1 Introduction

Environmental problems associated with energy use pose great challenges for sustainable development. Many countries are concerned with reducing energy consumption and greenhouse gas emissions from industrial sectors. Considered from a worldwide perspective, the transportation sector has become the world’s largest oil consumer and the second largest greenhouse gas emitter; in 2012, this sector consumed 61% of the world’s oil and accounted for 22% of the world’s carbon dioxide (CO2) emissions (International Energy Agency 2013). Therefore, controlling CO2 emissions from transportation is important for sustainable development. Many countries and regions have imposed CO2 emissions caps on the this sector, including the USA (Farrell and Sperling 2007), Germany (Blesl et al. 2007), Canada (Steenhof and McInnis 2008), UK (Hickman et al. 2009), Brazil (Machado-Filho 2009), and Taiwan (Trappey et al. 2012).

China produces the most CO2 emissions (Hu and Lee 2008) and the largest energy consumer in the world (BP 2011), and the country’s transportation sector is one of its high-energy-consumption and high-emission industries. Between 2005 and 2010, transportation energy consumption grew by 75%. Transport energy consumption was responsible for more than 20% of total final energy consumption in 2010 (National Bureau of Statistics of China 2011) and continues to trend upward. This significant energy consumption has generated more carbon emissions. Among the five major industries (agriculture, industry, construction, commerce, and transportation) in China, the transportation sector is the only one showing continuous increases in carbon intensity (Chen 2010). In particular, the transportation sector’s carbon intensity has been rapidly rising since 2004, with an annual growth rate of more than 20%. This is far higher than the growth of the national economy (Ding 2012). As a result, there is a great public interest in the environmental problems associated with the transportation sector.

The 11th Five Year Plan (2006–2010) issued by China’s Ministry of Transport (MOT) initiated several major projects, including promoting the energy-saving and new energy vehicles and the use of natural gas for taxis and buses. In the 12th Five Year Plan (2011–2015), MOT issued an low-carbon transportation planning. The plan was “low-carbon transport special action,” “energy-saving and new energy vehicle demonstration and extension project” and “energy-saving and emission reduction technology promotion project on highway construction and operation.” To permanently promote increased sustainability in the transportation sector, it is critical to identify the effect of these new policies. In addition, regional differences should be emphasized since the divide of regions in China and decades of unbalanced policy lead to development gaps among different regions (Wang et al. 2012a).

This paper evaluated the dynamic changes in the energy–carbon performance of China’s transportation sector, assessing the effects of these new policies and measures. This included assessing regional heterogeneity and the more innovative provinces. This analysis may help policy makers select appropriate strategies to support the sustainable development of China’s transportation sector.

The remainder of this paper is organized as follows. Section 2 presents the related literature review. Section 3 introduces the methodologies. Section 4 discusses the data and the results of energy–carbon performance. Section 5 provides conclusions and policy implications.

2 Literature review

Production processes are accompanied by undesirable outputs. The efficiency that includes undesirable outputs is referred to as environmental efficiency (Arocena and Price 1999). Pittman (1983) incorporated undesirable outputs into a multilateral productivity index based on ratio figures. Pittman’s approach required an assessment of shadow price of environmental regulatory compliance. However, it is still difficult to evaluate the shadow price of pollutants (Zhou et al. 2007). Other approaches for measuring energy and environmental efficiency include the stochastic frontier analysis (Cullinane and Song 2006; Cook and Seiford 2009; Lee and Jin 2012), free disposal hull model (Cook and Seiford 2009), and data envelopment analysis (DEA). The first two approaches do not incorporate undesirable outputs into the models; as such, they are not used as often.

DEA has become dominant in this area because it can be applied in cases with multiple outputs, including undesirable outputs. Traditional DEA assumes that all outputs should be maximized for a given input level. This approach does not accommodate the fact that undesirable outputs are also generated as by-products of desirable outputs. Hence, several methods have been proposed to accurately handle undesirable outputs based on the traditional DEA framework. Dyckhoff and Allen (2001) suggested treating the undesirable outputs as inputs. However, this does not reflect the true production process during modeling (Seiford and Zhu 2002). Färe et al. (1994) treated the undesirable outputs as a by-product of the production process. However, this approach does not address the negative externalities of pollution emissions.

To effectively treat the undesirable output, some approaches directly apply undesirable output data into the modified DEA model. These approaches include the hyperbolic efficiency (HE) measure (Färe et al. 1989), slack-based measure (SBM) model (Tone 2001), the directional distance function (DDF) model (Chung et al. 1997), and the range adjusted measure (RAM) model (Cooper et al. 1999). DDF has become widely used to examine energy and environmental efficiency, because it can reduce inputs and expand outputs (Picazo-Tadeo et al. 2005; Färe et al. 2007). Chambers et al. (1996) proposed the traditional DDF. They regarded undesirable outputs as special outputs, with negative externalities, by defining a directional vector. The traditional DDF is designed to reduce inputs and expand outputs at the same rate; as such, it is considered a radial efficiency measure. However, this radial measure has several limitations. Primarily, it does not provide efficiency information for specific factors, such as unequal environmental performance (Yu et al. 2015). In addition, radial efficiency measures overestimate efficiency when there is slack (Fukuyama and Weber 2009). Therefore, it has a relatively weak discriminating power when ranking the entities being evaluated (Zhou et al. 2012).

