Chapter 4. Model Design and Analysis
4. Analysis of Structural Changes of the City Gas Function for the Fabricated Metal Industry
4.2. Test for Structural Changes in the City Gas Demand Function for the Fabricated Metal Industry 77
This section examines the structural changes in the city gas demand function for the fabricated metal industry. The results of the Bai-Perron test, with a focus on the relative price elasticities of Bunker C/gas and LPG/gas, are as follows:
Table 4-16. Test Results of Structural Changes in the City Gas Demand Function for the Fabricated Metal Industry
Structural change Scaled F-stat critical-value Structural breakpoints
0 vs. 1* 85.836 13.98 2011.04
1 vs. 2* 47.163 15.72 2007.01
2 vs. 3* 20.806 16.83 2013.07
3 vs. 4* 37.139 17.61 2016.04
4 vs. 5 0.000 18.14 -
Note: The significance level is five percent. The values in Bai and Perron (2003) were used as critical values.
As can be seen from the table above, the number of structural changes in the price elasticity of the city gas demand function for the fabricated metal industry were estimated at four: January 2007, April 2011, July 2013, and April 2016.56
Figure 4-3. Structural Breakpoints in the Price Elasticity of City Gas Demand in the Fabricated Metal Industry
Note: City gas consumption was calculated with the data from Monthly Energy Statistics, while relative energy prices were calculated with the data from Petronet (https://www. petronet.co.kr) and the Korea City Gas Association (https://www.citygas.or.kr).
도시가스 소비 City gas consumption
4.3. Estimation of the City Gas Demand Function for the Fabricated Metal Industry That Accounts for Structural Changes
In this section, I estimate the city gas demand function that accounts for structural changes by applying the estimated structural breakpoints to the city gas demand function for the fabricated metal industry in
56 A detailed explanation of the principle of operation and the table of results of the Bai-Perron test is omitted in this section, as it has already been provided in Section 2.2 of Chapter 3 and Section 2.2 of Chapter 4.
0.6 0.8 1 1.2 1.4 1.6 1.8 2
40 90 140 190 240 290
2004.01 2006.01 2008.01 2010.01 2012.01 2014.01 2016.01 2018.01
백만m3
도시가스 소비 BC/gas 가격 LPG/gas 가격
Equation (9). This equation is expressed as below:
ln yt=β0+β1ln RPBC,t+β2lnRPLPG,t+β3lnIPvehc,t+β4lnIPict,t +β5lnIPmetal,t+β6HDDt+
∑ β11 6+i
i=1 di,tm+β01d1+β02d2+β03d3+β04d4 +β11d1 lnRPBC,t+β12d2 lnRPBC,t+ β13d3 lnRPBC,t+β14d4 lnRPBC,t+β21d1 lnRPLPG,t+ β22d2 lnRPLPG,t +β23d3 lnRPLPG,t + β24d4 lnRPLPG,t +εt
(10) Here, the following definitions are given:
d1=�1 if 2007.01≤t〈 2011.04, 0 otherwise d2=�1 if 2011.04≤t〉2013.07,
0 otherwise
d3=�1 if 2013.07≤t〉2016.04, 0 otherwise
d4=�1 if t≥2016.04, 0 otherwise
The estimation results of the above equation are shown in the following table. Let’s examine the results by focusing on the relative price elasticity.
Table 4-17. Estimation Results of the City Gas Demand Function for the Fabricated Industry That Accounts for Structural Changes
Variable Coefficient
estimate Standard error t-stat p-value
Constant term 3.063*** 0.511 5.992 0.000
d1 0.149*** 0.039 3.807 0.000
d2 0.410*** 0.060 6.803 0.000
d3 0.548*** 0.049 11.128 0.000
d4 0.387*** 0.056 6.894 0.000
Bunker C/gas -0.103 0.142 -0.730 0.467
Bunker C/gas·d1 0.188 0.156 1.204 0.230
Bunker C/gas·d2 -0.229 0.217 -1.056 0.293
Bunker C/gas·d3 0.667*** 0.231 2.889 0.004
Bunker C/gas·d4 0.504** 0.215 2.341 0.021
LPG/gas -0.039 0.139 -0.281 0.779
LPG/gas·d1 0.285* 0.157 1.812 0.072
LPG/gas·d2 0.635*** 0.209 3.038 0.003
LPG/gas·d3 -0.110 0.228 -0.481 0.631
LPG/gas·d4 0.075 0.201 0.371 0.711 Electronic component production
index 0.124** 0.051 2.422 0.017
Automobile manufacturing
production index 0.214*** 0.069 3.093 0.002
Metalworking production index -0.075 0.142 -0.527 0.599
HDD 0.001*** 0.000 5.842 0.000
dm1 - dm111) - - - -
R2 0.978 Adj-R2 0.974
F-stat 231.402 P-value 0.000
Note: These are the results of the OSL estimation of Equation (10). *, **, and *** refer to statistical significance at the 10- percent, 5-percent, and 1-percent levels, respectively. 1) The estimation results for the coefficients of dm1 through dm11 have been omitted due to lack of space.
