Accessing performance of transport sector considering risks of climate change and traffic accidents: joint bounded-adjusted measure and Luenberger decomposition

Green transformation of energy use in China’s transport sector will promote sustainable development in the country. This paper extends the Bounded-adjusted Measure and Luenberger indicators to detect the performance of China’s inland transport sector across 2006–2015. In the framework, the climate change and traffic accident risks are taken as undesirable outputs. In addition, source-specific and variable-specific decomposition are proposed for investigating the sources of inefficiency and productivity, and quantifying the contributions of climate change and traffic accident risks. This paper opens up the “black box” of technological progress, identifying the different channels (i.e., quantity and time-dimensions) through which affect economic growth. Therefore, policymakers can find out the most effective pathway to boost productivity growth and mitigate climate change and traffic accident risks in the transport sector, which are ignored in the conventional framework. Empirical results indicate great variances exist among 30 provinces in inefficiency scores, productivity change, and technological progress. Hence, classified regulations help to tackle this issue. We clustered 30 provinces into 4 groups according to their technological progress along quantity and time-dimensions. Variable-wise, CO2 emission-reduction and civil vehicle gains promote the TFP gains most. Also, we verify that economic development and environmental regulations can coordinate to promote the sustainable development of the transport sector.


Introduction
Transport sector, plays an important role in promoting sustainable development worldwide (Legacy 2015;Li et al. 2019;Monios 2019). Economic growth brings rapid progress of industrialization and urbanization, which will mainly in turn result in traffic pressures (e.g., traffic congestion, traffic accidents and greenhouse gas emissions) (Liu et al. 2010;Hao et al. 2015;Zhao and Hu 2019;Huang et al. 2019). Hence, properly addressing the aforementioned posers requires us to figure out the impacts of traffic congestion, traffic accidents, and GHG emissions on transport sector. On one hand, World Health Organization (WHO) (2018) issued an Analysis report on global road traffic safety situation claimed that annual fatalities due to traffic accidents reached 1.35 million worldwide. On the other hand, climate change has been a global poser facing humankind (Pilli-Sihvola et al. 2010;Jin et al. 2015;Bohr 1997). As the most important contributor to greenhouse gases (GHG), carbon dioxide (CO 2 ) is the main factor resulting in global warming, accounting for nearly 90% of the global average temperature rise (Huang et al. 2019). Indeed, transport sector, as the major CO 2 emitter, contributed to about 23% of overall CO 2 emissions globally (IEA 2014). In face of the aforementioned undesirable outputs, policy regulations on transport sector are promulgated internationally.
Properly addressing the aforementioned problems needs international efforts, including the developing countries. Notably, China, as the largest developing country, is regarded as the engine for economic growth (Boussemart et al. 2019;Huo et al. 2019;Wang et al. 2019Wang et al. , 2020. Also, the rapid development brings by-products. Encountering these issues, authorities in China have been dedicated to formulating regulations on transport sector. Recently, the Development Planning of Modern Comprehensive Transportation System issued by the State Council in China in the 13th Five-Year Plan pointed out that by 2020, the country will achieve the following goals 1 : (1) In general, the country will build an overall safe, convenient, efficient and green modern comprehensive highway transport sector.
(2) Some particular regions and areas must take the lead in basically realizing the modernization of transportation. The plan further detailed that the overall investment in the highway transportation sector will reach 15 trillion CNY, among which railway will reach 3.5 trillion, the highway will reach 7.8 trillion, civil aviation will reach 0.65 trillion, and water transportation will reach 0.5 trillion (National Development and Reform Commission, 2017).
The rapid development of the Chinese transport sector brings by-products, e.g., traffic accidents, traffic congestion and CO 2 emissions. Indeed, the overall deaths resulting from traffic accidents reached 63,194 in 2018(National Bureau of Statistics 2019. Looking at traffic congestion, the direct economic loss caused by traffic congestion is equivalent to 5-8% of GDP every year, up to 250 billion CNY (Ministry of Transport of the People's Republic of China 2019). Turning to CO 2 emissions in transport sector, the CO 2 emissions of the transportation industry are 781 million tons, accounting for 8.7% of the total CO 2 emissions of fuel consumption (IEA 2016).

