IIES Quarterly Energy Economics Review Vol 4 No 12 Sp 2007

Quarterly

Energy Economics Review

Volume 4, Number 12, Spring 2007

Proprietor: Institute for International Energy Studies

Responsible in Charge:

Editor in Chief: Mohammad Mazraati, Ph.D.

Managing Editor: Shohreh Khoshnoudi Nejad

Persian Editor: Raouf Shahsavari

Translater: Alireza Hamidi Younessi English Editor: Homayoon Nassimi Art Editor: Latif Rafizadeh

Editoral Editoral Editoral Editoral Board:Board:Board:Board: Hamid Abrishami(Ph.D.)/ Tehran University, Abolghasem Emamzadeh(Ph.D.)/ Petroleum Industry University, Ahmad R. Jalali-Naini (Ph.D.)/ Institute for education and research in management and planning, Mohammad-bagher Heshmatzadeh (Ph.D.)/ Shahid Beheshti University, Majid Abbaspour (Ph.D.)/ Azad University, Energy and environment faculty, Mehdi Assali (Ph.D.)/ Econometrician, OPEC, Morteza Mohammadi-Ardehali (Ph.D.)/ Amirkabir Industrial University, Mohammad Mazraati (Ph.D.)/ OPEC, Vienna, A. Shaabani (Ph.D.)/ Emam Sadegh University, M. H. Zahedivafa (Ph.D.)/ Emam Sadegh University, A. M. Seyf (Ph.D.)/Emam Sadegh University

ConsultantConsultantConsultantConsultants:s:s:s: Ali Emami-Meibodi (Ph.D.), Ebrahim Bagherzadeh (Ph.D.), Fereidoun Barkeshli (Ph.D.), Ali Geranmayeh (Ph.D.), Saeed Moshiri (Ph.D.)

Referees: H. Abbasi Nejad (Ph.D.), S. Adibi, M. Amirmoeini, F. Barkeshli (Ph.D.), M. Behrouzifar, A. Boghosian(Ph.D.), M. Bozorgzadeh Yazdi, A. Delparish, A. Emamzadeh (Ph.D.), A. Farzinvash, M.A. Hajimirzaei, M.R. Jalali Naeini(Ph.D.), A. Kadkhodazade, Sh. Khaleghi, M. Mazraati (Ph.D.), M. Sadeghi (Ph.D.), D. Vafi Najjar, H. Yadegari

Quarterly Energy Economics Review

Vol. 4, No. 12 / Spring 2007 / 1 INSTITUTE FOR INTERNATIONAL ENERGY STUDIES

P.O. Box: 19395/4757 Tehran, I.R. Iran

Tel: 2202 9351-60 Fax: 22029388 www.iies.org

.

Quarterly

Energy Economics Review

Volume 4, Number 12, Spring 2007

CONTENTS

Dynamics of Petroleum Markets in OECD Countries In a

Monthly VAR Model Mehdi Asali

2

Allocation of CO2

emissions in petroleum refineries to

petroleum joint products: a case study Alireza Tehrani Nejad M. - Valérie Saint-Antonin

71

Abstracts

Age Estimation of Car Fleet and its Impact on Fuel

Consumption in Iran: Efficiency vis-à-vis Renovation Mohammad Mazraati

101

Impacts of Oil Price Shocks on Economic Variables in a

VAR Model A. Sarzaeem

103

Recent Crude Oil Market Developments: Making

Structural Models M. Zamani

104

A Survey of New Structure of LNG and Natural Gas

Industry in the World E. Mansour Kiaee

106


2 / Vol. 4, No. 12 / Spring 2007

Dynamics of Petroleum Markets in OECD Countries

In a Monthly VAR Model

Mehdi Asali1

Abstract

This paper contains results of the first part of a study in which a Vector Auto-Regression (VAR)/Vector Error Correction (VEC) model is developed and estimated to investigate dynamics of petroleum markets in OECD. Time series of the model comprises monthly data for the variables: demand for oil in OECD, WTI in real term as a benchmark oil price, industrial production in OECD as a proxy for income and commercial stocks of crude oil and oil products in OECD for the time period of January 1995 to March 2007. The detailed results of this empirical research are presented in different sections of the paper, nevertheless, the general result that emerges from this study could be summarized as follows: (i) There is convincing evidence of the series being non-stationary and integrated of order one I(1) with clear signs of co-integration relations between the series. (ii) The VAR system of the empirical study appears stable and restore its dynamics as usual following a shock to the rate of changes of different variables of the model taking between 5 to 8 periods (months in our case). (iii) It appears that the null hypothesis of ‘the expected mean of the series being insignificant from zero’, cannot be rejected in 5% level for each of four time-series indicating lack of statistical proof for presence of the deterministic trend in time-series of concern, (iv) Normality tests and histograms of the series reveals that while distribution of the samples in level differ from theoretical normal

1. Econometrician, PMAD Department, Research Division, OPEC Secretariat, [email protected]


Vol. 4, No. 12 / Spring 2007 / 3

distribution however this is not the case for the differenced time series and for the residuals, on the other hand autocorrelation functions of the series are consistent with unit root process .(v) We find the lag length of 2 as being optimal for the estimated VAR model. (vi), Significant impact of changes in the commercial crude and products’ inventory level on oil price and on demand for oil is highlighted in our empirical study and in different formulations of the VAR model indicating importance of changes in stocks’ level on oil market dynamics. (vii) Income elasticity of demand for oil appear to be prominent and statistically significant in most estimated models of the VAR system, while price elasticity of demand for oil is found to be negligible and insignificant in the short-run.

Key terms: Petroleum market, dynamics, OECD, VAR model,

stationary.

1. Introduction

Structural changes in petroleum markets and its pricing systems in the last decades and increasing exposure of the financial markets to international oil trade have contributed to growing complexity of oil markets dynamics and volatility of its prices. These complexities are due to, and in turn intensify, uncertainties surrounding the oil markets and most often than not undermine robust and accurate prediction of the oil market developments. Growing demand for energy and oil particularly in major developing countries with considerable pace, increasing number of oil producing and exporting nations, technological changes in` upstream and downstream activities, integration of oil in the global commodity markets, movements of open interest in global financial markets on oil trade, impacts of geopolitical and environmental concerns on petroleum sector and climate changes are amongst numerous factors effecting oil markets and its prices. In fact, oil prices have been the most volatile price of all in commodity markets in recent years.

Because of its significant share in energy mix, which is crucial for well functioning of every modern society, its important role in the world economy’s development, and also its exhaustibility, petroleum


4 / Vol. 4, No. 12 / Spring 2007

markets and its dynamics have always been watched carefully not only by major consumers and producers but also by economic agents involved with commodity and financial markets and indeed by the governments of the producing and consuming nations alike. Understandably studies related to different aspects of economics of petroleum have been expanding fast in different directions, particularly after the oil shocks of 1970s and early 1980s. Turbulences in oil markets of the late 1990s when oil price reduced drastically due to the excess supply amid a recession in South East Asian countries, and continuous upward trend in oil prices on back of persistent tight markets dominated by growing demand for energy and oil particularly in major developing countries in last few years, have added yet more dimensions to dynamics of petroleum sector; further complicating its analysis.

Although this study is confined to the oil markets in OECD countries, nevertheless, given this region’s share in the global demand for oil, investigating developments of petroleum markets in OECD could contribute to our comprehension of the dynamics of global petroleum markets. This is a fact that any significant changes in demand for oil in OECD have always had far-reaching effects on petroleum markets. Although OECD’s share of global demand for oil has been continuously declining, due to a fast growing demand for energy and oil in developing nations; particularly in China, India and the Middle East, however, in 2006 OECD still was consuming about 60% of global oil supply and according to IEA (2007) OECD will continue to dominate the oil markets in the foreseeable future with a 55% share of global demand in 2011. The same applies for the crude and oil products stocks particularly when it comes to commercial crude and product inventories.

Our study examines relationship between major variables of oil market in OECD countries for the time period of 1995 to 2007 employing a monthly Vector Auto-regression (VAR)/Vector Error Correction (VEC) model. The estimated model then is used to forecast short term demand for oil in OECD. Typically, these relationships are explored using simple correlation and deterministic trends which in


Vol. 4, No. 12 / Spring 2007 / 5

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

1970 1975 1980 1985 1990 1995 2000 2005

OIL Consumption OECDOIL Consumption World

Fig. 1. Oil Consumption in OECD and the World (000 b/d)

most cases could not yield consistent and robust results. Advantage of the VAR modeling approach for our purpose in this study over possible alternative econometric techniques will become clearer as we proceed further. However, we have briefly pointed out here to the shortcoming of the traditional econometric models in oil market analysis.

Economic theory suggests existence of equilibrium relationship between demand for crude oil; income and oil prices. Also economic theory could have been thought of predicting a meaningful long-run relationship between inventory of oil and its prices, for oil supply comprises oil consumption and its inventory and any short run disequilibrium in oil demand and its supply is usually absorbed by changes in inventory; hence a close relationship between oil prices and oil stocks. Although in general the observed pattern of demand for crude oil, GDP, oil inventory and oil prices tend to support this theory however, there have been periods in which oil prices, output, oil

Fig 1. Oil Consumption in OECD and the World (000 b/d)


6 / Vol. 4, No. 12 / Spring 2007

demand and inventory have appeared to move independently of each other.

Now, if one try to explain these relationships by a single equation structural econometric model, for example as following linear model:

ttttt SPYD εαααα ++++= 3210 )1(

Where, Dt, Yt , Pt and St are demand for oil, gross domestic product, oil price and crude and products stocks respectively, there could be in most part, inadequacy on the part of estimated parameters due to the fact that important variables of the equation such as the scale variable of GDP for example, has to be treated as exogenous factors while in reality these variables are endogenous to the economic system. One of the major problems with this specification is that GDP is clearly an endogenous variable, and price may or may not be endogenous. Given these conditions OLS estimates of 1α or income

elasticity of demand are poorly defined from econometric point of view. This leads to application of a variety of econometrics techniques through which the endogeneity of the variables on the right hand side of equation (1) could be removed from the equation, and iα can be

properly estimated. Ignoring these facts in modeling oil market developments would leave the model an inadequate device of data generating process of oil markets. On the other hand a dynamic simultaneous equations model will be difficult to identify as economic theory still is not rich enough to provide a dynamic specification that identifies all of the restrictions required for such complex relationships.

However, empirical studies show that time series analysis of oil market could reveal, if existed, the underlying and lasting relationship between the important variables of oil market despite apparently inapprehensible developments in this market. Suppose in our oil demand equation discussed above, we treated all the variables that we believed exerted significant impact on oil market dynamics, as endogenous variables of the system; in this case if the right hand side variables of equation (1) were assumed endogenous, then we would


Vol. 4, No. 12 / Spring 2007 / 7

have needed to formulate explanatory equations for each of these variables. A VAR can be viewed as a natural extension of the question of endogeniety and feedback amongst the variables in question. In a VAR model all variables are treated symmetrically. That is, if we are interested in demand for oil, GDP, oil price and stocks, then we should expand our model to a four variable VAR.

A VAR-VEC modeling of petroleum markets would allow us to investigate the salient features of the economic and statistical relationship between these variables for the sample period of the study that covers January 1995 through March 2007. This time period includes oil price collapse from the supply glut in late 1990s coincident with economic downturn of many developing countries of the South-East Asia and sustained oil price increase from 2002 to mid 2006 due to strong global economic performance particularly major developing countries (e.g. China and India) surge of demand for energy and oil. So the time period covers sub-periods of both excess supply and excess demand with their impacts on oil markets developments.

Nevertheless, the required assumptions, on the basis of which time-series modeling inferences and forecasts are believed to be valid, may not hold in every given instance. So the first step in any empirical analysis using a Vector Auto-Regressive (VAR) or Vector Error Correction (VEC) model is to test if these assumptions are indeed appropriate. In the remainder of the paper we first review the main features of VAR/VEC modeling approaches and then proceed with estimation and forecasting part of the study. (See appendix for a brief description on the methodology).

2. A monthly oil market VAR model for OECD

In this section we will develop the VAR model of our study. Studying demand for oil, similar to other commodities, immediately postulate presence of income and price in the model. However, in congruity with the literature (see for example M. Ye, et. al.(2002)), as discussed earlier, we recognize the significant effect of oil inventory (crude and


8 / Vol. 4, No. 12 / Spring 2007

products) on dynamics of oil markets, i.e. on oil price and through this variable on demand for oil, thus in this study, our specification of the four variable VAR model takes in account the effects of oil stock changes on oil market developments. This is also important to note that WTI in our VAR is in real term. In other words nominal oil price is deflated by OECD consumer price index. One can find many examples of VAR models of oil market treating oil price in real terms (see for example R. Jimenez-Rodrigues and Marcelo Sanches, 2004). In fact in this version of the VAR model we are mainly interested in oil demand in OECD, which is suppose to be a function of real oil price, rather than impacts of nominal oil price shocks on inflation and economic activities in his region. In a next attempt we will extend the VAR model to consider nominal oil prices and other variables as well. This would be interested to compare the results of this version of the VAR model with one where impacts of oil price on inflation and economic growth are examined. The VAR model of four variables in our study in its most general structure could be introduced as follows:

(2) Where, as defined before, Dt, Yt, Pt and St stands for Demand for

oil in OECD, an index of monthly industrial production in OECD, WTI benchmark oil prices and oil stock (crude and product) in OECD countries at time t and respectively. Coefficients of the model “ iβ ”

and intercepts iα are to be estimated.

2.1 Time series properties of the VAR model variables

A simple graphical and statistical analysis would enhance our

∑ ∑ ∑ ∑

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1 1 1 14161514134

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εββββα

εββββα

εββββα

εββββα


Vol. 4, No. 12 / Spring 2007 / 9

comprehension of the VAR system of concern. Using 12 years of monthly data drawn from January 1995 to March 2007, time series of demand for oil, industrial production and oil and crude commercial stocks in OECD and WTI prices in real terms are analyzed, focusing on short-run effects of changes in these variables on the system of time-series. Monthly time-series were used because they have sufficient characteristics to capture short-run movements of the variables of concern over time, without adding unnecessary complexity to the analysis. This is relevant to the monthly analysis and forecast of oil market developments in OPEC monthly reports. Entire data is collected from Data Service Department (DSD) of the OPEC Secretariat

The statistical and graphical analysis of the time-series of the VAR system consists of inspecting the levels and differences of the variables. The logarithmic transformation of series used to remove the scale effects in the variables and reduce the possible effect of heterokedasticity. This transformation also allows the estimated coefficients to be interpreted as constant elasticities and circumvent the problem of different units of the time series.

Table (1) reports some descriptive statistics for the logarithms of the variables in levels, differences and for the residuals. Since the variables appear to be non-stationary in level, the empirical density of distributions of the variables as were depicted in Figure (5) below do not seem to be normal. The differences of the variables, which indicate changes to these variables on the other hand, seem stationary around a constant mean. From table (1), the mean for differences of all four variables of the model is not significantly different from zero,

(with largest value being around 0.005 for [ ]CPI

WTIP ∆=∆ ).

Normality is tested with Jarque-Bera test, distributed as )2(2χ

under the null. Jarque-Bera is a test statistic for testing whether the series is normally distributed. The test statistic measures the difference of the skewness and kurtosis of the series with those from the normal distribution. The statistic is computed as:


10 / Vol. 4, No. 12 / Spring 2007

(3)

Where S is the skewness, and K is the kurtosis (see: Eviews, 6, 2007). Under the null hypothesis of a normal distribution, the Jarque-

Bera statistic is distributed as 2χ with 2 degree of freedom. The

reported Probability is the probability that a Jarque-Bera statistic exceeds (in absolute value) the observed value under the null hypothesis- a small probability value leads to the rejection of the null hypothesis of normal distribution. So for example if in a test of normality J-B statistic’s probability was reported to be about 0.04 we could say the hypothesis of normal distribution is rejected in 5% but not at the 1% significant level. In estimated VAR model, the J-B test statistic is a multivariate extension of the test, which compare the third and fourth moments of the residuals to those from normal distribution. Usually Doornik and Hansen (1994) approach to normality test is adopted.

From table (1) we can see that, probability of the normality of the distributions of variables in first difference and also the VAR residual is higher than that of the variables in level. This is also evident from visual inspection of the histograms of the model’s variables in level and first difference.

Generally speaking we cannot reject normality of these variables in difference and residuals of the VAR model except for variable LTSOECD- stock of crude and products in OECD. The test provides normality of distribution of this variable in level form. Since the normality test, along with AR and ARCH tests is usually considered a test of mis-specification, so having found evidence of the residuals of the VAR model being derived from normal distribution is encouraging on the basis that this is an indication of proper specification of the model.

While it is difficult to discern if a time-series is nonstationary by

visual examination of level data, however, it is always a good idea to start with a visual inspection of the data and their time series

]4

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6

22 −

+=−K

SN

BJ


Vol. 4, No. 12 / Spring 2007 / 11

properties as a first check of the assumptions of the VAR model. Based on the graphs we can get a first impression of whether tix ,

looks stationary with constant mean and variance, or whether this is the case for tix ,∆ . If the answer is negative to the first but positive to

the next one, we can solve the problem by re-specifying the VAR in error-correction form as will be illustrated in the following sections of the paper.

Table 1. Descriptive statistics of the VARModel Variables

[ ]___________________________________________________________________________

,(*)..

___________________________________________________________________________

....03.0.........65.0..........002.0............09.0.............03.0........78.0.......................

......01.0.........75.0............44.0............92.0.............01.0........46.0.....................Pr

....93.9.........57.0............61.1............16.0...............9.8..........5.1.................

......01.4.........06.3............65.2............14.3............64.3.........88.2.........................

......41.0.......15.0......195.0.........04.0............52.0......24.0....................

.........01.0.........068.0.........004.0..........025.0..........015.0.........07.0...........................

.....05.0.....195.0.......010.0...........06.0.........06.0......20.0....................

.....039.0.........180.0.........011.0...........07.0...........038.0........198.0.....................

.....001.0.........005.0....0002.0.........001.0...........002.0........013.0.........................

.......0.0.............0.0.............0.0.............0.0.........0002.0........005.0............................

__________________________________________________________________________

...ˆ..............ˆ...............ˆ................ˆ..................................................................

__________________________________________________________________________

.....002.0.............14.0.........17.0............54.19..........86.0.........22.0......................

........37.0.............22.0.........58.0............20.0............05.0.........10.0....................Pr

...........9.1.............98.2.........09.1..............1.3............56.5.........46.4................

.......95.2.............95.2.........76.2.............83.2............23.2........02.3.........................

......28.0..........35.0......17.0.........35.0............31.0.....43.0....................

.......002.0.............03.0..........03.0............37.0.........078.0.........04.0...........................

......01.0.........09.0.......68.14............2.2........41.4.........65.10.....................

.......014.0..........062.0..........84.14............4.0........70.4.........85.10....................

...........002.0..........003.0..........77.14..........32.1........58.4.........77.10........................

.........002.0...........001.0.........76.14..........28.1.........56.4........77.10...........................

_________________________________________________________________________

...........................................................................................................................

CPIWTIP

DevSqSum

obability

BeraJarque

Kurtosis

Skewness

DevStd

Minimum

Maximum

Median

Mean

SP

DevSqSum

obability

BeraJarque

Kurtosis

Skewness

DevStd

Minimum

Maximum

Median

Mean

YDSPYD

SPYD

=

−

−−−−−

−−−−−

−

∆∆

−

−−−−−

−−−

−

−

−

∆∆∗

εεεε


12 / Vol. 4, No. 12 / Spring 2007

If in rare cases we found answers to both questions negative, it would be wise to investigate whether any significant departure from the constant mean and constant variance coincides with specific economic reforms or intervention at specific date in the time period of concerned. The next step in this case would be inclusion of this information in the model to find out about the intervention has had a permanent or transitory characteristic or whether it appear to be additive to the model or has fundamentally changed the parameters of the model. In the latter case the intervention is likely to have caused a regime shift and the model would need to be re-specified allowing for the appropriate change in the structure (see: Juselius, 2003).

Inspecting the graphs of the level of time series of our VAR model in different panels of Figure (2) suggested existence of non-stationary processes in the model while visual study of first differenced based graphs of the model variables do not indicate non-stationarity. Graphs of Figure (3) illustrate that these type of stochastic process are capable to adequately describe the data, independently of whether one takes a close-up or a long-distance look at the time series.

Figure (4) presents WTI in real term in first differences and 12-month differences respectively. Both series appear stationary in their differences although it seems that the departure from the mean appear more prolonged in monthly difference case. Also the outliers appear to be present in both cases. These might cause non-stationarity in an stable time-series system.

