MIT Global Change Joint Program Report 29

Massachusetts Institute of Technology
Joint Program on the Science and Policy of Global Change


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Report #29. Analysis of CO2 Emissions from Fossil Fuel in Korea: 1961-1994

by Ki-Hong Choi, November 1997

1. Introduction

This study analyzes the trend of CO2 emissions from energy (especially fossil-fuel) consumption in Korea to better understand the relationship between economic growth and CO2 emissions in rapidly growing Asian economies. Korea is a particularly interesting example, as it typifies the export-led industrialization believed likely to be repeated elsewhere in East Asia.

The study spans the period 1961-94, during which Korea experienced dramatic changes in energy consumption stemming from rapid economic development. The former date is sufficiently far from the Korean War to avoid its distorting effect and the latter date is dictated by data availability. During this period, Korea shifted in common perceptions from a non-industrialized nation to one that would soon accede to membership in the Organization of Economic Cooperation and Development (OECD). Walt W. Rostow[1] has suggested that the Korean economy entered the "take-off stage" of sustained growth in 1961, estimating its drive to technical maturity to be essentially completed by the end of the 1980s--in roughly one-third the time required by currently industrialized countries.

This study explores the relationship between national output and total CO2 emissions by analyzing CO2 intensity, which is defined as the ratio of CO2 emissions to national output. The analytical method used is Divisia decomposition (or index) analysis, a useful tool for quantifying factors contributing to changes in a variable of interest. A number of studies have examined the two factors (i.e., improvement in energy efficiency and structural change in industry) contributing to changes in aggregate energy intensity using this approach[2]. Only a few studies, however, notably Tornvager (1991), Ogawa (1990), and Shrestha and Timilsina (1996), have addressed the issue of changes in CO2 emission intensity.

The following section describes the data set and analytical method employed by the present study. The third section first analyzes the changing pattern of energy consumption descriptively, then proceeds to a detailed analysis of CO2 intensity by Divisia decomposition. The final section summarizes results of the analysis and their implications. Several appendices provide lengthy technical details and data used in the analysis.

2. Data and Analytical Method

2.1 Data

Our data set (depticted in Figure 1) includes sectorial energy data (collected over a longer period than is usually available for a rapidly industrializing country), real GNP, and CO2 emission coefficients.

2.1.1 Energy Data

This study draws upon sectorial energy consumption data generated since the early 1960s that has not been readily available, which we obtained from:
* The official Yearbook of Energy Statistics, compiled by KEEI (Korea Energy Economics Institute), for the period 1975-94 (sectorial energy data began to be collected officially by Korea during 1975 as a result of the 1970s oil crisis--which also spurred the Korean government to establish its Ministry of Energy and Resources in 1978).

* A report by the Korea Institute of Energy and Resources (KIER), for the period 1961-74[3], a data set compiled by disaggregating the official energy supply data, based on a Korean input-output table produced by Bank of Korea.
The "intersection" of these two smoothly connecting data sets defines the data used in this study (Table 1). Note that:
* The sectorial classification does not include the power sector, which consumes a huge amount of fossil fuel in the conversion to electricity. We therefore drew upon supplementary data from the Yearbook of Energy Statistics for power-sector fuel input, to include all the primary energy data needed to compute CO2 emissions in Korea. The supplementary information is used indirectly, through the emission coefficient of electricity.

* Wood was used as fuel mostly for residential, noncommercial purposes; we include it because it has generally been replaced by commercial anthracite briquette.

Figure 1. Graphical depiction of energy data used in this study (1961-94).

Table 1. Specifications for Korean Energy Data (1961-94)
Number of sectors: 4 Industry; Transportation; Residential and commercial; Public, etc.
Number of fuel types: 6
 Anthracite; Bituminous coal; Petroleum; Gas; Electricity; Wood
Unit: TOE
 All fuel converted to tons of oil equivalent (TOE = 107 Kcal)

2.1.2 Emission Coefficients

The CO2 emissions from fossil fuel are not so much related to specific burning conditions as they are proportional to the carbon content of the fossil fuel. Thus, the amount of carbon C emitted from a fossil fuel can be determined from the emission coefficient (in units of tons of carbon per ton of oil equivalent, TC/TOE) for the fossil fuel:

[1]

where Eks is the energy of type k consumed in sector s and , is the corresponding emission coefficient.

The emission coefficient of electricity is unique in this study, being defined as the amount of CO2 emitted during the generation of one unit of electricity consumed by a final user (as noted above in the description of our data set, power sector emissions are included indirectly through the emission coefficient of electricity). According to this definition, the emission coefficient of electricity is determined by the formula (for k = electricity, s = all sectors):

[2]

The fossil-fuel input data necessary to compute this parameter are provided in Appendix 3. Figure 2 displays trends for all emission coefficients examined, during the study period. For electricity, the fuel mix used in power generation appears to be a determining factor[4] in the value of the emission coefficient: nuclear power generation, in particular, has served a primary role in lowering the emission coefficient of electricity in Korea since the late 1970s--in fact, the sharp decrease in the emission coefficient of electricity to an all-time low in 1987 can be attributed primarily to two nuclear power units (2 x 900 MW) introduced in late 1986. (Only one unit generally has been introduced during any given year.)

Figure 2. CO2 emission coefficients for Korea (1961-94).

2.2 Analytical Method

This study employs Divisia decomposition (or index) analysis, a useful tool for quantifying factors contributing to changes in a variable of interest. Since Boyd et al. (1987) first applied the Divisia index[5] method to analyze sources of change in U.S. manufacturing energy intensity, a fair number of studies have utilized the method. A recent survey by Ang (1995) lists more than 50, among which a number have examined the factors (i.e., improvement in energy efficiency and structural change in the industrial energy intensiveness) contributing to changes in aggregate energy intensity using this approach. However, only a few studies in the literature, notably Tornvager (1991), Ogawa (1990), and Shrestha and Timilsina (1996), have addressed the issue of changes in CO2 intensity.

