ÖREBRO UNIVERSITY Örebro Business School Economics, Master Thesis Supervisor: Pär Österholm Examiner: Dan Johansson Fall 2017
Foreign macroeconomic fluctuations and monetary policy in
open economies
A study of US macroeconomic shocks on the United Kingdom and Sweden
Author:
Abstract
The UK and Sweden were among the first countries which adopted inflation targeting regimes in the early 1990s. Since inflation targeters have imperfect information about the economy when they determine interest rates, it is of interest to study the effect of different economic shocks on interest rates.
This paper investigates whether US macroeconomic fluctuations as proxies of the worldwide shocks have impact on monetary policy in the UK and Sweden. For this purpose, quarterly data for the period 1994:Q1-2016:Q4 is extracted. US real GDP growth, US inflation rate and US short-term interest rate are used as proxies of external variables. Domestic real GDP growth, unemployment rate, inflation rate and short-term interest rate for the UK and Sweden are used as domestic variables.
Vector Autoregression (VAR) models are implemented and impulse-response functions along with variance decompositions are analyzed in this study.
Major findings confirm the important role of US economic fluctuations on the short-term interest rate in the UK and Sweden. Foreign shocks increase domestic short-term interest rate in both countries. Among the external shocks, the US real GDP growth shock is the most important one which explains more than half of the contribution of external shocks. Monetary policy in the UK and Sweden reacts to fluctuations in order to offset the transitory effects of shocks.
Keywords: Monetary policy, foreign shocks, VAR, impulse-response functions, variance decompositions.
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1. Introduction
Exogenous disturbances or shocks to the macroeconomy affect the interest rate and monetary policy (Burda, 2013). By shock, we mean an unexpected and unpredictable event that has a positive or negative effect on the economy (Black et al, 2012). Some of these shocks are external and therefore more difficult to be tackled by domestic fiscal and monetary policies. A shock in the supply of oil can be named as an example of an external shock which can cause prices to rise rapidly, making it expensive to use for business purposes1.
The relation between external shocks and domestic monetary policy is widely studied in numerous studies, using different foreign shocks and focusing on different countries.
Summarized results of these studies confirm the effect of worldwide shocks on the domestic economy. The effect of US economic fluctuations is analyzed by Mackowiak (2007) who finds that external shocks (US monetary policy) are an important source of macroeconomic fluctuations in emerging markets. The effect of oil price shocks on domestic aggregate economy and monetary policy is studied in several countries including the US by Hamilton (1983). Hamilton and Herrera (2004) also claim that the effect of oil price shocks on the domestic economy is so great that it cannot be offset by monetary policy. As McCallum (1997) emphasizes, limited knowledge of how the macroeconomy works is the key problem for monetary policy formation. Thus, the policy design problem is to characterize how the short-term interest rate which is the instrument of monetary policy, should adjust to the current state of the economy (Clarida et al, 1999).
Respecting this background, the purpose of my study is to investigate whether external shocks can affect domestic monetary policy or not. The focus of this study is on the monetary policy in the UK which is the fifth largest economy in the world and in Sweden which is a small open economy. According to Nicky Morgan (former financial secretary to the treasury of the UK), Europe`s economy is vulnerable to external shocks (Evening post, 2014). Richard Sharp, a member of the UK central bank's financial policy also emphasizes on the vulnerability of the UK economy to external shocks (The Gardian, 2014). Becker et al (2012) have a similar attitude towards the economy of Sweden. They declare that Swedish economy is significantly vulnerable to financial shocks originating abroad.
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The question of this study can hence be formulated as:
Do US macroeconomic fluctuations affect monetary policy in the UK and Sweden?
The reason why particularly these two countries are chosen in this study is that both are open economies which have been EU members during the period studied in this article and have lots of common characteristics regarding European and WTO (World Trade Organization) regulations. But because of different size and power in the world economy, they may be affected differently by external shocks. Ball (2000) emphasizes that optimal monetary policy rules in the open economies differ from closed economies.
Furthermore, both countries have more than two decades experience with inflation targeting. New Zealand’s central bank became the first to declare target inflation in april 1988. Within just a few years, central banks of several other countries – Canada, the United Kingdom, Sweden and Australia adopted similar frameworks (Beechey & Österholm, 2010).
Respecting features of monetary policy, selection of relevant explanatory variables is a major challenge. As Calmfors et al (1997) argue, demand on monetary policy depends on the nature of shocks. These shocks which affect domestic monetary policy can be from sudden oil price changes to foreign income or monetary policy. I aim to focus on US variables as proxies of foreign factors in this study, because the economy of the US is the largest in the world, and this economy represents a quarter share of global economy (World economic forum, 2017). Moreover, the association between the US economy as the proxy of world economy with domestic variables is studied in several previous studies, including Österholm and Zettelmeyer (2008), Abrego and Österholm (2010), Mackowiak (2007) and Zulkefly and Bakri (2016).
This paper aims to achieve its purpose by using VAR models in which impulse-response functions and variance decomposition of forecast errors are analyzed. With respect to variance decomposition of forecast errors which indicate the percentual amount of contribution of each variable, incorporating some relevant domestic variables can help me gain more detailed information about the effect of external shocks in comparison to internal ones. Therefore, some domestic macroeconomic variables are also incorporated in the study.
Quarterly data for the period 1994:Q1-2016:Q4 is used for all variables. US real GDP growth, US inflation rate and US short-term interest rate are used as proxies of external variables.
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Domestic real GDP growth, unemployment rate, inflation rate and short-term interest rate for the UK and Sweden are used as domestic variables.
The main results are as follows:
External shocks, i.e. US real GDP growth, US inflation rate and US short-term interest rate explain more than half of the forecast error variance of the domestic short-term interest rate of the UK and Sweden at the sixty-quarter forecast horizon (0.55 of the Swedish interest rate and 0.67 of the UK interest rate). Of these external shocks, the US real GDP growth shock is the most important variable, explaining more than half of the contribution of external shocks (0.65 of the contribution of external shocks in Sweden and 0.58 in the UK).
Impulse-response functions confirm the dynamic impact of various external shocks on domestic interest rates. A standard deviation shock to the US real GDP growth leads to a increase of 0.30 percentage point in the Swedish interest rate and 0.35 percentage point in the UK interest rate after four and five quarters respectively. A similar shock to the US inflation rate leads to an increase of 0.14 and 0.12 percentage points in the respective country after two quarters, while a shock to the US interest rate increases respective country`s interest rate by 0.17 and 0.19 percentage points after seven and ten quarters.
