Effekten av oljeprischocker på den svenska ekonomin : En Vektor Autoregressiv analys

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Effekten av oljeprisstörningar på den svenska ekonomin

En vektorautoregressiv analys

The effect of oil price shocks on the Swedish economy

A Vector Autoregressive analysis

Author: Gabriel Kasto

Spring 2018

Economic thesis, advanced level, 30 credits Master of Economics

Örebro University, School of Business

Supervisor: Pär Österholm, Professor, School of Business Examiner: Dan Johansson, Professor, School of Business

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Abstract

A multivariate Vector Autoregressive model is used to analyze the effect of oil price shocks on the Swedish economy. The variables used in the VAR model are oil prices, unemployment, real GDP growth rate, CPIF inflation and 3-month treasury bill rate and the sample ranges from 1994Q1 to 2017Q3. The results from the impulse response functions show that the unemployment rate decreases and real GDP growth rate increases when oil prices are shocked. These responses indicate that they are, at least partially, the consequence of an aggregate demand shock and not the consequence of a cost-push shock as expected. In the sensitivity analysis, US real GDP growth rate is included in the system as a proxy to study if oil price shocks are in line with the expected effects of a cost-push inflation shock. However, the responses are somewhat similar to the initial results.

Keywords: Vector Autoregressive, VAR, oil price shocks, impulse response functions,

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1. Introduction

Oil price shocks have a significant impact on the economic activity in oil-dependent countries. Previous research show that oil price shocks have a negative impact on the world economy (Hamilton, 1983; Jiménez-Rodríguez and Sanchéz, 2004; Lescaroux and Mignon, 2009). In times of increasing oil prices, the world economy experiences low growth rate rendering less international trade between countries. Under these circumstances, the demand for oil-related goods is generally low. In the case of Sweden, a highly export dependent country, such impact may weaken the Swedish economic outlook (National Institute of Economic Research, 2016).

Sweden is the 22nd highest oil importing country in the world (Statistics Sweden, 2016). According to Statistics Sweden, Sweden imported approximately 23 million cubic meters crude oil, which amounted to 14 percent of the total import during 2016. At the same time, Sweden’s oil-related exports amounted to 9 percent of total export, which makes Sweden an oil dependent country (Statistics Sweden, 2016). As a result, an increase in oil prices could affect the economy of Sweden.

Increasing oil prices have direct and indirect effects on the economy. For example, increasing oil prices lead to higher fuel and heating oil prices. As fuel and heating oil together correspond to a weight of 3.2 percent of the consumer price index (CPI), increasing oil prices have a direct effect on consumer prices. To shed more light on the matter, during the financial crisis of 2008 high-octane petrol prices increased from 12 SEK (Swedish Krona) per liter to over 16 SEK. And a similar price hike was seen again during the conflict in the Middle East in 2012 (National Institute of Economic Research, 2016).

The indirect (delayed) effect on consumer prices is mainly influenced by factory expenses. For instance, forwarding agents and transfer companies take increasing prices of fuel into account when they transport goods to costumers. In other words, higher prices for transportation services result in higher costs for companies further down in the production chain (National Institute of Economic Research, 2016). Moreover, production factories shift higher oil prices to selling prices. This phenomenon of direct and indirect effects is called cost-push inflation.1

Furthermore, if higher oil prices remain for a longer period, the economic growth may be affected negatively in oil dependent countries (Lescaroux and Mignon, 2009).

1_{Cost-push inflation decreases the total production in the economy due to higher costs of production factors. As}

demand for oil related goods is increasing over time and supply weakens due to higher crude oil prices, the inflation in oil-dependent countries due to higher prices of finished goods increases (Gottfries, 2013).

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The direct and indirect effects on the Swedish inflation has been studied by Bjellerup and Löf (2008). The authors used a Vector Autoregressive (VAR) model to analyze the impact of a 10 percent increase in oil prices on CPI inflation. The direct (indirect) effect of such impact amounted to 0.15 (0.10) percentage points increase in CPI inflation after 5 years. The National Institute of Economic Research (2016) provided a similar and more recent study but employed a different model, namely a Bayesian VAR (BVAR). Although the National Institute of Economic Research (2016) only analyzed the indirect effect, the results were somewhat similar to the study of Bjellerup and Löf. The indirect effect corresponded to an increase of 0.14 percentage points in CPI inflation with fixed interest rates after 5 years.2 Furthermore, Bjellerup and Löf (2008) argued that although the effects may seem small historically, these numbers should not be underestimated in the case of an inflation target of 2 percent and with persistently increasing oil prices.

In economies with an inflation target, increasing oil prices will lead to interventions by central banks. In such events, central banks will adjust the interest rates to keep the inflation on target. Higher interest rates will further slow down the economic growth of oil importing countries and this effect is presented in numerous previous literature (Du et al. 2010; Lescaroux and Mignon, 2009; Hamilton and Herrera, 2004 and more). Furthermore, if higher oil prices remain for a longer period of time, the economic growth may be affected negatively (Lescaroux and Mignon, 2009). With lower economic growth the unemployment rate will eventually grow as well. Thus, it is expected that when oil prices are shocked, the Swedish economy may response in the manner of a cost-push shock.

Given this background, the purpose of this paper is to analyze the effect of oil price shocks3 on the Swedish economy. To perform this study, we applied a multivariate VAR model with five variables. By using the Choleski decomposition of the covariance matrix, forecast error variance decomposition and impulse response functions are enabled to answer the purpose of the paper. Four macro variables are used in the analysis, namely real GDP, CPI with fixed interest rates (CPIF), unemployment rate and 3-month treasury bill rate, which represents the nominal interest rate. Global Brent crude oil prices is the fifth variable employed in the VAR system and represents oil prices. Quarterly data was used for all the variables, ranging from 1994Q1 to 2017Q3.

2_{Both studies are presented in more details in previous literature (section 2).}

3_{Shocks, innovations and impulses will be used throughout the paper and refers to oil price hikes (Lütkepohl,}

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With this paper, we aim to provide a recent view on how the Swedish economy is affected by oil price shocks and to which extent, by including the set of variables mentioned above. Moreover, we included as much data as possible in order to provide a fresh view on the subject.