2.2.1 CO2 Intensity

CO2 intensity, defined as the ratio of CO2 emissions (C, defined in Equation [1]) to national output (Y, usually measured by gross national product, GNP, or gross domestic product, GDP), can be represented as the product of the term C/E and conventional energy intensity (E/Y) as follows:

[3]

where is the total energy consumtiopn of the (Korean) economy. Rewriting the first term on the right-hand side yields the following weighted average of individual emission coefficients:

[4]

where fks = Eks / E is the share of energy type k consumed in sector s, from the total energy consumption (cf., Table 1). Thus we define C/E as the aggregate CO2 emission coefficient.

2.2.2 Divisia Analysis

Divisia analysis, which can be understood as a numerical technique for index analysis, assumes all variables to be functions of time, and positive[6]. Applying Divisia analysis to Equation [3] yields the following identity [7]:

[5]

where we denote the logarithmic differentiation operator dlog()/dt by a "hat" over variables. We can further analyze the aggregate emission coefficient identity, Eq. [4], as follows[8]:

[6]

The right-hand side (RHS) of Eq. [6] is the product of two Sato-Vartia indices (cf. Ang and Choi, 1997), which can be interpreted as the energy share effect and the Divisia aggregate emission coefficient, respectively. Though the Tornqvist index has conventionally been used for such applications as this, we needed to use the Sato-Vartia formula here because of the following "zero-value problem."

2.2.3 Zero-Value Problem

As mentioned in the previous section, Divisia analysis assumes all variables to be positive. Our data set, however, contains 31% zero values[9] (mostly relating to emerging new gas energy and the disappearing use of traditional wood), so the Tornqvist index formula cannot be used consistently over the entire study period (cf. Shrestha and Timilsina, 1996, p. 290). In principle, this "zero-value problem" is trivial if the formula converges to some finite value when a variable tends from the positive toward zero[10]: though zero is not a legitimate argument of the logarithmic function, we can define the function at zero to be the limiting value. The problem lies in the fact that the conventional Tornqvist index formula has no limiting value at zero: the numerical experiment in Appendix 2 shows the formula to be unreliable for data including zero or near-zero values. The Sato-Vartia index formula, on the other hand, has a limiting value at zero, so we can apply Divisia analysis to the whole study period, regardless of zero values.

3. Analysis of Korean Emissions Growth

This section presents results of our case study of Korea to better understand the relationship between national output and total CO2 emissions, based on the data and analytical method developed in the previous section. The approach is to analyze CO2 intensity (the ratio between CO2 emissions and national output), which can be represented as the product of conventional energy intensity and aggregate emission coefficients, as defined in the previous section. First, we provide a detailed descriptive analysis of the data, then present results of a Divisia decomposition analysis of CO2 intensity.

3.1 Macro Trend

Figure 3 displays the GNP, energy consumption, and carbon emissions indices for Korea from 1961 through 1994. During this period, Korean GNP increased more than 14 times, at a rate of about 8.0% per annum. While the nation's well-known economic growth has served as its primary driver of energy demand and CO2 emissions, these have grown more slowly (roughly 7.5% and 7.0% per annum, respectively) than GNP over the study period.

Figure 3. Aggregate GNP, energy consumption, and carbon emissions in Korea (1961-94).

3.2 Energy Consumption and CO2 Emissions

3.2.1 Energy Consumption Pattern

During the 34-year study period, Korea's pattern of energy consumption changed completely, as Figure 4 depicts. Traditional energy sources such as wood and anthracite (South Korea's only native fossil fuels) were replaced by such imported fossil fuels as petroleum, bituminous coal, and liquefied natural gas (LNG). Non-carbon nuclear power plants' introduction to Korea in recent years has clearly played an important role in reducing CO2 emissions.

Figure 4. Primary energy consumption shares in Korea (1961-94).

3.2.2 CO2 Emission Pattern

CO2 emission was computed by applying the emission coefficients to the nation's energy consumption data. Figures 5 and 6 depict the sources of Korea's CO2 emissions, by energy source (fossil fuel) and by sector, respectively. Figure 5 may illustrate three points:
* Korea's entire increase in carbon emissions during the 34-year study period is attributable to the use of imported fuels that accompanied the nation's economic transformation.

* CO2 emissions rose sharply after the mid-1980s, mainly due to increased petroleum use (primarily for industry[11] and transportation purposes, as shown in Figure 6).

* Nuclear power has reduced the country's emissions significantly: had Korea installed bituminous-coal rather than nuclear-power plants, the nation would have emitted, as of 1994, more than 15% of its total CO2 emissions in addition to its actual emissions, as shown by the hatched area.

Figure 5. Korea's CO2 emissions, by fossil fuel (1961-94).

Figure 6 illustrates the changes in sectorial composition that occurred. The residential and commercial (R&C) CO2 emissions component--more than 80% in 1961--declined to less than 25% in 1994, while the industry component--less than 30% in 1961--increased to more than 60% in 1994. The transportation sector's change in share of emissions was also remarkable. Another point of note is that after the mid-1980s, emissions from R&C essentially stabilized, as the rapid drop in residential consumption of carbon-intensive anthracite (see Figure 1) essentially canceled out that sector's natural increase in energy demand.

Figure 6. Korea's CO2 emissions, by sector (1961-94).

3.3 Divisia Decomposition

The framework of our Divisia decomposition can be depicted as follows: Eqs. [5] and [6] correspond to the first level and the second level, respectively. Note that only the aggregate emission coefficient is analyzed to the second level (Eq. [6]). Most studies further analyze energy intensity, as well, to determine the contributions of individual energy intensities and industrial structure. However, we cannot analyze the energy intensity further, because our sectorial classification prevents a clear interpretation of sectorial output share.