Recent research has extended the radial DDF to non-radial DDF, incorporating slack. Fukuyama and Weber (2009) developed a slack-based inefficiency measure based on DDF. Färe and Grosskopf (2010) proposed a generalized non-radial DDF. Barros et al. (2012) proposed a weighted Russell DDF. Zhou et al. (2012) defined a non-radial DDF following an axiomatic method to measure efficiency. Zhang and Choi (2013) incorporated the meta-frontier approach into a non-radial DDF. Wang et al. (2014) analyzed China’s energy efficiency from both static and dynamic perspectives based on provincial panel data for the period of 2001–2010 using the global DEA. Wang and Feng (2015a) estimated China’s energy, environmental, and economic (“E3”) efficiency and the sources of E3 productivity growth using the global DEA. Wang et al. (2016) proposed an alternative three stage approach and measured total-factor CO2 emission performance and technology gaps.

Instead of taking a methodological orientation, much of the existing research is empirically oriented using DEA method. Examples of such studies included Guo et al. (2011), Lin et al. (2011), Wang et al. (2012b, 2013, 2015), Song et al. (2013), Meng et al. (2013), Zhang and Da (2013), Zhang et al. (2016), Lu et al. (2014), Wang and Feng (2015b), Liu et al. (2015), and Wu et al. (2016). These studies have focused on energy and environmental efficiency for China’s provincial-level or city-level regions. Most up-to-date researchers examined energy and environmental efficiency at the sector level for each province in China. Examples of such studies included Zhou et al. (2013), Tao and Zhang (2013), Zhang and Wang (2014), Lin and Fei (2015), Zhang et al. (2016), Yu et al. (2016), Emrouznejad and Yang (2016) and Tian et al. (2016).

A few researchers have focused on the energy and environmental efficiency of China’s transportation sector. Chang et al. (2013) proposed a non-radial DEA model with a SBM model to analyze the environmental efficiency of the sector. Bi et al. (2014) presented a non-radial DEA model with multidirectional efficiency analysis to measure the regional energy and environmental efficiency of the sector. Zhang et al. (2015) proposed a non-radial Malmquist CO2 emission performance index for measuring dynamic changes in total-factor CO2 emission performance of the sector. Zhang and Wei (2015) further examined and decomposed dynamic changes in total-factor carbon emissions performance incorporating the impact of regional heterogeneity. Sun et al. (2015) proposed a centralized DEA model, using it to determine the optimal path for controlling CO2 emissions at the sector level for each province in China. Song et al. (2016) proposed a panel beta regression with fixed effects to model the impact of railway transportation on environmental efficiency. Wu et al. (2016) treated transportation as a parallel system and then extended a parallel DEA approach to evaluate the energy and environmental efficiency of each subsystem.

Previous studies have comprehensively reviewed energy and environmental efficiency for the transportation sector. However, there remain open questions. First, most previous studies did not address regional technology heterogeneity. Technological sets can vary significantly in a country as large as China, so not including group heterogeneity may lead to biased efficiency score estimates. Second, many studies of the transportation sector have not considered changes over longer timescales. As such, trends in energy and environmental efficiency variability over time were not assessed. Finally, the existing literature often uses contemporaneous benchmark technology (CBT) or cross-benchmark technology, which may lead to a lack of circularity or infeasibility. This could affect the accuracy of the results. In contrast, global benchmark technology (GBT) can improve the discriminating power and comparability (Pastor and Lovell 2005).

This paper addresses the above empirical gap, making contributions in three key areas. First, we propose an approach combining meta-frontier method and non-radial DDF (M-G-NDDF) and then use the approach to evaluate the dynamic changes of the energy–carbon performance. The approach simultaneously considers the regional technology heterogeneity and the potential of slack in technological constraints. This may generate estimates that more accurately characterize China’s transportation sector. Second, we incorporate GBT into our model. This improves discriminating power and comparability, providing a more accurate assessment of energy–carbon performance. Third, we decompose the energy–carbon performance index into the efficiency change (EC), best-practice gap change (BPC), and technology gap change (TGC). This helps identify the source of changes in energy–carbon performance, facilitating targeted energy and environmental policy development and implementation in different regions.

