The life cycle assessment (LCA) is used to assess the overall environmental impact of goods or services, including the entire life cycle of a product: extraction and processing of raw materials, manufacturing, distribution, use, reuse, maintenance, recycling, and final disposal[20][21]. LCA analysis can be performed based on two main approaches: process-based model and input-output based analysis [22]. Compared with the method of process-based model, the input-output analysis (IOA) can be applied to more macro level life cycle assessment. The Input-output analysis (IOA) can comprehensively include the direct and indirect contributions of all economic activities in an impact assessment, and it can be more easily adopted as a basis for assessing the impact of anticipated technological changes in a defined economic system[20]. With the ability to extend the analysis to the entire economic system, IOA-LCA allows for a more comprehensive assessment of environmental impacts, considering emissions that may be hidden in upstream production processes, which contributes to the reduction of emissions throughout the economic system[14].

The central formula of the input-output model is that for an economy consisting of \(n\) industries, total output \(X\) can be expressed as the sum of intermediate use \(AX\) and final demand (i.e., products that are no longer processed for production) \(Y\) in each industry:

Where, I is the identity matrix; \((\text{I-A}{)}^{-1}\) is the Leontief inverse matrix, also known as the complete demand factor; \(X\) is a N × N matrix.

In order to investigate the difference between final production emissions and final demand emissions and the reasons for their formation, Skelton et al.[14] proposed a method for mapping embodied emission flows through the Leontief production system. This method is considered as an extension of the traditional SPA and can show a detailed flow analysis map of the supply chain between final production and consumption attribution. The SPA model has been widely used to identify key industrial sectors and supply chain pathways that lead to resource use and associated environmental impacts[23][24], and is a suitable and effective method for quantifying demand-driven environmental emissions.

An advantage of the Leontief model is the ability to track the intermediate purchasing chain through the layers of the production system triggered by the final demand. This is achieved by solving the Leontief inverse using its power series approximation, as follows [14]:

$$L=(I-A{)}^{-1}=I+A+{A}^{2}+{A}^{3}+\text{...}+\text{proveded that li}{\text{m}}_{t\to {\infty }}{A}^{t}$$

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The relationship between each two production layers (PL) is as follows:

$$\text{P}{\text{L}}^{t+1}=\text{P}{\text{L}}^{t}A$$

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Each sector relates to the environment through a number \(m\) of exogenous transactions (resources consumption or waste emissions), collected into the exogenous transactions coefficients vector \(\theta\),w, ich is a vector of direct emission coefficient, that is the amount of pollutant emissions generated per unit of economic output in each industry.\(\theta =E/X\), where \(E\) is the direct pollutant emission vector for each sector and \(X\) is the total output vector for each sector. In this paper, we consider CO2 and NOx emissions where the transportation sector is the main contributor[25].

The consumption of final products in each sector forms the final demand, which pulls upstream sectors along the production layer to produce intermediate products. Each sector generates direct emissions of pollutants from each production tier as it performs production activities at each production tier. Similarly, the consumption of intermediate goods by each production layer forms the reverse implied pollution flow from final production emissions back through each production layer to final demand emissions. The direct emissions \({D}^{t}\), indirect production embodied emissions \({P}^{t}\) and consumption emissions \({E}^{t}\) for sector \(i\) at production layer 0 and production layer \(t\) are calculated as follows.

Table 2

Direct, Consumption, and Production Attribution Equations for PL0 to PL3

| Direct | Consumption | Production |

Final attribution at PL0 | \({D}_{i}^{0}={\theta }_{i}{y}_{i}\) | \({E}_{i}^{0}={m}_{i}{y}_{i}\) | \({P}_{i}^{0}=\text{M*Y}\) |

Intermediate attribution at PL1 | \({D}_{i}^{1}={\theta }_{i}\text{*A*Y}\) | \({E}_{i}^{0}={m}_{i}\text{*A*Y}\) | \({P}_{i}^{1}=\text{M*A*Y}\) |

Intermediate attribution at PL2 | \({D}_{i}^{2}={\theta }_{i}\text{*}{\text{A}}^{2}\text{*Y}\) | \({E}_{i}^{2}={m}_{i}\text{*}{\text{A}}^{2}\text{*Y}\) | \({P}_{i}^{2}=\text{M*}{\text{A}}^{2}\text{*Y}\) |

Intermediate attribution at PL3 | \({D}_{i}^{3}={\theta }_{i}\text{*}{\text{A}}^{3}\text{*Y}\) | \({E}_{i}^{3}={m}_{i}\text{*}{\text{A}}^{3}\text{*Y}\) | \({P}_{i}^{3}=\text{M*}{\text{A}}^{3}\text{*Y}\) |

