Translog function in government development of low-carbon economy

A low-carbon economy fully balances the contradiction between high-speed economic growth and the gradual increase of greenhouse gas emissions, and is highly coupled with technology, environment, economy, and the industry sectors [1, 2]. It is a comprehensive economic form. This concept first appeared in researchers’ field of vision, and it was stated in the energy White Paper in 2003 that ‘it is essential to make Britain a low-carbon economy country’ [3]. On 16 February 2005, the Kyoto Protocol first restricted greenhouse gas emissions in the form of regulations [4]. The formulation of the Bali Roadmap in 2007 clarified the shared responsibility of each country based on the ratio, requiring developed countries to reduce greenhouse gas emissions by 25–40% by 2020 [5]. At this point, carbon emissions and related issues have become a political issue that is generally valued, and countries have begun to explore new driving forces and models for economic development [6, 7].

Denmark is the first country to implement a carbon tax, and its per capita carbon emissions have fallen sharply since 1996. EU-ETS, as the world's most active carbon emissions trading market, was started in the European Union in 2005. After implementing this policy, the per capita carbon emissions decline trend is obvious, and the EU is expected to achieve the goal of 21% carbon emissions reduction in the 2020s [8]. After the United States launched the Regional Greenhouse Gas Emission Reduction Initiative (RGGI) in 2009, the per capita carbon emissions declined rapidly. The ‘low-carbon economy’ is no longer the exclusive property of developed countries, but has gradually become an inevitable trend of global development [9].

With the continuous development of the economy and society, people are benefiting from development while facing increasingly serious environmental pollution, energy shortages and climate change [10, 11]. Especially, global warming caused by greenhouse gases such as carbon dioxide has become the international community.

One of the most serious challenges currently facing people's understanding of the impact of greenhouse gas emissions on the environment has also gone through a long process. The Swedish scientist, Arrhenius, had already found the possibility of global warming by burning fossil fuels through related research as early as 1896, because the use of fossil fuels would increase the concentration of carbon monoxide in the atmosphere, but people were not aware of the limits of economic and social conditions.

After the importance of this cutting-edge research achievement at that time, after >50 years of silence, until the late 1950s, Western scholars slowly realised the link between greenhouse gases and global climate change, and carried out relevant research. However, although the knowledge that greenhouse gas emissions will cause global climate change is gradually understood and accepted, no practical measures have been taken to control greenhouse gas emissions. Until the early 1990s, large-scale melting of glaciers in the North and South Arctic occurred, and global sea levels are constantly rising, climate anomalies in various countries frequently occur, and all sectors of the global community have to face the fact that the global climate is warming. The important fact is that people are continuously emitting greenhouse gases. In view of this grim situation, policymakers from various countries have begun to investigate the scientific sources of information about the causes of climate change, the impact of socio-economic development on the potential environment, and how to respond effectively. Under the planning of the United Nations Environment Programme (UNEP) and the World Meteorological Organization (WMO), the United Nations Intergovernmental Panel on Climate Change (IPCC) was established in 1988. The role of the organisation is to professionally evaluate the scientific, technological, and economic and social factors that affect global climate change based on the research results and academic literature published by scientists from various countries, based on open, transparent and objective conditions.

PCC has now become the most authoritative assessment agency for global research on climate change. Since its establishment, it has carried out four systematic assessments of global climate change. It has clearly put forward that people's daily economic and social activities affect the global climate by collating the research results of various countries. The IPCC's fourth and most recent assessment report was released in 2007. This report shows that global warming will continue for hundreds of years. The daily economic and social activities of humans and the periodic fluctuations of the atmospheric system cause the greenhouse effect, leading to global warming. Carbon dioxide is the most important of various greenhouse gases, accounting for more than two-thirds of the total. The severe situation of global warming has caused widespread concern in various countries and regions, and practical actions have been taken to participate in energy conservation and emission reduction of greenhouse gases. For example, the formulation of the United Nations Framework Convention on Climate Change, the Kyoto Protocol, and the Copenhagen Climate Conference held in 2009 all show that the international community is working together to develop a low-carbon economy and formulate energy-saving and emission reduction target plans to cope with global warming.

