Negative-value problems of the logarithmic mean Divisia index decomposition approach

An issue that has not been fully resolved in the Logarithmic Mean Divisia Index (LMDI) decomposition approach is how to deal with negative values in the data set. We provide an analytical solution to this problem and illustrate with an example. With the issue resolved, the LMDI approach can now be generally applied to any decomposition situation.     

Zero-value problems of the logarithmic mean divisia index decomposition method

Recently, the Logarithmic Mean Divisia Index (LMDI) approach to energy decomposition has been espoused as the preferred indexing method. Whilst the LMDI method provides perfect decomposition, and is time-reversal invariant, its strategy to handle zero-values is not necessarily robust. In order to overcome this problem, it has been recommended to substitute a small value δ=10^-10–10^-20$\delta =10^{-10}–10^{-20}$ for any zero values in the underlying data set, and allow the calculation to proceed as usual. The decomposition results are said to converge as δ$\delta$ approaches zero. However, we show that under this recommended procedure the LMDI can produce significant errors if applied in the decomposition of a data set containing a large number of zeroes and/or small values. To overcome this problem, we recommend using the analytical limits of LMDI terms in cases of zero values. These limits can be substituted for entire computational loops, so that in addition to providing the correct decomposition result, this improved procedure also drastically reduces computation times.     

CO2 emissions in Greece for 1990–2002: A decomposition analysis and comparison of results using the Arithmetic Mean Divisia Index and Logarithmic Mean Divisia Index techniques

This paper deals with the decomposition analysis of energy-related CO₂ emissions in Greece from 1990 to 2002. The Arithmetic Mean Divisia Index (AMDI) and the Logarithmic Mean Divisia Index (LMDI) techniques are applied and changes in CO₂ emissions are decomposed into four factors: income effect, energy intensity effect, fuel share effect and population effect. The period-wise and time series analyses show that the biggest contributor to the rise in CO₂ emissions in Greece is the income effect; on the contrary, the energy intensity effect is mainly responsible for the decrease in CO₂ emissions. A comparison of the results of the two techniques gave an insight in the intricacies of energy decomposition. Finally, conclusions and future areas of research are presented.     

Properties and linkages of some index decomposition analysis methods

We study the properties and linkages of some popular index decomposition analysis (IDA) methods in energy and carbon emission analyses. Specifically, we introduce a simple relationship between the arithmetic mean Divisia index (AMDI) method and the logarithmic mean Divisia index method I (LMDI I), and show that such a relationship can be extended to cover most IDA methods linked to the Divisia index. We also formalize the relationship between the Laspeyres index method and the Shapley value in the IDA context. Similarly, such a relationship can be extended to cover other IDA methods linked to the Laspeyres index through defining the characteristic function in the Shapley value. It is found that these properties and linkages apply to decomposition of changes conducted additively. Similar properties and linkages cannot be established in the multiplicative case. The implications of the findings on IDA studies are discussed.     

Decomposition analysis and the mean-rate-of-change index

The mean-rate-of-change index (MRCI) is a recent addition to the suite of decomposition analysis (DA) methods. In addition to the arithmetic mean used by its originators, the MRCI can be formulated incorporating any type of mean. When the logarithmic mean is used, the MRCI is equivalent to the logarithmic mean Divisia index. The MRCI is said to produce plausible decompositions, and to be able to handle negative values. However, regarding the sign and magnitude of decomposition terms, the MRCI is affected by the same distortions and inconsistencies as other DA methods, and generally does not produce more plausible results. Moreover, the MRCI’s ability to handle negative values is not necessarily an advantage in DA studies using input–output data. Finally, the MRCI is not robust.     

Analysis of CO2 emissions in APEC countries: A time-series and a cross-sectional decomposition using the log mean Divisia method

We decompose the changes of CO₂ emissions in APEC countries over time as well as the differences of CO₂ emissions among three income groups of APEC countries at a given period of time based on the logarithmic mean Divisia decomposition approach. Among the major findings of the paper the growth in per capita GDP and population are the two dominant contributors to the increase in CO₂ emissions in most cases. Furthermore, energy efficiency and fuel switching are found to be the two most promising fields for possible cooperation between APEC member countries.     

