Energy Efficiency (2010) 3:317–329 DOI 10.1007/s12053-009-9075-5
Comparing ODEX with LMDI to measure energy efficiency trends Caiman J. Cahill & Morgan Bazilian & Brian P. Ó Gallachóir
Received: 4 August 2009 / Accepted: 28 December 2009 / Published online: 26 January 2010 # Springer Science+Business Media B.V. 2010
Abstract This paper examines the effectiveness of ODEX in measuring energy efficiency improvements by comparing it to an alternative proxy for energy efficiency, namely an index of energy intensity with structural effects removed, calculated using the Logarithmic Mean Divisia (LMDI) decomposition technique. Both approaches are subjected to tests to determine their accuracy, using the industry sector in Ireland as a case study. While the LMDI performs better than ODEX, the results yielded by both in their chained forms are influenced by fluctuations in the data used to calculate them. A method is proposed to quantify the effects of fluctuations on the results. For Irish industry data, these effects are found to be significant. It is recommended that the effects of data
C. J. Cahill : B. P. Ó Gallachóir Sustainable Energy Research Group, Department of Civil & Environmental Engineering, University College Cork, Cork, Ireland C. J. Cahill (*) : B. P. Ó Gallachóir Environmental Research Institute, University College Cork, Lee Road, Cork, Ireland e-mail:
[email protected] URL: www.ucc.ie/serg M. Bazilian United Nations Industrial Development Organization (UNIDO), Vienna International Center, D1579, PO Box 300, 1400 Vienna, Austria
fluctuations be evaluated when calculating a chained top-down indicator to measure energy efficiency. Keywords ODEX . Energy efficiency indicator . Energy intensity . LMDI . Divisia . Decomposition analysis . Index theory
Introduction Energy efficiency is growing in significance as a key plank of energy and climate policy. The emergence of increasingly complex legislative requirements requires improved modelling for projecting, monitoring and evaluating energy savings associated with policy measures, as outlined for example by Hull et al. (2009) and Taylor et al. (2009). Within the European Union, Member States are seeking an amount of energy savings equal to or higher than 9% of the average annual energy consumption in a base period over the 9-year period 2008–2016 in accordance with Directive 2006/32/EC (European Union 2006), referred to hereafter as the Energy Services Directive (ESD). The 9% target is quantified in terms of energy savings, i.e. a reduction in energy demand relative to a counterfactual that can be attributed to energy efficiency improvement measures. Annex 1 of the Directive defines the methodology to be utilised in quantifying the target based on the preceding 5-year annual average final energy demand. The target is
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thus quantifiable, fixed and independent of future energy demand growth. In addition, the ESD target excludes those participating in the EU Emissions Trading Scheme. It allows the impact of measures introduced since 1995 (and in certain cases since 1991) that have a lasting effect to be included. The focus of the ESD is on quantified national measures, although there are some concerns regarding the absence of precise restrictions on the inclusion of autonomous progress (Thomas et al. 2009). When modelling anticipated energy savings or quantifying achieved energy savings, a clear distinction occurs between top-down and bottom-up methods. The bottom-up approach (Vreuls et al. 2009) uses data at the level of a specific energy efficiency improvement measure (e.g. energy savings per participant and number of participants) and then aggregates results from all the measures. By contrast, top-down methods (Lapillone et al. 2009) for evaluating savings use aggregated sectoral levels of energy savings. A top-down indicator provides a useful starting point as less data is required to calculate it. However, top-down indicators do not identify specific savings achieved as a result of policies. Instead, they reflect aggregate changes brought about by a variety of factors, such as price effects, autonomous effects, direct rebound effects, hidden structure effects, as well as the effects of old and new policies. This paper focuses on top-down methods for measuring energy efficiency and quantifying energy savings. The ESD states that “in developing the topdown calculation method used in this harmonised calculation model, the Committee shall base its work, to the extent possible, on existing methodologies such as the ODEX model”. The ODEX method for quantifying energy savings uses ODEX indicators or energy efficiency indices. This approach to measuring energy efficiency has been developed within the ODYSSEE project (ADEME 2007). These indices aggregate trends in unit consumption by sub-sector or end-use into one index by sector based on the weight of each subsector/end use in the total energy consumption of the sector. According to Bosseboeuf et al. (2005), ODEX “provides a good “proxy” of the energy efficiency progress from a policy evaluation viewpoint”. Within industry, ODEX relates energy use of manufacturing branches, or sub-sectors, to their physical output given by a production index for most branches, rather
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than to their value-added, to calculate their changes in energy efficiency. The calculated values for all subsectors are then weighted and aggregated to give an overall result for the sector. The ODEX thereby removes the distorting effects of changes in value added that are unrelated to production output. By disaggregating the sector into a number of distinct defined branches, the index attempts to remove changes in energy consumption patterns brought about by changes in the industrial production mix. However, few academic studies could be identified where the ODEX energy efficiency indicator is tested with scientific rigour or compared to existing decomposition methods. Boonekamp (2006) evaluates a number of bottom-up and top-down methods of calculating energy savings, among them ODEX, and finds that ODEX lacks a method of calculating uncertainty margins. Horowitz (2008) shows that changes in an