Due to this severe problem of climate change, the term ‘low-carbon economy’ was mentioned in the White Paper, ‘Our Future Energy: Creating a Low-Carbon Economy’ published by the British Government in 2003. This is the earliest authoritative report that puts forward the term. This is the essence of the concept. It focuses on the issues of energy use efficiency and energy consumption structure, with energy system innovation and technological innovation as the core, and promoting the sustainable development of society and mitigating the negative impact of climate change as the ultimate goal. Figure 1 shows the proportion of global energy.

Fig. 1

Another research direction focuses on the relationship between economic growth, energy efficiency and incremental carbon emissions. Aviral (2016) used the Granger test to track the development of CO₂ emission levels, total social energy demand and GDP in the developed world in the future, and pointed out that there is a two-way causal relationship between the total energy demand and carbon emissions in developed countries; Schipper (2010) decomposed the LMDI model of the carbon emission influencing factors of several IEA member states, and proposed that the change in carbon emission levels in most countries was due to changes in energy output intensity and total energy demand; Emmanuel Ziramba (2009) and Ertugrul Yildirim (2012) used econometric methods to explore the co-integration relationship between industrial production and energy consumption in South Africa, and the relationship between US fuel demand and unemployment and factory output rates; B. Liddle's (2013) research finds that the urbanisation rate and the size of urban households have an impact on the energy structure and carbon emissions, but the relationship between the two and carbon emissions is the opposite; foreign scholars in order to study the degree of economic development, technological progress, and population size have conducted research on carbon emissions and introduced the IPAT model for calculation. At present, OECD has proposed theories that can better explain the relationship between low-carbon economic development and carbon emission levels that are limited to the ‘decoupling’ theory, which is intended to realise the simultaneous implementation of social development and a decline in energy demand. Roman Vavrek (2016) quantitatively evaluated the relationship between economic development and greenhouse gas emissions based on the decoupling model theory. Studies in the V4 countries found that there is a strong decoupling between economic growth and carbon emissions, which can be met by accelerating the implementation of new policies and restructuring the energy structure and energy demand. Patrik Thollandera, Osamu Kimurab (2015) and others start with the harm caused by greenhouse gases to the global climate, and analyse the 2011 earthquake in Japan as the research background.

Concerning the important role of energy use efficiency in the face of energy supply shortages, Andrea M's (2009) research found that the implementation of relevant regulations to reduce carbon emissions can indeed reduce greenhouse gas emissions, but it would affect the price of fossil energy by a reduction in it. P Salas (2013) demonstrated the impact of energy investment and resource endowments on carbon emissions using energy-saving models, and suggested that the government introduce policies to promote energy technology development from a low-carbon economy.

The energy structure is the composition and proportion of fossil energy and other primary energy and secondary energy in the total energy output and total consumption. Economic development needs to be guaranteed by energy input. The types of energy consumption and their allocation are important factors affecting CO₂ emissions and economic development. At present, the economic growth rate is relatively fast, and the stepwise nature of its growth pattern has also led to an increasing proportion of fossil energy investment. As far as the current situation is concerned, the coal-based energy structure can best meet this development demand, but at the cost of a relatively fast carbon emission growth rate. Coal has always dominated China's energy supply and consumption structure, but its utilisation efficiency is low, which is 23% lower than oil efficiency and 30% lower than natural gas. Therefore, the coal-based energy structure is very uneconomic, and the growth of unit GDP depends on the large consumption of coal, which will directly lead to problems such as low energy efficiency and shrinking economic benefits, which seriously hinder economic development.

The research purpose of this article is to quantitatively analyse the existing problems of low-carbon economic structure by defining the concepts of low-carbon economy and energy structure. To target the problem is to set up three scenarios for the low-carbon economic demand structure and make scenario predictions of the energy supply structure based on the conclusions. In order to predict and optimise the low-carbon economic structure, finally, based on the above research results, countermeasures and suggestions are put forward for the government in the grey forecast management of the low-carbon economy.

