# Long-Run Forecasting of Energy Prices: Analysing natural gas, steam coal and crude oil prices for DELTA Energy →

## Long-Run Forecasting of Energy Prices: Analysing natural gas, steam coal and crude oil prices for DELTA Energy →

**Long-Run Forecasting of Energy Prices: Analysing natural gas, steam coal and crude oil prices for DELTA Energy As presented at the Energy Forum ”Modelling & Measuring Energy Risk” conference, London, UK, 24th November 2008 Master Thesis in Applied Econometrics By Koen den Blanken 279550kb@student.eur.nl Erasmus University Rotterdam Commissioned by: Portfolio Analytics DELTA Energy B.V. Supervisor DELTA A. Bosschaart MSc. Coreader DELTA F. Schlichter MSc. Supervisor EUR Dr. L. Hoogerheide Coreader EUR Dr. C. Heij 16th December 2008**

3 Executive Summary DELTA Energy relies for its investment decisions on long-run forecasts and scenarios.

Fuel costs are an extremely important component of total costs of most energy generating units and reliable forecasts for fuel prices are therefore needed. Besides a thorough anal- ysis of the fuel commodity and emission allowance prices, research needs to be conducted in the long-run availability, supply and sustainability of the various resources. Despite of the rapid development of renewable energy sources, it is expected that in the next 30 years fossil fuels remain the main portion of power generating capacity. The research question dealt by this report is therefore: to what extent is the long-run behaviour of various commodities used for energy production predictable and what are the implications for DELTA Energy’s asset investment strategy? The focus in the research is on modelling the interdependencies of the fossil fuel price series and assess investment implications.

The main goal is to develop a framework for DELTA Energy to simulate realistic long-run scenarios for natural gas, crude oil and steam coal prices. Besides an application of these price scenarios is given by comparing a coal and gas fired power plant investment.

To answer the research question quarterly price data for natural gas, crude oil and steam coal applicable to the Northwest European region over the period 1970:Q1-2008:Q3 are used. Predictability of the price level is tested by the Augmented Dickey-Fuller, Variance Ratio and KPSS random walk tests. The results are not conclusive though and rule out nor long-run mean-reversion nor the random walk hypothesis. From depletable resource theory it can be expected that long-run prices revert in the long-run to the unobservable marginal cost of extraction, which follows a trend and has continuous fluctuations in both the level and slope of that trend.

Deviations from that trend can be severe due to short- run supply and demand shocks.

**The prices series are modelled by a univariate stochastic long-run mean reverting model, a vector error correction model (VECM) and a multivariate unobserved components model (MUCM). The VECM exploits the significant cointegration relationships between the commodities while the unobserved component models use unobserved underlying (com- mon) factors as explanatory variables. By comparing various methodologies it is possible to judge the models applicability, reducing model uncertainty and likewise improve fore- casting performance.**

The results indicate, especially from 1978:Q1 onward, strong cointegration between nat- ural gas and crude oil prices and cointegration with steam coal prices as well.

Deviations from the price equilibrium however have been significant and long lasting. The univariate stochastic long-run model is not capturing the common trend effect and therefore results

4 in unsatisfactory out-of-sample performance as a result of uncertainty in the trend param- eter. This is evidence in favour of a multivariate approach in energy price modelling. The VECM performs better in capturing the common trend in the long-run energy prices. A negative trend in the long-run relationship between crude oil and natural gas versus steam coal is identified, implying that in the long-run crude oil and natural gas are expected to become relatively more expensive relative to steam coal. The multivariate unobserved components model confirms these long-run relationship between the fuels without assum- ing cointegration of the price series a priori.

It seems to succeed in capturing the slow mean-reversion to long-run equilibrium better than the VECM.

Long-run forecasts for the main energy prices are generated by multiple commercial and government institutions. This makes it possible to compare forecasts from these insti- tutions with the model forecasts. The fuels prices and thereby the interdependencies of the fuels prices from the models are compared to primarily IEA forecasts from the World Energy Outlook from 1994 onward. These results reveal that forecast performance of the models relative to IEA predictions is mixed. It seems that IEA does not predict much changes in the prices ratios of the fuels in most periods. The models do succeed in de- scribing most of the fuel price interdependencies accurately.

**This is evidence in favour of an approach in which the fuel prices are modelled coherently as is done in this research using multivariate models.**

High economic growth and quick depletion of crude oil reserves are the most likely ex- planations for crude oil prices increasing more quickly than natural gas and steam coal prices. Supply of natural gas, uranium and steam coal is currently less problematic. A significant increase in energy demand from emerging markets could in the long-run result in an increasing depletion rate of steam coal reserves and likewise increase coal prices. Greenhouse gas reduction targets and emission trading on the other hand increase total coal usage costs and can potentially decrease total steam coal demand in favour of natural gas demand.

The limited availability of natural gas reserves is an issue which could lead to political instability and security problems resulting in supply disruptions and additional price volatility for this commodity. From a sustainable point of view natural gas has an absolute advantage over steam coal, which currently has higher greenhouse gas emissions per MWh power produced. Technological developments could potentially overcome these difficulties but will most likely increase fuel switching opportunities and further strengthen common trends in prices as well. Uranium poses an interesting alternative to fossil fuels as it is not associated with greenhouse gas emissions.

The costs of uranium represent only a small part of total operation costs of a nuclear power plant. Political concerns on safety and waste disposal on the other hand make investment in nuclear power highly uncertain. Based on the price forecasts generated by the various models and the qualitative aspects four scenarios are constructed. By identifying these scenarios it is possible to describe the likely future development of the fuel prices in a stylized and practical fashion. The

5 scenarios are constructed along two dimensions, energy price levels and trends in relative prices. High versus low crude oil prices representing general energy price levels and a stable versus a continuation of the negative trend in natural gas prices relative to steam coal prices. Fuel price uncertainty combined with technological change and high capital cost of invest- ment pose an interesting challenge to energy companies willing to invest in new generating capacity. By constructing a portfolio of assets it is possible to diversify and hedge risks associated to this investment decision.

A physical investment in a power plant is irre- versible and can only be adjusted at the margin. The investment decision should be based therefore not only on expectations, but on the associated risks as well. Fuel price risk is a major component of total risk and should therefore be considered if the invest- ment decision is made. An important result is that fuel price variance or technological variance with respect to some technology, reduces investment in that technology. The higher fuel price variance of natural gas is therefore an important disadvantage. If total costs are considered though uncertainty will push towards flexible, less-capital intensive technologies, which is in favour of natural gas fired power plants.

**If DELTA Energy could reduce fuel price uncertainty by hedging or using long-term contracts then this could po- tentially increase power plant value. Another important option is considering to delay the investment decision until uncertainties are reduced. The described framework in this research allows DELTA Energy to make careful investment decisions. Given the four earlier constructed scenarios and by making assumptions for the technolog- ical development of natural gas and coal fired power plants, it can from a costs perspective be concluded that a coal fired power plant will probably have over the long-run the low- est power generation costs. **

Only if natural gas prices are substantially lower relative to steam coal prices or if emission costs are extremely high, natural gas fired power plants could potentially have lower generation costs. Furthermore, the additional volatility in natural gas prices could potentially outweigh the impact of emission price uncertainty. It is therefore expected that the historic merit order with coal power plants having lower marginal costs than natural gas fired power plants remains intact. The decision for DELTA Energy to invest in a specific type of power plant depends, besides costs, highly on the power price development.

The growth of renewables and energy savings can have a significant influence on long-run power price levels and volatility. It is expected that renewables will increase demand for peak-load capacity which could be generated by flexible natural gas fired power plants. A phase out of nuclear power generating capacity on the other hand could increase demand for base-load capacity as well. A further in detail analysis of the power market and the development of generating capacity is therefore needed to facilitate a strategic investment decision.

6 Preface This master thesis is the result of my efforts at DELTA Energy B.V. in Middelburg, which started in April 2008 and is the completion of my Master of Science degree in Economet- rics & Management Science at the Erasmus University Rotterdam. The idea for this research came after the observation that long-run energy price assump- tions in many energy studies and scenarios were highly influencing results and likewise research conclusions. To improve long-term decisions making therefore in my opinion a more in depth analysis was needed.

I would like to thank the following persons for being my supervisor: André Bosschaart at DELTA Energy and Lennart Hoogerheide at Erasmus University Rotterdam.

Also thanks to Felix Schlichter for comments regarding my thesis and discussions about energy related topics in general. I want to thank Koen Minderhoud for giving me the opportunity to present my results at the Energy Forum conference about Measuring & Modelling Energy Risk in London in November 2008. Finally, I would also like to thank Ruben van den Berg and Pier Stapersma for feedback on this report and Robert S. Pindyck for generously providing his dataset.

**Middelburg, December 15th, 2008. Koen den Blanken**

CONTENTS 7 Contents Executive Summary 3 Preface 6 Contents 7 1 Introduction 9 1.1 Context of the Research . 9 1.2 Research Objective and Problem Statement . 10 1.3 Research Questions . 10 1.4 Structure and Contents of the Report . 12 2 Data 13 3 Trend line for a Depletable Resource 17 4 Econometric Methodology 19 4.1 Random Walk Tests . 19 4.1.1 Augmented Dickey-Fuller test . 19 4.1.2 Variance Ratio Test . 20 4.1.3 KPSS Stationarity Test . 20 4.2 Stochastic Long-Run Mean-Reverting Model . 21 4.3 Vector Error Correction Model .

22 4.3.1 Johansen Cointegration Test . 23 4.3.2 Granger Causality . 24 4.4 Multivariate Unobserved-Components Model . 24 5 Results Forecast Models 26 5.1 Random Walk Tests . 26 5.2 Stochastic Long-Run Mean-Reverting Model . 28 5.3 Vector Error Correction Model . 30 5.4 Multivariate Unobserved-Components Model . 37 5.5 Summary . 41 6 Comparing Long-Run Forecasts 42 6.1 Stochastic Long-Run Mean-Reverting Model . 44 6.2 Vector Error Correction Model . 46 6.3 Multivariate Unobserved Components Model . 49 6.4 Conclusion and Summary . 51

CONTENTS 8 7 Qualitative Aspects 54 7.1 Crude Oil . 54 7.2 Natural Gas . 56 7.3 Steam Coal . 57 7.4 Uranium . 58 7.5 Emission allowances . 59 7.6 Summary . 61 8 Scenario Analysis 63 8.1 Expert Scenarios . 63 8.2 DELTA Energy’s Scenarios . 65 9 Investment under uncertainty 68 9.1 Real Options Theory . 68 9.2 DELTA Energy’s perspective . 70 9.3 Conclusion and Summary . 75 10 Research Conclusion 76 10.1 Problem Statement Revisited . 76 10.2 Research Conclusion . 76 10.3 Further Research . 78 References 80 A State Space format and the Kalman filter 84 A.1 Stochastic long-run mean-reverting model .

84 A.2 Multivariate unobserved components model . 85 B Abbreviations and Definitions 86

1 INTRODUCTION 9 1 Introduction In this chapter an introduction to the research is presented. First the context of the research is described, followed by the research objective and problem statement. Then several specific research questions to guide the research and their approach are formu- lated. Finally, a short description of the structure and content of the report is supplied. 1.1 Context of the Research Faced with ageing power utilities and increasing demand for electricity energy companies investigate opportunities to invest in new power plants. The choice on the type of power plant is very difficult because of uncertainty surrounding energy prices, fuel supply, regu- lation and investment costs.

**Reducing these uncertainties would help energy companies to reduce investment risk and accelerates the development of new power generating capacity. In recent years commodity prices increased dramatically as a result of high growth ex- pectation for the world economy and depletion of resources. Crude oil prices peaked in July 2008 at 147 USD, but came down quickly thereafter as a result of the downward adjustment of economic growth expectations. The high volatility in recent energy fuel prices clearly reveals the uncertainty in fuel prices and therefore indicates the importance for energy companies to develop a framework for long-run forecasting of energy prices. **

Meanwhile, energy markets in Europe are changing rapidly as a result of market liberal- ization and the search for alternative sources of energy. By an EU directive designed in 1996 the liberalization of the European energy market began. In January 2005 the Euro- pean Union introduced the Emissions Trading Scheme (EU ETS) which for the first time put a price on CO2 emissions for the power sector. Currently, the EU is considering the emission reduction targets for 2020. Furthermore, technological developments are chang- ing the market with, for example, the rapid growth of the liquified natural gas (LNG) market, increased power plant efficiency and decreasing capital costs of renewables.

All these developments are further complicating the investment decision. DELTA Energy owns several large power generating facilities and targets to expand power generation to 2000 MW in 2015 by investing in nuclear, biomass, wind and solar power. For the long-run DELTA wants to expand power generation capacity even further and is continuously investigating the various investment opportunities. DELTA is already in- vesting in a natural gas power with the construction of the Sloe plant which is expected to be completed in 2009.

1 INTRODUCTION 10 1.2 Research Objective and Problem Statement DELTA is planning to extend power generating capacity in the near future. To do so a detailed analysis of the various fuel options is needed. Besides a thorough analysis of the fuel commodity and emission allowance prices, research is conducted in the long-run avail- ability, supply and sustainability of the various resources. The long-run in this research is defined as the period until 2040. This is based on the assumption that the life span of a power plant is approximately 30 years. The fuels considered in this research are: Natural Gas, Steam Coal, Crude Oil and Uranium.

The research is limited to these fuels because fossil fuels will, despite of the rapid development of renewable energy sources, remain the main portion of power generating capacity in the long-run as defined above. In IEA (2008a), it is expected that by 2050 only 46% of global power in the BLUE Map (most optimistic) scenario comes from renewables. Uranium is included in this research as well because it is an important alternative for coal power and DELTA Energy currently has a significant part of nuclear power in its production mix. The objective of the research presented here is to provide DELTA Energy with insight into future developments of the main fuels for power generation and to outline implications for DELTA Energy’s assets and power plant investment planning decisions.

To what extent is the long-run behaviour of the various commodities used for energy pro- duction predictable and what are the implications for DELTA Energy’s asset investment strategy? Fuel availability and prices may have significant impact for DELTA Energy due to changes in the merit order of the power plants and altering operations. These effects can be direct via higher fuel costs, for example through the purchase of coal for power plants, effecting short-run marginal costs. Or emerging indirect via higher fuel costs effecting long-run marginal cost and changing power plant investments.

**Overall, DELTA Energy’s future asset allocation varies with the long-run outlook for the different fuels. 1.3 Research Questions Five research questions guide the research and subsequently build a framework to handle the problem statement.**

1. What are the long-run fuel price behaviours and their interdependencies? 2. What are the long-run effects of availability, supply and sustainability of the fuel types? 3. Which scenarios are realistic for the long-run fuel price developments? 4. What is the effect of fuel price uncertainty on power plant investment decisions?

1 INTRODUCTION 11 5. What are the implications for DELTA Energy’s assets and investment decisions? The first research question is answered by analysing the historic price series of the vari- ous commodities. This analysis is carried out from a time series modelling perspective.

First the individual commodities are analysed in univariate models. By modelling the price series development through time it is possible to better understand the historic de- velopments and to identify the key drivers. Special attention is given to the stochastic long-run mean-reverting process as suggested by Pindyck (1999). To establish this, first long-run mean-reversion opposite to the random walk has to be tested. Subsequently, an analysis of the interdependencies between the series is conducted by analysing the fuel switching opportunities, cointegration tests and by modelling the price series using vector error correction models.

The second research question addresses both historic and future availability and supply limitations. Furthermore, a summarizing analysis of the sustainability of the various fuel types is presented. All these factors add insights in the risks to the use of a specific fuel and helps identifying potential structural changes in the energy market supplementing the statistical analysis. The second research question is answered using literature review and relevant expert reports. The third research question dealt with by this report is the construction of several sce- narios for the future. Using the statistical models constructed in the first section and the qualitative remarks several forecasts are generated.

These forecasts are compared with other expert views and judged on realism. By doing so four plausible scenarios, which are easier to interpret, are identified. By creating these scenarios it is easier to describe the impact of long-run developments in stylized examples.

**The fourth research question is focused on the investment decision in a new to build power plant of given fuel type. Using the existing literature on investment under uncertainty the impact of the long-run fuel price behaviour on investment is assessed. This research question is investigated by considering several articles from portfolio and the real option theory. The fifth research question aims at answering the problem statement. The focal point lies in the impact for DELTA Energy’s assets and future investments plans. In this part specific characteristics of the Dutch Energy market are included.**

1 INTRODUCTION 12 1.4 Structure and Contents of the Report First the process of data collection and transformation is described in Section 2. Sub- sequently, in section 3 the economic theory behind the long-run price development of depletable resources is presented. In this way the expected behaviour and price drivers of long-run energy prices are identified. In the econometric methodology section 4, there- after, statistics are formulated to test these hypotheses and models are proposed to de- scribe the long-run price paths. Results and forecasts from this analysis are given in section 5.

Thereby the first research question is answered in the results summary. In section 6 out-of-sample forecasts from the models are compares with historic expert views. In this way the forecasting performance of the models can be determined. To improve current forecasts with qualitative aspects a discussion of possible future devel- opments in the energy markets is included in section 7, answering the second research question in the summary.

Consequently, scenarios from experts are discussed and to answer the third research ques- tion several scenarios for DELTA Energy are formulated in section 8. The fourth and fifth research question are answered in section 9, where the theory and consequences for DELTA Energy of investment under uncertainty are discussed. The conclusive answer to the research question is formulated in section 10 as well as a discussion of the research and suggestions for further research. In the appendix a detailed description of the state space models and the Kalman filter is presented as well as an overview of the abbreviations and definitions used in this research.

