Chapter 4. Model Design and Analysis
3. Structural Changes in the City Gas Demand Function for the Steel Industry
3.3. Estimation of the City Gas Demand Function for the Steel Industry That Accounts for Structural
In this section, the estimated structural breakpoints are applied to the city gas demand function for the steel industry in Equation (7) to set and estimate the city gas demand function for the steel industry that accounts for structural changes. This is expressed as an equation as below:
ln yt=β0+β1ln RPBC,t+β2lnRPLPG,t+β3lnIPiron,t+β4HDDt +β01d1+β02d2+β03d3
+β11d1 lnRPBC,t+β12d2 lnRPBC,t+β13d3 lnRPBC,t +β21d1 lnRPLPG,t+ β22d2 lnRPLPG,t +β23d3 lnRPLPG,t +εt
(8)
Here, the following definitions are given:
53 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 60 80 100 120 140 160
2004.01 2006.01 2008.01 2010.01 2012.01 2014.01 2016.01 2018.01
백만m3
철강 BC/gas 가격 LPG/gas 가격
d1=�1 if 2006.11≤t〈 2011.04, 0 otherwise d2=�1 if 2011.04≤t〉2013.08,
0 otherwise d3=�1 if t≥2013.08,
0 otherwise
The estimation results of Equation (8), which is a city gas demand function for the steel industry that accounts for structural changes in price elasticity, are as follows:
Table 4-11. Estimation Results of the City Gas Demand Function for the Steel Industry That Accounts for Structural Changes
Variable Coefficient
estimate Standard error t-stat p-value
Constant term 0.191 0.341 0.561 0.576
d1 0.196*** 0.038 5.204 0.000
d2 0.060 0.054 1.121 0.264
d3 -0.098** 0.041 -2.401 0.018
Bunker C/gas 0.370** 0.145 2.547 0.012
Bunker C/gas·d1 -0.334* 0.175 -1.911 0.058
Bunker C/gas·d2 -0.251 0.229 -1.096 0.275
Bunker C/gas·d3 -0.399** 0.169 -2.355 0.020
LPG/gas -0.077 0.147 -0.528 0.599
LPG/gas·d1 -0.076 0.164 -0.466 0.642
LPG/gas·d2 -0.166 0.227 -0.729 0.467
LPG/gas·d3 0.306* 0.185 1.657 0.100
Production index 0.959*** 0.078 12.231 0.000
HDD 0.000*** 0.000 8.443 0.000
R2 0.823 Adj-R2 0.810
F-stat 59.572 P-value 0.000
Note: These are the results of the OSL estimation of Equation (8). *, **, and *** refer to statistical significance at the 10- percent, 5-percent, and 1-percent levels, respectively.
Let’s take a look at the above estimates, focusing on the price elasticity. First, for the relative price elasticity of Bunker C/gas in city gas consumption, the elasticity value in the first interval is 0.370.
However, it falls to 0.036 in the second interval and further to 0.119 in the third interval.54 In the last interval, it is -0.029. The elasticity, which was close to 0.4 in the first interval, plummets to around zero over time.
This is related to the structural changes in the steel industry’s energy consumption, as discussed in Section 2.2 of Chapter 2. In the early stages of the sampling period, the proportion of Bunker C consumption was quite high, and as it was in a competitive relationship with city gas, the city gas demand responded somewhat to the changes in the relative price of Bunker C/gas. However, as the proportion of Bunker C consumption declined rapidly and city gas began to be used solely in the steel industry, the analysis shows that city gas consumption came to be almost unaffected by the changes in the relative price of Bunker C/gas.
Next, let’s examine the relative price elasticity of LPG/gas in city gas consumption. Unlike the relative price elasticity of Bunker C/gas, most of the estimates are not significant. In the first three intervals, the elasticity estimates are not significant at all. In the last interval, the elasticity estimate is 0.306, which is significant at the 10-percent level. However, the p-value, which determines the level of significance, is 0.100, which means that significance may or may not be present. This is because the proportion of LPG consumption in the steel industry is too small, as described in the analysis of the estimation results of the city gas demand function for the steel industry without accounting for structural changes.
In addition to price elasticity, another point to note is the model’s explanatory power. When structural changes were not accounted for, the values of R2 and Adj-R2 were only 0.498 and 0.487, respectively.
However, when the structural changes were taken into account, these values rose to 0.823 and 0.810, respectively. This shows the importance of accounting for structural changes in model construction.