The results of this paper have shown that interpreting oil price shocks as a cost-push shock may be misleading. The responses of the unemployment and real GDP growth rate have shown to be consistent with an aggregate demand shock where unemployment decreases and real GDP growth rate increases when oil prices are shocked. Moreover, both CPIF inflation and nominal interest rate increase when oil prices are shocked, which was in line with our expectations. Furthermore, we included US real GDP growth rate as a proxy to analyze the sensitivity of the results, such that oil price shocks on the Swedish economy would show a cost-push shock. The results from the sensitivity analysis are somewhat similar to our main findings which indicate that oil price shocks partially illustrate an aggregate demand shock on the Swedish economy.

This paper is organized as follows: In section 2 we highlight relevant previous studies that have analyzed oil price shocks on numerous countries using different models. The VAR model, impulse response function and forecast error variance decomposition are presented in section 3. In section 4 the data is presented along with unit root tests. The main findings of this paper are illustrated in section 5 and discussed in section 6. This paper ends with a conclusion in section 7.

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2. Previous literature

In the report published by National Institute of Economic Research (2016), the indirect effect of a 10 percent fall in oil prices on the Swedish inflation is analyzed. To investigate this impact, a BVAR model was used with six variables, namely the GDP for OECD4 countries, oil prices, unit labor cost, CPIF inflation excluding energy, 3-month treasury bill rate and nominal exchange rate. The timespan ranged from 1987Q2 to 2015Q3. The results showed that a 10 percent decrease in oil prices caused the CPIF inflation to decrease by 0.14 percentage points.

Du et al., (2010) studied the impact of increasing oil prices on China’s economy, mainly focusing on the economic growth and inflation. The authors used a VAR model with five variables in monthly frequency that ranged from 1995:1 to 2008:12. The variables were real GDP growth rate, CPI inflation, real oil prices, 6-months treasury bill rate and money supply. The results through impulse response functions showed that shocks to oil prices had a large negative impact on China’s GDP growth rate and CPI inflation. However, Du et al., (2010) argued that if increasing oil prices are not driven by the US or OECD countries, China’s GDP may remain unaffected.

Similar analysis to that mentioned above was carried out by Lescaroux and Mignon (2009) but by estimating a factor augmented VAR (FAVAR) model. The authors included 13 variables in FAVAR with quarterly data ranging from 1980-2006. Among the 13 variables, GDP, CPI inflation, unemployment rate and 1-year interest rates were economic indicator variables included in the analysis. Through generalized impulse response functions, Lescaroux and Mignon (2009) results show that oil price shocks had a short-lived increase in CPI inflation which in turn induced interest rates to rise. Furthermore, GDP was negatively affected by increasing oil price, but with a delayed impact. However, the authors underlined that the unemployment rate in China was not significantly affected by increasing oil prices because of the well-known fact that unemployment figures are misleading.

Bjellerup and Löf (2008) studied the direct and indirect effect of a 10 percent increase in oil prices on the CPI in Sweden. The authors used a VAR model and applied world GDP, trade-weighted exchange rate, oil prices, unit labor cost, CPI inflation excluding petroleum products and 3-months treasury bill rate. The used data was quarterly and ranged from 1990-2005. The choice of these variables was based on the assumption that they may have an impact on the Swedish inflation. The results showed that the indirect effect had the biggest impact after two

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years, where inflation rose by 0.13 percentage points. The direct effect amounted to a 0.15 percentage points increase in inflation after one year. However, after five years the total (direct and indirect) effect summed up to 0.25 percentage points (0.15 and 0.10, respectively).

The effect of oil price shocks on the monetary policy in the US was studied by Hamilton and Herrera (2004) using a VAR model. Quarterly data for real GDP growth rate, CPI inflation, oil prices and nominal interest rate was used for the period 1978 to 1993. The authors concluded that the greatest effect of an oil shock appeared after three to four quarters after the shock hit the economy.

Jiménez-Rodríguez and Sanchéz (2004) applied linear and non-linear VAR models to analyze the impact of oil price shocks on OECD countries. The variables included in the models were real GDP, CPI inflation, nominal interest rates and oil prices for all OECD countries with the time period of 1972Q3 to 2001Q1. The results from both the linear and non-linear VAR models show that real GDP is negatively affected by increasing oil prices in oil importing countries. However, oil price hikes led to positive growth in oil exporting countries, such as Norway.

Bernanke, Gertler and Watson (1997) used monthly structural VAR (SVAR) with seven variables to study oil price shocks on the US monetary policy. Real GDP growth rate, GDP deflator, commodity price index, oil prices with different measures, the federal funds rate, 3-month treasury bill rate and 10-year treasury bond rate were variables included in SVAR. The samples ranged from 1965:1 to 1995:12. The authors analyzed a shock to oil prices and the results showed that real GDP took on a slower growth by 0.25 percentage points and commodity prices increased by 0.2 percent after two years. Moreover, the federal funds rate increased by 8 basis points after the first year. Bernanke, Gertler and Watson (1997) concluded that a tighter monetary policy in response to higher oil prices is the contributing factor that affects the US economy negatively.

To sum up, the previous studies mentioned above analyze the effect of oil price shocks on the economy in numerous countries. Although most of the studies are in agreement that increasing oil prices have a negative effect on the economic growth, the impact of increasing oil prices vary across studies because of different models, choice of variables, time periods and countries. In this study, we assume that by including similar variables as researchers mentioned above we may be able to identify the impact of increasing oil prices on the Swedish economy.

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3. Empirical Methodology

In this section we begin by presenting the VAR model. Thereafter, impulse response

functions, forecast error variance decomposition and some limitations of the VAR model are presented and highlighted. Lastly, the section ends by pointing out the importance of

determining the appropriate lag length for the VAR model.

3.1 Vector Autoregressive (VAR)

Sims (1980) addressed criticism against large-scale macroeconomic models because they have unreasonable restrictions that are inconsistent with reality. At that time, these macroeconomic models used a lot of variables and equations which resulted in large and complex models. The popularity of such models has decreased significantly after the introduction of the VAR by Sims (1980) due to its simplicity to carry out an economic analysis with a handful of equations.

The VAR is used to empirically investigate the relationship between macroeconomic variables and oil prices. Brooks (2008) underlined several advantages of using VARs. One of the main advantages is that all variables are treated as endogenous in a VAR.5 This means that the researcher does not need to specify the response and explanatory variables and each variable depends upon the lagged values of all the variables in the VAR system.6 Thus, VAR models offer a richer data structure, meaning that the unrestricted model can capture the complex dynamic properties in the data (Brooks, 2008).