3
The total factor productivity (TFP) denotes the share of outputs that cannot be explained by the change in inputs. As a comprehensive indicator, TFP accounts for a large percent for economic growth (Ilmakunnas and Miyakoshi 2013). Hence, many studies have been dedicated to seeking for the driving force of TFP growth in firm-level, city-level, nationallevel and international level. However, they all focused on the "all-in-one" composite productivity indicator, this fails to reveal the impact mechanism of productivity on economic growth. On this basis, this paper opens up the "black box" of productivity, revealing the channels or pathways through which it affects the economic growth.
Previous scholars provided theoretical and empirical guidance in the related field for the current paper (Cooper et al. 2001;Cullinane et al. 2005;Fleisher et al. 2010;Venturini 2015;Gehringer 2015;Beier 2019). Indeed, the operation performance of transportation has been widely investigated (Tian et al. 2014;Kannan and Hirschberg 2016;Pettersson et al. 2018). Importantly, Oum et al. (2013) employed a DEA-based approach, together with alternative approaches for the measurement and comparison of social efficiency across firms in different transport modes. Seufert et al. (2017) developed a DEA-based Luenberger-Hicks-Moorsteen productivity indicator to measure the airline operational performance. Mahmoudi et al., (2019) introduced a DEA considering game-DEA for the sustainability assessment of urban transportation systems. Saeedi et al. (2019) extended a network DEA method to measure the performance of different intermodal freight transport chains inside a freight network. Indeed, data envelopment analysis (DEA) proposed by Charnes et al. (1978) can be an effective approach in measuring relative efficiency among Decision-making Units (DMUs). The approach can be used to measure the environmental efficiency in transport sector and we can obtain the corresponding TFP changes and technological progress with various approaches (e.g., Luenberger productivity indicator (LPI); Mamlquist index; Hicks-Moorsteen index) (Daraio et al. 2016;Liu et al. 2019). Chang and Tovar (2017) performed a Meta-frontier analysis on productivity change in the West Coast of South Pacific terminals with a DEA-Malmquist approach and further explained the differences in productivity change with a dynamic panel estimation, and revealed that catch-up effect and technological regress prevail. Feng and Wang (2018) introduced a global meta-frontier DEA for measuring energy efficiency in transport sector, and revealed that technological progress is the main factor for productivity gains.
Though the aforementioned conventional DEA models and approaches contributed to the accuracy of TFP measurement, these methods can not satisfy the multi-objective decision making and suffer certain drawbacks. For example, the subjective parameter setting is required for Slack-based Measure, which renders the deviation to the real productivity change. As for Range-adjusted Measure (RAM), the range composes the parameter that will destroy the discriminatory power and induce infeasible solutions assuming constant returns to scale (CRS). The Bounded-adjusted Measure proposed by Cooper et al. (2011), on the basis of additive structure, can address these drawbacks well. Furthermore, the treatment of static inefficiency determines the accuracy of productivity change. Additive-based Luenberger Productivity Indicator and multiplicative-based Mamlquist index have been the most prevailing approaches for measuring productivity change. Indeed, an additive-based LPI is a more flexible one that can perform the source-specific decomposition and variable-specific decomposition. Boussemart et al. (2020) did an expended decomposition on Luenberger Productivity Indicator and applied the model to the Chinese healthcare sector, found that productivity growth is mainly driven by technological progress.

3
The current paper mainly provides contributions methodologically and empirically as follows. Firstly, we construct a framework that incorporates multi-inputs and multi-outputs involving passenger and freight systems. Then, the managerial disposability is set for transportation-related energy use, implicating that clean energy use and structural adjustment are obtained. Thirdly, a systemic decomposition framework for Luenberger indicators is introduced, i.e., a source-specific and variable-specific one (as shown in Fig. 1). Last but not the least, the channels of technological progress on economic growth are revealed from the quantity and time-dimensions.
The following parts are organized in a coherent manner. Section 2 introduces the quantitative methods in computing TFP, along with the approach illustration on novelty. Data source and settings are investigated in Sect. 3. Section 4 brings empirical analysis which details the inefficiency and productivity change, as well as the decomposition results. Conclusion remarks and policy recommendations are provided in Sect. 5.

Quantitative methods
In order to perform variable-specific and source-specific decomposition analysis of the productivity change of transport sector in the China's regional level, we extend the approach for productivity change decomposition introduced by Chen et al. (2020). Specifically, we first need to establish the current and global frontier on the basis of the panel data from multiple time spans (i.e., 2006-2015 in the study). Then, province-level panel data in China are used, and a province-level region is taken as a decision-making unit (DMU). This section shows the detailed calculation process of inefficiency scores through BAM and productivity change relying on the LPI.

