# Interest rate behaviour in europe

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### Interest Rate Behaviour in Europe

### 1. Introduction

### 1.1 Background

Interest rates are considered center-pieces of macroeconomics because of the impact that they have on the social, economic and political aspects of a nation. The recent recession in many developed countries in the America and Europe saw an unprecedented level of coordination and swiftness in the manner in which central bank engaged in interest rate cuts. Such actions are founded on the economic justification that the reduction of interest rates stimulates the economy through monetary expansion. The inter-woven nature of different countries in the globalised era comes to the surface during turbulent economic times such as these. This research attempts to study the relationships that exist among the different European countries' monetary policies by studying the co-movements among their interest rates. An attempt is also made to study the relationship between the interest rates in the UK and the US, the two long-time economic partners. This research uses quantitative methods and modelling techniques to study the causal effect of certain critical factors on the interest rates of different monetary policy regimes in Europe.

### 1.2 Rationale

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The recent coordinated acts by the central banks of the world drive home the importance of taking the interdependence of countries into account. Ever since Euro Area was created and all the 16 countries adopted a common monetary policy and a single Central bank, the significance of Euro Area has increased in global economics. In regional economics, its importance is second to none. It is to be expected that such a large monetary area would have significance influence upon the interest rate changes in other states in the region. This perceived importance of Euro Area and the importance of studying the inter-dependence of different countries' monetary policies form the underlying rationale for this study. Euro Area was primarily created to ensure that the synergy of the members would lead to better economic strength. It would be appropriate to assess this factor through measurement of the impact of Euro Area's monetary policy on other states'.

### 1.3 Aims and Objectives

The aim of this research is to ascertain the extent of inter-relationships among the monetary policies of different monetary regimes in Europe. The primary objective of this research is to study the relationships among the interest rates in Euro Area and other member states of the European Union. Besides, this research also strives to establish the causal impact of changes in Euro Area's interest rates upon the interest rates in other European Union states. The overall purpose underlying this research is that it would provide some insights into relative behaviour of interest rates in Europe.

### 1.4. Methodology

This research is based on empirical research methodology where real historic data are used to build models and validate hypotheses. Quantitative research methods are used to explore the relationships among the critical variables whose characteristics are purported to be studied by this research. Two main quantitative methods used are - Correlation and Regression.

Correlation is a measure of the extent of co-movement between two data series. Correlation measures both the direction and the magnitude of changes in two variables (Levin and Rubin, 1997). The most popular measure of correlation is based on the covariance between the data series. The formula is presented below:

r = Sxy / [Sx2 X Sy2]0.5

Where,

x and y represent the two data series and

r is the correlation coefficient.

In this research correlation analysis is used to ascertain the relationship

- between pairs of different kinds of short term interest rates in Euro Area
- between interest rates of pairs of other European Union economies
- between interest rate of each one of the member of EU and the interest rate of Euro Area
- between LIBOR and US Fed rate

Correlation coefficient, as calculated above, takes a value between -1 and +1. A value of -1 denotes that the two variables move exactly in opposite directions while a value of +1 indicates that the movement of the two variables are perfectly matched. A value of zero denotes the presence of no significant correlation between the variables. Correlation shows only the extent of co-movement and not causation.

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The other quantitative technique used in this research is linear regression. Linear regression models the changes in dependent variable as functions of changes in one or more independent variables. Regression is used to measure the causal impact that changes in one or more variables have on the dependent variable (Newbold et al., 2003). In this research regression is used to measure the causal impact of money supply and inflation on the interest rate of Euro Area. This can be expressed in an equation as follows:

Ii = ai + ß1 . Mi + ß2 . Ci

Where,

Ii is the rate of interest during the period i

Mi is the quantity of money supply during period i with coefficient ß1

Ci is the rate of inflation during period i with coefficient ß2

The values of betas are tested for null hypotheses that ß1=0 and ß2=0 using a t-test. The regression function is also evaluated using a F-test. If the null hypotheses of t-tests get rejected it would be concluded that money supply and inflation have significant impact on the changes in interest rates during the period under consideration. If the null hypotheses are not rejected then the conclusion would be that money supply and inflation do not determine the changes in interest rates. It is expected that both money supply and inflation would have significant impact. Also, it is expected that money supply and inflation would have positive coefficient values.