2 DATA 13 2 Data Data from various sources are collected to answer the research questions as formulated in the introduction section. In this section a brief description of the data and its origination is given. All series are prices applicable to the Northwest European energy market. An overview of the data and sources is given in Table 1. Data on fuel prices were collected on a quarterly basis starting in the first quarter of 1970 till the third quarter of 2008. Quarterly data have the benefit over yearly data that it increases the number of observations significantly. Although quarterly data potentially induces seasonality, regressions using dummy variables for specific quarters indicate that this effect is present but negligible, see Table 2 and 3 for results on natural gas and crude oil.

An explanation for this seasonality effect is that in the winter more natural gas is used for heating as a result of the denser population of the Northern hemisphere. In the summer the demand for crude oil would be higher due to holiday traffic. Increasing the observation frequency to monthly data is not possible simply because of limited availabil- ity of high frequency data over the entire sample period. The seasonality was removed and the abbreviation SA was included to those series.

**The prices series of the most traded fossil fuel series by DELTA Energy for natural gas, steam coal and crude oil are used in the statistical analysis of this research. Quarterly average prices are calculated by taking the average price over the mid-day-prices over the months with delivery in the concerning quarter. The 1 month forward price is considered to be a good approximation of the spot price for most commodities. In practise this implies that to obtain for example the Q1 price the average prices of the December, January and February contracts are used. Crude oil price data for West Taxes Intermediate (WTI) and North Sea Brent are available over the entire sample period. **

The natural gas and steam coal series from the traded data are only available starting from 2000:Q1. To obtain the natural gas price series the Dutch gas hub prices, Title Transfer Facility (TTF), are used. This price is over the entire sample period strongly related to the UK National Balancing Point (NBP) and Belgium Zeebrugge (ZB) natural gas prices. For the period 2000:Q1- 2000:Q4, where data for TTF were not yet available, ZB prices were used instead. For steam coal prices the API]2 price is used which denotes coal imported from Columbia in- cluding freight and insurance charges for delivery in Amsterdam, Rotterdam or Antwerp.

Alternatively, API]4 for coal imports from South-Africa could have been used. The re- lationship between these two series is extremely tight and choice of either one of these two coal series is therefore not relevant for the long-run analysis. For crude oil North-Sea Brent is selected as proxy for European oil prices. To cover the period 1978:Q1-1999:Q4 quarterly data from the OECD/IEA publications Energy End-Use Prices for the sector Electricity and Import Costs and Indices by Importing Country for the Netherlands and Belgium were used. This data is available up to current quarter and has high correlation with the market traded series.

Data over the period 1970:Q1-1977:Q4 were constructed

2 DATA 14 Period Series Source Natural Gas (EUR / MWh) 1970:Q1-1977:Q4 U.S. natural gas PPI and ECN points DOE/EIA, ECN 1978:Q1-1999:Q4 Dutch import prices OECD/IEA 2000:Q1-2000:Q4 ZB market data Bloomberg 2001:Q1-2008:Q3 TTF market data Bloomberg Steam Coal (EUR / tonnes) 1970:Q1-1977:Q4 US Coal PPI and ECN points DOE/EIA, ECN 1978:Q1-1999:Q4 Dutch import prices OECD/IEA 2000:Q1-2008:Q3 API]2 market data Bloomberg Crude Oil (EUR / brl) 1970:Q1-2008:Q3 Crude North-Sea Brent Bloomberg Uranium (EUR / kgU), annual data 1970-2008 NUEXCO EV (Spot) OECD Red Book CO2 Emission (EUR / tonnes), daily data 2005-2008 EU ETS Bloomberg Producer Price Index 1970:Q1-2008:Q3 Netherlands PPI All Items OECD Table 1: Data series and sources.

by single point observations from various sources and linked by assuming high correlation with U.S. commodity prices indexes. The 1970:Q1-1977:Q4 price data are not used in the ultimate model estimation and therefore only have illustrative purposes. All prices are excluding taxes and transportation costs to the end-user.

**Furthermore, for illustration annual prices of uranium were collected from the OECD Red Book, as well as prices of emission allowances which are included in section 7. Sufficient historic data of electricity prices are not available due to the non-existence of a free market for electricity in Europe until the late nineties. This is also the reason why this research focusses only on the interdependencies between the various fossil fuels without considering the long-run relationship to electricity prices directly.**

After having constructed the price series for natural gas, steam coal and crude oil from the different sources, the series are deflated to 2008:Q1 chained euro’s using the OECD Netherlands PPI All Items.

Average annual producer price inflation in the Netherlands over the period 1970-2008 denoted 3.0%, Figure 1. As a next step the price series, which will be indicated by Pt, are transformed by the natural logarithm. This transformation is done to remove skewness in the returns and to prevent models from predicting negative values. The transformed series will be denoted by the lower case version pt. The real price series before transformation to log prices are visible in Figure 3. The standard deviation of the returns ∆pt over the sample period 1978:Q1-2008:Q3 are σ = 5.9%, 2.0% and 4.9% per quarter for natural gas, steam coal and crude oil respectively.

2 DATA 15 Dependent Variable: PGASLOG Method: Least Squares Sample (adjusted): 1978Q2 2007Q4 Included observations: 119 after adjustments Coefficient Std. Error t-Statistic Prob. DUMMY*PGASLOG(-1) -0.0222 0.0113 -1.966 0.052 PGASLOG(-1) 1.0113 0.0080 126.173 0.000 R-squared 0.8335 Mean dependent var 2.3692 Adjusted R-squared 0.8321 S.D. dependent var 0.3588 S.E. of regression 0.1470 Akaike info criterion -0.9797 Sum squared resid 2.5293 Schwarz criterion -0.9330 Log likelihood 60.2919 Hannan-Quinn criter. -0.9607 Durbin-Watson stat 1.7240 Table 2: Seasonality regression - Natural Gas. The dummy is 1 in Q2,Q3 (summer) and 0 in Q4,Q1 (winter).

Dependent Variable: POILLOG Method: Least Squares Sample (adjusted): 1978Q2 2007Q4 Included observations: 119 after adjustments Coefficient Std. Error t-Statistic Prob. DUMMY*POILLOG(-1) 0.0203 0.0076 -2.684 0.008 POILLOG(-1) 0.9910 0.0053 185.316 0.000 R-squared 0.9093 Mean dependent var 3.1744 Adjusted R-squared 0.9085 S.D. dependent var 0.4369 S.E. of regression 0.1322 Akaike info criterion -1.1930 Sum squared resid 2.0434 Schwarz criterion -1.1463 Log likelihood 72.9839 Hannan-Quinn criter. -1.1740 Durbin-Watson stat 1.6416 Table 3: Seasonality regression - Crude Oil. The dummy is 1 in Q2,Q3 (summer) and 0 in Q4,Q1 (winter).

2 DATA 16 Figure 1: Producer Price Index All Items - Annual percentage change. Figure 2: U.S. dollars per euro (1970:Q1-2008:Q3). Figure 3: Real 2008:Q1 chained quarterly prices in euro’s of natural gas, steam coal, crude oil and uranium (1970:Q1-2008:Q3).

**3 TREND LINE FOR A DEPLETABLE RESOURCE 17 3 **Trend line for a Depletable Resource Price fluctuations for depletable resources are the result of shocks to supply and demand. For a standard competitive produced good this would imply that the price in equilibrium is equal to the marginal costs of production.

Commodities though are not produced but mined. This leaves the producer with the option to store the commodity in the ground rather than extracting it. The price path should therefore exceed marginal costs and follow a specific dynamic behaviour special to depletable resources, Hotelling (1931). In this section a brief introduction to the economic theory behind price fluctuations for de- pletable resources is given.

Price changes can emerge from fluctuations in demand, extraction costs and reserves. These shocks affect both the log price level and its slope over time. To see this consider the basic model of a depletable resource produced in a competitive market with constant marginal costs of extraction c, Hotelling (1931). In his model the price trajectory, the change of the price P through time t is dP/dt = r(P − c), where r is the interest rate or the desired return on investment. Hence the price level is given by Pt = P0 0ert + c (1) where P0 0 = P0 −c is the net price. The gap between the price Pt and the marginal costs, c, is also known as the scarcity rent.

This difference can be seen as the compensation to the producer for selling the nonreproducible resource which leaves him indifferent between producing now or producing in the future. At lower prices the producer could decide that it is more profitable to store the resource in the mine or reservoir instead of selling it to the market. If the market price is above the desired compensation than naturally production will be increased. In principle this scarcity rent is increasing over time by the rate of interest.

If the demand function is isoelastic, of the form Qt = AP−η t then the trajectory of the production rate is given by Qt = A(c + P0 0ert )−η , (2) where η denotes the elasticity of demand, so the sensitivity of demand to price changes. Using the fact that cumulative production over the life of the resource must equal initial reserves, R0, the initial net price can be obtained by solving R0 = Z ∞ Qtdt = Z ∞ A(c + P0 0ert )−η dt . (3) This function can be evaluated numerically for any given value of η. If unitary elasticity

**3 TREND LINE FOR A DEPLETABLE RESOURCE 18 **of demand (η = 1) is assumed the function reduces analytically to R0 = A rc log c + P0 P0 (4) or P0 0 = c ercR0/A − 1 .

(5) The price level for any time t is now given by Pt = c + cert ercR0/A − 1 , (6) with slope dPt dt = rcert ercR0/A − 1 (7) and log price trajectory d log Pt dt = rc (ercR0/A − 1)ce−rt + c . (8) These last three equations show that an increase in either the level of extraction costs c, an upward shift in the demand curve A or depletion of the resources, lower R, leads to a rise in the price level Pt, but also to increases in the slope and the log price trajec- tory. Although the scarcity rent would in general induce an upward sloping trend it is possible that changes in the underlying factors distort this pattern significantly.

For most depletable resources, one would expect demand, extraction costs and reserves to fluctuate continuously and unpredictable over time. In this way it is for example possible that an unexpected discovery of large resource fields lead to a significant drop in the scarcity rent. Another example would be the recent unexpected high economic growth in emerg- ing markets which has potentially let to much higher scarcity rents for various depletable resources.

Notice that the net price level P0 0 is itself unobservable. This implies that if the price level reverts to its long-term trend, which represents the long-run total marginal costs, that this trend is unobservable. If we want to model the price process under the belief that it reverts towards the long-run marginal cost, the marginal costs and its development through time needs to be estimated from the data. The next chapter introduces several econometric methodologies to test the properties of the historic price series and model the data for forecasting purposes. These tests and models are based on suggestions from depletable resource theory that fuel prices should follow a long-run marginal costs based trend and have continuous random fluctuations in both the level and slope of that trend.

**4 ECONOMETRIC METHODOLOGY 19 4 **Econometric Methodology In this section the various methodologies used in this report will be discussed. First in subsection 4.1 several tests to distinguish long-run mean reversion from the random walk are introduced. Next in subsection 4.2 the stochastic long-run mean-reverting process is handled. Definition of the vector error correction model and cointegration testing to determine the interdependencies between the variables are set-up in subsection 4.3. Subsequently, as alternative in subsection 4.4 the multivariate unobserved components model is introduced.

4.1 Random Walk Tests The purpose of random walk tests is to determine whether or not changes in time series are predictable.

If the random walk hypothesis (RWH) is valid then the concept is that the price serie pt wanders in an unpredictable manner. It is, therefore, for modelling purposes extremely important to know whether series are random walk or are predictable and consequently can be modelled using explanatory variables. The simple random walk hypothesis without deterministic trend is defined as E[pt] = E[pt+τ ] and Cov(∆pt, ∆pt+τ ) = 0 ∀ t ∧ ∀ τ > 0 . (9) Which implies that the expectation of future prices is equal to the current price and cur- rent prices changes are uncorrelated with future prices changes for all time periods t and lags τ.

This is equal to stating that the series is covariance non-stationary or has a unit root. Hence, the best forecast for future prices under the RWH without trend would be the price in the current period.

Alternatively, the series is covariance stationary, has no unit root and is (long-run) mean- reverting. To distinguish the random walk from mean-reversion the ADF, Variance ratio and KPSS test are presented in the following subsections. Different tests are used to avoid limitations in each of the individual tests and establish a robust conclusion. 4.1.1 Augmented Dickey-Fuller test The Augmented Dickey-Fuller test looks whether lagged levels supply any information helpful in explaining changes over and above that contained in lagged changes, Hamilton (1994b). The testing procedure is based on the model ∆pt = α + βt + γpt + δ1∆pt−1 + δp∆pt−m + εt , (10) where m is the lag order of the autoregressive process.

The unit root test is performed by testing the null hypothesis γ = 0 versus the alternative hypothesis γ > 0. Critical values can be obtained by simulation from non-standard distributions and are supplied

**4 ECONOMETRIC METHODOLOGY 20 by MacKinnon (1991). 4.1.2 Variance Ratio Test The Variance Ratio test is based on work by Cochrane (1988) and Campbell and Mankiw (1987). If the series follows a random walk then the variance of n-lags differences should grow linearly with n. The n-th order variance ratio is defined as V R(n) = 1 n Var[pt+n − pt] Var[pt+1 − pt] . (11) The ratio of the variance of the 1-lag difference and n-lags difference should, if the series is a random walk, be close to one. 4.1.3 KPSS Stationarity Test A different approach to test the random walk hypothesis was suggested by Kwiatkowski et al. **

(1992), hereafter KPSS. The difference in their approach is that they take the mean-reversion case as the null hypothesis and the random walk as the alternative. They take the following unobserved components time-series model as starting point, where they decompose the series in a deterministic trend, a random walk and a stationary error: pt = δt + rt + εt . (12) Here rt is a random walk: rt = rt−1 + ηt , (13) where ηt is a stationary error as well. Under mild regularity assumptions, they suggest that testing the null hypothesis of co- variance stationary of the time series pt is equal to whether or not σ2 η is equal to zero by employing the test statistic: LM = T−2 PT t=1 S2 t ˆ ση 2 , (14) In which, the partial sum process St = Pt i=1 ηi, where ηi is the least squares residual obtained from the regression of the de-trended time series pt.

Furthermore, ˆ ση 2 in the denominator of equation (14) is a variance estimator that is intended to relieve the asymp- totic distribution of the LM statistic from nuisance parameters under the null hypothesis. As suggested by KPSS, this variance can estimated by the long-run variance estimator of the residuals ηt.

4 ECONOMETRIC METHODOLOGY 21 ˆ ση 2 = γ̂0 + q−1 X i=1 1 − i q + 1 γ̂i , (15) where the truncation lag q = 4bT/100c2/9 as suggested by Newey and West (1987) and γ̂i are the i-th order autocorrelations. Critical LM values for the KPSS stationarity test with deterministic trend are: 0.216, 0.146 and 0.119 at the 1%, 5% and 10% significance levels respectively. 4.2 Stochastic Long-Run Mean-Reverting Model Modelling the long-run price series for energy resources using a stochastic long-run mean reverting process was first introduced by Pindyck (1999). Pindyck’s long-run model is based on depletable resources theory and postulates two observations on commodity prices: • Reversion to an unobservable long-run marginal cost, which follows a trend; • Continuous random fluctuations in both the level and slope of that trend.

Both observations are based on depletable resource theory as discussed in section 3. Pindyck’s model for annual U.S. data (1870-1996) renders quite reasonable results for crude oil, but experiences some model identification difficulties for coal and natural gas. Later Bernard et al. (2004), using the same data set, find using Monte Carlo simulations instabilities in the mean-reversion parameters for natural gas and coal, but not for crude oil. Furthermore, an extension to Pindyck’s model has been developed by Radchenko (2005) using Bayesian estimation methods and model combination, again for U.S.

data. In this research the stochastic long-run mean-reverting model is imputed with European data and results function as reference to the alternative models of section 4.3 and 4.4. The stochastic long-run mean-reverting process as used by Pindyck with two state equa- tions is defined as: pt = α1 + β1pt−1 + φ1t + φ2tt + εt (16) φ1t = α2 + γ1φ1t−1 + η1t (17) φ2t = α3 + γ2φ2t−1 + η2t , (18) where Pindyck sets α2 = α3 = 0, for identification of the steam coal model γ2 = 1 and for identification of the natural gas model he removes the entire first state equation. This model can be estimated re-writing it in state space format and applying the stan- dard Kalman filter algorithm, Hamilton (1994a).

**General linear state space format is**

4 ECONOMETRIC METHODOLOGY 22 described in detail in appendix A. In the same appendix also the state space format of the stochastic long-run mean-reverting model is given. Forecasts from the model are constructed from the quarters 1998:Q3, 2003:Q3 and 2008:Q3 to reveal the effect of changes in the parameters over time. To reflect forecast uncertainty a 90% confidence bound is used. The parameter uncertainty is simulated using 5000 simulation from the multivariate normal distribution over the parameter space. Forecast uncertainty is simulated by random drawing from the estimation residuals. 4.3 Vector Error Correction Model If the energy commodity prices have a common stochastic trend then it is maybe possible to improve the forecast for these series by using a vector error correction model (VECM).

Besides by modelling the series in a multivariate model, common features can be exploited and if cointegration exists the number of parameters to be estimated remains limited. A common stochastic trend would give a more sophisticated way to describe the independen- cies between the various fuels. To establish this first an investigation into the existence of common stochastic trends or cointegration of the series has to carried out by testing for a unit root, Granger (1981) and Engle and Granger (1987), as presented in subsection 4.3.1. Furthermore, it is possible to include additional lags of the variables in the VECM to explain additional variation in the returns of the series.

