2009:034

M A S T E R ' S T H E S I S

Unit Root Tests and Structural Breaksin the Swedish Electricity Price

Isabelle Nilsson

Luleå University of Technology

D Master thesis Economics

Department of Business Administration and Social SciencesDivision of Social sciences

2009:034 - ISSN: 1402-1552 - ISRN: LTU-DUPP--09/034--SE

”Unit Root Tests and Structural Breaks in the

Swedish Electricity Price”

Isabelle Nilsson

Social Science and Business Administration Programmes

ECONOMICS PROGRAMME

Department of Business Administration and Social Sciences

Division of Economics

Supervisor: Linda Wårell

I

ABSTRACT

The purpose of this thesis was to examine the Swedish electricity price in order to determine

whether there are any structural breaks in the time series. Both the nominal and the real price

of electricity under the period 1900 to 2006 are examined. The theoretical framework used in

this thesis is different tests for unit root and structural breaks in time series. Tests for both

exogenously and endogenously determined breaks are performed. Different quantitative

methods for measuring structural breaks are applied in order to compare any differences. The

results showed that both the nominal and real electricity price exhibits unit root and that

breaks are most likely to occur rapidly. Both series exhibits a break around 1945 a time when

the Swedish economy was growing and the demand for electricity was increasing. The results

implies that more than one test should be used and compared when testing for structural

breaks in time series.

II

SAMMANFATTNING

Syftet med den här uppsatsen var att undersöka det svenska elpriset för att se huruvida det

finns några strukturella förändringar i denna tidsserie. Den teoretiska referensram som

användes var olika test för icke-stationaritet och strukturella förändringar i tidsserier. De olika

testen tillät både exogent och endogent bestämda förändringar, detta för att kunna jämföra

eventuella skillnader. Analysen baserades på data för både det reala och det nominella elpriset

under perioden 1900 och 2006. Resultaten visar att både den nominella och reala tidsserien

för elpriset är icke-stationär och serierna lämpligast förklaras av snabba förändringar. Båda

serierna uppvisade strukturella förändringar kring 1945, en period då den svenska ekonomin

växte och efterfrågan på elektricitet steg. Resultaten visar också på att fler än ett test bör

användas och jämföras vid test för strukturella förändringar i tidsserier.

III

TABLE OF CONTENTS

ABSTRACT ................................................................................................................................ I 

SAMMANFATTNING ..............................................................................................................II 

TABLE OF CONTENTS ......................................................................................................... III 

LIST OF FIGURES AND TABLES ........................................................................................ IV 

Chapter 1 INTRODUCTION ..................................................................................................... 1 

1.1 Background....................................................................................................................... 1 

1.2 Purpose ............................................................................................................................. 2 

1.3 Methodology .................................................................................................................... 3 

1.4 Scope and Limitations ...................................................................................................... 3 

1.5 Outline .............................................................................................................................. 3 

Chapter 2 BACKGROUND ....................................................................................................... 4 

2.1 The Swedish Electricity Price .......................................................................................... 4 

Chapter 3 THEORY ................................................................................................................... 9 

3.1 Time Series Analysis ........................................................................................................ 9 

3.2 Stationary and Non-stationary Time Series ..................................................................... 9 

3.3 Unit Roots Test: The ADF Test ..................................................................................... 12 

3.4 Unit Root Tests with Structural Breaks .......................................................................... 13 

3.4.1 Exogenous Structural Break .................................................................................... 14 

3.4.2 Endogenous Structural Break .................................................................................. 15 

3.4.3 Multiple Structural Breaks ...................................................................................... 17 

Chapter 4 EMPIRICAL RESULTS AND ANALYSIS ........................................................... 19 

4.1 Reliability and Validity .................................................................................................. 19 

4.2 Unit Root Tests ............................................................................................................... 20 

4.3 Exogenous Structural Break Test ................................................................................... 21 

4.4 Testing Unit Root Allowing for Endogenous Breaks .................................................... 22 

4.5 Testing Unit Root Allowing for Two Breaks ................................................................. 24 

4.6 Comparison .................................................................................................................... 27 

Chapter 5 CONCLUSIONS ..................................................................................................... 30 

REFERENCES ......................................................................................................................... 32 

IV

LIST OF FIGURES AND TABLES

Figure 2.1 The Swedish Electricity Price and the Oil Price, Nominal, 1900- 2000 .................. 5 

Figure 2.2 The Swedish Electricity Price, Nominal and Real, 1990- 2006 ............................... 6 

Table 4.1 ADF Unit Root Test ................................................................................................. 20 

Table 4.2 Zivot-Andrews Unit Root Test Allowing for One Break ......................................... 22 

Figure 4.1 Zivot-Andews Test, Nominal Electricity Price ....................................................... 23 

Figure 4.2 Zivot-Andews Test, Real Electricity Price ............................................................. 24 

Table 4.3 Clemente-Montañés-Reyes Unit Root Test with Double Mean Shift ...................... 24 

Figure 4.3 Clemente-Montañés-Reyes AO Test, Nominal Electricity Price ........................... 25 

Figure 4.4 Clemente-Montañés-Reyes IO Test, Nominal Electricity Price ............................. 25 

Figure 4.5 Clemente-Montañés-Reyes AO Test, Real Electricity Price .................................. 26 

Figure 4.6 Clemente-Montañés-Reyes IO Test, Real Electricity Price .................................... 27 

Table 4.4 Summary of Unit Root Tests .................................................................................... 27 

Table 4.5 Summary of Break Points ........................................................................................ 28 

1

Chapter 1

INTRODUCTION

1.1 Background

For about 100 years ago it became possible to use electricity in Sweden. Until the First World

War not many households had electricity. It was not until the 1920’s the demand for

electricity increased significantly. The first two decades in the previous century is

characterized by varying electricity prices. In 1945 almost every household in Sweden had

electricity. Between the years 1930 and 1960 the prices stayed at a low level (Energy Markets

Inspectorate, 2007). Following the oil crises in 1973 the nominal price of electricity increased

rapidly and continued to do so until a couple of years after the deregulation in the Swedish

electricity market in 1996.

The main purpose of the deregulation was to increase the competition on the electricity

market and thereby decrease the price of electricity. First, there was only Sweden and Norway

that had a common electricity market, a couple of years later both Finland and Denmark

joined the market. This resulted in a common electricity market called Nord Pool which was

the first multinational exchange for trade in electric power contracts (Flatabo et al., 2003).

Around two years after the reform in the Swedish market the prices fell. In 2000 the price

increased and reached a peak during 2003. It decreased a little in 2004 but then went up again

in 2005 (Swedish Energy Agency, 2006).

When looking at the all over pattern for the Swedish electricity price the last century it

fluctuates in correspondence with international crises, such as the Great Depression in 1929

and the first oil crisis in 1973. These years can be treated as points of structural breaks in the

electricity price. This means that at least one of the parameters affecting the electricity price

might have changed at these dates in the sample period. These effects can be transitory or

permanent (Hansen, 2001). However, even if it is reasonable to believe that structural breaks

2

have occurred at these dates, it would be interesting to see whether the break dates of these

crises fits endogenously determined break dates.