The remainder of this paper is organized as follows: Section 2 presents related theoretical background. Section 3 summarizes some related previous studies. Section 4 presents collected data. Section 5 presents briefly the basic structure of the model. Section 6 describes the empirical implementation of the model. Section 7 discusses the estimation results, including impulse-response functions and variance decompositions. Section 8 is a short discussion and finally section 9 concludes.
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2. Theory
2.1 Background
A stream of empirical work was done in the late 1980s implying broad agreement about the impact of choice of monetary policy on aggregate activity (Clarida et al, 1999). One of those empirical works written by the American economist John Taylor is an influential article which suggests that central bank can simply adjust short-term interest rate in reaction to observed deviations of inflation and output from their target (Sorensen & Whitta-Jacobsen, 2010). Paying attention to the "reaction to deviation", this emphasizes on changing the short-term interest rate once after demand or supply shocks occur.
The Taylor rule framework is i= r + +h( - )+b( - ) where i stands for short-term
nominal interest rate, r stands for real interest rate, and note actual and target inflation rate, and stand for actual and potential output respectively and finally h and b are positive coefficients (Sorensen & Whitta-Jacobsen, 2010).
Taylor rule has inspired many researchers to develop and modify this benchmark ruleso that it matches to different economies. Inspired by the Taylor rule, Clarida et al (1999) provide theoretical underpinnings by incorporating the techniques of dynamic general equilibrium theory in real business cycle analysis. Clarida et al (1999) summarize what they have learned from recent research on monetary policy in a pedagogical way. They implement a monetary policy design problem in a simple theoretical model. Starting with a baseline model in order to characterize some broad principles which are vital for an optimal policy management, they continue to improve their model by adding various real world complications. Different scenarios are studied with respect to presence or absence of commitments along with practical problems in real world.
The model described here is based on how Clarida et al (1999) have improved the baseline model in the presence of imperfect information.
2.2 Model
In the baseline framework in the new Keynesian model studied by Clarida et al (1999), represents the output gap gained from the difference between and which stand for actual and potential output respectively ( = - ), is the period t inflation rate, defined as the
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percentage change in the price level from t-1 to t, and is the nominal short-term interest rate. Each variable is expressed as a deviation from its long-run level (Clarida et al, 1999). So, the baseline model can be presented in terms of two separate equations:
=-φ[ - ]+ + (2.1)
is the IS curve that relates the output gap expectation inversely to real interest rate, where φ corresponds to the intertemporal elasticity of substitution and the disturbance is a function of expected changes in the government purchases relative to the expected changes in the potential output. Since shifts IS curve, it can be interpreted as a demand shock.
= λ +β + (2.2)
is the Phillips curve in form of expectations2 where is a cost-push shock and λ represents output loss (Clarida et al, 1999).
Disturbance terms, and can be defined as:
=μ + (2.3)
=ρ + (2.4)
where 0≤ μ, ρ≤1 and both and are i.i.d random variables with zero mean and variances
and respectively (Clarida et al, 1999).
This is the baseline model presented by Clarida et al (1999) which can be regarded as benchmark. From the benchmark model, new equations are derived with respect to different situations. In practice, the central bank has imperfect information due to imperfect obeservability. Thus, we assume that it cannot directly observe all different shocks currently hitting the economy (Sorensen & Whitta-Jacobsen, 2010). Therefore, in this study, the baseline model gets modified with regard to an "imperfect information" situation. Supposing that the central bank cannot observe the contemporaneous values of output, inflation or any of the random shocks, stands for the central bank`s information set at the time it fixes the interest rate that prevails at time t. The optimality condition for monetary policy can therefore be expressed in terms of expected as opposed to realized target variables (Clarida et al, 1999).
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E{ | }= -λ E{ | } (2.5)
where ɑ is the relative weight on the output deviation. In this situation with imperfect information, the IS and Phillips curve equations are given by:
= -φ[ |Ώ)- ]+ + (2.6)
= λ +β + (2.7)
Supposing there is no serial correlation in the cost-push shock as well as demand shock, so = and = When = : = (2.8) = (2.9)
meaning that the output gap and inflation rate at time t are the functions of supply-side shock. So the implied equilibrium values of the target variables under imperfect information are given by:
= + [
+ ]= (2.10)
=[1+ ] + = + (2.11)
meaning that the output gap under the imperfect information is a function of demand-side shock, while inflation rate under the imperfect information is a function of both demand and supply-side shocks. Clarida et al (1999) note that imperfect information implies greater volatility of inflation, since the central bank cannot immediately act to offset the impact of shocks. The net effect on the volatility of the output gap is on the other hand unclear.
Considering {μ, ρ}=0, i.e. no serial correlation in and exists which implies that shock in one period cannot affect the economy in future, equation (2.6) can be rewrite as follow:
= -φ + (2.12)
Ball (1998) says that in an open economy, policy can affect inflation in one period through the direct exchange rate channel. When policy makers minimize the variance of inflation, they
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set the next period`s expected inflation to zero ( =0). A similar motivation can be brought for minimizing the variance of the output gap =0). Sorensen and Whitta-Jacobsen (2010) argue that central bank focuses on minimizing fluctuations in the inflation and output gap so that
= = 0. So, equation (2.6) can be modified to equation (2.12)3.
Substituting =
and = , solving for , we gain:
=
+ (2.13)
where the monetary policy instrument is a function of shocks ( , )4. Size of the nominal interest rate depends on φ and λ, i.e. the size of intertemporal substitution of consumption, along with output loss (Clarida et al, 1999).
The new Keynesian model discussed by Clarida et al (1999) analyzes monetary policy in a closed economy. In order to see differences from an open economy, this model is compared with monetary policy of an open economy studied by Ball (1998) and Ball (2000). By adding the real exchange rate to the IS and Phillip curve, Ball (1998) concludes that inflation targeting and Taylor rules must be modified quite a bit in order to perform powerfully in an open economy, meaning that the policy instrument should be based on both the interest rate and the exchange rate.
Ball (2000) discusses the differences between open and closed economies regarding stabilization of output and inflation, using monetary policy. He emphasizes that optimal monetary policy rules in open economies differ from optimal rules in closed economies. Adding an exchange rate term to the Taylor rule and targeting long-run inflation along with choosing between the interest rate and the monetary condition index are his suggestions for open economies. He concludes that the nature of shocks to the exchange rate determines whether the interest rate or a monetary condition index keeps output and inflation stable.