A visual inspection reveals that, apart from significant volatility of the processes in the level and the differenced cases, which is a reflection of the magnitude of changes to the level of the variables, neither the assumption of a constant mean or a constant variance seem appropriate for the levels of the time-series, whereas the differenced time-series look more satisfactory in this respect. If marginal processes are normal then the observations should lie systematically on both sides of the mean. This seems approximately to be the case for real WTI but for oil stock and to some extend for industrial production there are some outlier around year 2000. This is a good


Vol. 4, No. 12 / Spring 2007 / 13

-.06

-.04

-.02

.00

.02

.04

1996 1998 2000 2002 2004 2006

d. Difference of (Log of) Total Commercial Stock OECD

-.3

-.2

-.1

.0

.1

.2

.3

1996 1998 2000 2002 2004 2006

b. Difference of (Log of) Real WTI

-.015

-.010

-.005

.000

.005

.010

.015

1996 1998 2000 2002 2004 2006

c. Difference of (Log of) Industrial Production Index OECD

-.12

-.08

-.04

.00

.04

.08

1996 1998 2000 2002 2004 2006

a. Difference of (Log of) Monthly Demand for Oil OECD

Fig. 3 Differences of the Model's Time-series

idea to find out whether the outlier observations can be related to some significant economic developments including economic or energy policy intervention in OECD level or whether these observations are too far away from the mean to be considered realizations from a normal distribution.

As was mentioned before, there seem to be some outlier observations, which apart from the series in level, this seems to be the case both in the differenced time-series and the residuals. As it is well known an outlier in a regression is a data point which has a large residual. Large in this context does not refer to the absolute size of a

Fig. 2. Differences of the Model's Time-series


14 / Vol. 4, No. 12 / Spring 2007

-3

-2

-1

0

1

2

3

1996 1998 2000 2002 2004 2006

1-Month Difference (WTI)

-3

-2

-1

0

1

2

3

1996 1998 2000 2002 2004 2006

12-Month Differenc (WTI)

Fig.4 WTI Prices: First and 12-Month Difference in Logarithms

Price

s C

ha

ng

es (

in L

og

arith

ms)

residual but to its size relative to most of the other residuals in the regression. Some of most outstanding outliers for WTI series appear to be around year 2000, 2001 and 2005. The Katrina hurricane in July 2005 in Golf of Mexico and the South East of the USA appears to be the reason behind price violation of mid 2005 reflected in the time series residuals.

Fig. 3. WTI Prices: Firstand 12-Month Difference in Logarithms


Vol. 4, No. 12 / Spring 2007 / 15

As was mentioned before, there seem to be some outlier observations, which apart from the series in level, this seems to be the case both in the differenced time-series and the residuals. As it is well known an outlier in a regression is a data point which has a large residual. Large in this context does not refer to the absolute size of a residual but to its size relative to most of the other residuals in the regression. Some of most outstanding outliers for WTI series appear to be around year 2000, 2001 and 2005. The Katrina hurricane in July 2005 in Golf of Mexico and the South East of the USA appears to be the reason behind price violation of mid 2005 reflected in the time series residuals.

-.08

-.04

.00

.04

.08

1996 1998 2000 2002 2004 2006

LDOECD Residuals

-.012

-.008

-.004

.000

.004

.008

.012

1996 1998 2000 2002 2004 2006

LIPIOECD Residuals

-.2

-.1

.0

.1

.2

1996 1998 2000 2002 2004 2006

LRWTI Residuals

-.06

-.04

-.02

.00

.02

.04

.06

1996 1998 2000 2002 2004 2006

LTSOECD Residuals

Fig. 4.The graphs of the residuals from the VAR model

Fig. 4. The graphs of the residuals from the VAR model


16 / Vol. 4, No. 12 / Spring 2007

.0

.2

.4

.6

.8

2 4 6 8 10 12 14 16 18 20 22 24

Actual Theoretical

Au

toc

orr

ela

tio

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LDOECD

0.0

0.2

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1.0

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Actual Theoretical

Au

toc

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0.0

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Actual Theoretical

Au

toc

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LTSOECD

0.2

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Actual Theoretical

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LIPIOECD

Fig. 5. Histograms and Autocorrelation Functions of the Series

0

4

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12

16

10.60 10.65 10.70 10.75 10.80 10.85 10.90

Density

LDOECD

0

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4.3 4.4 4.5 4.6 4.7

Density

LIPIOECD

0.0

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1.6

2.0

-2.5 -2.0 -1.5 -1.0 -0.5 0.0

Density

LRWTI

0

4

8

12

16

14.64 14.68 14.72 14.76 14.80 14.84 14.88

Histogram Kernel Normal

Density

LTSOECD

Fig. 5 Histograms and Autocorrelation Functions of the Series


Vol. 4, No. 12 / Spring 2007 / 17

0

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-.12 -.08 -.04 .00 .04 .08 .12

Density

DLDOECD

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ensity

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-.3 -.2 -.1 .0 .1 .2 .3

Density

DLRWTI

0

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-.08 -.04 .00 .04 .08


Density

DLTSOECD

Fig. 6 Histograms and Autocorrelation of the First Differences of the Series

-.2

-.1

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.1

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.3

.4

2 4 6 8 10 12 14 16 18 20 22 24

Actual Theoretical

Au

toco

rre

lati

on

DLIPIOECD

-.3

-.2

-.1

.0

.1

.2

2 4 6 8 10 12 14 16 18 20 22 24

Actual Theoretical

Au

toc

orr

ela

tio

n

DLRWTI

-.4

-.2

.0

.2

.4

2 4 6 8 10 12 14 16 18 20 22 24

Actual Theoretical

Au

toc

orr

ela

tio

n

DLTSOECD

-.4

-.2

.0

.2

.4

.6

2 4 6 8 10 12 14 16 18 20 22 24

Actual Theoretical

Au

toc

orr

ela

tio

n

DLDOECD

Fig. 6. Histograms and Autocorrelation of the First Differences of the Series


18 / Vol. 4, No. 12 / Spring 2007

It appears that all four time series of the VAR model are integrated of order one or in other word first differences of these process are stationary which will be investigated along with other statistical properties of the model in the next sections. The probability distribution and autocorrelation functions (ACF) for the level and first differences of the series are presented in figures (5) and (6). Histograms summarize the frequency of occurrence that a variable falls within a certain range of values. As such, histograms provide insights into the mean, standard error and probability distribution of given variable. Histograms of the demand for oil (D=LDOECD) and Industrial production Index (Y=LIPIOECD) in OECD, and histograms of (P=WTI) bench mark oil prices and total commercial stock (S=LTSOECD) are presented in the top panel of Figure (5) and Figure (6) respectively, with a plot of nominal distribution superimposed over the histogram and a smooth line generated from the histogram.

It is apparent that none of the time series in level distributed normally, hence the variables are skewed differently relative to the normal distribution. The ACFs through 24 lags of the variables are presented in the lower panel of the figures. The ACFs are highly significant. The wavy cyclical correlogram with a seasonal frequency for demand for oil and also commercial stocks suggest a seasonal pattern for these variables. These graphical and statistical finding are consistent with unit root processes.

Panels of Figure (6) depict histogram and ACFs for the first differences of all the variables of the model. In each case, the differencing transformation appears to have resolved the non-stationarities in the four series for the most parts. In all cases, the probability distributions of the differenced series appear to be approximately normally distributed. Further, the autocorrelations are also much smaller, and statistically insignificant at most lags. These results lend support to the inference that the time series of our VAR/VEC model are unit roots in level and integrated processes of order one, I(1).

Therefore the problems associated with non-stationary data will be a key consideration in the model specification and estimation that follows.


Vol. 4, No. 12 / Spring 2007 / 19

0

5

10

15

20

25

-.10 -.05 .00 .05 .10

Density

0

20

40

60

80

100

120

-.02 -.01 .00 .01 .02D

ensity

RESIDUALS LIPIOECD

0

2

4

6

8

10

-.3 -.2 -.1 .0 .1 .2 .3

Density

RESIDUALS LRWTI

0

10

20

30

40

50

-.08 -.04 .00 .04 .08


Density

RESIDUALS LTSOECD

Fig. 14 The Empirical and Normal Density of the Four VAR Residuals

RESIDUALS LDOECD

In Figure below, the histograms and auto-correlograms are reported for four VAR residuals. There should be no significant autocorrelation, if the truncation after the second lag is appropriate. Since all the autocorrelations are quite small, this seems to be the case. As discussed earlier the presence of auto-correlation in the residuals of the estimated model is often a result of model misspecification rather than ‘genuine’ auto-correlation of the model error terms. Recall that formal tests of the properties of the error term are carried out on the residuals. But, whilst the errors are a part of the data generation process, the residuals are a product of our model specification (Mukherjee et al, 1998). Hence testing for autocorrelation should in the first instance be interpreted as a test for misspecification. The classical linear regression model assumes lack of serial correlation between the error terms, i.e a zero covariance between the error terms of different observation. In other words, it assumes that because the

Fig. 7. The Empirical and Normal Density of the Four VAR Residuals


20 / Vol. 4, No. 12 / Spring 2007

-.8

-.4

.0

.4

.8

2 4 6 8 10 12 14

Correlogram Residual LDOECD

-.8

-.4

.0

.4

.8

2 4 6 8 10 12 14

Correlogram Residual LIPIOECD

-.8

-.4

.0

.4

.8

2 4 6 8 10 12 14

Correlogram Residual LRWTI

-.8

-.4

.0

.4

.8

2 4 6 8 10 12 14

Correlogram Residual LTSOECD

Fig. 15 Autocorrelogram of the Four VAR Residuals

error for one observation is large this dose not mean that the next error term also will be large. Indeed, the fact that an term is positive should have no implications for whether the next term is positive or negative.

To understand the implication of auto correlation for residual plots observe that if the different (residual) terms are independent then we should not see any patterns in the data- for example, there should not be long runs of positives followed by long runs of negatives, when a run is defined as successive values of the same sign. Eventually, a positive value in on period should not imply a negative value in the following period, so the plot should not be exceptionally jagged (i.e. have many short runs of positive and negative values). Also we realize that the empirical density functions are not deviated too much from the normal density and the residuals seem homo-scedastic, i.e. have similar variances over time. A couple of empirical densities, (LDOECD and LIPIOECD) seem to have longer tails (excess kurtosis), that are likely to be influenced by poor economic performance of 2000 to 2002 causing non-normality of these time series as pointed out earlier.

Fig. 8. Autocorrelogram of the Four VAR Residuals


Vol. 4, No. 12 / Spring 2007 / 21

2.2 The statistical adequacy of the model

To comprehend when a VAR is an adequate description of reality, it is important to know the limitations as well as potentials of that model. It was briefly mentioned that a VAR model can be a convenient way of summarizing the information given by the autocovariances of the time series data under certain assumptions about the data generating process (DGP) (Hendry, 1995a). However, the required assumptions may not hold in any given instance, so the first step in any empirical analysis of a VAR model is to test if these assumptions are indeed appropriate.

We could write our VAR system in a more compact manner as follows:

∑=

− Ω+Π+Φ=k

i

pttititt INXDX1

],0[~............)4( εεε

Where X is a vector of variables, i.e. X=[D, Y, P, S] and Π is a

vector of parameters, 2,,1 ,....,1],......,[ mjkjj ==Π ββ m being the

number of the variables of the model . t=1,…,T and the parameters ),,( εΩΠ itD are constant and unrestricted, except for εΩ being

positive-definite and symmetric. Given (3), the conditional mean of Xt is:

,.ˆ][)5(1∑

=

−− =Π+Φ=k

i

titititt XXDXXE

And the deviation of Xt defines tε as:

ttt XX ε=− ˆ

Hence, if the assumptions of multivariate normality, time-constant covariance, and the lag structure of the VAR are correct, then system (3):

i) is linear in the parameters; ii) has constant parameters; iii) has normally distributed errors tε , with:

iv) independence between tε and ,...2,1,.... =− hhtε

These conditions provide the model builder with testable


22 / Vol. 4, No. 12 / Spring 2007

hypothesis on the assumptions needed to justify the VAR (see: Hendry, 1995). In economic applications however, the multivariate normality assumption is seldom satisfied. This is potentially a serious problem, since derivation of a general DGP rely heavily on multivariate normality, and statistical inference is only valid to the extent that the assumptions of the underlying model are correct, (Hendry and Juselius, 2000). An important question is, therefore, how we should modify the standard general VAR model (2) in practice. We would like to preserve its attractiveness as a reasonably tractable description of the basic characteristics of the data, while at the same time, achieving valid inference. Thus it seems advisable to ensure validity of the first three assumptions. It is often useful to calculate descriptive statistics combined with a graphical inspection of the residuals as a first check of adequacy of the VAR model, as we did above, and then undertake formal mis-specification tests of each key assumption, that we are about to do in next sections of the paper. Once we understand why a model fails to satisfy the assumptions we can often modify it to end with a well-behaved model.

2.3 A Tentatively unrestricted VAR (2)

As a first step in the analysis, an unrestricted VAR(2) version of the model with a constant term and without dummy variables is estimated for the all four variables.

Observe that under the assumption that the parameters ,,......,, 21 ΩΠΠΠ=Θ k in the VAR model (3) above are

unrestricted, OLS estimator will be identical to Full Information Maximum Likelihood (FIML) estimator (see Hendry, 1995 and Juselius, 2003). However, when the data contain unit-roots we need to derive the likelihood estimator subject to reduced rank restriction. This will be discussed later but in this part of the paper, given the assumptions just mentioned we will conduct estimation of an unrestricted VAR (2) model of the system of time-series of concern to use in our analysis of oil market dynamics in OECD countries. The estimation results of our unrestricted VAR(2) model, i.e:


Vol. 4, No. 12 / Spring 2007 / 23

________________________________________________________________________

20,.,21,..86.32ˆlog,.....9.1534max)(

)(..),(..,...

70.4716...37.79........73.478........90.25..........................................

99.0........81.0..........96.0............59.0...............................................

99.0.......82.0..........96.0............60.0.........................................................

....................................................var.....

00002.0

00022.0

00502.0

00066.0

ˆ,..

0.1......096.0.......086.0........76.0

0.1.......26.0......051.0

0.1......109.0

0.1

04.0......02.0......02.0..........003.0

45.0......05.0.......01.0.........02.0

99.0.....7.1......10.0.....23.0

67.0....4.0...03.0........02.0

94.0....002.0...02.0..001.0

39.0..83.0......01.0.....13.0

4.1....93.1.05.1......25.0

82.0......50.0......03.0..60.0

24.0

67.2

8.6

12.2

)7(

________________________________________________________________________

.................................

2

2

,4

,3

,2

,1

2

2

2

21

1

1

1

1

2211

−=−=−=Ω=

−

−

=

=Ω

+

−

−−−

−−−

+

−−

−−

−−

−

+

−

=

+Π+Π+Φ=

−

−

−

−

∗

∗

∗

−

−

−

−

∗∗

∗∗

∗∗

∗∗

∗

−−

SCAICLLog

SCCriterionSchwartzandAICCriterionnInformatioAkaikstatisticssampleCommon

statisicF

RAdj

R

YSPDiablesindividualforStatistics

Y

S

P

D

Y

S

P

D

Y

S

P

D

XXDXModelEstimatedThe

t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

tttt

εσ

ε

ε

ε

ε

ε

),0(~..,,....,1

)6( 2211

Ω=

+Π+Π+Φ= −−

pt

ttttt

NandTt

XXDX

ε

ε

where Dt contains constant values, are reported below. An inspection of the estimated coefficients reveals more significant coefficients at lag 1 than lag 2. Also we realize that most of the coefficients with large t-ratios are on the diagonal, implying a highly autoregressive character of the variables. Also the significance of the crude and product stocks in oil demand and oil price equations is worth noting. These results support our earlier remark on the importance of the crude and product stocks for oil price and oil demand.


24 / Vol. 4, No. 12 / Spring 2007

As mentioned above these estimates are ML estimates as long as no restrictions have been imposed on the VAR model. To increase readability we have omitted standard errors of estimates and “t” ratios. Instead, coefficients with a “t”-ratio greater than 1.70 have been given an asterisk indicating statistical significance (at 5% level) of these parameters in the model. For the reason that will be discussed below related to the existence of unit-root in the system and since Xt is not likely to be stationary. In this case the “t” ratios are more likely to be distributed as the Dickey-Fuller’s “τ” (Juselius, 2003) and should, therefore, be interpreted as Student’s t.

It is obvious that a typical VAR model will be greatly over parameterized, in the sense that many of the coefficients (especially in a VAR that has lag length greater than one) will be individually insignificant. Our VAR model is no exemption. For example in our small VAR model of oil market, assuming only two lag length for the model, we will have 32 (m2×k) of β parameters to estimate where m is the number of endogenous variables in the system.

It should be noted that, in a standard VAR model, the right hand side contains only pre-determined variables (mostly lagged ones) and the disturbance terms are assumed to be serially uncorrelated. Thus, each equation of the VAR system can be estimated by ordinary least square without loss of efficiency (Atkins, 2005).

Dynamics of the VAR(2) unrestricted model depicted in this graphs, seem to be in accordance with our expectations of the oil markets and prediction of economic theory. An increase in oil price reduces oil demand while on the other hand an increase on oil demand has an positive impact on oil prices. A positive shock on economic activities increases demand for oil and an increase of demand for oil decreases the level of crude and product stocks which later rebound back to its initial level.

While the unrestricted estimated VAR model’s behavior seems plausible in an economic sense, this is still advisable to remind ourselves, briefly, of the exact interpretation of the VAR models before proceeding further with our analysis of oil market dynamics exhibited in different representations of the VAR-VEC models. This


Vol. 4, No. 12 / Spring 2007 / 25

-.06

-.04

-.02

.00

.02

.04

.06

14.68

14.72

14.76

14.80

14.84

95 96 97 98 99 00 01 02 03 04 05 06

Residual Actual Fitted

Fig. 10.c Commercial Stocks of Crude and Products, Fitted values and Residuals

will give us the necessary justification for addressing the non-stationarity issue of the series of our VAR system for some specification of the model even in price of losing information pertaining to the long-run relationships between the variables.

-.2

-.1

.0

.1

.2

.3

-2.4

-2.0

-1.6

-1.2

-0.8

-0.4

95 96 97 98 99 00 01 02 03 04 05 06


Fig. 10.b Real WTI, Fitted values and Residuals

-.03

-.02

-.01

.00

.01

.02

.03

10.68

10.72

10.76

10.80

10.84

95 96 97 98 99 00 01 02 03 04 05 06


Fig. 10.a Monthly Demand for Oil in OECD, Fitted Values and Residuals

Fig. 9.a. Monthly Dem and for Oil in OECD Fitted Values and Residuals

Fig. 9.b. Real WTI Fitted values and Residuals

Fig. 9.c. Commerclal Stocks of Crude and Products. Fitted values and Residuals


26 / Vol. 4, No. 12 / Spring 2007

-.015

-.010

-.005

.000

.005

.010

.015

4.4

4.5

4.6

4.7

4.8

95 96 97 98 99 00 01 02 03 04 05 06


Fig. 10.d Industrial Production Index, Fitted Values and Residuals

-.01

.00

.01

.02

.03

1 2 3 4 5 6 7 8 9 10

Response of LD to LP

-.01

.00

.01

.02

.03

1 2 3 4 5 6 7 8 9 10

Response of LD to LY

-.050

-.025

.000

.025

.050

.075

.100

1 2 3 4 5 6 7 8 9 10

Response of LP to LD

-.050

-.025

.000

.025

.050

.075

.100

1 2 3 4 5 6 7 8 9 10

Response of LP to LS

-.050

-.025

.000

.025

.050

.075

.100

1 2 3 4 5 6 7 8 9 10

Response of LP to LY

-.02

-.01

.00

.01

.02

1 2 3 4 5 6 7 8 9 10

Response of LS to LD

Fig. 5 Response to Cholesky One S.D. Innovations ± 2 S.E.

in the Model (20)

Fig. 9.d. Industrial Production Index, Fitted Values and Residuals

Fig. 10. Response to Cholesky One S.D. Innovations ±±±±2 S.E. in the Model (20)


Vol. 4, No. 12 / Spring 2007 / 27

2.4 Economic interpretation of the VAR models

The Vector Autocorrelation (VAR) process based on Gaussian errors has frequently been a popular choice as a description of economic time series data. There are many reasons for this: the VAR model is flexible, easy to estimate, and it usually gives a good fit to economic data. However, the possibility of combining long run and short run information in the data by exploiting the co-integration property is probably the most important reason why the VAR model continuous to receive the interest of both economists and econometricians (Juselius, 2003).

Theory based economic models have traditionally been developed as non-stochastic mathematical entities and applied to empirical data by adding a stochastic error process to the mathematical model. However, from an econometric point of view the two approaches are quite different: one starting from an explicit stochastic formulation of all data and then reducing the general statistical dynamic model by imposing testable restrictions on the parameters, the other starting from a mathematical formulation of a theoretical model and then expanding the model by adding stochastic components.

As discussed in Hendry (1995a), the conditional mean of a VAR model can be given an econometric interpretation as the agents’ plan at time t-1 given the past information of the process (derived from of the lagged variables) of the model. The assumptions in (19) concerning the residuals of the model being independent and normally distributed implies that the market players are rational, in the sense that the deviation between the actual outcome Xt and the plan

][ 011 −− ttt XXE is a white noise innovation, not explicable by the past of

the process. Thus the VAR model is consistent with economic agents who seek to avoid systematic forecast errors when they plan for time t based on the information available at time t-1. On the contrary, a VAR with auto-correlated residuals would describe agents that do not use all information in the data as efficiently as possible. This is because they could do better by including the systematic variation left in the


28 / Vol. 4, No. 12 / Spring 2007

residuals, thereby improving the accuracy of their expectations about the future. Therefore, checking assumptions of the model is not only crucial for correct statistical inference, but also for the economic interpretation of the model as a description of the behavior of rational agents.

