prefer the model
including an interest rate smoothing component to the second version of the model.
Concerning the in sample fit, we again think the estimated rule is performing fairly well. But,
as we observed also for the United Kingdom, our fitted series seems to be lagging one
observation on the actual series.
The forecasts
In order to arrive at our definitive forecasts, we use the predictions as they were mentioned
earlier in the data description section. As can be seen from our forward-looking Taylor rule,
we need predictions on the output gap and the expected inflation to plug into our estimated
Taylor rule as independent variables. We will report our forecasts using our estimated Taylor
rule, which includes an interest rate smoothing term, and the original Taylor rule, which
includes no interest rate smoothing term and which has a constant of 2 and coefficients of 0.5
for both inflation and output gap.