index based on the ODEX calculation methodology or any other top-down energy efficiency index are virtually unrelated to changes due to energy policies and uses a Monte Carlo simulation to show that estimates of policy impacts based on such indices have an unacceptable level of error. Bosseboeuf and Lapillone (2009) have suggested, however, that a careful comparison of historic trends in technical and observed ODEX could provide a basis for forecasting the counterfactual needed to calculate policy impacts. In this paper, the effectiveness of the ODEX in capturing energy efficiency achievements of Irish industry is scrutinised by comparing the results of the ODEX methodology with those based on using a Logarithmic Mean Divisa Index (LMDI) approach. The paper devises and applies tests to examine and compare the behaviour of the two and to determine which method is the most appropriate for Ireland. The LMDI method belongs to a family of more established (Divisia and Laspeyres) decomposition methods that in practical application to date use energy intensity as a starting point rather than (in the case of ODEX) unit consumption. Greening et al. (2007) provide a larger overview of a variety of topdown, bottom-up, econometric and decomposition methods of modelling energy consumption in the industrial sector. Decomposition methods typically calculate sub-sector energy intensity, i.e. the ratio of energy use to industrial output, and thereby endeavour to account for and remove the impact of changes in industrial production mix from the calculated
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overall energy performance result. The resultant energy intensity at constant structure has subsequently been used as a proxy for energy efficiency. According to Ang and Zhang (2000), this technique was first used in the late 1970s to study the impact of the changes in industrial mix on industrial energy demand. Their survey identified 124 studies on decomposition methods by 2000. Greening et al. (1997) undertook a comparison of six of the more common decomposition methods using data sets for ten OECD countries and concluded that methods using the Divisia decomposition approach yielded the smallest residual term, or error. Ang (2004) highlighted the lack of consensus on the “best” decomposition method and referred to the ad hoc choices made by researchers and analysts. He distinguished between the two main groups of decomposition methodology: those linked to the Laspeyres index and those linked to the Divisia method. The Laspeyres index measures the percentage change in some aspect of a group of items over time, using weights based on values in some base year. The Divisia index is a weighted sum of logarithmic growth rates, where the weights are the components’ shares in total value, given in the form of a line integral. In simple terms, the building block of methods linked to the Laspeyres index is based on the familiar concept of percentage change, whereas the building block of methods linked to the Divisia index is based on the concept of logarithmic change. As Ang (2004) points out, New Zealand, the US Department of Energy and the European funded ODYSSEE project all use the Divisia method, citing as reasons the small residual term and the fact that the approach is invariant to the choice of base year. The Laspeyres approach has been adopted by the International Energy Agency. Ang (2004) summarises the two approaches, stating that the Laspeyres index is easier to understand, but the Divisia index is more scientific, and generally recommends the use of the LMDI method due to its “theoretical foundation, adaptability, ease of use and result interpretation, and some other desirable properties in the context of decomposition analysis”. The LMDI approach has become an increasingly popular top-down method for analysing energy consumption trends and associated greenhouse gas emissions trends in all economic sectors. Canada had used the Laspeyres index until increasing difficulties with residual terms prompted a switch to LMDI in 2006 (Natural Resources Canada
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2006). Australia also recently adopted LMDI to bring the country’s approach “in line with recent similar studies for other advanced economies” (Sandu and Sayed 2008). Liu et al. (2007) apply the method to identify the sub-sectors of Chinese manufacturing industry that contribute most to the country's increase in CO2 emissions from fuel use. Sorrell et al. (2009) use the LMDI decomposition approach to assess the relative contribution of several factors to the decoupling of road freight energy use from gross domestic product (GDP) in the United Kingdom and determine that the decline in the value of domestically manufactured goods relative to GDP is the most significant factor. In Ireland, the ODEX indicator is the prevalent top-down methodology for measuring energy efficiency improvements in all sectors of the economy. O’Leary et al. (2007a) concluded that Ireland achieved an 8.1% improvement in energy efficiency over the period 1995–2005 based on the ODEX approach. Ireland is an interesting case study for a number of reasons; not least its significant growth in energy demand since 1995 coupled with relatively low and reducing energy intensity (Howley et al. 2008). Ireland also has experienced poor performance in limiting greenhouse gas emissions and faces significant challenges in the future, with greenhouse gas emissions already 25% above 1990 levels in 2007. The industry sector in Ireland is particularly interesting due to the gradual disappearance of energy-intensive manufacturing industry, brought about in part by economic policies targeting inward investment from companies in large value-added sub-sectors, including pharmaceuticals and information technologies. “Methodology” section develops the methodology used in this paper. It explains how the ODEX and an index based on the LMDI approach (referred to hereafter simply as LMDI) are calculated and outlines the tests used to scrutinise their effectiveness. “Results” section presents the results of both calculations and the tests. “Summary and Conclusion” section discusses the results and their implications and concludes.