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3. Equation (2.12) does not exist in Clarida.et.al (1999). Based on motivations in Ball (1998), and Sorensen and Whitta-Jacobsen (2010),
and are set equal to zero, so that equation (2.6) can be rewritten as equation (2.12).
4. Equation (2.13) indicates that nominal interest rate is a function of shocks. In these modifications, I have been inspired by a master thesis written by Gajic.R (2012).
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2.3 Background of using the VAR models in macroeconomy
Studying the US unemployment rate, inflation rate and interest rate, Stock and Watson (2001) claim that the VAR model provided by Sims (1980) is a powerful and reliable tool in everyday use, regarding data description and forecasting. But when it comes to policy analysis, identification problem occurs. This means that policy makers require differentiating between correlation and causation. This problem cannot be solved by statistical tools, even by a powerful one like VAR. Rather, economic theory or institutional knowledge is required to solve the identification, i.e causation versus correlation.
Additionally, analyzing the response of US monetary policy to economic disturbances, Bernanke et al (1997) summarize two common findings in monetary policy literature based on VARs. First, identified shocks to monetary policy explain relatively little of the overall variation in output (typically, less than 20 percent). Second, most of the observed movements in the instruments of monetary policy are endogenous, that is changes in monetary policy are largely explained by macroeconomic conditions.
Furthermore, VAR models are widely used for analyzing the relation between different external and domestic macroeconomic variables.
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3. Previous studies
In recent years, there have been a large number of studies written in order to analyze the possible effects of external shocks on domestic macroeconomic variables or monetary policy in different countries. Introducing the VAR model by Sims (1980) seems to have provoked an interest in such studies. All reviewed articles in this thesis are written after providing of VAR model by Sims (1980), and most of them use some form of VAR model.
In a thorough study, Bernanke et al (1997) analyze the US economy by using a VAR model. The effect of oil price shocks on domestic monetary policy is studied where "net oil price increase" variable is used as the suitable indicator of external shocks. Domestic fund rate, real GDP, the GDP deflator and CPI are among domestic variables. The study uses monthly data which covers three decades (1966-1975, 1976-1985, 1986-1995) and results show the important effect of oil price shocks on US monetary policy. Bernanke et al (1997) state that tightening of monetary policy which is the reaction to oil price changes affect the economy.
Hamilton and Herrera (2004) use also a VAR model to analyze the correlation between world oil price shocks and monetary policy in the US. Oil price, real GDP growth, CPI and interest rate are used in this study. Quarterly data for the period 1978-1993 is examined by Hamilton and Herrera (2004) who find that the effect of oil price shocks on domestic economy is so great that it cannot be offset by monetary policy.
A similar method is used by Österholm and Zettelmeyer (2008) who examine how sensitive Latin American GDP growth is to external developments. Quarterly data for the period 1994-2007 and a BVAR (Bayesian vector autoregressive) model is used in this study in order to analyze the effect of external demand, commodity prices and global financial conditions on GDP growth in the weighted index for some Latin American countries. Österholm and Zettelmeyer (2008) conclude that although financing shocks explain more than half of the effect of external shocks, external growth shocks and commodity price shocks are important as well.
Using quarterly data from 1995:Q2 to 2007:Q2, Abrego and Österholm (2010) examine the sensitivity of Colombian GDP growth to both domestic and external variables. In this study, variables capturing both domestic and external determinants of growth are included in BVAR model. Results show that domestic investment climate and fiscal policy along with global economic growth are the most important factors behind Colombian growth.
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A Bayesian approach is used by Allegret and Benkhodja (2011) to investigate the dynamic effect of four external shocks, namely oil price shock, USD/EUR exchange rate shock, international inflation shock and international interest rate shock as well as the reaction of domestic monetary policy in Algeria. Their findings state that both domestic output and inflation can be better stabilized by a core inflation5 monetary rule.
Zenansi and Benhabib (2013) study the importance of external shocks in domestic and external variable`s fluctuations for a sample of three North African countries by using VAR estimation and quarterly data during the period 1990-2010. Real GDP, financial integration, foreign direct investment and export are among the used variables. Their findings indicate that external shocks negatively affect domestic growth of named countries. Gained results from impulse-response functions and variance decompositions show that these countries are sensitive to external shocks.
Zulkefly and Bakri (2016) investigate the effect of foreign shocks on domestic macroeconomic fluctuations and monetary policy in Malaysia. Furthermore, they examine how domestic monetary policy could deal with external shocks. Macroeconomic variables studied in this case include world oil price, foreign income and foreign monetary policy shocks. All data are at a monthly frequency spanning from January 1980 until May 2009. They implement a SVAR (Structural vector autoregressive) model in their analysis. Results show an important role played by foreign shocks on domestic macroeconomic variables and monetary policy. In addition, domestic monetary policy has a vital role in minimizing the negative effect of external shocks on domestic economy.
These are some studies which analyze the possible effect of external shocks on domestic macroeconomic variables or monetary policy. All reviewed studies use some type of VAR model in their analysis. Stock and Watson (2001) on the other hand study the relation between three domestic variables, i.e. US inflation rate, unemployment rate and short-term interest rate using a VAR model for a monthly data set which covers the period of 1960:M01-2000:M05.
The purpose of this study is to figure out how well a VAR can address four macroeconometric tasks. These tasks are: 1. To describe and summarize macroeconomic data. 2. To make ___________________________________________________________________________
5. Core inflation is the rate of inflation calculated to exclude certain items that are subject to sudden and short-lived price movements, mainly food and energy. Core inflation is considered a better indicator of overall long-term trends than so-called headline inflation. (Black et al, 2012). By core inflation, Allegret and Benkhodja (2011) mean inflation in the non-oil goods sector.
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macroeconomic forecast. 3. To quantify what can be done about the true structure of macroeconomy. 4. To give advice to macroeconomic policymakers. They conclude that the VAR has proven to be a powerful and reliable model in case of analyzing data and forecasting.
Ribba (2006) uses a VECM (Vector Error Correction Model) model to study dynamic interaction of the same three domestic variables, i.e. US inflation rate, unemployment rate and short-term interest rate, at different frequencies. Monthly data covering the periods of 1961-1979 and 1980–2001 is used in this study. The result states a weak reaction of the interest rate to movements in inflation and unemployment rate.
To sum up, the effect of different external shocks on domestic macroeconomic variables and monetary policy in different countries are investigated in several papers. The most common used method is some form of the VAR model. Summarizing results, two main conclusions can be drawn: 1.Foreign shocks have impact on the behavior of domestic macroeconomic variables and monetary policy. 2. The VAR is a powerful and reliable model in analyzing data and forecasting.