To derive a full-information maximum likelihood (FILM) estimator requires an explicit probability formulation of the model. Doing so has the advantage of forcing us to take the statistical assumptions seriously. Suppose that we have derived an estimator under the assumption of multivariate normality. We then estimate the model and find that the residuals are not normally distributed, or that residual variance is heteroscedatic instead of homoscedastic, or that residuals exhibit significant autocorrelation, etc. The parameter estimate may not have any meaning, and since we do not know their ‘true’ properties, inference is likely to be misleading as well. Therefore, to claim that conclusions are based on FIML inference is to claim that the empirical model is capable of accounting for all the systematic information in data in a satisfactory way.

Although the derivation of a FILM estimator subject to parameter restrictions can be complicated, this is not so when the parameters of the VAR model (18) are unrestricted. In that case, the ordinary least squares (OLS) estimators are equivalent to FILM. After the model has been estimated by OLS, the IN distributional assumption can be checked against the data using the residuals

tε (Hendry and Juselius, 2000).

2.5 Stability and unit-root properties of the model

Up to this point, the VAR model of our study is estimated and discussed as if its time-series were stationary. But in light of the last sections discussion we realize that presence of unit-roots in time-series of the VAR system could cause serious problems regarding inference of the estimation results and the accuracy of the model’s predictions. In this section we examine the unit-roots of the time-series of the VAR model and its characteristics prior to proceeding


Vol. 4, No. 12 / Spring 2007 / 29

with estimation of the different versions of the model.

The dynamic stability of the process (4) which is repeated below for convenience;

∑=

− Ω+Π+Φ=k

i

pttititt INXDX1

],0[~............)4( εεε

can be investigated by calculating the root of (5):

tt

k

kp XLLLL )(),......,()8( 221 Π=ΧΠ−Π−Π−Ι

Where .itt

iL −Χ=Χ For a VAR (2) model of our case the

characteristic polynomial could be defined as:

).()()9( 221 zzp Π−Π−Ι=ΖΠ

The roots of 0)( =Π z contain all necessary information about

the stability f the process and therefore, whether it is stationary or non-stationary. In econometrics, it is usual to discuss stability in terms of the companion matrix of the system (Hendry, and Juselius, 2000), which is obtained by staking the variables of the model as a first order dynamic system:

,00.......,

,....,)10(

2

1

,

21

1

+

ΠΠ=

−

−

−

t

t

t

pt

t

X

X

IX

X ε

Where the first block is the original system and the second block is merely an identity for .1−tX Stability of the system depends on the

Eigen-values of the coefficient matrix in (10), and these are precisely

the roots of 0)( 1 =Π −z (Hendry and Juselius, 2000, Banerjee et al.

1993). For a p-dimensional VAR with 2 lags, there are 2p eigen-values. The following results apply:

(a) if all eigenvalues of the companion matrix are inside the unit circle, then Xt is stationary;

(b) if all the eigenvalues are inside or on the unit circle, then Xt is non-stationary;


30 / Vol. 4, No. 12 / Spring 2007

(c) if any of the eigenvalues are outsise the unit circle, then Xt is explosive.

For the multivariate (four variable) demand for oil VAR(2) model, we will have 4×2=8 roots, the model of which are reported directly from the computer output in table (2) below (rounded to point three digits):

conditionstabilitythesatisfiesVAR

circleunittheoutsideliesrootNo

Modulus

iRoot

ionspecificatLag

CiablesExogenous

SLTSOECDPLRWTRYLIPIOECDDLDOECDiablesEndogenous

PolynomialsticCharagteriofRootsTable

....

.......

_________________________________________________________________________

024.0......,.........230.0............,.........230.0,......326.0,..482.0,..855.0,..945.0,..999.0...

024.0,...229.0021.0,...229.0216.0,...326.0,..482.0,..855.0,..945.0,..999.0.........

_________________________________________________________________________

12:.

:var.

)(),..(),.(),.(:var.

________________________________________________________________________

....2

+−−−

Figure (10) illustrate these Eigen-values in relations to the unit circle. We note that the system is stable and no explosive roots are found in the system of time series, however, there are two near-unit roots, suggesting the presence of stochastic trends as well a couple of complex roots. The distinction between a unit-root process and a near unit-root process need not be crucial for practical modeling. Even though a system is stable but a couple of rots close to unity (say

)95.0≥ρ as in our case, it is often a good idea to act as if there are

unit roots to obtain robust statistical inference. Now, in our empirical exercise since there are two roots close to unity for the four variables, the series seem non-stationary and possibly co-integrated.

Now that our VAR system is shown to be stable, albeit containing near unit roots characteristics, we could address the non-stationarity issue in the time-series of the model to obtain a set of robust and consistent results from our estimation exercises. Theoretically, the unit-root assumption implies an ever-increasing


Vol. 4, No. 12 / Spring 2007 / 31

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Inverse Roots of AR Characteristic Polynomial

Fig. 10 The eigenvalues of the companion matrix

variance to the time series (around a fixed mean), violating the constant-variance assumption of a stationary process. Of course the stability of the system was detectable given the estimation results of the unrestricted VAR model in the level of time-series and dynamic responses of the variables to the shocks, in the previous section of the paper.

In this part of the paper we will estimate the model after having examined the hypothesis of the variables of the system being I(1). Given the time series of the model are I(1) we first will discuss its short-run features by transferring data to a set of stationary time-series. In the next part of the paper we will embark on a VEC modeling of the time-series examining the co-integration relations and the long-run characteristics of the system. On the basis of the preceding discussion our analysis would proceed with a formal test of the integration of the VAR model time-series. Two forms of the

Fig. 11. The eigenvalues of the companion matrix Inverse Roots of AR Characteristic Polynomial


32 / Vol. 4, No. 12 / Spring 2007

augmented Dickey-Fuller (ADF) tests were estimated where each form differs in the assumed deterministic component(s) in the series i.e:

....tan....;..)12(

.tan........;.........)11(

11

41321

11

3121

trendandtconsXXtX

onlytconsXXX

tt

P

i

tt

tt

P

i

tt

εββββ

εβββ

+∆+++=∆

+∆++=∆

−

=

−

−

=

−

∑

∑ As usual tε is assumed to be a Gaussian white noise random

error and t=1,..,T (number of observations in the sample) is a time trend term.

Although the tests were conducted for both forms of the ADF tests mentioned above, but in fact we needed to examine only the first test, i.e. the expression (11), because according to the descriptive statistics reported on table (1) the hypothesis “ 0][ =∆ iXE ” could not

be rejected for non of the variables of the model. However, estimating

the second expression i.e .11

41321 tt

P

i

tt XXtX εββββ +∆+++=∆ −

=

− ∑ for

all four variables of the model yielded the following results:

____________________________________________________________

).3.1..().........61.0().........11.2..().........02.5.....(....................

00004.0.....00001.0......0004.0.........0004.0...........

............................................................................

___________________________________________________________

)12..(..var

........3

Statisticst

tCoefficienterndTime

LYLSLPLDVariables

equiniables

theoftscoefficientrendtimeforresultsEstimationTable

−

−

As we can see coefficients of LD and LP are very small indeed and coefficients of the two other variables are small and statistically insignificant. Therefore, since we had found 0][ =∆ iXE , [the

hypothesis that the mean of the first difference of the variables is not significantly different from zero cannot bee rejected], which is now supported with these statistical evidence, applying the ADF test with


Vol. 4, No. 12 / Spring 2007 / 33

constant term only is what would be needed for a statistical unit-root test of the time-series of our VAR model.

Table (4) contains the results from the ADF test. The number of lagged differences, p, is chosen to ensure that the estimated errors are not serially correlated based on the Akaike information Criterion (AIC). The Akaike Information Criterion (AIC) is computed as:

[ ]nsobservatiosampletheofnumberisTandresidualtheis

TTl

followsasdefinedoodthelikelihislandestimateparametersofnumberisnwhere

TnTlAIC

...........ˆ

)/ˆ'ˆlog()2log(12

:.............

/2/2)13(

ε

εεπ ++−=

+−=

The AIC is often used in model selection for non-nested alternative-smaller values of the AIC are preferred. For example one can choose the length of a lag distribution by choosing the specification with lowest value of the AIC. The Schwarz Criterion (SC) is an alternative to the AIC that impose a large penalty for additional coefficients [see also eq. (16) below].

Table (4) and (5) contains the results from the ADF tests for the variables in level and in first difference respectively. Between them these two tables test the hypothesis whether the time-series of the model are I(1). The first column of the tables refer to the number of lags, p,, in each regression. This is followed by set of three figure for each lag under each variable.

The first figure is the t-statistic for the ADF test that is associated with the last lagged difference variable in each equation, followed by the MacKinnon one sided p value and the AIC. The null hypothesis in each set is that there is a unit-root in the equation of concern or equivalently the series is I(1). This implies of the coefficient being zero. It is well known that because of the properties of non-stationary process, the distributions of the statistics are different. The critical values are given at the bottom of the tables. AIC criterion is used in evaluating the appropriate number of lags in the testing procedure that remove serial correlation in the residuals with smaller values of information criteria being preferred.


34 / Vol. 4, No. 12 / Spring 2007

1%at t Significan

5%at t Significan

values.-p sided-one (1996)MacKinnon

2.578788level ..10%2.883930,.level ..5%3.481623,.level 1%: valuescriticalTest

______________________________________________________________________________

81.7/87.0/57.0.....51.5/21.0/75.2......35.2/86.0/87.1.....23.4/00.0/16.5)..00(

780/86.0/60.0......53.5/15.0/94.2......35.2/53.0/11.2.....25.4/00.0/81.3)..01(

81.7/86.0/61.0.....54.5/08.0/22.3......33.2/59.0/99.1.....28.4/04.0/92.2)..02(

782/85.0/67.0.....59.5/02.0/81.3.....32.2/50.0/05.2.....32.4/07.0/50.3)...03(

84.7/83.0/56.0.....56.5/05.0/34.3......32.2/50.0/05.2.....32.4/01.0/66.3)..04(

84.7/81.0/82.0......58.5/20.0/01.2......29.2/50.0/17.2.....33.4/03.0/14.3)...05(

83.7/76.0/96.0......14.5/18.0/85.2.....28.2/49.0/19.2......33.4/01.0/35.3)...06(

82.7/70.0/15.1......62.5/59.0/00.2......26.2/50.0/17.2.....47.4/12.0/49.2).....07(

82.7/81.0/83.0.......60.5/58.0/01.2......24.2/46.0/24.2....47.4/16.0/.32.2).....08(

80.7/78.0/92.0......58.5/53.0/10.2.....22.2/51.0/14.2......52.4/14.0/46.2).....09(

80.7/74.0/02.1......59.5/34.0/48.2......26.2/22.0/74.2.....65.4/19.0/25.2).....10(

82.7/83.0/75.0.....56.5/36.0/42.2.....27.2/08.0/20.3....18.5/03.0/13.3)...11(

81.7/88.0/51.0.....77.5/03.0/61.3.....25.2/08.0/21.3....17.5/09.0/63.2).....12(

81.7/79.0/88.0.....77.5/04.0/50.3.....25.2/26.0/63.2.....15.5/13.0/46.2).....13(

81.7/77.0/94.0.....75.5/02.0/80.3.....26.2/16.0/90.2.....25.5/73.0/73.1).....14(

_____________________________________________________________________________

/Pr/.../Pr/.../.Pr/.../Pr/....

.........................................................................................................................

_____________________________________________________________________________

)....(.....4.

∗∗

∗

×

∗∗

∗∗

∗∗

∗∗

∗∗

∗

∗

∗∗

∗∗

∗

∗

×

===

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−

−

AICobADFtAICobADFtAICobADFtAICobADFtLags

LYLSLPLD

levelinVariablesRootUnitfortestsADFTable


Vol. 4, No. 12 / Spring 2007 / 35

All four variables of the model, i.e. LD, demand for oil; LP, WTI oil bench mark price; LS, stock of crude and products and LY, an index of industrial production in OECD appear to be I(1) processes. The LY series is clearly an I(1) process, failing to reject the null hypothesis of a unit-root at each of the 14 lags. The t-ADF tests for the first three of the four variables seem to be significant for some legs. This could lead to a rejection of the null hypothesis of a unit root particularly in case of LD, nevertheless, further testing revealed that theses series were non-stationary particularly because of presence of large outliers. As Hendry and Juselius (2000) argue, “most economic time series are non-stationary, and at best become stationary after differencing. Therefore, stationarity is considered for a differenced

1%at t Significan

5%at t Significan

includedconstant a have testsdifference-First

values.-p sided-one (1996)MacKinnon

2.578788level ..10%2.883930,.level ..5%3.481623,.level 1%: valuescriticalTest

______________________________________________________________________________________

80.7/00.0/7.11...50.5/00.0/1.11...34.2/00.0/5.10...16.4/00.0/1.16)..00(

82.7/00.0/77.6...50.5/00.0/69.7...33.2/00.0/36.8...23.4/00.0/7.12)..01(

83.7/00.0/94.4...50.5/00.0/62.5...31.2/00.0/94.6...24.4/00.0/76.7)..02(

785/00.0/73.3...51.5/00.0/90.5...29.2/00.0/99.5...28.4/00.0/40.7)..03(

85.7/00.0/55.3...54.5/00.0/49.6...28.2/00.0/67.4...28.4/00.0/3756)..04(

84.7/03.0/07.3...52.5/00.0/75.5...27.2/00.0/18.4...26.4/00.0/52.6)..05(

82.7/03.0/09.3...61.5/00.0/97.6...25.2/00.0/03.4...44.4/00.0/72.8)..06(

83.7/02.0/17.3...59..5/00.0/94.5...26.2/50.0/67.3...45.4/00.0/02.8)..07(

80.7/03.0/04.3...58.5/00.0/95.4...21.2/01.0/59.3...49.4/00.0/36.8)..08(

80.7/03.0/37.3...57.5/00.0/92.3...23.2/07.0/74.2...62.4/00.0/70.9)..09(

81.7/01.0/84.3...58.5/00.0/87.3.......21.2/14.0/39.2...12.5/00.0/3.15)..10(

83.7/00.0/68.3......60.5/06.0/79.2......19.2/15.0/37.2...13.5/00.0/86.7)..11(

84.7/00.0/92.3...68.5/03.0/03.3...22.2/04.0/90.2...12.5/00.0/18.6)..12(

82.7/01.0/55.3...66.5/03.0/04.3...21.2/06.0/75.2...24.5/00.0/90.3)..13(

80.7/03.0/05.3...65.5/04.0/93.2...25.2/01.0/38.3...21.5/07.0/59.3)..14(

______________________________________________________________________________________

/Pr/.../Pr/.../.Pr/.../Pr/....

.........................................................................................................

______________________________________________________________________________________

)......(.....5.

∗∗

∗

××

×

∗∗∗∗∗∗∗∗

∗∗∗∗∗∗∗∗

∗∗∗∗∗∗∗∗

∗∗∗∗∗∗∗∗

∗∗∗∗∗∗∗∗

∗∗∗∗∗∗∗

∗∗∗∗∗∗∗

∗∗∗∗∗∗∗

∗∗∗∗∗∗∗

∗∗∗∗∗∗

∗∗∗∗∗

∗∗∗∗

∗∗∗∗∗∗

∗∗∗∗∗∗

∗∗∗∗∗

×

××

===

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−−−−−

−−−−

∆∆∆∆

−

AICobADFtAICobADFtAICobADFtAICobADFtLags

LYLSLPLD

differencefirstinVariablesRootUnitfortestsADFTable


36 / Vol. 4, No. 12 / Spring 2007

series tX∆ or for the terrorsIID ε.. . The distinction between a unit-

root process and a near unit-root process need not be crucial for practical modeling. Even though a variable is stationary, but with a root close to unity (say, )95.0>ρ , it is often a good idea to act as if

there are unit roots to obtain robust statistical inference”.

3. Specification of the VAR Model

Now that we have established the fact that the time series composing our VAR model are I(1) processes and there are clear signs of co-integration or long-run relationship between them, we are in a opposition to proceed with specification and estimation the VAR model prior to testing for co-integration and then estimation the VEC model to use it for forecasting the market developments.

A general to specific approach is adopted here as Hendry (1986) and Hendry and Juselius (2000, 2001). First we will determine the lag structure of the VAR model. The VAR model (2) is general enough to accommodate any number of lag structures, so this must be determined prior to conducting the analysis. Then using the results of estimation the unrestricted VAR model in the preceding section, the VAR model will be re-estimated. Once a correctly specified model emerges from this process, restrictions are imposed on the model to give an economic interpretation for a statistically sound and robust model.

The test for a long-run relationship between demand for oil, industrial production, stocks of crude and products and crude oil prices starts with the estimation of the four variables VAR model. The VAR model can be specified in matrix form as:

The time series have been transformed to logarithms to address heterokedasticity issues. Constant (and trend) terms are included in each equation; their role will be modified at a later stage on the basis

+

Π+

Φ=

−

−

−

−

t

t

t

t

it

it

it

it

i

i

t

t

t

t

t

LY

LS

LP

LD

Ltimrtrend

tcons

oductionIndustrialLY

oductsCrudeofStockLS

WTIiceOilLP

OilforDemandLD

4

3

2

1

)(tan

)Pr.(

)Pr&..(

).Pr.(

)..(

)14(

ε

ε

ε

ε


Vol. 4, No. 12 / Spring 2007 / 37

of statistical examination of the series behaviors. The error terms are assumed to be white noise and can be contemporaneously correlated. The expression ( )LΠ is a lag polynomial operator indicating that p

lags of each series is used in the VAR. The individual iΠ terms

represent a 4×4 matrix of coefficients at the ith lag and the Φ matrix is a 4×2 matrix. The other variables, LD, LP, LS,LY, constant, time trend and error terms are scalar.

The number of lags to the variables is unknown at the beginning. The selection methodology starts with an initial maximum number of p lags which are assumed to be in excess to the minimum required lags. Residual diagnostics tests like normality, serial correlation and heterokedasticity are conducted and the VAR model is tested for stability. The main objective of these tests is to make sure that the results are close enough to the assumption of white noise residuals. A large number of lags are most likely to produce over-parameterized model. Nevertheless, a convincing econometric analysis needs to start with a statistical model of the data generation process and then conduct the relevant tests to achieve parsimony with fewest number of lags capable of explaining the dynamics of the system.

3-1. Lag length selection

The selection criteria for the appropriate lag length of the unrestricted

VAR models employ 2χ tests and F-tests. Table (5) shows results of

tests of lag length on the basis of 2χ tests. The selection procedure

involves choosing the VAR (p) model with the highest value of AIC, SBC or the HQ and lowest value of FPE. In practice, the use of SBC is likely to result in selecting a lower order VAR model than when using the AIC. However, in using both criteria it is important that the maximum order chosen for the VAR is high enough for high-order VAR specification. As it can be seen we have chosen Max. order of eight lags which is supposed to be sufficient. All the nine VAR (p), 0=0, 1,…, 8, are estimated over the same sample period. As to be expected the maximized values of log-likelihood function given under


38 / Vol. 4, No. 12 / Spring 2007

the column LogL increase with p. The Hannan-Quinn (HQ) and the Schwartz (SC) criterions select the order 1 while the Akaike (AIC) and the Final Prediction Error (FPE) select the order 2. However, the log-likelihood ratio statistics rejects order 1, but do not reject a VAR of order 2.

The log-likelihood ratio statistics (LR column on table 5) are computed for testing the hypothesis that the order of the VAR is (p) against the alternative that it is P (the Maximum expected order), for p=1,2… ,P-1. To test this hypothesis one should construct the relevant log-likelihood statistics for these tests by using the maximized values of the log-likelihood function given in the relevant column of the result table. For example, to test the hypothesis that the order of the VAR model is 2 against 3 the relevant log-likelihood ration statistics is given by:

Where LogLp =p=1,2,..,p refers to the maximized value of the log-likelihood function for the VAR(p) model. Under the null hypothesis, LR (2:3) is distributed asymptotically as a chi-squared

variate with 22 )23( mm =− degrees of freedom, where m is the

dimension of coefficient vector of the variables in an standard VAR(p) model.