3 Methodology

3.1 Non-radial directional distance function

This paper uses the non-radial directional distance function to model a transportation technology that jointly produces a desirable and an undesirable output. Based on Färe and Grosskopf (2010), assume there is a transportation process that consumes capital stock (K), labor force (L), and energy (E) as inputs under the given production technology condition (T). This process generates the gross product (Y) of transportation as a desirable output and CO2 emissions (C) as an undesirable output. The production possibility set (PPS) is expressed as:

$$P(K,L,E) = \left\{ {\left. {(Y,C):(K,L,E,Y,C) \in T} \right\}} \right.$$
(1)

The directional distance function (DDF) was provided by Chambers et al. (1996) and extended by Chung et al. (1997). It is a relatively new methodology for measuring performance. The conventional DDF is a radial efficiency measure that may overestimate efficiency when the slack exists (Fukuyama and Weber 2009). Zhou et al. (2012) proposed a formal definition of the non-radial DDF (NDDF). Following Zhou et al. (2012), the DEA-type model for calculating the NDDF value can be defined as follows:

$$\mathop D\limits^{ \to } (K,L,E,Y,C) = \hbox{max} w_{E} \beta_{E} + w_{Y} \beta_{Y} + w_{C} \beta_{C}$$
(2)
$$\begin{aligned} &s.t.\sum\limits_{n = 1}^{N} {\lambda_{n} NE_{n} } \le NE_{j} \hfill \\ &\sum\limits_{n = 1}^{N} {\lambda_{n} E_{n} } \le E_{j} + \beta_{E} g_{E} \hfill \\ &\sum\limits_{n = 1}^{N} {\lambda_{n} Y_{n} } \ge Y_{j} + \beta_{Y} g_{Y} \hfill \\ &\sum\limits_{n = 1}^{N} {\lambda_{n} C_{n} } { = }C_{j} + \beta_{C} g_{C} \hfill \\ &\lambda_{n}^{{}} \ge 0,n = 1,\,2,\, \ldots ,N,\,\beta_{E} \ge 0,\,\beta_{Y} \ge 0,\,\beta_{C} \ge 0 \hfill \\ \end{aligned}$$

Here, \(\lambda\) is the intensity variable; \(g_{E}^{{}}\), \(g_{Y}^{{}}\), and \(g_{C}^{{}}\) denote the direction vectors associated with energy inputs, desirable outputs, and undesirable outputs, respectively. The directional vector \(g\) can be set differently, based on different policy goals. \(\beta\) is the measure of inefficiency. \(w_{E}\), \(w_{Y}\), and \(w_{C}\) are the components of a weighting vector.

According to Zhou et al. (2012), assume that \(s_{E}\), \(s_{Y}\) \(s_{C}\) are nonnegative slack variables associated with energy input, the gross product and CO2 emissions. If \(\beta_{E}\), \(\beta_{Y}\), and \(\beta_{C}\) are, respectively, set equal to \(- s_{E} /g_{E}\), \(s_{Y} /g_{Y}\) and \(- s_{C} /g_{C}\), then \(\mathop D\limits^{ \to } (K,L,E,Y,C)\) would be a weighted version of the slacks-based inefficiency measure defined in Fukuyama and Weber (2010) and Fukuyama et al. (2011). If the direction vector is set equal to (−1, 1,−1), Eq. (2) without undesirable output is almost the same as the generalized directional distance function proposed in Färe and Grosskopf (2010) except that the latter does not consider the numbers of inputs in the objective function.

In order to simultaneously model energy and CO2 emission performance in logistics sector, the energy–carbon performance indexFootnote 1 (ECPI) can be defined based on Zhou et al. (2012). Then, we can formulate the ECPI as

$${\text{ECPI}} = \frac{{1 - 1/2(\beta_{E}^{ * } + \beta_{C}^{ * } )}}{{1 + \beta_{Y}^{ * } }}$$
(3)

3.2 Meta-frontier and group frontier technologies

To investigate regional heterogeneity of China, we combine the meta-frontier DEA approach proposed by O’Donnell et al. (2008) with the NDDF model proposed in this paper. Based on Zhang and Wei (2015), assume that H groups show technological heterogeneity: \(h = 1, \ldots ,H\). The contemporaneous production technology for group R h at time t can be defined as \(T_{{R_{h} }}^{c} = \left\{ {(K^{t} ,L^{t} ,E^{t} ,Y^{t} ,C^{t} ):(K^{t} ,L^{t} ,E^{t} )} \right.\) can produce \(\left. {(Y^{t} ,C^{t} )} \right\},\) where \(t = 1, \ldots ,T\). The contemporaneous benchmark technology constructs a reference production set at each point in time t, from the observations made at that time only (Pastor and Lovell 2005; Tulkens and Eeckaut 1995). Then, altering the definition of intertemporal benchmark technology by Oh and Lee (2010), the intertemporal benchmark technology of group \(h\) can be defined as \(T_{{R_{{_{h} }} }}^{I} = T_{{R_{h} }}^{1} \cup T_{{R_{h} }}^{2} \cup \cdots \cup T_{{R_{h} }}^{T} ,\). The intertemporal benchmark technology contains all the observations from the full time period for the specific group h (Tulkens and Eeckaut 1995). The global production technology can be defined as \(T_{{}}^{G} = T_{{R_{1} }}^{I} \cup T_{{R_{2} }}^{I} \cup \cdots \cup T_{{R_{h} }}^{I} ,\). This is constructed from all observations for the full time period for all groups. As proposed by Oh and Lee (2010), global production technology needs to be incorporated into the model (2) to improve the discriminating power and comparability of intertemporal observations.