### 1.5 Outline

The next chapter of this dissertation reviews a cross-section of literature that have studied the behaviour of interest rates in Euro Area and greater Europe and makes observations on the basis of the conclusions drawn in those researches. The third chapter is concerned with the study of correlation between different sets of data, which has been explained in the earlier section of this chapter. The fourth chapter builds a simple model to forecast interest rate of Euro Area from two variables - money supply and inflation. Finally the conclusion chapter summarises the discussion in the dissertation and spells out the conclusions arrived at on the basis of the observations made using various analysis methods.

### 2. Literature Review

The objective of this research is to study the behaviour of interest rates in Europe. A number of researchers have conducted various different researches on the same topic and have made valuable contributions to the academic knowledge. A review of the conclusions made by some of these researchers would help to pre-empt the results of the empirical research that will be conducted as part of this study and would also help to compare the results of this research to those of the earlier researchers. This chapter of this dissertation studies a cross-section of academic researches that have studied the nature and inter-relationships between different interest rates in Europe. The first part of this section focuses on the relationship between interest rate and inflation rates in different countries of EMU; the second part is focussed on financial and monetary integration within the EMU and the third section reviews literature that have studied the linkages between EMU and the other countries, particularly the US.

### 2.1. Interest Rate and Inflation rates in EMU

The most prominent feature of Economic and Monetary Union (EMU) of European Union is that the fiscal policy of each country is determined by the national governments that rule the particular state while the monetary policy is determined centrally for all the countries in the EMU. The monetary policy aims to achieve a stable monetary condition through appropriate control of the inflation and interest rates. However inflation and general economic growth is affected by fiscal policies followed by each government. When a government engages in expansionary fiscal policy funded mostly by borrowed capital, it could result in poor quality of growth coupled with high inflation. Thus the success of central monetary policy is dependent upon the fiscal discipline of the member states. Knowing this fully well, the EMU created a 'Stability and Growth Pact' that requires that the deficit to GDP ratio should not exceed 3% for any member state. Any state that violated the requirements is handed out punishments in the form of sanctions. The idea of creating a stability and growth pact is to ensure that the minimum level of fiscal prudence may be ensured so that monetary policy can be focussed on stability of the economy as well as growth. A number of researchers have enquired into the relationship between fiscal conditions of members of EU and the impact of fiscal excesses on the inflation rate. When inflation rate changes in the state, the real interest rates could vary across different states in the EU even though the nominal interest rates are all fixed at same level.

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Examples of our workHonohan and Lane (2003) study the inflation rates in different countries of the Economic and Monetary Union (EMU) of the European Union. The authors find that the inflation rates have been significantly different during the period under study. Particularly, the inflation rates in the countries in the periphery such as Ireland have had consistently high inflation while Germany's inflation has been below the Euro Area average. The authors identify that most of the researchers in this area have tended to focus on the productivity factor. However the authors argue that the productivity factor differentials have not yet been taken into account. The ongoing differences in inflation rates across different states with the EMU are attributable to the differential impact of Euro weakness on the external sectors of each one of the member states of the EMU. The authors assert that the productivity differentials are yet to be reflected in the inflation rates and when they get accounted for, the inflation rates will vary even widely and the real interest rates in different states of EMU will diverge even further. Thus, even though the ECB fixes a single interest rate for all of EMU, the real interest rates could be different in each country depending on the inflation rates prevailing. In an important research paper, Faini (2005) shows how the imprudent fiscal policies followed by some members of the EMU could cause the interest rates of the entire union to rise. The author observes that the punishment meted out to the countries that violate the stability and growth pact by incurring larger than allowed fiscal deficits is not adequate. He states that the impact of a member country running a large fiscal deficit could be two - firstly, the overall country spread increases and secondly, the interest rate of the entire EMU also increases.

### 2.2. Financial and Monetary Integration in EMU

Poghosyan and Haan (2007) remark that one of the main objectives of the EMU is to achieve financial integration. The authors study the extent of financial integration using threshold vector error-correction model. In this model the transaction costs are analysed and any indication of co-movements in financial environments are noted. This is applied on interest rates from different financial markets in a number of EMU countries. Based on the results the authors conclude that "only for some country pairs and financial market segments there is evidence in support of financial integration". Borio and Fritz (1995) study the response of short-term lending rates to changes in policy rates using a sample of 12 developed countries. The authors identify that the degree of competition in lending market and clarity of signal are the two important factors that determine the extent of relationship between these two rates. Besides, the authors find that there was no asymmetric relationship between these two with respect to increases and decreases.