The Ordinary Least Square (OLS) method of estimating a standard regression model assumes

that mean and variance of the variables being tested are constant over time. Most macro

economic variables have means and variances that changes over time, these are called non-

stationary or unit root variables. The OLS method therefore gives misleading interpretations

when the regression equation contains non-stationary variables (Glynn et al., 2007).

Literature treating time series analysis have for a long time stressed the importance of testing

for structural breaks in economic data sets. Structural breaks can reflect institutional,

legislative or technical change. These breaks can also reflect changes in economic policies or

large economic shocks such as the oil crises in 1973. One particular problem that is common

when dealing with empirical modelling is that often one or more of the time series being used

have a unit root. Most macroeconomic data exhibits unit root processes therefore it is

suggested that it might be necessary to isolate some unique economic events and see them as

a permanent change in the pattern of the time series (Perman and Byrne, 2006).

This has implications for how the time series can be modelled. There are different kinds of

structural breaks, they can be determined endogenously or exogenously. They can also be

multiple, which means that the time series contains more than one structural break. Different

kinds of models are developed in purpose to capture and test for these breaks (Perman and

Byrne, 2006). Testing for unit root and at the same time allowing for structural breaks has

some advantages. Firstly, it prevents the test results from being biased towards non-

stationarity and unit root. Secondly, these tests can identify when the possible break occurred

(Glynn et al., 2007). The question of this thesis becomes what structural breaks can be

identified in the case of the Swedish electricity price? Do endogenously determined breaks

occur at the dates of international crises? If not what can be the underlying explanation for

these breaks?

1.2 Purpose

This thesis examines the Swedish electricity price in order to determine whether there are any

structural breaks in the time series. Different quantitative methods for measuring structural

breaks will be applied in order to compare any differences.

3

1.3 Methodology

The theoretical framework used in this paper considers an autoregressive model using time

series data. An econometric approach will be used to analyze the Swedish electricity price.

Statistical data on the price of electricity in Sweden from 100 years have been collected. One

of the methods used is the traditional Augmented Dickey-Fuller test to test whether the series

contains a unit root or not. To test for one exogenous structural break a Chow test will be

performed, this test does not test for unit root. The third test is a Zivot-Andrews unit root test

with one endogenously determined structural break. Finally a test proposed by Clemente,

Montañés and Reyes for two breaks is performed.

1.4 Scope and Limitations

The thesis will only consider the price of electricity in Sweden. The data that is received from

Kander (2002) concerns the nominal price of electricity and covers the years between 1892

and 2000, but to avoid some extreme values in the middle of 1890 the years used will be

limited to the time from 1900 to 2000. The statistics concerning the electricity price between

2001 and 2006 is received from SCB. The nominal prices will be converted into real prices

with the price level of 2006 as the base year. The data concerns the price of electricity without

taxes. Both the nominal and the real prices will be used and compared. The thesis will only

perform the structural breaks test that is presented above.

1.5 Outline

This thesis is divided into five chapters. The introduction in chapter 1 gives a general

description of the problem and further it presents the purpose, methodology, scope and

limitations of the thesis. Chapter 2 describes the background of the subject which includes a

historical approach of the Swedish electricity price. Chapter 3 presents the theoretical models

and tests used in this thesis. It also explains the concept of stationarity. In chapter 4 the results

from the tests for unit root and structural breaks are presented. It also includes a discussion

about the data used. The chapter ends with a comparison and an analysis of the results and the

methods used. Final conclusions can be found in chapter 5.

4

Chapter 2

BACKGROUND

This chapter will start with a historical presentation of the Swedish electricity price. The

presentation will focus on the years where there have been significant changes in the trend of

the price and look at what factors that might have caused these trend breaks.

2.1 The Swedish Electricity Price

The demand for electricity is decided by the general economic situation and the temperature.

Factors that affect the electricity price can be found in the conditions and factors that affect

the cost of producing electricity. In Sweden the most important of these is the hydrological

development, the development of capacity, the interaction on the Nordic electricity market

(since 1996), fuel prices, market competition and since 1995 the trade with emission permits

(Swedish Energy Agency, 2006).

For about 100 years ago it became practically possible to use electricity in Sweden. In the

beginning the electricity was produced by steam plants and only used for lighting. In this

period the electricity price was around today’s level in nominal terms. Around the turn of the

century Sweden started to build their first hydro power plants which became the main

electricity source. Private and communal power producing companies were given the

assignment to produce and distribute electricity. When it became a lack of paraffin during the

First World War the development of energy plants increased. Figure 2.2 shows that both the

real and the nominal electricity price increased to high levels during the First World War. In

1920 many household appliances were introduced in the Swedish homes and the households

became more dependent on electricity. This increased the demand for electricity and in 1945

almost every household in Sweden had electricity (Energy Markets Inspectorate, 2007).

Additionally, after the end of the Second World War the Swedish economy was strong. The

manufacturing industry developed and hence this sectors demand for electricity increased

(NE, 2009b).

5

As one can see in figure 2.1 the electricity price almost doubled between the years 1915 and

1920. With an increasing demand and supply during the early 1920 the prices started to

decline rapidly in both nominal and real terms. The decrease continued after the middle

1920’s but at a lowering rate (Energy Markets Inspectorate, 2007). An international crisis that

affected the world economy at this time was when the New York stock market crashed in

1929 which was the starting point of the Great Depression in the 1930’s (NE, 2008b).

In Sweden the first nuclear power plant was taken into production in 1972. However, with a

strong opinion against further development of nuclear power plants together with the oil crises

in 1973 and 1979 the Swedish government realised the weaknesses in their electricity

production. So they began to look for renewable energy sources (Rönnborg, 2003). Electricity

produced from nuclear power is relatively cheap compared to electricity that comes from

wind power for example. Although the demand for electricity has continued to increase since

1970 it has been doing so at a declining rate. At the same time the price of electricity has

increased significantly. One important factor contributing to the massive increase in the

electricity price and the demand for electricity is the relative price of oil, see figure 2.1.

Figure 2.1 The Swedish Electricity Price and the Oil Price, Nominal, 1900- 2000.

Source: Kander (2002).

0,0000

0,1000

0,2000

0,3000

0,4000

0,5000

0,6000

1900

1906

1912

1918

1924

1930

1936

1942

1948

1954

1960

1966

1972

1978

1984

1990

1996

Oil an

d electricity price SEK/KW

h

Oil price SEK/KWh Nominal

Electricity price SEK/KWh Nominal

6

After the oil crises in the 1970’s oil became substituted for electricity, especially when it

came to heating (Andersson, 1997). Another reason for the increase can be the less oil

intensive electricity production that could not generate the electricity that was being

demanded. Therefore it became an excess demand on the market which created an increase in

the price of electricity. Comparing the nominal and the real price of electricity one can see

that they are following different patterns, see figure 2.2. Before the oil crises in the 1970’s

both series are declining at different rates, after this period the nominal price increased

significantly while the real price continued to decline due to a lower rate. One explanation for

this is the high inflation rates in Sweden between 1970 and 1990 (SCB, 2007). One important

year in the Swedish economy is 1982 when the Swedish central bank devaluates the Swedish

currency by 16% after years of depression in the 1970’s. This action was named the “Big

bang”. At the same time the U.S. trade cycle went up and a long period of prosperity had

begun (Bergström, 1999). Furthermore, the Swedish economy went through a financial crisis

in the beginning of 1990. The crisis was caused by a major credit expansion that came after a

deregulation of the monetary system in 1989 (NE, 2009a).