A meta-frontier results from enveloping the production frontier of all groups. Therefore, the meta-frontier is defined as \(T_{m} = \left\{ {T_{1} \cup T_{2} \cup \cdots \cup T_{H} } \right\}\). Assume there are N h observations for group h. Based on the region’s technology heterogeneity, the meta-frontier should be incorporated into model (2). Here, we propose the meta-frontier global non-radial DDF model (M-G-NDDF) exhibiting constant returns to scale (CRS):

$$\mathop {D^{m} }\limits^{ \to } (K,L,E,Y,C) = \hbox{max} \,w_{E} \beta_{E}^{m} + w_{Y} \beta_{Y}^{m} + w_{C} \beta_{C}^{m}$$
(4)
$$\begin{aligned} &s.t.\sum\limits_{t = 1}^{T} {\sum\limits_{h = 1}^{H} {\sum\limits_{n = 1}^{{N_{h} }} {\lambda_{n}^{h} NE_{n}^{h} } \le NE_{j}^{h} } } \hfill \\ &\sum\limits_{t = 1}^{T} {\sum\limits_{h = 1}^{H} {\sum\limits_{n = 1}^{{N_{h} }} {\lambda_{n}^{h} E_{n}^{h} } \le E_{j}^{h} + \beta_{E}^{m} g_{E} } } \hfill \\ &\sum\limits_{t = 1}^{T} {\sum\limits_{h = 1}^{H} {\sum\limits_{n = 1}^{{N_{h} }} {\lambda_{n}^{h} Y_{n}^{h} } \ge Y_{j}^{h} + \beta_{Y}^{m} g_{Y} } } \hfill \\ &\sum\limits_{t = 1}^{T} {\sum\limits_{h = 1}^{H} {\sum\limits_{n = 1}^{{N_{h} }} {\lambda_{n}^{h} C_{n}^{h} } = C_{j}^{h} + \beta_{C}^{m} g_{C} } } \hfill \\ &\lambda_{n}^{h} \ge 0,n = 1,2, \ldots ,N_{h} ,h = 1,2, \ldots ,H,t = 1,2, \ldots ,T,\beta_{E}^{m} \ge 0,\beta_{Y}^{m} \ge 0,\beta_{C}^{m} \ge 0 \hfill \\ \end{aligned}$$

Similar to Zhang and Choi (2013), and based the above models, we generate the following energy–carbon performance under three different production technologies:

$${\text{ECPI}}^{d} = \left( {\frac{{1 - 1/2(\beta_{E}^{ * } + \beta_{C}^{ * } )}}{{1 + \beta_{Y}^{ * } }}} \right)^{S}$$
(5)

Here, \(d \equiv (C,I,G),\,s = t,\,t + 1\). C, I, and G represent contemporaneous, intertemporal, and global technology, respectively. Following the formulation of meta-frontier Malmquist index in Oh and Lee (2010), we define the global meta-frontier non-radial Malmquist energy–carbon performance index (GMNMECPI), based on the global production technology set (\(T_{{}}^{G}\)), as follows:

$${\text{GMNMECPI}}\left( {K^{s} ,L^{s} ,E^{s} ,Y^{s} ,C^{s} } \right) = \frac{{{\text{ECPI}}^{G} \left( {K^{t + 1} ,L^{t + 1} ,E^{t + 1} ,Y^{t + 1} ,C^{t + 1} } \right)}}{{{\text{ECPI}}^{G} \left( {K^{t} ,L^{t} ,E^{t} ,Y^{t} ,C^{t} } \right)}}$$
(6)

If \({\text{GMNMECPI}} > 1\), the observation is close to the global best-practice frontier; if \({\text{GMNMECPI}} < 1\), the observation is shifting from the global best-practice frontier.

According to Oh and Lee (2010), the GMNMECPI can be decomposed into a technical efficiency change (EC), a best-practice gap change (BPC), and a meta-frontier technology gap change (TGC). The decomposition process is as follows:

$$\begin{aligned} {\text{GMNMECPI}}\left( {K^{s} ,L^{s} ,E^{s} ,Y^{s} ,C^{s} } \right)& = \frac{{{\text{ECPI}}^{G} \left( {K^{t + 1} ,L^{t + 1} ,E^{t + 1} ,Y^{t + 1} ,C^{t + 1} } \right)}}{{{\text{ECPI}}^{G} \left( {K^{t} ,L^{t} ,E^{t} ,Y^{t} ,C^{t} } \right)}} \hfill \\& = \left[ {\frac{{{\text{ECPI}}^{C} (.^{t + 1} )}}{{{\text{ECPI}}^{C} (.^{t} )}}} \right]\left[ {\frac{{{\text{ECPI}}^{I} (.^{t + 1} )/{\text{ECPI}}^{C} (.^{t + 1} )}}{{{\text{ECPI}}^{I} (.^{t} )/{\text{ECPI}}^{C} (.^{t} )}}} \right]\left[ {\frac{{{\text{ECPI}}^{G} (.^{t + 1} )/{\text{ECPI}}^{I} (.^{t + 1} )}}{{{\text{ECPI}}^{G} (.^{t} )/{\text{ECPI}}^{I} (.^{t} )}}} \right] \hfill \\ &= \left[ {\frac{{{\text{TE}}^{t + 1} }}{{{\text{TE}}^{t} }}} \right]\left[ {\frac{{{\text{BPG}}^{t + 1} }}{{{\text{BPG}}^{t} }}} \right]\left[ {\frac{{{\text{TGR}}^{t + 1} }}{{{\text{TGR}}^{t} }}} \right] \hfill \\ & = {\text{EC}} \times {\text{BPC}} \times {\text{TGC}} \hfill \\ \end{aligned}$$
(7)