By the Granger Causality test, as described in subsection 4.3.2, the usefulness of this approach can be tested. Cointegration is a familiar technique in energy price series modelling. This can be ex- plained from economic theory by the explanation that fuels are competitive substitutes and complements in electricity generation as well as in industrial applications. Siliver- stovs et al. (2005), Villar and Jouth (2006), Hartley et al. (2007) and Benchivenga et al. (2008) are just a glimpse of recent articles which find cointegration between crude oil and natural gas prices over various time periods for U.S.

and European markets. Bachmeier and Griffin (2006) investigate, using U.S. data since 1990, cointegration of coal prices with crude oil and natural gas prices, but conclude that these markets are weakly integrated and therefore adjust only slowly towards long-run equilibrium. To define the VECM, first consider the vector autoregressive (VAR) model: Yt = µ + Φ1Yt−1 + Φ2Yt−2 + ΦpYt−p + et , (19) where in this application Yt = pt,gas pt,coal pt,oil 0 and the Φ’s are 3 × 3 coefficient matrices. In error correction format, that leads to the VECM ∆1Yt = µ + Γ1∆1Yt−1 + Γp−1∆1Yt−p+1 + ΠYt−1 + et, (20)

4 ECONOMETRIC METHODOLOGY 23 where ∆1 denote first differences and where Γi = (Φ1 + Φ2 + Φi) − Im , for i = 1, 2 , p − 1 , (21) Π = Φ1 + Φ2 + Φp − Im , (22) where Π is the 3×3 matrix containing the information on possible cointegration relations between the elements of Yt and I is the identity matrix. Note that due to the logarithmic specification of the price series pt, the first differences ∆1Yt represent quarterly returns. Expanding parameter estimates are calculated by estimating the VECM with maximum likelihood in Matlab version R2007a using a customized version of the LeSage Toolbox1 .

**Forecasts from the VECM are constructed from the quarters 1998:Q3, 2003:Q3 and 2008:Q3 to reveal the effect of changes in the parameters over time. **

To reflect parameter and forecast uncertainty a 90% confidence bound is used. The parameter uncertainty is simulated using 5000 simulation from the multivariate normal distribution over the pa- rameter space. Forecast uncertainty is simulated by random drawing from the estimation residuals. 4.3.1 Johansen Cointegration Test By first regressing equation (20) by row wise OLS, the residuals rt,1, rt,2 and rt,3 and the 3 × 3 residual product matrices Sij = (1/n) n X t=1 rt,irt,j , for i, j = 1, 2, 3 (23) are created. The Johansen (1988) maximum likelihood cointegration test focusses on the rank of Π.

If it is possible to construct the rows of Π by a linear combination of the other rows the rank of the matrix is reduced. If the rank of Π = 0, all series are non- stationary and have no common stochastic trend, but there are as many stochastic trends as variables. If on the other hand the matrix has full rank then all series are stationary and have no common stochastic trend as well. If a common stochastic trend or common trends are present the rank is between these two cases. The rank r is tested by the Trace likelihood ratio test, under the null hypothesis of the existence of at most r unit roots and is given by Trace = −n m X i=r+1 log(1 − λ̂i) , (24) where λi represent the i-th eigenvalue of the matrix S.

A value of the test above the critical value implies the rejection of the null hypothesis.

1 The Econometrics Toolbox by James P. LeSage is freely available at www.spatial-econometrics.com.

**4 ECONOMETRIC METHODOLOGY 24 4.3.2 **Granger Causality Granger causality implies that a variable contains leading information on other variables. This does not mean that the variable actually drives the underlying data generating pro- cess and actually causes the other variable to change, but only in the statistical sense. It contains information in addition to the information in the series own history, which is potentially useful for forecasting purposes when specifying the correct lag structure, Granger (1969).

Granger causality can be tested for normal-distributed, stationary series by regressions of the form y1t = α + β11y1t−1 + β21y2t−1 + βp1y1t−p + βp2y2t−p, for lags p = 1, 2 , T, (25) where y2 is the variable that possibly Granger causes y1. Due to the near-random walk properties of the natural gas, crude oil and steam coal series in our sample the data are transformed to first differences to construct stationarity. Sta- tionarity is required to perform the standard Granger causality test. Subsequently, the Granger causality test is performed on all six possible combinations of the three return series.

4.4 Multivariate Unobserved-Components Model As alternative to the standard cointegration analysis a multivariate unobserved com- ponents model (MUCM) can be proposed. This model can be seen as a multivariate extension of the stochastic long-run mean reverting model as defined in section 4.2. An important drawback of standard cointegration analysis as discussed in section 4.3 is that all variables constituting the stationary equilibrium relation should be included in the analysis. Additionally, Engel (2000) shows that standard cointegration tests are biased toward accepting the cointegration hypothesis in the presence of omitted integrated vari- ables.

Furthermore as Morley (2007) suggests the speed of adjustment in terms of restoring their long-run equilibrium relationship is the same for all variables. That means speed of adjustment measured as the half-life response of a variable to a shock. So although for example the natural gas price adjusts in terms of magnitude more than crude oil the speed of adjustment of both is equal in the VECM. This limits the ability of the VECM to discriminate between alternative price behaviours.

In Section 3 it is argued that commodity prices are determined by a combination of shocks in demand, changing extraction costs and depletion of the resource. The energy prices are in the long-run determined by changes in the underlying long-run marginal cost factors. It can be expected that changes in the marginal costs for crude oil will correspond with

4 ECONOMETRIC METHODOLOGY 25 similar hikes in marginal costs for natural gas and steam coal. For example, cost increases in extraction costs as a result of rising building and labor costs, resource increases as a result of intensified search by energy companies or in case of demand shocks by increased growth of the global economy.

**In the unobserved components framework these omitted integrated variables can be filtered from the long-run relations between the price series. For the set up of the multivariate unobserved components model I follow the method- ology in Morley (2007). He expands the work of Stock and Watson (1988) who suggest decomposing time series into common stochastic trends (random walks) and idiosyncratic stationary components. To apply this model to the fuel price series I add a level shift α and the possibility to have a deterministic drift in the common stochastic trend rela- tionship δ. The multivariate unobserved components model with p3 as base series is than defined as p1,t = β1p1,t−1 + α1 + γ1τt + δ1t + ε1,t (26) p2,t = β2p2,t−1 + α2 + γ2τt + δ2t + ε2,t (27) p3,t = β3p3,t−1 + τt + ε3,t , (28) where τt is the common stochastic trend, βipi the idiosyncratic stationary component and εi ∼ N(0, σ2 εi ). **

The common trend follows an unobservable random walk and is allowed to have deterministic drift µ to capture positive growth in long-run marginal costs: τt = µ + τt−1 + ηt , (29) where ηt ∼ N(0, σ2 η). To allow for additional dynamics of the model, as explained in Morley (2007), I facilitate the innovations in the MUCM to be correlated: ρηεi = corr(ηt, εi,t) for i = 1, 2, 3 (30) ρεiεj = corr(εi,t, εj,t) for i, j = 1, 2, 3 and i 6= j . (31) For estimation, the model is casted into state space format as defined in appendix A. Subsequently the Kalman filter and maximum likelihood estimation is applied to obtain expanding parameter and state variable estimates.

The Matlab optimisation routine for the Kalman filter is available from the author upon request. Forecasts from the MUCM are constructed from the quarters 1999:Q4, 2004:Q4 and 2008:Q3 to reveal the effect of changes in the parameters over time. To reflect parameter and forecast uncertainty a 90% confidence bound is used in which the parameter uncer- tainty is simulated using a multivariate normal distribution over the parameter space.

**5 RESULTS FORECAST MODELS 26 5 **Results Forecast Models Results from the tests and models as described in section 4 are presented in this chapter. First the outcomes of the various random walk tests are given in section 5.1. Subsequently, in section 5.2 results from the stochastic long-run mean-reverting process, followed by the vector error correction model in section 5.3. Finally, the estimation and forecast results from the multivariate unobserved components model can be found in section 5.4. By comparing results from various models it is possible to judge the models’ applicability, reducing model uncertainty and likewise improve forecasting performance.

A summary of the results and an answer to the first research question is formulated in section 5.5. 5.1 Random Walk Tests The Augmented Dickey-Fuller (ADF) unit root test for various lag lengths with determin- istic trend fails to reject the null-hypothesis of a unit root in the series. This implies that it can’t be ruled out that the series behave as a random walk. Autoregressive parameters for all series are close to one, with coal 0.98, natural gas 0.95 and crude oil 0.95. This suggests that a significantly larger sample is necessary to make rejection possible in the first place. The power of the ADF test for series with high autoregressive parameters is very limited.

The failure to reject the unit root does not imply the acceptance of the random walk hypothesis. It therefore leaves the discussion open to the reader. The results of the Variance Ratio test in Figures 4, 5 and 6 for natural gas, steam coal and crude oil respectively indicate that for increasing lag differences the ratio clearly starts to deviate from 1. The decline in the variance ratio is slow, but comparable with the variance ratios found by Pindyck (1999). He also reports variance ratios of approximately 40% after 15 years (60 quarters). This is evidence in favour of long-run mean-reverting behaviour in the logarithm of the series.

If we, however, test for significance of the differ- ence of the variance ratio from 1, a simple z-test fails to reject the random walk hypothesis. LM values for the KPSS test for natural gas, steam coal and crude oil are respectively 0.1116, 0.0198 and 0.0995. All values are below the 10% significance level of 0.119 and therefore indicate that there is no argument to reject the null hypothesis of stationarity. This result though can be the consequence of low rejection power of the KPSS test due to the short sample of the series. The results for crude oil deviate from Hamilton (2008) who rejects the null hypothesis for U.S.

dollar prices over the sample period 1970:Q1-2008:Q1. The conclusion is that the ADF, Variance Ratio and KPSS test produce seemingly con- tradicting results. The failure to reject the unit root does not imply the acceptance of the random walk hypothesis. Nor does the failure to reject the mean-reverting hypothesis imply the acceptance of long-run memory. Therefore it is statistically impossible to rule out one of these options based on these test results.

5 RESULTS FORECAST MODELS 27 Figure 4: Variance Ratio - Natural Gas, lag in quarters Figure 5: Variance Ratio - Steam Coal, lag in quarters Figure 6: Variance Ratio - Crude Oil, lag in quarters

**5 RESULTS FORECAST MODELS 28 5.2 **Stochastic Long-Run Mean-Reverting Model The model as defined in section 4.2 resulted in coefficients for γ1 and/or γ2 higher than 1 for all series. This caused that the recursive estimates of the state equations can explode. Therefore some of the γ coefficient were restricted to 1 and the models re-estimated. The problem remained for all series and eventually all γ coefficients were eventually set to 1.

To facilitate identification the constant terms α were set to zero. Results of the remaining parameters estimates are given in Table 4.

The Kalman filter results deviate quite substantially from Pindyck (1999). The low au- toregressive coefficients of crude oil and natural gas suggest high mean-reversion, but most of the variation in the log price series is captured by the unobserved components. Remarkable is the small negative coefficient of the stochastic trend for steam coal prices, which illustrates the slow downward moving trend in recent decades. Forecasting results from 1998:Q3, 2003:Q3 and 2008:Q3 for natural gas, steam coal and crude oil are given respectively in Figure 7, 8 and 9. For all three series it is clear that the forecasted trend has changed in the recent years.

This is mainly due to the fact that the trend line depends highly on the sign of slope of the stochastic trend. For steam coal the trend recently changed from decreasing into relatively flat. It is clear that forecasting results from these univariate models are unsatisfactory. The confidence intervals reveal that the uncertainty of the forecasts is very high. A small estimation error or change in the trend parameter has a large effect on the forecasted commodity prices. Furthermore, the model estimates give no insight in the interdepen- dencies between the fuel prices in the long-run. This supports the multivariate approach as followed in the subsequent sections.

Stochastic long-run mean-reverting model Estimates, 1978:Q1-2008:Q3 Natural Gas β1 φ1,T φ2,T σε ση1 ση2 Log likelihood 0.119 1.581 0.012 0.000 0.000 0.000 60.96 (0.354) (1.826) (0.059) (0.000,0.000) (0.000,0.000) (0.000,0.000) Steam Coal β1 φ1,T φ2,T σε ση1 ση2 Log likelihood 0.629 1.784 -0.000 0.007 0.000 0.000 125.61 (0.241) (2.384) (0.053) (0.000,0.016) (0.000,0.000) (0.000,0.000) Crude Oil β1 φ1,T φ2,T σε ση1 ση2 Log likelihood 0.161 1.784 0.016 0.000 0.019 0.000 66.46 (0.377) (1.203) (0.050) (0.000,0.000) (0.003,0.100) (0.000,0.000) Table 4: Parameter estimates calculated using MLE. Standard errors reported in parentheses.

5 RESULTS FORECAST MODELS 29 Figure 7: Forecasts univariate stochastic mean-reverting model - Natural Gas (log prices). Dotted lines represent the 90% confidence interval, inner forecast uncertainty, outer including parameter uncertainty. Figure 8: Forecasts univariate stochastic mean-reverting model - Steam Coal (log prices). Dotted lines represent the 90% confidence interval, inner forecast uncertainty, outer including parameter uncertainty. Figure 9: Forecasts univariate stochastic mean-reverting model - Crude Oil (log prices). Dotted lines represent the 90% confidence interval, inner forecast uncertainty, outer including parameter uncertainty.

**5 RESULTS FORECAST MODELS 30 5.3 **Vector Error Correction Model Before estimating the vector error correction model (VECM) the steam coal, crude oil and natural gas series are tested for common stochastic trends and Granger Causality. Thereafter the VECM is estimated and forecasts are generated. Expanding estimates of the Trace statistic for cointegration with and without linear trend are presented in Figure 11. The horizontal dashed lines represent the critical values for the null hypothesis test of none up to at most 2 cointegration relation at the 95% sig- nificance level. Values above this line indicate a rejection of the null hypothesis.

The test rejects the null-hypothesis of no common stochastic trends at the 95% significance level. The hypothesis of at most one stochastic trend is rejected only in the some years between 1990 and 2005. The existence of two common trends is therefore left open to discussion. It seems that the linear trend model with two cointegration relationships is the most attractive and theoretically sound model. The linear trend coefficients in the cointegration relationships are small, but significant.

The coefficient estimates of the linear trend in the cointegration relationships with 2 unit roots are shown in Figure 10. These graphs indicate that the trend has become more im- portant since 2000 and resulted in a shift in the cointegration relationship, especially in the long-run relationship describing steam coal and crude oil. Crude oil is getting increas- ingly expensive while the steam coal price increases less quickly. A possible explanation for this change in the cointegration relationship could be a change in relative efficiency or changes in the underlying marginal cost drivers.

An example of such a change could be the higher depletion rate of crude oil reserves relative to the more widely available steam coal reserves. An increase in the relative efficiency by technological change in favour of oil and gas on the other hand could lead to a permanent demand shock as a result of fuel switching by electricity generators and industrial users in the direction of gas and oil products away from coal.

Results for the Granger Causality test can be found in Table 5. Using 95% as confidence level the test indicates that out of the six combinations only crude oil returns Granger cause natural gas returns significantly. This implies that crude oil prices contain poten- tially valuable information in predicting natural gas prices. Including one lag into the VECM therefore could potentially improve forecast accuracy. Furthermore, at the 90% confidence interval natural gas return Granger cause steam coal returns as well. Remark- ably crude oil returns do not Granger cause steam coal returns which would be expected through natural gas returns.

Apparently, the information in natural gas returns which helps explaining the variation in the coal returns is not the same part of the information which is explained by crude oil returns.

**In Figure 12 the development of the cointegration residuals is shown. The error cor-**

5 RESULTS FORECAST MODELS 31 Null Hypothesis: Obs F-Statistic Prob. ∆poil does not Granger Cause ∆pgas 115 9.27828 2.E-06 ∆pgas does not Granger Cause ∆poil 0.25518 0.9059 ∆pcoal does not Granger Cause ∆pgas 115 0.73885 0.5675 ∆pgas does not Granger Cause ∆pcoal 2.17035 0.0773 ∆pcoal does not Granger Cause ∆poil 115 0.76065 0.5532 ∆poil does not Granger Cause ∆pcoal 0.79592 0.5304 Table 5: Pairwise Granger Causality Test: lags 4 - quarterly returns natural gas, steam coal and crude oil (1978:Q1-2007:Q4).

rection mechanism is clearly visible, but deviations from equilibrium can be large and mean-reversion is slow. Especially for the cointegration relationship between crude oil and steam coal where deviations can hold on for several years. These deviations though are not surprising as Hartley et al. (2007) already indicated that severe short-run deviations can occur as a result of seasonality, weather shock and changes in storage. Cointegration between natural gas and crude oil is much stronger and estimation results are inline with results found in the literature. Error correction is much stronger for natural gas than crude oil as can be seen from the much smaller, even insignificant, coefficients for the er- ror correction terms.

This confirms that crude oil is still the main determinant of energy price levels in the market.

In Figures 13, 14 and 15 forecasts from the VECM with linear trend for 1 and 2 coin- tegration relations can be found. Predictions are shown from 1998:Q3 and 2008:Q3 on, results for the 2003:Q4 predictions were similar but are available at the author on request. The inner dotted lines are the 90% confidence interval representing forecast uncertainty and the outer include parameter uncertainty. The confidence intervals around the price forecasts seem large certainly if you remember that prices are in logs, but considering the correlation between the fuel prices this is misleading. Both models predict a positive trend for crude oil and natural gas prices relative to steam coal prices which are predicted to remain stable.

To give more insight in the interdependencies the price ratios of the forecasts are consid- ered in Figures 16, 17 and 18. Predictions for the coal-oil ratio are decreasing towards 0.5 by 2040. Gas-oil decreases towards 0.22 and gas-coal increases towards 0.52 by 2040. Parameter uncertainty has limited effect on the eventual outcomes. This is due to the two cointegration relationships which forces the prices back to their long-run equilibrium. This is a huge advantage over the univariate stochastic long-run mean reverting model of section 5.2. In the VECM with one cointegration relationship the uncertainties are larger because of limited reversion of the steam coal series in that case.