A VAR model of order p (VAR(p)) may be written as follows (Lütkepohl, 2005):

𝒚_𝒕 = 𝝂 + 𝑨_𝟏𝒚_𝒕−𝟏+ ⋯ + 𝑨_𝒑𝒚_𝒕−𝒑+ 𝒖_𝒕, t = 0, ±1, ±2,…, (1) where 𝒚_𝒕 is a (K * 1) vector of endogenous variables, 𝝂 is a (K * 1) vector of intercepts, 𝑨_𝟏 through 𝑨𝒑 are (K * K) matrices of parameters. Lastly, 𝒖𝒕 is a (K * 1) vector of white noise

disturbance term fulfilling 𝑬(𝒖𝒕) = 𝟎, 𝑬(𝒖𝒕𝒖′𝒕) =𝒖 for all t, where 𝒖 is positive definite

covariance matrix and 𝑬(𝒖_𝒕𝒖′_𝒔) = 𝟎 for s ≠ t (Lütkepohl, 2005).

5_{Exogenous variables and behaviors, such as trends and seasonals, may also be included in a VAR system (often}

denoted as 𝐵𝑥𝑡), with the restriction that they are added in all equations and if theoretical considerations suggest

it (Diebold, 2001; Brooks, 2008).

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Moreover, the VAR(p) process is covariance-stationary if it has finite and time invariant first and second order moments. In this case, VAR can be expressed in a vector moving average (VMA) form of infinite order

𝒚𝒕 = 𝛍 + ∑∞ 𝒊=𝟎𝚽𝒊𝐮𝒕−𝒊 (2)

Where the 𝛍 (K * 1) vector is the time invariant mean of the process. 𝚽𝒊 is a series of moving

average coefficients, representing impulse response function at time i and 𝐮_𝒕−𝒊 are the error terms at time t-i (Lütkepohl, 2005).

3.2 Impulse response function

Impulse response functions (IRFs) is used to study the dynamics of the model. Impulse responses show the effect of innovations to one variable that enters through the residual vector (𝑢_𝑡) to induce changes on the current and future values of another variable in the system (Lütkepohl, 2011).

Lütkepohl (2005) claim that a problem in the impulse response analysis is that the residuals are correlated with each other. This means that the residuals are not independent and a shock to one variable is assumed to be influenced by other variables being shocked contemporaneously in the system. To perform the IRFs in terms of the VMA representation, the residuals must be rewritten in such a form that they are orthogonal7.

To relate the statement mentioned above, we recall equation (2) and rewrite the expression such that the residuals are uncorrelated. In that purpose, using Choleski decomposing of the white noise covariance matrix will give 𝑷𝑷′. In this case, _𝒖 can be expressed as _𝒖= 𝑷𝑷′, where 𝑷 is a lower triangular matrix with variances of the residuals on the main diagonal and 𝑷′ is the transpose of the matrix. Writing this in the following equation gives us8

𝒚_𝒕 = ∑ (𝚽_𝒊𝑷)(𝑷−𝟏_𝐮 𝒕−𝒊) ∞

𝒊=𝟎

∑∞ _𝒊=𝟎𝜣_𝒊𝒘_𝒕−𝒊 (3)

where 𝜣_𝒊 = (𝚽_𝒊𝑷) and defines the response of innovations to the system and 𝒘_𝒕−𝒊= (𝑷−𝟏_𝐮

𝒕−𝒊)9 are uncorrelated components with unit variance in each component. In this form, a

7_{Variables that are linearly independent of each other are orthogonal. For example,}_𝑦

𝑡 and 𝑥𝑡 are orthogonal if

they are perpendicular to each other (Verbeek, 2012).

8_Parameter_μ_{have been excluded in equation (3) because it is no longer of interest (Lütkepohl, 2005).} 9_{A matrix is orthogonal if the transpose is equal to the inverse, 𝑃}′_{= 𝑃}−1_.

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unit innovation is just the innovation of size one standard deviation. Moreover, Lütkepohl (2005) states that it is reasonable to assume that one standard deviation shock to 𝒘_𝒕 has no

effect on other components since the components are orthogonal.

Note that 𝜣_𝟎 = 𝑷 is lower triangular and the elements (𝜽_𝑗𝑘) of 𝜣_𝟎 are interpreted as responses

to innovations in the system. We can depict 𝜣_𝟎 in a matrix form such that 𝜽_𝑗𝑘 is the j-th row

and k-th column of 𝜣_𝟎 and represents the reaction of variable j to an innovation in variable k

𝜣_𝟎= [ 𝜃₁₁ 0 0 ⋯ 0 𝜃₂₁ 𝜃₂₂ 0 ⋯ 0 𝜃31 𝜃32 𝜃33 ⋱ ⋮ ⋮ ⋮ ⋱ 0 𝜃_𝐾1 𝜃_𝐾2 𝜃_𝐾3 𝜃_𝐾4 𝜃_𝐾𝐾] (4)

Typically, the ordering of the variables matters since the fact that 𝜣_𝟎 is a lower triangular with one standard deviation elements in the main diagonal (𝜃₁₁, 𝜃₂₂, … , 𝜃_𝐾𝐾) (Lütkepohl, 2005). The ordering in the Choleski decomposition means that the first variable has a potential immediately impact on all the variables in the system, but not the other way around. The second variable may have an immediate impact on the remaining variables but not the first variable, and so on. However, there are no statistical tools to determine the ordering of the variables of interest and has to be specified by the researcher (Lütkepohl, 2005). To motivate the ordering of variables to elude dynamic misspecifications, we rely on the economic theory slow-to-fast.10

The meaning of the slow-to-fast ordering is that the first variable in the system is a slow-moving variable and the last variable in the system is a fast-moving one (Stockhammar and Österholm, 2017). For example, oil prices react quickly to news, such as higher or lower production levels, natural disasters and political instabilities (OPEC, 2018), hence oil prices are a fast-moving variable. On the other hand, changes to oil prices do not affect companies in the short run when they decide whether to hire or fire workers, thus unemployment is a slow-moving variable (Stockhammar and Österholm, 2017). The 3-month treasury bill rate is given by the Swedish National Debt Office11 and have a maturity up to three months. Furthermore, changes in the interest rates have a delayed effect on the economic growth. For instance, changes in the interest rates will take up to two years to see the full effect on inflation (Riksbanken, 2018). This also affects GDP because inflation and GDP are interdependent (Gottfries, 2013).