Figure 2.2 The Swedish Electricity Price, Nominal and Real, 1990- 20061.

Source: Kander (2002) and SCB (2007).

1 To make the pattern more visible the nominal price has been multiplied by 10.

0,0000

2,0000

4,0000

6,0000

8,0000

10,0000

12,0000

14,0000

1900

1907

1914

1921

1928

1935

1942

1949

1956

1963

1970

1977

1984

1991

1998

2005

Electricity price SEK/KW

h

Electricity price SEK/10 KWh Nominal

Electricity price SEK/KWh Real (Base year: 2006)

7

In 1992 the first step towards a deregulated electricity market was taken when the

government’s hydroelectric power company was divided into Vattenfall AB and Svenska

Kraftnät. Until then the Swedish government was the only supplier of electricity in Sweden.

The deregulation continued in 1996. The purpose of the reform was to increase the

competition on the electricity market and in that way decrease the price of electricity. This

resulted in integration between the Swedish and Norwegian market into one deregulated

electricity market called Nord Pool (Andersson, 1997). In 1998 Finland entered the common

market and Denmark followed in 1999/2000. Nord Pool was the first multinational exchange

for trade in electric power contracts (Flatabo et al., 2003).

The market consists of one market operator (Nord Pool) and five system operators in the

member countries where each country has their own regulatory agency. In this market all

countries prices are equal to the system price. This system price is calculated by Nord Pool

and decided by the trade on the market. If the price calculation exceeds grid capacity limits

then two or more area prices are calculated. Generally, the spot price reflects the households’

prices which indicate that the retail market works efficient. The market for power trading is

called Elbas and the trade leads to physical delivery. It has the function of an aftermarket to

the spot market at Nord Pool. The involved actors in this market are the power producers,

distributors, industries and brokers from Sweden and Finland (Flatabo et al., 2003). In 2005

Nord Pool continued to grow when it opened the KONTEK bidding area in Germany, which

gave them access to the Vattenfall Europe Transmission control area (Nordpool, 2008).

The demand for electricity in Sweden increased about three percent during the years between

1996 and 2005. The interaction between the Nordic countries different production structures

is important for the electricity price on the Nordic market. The limited trade capacity between

the countries sometimes results in differences in prices between the price areas (Swedish

Energy Agency, 2006).

The system price was declining the years after 1996. In the year of 2000 the average price

was facing its lowest level. After 2000 the price increased and reached a peak during 2003. It

decreased a little in 2004 but then went up again in 2005. One of the main reasons for this is

the trade of emission permits that was introduced in 2005. Another important factor was the

very high prices on fossil fuels. The prices of oil and gas decreased between 1996 and 1999

8

but have thereafter increased, especially between the years 2004 and 2005. Furthermore, the

nuclear plant Barsebäcks second reactor was deactivated in May 2005 (Swedish Energy

Agency, 2006).

9

Chapter 3

THEORY

This chapter begins with discussing time series analysis and the autoregressive model that will

be used is presented. Further, the basic concepts of stationary and non-stationary time series

are explained. The chapter continues with tests for unit roots and the different kinds of

structural breaks.

3.1 Time Series Analysis

Time series analysis concerns observations that are ordered over time, the electricity price is

an example of a time series variable. This variable is random, i.e. its value cannot be

determined before it has actually been observed. Time series analysis is often used in the

finance sector, in research and the raw material market to name a few examples (Westerlund,

2005).

When estimating OLS regressions using time series data the time series is assumed to be

stationary. The problem is that most macroeconomic variables are non-stationary which can

cause serious econometric consequences. A common situation that occurs when dealing with

time series data is autocorrelation (Westerlund, 2005). The standard test for autocorrelation is

the Durbin-Watson (DW) test which is usually included in the basic diagnostic statistics. This

can however be corrected for by using an autoregressive model. Autocorrelation might

indicate omission of one or more lagged variables, or the omission of any important variable

in the model specification (Dougherty, 2007).

3.2 Stationary and Non-stationary Time Series

As mentioned above, performing OLS regressions assumes stationary time series. This means

that the time series exhibits a mean and variance that is constant over time. The problem with

most macroeconomic and financial variables is that they are non-stationary. This means that

10

the time series mean and variance varies over time, which can have serious econometric

consequences (Westerlund, 2005). The non-stationary series have no tendency to return to a

long-rung deterministic trend and the variance of the time series is dependent on time (Glynn

et al., 2007). The problem with for example two non-stationary variables is that they can

separate from each other over time and lose their joint relationship. This phenomenon is

usually called a spurious regression (Westerlund, 2005).

Most recent work has been focusing on the fitting of single variable processes where the

variable is a linear function of previous values of itself and the error term (Dougherty, 2007).

This model says how many lagged values of the dependent variable y that lies on the right

hand side of the equal sign in the regression model:

(1)

This time series is autoregressive of order ρ called the AR(ρ)-model. The model has an

intercept β0, the autoregressive parameters β1, β2,…, βρ, an error term εt and it does not include

any explanatory variables. t represents the time period. For simplicity assume only one lagged

value:

(2)

This thesis and the following discussion will focus on this simplified version of the previous

model. Though, the results from this AR(1)-model can normally be generalized to the regular

AR(ρ)-model in equation (1) (Westerlund, 2005).

If the regressive parameter β1 is:

1 1 (3)

Then yt is a stationary variable. Further, if β1 is equal to 1 then the AR(1)- model in equation

(2) and yt is said to be non-stationary. If β1 is greater then 1 this would cause yt to explode and

be infinitely large over time. However, this is not reasonable and therefore should the cases

where β1 > 1 and where β1 < -1 be ignored. If β1 = 1 the variable yt has what is called a unit

11

root and is therefore non-stationary. To test whether a time series variable is non-stationary or

not one can use the Augmented Dickey Fuller model (see section 3.4). This model tests if the

variable contains a unit root (Westerlund, 2005).

If the variable contains a unit root, i.e. β1 = 1, equation (2) becomes:

(4)

This is an example of a non-stationary process known as a random walk (Dougherty, 2007).

This means that the non-stationary time series suffer permanent effects from random shocks.

(Glynn et al, 2007). If the series starts at y0 at time 0, its value at time t become:

(5)

In this process the contribution of each shock ε is permanently built into the time series.

Because the series includes the sum of the shocks, it is said to be integrated. If expectations

are taken into account at time 0, the expected value of yt at any future time t is independent of

t but its variance is increasing over time:

(6)

(Dougherty, 2007). If a non-stationary variable is present this could be rewritten into

stationary variables before an estimation of the model is done. This implies that the

interpretation of the parameters should be slightly different (Westerlund, 2005). If one can

transform the non-stationary process in this way, it is said to be difference-stationarity. If it

becomes stationary by differencing y once it is integrated of order 1, I(1). If it becomes

stationary by differencing twice it is called I(2) and so on. Trend-stationarity, on the other

hand, is when a non-stationary time series can be transformed into a stationary process by

extracting a time trend. The difference between these two types of stationarity is important in

the analysis of time series (Dougherty, 2007).