**The results do confirm the same results as with the stochastic long-run mean-reverting**

**5 RESULTS FORECAST MODELS 32 VECM **Estimates, 1978:Q3-2008:Q3 Cointegration Equation 1 Equation 2 Relation PGASLOGSA 1.0000 0.0000 PCOALLOG 0.0000 1.0000 POILLOGSA -0.844 -0.737 (0.072) (0.034) Trend (’78:Q1) 0.006 0.025 (0.003) (0.002) Constant -0.286 -3.903 (0.532) (0.208) Error D(PGASLOGSA) D(PCOALLOG) D(POILLOGSA) Correction CointEq1 -0.617 0.046 -0.028 (0.076) (0.055) (0.092) CointEq2 0.204 -0.139 0.144 (0.069) (0.050) (0.084) D(PGASLOGSA(-1)) 0.278 0.092 0.120 (0.078) (0.056) (0.095) D(PCOALLOG(-1)) -0.013 0.293 -0.005 (0.125) (0.090) (0.152) D(POILLOGSA(-1)) -0.179 0.025 0.220 (0.091) (0.065) (0.110) Constant 0.008 0.000 0.007 (0.010) (0.007) (0.010) Table 6: Cointegration coefficients linear trend VECM with 2 unit roots.

Standard deviation error in parentheses.

model that in the long-run steam coal prices are decreasing relatively in relation to nat- ural gas and crude oil prices. Furthermore, crude oil prices are rising more quickly than natural gas prices. Advantage of the VECM is deeper insight in the interdependencies and associated uncertainties. Although, the selection of number of cointegration relationship remains important for the model outcomes.

5 RESULTS FORECAST MODELS 33 Figure 10: Expanding estimate of linear trend parameters of cointegration equations and corresponding t-statistic values. A absolute value higher that 1.96 indicates significance of the linear trend at the 95% confidence level, represented by the dotted line.

Figure 11: Trace test statistic values for no-trend and linear trend VECM specification, data 1978:Q1- 2008:Q3. The horizontal dashed lines represent the critical values for the null hypothesis test of none, at most 1 and at most 2 cointegration relation(s) at the 95% significance level.

5 RESULTS FORECAST MODELS 34 Figure 12: Development of cointegration residuals in linear trend VECM with 2 cointegration relations, 1978:Q1-2008:Q3. Relation 1 is natural gas versus crude oil and relation 2 describes steam coal versus crude oil. Figure 13: Forecasts VECM 1998:Q3 - linear trend and 1 cointegration relation. Dotted lines are 90% confidence intervals, inner forecast uncertainty, outer including parameter uncertainty.

**5 RESULTS FORECAST MODELS 35 Figure 14: Forecasts VECM 2008:Q3 - linear trend and 1 cointegration relation. Dotted lines are 90% confidence intervals, inner forecast uncertainty, outer including parameter uncertainty. **

Figure 15: Forecasts VECM 2008:Q3 - linear trend and 2 cointegration relations. Dotted lines are 90% confidence intervals, inner forecast uncertainty, outer including parameter uncertainty.

5 RESULTS FORECAST MODELS 36 Figure 16: Forecasts price ratio steam coal and crude oil - VECM 2008:Q3 2 cointegration relations. Red dotted line represents 90% confidence intervals. Blue dotted line represents 90% confidence interval including parameter uncertainty. Figure 17: Forecasts price ratio natural gas and crude oil - VECM 2008:Q3 2 cointegration relations. Red dotted line represents 90% confidence intervals. Blue dotted line represents 90% confidence interval including parameter uncertainty. Figure 18: Forecasts price ratio natural gas and steam coal - VECM 2008:Q3 2 cointegration relations.

Red dotted line represents 90% confidence intervals. Blue dotted line represents 90% confidence interval including parameter uncertainty.

**5 RESULTS FORECAST MODELS 37 5.4 **Multivariate Unobserved-Components Model The multivariate unobserved components model is estimated for the trivariate system of the price series natural gas p1t, steam coal p2t and crude oil p3t. Parameter estimates from maximum likelihood estimation are available in Table 7. Correlated MUCM Estimates, 1978:Q1-2008:Q3 Natural Gas α1 δ1 γ1 β1 σε1 0.102 -0.002 1.141 0.503 0.018 (0.690) (0.006) (0.048) (0.100) (0.002,0.0180) Steam Coal α2 δ2 γ2 β2 σε2 0.951 -0.006 0.662 0.732 0.006 (0.508) (0.005) (0.050) (0.028) (0.001,0.038) Trend Crude Oil µ τT ση β3 σε3 0.003 1.123 0.001 0.709 0.011 (0.003) (0.043) (0.000,0.001) (0.033) (0.001,0.098) Correlations ρε1ε2 ρε1ε3 ρε2ε3 ρηε1 ρηε2 ρηε3 0.145 -0.382 -0.258 -0.496 0.167 0.866 (0.076) (0.092) (0.059) (0.305) (0.231) (0.292) Table 7: Parameter estimates calculated using MLE.

Standard errors parameters reported in parentheses, except for the σ’s which are reported as 95% confidence interval. Log likelihood 279.8. The results for the trend parameters confirm the positive growth of long-run marginal costs. The small negative δ parameters suggest an increase in the crude oil price relative to natural gas and steam coal prices in the long-run. Second, contrary to the VECM, the difference in the autoregressive parameters of the transitory price components allows for individual speeds of adjustments of the price series. Although, likelihood ratio tests for H0 : β1 = β3, β2 = β3 indicate that the 5% critical value of 3.84 is not exceeded.

Mean- while, the parameter estimates are robust over the sample. The correlation estimates reveal the presence of some remaining dynamics in the errors term not yet captured by the model. The likelihood ratio test for H0 : pij = 0 is 23.4, which exceeds the 5% critical value of 12.59 indicating that the correlations significantly improve model fit. Forecasts for the natural gas, steam coal and crude oil prices from 1999:Q4 and 2008:Q3 are shown in Figure 19 and 20. The 2003:Q4 forecasts not show here produced similar results. The common stochastic trend is presented in the same figure by the black line.

The confidence intervals indicated by the dotted lines around the price forecasts seem large certainly if you remember that prices are in logs, but considering the correlation

5 RESULTS FORECAST MODELS 38 between the fuel prices this is misleading. If a high oil price is realized it is probable that the coal and natural gas price will be high as well. Notice that the confidence interval around steam coal prices is relatively small reflecting the lower variation in steam coal prices. The forecasted energy price levels have changed significantly since 2000 due to the strong increase in recent years. The MUCM has preserved the relationships between the fuel prices. The relative price decrease of steam coal prices in relation to gas and oil prices is still intact. Furthermore, natural gas and crude oil prices are both steadily increasing.

To give more insight in the interdependencies the price ratios are considered in Figures 21, 22 and 23. Predictions for the coal-oil ratio are decreasing towards 0.3 by 2040. Gas-oil decreases towards 0.21 and gas-coal increases towards 0.7 by 2040. Parameter uncertainty has a large effect on the eventual outcomes. This effect is much larger than at the VECM due to the fact that cointegration is not assumed in this model. Thanks to the mean-reversion the forecast uncertainty remains limited which is a huge advantage over the univariate stochastic long-run mean reverting model of section 5.2.

**The results do confirm the same analysis as in the SMRM and VECM that in the long- run steam coal prices are decreasing relatively in relation to natural gas and crude oil. Furthermore, crude oil prices are rising more quickly than natural gas prices.**

5 RESULTS FORECAST MODELS 39 Figure 19: Realized and forecasted log prices of natural gas, steam coal and crude oil - MUCM 1999:Q4. Dotted lines are 90% confidence intervals, inner forecast uncertainty, outer including parameter uncer- tainty. Black line represents estimated common stochastic trend τ and forecast. Figure 20: Realized and forecasted log prices of natural gas, steam coal and crude oil - MUCM 2008:Q3. Dotted lines are 90% confidence intervals, inner forecast uncertainty, outer including parameter uncer- tainty. Black line represents estimated common stochastic trend τ and forecast.

5 RESULTS FORECAST MODELS 40 Figure 21: Realized and forecasted price ratio steam coal and crude oil - MUCM 2008:Q3. Red dotted line represents 90% confidence interval. Blue dotted line represents 90% confidence interval including parameter uncertainty. Figure 22: Realized and forecasted price ratio natural gas and crude oil - MUCM 2008:Q3. Red dotted line represents 90% confidence interval. Blue dotted line represents 90% confidence interval including parameter uncertainty. Figure 23: Realized and Forecasted price ratio natural gas and steam coal - MUCM 2008:Q3. Red dotted line represents 90% confidence interval.

Blue dotted line represents 90% confidence interval including parameter uncertainty.

**5 RESULTS FORECAST MODELS 41 5.5 **Summary This chapter addressed the first research question, i.e. what are the long-run fuel price behaviours and their interdependencies? It did so by considering statistical tests of the random walk hypothesis (RWH) and modelling the historic price series of the various fossil fuels. The results of the tests though are not conclusive and rule out nor long-run mem- ory nor the RWH. Therefore, models considering the RWH and long-run mean-reversion are used in this research to describe energy prices. The prices series are modelled by a univariate stochastic long-run mean reverting model, a vector error correction model (VECM) and a multivariate unobserved components model (MUCM).

The VECM exploits the significant cointegration relationships between the commodities while the unobserved component models use unobserved underlying (common) factors as explanatory variables. The results indicate historically strong cointegration between natural gas and crude oil prices and cointegration with steam coal prices as well. This implies that the fossil fuel prices are closely related and do not move independently. Deviations from the long-run price equilibrium though have been significant and long lasting. The univariate stochas- tic long-run model is not capturing the common trend effect and therefore results in unsatisfactory out-of-sample performance as a result of high uncertainty in the trend pa- rameters.

This is evidence in favour of a multivariate approach in energy price modelling. The VECM performs well in capturing the common trend. The multivariate unobserved components model confirms the long-run relationship between the fuels without assuming cointegration of the price series. A negative trend in the long-run relationship between crude oil and steam coal is identified in both models, implying that in the long-run crude oil and natural gas are expected to become relatively more expensive in comparison to steam coal. Moreover, crude oil prices are expected to increase slightly faster than natural gas prices.

The next chapter supplements this chapter by testing the out-of-sample performance of the various forecasting models. By comparing the forecast from the VECM and MUCM with the expert opinion from the International Energy Agency (IEA) and other professional institutions it is possible to judge the model estimates of the fuel price interdependencies.

**6 COMPARING LONG-RUN FORECASTS 42 6 **Comparing Long-Run Forecasts Long-run forecasts of energy prices are of vital interest to many business and government institutions for investment and policy decisions. Therefore government agencies as the International Energy Agency (IEA) and the Energy Information Administration (EIA) part of the U.S.

Department of Energy (DOE) make regular forecasts. In the Netherlands the Central Planing Bureau (CPB) does not publish energy price forecasts on a regular basis, but does on occasions publish special reports. Furthermore, a wide spectrum of commercial forecasting agencies is active in the market place. In this section (historic) forecasts from the IEA and various other agencies will be discussed and compared to the model results from section 5. The focus in forecast performance is on the ratios of the fuel prices, because this is the most relevant for the interdependencies of the fuel prices.

Forecast from OECD/IEA for world crude oil, EU natural gas import and EU steam coal import prices are presented in Table 8, 9 and 10 respectively. The forecasts are given as an average annual price for consecutive 5 year periods ahead up to 2030. The first forecasts were published in the World Energy Outlook (WEO) 1994 edition and the last in 2006. The World Energy Outlook 2008 is not expected before November 2008 and is therefore at the moment of writing not included in this report. World crude oil price forecasts from DOE can be found in Table 11. The DOE does sadly enough not report European steam coal or natural gas price forecasts.

All forecasts in U.S. dollars were converted to 2008:Q1 chained euro prices. The Four Scenarios report, CPB (2004), forecasted a steady increasing oil price to 40 euro’s for 2025 inline with IEA and EIA predictions at that time. Notice that all forecasts underestimated 2005 crude oil and natural gas prices significantly. A comparison of the price ratio forecasts of natural gas versus crude oil and steam coal versus crude oil from the IEA with the stochastic long-run reverting model (SMRM), the vector error correction model (VECM) and the multivariate unobserved components model (MUCM) is given in subsequent subsections.

To reflect uncertainty in the number of cointegration relations in the VECM both the 1 and 2 cointegration relationships options are presented. Additionally, an equal weighted (EW) forecast is produced by averaging the forecasts from the three models (SMRM, VECM trace and MUCM) into a single forecast. This technique potentially reduces forecast errors and avoids the issue of model selection, Timmerman (2006) and Capistran and Timmerman (2007). To make a fair comparison only data until the year of the IEA publication is used in the model estimation. To calculate forecast errors the IEA forecasts were interpolated by the pchip function in Matlab which produces a piecewise Cubic Hermite interpolation polynomial.

Absolute and relative root mean squared prediction errors (RMSPE) of the various models are summarized in Table 12 in the final subsection. The RMSPE values were estimated by calculating the weighted average RMSPE of the seven IEA forecasts (0 94,0 96 , 0 06) weighted by the number of forecasted quarters (60, 52 , 12).

**6 COMPARING LONG-RUN FORECASTS 43 **Forecasts IEA - world crude oil prices (2008:Q1 euro’s per barrel) Year WEO’94 WEO’961 WEO’98 WEO’00 WEO’02 WEO’04 WEO’06 1995 22.40 22.342 2000 29.64 23.29 22.87 18.702 2005 36.89 34.25 22.87 22.20 33.94 35.56 54.872 2010 36.89 34.25 22.87 22.20 33.94 35.56 55.83 2015 33.63 26.23 37.18 38.79 51.82 2020 33.63 30.27 40.41 42.02 54.42 2025 43.64 44.45 57.02 2030 46.87 46.87 59.92 Table 8: Long-run forecasts world crude oil prices in real 2008:Q1 chained euro’s per barrel as published in the biannual World Energy Outlook by OECD/IEA. 1) Forecasts from WEO 1996 are those of the Capacity Constraints Case, IEA (1996).

2) Not forecasted, but actual price realisation. Forecasts IEA - EU natural gas import prices (2008:Q1 euro’s per MWh th) Year WEO’94 WEO’961 WEO’98 WEO’00 WEO’02 WEO’04 WEO’06 1995 11.10 11.852 2000 14.95 12.34 11.91 7.782 2005 18.80 17.96 11.91 8.64 15.99 18.20 21.382 2010 18.80 17.96 11.91 9.36 15.44 18.20 21.97 2015 17.35 12.36 16.82 19.58 20.53 2020 17.35 15.36 18.20 20.96 21.74 2025 19.58 22.34 22.94 2030 20.96 23.72 24.15 Table 9: Long-run forecasts EU natural gas import prices in real 2008:Q1 chained euro’s per MWh as published in biannual World Energy Outlook by OECD/IEA. 1) Forecasts from WEO 1996 are those of the Capacity Constraints Case, IEA (1996).

2) Not forecasted, but actual price realization. Forecasts IEA - EU steam coal import prices (2008:Q1 euro’s per ton) Year WEO’94 WEO’961 WEO’98 WEO’00 WEO’02 WEO’04 WEO’06 1995 53.75 61.242 2000 65.21 65.71 56.50 39.412 2005 72.46 69.23 56.50 50.31 59.80 71.12 67.702 2010 72.46 69.23 56.50 50.31 63.04 64.65 59.62 2015 61.88 50.31 64.65 66.27 60.49 2020 61.88 50.31 66.27 67.89 62.00 2025 68.69 69.50 63.52 2030 71.12 71.12 65.04 Table 10: Long-run forecasts EU steam coal import prices in real 2008:Q1 chained euro’s per ton as published in biannual World Energy Outlook by OECD/IEA. 1) Forecasts from WEO 1996 are those of the Capacity Constraints Case, IEA (1996).

2) Not forecasted, but actual price realization.

**6 COMPARING LONG-RUN FORECASTS 44 **Forecasts DOE - world crude oil prices (2008:Q1 euro’s per barrel) Year AEO’96 AEO’98 AEO’00 AEO’02 AEO’04 AEO’06 AEO’08 2000 24.43 21.67 18.701 2005 27.83 23.07 27.87 36.74 34.18 54.871 2010 31.22 24.47 28.57 37.76 35.46 52.29 73.42 2015 33.50 25.87 29.29 38.79 36.78 52.85 59.35 2020 27.28 29.98 39.89 38.17 56.07 59.20 2025 39.61 59.80 63.95 2030 63.00 69.87 Table 11: Long-run forecasts world crude oil prices in real 2008:Q1 chained euro’s per barrel as published in the Annual Energy Outlook (AEO) by DOE/EIA. 1) Not forecasted, but actual price realization.

6.1 Stochastic Long-Run Mean-Reverting Model The stochastic long-run mean-reverting model (SMRM) performs surprisingly well in pre- dicting the price ratios of the fuels, Figures 24 and 25. This is surprising because the model isn’t specially designed to describe the fuel interdependencies. The forecasts for the coal-oil ratio are more accurate than the IEA predictions, while the gas-oil ratio fore- casts seem quite similar.

The SMRM does succeed in capturing the downward trend in the coal-oil ratio with es- timates converging to a price ratio somewhere between 0.5 and 1.0 in the long-run. The IEA predicts a slowly decreasing price ratio towards about 1.0 by 2030. This confirms the view that crude oil prices are in the long-run increasing relatively faster than steam coal prices. The gas-oil ratio estimates for the years 1994, 1996 and 1998 closely resemble IEA fore- casts. From 2000 onward though the SMRM forecasts are substantially lower. This can be explained from the time-varying coefficients in the model which allow for a quick adjust- ment to the lower gas-oil ratio since 2000.

Long-run forecasts from the SMRM indicate a decreasing gas-oil price ratio around 0.3 by 2040, while IEA predicts a slightly increasing ratio towards 0.4. This implies that the IEA doesn’t assume a positive long-run trend with crude oil prices increasing faster than natural gas prices.

**6 COMPARING LONG-RUN FORECASTS 45 **Figure 24: Comparison of price ratio forecasts for steam coal and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook. The corresponding forecast lines are the ratio forecasts produced by the SMRM based on the IEA oil price scenario. Figure 25: Comparison of price ratio forecasts for natural gas and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook.