10_{An alternative approach is to try different ordering of the variables in the system and see if the results are robust}

(Lütkepohl, 2005)

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At first glance, with the motivation mentioned above, it seems appropriate to order the unemployment rate first, followed by the growth rate of real GDP and CPIF inflation, 3-month treasury bill rate and oil prices last. However, it is likely to assume that changes in oil prices are due to exogenous oil price shocks. Such exogenous developments are the OPEC embargo in 1973, Iran-Iraq war in the early 1980s, Persian Gulf war in the early 1990s, financials crisis in 2007-2008 and most recently, the conflict in the Middle East since 2010. Thus, by ordering the oil prices first in the system, it is assumed that oil prices will contemporaneously affect itself and the remaining variables in the system, but not the other way around.12

To illustrate the identification of the model on impact with the variables employed, it is presented by the relation 𝜺_𝒕 = 𝜣_𝟎𝒘_𝒕 in equation (5) below

[

𝜀

_𝑡△𝑜𝑖𝑙

𝜀

_𝑡𝑢

𝜀

_𝑡𝑟𝑔𝑑𝑝

𝜀

_𝑡𝑐𝑝𝑖𝑓

𝜀

_𝑡𝑖

_]

= [ 𝜃₁₁ 0 0 0 0 𝜃₂₁ 𝜃₂₂ 0 0 0 𝜃₃₁ 𝜃₃₂ 𝜃₃₃ 0 0 𝜃41 𝜃42 𝜃43 𝜃44 0 𝜃51 𝜃52 𝜃53 𝜃54 𝜃55] x [ 𝑤_𝑡△𝑜𝑖𝑙 𝑤_𝑡𝑢 𝑤_𝑡𝑟𝑔𝑑𝑝 𝑤_𝑡𝑐𝑝𝑖𝑓 𝑤_𝑡𝑖 _] (5)

The equation that is written first in the system is not affected by the following variables at time

t. Furthermore, the second equation in the order is affected only by the first residual and not the

remaining residuals. Finally, the last equation is affected by all the residuals in equation (5).13

The Choleski decomposition also enables forecast error variance decomposition. Variance decomposition is related to IRF, but has a different focus. Variance decomposition answers the question “How much of the h-steps-ahead forecast error variance of variable i is explained by

innovations to variable j?” (Diebold, 2001, p.235). Just like with the IRFs, the ordering matters

in the variance decomposition. We use the same ordering presented in equation (5). In this study we employ variance decomposition and IRF to analyze the dynamics of the variables.

A limitation of VAR models, besides ordering the variables using economic theory, is that VAR models have to be estimated to lower order systems (Lütkepohl, 2005). Hendry (1995) states that the effects of omitted variables will end up in the residuals which in turn may lead to major

12_{It is worth noting that the Swedish variables may have a lagged effect on the oil prices. This is tested and}

illustrated in the IRFs in the Appendix. For instance, figures A.2 and A.4 (first row) show that a shock to the macro variables have no effect on oil prices. Furthermore, ordering oil prices last in the system is tested. By doing this we allow the residuals of oil prices to be affected by all the Swedish variables in the system. This is performed to test the robustness of the ordering. The results from IRFs are presented in Figure A.6 in the Appendix and discussed in section 6.

13_{The expression ∆ indicates the first difference of the log oil prices. See section 4.1 for more details on the results}

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distortions in the IRFs and variance decomposition. This makes the structural interpretation of the system inconsistent. Furthermore, another limitation is that the IRFs needs to be interpreted with caution by the analysist. However, the system may still be useful for predictions (Hendry, 1995). In the following sub-section, we will address another weakness of VAR, which is determining the appropriate lag length.

3.3 Lag length criteria

Fitting VAR models to the data does not come fuss-free. Brooks (2008) claim that a weakness of the VAR is determining the appropriate lag length (the order of p). Setting the lag length too large, degrees of freedom will be used up which may lead to inconsistent results. Choosing a small lag length may not be a sufficient number of lags to capture the dynamic properties of the data (Lütkepohl, 2011). To choose the appropriate order of lags in the VAR, model selection criteria is often used in empirical work.14 Lütkepohl (2011) states 3 types of information criteria that are often employed by researchers, namely Akaike’s information criterion (AIC) (Akaike, 1973), Hannan-Quinn information criterion (HQ) (Hannan and Quinn, 1979) and Schwarz information criterion (SIC) (Schwarz, 1978).

These three criteria choose the appropriate lag order (p) such that the criterion is minimized (Lütkepohl, 2005). Moreover, Lütkepohl (2005) underlines that AIC may overestimate the lag order and always suggest the largest order, while HQ and SIC are consistent since SIC chooses the smallest order and HQ is in between. That being said, we will rely on SIC and HQ to determine the optimal lag order.

After determining the appropriate lag length, it is ideal to investigate the residuals in the chosen VAR model to be white noise (Henriques and Sadorsky, 2008). Lütkepohl (2005) argues that it is necessary to check the whiteness of the residuals when the order of the variables in VARs are based on economic theory. Moreover, Lütkepohl (2005) suggests employing different statistical tools to investigate the white noise of the residuals because different tools emphasize different aspects. We use two autocorrelation tests, namely Lagrange Multiplier (LM) test and

Portmanteau test. The null hypothesis in the LM test (Portmanteau test) is that there is no

residual autocorrelation (up to lag h). If the null hypothesis is rejected then the specified VAR model is not appropriate and must be redefined until the autocorrelation tests are satisfied.

14_{An alternative approach to choose the lag length is the cross-equation restrictions (See Lütkepohl, 2005; 2011}

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4. Data

The empirical analysis is carried out using five variables with quarterly data for the period 1994Q1 to 2017Q3 (95 observations). The variables at hand are real GDP (RGDP) and represents the economic growth of Sweden without including the effect of inflation. Consumer price index with fixed interest rates15_{(CPIF inflation) is the main measure of underlying}

inflation and aims to remove the effect of changed interest rates from the CPI. Sveriges Riksbank (central bank of Sweden) has replaced CPI with CPIF as inflation target variable for monetary policy since 2017 (Sveriges Riksbank, 2017). Therefore, we believe it is reasonable to include CPIF in the analysis. Both RGDP and CPIF are calculated as year-on-year growth rates, which is a commonly used formula when modelling macroeconomic variables in time series (Stockhammar and Österholm, 2017)16. Unemployment (U) represents the age group of 15-74 years, Brent crude oil prices are expressed in logarithm (LOIL) and 3-month treasury bill rate (I) is the nominal interest rate. LOIL data is taken from FRED St. Louis, the remaining variables are extracted from Macrobond. RGDP and U are seasonally adjusted. The variables are presented in figure 1.