There are two reasons why one should be careful when doing regressions with non-stationary

time series. The first is that the properties of the regression estimators are likely to be

12

critically affected. The second is regarding the risk of spurious regressions (Dougherty, 2007).

Signs of a non-stationary variable in a regression are that the DW statistics for the

autocorrelation is too small, that the R2-statistic is near 1 and that the explanatory variable is

very statistical significant, despite the fact that it is not a determinant of the dependent

variable (Westerlund, 2005). This type of spurious regressions can be avoided by detrending

the variables before doing the regression, i.e. by including a time trend in the regression. The

Monte Carlo experiment showed that spurious regressions also can occur in regressions with

integrated time series and with regressions using stationary time series, if autocorrelation in

the disturbance term is ignored (Dougherty, 2007).

Moreover, if the non-stationary variables are cointegrated, i.e. that the two variables includes

the same unit root or stochastic trend, the variables have a joint component. Therefore they

are not independent despite that they are non-stationary, which implies that they are related in

some way. Cointegration can be interpreted as a sort of long run equilibrium. For the

stochastic trend in the variables to take out one another the disturbance term in the

cointegration regression has to be stationary, which it will be if the variables have the same

stochastic trend. To test for cointegration is to test whether the disturbance term in the

regression model is stationary or not (Westerlund, 2005). There will however be no focus on

this phenomenon during this thesis, but worth mentioning.

3.3 Unit Roots Test: The ADF Test

One way of detecting non-stationarity is often described as testing for unit roots. The standard

test by Dickey and Fuller (1979) is based on the model:

(7)

rewritten as

∆ 1 (8)

Where Δyt = yt – yt-1. The time series is non-stationary if the coefficient of yt-1 is zero, the

series is then difference-stationary. If the coefficient of t not is zero the series is trend-

stationary. One property of the Dickey-Fuller test is that the disturbance term is not

autocorrelated. However, if it is autocorrelated more lagged values of yt should be included on

13

the right hand side of equation (7). Rewriting equation (8) yields the so-called Augmented

Dickey-Fuller (ADF) model (Dougherty, 2007):

∆ 1 ∆ (9)

This model tests whether a time series is affected by transitory or permanent shocks, by

testing the null hypothesis that the (β1 + β2 – 1) = 0. This means that the series exhibits unit

root, i.e. it is non-stationary. This hypothesis is tested against the alternative hypothesis that

(β1 + β2 – 1) < 0, i.e. that the series is stationary (Perman and Byrne, 2006). Here Δ denotes

the first difference of the time series yt that is being tested (Glynn et al., 2007). It should

however by mentioned that in practice the test tends to have low power and rejecting the null

hypothesis does not always mean that the time series is non-stationary (Perman and Byrne,

2006). Perron (1989)2 showed that without considering a possible existing break when doing

the ADF test could lead to a bias that reduces the ability to reject a false unit root null

hypothesis. To correct for this type of failure Perron suggested an ADF test allowing for a

known or exogenous structural break (Glynn et al., 2007).

3.4 Unit Root Tests with Structural Breaks

A structural break may be the change in the time series as a result of some unique economic

event (Glynn et al., 2007). Structural breaks can reflect institutional, legislative or technical

change. It can also be changes in economic policies or large economic shocks, such as the oil

crises in 1973. Most macroeconomic time series variables are non-stationary, i.e. they contain

a unit root (Westman, 2005). This means that a structural break can have a permanent affect

on the pattern of the time series (Perman and Byrne, 2006). Testing the unit root hypothesis

allowing for structural breaks has some advantages. One is that it prevents test results from

becoming biased towards unit root. Another advantage is that it can identify when the possible

break occurred. Two important issues with this type of procedure is that some authors claims

that there is a trade-off between the power of the test and the amount of information included

with respect to the choice of break date. A second issue is that the tests only capture the single

most significant break in the series, this can however be corrected for by using tests allowing

for multiple breaks (Glynn et al., 2007).

2 Hereafter referred to as Perron.

14

3.4.1 Exogenous Structural Break

Structural breaks in time series can affect the results of unit root tests (see section 3.4). Perron

argued that the ADF tests become biased towards the non-rejection of the null hypothesis

when a structural break is present. Further, he claims that most macroeconomic series do not

actually exhibit unit root. This characteristic has rather come from large and infrequent shocks

which indicate that the economy returns to a deterministic trend after small and frequent

shocks. Perron therefore modified the standard ADF test to a procedure that includes dummy

variables to account for a single exogenous (known) break. This test allows for a break under

both the null and the alternative hypothesis (Glynn et al., 2007). When an ADF test indicates

that a unit root is present in a time series, the unit root should be considered as a single

permanent break in a deterministic part of a stationary or trend-stationary process (Perman

and Byrne, 2006).

The following three trend break models are developed from Perron. These tests for the

existence of unit root taking three types of structural breaks into account. At first there is a

crash model that allows for a break in the intercept (level) of the time series:

∑ ∆ (10)

The second model is called a changing growth model that allows for a change in the slope

(rate of growth) of the linear trend and the two segments joined at the break date:

∑ ∆ (11)

An example of this can be a productivity slowdown. The third model allows for both an

intercept and a slope change to occur simultaneously, this means a time change in both the

level and the slope.

∑ ∆ (12)

TB represents the break date. The intercept dummy DUt shows a change in level where DUt =

1 if (t > TB) and DUt = 0 otherwise. The slope dummy DTt and DTt* corresponds to a change

in the slope of the trend function DT* = t-TB or DTt* = t if t > TB and zero otherwise. These

15

three models have a unit root with break under the null hypothesis because the dummy

variables are included in the regression under the null hypothesis. The alternative hypothesis

indicates a broken trend stationary process, i.e. that the break was identified ex ante by

economic information (Glynn et al., 2007). This test will not be used in this thesis, however,

the Zivot and Andrews test that will be presented in section 3.5.2 is based upon one of these

models suggested by Perron.

Another test for structural change is the Chow test. The testing procedure divides the sample

into two sub-periods and estimates the same equation for each sub-period separately. Then the

equality of the two sets is tested using the F-statistic to see whether there is some structural

change between the periods before and after the exogenously chosen break date. There are

two ways to pick the date: either by picking an arbitrary candidate break date or picking a date

based on some known characteristic of the data. There are however problems with both ways.

In the first case the true break date can be missed so the test may be uninformative. In the

second case the test can be misleading because the break date is correlated with the data and

the test might indicate a break even though no break exists (Hansen, 2001). The null

hypothesis is that the coefficient for the two sub-periods is equivalent and that there is no

structural change between the two periods. A rejection of the null hypothesis indicates that

there is a structural change between the two sub-periods (Dougherty, 2007).

3.4.2 Endogenous Structural Break

The break date can also be endogenous, i.e. it is correlated with the data (Hansen, 2001). The

test for these kinds of breaks is the same as for exogenous breaks. One tests for each possible

break date in the sample, or some specific part of the sample, and then chooses the date with

strongest evidence against the null hypothesis of unit root. That is where the t-statistic from

the ADF test of unit root is at a minimum (Perman and Byrne, 2006).