Energy is an important material foundation for the transformation of mankind from its primitive existence to modern civilisation, and it is also the driving force for the continuous development of today's society. In the context of the increasingly fierce political and economic competition in various countries, all countries have clearly realised that according to the current energy consumption rate, nonrenewable energy sources such as oil and coal will one day face depletion, which will bring forth extreme lack of development globally, followed by severe threats and tests. As a country with a rapidly growing economy, China has a huge energy demand. The actual situation is that the geographical distribution of different energy varieties in our country is extremely uneven and the per capita reserves are limited. This is reflected in the transportation of energy. Affected by transportation infrastructure conditions, energy supply in some areas cannot be effectively met, and the limited supply of domestic energy itself has further become a key factor affecting the sustainable development of China's economy and society. According to data from 2018, China has surpassed the United States to become the world's largest net oil importer, which can also confirm the embarrassing situation of China's high dependence on foreign energy and a huge demand gap. In addition to the problem of energy shortage, by contrast, the energy waste caused by the extensive consumption of energy, environmental damage and climatic anomalies caused are becoming more and more serious, which is mainly caused by the increase of SO₂, CO₂ and other gas emissions caused by the extensive consumption of energy Air pollution such as haze and acid rain, and climate change are caused by the greenhouse effect.

Energy issues have become increasingly restrictive of socio-economic development and have become a global problem. With the increasing attention of society and governments to carbon emissions, saving energy consumption and achieving low-carbon development in industries are particularly important. The core sector of the logistics industry consumes even more energy. Therefore, the current research on the energy efficiency and energy consumption structure of the logistics industry has positive practical significance in order to save energy consumption and develop low-carbon logistics. Starting with labour factors, and decomposing the energy consumption input factors of logistics into oil, coal, natural gas and electricity, it is believed that the various energy types can be replaced with each other to a certain extent, and are affected by the difference in technological level. According to this, on the basis of fully considering the ease of substitution of energy consumption varieties at the current stage of the logistics industry, by changing the combination of different energy consumption varieties in the logistics industry, the dual goals of a stable development of the logistics industry and energy conservation and consumption reduction are achieved. Two questions will arise here: in the production activities of daily logistics, what are the benefits generated by different energy types, and to what extent can they replace each other? And what effect will this substitution effect have on the sustainable development of the future logistics industry based on energy conservation? In the existing literature, some scholars have conducted in-depth research on the above two issues by empirically examining the output and substitution effects of different energy varieties in a certain industry or locality. Figure 2 shows the logistics operation.

Fig. 2

The scientific and reasonable model method is used to objectively reflect the degree of influence of different input factors on the development of China's logistics industry, especially its energy utilisation efficiency and energy consumption structure. It is important to sort it out according to relevant research literatures and summarise the following issues:

Most of the current related researches are based on time series data between energy factors and non-energy factors such as capital and labour to perform substitution elasticity analysis. This is feasible for most industrial research, but for the characteristics of the high-energy consumption industry (logistics, extractive industry), the rationality of the analysis of the substitution effect of energy elements separately from non-energy elements remains to be discussed. Han's research results on the energy efficiency and energy consumption structure confirm this view, because energy elements of the internal energy structure and technology-based differences make the impact of output substitution of energy varieties on output variables different.

Beyond the logarithmic production function, a variable elastic production function model that is easier to estimate than other function models and has a strong inclusiveness was first proposed by Christensen et al. According to the actual development of the logistics industry, the input factors of various types of energy interact with each other, and do not affect the development of the logistics industry in isolation.