Methodology Trends in energy consumption in all sectors of the Irish economy are analysed and published regularly
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by Sustainable Energy Ireland, Ireland’s national energy agency. The most recent publication for the Industry sector includes an ODEX energy efficiency indicator and an index of energy intensity at constant structure calculated using a Divisia method (O’Leary et al. 2007b). In the work detailed in this document, the ODEX and LMDI are calculated using the methods outlined below. Both ODEX and LMDI are subjected to a number of tests to determine which index calculation method performs more reliably when applied to the data set for the Irish industry sector. Calculating ODEX: an energy efficiency index To calculate ODEX for industry, the sector is broken down into a number of sub-sectors or branches for which both final energy consumption data and production output data are available. A unit consumption value I is calculated for each sub sector by simply dividing its energy consumption E by its production output P. I¼
E P
ð1Þ
As ODEX calculates savings of each sub-sector separately relative to the previous year’s performance and all sub-sectors’ savings are then aggregated, the units used for measuring production output may be different from sub-sector to sub-sector. A unit consumption value is calculated for each year of the period under analysis and may be indexed such that the value for any year is given relative to a base year value. Then, for any given year t, the unit consumption index for a sub-sector i can be calculated as: Iit
E t » P0 ¼ i0 it Ei » Pi
tion values by sub-sector in accordance with the ODYSSEE definition (Enerdata 2008). Each subsector is weighted on the basis of its share of total energy consumption of the sector. For each subsector, the variation of the overall ODEX between consecutive years t−1 and t is calculated according to the following formula: It I t1
¼P i
1 ðEit =E t Þ:ðIit1 =Iit Þ
ð3Þ
where It is the ODEX value for the sector in year t and Et is the total energy consumption of the sector in that year. The base year ODEX value, I0, is typically set to 100. Calculating LMDI: a composite index of energy intensity The LMDI decomposition method typically decomposes changes in industrial energy consumption into contributions from changes in activity levels, changes in the structure of industry and changes in the subsectoral energy intensities. As this study is concerned with top-down energy efficiency measurements and as ODEX provides no method of assessing energy consumption associated with changes in activity levels or structure, the energy intensity component of the LMDI methodology only will be examined. The LMDI formula for the ratio of change in energy consumption due to changes in energy intensity is given by Ang (2005) as: Dint
T ! X EiT Ei0 = loge EiT loge Ei0 N :loge i0 ¼ exp ðE T E 0 Þ=ðloge E T loge E 0 Þ Ni i
ð4Þ ð2Þ
where Ei 0 and Ei t and are the energy consumption values for a sub-sector i in the years 0 and t, respectively, Pi 0 and Pi t are the corresponding production output values for the same years. However, the ODEX result will be the same regardless of whether the unit consumption value used is an absolute value or a value relative to a base year value. The unit consumption value is calculated for each sub-sector for each year. The overall industry ODEX is calculated as a weighted average of unit consump-
where Ni 0 represents the energy intensity of the subsector i in the base year. Energy intensity in industry is typically measured as energy consumption per unit of gross value added (GVA). Similarly, GVA is used for calculating the activity and structural components of the LMDI approach. However, Ang (2006) shows that if only the intensity component of the LMDI is of interest and the structural and activity components are not required to be analysed, then the LMDI approach could be applied using physical indicators rather than value added. In other words, energy intensity values Ni could be substituted with unit consumption values
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Ii calculated from production output as shown in Eqs. 1 and 2. To enable a direct comparison with
It I t1
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ODEX, which is a chained index of energy efficiency, the chained form of LMDI can be applied, as follows:
t ! X Eit Eit1 = loge Eit loge Eit1 Ii :loge t1 ¼ exp t E t1 Þ=ðlog E t log E t1 Þ ð E I e e i i
where Ii t represents the unit consumption value of the sub-sector i in the year t. The chained version of LMDI will be used here when comparing it to ODEX. To facilitate a direct comparison of LMDI and ODEX results in this paper, the value of I0 for both will be set to 100. Determining the most appropriate indicator for Irish industry Both ODEX and LMDI are subjected to tests to compare the behaviour of the two indices, to determine which of the two provides the most accurate view of energy consumption trends in Irish industry and to examine the appropriateness of using either index value to calculate real energy savings. Several test methods exist in index number theory to determine the likely accuracy of a particular index result. Diewert (1993) lists some of the most common tests. Two tests more commonly employed in assessment of energy decomposition analysis techniques are examined, namely a zero values robustness test and a time reversal test. Additional tests are designed here specifically to assess the behaviour of the two indices when there are fluctuations in the data used to calculate them. The relevance of the tests to Irish industry is assessed, and a method of quantifying the effect of the fluctuations on each result is proposed.