3.3.1 First-Level Analysis

Figure 7 results from our index analysis based on the identity in Eq. [5], which indicates that changes in CO2 intensity can be analyzed in terms of both the change in energy intensity (energy per unit of national output, e.g., GNP) and the change in aggregate emission coefficients (CO2 emission per unit of aggregate energy)[12]. We rewrite Eq. [5]:

[5']

Figure 7 indicates that the energy intensity and aggregate emission coefficient, overall, combined to lower the CO2 intensity more than 30% during 34 years of condensed growth. The analysis shows, in addition, that the aggregate emission coefficient contributed more to CO2 intensity than did energy intensity.

The first component, energy intensity, which fell rapidly during the 1960s and 1980s, increased considerably in the early 1980s[13] and since the late 1980s. In fact, despite considerable fluctuation during the intervening years, energy intensity in 1994 was at the same level it had been in the late 1960s. The second component--aggregate emission coefficient (CO2 emission per unit of aggregate energy input)--declined more steadily, proving by the end of the study period to be slightly more important than the decline in energy intensity.

Figure 7. Analysis of CO2 intensity of Korea (1961-94).

3.3.2 Second-Level Analysis

As explained in the previous section, the change in aggregate emission coefficient (as determined by our first-level analysis) can be analyzed further to yield the energy share effect (weighted changes in energy share, e.g., substitutions of lower-carbon energy forms) and the emission coefficient effect (weighted changes in individual emission coefficients):

[6]

Figure 8 results from our index analysis based on the identity in Eq. [6]. For purposes of comparison, the figure is drawn to the same scale as Figure 7. Figure 8 indicates that changes in energy share and in individual emission coefficients combined to lower the aggregate emission coefficient during the study period. Interestingly, until the first nuclear power plant was introduced in 1977, the effect of energy share on the aggregate emission coefficient overshadowed the effect of changes in the emission coefficient, while the relative magnitudes of these two factors reversed following the introduction of nuclear power.

Possible explanations follow for the trends in energy share:

* The increase from the mid-1970s through the mid-1980s resulted from rising use of bituminous coal, as well as electrification (electricity is a carbon-intensive energy source because of its significant conversion losses; see Figure 2).

* The decline after the mid-1980s reflects the rapid disappearance of anthracite (use of which peaked in 1987) in residential and commercial use, and rapid improvement in the electricity emission coefficient due to the introduction of nuclear power on a large scale.

The emission coefficient effect[14] derives essentially from the electricity emission coefficient and the share of electricity in total energy usage. The electricity emission coefficient declined steadily as the power sector began to use oil since the early 1960s, and then nuclear power after 1977. Since the early 1990s, however, the electricity emission coefficient has increased, reflecting the decline of nuclear power in electricity generation and increased use of more conventional fuels, including LNG.

Figure 8. Analysis of the aggregate emission coefficient for Korea (1961-94).

4. Summary and Conclusions

The present study was conducted to determine the relationship between national output and total CO2 emissions from fossil-fuel consumption. For purposes of this research, Korea during 1961-94 seemed especially suitable, as that case typifies the export-led industrialization believed likely to be repeated elsewhere in East Asia: during the 34-year study period, Korea's energy consumption pattern changed completely--a phenomenon that generally required more than a century for countries that industrialized earlier.

We analyzed the observed CO2 intensity (the ratio of CO2 emission to national output) through two levels of Divisia decomposition:

* The first level splits CO2 intensity into the contributions of energy intensity and aggregate emission coefficient (the ratio of CO2 emissions to aggregate energy).

* The second level further analyzes the aggregate emission coefficient, splitting it into the contributions of energy share and individual emission coefficients.
Our major findings regarding the sources of change in Korean CO2 intensity during 1961-94 are:
* The aggregate emission coefficient contributed to CO2 intensity more than did energy intensity, emphasizing the significant role of energy substitution in reducing CO2 emission in a rapidly developing economy.

* The emission coefficient contributed to the aggregate emission coefficient more than did energy share (mainly due to nuclear power's significant share in the Korean power sector), implying the importance of the power sector in reducing CO2 emissions.
Since Korea has unique characteristics (in terms of natural resource endowment and industrial structure, for example), international comparisons using the type of analysis presented here would be helpful to determine the validity of these findings more broadly.

References

Anderson, R.G. and B.E. Jones and T.D. Nesmith (1997), "Monetary Aggregation Theory and Statistical Index Numbers," in Review, Federal Reserve Bank of St. Louis, January/February, pp. 31-51.

Ang, B.W. and Ki-Hong Choi (1997), "Decomposition of Aggregate Energy and Gas Emission Intensities for Industry: A Refined Divisia Index Method," The Energy Journal, Vol. 18, No. 3, pp. 59-73.

Barnett, W.A. (1982), "Divisia Monetary Aggregate: Compilation, Data, and Historical Behavior," Staff Study 116, Washington, Board of Governors of the Federal Reserve System.

Boyd, G., J.F. McDonald, M. Ross and D.A. Hanson (1987), "Separating the Changing Composition of US Manufacturing Production from Energy Efficiency Improvements: A Divisia approach," The Energy Journal, April, pp. 77-96.

Diewert, W.E. (1976), "Exact and Superlative Index Numbers," Journal of Econometrics, May, pp. 115-145.

Farr, T. and D. Johnson (1985), "Revision in the Monetary Services (Divisia) Indices of the Monetary Aggregate, Staff Study 147, Washington, Board of Governors of the Federal Reserve System.

Hulten, C.R. (1973), "Divisia Index Numbers," Econometrica, Vol. 41, No. 6, November, pp. 1017-1025.

Lau, L. (1979), "On Exact Index Numbers," Review of Economics and Statistics, Vol. 61, February, pp. 73-82.

Korea Institute of Energy and Resources (1982), "A Study on the Planning of Energy Demand and Supply," KE-82P-40, pp. 308-326.

Ministry of Trade, Industry, and Energy and Korea Energy Economics Institute (1996), Yearbook of Energy Statistics, Seoul, Republic of Korea.

Frisch, R. (1930), "Necessary and Sufficient Conditions Regarding the Form of and Index Number Which Shall Meet Certain of Fisher's Tests," Journal of American Statistical Association, December, pp. 397-406.