Production technology
Transport sector, as a comprehensive system network, can be regarded as a production process that transforms energy use and conventional input (i.e., non-energy inputs, e.g., labor force, capital stock and vehicle quantities) into desirable outputs (e.g., transport turnover and economic outputs) and undesirable outputs (e.g., traffic casualties and CO 2 emissions) (Wang et al. 2011;Fan and Lei 2016;Hang et al. 2019;Chen et al. 2019).
In the current paper, we consider possession of registered civil vehicles, fixed capital stocks, labor force, and energy use in transport sector as inputs, transport turnover and output as desirable outputs and traffic casualties, and CO 2 emissions as undesirable outputs . Equation (1) presents the details.
As is shown in Eq. (1), the variable set (E t 1 , P t , K t , L t ) represents the energy use of inland transport (E), possession of registered civil vehicles (P), fixed capital stock in transport sector, storage, and post (K) and employment in transport, urban units, traffic, storage, and post (L), respectively. The variable set (D t , Y t , T t 1 , E t 2 , T t 2 , C) denotes the value added of the inland transport sector (Y), transport turnover (T1), traffic deaths (T2), and CO 2 emissions in transport sector (C). Indeed, the variable set PT t is defined as a close-set, suggesting that the transformation from inputs to outputs is limited and null-jointness and strong disposability can be assumed (Färe and Grosskopf 2004).
In the aforementioned Eq. (2), represents the positive intensity vector, whereas i denote i-th decision-making unit (DMU). Further on, e, p, k, l, y, e 2 , t 1 , t 2 , c is the matrices of quantities of inputs, desirable outputs, and undesirable outputs, respectively. With constraint ∑ = 1 , the underlying technology becomes variable returns to scale (VRS) one. When there are no constraints on , constant returns to scale (CRS) is maintained. (1) 1 3

BAM model assuming managerial disposability for energy use
Bounded-adjusted Measure (BAM) is a non-radial and non-oriented model that can detect subtly differences among decision-making units (DMUs) (Cooper et al. 2011). This indicates the model has strong discriminatory power which can be attributed to its parameter. 2 In addition, the model is flexible and suitable for any returns to scale (RTS). Indeed, the basic model treats all input-oriented variables in the same manner (i.e., natural disposability). The natural disposability implies that producers may reduce the generation of the undesirable outputs by adjusting production, i.e., given a reduction in the input vector leading to reduced undesirable outputs, maximize the desirable outputs. However, with the rapid process of urbanization and industrialization, the energy use has greatly turned into a cleaner mode. Therefore, the novel treatment manner for energy use variable is necessary. For addressing the problem, Goto (2011, 2012) introduced the managerial disposability, which has certain policy implications. Specifically, assuming managerial disposability, producers maximize production of the desirable outputs while minimizing generation of the undesirable outputs and increasing the use of inputs. With regards to the energy use, this can be explained as using cleaner energy instead of coal, oil and other fossil energy related to pollutant emissions.
The current paper will apply natural disposability to conventional input variables and managerial disposability to energy use. For simplicity, we arrange possession of registered civil vehicles (P), fixed capital stock in transport sector, storage, and post (K), and employment in transport, urban units, traffic, storage, and post (L) into conventional inputs, and separate energy use. In addition, value added of the transport sector (Y) and transport turnover (T1) are incorporated into desirable outputs and traffic death (T2) and CO 2 emissions in transport sector (C) into undesirable outputs. The introduced model is for calculating the static inefficiencies of the transport sector. The additive structure of BAM can be described as: (3) i e ri − S e r = e ri ; i e ri ≤ max(e ri ); where variable set (x pi , e ri , y vi , z wi ) denotes the quantities of conventional inputs, energy inputs, desirable outputs and undesirable outputs of the i-th DMU in time period t, respectively. Variable set (S x q , S e r , S y v , S z w ) represents slack variable set of conventional inputs, energy use, desirable outputs and undesirable outputs, respectively. Variable set (L x q , U e r , U y v , L z w ) defines the difference between lower bound (upper bound) and the observed values of conventional inputs, energy use, desirable outputs and undesirable outputs as follows: In addition, it is noteworthy that if i-th input satisfies x qi = min(x qi ) , the optimal condition is found (i.e., S * x q ). Then, we define S * x q L x q = 0 . Likewise, we can define: Further on, the investigation of productivity change forces us to perform the variablespecific decomposition. Cooper et al. (1999) introduced the input-oriented and outputoriented decomposition that attribute inefficiency to overall inputs and overall outputs. Cooper et al. (2007) proposed the variable-specific decomposition method for Slack-based Measure (SBM). On this basis, the current paper introduces a decomposition approach that can attributes overall inefficiency to individual variable for BAM.