Table 5. Testsoflaglengthor Model Reduction for VAR

criterionn informatioQuinn -Hannan :HQ

criterionn informatio Schwarz :SC

criterionn informatio Akaike :AIC

error prediction Final :FPE

level) 5%at (each test statistic test LR modified sequential :LR

criterion by the selectedorder lag indicates *

_____________________________________________________________________________

-19.80511-18.12694-20.9539315-9.71e 15.36716 1556.867 8

-20.03046-18.55570-21.0400315-8.79e *31.10212 1546.722 7

-20.11433-18.84299-20.9846515-9.20e 21.97606 1526.956 6

-20.29089-19.22297-21.0219615-8.80e 31.12377 1513.493 5

-20.39480-19.53028-20.9866115-9.08e 28.63356 1495.090 4

-20.52872-19.86762-20.9812915-9.10e 21.57805 1478.728 3

-20.72784-20.27015*21.04115- *15-8.56e 30.23674 1466.798 2

*20.86430- *20.61003- -21.0383615-8.58e 1376.453 1450.608 1

-10.73156-10.68071-10.7663810-2.48e .............NA ....736.1135 0

____________________________________________________________________________

HQ....................SC................AIC..............FPE..............LR..............LogLLag

)(2)3:2()15( 23 LogLLogLLR −=


Vol. 4, No. 12 / Spring 2007 / 39

To decide on the most desirable order of the VAR model we note that the BSC, HQ and AIC statistics are all closely related. In each case, the log determinant of the estimated residual covariance matrix is computed and added to term that exacts as a penalty for the increased number of parameters used in the estimation. The BSC, HQ and AIC differ in the magnitude of the penalty term. Each used as alternative criterion in testing, because each reflects the tradeoff between increasing the precision of the estimates and the possible over-parameterization associated with the loss of parsimony and degree of freedom. The expression for the three criterions could be given as follows (Villar, and Joutz, 2006):

( )( ) ( )

( ) ( )( ) 1

1

1

loglog2ˆlog

log2ˆlog

2ˆlog)16(

−

−

−

×××+Σ=

×××+Σ=

××+Σ=

TTcDetHQ

TTcDetBSC

TcDetAIC

The first terms on the right-hand side of the equations are the log determinants of the estimated residual covariance matrix. The log determinant of the estimated residual covariance matrix will decline as the number of regressors, just as in a single equation ordinary least squares regression. It is similar to the residual sum of squares or estimated variance. The second term on the right-hand side acts as a penalty for including additional regressors (c) which scaled by the inverse of the number of observations (T). The lag length chosen is the model with minimum value for the Statistics. The three tests do not always agree on the same number of lags. In practice, the use of the SBC is likely to result in selecting a lower order VAR model than when using AIC. Notice that it is quite usual for the SBC to select a lower order VAR as compared with the AIC. Also as was discussed in our case and according to the statistics given on table (5) order 1 is rejected by the log-likelihood ratio. In the light of these reasons we choose the VAR (2) model.


40 / Vol. 4, No. 12 / Spring 2007

3.2 Estimation results of the VAR (2) model

Having decided on the order of the VAR model we could now proceed with estimation of our VAR (2) model. In section (4.3) “a tentative VAR(2) model” we in fact estimated the VAR(2) model in level of time-series. However, now that we have found the time series of our system are I(1) and since on the other hand in this part of the study we are mainly concern with the short-run developments of the oil markets in OECD, therefore we will estimate the first differenced form of the VAR (2) model as follows:

......)17( 2211' ε+∆Π+∆Π+Φ=∆ −− tttt XXDX

Which in extended form of or fourvariate VAR (2) model becomes:

The estimation results are given below. As can be seen from these results in the time period of concern, income elasticity of demand for oil in OECD has been around 1 and statistically significant, indicating a 1% increase in industrial production, in previous time period, would cause an increase in demand for oil with a magnitude of slightly less than 1% (0.96%). Also it is interesting to see that changes in stocks of crude and products has significant impacts on the both rates of oil demand and particularly oil price with expected signs. We also notice that oil prices changes have no significant impact on demand for oil in the short-run but, perhaps surprisingly, exert some negligible impact on industrial production rate.

+

∆

∆

∆

∆

Π+

∆

∆

∆

∆

Π+Φ=

∆

∆

∆

∆

−

−

−

−

−

−

−

−

4

3

2

1

2

2

2

2

2

1

1

1

1

1')18(

ε

ε

ε

ε

t

t

t

t

t

t

t

t

t

t

t

t

t

Y

S

P

D

Y

S

P

D

D

Y

S

P

D


Vol. 4, No. 12 / Spring 2007 / 41

-.08

-.04

.00

.04

.08

1996 1998 2000 2002 2004 2006

D(LD) Residuals

-.2

-.1

.0

.1

.2

1996 1998 2000 2002 2004 2006

D(LP) Residuals

-.06

-.04

-.02

.00

.02

.04

1996 1998 2000 2002 2004 2006

D(LS) Residuals

-.015

-.010

-.005

.000

.005

.010

.015

1996 1998 2000 2002 2004 2006

D(LY) Residuals

10.20,..80.20,..10.14ˆlog,....1501max)(

..),.(.inf..,.

00.2......70.1......52.2........77.6..........................................

05.0......03.0.......08.0........24.0....................................

11.0......10.0......13.0........29.0.........................................................

..........................................var...

00002.0

00022.0

00515.0

00073.0

ˆ................

.1.....11.0......10.0.....021.0

0.1......10.0.......72.0

0.1.......06.0

1

.

%.5...

18.0....03.0......00.0.........00.0

11.0..32.0.......00.0........04.0

24.0....38.0.......06.0.....23.0

66.0.......03.0....02.0.....14.0

.02.0....01.002.0........01.0

.041....14.0...03.0......17.0

11.1.....79.1...11.0........19.0

96.0.....87.0......03.0,....10.0

002.0

001.0

004.0

002.0

)19(

____________________________________________________________________________

':).2.(....Re.

2

41

3

2

1

2

2

2

2

1

1

1

1

2211

−=−=−=Ω=

−

−

=

=Ω

+

∆

∆

∆

∆

−−

−−

−−−

−−−

∆

∆

∆

∆

−−−

−−−

−−

−−

+

−

=

∆

∆

∆

∆

+∆Π+∆Π+Φ=∆−

∗

−

−

−

−

∗

∗

−

−

−

−

∗

∗

∗

∗∗

∗

−−

SCAICLLog

CriterionSchwartzandAICCriterionormationAkaikSampleCommon

StatisticF

SquaredRAdj

R

YSPDiablesindividualforlStatistica

levelattSignifican

Y

S

P

D

Y

S

P

D

Y

S

P

D

XXDXModelVARrunShorttheofsultsEstimation

t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

ttttt

εσ

ε

ε

ε

ε

ε


42 / Vol. 4, No. 12 / Spring 2007

Inspecting the graphs of residuals series of the variables of the estimated VAR model together with the residuals’ empirical distribution (below) clearly shows that standard assumption of OLS estimation regarding stationarity of the residuals and normality of their distribution are satisfied supporting statistically robustness of the estimation results.

It is worth noting that the volatility of oil markets reflected particularly on rate of changes of oil prices and inventory levels, and also existence of outliers in the time series inevitably contribute to low explanatory power of the estimated model. This should be mentioned that we have not used dummy variables in the estimated models. Dummy variables could capture effects of particular events enhancing models goodness of fit especially when there are many outliers in the time series of the model.

Below we have presented graphs illustrating response of our VAR (2) model’s variables to different shocks. As was discussed very briefly at the beginning of the paper, a Vector Auto-Regression (VAR) system and closely related Vector Error Correction model possess a very rich set of dynamics which uncovered through the use of impulse response functions. It is well known that any single variable auto-regression has a moving average representation. Therefore, a natural generalization of this is that any VAR (or respected VEC) models have a vector moving average (VMA) representation. For example it can be shown that one can arrive to the following VMA by necessary manipulation of our four variables VAR model:

0

5

10

15

20

25

-.08 -.04 .00 .04 .08 .12

Density

D(LD)

0

2

4

6

8

-.3 -.2 -.1 .0 .1 .2 .3

Density

D(LP)

0

10

20

30

40

50

-.08 -.04 .00 .04 .08

Density

D(LS)

0

20

40

60

80

100

120

-.02 -.01 .00 .01 .02


Density

D(LY)

Fig. Implied Empirical Density of VAR(2) in First Differenced Fig. 12. Implied Empirical Density of VAR (2) in First Differenced


Vol. 4, No. 12 / Spring 2007 / 43

∑∞

=

−

−

−

−

+

=

0

,4

,3

,2

,1

44434241

34333231

24232221

14131211

4

3

2

1

)().....()......().....(

)().....()......().....(

)().....()......().....(

)().....()......()......(

)20(i

it

it

it

it

t

t

t

t

iiii

iiii

iiii

iiii

Y

S

P

D

ε

ε

ε

ε

φφφφ

φφφφ

φφφφ

φφφφ

α

α

α

α

There is an analogous VMA for the VEC model. The sixteen sets of coefficients )(iijφ are the impulse response functions. These

give us the effect of the shocks tt 21 ,.εε , t3ε and t4ε on the entire time

paths of the entire sequences of Dt, Pt, St and.Yt. Notice that for i=0, the coefficients give the impact response. After n periods, the cumulative sum of the effects of, say t2ε , which can be thought of as

impact of a shock to Pt, on Dt is given by:

Of interest in this study is the elasticity of response of one

variable to another. This can be calculated as the dynamic correlation. Suppose that we are interested in the dynamic path of the elasticity of response of demand to a shock in Yt . This is given by the dynamic correlation:

This would give us the time path of the elasticity. It should be noted that analysis using the impulse response function is completely analogous to forecasting. In an impulse response function framework, if we shock one variable, say P, and trace the response of another variable say D, in fact we are forecasting the future path of D, given some future values of P.

Some interesting observations could be detected inspecting dynamics of the responses of the rate of changes of the variables of the model to innovations. For example, while impact of a shock to the rate of changes of demand for oil on the rate of changes of oil priced is as expected opposite to the impact of an impulse to the rate of

∑=

n

i

i0

12 )().......21( φ

∑

∑

=

==n

i

n

i

i

i

i

044

014

)(

)()()22(

φ

φ

ρ


44 / Vol. 4, No. 12 / Spring 2007

-.02

-.01

.00

.01

.02

.03

.04

1 2 3 4 5 6 7 8 9 10

Response of D(LD) to D(LP)

-.02

-.01

.00

.01

.02

.03

.04

1 2 3 4 5 6 7 8 9 10

Response of D(LD) to D(LY)

-.04

.00

.04

.08

.12

1 2 3 4 5 6 7 8 9 10

Response of D(LP) to D(LD)

-.04

.00

.04

.08

.12

1 2 3 4 5 6 7 8 9 10

Response of D(LP) to D(LS)

-.015

-.010

-.005

.000

.005

.010

.015

1 2 3 4 5 6 7 8 9 10

Response of D(LS) to D(LP)

-.002

.000

.002

.004

.006

1 2 3 4 5 6 7 8 9 10

Response of D(LY) to D(LD)

Fig. Dynamics of the Short-run Model (39)

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

changes of oil prices on demand for oil but the magnitudes of impacts are different as a shock to the rate of changes of demand for oil has greater effect on the rate of oil price changes vice versa. Also we notice that almost all the shocks are faded in 5 to 7 time periods. So, although a shock to the rate of changes of stocks (crude and products) on oil price is almost twice as its impact on demand for oil (in absolute terms), however, both impulse impacts fade away in approximately the same time period.

Fig. 13. Dynamics of the Short-run Model (39) Response to Cholesky

One S.D. Innovations±±±± 2 S.E.


Vol. 4, No. 12 / Spring 2007 / 45

3.3 Different EC representation of the unrestricted VAR

The unrestricted VAR model that we estimated and discussed its various characteristics in the preceding sections of this paper, can be given different parameterization without imposing any binding restrictions on the model parameters, i.e. without changing the value of the likelihood function (Juselius, 2003). The formulation of the VAR model in the so called vector error correction (VEC) or equivalently, vector equilibrium correction (VEq.C) model (Hendry, 2000) gives a convenient formulation of the model (20) i.e.

),0(~..,,....,1

)6( 2211

Ω=

+Π+Π+Φ= −−

pt

ttttt

NandTt

XXDX

ε

ε

in terms of differences, lagged differences, and levels of the process. The analysis could benefit from these representations in several ways:

(i) The multicollinearity effect which typically is strongly present in time series data is significantly reduced in error-correction form. Differences are much more ‘orthogonal’ than the levels of variables.

(ii) All information about effects are summarized in the levels matrix Π which can, therefore, be given special attention when solving the problem of co-integration.

(iii) The interpretation of the estimates is more intuitive, as the coefficients can be naturally classified into short-run effect and long-run effects.

(iv) The VEC formulation directly addresses the reasons behind the changes to the variables of the system.

Here we discuss three different versions of the VAR(k), following the same procedure adopted in Hendry and Juselius(2000) and Juselius(2003). As we found the optimal lag length of our VAR model 2 so the lag length of all representation models also are confined to


46 / Vol. 4, No. 12 / Spring 2007

k=2. It would enable us to explain the main points of our argument without loss of generality. The purpose is to illustrate how the estimates could look different although the model is exactly the same.

As discussed earlier, so long as the parameters ( )ΩΠΠΦ ,,, 21 in

(6) formulation are unrestricted, OLS can be used to estimate them. Therefore, any of the three formulation of the VAR model that will be discussed below, can be used to obtain the unrestricted estimates of the VAR model. The important point is that although the parameters differ in the four representations, each of them explains exactly as much of variation in Xt.

The first reformulation of model (6) is into the following error (equilibrium) correction form:

[ ]tpt

ttttt

INandwhere

XXDX

ΩΠ−=ΓΠ−Π−Ι=Π

+Π+∆Γ+Φ=∆ −−

,0~,...,..

)23(

,2)1(

121

11)1(

1

ε

ε

In (23) the lagged levels matrix Π has been placed at time t-1, but could be chosen at any feasible lag without changing the likelihood.

The estimated coefficients reported below. As it can be seen most of the significant coefficients are now located in the lagged level

matrix Π whereas only 3 out of 16 coefficients in the )1(1Γ matrix

seem significant. Among the Π matrix coefficients three are placed on the diagonal indicating (autoregressive) significant effects of the changes in last period (last months) levels of demand for oil, oil price and the commercial crude and product stocks on the rate of the changes of these variables in the present period (month). The remaining three illustrate significant impacts of the changes in (lagged) level of production on oil demand and oil price and that of oil price on production.


Vol. 4, No. 12 / Spring 2007 / 47

________________________________________________________________________

20,.,21,..86.32ˆlog,.....9.1534max)(

)(..),(..,...

97.1...........9.1............9.2...........26.9............................................

05.0........05.0..........10.0............32.0...............................................

10.0.......10.0..........15.0............36.0.........................................................

....................................................var.....

00002.0

00022.0

00502.0

00066.0

ˆ,..

0.1......087.0......13.0........03.0

0.1.......10.0......75.0

0.1......05.0

0.1

02.0......02.0......003.0......004.0

06.0....12.0...001.0.....11.0

43.0.....25.0....05.0.....48.0

15.0........11.0....002.0...42.0

.

04.0....02.0...02.0..003.0

45.0.....05.0..013.0...02.0

00.1......65.1....10.0......23.0

67.0......39.0......026.0..02.0

24.0

67.2

8.6

12.2

)24(

________________________________________________________________________

....

2

2

,4

,3

,2

,1

1

1

1

1

1

1

1

1

11)1(

1

−=−=−=Ω=

−

−

=

=Ω

+

−−

−−−

−−−

−−

+

∆

∆

∆

∆

−−

−−−

−

−

+

−

=

∆

∆

∆

∆

+Π+∆Γ+Φ=∆

−

−

−

−

∗

∗∗

∗∗

−

−

−

−

∗

∗

∗

∗

−−

SCAICLLog


statisicF

RAdj

R


Y

S

P

D

Y

S

P

D

Y

S

P

D


t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

tttt

εσ

ε

ε

ε

ε

ε

Altogether, estimating the model exclusively in difference, i.e. setting 01 =Π −tX would not provide many interesting results. But, on

the other hand including this 1−Π tX in the model raises the question

of non-stationarity problem. Since a stationary process cannot be equal to a non-stationary process, the estimation results can only make sense if 1−Π tX defines stationary linear combinations of the variables.

For example the first and third row of 1−Π tX can be respectively

reformulated as:


48 / Vol. 4, No. 12 / Spring 2007

)5.001.092(.12.0...

)36.026.0005.0(42.0....)25(

1111

1111

−−−−

−−−−

−++−

−−+−

tttt

tttt

YSPDrowThird

YSPDrowFirst

If the linear combination in the parentheses defined two stationary variables, then all parts of the first and third equation in the system would be stationary and, therefore, balanced. This is in fact what co-integration analysis does: it defines stationary linear combinations between non-stationary time-series so that an I(1) process can be reformulated exclusively in stationary variables. However, it is important to have economically meaningful interpretation to these linear combinations by imposing relevant restrictions for identifying the parameters. For example the above relations might be interpreted as the deviation of observed demand for oil (in case of the first row) from a steady state oil demand relation,

*11 −− − tt DD or actual inventory level(in case of the third row)

*11 −− − tt SS of the commercial crude and products in OECD from a

steady state level of stocks where:

111*

111*

5.001.092.

36.026.0005.0)26.(

−−−

−−−

+−−=

++−=

tttt

tttt

YPDS

YSPD

In order to make these issues clear we should find-out whether demand for oil (or stock levels) has a unit coefficient or possibly some coefficients could be set zero.

Note that )( maxLLog and Ωlog are exactly the same as for the

unrestricted VAR in the

previous section. This clearly shows that from a likelihood point of view the models are identical because the residuals are the same in all VEC representatives and all residual tests of information criteria are identical, whereas tests of the significance of single variables need not be and usually are not. For example, the single F-tests of the lagged variables in differences are very different when compared to the two successive specifications, whereas the tests values for the lagged variables in levels are identical. This illustrate that Π matrix is

invariant to linear transformations of the VAR system but not the m

1Γ


Vol. 4, No. 12 / Spring 2007 / 49

-.02

-.01

.00

.01

.02

.03

1 2 3 4 5 6 7 8 9 10


-.02

-.01

.00

.01

.02

.03

1 2 3 4 5 6 7 8 9 10


-.04

-.02

.00

.02

.04

.06

.08

1 2 3 4 5 6 7 8 9 10


-.04

-.02

.00

.02

.04

.06

.08

1 2 3 4 5 6 7 8 9 10


-.04

-.02

.00

.02

.04

.06

.08

1 2 3 4 5 6 7 8 9 10

Response of D(LP) to D(LY)

-.015

-.010

-.005

.000

.005

.010

.015

1 2 3 4 5 6 7 8 9 10

Response of D(LS) to D(LY)

Fig. 12 Response to Cholesky One S.D. Innovations ± 2 S.E. in Model (22)

matrices, which depends how we chose m (Juselius, 2003).

Fig. 14. Response to Cholesky One S.D. Innovations ±±±± 2 S.E. In Model (22)


50 / Vol. 4, No. 12 / Spring 2007

We now turn to an alternative formulation of the ECM where we set m=2. In this case our VAR model in VEC mode becomes:

Thus, the matrix Π remains unchanged, but )1(1Γ matrix changes

to )2(1Γ . This latter matrix measures the cumulative long-run effect,

whereas )1(1Γ in (23) describe ‘pure’ transitory effects measured by

the lagged changes of the variables. While the explanatory power is identical for the two model versions, the estimated coefficients and their p-values can vary considerably. Usually many more significant coefficients are obtained with formulation (27) compared with (23). Estimated model of formulation (27) is reported in (28) below. We notice some interesting changes in this representation compared the previous one. Impacts of (lagged) changes in stocks level on (rate of changes of) demand for oil and oil prices have increased to 0.51 and -1.94 respectively as compared to 0.39 and -1.65 in formulations (23). Also impact of the (lagged rate of) changes of industrial production (Y) on the rate of change of demand for oil is now significant and with a magnitude larger (0.82) than the same coefficient at the previous formulation. This indicates that even if in the transitory and very short periods of time (say several months in our model) changes in production growth would have insignificant effect on rate of changes in oil demand, its cumulative effect in the long run could be significant.

Generally speaking inspecting estimated model (28) will show

that the number of ‘significant’ coefficients in )2(1Γ (coefficient matrix

of 1−∆ tX in equation (27)) is larger than 1)1(Γ (coefficient matrix of

1−∆ tX in equation (23)), but that of Π matrix is not changed.

Therefore, more significant coefficients do not necessarily imply high explanatory power, but may as well be a consequent of the parameterization of the model (Juselius, 2003). This means that the

( )1)2(

121

21)2(

1

...

)27(

Π−Ι=ΓΠ−Π−Ι=Π

+Π+∆Γ+Φ=∆ −−

andwith

XXDX ttttt

ε


Vol. 4, No. 12 / Spring 2007 / 51

interpretation of the estimated coefficients in dynamic models is more complicated compared to static regression models.

In graphs below response of different variables of the model (27) to innovations are illustrated. Larger values of statistically significant estimated coefficients in model (27) compared to the coefficients of model (23) are manifested in dynamics of the reaction of the variables of model (27) to innovations. The graphs provided below show that reactions to impulse are more vigorous and wavier in this case implying cumulated effects of the shocks on the system of time series variables. However, the impacts of innovations on the VAR system require almost the same span of time to spent out as the previous case.