Table 3

Embodied Emissions Flow Equations

| from sector at PL1 to sector at PL0 | from sector at PL2 to sector at PL1 | from sector at PL3 to sector at PL1 |

Embodied Emissions Flow | \({E}_{\text{ij}}^{1\to 0}={m}_{i}\text{*}{\text{a}}_{\text{ij}}\text{*}{\text{y}}_{i}\) | \({E}_{\text{ij}}^{2\to 1}={m}_{i}\text{*}{\text{a}}_{\text{ij}}\text{*A*Y}\) | \({E}_{\text{ij}}^{3\to 2}={m}_{i}\text{*}{\text{a}}_{\text{ij}}\text{*}{\text{A}}^{2}\text{*Y}\) |

In Tables 2 and 3, \(M\) is the N × N matrix of emission multipliers and \(m\) is the row vector (1×N) in \(M\). \(M\) and \(m\) can be calculated according to Eqs. (5) and (6), respectively:

$$M=\stackrel{\wedge }{\theta }L$$

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Where \(\stackrel{\wedge }{\theta }\) is the diagonal form of the emission intensity and \({\theta }^{T}\) is the row vector form of the emission intensity.

Finally, we should also note that the sum of the final production attributes equals the sum of the final demand attributes (\({\sum }_{i=1}^{n}{P}_{i}^{0}={\sum }_{i=1}^{n}{E}_{i}^{0}\)).

In this paper, it is assumed that the supply relationship between sectors remains unchanged during the life cycle of the technology implementation (set to 15 years in this paper, based on the current end-of-life requirements for most vehicle models in China), and that the industry emission intensity and product prices remain constant. A similar hypothesis has been set in many studies[26][27][28].

The implementation of vehicle related emission reduction technologies requires additional investment costs, which is an important reference for countries or enterprises to adopt emission reduction strategies. The application of emission reduction technologies will cause changes in the final consumption. When the increased costs or benefits of applying energy-efficient technologies lead to changes in the final consumption of key sectors, the economic output of other sectors will be indirectly affected due to sectoral linkages, which will lead to changes in pollutant emissions in each sector.

In order to obtain the net emission abatement potential of each technology, the direct emission reductions during the use stage and the indirectly induced emissions during the production stage are considered in this paper, using 2018 as the base year.

Considered from the whole life cycle, the equipment and power used in these abatement technologies generate additional pollutant emissions during the production phase. In addition, the reduction in fuel consumption also reduces the pollutants emitted during production stages. The addition emissions in production stage generated through industry linkages, is denote as \(AD{E}_{production}\). The top-down IOA method can be used to estimate the impact on the whole economic sectors from the final demand shock (reflected in monetary value) caused by the application of the technology, resulting in associated additional emissions in production stage. The SPA model introduced above can calculate the emissions in the production stage, and this method does not need too much micro production process data. We use the SPA model to estimate the additional emissions from the production phase of the technology, as described in Eqs. (3)- (6) and Tables 2 and 3, where it is important to note that when calculating the additional emissions of a technology, the variable \(Y\) is set to zero in all sectors except for the shock sector, which is a change in value (denoted as *y**1*, *y**2* and *y**3*, *in million of yuan*). The \({y}_{1}\) is the fuel cost, which is the final demand reduction in the refined oil sector in the IO table. The \({y}_{2}\) is the technology investment cost, which is the increase in final demand in the IO table for the automotive parts sector, rubber and related industries such as the complete vehicle manufacturing sector (see Table 4) due to the implementation of the motor vehicle retrofit technology. The \({y}_{3}\) is the electricity cost, which in the IO table is the increased final demand in the electricity sector due to the implementation of motor vehicle electrification technology. Here we set the fuel cost (\({y}_{1}\)) and electricity cost (\({y}_{3}\)) increase by a discount rate of 5% p.a. in the 15 year[11], and the technology investment cost (\({y}_{2}\)) is completed in the first year, without considering discounting. The variation of these three final requirements could be estimated by the following formula.

$${\text{y}}_{1}=\sum _{i=1}^{n}(\text{O}\text{P}\times \text{F}\text{E}\times \text{A}\text{M}\times \text{V}\text{O}\times \text{S}\times {10}^{-6}\times {\left(1+5\text{\%}\right)}^{n-1})$$

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$${\text{y}}_{2}=\text{I}\text{C}\times \text{V}\text{O}\times {10}^{-6}$$

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$${\text{y}}_{3}=\sum _{i=1}^{n}(\text{E}\text{P}\times \text{P}\text{M}\times \text{A}\text{M}\times \text{V}\text{O}\times {10}^{-6}\times {(1+5\text{\%})}^{n-1})$$

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In which, \(OP\) (yuan/L) is the oil price, and the average oil price in China in 2018 is 7.27 yuan /L for gasoline and 6.88 yuan/L for diesel[29]; the variables \(FE\), \(AM\), \(VO\) and \(S\) are described in Eq. (7); \(IC\) (yuan) is the technology investment cost (see Table S1); \(EP\) (yuan/kW·h) is the electricity price, and the average feed-in tariff for power producers in China in 2018 is 0.374 yuan/kW·h[30]; \(PM\) (kW·h/100km) is the power consumption per unit mileage (see Table S2); \(n\) is the year of technology use, ranging from 1 to 15.