Determinants of energy demand in the French service sector: A decomposition analysis

This paper analyzes the changes in the energy consumption of the service sector in France over the period 1995–2006, using the logarithmic mean Divisia index I (LMDI I) decomposition method. The analysis is carried out at various disaggregation levels to highlight the specifics of each sub-sector and end-use according to their respective determinants. The results show that in this period the economic growth of the service sector was the main factor that led to the increase in total energy consumption. Structure, productivity, substitution and intensity effects restricted this growth, but with limited effect. By analyzing each end-use, this paper enables a more precise understanding of the impact of these factors. The activity effect was the main determinant of the increase in energy consumption for all end-uses except for air conditioning, for which the equipment rate effect was the main factor. Structural changes in the service sector primarily impacted energy consumption for space heating and cooking. Improvements in productivity limited the growth of energy consumption for all end-uses except for cooking. Finally, energy efficiency improvements mainly affected space-heating energy use.     

Changes in the GHG emission intensity in EU-15: Lessons from a decomposition analysis

This paper analyses the reduction in greenhouse gas emissions in 15 countries of the European Union between 1990 and 2007 to find out the contribution of different countries. Using the log-mean Divisia index decomposition approach, it identifies the driving factors of emissions related to energy and other industrial activities. It also focuses on two success cases (namely Germany and the United Kingdom) and contrasts the developments with two less successful cases (namely Spain and Italy). A scenario analysis is then used to indicate the emission reduction possibility through cross-learning. The study shows that the emission intensity has reduced significantly in both energy-related activities and other processes at the aggregate level, while the performance varies significantly at the individual country level. Changes in the energy mix, a reduction in energy intensity and a reduction in the emission intensity from other process-related emissions were mainly responsible for the success in the EU-15.     

Decomposing the change of CO2 emissions: A joint production theoretical approach

This paper presents an alternative decomposition method to explore the driving forces of change in carbon emissions by using distance functions estimated by data envelopment analysis. The proposed approach can isolate the effects of changes in GDP composition and energy supply composition on the change of carbon emissions. In addition, it is capable of identifying the effects of changes in different input ratios, which may be very important if there are substitution effects among different inputs. Moreover, the proposed model can measure the effects of changes in good and bad output technical efficiencies. Consequently, this decomposition technique allows a change of carbon emissions to be decomposed into contributions from ten factors, which provides more insights for policy makers. We apply this model to decompose carbon emissions in 25 OECD counties and China. For the sample countries as a whole, the empirical results indicate that the economic growth is the crucial driver to carbon emissions increase, while the changes in GDP composition and capital–energy ratio are two main drivers to carbon emissions reduction. In particular, we discuss in detail the driving forces of China's carbon emissions change in order to propose some valuable policy implications for China from an international perspective.     

Variance analysis of global CO2 emission - A management accounting approach for decomposition study

In the context of the present worldwide concern and desperate search for policies to curtail carbon dioxide emission, the paper aims to determine the roles of major driving forces in aggravating emission and examine the possibility of emission cut without compromising economic growth. Variance analysis method, in the line of management accounting, is used to decompose the changes in emission of 156 sample countries over the period 1993-2007. The major findings suggest that in aggregate, rising per capita GDP has been about seven times more responsible than that of population in accentuating emission; decline in energy intensity has been instrumental in offsetting nearly half of their potential effects, while inter-fuel substitution and change in emission intensities have meager roles. However, wide disparities in structural composition of energy intensity and emission intensity of fuels among countries over the period, point towards the crucial role of proper energy management in lowering emission concomitant with high economic growth. Management accounting control, particularly variance analysis, at the national level can be an effective tool in identifying the weaknesses and exploring the areas where emission reduction can be possible.     

Decomposition of changes in energy intensity : A comparison of the Divisia index and other methods

The desirability of separating the effects of underlying shifts in the composition of the economy from changes in energy use patterns has been recognized by many researchers. The similarity between this decomposition of aggregate measures of energy intensity into its component parts and decomposition of aggregate output (cost) data into price and quantity indices is less well known. This paper makes some comparisons between energy intensity decomposition and the formulation of economic indices. We illustrate the useful properties of one particular index, the Divisia index in performing energy intensity decomposition.     

Criteria for the decomposition of energy systems in local/global optimizations

The decomposition of an energy system into subsystems of reduced complexity, to be optimized separately, but in a way compatible with the optimum of the global system, has been recognized as a viable solution to the problem of the design optimization of highly integrated, complex energy systems. Iterative Local/Global Optimization (ILGO) and its dynamic extension (DILGO) permit the decomposition of the global problem into smaller subproblems to be optimized separately, guaranteeing in the process that the subproblem optima eventually converge after a small number of iterations to or near to the optimum of the original global problem. The aim of this paper is to analyze the criteria for energy system decomposition, in particular with regard to the formulation of the separate subproblems and to the imposition of the constraints that affect the coupling of two or more subsystems. Three general decomposition criteria are identified and discussed with simple examples to let the mathematical formulation be analyzed critically.     