________________________________________________________________________

20,.,21,..86.32ˆlog,.....9.1534max)(

)(..),(..,...

97.1...........9.1............9.2...........26.9............................................

05.0........05.0..........10.0............32.0...............................................

10.0.......10.0..........15.0............36.0.........................................................

....................................................var.....

00002.0

00022.0

00502.0

00066.0

ˆ,..

0.1......087.0......13.0........03.0

0.1.......10.0......75.0

0.1......05.0

0.1

02.0..02.0.....003.0......004.0

06.0....12.0...001.0.....11.0

43.0.....25.0...05.0.....48.0

15.0.....11.0......002.0...42.0

06.0.......002.0...02.0...001.0...

39.0....17.0....013.0...14.0

42.1.....94.1....05.0.......25.0

82.0......51.0......03.0..40.0

24.0

67.2

8.6

12.2

)28(

________________________________________________________________________

....

2

2

,4

,3

,2

,1

2

2

2

2

1

1

1

1

21)2(

1

−=−=−=Ω=

−

−

=

=Ω

+

−−

−−−

−−−

−−

+

∆

∆

∆

∆

−

−−−

−−

−−

+

−

=

∆

∆

∆

∆

+Π+∆Γ+Φ=∆

−

−

−

−

∗

∗

∗∗

∗∗

−

−

−

−

∗

∗

∗

∗∗∗

∗

−−

SCAICLLog


statisicF

RAdj

R


Y

S

P

D

Y

S

P

D

Y

S

P

D


t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

ttttt

εσ

ε

ε

ε

ε

ε


52 / Vol. 4, No. 12 / Spring 2007

-.03

-.02

-.01

.00

.01

.02

.03

1 2 3 4 5 6 7 8 9 10


-.03

-.02

-.01

.00

.01

.02

.03

1 2 3 4 5 6 7 8 9 10


-.04

.00

.04

.08

.12

1 2 3 4 5 6 7 8 9 10


-.04

.00

.04

.08

.12

1 2 3 4 5 6 7 8 9 10


-.04

.00

.04

.08

.12

1 2 3 4 5 6 7 8 9 10

Response of D(LP) to D(LY)

-.015

-.010

-.005

.000

.005

.010

.015

1 2 3 4 5 6 7 8 9 10

Response of D(LS) to D(LP)

Fig. 13 Response to Cholesky One S.D. Innovations ± 2 S.E. in Model (26)

Another convenient formulation of the VAR model is in second

order difference (acceleration rates), changes and levels (see Hendry and Juselius, 2000). It is argued that this formulation is particularly useful when there are I(2) time series in the VAR model of concern, but this formulation is in general more convenient representation of a

Fig. 15. Response to Cholesky One S.D. Innovations ±±±±S.E. In Model (26)


Vol. 4, No. 12 / Spring 2007 / 53

VAR model when the sample contains periods of rapid changes, so that acceleration rates (in addition to growth rates) become relevant determinants of agents’ behavior.

So we have estimate our four variables VAR(2) model in this formulation which in matrix form would be similar to (28):

211

212

.,..

)29(

Π−Π−Ι=ΠΓ−Ι=Γ

+Π+Γ∆+Φ=∆ −−

andwhere

XXDX ttttt

ε

The estimation results which are reported in (30) may look at first sight quite different from the previous exercises. But in fact we have more or less the same matrices of estimated coefficients save for the diagonal elements of the differenced variables vector. a closer investigation would reveal that a factor of -1 has been added to the diagonal elements of the differenced variables. Thus, the significance of the diagonal elements are only a consequence of applying the difference operator once more to .tX∆ For this reason it could be

more meaningful to test whether the diagonal elements are significantly different from -1 than from zero. The F statistics on the significance of the regressors have obtained large values, which is just

an artifact of the 2∆ transformation, and they do not say much about the importance of the lagged t-1 variables in explaining the variations in Xt .

Although the above reformulations are equivalent in terms of explanatory power, and can be estimated by OLS without considering the order of integration, however, inference on some of the parameters will not be standard unless ( )0~ iX t . For example, when Xt is not

stationary, the joint significance of the estimated coefficients cannot be based on standard F-tests (see Hendry and Juselius, 2000). It is worth nothing that since we have estimated the VAR model with optimal order determined by the relevant criteria and information statistics, according to the VARDL modeling approaches (see Pesaran and Shin, 1997 and Pesaran et al 2001) the estimation results could be considered efficient and consistent. Nevertheless, we would not prolong our paper which is concluded here, and will leave the issue of


54 / Vol. 4, No. 12 / Spring 2007

VARDL to the second part of the study to be discussed in association with the issue of co-integration in the VAR.

________________________________________________________________________

20,.,21,..86.32ˆlog,.....9.1534max)(

)(..),(..,...

13.20.......96.17.......05.18...........13.51...........................................

52.0.........49.0..........49.0.............73.0...............................................

54.0.........51.0..........52.0.............75.0.......................................................

.......................................................var.....

00002.0

00022.0

00502.0

00066.0

ˆ......,.........

0.1......087.0......13.0........03.0

0.1.......10.0......75.0

0.1......05.0

0.1

02.0..02.0.....003.0......004.0

06.0....12.0...001.0.....11.0

43.0.....25.0...05.0.....48.0

15.0.....11.0......002.0...42.0

06.1..002.0..02.0.......001.0...

39.0....17.1..013.0.......14.0

42.1.....94.1...95.0......25.0

82.0......51.0......03.0..40.1

24.0

67.2

8.6

12.2

)30(

________________________________________________________________________

....

2

2

,4

,3

,2

,1

2

2

2

2

1

1

1

1

2

2

2

2

212

−=−=−=Ω=

−

−

=

=Ω

+

−−

−−−

−−−

−−

+

∆

∆

∆

∆

−−

−−−

−−−

−−

+

−

=

∆

∆

∆

∆

+Π+Γ∆+Φ=∆

−

−

−

−

∗

∗

∗∗

∗∗

−

−

−

−

∗∗

∗

∗

∗∗∗

∗

−−

SCAICLLog


statisicF

RAdj

R


Y

S

P

D

Y

S

P

D

Y

S

P

D


t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

ttttt

εσ

ε

ε

ε

ε

ε

Although the above reformulations are equivalent in terms of explanatory power, and can be estimated by OLS without considering the order of integration, however, inference on some of the parameters will not be standard unless ( )0~ iX t . For example, when Xt is not

stationary, the joint significance of the estimated coefficients cannot be based on standard F-tests (see Hendry and Juselius, 2000). It is worth nothing that since we have estimated the VAR model with optimal order determined by the relevant criteria and information statistics, according to the VARDL modeling approaches (see Pesaran and Shin, 1997 and Pesaran et al 2001) the estimation results could be


Vol. 4, No. 12 / Spring 2007 / 55

considered efficient and consistent. Nevertheless, we would not prolong our paper which is concluded here, and will leave the issue of VARDL to the second part of the study to be discussed in association with the issue of co-integration in the VAR.

4. Summary and concluding remarks

In this paper we developed and estimated a four variate VAR model to investigate dynamic of oil markets in OECCD countries. The time period of study covers January 1995 t o March 2007 and the time series contain monthly data on demand for oil, industrial production, stock of commercial crude and products in OECD and WTI. Data sets are collected from Data Service Department (DSD) of OPEC Secretariat.

Having found the time series of the VAR model integrated of degree one I(1), with co-integration relationships we determined the optimal lag length of the VAR model and then estimated the unrestricted VAR model in different representations. Estimation results considering different formulation of the model all show clear signs of the important effects that production (economic growth) and also changes in stocks’ level of crude and products exert on demand for oil and on oil prices. To be more precise we find income elasticity of demand for oil to be in the range of 0.67 to 0.96 and proportional changes of oil price in response to an increase of 10% in the crude and product stocks to be between -16.5% to 19.5% in the short run. On the other hand, in congruity with the mainstream empirical works on oil markets we also find oil price impact on demand for oil in OECD countries statistically insignificant and negligible in absolute term. One particular point that emerges worthy of emphasizing, is imperative requirement of inclusion of the crude and products’ commercial stocks time series in any modeling attempt for estimating and forecasting oil demand and oil prices in OECD. The estimation of the VAR model resulted in identifying evidence of a stable relationship between the four time series of concern.

The analysis of this paper also has provided statistical evidence


56 / Vol. 4, No. 12 / Spring 2007

supporting the hypothesis that like many economic series, demand for oil, oil prices, industrial production and stock of crude and products are non-stationary time series. This can have important implication with respect to estimation, forecasting and policy analysis as not taking into account possible non-stationarity in the data could lead to misleading results and failing to catch important properties of the data. While this does not mean that VAR-VEC modeling approach are always superior to the other modeling techniques, nevertheless, VAR-VEC analysis can provide a useful benchmark for empirical investigation of oil markets dynamics.

References

Atkins, J. F. (2005) “Final Report on VAR Estimation of Oil Consumption, Price and GDP Relationship” University of Calgary and PMA Department of OPEC Secretariat

Barrel, B. and O. Pomerantz (2004) “Oil Price and theWorld Economy” NIESR, London

Barsky, R. and L. Kilian (2004) “Oil and the Macroeconomy Since the 1970s” Centre for Economic Policy Research, London

Bernanke, B. S., M. Gertler and M. Watson (1997) „Systematic Monetary Policy and the Effect of Oil Price Shocks“ Brooking Papers on Economic Activity.USA

Boswijk, H. P. (1995) “Identifying of Cointegrated Systems” Working Papers, Tinbergen Institute and Department of Actual Science and Econometrics, University of Amsterdam, the Netherlands

Box, G. E. P., G. M. Jenkins and G. C. Reinsel (1994) “Time Series Analysis” Prentice Hall, New Jersey

Brown, S. P. A. and M. K. Yuecel (2001) “Energy Prices and Aggregate Economics Activity” Federal Reserve Bank of Dallas.

Brown, S. P. A., M. K. Yuecel and J. Thompson (2003) “Business Cycle: The Role of Energy Prices” Federal Reserve Bank of Dallas.

Cziraky, D. (2001) “Cointegration Analysis of the Monthly Time-Series Relationship Between Retail Sales and Average Wages in


Vol. 4, No. 12 / Spring 2007 / 57

Crotia” Department for Resource Economics, IMO, Zagreb, Coratia

Cunado, J. and F. P. de Gracia (2004) “Oil Price, Economic Activity and Inflation” Workingh Papers, University of Navarre.

Doornik, J. A. (1995) “Testing Restrictions on the Cointegrating Space” Working Papers, Nuffied Colleage, Oxford University, UK.

EViews 6 (2007), Quantitative Micro Software, LLC Irvine CA, USA

Harvey, A. C. (1989) “Forecasting, Structural Time-Series Models and Kalman filter” University of Cambridge.

Hendry, F. H. (1996) “Dynamic Econometrics” Oxfored University Press

Hendry, F. D. and K. Juselius (1999 and 2000) “Explaining Co-integration: Part I and II” Nuffield College Oxford and European University Institute, Florence

Hunt, B. P. Isard and D. Laxton (2002) “The Macroeconomic Effects of Higher Oil Prices” National Institute for Economic andSocial Research, London.

Jimenez-Rodrigues, R. and M. Sanchez (2004) “Oil Price SOC and Real GDP” Working Papers European Central Bank

Juselius, Katarina (2003) “The Cointegrated VAR Model: Econometrics Methodology and Macroeconomic Application” European University Institute.

Maddala, G. S. (1992) “Introduction to Econometrics” Macmillan Publishing Company, New York, USA

Mukherjee, C., H. White and M. Wuyte (1998) “Econometrics and Data Analysis for Developing Countries” Routledge, London

Lanza, A. M. Manera, M. Giovannini (2005) “Modeling and Forecasting Cointegration Relationships Among Heavy Oil and Product Prices” Energy Economics, 27, 831-848

Keuk-Soo, K. and W. D. McMillan (2005) “Estimating the Effects of Monetary Policy Shocks: Does Lag Structure Matter?” Working Papers, Korea International Trade


58 / Vol. 4, No. 12 / Spring 2007

Association and Department of Economics, Louisiana State University.

Ozcicek O. W. D. McMillan, (1995) “Lag Length Selection in Vector Autoregressive Models”

Pesaran, M. H. and Y. Shin (1997) “An Autoregressive Distributed Lag Modeling Approach to Cointegration Analysis” Department of Applied Economics, University of Camridge.

Pesaran, M.H. (2003) “System Approaches to Co-integration Analysis” Presentation, Department of Applied Economics, University of Cambridge.

Shrestha, M. B. (2004) “ARDEL Modeling Approach to Cointegration Tests” Working Papers, University of Wollongong, Australia

Villar, J.A and F. L. Joutz (2006) “The relationship Between Crude Oil and Natural Gas Prices” EIA


Vol. 4, No. 12 / Spring 2007 / 59

Appendix

A short description of the modeling Methodology

Vector Auto-regression (VAR) and vector error correction (VEC) modeling approaches have found wide spread application in petroleum economics since introduction of time series analysis to econometrics literature. As for financial and commodity markets, time series modeling are employed to analyze developments of oil markets and to predict changes in variables of interest in this industry. This is mainly due to the fact that economists and econometricians have found time-series modeling a convenient way of summarizing information given by the data generating process (DGP) of these markets.

The use of VAR models in economics arose largely due to the influential work of Sims “Macroeconomic and Reality, (Econometrica, 1980). Prior to Sims’ pioneering work, economists tended to model time series relationship as either a system of structural equations, estimated one by one, or as on or more reduced form equations. Sims argued quite strongly that the “incredible identification restrictions” which are inherent in structural modeling required an alternative estimation strategy.

One can also think of VAR modeling strategy as arising naturally out of the seminal work of Box and Jenkins (1976) They argued that a prudent manner to forecast the future path of any stochastic process is to statistically model the past realization of the variables. This lead to the explosion of autoregressive integrated moving average (ARIMA) models. VAR analysis extends the Box and Jenkins work to more than one variable. (Atkins 2005).

VAR models are shown to be essentially reformulations of the co-variances of the data, (Juselius, 2003). The question, in application of VAR modeling techniques in economic problems, is whether a VAR model can be interpreted in terms of rational behavior of economic agents. According to the assumption of the VAR model the difference between the mean and the actual realization of data is white


60 / Vol. 4, No. 12 / Spring 2007

noise process. This assumption is consistent with economic agents’ behavior that are assumed to be rational in the sense that they do not make systematic forecast errors when they make plans for time t based on the available information at time t-1. For example, a VAR model with auto-correlated and or heteroscedastic residuals would describe agents that do not use all information in the data efficiently as possible. This is because they could do better by including the systematic variation left in the residuals, thereby improving their expectations about the future. Therefore checking the white noise requirement of the residuals is not only crucial for correct statistical inference, but also for the economic interpretation of the model as a rough description of the behavior of rational agents (Hendry, Juselius, 2000).

One of the major advantage of a standard VAR is that all the variables of the model are treated as endogenous (of course we could consider exogenous variables in a VAR model as well) and right hand side variables are pre-determined (that is non-contemporaneous , or lagged values), we can avoid the ubiquitous problems associated with simultaneous equation bias. In a sense we allow the data speak, by uncovering a rich set of dynamics amongst the variables which we consider to be important. The VAR model may be viewed as a system of reduced form equations in which each of the endogenous variables is regarded on its own lagged values and the values of all other variables in the system.

The VAR methodology requires determining the appropriate variables to be included in the VAR system (which in our example above is three) and determining the appropriate lag length (k). Inclusion of variables in a VAR system could be assisted by economic theory or some prior knowledge from observations or reflected in the literature and the latter is accomplished through the use of some system model selection criteria, such as Akaike Information Criterion (AIC). Obviously a typical VAR will be greatly over parameterized in the sense that many of the coefficients will be individually statistically insignificant.


Vol. 4, No. 12 / Spring 2007 / 61

We noticed that in a standard VAR the right hand side contains only pre-determined variables (mainly lagged variables) and the error terms are assumed to be serially uncorrelated. Now the question is whether we can estimates each equation of a standard VAR by OLS without loss of efficiency? The answer is that if all the time-series of the model were stationary then our VAR was considered a stationary VAR and OLS technique would yield consistent and efficient estimation results. However, most economic time series are non-stationary and for this reason we will have to address this issue before proceeding with the estimation exercise.

1. Stationarity

From the preceding discussion it becomes clear that a time series analysis of oil markets would require, from the outset, verification of the classical econometric theory assumption of stationarity of the data generating processes representing the market of concern. These assumptions intend that means and variances of the process are constant over time. However, graphs of monthly data of the petroleum markets variables for the time period under study (1995-2007) some of which are depicted in different panels of Fig. 2 and the historical record of economic forecasting of these variables would suggest otherwise.

Petroleum markets evolve, grow and change over time in both real and nominal terms, some times dramatically- and economic forecasts of oil prices, its supply and demand are often badly wrong, whereas forecasting failure of this magnitude should occur relatively infrequently in a stationary process (see Hendry, and Juselius, 1999). A significant deterioration in forecast performance relative to the anticipated outcome confirms that petroleum markets’ data are not stationary because even poor models of stationary data would forecast on average as accurately as they fitted, yet that manifestly does not occur empirically.

Figure 1 shows the four time series of the petroleum market in OECD that we are trying to establish the relationship between them. The first panel reports the monthly time series of demand for oil


62 / Vol. 4, No. 12 / Spring 2007

(LDOECD) in OECD. Panel b shows industrial production (LIPIOECD). Panel d records total stock of commercial crude and oil products reserves (LTSOECD) and finally panel d depicts monthly WTI in real term (LRWTI) in the time period of concern. Since the variables are expressed in logarithmic scale therefore every graphs show proportional changes in the respected variables: hence apparently small movements over the time intervals sometimes represents quite large changes. In some cases such as industrial production index of panel b regarding the scale of the graph, much smaller range of variation is observed in equal intervals of time, but again, the notion of a constant mean seems untenable. In general we can say that there is considerable evidence of changes in means of petroleum markets’ time series and it is hard to imagine any revamping of the statistical assumptions such that these outcomes could be construed as drawing from stationary processes.

10.65

10.70

10.75

10.80

10.85

10.90

1996 1998 2000 2002 2004 2006

Monthly Demand for Oil: OECD

LDOECD

4.40

4.44

4.48

4.52

4.56

4.60

4.64

4.68

4.72

1996 1998 2000 2002 2004 2006

Monthly Industrial Production: OECD

LIPIOECD

-2.4

-2.0

-1.6

-1.2

-0.8

-0.4

1996 1998 2000 2002 2004 2006

WTI in Real Term

LRWTI

14.65

14.70

14.75

14.80

14.85

1996 1998 2000 2002 2004 2006

Total Commercial Stock of Crude and Products: OECD

LTSOECD

Fig. 2. Monthly Demand for oil, Industria Production, WTI and Total Oil andProduct Stock in OECD (1995-2007)

Fig. 1. Monthly Demand for Oil, Industria Production, WTI and Total and Product Stock in OECD (1995-2007)


Vol. 4, No. 12 / Spring 2007 / 63

While it is quite difficult to tell, by visual examination of level data, if a time series is non-stationary, it seems that time-series of concerned do have characteristics consistent with non-stationary data. All appear to have a trend and meandering quality, with variables wandering up and down. The means of the series however, do not look constant overtime, except perhaps for the crude and product inventory variable, LTSOECD, and in fact may be drifting upward, suggesting the possibility of a stochastic trend. The price series, LRWTI, also appear to be serially correlated, with prices drifting up for a while followed by periods of successive declines. Furthermore, the volatility of the series vary over time. Nevertheless, variation of the time series might be consistent with the possibility that these processes share a common trend, fluctuating around a certain level meaning that these time series may be co-integrated.

As Hendry and Juselius (1999) argue “the practical problem facing econometrician is not a plethora of congruent models from which to choose, but to find any relationships that survive long enough to be useful”. For these reasons while in this study we try to establish and identify the relationships between some important variables of the petroleum markets, ignoring the fact that all or some of the time-series of petroleum markets might exhibit non-stationarity, could have severe consequences of spurious regressions and invalid statistical inference undermining robustness of the forecasts of the econometric model.

When data means and variances are non-constant, observations come from different distributions over time, posing difficult problems for empirical modeling. Assuming constant means and variances when they are not can induce serious statistical mistakes.

Non-stationarity can be due to evolution of the economy, legislative changes, technological change, and political turmoil among other things. In practice, it is useful to classify exhibiting a high degree of time persistence (insignificant mean reversion) as non-stationary and variables exhibiting a significant tendency to mean reversion as stationary. However, it is important to stress that the


64 / Vol. 4, No. 12 / Spring 2007

stationarity/ non-stationarity or alternatively the order of integration of variable, is not in general a property of an economic variable but a convenient statistical approximation to distinguish between the short-run, medium-run and long-run variation in the data (Juselius, 2003). Econometrically it is convenient to let the definition of long-run or short run depend on the time perspective of the study. From economic theory point of view the question remains in what sense a “unit root” process can be given a “structural” interpretation. For example, oil price is considered stationary in one study and non-stationary in another, where the latter is based, say, on a sub sample of the former might seem contradictory. This need not be so, unless a unit root process is given a structural interpretation. However, given the time period of our study that at best could be regarded a medium-term time period we could expect finding our time series non-stationary.

