# The Non-Linear Effect of Chinese Financial Developments on Energy Supply Structures

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. The Evolvement of Financial Development Indicators

_{2}, total stock value, the balance of treasuries, financial bonds, and corporate bonds. In fact, FIR is more often used to analyze the change of financial structure. In the 1990s, the wave of empirical research on financial development and economic growth forced scholars to create new financial indicators. King and Levine made a great contribution to it, making up the shortfall of Goldsmith’s indicator [6]. In order to investigate the relationship between financial development and economic growth, they took a sample of 77 countries from the period 1960–1989, and controlled for other potential factors that might impact on economic development. The following financial development indicators are used in their research: (1) the ratio of liquid liabilities of financial intermediary to GDP (in reality, this is always measured by M

_{2}/GDP); (2) CMB/(CMB + CEB), CMB means the total assets of commercial banks for one country, and CEB is the assets of central bank for one country. The indicator reflects financial system’s efficiency in a country, because commercial banks are usually believed to be more efficient in capital allocation than central banks; (3) the ratio of domestic credit to private sector/GDP is also used to denote financial efficiency. However, the shortcomings of their findings are the sole focus on the banking sector, and ignoring the influence of other financial markets like stocks and bonds. In 1998, Levine and Zervos supplemented several stock indexes, including stock market capitalization to GDP, stock market value traded to GDP, and stock market turnover [7,8]. Nowadays, cointegration and causality tests are still mostly used to investigate the long-running relationship among financial development, economic growth, and energy consumption [9,10,11,12,13]. In addition to the financial indicators put forward by King and Levine [6], they constructed other banking indicators like the ratio of deposit money bank assets to GDP, the ratio of financial system deposits to GDP, the ratio of liquid liabilities to GDP, and stock market variables like the number of listed companies per 10,000 people.

#### 2.2. Why Does Non-Linear Analysis Matter in the Energy Supply Model?

## 3. Data, Variables, and Model Introduction

#### 3.1. Data and Variables

_{2}, total stock value, the balance of treasuries, financial bonds, and corporate bonds when calculating the financial interrelation ratio (FIR). However, the related data are not published in a single province in China. Since that FIR is used to signify the total financial activities during one period, this paper replaces the total financial assets with the added value in the financial industry. Thus, we use the ratio of the added value in the financial industry to GDP to represent the financial correlation ratio and reflect the general financial industry development degree in a province.

#### 3.2. PSTR Model Specification

_{0}: $\gamma $ = 0, expressing no regime-switching effect in the model. However, as mentioned above, the model collapses into a linear panel regression model under the null hypothesis, thus the classical tests have no standard distribution, which results in the so-called Davies Problem [38]. One way to solve this problem is to replace the transition function $g({q}_{it-1};\gamma ,c)$ with its first-order Taylor expansion around the null hypothesis $\gamma $ = 0 [20]. When m = 1 and m = 2, respectively, the first-order Taylor expansions around $\gamma $ = 0 of the transition function $g({q}_{it-1};\gamma ,c)$ are:

_{0}: ${\varpi}_{1}={\varpi}_{2}=0$ in these auxiliary regressions. According to Colletaz and Hurlin [39], the three nonlinear statistical tests are as follows:

_{0}is the panel sum of squared residuals under H

_{0}(linear panel model with individual effects), SSR

_{1}is the panel sum of squared residuals under H

_{1}(PSTR model with two regimes), and K is the number of explanatory variables. If the linearity hypothesis is rejected, we can continue testing for no remaining nonlinearity to explore whether there are another transition functions. The test will not stop until the null hypothesis cannot be rejected.

## 4. Empirical Analysis

#### 4.1. Unit Root Test

#### 4.2. Nonlinearity Test and Transition Regime Determination

_{it-1}, LLAN

_{it-1}, LFDI

_{it-1}, and LCIR

_{it-1}to the non-linear test. There are three targets in the process of non-linear testing: (1) examine whether there is non-linearity between financial development indicators and energy supply structures; (2) pick the optimal transition variable; and (3) determine the number of transition functions and location parameters. The testing procedure works as follows. First, test a linear model (r = 0) (r is the number of transition function) of the LCSR and LTPG specifications against a model with one threshold function (r = 1). If the null hypothesis H

_{0}is rejected, this indicates the existence of nonlinearity of the model. Then proceed to the second step: test for remaining non-linearity and determine the number of transition functions. Test a one threshold (r = 1) model against a double threshold model (r = 2). The procedure is continued until the null hypothesis (H

_{0}: r = r*) is not rejected, and then r* is the optimal number of transition functions. For each specification, we compute the LM, LM

_{F}, and LRT statistics for the linearity tests. Since previous studies have documented that the F-version of the test has better size properties in small samples than the ${\chi}^{2}$ asymptotic-based statistic [7], we only report the LM

_{F}statistic of LCSR and LTPG specifications in Table 2. The LM

_{F}has an asymptotic $F(mK,TN-N-m(K+1))$ distribution under H

_{0}, where m is the number of location parameters and K the number of explicative variables. In our specifications we have K = 4.