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Table 3.1 Summary of previous studies
_________________________________________________________________________________________ Study Method Result
__________________________________________________________________________________________ Bernanke.et.al (1997) VAR Oil price shocks affect US monetary policy.
Hamilton and Herrera (2004) VAR Oil price shocks affect US monetary policy.
Österholm and Zettelmeyer (2008) BVAR Financing shocks explain more than half of the
effect of external shocks.
Abrego and Österholm (2010) BVAR Domestic investment climate and fiscal policy along with global economic growth are the most important factors behind domestic growth.
Allegret and Benkhodja (2011) BVAR Domestic output and inflation can be better stabilized by core inflation monetary rule.
Zenansi and Benhabib (2013) VAR External shocks negatively affect domestic growth.
Zulkefly and Bakri (2016) SVAR Foreign shocks play an important role on
domestic macroeconomic variables and monetary policy.
Stock and Watson (2001) VAR VAR is a powerful and reliable model for analyzing data and forecasting.
Ribba (2006) VECM Interest rate reacts weakly to movements in
inflation and unemployment rate.
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4. Data
4.1 Data description
As mentioned previously, although the purpose of this thesis is to investigate the effect of external fluctuations on domestic monetary policy in the UK and Sweden, some relevant domestic variables are also included in the VAR models in order to distinguish the effect of external variables.
Quarterly data for the period 1994:Q1-2016:Q4 is used in this study and the choice of variables is based on those variables which are associated with monetary policy according to the Taylor rule, Phillip curve and new Keynesian theory. Moreover, all chosen variables are used in previous studies. Variables used in this study are: real GDP growth for the US, Sweden and the UK, inflation rate for the US, Sweden and the UK, short-term interest rate for the US, Sweden and the UK, and unemployment rate for the Sweden and the UK.
Used data in this study is in the form of quantitative secondary data which is extracted from different databases. Nominal short-term interest rate, real GDP growth and inflation rate based on CPI6 for all three countries are extracted from OECD. UK unemployment rate is brought from the UK office for national statistics and Sweden unemployment rate is extracted from FRED.
Data is quarterly data for the period 1994:Q1-2016:Q4 which consists of 92 time series observations for each variable as seen in the table 4.1. The reason why the time period studied in this paper starts at 1994 is because the UK and Sweden adopted their inflation targeting regimes on October 1992 and January 1993 respectively. Fromlet (2010) argues that it takes some time for this regime change to fully affect the economy. In this paper, it is assumed that it takes at least one year for inflation targeting to show its effect on the whole economy.
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6. Inflation rate is measured by consumer price index (CPI) where 2010 is the base year (OECD, 2017). Inflation rate is given as percentage changes compared to base year by OECD, not as index.
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Table 4.1 Descriptive statistics
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Variable Number of observations Mean % Standard deviation % Min % Max% __________________________________________________________________________________________ Interest rate US 92 2.88 2.35 0.11 6.63 Inflation rate US 92 2.24 1.14 -1.6 5.3 Real GDP growth US 92 0.61 0.61 -2.1 1.9 Unemployment rate UK 92 6.42 1.43 4.7 9.9 Interest rate UK 92 3.81 2.44 0.38 7.58 Inflation rate UK 92 1.98 1.04 0 4.8 UK real GDP growth 92 0.54 0.6 -2.3 1.8
Unemployment rate Sweden 92 7.52 1.20 5.1 10.3
Interest rate Sweden 92 2.88 2.35 -0.78 9.11
Inflation rate Sweden 92 1.16 1.18 -1.4 4.3
Sweden real GDP growth 92 0.67 0.91 -3.7 2.4
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Note: This own structured table shows descriptive statistics over the quarterly data for all external and domestic variables for the period 1994:Q1-2016:Q4. Sources are OECS, FRED and UK office for national statistics. Eviews program is used for preparing this table.
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4.2 Unit root tests
With respect to whether each time series has stochastic trend or not, appropriate ADF (Augmented Dickey-Fuller), Phillip-Perron and KPSS (Kwiatkowski-Phillips-Schmidt-Shin) unit root tests were run for all time series. Null hypothesis in the first two tests is that the time series in question has a unit root vs. the alternative hypothesis is in favor of stationarity. The KPSS test on the other hand has stationarity under null hypothesis (Österholm & Zettelmeyer, 2008).
Table 4.2 Unit root tests (Results at 5 percent level)
__________________________________________________________________________________________ Variable ADF Phillip-Perron KPSS
__________________________________________________________________________________________ Interest rate US non-stationary non- stationary stationary Inflation rate US stationary stationary stationary
Real GDP growth US stationary stationary non-stationary
Unemployment rate UK non- stationary non- stationary stationary Interest rate UK stationary non- stationary stationary Inflation rate UK stationary non- stationary stationary UK real GDP growth stationary stationary stationary
Unemployment rate Sweden non- stationary non- stationary stationary Interest rate Sweden stationary non-stationary stationary
Inflation rate Sweden stationary stationary stationary
Sweden real GDP growth stationary stationary stationary
_________________________________________________________________________________________________________________ Note: In this own structured table, results from three different tests are shown. Eviews program is used, and the gained numbers from each test can be found in table A.1 in the appendix.
As seen in the table, interest rates for the UK, the US and Sweden are not stationary according to Phillip-Perron test, while the US interest rate is not stationary even according to ADF test. Beechey, Hjalmarsson and Österholm (2009) discuss that nominal interest rates are highly persistent and the poor power of traditional univariate Dickey–Fuller type tests cannot be reliable. Although, nominal interest rates have varied substantially in recent decades, they have wandered within reasonable bounds over the long-run. Furthermore, private nominal interest rates are in a stable range which is impossible if interest rates possessed a unit root.
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By applying near-integration methods of co-integration and testing the expectations hypothesis on term-structure data from numerous countries, Beechey, Hjalmarsson and Österholm (2009) conclude that nominal interest rates are likely to be stationary.
The UK and Swedish unemployment rates are not stationary according to ADF and Phillip-Perron tests, but stationary according to KPSS test. When unit root tests are applied to unemployment rates, Gustavsson and Österholm (2007) find mixed evidence for unit root in different countries, depending on which unit root test and which measure is applied. Their results show overall transitory (temporary) effect of one-time shock on unemployment rate which implies that unemployment rate is stationary.