Perron and Vogelsang (1992) and Perron (1997) suggested a test that allows for two different

forms of structural break called the Additive Outlier (AO) and the Innovational Outlier (IO)

models. The AO model changes are assumed to take place rapidly allowing for a break in the

slope, while in the IO model changes are assumed to take place gradually. The latter one

allows for a break in both the intercept and the slope. Common for both models is the

assumption of no break under the null hypothesis of unit root (Glynn et al., 2007).

16

Zivot and Andrews (1992)3 transforms Perron’s unit root test that is based upon an

exogenously determined break date into an unconditional unit root test, i.e. instead of treating

the break date as fixed these authors purpose a test where the break date is estimated. The test

allows for a single break in the intercept and the trend (slope) of the series (Zivot and

Andrews, 1992). They suggest a sequential test using the full sample and a different dummy

variable for each possible break date (Perman and Byrne, 2006).

Zivot and Andrews uses the intervention outlier model for the changing growth model in

equation (11) instead of the additive outlier model used by Perron. The regression is written:

ŷ â ŷ ∑ ĉ ∆ŷ ê (13)

where ŷBt is the residuals from a regression with yt as the dependent variable and where the

explanatory variables contains a constant, time trend and DT*t. Further, they treat the

structural break as an endogenous occurrence and the null hypothesis for the three models

presented in equations (10), (11) and (12) is:

(14)

The selection of the breakpoint for the dummy variable in equations (10), (11) and (12) is

viewed as an outcome of an estimation procedure that is designed to fit yt to a certain trend

stationary representation. In other words, Zivot and Andrews assume that the alternative

hypothesis specifies that yt can be a trend stationary process with one break in the trend that

occurs at an unknown point in time. The goal with this test is to find the breakpoint that

supports this alterative hypothesis the most (Zivot and Andrews, 1992). The time of the break

is detected based on the most significant t-statistics for α (Saatcioglu and Korap, 2008). This

is where the t-statistic from the ADF test of unit root is at a minimum, i.e. a break date is

selected where the strongest evidence against the null hypotheses of unit root is found. A

break under the null hypothesis is not allowed in this test (Perman and Byrne, 2006).

3 Hereafter referred to as Zivot and Andrews.

17

3.4.3 Multiple Structural Breaks

Some variables do not show just one break. Relaxing the assumption about only one structural

break makes it possible to test for multiple breaks. In this case the distinction between a non-

stationary and stationary series becomes less clear (Perman and Byrne, 2006).

Clemente, Montañés and Reyes (1998) extend the Perron and Vogelsang (1992) statistics to

the case of two changes in the mean. They wish to test the null hypothesis H0 against the

alternative hypothesis H1.

: (15)

: (16)

In these equations DTBit is a pulse variable equal to one if t = TBi +1 and becomes zero

otherwise. Further, DUit = 1 if t > TBi (i = 1,2) and zero otherwise. TB1 and TB2 represents the

time periods when the mean is being modified. For simplicity, assume that TBi = λiT (i = 1,2)

where 0 < λi < 1 and λ2 > λ1 (Clemente et al, 1998).

If the two breaks belong to the innovational outlier one can test the unit root hypothesis by

estimating the following model:

∑ ∆ (17)

From this estimation the minimum value of the simulated t-ratio is obtained and this value can

be used for testing if the autoregressive parameter is 1 for all break time combinations. To

make it possible to derive the asymptotic4 distribution of this statistic assume that 0 < λ0 < λ1,

λ2 < 1 – λ0 < 1. By implementing the largest possible window, λ1 and λ2 take values in the ((t

+ 2)/T, (T – 1)/T)) interval. Further, assume that λ2 > λ1 + 1 which implies that cases where

the breaks occur in consecutive periods are eliminated (Clemente et al, 1998).

4 Definition asymptote: asymptote to a curve is a straight line that the curve approaches unrestrictive without

coincides with it (NE, 2008a).

18

If the shifts are better described as additive outliers the unit root hypothesis can be tested

through a two-step procedure. First, eliminate the deterministic part of the variable by

estimating the following model:

ỹ (18)

The second step involves taking out the test by searching for the minimal t-ratio for the

hypothesis that ρ = 1 in the following model:

ỹ ∑ ∑ ỹ ∑ ∆ỹ (19)

The dummy variable DTBit is included in the model to make sure that min ^ (λ1, λ2)

converges to the distribution (Clemente et al, 1998):

min ^ , ½ ½ (20)

The thesis continues to examine whether there are structural breaks in the Swedish electricity

price and if these coincide with the international crises. First, a Chow test for one exogenously

determined break will be used. Second, the Zivot and Andrews test that assumes one

endogenous break is performed. Finally, the Clemente, Montañés and Reyes test is used to

test for two structural breaks.

19

Chapter 4

EMPIRICAL RESULTS AND ANALYSIS

The chapter begins with a discussion of the reliability and validity of the data and the

methods. Five different methods have been used to detect unit root processes and structural

breaks in both the nominal and the real Swedish electricity price. Firstly, a Dickey-Fuller and

an Augmented Dickey-Fuller test not allowing for any breaks is used to determine whether

the variables exhibits unit root. Secondly, exogenously determined breaks are detected by the

Chow test for structural change. Furthermore, a Zivot and Andrews test is performed to test

for unit root allowing one endogenous structural break and also a test for two breaks purposed

by Clemente, Montañés and Reyes. The results from these tests are presented in order and

analyzed in a comparison in the end of the chapter.

4.1 Reliability and Validity

The data is based on the nominal value of the electricity price, which implies bias in form of

inflation included in the data. However, when examining structural breaks it is also interesting

to analyse time series with much variation. Furthermore, it is interesting to compare any

differences that might occur between the two time series. That is why tests on both nominal

and real prices will be done. Another limitation is that the years between 1892 and 1900 are

excluded. The main reason is to avoid some extreme values, which might warp the results. In

addition, the use of electricity was very low during these years. The statistics considering the

years between 1892 and 2000 is received in nominal prices from Kander (2002) and is

believed to be reliable. To capture the effects from the deregulation in 1996 the time series

has been extended to 2006. The additional data have been collected from the Statistics of

Sweden and is assumed to be reliable as well. The data concerns the spot price of electricity

without taxes.

The Chow test is a commonly used test for exogenously determined structural change.

Though there are some problems concerning the choice of break point. The true break date

20

can be missed so the test becomes uninformative or the date can be correlated with the data

which gives misleading results (Hansen, 2001). The Dickey-Fuller and the ADF test are

considered as the traditional unit root test. However, there exists some criticism against these

as mentioned before. Firstly, some authors claim that in practice the test tends to have low

power and rejecting the null hypothesis does not always mean that the time series is non-

stationary (Perman and Byrne, 2006). Secondly, not considering a possible existing break

could lead to a bias that reduces the ability to reject a false unit root null hypothesis (Glynn et

al., 2007). That is why the Zivot-Andrews is used. This method has been criticised for not

allowing for break under the null hypothesis, gradual breaks or multiple breaks (Perman and

Byrne, 2006). It is reasonable to think that the series might exhibit more than one structural

break and that breaks occur gradually. That is why the Clemente-Montañes-Reyes test is

performed. For estimation purposes Stata has been used for all tests performed and the tests

have been chosen from those tests that have been available in this programme.