An examination of the relative price elasticity of Bunker C/gas shows that the coefficient estimates are not significant in the first three intervals. In the fourth and fifth intervals, however, the estimates are significant, with values of 0.667 and 0.504, respectively. For the relative price of LPG/gas, the estimates are significant in the second and third intervals but not in the rest of the intervals.
These results do not provide sufficient information to identify any particular trend. In addition, the confidence in the results may be low due to multicollinearity arising from the correlation between the variables related to the relative price of Bunker C/gas and the relative price of LPG/gas, as in previous analyses. Therefore, the estimates were calculated using one type of relative price variable, as was done for the petrochemical and steel industries.
Table 4-18. Estimation Results of the City Gas Demand Function for the Fabricated Industry That Accounts for Structural Changes (excluding the relative price of LPG/gas)
Variable Coefficient
estimate Standard error t-stat p-value
Constant term 3.446*** 0.506 6.814 0.000
d1 0.222*** 0.027 8.212 0.000
d2 0.504*** 0.058 8.698 0.000
d3 0.606*** 0.047 12.992 0.000
d4 0.449*** 0.056 8.055 0.000
Bunker C/gas -0.069 0.129 -0.538 0.592
Bunker C/gas·d1 0.405*** 0.139 2.912 0.004
Bunker C/gas·d2 0.063 0.197 0.319 0.751
Bunker C/gas·d3 0.531*** 0.161 3.298 0.001
Bunker C/gas·d4 0.520*** 0.175 2.974 0.003
Electronic component
production index 0.060 0.049 1.206 0.230
Automobile manufacturing
production index 0.250*** 0.069 3.632 0.000
Metalworking production index -0.140 0.138 -1.019 0.310
HDD 0.001*** 0.000 5.511 0.000
dm1 ~ dm111) - - - -
R2 0.975 Adj-R2 0.971
F-stat 247.569 P-value 0.000
Note: These are the results of the OSL estimation of Equation (10), excluding the interaction terms related to the relative price of LPG/gas. *, **, and *** refer to statistical significance at the 10-percent, 5-percent, and 1-percent levels, respectively. 1) The estimation results for the coefficients of dm1 through dm11 have been omitted due to lack of space.
The table above shows the estimated results after removing the relative price variables of LPG/gas and the interaction terms. The estimates for the relative price elasticity of Bunker C/gas appear to be close to zero in the first and third intervals and are not significant. The estimates for the second, fourth, and fifth intervals have a value ranging between 0.4 and 0.5, which is highly statistically significant.
Next, let’s take a look at the results of the estimation after removing the relative prices of Bunker C/gas and the interaction terms.
Table 4-19. Estimation Results of the City Gas Demand Function for the Fabricated Industry That Accounts for Structural Changes (excluding the relative price of Bunker C/gas)
Variable Coefficient
estimate Standard error t-stat p-value
Constant term 3.350*** 0.477 7.025 0.000
d1 0.116*** 0.033 3.487 0.001
d2 0.348*** 0.054 6.470 0.000
d3 0.512*** 0.046 11.146 0.000
d4 0.418*** 0.050 8.346 0.000
LPG/gas -0.096 0.125 -0.769 0.443
LPG/gas·d1 0.418*** 0.140 2.992 0.003
LPG/gas·d2 0.505*** 0.187 2.696 0.008
LPG/gas·d3 0.407** 0.161 2.520 0.013
LPG/gas·d4 0.379** 0.161 2.358 0.020
Electronic component
production index 0.147*** 0.046 3.155 0.002
Automobile manufacturing
production index 0.241*** 0.070 3.425 0.001
Metalworking production index -0.189 0.140 -1.350 0.179
HDD 0.001*** 0.000 5.993 0.000
dm1 ~ dm111) - - - -
R2 0.975 Adj-R2 0.972
F-stat 255.590 P-value 0.000
Note: These are the results of the OSL estimation of Equation (10), excluding the interaction terms related to the relative price of Bunker C/gas. *, **, and *** refer to statistical significance at the 10-percent, 5-percent, and 1-percent levels, respectively.