Frisch, R. (1936), "Annual Survey of General Economic Theory: The Problem of Index Numbers," Econometrica, January, Vol. 4, No. 1, pp. 1-38.

Samuelson, P.A., and S. Swamy (1974), "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, Vol. 64, pp. 566-593.

Sato, K. (1976), "Ideal Log-Change Index Number," The Review of Economics and Statistics, 58, pp. 223-228.

Shrestha, R.M. and G.R. Timilsina (1996), "Factor affecting CO2 intensities of power sector in Asia: A Divisia decomposition analysis," Energy Economics, 18, pp. 283-293.

Torvanger, A. (1991), "Manufacturing Sector Carbon Dioxide Emissions in Nine OECD Countries, 1973-87," Energy Economics, July, pp. 168-186.

Theil, H. (1973), "A New Index Number Formula," Review of Economics and Statistics, 55, November, pp. 498-502.

Vartia, Y.O. (1976), "Ideal Log-change Index Numbers," Scandinavian Journal of Statistics, pp. 121-126.

Appendix 1. Divisia Decomposition of the Aggregate Emission Coefficient

First, we apply Divisia analysis to the identity of the aggregate emission coefficient, breaking the coefficient down to two Divisia integral indices (see Eq. [5] in the main text). Our next task is to find a discrete approximation formula for the continuous integral index formula.

A1.1 Divisia Integral Index

Logarithmic differentiation (dlog /dt ) of both sides of the aggregate emission coefficient identity, (see Eq. [3] in the main text), yields:

, where (dlog /dt = ^) [A1-1]

Integrating both sides of Eq. [A1-1] over the interval [0, T] yields:

[A1-2]

Taking the natural exponential for both sides results in the form:

[A1-3]

The first term of the right-hand side (RHS) can be interpreted as the Divisia integral index of energy share, and the second term as the Divisia integral index of emission coefficients. We next determine a discrete version of this formula.

A1.2 Discretization

The following log-change identity approximates the Divisia integral index:

[A1-4]

where is the value of the weight function (see Eq. [A1-2]) at point t*[0,T]; since the precise point is unknown, the log-change formula is an approximation. The conventional Tornqvist log-change formula uses a weight function that is the arithmetic average of two end-point weights:

[A1-5]

The Tornqvist formula, however, has the functional flaw of the "zero-value problem" described in the main text--a weakness that necessitates our using a different weight function.

A1.3 Sato-Vartia index

Sato (1976[15]) proposed a weight function termed the normalized logarithmic mean (log-mean) weight[16]. The "log-mean" of two positive numbers is defined by:

, for x, y greater than 0 , and x not = y [A1-6]

We define L(x,x) = x, the limit of L(x,y) as y -> x. Substituting the normalized log-mean weight in Eq. [A1-4] produces an identity, even though we do not know the exact point t*[0,T].

The normalized log-mean weight is defined:

[A1-7]

where . Inserting the weights defined by Eq. [A1-7] into Eq. [A1-4] yields the following identity:

[A1-8]

We can prove Eq. [A1-8] is an identity by comparing the natural exponents of its right- and left-hand sides:

[A1-9]

The exponent of the RHS in Eq. [A1-9] leads to that of the LHS, as follows:

[A1-10]

[A1-11]

[A1-12]

[A1-13]

Our analysis is based on the identity, Eq. [A1-8]; Appendix 2 shows that this Sato-Vartia formula does not have the zero-value problem.

Appendix 2. Numerical Treatment of a Zero-Value Problem with the Log-Change Index

This appendix explains the numerical techniques used in Divisia decomposition analysis, especially its second-level analysis, described in the main text. The mathematical definitions used here are identical to those given in Appendix 1.

Even though a zero value is not allowed in the log-change formula, the formula can be defined for zero if a limit (approached from the right-hand side of zero) for the formula exists. It can be shown that the Sato-Vartia index formula (defined in Appendix 1) has a limit at zero, by determining the limit of Eq. [A2-1] analytically:

[A2-1]

If the assumption is plausible, we can proceed as follows:

[A2-2]

[A2-3]

[A2-4]

[A2-5]

[A2-6]

[A2-7]

[A2-8]

Thus, we can define . Such a definition is not possible for the Tornqvist formula, however, because . Since this limiting property is rather qualitative, we quantify its significance through the following numerical experiment.

A2.1 Numerical Experiment

The data set for this experiment is that specified in the main text, containing 31% zero values. In the identity of the aggregate emission coefficient (Eq. [6] in the main text). Obviously the right-hand side (RHS) cannot be applied to such a data set, since zero is not permitted for logarithmic functions.

[A2-9]

Let us therefore denote the original data set by D and define a sequence of new data sets, D1, D2, D3,..., Dn, such that (Dn -> D) to be used for the RHS in place of the original data set. They are constructed by replacing every zero in the original data set D with an arbitrary small positive number, e.g., 10-1, 10-3, 10-5, 10-7, 10-9, 10-12, 10-15, 10-18.

After applying the original D to the LHS of Eq. [A2-9] and the data set Dn constructed to the RHS, we check the discrepancy between the two sides of the equation. If the discrepancy shrinks as we apply (Dn -> D) to the log-change formula of RHS, then the formula do not have the zero-value problem.

A2.1.1 Unsuitability of the Tornqvist Formula

The following figure was prepared by applying the Tornqvist formula to the RHS of Eq. [A2-9], for each data set, D1, D2, D3,..., Dn. Note that the discrepancy between the two sides of the equation increases as (Dn -> D).