EC is the efficiency change measure presented by Färe et al. (1994). The BPC measures changes in the best-practice gap ratio between contemporaneous technology and intertemporal technology during the two periods. Here, a value of \({\text{BPC}} > 1\) indicates that the contemporaneous technology frontier moves toward the intertemporal technology frontier. A value of \({\text{BPC}} < 1\) indicates that the contemporaneous technology frontier is moving away from the intertemporal technology frontier. Because BPC measures frontier moves related to contemporaneous technology, it is also an innovation effect equivalent to the technical change (TC) term in the conventional Malmquist index.

TGC measures the changes in the technology gap ratio (TGR) between the intertemporal production technology frontier and the global frontier in two periods. \({\text{TGC}} > ({\text{or}} < )1\) indicates a decrease (increase) in the technology gap between the intertemporal technology for a specific group and the global technology. TGC can be used to measure changes in technology leadership for a given group.

3.3 Data

This paper examines the effect of policies in place during the 11th and 12th Five Year Plans (2006–2015); as such, the sample observation interval comes from the same period. Energy data are not available for Tibet, and the price index data for Chongqing are incomplete. As such, these two areas were omitted from the analysis. The study used a panel data set for China’s remaining 29 provincial regions. The data were obtained from “China Statistical Yearbook,” “China Energy Statistical Yearbook,” and “China Environmental Yearbook.”

  1. (1)

    Desired output. Past studies have generally adopted the transportation sector’s gross product (Bi et al. 2014; Zhang et al. 2015; Song et al. 2015) or the turnover (Zhou et al. 2013, 2014; Cui and Li 2015) as the desired output. China’s statistical yearbook includes some turnover data that are not associated with a specific area. Omitting these data could lead to underestimates of the sector’s energy–carbon performance. As such, gross product (Y) was used as the desired output, and the data were converted into 1990 constant prices.

  2. (2)

    Undesired output. As transportation activity is a main CO2 emission source, this study adopted the CO2 emission (C) generated during transportation sector operations as the “undesired” output indicator. This approach is consistent with other researchers (Bi et al. 2014; Zhang et al. 2015; Song et al. 2015; Zhou et al. 2013, 2014; Cui and Li 2015). Official data on provincial CO2 emissions from the transportation sector are not available for China. Based on Chang et al. (2013), we instead used a fuel-based carbon calculation model, based on the conversion factor to estimate provincial transportation CO2 emissions.

  3. (3)

    Energy input. The volume of energy consumed (E) by the transportation sector was adopted as the energy input, including all types of energy, such as coal, oil, and gas (National Bureau of Statistics of China (NBSC), China statistical year book, 2007–2016). All forms of energy consumption are converted into the standard coal equivalent and then aggregated.

  4. (4)

    Labor input. We adopted the annual number of employees (L) in the transportation sector as an alternative to a labor input indicator. This approach is used elsewhere in the literature (Zhang et al. 2015; Wang et al. 2013).

  5. (5)

    Capital input. This paper adopted capital stock (K) as the indicator of capital input. This variable has been widely accepted as a form of non-energy input (Zhang et al. 2015; Wang et al. 2013). The most common estimation method using the comparative price of capital stock is the “perpetual inventory method.” The data were converted into 1990 constant prices.

Table 1 provides descriptive statistics of the transportation sector data.

Table 1 Descriptive statistics of the input and output data of transportation sector (2006–2015)
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In the “China Statistical Yearbook,” economic zones are divided into the eastern, central, and western regions.Footnote 2 Many researchers have used this classification approach; as such, this paper also adopted these same three regions and compared the differences between them.

4 Results and discussion

4.1 Empirical results

4.1.1 Energy–carbon performance index and the decomposition

To examine changes in the transportation sector’s energy–carbon performance, and to incorporate regional heterogeneity, we computed the energy–carbon performance index (GMNMECPI) and its decomposition for each of the 29 provinces.

Table 2 shows that the average energy–carbon performance of China’s transportation sector decreased by approximately 1.636% using the GMNMECPI. This indicates that the ratio of target carbon emission to the actual carbon emission decreased annually by 1.636% in the sample period. The eastern, central, and western China showed a negative trend, with an average rate of −0.373, −2.416 and −2.386%, respectively.