AAT-TFP measurement
In order to continue on the analysis of Average Annual Transport Total Factor Productivity (AAT-TFP) of China's 30 province-level regions, the study considers energy use of (4) transport (E), possession of registered civil vehicles (P), fixed capital stock in transport sector, storage, and post (K), and employment in transport, urban units, traffic, storage, and post (L), value added of the transport sector (Y), transport turnover (T1), traffic death (T2) and CO 2 emissions in transport sector (C) as variables. Furthermore, the component of inefficiency is given in Eqs. (6)-(9) can be further broken down in terms of individual variables as shown in Eq. (10).
Take all observations associated with different time spans into consideration for constructing a global frontier, technical efficiency can then be captured for each sample time period. In addition, the relevant productivity change can then be calculated by considering the dynamics in the global inefficiencies for the adjacent time periods. Indeed, the mixed disposability for inputs in BAM is employed for computing technical inefficiency (IE). On the one hand, technical inefficiency measured against the global frontier is termed global inefficiency (GIE). On the other hand, technical inefficiency measured against the frontier-spanning observations from a sample period is termed contemporaneous inefficiency (CIE). What is more, the technology gap (TG) is comprised of the difference captured between these two measures. Note that subscript index v is employed to represent the variable returns to scale (VRS) estimators, whereas subscript index c denotes the constant returns to scale (CRS) estimators. Furthermore, the comprehensive relationship of the aforementioned two measures associated with the global and contemporaneous frontiers is shown as follows: Drawing from Oh (2010), the Average Annual Total Factor Productivity change of transport sector is calculated as: Indeed, AATFP > 0 indicates productivity gains, whereas AATFP < 0 suggests productivity decline. In addition, the measures of TG and CIE set off the two terms of the LPI, namely catch-up effect (efficiency change, AAEC) and frontier movement (technological progress, AATP): Assuming VRS estimator permits expanding the source-specific decomposition. On the one hand, average annual efficiency change (AAEC) term can be further broken down into pure efficiency change (LPEC) and scale efficiency change (LSEC). On the other hand, technological progress (ATTP) can be further broken down into average annual pure technological progress (LPTP) and average annual technological progress of scale change (LTPSC). The calculation process is presented below: As this study focuses on the operation performance of transport sector, we decompose the productivity change in Eq. 12 (and its terms in Eqs. 15-18) in terms of the eight variables presented in Eq. 10. Note that one can identify the productivity changes related to energy use or other variables of interest. Since the paper focuses on the transport sector, we then term the presented productivity change as Average Annual Transport Total Factor Productivity (AAT-TFP) in the following parts.
Note that the DEA model shown in this sub-section implies specific assumptions which could possibly influence the inefficiency scores and productivity changes obtained. Indeed, the underlying technology and the inefficiency measurement can be defined in DEA models. In addition, when constructing the AAT-TFP indicator, the use of the inefficiency measurement also varies greatly in terms of the decomposition approach. In the current paper, natural disposability technology is set for non-energy inputs, whereas managerial disposability is considered for energy inputs. This delivers certain policy implications, where natural disposability decreases inefficiency scores through curbing inputs and managerial disposability decreases inefficiency scores by expanding inputs.
What is more, Miao et al. (2021) and Wang et al. (2021) emphasized that the sustainable development of the economy depends on technological progress to a great extent. Indeed, the sustainable development of transport sector also remarkably relies on technological progress (Cohen and Jones 2020). Especially, against the background of fast industrialization and urbanization in China, transport production technologies are dedicated to promoting a comprehensive transport network and gaining output value added, whereas ignoring traffic accidents and greenhouse gas emissions. Hence, exploiting the paths of technological change has been a necessity, whereas ignored by the existing literature. In order to comprehensively model the effects of technological change on AAT-TFP, specific problems ought to be addressed in perspective (Miao et al. 2019). Specifically, (1) from longterm time-dimension, how can we measure the technological progress? (2) from long-term quantity-dimension, how can we quantify the technology gap between the worst-performance time period and a certain time period? (3) from technological progress perspective, how can we investigate the relationship between long-term time-dimension and quantitydimension? The decomposition of Eq. (14) fails to address these questions. The further decomposition of technological change components in transport sector can proclaim the differences in technological change patterns across different regions. Then, the suitable and reasonable technologically innovative transport strategies for promoting comprehensive and sustainable development.
By exploring Eq. (14), we can model the average annual technological in the long term: As presented in Eq. (19), TG c (i) − TG c (t + 1) denotes technological gap between i-th time period and t + 1-th time period, further referred to as PT t+1 refers to the technological gap between i-th time period and t-th time period, further referred to as PT t i . In particular, when we set constraints on parameter i, certain implications can be delivered.
Assumption (1): when i = 1(in Eq. 20), the technology gap between the initial time period and t-th time period and t + 1-th time period can then be presented, respectively. Miao et al., (2019) Assumption (2): when i is defined as the time period that owns the maximum technological change, then TG c (i) is termed as TG max c (presented in Eq. 21). In brevity, PQ max , i.e., the technological gap between a certain time period t + 1 (t) and a specific sample point with worst-technology performance.
In addition, by exploiting Eqs. (19)-(21), the combined assumption of (1) and (2) (i.e., time-dimension and quantity-dimension) decomposition results can be obtained: In Eq. (22), is defined as a weight parameter that belongs to [0, 1]. In particular, when = 1∕2 , average time-and quantity-dimension decomposition results are then obtained (the particular situation is employed in Miao et al. 2019b). The decomposition process is presented in Fig. 1.
In conclusion, one can attribute the overall inefficiency scores and overall productivity change into individual variables. In addition, the source decomposition can then be performed for productivity change into efficiency change and technological change. What is more, we can explain the trends of technological change along time-and quantity-dimensions by comparing technological gap (TG) against different assumptions. Noteworthy, a similar decomposition process can be applied to average annual pure technological progress (PTP) and average annual technological progress of scale change (TPSC) with interest.