The oil price series show a number of events throughout the studied period. In particular, during the financial crisis in 2008 and the conflict in the middle east in 2011 where crude oil reaches its highest price. The economic growth of Sweden drops to almost minus 4 percent in the financial crisis but recovers to positive growth in the following year. CPIF growth rate reaches its highest values of approximately 3.6 percent during the financial crisis but thereafter drops to about 0 percent to then rise at the end of the studied period. The unemployment rate amounts to 10.3 percent in 1997 but takes on a negative trend until 2000 and thereafter reaching approximately 9 percent during the financial crisis and then stabilizing at 6.8 percent. The treasury bill rate was at 9.1 percent in 1995, then dropping and following a negative trend with some upswings throughout the period.

15_{Statistics Sweden measure the CPIF, on behalf of Sveriges Riksbank, in monthly frequency. To our knowledge,}

quarter frequency is not available for this variable, hence we use the last monthly values in each quarter.

16_{Real GDP is calculated by ((𝑌}

𝑡/𝑌𝑡−4− 1) ∗ 100) where 𝑌𝑡 is real GDP and CPIF is calculated by ((𝑍𝑡/𝑍𝑡−4−

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Figure 1. Time series data.

2.0 2.5 3.0 3.5 4.0 4.5 5.0 94 96 98 00 02 04 06 08 10 12 14 16 LOIL -4 -2 0 2 4 6 8 10 94 96 98 00 02 04 06 08 10 12 14 16 RGDP -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 94 96 98 00 02 04 06 08 10 12 14 16 CPIF 5 6 7 8 9 10 11 94 96 98 00 02 04 06 08 10 12 14 16 U -2 0 2 4 6 8 10 94 96 98 00 02 04 06 08 10 12 14 16 I

Note: All time series are given in percent. Source: Macrobond and FRED St. Louis.

4.1 Unit root tests

Unit root tests are often employed in order to get a stable VAR(p) model. Unit root tests are statistical tests that controls for the stationarity of time series and are desirable tools to generate robust results. Non-stationary variables may have different forms. Such forms can be that a time series is trending over time which indicate deviations from stationarity or that the variance of a time series is not constant over time (Lütkepohl, 2005). In this case, a time series have a unit root and can be integrated of order one (I(1)) or order two (I(2)). In a scenario where a variable

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have a unit root (either I(1) or I(2)), taking the first or second difference will make the variable stationary (I(0)).

To test whether the time series are stationary, we employ Augmented Dickey Fuller (ADF) and

Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root tests. The null hypothesis for the ADF

test is that the data series has a unit root and the alternative hypothesis is that the series has less than a unit root. ADF test is developed to adjust for the correlation in the residuals by adding lagged values to the dependent variable ∆𝑌𝑡 where the optimal lag length is chosen by SIC

(Gujarati, 2009). KPSS is an alternative test based on a Lagrange multiplier testing principal and is assumed to decompose the univariate series into a sum of deterministic component, random walk and stationary disturbances (Syczewska, 2010). The KPSS test has the null hypothesis that the data series is stationary and the alternative hypothesis is that the data series have a unit root.

The purpose of using ADF and KPSS unit root tests is that the ADF test is known to have low power against the alternative hypothesis of (trend) stationarity (Toda and Yamamoto, 1995). Thus, the KPSS is a preferred alternative unit root test and rejects the null hypothesis of stationarity only when there is strong evidence of unit root in the series. In table 1 below we present the results of the ADF and KPSS tests.

Table 1. Results for the ADF and KPSS unit root tests.

ADF and KPSS in levels ADF and KPSS in first differences

Variables ADF KPSS ADF KPSS

LOIL -1.602(1) 1.029(7)*** -7.598(0)*** 0.132(1) RGDP-growth -3.093(8)** 0.223(6) -5.213(7)*** 0.027(5) CPIF-inflation -2.856(4)* 0.308(6) -7.890(4)*** 0.033(1) U -2.305(1) 0.208(7) -5.389(0)*** 0.099(6) I -2.501(1) 1.087(7)*** -5.534(1)*** 0.034(4)

Statistically significance at levels 10%, 5% and 1% are denoted as *, ** and *** respectively. Both unit root tests are estimated with a constant in levels and first difference. Numbers in the parentheses are the optimal lag length determined by SIC for ADF and Newey-West bandwidth for KPSS. See Tables A.1 and A.2 in the appendix for the critical values for ADF and KPSS tests respectively.

For the log oil prices, the ADF and KPSS tests are in agreement that the series is non-stationary in levels. Taking the first difference of log oil prices, both tests show that the series is stationary.

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Moreover, both ADF and KPSS tests agree that real GDP growth rate and CPIF inflation growth rate are stationary in levels.

Turning to the unemployment rate, the ADF and KPSS tests are in conflict where the latter test indicate that the series is stationary in levels while the prior test states the opposite. In this case, transforming the unemployment series to stationary may seem appropriate. However, Gustavsson and Österholm (2007) provide mixed evidence when applying several unit root tests to unemployment series for numerous countries. Gustavsson and Österholm (2007) state that there is some evidence of stationarity in the unemployment rate in levels when the process is near integrated which univariate unit root tests may fail to observe because of their low power against stationary alternative.

The low power of Dickey-Fuller tests is criticized in the same fashion as mentioned above by Beechey, Hjalmarsson and Österholm (2009), where the long and short run interest rates are investigated. Due to the high persistence of the nominal interest rates, Dickey-Fuller tests may fail to conclude if the interest rates are stationary in levels. Beechey, Hjalmarsson and Österholm (2009) explain that the nominal interest rates have historically fluctuated within reasonable boundaries which indicates that it is nearly impossible that the interest rates hold a unit root.17

To conclude the results of the unit root tests with the motivation above in hand, it seems appropriate to apply real GDP and CPIF growth rates, the unemployment and nominal interest rate in levels in the VAR system. As for the oil prices, the ADF and KPSS tests agree that the series is non-stationary in levels and by taking the first difference of log oil prices the series is transformed to a stationary process. To see how the system operates on impact with the transformed variables, we refer to equation (5) in section 3.2.

4.2 Optimal lag length and residual tests

To determine the optimal lag length (p) for the VAR model, SIC and HQ are employed. With the variables included in the form specified in the section above (4.1), SIC suggest a lag order of 1 (VAR(1)) and HQ suggest lag order 2 (VAR(2)). Furthermore, turning to the Portmanteau and LM autocorrelation tests to investigate the whiteness in the residuals of the VAR(1) model.