ð5Þ
It can be seen that the two approaches yield different results. ODEX shows a 26.7% improvement in energy performance up to 2007, while chained LMDI gives a figure of 23.8% improvement over the same period. In some economies, production output figures for many of the defined energy-intensive industry branches can be relatively easily quantified, in terms of tonnes of steel or cement produced for instance, and can be used directly in the index calculation. In Ireland, however, these energyintensive branches in some cases do not exist, and production figures are not released for those that do. Instead, production output figures are aggregated at a two-digit NACE level and published for 13 manufacturing sub-sectors, with each sub-sector producing a range of similar goods. The production output data are derived from a national Census of Industrial Production. As each of the 13 sub-sectors includes a range of different products, it is necessary for the publishers of the data to apply a weighting to each product based on its value added, in order to derive an aggregate unitless production output figure for the
100
90
Results Index results for Irish industry Using production output data for Ireland published by the Central Statistics Office (2006) and energy consumption data provided by Sustainable Energy Ireland, both ODEX and LMDI in its chained form have been calculated annually from 1995 onwards and are presented in Fig. 1.
80 76.2 73.3 70
1995
2000 ODEX
2005 LMDI (chained)
Fig. 1 Irish Industry: ODEX versus LMDI (chained)
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sub-sector. As the relative values of these products change over time, the sub-sector’s production output figure is adjusted every few years using GVA data, to account for these changes. As a result, production output trends for the sub-sectors are similar to their trends in GVA. According to Ademe (2007), “energy savings can be directly derived from the ODEX indicator since this also represents the ratio between energy consumption and a fictive consumption that would have occurred without the savings”. In this manner, O’Leary et al. (2007a) use the Irish industry ODEX value to calculate total yearly energy savings brought about by improved energy efficiency in the sector, according to the formula: 100 Savingst ¼ E t » 1 It
ð6Þ
where It is the ODEX value in year t. For instance, the savings achieved by the industrial sector in Ireland in 2007 is calculated as 980 ktoe, using the ODEX and sector energy consumption values for that year. However, if the ODEX value in Eq. 6 is replaced with the LMDI value for Irish industry, the calculated savings will be considerably lower at just 840 ktoe. It should be noted that both results include all energy savings due to energy efficiency improvements, whatever their cause, that influence the development of the indices over time. Also, while both methods attempt to remove the effect of structural changes on energy consumption by disaggregating into subsectors, the effect of structural changes within subsectors cannot be decomposed from the result. In order to determine which result best reflects the energy efficiency achievements of Irish industry, both will be subjected to a series of tests appropriate to the Irish data set. Tests from index number theory Some of the tests commonly performed on index numbers and decomposition methods cannot be applied to ODEX as, unlike LMDI, it does not decompose changes in energy use into separate determinant effects. For instance, Hoekstra and van den Bergh (2003) suggest analysing properties of an index by using Completeness, Time Reversal and Zero Value Robustness tests. The completeness test
evaluates whether a decomposition technique has a residual component. A residual shows that the sum of the determinant effects has overestimated or underestimated the change. The completeness test cannot be applied to ODEX as no residual can be calculated. By contrast, Ang and Liu (2001) have shown that LMDI is perfect in decomposition and that no residual exists. The zero value robustness test assesses how the method performs when there are zero values in the data set used to calculate the index. Computational problems that occur when zero values are used in the LMDI calculation can be addressed by replacing each zero either with a small positive number δ, as described by Ang et al. (1998), or with the analytical limit of each affected LMDI term if there are many zero values in the data set, as recommended by Wood and Lenzen (2006) and further analysed by Ang and Liu (2007). Zero values also lead to problems when calculating ODEX, but