The corresponding forecast lines are the ratio forecasts produced by the SMRM based on the IEA oil price scenario.

**6 COMPARING LONG-RUN FORECASTS 46 6.2 **Vector Error Correction Model The vector error correction model (VECM) performs reasonable in predicting the price ratios of the fuels, Figures 26-29. In the case of one cointegration relation, the forecasts for the coal-oil ratio are more accurate than the IEA predictions, but the gas-oil ratio forecasts deviate quite substantially. With two cointegration relationships the predictions are a bit more conservative and seem to perform a bit less accurate. Notice that realized coal-oil ratio in the period 2000-2005 is much lower than both IEA and the VECM initially predicted, Figures 26 and 28.

Remarkable as well is the differ- ence in the ratio prediction in 2006 with IEA close to 1 by 2030 and the VECM close to 0.5. These two observations clearly indicate the difference between the IEA and the VECM estimates. In the VECM it is assumed that the low ratio as realized in the period 2000-2005 is a deviation from long-run equilibrium prices. The steam coal price is simply to low in comparison to the crude oil price and a correction is therefore expected. As a result, the VECM predicts a sharp increase in 1994. These first predictions were far from accurate but do not necessarily indicate a failure of the model due to the fact that short-run deviations from equilibrium can sustain for several years.

As noticed in section 5.3, figure 10 the linear trend parameter in the VECM became relevant only in the recent decade. This implies that coal and oil prices were actually converging faster towards each other than the model initially predicted. This partly explains the overestimation of the ratio by the VECM in 1994 and explains the much lower ratio equilibrium in the years thereafter, when the linear trend parameter was more pronounced. The gas-oil ratio as shown in Figures 27 and 29 were in the period 2000-2005 low as well. The VECM forecast until 2000 predicted the sharp increases in prices but seem to describe unacceptable high ratios in the long-run.

This is due to the negative value of the linear trend coefficient in the cointegration relationship, as noted before. Apparently the uncertainty in the coefficient of the linear trend has considerable influence on long-run forecasting results of the VECM. This fact stresses the importance of continuous updat- ing and re-estimation of model parameters. The IEA forecasts of 1994 and 1998 both missed the lower gas-oil ratios as well. The IEA ratios in recent forecasts seem to be structurally lower for upcoming decades while the VECM estimates slightly higher values in the medium-run and decreasing in the long-run.

It seems that there is some consensus over the long-run with expected ratios for gas-oil varying between 0.4 and 0.5 by 2030 for gas-oil and between 0.5 and 1 for coal-oil prices. These ranges are still quite large but reflect the degree of uncertainty as can be seen from the historic variation in the price ratios.

**6 COMPARING LONG-RUN FORECASTS 47 **Figure 26: Comparison of price ratio forecasts for steam coal and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook.

The corresponding forecast lines are the ratio forecasts produced by the VECM with one cointegration relationship. Figure 27: Comparison of price ratio forecasts for natural gas and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook. The corresponding forecast lines are the ratio forecasts produced by the VECM with one cointegration relationship.

**6 COMPARING LONG-RUN FORECASTS 48 **Figure 28: Comparison of price ratio forecasts for steam coal and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook. The corresponding forecast lines are the ratio forecasts produced by the VECM with two cointegration relationships. Figure 29: Comparison of price ratio forecasts for natural gas and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook.

The corresponding forecast lines are the ratio forecasts produced by the VECM with two cointegration relationships.

**6 COMPARING LONG-RUN FORECASTS 49 6.3 **Multivariate Unobserved Components Model The multivariate unobserved components model (MUCM) performs reasonable in predict- ing the price ratios of the fuels, Figures 30 and 31. The ratio forecasts reveal the smooth reversion of the MUCM towards the long-run equilibrium contrary to the VECM where reversion is more quickly. This is due to the fact that the MUCM allows for a commodity specific mean-reverting behaviour towards equilibrium. The forecasts for the coal-oil ratio are (ignoring the 1994 forecast) more accurate than the IEA predictions and the same holds for the gas-oil ratio forecasts.

The 1994 MUCM forecast suffers from the same change in the trend parameter as the VECM does. Thanks to the stochastic nature of the state variables the model adjusts quickly but not fast enough to prevent the 1994 error. The adjustment is slower than in the SMRM where more unobserved components were included to capture the stochastic trend. The MUCM succeeds in capturing the lower coal-oil ratios trend in the period 2000-2005. IEA predicts a similar development but the ratio is consequently too high. Long-run forecasts from the MUCM for the coal-oil ratio are approximately 0.75 by 2030, while IEA predicts a ratio decreasing slowly towards 1.

This confirms the view that crude oil prices are in the long-run increasing relatively faster than steam coal prices. For the gas-oil ratio the MUCM fails to capture the lower ratios in the period 2000-2005. By 2000 though the model has adjusted and does predict consequently lower price ratios while the IEA is still aiming a bit too high. Long-run forecasts from the MUCM for the gas-oil ratio are as low as 0.3 by 2030 while IEA predicts 0.4. This implies that the IEA doesn’t foresee a positive long-run trend with crude oil prices increasing faster than natural gas prices.

**6 COMPARING LONG-RUN FORECASTS 50 **Figure 30: Comparison of price ratio forecasts for steam coal and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook. The corresponding forecast lines are the ratio forecasts produced by the MUCM based on the IEA oil price scenario. Figure 31: Comparison of price ratio forecasts for natural gas and crude oil. The blue line represents the true realized price ratio. The asterisks values are those ratios as forecasted by the IEA in its biannual publication the World Energy Outlook.

The corresponding forecast lines are the ratio forecasts produced by the MUCM based on the IEA oil price scenario.

**6 COMPARING LONG-RUN FORECASTS 51 6.4 **Conclusion and Summary In this section various models have been compared to the IEA forecasts and out-of-sample performance has been assessed. It should be kept in mind that even the longest out-of- sample period is relatively short (60 quarters) and the results should therefore be inter- preted cautiously. Average absolute and relative prediction errors of the various models over the seven forecast periods are summarized in Table 12. Gas Coal Oil Gas/Oil Coal/Oil Gas/Coal IEA 5.40 18.16 17.30 0.13 0.81 0.10 SMRM 6.722 22.75 20.8812 0.152 0.5312 0.08 VECM - trace 6.662 23.12 22.7212 0.161 0.5512 0.082 VECM - 1 CR 6.662 24.17 22.0912 0.162 0.552 0.082 VECM - 2 CR 7.172 21.51 24.3112 0.191 0.8812 0.092 MUCM 7.4512 22.75 20.8812 0.142 0.822 0.0812 EW 6.862 22.54 22.5112 0.1412 0.602 0.08 Relative RMSPE w.r.t.

IEA = 1.00 SMRM 1.252 1.25 1.2112 1.122 0.6512 0.79 VECM - trace 1.232 1.27 1.3112 1.261 0.6812 0.832 VECM - 1 CR 1.242 1.33 1.2812 1.262 0.682 0.822 VECM - 2 CR 1.332 1.18 1.4112 1.451 1.0812 0.942 MUCM 1.3812 1.21 1.3912 1.112 1.022 0.9012 EW 1.272 1.24 1.3012 1.0812 0.742 0.77 Table 12: Absolute and relative average root mean squared prediction errors of the IEA forecasts compared to stochastic long-run mean reverting model (SMRM), vector error correction model (VECM) and multivariate unobserved components model (MUCM) and equal weighted average forecast over the three models (EW). 1) Significantly different forecast performance according to Diebold-Mariano test at 5% confidence level.

2) Significantly different forecast performance according to Giacomini-White test. Out-of-sample period 1994:Q1-2008:Q3.

None of the models succeeds in predicting the commodity price levels more accurately than the IEA. Even the equal weighted model isn’t able to lower the prediction errors. Apparently, the biannual IEA analysis seems to include additional information in the forecasts over historic and current prices. This is evidence in favor of including expert information to improve forecasting performance as is common practise in professional forecasting, Lawrence et al. (2006). According to the Diebold and Mariano (1995) test procedure though only the crude oil forecast performance is on average significantly dif- ferent from the IEA.

This test takes into account the sample variability of the forecasts. The alternative Giacomini and White (2006) test, which allows for misspecified models, indicates a significant difference in forecast performance on all series except for the steam coal forecasts. Full overview of significant different forecast performance is given in Ta-

**6 COMPARING LONG-RUN FORECASTS 52 **ble 13. Actual test values are available at the author upon request. If we consider the price ratios it seems that the models significantly predict the coal/oil and coal/gas ratio more accurately. The SMRM even predicts the price ratios the most accurately but this model is not informative on the associated uncertainties. The out- of-sample information indicates that the VECM with 1 cointegration relationship seems more accurate than a VECM with 2 common trends. The MUCM performance is slightly disappointing while the EW model performs reasonably well in predicting all price ratios.

It seems that model combination is not improving forecast performance significantly in this case. This is due to the high correlation between the different forecasting models. Overall it can be concluded that the VECM with one cointegration relationship is a rea- sonable model to describe the fuel price interdependencies. Moreover the VECM allows us to describe the uncertainties in the fuel price forecasts and the relative prices. This is an important gain over the IEA forecasts which consist of purely point forecasts. Insight in these uncertainties are highly relevant for risk assessments in long-run investment de- cisions.

Long-run forecasts of the coal-oil price ratio of the models seem to converge to a ratio somewhere around 0.75 by 2030. This number is somewhat below the IEA forecast of 1. The IPA, a commercial forecasting agency, predicts a coal-oil ratio of 1.16 by 2030 IPA (2008). In their report though also values as low as 1.00 by 2013 are predicted. The gas-oil price ratio forecasts of the models seem to converge to a ratio somewhere around 0.3 by 2030. This number is significantly below the IEA forecast of 0.4 and below the stable coal-oil ratio of 0.42 until 2030 as foreseen by IPA (2008). The next chapter addresses the second research question, i.e.

what are the long-run effect of availability, supply and sustainability of the fuel types? It supplements the statistical models in the sense that not all future information is contained in current prices and by the fact that upcoming structural changes in the energy market could change historic trends.

**6 COMPARING LONG-RUN FORECASTS 53 **Gas Coal Oil Gas/Oil Coal/Oil Gas/Coal Diebold-Mariano w.r.t. IEA SMRM 0 96− 0 98− 0 00− 0 94− 0 96− 0 96− 0 02+ 0 94+ 0 96+ 0 98+ 0 00+ 04− 0 98− 0 00+ 0 04+ 0 98+ 0 00+ 02− 0 04− 0 02+ 0 04+ VECM - trace 0 96− 0 98− 0 00− 0 94− 0 96− 0 94− 0 02− 0 94− 0 96+ 0 96+ 0 00+ 00+ 0 98− 0 00+ 0 04+ 0 98+ 0 00+ 02− 0 04− 0 04+ VECM - 1 CR 0 96− 0 98− 0 00− 0 94− 0 96− 0 94− 0 98− 0 94− 0 96+ 0 96+ 0 00+ 00+ 0 98− 0 00+ 0 02− 0 04+ 0 98+ 0 00+ 02− 0 04− 0 04+ VECM - 2 CR 0 96− 0 98− 0 00− 0 94− 0 96− 0 94− 0 02− 0 94− 0 96+ 0 94− 0 96− 00+ 0 98− 0 00+ 0 04+ 0 98+ 0 00+ 0 98+ 0 00+ 02− 0 04− 0 04+ MUCM 0 94− 0 96− 0 00− 0 94− 0 96− 0 94− 0 00− 0 94− 0 98+ 0 94− 0 98+ 98− 0 00+ 0 98− 0 00+ 0 02+ 0 04+ 0 00+ 0 02+ 0 00+ 04− 0 04− 0 04+ EW 0 96− 0 98− 0 00− 0 94− 0 96− 0 94− 0 96− 0 94− 0 96+ 0 96+ 0 98+ 00+ 0 04− 0 98− 0 00+ 0 04+ 0 98+ 0 00+ 0 00+ 02− 0 04− 0 02+ 0 04+ Giacomini-White w.r.t.

IEA SMRM 0 94− 0 96− 0 94− 0 96− 0 94− 0 96− 0 94− 0 96− 0 94+ 0 96+ 0 96+ 0 98+ 98− 0 00+ 0 00− 0 04− 0 98− 0 00+ 0 98+ 0 00− 0 98+ 0 00+ 0 00+ 0 04+ 02− 0 04− 0 02+ 0 04− 0 02+ 0 04+ 0 02+ 0 04+ VECM - trace 0 94− 0 96− 0 00− 0 02− 0 94− 0 96− 0 94− 0 96+ 0 94− 0 96+ 0 96+ 0 98+ 98− 0 00+ 0 98− 0 00+ 0 98+ 0 02− 0 98+ 0 00+ 0 00+ 0 02− 02+ 0 04− 0 02− 0 04− 0 04+ 0 02+ 0 04+ 0 04+ VECM - 1 CR 0 94− 0 96− 0 00− 0 02− 0 94− 0 96− 0 94− 0 96+ 0 94− 0 96+ 0 96+ 0 98+ 98− 0 00+ 0 98− 0 00+ 0 98+ 0 02− 0 98+ 0 00+ 0 00+ 0 02− 02+ 0 04− 0 02− 0 04− 0 04+ 0 02− 0 04+ 0 04+ VECM - 2 CR 0 94− 0 96− 0 94− 0 96− 0 94− 0 96− 0 94− 0 96− 0 94− 0 96− 0 94− 0 96− 98− 0 00+ 0 00− 0 98− 0 00+ 0 98− 0 02− 0 98+ 0 00+ 0 98+ 0 00+ 02+ 0 04− 0 02− 0 04− 0 04+ 0 02+ 0 04+ 0 02− 0 04+ MUCM 0 94− 0 96− 0 94+ 0 00− 0 94− 0 96− 0 94− 0 96+ 0 94− 0 96− 0 94− 0 96− 98− 0 00+ 0 98− 0 00+ 0 98+ 0 02+ 0 98+ 0 00+ 0 98+ 0 00+ 02− 0 04− 0 04− 0 04+ 0 02+ 0 04+ EW 0 94− 0 96− 0 94− 0 00− 0 94− 0 96− 0 94− 0 96− 0 94− 0 96+ 0 96+ 0 98+ 98− 0 00+ 0 98− 0 00+ 0 98+ 0 02− 0 98+ 0 00+ 0 00+ 0 04+ 02− 0 04− 0 02− 0 04− 0 04+ 0 02+ 0 04+ Table 13: Significantly different forecast performance according to Diebold-Mariano and Giacomini- White tests at 5% confidence level.

Out-of-sample period 1994:Q1-2008:Q3. +) Better forecast perfor- mance. -) Worse forecast performance. 5% confidence level.

7 QUALITATIVE ASPECTS 54 7 Qualitative Aspects In this section some of the underlying factors of the fuel prices will be discussed. This analysis is conducted by considering each of the commodities separately in the subsec- tions below. In this way it is possible to identify arguments which would augment the statistical price analysis and forecasts of the previous sections. Attention is given to the depletion rate of the resource (supply), development of demand, geographic availability and sustainability in the long-run. Uranium is included in this part of the analysis as well because it is an important alternative to coal power and DELTA Energy has a sig- nificant part of nuclear power in its production mix.

Furthermore, some remarks will be made on the technological application of the fuels in actual electricity generation. Next, implications of emission allowance prices on fuel prices are given. Finally, a summary of the qualitative aspects answering the second research question is presented. 7.1 Crude Oil Crude oil is the most important fuel in energy consumption, accounting for about 36% of total energy use. In the Netherlands the share of oil in primary energy use declined from 49.3% in 1973 to 40.9% in 2006, IEA (2007). Primary energy use refers to total energy use in its initial form, after production or importation, so excluding losses by transformation or distribution.

For electricity generation only, crude oil has in recent decades become less important. The share of oil usage in heating and electricity generation declined, 3.0% per year on average, but this was compensated by an increased use of oil in transportation services. The decrease in energy generation has been the result of high oil prices in the eighties, environmental policies and the increased relative efficiency of natural gas and coal fired-power plants. The reason that crude oil is still considered in this research is its leading role in the energy markets. Many long-term natural gas contracts are for example linked to crude oil prices, CIEP (2008b) and crude oil markets are the among the most liquid of all energy markets.

**In the long-run though it is expected that the leading role of oil as main driver of energy prices will diminish as reserve get depleted. The level of crude oil prices is extremely difficult to predict. Factors driving the oil price upwards list: increasing world demand for oil, supply disruptions, political instability, lack of production capacity, the weak US Dollar and price speculation. Hamilton (2008) suggests that if speculation and short-run price inelasticity are the key driving factors, we would expect to see dramatic moves in prices, rendering forecasting the level virtually impossible. **

Supply disruptions like the Iran-Iraq (1980) and Iraq-Kuwait war (1990) re- sulted in large price swings before demand eventually adjusted as a result of the high price. The relation between oil prices and economic growth has not been stable over the entire sample period. Between 1978 and 1981 oil demand in the U.S. actually fell by 16.0% as a result of the high prices, despite economic growth of 5.4% over the same period. Between 2002 and 2006, when oil prices increased 108.8%, U.S. oil consumption actually increased

7 QUALITATIVE ASPECTS 55 4.1%. U.S. real GDP growth over this period was 11.9%. This indicates that low price elasticity in combination with supply disruptions makes it extremely difficult to predict oil price behaviour, Hamilton (2008). In the long-run though with depletion of resources in sight strong demand will have more effect on the scarcity rent, resulting eventually in higher prices. In recent years there is heavy debate about the depletion of oil reserves, the so called ’Peak Oil’ theory which advocates that the peak in production has already occurred several years ago. In Figure 32 the production profile of oil and gas liquids as expected by the World Energy Council in 2007 is given, WEC (2007).