Codogno et al. (2003) state that EMU is expected to create a substantially integrated government debt market in Europe. However it is noted that the interest rates on Euro-denominated bonds issued by different governments in EMU have not converged. Substantial spreads are found between them due to reasons such as liquidity and fiscal conditions prevailing in respective countries, which affect their creditworthiness. Gerlach and Schnabel (2000) find from their research that between 1990 and 1998, excluding the period of market turmoil during 1992-1993, the interest rates in EMU moved very closely with average output gaps and rates of inflation. The authors refer to the Taylor rule, which is vindicated by these findings. Toolsema et al. (2001) examine the extent of monetary policy transmission among 6 EMU countries - Belgium, France, Germany, Italy, the Netherlands and Spain. They conclude that there was little evidence to prove that monetary policy transmission was working. They find that major differences exist in the sample both in the short-term and long-run changes in interest rates caused by monetary policy changes.

Gerlach and Smets (1999), on the basis of their study of relationships between inflation and output gaps in different countries in the EMU area, suggest that the ECB should react to changes in output gap in the entire region, even if the bank cares only about inflation as the authors find significant relationship between inflation and output gaps in different countries of the region. Martin (2001) studies various kinds of convergence that have taken place among different countries of the Europe region and conclude that the central bank has a very important to play in ensuring that real convergence develops among the different members states of the EMU region. The author finds significant scope for growth of convergence among the countries.

Prior to EMU, Europe had a functional monetary cooperation among a number of states in the form of Europe Monetary System (EMS). EMS was introduced in 1979 after the collapse of Brettonwoods system. Under EMS, the members countries agreed to peg their currencies on the basis of a pre-determined calculation. There was no specific anchor country chosen even though Germany, with its Deutsche Mark, was considered the leader of the system, as its currency was one of the strongest and most stable at that time. EMS restricted the movements in currency exchange rates within the range of 2.25%. EMS is considered the trial run for the greater cooperation in the form of EMU, which replaced EMS later down the line. One of the most important aspects of studying EMS in comparison to today's EMU is that under EMS, the monetary policy was determined independently by the central banks of the members of the union.

Karfakis and Moschos (1990) study the relationships among interest rates of different members of the old EMS system. The author conducts Granger Causality tests to identify the dependence of interest rate of each state on that of the other state. The tests show that there existed a unidirectional causality between German interest rate and the interest rates of other states. Thus the states followed the changes in monetary policy of Germany, which was the largest economy in the Union. The author asserts that when a number of countries enter into a union, they tend to follow the trend set by the largest player in the union even though they may have the freedom to choose their own policies. The authors on the basis of their findings suggest a German dominance theory, which asserts that Germany played the pivotal role even in EMS where the individual states could actually choose their own policies. Fratianni and von Hagen (1990) find simple Granger causality tests to be inadequate to make the conclusions that Karfakis and Moschos (1990) have made in their research. They use a system of equations, which employ the short term interest rate variable to capture changes in the monetary policy of individual states. They also use United States short-term interest rates as proxy for the interest rates in other countries outside the EMS. The authors observe that the changes in short term interest rates of the states of EMS respond to a number of different factor including changes in inflation and output growth rates in domestic economy, changes in short term interest rates in other states in EMS and also outside the EMS besides other factors. On the basis of these observations, the authors conclude that "in the short-run, the EMS is best portrayed as an interactive web of monetary policies, where Germany is an important player but not the dominant one" (p. 21).

Koukouritakis and Michelis (2005) study the linkages between the term structures of two of the early entrants into EU (Germany and France) and 10 latter entrants (Cyprus, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Malta, Poland, the Slovak Republic and Slovenia). The authors decompose terms structures into transitory and permanent components. They attempt to analyse the short-term and long-run linkages among the interest rates. They find that there existed weak short-term but strong long-term relationships among the term structures of different countries in the EU. On the basis of these observations the authors conclude that the countries even before they entered into the EU had a habit of closely following the two larger economies on Europe - Germany and France.

### 2.3. Relationship between Interest Rates in Europe and Other countries

Cumby and Mishkin (1987) study the relationship between the interest rates in the US and the UK and ascertain the reasons for this relationship. The authors observe that the interest rates in the US and Europe increased substantially during the 1970s and 1980s. This rise was seen not only in nominal interest rates but also in real rates. The authors conclude that "There is a positive association between movements in U.S. real rates and those in Europe. However, European real rates typically do not move one-for-one with U.S. real rates, still leaving open the possibility that European monetary policy can influence domestic economic activity".