Data sources
This paper relies on the non-parameter model (BAM) and Luenberger indicators that involve the transformation from inputs to outputs. Note that the lack of data in the Tibet autonomous region forces us to consider the remaining 30 province-level regions in mainland China as decision-making units. The time span across 2006-2015 that corresponds to the China's 11th-12th Five-Year Plan is taken as a research sample. Note that part of the data is from Stefaniec et al. (2020) Specifically 3 : (1) (1) Energy use (E, Mtce): E denotes the energy use in transport sector. Indeed, energy use is considered as an important variable in transport sector. Following Chen et al. (2019) and Huang et al., (2019), energy use is considered as an input variable. In addition, we assume the converse disposability for energy use and other input variables in transport sector. The primary data set was drawn from the China Energy Statistical Yearbook. Drawing from CESY (2016), conversion factors to coal equivalent are employed.
Wang (2019) and Stefaniec et al. (2020) incorporated civil vehicles as their input variable, which has been the theoretical basis for the current paper. Indeed, the data set was derived from the online database of the National Bureau of Statistics of China (NBSC 2020).  (2014), which takes value added as desirable outputs. The data was drawn from the online database of the National Bureau of Statistics of China (NBSC 2020). (6) Turnover (T1, 10 8 ton-km): T1 represents the total passenger and freight turnover of highways, railways, and waterways. We refer to Stefaniec et al. (2020), and set transport turnover as desirable output. The data was drawn from the online database of the National Bureau of Statistics of China (NBSC 2020). Note that, according to Chang et al. (2013), passenger turnover was transformed into freight turnover units in the paper. (7) Traffic casualties (T2, persons): T holds a number of deaths and people injured in traffic accidents. Indeed, according to Chen et al. (2020), traffic accidents are considered undesirable outputs. However, some minor traffic accidents are hard to identify and thus we consider traffic casualties as a proxy variable. The data was drawn from the online database of the National Bureau of Statistics of China (NBSC 2020). (8) Carbon dioxide emissions (C, Gg CO 2 ): CO 2 emissions from the fossil fuel combustion of transport vehicles. Following Mahdiloo et al. (2018), CO 2 emissions are treated as undesirable outputs. According to IPCC (2006), the fuel-based carbon footprint model is used to calculate the emissions, while electricity usage is excluded. The data set was from China Energy Statistical Yearbook. increasing trend. Conversely, energy use in transport sector decreased, indicating regulations have positive effects in general. As regards output-oriented variables, value added and turnover volume display a rapid increasing trend. On the contrary, traffic casualties show the opposite trend. Noteworthy, the effects of CO 2 emissions abatement policies are limited. Table 2 shows the changing rates of input/output variables across 2006-2015 in China.
For simplicity, Table 2 lists the changing rates of eight core variables in China's transport sector across 2006-2015. Specifically, among 30 provinces, as regards energy use, most provinces have rates of change larger than − 90.00%, apart from HAN, AH, and QH (− 89.79, − 88.91, and − 83.87% resp.). This indicates that these province-level regions are lagged in transport energy-conversation as a whole. For civil vehicle possession, GS and NX are possessed with the highest rates of change (542.40 and 498.70% resp.), whereas SH and BJ have the opposite trend (123.24% and 163.67% resp.). Looking at capital stock, CQ and FJ have the best performance (110.98 and 73.10% resp.), while JL and HLJ hold the other extreme (4.36 and 2.93%). Turning to the labor force, SC and GZ show explosive growth on changing rates (1156.92 and 1017.25% resp.), whereas SH and JX have converse trend (224.57 and 276.10% resp.). As for value added, GX and GZ increase greatly (240.70 and 376.99% resp.) whereas YN and GS are lagged (74.49 and 61.96% resp.). Looking at traffic turnover, only TJ has decreasing trend. For traffic casualties, only TJ shows increasing trend. Hence, the performance obtained in rates of change in TJ is terrible. Finally, the decreasing rate of change relative to CO 2 emissions is observed in TJ, IN-MON, and SD (− 2.37, − 10.31, and − 0.64).
Generally speaking, the average changing rates associated with energy use and traffic casualties hold an obvious decline trend (− 93.19 and − 43.65% resp.), whereas that of civil vehicles and employment display a steep increasing trend (371.84 and 635.32% resp.). For K, L and C, spatial distribution characteristics of performance are better in southeastern coastal areas and go decreasing in northwestern provinces.