the approach of replacing these with small values will not yield satisfactory results. No method has been identified in existing literature to handle zero values when calculating ODEX. The time reversal test, as first proposed by Fisher (1922), requires that if the time sequence between first and last years being analysed is reversed, the new index should be the reciprocal of the original. In other words, the improved energy efficiency calculated in one direction in time should be equal to the deterioration in energy efficiency calculated in reverse time. Here, the data set for Irish industry is used to perform the test. For each index, the most recent index value is taken as the base year value, and the index is calculated for each year in reverse chronological order. To pass the test each index must return to its original value of 100 in 1995. Taking 76.2, the 2007 value, as the base year value for the LMDI, and working backwards, it can be seen in Fig. 2a that the LMDI adheres to its original path and yields a value of 100 in 1995. For ODEX, the 2007 value of 73.3 is taken as the base year value. When the index value for preceding years is calculated, the path diverges from the original until a value of 92.5 is reached in 1995, see Fig. 2b. This is considerably lower than the expected value. ODEX fails the time reversal test for two reasons. Firstly, the change in unit consumption for each subsector between years t−1 and t is weighted using the energy consumption share in year t only. This means
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sumption symmetry where loge Ii t =Ii t1 ¼ t1provides loge Ii =Ii t .
a 100
100.0
Index behaviour with fluctuating sub-sector values
90
80 76.2
70 1995
2000 LMDI Industry (chained)
2005 LMDI Industry (chained) Reversed
b 100
92.5 90
80
73.3 70 1995
2000 ODEX Industry
2005 ODEX Industry Reversed
Fig. 2 a Time reversal test—LMDI. b Time reversal test— ODEX
that, working backwards, the unit consumption change between t and t−1 gets a different weighting, namely the energy consumption share in year t−1. Secondly, the change in unit consumption between two consecutive years is calculated as a simple fraction, so that for example, a 25% increase between years t−1 and t would be just a 20% decrease when the time is reversed. The LMDI approach does not encounter either of these difficulties as the logarithmic mean of two energy consumption values in years t and t−1, used to calculate the weights, is obviously the same in either direction, and the use of logarithms in calculating the change in unit con-
A new test is introduced here to examine the response of each indicator to fluctuating sub-sector data values. The test has been devised after observing large fluctuations in the historical data set used to calculate top-down indicators for Irish industry. In the test, three scenarios are examined. In all scenarios, the industry sector comprises two sub-sectors, A and B, each consuming the same amount of energy in year 0. In each scenario, the energy efficiency performance of the sector is tracked over a 3-year period using both ODEX and LMDI indices. In all cases, the energy efficiency of each sub-sector, measured by its unit consumption value, is the same at the end of the period as it was at the start, i.e. there has been no net change in the energy efficiency of the sector. In the first scenario, the production output of subsector A increases by 20% in year 1 and returns to its base year value in year 2. The production output of sub-sector B remains unchanged for all years, see Table 1. The unit consumption values in year 2 show that there has been no net change in the energy efficiency of either sub-sector in the period. As there has been no change in efficiency at the end of the period, each index should return a value of 100. However, ODEX yields a value of 99.2 in year 2 indicating a 0.8% improvement in energy efficiency while LMDI returns to its base year value of 100. In order to get an index value that returns to base year value in year 2, the It value calculated for year 2 should be the reciprocal of the year 1 value. For ODEX, this is not the case as it uses simple fractions to account for changes in sub-sector unit consumption values, as was evident in the time reversal test. The LMDI on the other hand, uses logarithms, so that the changes in years 1 and 2 are symmetrical. In the second scenario, each sub-sector’s share of total energy consumption changes over the period. The production output of sub-sector A changes such that the unit consumption value increases in year 1 and returns to its original value in year 2. The unit consumption value of sub-sector B remains constant over the 3 years, see Table 2. Again the energy efficiency of both subsectors are the same at the end of the period as they were at the start, so index values would be expected to