2. Addressing non-stationarity

As was mentioned non-stationarity is observed in economic time series very frequently so much that it seems natural feature of economic life. Legislative changes are one obvious source of non-stationarity, often inducing structural breaks in time series, but it is far from the only one. Economic growth, perhaps resulting from technological progress, ensures secular trends in many time series. Such trends need to be incorporated into statistical analysis. In time series analysis of economic systems such as petroleum markets focus usually are on a type of stochastic non-stationarity induced by persistent accumulation of past effects, called unit-root process. Such process can be interpreted as allowing a different ‘trend’ at every point in time, so are said to have stochastic trends.

There are many plausible reasons why economic data may contain stochastic trends. Economic variables depending closely on technological progress are most likely to have stochastic trend. Because technology involves the persistence of acquired knowledge, so the present level of technology is the accumulation of past discoveries and innovations. The impact of structural change in the


Vol. 4, No. 12 / Spring 2007 / 65

world oil markets is another example of non-stationarity. Other variables related to the level of any variable with a stochastic trend will ‘inherit’ that non-stationarity, and transmit it to other variables in turn: oil income for oil exporting countries may led to structural changes in investment, economic growth employment and so on and its decline might cause a significant increase in exchange rate inflation and unemployment in these countries. In annex to this paper we have provided an illustration of the main concepts of VAR-VEC modeling approach.

3. Testing for Unit-Roots and Integration of the VAR model

variables

When testing stability of the system we do not need to specify the order of integration of the model’s variables (Xt ) because, as was discussed, as long as the parameters of the model were unrestricted, OLS could be used to estimate them consistently. However, when we want to set the scene for conducting an analysis based on stationary series we will have to determine first the order of the integration of the non-stationary series of our VAR system.

One can test formally for stationarity by testing if the variable may be described as a random walk, either with or without drift. This procedure is also called testing for unit root as an I(1) process has a unit root. If we find we cannot reject the hypothesis that the variable is a unit root (e.g. follow a random walk) then we have found that variable is not stationary and must proceed accordingly.

It might seem that the test for stationarity is a parameter test on the AR(1) model given its general case: .121 ttt XX εββ ++= −

Specially we can test the hypothesis that 1,.,.0 11 == ββ and , in which

case the series is a random walk. Whilst this approach is intuitively appealing it requires modification for the following reasons:

(i) Equation .121 ttt XX εββ ++= − is a restricted version of

the general model which includes also a deterministic time trend. So we must use a more general model such


66 / Vol. 4, No. 12 / Spring 2007

as: ttt XtX εβββ +++= −1321 as the basis for our initial

testing.

(ii) It can be shown that if the series is non-stationary then the estimate of 3β

will be downward bias. For this reason we cannot use the standard t-or F statistics when looking at critical values to conduct significant tests. Alternative critical values have been provided by Dickey and Fuller.

(iii) A modified Version of the equation

ttt XtX εβββ +++= −1321 is used called the

Augmented Dickey –Fuller (ADF), which includes the lagged difference of the variable.

tttt XXtX εββββ +∆+++= −− 141321 ; the inclusion of

this term means that the critical values are valid even if there is residual autocorrelation.

4. From Co-integration Relationships to Error Correction

Models

Co-integration analysis is inherently multivariate, as a single time series cannot be co-integrated. Consequently, in a set of integrated variables, such as crude oil demand and its price, level of crude and product inventory, where each process is individually I(1), but follows a long-run path, affected by industrial production, co-integration between these variables could arise, for example, if there was a linear combination of these variables constructing a stationary process. However, co-integration as such does not say anything about the direction of causality. So if the assumptions about these relationships directions were incorrect, then the estimates of the co-integration relations would be inefficient, and could be biased. To find out which variable adjust and which variable do not adjust, to the long-run co-integration relations, an analysis of the full system of equations is required (Hendry, Juselius, 2000)

From the last section it became clear that the remedy for a unit


Vol. 4, No. 12 / Spring 2007 / 67

root would be to estimate the VAR in first difference form. However, many economists and econometricians (see for example: Sims,(1890), Sims, Stock and Watson, Econometrica, (1990), Hendry and Juselius(2000)), argue against differencing even if the time series that do contain a unit root are difference stationary. The main point against the procedure of differencing time series to reach stationarity is the loss of information related to the long run relationship between the variables, in the process. This potential problem of losing information leads to the concept of an error correction model, which bears a very close relationship to a VAR methodology.

5. Uncovering the Dynamics

A Vector Auto-Regression system and closely related Vector Error Correction model possess a very rich set of dynamics which uncovered through the use of impulse response functions. It is well known that any single variable auto-regression has a moving average representation. Therefore, a natural generalization of this is that any VAR (or respected VEC) models have a vector moving average (VMA) representation. For example if we had a VAR system consistent of four endogenous variables, it can be shown that one can arrive to a VMA by necessary manipulation of the four variables VAR model. There is an analogous VMA for the VEC model. The 16 sets of coefficients )(iijφ in our VAR model are the impulse response

functions. These give us the effect of the shocks tt 21 ,.εε t3ε and t4ε on

the entire time paths of the entire sequences of X1t, X2t,X3tand X4t. Notice that for i=0, the coefficients give the impact response.

Of interest in this study is the elasticity of response of one variable to another. This can be calculated as the dynamic correlation. This would give us the time path of the elasticity. It should be noted that analysis using the impulse response function is completely analogous to forecasting. In an impulse response function framework, if we shock one variable, say P, and trace the response of another variable say D, in fact we are forecasting the future path of D, given some future values of P.


68 / Vol. 4, No. 12 / Spring 2007

6. Model selection

The most difficult aspect of working with time series data is model selection. The crucial point to understand is setting up models in terms of components which have a direct interpretation. This enables the researchers to formulate, at the outset, a model which is capable of reflecting the salient characteristics of the data. Once the model has been estimated, its suitability can be assessed not only by carrying out diagnostic tests to see if the residuals have desirable properties but also by checking whether the estimated components are consistent with any prior knowledge which might be available. Thus for example, if a cyclical component is used to model the oil trade cycle, knowledge of the petroleum economics history of the period should enable one to judge whether the estimated parameters are reasonable. This is in the same spirit as assessing the plausibility of a regression model by reference to the sign and magnitude coefficients.

Classical time series analysis is based on the theory of stationary stochastic process, and this is starting point for conventional statistical time series model building. It can be shown that most stationary process can be approximated by a model from the class of autoregressive moving average (ARMA) models. However, a much wider class of models, capable of exhibiting non-stationary behavior, can be obtained by assuming that a series can be represented by an ARMA process after differencing. This is known as the autoregressive integrated moving average (ARIMA) class of models and a model selection strategy for such models was developed by Box and Jenkins (1976).

The following criteria for a good model have been proposed in the econometrics literature. (Hendry and Richard(1983), Mizon and Richard(1986), Ericson and Hendry (1985) Mizon(1984) and Haevey(1981a). They apply to both structural time series and pure time series modeling.

(a) Parsimony A parsimonious model is one which contains a relatively small number of parameters and other things being equal, a simpler model is to be preferred to a complicated one.


Vol. 4, No. 12 / Spring 2007 / 69

(b) Data coherence Diagnostic checks are performed to see if the model is consistent with the data. The essential point is that the model should provide a good fit to the data, a the residuals, as well as being relatively small, should be approximately random.

(c) Consistency with prior knowledge In an econometric model, economic theory may provide prior information on the size or magnitude of various parameters and the estimated model should be consistent with this information.

(d) Data admissibility A model should be unable to predict values which violate definitional constraints. For example many variables cannot be negative,

(e) Structural stability As well as providing a good fit within the sample, a model should also give a good fit outside the sample. In order for this to be possible, the parameters should be constant within the sample period and this constancy should be carry over into the post-sample period.

(f) Encompassing A model is said encompass a rival formulation if can explain the results given by the rival formulation. If it is the case, the rival model contains no information which could be used to improve the preferred model.

We have tried to observe most of these criterions in our exercise, however, it remains to be seen whether these criteria are satisfied in our time-series modeling exercise. A pure time series model contains no explanatory variables apart from variables which are solely functions of time. Forecasts of future observations are therefore made by extrapolating the components estimated at the end of the sample. Since the forecasts are based on a statistical model, the mean square errors (MSE) associated with them may be computed.

When a model contains explanatory variables, forecasts can only be made conditional on future values of these variables. If lagged values of an explanatory variable enter into a model, some of the values which are needed to generate forecasts of the dependent variable are known and the explanatory variable is then referred to as


70 / Vol. 4, No. 12 / Spring 2007

a leading indicators.

A multivariate time series model offers the possibility of allowing for interactions among the variables when forecasts are made. As with univariate time series modeling, the effectiveness of a multivariate model depends on the extent to which it remains stable over time.

Having reviewed the main features of the VAR modeling approach in context of our empirical study of the oil market dynamics in OECD we now turn to specify the VAR model outline of which was discussed above briefly.


Vol. 4, No. 12 / Spring 2007 / 71

Allocation of CO2 emissions in

petroleum refineries to petroleum joint products: a case study

Alireza Tehrani Nejad M.1 Valérie Saint-Antonin2

Abstract

Oil refining is a joint production system because the production of one oil product makes technically inevitable the production of other oil products. Due to the complex nature of the process involved and the vast number of joint product outputs that are strongly correlated, it is very difficult to establish any meaningful CO2 emissions allocation between oil products. Nevertheless, the allocation of petroleum refinery energy use and the resultant CO2 emissions among different oil products is necessary in “well to wheel” analysis in order to evaluate the environmental impacts of individual transportation fuels.

In practice, allocation methods used so far for the petroleum-based fuel are traditionally based on two fundamental approaches: physical measures (mass, volume, energy contents or other relevant parameters) or market value of individual oil products from a given refinery. These methods are open to discussion on two points. Fist, an a priori assumption about the allocation procedure (i.e., mass, volume, energy contents, market value, etc.) is in some ways completely

1. [email protected] 2. [email protected]


72 / Vol. 4, No. 12 / Spring 2007

arbitrary and consequently of little use for economic decision making purposes. Second, these approaches ignore the opportunity cost effects and the interdependencies which might exist among the refinery process units, and systematically assign more emissions to the oil products that utilize more process units.

More sophisticated proposals to energy consumption and emissions allocation have been developed based on the concept of duality in linear programming (LP). Unfortunately, in refinery LP models constraints on (fixed) unit process capacities or input availabilities might destroy the additivity property of the marginal-based allocations. In fact, due to a technical feature inherent in LP, the petroleum product allocation coefficients might underestimate or overestimate the total volume of the refinery’s CO2 emissions. This handicap is a valid objection to LP as an allocation tool in retrospective or accounting LCA studies and might limit its use for problems in which the objective is to assign unambiguously the whole refinery’s emissions among the oil products.

This practice-oriented paper is aimed to provide a two-stage

procedure, based on LP, to fully allocate the refinery’s CO2 emissions

among the refinery’s petroleum joint products. The procedure is

applied to the IFP (Institut Français du Pétrole) oil refinery. The

average contribution of petroleum oil products to the refinery’s CO2

emissions are then compared with the other accounting allocation

methods. We show that, contrary to these latter, gasoline has not

always a higher average CO2 content than that of diesel within the

European refineries.

Key words: Co2 emission, refineries, well to wheel emission, joint

products.

1. Introduction

Life Cycle Assessment (LCA) is one of the engineering methods that has increasingly gained attention and is regarded today as an important tool for environmental policy and strategic decision making.


Vol. 4, No. 12 / Spring 2007 / 73

According to the Society of Environmental Toxicology and Chemistry (SETAC, 1993), this method aims at evaluating the environmental burdens associated with a product, process or activity throughout its life cycle from the extraction of raw materials through processing, transport, use, disposal and recycling. By relating environmental issues to the whole production chain, this method is regarded to have a holistic system-level approach which is well suited for assessment of complex systems.

Well-to-Wheel (WTW) studies are similar to LCAs but they cover a narrower system boundary by only focusing on the transport applications. They calculate the energy consumption and the associated greenhouse gas emissions along fuel chains and consist of two parts. The first part assesses the stage from the extraction of feedstock until the delivery of automotive fuels to the vehicle tank and is usually referred to as Well-to-Tank (WTT) analysis. The second part corresponds to Tank-to-Wheel (TTW) studies and aim at evaluating the performance of automotive fuels in the engine.

By analogy to LCAs, WTW studies can be also categorized in retrospective and prospective approaches (e.g., Ekvall et al., 2005). Retrospective studies look back at historic environmental impacts and use plant-specific or average data to illustrate the environmental burdens (e.g., CO2 emissions) associated with the average production of a given automotive fuel.

These kind of studies are useful for environmental accounting purposes. On the other hand, prospective or change-oriented studies look forward and consider the effects of different decisions. They are based on marginal data and attempt to explore the environmental effects associated with the marginal production of a given automotive fuel. As mentioned by EUCAR et al., (2004), when the ultimate purpose of a study is to guide the policy makers, prospective or marginal approach should be considered. In this study, we focus on both retrospective and prospective WTT analysis.

Since in WTT studies the main difference among the CO2 content of automotive fuels are exclusively due to the refining process (EUCAR et al., 2004), especial care should be taken on this


74 / Vol. 4, No. 12 / Spring 2007

component. Oil refining is a joint production system with a very complex technical structure and a vast number of outputs that are strongly correlated. Therefore a key methodological problem which inevitably arises is how to correctly identify and quantify the real cause-effect chains that should be considered in estimating the marginal and aver-age CO2 content of automotive fuels at the gate of the refinery1 within refineries. Neither the traditional WTT approaches, nor the existing databases can be useful because they fail to capture the complex interdependencies and synergies which exist among the refinery oil products and process units. This paper attempts to illustrate that a practical way to perform such an analysis is to use Linear Programming (LP) models. In contrast to the traditional WTT methods, the information created through the duality in LP incorporates the complete interdependency and economic effects associated with any marginal variation in the refinery; these information can be directly used for prospective WTT studies but need some more computations for retrospective analysis. The proposed methodology is then applied to a real-type refinery model in order to estimated the CO2 content associated with the marginal and average production of the automotive fuels. Three simulations for years 2005, 2008 and 2010 are performed to evaluate the impact of the sulfur tightening policy on the CO2 content of automotive fuels at the gate of the refinery. This question is of importance because the reduction of the environmental impacts of automotive fuels constitutes one of the prime objectives of the European environmental policies.

2. General Linear Model of the Refinery and the CO2

Emissions

The use of LP in the refining industry spans a period of well over 50 years. The blending of gasoline was among the first popular applications of LP in refineries (Charnes et al., 1952). Today,

1. Throughout this paper, by marginal (average) CO2 content of a given oil product we mean the additional CO2 emissions associated with the marginal (average) production of that oil product within the refinery.


Vol. 4, No. 12 / Spring 2007 / 75

designing new units, fixing the operating conditions, making a choice of feedstocks, improving the operations planning, oil product costing, policy analysis and forecasting are among the routine utilization of LP in oil refineries.

Refineries are very large complex industrial plants converting crude oil to a large number of petroleum products. Here, we develop the following static single-refinery LP model which operates in a competitive environment.

(product demand constraints) (material balance and quality constraints) (CO2 balance equation) (capacity constraints)

The main variables of our model are non negative physical

flows xj (j =1, 2,...,n) between refining units from crude oils to end-use oil products along with intermediate products, utility consumptions, exchange products and pollutant emissions. The term c is the given n-vector of acquisition input costs and includes the cost of crudes, feedstocks, operating variable cost (e.g., cost of catalysts, solvents and chemicals) and the exchange cost of finished products. In a cost minimizing framework, the refiner’s objective is to satisfy demand for a product (in terms of both quantity and quality), denoted by the m-vector b, at minimum cost subject to the prevailing technology, input costs and availability. The oil product categories considered in this model are liquefied petroleum products (propane and butane), naphtha, gasoline, middle distillates (jet fuel, diesel and heating oils), heavy fuel oils with 1% and 3.5% mass sulfur contents and bitumen.

The linear technology used is represented by the fixed coefficient matrix A of dimensions m × n. The most common types of other constraints are the material balance and product quality

≥≥

≤

=−

=

≥

.0,0

0

0

..

min

ε

ε

x

fFx

Ex

Dx

bAx

ts

xcT

(1)


76 / Vol. 4, No. 12 / Spring 2007

constraints. The latter guarantee the expected quality and technical requirement of finished products in blending problems such as octane number (for gasoline), cetane number1 (for diesel), viscosity (for fuel oil) and sulfur content (for all the above products). The material balance constraints represent the fact that the sum total of quantities going into some unit process or blending pool equals the sum total coming out. These constraints are represented in a standard form by the block Dx = 0.

We have also defined an emission balance equation, Ex, capturing the numerous source of CO2 emissions in the refinery. In general, a refinery’s emissions depend on the crude oil’s weight (API2) and the conversion degree required for achieving the oil production target b: a high share of more valuable products (i.e., gasoline and diesel) requires higher processing and more CO2 emissions. Modern and more complex refineries that are equipped to process heavier crude slates and produce lighter products record higher CO2 emissions. Different types of fuels are burnt to provide the required energy for refining processes. In our LP model, the total

carbon dioxide emissions ε are generated from burning fuel gas (ethane and propane), liquefied fuel (e.g., vacuum residue) and the coke of the catalytic cracker, each of which being assigned a specific CO2 emission coefficient E of dimension 1 × n.

Finally, since our study concerns the short and medium term the availability of some process units is limited to their installed capacity in the short term, .fFx ≤ That is, no invest-ment occurs in new

technology and no capital investment is depreciated or retired. For the medium term simulations, however, some realistic investments could occur.

For a general solution, let M and S be the sets of active demand constraints and scarce unit processes at the optimum. In words, the

1. The cetane number measures the speed at which diesel burns in an engine when subjected to high temperature and pressure (Favennec, 1998). 2. The degree API is an arbitrary scale for the measurement of the density of crude oil. The relationship between relative (with respect to water) density and degree API is given by the formula: °AP I = 141.5/d −131.5 (Favennec, 1998).


Vol. 4, No. 12 / Spring 2007 / 77

optimal combination of inputs are such that all final product demands are satisfied without any excess of production. This assumption is justified within a static LP model in which no inventory or exportation variable is defined. Moreover, we denote Β the (k × k) basic matrix and β the set of basic index. Sections 3 and 4 describe how the optimal LP solution could be used in order to yield non arbitrary prospective and retrospective WTT information.

3. Prospective LP-based emission coefficients

The exposition of this approach in this paper differs from the existing literature known as the marginal allocation methodology (see Azapagic and Clift, 1994, 1995, 1998, 1999a,b; Babusiaux, 2003).

Following the definition of a primal feasible basic variable,

(2)

where xB represents the vector of basic variables and B

−1

corresponds to the inverse of the basis (a matrix) which is pre-multiplied by the right-hand-side (RHS) vector. At the optimum, the

emission variable ε is always positive and can be expressed as follows,

(3)

where eε is the ε th unit vector ( 0=teε for ε≠t and 1=εεe ) and 1−

BeT

ε corresponds to the row of 1−B associated with the basic CO2

variable ε. Simplifying (3), we get:

(4)

= −

f

b

BxB 0

01

= −

f

b

BeT

0

01εε

∑∑∈∈

+=Sj

jjMi

ii fb ,γαε


78 / Vol. 4, No. 12 / Spring 2007

where iα and jγ correspond to the blocs which relate ε respectively to

the demand and capacity slack variables in the final simplex tableau. According to the optimal technology, iα and jγ can be positive,

negative or zero (see Section 6.2). In economic words, relation (4) implies that when the production functions Ax = b are linear homogeneous and exhibit constant return to scale, the attribution of the carbon dioxide emissions to primal constraints (i.e., oil products and limiting unit processes) according to their marginal contributions (i.e., iα and jγ ) is exactly equal to the whole CO2 emissions

generated within the refinery. The partitioned emissions reflect the underlying technical interdependencies embodied in the re-finery model and are not necessary in proportion to physical measures (e.g., mass or energy content, etc.).

To better appreciate the use of these product-related coefficients )( Miai ∈ in WTT studies, we differentiate the emission balance

constraint with respect to bi as follows

(5)

where the row-vector Ek corresponds to the input-emission coefficients as they appear in the basic index β. The vector (dxk/dbi) represents the inverse of the marginal production of the kth unit process with respect to the ith oil product. As shown in (5), the

)( Mii ∈α is calculated by tracking emissions through individual

active unit processes )( β∈kxk and is adjusted by the inverse of the

marginal production vector. Thanks to this vector, the complex substitution and synergy effects among crude oils, active unit processes and various intermediate and final oil products are also captured in the computation of each )( Mii ∈α . In other words, these

product-related coefficients1, as opposed to the ones in traditional methods, include all consequences of the desired change on the

1. We borrowed these terminologies from Azapagic and Clift

∑∉∈

=−

εβ

α

ε

kk

i

ii

kk

db

d

db

dxE ,0


Vol. 4, No. 12 / Spring 2007 / 79

operation of the refinery as well as compositional changes of the oil products. Therefore, these simplex-based substitution coefficients are well suited for assessment of the marginal CO2 content of automotive fuels for prospective WTT studies.