Transport inefficiency
The framework introduced in Sect. 2 will induce inefficiency scores both under CRS and VRS assumptions. 4 We can obtain the inefficiency scores in transport sector for 30 province-level regions. In addition, we term the inefficiency as global inefficiency (i.e., GIE)  Table 2, and in the following context we will mainly use the abbreviation for sake of brevity  due to the construction of the global frontier. What is more, the additive structure BAM permits the variable-specific decomposition, as shown in Table 3. As Table 3 shows, the average scores of GIE for 30 province-level regions in China's transport sector during 2006-2015 is 0.12. Generally speaking, inefficiency scores associated with energy use (E), value added (Y) and CO 2 emissions (C) induced by the BAM model are zero. Note that the zero inefficiencies for value added (Y) is coherent with most previous researches (e.g., Miao et al. 2019a). However, the nil inefficiency for energy-environment variables (i.e., E and C) vary greatly from that in Miao et al., (2019a), where inefficiency scores relative to energy-environment variables account for 82% of the overall inefficiency. As we set managerial disposability for E, the nil inefficiency scores indicate expanding clean energy use in transport networks should be promoted. Turning to Y, the additive approach indicates there is limited potential for gaining the value added in transport sector given the existing levels of inputs. Hence, input-oriented structural adjustments are prioritized over input-oriented extensive growth. Looking at C, the zero inefficiency score corresponds to the strong assumption for energy use, suggesting that complete clean energy use will result in optimal CO 2 emissions. Looking at transport turnover (T1), the GIE is low but no longer equal to zero, which can be attributed to the redundancy for P, K and L (all 0.02). Noteworthy, the GIE scores relative to traffic casualties is highest (0.04), accounting for 33.33% of the overall inefficiency scores, and this corresponds to the results reported in Chen et al. (2019). This indicates traffic casualties have been the roadblock for achieving high efficiency and large potentials exist for improvements in this regard.
Region-wise, substantial variances can be observed for 30 province-level regions and certain patterns can be concluded. For example, HB and GZ have been in the frontier for their nil inefficiency scores. Look at HB, the province is possessed with more outputs (value added) in transport sector, whereas it can better coordinate the relationship among energy use, value added and traffic casualties. Hence, its technical efficiency in transport sector is at the forefront of the whole country. Turning to GZ, though its total economic output in transport sector is not high, the level of energy use, civil vehicle possessions, traffic casualties and pollutant emissions can be coordinated with economic development. Due to the relatively high possession intensity of civil vehicle possession per unit area, the level of inefficiency scores in BJ, TJ and SH are generally low (0.03, 0.07 and 0.03 resp.) whereas they still bear certain pressure of regulations in transport sector. Spatially, the sum of the static inefficiencies of transport sector in central China (e.g., AH, JX, HEN and HUN; 0.23, 0.18, 0.12 and 0.16 resp.) and parts of Western China (i.e., CQ, SC, YN and XJ; 0.26, 0.27, 0.24 and 0.20 resp.) exceed that of other parts in the country. For local officials, the situation of atmospheric environment harnessing is grim.