_{0}: r = 0 vs. H

_{1}: r = 1) for all four models proved the existence of nonlinearity in LCSR and LTPG specifications. For LCSR specifications, the subsequent tests show that Model 1 and Model 2 are four-regime models, Model 3 is a three-regime model, and the number of regimes in Model 4 depends on the number of location parameters. Furthermore, the strongest rejection of the null hypothesis of linearity (H

_{0}: = 0 vs. H

_{1}: = 1) is obtained from Model 1 whenever the position parameter m = 1 or m = 2. According to González et al. (2005) [23], the variable that most strongly rejects linearity should be selected as the transition variable. Thus, in the LCSR specification, the optimal model would be Model 1, which uses the lagged one value of the ratio of added value in the financial industry to GDP (LFIR) as a threshold variable with the number of transition function r* = 3. For LTPG specification, the subsequent tests show that all four models are two-regime models. The strongest rejection of the null hypothesis of linearity (H

_{0}: = 0 vs. H

_{1}: = 1) is obtained from Model 4 whenever the position parameter m = 1 or m = 2; thus, the optimal model would be Model 4, which uses the lagged one value of the investment in the coal mining and washing industry/GDP (LCIR) as a threshold variable with the number of transition function ${r}^{*}$ = 1.

_{it-1}as the transition variable. For the LTPG specification, when m = 1, the AIC and BIC values are relatively smaller, and the corresponding optimal number of transition functions is ${r}^{*}$ = 1, thus, the model format is to be set as $({r}^{*},{m}^{*})$ = (1, 1), with LCIR

_{it-1}as the transition variable.

#### 4.3. PSTR Model Estimation

_{1}, transition function g

_{2}is nearly a zero indicator function. In Regime 3 for the third transition function, the slope parameter and corresponding location parameter are 2.9 and −3.989, respectively. In Figure 1c, the transition function has a relatively gradual incline, and the majority of threshold variables are larger than the location parameter −3.989; almost all of the transition functions g

_{3}range from 0.5 to 1.

^{–3.989}= 0.0185, e

^{–3.677}= 0.0253, e

^{–3.014}= 0.0491. According to ${\alpha}_{k}+{\beta}_{k}\times {g}_{1}+{\lambda}_{k}\times {g}_{2}+{\eta}_{k}\times {g}_{3}(k=1,\cdots ,4)$, we can calculate the threshold value in each non-linear regime. We find the elastic coefficient for LFIR ranges from 0.049 to ~0.095, indicating that the expansion of the whole financial scale is not helpful for the reduction of coal supply structure. The elastic coefficient for LLAN changes from −0.498 to −0.077, meaning that the increase of credit proportion exerts a reduction effect on the coal supply structure. In addition, when the LFIR

_{it-1}> 0.491, the elasticity increases with the increase of LFIR. When LFIR

_{it-1}< 0.0185, the elastic coefficient for FDI is small but negative, but with the increase of LFIR

_{it-1}, the elastic coefficient for FDI gradually increases. In the regime 4 with LFIR

_{it-1}= 0.0491, the coefficient is −0.126. It can be deduced that as the financial sector plays a more and more important role in the future, foreign direct investment will make a greater contribution to decreasing the coal supply. The elastic coefficient for LCIR is negative when LFIR

_{it-1}< 0.0253, and then turns positive afterwards. Based on the coefficient analysis above and considering that the ratio of added value in the financial sector/GDP will continue to increase in the future, banks should lend more money to qualified coal production businesses so as to squeeze out the inefficient enterprises. On the other hand, local governments should introduce more foreign direct investment, such that the local energy business can learn about advanced technology and management skills, and improve the energy utilization efficiency.