Similarly, )( Sji ∈γ refers to the quantities of CO2 attributable

to the last unit of the jth scarce capacity process. These marginal process-related emissions are also useful in prospective WTT studies where the implications of both final products and unit process expansion are of interest (Azapagic and Clift, 2000).

4. Retrospective LP-based emission coefficients

Retrospective WTT studies aim to assess the environmental burdens (specially the CO2 emissions) associated with the average production of a given automotive fuel within the refinery. As opposed to the prospective approach, retrospective WTT studies require the allocation of the total CO2 emissions of the refinery over the petroleum products. As mentioned before, oil refining is a joint production system and due to the complex nature of the process involved and the vast number of joint product outputs that are strongly correlated, it is very difficult to establish any non-controversial allocation scheme for oil products.

In the allocation theory, it is well-known that any theoretically justified or non-arbitrary allocation method should be additive, unambiguous and defensible. The additivity property requires that the total refinery CO2 emissions be equal to the sum of the parts, meaning that all of the refinery’s carbon dioxide emissions are allocated among the oil products, no more no less. The unambiguity condition requires the uniqueness of the allocated parts, and the defensibility criterion, which is the most important one, needs to provide conclusive proof for choosing a particular allocation method among all possible alternatives. Moreover, the allocation procedure should also take into account the ISO 14041 recommendations which could be summarized as follows (Frischknecht 2000):

1. Where allocation cannot be avoided, the system inputs and outputs should be partitioned between its different products or


80 / Vol. 4, No. 12 / Spring 2007

functions in a way which reflects the underlying physical

relationships between them;

2. Where physical relationships alone cannot be established or used as the basis for al-location the inputs should be allocated between the outputs and functions in a way which reflects other relationships between them (e.g., physical measures or economic relations).

In practice, most of the allocation rules used so far for the petroleum-based fuel are traditionally based on two fundamental approaches: physical measures (mass, volume, energy or exergy1 contents, molecular mass or other relevant parameters) or market value (gross sale value) or expected economic gain of individual oil products from a given refinery. Both of these approaches inevitably involve the use of arbitrary allocation rules and correspond to the second recommendation of ISO 14044. Furthermore, these approaches provide an incomplete picture of the whole system as they ignore the complex interactions, interdependencies and synergies which exist among the refinery oil products and process units.

In this section we provide an original two-stage approach to yield some LP-based coefficients in such a way that it best satisfies the desired characteristics of a non-arbitrary allocation method as well as the ISO 14041 recommendations. To this end, let us first observe that in relation (4) due to the presence of the active capacity constraints at the optimal solution the refinery’s CO2 emissions ε are inevitably shared between both oil products and scarce unit processes. Therefore, the product-related coefficients )( Mii ∈α derived from

relation (4) does not respect the additivity criterion required for an allocation rule and can not be directly used in retrospective-oriented studies. For instance, in a LP-based refinery case study, Tehrani Nejad M. (2007b) observes that the total allocated CO2 to the petroleum products based on their respective marginal contents )( Mii ∈α might

1. The exergy content of a system indicates its distance from the thermodynamic equilibrium. The higher the exergy content, the farther from the thermodynamic equilibrium (definition from, http://www.holon.se/folke).


Vol. 4, No. 12 / Spring 2007 / 81

be 3.5 times more than the total unallocated CO2 emissions due to the

total process-related emissions, i.e., ∑ j ji fγ .

Achieving retrospective LP-based coefficients requires the reassignment of the total process-related emissions over the oil products. We achieve this objective within a two stage procedure from the optimal emission function in relation (4) (For a complete discussion and a numerical example, see Tehrani Nejad M., 2007a). In this regard, care should be taken not to fall in the realm of any arbitrary or ad hoc measures.

4.1 First stage

For some technical reasons that will be discussed in the second stage, we begin the first step by introducing an artificial constraint into model (1) which can be readily interpreted as a material balance constraint for the process loss. In fact, this constraint might already exist in most refinery models in order to capture the quantity of total process loss. In cost accounting systems, process loss is usually expressed as a percentage of the input activity volume. The new LP model takes on the following specifications

(6)

where the n-vector ],...,,[ 21 n

Tllll = represents the loss

coefficients for each input activity, and the variable l measures the total losses inherent in the production process. We also assume that

there is no abnormal loss so that 1=+ jj

T lAe for all input activities,

where ]1,...,1,1[=Te .

The concept of the process-related emissions )( Sji ∈γ and their

technical connection with the oil products are key to our analysis. For

≥≥≥

≤=−

=−

≥

.0,0,0

0

0

..

min

ε

ε

l

l

x

fFxxE

xl

bAxts

xc

T

T

T


82 / Vol. 4, No. 12 / Spring 2007

any jSj γ ,∈ can be formulated by differentiating the emission

balance constraint in (6) with respect to xj as follows (7) Where the vector Ek corresponds to the emissions row in B, from

which the (-1) coefficient associated with ε is omitted; and, the vector

)( jk dxdx corresponds to the column of B−1

associated with the slack

variable of the jth scarce unit process, from which γj is extracted. In economic terms, )( jk dxdx represents the vector of marginal rates of

technical substitution (MRTS) between the jth scarce unit process and all the unit process activities involved in the production plan. More precisely, this vector shows the rate at which basic inputs should be substituted along the given oil product isoquant b, whenever an extra unit of jth scarce input were made available at the optimum. For notational convenience, we set jjk dxdx ς=)( . These marginal

coefficients are a powerful tool to capture the technical characteristics between unit processes and oil product outputs at each stage of the refining process. To the best of our knowledge, and surprisingly, these

coefficients have never been used in any empirical LP study. Now to reveal the physical relationships between the marginal

CO2 content of jth scarce unit process and final oil products, we introduce the optimal adjustment of final outputs (oil products and losses) into relation (7), which leads to

(8)

where, by construction, ∑ ∈=+

Mi kik la 1. To separate the part of

each output in γj, we introduce the following (k−1)×(k−1) allocating matrix iΩ and lΩ :

,0=−

=≠∈

∑

j

jKK j

kK

dx

d

dx

dxE

γεβ

ε

jk

kk Mi

kikKi laE ςγ

εβ∑ ∑

≠∈ ∈

+=


Vol. 4, No. 12 / Spring 2007 / 83

(9)

Where the coefficients aik are the average productivity of crude oils

associated with the I th row of B. Similarly, the coefficients lk

correspond to the loss coefficients associated with the material balance row for losses in B.

Using definition (9), relation (8) can be rewritten as (10)

Where construction, )1,...,1,1( diagMi i =Ω+Ω∑ ∈ l

Rearranging (10), we sp separate the part of oil product outputs from process loss in γj.

(11) Relation (11) relates each γj to the refinery's outputs (including the

process losses) through a realistic technical relationship which emerges from the equilibrium behavior of the firm.

Now, using the decomposition relation (11) and doing some algebraic manipulations the optimal emission function (5) can be expressed as

(12)

The economic interpretation of relation (12) runs as follows: at

the optimal solution of model (6), the carbon dioxide emissions of the refinery is quasi fully allocated among the oil products through their marginal contributions iα and the production elasticity ijδ of the scarce

unit processes. The obtained (re)allocation coefficients iα depend

totally upon the technical and physical relationships that define the operating state of the refinery and its associated cost efficient

≠∈=Ω

≠∈∈=Ω

),,,(

),,(

εβ

εβ

kkldiag

kkMiadiag

k

iki

,

,

l

∑∈

Ω+Ω=Mi

ji

T

Bj E ςγ )( l

4847648476

l

lossofpart

j

T

B

productsoilofpart

Mi

ji

T

Bj EE

.ςςγ Ω+Ω= ∑

∈

.)()( l

4847644 844 76

l

θα

δδαε ∑∑∑∈∈∈

++=Sj

j

T

Bi

Sj

ij

T

Bi

Mi

EbE

i


84 / Vol. 4, No. 12 / Spring 2007

equilibrium and accounts for all interdependencies in the production plan.

From relation (12), we observe that a rather small residual part

remains still unallocated to the oil products, i.e., lθ . We define the

relative error term of the first step by є εθ /l= , which is essentially

proportionate to the normal loss coefficients. While in almost real-world refinery production models the loss coefficients are small, the relative error of this first step should be very small too. So in empirical studies, iα is a good estimator of the average contribution of

the ith oil product to the refinery’s CO2 emissions and the reallocation procedure can be successfully stopped here. In the following numerical simulations in Section 6, the allocation procedure is stopped at the end of the first stage.

4-2. Second step

The problem considered in the second step is how much of lθ should be shared by each product. In effect, this stage is of importance in models in which the loss coefficients associated with some unit processes are relatively high.

The quantity of the refinery loss l is a basic variable (because always positive) and can be allocated among the primal constraints in the same way as we did for the emissions variable

ε . By an analogous logic to that developed in the first step, we decompose the loss variable l of the LP model (6) according to the optimal basic variable definition:

(13)

where le is the l th unit vector ( tel = 0 for l≠t and 1=lle ) and 1−

BeT

l corresponds to the row of B-1associated with the basic variable

l and contains several blocks referred to the slack variables of model (6). Rewriting (13), we get the following relation

= −

f

b

BeT

0

01ll


Vol. 4, No. 12 / Spring 2007 / 85

(14)

that relates the total process loss of the refinery to the oil products b and the limited (fixed) unit processes x through the marginal allocation coefficients, )( Mii ∈ϑ and )( Sji ∈υ .

Relating the refinery loss to solely oil products needs reallocating the loss contribution of scarce unit process over oil products. By analogy to jγ , the marginal coefficient jυ can be

formulated by differentiating the loss constraint in (6) with respect to

jx as follows

(15)

where the vector kl corresponds to the loss row in B, from which the (-

1) coefficient associated with l is omitted. The vector )(j

k

dx

dx

corresponds to the column of 1−B associated with the slack variable of the jth scarce unit process, from which jυ is extracted. For notational

convenience, we set j

j

k

dx

dxς~)( = .

By using the same procedure as the first stage, relation (15) can be rewritten as

(16)

where the (k − 1) × (k − 1) allocating matrix iΩ~

is defined as

(17)

With ∑ ∑∈∈

+Mi

i

Sji

nij

TBi bl

44 844 76ϑ

δϑ )( .

An exact reallocation scheme for )( Sji ∈υ requires normalizing

the input-output coefficients associated with each column of the

∑ ∑= ∈

+=Mi Sj

jiii fb ,υϑl

∑≠∈

=

=−

l

l

kk jj

kk

j

dx

d

dx

dxl

β

υ

,0

∑∈

Ω≈Mi

jiTBj l ςυ ~)

~(

),,,(~

, l≠∈∈=Ω kkMiadiag iki β


86 / Vol. 4, No. 12 / Spring 2007

matrix A, so that for any 1, =∈ nj

TAej β . While the loss coefficients

are relatively small, the required normalization condition does not skew the CO2 reallocations. Note that, in the first step, the material balance constraint for the process losses plays a “justified” normalization role and let us extract the maximum information from the technical data that are put into the model. The relation (16) becomes then,

(18) ∑ ∈=Ω

Mi

n

i diag ).1,...,1,1(~

where Using relation (18) and making some algebraic manipulations, the

optimal loss respond function becomes

(19)

where the expression n

ijδ corresponds to the production elasticity of

the jth scarce unit process at the optimum. At this stage, we are finally ready to extract the exact average

contribution of each oil product to the refinery’s carbon dioxide emissions. By using the relation (19) in (12) and simplifying, we get

(20)

In relation (20), the expression ∑ ∈+

Sj iij

T

BE ϑθδ represents the

net contribution of the ith oil product to the process-related carbon dioxide emissions (i.e.,∑ ∈Sj jj fγ in relation 4). These net

contributions are based on the production elasticity of the unit processes involved in the production plan and vary following the optimal technology of the multi-product refinery.

Let us re-state the meaning of relation (20) as follows: in a

∑∈

Ω=Ii

jni

TBj l ςυ ~)

~(

∑ ∑∈ ∈

+=Mi Sj

i

n

ij

T

Bi

i

bl

44 844 76

l

ϑ

δϑ ,)(

∑ ∑∈ ∈

++=Mi

Ai

iSj

ijTBi bE

4444 34444 21

α

ϑθδαε .)(


Vol. 4, No. 12 / Spring 2007 / 87

competitive situation and within a linear production technology Ax =

b, the whole CO2 emissions of the refinery can be fully assigned to the

oil products through the “average allocation” coefficients )( MiAi ∈α .

These latter include the direct and the indirect contribution of each oil product to the refinery’s CO2 emissions. The direct contribution

ia corresponds to the marginal CO2 content of the ith oil product and

is directly obtainable from the final Simplex tableau as explained in

Section 3. The indirect contribution, ∑ ∈+

Sj iij

T

BE ϑθδ , depends upon

the production elasticity of unit processes and should be calculated, ex-post, at the optimal solution of the LP model. Note that both the direct and indirect contributions, (i) are based on the same cost efficient equilibrium (i.e., they are extracted from the same final simplex tableau) and are perfectly coherent with each other; and, (ii) they depend totally upon the technical and physical relationships that define the operating state of the refinery and are perfectly consistent with the ISO 14044 recommendations.

Furthermore, if we suppose that 0=iϑθ in relation (20), then

one could conclude that for each oil product, the percentage deviation of average CO2 contents from marginal CO2 content must be directly proportional to its production elasticity of supply. Note that, relation (20) is based on any exogenous information and can be easily computed from the optimal simplex tableau.

5. General framework and data of the refinery LP

model

The refinery model retained here is based on the LP model presented in (6) and corresponds to a typical European Fluid Catalytic Cracking (FCC) refinery developed by Institut Français du Pétrole. It contains 650 constraints and more than 1800 variables. Its general framework can be summarized as follows.

5-1. Crude oil supply

Several dozen of different crude oils with different physical


88 / Vol. 4, No. 12 / Spring 2007

characteristics are daily processed in European refineries. Because the size of a LP model is approximately proportional to the number of crude oils considered, it is impossible to represent all of them in a refining model (Babusiaux et al., 1983). In this study, the number of crudes is reduced to Brent (generic name for North Sea sweet crude oil), Arabian Light and Arabian Heavy crudes1. However, due to aggregation problems and the lack of complete technical information, the optimal crude structure deduced from the LP model could not reflect the given European oil market structure. For this reason, the crude oil shares have been fixed in the model (see Table 1).

In addition to crude oils, a variety of other specialized inputs such as partly refined oil products or imported residual fuel oils, enhance the refiner’s capability to make the desired mix of products. For simplification purposes, we only considerd some imported feedstocks of atmospheric residue type as input to a vacuum distillation unit. Moreover, the use of natural gas is also modeled for meeting the refinery fuel’s specifications and producing hydrogen from a steam reforming unit. The natural gas price used is 6.33 $US/MTBU which corresponds to its average price in year 2005 (source: World Gas Intelligence, 2005).

Table 1. Typical crude oil in the LP model

Crude oil %mass API* Sulfur content* (% mass)

Brent 40 37.0 0.32

Arabian light 40 33.0 1.86

Arabian heavy 20 27.0 2.69

Feedstocks 16.0 3.23 * Source: Favennec, 1998

5-2. Crude oil prices

The selling price of crude oils is a Custom-Insurance-Fret (CIF) price which is deduced from the Free-On-Board (FOB) price in two steps. First, a freight cost calculated according to a reference scale is added to the FOB price. Then the obtained price is multiplied by an

1. These are considered to be typical of the quality of crudes currently available in European refineries (Saint-Antonin, 1998).


Vol. 4, No. 12 / Spring 2007 / 89

insurance and commission rate. Here, we used the average CIF prices for year 2005 (Table 2).

5-3. Refinery Scheme

The refinery configuration used in this paper corresponds to the most commonly found process scheme arrangements in Europe; that is a typical fluid catalytic cracking refinery which is mainly oriented to produce gasoline. Below, we briefly review the main process units.

Table 2: Crude oil prices for year 2005a

Crude oil Conversion

factorsb $/b $/t

Brent 7.50 53.3 400

Arabian light 7.32 49.2 360

Arabian heavy 7.10 45.9 326

Feedstocks 7.32 40.9 300 a Source: Platt’s, 2005

b Conversion factors from ton to barrel

The first standard process is the topping unit, in which crude oils are distilled at atmospheric pressure and separated into various fractions according to their boiling points. Light fractions (with a boiling point lower than 180°C) are used to make light petroleum gas (i.e., propane and butane), naphtha and gasoline whilst middle fractions (distilled between 180 and 360°C) contribute to the production of jet fuel and diesel oil. Straight-run cuts can not be used directly to blend pools since their characteristics are too far from end-product specifications.

Various process units operate in order to improve these intermediate products. In particular, acatalytic reforming unit upgrades the heavy naphtha cut into an aromatic gasoline component with significantly higher octane numbers. This unit provides, as a precious by-product, the hydrogen required for the hydro-treating and desulfurization units. Moreover, two different isomerization units are also modeled to convert n-paraffins into isoparaffins1

of substantially

1. It is a paraffin with branched chain molecules.


90 / Vol. 4, No. 12 / Spring 2007

higher octane number. The heaviest fractions (boiling range over 360°C) are distilled

again under vacuum to pro-duce vacuum distillate and vacuum residue. The major portion of vacuum residue is fed to a visbreaker to reduce the viscosity of the fuel oil products; this minimizes the contribution of light distillate products, and the excess vacuum residue is used as refinery fuel. The visbreaker is today the cheapest process unit of fuel oil excess conversion into more valuable products. However, a serious post-treatment is required - to meet the octane numbers and sulfur contents - before blending the visbreaker’s outputs into end-products.

The vacuum distillate is converted by a FCC to a gasoline blending component and light cycle oil for blending into the diesel pool. The FCC is today the most important process unit which is used to increase the ratio of light to heavy products from crude oils by operating at 500-550°C, and using a fluidised bed of zeolite catalyst. This conversion unit also produces light olefines whose reaction with iso-butane provides isoparaffins that constitutes a non-aromatic gasoline blending component with high octane numbers. In our model, the FCC is combined with an alkylation unit and operates following

two severities18 .

The other major unit in the model is the hydro-cracking process which is simply defined as a combination of catalytic cracking and hydrogenation reactions; this unit requires a dual-function catalyst and a very high amount of hydrogen. As the reforming unit can not satisfy alone the total requirement of hydrogen, a specific hydrogen production plant (steam reforming) is also modeled.

Besides, the sulfur specifications for gasoline, middle and heavy oil products requires the use of various hydrodesulfurization units (HD, HX and HA). A Claus sulfur recovery processing is also modeled to convert the H2S to liquid sulfur.

1. Severity is a way of defining the operating conditions, which can be more or less severe, of a process unit.


Vol. 4, No. 12 / Spring 2007 / 91

Figure 1. Typical refinery scheme

5-4. Petroleum products specifications

European and U.S. refineries are subject to environmental specifications. Specially, gasoline and “on-road” diesel sulfur contents were significantly reduced to 50 ppm in 2005 and will be set to 10 ppm by January 2009. In addition, the total aromatic content is reduced from 42 vol% to 35 vol% in 2005. Since 2000, the olefins and benzene contents have been limited to 18 vol% and 1 vol% respectively. A review of European Union diesel specifications is scheduled for 2006 (Houdek, 2005).

Between Europe and the rest of the world, trade of oil products can only take place if the sulfur levels of petroleum products comply with the European regulations. This point is of importance because most countries in Asia, Africa and South America adopt sulfur specifications that set levels far above European standards. For instance, the national specifications for sulfur levels in gasoline and


92 / Vol. 4, No. 12 / Spring 2007

diesel in China are respectively 800 ppm and 2000 ppm, or 16 and 40 times higher than European specifications. For our base case study (year 2005), we considered the European specifications of the year 2005 for automotive fuels (Table 3).

Table 3. Specifications of gasoline and diesel in Europe

Quality Gasoline Diesel

Sulfur, max. (% m) 50 ppm 50 ppm Cetane, min. (number) – 51 Poly Aromatics, max. (% vol.) – 11 Density – 845 RON, min. (point) 95 – MON, min. (point) 85 – Aromatics, max. (% vol.) 35 – Olefins, max. (% vol.) 18 – Oxygen, max. (% m) 2.7 – Benzene, max. (% vol.) 1.0 – Oxygen, max. (% wt.) 2.7 –

Source: Panorama IFP, 2005

6. Scenarios and simulations

6-1. Scenarios specifications

The objective of our simulations is to evaluate the impact of the sulfur reduction policy on the marginal and average CO2 content of automotive fuels at the gate of a European-type refinery. Three sulfur specification scenarios based on 2005 (the base case), 2008 and 2010 have been defined (see Table 4). For simplicity purposes, we suppose that there is no distinction between product specifications and the actual levels required at the refinery gate to cover for possible contamination in the distribution systems1.