4.2 Unit Root Tests

First, equation (9), the Augmented Dickey-Fuller test, was used to test for unit root without

allowing for any structural breaks. The variables tested are the logarithm of the nominal

electricity price (LELN) and the logarithm of the real electricity price (LELR) under the

period 1900 to 2006. Table 4.1 shows the results from the tests.

Table 4.1 ADF Unit Root Test

Levels

T-stat (lags)

1st difference

T-stat (lags)

Decision

LELN

Intercept

-0.841 (0) Non-stationary

-4.146 (2) Stationary

Unit root

Intercept + trend

None

LELR

Intercept

Intercept + trend

None

-1.240 (0) Non-stationary

-0.622 (0) Non-stationary

-1.437 (0) Non-stationary

-2.136 (0) Non-stationary

-4.033 (2) Stationary

-4.361 (2) Stationary

-4.157 (2) Stationary

-9.006 (1) Stationary

-9.109 (1) Stationary

-4.488 (2) Stationary

Unit root

Unit root

Unit root

Unit root

Stationary

21

The ADF test for unit root in levels shows that the series are non-stationary both in intercept

and trend. Taking the first difference of the series and testing these with and without intercept

and trend makes the series stationary. These results indicate that both of series exhibits unit

root processes. The criticism against the ADF test was that it did not allow for existing

structural breaks and therefore became biased towards unit root which reduces the ability to

reject a false unit root null hypothesis (Glynn et al., 2007). It should also be mentioned that

this test tends to have low power and rejecting the null hypothesis does not always mean that

the series is non-stationary (Perman and Byrne, 2006).

4.3 Exogenous Structural Break Test

To perform a Chow test on the nominal price an autoregressive model of order one was used

to regress the whole sample between 1900 and 2006. The AR(1) model was used because

including more lagged variables did not make the test statistics more significant so for

simplicity only one lag was included. A break date at 1977 was chosen, this because when

looking at figure 2.2 it seems that the series change pattern after this date. The first sub-period

therefore includes the observations between 1900 and 1976. The second sub-period includes

the observations from 1977 to 2006. The same AR(1) model was used to regress the two sub-

periods separately. The result of the residual sum of squares (RSS), the number of parameters

(k) and the number of observations for each period (n1 and n2) was used to perform an F-test.

/ /

(21)

An estimation of the equation above gave the F-value: 7.8483 and the critical F-value5 gives

4.82. The estimated F-value is larger than the critical value and therefore the null hypothesis

of no structural change can be rejected. The alternative hypothesis indicates that there is a

structural change between the two sub-periods in the nominal electricity price. The Chow test

therefore indicates that a structural break in this time series occurs at 1977. The test was also

performed on the real electricity price. A regression of an autoregressive model of order one

was used on the whole sample and the sub-periods. Including more than one lagged variables

made these variables not statistical significant. The chosen break date was at 1968. This break

5 Critical F-value with 1% significance level.

22

date seemed most reasonable when studying figure 2.2. At this point the pattern changes

significantly in the real price series. The estimated F-value becomes 14.2391 which is higher

than the critical F-value6: 4.82. One can reject the null hypothesis which indicates that 1968 is

a structural break in the real electricity price series.

4.4 Testing Unit Root Allowing for Endogenous Breaks

Equation (13), the Zivot-Andrews test, was used to test for unit root allowing for one

endogenously determined structural break. Both the logarithm of the nominal electricity price

(LELN) and the logarithm of the real electricity price (LELR) under the period 1900 to 2006

were estimated. Table 4.2 shows the results of the tests.

Table 4.2 Zivot-Andrews Unit Root Test Allowing for One Break

LELN LELR

Lags included* 3 3

Minimum t-statistics -3.571 -3.009

at year 1977 1990

1% Critical Value -5.43 -5.43

5% Critical Value -4.80 -4.80

* lags for the difference of the series selected via TTest.

When using the Zivot-Andrews test the break date is chosen where the t-statistics for α is

most significant, this is where the t-statistic from the ADF test of unit root is at a minimum.

This is the break date where there is strongest evidence against the null hypothesis of unit

root. For the nominal electricity price the null hypothesis of unit root cannot be rejected

despite that a break has been included. The breakpoint for this variable does not exactly

coincide with any international crises. The break date lies between the first and the second oil

crises in 1973 and 1979. Additionally, the years between 1976 and 1978 were characterized

by high inflation rates. As mentioned before the Zivot-Andrews test does not allow for a

break under the null hypothesis which makes the chosen break date for the nominal electricity

price not significant. This does not necessarily mean that there is no break in 1977. However,

the break date is chosen from the minimum t-statistics and because the t-statistics is calculated 6 Critical F-value with 1% significance level.

from th

fully tru

with the

Figure

This ho

rejected

the one

exogeno

test was

1990 th

also tw

explain

endogen

series fo

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usted. This

e exogenous

4.1 Zivot-A

olds for the

d and theref

es found in

ously and t

s 1968. The

hat was caus

wo years be

a change

nous determ

or the real p

that varies

result is in

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real electr

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over time w

nteresting b

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st, Nomina

icity price

ult cannot b

nal series w

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drews test in

eregulation

rst deregula

in the elect

k differs mi

ctricity.

23

when a seri

because the

n the Chow

al Electricit

as well. Th

be fully trus

where the br

rmined bre

ndicates a b

of the mon

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tricity price

ight be that

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ty Price

he null hyp

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e. The reas

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detect exo

The date c

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electricity

son why th

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y this test c

unit root ca

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hosen in th

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edit expansi

market wh

he exogenou

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annot be

coincides

annot be

fers from

Here the

he Chow

Sweden

ion. It is

hich can

usly and

ak in the

Figure

4.5 Test

Equatio

two stru

logarith

Table 4

Append

Table 4

Variable

LELN

LELR

* Min. t

Remem

break in

for a br

price th

AO mo

4.2 Zivot-A

ting Unit R

on (19), the

uctural brea

hm of the re

4.3 shows

dix 2.

4.3 Clement

e

M

-

-

t is the mini

mber that in

n the slope.

reak in both

e null hypo

del picks 1

Andews Tes

Root Allowi

Clemente-M

aks. Both t

eal electricit

the results

te-Montañé

Additiv

Min t *

-4.700

-3.684

imum t-stati

the AO mo

In the IO

h the interce

othesis of un

945 and 19

st, Real Ele

ing for Two

Montañes-R

the logarith

ty price (LE

from the

és-Reyes U

ve Outlier (

Optimal B

1945 an

1943 an

istics calcul

odel chang

model chan

ept and the

nit root cann

982 as the o

24

ectricity Pr

o Breaks

Reyes test, w

m of the n

ELR) under

tests, for m

Unit Root T

(AO)

reakpoints

nd 1982

nd 1966

lated. 5% cr

es are assu

nges are ass

e slope. Des

not be rejec

optimal brea

rice

was used to

nominal ele

r the period

more test s

est with Do

In

Min t

-3.726

-2.795

ritical value

med to tak

sumed to ta

spite the bre

cted in eithe

ak dates for

o test for un

ctricity pric

1900 to 20

statistics fro

ouble Mean

nnovational

* Opti

6 1

5 1

e for two bre

e place rap

ake place gr

eaks in the

er the AO or

r this series.

nit root allow

ce (LELN)

006 were es

om these t

n Shift

Outlier (IO

imal Breakp

917 and 19

938 and 20

eaks: -5.490

pidly allowi

radually and

nominal el

r the IO mo

. The t-stati

wing for

and the

stimated.

tests see

O)

points

75

00

0.

ing for a

d allows

lectricity

odel. The

istics for

the dum

shows t

IO mod

place ra

Figure

1945 w

Sweden

period a

demand

currency

nominal

rates at

the 1970

Figure

mmy variabl

that the AO

del. This ind

apidly rather

4.3 Clemen

as the last y

n had electr

after 1945, t

ded more e

y by 16%.

l electricity

26,2% and

0’s.