17_{In the articles by Gustavsson and Österholm (2007) and Beechey, Hjalmarsson and Österholm (2009) where}

unemployment and interest rates are studied in the prior and latter articles, respectively, Sweden is among the many countries included in the author’s research. Therefore, motivating the choice of employing unemployment and 3-month treasury bill rate in levels with the statements above seems reasonable.

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In this case, the results show that the null hypothesis of no serial autocorrelation is rejected by both tests.18

Moving on to test if there is white noise in the residuals in the VAR(2) model suggested by HQ, the autocorrelation tests are in conflict. Portmanteau test rejects the null hypothesis up to lag 2, while the LM test cannot reject the null hypothesis of no serial autocorrelation in the residuals. The results from the Portmanteau test is in line with the statement of Patilea and Rïssi (2013) that the test is unreliable when investigating the whiteness of the error terms in VAR models with variables in levels included in the system, such as in our case. That being said, we deviate from the result indicated by the Portmanteau test and we only rely on the LM test, concluding that VAR(2) is the appropriate model as suggested by HQ.19

18_{The IRFs and variance decomposition for the VAR(1) model are presented in Figure A.2 and A.3 respectively}

in the Appendix.

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5. Results

In this section forecast error variance decomposition and IRFs for the ordering specified in section (3.2) are presented. The simulations are generated using the Choleski decomposition of the covariance matrix. We mainly focus on the innovations to oil prices and how such innovations affect the Swedish variables included in VAR(2) to answer the purpose of the paper. Results for the full set of IRFs and variance decomposition are presented in the Appendix in Figure A.4 and Figure A.5, respectively.

Figure 2. Variance decomposition from VAR(2) model. Shown over a 40-quarter horizon.

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent U variance due to D(LOIL)

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent RGDP variance due to D(LOIL)

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent CPIF variance due to D(LOIL)

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent I variance due to D(LOIL)

Note: The figures above illustrate one standard deviation shock to oil prices to each variable to the forecast error variance of unemployment rate, real GDP, CPIF and 3-months treasury bill rate. On the vertical axis the percentage contribution due to a shock and on the horizontal axis the number of quarters is presented.

From the figures above, we can see that oil price shocks contribute to 10 percent of the forecast error variance of the unemployment rate. The contribution of oil price shocks to the forecast error variance of real GDP and inflation amount to 12 and 11 percent, respectively, after 40 quarters. Lastly, an innovation to oil prices contribute to 24 percent of the fluctuations in the Swedish interest rate. Interestingly, the short-term interest rate is substantially affected by oil price shocks compared to the remaining variables in the system.

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Figure 3. Response of macro variables due to One Standard Deviation shock to oil prices.

-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to D(LOIL) -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to D(LOIL) -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40

Response of CPIF to D(LOIL)

-.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to D(LOIL)

Note: The figures above show the response of One Standard Deviation shock to oil prices. The dashed (red) lines are ± 2 Standard Errors.

The results from the IRFs show that a one standard deviation shock to oil prices leads to a decline in the unemployment rate by 0.11 percentage points up to four quarters ahead. The unemployment rate rises after four years to 8 basis points and thereafter dies out. The effect on real GDP growth rate due to an oil price shock leads to a slight increase in the first quarter but then rises to 0.5 percentage points at the third quarter. Thereafter, the effect declines to a negative value of 0.2 percentage points at quarter ten. The inflation (CPIF) have a direct response of an impulse to oil prices. Inflation decreases to 4 basis points in the second quarter to then rise back to 0.13 percentage points after one year. Thereafter, CPIF decreases approximately four years ahead and then dies out. Lastly, the interest rate rapidly increases due to a shock to the oil prices and reaches 0.35 percentage points after four quarters and thereafter dies out in long run. The wide standard error bands indicate that oil price shocks on the Swedish macro variables are only significant for a few quarters.

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6. Discussion

To analyze the impact of oil price shocks on the Swedish economy, a VAR(2) model (as suggested by HQ) has been employed. By using the Choleski decomposition of the white noise covariance matrix, forecast error variance decomposition and IRFs are enabled for the analysis. Moreover, relying on economic theory for the ordering of the variables in the system (see section 3.2) we acquire the results presented in section (5).

Firstly, as mentioned earlier20_{that the Swedish variables may have a lagged impact on oil}

prices, is tested with VAR(1) and VAR(2) models (first row in figures A.2 and A.4 in the Appendix). These results are what to be expected which indicates the Swedish variables do not affect oil prices. Moreover, we order oil prices last in the system. The results from IRFs and variance decomposition are found in figures A.6 and A.7 in the Appendix. These results show that the Swedish variables do not have an effect on oil prices which is what we had expected. Hence ordering oil prices first in the system (as depicted in equation (5)) seems reasonable. Furthermore, we compare the results of VAR(1) (suggested by SIC) and VAR(2) (suggested by HQ) where the latter model have white noise residuals according to LM test. The results from the two models are quite similar which indicates that the specified VAR(2) is robust.

The response of unemployment to one standard deviation shock in oil prices show that in the short run unemployment decreases and this decline is significant. However, after ten quarters unemployment raises. Furthermore, the response of the economic growth to a shock in oil prices show that real GDP growth increases until 3-quarters ahead (and is significant) and then decline to negative growth. However, these results are not what we had expected by defining oil price shocks as cost-push shocks. In the case of a cost-push shock, we would expect that an oil price hike would lead to an increase in the unemployment rate and real GDP growth to decrease and then stabilize in the long run (assuming increasing oil prices are not persistent). As the result indicate that these responses are in the opposite direction of what we had expected, it is reasonable to assume that oil price shocks, at least partially, illustrate an aggregate demand shock. In line with previous studies21_{, we find that shocks to oil prices have a negative effect}

on the economic growth of oil importing countries.

Investigating the response of CPIF inflation and the nominal interest rate, the results show that both series increase (and are significant) in the short run due to innovations in oil prices. These

20_{See footnote 12.}

21_{See Du et al., (2010), Lescaroux and Mignon (2009), Hamilton and Herrera (2004) and Bernanke, Gertler and}

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responses can be explained by cost-push inflation shock but also by an aggregate demand shock, such that increasing oil prices lead to higher prices of oil-related goods and high-octane petrol which in turn leads to an increase in the CPIF inflation. This further leads the central banks to increase the interest rate to keep inflation on target which is similar to the response of the nominal interest rate in this analysis. This coincides with the results of Du et al., (2010) and Bernanke, Gertler and Watson (1997), such that increasing oil prices will induce higher interest rate. Moreover, the inflation response is somewhat similar to the study of Bjellerup and Löf (2008) that inflation rises to 0.15 percentage points in the short run (direct effect) due to an oil price shock whereas in this study such impact amounts to 0.13 percentage points after 4 quarters.