In this study, stationarity of all included variables at 5 percent level is confirmed at least by one of the tests. Relying on the results of unit root tests and stationary nature of interest rate and unemployment rate discussed in several scientific papers including Beechey, Hjalmarsson and Österholm (2009) and Gustavsson and Österholm (2007), I conclude that all time series in this study are stationary.
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5. Method
In this study, VAR models are used to investigate the effect of external shocks on domestic monetary policy. Before going to the practical implementation of the VAR model, I would briefly explain what VAR model is.
5.1 Vector Autoregression model (VAR)
Before 1980, traditional econometric analysis used to rely on the specification and estimation of large scale structural simultaneous models, in order to analyze the interactions between sets of macroeconomic variables. These traditional models suffered from several shortcomings and were criticized by a number of economists including Sims (1980, 1982) who emphasized two methodological weaknesses: 1. Specification of simultaneous equations systems was largely based on the aggregation of partial equilibrium models, without any concern for the resulting omitted interrelations. 2. The dynamic structure of the model was often specified in order to provide restrictions necessary to achieve identification of the structural form (Amisano & Giannini, 1997).
Motivated by these shortcomings, Sims (1980) provided the Vector Autoregression (VAR) model. The VAR is a multivariate autoregression with n-equation, n-variable linear model in which each variable is explained by its own lagged value, plus past values of the remaining
n-1 variables. The VAR provides a systematic way to capture rich dynamics in multiple time
series (Stock & Watson, 2001).
This model is used to capture the interaction of several endogenous time series. In other words, the VAR is a forecasting model by which the way how some endogenous factors interact and influence the future path of each other is investigated by introducing a multivariate AR(ρ) model (Becketti, 2013). VAR models have several advantages; for example, they impose very few restrictions on the dynamics of the system and are considered to perform reasonably well in forecasting (Abrego & Österholm, 2010).
While in an autoregressive model, we model a single series ( ), in terms of its own past, in vector autoregressive models, several series in terms of their past are modeled. Suppose having two series, and , a vector autoregression consists of equations that look like
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and
= + β + ρ + β + ρ + ....+ (5.2)
where each equation contains an error that has zero expected value given past information
on y and z ( ~WN(0, ) (Wooldridge, 2012).
5.2 Impulse-response functions
An important device which makes it possible to understand the dynamic properties of vector autoregressions of interest to forecasters, is the impulse-response function (Diebold, 2006). Impulse-response functions trace out the response of current and future values of each of the variables to one standard deviation shock to the current value of each of the VAR errors, assuming that this error returns to zero in subsequent periods and all other errors are equal to zero (Stock & Watson, 2001). In fact, VAR errors are regarded as transitory shocks with transitoryeffects7.
To illustrate the situation more concrete, suppose a bivariate VAR (1) case.
= + + (5.3) = + + (5.4)
where ~ WN(0, ), ~ WN(0, ), and cov ( , ) = , meaning that error terms ( ) are white noise8 distributed with zero mean value and variance of ( ).
The standard moving average representations are:
= + +... (5.5)
= + +... (5.6)
As in the univariate case, it is useful to adopt a different normalization of the moving average representation for impulse-response analysis. The multivariate analog of the univariate normalization by standard deviation is called normalization by the Cholesky factor (Diebold, 2006). In the resulting vector moving average representation, the innovations of transformed system are in standard deviation units. Better said, the question is "How does a standard deviation rise to affect , now and in the future, for all the various combinations
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7. A shock is permanent if it has a long-run effect, otherwise it is said to be transitory with no long-run effect ( Black et al, 2012). In other words, a transitory effect is a temporary effect, not permanent.
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of i and j (Diebold, 2006. P, 233)?
Another important issue in the impulse-response functions is that the first equation has only one current innovation The second equation has both current innovations. So, the ordering of the variables in VAR model can matter (Diebold, 2006). Using economic theories in order to choose the ordering, or testing different orderings to decide about the robustness of the results can be useful.
What is discussed here is in the case orthogonalized impulse-response functions are implemented, where the ordering of the variables in the model is important. Generalized impulse-response functions on the other hand do not care about the ordering. As Pesaran and Shin (1998) argue, orthogonalized and generalized impulse-response functions differ in a number of respects. The generalized impulse-responses are invariant to the reordering of the variables in the VAR, but this is not the case with the orthogonalized ones where many alternative reparametrizations could be employed to compute orthogonalized impulse-responses, and there is no clear guidance as to which one of these possible parameterizations should be used. In contrast, generalized impulse-responses are unique and fully take account of the historical patterns of correlations observed amongst different shocks (Pesaran & Shin, 1998)
5.3 Variance decompositions
Variance decomposition is another way of characterizing the dynamics associated with VAR model. Variance decompositions which are closely related to impulse-response functions aim to answer to the question "How much of the h-step-ahead forecast error variance of variable i is explained by innovations to variable j, for h = 1, 2 , . . . ?" (Diebold, 2006. P,235). Better said, in each linear regression of a VAR model, how many percent of the dependent variable`s forecast error variance can be clarified by innovations to each of the regressors?
Impulse-response functions and variance decompositions are highly complementary and variance decompositions have a nice forecasting motivation (Diebold, 2006).
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6. Empirical implementation of the model
6.1 VAR (1)
As mentioned earlier, VAR is a forecasting model. Thus, we would like variables mean and covariance structure to be stable over time, in which case the series is called for covariance stationary (Diebold, 2006). Going back to the data section, we concluded that all variables are assumed to be stationary. Thus, relying on the stationary tests and Granger-causality9 test
which implies that all time series are useful for forecasting the interest rates, and interest rates are predictable by explanatory variables10, the VAR model is implemented in this study, using all variables in the original form, because using differences causes lost information.
There are different lag selection criteria for choosing an appropriate model. Most model selection criteria attempt to find the model with the smallest out-of-sample 1-step-ahead mean squared prediction error (Diebold, 2006). Because all of the criteria are effectively estimates of out-of-sample mean square prediction error, they have a negative orientation (the smaller, the better) (Diebold, 2006).
Among different lag selection criteria, in both cases (the UK and Sweden), SIC (Schwarz information criterion) and HQIC (Hannan-Quinn information criterion) preferred lag 1. But FPE (final prediction error) and AIC (Akaike information criterion) suggested different lag selections for the UK and Sweden`s cases. FPE and AIC preferred lag 2 in the UK case, and lag 7 in the Sweden`s case. According to Lutkepohl (2005), SIC and HQIC provide consistent estimates of the true lag order, while FPE and AIC overestimate the lag order with positive probability (Becketti, 2013).