Bremnes et al. (2001) study the relationships among the long-term interest rates in Norway, Germany and the United States using large samples. The authors use a Johanssen multivariate cointegration procedure to achieve the research objectives. They observe that US interest rates have a significant includes on the changes in Norwegian interest rates as well as EU interest rates, which are applicable to Germany. The authors also find that Norway's interest rates were closely associated with those of Germany. Thus the authors conclude that small countries tend to associate their monetary policies to that of the large countries.

Ehrmann and Fratzscher (2004) acknowledge that there has been a strong degree of interdependence between the economic and monetary policies and performances of the European Union and US. However the authors investigate if the nature of this interdependence has undergone any significant change after the creation of EMU within EU. The authors, instead of using historic data, use real-time data to ascertain the changes in the interest rates of these two monetary regimes. The authors observe that the interdependence has increased significantly after the creation of EMU. It has always been the case that changes in important macroeconomic variables in the US have an important impact on the changes in interest rates in the EU. However after the advent of EMU into picture, it is noted that certain important macroeconomic news from the EU have begun to have causal impact on the changes in macroeconomic variables in the US as well. Thus the authors identify that the one-way causality has slowly been transformed into bi-directional relationship between these two regions. This, according to the authors has led to the apparent increase in the degree of interdependence between the two economic regimes. The authors take this relationship to the next level by stating that "US macroeconomic news have become good leading indicators for economic developments in the euro area".

### 2.4. Chapter Summary

The detailed review of literature that have studied the relationship among the monetary variables of the states within the EU and also outside the EU clearly shows that there are strong linkages visible among the interest rates. There are also very strong monetary linkages visible between the EMU and UK. This shows that the normal interest rates are to a great extent inter-linked not only within Europe but also outside Europe as there are strong relationships found between Interest rates in EMU and US. However, it is observed that are differences in inflation rates within the states that are members of EMU. Besides, the fiscal policies of the states in EMU are also quite different with some states engaging in active deficit financing of the economies. Due to these inherent variations, inflation rates differ, which in turn cause wide spread variations in real interest rates. These observations could prove valuable while conducting empirical enquiries into the nature and relationships between interest rates in Europe, within and outside the EMU and EU. The observations made from empirical research in the next chapters of this dissertation will be compared to the observations made from literature review in this chapter.

### 3. Co-movements of interest rates

The objective of this research is to ascertain the behaviour and nature of interest rates in the European countries. It is seen that the Europe is dominated by the European Union which comprises 27 countries. 16 of these countries have unified to form a single monetary union under which they share a single central bank, monetary policy and Euro currency. This group is officially known as Euro Area (ECB, 2009). It is also referred to as Euro Area in contemporary literature. For the countries in Euro Area, because of single monetary policy and currently, there is only one set of common interest derived from the money market (Gali, 2004). On the other hand, the other members of the European Union have individual monetary policies and interest rates. The first part of this section is concerned with the study of co-movement of different kinds of interest rates within the Euro Area. It is followed by an analysis of the co-movement of interest rates in other EU states. The third part studies using quantitative methods, the extent of co-movement of interest rates between EA and each one of the EU countries. Finally, the co-movement of interest rates between UK and US in the form of a study of relationship between LIBOR and US Fed rate is performed. It is believed that the above mentioned studies would help to understand the relationship in interest rates of three important groups or countries - EA, other states in EU and US. The outcomes of these studies are useful in the next chapter which ascertains the impact of other variables on interest rates of these zones or countries. The studies related to the co-movements of interest rates, as mentioned above, are conducted using correlation method which is explained in the earlier chapter of this dissertation.

### 3.1 The Co-movement of interest rates in Euro Area nations

Following table shows the results of correlation between pairs of different short and medium term interest rates in the Euro Area.

The above table shows both correlation coefficients and corresponding p-values for a null hypothesis test that the correlation is zero between the pairs of series. It can be seen that all of the interest rate series have very strong correlation with each other. The strongest correlation is found between 3 months Euribor and 1 month Euribor as well as between 1 year Euribor and 6 months Euribor. The p-values are 0.000 for all pairs indicating that the null value that correlation is zero is rejected for each one of the pairs.