Figure A2-1. Test of the Tornqvist Formula for Zero Values

A2.1.2 Suitability of the Sato-Vartia Formula

Employing the Sato-Vartia formula in a similar experiment, we can confirm that the LHS rapidly converges to the RHS: Except for the case of a data set in which every zero of the original data set is replaced by a (rather large) 0.1, the RHS and LHS are essentially equal, within a precision range of 10-5. Even in that case of 0.1, the maximum discrepancy between the LHS and RHS is negligible (less than 0.003%). Results of this experiment follow:

Table A2-1. Test of the Sato-Vartia Formula for Near-Zero Values

LHS
 RHS(10^-1) Difference % Difference
61 1.00000 1.00000 0.00000 0.00000%
620.99449 0.99449 0.00000 0.00000%
63 0.99226 0.99226 0.00000 0.00000%
64 0.99765 0.99765 0.00000 0.00000%
65 0.99801 0.99802 -0.00001 0.00100%
66 0.98005 0.98005 0.00000 0.00000%
67 0.97177 0.97178 -0.00001 0.00103%
68 0.95731 0.95732 -0.00001 0.00104%
69 0.93151 0.93152 -0.00001 0.00107%
70 0.91590 0.91592 -0.00002 0.00218%
71 0.90831 0.90832 -0.00001 0.00110%
72 0.90419 0.90420 -0.00001 0.00111%
73 0.90927 0.90929 -0.00002 0.00220%
74 0.90866 0.90868 -0.00002 0.00220%
75 0.92567 0.92568 -0.00001 0.00108%
76 0.91874 0.91876 -0.00002 0.00218%
77 0.91634 0.91636 -0.00002 0.00218%
78 0.90269 0.90271 -0.00002 0.00222%
79 0.89202 0.89203 -0.00001 0.00112%
80 0.89555 0.89557 -0.00002 0.00223%
81 0.90414 0.90416 -0.00002 0.00221%
82 0.91174 0.91176 -0.00002 0.00219%
83 0.90223 0.90225 -0.00002 0.00222%
84 0.89770 0.89772 -0.00002 0.00223%
85 0.88172 0.88174 -0.00002 0.00227%
86 0.84685 0.84687 -0.00002 0.00236%
87 0.81097 0.81099 -0.00002 0.00247%
88 0.82707 0.82709 -0.00002 0.00242%
89 0.80851 0.80853 -0.00002 0.00247%
90 0.79615 0.79617 -0.00002 0.00251%
91 0.79394 0.79396 -0.00002 0.00252%
92 0.79396 0.79397 -0.00001 0.00126%
93 0.79531 0.79533 -0.00002 0.00251%
94 0.80619 0.80621 -0.00002 0.00248%

Appendix 3. Emission Coefficient of Electricity

Input Energy (1000 TOE) (Ton of Oil Equivalent) CO2 Emissions Output Energy
Anthracite Bituminous B-C Other Oil Diesel Naptha LNG Nuclear Hydro TC/TOE 1000TC 1000 TOE TC/TOE
1961 247.0 27.6 86.5 3.1 13.0 0.0 0.0 0.0 143.9 1.12 396.5 102.2 3.880
1962 302.9 33.9 106.1 3.8 16.0 0.0 0.0 0.0 176.4 1.08 486.1 126.1 3.855
1963 377.1 31.0 127.7 13.3 6.6 0.0 0.0 0.0 182.3 0.88 585.5 145.5 4.024
1964 513.6 14.1 145.4 12.3 7.9 0.0 0.0 0.0 187.7 0.88 736.0 174.8 4.211
1965 711.5 1.0 113.7 7.1 4.1 0.0 0.0 0.0 177.6 0.85 907.7 210.5 4.312
1966 605.4 0.0 321.7 9.5 4.7 0.0 0.0 0.0 245.7 0.84 973.5 260.6 3.736
1967 587.4 0.0 618.5 24.9 85.5 0.0 0.0 0.0 237.8 0.64 1296.7 332.8 3.896
1968 592.8 0.0 791.1 26.4 228.4 18.9 0.0 0.0 230.3 0.00 1593.4 414.3 3.846
1969 463.5 0.0 1218.0 15.7 134.3 49.3 0.0 0.0 358.2 0.00 1760.3 542.3 3.246
1970 280.0 0.0 1822.5 10.0 52.5 30.0 0.0 0.0 305.0 1996.0 659.9 3.025
1971 219.8 0.0 2165.4 2.7 24.7 5.5 0.0 0.0 329.8 2179.9 751.2 2.902
1972 253.3 0.0 2406.8 0.0 15.1 0.0 0.0 0.0 340.8 2414.5 838.4 2.880
1973 412.7 0.0 3072.1 0.0 19.1 0.0 0.0 0.0 317.1 3181.9 1029.7 3.090
1974 205.7 0.0 3539.4 0.0 60.0 0.0 0.0 0.0 479.9 3396.0 1186.5 2.862
1975 313.0 0.0 4256.3 5.0 50.5 5.0 0.0 0.0 419.1 4147.8 1321.7 3.138
1976 408.7 0.0 4835.9 0.0 51.8 11.5 0.0 0.0 449.0 4767.1 1678.4 2.840
1977 413.2 0.0 5657.7 0.0 219.9 6.7 0.0 20.0 346.5 5634.1 1953.9 2.884
1978 270.6 0.0 6040.1 8.0 612.8 0.0 0.0 580.9 445.6 6146.2 2393.3 2.568
1979 351.4 0.0 6703.0 8.8 351.4 0.0 0.0 790.7 579.8 6598.6 2678.5 2.464
1980 686.7 0.0 6731.1 153.6 108.4 0.0 0.0 867.4 487.9 6919.7 2815.0 2.458
1981 699.3 0.0 6992.7 411.9 67.1 0.0 0.0 728.0 680.1 7356.2 3046.5 2.415
1982 723.4 0.0 7325.9 611.3 91.7 0.0 0.0 947.6 489.1 7872.9 3257.7 2.417
1983 1110.5 335.5 6848.3 590.0 92.5 0.0 0.0 2244.2 347.0 8230.4 3665.3 2.245
1984 878.7 2292.3 5386.9 509.4 127.4 0.0 0.0 2954.5 585.8 8756.8 4046.4 2.164
1985 774.4 3318.7 4300.5 193.6 83.0 0.0 0.0 4189.9 968.0 8476.8 4363.0 1.943
1986 640.7 3625.5 2828.5 312.5 78.1 0.0 62.5 7079.0 1000.1 7503.6 4842.7 1.549
1987 723.8 3003.9 904.8 235.2 72.4 0.0 1972.5 9826.1 1357.2 6382.1 5518.5 1.156
1988 890.1 3767.6 2090.8 517.5 82.8 0.0 2442.7 10019.3 890.1 8995.0 6391.3 1.407
1989 824.3 3549.0 2793.4 480.8 91.6 0.0 2152.3 11837.7 1167.7 9092.9 7068.5 1.286
1990 703.5 3908.3 3595.6 573.2 234.5 0.0 2240.7 13209.9 1589.4 10310.7 8117.0 1.270
1991 686.0 3944.3 4830.4 1200.4 257.2 0.0 2315.1 14090.9 1257.6 12035.6 8976.3 1.341
1992 784.1 4328.0 5457.0 2007.2 564.5 0.0 2916.7 14144.3 1160.4 14467.3 9911.0 1.460
1993 924.8 6165.5 5549.0 1986.7 308.3 0.0 3288.3 14523.3 1507.1 16692.5 10985.1 1.520
1994 963.1 8514.0 6433.7 2195.9 385.3 0.0 4353.3 14678.0 1001.7 20981.5 12602.5 1.665
Source: Yearbook of Energy Statistics, Ministry of Trade, Industry, and Energy and Korea Energy Economics Institute, 1996.