^{–4.724}= 0.0089), resulting in most of the circles standing for transition function values greater than 0.5 and distributing around 0.8~1. According to ${a}_{k}+{b}_{k}\times g(k=1,\cdots ,4)$, the elastic coefficient for LFIR at LCIR

_{it-1}= 0.0089 equals −0.1975, meaning that a 1% increase in the LFIR will lead to a 0.1975% reduction in the ratio of thermal power generation. With the increase of LCIR

_{it-1}, the reduction effect will be greater. To identify the exact threshold value from positive to negative of the transition function for LLAN, we transform the format of the transition function to obtain the turning point, and calculated 0.0374, indicating that when the coal mining and washing industry investment proportion (LCIR) is larger than 0.0374, there is a negative correlation between LLAN and LTPG. Conducting the same conversion for the transition function for LFDI, we achieve the turning point at 0.0234. This means when LCIR

_{it-1}is larger than 0.0234, the elastic coefficient between LFDI and LTPG is negative, and vice versa. The coefficients for LCIR are not significant in either regime, so we did not perform a detailed analysis. Based on the coefficient analysis above, augmented investment in the coal mining and washing industry is encouraged. With the increase of LCIR, the financial sector, credit market, and foreign investors will have a reduction effect in the proportion of thermal power generation. More detailed analysis of the impact of financial development and LCSR and LTPG specifications will be given in Section 5.

## 5. Discussion

#### 5.1. The Time-Varying Elasticity Analysis of the LCSR Specification

#### 5.2. The Time-Varying Elasticity Analysis of the LTPG Specification

^{−4.724}= 0.0089). When LCIR is higher than 0.0089, the model gradually moves towards a high regime state as the threshold variable increases. Otherwise, the model gradually falls towards a low regime state as the threshold variable is reduced. In the observation of 255 LCIR series, only 15 of them were smaller than the position parameter: Guangxi (2000–2003), Hubei (1999–2004), Qinghai (2000–2002, 2004), and Jiangsu (2013) accounted for 5.9% of the whole interval range. This feature can also be seen in Figure 2, which shows the transition function for LTPG specification. The intensive degree of the values of transition functions on the right of the location parameter is significantly higher than that on the left side, meaning that most observed values are above the position parameter. Thus, the thermal power generation proportion (LTPG) specification is mainly located in the high regime.

_{it-1}= 0.89% divides the model into a linear part (low regime) and a nonlinear part (high regime). Figure 2 shows that values of transition function smaller than the threshold value 0.89% were observed in Guangxi (2000–2003), Hubei (1999–2004), Qinghai (2000–2002, 2004), and Jiangsu (2003). This denotes that the elasticity coefficients in the corresponding provinces and years are in the low regime, while the others tend towards the high regime. In order to identify the transition characteristics, in Table 6 we present the individual time-varying elasticity coefficients and make a simple analysis for the four provinces (Guangxi, Hubei, Qinghai, and Jiangsu).

## 6. Conclusions and Recommendations

- (1)
- Improving the ratio of the financial industry to GDP is helpful for hindering the overproduction of thermal power generation by 0.066%~0.117%. However, it is not helpful for the decrease of the ratio of coal production in high financial development regions such as Ningxia. Therefore, the financial sector can play a useful role in resolving the coal overcapacity. As is emphasized by numerous experts, finances play a dominant role in the process of supply-side reform, so the local government should make great effort to develop the financial industry in the future, which will be very helpful in reducing the coal overcapacity.
- (2)
- The impact of loans in financial institution/GDP on the ratio of coal supply is negative in high financial development regions such as Ningxia. In middle financial development region like Sichuan, the influence is mainly negative. In Guangxi, with the development of the financial industry, the impact is first positive and then negative. The impact on thermal power generation is also first positive and then negative with the increase of investment in the coal industry. Therefore, for the region with developed finances, the bank lending more money to energy enterprises is beneficial for resolving the problems of coal overcapacity, but in low financial development regions, banks should not give credit to debased businesses. For the local government, more investment in the coal industry will result in a decrease of thermal power generation.
- (3)
- The impact of foreign direct investment/GDP on the ratio of coal supply remained negative, ranging from−0.2 to −0.1. However, its influence on thermal power generation is negligible. In the past few decades, some local governments have been actively introducing FDI to promote economic development, such that local energy businesses can learn about advanced technology and management skills and improve energy efficiency. Meanwhile, they can also optimize their energy supply structure.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Transition function for LCSR specification. (