In this scenario the production peak lies around 2010. Notice that the share in production from the Middle East is rising steadily, increasing the energy dependence on this region and the importance of the OPEC cartel. Furthermore, it is expected that the share of non-conventional oil, dense and viscous oil as well as oils derived from coal and immature source rocks, rises to approximately 9% of total production. Large reserves of non-conventional oil are available in Canada and the former Soviet-Union. Extracting these oils will increase marginal costs significantly and therefore prices in the long-run are most likely to increase, especially within a decreasing production environment.

High oil price expectation have led to severe price increases in the oil markets in the second quarter of 2008. North-sea brent prices peaked at nearly 147 U.S. dollars, but came down rapidly in the third and fourth quarter of 2008. The VECM and MUCM predictions already (partly) capture the effect of an increasing crude oil price relative to natural gas and steam coal prices. The MUCM, thanks to its stochastic trend, even captures the recent surge in prices which has resulted in higher long-run forecasts. High growth from emerging markets and quick depletion of current resources justifies this prediction.

Figure 32: Production profile of oil and gas liquids. Source: 2006 Scenario, Association for the Study of Peak Oil & Gas, 2007. NGL stands for natural gas liquids.

**7 QUALITATIVE ASPECTS 56 7.2 Natural Gas In many expert reports natural gas is seen as the fuel of the 21st century. Major break- throughs in the drilling, transportation and storage have helped to reduce the costs of natural gas significantly and made trade between countries and even continents econom- ically feasible. Further advances in liquified natural gas (LNG) and gas to liquids (GTL) can be expected, leading to more globalisation of natural gas markets. Furthermore, ad- vances in the technology of natural gas fired power plants like the combined-cycle have in recent years increased efficiency to nearly 60%. **

Besides, natural gas power plants can be smaller and are faster to construct reducing capital costs and likewise investment uncer- tainty, WEC (2007). Typical advantage of gas fired power plants are their flexibility to react to market changes and the possibility to turn off production at low energy prices. This makes gas power plant ideal at peak hours where energy prices are more volatile. The share of natural gas in the total energy mix in the Netherlands over the period 1973- 2006 decreased from 45.6% to 42.6%. Average annual growth of input for heating and electricity generation was only 0.7%, but since 1990 growth accelerated to 3.3% per year, IEA (2007).

Natural gas usage in the Netherlands was in 1973 already high thanks to the early discovery of large domestic natural gas reserves in Slochteren in 1959. For Europe as a whole natural gas usage increased from 5.4% in 1973 to 23.9% in 2006. Availability of natural gas is in the long-run the main disadvantage of the commodity. Around 73% of all proven reserves is situated in the former Soviet Union and Middle- East region. It is expected that current resources are sufficient to supply the world for at least another 130 years. The exploration of natural gas resources is more successful than that of crude oil and it is therefore expected that more resources will be discovered in the future.

The new resources of gas have higher delivery costs than the old reserves. Long-run marginal costs are therefore likely to rise if supply and demand in the long-run is tight. The dependence of LNG could further bring about global competition for gas resources, potentially increasing gas price volatility, if the market is tight, CIEP (2008a). Another disadvantage of natural gas power plants is the relative high sensitivity to fuel price volatility. Fuel costs in natural gas plants account for 60% to 75% of total generation costs, IEA (2008a).

As for crude oil prices, natural gas prices peaked in 2008 reflecting high growth expecta- tions for the world economy. Natural gas prices are in the VECM and MUCM already expected to increase relative to steam coal prices. The MUCM is capturing the recent surge in energy price levels as well which results in higher long-run energy price levels. Limited supply and environmental advantages of natural gas support scenarios with higher natural gas prices in the long-run.

7 QUALITATIVE ASPECTS 57 7.3 Steam Coal Steam coal is the best available resource with proven reserves for at least another 150 years, WEC (2007).

**Coal is widely accessible with as major producers the United States, the Russian Federation, China, Australia and India. Coal usage is expected to grow mod- estly in the OECD countries. In recent years though coal usage by emerging economies has increased significantly, Figure 33, transforming China as well as India from a coal exporting country into a coal importing country, Hartley and Medlock (2008). Most coal exports therefore originate from Australia, Columbia, Indonesia, the Russian Federation and South-Africa, BP (2008). Strong growth from emerging markets could speed up de- pletion of steam coal resources and increase long-run prices more than currently expected by the model forecasts. **

Long-run availability is an advantage with only about 23% of proven reserves situated in Columbia, Indonesia, the former Soviet Union, the Middle- East region and South-Africa, IEA (2008b). This reveals the wider dispersion of this resource.

The share of coal in the energy mix in the Netherlands increased from 4.6% in 1973 to 9.5% in 2006. The average annual input growth for heating and electricity generation accounted 6.3% over the same period. Since 1990 though coal usage in the Netherlands is declining by an average rate of 0.6% per year, IEA (2007). Coal power generation is less flexible than natural gas and is therefore mainly used for shoulder-load power production. Efficiencies have been increasing steadily from 30% in 1970 to currently 47%. Figure 33: Global coal use (1980-2006). Source: Energy Information Administration.

Three interesting long-run developments in coal technology are coal-to-liquids (CTL), underground coal gasification (UCG) and carbon capture and storage (CCS). CTL and UCG increase the opportunities for fuel switching when at high oil and gas prices coal

7 QUALITATIVE ASPECTS 58 can be liquified or gasified. If economically feasible these technologies will reduce oil and gas price volatility and strengthen the common trend with these commodity prices. CCS which aims at storing CO2 emission underground can be an interesting temporarily so- lution to the environmental concerns associated with coal combustion and will increase the attractiveness of coal significantly, WEC (2007). It is difficult to predict whether CCS will be commercial viable or that direct investment in renewables is more effective. If CCS is viable than this would increase steam coal demand significantly as a result of reduced emission costs but also via the reduced efficiency of approximately 25%.

Heuvel (2008) concludes in a CCS analysis for the Dutch market that it can’t be ruled out that somewhere between 2015 and 2025 CCS might become commercially attractive at CO2 prices above 70 euro’s. Albeit, government support to remove the liability for long-run storage is necessary even in that scenario.

**7.4 Uranium Uranium is available in a wide variety of nations with over 50% of identified resources located in Australia, Kazachstan, Canada and the United States, Figure 34. Proven reserves are plentiful and sufficient to provide uranium for at least another 85 years. Con- ventional resources and unconventional resources could amount to potentially 270 and 675 years respectively. The availability of uranium though depends highly on the chosen level of extraction costs and likewise the price of uranium itself. Vast amounts of uranium are available, but only at higher costs of extraction and purification, NEA (2006). **

The restricting factor is timely investment in new mines and production facilities. Current reactor requirements exceed uranium production and despite of heavy investments in re- cent years it is expected that output from new mines takes up to ten years to emerge, WEC (2007). The last few years the price of uranium increased dramatically reflecting the short-term uranium shortage, but this increase creates sufficient investment opportu- nities in the long-run.

The share of nuclear power in European energy generation has risen sharply in the seven- ties and eighties when fossil fuel prices were high and nuclear energy formed an alternative energy source. Since 1986 though the number of new built plants decreased rapidly due to environmental and safety concerns and lower fossil fuel prices. In the Netherlands only 1% of the primary energy supply comes from nuclear resources, IEA (2007). In recent years, with renewed high fossil fuel prices, a lot of plans exist to expand the number of nuclear power plants once again. In Europe this interest can also be explained by the fact that electricity generation by nuclear power does not produce any emissions.

Moreover in some oil and gas exporting countries there exists interest in nuclear power as a way to reduce current high rates of oil and gas depletion, WEC (2007). It can therefore, if fossil fuel prices remain high, be expected that the demand for uranium will be high as well.

7 QUALITATIVE ASPECTS 59 Figure 34: Distribution of Identified Resources at USD 130/kgU. Source: NEA/IAEA, 2006. Besides the waste and safety issues nuclear power plants have the disadvantage that the capital costs for building new plants are very high relative to gas and coal power plants. The advantage is the relatively low operating costs. The share of uranium costs, only about 5%, is low compared to total costs reducing the impact of uranium price volatility, WEC (2007). 7.5 Emission allowances Natural gas combustion has in comparison to the other fossil fuels the lowest environmen- tal impact.

For every megawatt hour of electricity produced using natural gas currently an average of approximately 0.4 tons of CO2 is emitted. For steam coal this number is approximately 0.85 ton. This advantage of natural gas can grow in importance over time if the price of CO2 emission allowances increases in future trading periods or if natural gas fired power plant efficiencies increase quicker than coal power plants. CO2 emission allowance prices for the European Union for emissions in the period 2008- 2012 hover around 25 euro’s per ton, Figure 35. In the light of the Kyoto commitments, an increased usage of natural gas by the (energy) industry can be expected.

**The magnitude of this advantage is difficult to predict due to a lack of historic data, the first European Union Emissions Trading Scheme (EU ETS) emission period started in 2005 and political uncertainty on the framework for future periods remains. Uncertainty exists around the reduction targets, industries involved, length of the trading periods, banking of allowances to subsequent periods, allocations and the option to reduce emissions abroad, Stapersma (2008). Point Carbon predicted in its recent June edition a steady increasing carbon price**

7 QUALITATIVE ASPECTS 60 towards 39 euro’s per ton in 2012, PointCarbon (2008). They point out that carbon prices seem to stay strong independent of changes in fundamentals. Changes in the relative prices of natural gas and steam coal though have an effect on carbon prices via fuel switching opportunities. If, for example, the price of steam coal increases relative to natural gas it gets more attractive to use natural gas as a substitute fuel. As a result more producers will shift towards natural gas and therefore carbon emis- sions will be lower. Lower demand for emission allowances and therefore lower carbon prices will be the result.

On the other hand, lower carbon prices reduce the total costs associated with the usage of steam coal relative to natural gas. You could therefore ex- pect as a result an increase in the demand for coal and likewise an increase in the relative price of steam coal to natural gas. This second effect though is in the current situation less pronounced. Not all energy fuel users participate in an emission trading scheme and at current prices the emission allowance costs represent a smaller fraction in total costs than the cost of the fuel itself. It is expected that emerging markets as China and India will for the time being not participate in an emission trading scheme that caps their total emissions.

Therefore, it is likely that high CO2 prices in the long-run will only have a limited negative effect on coal prices. Meanwhile, China and India do participate in the Clean Development Mechanism (CDM) in which reductions are financed by the West and Certified Emission Reductions (CER’s) are earned in return. In the long-run it is possible that more European industries and countries outside the European Union will participate in some sort of capping emission allowance trading scheme. More participants will mean that it is easier to distribute the reduction costs over the participants efficiently, which would result in a lower overall carbon price level, Stapersma (2008), which would be in favour of steam coal.

On the other hand, it is likely as well that in the future a major part of total coal usage costs will consist of carbon costs.

Figure 35: EU ETS prices for trading periods 2005-2008 and 2008-2012. Source: Danish Environmental Protection Agency.

**7 QUALITATIVE ASPECTS 61 Point Carbon expects that an increase of 25% in the natural gas price relative to steam coal prices increases average carbon prices by approximately 19% as a result of fuel switch- ing to coal usage. A similar increase in coal prices would on average decrease carbon prices by approximately 9%, PointCarbon (2008). In this sense it can be concluded that carbon prices have a dampening effect on changes in the commodity prices difference of natural gas and coal. **

This does not mean though that predicting the carbon price level is not an essential part in comparing total fuel costs and power plant investment decisions. 7.6 Summary This chapter addressed the second research question, i.e. what are the long-run effects of availability, supply and sustainability of the fuel types? Availability is defined as the ease to obtain the fuel in the market reflected by geographical dispersion of the resources and market domination by cartels. Supply captures the remaining resources influenced by the rate of depletion. Sustainability indicates the long-run durability of the fuel and the environmental impact.

To summarize the results Table 14 is constructed. Market Price Availability Supply Sustainability Crude oil high medium low low Natural gas high low medium medium Steam coal medium high high low Uranium medium high high medium Table 14: Summary long-run outlook in qualitative analysis. If long-term fundamentals remain positive, crude oil demand is expected to remain high as a result of high demand from the transportation sector and emerging markets. Com- bined with quick depletion of conventional reserves the outlook for crude oil prices is high. Availability is considered medium as a result of wider dispersion of non-conventional oil reserves.

Sustainability is set low as crude oil is considered inefficient for power generation. Natural gas prices are often closely linked to crude oil prices by price formulae in long-run contracts. Assuming positive economic conditions high demand growth from the (energy) industry and transportation will drive natural gas prices upward. Reserves are concen- trated in only a few regions which limits availability substantially. Thanks to the relatively low carbon emission from natural gas and sufficient reserves it is expected that natural gas will play an important role in future energy markets and therefore scores medium on sustainability.

Abundant resources of steam coal exist. Above all these resources are widely available. Steam coal is likewise an attractive fuel in terms of supply and availability. As a result,

7 QUALITATIVE ASPECTS 62 demand for this fuel is expected to increase, especially from emerging markets with no carbon emission cap in place. In Europe the success of this fuel very much depends on carbon prices, which are highly uncertain and mainly determined by political factors. A low score on sustainability is therefore in place. Uranium is without CO2 emissions an interesting alternative for the fossil fuels.

**Despite of short-run supply shortages, resources are widely available and supply in the long-run is not problematic. The costs of uranium represent only a small part of total operation costs of the nuclear power plant. Political and environmental concerns though threaten long-run sustainability.**

The next chapter addresses the third research question, i.e. which scenarios are realistic for the long-run fuel price developments? It combines the forecasts from the statistical model results in section 5 and their out-of-sample performance of section 6 with the qualitative aspects of this section into several scenarios. In this way it is possible to efficiently incorporate all available information into the price forecasts and to describe associated risks.

8 SCENARIO ANALYSIS 63 8 Scenario Analysis Based on the statistical forecasting models and the qualitative considerations four sce- narios for the long-run energy price development are constructed in this section.

First scenarios as constructed by the International Energy Agency (IEA), the Union of Electric- ity Industry (Eurelectric) and the Central Planning Bureau (CPB) in the Netherlands are considered. Subsequently, the long-term view as developed for DELTA Energy is given. By combining the forecasts from the statistic models with the qualitative aspects into several scenarios it is possible to efficiently incorporate all available information into the price forecasts and to describe associated risks in a stylized way. 8.1 Expert Scenarios An interesting scenario analysis incorporating both fuel prices and technological develop- ment is given in Energy Technology Perspectives: Scenario and Strategies to 2050, IEA (2008a).

In this research three scenarios are identified: Baseline, ACT Map and BLUE Map. The ACT Map scenario is based on technologies that already exist and global CO2 emissions should by 2050 be reduced to 2005 levels, while the BLUE Map scenario targets a 50% reduction by 2050 as advised by the Intergovernmental Panel of Climate Change (IPCC) and deployment of technologies still under development. In all three scenarios fossils fuel continue to play a key role. In the baseline scenario oil and gas prices are high and security concerns increase as import costs rise. Prices are set relatively stable at 62 USD per barrel crude oil, 61 USD per ton steam coal and 25.01 USD per MWh natural gas.

This suggests a coal-oil ratio close to 0.98 and a gas-oil ratio of 0.40. CO2 emissions continue to increase as well as oil demand. The baseline scenario is considered to be unsustainable in the long-run. Interestingly, IEA notices that increased coal usage in the production for liquid transport fuels will increase CO2 emissions significantly. In the ACT scenario CO2 prices of around 50 USD/t CO2 by 2050 are expected. The share of renewables in energy production is still only 35%, Figure 36. Remarkable is the sharp decline in coal usage to only 7% without CCS and 14% with CCS technology, down from 40% globally in 2005.

**This indicates that even at a moderate CO2 price it is unattractive to invest in coal power plants. Gas usage on the contrary remains relatively stable at 33% without CCS and 29% with CCS technology, up from 20% globally in 2005. Results are of course sensitive to the long-run fuel price outlook. In the BLUE Map the share of renewables increases to 46% by 2050. CO2 prices in the BLUE Map are as high as 200 USD/t CO2 and the share of gas fired plants declines to 17% with CCS and 11% without CCS technology. Coal in this case declines to only 13% with CCS and 0% without CCS, 36. The decline in coal usage is much larger in the CCS scenario due to the fact that CCS is significantly more expensive per tonne of CO2 saved for natural gas than for steam coal. **

An alternative scenario analysis for Europe has been developed by the Union of the Elec-

8 SCENARIO ANALYSIS 64 Figure 36: Share of global power generation in baseline, ACT Map and BLUE Map scenarios. Source: IEA Statistics, IEA 2006. tricity Industry, Eurelectric (2007). In their analysis four scenarios for the European energy industry are defined: Baseline, Efficiency & Renewable Energy Sources (RES), Supply and Role of Electricity. In all scenarios oil and gas prices are closely linked and relatively high reaching 100 euros in 2008 price per barrel and 57 euros per MWh by 2050 respectively. Coal prices are expected to rise at far lower rates deteriorating the coal-oil ratio dramatically (towards 0.69) with a coal price of approximately 72 euro’s per tonne by 2050.

Remarkable is that all alternative scenarios indicate a smaller share of coal in the power generating mix with CO2 prices varying between 50 and 120 euro’s per tonne. The scenarios which include CCS technology as viable option indicate a revival of coal usage starting in 2020 reaching a share of about 20% by 2050. This re-emergence is the result of high gas and oil prices and high gas demand for energy generation in the medium run, until 2020. The same holds for nuclear energy which takes a considerable share in generation beyond 2030.

In 2004 the Central Planning Bureau (CPB) in the Netherlands constructed four sce- narios for the energy markets and climate change until 2040, CPB (2004). Despite the dramatic rise in energy prices in recent years it is still worthwhile to analyze the forecasts and argumentation given in their report. The scenarios are defined as: Global Economy, Transatlantic Market, Regional Communities and Strong Europe. In all scenarios the price path of oil is nearly similar at a stable price between 30 an 45 euro’s per barrel by 2040 in chained 2008 prices. Striking is the quote: ”technological developments and market incentives prevent a Hubbert peak in global oil production with a rather flat price pattern in all scenarios as result (see also Ryan (2003))”.