Multiple calibration decomposition analysis: Energy use and carbon dioxide emissions in the Japanese economy, 1970–1995

The purpose of this paper is to present a new approach to evaluating structural change of the economy in a multisector general equilibrium framework. The multiple calibration technique is applied to an ex post decomposition analysis of structural change between periods, enabling the distinction between price substitution and technological change to be made for each sector. This approach has the advantage of sounder microtheoretical underpinnings when compared with conventional decomposition methods. The proposed technique is empirically applied to changes in energy use and carbon dioxide (CO₂) emissions in the Japanese economy from 1970 to 1995. The results show that technological change is of great importance for curtailing energy use and CO₂ emissions in Japan. Total CO₂ emissions increased during this period primarily because of economic growth, which is represented by final demand effects. On the other hand, the effects such as technological change for labor or energy mitigated the increase in CO₂ emissions.     

Analysis and decomposition of energy consumption in the Chilean industry

With rising energy costs and climate change concerns, energy efficiency will be important in maintaining competitiveness and reducing the environmental impact of industrial activities. In this paper we study the Chilean industrial sector, which is the largest consumer of energy within the country. Energy demand and CO₂ emissions in Chile have grown rapidly in recent years while energy supply is mostly imported and subject to disruption. Therefore, it is important to understand energy consumption in this sector and determine which sub-sectors have the greatest potential to reduce energy consumption. We used the Index Decomposition Analysis (IDA), applying the Logarithmic Mean Divisia Index method I (LMDI-I), to quantify the impact of diverse driving factors on energy consumption. Furthermore, a panel data analysis was used to determine whether there are differences in energy intensity across firms with different characteristics. Our results show that energy intensity has risen over time although energy consumption remains stable. This fact supports the idea that energy efficiency policies could play an important role for the industrial sector. Additionally, energy consumption and energy intensity follow different patterns in each sub-sector; therefore we conclude that the application of differentiated sectoral policies is preferable over a single global policy.     

CO2 emissions from electricity generation in seven Asia-Pacific and North American countries: A decomposition analysis

The Logarithmic Mean Divisia Index (LMDI) method of complete decomposition is used to examine the role of three factors (electricity production, electricity generation structure and energy intensity of electricity generation) affecting the evolution of CO₂ emissions from electricity generation in seven countries. These seven countries together generated 58% of global electricity and they are responsible for more than two-thirds of global CO₂ emissions from electricity generation in 2005. The analysis shows production effect as the major factor responsible for rise in CO₂ emissions during the period 1990–2005. The generation structure effect also contributed in CO₂ emissions increase, although at a slower rate. In contrary, the energy intensity effect is responsible for modest reduction in CO₂ emissions during this period. Over the 2005–2030 period, production effect remains the key factor responsible for increase in emissions and energy intensity effect is responsible for decrease in emissions. Unlike in the past, generation structure effect contributes significant decrease in emissions. However, the degree of influence of these factors affecting changes in CO₂ emissions vary from country to country. The analysis also shows that there is a potential of efficiency improvement of fossil-fuel-fired power plants and its associated co-benefits among these countries.     

Disaggregated analysis of US energy consumption in the 1990s: evidence of the effects of the internet and rapid economic growth

This paper decomposes US energy use from 1988 to 1998 and attributes the changes in energy use to three underlying factors: activity, structure, and intensity. For this study we use a bottom-up methodology, by separately decomposing delivered energy use in six sectors: travel, freight, manufacturing industries, non-manufacturing industries, residential, and services. The most commonly used indicator of energy efficiency in the total economy, the ratio of energy consumed to unit of GDP (E/GDP) created can often be misleading. The rapid decline in the E/GDP ratio in recent years has been used to support assertions that the internet and information technologies in general have enabled improvements in energy efficiencies. However, our disaggregate analysis suggests that energy intensities on average are falling more slowly than ever before while actual energy use increased faster than at any time since 1970. The decline in the E/GDP ratio in the mid- to late 1990s owes much more to structural changes in the demand for energy services than to falling energy intensities.     