**a**) The first transition function with slope parameter equaling to 13.027; (

**b**) the second transition function with slope parameter equaling to 9.97; (

**c**) the third transition function with slope parameter equaling to 2.90.

Variables | Statistics | p-Value | Stable or Not |
---|---|---|---|

LCSR | −3.2504 | 0.0006 | Stable |

LTPG | −7.42329 | 0.0000 | Stable |

LFIR | −2.5808 | 0.0049 | Stable |

LLAN | −5.9363 | 0.0000 | Stable |

LFDI | −4.3104 | 0.0000 | Stable |

LCIR | −3.52612 | 0.0002 | Stable |

LCSR Specification | ||||||||

Model 1 | Model 2 | Model 3 | Model 4 | |||||

Transition Variables | LFIR_{it-1} | LLAN_{it-1} | LFDI_{it-1} | LCIR_{it-1} | ||||

Number of Location Parameters | m = 1 | m = 2 | m = 1 | m = 2 | m = 1 | m = 2 | m = 1 | m = 2 |

H_{0}: $r$ = 0 vs. H_{1}: $r$ = 1 | 25.195 *** (0.000) | 16.771 *** (0.000) | 6.264 *** (0.000) | 4.963 *** (0.000) | 14.575 *** (0.000) | 7.969 *** (0.000) | 5.740 *** (0.000) | 7.934 *** (0.000) |

H_{0}: $r$ = 1 vs. H_{1}: $r$ = 2 | 3.207 ** (0.014) | 5.921 *** (0.000) | 5.336 *** (0.000) | 3.701 *** (0.000) | 1.097 (0.359) | 1.404 (0.196) | 3.157 ** (0.015) | 0.310 (0.962) |

H_{0}: $r$ = 2 vs. H_{1}: $r$ = 3 | 5.912 *** (0.000) | 3.474 *** (0.001) | 2.561 *** (0.039) | 1.941 ** (0.055) | - | - | 0.697 (0.595) | - |

H_{0}: $r$ = 3 vs. H_{1}: $r$ = 4 | 0.385 (0.819) | 0.479 (0.870) | - | - | - | - | - | - |

LTPG Specification | ||||||||

Model 1 | Model 2 | Model 3 | Model 4 | |||||

Transition Variables | LFIR_{it-1} | LLAN_{it-1} | LFDI_{it-1} | LCIR_{it-1} | ||||

Number of Location Parameters | m = 1 | m = 2 | m = 1 | m = 2 | m = 1 | m = 2 | m = 1 | m = 2 |

H_{0}: $r$ = 0 vs. H_{1}: $r$ = 1 | 2.188 * (0.071) | 4.466 *** (0.000) | 2.584 ** (0.038) | 4.544 *** (0.000) | 4.817 *** (0.001) | 3.728 *** (0.000) | 10.395 *** (0.000) | 8.591 *** (0.000) |

H_{0}: $r$ = 1 vs. H_{1}: $r$ = 2 | - | 1.404 (0.196) | - | 1.513 (0.154) | 0.670 (0.614) | 0.732 (0.664) | 1.521 (0.197) | 1.311 (0.239) |

_{0}is rejected at 1% significance level; ** denotes the null hypothesis H

_{0}is rejected at 5% significance level; * denotes the null hypothesis H

_{0}is rejected at 10% significance level.

Specification | LCSR | LTPG | ||
---|---|---|---|---|

Number of Location Parameter | m = 1 | m = 2 | m = 1 | m = 2 |

Transition Variables | LFIR_{it-1} | LFIR_{it-1} | LCIR_{it-1} | LCIR_{it-1} |

${r}^{*}$ ($m$) | 3 | 3 | 1 | 1 |

AIC | −4.275 | −4.264 | −4.672 | −4.666 |

BIC | −3.969 | −3.917 | −4.533 | −4.513 |

Transition Variables $({\mathit{r}}^{*},{\mathit{m}}^{*})$ | LFIR_{it-1} (3, 1) | |||
---|---|---|---|---|

Liner Part | Nonlinear Part | |||

Regimes | Regime 1 | Regime 2 | Regime 3 | Regime 4 |

LFIR (${\widehat{\alpha}}_{1},{\widehat{\beta}}_{1},{\widehat{\lambda}}_{1},{\widehat{\eta}}_{1}$) | −0.135 * (−1.803) | −0.266 *** (−3.056) | 0.151 ** (2.221) | 0.445 *** (2.836) |

LLAN (${\widehat{\alpha}}_{2},{\widehat{\beta}}_{2},{\widehat{\lambda}}_{2},{\widehat{\eta}}_{2}$) | −1.644 *** (−6.170) | −0.136 (−0.545) | −1.154 *** (−3.702) | 2.297 *** (4.542) |