Table 2 Changes in the GMNMECPI of China’s transport sector, 2006–2015
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At the province level, 6 provinces (54.55% of total) in eastern China, 7 provinces (87.5% of total) in central China, and 8 provinces (80% of total) in western China showed a decrease. Guangdong was the province with the largest increase (3.064%) in average energy–carbon performance; Qinghai showed the largest decrease (−8.267%).

To investigate sources of energy–carbon performance change, the GMNMECPI estimates were decomposed into the efficiency change (EC), best-practice gap change (BPC), and technology gap change (TGC) components. Tables 3, 4, and 5 show the results. Table 3 shows that average EC index for the total country from 2006–2015 under the GMNMECPI framework was 0.999. This indicates an average annual growth of −0.144%. This suggests that provincial transportation generally moved slightly away from the production technology frontier over the sample period. At the regional level, central China showed an increasing trend, with an average energy–carbon performance growth rate of 1.401%. The EC index decreased at an average rate of −0.733 and −0.721% in eastern and western China, respectively.

Table 3 Efficiency change component of the GMNMECPI, 2006–2015
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Table 4 Best-practice gap change component of the GMNMEPI, 2006–2015
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Table 5 Technology gap change component of the GMNMEPI, 2006–2015
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For individual provinces, 10 provinces experienced a decrease in efficiency change of energy–carbon performance, and 8 provinces saw an increase. The EC remained unchanged in the other provinces. In eastern China, Tianjin had the highest EC, with an average of 2.438%; Shandong had the lowest EC (−3.871%). In the central region, Hunan saw the highest increase in EC (5.448%). In the western area, Guizhou had the highest increase (1.43%); Yuan showed the most significant decline in efficiency change (−4.687%). This indicates that these provinces would need to expend significant effort to improve energy–carbon performance.

Table 4 shows that the average best-practice change (BPC) index of the full country is 0.995 under the GMNMEPI, indicating a slight decrease in technology change. This also implies a technological decline in energy use and CO2 emission reduction in China’s transportation sector during the sample period. In eastern China, there was a positive trend, with an average growth rate of 0.380%. The central and west China showed a decreasing trend, with an average rate of −2.040, and −0.148%, respectively.

At the province level, 13 provinces experienced a technological decline, while 14 provinces showed technological progress. Two provinces (Inner Mongolia and Hunan) remained unchanged. Zhejiang was the province with the highest technological progress (2.885%). Jilin had the lowest (−5.877%). In eastern China, Beijing, Tianjin, Fujian, and Hainan experienced a technological decline, at an average rate of −1.324, −1.125, −0.518, and −4.247%, respectively; in western China, Guangxi, Qinghai, and Ningxia saw a technological decline, at an average rate of −0.646, −4.637, and −1.692%, respectively. In addition to Henan and Hunan, the other provinces in central region experienced a technological decline. This indicates that the central China lacked technological innovation in low-carbon technology for the transportation sector. Efficiency also decreased in the central area during the latter part of the period. This was accompanied by a technical regression, resulting in declined energy–carbon performance in central area, at a level lower than the western area.

The technology gap change (TGC) index measures the gap between the intertemporal technology frontier and the global frontier, reflecting the change in technology leadership for a given group. Table 5 shows that the average TGC value is 0.997. This indicates there was little change in the gap between the intertemporal technology frontier and the global frontier. This result suggests a lack of technological leadership in China’s regional transportation sectors during the study period.

Figures 1, 2, 3 and 4 present trends in the cumulative energy–carbon performance index and its decomposition. The 2006 value was set to unity, allowing an estimate of the trend in the cumulative index. Figure 1 reports the cumulative changes in GMNMECPI and its decomposition for the three regions. As Fig. 1 shows, the GMNMECPI in the eastern area shows a downward trend from 2007–2010, indicating the GMNMECPI worsened in this period. The GMNMECPI then experienced an upward trend from 2010–2015. The GMNMECPI in the east decreased 3.31% across the study period. For the central area, the GMNMECPI experienced a significant downward trend from 2006–2012, followed by an slight upward trend; the overall GMNMECPI in central China decreased 19.757% over the period. The GMNMECPI in western trended downward in the sample period; the overall GMNMECPI in the region decreased 19.538%. These results indicate that the central and western areas experienced energy–carbon performance loss during the study period.

Fig. 1
figure 1

Trends of cumulative GMNMECPI at the area level

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Fig. 2
figure 2

Trends of cumulative EC at the area level

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Fig. 3
figure 3

Trends of cumulative BPC at the area level

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Fig. 4
figure 4

Trends of cumulative TGC at the area level

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Figure 2 shows that central China experienced a significant upward trend in efficiency change (EC); this area had the highest efficiency change, with a growth rate of 13.336% during the study period. In contrast, there was a downward trend both in eastern and western regions. In western China, the efficiency change decreased 6.301% during the sample period. Eastern China experienced the lowest efficiency change, with a decrease of approximately 6.41%. This implies that production technology for the eastern region’s transportation sector has not been fully used; the reasons for this require further investigation.