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Table 1 ODEX indicates energy efficiency improvement; LMDI does not Year t
Sub-sector i
Energy consumption Ei t
Production output Pi t
Unit consumption Ii t
ODEX
LMDI
0
Sub-sector A Sub-sector B
100.0 100.0
100.0 100.0
100.0 100.0
100.0
100.0
1
Sub-sector A Sub-sector B
100.0 100.0
120.0 100.0
83.3 100.0
90.9
91.3
2
Sub-sector A Sub-sector B
100.0 100.0
100.0 100.0
100.0 100.0
99.2
100.0
return to their base year values of 100. The values of both ODEX and LMDI increase in year 1 to account for the decreased energy efficiency of sub-sector A. In year 2, both indices show an improvement in energy efficiency relative to the base year, with ODEX showing the greater improvement. Both ODEX and LMDI show an improvement over 3 years where none exists. In this example, the energy efficiency gains in year 2 are given a greater weighting than the losses in year 1 due to the fact that sub-sector A has a greater share of total energy use in year 2. The energy consumption shares are calculated using a logarithmic mean of values in years t and t−1 in the case of LMDI, while ODEX uses a simple annual fraction. Additionally, as in the first scenario, the ODEX result is influenced by the unsymmetrical calculation of the fluctuation in unit consumption value. The third scenario is similar to the second except that this time, the production output of sub-sector A changes such that its unit consumption value decreases in year 1 and returns to its original value in year 2, see Table 3. As unit consumption values at the start and at the end of the period are the same, index results showing no change in energy efficiency after 3 years would be expected. ODEX and LMDI values reflect the improved energy efficiency in year 1 but both give values for year 2 that are greater than
the base year values, indicating a deterioration of energy efficiency in the sector over the 3-year period. This is because the energy efficiency losses in year 2 are given a greater weighting than the gains in year 1 due to sub-sector A’s increased share of total energy consumption in year 2. In the case of ODEX, this effect is somewhat reduced by the error brought about by its handling of fluctuations in the unit consumption value, shown in the first scenario. The three scenarios show that the values yielded by both indices can be affected by fluctuations in the data used to calculate the indices. In the first scenario, fluctuations are brought about by changes in production output while energy consumption remains constant. In the second and third scenarios, unit consumption values fluctuate around the base year values and energy consumption shares change. In all cases, an energy efficiency improvement achieved by a sub-sector carries a greater weight if its share of energy consumption is greater. As in the examples above, this can lead to an overestimation or underestimation of total achievements if the improvement is cancelled out by a deterioration in energy efficiency prior to it or after it. Typically, energy efficiency indices are employed in this fashion to provide an indication of the energy efficiency achievements of a sector over a time period of greater than 2 years, such
Table 2 ODEX and LMDI indicate energy efficiency improvement Year t
Sub-sector i
Energy consumption Ei t
Production output Pi t
Unit consumption Ii t
ODEX
LMDI
0
Sub-sector A Sub-sector B
100.0 100.0
100.0 100.0
100.0 100.0
100.0
100.0
1
Sub-sector A Sub-sector B
110.0 90.0
88.0 90.0
125.0 100.0
112.4
112.4
2
Sub-sector A Sub-sector B
120.0 80.0
120.0 80.0
100.0 100.0
97.7
98.9
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Table 3 ODEX and LMDI indicate deterioration in energy efficiency Year t
Sub-sector i
Energy consumption Ei t
Production output Pi t
Unit consumption Ii t
ODEX
LMDI
0
Sub-sector A Sub-sector B
100.0 100.0
100.0 100.0
100.0 100.0
100.0
100.0
1
Sub-sector A Sub-sector B
110.0 90.0
125.0 90.0
88.0 100.0
93.0
93.5
2
Sub-sector A Sub-sector B
120.0 80.0
120.0 80.0
100.0 100.0
100.2
100.6
that the value for any particular year is compared to the value in a base year. Chained indices such as the ones analysed here give an accurate measure of energy efficiency changes from 1 year to the next. Their accuracy over a longer time period will be influenced by the extent of change and fluctuation in the data set used to calculate them.