Within these scenarios, oil products’ demand, crude oil supplies and all other input and output prices (such as crudes and petroleum products) are supposed to be the same as the base case. For the medium term scenarios (2008 and 2010), only some realistic investments could occur in the reforming and hydro-cracking units.

1. In order to guarantee a 10 ppm sulfur level at the pump, generally refineries aim at a level of 6 or 7 ppm to take into account the pipeline contamination issues.


Vol. 4, No. 12 / Spring 2007 / 93

Table 4. Sulfur scenarios for 2005, 2008 and 2010 Oil products Base case Scenario 2008 Scenario 2010

Gasoline 50 30 10 Diesel 50 30 10

Heating oil 2000 1000 1000 Unites: ppm

6-2. Marginal CO2 contributions of automotive fuels: a

prospective study

The results per automotive fuels featured in Table 5 correspond to the marginal CO2 contribution of gasoline and diesel at the gate of the refinery. They show that the gap between the marginal CO2 contribution of gasoline and diesel will be enlarged until 2010. This important conclusion can be explained as follows. By 2005, European refineries have already expanded the diesel fraction from oil refining beyond its optimum balance with gasoline yield to meet the diesel-oriented market demand. Technically, this imbalanced production ratio has most probably resulted in higher production cost and energy consumption for diesel, as compared to gasoline (for technical details, see Kavalov and Peteves, 2004). Table 5 shows that, adding the ultra-low sulfur specifications into the current imbalanced production situation will further increase the marginal energy consumption and the resultant CO2 emissions associated with diesel.

On the other hand, the marginal CO2 content associated with gasoline continues to decrease and becomes even negative from 2008. This unconventional result is mainly due to the catalytic reforming unit, whose major function is to contribute to the gasoline blend but also provides hydrogen as a by product. Meeting the ultra-low sulfur diesel from 2008 would require to use more intensively the hydrodesulfurisation and hydro-cracking units for which hydrogen is a crucial input. For cost reasons, it happens that catalytic reforming unit would operate at full capacity not in order to meet the gasoline demand (which is decreasing in Europe) but to meet the increasing hydrogen requirement of the refinery. This unusual situation would inverse the major function of the reforming unit and would push


94 / Vol. 4, No. 12 / Spring 2007

gasoline to become more and more as a “by-product” of this unit as compared to hydrogen. Since the optimal solution of LP accounts for all the interdependencies among process units, it does not wrongly penalize the reforming unit for its intensive operation; and, therefore, the gasoline pool receives a much lesser CO2 emissions than diesel. The negative CO2 content of gasoline could confirm the “by-product” nature of this product in European refineries in the near future. Note that, however, the emission coefficients in Table 5 must be interpreted with great care as they only correspond to the marginal production of automotive fuels in the refinery. As far as the total CO2 emissions are not fully allocated over oil products (because of the “non product” active constraints), these marginal coefficients are only useful for prospective WTT analysis. In other words, these marginal product-related coefficients should not be compared with the results of the accounting WTT studies in which gasoline production is in general more energy-and CO2-intensive than diesel (e.g., IAE, 2005). An optimal departure1

from the marginal CO2 content to average CO2 content associated with automotive fuels is the subject of the next section.

Table 5. Evolution of the marginal CO2 contents

Oil products Base case Scenario 2008 Scenario 2010

Gasoline 0.205 -2.483 -1.010 Diesel 0.357 0.690 0.800

Unites:tCO2/t

6.3 Average CO2 contributions of automotive fuels: a

retrospective study

Retrospective LP-based coefficients require the reassignment of the process-related CO2 emissions over oil products. Following the methodology presented in Section 4, we extract the MRTS coefficients associated with the “non product” active constraints from

1. Here, an optimal departure means to preserve the cost efficient equilibrium of the refinery.


Vol. 4, No. 12 / Spring 2007 / 95

the final simplex tableau, that is the optimal vector .iϑ . Table 7

summarizes these information in order to perform the first phase calculations. Commercially available software for large scale models include some especial commands to extract these coefficients. The mathematical software we use is LAMPS (Linear And Mathematical Programming System) and the available command is TRANSFORMCOLUMNS (Advanced Mathematical Software Ltd., 1991).

The quasi average CO2 contents )( Mii ∈α are calculated

according to relation (12) in Table 6. As it was expected, the relative

error term of the first step, є = εθ /l , for the three simulations were respectively 2%, 3% and 5%1

. We consider that these first-stage CO2 allocations are good estimations of the final average CO2 content

)( MiAi ∈α and the procedure can be successfully stop here.

Table 6. Evolution of the average CO2 contents Oil products Base case Scenario 2008 Scenario 2010

Gasoline 0.302 -1.189 -0.931

Diesel 0.567 0.752 1.503 Unites: tCO2 /t

The results per automotive fuels featured in Table 6 are now

comparable to those which are based on traditional accounting WTT studies. Most of these latter overestimate the energy use and CO2 emissions of gasoline, as compared to diesel, due to the higher number of gasoline processing units in European refineries. In our LP model, the average CO2 content associated with automotive fuels are totally in line with their respective marginal CO2 contents. That is, since the equilibrium extent of gasoline-to-diesel conversion has been reached, adjusting the a European-type refinery’s output to meet the new ultra-low diesel demand, would be in average more energy-and CO2 -intensive for diesel as compared to gasoline. Moreover, the gap between diesel and gasoline average CO2 contribution would also be

1. The complete computations are available upon request from the first author.


96 / Vol. 4, No. 12 / Spring 2007

widen further, because of the more expensive adjustment of diesel properties to the new European standard requirements.

Table 7. Production elasticities associated with capacity and

calibrating constraints

Year 2005 DI RF IS IR PE HA HO

imp. BT

imp. JFimp. HA+HX

Propane 0.00 -0.14 -0.04 -0.05 0.01 0.00 0.00 0.00 -0.03 -0.64 Butane 0.00 -0.05 -0.01 -0.01 0.01 0.00 0.00 0.00 -0.01 -0.43

Naphtha 0.00 -0.06 -0.02 -0.03 -0.06 0.00 -0.00 -0.01 0.01 0.41

Gasoline 0.00 0.01 0.01 0.01 0.01 0.00 0.00 0.00 -0.01 -0.12 Jet fuel 0.00 -0.11 0.01 0.01 0.01 0.00 0.00 0.00 0.01 -0.28

Diesel 0.00 -0.06 -0.01 -0.01 0.01 0.00 0.00 0.00 0.00 -0.15

Heating oil 0.00 -0.07 -0.02 -0.03 -0.04 0.00 0.00 -0.01 0.01 0.22

Heavy fuel 1%S 0.00 -0.57 -0.17 -0.26 -0.26 0.00 -0.02 -0.05 0.01 0.88

Heavy fuel 3.5%S

0.00 -0.98 -0.30 -0.46 -0.73 0.00 -0.05 -0.13 0.01 0.97

Bitumen 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Year 2008 DI RF IS IR PE HA HO imp.

BT imp.

JFimp. HA+HX

Propane -2.28 0.00 -0.10 0.00 -2.23 0.09 0.00 0.01 0.00 0.04 Butane -1.78 0.00 -0.08 0.00 -1.78 0.06 0.00 0.00 0.00 0.02

Naphtha 0.07 0.00 0.02 0.00 0.09 0.01 0.00 -0.01 0.00 0.07

Gasoline -0.63 0.00 -0.03 0.00 -0.65 0.02 0.00 0.00 2.40 0.00 Jet fuel 0.27 0.00 -0.01 0.00 0.09 0.04 0.00 0.00 0.00 0.18

Diesel -0.03 0.00 -0.01 0.00 -0.06 0.01 0.00 0.00 0.00 0.03

Heating oil -0.18 0.00 0.01 0.00 -0.15 0.02 0.00 -0.01 0.00 0.06

Heavy fuel 1%S -2.22 0.00 -0.01 0.00 -1.97 0.17 0.00 -0.03 0.01 0.38

Heavy fuel 3.5%S

-1.00 0.00 0.18 0.00 -0.64 0.25 0.00 -0.09 0.01 0.86

Bitumen 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Year 2010 DI RF IS PE PE HA HO imp.

BT imp.

JFimp. HA+HX

Propane 0.12 0.00 -0.26 0.00 -0.14 0.00 0.00 0.02 0.00 0.12 Butane 0.08 0.00 -0.29 0.00 -0.12 0.00 0.00 0.02 0.00 0.12

Naphtha -0.35 0.00 0.22 0.00 0.10 0.00 0.00 0.01 0.00 0.01

Gasoline 0.06 0.00 -0.15 0.00 -0.07 0.00 0.00 0.01 0.00 0.06 Jet fuel -1.16 0.00 -0.68 0.00 -0.52 0.00 0.00 0.14 0.00 0.47

Diesel -0.51 0.00 -0.27 0.00 -0.16 0.00 0.00 0.05 0.00 0.18

Heating oil -0.11 0.00 0.15 0.00 -0.04 0.00 0.00 0.01 0.00 0.02

Heavy fuel 1%S -0.65 0.00 0.85 0.00 -0.21 0.00 0.00 0.04 0.00 0.15

Heavy fuel 3.5%S

-1.94 0.00 2.51 0.00 -0.32 0.00 0.00 0.09 0.00 0.28

Bitumen 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

DI = topping unit, RF = Reforming unit, IS = isomerization unit of type A IR = isomerization unit of type B, PE = FCC feed Pretreatment, BT prod. = Bitumen production HA = revamp of the desulfurisation unit, HO imp. = Heating oil importation JF = Jet fuel importation, HA + HX = Total capacity of desulfurisation units.


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7. Conclusion

In this paper we distinguished between prospective (marginal) and retrospective (accounting) WTT analysis. We argued that prospective analysis should be considered when the objective is to explore the environmental effects associated with the marginal production of a given automotive fuel. On the other hand, retrospective analysis is of interest when the main objective is to evaluate the average environmental impacts of a given automotive fuel in transportation studies. It was also explained that, an exact prospective/retrospective study for the production of automotive fuels requires to assess the marginal/average contribution of gasoline and diesel to the total CO2 emissions generated within the refinery. Oil refining is one of the most complex joint production system, and traditional WTT methods fail to account for the complete interaction and substitution effects among the process units.

In order to compute the marginal/average contribution of automotive fuels at the gate of refineries, a practical method based on linear programming was developed. We illustrated that the marginal/average LP-based emission coefficients which emerge from the optimal solution, as opposed to the ones computed by traditional methods, include all consequences of the desired change on the operation of the refinery as well as compositional changes of the oil products. In other words, these emission coefficients embody the physical and process relationships in the refinery system and provide a more realistic estimates of the environ-mental impacts of automotive fuels.

Using the LP model developed in Sections 3 and 4, we estimated the marginal/average CO2 contribution of the petroleum products for a typical European refinery. Then, three simulations for years 2005, 2008 and 2010 were performed to evaluate the impact of the sulfur reduction policy on the CO2 content of automotive fuels at the gate of the refinery. Based on the obtained numerical results, the following core conclusions can be highlighted. Due to the transport and fiscal policies in most of the European countries, the demand for automotive diesel, at the expense of gasoline, has been drastically


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increased from the past 10 years. Since the equilibrium extent of gasoline-to-diesel conversion has been reached, adjusting the European refineries output to meet the new oil product quantities, would be more energy-and CO2 -intensive for diesel. Moreover, our estimates follow the general conclusions driven by Kavalov and Peteves (2004) who claimed that the gap between diesel and gasoline CO2 contribution would be widen further, because of the more expensive adjustment of diesel properties to the new European standard requirements.

A surprising result was the negative marginal/average CO2 contribution of gasoline at the gate of the refinery from 2008. This fact, however, could be perfectly explained by the continuously declining demand of gasoline, on the one hand and, on the other hand by the increasing hydrogen requirement in the refineries due to the new quality specifications. This imbalanced situation would inverse the major function of the catalytic reforming unit and, would cause gasoline to become more and more as a “by-product” of this unit and the whole refining system. Hence, the negative CO2 content of gasoline should be interpreted rather as a confirmation of the “by-product” nature of this oil product in Europe in the near future.

References

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Azapagic, A., Clift, R., 1994. Allocation of Environmental Burdens by Whole-System modeling – The Use of Linear Programming. In: Allocation in LCA, Huppes and Schneider (Eds.), SETAC, Brussels, 54-60.

Azapagic, A., Clift, R., 1995. Life Cycle Assessment and Linear Programming – Environ-mental Optimization of Product System. Computers Chemistry Engineering 19 (Suppl.), S229-S234.

Azapagic, A., Clift, R., 1998. Linear Programming as a tool in Life Cycle Assessment. International Journal of LCA 6 (3), 305-316.

Azapagic, A., Clift, R., 1999a. Allocation of Environmental Burdens


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in Multiple–function Systems. Journal of Cleaner Production 7 (2), 101-119.

Azapagic, A., Clift, R., 1999b. Allocation of Environmental Burdens in Co-product Systems: Product-related Burdens (Part 1). International Journal of LCA 1999b 6 (4), 357-369.

Azapagic, A., Clift, R., 2000. Allocation of Environmental Burdens in Co-product Systems: Process and Product-related Burdens (Part 2). International Journal of LCA 5 (1), 31-36.

Babusiaux, D., 2003. Allocation of the CO2 and Pollutant Emissions of a Refinery to Petroleum Finished Products. Oil & Gas Science and Technology – Rev. IFP 6 (58), 685-692.

Babusiaux, D., Champlon, D., Valais, V., 1983. Aggregate oil refining models, the case of Energy Economy interactions in France. Energy Exploration and Exploitation 2(2), 143-153.

Charnes, A., Cooper, W.W., Mellon, B., 1952. Blending aviation gasoline – a study in programming interdependent activities in an integrated oil company, Econometrica 20 (2), 135-139.

Ekvall, T., Tillman, A. M., Molander, S., 2005. Normative ethics and methodology for life cycle assessment. Journal of Cleaner Production 13, 1225-1234.

EUCAR, CONCAWE and JRC, 2004. Well-to-Wheels Analysis of Future Automotive Fuels and Associated Powertrains in the European Context. Well-to-TANK Report, Version 2b.

Favennec, J.P., 1998. Exploitation et Gestion de la Raffinerie. Le Raffinage du Pétrole. Edition Technip, Paris.

Frischknecht, R., 2000. Allocation in Life Cycle Inventory Analysis for Joint Production. International Journal of LCA 5 (2), 31-36.

Houdek, M.J., 2005. Rebalance Gasoline Surplus by Maximizing FCC Propylene, Presented at the ERTC 10th Annual Meting in Vienna.

International Energy Agency (IEA), 2005. The European Refinery Industry Under the EU Emissions Trading Scheme, Competitiveness, trade flows and investment implications, Paris.

Kavalov, B., Petevs, S.D., 2004. Impacts of increasing automotive diesel consumption in the EU. European Commission, Directorate General Joint Research Center, Petten, The Netherlands.


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Saint-Antonin, V., 1998. Modélisation de l’offre de produits pétroliers en Europe. Ph.D dissertation (in french). Université de Bourgogne-ENSPM.

SETAC, 1993. Guidelines for Life Cycle Assessment: “A code of practice”.

Tehrani Nejad M., A., 2007a. Allocation of CO2 Emissions in Petroleum Refineries to Petroleum Joint products: a Linear Programming Model for Practical Application. Energy Economics, 29, 974-997.

Tehrani Nejad M., A., 2007b. Application of Linear Programming to the Allocation of an Environmental Burden (CO2 emissions) in a Life Cycle Assessment of a Co-product System (Petroleum Oil Refinery). Oil & Gas Science and Technology-Revue IFP, In press.

World Gas Intelligence, 2005


Vol. 4, No. 12 / Spring 2007 / 101

Age Estimation of Car Fleet and its Impact on Fuel Consumption in

Iran: Efficiency vis-à-vis Renovation

Mohammad Mazraati1

Abstract

Volume of gasoline consumed in Iran is determined by such different factors as gasoline price as well as efficiency, age, and number of cars in use among many other structural and cultural variables. This paper considers the average age and efficiency of cars and gasoline demand models as a function of the age, efficiency, price and other explanatory variables to prove that although renovation of the fleet could have positive impact on fuel saving, it is yet to be the most effective approach. It also shows that mandatory efficiency standards for car manufactures and imported cars like the CAFÉ standards in US, could lead to improved efficiency of car fleet, where lower cost within a shorter period of time are incurred. The short term efficiency elasticity of gasoline demand is -3.5 which proves the above mentioned hypothesis. One percent increase in the efficiency of the fleet would lead to about 3.5 percent decrease in gasoline demand in the short run denoting a considerable fuel saving. The short term price

1. Energy Models Analyst, OPEC secretariat, Vienna, Austria, [email protected] and [email protected]


102 / Vol. 4, No. 12 / Spring 2007

elasticity of gasoline demand is estimated at -0.17 demonstrating insignificant response of demand to price in short term although a higher impact can be envisaged in long term. The car age and elasticity of gasoline demand by the fleet of cars are estimated at 0.16 and 0.43 respectively. The elasticity of the number of cars is less than unit but it is still considerable and indicates the considerable impacts of growing size of the fleet on fuel demand. The current development of the fleet size is indicative of a dramatic rise in the number of registered cars which in turn translates to sharp increase in gasoline demand in the future. The paper concludes that in order to get better results, such measures as rationalizing gasoline prices, decreasing average lifetime of car fleet, enforcing the CAFÉ standards to improve the efficiency of cars, levying higher taxes on old cars, scrapping down the old vehicles among other policies should be considered as a part of general policy.

Keywords: average age of car fleet, Iran, Café standards, fuel

efficiency, renovation of car fleet, scrappage, transportation,

gasoline consumption


Vol. 4, No. 12 / Spring 2007 / 103

Impacts of Oil Price Shocks on Economic Variables

in a VAR Model

A. Sarzaeem 1

Abstract

In recent decades, volatility of oil prices has led to such consequences as macroeconomic turbulences. Most of the researches look at the matter from oil importer's point of view while oil producers are usually neglected. This paper explains the relationship between oil price shocks and economic growth and inflation by the econometric methods like VAR model and OLS regression. Based on quarterly data, an unrestricted autoregressive model is estimated in order to gauge short run effects of oil shocks on different variables such as exchange rate, money, government expenditure, inflation and GDP. Long run effects are also measured by the aid of a co-integration autoregressive model. Impulse-response technique is used to estimate reaction of aforementioned variables to different shocks. At the end, the paper proposes the economic policies based on statistical results.

Keywords: Oil price shocks, VAR model, macro economics.

1. Expert, Institute for International Energy Studies (IIES), [email protected]


104 / Vol. 4, No. 12 / Spring 2007

Recent Crude Oil Market Developments:

Making Structural Models

Mehrzad Zamani1

Abstract

The recent oil market conditions, have confronted analysts with serious challenges in their efforts to analyze oil price trends and the reasons behind them. They have, so far, addressed the issue on the basis of structural changes, periodical behavior and speculation. The roots of those challenges, in their view, are embedded in the influential development of fundamental elements on the price of oil. OPEC's oil production in the 1990s, is a case in point, which materialized the organization's price objectives very effectively. The organization, however, has lost its price controlling mechanisms and capabilities in recent years. The relationship of crude oil prices and commercial stockpilings has also reversed. This study reviews changes in the fundamental factors on the basis of econometric models. According to results, OPEC's excess or surplus production capacity in recent years (post 2003) has affected the relationship of oil stockpilings and prices. OPEC's surplus production capacity had no impact on oil prices prior to 2003, when it began to demonstrate its influence. Thus, OPEC which set its members' production quotas in

1. Expert, Modeling and Long term energy studies Group, IIES, E-mail: [email protected]


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light of stockpiling levels, in its pursuit of price objectives, is presently influencing the oil market with its excess capacity. Therefore, through its quota setting mechanism, OPEC is facing two opposing effects of the changing stock-levels and the surplus capacity, and currently the role of the second is superior.

Key words: Oil price, Oil market fundamentals, OPEC. Reversing

factors


106 / Vol. 4, No. 12 / Spring 2007

A Survey of New Structure of LNG and Natural Gas Industry in

the World

Eshagh Mansour kiaee1

Abstract

Hegelian process of change dictates that when entity (thesis) is transformed into its opposite (antithesis), the combination would be resolved in a higher form (Synthesis). It seems that global liquefied natural gas industry is undergoing such a process. The process of restructuring traditional monopoly in LNG industry materialized by market liberalization and privatization requires a new form of structure that benefits from competitive markets. This paper discusses the probable impacts of liberalization on the future developments of LNG industry. The paper also examines the probability that whether Hegel's invisible hand would be able to transform the traditional monopoly in LNG industry into the restructured one involving viable competitive markets.

Key terms: Hegel's Dialectic Theory, LNG, Traditional Model of

Natural Gas Trade, Competitive Markets Model, Liberalization,

Prices, long-term contracts, spot market.

1. National Iranian Gas Export Company (NIGEC), LNG marketing expert , [email protected]

IIES Quarterly Energy Economics Review Vol 4 No 12 Sp 2007

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