With respect to the best-practice gap change (BPC) in Fig. 3, only the eastern region saw increases, at rates of 3.47%. The central and western areas experienced a decline, at a rate of −16.931 and −1.327%, respectively. This indicates that central China experienced a significant lag in innovation with respect to technologies in the transportation sector. Many provinces in the central region (such as Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, and Hubei) showed a significant decline during the sample period. This indicates that innovation may need more attention in these provinces. The results also suggest that the central region may have become a “pollution haven” while advancing. This possibility requires further investigation.

The technological gap change (TGC) provides a possible measure of the change in technological gap between groups and reflects technological heterogeneity. Figure 4 shows that the TGC in the eastern region is almost equal to unity during the study period. This indicates that most provinces in eastern China have advanced production technology in the transportation sector and are in the technology frontier. This reflects almost no technology gap between the eastern area frontier and the meta-frontier. The central regions experience a significant downward trend during most years in the sample period, indicating an expanding gap between this group frontier and the meta-frontier. There was a decline in the TGC in the western area in recent years. This indicates that the gap between relative technological level in western area and the potential technological level across the country may expand in the future, possibly worsening environmental problems.

As mentioned above, the paper covers two periods: the 11th Five Year Plan (2006–2010) period and the 12th Five Year Plan (2001–2015) period. In order to determine any significant methodological differences between the GMNMECPI in these two periods, we employ the Mann–Whitney U test and compare the difference in decomposition results. As shown in Table 6, all the results of GMNMECPI and the decomposition cannot reject the null hypothesis at least at the 5% level, indicating that the results for the two periods statistically have no significant differences in terms of GMNMEPI, EC, BPC, and TGC components. However, the Chinese government proposed energy-saving and carbon intensity reduction targets during the 11th and 12th Five Year Plan periods (2006–2015). However, our results show that energy–carbon performance did not improve from 2006–2015, suggesting the low-carbon transportation policy had no effect.

Table 6 Mann–Whitney U test for the GMNMECPI and the decomposition of the two periods
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4.1.2 Innovative provinces

In view of the sustainable development of transport sector, it would help to identify the most innovative provinces, so that the provinces that are overusing energy and emitting excess CO2 emissions can target innovators who might help improve their energy–carbon performance.

The TGC index only indicates the change in the technological gap between a specific group and the whole country. A more in-depth analysis is needed to identify the innovators. There are two types of innovative provinces: group and meta-frontier. Group innovators include provinces that invent new technology within a specific group. Meta-frontier innovators are a subset of group innovators that take an integrated perspective. Färe et al. (1994), Oh and Lee (2010), and Zhang and Choi (2013) specify three conditions to determine group innovators:

$${\text{BPC}} > 0,$$
(8a)
$$E^{t} (K^{t + 1} ,L^{t + 1} ,E^{t + 1} ,Y^{t + 1} ,C^{t + 1} ) > 1,$$
(8b)
$$E^{t + 1} (K^{t + 1} ,L^{t + 1} ,E^{t + 1} ,Y^{t + 1} ,C^{t + 1} ) = 1,$$
(8c)

Condition (8a) specifies that the contemporaneous production technology frontier should shift toward the intertemporal production technology frontier. Condition (8b) indicates that the production activity of innovative provinces in period t + 1 should be outside the technology frontier of period t. Condition (8c) indicates that the innovative provinces should be located on the contemporaneous technology frontier in period t + 1.

To be an innovative province on the meta-frontier, the following two additional conditions are required:

$${\text{TGC}} > 1,$$
(9a)
$$E^{G} (K^{t + 1} ,L^{t + 1} ,E^{t + 1} ,Y^{t + 1} ,C^{t + 1} ) = 1,$$
(9b)

Condition (9a) specifies that a meta-frontier innovator should be a technological leader that has achieved a decrease in the gap between the intertemporal technology frontier and the global technology frontier. Condition (9b) states that a meta-frontier innovative province should be located on the global production technology frontier.

Table 7 shows the innovative provinces for low-carbon transport technology under the group frontier and meta-frontier. In eastern China, Hebei and Fujian are identified as group innovators five and three times, respectively; Shandong appears twice; and Hainan only once. In central China, Shanxi, and Jilin are recognized as innovative provinces five and two times, respectively; Anhui appears only once. In the west, Gansu is recognized as an innovative province twice; Guizhou, Shaanxi, Inner Mongolia, Xinjiang, Guangxi, and Sichuan appear once. From the meta-frontier perspective, two provinces are nationwide innovators. Hebei ranked highest in 2006–2007, 2009–2010, 2011–2012, 2012–2013, and 2013–2014. Fujian ranked first from 2008 to 2009. The meta-frontier innovators are all in the eastern region, suggesting that this region is a leader in innovating low-carbon transportation technology.