Respecting seven variables and one lag (VAR (1)), the baseline equation for the Swedish interest rate as dependent variable looks like:
= + + + + + + + + (6.1)
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9. Granger-causality is a limited notion of causality where past values of one series are useful for predicting future values of another series (Wooldridge, 2012).
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Having seven variables and seven lags (VAR (7)), the baseline equation for the Swedish interest rate as dependent variable looks like:
= + + + + + +
+ (6.2)
Respecting seven variables and one lag (VAR (1)), the baseline equation for the UK interest rate as dependent variable looks like:
= +
+ + + + + + + (6.3)
Having seven variables and two lags (VAR (2)), the baseline equation for the UK interest rate as dependent variable looks like:
= +
+ + + + + + (6.4)
Where denotes US real GDP growth, stands for US inflation rate, stands for US Interest rate, represents Swedish GDP growth, denotes Swedish unemployment rate, is the inflation rate of Sweden, represents Swedish interest rate, represents UK GDP growth, denotes the UK unemployment rate, is the inflation rate of the UK and
represents the UK interest rate,
Similar regressions are run for all seven variables in each case, meaning that in each case (the UK and Sweden) there are seven equations in the model. In each equation, one variable is dependent variable and the lag forms of all seven variables are explanatory variables.
A VAR process is stationary if all roots of the process lie outside the unit circle. Equivalently, all the eigenvalues of the companion matrix must lie inside the unit circle (Becketti, 2013).
The results of VAR (1) and VAR (7) for the Sweden`s case and VAR(1) and VAR(2) for the UK case show regardless which lag criterion we respect, there is no unit root in the process, meaning that all of the eigenvalues of the companion matrix lie inside the unit circle. In this study, respecting SIC and HQIC criteria, I rely on the results of VAR (1) for both cases in the rest of this study.
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Figure 6.1 VAR(1) Sweden`s case, Figure 6.2 VAR(1) UK case,
characteristic Polynomial graphs characteristic Polynomial graphs
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Note: These figures are extracted from Eviews program after running VAR (1) models in Eviews.
6.2 Impulse-response functions and variance decompositions
As discussed earlier, ordering of the variables in the VAR model can matter because the first equation has only one innovation The second equation has both current innovations and so on (Diebold, 2016). In other words, the first variable affects contemporaneously all other variables in the model, while the second variable is supposed not to have any effect on the previous variable and just to affect contemporaneously the rest of the variables and so on. Finally, the variable which is ordered last, assumed not to be able to affect previous variables in the ordering. Hence, based on the economic theories and purpose of the study, external variables are ordered first in this study. The ordering of the variables in this study is: 1. US real GDP growth, 2. US inflation rate, 3. US interest rate, 4. Domestic real GDP growth, 5. Domestic unemployment rate, 6. Domestic inflation rate, 7. Domestic interest rate.
This ordering implies that US real GDP growth is assumed to contemporaneously affect itself and all other variables in the model, but the other variables are not assumed to be able to contemporaneously affect US real GDP growth. It means that a standard deviation shock to the US real GDP growth in the first equation will contemporaneously affect US real GDP, US inflation rate, US interest rate, domestic real GDP growth, domestic unemployment rate, domestic inflation rate, and domestic interest rate in all equations, but a standard deviation shock to the latter variables will not contemporaneously affect the US real GDP growth.
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Inverse Roots of AR Characteristic Polynomial
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
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On the other hand, domestic interest rate which is ordered last is assumed to be affected contemporaneously by the standard deviation shocks to all variables, but not to be able to affect any of the previous variables. Following many previous authors, Bernanke et al (1997) say that macroeconomic variables are the world-causally prior to interest rates. It implies that macroeconomic variables must be ordered before interest rate.
Clarida et al (1999) note that much of the available evidence suggests a lag of six to nine months in the effect of a shift in interest rate on output as well as a lag which covers one year and a half for the effect of the interest rate on the inflation rate. This also implies that the interest rate acts slower compared to inflation rate and output gap. Likewise, Sorensen and Whitta-Jacobsen (2010) emphasize that it takes about two years for a change in the interest rate to attain its maximum impact on the rate of inflation. In addition, as highlighted in the purpose of this thesis, the possible effects of variables on domestic interest rate is aimed to be analyzed in this paper. So, it is assumed that external variables can contemporaneously affect domestic ones, and among domestic variables, the interest rate is ordered last.
Although presented results in this study are based on the orthogonalized impulse-response functions with the ordering discussed previously, generalized impulse-response functions (generalized ones do not care about ordering of the variables) were also tried as a robustness test in order to capture differences in the figures. Almost no notable differences were observed in the figures.
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7. Results
In this section, I present the results for the UK and Swedish interest rates. Two sets of impulse-response functions and variance decompositions are presented in this paper, based on VAR (1) models for the UK and Sweden.
Full set of impulse-response functions and variance decomposition results are shown in Figures A1, A2, A4 and A5 in the appendix while impulse-response functions and variance decomposition results of the interest rates are shown in Figures 7.1-7.4 in this section.
Cholesky decomposition is used to identify the response of each variable to one standard deviation shock to each explanatory factor. The magnitudes of standard deviation shocks are as follows:
In Sweden`s case: about 0.53 percentage point for the US real GDP growth, 0.69 percentage point for the US inflation rate, 0.36 percentage point for the US interest rate, 0.66 percentage point for the Swedish real GDP growth, 0.20 percentage point for the Swedish unemployment rate, 0.39 percentage point for the Swedish inflation rate and 0.29 percentage point for the Sweden interest rate.
In the UK case: about 0.48 percentage point for the US real GDP growth, 0.67 percentage point for the US inflation rate, 0.36 percentage point for the US interest rate, 0.42 percentage point for the UK real GDP growth, 0.15 percentage point for the UK unemployment rate, 0.32 percentage point for the UK inflation rate and 0.27 percentage point for the UK interest rate. These shocks are estimated to have the effects which are presented in Tables 7.1, 7.2 and 7.311.
Table 7.1 presents results for the Swedish interest rate. In this table, the size of each standard deviation shock in percentage points, time after which maximum effect of each shock on interest rate is reached, and the percentage effect of each standard deviation shock on the interest rate are summarized. As the table illustrates, standard deviation shocks to the US and Sweden real GDP growth have the most significant effects to the Swedish interest rate.