LFDI (${\widehat{\alpha}}_{3},{\widehat{\beta}}_{3},{\widehat{\lambda}}_{3},{\widehat{\eta}}_{3}$) | 0.425 *** (4.096) | 0.268 *** (3.914) | −0.008 (−0.133) | −0.863 *** (−4.595) |

LCIR (${\widehat{\alpha}}_{4},{\widehat{\beta}}_{4},{\widehat{\lambda}}_{4},{\widehat{\eta}}_{4}$) | −0.266 *** (−4.854) | 0.112 ** (2.286) | −0.009 (−0.317) | 0.254 ** (2.539) |

Location parameter ${c}_{j}$ | −3.677; −3.014; −3.989 | |||

Slope parameter ${\gamma}_{j}$ | 13.027; 9.97; 2.90 |

Transition Variables $({\mathit{r}}^{*},{\mathit{m}}^{*})$ | LCIR_{it-1} (1,1) | |
---|---|---|

Liner Part | Nonlinear Part | |

Regimes | Regime 1 | Regime 2 |

LFIR (${\widehat{a}}_{1},{\widehat{b}}_{1}$) | −0.344 *** (−2.797) | 0.293 ** (2.351) |

LLAN (${\widehat{a}}_{2},{\widehat{b}}_{2}$) | 1.833 *** (4.466) | −1.964 *** (−4.650) |

LFDI (${\widehat{a}}_{3},{\widehat{b}}_{3}$) | 0.122 ** (1.976) | −0.142 ** (−2.330) |

LCIR (${\widehat{a}}_{4},{\widehat{b}}_{4}$) | 0.073 (1.118) | −0.085 (−1.240) |

Location parameter $c$ | −4.724 | |

Slop parameter $\gamma $ | 1.840 |

Time-Varying Elasticity between LTPG and Financial Development Indexes | Results Explanation |
---|---|

The influence of LFIR on LTPG in all provinces was negative all the time. Guangxi: In 2001–2004, the elastic coefficient was in the low regime (−0.25, −0.21), and then shifted to the high regime (−0.153, −0.062). Hubei: In 2000–2004, it was in the low regime (−0.35, −0.23), and then shifted to the high regime (−0.18,−0.055). Jiangsu: In 2014 it was in the low regime (–0.245); in other years it was in the high regime (−0.162, −0.058). Qinghai: In 2000–2002 and 2004, it was in the low regime (−0.344, −0.172). In other years, it was in the high regime, and the elastic coefficients were stabilized between −0.086 and −0.055. | |

Guangxi: Except for 2000, 2012, and 2013, the elastic coefficients were positive; in the other years they were negative. The absolute values of the elastic coefficients had a decreasing tendency before and after the turning point between the low and high regime. Hubei: The variation tendency of elastic coefficients was similar to Guangxi. In 2012–2014, the influence effect changed to be negative, and was stabilized around −0.1. Jiangsu: The elastic coefficient in 2014 was in the low regime (1.167); in other years it fluctuated around 0.1. Qinghai: The elastic coefficients in 2000–2005 were positive (0.1~1.44), but in 2006–2014 changed to be negative (−0.1~−0.023). | |

Guangxi: Generally, the absolute values of elastic coefficients showed a declining tendency, and they changed to be negative after 2010, between −0.015 and −0.003. Heilongjiang: The elastic coefficients in 2000–2009 were positive, between 0.04 and 0.12, but changed to be negative after 2010, between −0.019 and −0.007. Qinghai: In the low regime (2000–2002, 2004), the elastic coefficients were positive, between 0.038 and 0.12. The elastic coefficients in the high regime were negative, fluctuating slightly between −0.019 and −0.004. |

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Chai, J.; Xing, L.; Lu, Q.; Liang, T.; Lai, K.K.; Wang, S.
The Non-Linear Effect of Chinese Financial Developments on Energy Supply Structures. *Sustainability* **2016**, *8*, 1021.
https://doi.org/10.3390/su8101021

**AMA Style**

Chai J, Xing L, Lu Q, Liang T, Lai KK, Wang S.
The Non-Linear Effect of Chinese Financial Developments on Energy Supply Structures. *Sustainability*. 2016; 8(10):1021.
https://doi.org/10.3390/su8101021

**Chicago/Turabian Style**

Chai, Jian, Limin Xing, Quanying Lu, Ting Liang, Kin Keung Lai, and Shouyang Wang.
2016. "The Non-Linear Effect of Chinese Financial Developments on Energy Supply Structures" *Sustainability* 8, no. 10: 1021.
https://doi.org/10.3390/su8101021