At the same time, the technological progress between the input factors is differentiated and exceeds the logarithm. The production function belongs to the square reflection surface model in structure, and can fully reflect the mutual influence of the input factors under the difference in technological progress. This section intends to use the time-series data of the logistics industry's value-added and consumption of major energy types in the logistics industry from 2002 to 2018. As determined by the development situation, the lagging period of value-added logistics is used to replace other explanatory variables such as labour and capital, along with four different types of energy such as oil, coal, electricity and natural gas as input factors to construct a logistic production function model, as shown in formula (1): (1) βOO(τνOf)s+βCC(τνCf)s+βEE(τνEf)s+βGG(τνGf)s,(S−T)βOEτνOfτνEf+βOGτνOfτνGf+βCEτνCfτνEf+βCGτνCfτνGf+βEGτνEfτνGf+τνΓf=ε+ατνΓf−Γ+βOτνOf+βcτνCf+βEτνEf+βGτνGf+βOCτνOfτνCf \matrix{ {{\beta ^{OO}}{{\left( {\tau \nu {O^f}} \right)}_s} + {\beta ^{CC}}{{\left( {\tau \nu {C^f}} \right)}_s} + {\beta ^{EE}}{{\left( {\tau \nu {E^f}} \right)}_s} + {\beta ^{GG}}{{\left( {\tau \nu {G^f}} \right)}_s},(S - T)} \hfill \cr {{\beta ^{OE}}\tau \nu {O^f}\tau \nu {E^f} + {\beta ^{OG}}\tau \nu {O^f}\tau \nu {G^f} + {\beta ^{CE}}\tau \nu {C^f}\tau \nu {E^f} + {\beta ^{CG}}\tau \nu {C^f}\tau \nu {G^f} + {\beta ^{EG}}\tau \nu {E^f}\tau \nu {G^f} + \tau \nu {\Gamma ^f}} \hfill \cr { = \varepsilon + \alpha \tau \nu {\Gamma ^{f - \Gamma }} + {\beta ^O}\tau \nu {O^f} + {\beta ^c}\tau \nu {C^f} + {\beta ^E}\tau \nu {E^f} + {\beta ^G}\tau \nu {G^f} + {\beta ^{OC}}\tau \nu {O^f}\tau \nu {C^f}} \hfill \cr } In formula (1): Lt, Lt−1 indicate the value-added of logistics in t and t−1 years; Qt, Ct, Et, Gt represent the oil, coal, electricity and natural gas consumption of the logistics industry in t; α, β indicate the coefficient to be estimated, and ɛ is a constant. The parameters of ridge regression estimation model are used to analyse the output elasticity, substitution elasticity and technological progress difference of various energy in the logistics industry, so as to reflect the energy consumption of logistics industry, and then provide corresponding improvement measures for the development of low-carbon logistics.

The output elasticity refers to the relative change in output caused by the relative change of such input when the quantity of a certain input factor is changed separately when the other input quantities are fixed. The output elasticity of the energy input factors of the logistics industry can reflect the utilisation efficiency of different energy sources. The calculation formula is as follows.

The output elasticity of oil input is: (2) ηO=dLLdOO=dlnLtdlnOt=βO+βOClnCt+βOElnEt+βOGlnGt+2βOOlnOt {\eta _O} = {{{{dL} \over L}} \over {{{dO} \over O}}} = {{dln{L_t}} \over {dln{O_t}}} = {\beta _O} + {\beta _{OC}}ln{C_t} + {\beta _{OE}}ln{E_t} + {\beta _{OG}}ln{G_t} + 2{\beta _{OO}}ln{O_t} The output elasticity of coal input is: (3) ηC=βC+βCOlnOt+βCElnEt+βCGlnGt+2βCClnCt {\eta _C} = {\beta _C} + {\beta _{CO}}ln{O_t} + {\beta _{CE}}ln{E_t} + {\beta _{CG}}ln{G_t} + 2{\beta _{CC}}ln{C_t} The output elasticity of electricity input is: (4) ηE=βE+βEOlnOt+βEClnCt+βEGlnGt+2βEElnEt {\eta _E} = {\beta _E} + {\beta _{EO}}ln{O_t} + {\beta _{EC}}ln{C_t} + {\beta _{EG}}ln{G_t} + 2{\beta _{EE}}ln{E_t} The output elasticity of natural gas input is: (5) ηG=βG+βGOlnOt+βGClnCt+βGElnGt+2βGGlnGt {\eta _G} = {\beta _G} + {\beta _{GO}}ln{O_t} + {\beta _{GC}}ln{C_t} + {\beta _{GE}}ln{G_t} + 2{\beta _{GG}}ln{G_t} John Richard Hicks believed that the elasticity of factor substitution refers to the ratio between the rate of change of the ratio of the two input factors and the rate of change of the marginal technology substitution rate. In general, the larger the elasticity value, the stronger the substitution of these two input factors is. Chambers (1988) extended the Hicks substitution effect to the multi-factor production function. Combining the existing research results, the mutual substitution elasticity of the four main energy input factors of the logistics industry is calculated as follows:

The elasticity of oil and coal substitution is: (6) ω¯OC=d[OC]OC[d[MPCMPO]MPCMPO]−1=d[OC]d[MPCMPO]MPCMPOOC {\overline \omega _{OC}} = {{d\left[ {{O \over C}} \right]} \over {{O \over C}}}{\left[ {{{d\left[ {{{M{P_C}} \over {M{P_O}}}} \right]} \over {{{M{P_C}} \over {M{P_O}}}}}} \right]^{ - 1}} = {{d\left[ {{O \over C}} \right]} \over {d\left[ {{{M{P_C}} \over {M{P_O}}}} \right]}}{{{{M{P_C}} \over {M{P_O}}}} \over {{O \over C}}} (7) MPCMPO=ELECELEO=ηCηOOC {{M{P_C}} \over {M{P_O}}} = {{{{EL} \over {EC}}} \over {{{EL} \over {EO}}}} = {{{\eta _C}} \over {{\eta _O}}}{O \over C} (8) ωOC=d[OC]d[MPCMPO]ηCηO=ηCηO[d[MPCMPO]dOC]−1=ηCηO[d[ηCηOOC]d[OC]]−1 {\omega _{OC}} = {{d\left[ {{O \over C}} \right]} \over {d\left[ {{{M{P_C}} \over {M{P_O}}}} \right]}}{{{\eta _C}} \over {{\eta _O}}} = {{{\eta _C}} \over {{\eta _O}}}{\left[ {{{d\left[ {{{M{P_C}} \over {M{P_O}}}} \right]} \over {d{O \over C}}}} \right]^{ - 1}} = {{{\eta _C}} \over {{\eta _O}}}{\left[ {{{d\left[ {{{{\eta _C}} \over {{\eta _O}}}{O \over C}} \right]} \over {d\left[ {{O \over C}} \right]}}} \right]^{ - 1}} (9) d[ηCηOOC]d[OC]=ηCηO+OCd[ηCηO]d[OC] {{d\left[ {{{{\eta _C}} \over {{\eta _O}}}{O \over C}} \right]} \over {d\left[ {{O \over C}} \right]}} = {{{\eta _C}} \over {{\eta _O}}} + {O \over C}{{d\left[ {{{{\eta _C}} \over {{\eta _O}}}} \right]} \over {d\left[ {{O \over C}} \right]}} (10) d[ηCηO]=1ηOdηC−ηCηO2dηO d\left[ {{{{\eta _C}} \over {{\eta _O}}}} \right] = {1 \over {{\eta _O}}}d{\eta _C} - {{{\eta _C}} \over {\eta _O^2}}d{\eta _O} (11) d[OC]=1CdO−OC2dC d\left[ {{O \over C}} \right] = {1 \over C}dO - {O \over {{C^2}}}dC Substituting Eqs (10) and (11) into Eq. (9) and dividing the numerator and denominator together yield: (12) d[ηCηO]d[OC]=1ηOdηC−ηcηO2dηO1CdO−OC2dC1ηOdηCdC−ηcηO2dηOdC1CdOdC−OC2 {{d\left[ {{{{\eta _C}} \over {{\eta _O}}}} \right]} \over {d\left[ {{O \over C}} \right]}} = {{{1 \over {{\eta _O}}}d{\eta _C} - {{{\eta _c}} \over {\eta _O^2}}d{\eta _O}} \over {{1 \over C}{d_O} - {O \over {{C_2}dC}}}}{{{1 \over {{\eta _O}}}{{d{\eta _C}} \over {dC}} - {{{\eta _c}} \over {\eta _O^2}}{{d{\eta _O}} \over {dC}}} \over {{1 \over C}{{dO} \over {dC}} - {O \over {{C_2}}}}} By formulas (11) and (8), we get: (13) ωOC={1+[−βOC+ηOηCβCC](−ηO+ηC)−1}−1 {\omega _{OC}} = {\left\{ {1 + \left[ { - {\beta _{OC}} + {{{\eta _O}} \over {{\eta _C}}}{\beta _{CC}}} \right]{{\left( { - {\eta _O} + {\eta _C}} \right)}^{ - 1}}} \right\}^{ - 1}} In the same way, the elasticity of substitution of oil and electricity can be derived as: (14) ωOE={1+[−βOE+ηOηEβEE](−ηO+ηE)−1}−1 {\omega _{OE}} = {\left\{ {1 + \left[ { - {\beta _{OE}} + {{{\eta _O}} \over {{\eta _E}}}{\beta _{EE}}} \right]{{\left( { - {\eta _O} + {\eta _E}} \right)}^{ - 1}}} \right\}^{ - 1}} The elasticity of oil and gas substitution is: (15) ωOG={1+[−βOG+ηOηGβGG](−ηO+ηG)−1}−1 {\omega _{OG}} = {\left\{ {1 + \left[ { - {\beta _{OG}} + {{{\eta _O}} \over {{\eta _G}}}{\beta _{GG}}} \right]{{\left( { - {\eta _O} + {\eta _G}} \right)}^{ - 1}}} \right\}^{ - 1}} The substitution elasticity of coal and electricity is: (16) ωCE={1+[−βCE+ηCηEβEE](−ηC+ηE)−1}−1 {\omega _{CE}} = {\left\{ {1 + \left[ { - {\beta _{CE}} + {{{\eta _C}} \over {{\eta _E}}}{\beta _{EE}}} \right]{{\left( { - {\eta _C} + {\eta _E}} \right)}^{ - 1}}} \right\}^{ - 1}} The substitution elasticity of coal and natural gas is: (17) ωCG={1+[−βCG+ηCηGβCG](−ηC+ηG)−1}−1 {\omega _{CG}} = {\left\{ {1 + \left[ { - {\beta _{CG}} + {{{\eta _C}} \over {{\eta _G}}}{\beta _{CG}}} \right]{{\left( { - {\eta _C} + {\eta _G}} \right)}^{ - 1}}} \right\}^{ - 1}} The substitution elasticity of electricity and natural gas is: (18) ωEG={1+[−βEG+ηEηGβEG](−ηE+ηG)−1}−1 {\omega _{EG}} = {\left\{ {1 + \left[ { - {\beta _{EG}} + {{{\eta _E}} \over {{\eta _G}}}{\beta _{EG}}} \right]{{\left( { - {\eta _E} + {\eta _G}} \right)}^{ - 1}}} \right\}^{ - 1}} Taking 2002–2018 as the sample and 2020–2030 as the research period, the development of low-carbon logistics takes energy saving and emission reduction as its fundamental purpose, and at the same time meets the demand for value-added logistics industry and logistics energy consumption during the study period. In a low-carbon economy, the energy saving and emission reduction of the logistics industry mainly uses carbon intensity and energy consumption intensity as evaluation indicators, which can be achieved through logistics energy structure optimisation and technological progress. The carbon emission coefficient of unit energy is fixed after calculation. The unit energy carbon emission coefficient of each province adopts unified parameter values. Alternative energy technologies are feasible, and various types of energy used by the logistics industry can replace each other.