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11. Responses of all seven variables to different impulses (for the UK and Sweden) can be analyzed, using full set of impulse-response functions and variance decompositions in the appendix. But for the purpose of this study, just responses of domestic interest rates (for the UK and Sweden) to seven impulses (standard deviation shocks to explanatory variables) are of interest.
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Table 7.2 presents results for the UK interest rate. As observed in the table, standard deviation shocks to the US and UK real GDP growth have the most significant effects on the UK interest rate while the UK unemployment rate shows no significant effect.
Looking at the time after which maximum effect of each shock to interest rate is reached, we observe that the Swedish interest rate reacts more quickly to the shocks compared to the UK interest rate.
Table 7.3 shows variance decompositions of forecast errors in a forecast horizon of sixty-quarters. As this table illustrates, shocks to the US real GDP growth, domestic real GDP growth and US interest rate contribute significantly to the forecast error variance of the UK and Swedish interest rates. Domestic unemployment rates and inflation rates show no significant contributions to the forecast error variances. The US inflation rate seems not to be a significant variable either since a shock to the US inflation rate contributes just to 8 percent of the forecast error variance of the UK interest rate and 3 percent of the forecast error variance of the Swedish interest rate.
External shocks, i.e. US real GDP growth, inflation rate and short-term interest rate explain more than half of the forecast error variance of the domestic short-term interest rates in the UK and Sweden at the sixty-quarter forecast horizon (0.55 of the Sweden interest rate and 0.67 of the UK interest rate). Of these external shocks, the US real GDP growth shock is the most important variable, explaining more than half of the contribution of external shocks (0.65 of the contribution of external shocks in the Sweden and 0.58 in the UK).
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Table 7.1 Response of the Swedish interest rate to impulses
__________________________________________________________________________________________ Explanatory variable Size of standard Time after which Percentage effect of a deviation shock (in maximum effect is standard deviation shock
percentage point) reached on domestic interest rate __________________________________________________________________________________________
Real GDP growth US 0.53 4 0.30
Inflation rate US 0.69 2 0.14
Interest rate US 0.36 7 0.17
Sweden real GDP growth 0.66 3 0.31
Unemployment rate Sweden 0.20 2 -0.07
Inflation rate Sweden 0.39 3 0.15
Interest rate Sweden 0.29 10 0.14
__________________________________________________________________________________________
Note: In this own structured table, results of the orthogonalized impulse-response functions of short-term interest rate of Sweden are summarized. Ordering of the variables is as discussed previously. Quarterly data for the period 1994:Q1-2016:Q4 is used and Cholesky decomposition is adjusted for 60 coming quarters. Eviews program is used.
Table 7.2 Response of the UK interest rate to impulses
__________________________________________________________________________________________ Explanatory variable Size of standard Time after which Percentage effect of a deviation shock (in maximum effect is standard deviation shock percentage points) reached on domestic interest rate
__________________________________________________________________________________________ Real GDP growth US 0.48 5 0.35 Inflation rate US 0.67 2 0.12 Interest rate US 0.36 10 0.19 UK real GDP growth 0.42 5 0.31 Unemployment rate UK 0.15 9 0 Inflation rate UK 0.32 10 -0.07 Interest rate UK 0.27 11 0.12 __________________________________________________________________________________________
Note: In this own structured table, results of the orthogonalized impulse-response functions of UK short-term interest rate are summarized. Ordering of the variables is as discussed previously. Quarterly data for the period 1994:Q1-2016:Q4 is used and Cholesky decomposition is adjusted for 60 coming quarters. Eviews program is used.
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Table 7.3 Variance decomposition of forecast errors of the UK and Swedish interest rates ____________________________________________________________________________________ Explanatory variable Swedish interest rate UK interest rate ____________________________________________________________________________________ Real GDP growth US 36% 39%
Inflation rate US 3% 8%
Interest rate US 16% 20%
Domestic real GDP growth 19% 16%
Domestic unemployment rate 2% 4%
Domestic inflation rate 3% 2%
Domestic interest rate 21% 11%
Sum 100% 100%
_________________________________________________________________________________________________________________ Note: In this own structured table, results of the variance decomposition of forecast errors for short-term interest rate of the UK and Sweden in a forecast horizon of sixty-quarters are summarized. Percentage contribution of each explanatory variable to forecast error variance of the UK and Swedish interest rates are shown in this table. Eviews program is used.
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Figure 7.1 Impulse-response functions of the Swedish interest rate as dependent variable in the VAR (1) to Cholesky one standard deviation innovations to the error terms. ________________________________________________________________________________________________________
Note: These figures are gained from VAR (1) model in Eviews. In each figure, percentage effect can be observed on the vertical axel and the number of quarters can be seen on horizontal axel. Response of the Swedish interest rate to the standard deviation shocks to the US real GDP growth, US inflation rate, US interest rate, Swedish real GDP growth, Swedish unemployment rate, Swedish inflation rate and Swedish interest rate can be observed in the figures. -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_SWEDEN to REAL_GDP_GROWTH_US
-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_SWEDEN to INFLATION_US
-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_SWEDEN to INTEREST_RATE_US
-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_SWEDEN to REAL_GDP_GROWTH_SWEDEN
-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_SWEDEN to UNEMPLOYMENT_SWEDEN
-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 45 50 55 60
Response of INTEREST_RATE_SWEDEN to INFLATION_SWEDEN
-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_SWEDEN to INTEREST_RATE_SWEDEN
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Figure 7.2 Impulse-response functions of the UK interest rate as dependent variable in the VAR (1) to Cholesky one standard deviation innovations to the error terms.
____________________________________________________________________________________________________ Note: These figures are gained from VAR (1) model in Eviews. In each figure, percentage effect can be observed on the vertical axel and number of quarters can be seen on the horizontal axel. Response of the UK interest rate to the standard deviation shocks to the US real GDP growth, US inflation rate, US interest rate, UK real GDP growth, UK unemployment rate, UK inflation rate and UK interest rate can be observed in the figures.
-.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_UK to REAL_GDP_GROWTH_US
-.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_UK to INFLATION_US
-.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_UK to INTEREST_RATE_US
-.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_UK to REAL_GDP_GROWTH_UK
-.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_UK to UNEMPLOYMENT_UK
-.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_UK to INFLATION_UK
-.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 5 10 15 20 25 30 35 40 45 50 55 60 Response of INTEREST_RATE_UK to INTEREST_RATE_UK
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Figure 7.3 Variance decomposition of the Swedish interest rate as dependent variable in VAR (1).