Table 4

**Major industries where emission reduction technologies are causing** \({\mathbf{y}}_{2}\)**changes**

Technology | Description | Direct industries with increased final demand [31] |

Engine energy-saving technology | Engine and transmission parts improvement | Auto parts and accessories industry |

New energy technology | Adopt new power systems such as electrification and hybrid power | Automobile industry |

Drag reduction technology | Low friction lubricant | Lubricant improvement | Refined petroleum and processed nuclear fuel products industry |

Low rolling resistance tire | Rubber tire improvement | Rubber products industry |

Lightweight Or Air resistance reduction | Overall body design improvement | Automobile industry |

For vehicles, the emission reduction caused by energy-saving or substitution technology could be accounted by the coefficient method of pollutant emission per unit of gasoline. Assuming no change in vehicle ownership is considered, the direct CO2 abatement could be obtained by multiplying the CO2 generation factor by the amount of fuel that would be saved by each type of technology in the next 15 years. Since NOx emissions are more likely to be influenced by tailpipe control technologies, the relationship between NOx production factor and final emission factor of fuel consumption is highly uncertain. In the absence of sufficient data, this article set the current emissions multiplied by the corresponding energy-saving efficiency of various technologies as the emissions of this technology.

$${\text{A}\text{B}\text{E}}_{\text{u}\text{s}\text{e}-{\text{C}\text{O}}_{2}}\text{=α ×FE×VO×AM×S×ρ×1}{\text{0}}^{\text{-11}}\text{×15}$$

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$$\text{A}\text{B}{\text{E}}_{\text{u}\text{s}\text{e}-\text{N}\text{O}\text{x}}\text{=}\text{β}\text{×S×15}$$

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In which, the CO2 and NOx direct abatement emissions are denoted as \({ABE}_{use-{CO}_{2}}\) and \(A{BE}_{use-NOx}\), respectively; \(\alpha\) is the CO2 generation factor, for gasoline is 2.93t/t and for diesel is 3.10t/t; \(FE\) is the fuel consumption per unit mileage(L/100km); \(VO\) is the current total ownership of vehicles; \(AM\) is the average annual mileage (km); \(\rho\) is the fuel density, 0.73 kg/L for gasoline and 0.84 kg/L for diesel; 15 is the service life of the vehicle; \(\beta\) is the annual statistical NOx emissions (Kt) of current total quantity of vehicles; \(S\) is the energy-saving efficiency in %. Detailed data for \(FE\), \(VO\), and \(AM\) are shown in Table S2, and detailed data for \(S\)are shown in Table S1.

The potential for emission abatement over the whole life cycle is referred to as the net abatement potential/emissions, denoted as \({ABE}_{net}\)(CO2 in Mt, NOx in Kt). The net abatement potential is the direct emission reductions from the use phase of the technology deducting the additional emissions generated in the production phase, which could be expressed as:

$$\text{A}\text{B}{\text{E}}_{\text{n}\text{e}\text{t}}={\text{A}\text{B}\text{E}}_{\text{u}\text{s}\text{e}}-\text{A}\text{D}{\text{E}}_{\text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}\text{i}\text{o}\text{n}}$$

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From the perspective of the ife cycle, the adoption of vehicle energy-saving or substitution technology will produce additional investment costs of technological transformation (above \({y}_{1}\)). If electric vehicle technology is adopted, it will increase additional power costs (above \({y}_{2}\)), but it will also save fuel and generate energy-saving benefits (above \({y}_{3}\)). Economic benefits are the main driving force that may promote the long-term development of technology. We generally refer to emission reduction from the perspective of cost, however, but energy-saving technology may bring economic benefits. From the perspective of cost-benefit analysis, the net benefit (\(NB\)) is as follows.

$$\text{N}\text{B}={\text{y}}_{3}-{\text{y}}_{1}-{\text{y}}_{2}$$

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The net abatement benefit per unit emissions (\(AB\), CO2 unit yuan/t, NOx unit yuan/kg) could be calculated as follows:

$$\text{A}\text{B}=\text{N}\text{B}/{\text{A}\text{B}\text{E}}_{\text{n}\text{e}\text{t}}$$

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