Chapter 4. Model Design and Analysis
2. Analysis of Structural Changes in the City Gas Demand Function for the Petrochemical Industry
2.2. Test for Structural Changes in the City Gas Demand Function for the Petrochemical Industry
take into account the recent structural changes in city gas consumption. This shows that there is room for improvement in the future if it can be made to reflect the structural changes.
2.2. Test for Structural Changes in the City Gas Demand Function for the Petrochemical Industry
In this section, the Bai-Perron test was performed to detect structural changes in the relative price elasticity of Bunker C/gas and LPG/gas in Equation (5), which is the city gas demand function for the petrochemical industry. The results are presented in the table below:
Table 4-3. Test for Structural Changes in the City Gas Demand Function for the Petrochemical Industry Structural change Scaled F-stat Critical-value Structural breakpoint
0 vs. 1* 243.950 13.98 2016.03
1 vs. 2* 58.131 15.72 2008.08
2 vs. 3* 51.791 16.83 2012.10
3 vs. 4 9.895 17.61 -
Note: The significance level is five percent. The values in Bai and Perron (2003) were used as critical values.
As explained in Section 2 of Chapter 3, the Bai-Perron test is a method of sequentially identifying structural breakpoints and testing whether the structural changes are significant at those times. The table above51 shows that the largest value of the F-statistic calculated for all the remaining values excluding the first and last 15 percent of the total sample is 243.950, in March 2016. When compared with the critical value, the structural change was found to be significant. Therefore, the sample was divided into two at this breakpoint, and the F-statistic was calculated using the same process above for each subsample. The results showed that the next biggest value was 58.131, in August 2008. This point is also significant. By repeating the same calculation process, the last statistically significant structural breakpoint was found to be October 2012.
Through these processes, I was able to estimate three structural breakpoints in the price elasticity of
50 The coefficient estimates of heating degree days are small due to the large values of the heating days variable. Because this is a problem with the variable unit, it is necessary to focus on significance rather than the magnitude of the coefficient value.
On the other hand, as all other variables are log-transformed, the coefficient values can be interpreted as elasticity values, and more importance can be placed on the magnitude of the coefficient estimates.
51 As this section is the first in this study to interpret the Bai-Perron test results, the results are explained in detail.
Subsequently, descriptions with this level of detail will be omitted for the steel and fabricated metal industries.
the city gas demand function for the petrochemical industry: August 2008, October 2012, and March 2016.
Figure 4-1. Structural Breakpoints in the Price Elasticity of the City Gas Demand Function for the Petrochemical Industry
Sources: Calculated city gas consumption using data from Monthly Energy Statistics; and relative energy prices using data from Petronet (https://www. petronet.co.kr, last accessed on December 5, 2019) and the Korea City Gas Association (http://www. citygas.or.kr/ info/charge.jsp, last accessed on December 5, 2019).
석유화학
PetrochemicalBC/gas
가격
Bunker C/gas priceLPG/gas
가격
LPG/gas price2.3. Estimation of the City Gas Demand Function for the Petrochemical Industry That Accounts for Structural Changes
In this section, the structural breakpoints that were estimated using the Bai-Perron test are applied to the city gas demand function for the petrochemical industry in Equation (5) to establish and estimate the city gas demand function for the petrochemical industry that takes structural changes into account.
This is expressed as the following equation:
ln yt=β0+β1ln RPBC,t+β2lnRPLPG,t+β3lnIPchem,t+β4HDDt+β01d1+β02d2+β03d3
+β11d1 lnRPBC,t+β12d2 lnRPBC,t+β13d3 lnRPBC,t +β21d1 lnRPLPG,t+ β22d2 lnRPLPG,t +β23d3 lnRPLPG,t +εt
(6)
Here, the following definitions are given:
d1=�1 if 2008.08≤t〈 2012.10, 0 otherwise
0.6 0.8 1 1.2 1.4 1.6 1.8 2
0 50 100 150 200 250 300 350
2004.01 2006.01 2008.01 2010.01 2012.01 2014.01 2016.01 2018.01
백만m3
석유화학 BC/gas 가격 LPG/gas 가격
d2=�1 if 2012.10≤t〈 2016.03, 0 otherwise
d3=�1 if t≥2016.03, 0 otherwise
Since there are three structural breakpoints, the sample is divided into four parts based on each time point. The first subsample is expressed as the standard, while the remaining subsamples are expressed as dummy variables.