It is also noted by the CPB that: ”Disruptions within supply, caused for instance by geopolitical factors, are able to cause significant changes in the prices. In the medium and long-term, supply will, however, restore, supplemented sometimes by demand responses, bringing the price back to the long-term path. After all, history has shown that long-term price elasticity of demand, as well as supply, is fairly high, though the short-term elasticities are rather small causing

**8 SCENARIO ANALYSIS 65 the high volatility in the price of oil in the short run.” These arguments by the CPB clearly support the long-run mean-reversion hypothesis, but contradict the Peak Oil ar- gumentation. The same stable estimates are found for natural gas prices varying between 25 and 32 euro’s per MWh by 2040. A price prediction for steam coal is omitted in the report. The conclusion notices that the share of gas-fired plants increases in all scenarios as a result of economical and environmental advantages of the technique. Coal usage is expected to decline certainly with CCS projected to play a limited role and high global CO2 prices ranging from 16 to as high as 1212 USD per ton by 2040. **

8.2 DELTA Energy’s Scenarios The described scenarios above clearly reveal the degree of uncertainty which is associated with predicting long-run energy prices. Considering the forecasts from section 5, out-of- sample performance from section 6, the qualitative remarks from section 7 and the expert scenarios above four long-run scenarios for DELTA Energy are developed. The scenarios are developed along two dimensions of uncertainty, Table 15. The first uncertainty is the level of energy prices established by the development of the crude oil price. The second uncertainty is the long-run interdependency between natural gas and steam coal prices.

From the model estimates a negative trend was discovered implying steam coal prices increasing less quickly than natural gas prices. From the qualitative analysis we know that demand for coal from emerging economies could severely effect this trend. Actual prices for the scenarios are given in Table 16. This view is of course arbitrary but can be considered as a good mixture of the various aspects discussed in this research. In all scenarios it is assumed that the long-run relationship between crude oil prices and steam coal prices is expected to tighten as technological progress (CTL, UCG and potentially CCS) will increase fuel switching opportunities for these fuels.

Furthermore, it is expected that the link between natural gas and crude oil prices will remain strong despite of the decoupling of prices and liberalization of gas markets. Again fuel switching opportunities and technological progress (GTL) will provide sufficient conditions for prices to stay con- nected in the long-run.

Crude Oil prices High Low Gas/Coal Trend Negative Scenario 1 Scenario 3 Stable Scenario 2 Scenario 4 Table 15: Dimensions of various scenarios. The first scenario is constructed by generating prices from the VECM with one cointegra- tion relationship which had the best out-of-sample performance of the statistical models. Confidence intervals are generated without parameter uncertainty. The steam coal series

8 SCENARIO ANALYSIS 66 is relatively unaffected by the crude oil and natural gas price development in this model. The VECM produces high price estimates and is therefore classified as the high scenario.

**The coal-oil price ratio is expected to decline steadily towards 0.7 by 2040. The gas-oil ratio decreases towards 0.3. The main argument for the higher price increase of crude oil is the relative fast depletion of conventional oil resources. The second scenario is the scenario which crude oil prices are relatively low due to slower depletion of crude oil reserves. The long-run trend between natural gas and steam coal prices remains stable as emerging markets switch to coal usage as alternative to natural gas and crude oil. Price paths for this scenario are generated by the VECM with one cointegration relation as well but the cointegration trend parameter is set at 0.02 instead the original value of -0.004. **

The constant is adjusted to -1.34 to keep the intercept in the base year 2008 equal to 0.84. Thereby, the gas-coal price ratios remains relatively stable at a level of 0.2 until 2040, while crude oil prices remain increasing towards a coal-oil ratio of 0.65 by 2040.

The third scenario assumes the relatively low crude oil prices as projected by the IEA in 2006. The natural gas and steam coal prices are simulated using again the VECM with 1 cointegration relationship but conditional on the IEA crude oil price forecast. In this way the forecast can profit from the IEA expert information and also use the consistent interdependence of the VECM predictions. The resulting forecasts are relatively low but the negative trend between steam coal and natural gas prices remains intact. The gas-coal ratio increases to 0.5 by 2040.

Energy prices are quite stable as well as low in the fourth scenario.

Again price paths are generated with the VECM with 1 cointegration relationship and conditional on the IEA forecasts from 2006. In this case the cointegration trend parameter is again adjusted to 0.02 as in scenario 2, such that a stable trend between natural gas and steam coal prices is present. With the construction of these four scenarios a realistic coverage of the uncertainties within long-run energy prices can be given. The next chapter addresses the fourth and fifth research questions, i.e. what is the effect of fuel price uncertainty on power plant investment decisions and what are the implications for DELTA Energy’s assets and invest- ment decisions? Economic theory about investment under uncertainty and the scenarios as constructed in this chapter are used to answer these questions.

In this way the statis- tical models and qualitative remarks on long-run energy prices are used in practise.

**8 SCENARIO ANALYSIS 67 2005 2010 2015 2020 2025 2030 2035 2040 **Natural Gas (EUR / MWh) IEA 21.4 22.0 20.5 21.7 22.9 24.2 Eurelect 23.4 23.4 24.3 28.5 29.3 36.0 39.3 CPB 25.0 26.0 27.0 28.0 29.0 30.0 31.0 IPA 23.2 17.1 15.4 16.2 16.7 DELTA Energy Scenario 1 30.7 34.1 37.7 41.3 44.4 49.1 55.2 Scenario 2 29.9 29.1 28.6 27.8 27.4 27.0 26.5 Scenario 3 25.8 23.8 24.3 24.2 24.7 25.9 26.9 Scenario 4 25.1 20.8 18.8 16.8 15.2 14.0 12.9 Steam Coal (EUR / ton) IEA 67.7 59.6 60.5 62.0 63.5 65.0 Eurelect 55.4 60.9 62.6 64.2 66.5 69.2 72.0 IPA 60.0 45.9 44.6 45.6 46.5 DELTA Energy Scenario 1 126.6 128.1 128.1 130.2 132.2 132.3 132.3 Scenario 2 127.2 127.0 127.0 128.2 128.2 128.3 128.4 Scenario 3 85.5 77.7 72.1 67.3 61.6 58.8 54.9 Scenario 4 84.9 76.7 70.0 63.5 57.8 53.7 48.9 Crude Oil (EUR / brl) IEA 54.9 57.0 53.1 55.9 58.8 64.0 Eurelect 47.6 49.0 51.6 58.2 59.6 72.8 74.1 CPB 30.0 32.0 34.0 36.0 38.0 40.0 42.0 IPA 57.8 40.7 37.0 38.1 40.0 DELTA Energy Scenario 1 84.9 97.6 114.4 128.5 144.1 168.7 195.5 Scenario 2 85.2 97.7 110.9 127.7 145.6 174.0 197.1 Scenario 3 57.0 53.1 55.9 58.8 64.0 68.6 76.2 Scenario 4 57.0 53.1 55.9 58.8 64.0 68.6 76.2 Table 16: Assumed evolution of fossil fuel prices in chained 2008 prices by various scenarios.

IEA is the scenario as reported in the World Energy Outlook 2006. Scenario 1: high crude oil price, negative trend gas-coal. Scenario 2: high crude oil price, stable trend gas-coal. Scenario 3: low crude oil price, negative trend gas-coal. Scenario 4: low crude oil price, stable trend gas-coal.

**9 INVESTMENT UNDER UNCERTAINTY 68 9 **Investment under uncertainty Fuel price uncertainty combined with technological change and high capital cost of invest- ment pose an interesting challenge to energy companies willing to invest in new generating capacity. By constructing a portfolio of assets it is possible to diversify and hedge risks associated to this investment decision. A physical investment in a power plant though is irreversible and can only be adjusted at the margin, Zon and Fuss (2006). The investment decision should be based therefore not only on expectations, also know as the net present value, but on associated risks as well.

Fuel price risk is a major component of total risk and should therefore be considered in the investment decision. In the first subsection a brief introduction to the theory of investment under uncertainty based on the work of Dixit and Pindyck (1994) is given. Subsequently, DELTA’s perspective and the implica- tions for its investment strategy are given in the next subsection. A summary answering the fifth research question is given in the last subsection.

9.1 Real Options Theory The spark spread for steam coal and clean spark spread for natural gas are given by X(t) = PE(t) − HR [PC(t) − FCO2 PCO2 (t ( 32) where PE represents the power price, HR the heat rate or inverse efficiency, PC the com- modity price per MWh and PCO2 the costs of emitting a tonne CO2 all at time t. FCO2 is the commodity specific CO2 factor which in the Netherlands is determined by the Dutch Emission Authority. This amounts 0.34092 ton per MWh for steam coal and 0.20196 ton per MWh for natural gas.

The instantaneous cash flow by operating a coal or natural gas fired power plant is then D(t) = Q(t) [X(t) − G] , (33) where G are the (constant) variable operating costs, excluding fuel costs and Q the amount of the power supplied by the plant in MWh at time t.

Notice that this cash flow is theo- retically none negative as the power plant operator has the opportunity to turn off power generation, Q = 0, if variable costs exceed the clean dark/sprak spread. In practise though a large part of power generating capacity consists of must-run units and units have a power generating minimum. Further limitations like start-up costs and power price volatility naturally effect the precise value of Q(t) in determining when turning off or scale down operations is profitable.

The present value (at time 0) of receiving the uncertain cash flows D(t) is given by V0 = E0 e−rt D(t) , (34)

**9 INVESTMENT UNDER UNCERTAINTY 69 **where r is the risk-free rate or the desired return on investment. The value of a power plant Vp is then given by the expectation of the integrated cash flows over the life time T of the power plant, receiving the cash flows from date 0 until T Vp(P, t) = E0 Z T e−rt D(t)dt . (35) The value of the real option to invest is then given by W(t) = max Vp(P, t), e−r∆t W(t + ∆t)) , (36) where ∆t is the time interval between investment decisions and W(t + ∆t) the expected value of the option if delaying the investment decision one interval.

If future cash flows are highly uncertain than is it possible that it is more profitable to delay the investment several periods. The irreversible nature of the large capital investment makes accurate timing of the investment very important.

Calculation of the real option value is done by simulating power prices and commodity prices up to the life span of the power plant investment decision under consideration. In this way a lot of different spark spreads paths are constructed reflecting price uncertainty. Commodity prices could be simulated using fuel price models, as for example the VECM and MUCM as suggested in section 4 or by assuming any other price path distribution. Power and emission prices are of course the other important sources of price uncertainty, but modelling these is outside the scope of the thesis. Including long-run price interde- pendencies between fuels and power prices could constitutes a vital part of long-run power price modelling.

After having simulated the spread price paths, the cash flows can be calculated using equation (33). Finally, the value of the power plant at every instance t is obtained via equation (35) and the option value at every point in the future is estimated. Via backward induction starting at the maximum investment horizon the current real option value of investment can be determined. By simply comparing the option value of the natural gas power plant with the coal power plant and the value of possible other alternatives the optimal investment decision can be made. In practise the existing portfolio characteristics should be included in the analysis.

To complete the full picture, a thorough analysis of the investment costs of the various alternatives and uncertainty in the development of the investment costs over time is necessary as well.

The general result of this methodology as concluded by Dixit and Pindyck (1994) is that uncertainty will push towards flexible, less-capital intensive technologies. This would im- ply that high uncertainty would support investment in natural gas fired power plants. In a similar analysis for the UK market, focussed on energy policy, Zon and Fuss (2006)

**9 INVESTMENT UNDER UNCERTAINTY 70 **find that increased fuel price variance or technological variance with respect to some tech- nology reduces investment in that technology. Forecasting uncertainty for natural gas prices is higher than for steam coal prices and therefore investment in natural gas fired power plants seems less attractive by that argument.

Carbon price uncertainty should be included in the analysis which increases total uncertainty of steam coal prices signifi- cantly. Furthermore, Zon and Fuss (2006) conclude that increased risk aversion reduces fluctuations in investments over time as electricity production becomes more diversified over technologies to such a large extent that carbon emission will be reduced, mainly by switching towards nuclear energy production, rather than renewables. The explanation is that investors tend to delay the investment in a new technology until the ongoing em- bodied technological change reaches some optimal level where their productivity gain is maximized.

9.2 DELTA Energy’s perspective DELTA Energy is with approximately 750 MW in place a relatively small player on the Northwest European energy market and aims for sustainability of the company in the long-run. The fuel mix currently consists of nuclear, coal, natural gas, wind and biomass concentrated in the province Zeeland in the Netherlands, Table 18. To remain indepen- dent, the strategy of DELTA Energy is risk averse and focussed on a reasonable return under all probable scenarios. The target of DELTA is to expand power generation to 2000 MW in 2015 by investing in nuclear, biomass, wind and solar power.

For the long-run DELTA wants to expand power generating capacity even further and is actively investi- gating the various investment opportunities. DELTA is already investing in natural gas power with the construction of the Sloe plant which is expected to be completed in 2009. The Dutch power market is characterized by a large share of natural gas power plants. The use of power generating capacity depends on the situation in the power markets. This means power prices in the Netherlands but also abroad, fuel prices and emission costs. If for example energy prices abroad are low and natural gas prices are high than it is likely that power will be imported from abroad instead of produced locally lowering Dutch power prices.

The capacity of such imports though is limited but several plans exist to expand this so called interconnector capacity in the near future. Moreover en- ergy demand increase over the course of the day peaking at 5 p.m. and falling back in the evening and night. This effect results in higher, more volatile prices during the day, peak-hours, and more stable low prices in the night, off-peak hours. These fluctuations cause the need for flexible production capacity during peak-hours. The use of a power plant depends on the marginal costs of producing another unit of power. Therefore during the off-peak hours only the plants with the lowest marginal costs produce electricity and when power prices increase power plants with higher marginal costs are ac- tivated, this forms the so called merit order, Figure 37.

A power plant at the marginal cost

**9 INVESTMENT UNDER UNCERTAINTY 71 **Figure 37: The impact of renewable generation on the merit order in different segments of electricity supply. Source: Sensfuss et al. (2008). barrier is setting the price level while the other plants are price-takers. Plants with the lowest marginal costs therefore have also the highest load factor, the number of operation hours per year. Peak-load plants with a low load factor have a low number of operation hours but earn on average a higher power price than base-load units. Historically nuclear power plants with the lowest marginal costs were on the left, followed by steam coal, then natural gas and at the far most right reserve capacity mostly oil fired power plants.

Currently two important developments in the market are changing the historic merit or- der. Firstly, more renewable generation, mostly wind and biomass is entering the power market. Wind capacity enters the merit order from the left as it has very low marginal costs, while biomass is mostly used in combination with coal fired capacity. Both shift, as well as power imports, the supply curve to the right lowering average marginal costs. This is also know as the merit-order effect, Sensfuss et al. (2008). The growth of renewables will probably increase power price volatility as wind and solar capacity is dependent on weather conditions.

Secondly, the introduction of emission costs has changed the order as coal fired power plants are more strongly effected by increased carbon costs than natural gas plants. If coal prices are high than it sometimes even happens that marginal costs of coal fired plants exceed marginal costs of gas fired plants. This has already had a negative effect on the number of operating hours of coal fired plants. DELTA therefore uses the merit order in her models to assess the impact of fuel prices and emission costs on operations and investment decisions.

The impact of fuel price uncertainty for DELTA Energy’s assets can be analyzed by cal- culating the marginal costs of the various power plants under the scenarios as defined in section 8. To investigate the impact for DELTA Energy’s investment decisions also total costs have to be considered. To do so assumptions are needed for the investment costs, variable costs, load factor, efficiency of the power plant, capital costs and depreci-

**9 INVESTMENT UNDER UNCERTAINTY 72 **Power Plant Characteristic 2008 2010 2020 2030 2040 Natural Gas Efficiency (%) 58 59 61 62 64 Investment costs (EUR/kW) 465 435 400 400 400 CO2 emissions (g/kWh) 354 342 330 325 320 Variable costs (EUR/MWh) 4 4 4 4 4 Load factor (%) 79.9 79.9 79.9 79.9 79.9 Electricity generation costs Scenario 1 (EUR/MWh) 68.3 75.2 98.0 129.2 173.9 Scenario 2 (EUR/MWh) 68.3 73.5 79.6 86.6 96.2 Scenario 3 (EUR/MWh) 68.3 66.4 73.8 88.2 112.9 Scenario 4 (EUR/MWh) 68.3 65.2 62.5 63.8 70.0 Steam Coal Efficiency (%) 46 46 48 50 52 Investment costs (EUR/kW) 1030 1000 950 900 900 CO2 emissions (g/kWh) 744 728 697 670 644 Variable costs (EUR/MWh) 5 5 5 5 5 Load factor (%) 79.9 79.9 79.9 79.9 79.9 Electricity generation costs Scenario 1 (EUR/MWh) 70.9 74.3 84.2 96.7 112.2 Scenario 2 (EUR/MWh) 70.9 74.1 83.7 94.8 110.1 Scenario 3 (EUR/MWh) 70.9 62.5 68.5 77.3 88.1 Scenario 4 (EUR/MWh) 70.9 62.3 67.5 74.2 84.1 Table 17: Development of characteristic for steam coal and natural gas power plant technologies and calculated electricity generation costs including CO2 emissions costs.

Depreciation natural gas plant 15 years, steam coal 25 years. Interest rate 6%. Source assumptions: DLR (2007). ation. The total electricity generation costs under the four scenarios are given in Table 17. A steadily increasing CO2 price from 25 euro’s in 2008 up to 50 euro’s in 2040 has been assumed. To incorporate uncertainty CO2 prices have been simulated by log nor- mal random walk with a positive drift of 0.15% and variance 1.5% per quarter. The ratio of total and marginal generation costs of gas versus coal power plants is show in Figure 38. Total electricity generation costs in scenario 1 for steam coal are lower than for natural gas.