4.4 Clemen

les included

O model is m

dicates that

r than gradu

nte-Montañ

year of the

ricity which

the manufac

electricity.

The IO mo

y price. In

47,0%. The

nte-Montañ

d in the mod

more signif

t the series

ually.

ñés-Reyes A

Second Wo

h increased

cturing indu

In 1982 th

odel suggest

1917 and 1

e second br

ñés-Reyes I

25

dels and the

ficant in exp

is more lik

AO Test, N

orld War an

the demand

ustry in Sw

he Swedish

ts 1917 and

1918 Swed

reak in 1975

IO Test, No

e statistics fo

plaining the

kely to exh

Nominal Ele

nd at this ti

d for electr

eden develo

h central b

d 1975 as th

en suffers

5 can be exp

ominal Elec

for the nomi

e nominal p

ibit structur

ectricity Pr

ime almost

ricity. Addi

oped and he

bank deval

he optimal b

from extrem

plained by t

ctricity Pri

inal electric

price series

ral breaks t

rice

every hous

tionally, du

ence also th

luates the

break point

mely high

the two oil

ice

city price

than the

that take

sehold in

uring the

his sector

Swedish

s for the

inflation

crises in

In the c

reject th

the dum

explaini

graduall

exhibits

specific

model i

and 196

Figure

The yea

model. T

Great D

electrici

power c

level. O

market

end of

internat

Sweden

the dem

real ele

increase

substitu

case of the r

he null hypo

mmy variabl

ing the beh

ly is less li

s a unit ro

cation break

s significan

66.

4.5 Clemen

ars of 1938

The first br

Depression i

ity market a

contracts. D

One can say

started to s

the Secon

tional crises

n had electri

mand of elec

ctricity pric

e in the pric

uted for ele

real electric

othesis of un

les included

haviour of th

ikely to occ

oot process

ks are assum

nt in explain

nte-Montañ

8 and 2000

eak point ca

in the 1930

and Nord P

During this b

y that the e

show at this

nd World W

s. An additi

icity and the

ctricity. The

ce follows

ce of oil, s

ctricity and

ity price the

nit root. Ho

d shows tha

he real elec

cur in this

s despite t

med to take p

ning the real

ñés-Reyes A

have been

an only be e

’s. In 2000

ool became

break date t

ffects of th

s point. In t

War which

onal explan

e manufactu

e second stru

an even pa

ee figure 2

d since the 26

e results in

owever, in th

at only one

ctricity pric

series. The

the presenc

place rapidl

l electricity

AO Test, R

picked out

explained by

both Finla

e the first m

the average

he deregulat

he AO mod

h supports

nation is tha

uring indust

uctural brea

attern, see f

.1. When th

price of o

table 4.4 sh

he case of th

of the dum

e. This indi

e AO mode

ce of struc

ly. The dum

price and th

Real Electri

t as years o

y the beginn

and and Den

multinational

e price of el

tion and th

del the first

the theory

at around 19

try develope

ak takes pla

figure 2.2.

he oil price

oil has cont

hows that th

he IO mode

mmy variab

icates that b

el also sugg

ctural brea

mmy variabl

he test sugg

city Price

of structural

ning of the

nmark had j

l exchange

lectricity w

e more com

t break poin

y of breaks

945 almost

ed which ha

ace in 1966,

This can b

e started to

tinued to ri

he IO mode

el, the t-stati

bles is signi

breaks takin

gests that th

aks. In this

les indicate

gests breaks

l change by

recovering

joined the c

for trade in

was facing it

mpetitive el

nt occurs du

s occurring

every hous

ad a major a

, after this b

be explained

increase it

ise the dem

el cannot

istics for

ficant in

ng place

he series

s model

that this

s in 1943

y the IO

after the

common

n electric

ts lowest

lectricity

uring the

g during

sehold in

affect on

break the

d by the

became

mand for

electrici

Additio

where t

seemed

Figure

4.6 Com

In the fi

the nom

the nom

significa

tests the

breaks i

the nom

results i

at a five

and real

Table 4

Variable

LELN

LELR

ity has als

nally, this

the break w

likely that

4.6 Clemen

mparison

irst stage tes

minal and the

minal electri

ance level.

e results ten

in the Zivot

minal price f

in table 4.4

e percent si

l price of el

4.4 Summar

es AD

Unit

Unit

so continue

break date

was chosen

this series w

nte-Montañ

sts for unit r

e real electr

icity price

Perron arg

nd to be bia

t-Andrews

for electrici

shows that

gnificance

ectricity exh

ry of Unit R

DF test

Root U

Root U

ed to incr

coincides

from study

would exhib

ñés-Reyes I

root withou

ricity price.

cannot reje

gued that wi

ased toward

and Clemen

ity exhibits

for all mod

level. The c

hibits unit r

Root Tests

Zivot-And

Unit Root

Unit Root

27

rease which

with the br

ying the figu

bit two brea

IO Test, Re

ut allowing f

The results

ect the null

thout accou

ds unit root.

nte et al. tes

a unit root

dels the null

concluding

root even wh

drews

U

U

h is reflec

reak date s

ure of the s

aks.

eal Electric

for any stru

s in table 4.4

hypothesis

unting for st

However,

sts the resu

t process. F

hypothesis

remark is t

hen structur

Clemente e

AO mod

nit Root

nit Root

cted in a

suggested fr

series. As m

city Price

uctural break

4 indicate th

of unit roo

tructural bre

allowing fo

ults indicate

or the real

s of unit roo

therefore tha

ral breaks a

et al.

del

Un

Un

decrease in

from the Ch

mentioned b

ks was used

hat the ADF

ot at a five

eaks in the u

or both one

s the same,

electricity p

ot cannot be

at both the

are included

Clemente e

IO mode

nit Root

nit Root

n price.

how test

before it

d on both

F test for

e percent

unit root

and two

i.e. that

price the

rejected

nominal

d.

et al.

el

28

Table 4.5 Summary of Break Points

Variables Chow test Zivot-Andrews Clemente et al.

AO model

Clemente et al.