Catalytic decomposition of methane in the presence of in situ obtained ethylene as a method of hydrogen production

It is predicted that the catalytic decomposition of methane (CDM) can be a promising pro-ecological method of hydrogen production. The main drawback of this process is fast deactivation of the catalyst by the carbonaceous deposit formed on its surface. This problem can be effectively solved e.g. by methane decomposition in the presence of ethylene. However, as ethylene is expensive, an attempt was made to synthesise it in situ, in the process of oxidative coupling of methane (OCM), which was subsequently combined with the CDM process in one reactor. As OCM catalysts the sodium–calcium or lithium–magnesium oxide systems were tested, while the CDM catalyst was activated carbon. The optimum conditions of ethylene production were established and applied to conduct the combined OCM–CDM process. The combined process was found to produce hydrogen in higher yields than when only the activated carbon catalyst was used. This observation was explained by formation of catalytically active carbonaceous deposit appearing as a result of decomposition of ethylene.     

Long-term changes in CO(2) emissions in Austria and Czechoslovakia-Identifying the drivers of environmental pressures

This study presents fossil-fuel related CO(2) emissions in Austria and Czechoslovakia (current Czech Republic and Slovakia) for 1830-2000. The drivers of CO(2) emissions are discussed by investigating the variables of the standard Kaya identity for 1920-2000 and conducting a comparative Index Decomposition Analysis. Proxy data on industrial production and household consumption are analysed to understand the role of the economic structure. CO(2) emissions increased in both countries in the long run. Czechoslovakia was a stronger emitter of CO(2) throughout the time period, but per-capita emissions significantly differed only after World War I, when Czechoslovakia and Austria became independent. The difference in CO(2) emissions increased until the mid-1980s (the period of communism in Czechoslovakia), explained by the energy intensity and the composition effects, and higher industrial production in Czechoslovakia. Counterbalancing factors were the income effect and household consumption. After the Velvet revolution in 1990, Czechoslovak CO(2) emissions decreased, and the energy composition effect (and industrial production) lost importance. Despite their different political and economic development, Austria and Czechoslovakia reached similar levels of per-capita CO(2) emissions in the late 20th century. Neither Austrian "eco-efficiency" nor Czechoslovak restructuring have been effective in reducing CO(2) emissions to a sustainable level.     

Driving forces of residential CO2 emissions in urban and rural China: An index decomposition analysis

There exist many differences between urban and rural China among which residential CO₂ emissions arising from energy consumption is a major one. In this paper, we estimate and compare the energy related CO₂ emissions from urban and rural residential energy consumption from 1991 to 2004. The logarithmic mean Divisia index decomposition analysis is then applied to investigate the factors that may affect the changes of the CO₂ emissions. It is found that energy intensity and the income effects, respectively, contributed most to the decline and the increase of residential CO₂ emissions for both urban and rural China. In urban China, the population effect was found to contribute to the increase of residential CO₂ emissions with a rising tendency. However, in rural China, the population effect for residential CO₂ emissions kept decreasing since 1998.     

The stability of Pt–Ir/C bimetallic catalysts in HI decomposition of the iodine–sulfur hydrogen production process

Decomposition of HI is the key reaction of hydrogen production in the iodine–sulfur thermochemical water splitting cycle, so studies about the catalysts for HI decomposition have drawn increasing attention. In this study, a series of monometallic Pt/C((Pt/C-400, Pt/C-500, Pt/C-600, Pt/C-700 and Pt/C-800), Ir/C(Ir/C-400, Ir/C-500, Ir/C-600, Ir/C-700 and Ir/C-800) and bimetallic Pt–Ir catalysts supported on active carbon (Pt–Ir/C-400, Pt–Ir/C-500, Pt–Ir/C-600, Pt–Ir/C-700 and Pt–Ir/C-800 were prepared by the impregnation-reduction-calcination method. Their catalytic activities were evaluated for HI decomposition in a fixed bed reactor at 400 and 500 °C under atmospheric pressure. Their structures, metal particles size and distribution, and specific surface area were characterized by X-ray diffraction (XRD), Transmission electron microscopy (TEM) and Brunauer-Emmett-Teller (BET) surface area, respectively. The results showed that the bimetallic Pt–Ir catalyst had the excellent stability in terms of the anti-sintering structure and catalytic activity. Therefore, the bimetallic Pt–Ir catalysts are the good candidates to take the place of the traditional monometallic Pt/C catalyst for catalyzing the HI decomposition.