### 3.2 Co-movement of Interest Rates in Other EU states

Following table shows the results of correlation analysis conducted using short term interest rates in different countries which are part of the EU but not part of EA.

In the above table, p values are shown below the correlation coefficients. It can be seen that there are wide spread differences among the different states with respect to the relationships between their interest rates. The interest rates of Romania and Poland correlate 0.917 and a p-value of 0.000 means that the null hypothesis that correlation is zero can be rejected at 99% confidence level. Similarly, Poland and Estonia have a very strong positive correlation between their interest rates as indicated by a coefficient value of 0.81 and a p-value of 0.000. Latvia and Estonia share a very strong relationship and so do Chezh and Denmark. The interest rates of Sweden and Hungary share insignificant negative relationships with that of Denmark. These results clearly show that the relationships between pairs of states in EU which are not part of EA are mixed at best. While some of their share significant positive relationships, some have insignificant but negative relationships. Quite surprisingly, the interest rates in Estonia, Latvia and Poland share the strongest relationships with the interest rate in UK. These results partly support the observations made in the literature review. Researchers have noted that the states in EA area tend to have strong relationships among their nominal interest rates.

### 3.3 The Co-movement of interest rates in Euro Area and other EU member states

Estonia shares a very strong positive relationship with Euro Area. It is indicated by the correlation coefficient of 0.946 and p-value of 0.000. UK and Euro Area share strong positive relationship between their interest rates. The correlation coefficient between these interest rates is 0.694. P-value of 0.000 shows that the null hypothesis that correlation coefficient is equal to zero is rejected at 99% confidence level. The interest rates of Hungary and Sweden share insignificant negative relationships with the interest rate of Euro Area.

### 3.4 The relation between EURIBOR and US interest rates

This part of the chapter is concerned with the analysis of co-movement between interest rates in Europe and the US economies. The objective is to identify the relationship between the 3 months Euribor and 3 months US Treasury. The output of the correlation analysis is provided below.

Pearson correlation of 3m Euribor and 3m US Treasury = 0.430

P-Value = 0.000

It can be seen that the correlation coefficient between Euribor and US Treasury bill is 0.43. A p-value of 0.000 shows that the null hypothesis equating correlation coefficient to zero is rejected at both 99% and 95% confidence levels. This shows that the short term interest rates at Europe and US share a very strong positive relationship. It is observed from the review of a number of researchers including Bremnes et al. (2001), Cumby and Mishkin (1987) and Ehrmann and Fratzscher (2004) that US and Europe tend to share very strong monetary relationships. Researchers have attributed this to the fact that the two continents have had very strong financial and political relationships.

### 3.5. The relation between LIBOR and US interest rates

It is necessary to obtain the correlation coefficient between the interest rates in UK and US. This is done by using the 3 month US LIBOR and 3 month US Treasury. Following is the result of the correlation analysis

Pearson correlation of 3m Libor USD and 3m US Treasury = 0.966

P-Value = 0.000

As can be observed, the correlation coefficient is 0.966 and the p value is 0. This shows that the null hypothesis that there is no significant correlation can be rejected at 95% and 99% confidence levels. In other words, there is a very strong correlation between short-term interest rates in US and UK. This matches the observations made in literature review section where it is noted that a number of researchers have found empirical relationship between these two countries' monetary polices. This stems from the long-term political and economic association of US and UK. Particularly the monetary policies of both these countries have been long known to move in lock-steps with each other.

### 3.6. Chapter Summary

This chapter analyses the relationship between pairs of interest rates of different states in EU, EA and outside Europe. It is observed that there is very strong relationship between interest rates pertaining to different time periods as measured by 1 month, 3 months, 6 months and 1 year EURIBOR. An analysis of short-term interest rate of different states in Europe shows that some states such as Poland, Latvia and Lithuania share very strong correlation with UK LIBOR which indicates that small states tend to follow the monetary policies of larger economies in order to ensure monetary and economic stability in the countries. Among the countries outside the EA, Estonia shares the strongest relationship with EU. LIBOR and US Treasury rates are very closely correlated as may be expected on the basis of the strong economic ties that these two countries share with each other.

### 4. Interest Rates Modelling and Forecasting in Europe

This section of the report is concerned with ascertaining the impact of some important factors on the changes in short term interest rates in Europe. The first part of this section is concerned with factors affecting interest rates in Euro Area and the second part deals with the impact of changes in Euro Area interest rates upon other EU states' interest rates.