1) The estimation results for the coefficients of dm1 through dm11 have been omitted due to lack of space.
The relative price elasticity of LPG/gas in the table above shows that it follows a very similar trend to the relative price elasticity of Bunker C/gas. The estimate in the first interval has a value close to zero and is not statistically significant. On the other hand, the rest of the intervals have a value between 0.3 and 0.4, which are statistically significant.
A summary of the above results and the changes in the price elasticity of city gas demand in the fabricated metal industry is provided in the following table:
Table 4-20. Changes in the Price Elasticity of City Gas Demand in the Fabricated Metal Industry
Interval
Including all variables Excluding LPG/gas Excluding Bunker C/gas
Bunker C/gas LPG/gas Bunker C/gas LPG/gas
Jan. 2004 – Dec. 2006 -0.103 -0.039 -0.069 -0.096
Jan. 2007 – Mar. 2011 0.084 0.285 0.336 0.322
Apr. 2011 – Jun. 2013 -0.333 0.635 -0.006 0.409
Jul. 2013 – Mar. 2016 0.564 -0.110 0.462 0.311
Apr. 2016 – Dec. 2018 0.400 0.075 0.450 0.283
Note: The coefficient estimates that are not significant even at the 10-percent level have been marked in gray.
The price elasticity for all city gas demand functions in the first interval is not significant, and its value is close to zero. In the following intervals, the price elasticity ranges between 0.3 and 0.6, which becomes more evident in cases where only one price variable is included in the function than when all variables are included.
So, let us now examine what brought about these changes in price elasticity. The fabricated metal industry is made up of a wide variety of industries. Among them, three industries that consume large amounts of city gas are automobile manufacturing, electronic components, and metalworking. As discussed in Section 3 of Chapter 2, city gas is mainly used in the fabricated metal industry to provide heating for production facilities. Therefore, it can be helpful to examine how the production capacity or size of the production facilities of the three industries has changed during the sample period for the statistical analysis of this report. The figure below shows the production capacity indices for the automobile manufacturing, electronic components, and metalworking industries from 2014 to 2018.
Figure 4-4. Trend of Production Capacity Indices of the Automobile, Electronic Components, and Metalworking Industries
Source: Korean Statistical Information Service (http://kosis.kr, 2019.9.30.).
Note: The production capacity of each industry has been indexed with 2015 as the base year (100).
금속가공 Metalworking
전자부품 Electronic components
자동차 Automobile
It is noteworthy that, from 2004 to 2018, the production capacity of metalworking and automobile manufacturing remained somewhat stagnant, while that of electronic components rose sharply. City gas consumption is proportional to the size of the production facilities, because city gas is mainly used to provide heating for production facilities, as mentioned earlier. Therefore, it appears that the electronic components industry saw a rapid increase in its proportion of city gas consumption in the fabricated metal industry.
The table below estimates the relative price elasticity of the automobile manufacturing, electronic components, and metalworking industries using monthly data from January 2014 to December 2018.
Table 4-21. Estimation Results of the City Gas Demand Function for Sub-Industries of the Fabricated Metal Industry
Industry Variable Coefficient
estimate Standard error t-stat p-value
Automobile manufacturing
Constant term 4.830*** 0.801 6.028 0.000
LPG/gas -0.003 0.140 -0.018 0.986
Production
index 0.526*** 0.176 2.995 0.004
HDD 0.001*** 0.000 14.657 0.000
R2 0.814 Adj-R2 0.804
F-stat 81.470 P-value 0.000
Electronic Constant term 5.320*** 0.805 6.609 0.000
30 40 50 60 70 80 90 100 110 120
2004 2006 2008 2010 2012 2014 2016 2018
금속가공 전자부품 자동차
components LPG/gas 0.553*** 0.131 4.215 0.000 Production
index 0.318* 0.172 1.844 0.070
HDD 0.002*** 0.000 22.734 0.000
R2 0.909 Adj-R2 0.904
F-stat 186.976 P-value 0.000
Metalworking
Constant term 6.922*** 0.603 11.485 0.000
LPG/gas -0.036 0.075 -0.488 0.627
Production
index 0.039 0.131 0.298 0.767
HDD 0.001*** 0.000 13.968 0.000
R2 0.781 Adj-R2 0.770
F-stat 66.739 P-value 0.000
Note: These are the results of OSL estimations, which were calculated with one production variable, price variable, and temperature variable each because there were only 60 samples. *, **, and *** refer to statistical significance at the 10-percent, 5-percent, and 1-percent levels, respectively.