The estimation results of the city gas demand function for the petrochemical industry that accounts for structural changes in price elasticity are as follows:
Table 4-4. Estimation Results of the City Gas Demand Function for the Petrochemical Industry That Accounts for Structural Changes
Variables Coefficient
estimate Standard error t-stat p-value
Constant term -6.638*** 1.392 -4.767 0.000
d1 0.469*** 0.114 4.108 0.000
d2 0.739*** 0.133 5.578 0.000
d3 -0.581*** 0.169 -3.431 0.001
Bunker C/gas 1.032*** 0.360 2.869 0.005
Bunker C/gas·d1 -0.410 0.411 -0.997 0.320
Bunker C/gas·d2 -0.459 0.603 -0.762 0.447
Bunker C/gas·d3 1.799*** 0.609 2.952 0.004
LPG/gas 0.310 0.382 0.811 0.419
LPG/gas·d1 0.423 0.449 0.942 0.347
LPG/gas·d2 1.889*** 0.631 2.994 0.003
LPG/gas·d3 0.242 0.635 0.381 0.703
Production index 2.402*** 0.324 7.423 0.000
HDD 0.000*** 0.000 4.494 0.000
R2 0.911 Adj-R2 0.904
F-stat 130.962 P-value 0.000
Note: These are the results of the OSL estimation of Equation (6). *, **, and *** refer to statistical significance at the 10- percent, 5-percent, and 1-percent levels, respectively.
According to the estimation results of Equation (6), which is a city gas demand function for the petrochemical industry that accounts for structural changes, most of the remaining variables were considerably significant except for the interaction terms between some relative prices and dummy variables. And, as with the demand function that did not account for structural changes, the estimated coefficients had positive values for the relative price (oil/gas), production index, and heating degree
days, and thus were in line with economic theory.
As this study is interested in the way the relative price elasticity of city gas demand changes, let’s focus on the significant estimates to examine the ways in which the relative price elasticity of Bunker C/gas and LPG/gas changes for each sample interval. In terms of the relative price of Bunker C/gas, the elasticity in the first interval almost tripled from 1.032 to 2.831 (=1.032+1.799) in the fourth interval.
This is because fuel demand has become sensitive to fuel price changes due to the expanded supply of dual fuel boilers in the petrochemical industry, as discussed in Sections 1 and 4 of Chapter 2.
Similar results can be seen in the changes in the elasticity of the relative price of LPG/gas. In the first interval, the elasticity was only 0.310, but in the third interval, the elasticity rose nearly sevenfold to 2.199 (=0.310+1.889).52 As discussed in Sections 1 and 4 of Chapter 2, this result can also be attributed to the fact that the price sensitivity has increased due to the competition between city gas and LPG for use as feedstocks for hydrogen production and the expanded supply of dual fuel boilers in the petrochemical and refining industries.
However, some of the above estimation results are ambiguous. As discussed in Sections 1 and 4 of Chapter 2, the price elasticity of city gas demand was expected to rise continuously due to the increased use of city gas as a feedstock and the expanded supply of dual fuel boilers. However, the estimation results differed from those expected in some intervals. For example, although the estimation results were not significant, in the case of the interaction term between dummy variables and the relative price of Bunker C/gas, the price elasticity in the second and third intervals was lower than in the first interval.
In addition, in the case of the interaction term between dummy variables and the relative price of LPG/gas, the price elasticity in the fourth interval was lower than in the third.
These results can be attributed to multicollinearity due to the similarity between the two relative price variables. Multicollinearity between independent variables amplifies the variance of coefficient estimates, thereby reducing the significance of the estimates and the accuracy of estimate values. The following table shows the correlation coefficients between two relative price variables.
Table 4-5. Correlation Between Relative Price Variables
Original data Log-transformed data
Bunker C/gas & LPG/gas 0.557 0.543
Bunker C/gas·d1 & LPG/gas·d1 0.984 0.735
Bunker C/gas·d2 & LPG/gas·d2 0.996 0.810
Bunker C/gas·d3 & LPG/gas·d3 0.996 0.895
First, let’s look at the correlation of the original data. The correlation between Bunker C oil/gas and LPG/gas that are not interaction terms is 0.557, which is not very high. However, the interaction term has a correlation of almost 1. This problem occurs due to the process of generating an interaction term with dummy variables, which have a value of 0 except for certain intervals. Looking at the log-transform data, the correlation between Bunker C/gas and LPG/gas that are not interaction terms is similar at
52 However, since the elasticity estimate of the first interval is not statistically significant, if it is considered to be zero, the elasticity of the third interval would be 1.889.
0.543. The correlation of cross terms is between 0.7 and 0.9, which is slightly lower than in the original data, but the correlation between variables is still quite high.
Therefore, it is necessary to examine what happens when only one of the two types of relative prices is added to correct this issue. The table below shows the estimated results of Equation (6), excluding the relative price of LPG/gas and related interaction terms:
Table 4-6. Estimation Results of the City Gas Demand Function for the Petrochemical Industry That Accounts For Structural Changes (excluding the relative price of LPG/gas)
Variables Coefficient
estimate Standard error t-stat p-value
Constant term -4.983*** 1.354 -3.681 0.000
d1 0.534*** 0.069 7.739 0.000
d2 0.834*** 0.105 7.953 0.000
d3 -0.523*** 0.149 -3.510 0.001
Bunker C/gas 1.379*** 0.244 5.656 0.000
Bunker C/gas·d1 -0.250 0.312 -0.802 0.424
Bunker C/gas·d2 0.953** 0.389 2.449 0.015
Bunker C/gas·d3 1.910*** 0.396 4.828 0.000
Production index 2.027*** 0.316 6.418 0.000
HDD 0.001*** 0.000 5.874 0.000
R2 0.897 Adj-R2 0.891
F-stat 163.856 P-value 0.000
Note: These are the results of the OSL estimation of Equation (6), 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.