### 4.1 Factors affecting Interest rates in EA

This section attempts to model the interest rate changes in Euro Area using linear regression with two predictor variables - money supply changes and inflation (which is the equivalent of changes in general price level). Following table shows the results obtained from the regression function.

It can be observed that the both money supply (M3) and inflation have negative coefficients indicating that negative changes in these variables cause a positive change in interest rates. This is quite unlike the macroeconomic theory which states an increase in inflation is countered by the central banks through an increase in interest rates so that the extra supply of money gets sucked back into the system. However the results presented here are contradictory to conventional economic wisdom. It may be necessary to ascertain the significance of these variables. It is seen that the P-values of these two variables are 0.023 and 0.159. Both values are more than 0.01 indicating that at 99% confidence level, the null hypotheses, that the coefficient of the two predictor variables are equal to zero, are not rejected. This means that there is no significant impact of M3 and inflation on the interest rates. The overall strength of the regression function is observed from the P-value associated with F-test which is 0.033 in this case. As this value is also more than 0.01 it can be concluded that at 99% confidence level, the two predictor variables do not have any significant impact on the changes in short term interest rates. The adjusted R-squared value of 4.5% means that the change in money supply and inflation could together define only 4.5% of the total changes in the interest rates. In short, it can be concluded that money supply and inflation do not influence interest rates.

The reason for this odd conclusion could be that the interest rates do not change in tandem with money supply and inflation. The interest rates have a tendency to lag behind the macro economy as the central bank typically watches the macro economic variables over long term to make changes in monetary policies (Gali, 2008).

### 4.2 Factors affecting Interest rates in other EU states

It is seen in the earlier section of this chapter that money supply and inflation do not seem to have any direct impact on the changes in short term interest rates in the EA. This part of the chapter checks the impact of changes in Euro Area interest rates upon the changes in interest rates in other EU states. Following table shows the results of 11 regression functions performed with interest rates series of each one of the 11 other states in EU as the regressed variable and the 3m Euribor as the regressor variable.

The results as given above show that the interest rate changes in EA have had significant impact on the interest rates of only some countries. The interest rates of Estonia, Latvia, Poland, Romania and UK have significant positive relationships with the interest rate changes in the Euro Area as observed from the positive value of their respective coefficients and the p-value of less than 0.01. This observation is based on t-tests performed at 95% confidence level. On the other hand some countries including Bulgaria, Hungary and Sweden have negative coefficients but with insignificant values as their p-values are all greater than 0.01. Thus for these countries interest rate changes in EA have insignificant but negative impact. For other countries such as Denmark, Chezh Republic and Lithuania, the impact is positive but insignificant. Thus from the above regression results it can be concluded that short term interest rates in EA have significant positive impact only on a handful countries in EU that are not part of the EA.

### 5. Time series Analysis

The analysis so far has focussed on the relationships between interest rates of different economies or better different kinds of interest rates within the same country. This section is focussed on the time series aspect of the data. Since the data represent the value of the macroeconomic variable for a specific time period, the continuous set of data can be considered a time series. This section analyses the time series data using trend analysis. The presence of stationarity in time series is tested using autocorrelation function.

### 5.1. Trend Analysis

It is essential to understand the nature of time series data in order to enter it into forecast models. Most of the forecast models assume that the time series follow a linear trend. However it may not be true. Linear regression models assume that the independent variables have a linear causal impact on the dependent variable. However time series models are built on the basis of the historic values of the same series. The purpose of these models is to forecast the future course of the data series. Some of the most popular methods of forecasting used are linear, quadtratic and exponential. It is customary to begin with the linear model to ascertain the nature of the model. The accuracy of the model is ascertained by comparing modelled data to the actual data. Some of the key measures of accuracy of the forecast model are MAPE (Mean Absolute Percent Error), Mean Absolute Deviation (MAD) and Mean Squared Deviation (MSD). When these measures of error are minimised the model is stated to be get better. This section builds the forecast models for UK interest rate and EU interest rates.

### 5.1.1. 3m LIBOR

First, linear model is attempted for UK interest rates. Following is the typical structure of a linear model

Xt = b0 + b1t + e

Where

Xt = Data value for period t

t = time period

The value of b0 and b1 are ascertained using Minitab procedures for linear trend analysis. Following chart shows the equation and the graph for interest rate data series for UK

As can be observed, the forecasted value when fitted against the actual value, is quite off and does not represent the underlying trend in the data. The negative coefficient means that the slope of the line is negative and so the data is decreasing over time. However as can be observed from the data, the data series is actually an increasing function and not a decreasing function. Besides, the high values of MAD and MSD clearly indicate that the linear forecast model may not be appropriate for the UK interest rate data series.