The decision variable considered for the development of the logistics industry during the study period is the energy consumption of different energy sources in the t period χti \chi _t^i . The energy types mainly include petroleum, coal, natural gas and electricity, that is, α_i, i = 1, 2, and 3... Then the total energy carbon emissions Ttc T_t^c of the logistics industry in the t period is: (19) Ttc=∑i=1nχtiαi T_t^c = \sum\limits_{i = 1}^n \chi _t^i{\alpha _i} According to the definition of carbon intensity, if both sides of formula (19) are divided by the value-added value L_t of the logistics industry in period t, the carbon intensity expression of logistics industry in period t is: (20) ωtc=TtcLt=∑i=1nχtiαtLt \omega _t^c = {{T_t^c} \over {{L_t}}} = {{\sum\limits_{i = 1}^n \chi _t^i{\alpha _t}} \over {{L_t}}} The total consumption of different energy sources in the logistics industry in period t is: (21) Tte=∑i=1nχti T_t^e = \sum\limits_{i = 1}^n \chi _t^i According to the definition of carbon energy intensity, if both sides of Eq. (22) are divided by the value-added value L_t of the logistics industry in the t-th period, then the energy intensity expression of the logistics industry in the t-th period is: (22) ωt3=TteLt=∑i=1nχtiαtLt \omega _t^3 = {{T_t^e} \over {{L_t}}} = {{\sum\limits_{i = 1}^n \chi _t^i{\alpha _t}} \over {{L_t}}}

Ridge regression is a biased estimation regression method that is specifically applied to data research with collinearity. When there is obvious collinearity among the respective variables, generally the least squares method cannot be used to directly perform the regression analysis. Instead, the corresponding methods must be used to deal with it, that is, to give up the unbiasedness of the least squares method and lose a part of the information, reducing some precision used as a condition to get a more realistic regression coefficient.