attributable to the fluctuations in sub-sector data values. The method involves removing fluctuations from all unit consumption and energy consumption values. This is done by performing a linear interpolation between the values for year t and the base year value. The unit consumption values for all sub-sectors for all years between 0 and t are then given by the following equation:
Relevance of fluctuating values test to Irish industry It has been shown that fluctuations in the data used to calculate ODEX and chained LMDI can affect the result and that they can lead to a result that overstates or understates the energy efficiency progress over a period greater than 2 years. To determine if the fluctuating values test has any relevance to a real data set, the pattern of fluctuating energy and production output values tested here needs to be compared to actual data. Figure 3 shows the trends for unit consumption indices for the 13 sub-sectors of Irish industry that are used to calculate ODEX and LMDI. Most sub-sectors in Irish industry exhibit some degree of fluctuation, brought about by fluctuations in both production output and energy consumption values. For some sub-sectors, at least, the amplitudes of the fluctuations are considerable. Given their size, it is likely that some of the fluctuations are due to imperfect data rather than dramatic changes in the energy efficiency of sub-sectors from one year to the next. The extent to which these fluctuations will influence the index results will depend on the size of the fluctuations and on how the weighted sub-sector values change relative to each other from year to year. Quantifying the magnitude of the fluctuating effect A method is proposed here that helps quantify the magnitude of the change in index values that is
Iix ¼ Ii0 þ
x » I t I 0 for 0 < x < t i i t
ð7Þ
Furthermore, the energy consumption values for all sub-sectors for all preceding years are similarly calculated to remove fluctuations as follows: x » E t E 0 for 0 < x < t Eix ¼ Ei0 þ ð8Þ i i t This method requires that each year, both energy efficiency indices be recalculated for all preceding years. This means that the ODEX and LMDI values must also be recalculated each year for all preceding years. The method assumes that energy consumption for all sub-sectors followed a straight line path up to year t and that productivity was such that all unit consumption trends up to year t were also linear. The production output figures can be recalculated also to ensure consistency, by dividing the energy consumption values by the unit consumption values for each sub-sector. However, production output values from years 1 to t−1 will not affect the result for either index. When this straight-line method is used to calculate both ODEX and LMDI in the three scenarios of the fluctuating values test (Tables 1, 2 and 3), the effects of fluctuations are removed, and all index values return to their base year values in year 2. To quantify the effect that fluctuations of sub-sector values may have on the index results for Irish industry, both indices are recalculated using the
326
Energy Efficiency (2010) 3:317–329 250 Non-Energy Mining Food, beverages and tobacco
200 Unit consuption (1995=100)
Textiles and textile products Wood and wood products Pulp, paper, publishing and printing
150
Chemicals & man-made fibres Rubber and plastic products
100
Other non-metallic mineral p products Basic metals and fabricated metal products Machinery and equipment n.e.c.
50
Electrical and optical equipment Transport equipment manufacture
0 1995
Other manufacturing
2000
2005
Fig. 3 Unit consumption indices for 13 Irish industry sub-sectors
straight line method. The value for each year is recorded. The results are shown in Fig. 4a and b. The total improvement recorded by ODEX over the 13-year period drops from 26.7% to 23% when the linear interpolation approach is used for energy consumption and unit consumption values. This indicates that fluctuations in the data set for Irish industry led to an overestimation of energy efficiency achievements of around 0.3 percentage points per annum. The improvement indicated by LMDI dropped by 1.9% when fluctuations were removed, or an average of 0.15% per annum.
Summary and conclusion This paper has compared ODEX to LMDI in order to assess which index is most appropriate for measuring changes in energy efficiency in the Irish industry sector. It was demonstrated that LMDI passes the time reversal test from index number theory and that methods exist for handling zero values in the data set used to calculate the index. ODEX, on the other hand, fails the time reversal test due to its use of simple fractions to calculate changes in unit consumption and its use of just 1 years’ energy consumption when calculating the weight of each sub-sector’s contribution. ODEX has no documented approach for handling zero values. However, as the data used in this work to calculate the index is aggregate energy consumption and productivity data for two-digit sub-sectors, no zeros exist, and there-
fore, the handling of zero values is not critical to the choice of the most appropriate index for measuring energy efficiency in Irish industry. The LMDI approach enables the decomposition of changes in energy use into determinant effects, and the decomposition technique leaves no residual. Although full decomposition is not carried out here, the fact that the methodology leaves no residual provides greater confidence that its result is accurate. As ODEX provides no method for assessing its accuracy, it is concluded that LMDI provides the more reliable indicator of energy efficiency in Irish industry. The fluctuating values test has shown that fluctuations in the data set can lead to an underestimation or overestimation by both approaches of the savings achieved. Using the straight line interpolation method, the extent of the influence of the fluctuations on the result can be quantified. For Irish industry, both indices overestimate the savings, with ODEX showing the greater overestimation. The distortions of the result are a consequence of the chaining of the indices, i.e. the dependence of the value for year t on the value for year t−1. The fact that these distortions can arise when data values change significantly from one year to the next cannot be perceived as a failing of either index. The effect of fluctuations on chained index numbers is well documented in the field of economics (Ehemann 2007; Forsyth and Fowler 1981; Frisch 1936), where large fluctuations in prices or quantities are sometimes considered implausible or a sampling interval is recommended that filters the fluctuations. Nonetheless, it can be