Quadratic forecast model is used to ascertain if the data series of UK interest rates fit well into the quadratic function.

A quadratic model is built on the basis of the following structure.

Xt = b0 + b1 t + b2 t2+ e

Where

Xt = Data value for period t

t = time period

t2 = squared value of time period.

Following chart shows the quadratic model of the data series representing UK interest rates.

As it can be observed easily from the graph shown above, the quadratic model is able to predict the movement of the time series quite accurately. The MAD and MSD error measures are both significantly lower than that while using linear trend model and so quadratic model is chosen as the proper fit the UK interest rate data series. Following is the model that is obtained using quadratic modelling

Yt = 6.758 - 0.10561*t + 0.001045*t2

Where

Yt is the 3 month LIBOR during time period t

Exponential smoothing can be used to generate better fit for the data than quadratic modelling and linear modelling. Exponential smoothing is a process, which learns from the differences between the forecasted value and the actual value and adjusts the forecasting factor to represent the difference. Thus with every subsequent data item the model evolves and produces better forecasts. This is the reason for the wide popularity of exponential smoothing as the forecasting method. It is also observed that this method has the ability to take into account the changes that take place in the external environment and so the exponential smoothing method always includes the latest set of data in its forecasting model.

Exponential smoothing typically takes the following form

Yt = a.xt-1 + (1-a) Yt-1

Where

a is the smoothing factor

Following chart shows the alpha value as calculated using the exponential smoothing method. It also shows the close correlation between the fitted values and the actual values.

It can be observed that the Alpha value is positive at 1.4891 and the MAD is 0.0810.This MAD can be compared to the MAD value of 0.3406 obtained from quadratic model method. Thus it is easy to note that exponential smoothing does a better job of matching the actual values. Using an alpha value of 1.4891 it may be possible to accurately forecast the future changes in 3 month LIBOR.

### 5.1.2. 3m EURIBOR

The trend analysis of EURIBOR is also performed to ascertain the nature of underlying trend in the time series. As with the case of LIBOR, the EU interest rates are first fit into a linear model. Following is the result obtained.

The linear model estimated from the time series of 3 month EURIBOR is as follows

Yt = 3.754 - 0.0105t

Where

Yt is 3 month EURIBOR.

It is noted that the MAD and MSD values are significantly high. Besides, the above graph clearly shows that the fitted line is quite different from the actual line and so the model is not capable of forecasting the future movements in EURIBOR accurately. Quadratic modelling method is used to obtain a different model for the same data series. Following is the chart, which shows the quadratic model and its fit with the actual data.

It can be noted that the MAD and MSD for quadratic model is significantly less than those for the linear model estimated. Thus the forecast model for 3 month EURIBOR interest rate data series can be stated as follows:

Yt = 5.323 - 0.10467*t + 0.000951*t2

Where

Yt is the 3 month LIBOR during time period t

As seen in the case of LIBOR, it may be possible to obtain beter forecasting by usng the exponential smoothing method for EURIBOR as well. Therefore it is necessary to obtain alpha values for Euribor for the period under consideration. Following chart shows the exponential smoothing alpha value as well as the fit between the actual data and fitted values of the data series.

The smoothing constant obtained for EUROBOR is 1.89234. It can be noted that the MAD value for the forecasting done using exponential smoothing method is 0.06214 while it was 0.4845 for the quadratic model used earlier. Thus it is evident that the exponential smoothing method can produce more accurate forecasts. The alpha value to be used for accurate forecasting of EURIBOR is 1.89234.

### 5.2. Autocorrelation

Another property, which is necessarily studied while analysing the time series data is autocorrelation. Since the data series represents the changes in underlying variables over time, there is a very high probability that the subsequent changes may be dependent upon the previous changes in the series. Thus in the series, there may be significant correlation between one data item and subsequent data items. In order to ascertain if this property is present, typically the data series is correlated with itself at specific lags. It is noted that at lower lag levels, autocorrelation tends to be higher than at higher lag levels.