In fact, ridge regression is an improvement on the least square method. The main characteristic of ridge regression analysis is that although the remaining standard deviation is larger than the least square method, it fits some ill-conditioned data much more than the least square method, so as to obtain higher calculation accuracy. When there is obvious collinearity between the respective variables, the matrix determinant of the independent variables will be approximately equal to 0 or become singular. At this time, XX is also singular. But if XX is added to the normal number matrix KA, the singularity of XX + KA will be improved over XX. Therefore, β (K) = (XX + KA)−1XX is used as the estimated value of the regression coefficient.

This value will be more accurate and stable than the least squares estimation. β (K) will become the ridge of the regression coefficient. When K = 0, it obviously becomes the least square estimation. Although K value can be selected arbitrarily, when K → ∞, β (K) tends to 0, so the K value should not be too large. Therefore, an important concern when performing ridge regression analysis is the reasonable selection of K values. Based on ridge regression, biased estimates are made, and it is generally desirable to keep as much information as possible, that is, to keep the K value as small as possible. Therefore, you can observe the changes in the value of different K values, and then take the minimum K value that makes the equation stable. Another relatively simple and intuitive method is to observe the changes in the ridge trace and determine when it gradually stabilises.

In order to facilitate the calculation, the independent variable of the translog function is replaced by a special symbol; let lnL_t 1 = Y0, and the remaining variables are λ₀, λ₁, λ₂, λ₃, λ₄, λ₆, λ₇, λ₈, λ₉, λ₁₀, λ₁₁, λ₁₂, λ₁₃, λ₁₄.

According to the data source, the data of each variable from 2002 to 2018 were obtained. After calculation, the correlation coefficient value is basically >0.82, and the multicollinearity among the variables is more significant. In order to make the least squares (OLS) estimation result more reasonable, this study uses the ridge regression method to solve the multicollinearity problem to estimate, and uses the statistical software SPSS18.0 to calculate the different variables within a certain ridge parameter (K value) range. The coefficient changes are plotted into a ridge trace and the relationship between R2 and K values, as shown in Figures 3 and 4.

Fig. 3

Fig. 4

According to the ridge plots of the respective variables shown in Figure 1, it can be seen that when the K value is around 0.2, the ridge regression coefficient of each variable is estimated to be stable and does not show sharp fluctuations. According to Figure 2, it can also be seen that the K value from 0.2, R² showed a relatively steady decline. Using K = 0.2 to calculate the variance expansion factor, the results are shown in Table 1. Each VIF value is <5, indicating that the ridge estimate β (K) of the corresponding K value will be relatively stable. In sum, given K = 0.2 and its determinable coefficient R² = 0.9868, the calculation is based on the data of the energy consumption of the logistics industry from 2002 to 2018, and the final results of the ridge regression are shown in Table 1.

It can be seen from Table 1 that the statistical test results obtained after the ridge regression are not ideal, but the application of the ridge regression method is mainly whether it can effectively overcome the colinearity and whether the obtained parameters are reasonable. The regression coefficients of basically all variables in Table 1 are positive, except for the coefficients of coal and its cross-impact terms (λ₂, λ₅, λ₁₂). This is mainly because the energy consumption statistics of the logistics industry show that from 2002 to 2018, the coal energy consumption is continuously decreasing, and other energy consumptions are increasing, in the logistics industry. Therefore, the estimated value of this parameter is consistent with the actual situation of energy consumption in the logistics industry. Therefore, the parameter estimation results of the model can be considered to be meaningful.

According to the estimated values of the model parameters obtained above, the output and substitution elasticity of different energy inputs and their technological progress differences in the logistics industry from 2000 to 2018 can be calculated, as shown in Figures 5–7.

Fig. 5

Fig. 6

Fig. 7

In Figure 5, from 2002 to 2018, the output elasticity of different energy elements in China's logistics industry has been increasing, from large to small: natural gas, electricity, oil and coal. This is in line with the actual situation that natural gas and electricity are used as clean energy. Their utilisation efficiency is higher than that of high carbon emission energy such as oil and coal. Especially in the logistics field, the elasticity of natural gas energy output is much higher than that of oil and coal output elasticity. In 2008, the output elasticity of natural gas was 0.47, reaching 0.68 in 2018, an increase of 30.9%, and since 2008, this gap has continued to widen. The output elasticity value of electricity has been maintained at this relatively stable state of 0.3, although the output elasticity of petroleum and coal energy has also remained stable, but they are all <0.1. Among them, the output elasticity of coal energy in the logistics industry has been growing slowly but has been negative.