6.1 Sensitivity analysis

In this section, we analyze the responses of real GDP growth and unemployment rate that show the consequence of an aggregate demand shock rather than a cost-push shock. One possible explanation can be the long sample in the analysis. Under certain periods in the sample, high aggregate demand for crude oil from the US (among other countries) emerges within the studied period.22 According to International Energy Agency (2017) the global demand for crude oil has been steadily increasing in the past two decades with US contributing to the highest demand (IEA, 2017).

High aggregate demand in the US means that they demand both oil and Swedish export goods.23 This will lead the Swedish export industry to increase because among the class of goods Sweden exports to the US, oil related machinery is one of the most exported products (Regeringen, 2017). With this information in hand, the responses of the Swedish real GDP growth and unemployment presented in section 6 may seem appropriate when oil prices are shocked.

To analyze the sensitivity of our result, we will study if the responses show a cost-push shock by including year-on-year US real GDP growth rate24 as a proxy in the system. The ADF and KPSS unit root tests show that the US real GDP growth rate is stationary in levels (see table A.3 in the Appendix). US real GDP growth rate is ordered first in the system, followed by first

22_{China is the second in the list of highest demand for crude oil followed by India (IEA, 2017).}

23_{Most of the crude oil imported to the US is produced to transportation fuel, airplane fuel, heating oil and other}

factors that is consumed in the US. Only a small amount of oil related products is exported (IEA, 2017).

24_{US Real GDP growth rate is calculated by ((𝑋}

𝑡/𝑋𝑡−4− 1) ∗ 100) where 𝑋𝑡 is US real GDP. The time period

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difference of log oil prices and the Swedish variables.25 This ordering implies that the US real GDP growth is assumed to contemporaneously affect itself and the following variables in the system, but not the other way around. The impulses in the six-variable system are interpreted as one standard deviation shocks because of the Choleski decomposition. Moreover, both SIC and HQ suggest a lag length of 1 (VAR(1)) and both autocorrelation tests indicate that the residuals are white noise. The IRFs and variance decomposition from the six-variable VAR(1) model are presented in figures A.8 and A.9, respectively, in the Appendix.

The results from the IRFs indicate that a one standard deviation shock to the US real GDP growth leads to a (significant) decrease in the unemployment rate. The Swedish real GDP growth rate rises (and is significant) in the short run due to a shock to US real GDP growth. The CPIF inflation increase in the short run and remains around zero growth thereafter. Lastly, the nominal interest rate increases when the US real GDP growth is shocked.

More interestingly, analyzing shocks to oil prices (second column from the left in figure A.8) the results do not change by much in comparison to the results in section 5. Except for the nominal interest rate that show a significant increase, none of the remaining Swedish variables show significant responses to oil price shocks when US real GDP growth is included in the system. This further indicates that our results are somewhat the consequence of an aggregate demand shock. Thus, interpreting the effect of oil price shocks on the Swedish economy as a cost-push shock may be misleading. Assuming that our analysis is employed in an adequate manner, it may be difficult to measure the effect of oil price shocks on the Swedish economy with high precision.

One possible explanation can be because of the few observations included in the analysis since quarterly frequency is used in the data. Moreover, the Swedish real GDP used in this study is from 1993 and by transforming the series into year-on-year growth rate, four observations disappear in the calculation. Another explanation can be that including many variables in the VAR system will lead to degrees of freedom being used which in turn may lead to imprecise results.

25_{The US real GDP growth rate is an external variable and ordering it first in the system seems reasonable. One}

may also argue that the US is a big open economy and Sweden is a small open economy and shocks to the US economy may affect the Swedish economy but not the other way around. Hence this motivation may be an adequate one to order US real GDP growth first.

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7. Conclusion

The paper employed a multivariate VAR model with five variables, namely oil prices, unemployment, real GDP growth rate, CPIF inflation and 3-month treasury bill rate. Quarterly data is used and the sample ranges from 1994Q1 to 2017Q3. Through variance decomposition and IRFs we are able to analyze the effect of oil price shocks on the Swedish economy.

The findings of this study show that the responses of unemployment and real GDP growth are not what we had expected by defining oil price shocks as a cost-push shock. The results indicate that we partially have an aggregate demand shock. We analyze this by including US real GDP growth rate as a proxy to analyze if the responses show a cost-push shock. However, the results of oil price shocks on the Swedish economy do not change by much. Hence, interpreting a shock to oil prices as an aggregate demand shock may seem reasonable.

The implication of these results is that increasing oil prices have a partially adverse effect on the Swedish economy. However, it is necessary to keep in mind that VAR models are used to illustrate the responses of oil price hikes but do not reveal the true consequence of such events. In this case, it is necessary for macroeconomists and policy makers to analyze the impact of oil price shocks thoroughly before taking action in order to keep inflation on target. To increase the nominal interest rate according to our findings (0.35 percentage points) to induce tighter monetary policy in response to oil price hikes may lead to negative effects on the economic growth. This is because of the inflation target of 2 percent in Sweden and higher nominal interest rate may lead the inflation below its target in the long run.

An improvement of the study could be to use fewer Swedish variables with a longer sample. More observations in combination with fewer variables in a VAR model may lead to satisfactory results. Another improvement could be to use a different VAR model (such as SVAR or BVAR) and compare the results with this study.

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Appendix

Table A.1 Critical values for ADF test

Variables Critical values 1% 5% 10%

LOIL -3.502 -2.892 -2.583 RGDP growth -3.508 -2.895 -2.585 CPIF inflation -3.504 -2.894 -2.584 U -3.502 -2.892 -2.583 I -3.502 -2.892 -2.583 US RGDP growth -3.505 -2.893 -2.584

Note: The critical values presented are with a constant included for all variables.

Table A.2 Critical values for KPSS test

Critical values 1% 5% 10%

0.739 0.463 0.347

Note: The critical values presented are with a constant included.