It is possible to conduct hypotheses tests to check if the data involves any significant autocorrelation at a specific lag level. Lung-Box test is commonly used to ascertain the extent of autocorrelation and its statistical significance. Following is the formula used for Ljung-Box test.

Q =

Where

N is the sample size

R2t is the autocorrelation at lag t

k is the number of lags that are tested

Following are the hypotheses that are tested

H0 : autocorrelation at various lags is equal to zero

Ha: autocorrelation at various legs is not equal to zero

Following graphs show the autocorrelation values of LIBOR and EURIBOR at different lag levels. The red lines denote the statistical significance limits. Any value of autocorrelaiton which is outside the limit means that the autocorrelation is statistically significant till that lag level.

At Lag level of 1, LIBOR has an autocorrelation coefficient of 0.9647 while EURIBOR has 0.9808. It can be noted that EURIBOR has a higher rate of autocorrelation than LIBOR. It is also noted that the autocorrelation for both the interest rates are statistically significant till lag level 7. The fact that EURIBOR has a higher degree of autocorrelation denotes that the changes in EURIBOR are highly dependent upon the previous values of the data series. On the other hand, the changes in LIBOR appear to be more random than EURIBOR.

### 5.3. Chapter Summary

Interest rate modelling in EA shows that both money supply and inflation rate do not have any significant relationship with short-term interest rates. This may be due to the lag that is observed between the changes in monetary variables and the changes in interest rate as induced by the central bank. A set of regression function carried out to ascertain the impact of changes in EURIBOR on changes in interest rates in different states in Europe shows that some countries such as Estonia, Latvia, Poland, Romania and UK show significant impact of EURIBOR in their interest rate decisions. Other countries have insignificant relationships. It is observed that exponential smoothing provides the best fit of the historic data for both LIBOR and EURIBOR. An analysis of the autocorrelation of these data series clearly shows that there is significant autocorrelation in both these data series with LIBOR exhibiting slightly more random changes than EURIBOR.

### 6. Conclusion

One of the most important objectives of the formation of EU is to create financial and monetary stability in the region. Besides, the recent behaviour of central banks to act in tandem while making significant changes to monetary policies inspired this research which attempts to study the behaviour of interest rates in Europe using popular quantitative techniques. Correlation analysis shows that the different short term interest rates within Euro Area have very high degree of correlation among themselves. On the other hand, only some countries have strong correlations among their interest rates among the other states of EU. The short term interest rates in UK and EA correlate significantly and so do the short term interest rates in UK and US. Regression analysis shows that money supply and inflation do not have any significant predictive values for the short term interest rates as the interest rates typically tend to move on the basis of long term changes to the macro economic variables. Finally, it is seen that the interest rates in some countries such as UK, Estonia, Latvia, Poland and Romania exhibit high degree of sensitivity to changes in the EA interest rates. The results overall lead to a conclusion that the al the interest rates in Europe do not move together or get influenced by each other. Only a handful of countries including EA, UK, Estonia, Latvia, Poland and Romania appear to have achieved measureable levels of monetary integration. This shows that EU still has a long way to go in their ambition to achieve financial and monetary integration. EA, UK and US share strong monetary relationships as expected on the basis of literature review. The time series analysis of LIBOR and EURIBOR shows that alpha value of 1.4891 and 1.8923 respectively can be used to obtain accurate forecasts using exponential smoothing methods. It is noted that EURIBOR has a higher degree of autocorrelation than LIBOR. In other words, LIBOR is more random than EURIBOR. The conclusion that can be drawn from this observation is that BOE has a habit of making some quick unexpected changes in monetary policy than ECB. This conclusion is hardly surprising, given the fact that BOE does not even publish a detailed report whenever the short-term discount rates are left unchanged by the Monetary Policy Committee (MPC).

The final conclusion that can be drawn from the statistical tests conducted in this brief research is that the interest rates in Europe exhibit mixed relationships. While some states such as EU, Poland, Latvia and UK share very strong relationships among their monetary policies, other countries appear to be mostly independent. Even within the European Union there are states such as Denmark and Bulgaria, which do not have any significant relationships in terms of interest rates. Thus, the observation made in the literature review, that EU states tend to have strong monetary relationships appears only partly justified by the actual data. However it should be noted that this research is based on a limited set of data and the results may be different when a longer time horizon is involved. One conclusion, which emerges strong and resounding, is that both EMU and UK share very strong monetary relationships, which are reflected in the empirical analysis. This also matches the observations made by a number of researchers earlier.

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