Table 7 Group and meta-frontier innovators
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4.1.3 Kernel density estimate for the energy–carbon performance index

The results of the Kernel density analysis provide more information about the energy–carbon performance from the aspect of the peak and asymmetry of distribution. We compared the GMNMECPI and its decomposition through a Kernel density estimate, to visually explore the differences among the three China regions. Figure 5 shows that the GMNMECPI in the eastern China is to the right of the values for central and western China. This indicates higher energy–carbon performance in the east than in the other two regions. The east experienced a triple peak, highlighting a polarization phenomenon for energy–carbon performance in that region. The GMNMECPI in central and western regions are generally aligned, indicating a similar energy–carbon performance for these two regions. However, the latter has a high peak than the former, implying that the energy–carbon performance in the west is more decentralized than in central China. The results of Kernel density confirm that there are significant differences in energy–carbon performance between the three regions.

Fig. 5
figure 5

Kernel density for the GMNMECPI in three areas

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To provide detailed information about the change in energy–carbon performance in a specific area, we estimated the Kernel density of the GMNMECPI in typical years for the three regions (Figs. 6, 7, 8). Figure 6 shows energy–carbon performance in the eastern region: it decreased first and then increased. From 2006 to 2010, the GMNMECPI in the east declined and then increased slightly from 2010 to 2014. There was a small right peak in 2006, indicating several provinces have higher energy–carbon performance than the others in the eastern area. Peaks in 2010 and 2014 are lower than the 2006 peak. This implies that the energy–carbon performance in the east became more decentralized later in the study period.

Fig. 6
figure 6

Kernel density for the GMNMECPI in east area

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Fig. 7
figure 7

Kernel density for the GMNMECPI in central area

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Fig. 8
figure 8

Kernel density for the GMNMECPI in west area

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Figure 7 reports the change in energy–carbon performance for the transportation sector in central China from 2006 to 2014. The energy–carbon performance decreases significantly from 2006 to 2010; but there is no significant change in GMNMECPI from 2010 to 2014. In 2006, a slight double peak is seen, implying a polarization phenomenon related to energy–carbon performance that year. The peak in 2006 is much higher than in 2010 and 2014, indicating a decentralization trend related to energy–carbon performance in the central area.

The energy–carbon performance decreases slightly from 2006 to 2010 in western China during the sample period (Fig. 8). The GMNMECPI in 2006 shows a steep shape, contrasting with the more gradual patterns in 2010 and 2014. This indicates that the energy–carbon performance for the western area became more decentralized as time passed, compared to 2006. Similar to Fig. 7, there is a double peak in 2006, indicating a polarization phenomenon for energy–carbon performance in the region. This further validates the results presented above.

5 Conclusions

China’s transportation sector consumes significant energy and emits significant CO2. This makes it important to evaluate the energy–carbon performance of the sector, and the effects of current policies. This study was designed to explore gaps in the existing relevant research: the lack of information on regional heterogeneity may bias energy–carbon performance estimates; a lack of long-term studies prevents the exploration of energy–carbon performance variability over time; the use of the CBT or cross-benchmark technology may result in lower discriminating power and intertemporal incomparability. To address these areas, this paper proposed a M-G-NDDF model by combining meta-frontier method, GBT, and non-radial DDF. The new approach was then applied to evaluate the energy–carbon performance of the transportation sector across 29 provinces in China from 2006-2015.

The study generated the following main empirical results. First, on average, the energy–carbon performance of China’s transportation sector decreased by approximately 1.636% during the study period; the eastern, central, and western China showed a negative trend, with an average rate of −0.373, −2.416, and −2.386%, respectively. The gap between the central and western group frontiers and the meta-frontier expanded significantly. Second, the decomposition of the performance index reveals that energy–carbon performance reduction is primarily caused by a significant technology lag in the central area. In contrast, energy–carbon performance is mainly influenced by deteriorations in efficiency in the east and west. Third, the eastern area has the highest innovation effect in low-carbon transportation technology. The central area experienced a distinct catch-up effect, with the largest increase in efficiency. Finally, all three areas have become more decentralized with respect to energy–carbon performance in recent years.

Based on the results above, we propose the following policy steps to increase the sustainable development of China’s transportation sector. Deteriorating efficiency hinders energy–carbon performance improvement in the east. In addition, there is an obvious decentralization for the energy–carbon performance in this region. We suggest that local governments focus on improving the internal management of firms to fully use resources. It is also important to stimulate technology diffusion related to energy use and environmental protection, to reduce within-group differences.

In central China, the lowest energy–carbon performance is explained by technological lag. This area has many energy- and emission-intensive industries; CO2 emissions have significantly increased with the rapid development of heavy industries. Therefore, the government should upgrade the local industrial structure. This would include introducing environmental friendly industries and encouraging firms to carry out technological innovation and use the latest environmental control technologies. This would narrow the technology gap.

As environmental pollution controls strengthen, many energy- and emission-intensive enterprises will transfer from the east to the west of China. Due to the very fragile ecological environment in the west, it is vital that this region does not become a “pollution haven.” This can be facilitated by the west’s integration of industrial transfers from the east. To balance economic development and environmental protection in the west, the local government should accelerate resource and factor market reforms, encouraging spillover effects associated with advanced technology and management ideas.