________________________________________________________
Note: These figures are gained from VAR (1) model in Eviews. In each figure, percentage contribution of each variable to the forecast error variance of the Swedish interest rate can be observed on the vertical axel and number of quarters can be seen on the horizontal axel. Percentage contribution of the US real GDP growth, US inflation rate, US interest rate, Swedish real GDP growth, Swedish unemployment rate, Swedish inflation rate and Swedish interest rate to the forecast error variance of the Swedish interest rate can be observed in the figures.
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_SWEDEN variance due to REAL_GDP_GROWTH_US
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_SWEDEN variance due to INFLATION_US
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_SWEDEN variance due to INTEREST_RATE_US
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_SWEDEN variance due to REAL_GDP_GROWTH_SWEDEN
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_SWEDEN variance due to UNEMPLOYMENT_SWEDEN
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_SWEDEN variance due to INFLATION_SWEDEN
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_SWEDEN variance due to INTEREST_RATE_SWEDEN
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Figure 7.4 Variance decomposition of the UK interest rate as dependent variable in VAR (1).
________________________________________________________
Note: These figures are gained from VAR (1) model in Eviews. In each figure, percentage contribution of each variable to the forecast error variance of the UK interest rate can be observed on the vertical axel and number of quarters can be seen on the horizontal axel. Percentage contribution of the US real GDP growth, US inflation rate, US interest rate, UK real GDP growth, UK unemployment rate, UK inflation rate and UK interest rate to the forecast error variance of the UK interest rate can be observed in the figures.
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_UK variance due to REAL_GDP_GROWTH_US
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_UK variance due to INFLATION_US
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_UK variance due to INTEREST_RATE_US
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_UK variance due to REAL_GDP_GROWTH_UK
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_UK variance due to UNEMPLOYMENT_UK
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60
Percent INTEREST_RATE_UK variance due to INFLATION_UK
0 10 20 30 40 50 60 70 80 5 10 15 20 25 30 35 40 45 50 55 60 Percent INTEREST_RATE_UK variance due to INTEREST_RATE_UK
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8. Discussion
As noted in the method section, the VAR model lets us capture the interaction of all endogenous variables in the model. Focusing on the purpose of this thesis, responses of domestic short-term interest rates of the Sweden and UK to different shocks will be discussed in details.
Impulse-response functions suggest that central banks respond to domestic and external shocks in order to offset fluctuations. It takes shorter time for the Swedish central bank to react to fluctuations compared to the UK central bank since it takes less number of quarters for Swedish interest rate to respond to shocks. The transitory effect of shocks is confirmed by impulse-response figures in which the effects tend to die out after several quarters.
In the Swedish case, the short-term interest rate responds positively to the shocks on domestic real GDP growth and inflation rate and negatively to the unemployment rate in less than one year. Such reactions agree with Taylor rule and Phillips curve. Positive reaction of the interest rate to both domestic and external shocks can be traced back in the new Keynesian model since we concluded that interest rate is a function of shocks.
Similar results are gained in the UK case, though under longer time period. The negative response of the UK short-term interest rate to a shock to domestic inflation rate and no response of the UK interest rate to a shock to domestic unemployment rate are the only reactions which cannot be matched with theory.
In both cases, external shocks explain more than half of the forecast error variance of the domestic short-term interest rate. Such results are consistent with reviewed previous studies in which an important role of external shocks on domestic macroeconomic variables and monetary policy is confirmed12. Although, US real GDP growth plays the most noticeable role in explaining the forecast error variance of the domestic short-term interest rates, the US short-term interest rate and domestic real GDP growth are important as well. Effect size of the
___________________________________________________________________________
12. In previous studies, I did not find any article using exact the same variables which are used in this study, but all variables can be found in previous studies. The important role played by external shocks on domestic monetary policy is found in Bernanke et al (1997), Hamilton
and Herrera (2004) and Zulkefly & Bakri (2016) though proxies of external variables in these studies are not the same as used in my study.
The effect of external shocks on other domestic variables ( real GDP growth, unemployment rate and inflation rate) which are investigated and confirmed in some of previous studies, can be analyzed by using full set of impulse-response figures and variance decompositions which are in the appendix. But because the purpose of this study is to examine the effect of external shocks on domestic short-term interest rate, and domestic real GDP growth, unemployment rate and inflation rate are incorporated in the model just for letting me compare the percentage effect of external shocks to the percentage effect of domestic shocks, I do not care about the effect of external shocks on these three domestic variables in this study.
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external variables on domestic interest rates does not differ extremely in two countries.
In summary, results of this study show that US economic disturbances as proxies of worldwide fluctuations have effect on domestic interest rates in the UK and Sweden as two non-euro European countries which are among first countries who have adopted inflation targeting regime. The magnitude of external effects is greater than internal effects in both countries. The magnitude of external effects is greater in the UK compared to Sweden, but it takes shorter time for the Swedish monetary policy to respond to disturbances.
The VAR model also seems to act reliably in this study as the interaction of all variables is captured clearly. Going back to Stock and Watson (2001), in case of forecasting, VAR is reliable, but it cannot answer policy analysis. Better said, although the correlation between different external and internal variables with domestic interest rate is observed in this study, direct effect of these variables cannot be confirmed. That is why I repeated "possible effect" several times in the study. "Could better proxies be used? Are there some variables highly correlated with chosen variables which are missed in the study? How the poor power of stationary tests can affect the results?" are among those questions which may have impact on the results.
Eight out of nine previous reviewed studies use VAR model, but just in some of them stationarity of time series is discussed briefly. In this study, KPSS test was the only test which confirmed the stationary of all time series. This stationary test (KPSS) is used just in Österholm and Zettelmeyer (2008) and Zenansi and Benhabib (2013) papers.
Ribba (2006) was the only who used VECM (vector error correction model) persisting on the presence of unit root in time series. Although results of impulse-response figures in my study imply that all effects are transitory, using co-integration13 test and VECM model could lead to other results.
The biggest challenge during this study was whether to rely on the combination of three stationary tests and a large number of studies which are written in favor of stationary nature of chosen variables, or to be skeptical and run VECM model. I did not find any previous study in
_______________________________________________________________________________________________________________ 13. A co-integrating relationship is a stationary linear combination of two or more stationary variables. In case of observing non-stationary time series, we have a dilemma. If we estimate the equation in level, there is a risk of estimating a spurious regression. If we take first-differences, there is the risk of estimating a misspecified equation. So we need to see whether there is a co-integrating (long-lasting) relationship between variables (Becketti, 2013).