IO model

LELN 1977 1977 1945 and 1982 1917 and 1975

LELR 1968 1990 1943 and 1966 1938 and 2000

The results in table 4.5 for the nominal electricity price shows that the exogenously

determined break date in the Chow test coincides with the endogenously determined break

date in the Zivot-Andrews test. For the nominal electricity price the dummy variables

included in the Clemente et al. IO model only one were statistical significant. The only

significant endogenously determined breaks that can be identified in this series are the break

dates purposed by the Clemente et al. AO model. That is 1945 and 1982. This result is

interesting as one might have expected that the years around the First World War or at some

date near the oil crises to be characterized by structural change according to the data in figure

2.2. As mentioned before, almost every household in Sweden had electricity at 1945 and the

manufacturing industry developed demanding more electricity, which increased the demand

for electricity and the big devaluation of the Swedish krona is likely to be the reason for the

break in 1982.

The results for the real electricity price in table 4.5 shows that the Zivot-Andrews test

indicates a break during the financial crisis in Sweden in 1990, which does not coincides with

the exogenously determined break in the Chow test where the break date was chosen from

studying the figure of the real electricity price in chapter 2. However, looking at this figure

one might expect that the real electricity price exhibit more than one break. As mentioned

before only one of the dummy variables in the IO model was significant in explaining the real

electricity price. However, the second break in 2000 proposed by this model seems likely

according to the circumstances in the electricity market around this year. The AO model

allowing for two breaks taking place rapidly indicates two significant breaks. The first break

in 1943 cannot easily be detected in figure 2.2, while the second break almost coincides with

the exogenously determined break in the Chow test. After the break in 1968 the series clearly

changes pattern, it becomes almost flat. The change in pattern can be explained by the

substitution from oil towards electricity as the price of oil increases significantly from the late

29

1960’s and forward. This break is the one that coincides with the exogenously determined

break in the Chow test.

Comparing the results for the nominal and the real electricity price one concluding remark is

that something happened with the price of electricity during the period after the Second World

War that is around 1945 were the Clemente et al. AO model suggest a break for both the real

and nominal price. The exogenously and endogenously determined break coincides for both

series but while the nominal exogenously determined break coincides with the one-break

model the real electricity price series exogenously determined break coincides with the two-

break model. These results indicate that the nominal price most likely exhibits one break and

that the real electricity price is better explained by two breaks. This might be expected when

studying the series in figure 2.2 looking at parts where the series follows an even pattern.

30

Chapter 5

CONCLUSIONS

The purpose of this thesis was to examine the Swedish electricity price between the years of

1900 and 2006 in order to determine whether there are any structural breaks in the time series.

This was done by applying different quantitative methods for measuring structural breaks,

which made it possible to compare potential differences.

The analysis shows that for the nominal electricity price that exhibits much variation, none of

the tests that have been applied can reject the null hypothesis of unit root. The exogenously

determined break date suggested in the Chow test is being supported by the Zivot-Andrews

test for one endogenously determined break and partly by the Clemente-Montañés-Reyes IO

model. However, the significance of the two latter tests was not that high. It turned out that

the AO model was most significant in explaining the endogenous determined breaks in the

nominal electricity price series. This model assumes that the breaks takes place rapidly and

suggested 1945 and 1982 as break points in the series. The concluding remark according the

nominal price of electricity is that it exhibits unit root and that breaks are taking place rapidly.

Furthermore, the exogenously determined break did not coincide with the statistical

significant endogenous determined break date in this model. The expected break date was

between the two oil crises in the 1970’s. However, the AO model suggests 1945 and 1982 as

points of structural change.

The results suggested that the real electricity price is possessing unit root. The Zivot-Andrews

test indicates a break in 1990 that is during a financial crisis in Sweden that was caused by a

deregulation of the monetary system and a credit expansion. It is also two years before the

first deregulation of the Swedish electricity market which can explain a change in pattern in

the electricity price. The Clemente-Montañés-Reyes IO model indicates unit root in the real

electricity price but this model was not that significant in explaining the series. The AO model

was significant in explaining the series indicating two breaks taking place gradually in 1943

and 1966. The exogenous determined break in the Chow test takes place around the second

31

break suggested by the AO model. A concluding remark regarding the real electricity price is

that it exhibits unit root and that breaks most likely taking place rapidly. Most of the break

dates suggested by the different tests coincides with international and national crisis, policy

changes on the electricity market and changes in demand. The end of the Second World War

and the increase in demand during this period, the financial crisis in 1990, the massive

increase in the price of oil during the last four decades and the expansion of the common

Nordic electricity market in 2000 are changes that has affect the real price of electricity.

Because the exogenously determined break does not coincides with the endogenous

determined break in the one-break Zivot-Andrews model for the real electricity price one

concluding remark is that it is not always easy to detect a break only by studying a series

pattern. In the case of the real electricity price it seems more likely that the series exhibits

more than one break. These results implies that more than one test should be used and

compared when testing for structural breaks in time series.

As one might expect the nominal price is most affected by fluctuations in the inflation rate.

Both series are exhibits unit root and are best explained by structural changes that is taking

place rapidly. Additionally, the results indicate a break around 1945 for both series. This was

a period when the Swedish economy was strong, most households had electricity, the

manufacturing industry was growing and hence the demand for electricity was increasing.

32

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Appendix 1

ADF test statistics

Nominal ADF Levels

T-stat

Prob

Lag length

Decision

Intercept -0.841 0.803 0 Non-stationary

Intercept + slope -1.240 0.897 0 Non-stationary

None -0.622 0.446 0 Non-stationary

Nominal ADF 1st Diff

T-stat

Prob

Lag length

Decision

Intercept -4.146 0.001 2 Stationary

Intercept + slope -4.361 0.004 2 Stationary

None -4.157 0.000 2 Stationary

Real ADF Levels

T-stat

Prob

Lag length

Decision

Intercept -1.437 0.5617 0 Non-stationary

Intercept + slope -2.136 0.5196 0 Non-stationary

None -4.033 0.0001 2 Stationary

Real ADF 1st Diff

T-stat

Prob

Lag length

Decision

Intercept -9.006 0.0000 1 Stationary

Intercept + slope -9.109 0.0000 1 Stationary

None -4.488 0.0000 2 Stationary

Appendix 2

Clemente-Montañés-Reyes Regression Results

Clemente-Montañés-Reyes Unit Root Test for LELR, IO model

AR(2) Du1 Du2 (rho – 1) Constant

Coefficients 0.07633 0.17002 0.04225 0.22080

T-statistics -2.422 3.485 -2.795

P-values 0.018 0.001 -5.490*

* 5% critical value.

Clemente-Montañés-Reyes Unit Root Test for LELN, IO model

AR(5) Du1 Du2 (rho – 1) Constant

Coefficients -0.05645 0.14603 -0.13117 -0.22272

T-statistics -1.573 4.318 -3.726

P-values 0.119 0.000 -5.490*

* 5% critical value.

Clemente-Montañés-Reyes Unit Root Test for LELR, AO model

AR(12) Du1 Du2 (rho – 1) Constant

Coefficients -1.31289 -1.14709 -0.20113 6.28187

T-statistics -14.632 -12.570 -3.684

P-values 0.000 0.000 -5.490*

* 5% critical value.

Clemente-Montañés-Reyes Unit Root Test for LELN, AO model

AR(3) Du1 Du2 (rho – 1) Constant

Coefficients -0.43087 0.99141 -0.34527 -1.71438

T-statistics -7.900 15.315 -4.700

P-values 0.000 0.000 -5.490*

* 5% critical value.