The explanation is that the effect of rising natural gas prices is stronger than rising CO2 prices. The risk of a further increase of natural gas prices relative to steam coal prices, given the assumed CO2 price volatility, outweighs the risk of rising CO2 prices. If marginal costs, Figure 38, are considered than the effect is even stronger, because fuel costs are a large share of natural gas fired power plants marginal costs. It is therefore expected that the number of operating hours of natural gas fired power plants in scenario 1 will be negatively effected, making natural gas power even more expensive.

In scenario 2 the total generation costs of steam coal are slightly higher than for natural gas. The relative low price of natural gas and the stable relationship to steam coal prices in this scenario explain this difference to scenario 1. The marginal costs from the steam

**9 INVESTMENT UNDER UNCERTAINTY 73 **coal power plant on the other hand are slightly lower due to the fact that a smaller share of total costs consists of fuel costs. Therefore even in this scenario the risk of rising nat- ural gas prices is a serious threat to the number of operating hours of natural gas fired power plants. This is also visible from the historic pattern in which the total costs ratio is relatively stable and the marginal cost ratio much more volatile. Scenario 3 shows the situation with generally lower energy prices, but an increasing trend in the relative price of natural gas.

The lower price in the starting years is an advantage for natural gas power plants with a relatively high share of fuel costs but with rising prices this advantage is disappearing quickly. By 2015 total generation costs of steam coal power plants are lower and by 2040 the difference is quite substantial. Gas prices in the fourth scenario are low and stable in relation to steam coal prices. To- tal generation costs for natural gas fired power plants are lower and marginal costs by 2040 are still lower than for steam coal power plants. Carbon emission costs effect coal fired power plants significantly potentially reducing the number of operating hours.

Coal power plants are more heavy effect by a reduction in factor load due to the higher capital costs and total costs from coal generation will therefore increase rapidly in this case. On the other hand the volatility in natural gas prices still threatens profitability of gas fired power plants.

It seems that from a costs perspective in all scenarios coal fired power plants are relative to natural gas fired plants an attractive investment. High natural gas prices potentially outweigh the effect of high carbon emission costs for steam coal. Furthermore, the volatil- ity in natural gas prices adds more risk to the cost development of gas fired power plants. These observations though don’t mean that coal fired power plants will have the highest return on investment. Natural gas power is more flexible and earns on average higher power prices, but this result is a strong indication for the future development of the merit order.

It seems that the historic merit order will remain intact with coal power on average having the lowest marginal costs of these two alternatives.

Profitability of the power plants depends highly on the power prices. With the rapid growth of renewables it is expected that volatility of power prices will increase. This would be an advantage for natural gas fired power plants. Only if total power generation costs of coal fired power plants are lower than of renewables, then an investment in coal power remains profitable. The generation costs from renewables highly depends on the development of their investment costs, which falls outside the scope of this research. Currently already some wind projects are able to produce electricity competitively, IEA (2008a).

**The impact from renewables on long-run power prices should therefore not be underestimated.**

**9 INVESTMENT UNDER UNCERTAINTY 74 **Figure 38: Development gas/coal ratio total and marginal electricity generation costs for the various scenarios. Dotted lines represent 90% confidence interval. From left to right: high to low crude oil price. From top to bottom: negative to stable trend gas-coal price.

**9 INVESTMENT UNDER UNCERTAINTY 75 9.3 **Conclusion and Summary As a risk averse investor DELTA should invest more heavily in existing technologies. Nu- clear power is perhaps in the long-run under the assumption of political stability and controllable construction costs an alternative for coal power plants.

An analysis of the capital costs is essential for such a decision which falls outside the scope of this research. In the future though it can not be ruled out that an investment in nuclear power is an interesting alternative.

If we focus on the fossil fuels than coal power could from a costs perspective be a good investment. With the decommissioning of the Borssele coal power plant, the BS-12, ex- pected by 2021 DELTA has no longer coal power in its product mix, Table 18. By 2020 natural gas prices are expected to be relatively high and steam coal could even at increas- ing CO2 prices, to 50 euros by 2040, still pose a valuable alternative. This even holds if steam coal prices and natural gas prices remain stable at 2008:Q3 levels. Only a scenario in which natural gas prices are substantially lower relative to steam coal prices and low energy price levels or a scenario in which CO2 prices are extremely high would change this perspective.

Early investment in steam coal power generation can induce some risk and a possible outcome of a real option analysis, therefore, could be that the investment in a coal power plant is not (yet) economically viable despite of a positive expected return on investment. Mitigation of these risks by forming alliances with other potential investors as was done by the co-ownership of the Sloe plant with Electricité de France also helps DELTA Energy to construct a diversified sustainable portfolio. Power Plant Fuel Location Capacity Must-run Period BS-30 Uranium Borssele 200 n/a 1973 - 2033 BS-12 Steam coal Borssele 200 80 1988 - 2021 ELSTA Natural gas Terneuzen 175 90 1998 - 2028 Sloe plant Natural gas Vlissingen 430 260 2009 - 2039 Renewables n/a Zeeland 160 n/a 2008 (Unknown) Uranium Borssele 500 n/a 2025 - 2060 Table 18: DELTA Energy’s Assets.

Capacity and must-run in MW.

10 RESEARCH CONCLUSION 76 10 Research Conclusion Before formulating a conclusion in this chapter first the problem statement is revisited. Then the research questions as dealt with in the previous chapters are addressed. Subse- quently, a conclusion is drawn and suggestions for further research are presented. 10.1 Problem Statement Revisited The objective of the research presented here was to provide DELTA Energy with insight into future developments of the main fuels for power generation and to outline implica- tions for DELTA Energy’s assets and power plant investment planning decisions.

**The research question as formulated in the introduction was therefore: To what extent is the long-run behaviour of the various commodities used for energy pro- duction predictable and what are the implications for DELTA Energy’s asset investment strategy?**

Five research question were dealt with to guide the research: 1. What are the long-run fuel price behaviours and their interdependencies? 2. What are the long-run effects of availability, supply and sustainability of the fuel types? 3. Which scenarios are realistic for the long-run fuel price developments? 4. What is the effect of fuel price uncertainty on power plant investment decisions? 5. What are the implications for DELTA Energy’s assets and investment decisions? 10.2 Research Conclusion The first research question was answered in section 5. Predictability of the fuel price levels was investigated by the augmented Dickey-Fuller test, the variance ratio test and the KPSS stationarity test.

The statistical results were not conclusive and rule out nor long-run mean-reversion nor the random walk hypothesis. From depletable resource the- ory it is expected that long-run prices revert in the long-run to the unobservable marginal cost of extraction, which follows a trend and has continuous fluctuations in both the level and slope of that trend. Deviations from that trend can be severe due to short-run supply and demand shocks.

By modelling the price series using a stochastic long-run mean-reverting model, a vec- tor error correction model and a multivariate unobserved components model it could been established that significant long-run relationships between the fuel prices do exist. The VECM exploits the significant cointegration relationship(s) between the commodities

10 RESEARCH CONCLUSION 77 while the unobserved component models use unobserved underlying (common) factors as explanatory variables. A negative trend in the long-run relationship between crude oil and steam coal is identified in both models, implying that in the long-run crude oil and natural gas are expected to become relatively more expensive in comparison to steam coal.

Crude oil prices are expected to increase slightly faster than natural gas prices. Furthermore, all models indicate more uncertainty in long-run natural gas price forecasts than in steam coal prices.

**The comparison of the out-of-sample forecast performance of the statistical models in section 6 suggested that the models are not able to improve the fuel price level forecasts from IEA experts. Inclusion of forward looking information besides historic prices helps to improve forecasting performance. The models do succeed in describing most of the fuel price interdependencies accurately. This is evidence in favour of an approach in which the fuel prices are modelled coherently as is done in this research using multivariate models. The qualitative aspects as discussed in section 7 answered the second research question. **

High economic growth and quick depletion of crude oil reserves are the most likely expla- nation of crude oil prices increasing more quickly than natural gas and steam coal prices. Supply of natural gas, uranium and steam coal is currently less problematic. A significant increase in energy demand from emerging markets though could in the long-run result in an increasing depletion rate of steam coal reserves and likewise increase coal prices. Greenhouse gas reduction targets and emission trading on the other hand increase total coal usage costs and can potentially decrease total steam coal demand in favour of natural gas demand.

The limited availability of natural gas reserves is an issue which could lead to political instability and security problems resulting in supply disruptions and additional price volatility for this commodity. From a sustainable point of view natural gas has an absolute advantage over steam coal which currently has higher greenhouse gas emissions per MWh power produced. Technological developments could potentially overcome these difficulties but will most likely increase fuel switching opportunities and further strengthen common trends in prices as well. Uranium poses an interesting alternative to fossil fuels as it is not associated with greenhouse gas emissions.

The costs of uranium represent only a small part of total operation costs of a nuclear power plant. Political concerns on safety and waste disposal on the other hand render investment in nuclear power highly uncertain. Based on the statistical model, their performance, the qualitative remarks and other ex- pert scenarios the third research question is addressed in section 8. Four scenarios have been constructed reflecting uncertainty in energy price levels and the interdependencies between natural gas and steam coal prices. Energy price levels are extremely difficult to predict. Therefore a high and low crude oil price option have been included.

Furthermore uncertainty around the growth of emerging markets and their willingness to reduce carbon emissions have led to the inclusion of a negative and a stable gas/coal trend option in the scenarios. Using these scenarios DELTA Energy can construct a coherent long-term view

10 RESEARCH CONCLUSION 78 and make crucial strategic decisions. The fourth research question has been addressed by analysing the effect of fuel price uncertainty on power plant investment decisions in section 9.1. An important result is that fuel price variance or technological variance with respect to some technology reduces investment in that technology. The higher fuel price variance of natural gas is therefore an important disadvantage. If total costs are considered though uncertainty will push towards flexible, less-capital intensive technologies, which is in favour of natural gas fired power plants.

**If DELTA Energy could reduce fuel price uncertainty by hedging or us- ing long-term contracts then this could potentially increase power plant value. Another important option to consider is delaying the investment decision until uncertainties are reduced. The described framework allows DELTA Energy to make careful investment decisions.**

The implication for DELTA Energy’s assets and investment decisions is the ultimate goal of this research and was discussed in section 9.2. Given the four scenarios and techno- logical assumptions, it can from a costs perspective be concluded that a coal fired power plant will probably have over the long-run the lowest power generation costs. Only if natural gas prices are substantially lower relative to steam coal prices or if emission costs are extremely high, natural gas fired power plants could potentially have lower generation costs. Furthermore, the additional volatility in natural gas prices could potentially out- weigh the impact of emission price uncertainty.

It is therefore expected that the historic merit order with coal power plants having lower marginal costs than natural gas fired power plants remains intact.

The decision for DELTA Energy to invest in a specific type of power plant depends, be- sides costs, highly on the power price development. The growth of renewables and energy savings can have a significant influence on long-run power price levels and volatility. It is expected that renewables will increase demand for peak-load capacity which could be generated by flexible natural gas fired power plants. A phase out of nuclear power gener- ating capacity on the other hand could increase demand for base-load capacity as well. A further in detail analysis of the power market and the development of generating capacity is therefore needed to facilitate a strategic investment decision.

10.3 Further Research The results from the long-run stochastic mean-reverting model deviate substantially from Pindyck (1999). This can be the results of the short data set but also from deviations in the Kalman filter. The compounding of small numerical errors can cause these differences. To take a closer look the dataset of Pindyck who originally estimated his results in E-views 3.0, was plugged into E-views 6.0 and re-estimated. The numerical solver though didn’t

10 RESEARCH CONCLUSION 79 succeed in reproducing Pindyck’s results. It is therefore likely that model instability and consequently numerical problems explain the different results. The commodity prices are measured in euros to facilitate the analysis for DELTA En- ergy and the Northwest European energy market. From 1970 onwards though the U.S. dollar has decreased in value relative to the Dutch guilder and later on the euro. In the long-run purchase power parity is assumed and therefore the exchange rate effect is not incorporated in this research. A quick analysis of the vector error correction model based on dollar data didn’t change the results dramatically.

**A more in depth analysis or alter- natively the use of a basket of currencies could enhance the research conclusions. The multivariate unobserved components model has proved to be an interesting alterna- tive to the standard cointegration models. More research should be conducted to improve its forecasting performance. This could be done by including additional explanatory fun- damentals, unobserved components or price lags.**

Not considered in this research is the use of an ARFIMA model as for example proposed by Koopman et al. (2007) for daily electricity prices. The ARFIMA model is well know for its ability to describe long-run memory behaviour but has the disadvantage that it is difficult to estimate with a limited dataset as in this research. Forward prices for most of the commodities are available for several years ahead and could include viable information for the long-run development of energy prices. The inclusions of this information could potentially increase forecast accuracy. Furthermore it would be interesting to investigate whether the model predictions are consistent with forward expectations.

The scenarios in this research are simulated using the vector error correction model with one cointegration relationship. This model was selected based on its out-of-sample perfor- mance, but other methods could have been considered as well. An interesting alternative would have been a Bayesian approach in which the VECM could have been integrated over the number of cointegration relationship. Even more challenging, a complete Bayesian modelling approach could be considered. To address the issue of power plant investment decisions more accurately a more extent analysis is needed. The long-run power price development was not investigated in this research.

A distinction between base and peak-load prices would be needed in that case as well to assess the effect on the number of operating hours of different power plant types. Furthermore, the technological development of the power plants is assumed, but in reality investment costs are besides fuel costs uncertain as well. The same holds for the development of a long-run forecasting model for carbon emission prices which is material for further research.

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**A STATE SPACE FORMAT AND THE KALMAN FILTER 84 A **State Space format and the Kalman filter The general linear state space format is given by yt = A0 xt + H0 ξt + εt, εt ∼ N(0, R), t = 1 , T, (37) ξt+1 = M + Fξt + Sηt, ηt ∼ N(0, Q) , (38) where yt is a p × 1 vector of p observed endogenous variables and xt is a k × 1 vector of k explanatory variables, which can possibly be lags of yt.

The m × 1 vector of unobserved states ξt are modelled by the state equation. The matrices A, H, M, F, S, R and Q are time-invariant and contain (partially) unknown parameters, which can be estimated by maximum likelihood, provided that the model is identified. Forecasts from the model are supplemented with confidence intervals by quasi maximum likelihood estimation to identify forecasting and parameter uncertainty.

The Kalman update equations to obtain the states are given by: ˆ ξt+1|t = M + F ˆ ξt|t−1 + FPt|t−1H(H0 Pt|t−1H + R)−1 (yt − A0 xt − H0 ˆ ξt|t−1) , (39) Pt+1|t = FPt|t−1F0 − FPt|t−1H(H0 Pt|t−1H + R)−1 H0 Pt|t−1F0 + SQS0 , (40) where P denotes the states variance matrix. The model is estimated by iterating between estimating the parameters in the state space format given above and estimating the states using the Kalman update equations. For more information Hamilton (1994a). A.1 Stochastic long-run mean-reverting model In state space format the stochastic long-run mean-reverting model of section 4.2 can be written by observation equation pt = α β1 1 pt−1 + 1 t φ1t φ2t + εt (41) and state equation φ1t φ2t = γ1 0 0 γ2 φ1t−1 φ2t−1 + η1t η2t , (42) where R = σ2 ε and Q = σ2 η1 0 σ2 η2 .

All errors terms are assumed Gaussian and uncor- related.

**A STATE SPACE FORMAT AND THE KALMAN FILTER 85 A.2 **Multivariate unobserved components model In state space format the multivariate unobserved components model (MUCM) of section 4.4 can be written by observation equation p1,t p2,t p3,t = β1 0 0 0 β2 0 0 0 β3 p1,t−1 p2,t−1 p3,t−1 + α1 + δt α2 + δt + γ1 1 0 0 γ2 0 1 0 1 0 0 1 τt ε1,t ε2,t ε3,t (43) and state equation τt ε1,t ε2,t ε3,t = µ + 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 τt−1 ε1,t−1 ε2,t−1 ε3,t−1 + ηt ε1,t ε2,t ε3,t , (44) where R = 0 and Q = σ2 η ρηε1 σησε1 ρηε2 σησε2 ρηε3 σησε3 ρηε1 σησε1 σ2 ε1 ρε1ε2 σε1 σε2 ρε1ε3 σε1 σε3 ρηε2 σησε2 ρε1ε2 σε1 σε2 σ2 ε2 ρε2ε3 σε2 σε3 ρηε3 σησε3 ρε1ε3 σε1 σε3 ρε2ε3 σε2 σε3 σ2 ε3 .

All errors terms are assumed Gaussian and potentially correlated.

**B ABBREVIATIONS AND DEFINITIONS 86 B **Abbreviations and Definitions SMRM stochastic long-run mean-reverting model VECM vector error correction model MUCM multivariate unobserved components model IEA International Energy Agency OPEC organization of petroleum exporting countries CTL coal-to-liquids CCS carbon capture and sequestration GTL gas-to-liquids UCG underground coal gasification NGL natural gas liquids LNG liquified natural gas Watt measure of electrical capacity kW 1000 Watts kWh kilowatt-hour, measure of electrical output MWh megawatt-hour, 1000 kWh brl barrel, unit of crude oil, 159 litre Reserves Quantities which are anticipated to be technically (but not necessarily commercially) re- coverable from known accumulations.

Resources Refers to recoverable quantity (in addition to proved reserves) that is inferred to occur, based on direct geological evidence, in extensions of well-explored deposits and in de- posits in which geological continuity has been established, but where specific data and measurements of the deposits and knowledge of their characteristics are considered to be inadequate to classify the resource as a proved reserve, WEC (2007).