Energy Efficiency (2010) 3:317–329
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a 100
90
80 77.0
73.3 70
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2000 ODEX
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ODEX straight-line method
b 100
90
80 78.1
76.2
70 1995
2000 LMDI (chained)
its unchained form uses only data from the base year and the year being evaluated to calculate savings, as shown in Eq. 4, and is therefore independent of fluctuations in the intervening years. ODEX has no unchained form and is unsuited to being adapted to an unchained index, given that the weight of each subsector’s contribution is calculated using its share of energy consumption in one year only. LMDI in its unchained form indicates an energy efficiency improvement of 22.5% in the Irish industrial sector between 1995 and 2007, see Fig. 5, which is a smaller improvement than indicated by either the chained LMDI or ODEX. As LMDI has been proven to be a decomposition method that produces no residual and as it excludes the influence of fluctuations in its unchained form, this unchained result is likely to be the most accurate of the three. The total energy savings in 2007 calculated using Eq. 6 is now 781 ktoe, which is over 20% less than the savings indicated by the ODEX result. The results of this analysis have been considered in Ireland, and energy efficiency is currently calculated using a LMDI index for industry and ODEX for the transport and residential sectors (Dennehy et al. 2009). The ESD requires that Member States use a combination of top-down and bottom-up calculation methods in a harmonised model, to measure progress towards defined energy efficiency targets, and suggests ODEX as a top-down indicator. Each Member State should identify the top-down method that provides the most reliable and most accurate measurement of the true
2005
LMDI (chained) straight-line method
Fig. 4 a ODEX for Irish Industry: actual versus straight line path. b LMDI for Irish Industry: actual versus straight line path
seen that the fluctuations in the Irish data are considerable and persistent and that their effect on the results is not insignificant. The fluctuations may be due to the quality of data available. One approach to removing the effect of fluctuations is introduced in this work, namely, to recalculate all energy consumption and unit consumption values for preceding years such that their trends are linear. However, this method is cumbersome as it involves recalculation of all years for every new year calculated. Therefore, it may be more practical to use an unchained method to measure savings in Irish industry and in any other instances where large fluctuations occur. The LMDI method in
100
90
80
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Fig. 5 Unchained LMDI for Irish Industry
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energy efficiency improvements in its economy. If a Member State wishes to apply the ODEX top-down method, then the accuracy of the method should be determined using the historical data set for that Member State. The method to determine the influence of fluctuating values as documented here could be applied. Based on the analysis in this study, it can be expected that ODEX or any other chained index will yield a less reliable result in countries or sectors where there large annual changes in energy consumption shares or where there are large fluctuations in the data for more energyintensive sub-sectors. It is worth noting that if ODEX is proven to be accurate for a particular set of historical data, this does not guarantee that the calculation will remain accurate for all potential future energy data patterns. If its accuracy for relevant sets of data is not proven or if the error is not quantified, then it is difficult to justify using a chained top-down energy efficiency indicator to compare energy efficiency improvements of countries, or to compare sectors within a country, or indeed to aggregate energy savings of several countries. With both indices, the issue remains that the energy efficiency changes recorded are the result of a number of influencing effects and not just the effects of policies such as those implemented in response to the requirements of the ESD. Horowitz (2009) maintains that an alternative econometric approach using regression provides a means of calculating a counterfactual against which real policy savings can more reliably be measured. The EMEEES project, implemented under the European Commission’s Intelligent Energy Europe programme, has recently recommended that top-down methods be used only for individual disaggregated indicators for which reliable unit consumption values can be derived, as opposed to an ODEX aggregate indicator, as these are better suited to capture the effects of policies (Thomas et al. 2009). The authors intend to carry out the analysis developed here using data from other countries, in order to compare and contrast with the results from Ireland. Furthermore, it is worth assessing how the LMDI approach could be applied to all sectors of the economy, using a mix of different physical indicators, as used by ODEX, to achieve a reliable economywide energy efficiency indicator. Acknowledgements The authors wish to acknowledge the helpful input from Wolfgang Eichhammer and Martin Howley and the feedback and suggestions from Bruno Lapillonne. The authors also acknowledge the funding support for this research
Energy Efficiency (2010) 3:317–329 by Sustainable Energy Ireland. This research builds on work presented by the authors at the ECEEE Summer Study 2009.
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