Appendix 4. Energy Consumption Data: 1961-94

Table A4
1961-78 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978
Industry Anthracite 764.1 898.1 1021.3 1133.5 1243.5 1456.7 1286.4 1069.9 1042.7 863.3 748.3 653.7 769.5 1074.5 1418.3 1488.2 1381.4 1387.7

 Bituminous 29.2 80.8 63.1 81.5 56.3 42.8 31.6 67.3 60.0 52.8 37.0 21.7 428.4 553.6 518.8 1046.8 1386.0 1431.5

 Petroleum 268.2 394.6 508.3 595.2 689.0 932.7 1648.2 2553.8 3329.2 3861.5 4316.3 4638.0 5670.4 5455.4 6555.6 7460.6 8855.3 10053.5

 Gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Electricity 55.2 75.1 92.7 112.0 136.2 169.8 221.5 277.6 358.5 426.3 482.3 535.7 688.4 777.8 945.7 1136.1 1334.3 1682.9

 Wood 690.4 638.5 653.8 813.5 909.3 400.0 208.5 270.9 172.1 246.7 353.3 481.2 455.5 293.2 161.6 118.4 214.9 296.5

 Sum 1807.1 2087.1 2339.2 2735.7 3034.3 3002.0 3396.2 4239.5 4962.5 5450.6 5937.2 6330.3 8012.2 8154.5 9600.0 11250.1 13171.9 14852.1
Transportation Anthracite 167.0 160.2 151.4 118.0 97.6 159.6 180.2 152.0 115.1 30.0 20.1 16.4 36.3 59.3 52.0 51.5 59.5 65.1

 Bituminous 5.4 11.2 6.6 6.6 5.4 4.5 1.6 0.8 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Petroleum 392.8 403.7 373.6 333.2 493.6 761.7 1047.2 1490.4 1873.4 2317.7 2630.7 3122.3 3649.2 4065.7 3237.1 3544.7 4225.0 4605.2

 Gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Electricity 2.4 2.9 2.8 2.9 3.8 4.4 5.8 6.8 6.2 5.1 5.5 6.5 8.1 20.4 28.3 28.7 32.8 36.9

 Wood 11.5 10.8 10.6 10.7 10.5 5.7 1.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Sum 579.1 588.8 545.0 471.4 610.9 935.9 1236.6 1650.0 1995.1 2352.8 2656.3 3145.2 3693.6 4145.4 3317.4 3624.9 4317.3 4707.2
R&Commercial Anthracite 1489.1 1863.0 2414.1 2802.6 2987.0 3299.2 3064.1 3195.0 3560.5 4291.9 4468.4 4690.2 5485.8 5096.4 4970.0 5272.9 5920.4 6140.8

 Bituminous 0.4 0.6 0.9 0.8 0.7 0.6 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Petroleum 30.4 42.8 55.1 41.6 35.8 29.3 90.3 151.1 302.7 520.6 594.9 633.7 684.8 673.2 802.7 899.6 1068.9 1397.7

 Gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 1.1 1.3 2.1 4.2 5.8 6.5 7.3

 Electricity 36.1 37.1 37.1 45.5 54.7 68.5 85.0 106.3 144.6 185.3 218.0 248.9 283.7 322.3 266.6 417.5 472.4 536.2

 Wood 4808.4 4580.2 4355.9 4234.6 4117.0 3976.2 4161.0 4375.7 4164.7 3979.5 3717.0 3455.2 3169.6 3176.0 3185.8 3018.4 2854.8 2691.4

 Sum 6364.4 6523.7 6863.1 7125.1 7195.2 7373.8 7400.7 7828.1 8172.5 8977.3 8998.8 9029.1 9625.2 9270.0 9229.3 9614.2 10323.0 10773.4
Public & Others Anthracite 318.3 356.6 401.4 352.3 273.4 299.8 277.0 219.3 265.7 275.3 249.2 237.7 331.3 557.1 756.8 647.7 568.7 483.6

 Bituminous 0.0 0.1 0.0 0.0 0.0 0.0 0.1 0.4 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Petroleum 18.9 31.2 44.5 42.8 98.2 129.9 192.8 252.0 482.5 832.9 905.8 948.8 944.3 902.9 910.9 1043.9 1230.7 1450.6

 Gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Electricity 8.5 11.0 12.9 14.4 15.8 17.9 20.5 23.6 33.0 43.2 45.4 47.3 49.5 66.0 81.1 96.1 114.4 137.3