This shows that the use of natural gas energy is beneficial to the development of low-carbon logistics, while the use of coal energy will have a negative effect. The rapid increase in the output elasticity of natural gas in the logistics industry also indicates that the industry has significantly improved its energy efficiency.

In Figure 6, the elasticity of the substitution of electricity and natural gas is <1, which shows that the two types of energy in the logistics industry do not need to be replaced with each other in the logistics industry as electricity and natural gas as clean energy; instead, these two types of clean energy should be developed together. The substitution elasticity coefficients between oil and electricity, oil and gas, coal and natural gas, coal and electricity are all close to each other, and all are >1, indicating that clean energy is represented by natural gas and electricity and high carbon emissions are represented by oil and coal. Effective energy substitution can be carried out between energy sources and the substitution of coal and electricity is relatively high. The possible reason is that a considerable part of electricity energy is generated by using coal for thermal power generation as alternative elasticity. The highest elasticity of energy factor substitution in the logistics industry is oil and coal, which have basically remained >1.10. Since 2008, the elasticity of energy substitution between the two has become higher and higher. By 2018, the elasticity of substitution between the two has reached calendar years. The highest value is 1.19, mainly because petroleum and coal energy are high-carbon fossil fuels.

In Figure 7, the current progress in energy technology in the logistics industry is electricity, coal, natural gas and oil. The technological progress of electricity and coal is the fastest. The technological progress of electricity is in line with China's development needs for clean energy. However, the rapid progress of coal technology seems to contradict the previous conclusion that the output elasticity of coal energy is negative. The following may be the reasons for this scenario:

The use of coal energy has been extensive for a long time. A large amount of coal is directly burned and discharged without processing such as desulfurisation, which causes serious environmental pollution and low utilisation efficiency. Therefore, the technical starting point of coal utilisation is low, and there is a large space for improvement.

MATLAB2018b is used to compare the total energy demand observation with the grey forecast value from 2002 to 2018, as shown in Figure 8.

Fig. 8

Next, a gray forecast GM (1, 1) model is established for the demand for coal, oil, natural gas and other energy sources and forecasted. Using the data of energy consumption in 2009–2018 to simulate the training of the model and predict its demand in 2020–2030, the specific values are shown in Table 2.

The grey forecast GM (1, 1) model can be used to predict coal supply and demand from 2020 to 2030, as shown in Figure 9.

Fig. 9

The forecast of oil supply and demand in 2020–2030 is shown in Figure 10.

Fig. 10

The forecast of natural gas supply and demand from 2020 to 2030 is shown in Figure 11.

Fig. 11

The GM (1, 1) prediction method based on the grey system theory has the advantages of simple principles, unclear distribution rules, few research samples, convenient calculation and high prediction accuracy. However, the grey prediction method also has some disadvantages. Limited by the development coefficient, for decades of long-term forecasting, its accuracy is not very high, which is more suitable for short- and medium-term forecasting research. Compared with the large number of applicable samples, long-term regression equation prediction, BP neural network prediction, and genetic algorithm prediction is applicable to incomplete data. The complete time-series study sample for this study is 6, and the forecast for the next 6 years is till 2020. The value of logistics energy intensity and logistics carbon intensity before 2030 has a short forecast period, so it is more consistent with the use of GM (1, 1) forecasting model for research. After relevant tests, each of the GM (1, 1) prediction models has reached a relatively credible level. The prediction research results can objectively reflect the development expectations of the energy saving and emission reduction effects of the future logistics industry.

The objective of this article is to study the dynamic energy-saving and emission reduction effects of the logistics industry. First of all, by analysing the energy consumption structure and energy efficiency of the logistics industry, we can obtain the current energy consumption status of the logistics industry as a whole, highlighting the importance of ‘energy conservation’, and second by introducing the concept of carbon footprint The CO₂ emissions of the logistics industry are measured and calculated, and the dynamic regional distribution of the carbon footprint of the logistics is obtained. The purpose is to emphasise the meaning of ‘emission reduction’, and then introduce the two indicators of energy intensity and energy intensity in combination with government work. This paper sets the ‘double intensity’ target value of energy conservation and emission reduction in the logistics industry, and forecasts and analyses the completion of energy conservation and emission reduction in the logistics industry in the future.