The estimation results presented in the table above show that there is no significant change in the coefficient estimates other than the price variable. In addition, despite excluding four variables, the values of R2 and Adj-R2 are nearly the same as before (0.911 and 0.904, respectively). This is because the additional explanatory power of the excluded variables is insignificant due to multicollinearity.
However, there are significant differences in the estimates of price variables. While the estimate of Bunker C /gas·d2 was not significant and had a negative value (-0.459) previously, it was significant at the five-percent level and rose dramatically to 0.953. Therefore, these estimation results show that the elasticity of the relative price of Bunker C/gas in the city gas demand in the petrochemical industry was 1.379 in the first interval, but then increased dramatically to 2.332 and 3.289 in the third and fourth intervals, respectively. In other words, the increase in the relative price elasticity of energy due to the expansion of dual fuel boilers described in Sections 1 and 4 of Chapter 2 was confirmed numerically.
Next, let’s perform the same analysis but excluding the relative price of Bunker C/gas. The table below shows the estimation results of Equation (6), excluding the relative price of Bunker C/gas and related interaction terms.
Table 4-7. Estimation Results of the City Gas Demand Function for the Petrochemical 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 -8.965*** 1.284 -6.980 0.000
d1 0.591*** 0.108 5.444 0.000
d2 0.770*** 0.127 6.048 0.000
d3 -0.288* 0.159 -1.816 0.071
LPG/gas 1.105*** 0.272 4.070 0.000
LPG/gas·d1 0.020 0.357 0.056 0.956
LPG/gas·d2 1.600*** 0.426 3.754 0.000
LPG/gas·d3 1.758*** 0.431 4.080 0.000
Production index 2.907*** 0.303 9.603 0.000
HDD 0.000*** 0.000 2.709 0.007
R2 0.888 Adj-R2 0.882
F-stat 149.545 P-value 0.000
Note: These are the results of the OSL estimation of Equation (6), 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.
Similar to the previous case, the estimation results presented in the table above show no significant change in the coefficient estimates other than the price variable. The values of R2 and Adj-R2 also differ slightly from the previous ones (0.911 and 0.904, respectively).
However, the estimates of price variables have changed considerably. When all price variables were included, the estimated elasticity of the relative price of LPG/gas in the first interval was only 0.310, but the estimate increased to 1.105 after excluding the Bunker C oil/gas price variables. In addition, the estimate of LPG/gas·d3 was not significant, and the value was only 0.242 when all variables were included. In these results, however, it was found to be significant at even the one-percent level, and the value increased dramatically to 1.758.
Therefore, the results of this estimation show that the elasticity of the relative price of LPG/gas for city gas demand in the petrochemical industry was 1.105 in the first interval, but then increased dramatically to 2.705 and 2.863 in the third and fourth intervals, respectively. It is therefore possible to say that the increase in the elasticity of the relative energy price due to the expanded supply of dual fuel boilers and increased use of city gas for hydrogen production discussed in Sections 1 and 4 of Chapter 2 have been confirmed through an estimation model.
So far, model analyses were performed to examine the structural changes in city gas consumption in the petrochemical industry with a focus on price elasticity. The results of each analysis can be summarized as follows, focusing on changes in price elasticity:
Table 4-8. Changes in the Price Elasticity of City Gas Demand in the Petrochemical Industry
Interval
Including all variables Excluding LPG/gas Excluding Bunker C/gas
Bunker C/gas LPG/gas Bunker C/gas LPG/gas
Jan. 2004 – Jul. 2008 1.032 0.310 1.379 1.105
Aug. 2008 – Sep. 2012 0.622 0.733 1.129 1.125
Oct. 2012 – Feb. 2016 0.573 2.199 2.332 2.705
Mar. 2016 – Dec. 2018 2.831 0.552 3.289 2.863
Note: The coefficient estimates that are not significant, even at the 10-percent level, have been marked in gray.
As explained above, when the total price variable is included, the reliability of the estimation results is reduced due to multicollinearity. Therefore, the estimation results are more meaningful when excluding one of the two price variable groups. The results of each estimation are quite similar. Both the elasticity of the relative price of Bunker C/gas and the elasticity of the relative price of LPG/gas remained between 1.1 and 1.4 in the first and second intervals. However, they increased to between 2.3 and 2.7 in the third interval and further to between 2.8 and 3.3 in the fourth interval.
These results are in considerable agreement with the qualitative analytical results in Sections 1 and 4 of Chapter 2. In other words, as the energy consumption structure of the petrochemical industry has shifted in the direction of expanding the supply of dual fuel boilers and increasing the use of city gas for hydrogen production, it became easier for petroleum products and city gas to replace each other, and the elasticity of the relative energy prices has increased.