Table A.3. Results for the ADF and KPSS unit root tests for the US real GDP growth variable. ADF and KPSS in levels ADF and KPSS in first differences

Variable ADF KPSS ADF KPSS

US RGDP-growth -3.353(1)** 0.401(7)* -6.929(3)*** 0.031(3)

Statistically significance at levels 10%, 5% and 1% are denoted as *, ** and *** respectively. Both unit root tests are estimated with a constant. Numbers in the parentheses are the optimal lag length determined by SIC for ADF and Newey-West bandwidth for KPSS. See Tables A.1 and A.2 in the appendix for the critical values for ADF and KPSS tests respectively.

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Figure A.1. Time series of US real GDP growth rate

-6 -4 -2 0 2 4 6 94 96 98 00 02 04 06 08 10 12 14 16 us_rgdp

Note: The figure above shows US real GDP growth rate in quarter frequence for the time period 1994Q1 to 2017Q3.

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Figure A.2. Impulse response functions from VAR(1) as suggest by SIC with the ordering specified in equation (5). -.05 .00 .05 .10 .15 .20 5 10 15 20 25 30 35 40

Response of D(LOIL) to D(LOIL)

-.05 .00 .05 .10 .15 .20 5 10 15 20 25 30 35 40 Response of D(LOIL) to U -.05 .00 .05 .10 .15 .20 5 10 15 20 25 30 35 40 Response of D(LOIL) to RGDP -.05 .00 .05 .10 .15 .20 5 10 15 20 25 30 35 40

Response of D(LOIL) to CPIF

-.05 .00 .05 .10 .15 .20 5 10 15 20 25 30 35 40 Response of D(LOIL) to I -.4 -.2 .0 .2 .4 5 10 15 20 25 30 35 40 Response of U to D(LOIL) -.4 -.2 .0 .2 .4 5 10 15 20 25 30 35 40 Response of U to U -.4 -.2 .0 .2 .4 5 10 15 20 25 30 35 40 Response of U to RGDP -.4 -.2 .0 .2 .4 5 10 15 20 25 30 35 40 Response of U to CPIF -.4 -.2 .0 .2 .4 5 10 15 20 25 30 35 40 Response of U to I -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to D(LOIL) -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to U -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to RGDP -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to CPIF -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to I -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40

-.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to U -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to RGDP -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40

Response of CPIF to CPIF

-.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to I -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to D(LOIL) -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to U -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to RGDP -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to CPIF -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to I

Response to Cholesky One S.D. Innov ations ± 2 S.E.

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Figure A.3. Variance decomposition from VAR(1) as suggest by SIC with the ordering specified in equation (5). 0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent D(LOIL) variance due to D(LOIL)

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent D(LOIL) variance due to U

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent D(LOIL) variance due to RGDP

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent D(LOIL) variance due to CPIF

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent D(LOIL) variance due to I

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent U variance due to U

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent U variance due to RGDP

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent U variance due to CPIF

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent U variance due to I

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent RGDP variance due to U

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent RGDP variance due to RGDP

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent RGDP variance due to CPIF

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent RGDP variance due to I

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent CPIF variance due to U

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent CPIF variance due to RGDP

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent CPIF variance due to CPIF

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent CPIF variance due to I

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent I variance due to U

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent I variance due to RGDP

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent I variance due to CPIF

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent I variance due to I Variance Decomposition

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Figure A.4. Impulse response functions from VAR(2) as suggested by HQ based on the ordering specified in equation (5). -.1 .0 .1 .2 5 10 15 20 25 30 35 40

-.1 .0 .1 .2 5 10 15 20 25 30 35 40 Response of D(LOIL) to U -.1 .0 .1 .2 5 10 15 20 25 30 35 40 Response of D(LOIL) to RGDP -.1 .0 .1 .2 5 10 15 20 25 30 35 40

-.1 .0 .1 .2 5 10 15 20 25 30 35 40 Response of D(LOIL) to I -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to D(LOIL) -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to U -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to RGDP -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to CPIF -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to I -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to D(LOIL) -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to U -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to RGDP -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to CPIF -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to I -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40

-.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to U -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to RGDP -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40

-.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to I -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to D(LOIL) -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to U -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to RGDP -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to CPIF -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to I Response to Cholesky One S.D. Innovations ± 2 S.E.

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Figure A.5. Forecast error variance decomposition from VAR(2) as suggested by HQ based on the ordering specified in equation (5). 0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent D(LOIL) variance due to D(LOIL)

0 20 40 60 80 100 5 10 15 20 25 30 35 40

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent I variance due to I Variance Decomposition

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Figure A.6. Impulse response functions from VAR(2) with the ordering: unemployment, real GDP growth, CPIF inflation, nominal interest rate and log oil prices in first difference.

-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to U -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to RGDP -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to CPIF -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to I -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of U to D(LOIL) -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to U -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to RGDP -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to CPIF -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to I -1 0 1 2 5 10 15 20 25 30 35 40 Response of RGDP to D(LOIL) -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to U -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to RGDP -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40

-.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40 Response of CPIF to I -.4 -.2 .0 .2 .4 .6 5 10 15 20 25 30 35 40

-.8 -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to U -.8 -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to RGDP -.8 -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to CPIF -.8 -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to I -.8 -.4 .0 .4 .8 5 10 15 20 25 30 35 40 Response of I to D(LOIL) -.1 .0 .1 .2 5 10 15 20 25 30 35 40 Response of D(LOIL) to U -.1 .0 .1 .2 5 10 15 20 25 30 35 40 Response of D(LOIL) to RGDP -.1 .0 .1 .2 5 10 15 20 25 30 35 40

-.1 .0 .1 .2 5 10 15 20 25 30 35 40 Response of D(LOIL) to I -.1 .0 .1 .2 5 10 15 20 25 30 35 40

Response to Cholesky One S.D. Innovations ± 2 S.E.

Note: In the figure above, oil prices are ordered last in the system. For details on the responses of this specification see section 6 for details.

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Figure A.7. Variance decmposition from VAR(2) with the ordering: unemployment, real GDP growth, CPIF inflation, nominal interest rate and log oil prices in first difference.

0 20 40 60 80 100 5 10 15 20 25 30 35 40

0 20 40 60 80 5 10 15 20 25 30 35 40

Percent I variance due to I

0 20 40 60 80 5 10 15 20 25 30 35 40

0 20 40 60 80 100 5 10 15 20 25 30 35 40

Percent D(LOIL) variance due to D(LOIL) Variance Decomposition

Note: The last row illustrates the variance decomposition of shocks to the Swedish variables on the oil prices. As anticipated the results show that shocks to the Swedish variables explain very little of the forecast error variance decomposition in the oil prices.