As can be seen from the table above, the estimates of the price elasticity of the automobile manufacturing and metalworking industries are close to zero and not statistically significant. On the other hand, the estimate of the relative price elasticity of city gas demand for the electronic components industry is 0.553, which is not small and very statistically significant.
The price elasticity of total city gas demand for the fabricated metal industry can be expressed as a function of the price elasticity of the sub-industries. However, it seems that the proportion of city gas consumption in the electronic components industry, which has a high price elasticity, has increased, which resulted in the increased price elasticity of total city gas demand for the fabricated metal industry.57
5. Chapter Conclusion
In this chapter, I analyzed the presence of structural changes in city gas consumption in the petrochemical, steel, and fabricated metal industries using monthly data from 2004 to 2018 and an econometric method.
First, the unit roots of the time series data used in the analysis were tested. In the previous studies, the unit root test was performed without accounting for the mean or breaks in the time series data. However, this study used a unit root test that accounts for breaks and showed that the time series data used in this study are stationary, meaning that they do not contain unit roots.
57 I would like to note that these conclusions have been inferred through indirect analysis. This is a limitation due to the lack of data on city gas consumption in the sub-industries of the fabricated metal industry (the city gas consumption data for sub- industries was compiled from 2014).
The analysis of structural changes in the city gas demand function for the petrochemical industry showed that structural changes occurred three times, in August 2008, October 2012, and March 2016.
The sample was then divided into four intervals, using the times of the three structural changes as breakpoints, and analyzed. The results showed that the relative price elasticity of petroleum/gas of city gas demand in the petrochemical industry had a value close to one in the first interval but gradually increased to about three in the last interval. This means that the demand for city gas in the petrochemical increased by one percent when the relative price changed by one percent in the initial stage of the sampling period, but the demand recently began increasing by three percent for the same level of change in the relative price. This is because it has become easier to replace petroleum products with city gas (and vice versa) in the petrochemical industry with the recent expansion in the supply of dual fuel boilers and increased consumption of city gas as a feedstock.
The analysis of the structural change in the city gas demand function for the steel industry revealed the following results. An analysis of the timing of structural changes showed that there had been three structural changes (November 2006, April 2011, and August 2013), as was the case in the petrochemical industry. However, the estimation of the relative price elasticity revealed the complete opposite of the results from the petrochemical industry. In the first interval, the relative price elasticity of petroleum/gas for city gas demand was between 0.3 and 0.4, but in the second to fourth intervals, the elasticity declined to near zero. This result can be attributed to the fact that Bunker C was used as fuel for the steel industry along with city gas in the initial stage of the sampling period, but the use of Bunker C rapidly decreased due to environmental and facility management problems, giving way to the use of city gas as fuel.
The analysis of structural changes in the city gas demand function for the fabricated metal industry estimated four structural changes (January 2007, April 2011, July 2013, and April 2016). The relative price elasticity of petroleum/gas for city gas demand was close to zero at the beginning of the sampling period, but rose to between 0.3 and 0.5 over time, owing to the change in the proportion of the sub- industries that make up the fabricated metal industry. In the fabricated metal industry, there are three sub-industries that consume large amounts of city gas: automobile manufacturing, electronic components, and metalworking. The relative price elasticity of automobile manufacturing and metalworking is close to zero, and electronic components was estimated to have a value of about 0.6.
The trends of the production capacities of these three industries showed that the scale of production of electronic components, including semiconductors, increased rapidly during the analysis period, while the production capacity of the automobile manufacturing and metalworking industries remained stagnant. In other words, the rapid increase in the proportion of the sub-industry with high elasticity within the fabricated metal industry led to an increase in the relative price elasticity of the entire fabricated metal industry during the analysis period.
The analysis of structural changes in the city gas demand function for each industry revealed that the timing and causes of structural changes were different for each industry, and the price elasticity and trends of changes also differed by industry. Therefore, to understand the recent structural changes in city gas consumption in the industrial sector, it is essential to use a tailored city gas demand function for each sector.