 Wood 124.7 118.6 126.7 123.4 104.5 46.2 22.4 27.5 18.3 25.0 36.8 53.8 46.9 55.9 62.5 38.4 47.4 50.1
470.4 517.5 585.5 532.9 491.9 493.8 512.8 522.8 799.9 1176.4 1237.2 1287.6 1372.0 1581.9 1811.3 1826.1 1961.2 2121.6
All Sectors anthracite 2738.5 3277.9 3988.2 4406.4 4601.5 5215.3 4807.7 4636.2 4984.0 5460.5 5486.0 5598.0 6622.9 6787.3 7197.1 7460.3 7930.0 8077.2

 bituminous 35.0 92.7 70.6 88.9 62.4 47.9 33.6 68.5 60.8 52.8 37.0 21.7 428.4 553.6 518.8 1046.8 1386.0 1431.5

 petroleum 710.3 872.3 981.5 1012.8 1316.6 1853.6 2978.5 4447.3 5987.8 7532.7 8447.7 9342.8 10948.7 11097.2 11506.3 12948.8 15379.9 17507.0

 city gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 1.1 1.3 2.1 4.2 5.8 6.5 7.3

 electric 102.2 126.1 145.5 174.8 210.5 260.6 332.8 414.3 542.3 659.9 751.2 838.4 1029.7 1186.5 1321.7 1678.4 1953.9 2393.3

 wood 5635.0 5348.1 5147.0 5182.2 5141.3 4428.1 4393.7 4674.1 4355.1 4251.2 4107.1 3990.2 3672.0 3525.1 3409.9 3175.2 3117.1 3038.0
Total Sum 9221.0 9717.1 10332.8 10865.1 11332.3 11805.5 12546.3 14240.4 15930.0 17957.1 18829.5 19792.2 22703.0 23151.8 23958.0 26315.3 29773.4 32454.3


















Industry
1807.1 2087.1 2339.2 2735.7 3034.3 3185.0 3396.2 4239.5 4962.5 5450.6 5937.2 6330.3 8012.2 8154.5 9600.0 11250.1 13171.9 14852.1
Transportation
579.1 588.8 545.0 471.4 610.9 935.9 1236.6 1650.0 1995.1 2352.8 2656.3 3145.2 3693.6 4145.4 3317.4 3624.9 4317.3 4707.2
R&Commercial
6364.4 6523.7 6863.1 7125.1 7195.2 7373.8 7400.7 7828.1 8172.5 8977.3 8998.8 9029.1 9625.2 9270.0 9229.3 9614.2 10323.0 10773.4
Public & Others
470.4 517.5 585.5 532.9 491.9 493.8 512.8 522.8 799.9 1176.4 1237.2 1287.6 1372.0 1581.9 1811.3 1826.1 1961.2 2121.6
Total
9221.0 9717.1 10332.8 10865.1 11332.3 11988.5 12546.3 14240.4 15930.0 17957.1 18829.5 19792.2 22703.0 23151.8 23958.0 26315.3 29773.4 32454.3

1979-94
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Industry Anthracite 302.1 339.9 369.6 231.8 242.8 206.3 182.7 248.4 242.4 276.3 204.4 145.5 165.7 257.1 447.8 398.0

 Bituminous 2870.4 3321.1 4906.4 5612.0 5997.4 6206.0 6307.6 6551.9 7772.4 9038.8 10058.9 10662.0 12578.6 13131.0 14878.3 15005.1

 Petroleum 10812.0 10947.7 10140.5 9321.9 9671.0 10443.6 10697.3 11857.2 12915.3 14599.8 15935.5 20014.0 24250.8 30514.4 32654.2 35881.2

 Gas 0.0 0.0 0.0 0.0 0.0 1.0 15.1 39.9 75.0 110.1 158.3 234.2 313.0 377.2 460.0 600.4

 Electricity 1869.6 1970.5 2089.4 2187.9 2435.1 2650.8 2812.0 3167.7 3642.6 4175.2 4513.9 5095.4 5605.8 6063.4 6581.2 7397.6

 Wood 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 482.2 569.0 626.1

 Sum 15854.1 16579.2 17506.0 17353.5 18346.4 19507.7 20014.7 21865.0 24647.8 28200.3 30871.1 36151.0 42914.0 50825.3 55590.5 59908.5
Transportation Anthracite 1.4 2.4 1.9 1.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Bituminous 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Petroleum 5575.5 4868.5 3679.5 4173.2 5390.3 5954.9 6645.1 7623.7 9201.0 10667.0 12186.5 14086.3 16062.2 18429.8 21010.9 23735.8

 Gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Electricity 33.4 34.2 39.8 40.4 44.2 51.9 62.3 75.7 74.2 80.1 82.6 87.0 93.8 101.1 108.2 124.4

 Wood 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Sum 5610.3 4905.1 3721.1 4215.5 5434.5 6006.8 6707.4 7699.4 9275.2 10747.1 12269.1 14173.3 16156.0 18530.8 21119.1 23860.2
R&Commercial Anthracite 8172.0 8659.5 9104.8 8629.3 9040.2 10322.9 11399.3 12032.9 11721.3 11205.0 9810.7 9027.0 7169.9 5288.4 3731.3 2266.8

 Bituminous 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Petroleum 2162.3 2221.7 3525.4 3344.3 3073.1 3438.4 3524.8 3746.7 4284.4 5330.8 6694.4 8875.7 10161.3 12404.9 14669.1 15375.2

 Gas 8.1 14.7 23.1 27.5 37.4 50.6 69.1 92.4 124.1 228.8 461.1 776.9 1159.6 1760.0 2450.1 3313.2

 Electricity 593.9 610.9 690.8 778.6 909.9 1038.3 1155.4 1252.6 1434.6 1709.8 2011.2 2420.6 2732.2 3174.3 3663.1 4321.4

 Wood 2892.1 2516.9 2492.0 2417.2 2377.8 2492.0 2031.4 1480.4 1318.5 1163.7 1032.6 796.6 617.4 239.3 172.0 237.7