As described in Section 2.3 of this chapter, there is a high correlation between the relative price of Bunker C/gas (including interaction terms) and the relative price of LPG/gas, which creates multicollinearity. In addition, the role of the relative price of LPG/gas is very limited in the analysis of the demand function for city gas in the steel industry. Therefore, I also examined the results of an analysis that excludes the relative price of LPG/gas. The table below shows the estimation results:
Table 4-12. Estimation Results of the City Gas Demand Function for the Steel Industry That Accounts for Structural Changes (excluding the relative price of LPG/gas)
Variables Coefficient
estimates Standard error t-stat p-value
Constant term 0.053 0.337 0.158 0.875
d1 0.184*** 0.021 8.792 0.000
d2 0.057 0.046 1.262 0.209
d3 -0.091*** 0.031 -2.949 0.004
Bunker C/gas 0.336** 0.132 2.550 0.012
Bunker C/gas·d1 -0.441*** 0.151 -2.920 0.004
Bunker C/gas·d2 -0.367* 0.199 -1.849 0.066
Bunker C/gas·d3 -0.215 0.140 -1.531 0.128
54 Since the coefficient estimate for Bunker C/gas·d2 is not significant, if it is considered to be zero, the elasticity value becomes 0.370.
Production Index 0.987*** 0.078 12.652 0.000
HDD 0.000*** 0.000 8.584 0.000
R2 0.813 Adj-R2 0.803
F-stat 82.142 P-value 0.000
Note: These are the results of the OSL estimation of Equation (8), 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 table above show that there is no significant change in the overall coefficient estimates. In addition, despite excluding four variables, the values of R2 and Adj-R2, which represent the explanatory power of the model, remained almost the same. This is because the additional explanatory power of the relative price of LPG/gas is not large.
The relative price elasticity estimates for Bunker C/gas are also similar to the previous ones. In the first interval, the estimate was 0.336, but afterwards, the absolute value of the estimate declined significantly to -0.105, -0.031, and 0.121, which are near zero. The explanation for this can be found in the fact that while Bunker C and city gas competed in the steel industry in the initial sampling stage, as described above, the consumption of Bunker C has drastically decreased, resulting in an increase in the absolute amount of city gas consumption.
Table 4-13. Estimation Results of the City Gas Demand Function for the Steel 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 0.098 0.313 0.314 0.754
d1 0.253*** 0.029 8.834 0.000
d2 0.135*** 0.042 3.207 0.002
d3 -0.041 0.033 -1.257 0.210
LPG/gas 0.091 0.132 0.693 0.489
LPG/gas·d1 -0.223 0.144 -1.548 0.124
LPG/gas·d2 -0.275 0.196 -1.407 0.161
LPG/gas·d3 0.104 0.146 0.713 0.477
Production index 0.967*** 0.072 13.459 0.000
HDD 0.000*** 0.000 8.369 0.000
R2 0.816 Adj-R2 0.806
F-stat 83.714 P-value 0.000
Note: These are the results of the OSL estimation of Equation (8), 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.
The above table presents the results of the analysis using the relative price of LPG/gas as the price
variable, while excluding the relative price of Bunker C/gas.55 First, the coefficient estimates, excluding the price variable, are not much different from those of the previous analysis. On the other hand, none of the estimates of the relative price and the interaction terms appear to be not significant even at the 10-percent level. This is because LPG consumption accounts for only a small portion in the steel industry, as examined previously. Therefore, the results of the qualitative and quantitative analyses appear to be quite consistent.
The above model analysis examined the structural changes in city gas demand in the steel industry.
The results of the analysis, with a focus on changes in price elasticity, can be summarized as below:
Table 4-14. Changes in the Price Elasticity of City Gas Demand in the Steel Industry
Interval
Including all variables Excluding LPG/gas Excluding Bunker C/gas
Bunker C/gas LPG/gas Bunker C/gas LPG/gas
Jan. 2004 – Oct. 2006 0.370 -0.077 0.336 0.091
Nov. 2006 – Mar. 2011 0.036 -0.153 -0.105 -0.131
Apr. 2011 – Jul. 2013 0.119 -0.243 -0.031 -0.184
Aug. 2013 – Dec. 2018 -0.029 0.229 0.121 0.196
Note: The coefficient estimates that are not significant, even at the 10-percent level, have been marked in gray.
As can be seen from the table above, the relative price elasticity of Bunker C/gas in city gas consumption in the steel industry has a value of between 0.3 and 0.4 in the first interval, but then approaches zero afterward. This is because Bunker C was used in a significant proportion in the steel industry in the initial stages of the sampling period, and it was in competition with city gas. However, the proportion of Bunker C consumption fell sharply afterward, and city gas began to be used without competition.
In the case of the relative price elasticity of LPG/gas, it is difficult to find a significant value across all intervals, as the proportion of LPG consumption is insignificant in the steel industry.
55 Although the explanatory power of the relative price of LPG/gas is rather limited, this was also analyzed to maintain consistency with other sections.
4. Analysis of Structural Changes of the City Gas Function for the Fabricated Metal