 Sum 13828.4 14023.7 15836.2 15197.0 15438.4 17342.2 18180.0 18605.0 18882.9 19638.0 20009.9 21896.9 21840.4 22866.9 24685.5 25514.3
Public & Others Anthracite 80.7 103.2 94.9 73.5 55.3 70.8 50.4 54.3 42.2 45.3 42.2 21.1 0.0 12.0 0.0 0.0

 Bituminous 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 Petroleum 1415.3 1786.7 1566.9 1620.4 1786.5 1765.3 1712.5 1953.8 1971.6 1913.2 2150.9 2276.1 2200.5 1590.2 1541.4 1518.5

 Gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 67.6 82.0 117.2 143.3

 Electricity 181.6 199.4 226.5 250.8 276.1 305.4 333.3 346.8 367.1 426.2 460.9 513.9 544.4 572.2 632.7 759.1

 Wood 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
1677.6 2089.3 1888.3 1944.6 2118.0 2141.5 2096.1 2354.8 2380.9 2384.7 2654.0 2811.1 2812.5 2256.5 2291.3 2420.9
All Sectors anthracite 8556.2 9105.0 9571.2 8936.5 9338.4 10600.0 11632.3 12335.6 12006.0 11526.6 10057.3 9193.6 7335.6 5557.6 4179.1 2664.9

 bituminous 2870.4 3321.1 4906.4 5612.0 5997.4 6206.0 6307.6 6551.9 7772.4 9038.8 10058.9 10662.0 12578.6 13131.0 14878.3 15005.1

 petroleum 19965.1 19824.6 18912.4 18459.8 19920.9 21602.2 22579.7 25181.4 28372.2 32510.9 36967.3 45252.1 52674.8 62939.3 69875.7 76510.9

 city gas 8.1 14.7 23.1 27.5 37.4 51.6 84.2 132.3 199.1 338.9 619.4 1011.0 1540.3 2219.2 3027.3 4056.9

 electric 2678.5 2815.0 3046.5 3257.7 3665.3 4046.4 4363.0 4842.7 5518.5 6391.3 7068.5 8117.0 8976.3 9911.0 10985.1 12602.5

 wood 2892.1 2516.9 2492.0 2417.2 2377.8 2492.0 2031.4 1480.4 1318.5 1163.7 1032.6 796.6 617.4 721.5 741.0 863.8
Total Sum 36970.4 37597.3 38951.7 38710.7 41337.2 44998.1 46998.1 50524.2 55186.8 60970.2 65804.1 75032.3 83722.9 94479.6 103686.5 111704.0
















Industry
15854.1 16579.2 17506.0 17353.5 18346.4 19507.7 20014.7 21865.0 24647.8 28200.3 30871.1 36151.0 42914.0 50825.3 55590.5 59908.5
Transportation
5610.3 4905.1 3721.1 4215.5 5434.5 6006.8 6707.4 7699.4 9275.2 10747.1 12269.1 14173.3 16156.0 18530.8 21119.1 23860.2
R&Commercial
13828.4 14023.7 15836.2 15197.0 15438.4 17342.2 18180.0 18605.0 18882.9 19638.0 20009.9 21896.9 21840.4 22866.9 24685.5 25514.3
Public & Others
1677.6 2089.3 1888.3 1944.6 2118.0 2141.5 2096.1 2354.8 2380.9 2384.7 2654.0 2811.1 2812.5 2256.5 2291.3 2420.9
Total
36970.4 37597.3 38951.7 38710.7 41337.2 44998.1 46998.1 50524.2 55186.8 60970.2 65804.1 75032.3 83722.9 94479.6 103686.5 111704.0

[1] Rostow, W.W., Korea and the Fourth Industrial Revolution, 1960-2000, presented at the Federation of Korean Industries (September 1983, Seoul).

[2] Ang (1995) surveys more than 50 studies with many different decomposition methods; recent studies tend to use the Divisia decomposition (index) method.

[3] A Study on the Planning of Energy Demand and Supply (in Korean), KE-82P-40, pp. 308-26 (KIER: Korea Institute of Energy and Resources, formerly KEEI).

[4] Another, much smaller, factor reducing the emission coefficient of electricity is the generation efficiency improvement of the power sector. Our estimate is that the conversion efficiency of the power sector improved 0.95% annually during 1970-95, on average.

[5] The Divisia index is based on such basic economic principles as the linear homogeneity of an aggregate function, and competitive market prices.

[6] This assumption is relaxed in the following zero-value problem.

[7] Integrating the first identity over the interval yields the second identity.

[8] See Appendix 1 for the derivation. It also explain how the special functional form of the weight function transforms the approximation formula into an algebraic identity.

[9] Of 816 data elements (derived from 34 years, 6 energy types, and 4 sectors), 250 values are zero.

[10] This zero-value problem corresponds to the determiniteness test of index number theory. It should be noted that the determiniteness test is a bit controversial: Samuelson and Swamy (1974) disregard it as an old practice, saying "Frisch followed the old practice of adding a regularity conditionÉ It is so-called determiniteness test, which requires that, as some pj -> 0 or
*, the index should not go to 0 or infinity. This condition, it seems to us, is an odd one and not at all a desirable one." Sato (1976, p. 224, footnote 9) also disregarded this problem, raised by Theil (1973), by referencing Samuelson and Swamy (1974).

[11] These rising trends in energy intensity were largely due to the completion of large petrochemical complexes.

[12] This aggregate energy is sometimes referred to as the energy balance aggregate or heat-sum aggregate.

[13] During our 34-year study period, the Korean economy experienced only one period of negative growth, during 1980; that was due to political instability at the time.

[14]This term is designated in Figure 2 as Divisia Aggregate.

[15] Y. Vartia is also credited for this index.

[16] According to Tornqvist et al. (1985), the "log-mean" concept was first advanced in Tornqvist (1935, in Swedish). It is interesting that he proposed the Tornqvist index (1936), which is based on arithmetic average weight function instead of his log-mean weight function.

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