Variable-specific dimension decomposition
In this study, we perform the decomposition from two dimensions on the basis of the Luenberger productivity indicator. Note that the panel data representing all the time periods are used to construct the global frontier, and panel data from each particular time period are employed to build the current frontier (i.e., we handle data, respectively). Combined with Eqs. (11)-(18), the average annual change of TFP of transport sector in China's provincial-level region during 2006-2015 can be calculated. Moreover, according to the additive structure principle of the extended Luenberger productivity indicator, ATTFP growth is decomposed into the contribution of each variable. The results are shown in Table 4. As is presented in Table 4, the total growth rate of AAT-TFP is 2.32% across 2006-2015. The variable-specific decomposition indicates that all variables contributed positively to the overall productivity gains, with the highest share of C and L (0.57 and 0.48%). This indicates regulation policies on C and the labor force have achieved high-quality progress, whereas Y is comparatively lagged (0.11%). This corresponds to the inefficiency scores presented in. Specifically, higher inefficiency scores indicate more potential for improvements (e.g., P, K, L, and T2). Conversely, lower inefficiency scores suggest limited potentials for improvements (e.g., Y and E).
Regionally, substantial variances can be observed. Looking at GZ, the joint results of nil inefficiency (0.00) and negative productivity change (− 0.81) imply the existing inputs cannot achieve connotative development, and then input-oriented structure adjustments in transport sector are required. Turning to BJ, TJ and China's southeastern coastal areas, lower inefficiency scores are observed, e.g., 0.00% for BJ, 0.00 for SH, 1.61% for JS, and 1.59% for ZJ. Whereas western province-level regions hold relatively larger productivity gains, e.g., 5.72% for GS, 5.14% for NX. Spatially, the productivity change in transport sector presented is lower in southeast regions and going to increase in northwest regions gradually.

Time-dimension decomposition
Average annual transport productivity change can then be obtained. For simplicity, the results are shown in Supplementary materials (Table A1). Figure 2 then presents the changing trend of the annual productivity. For measuring the spatial variances, we further divide 30 province-level regions into 3 groups (i.e., Western regions, Central regions and Eastern regions). 5 In general, as shown in Fig. 2

Source-decomposition of productivity change
The growth rates of AAT-TFP and its corresponding decomposition results with respect to individual variables of China's transport sector have been obtained in the above part. However, the purposes of finding the driving effect of catch-up effect and frontier movement force us to seek for source-decomposition of the productivity changes. According to Eqs. The decomposition results for AAT-TFP reveal that the average productivity change in the transport of the whole state due to the catch-up effect is 0.03% (as shown in Fig. 3), whereas that due to frontier movement is 2.29%. This indicates technological progress contributes 98.7% of the overall productivity change, and efficiency change only has faint positive effects on TFP. Such results are basically consistent with those reported in Zha et al. (2019). Region-wise, substantial variances can be observed. Looking at technological progress, only HAN and GZ present negative growth rates (− 0.64 and − 0.81% resp.), which indicates relative lagged technology and the technological process is key in promoting TFP. Noteworthy, the growth rates of efficiency change in HAN is steep (1.07%), while that in GZ is nil. This suggests that though HAN holds bad performance, the province-level region is pursuing the province-level region that is located in the frontier, whereas GZ fails. On the contrary, the technological gains of transport sector in SHX, JS, AH, YN, GS, NX, and XJ are superior to the national average level (4.43%, 4.15%, 4.87%, 4.12%, 5.72%, 5.14%, and 4.52% resp.).
Turning to the efficiency change (0.03%), the subtle positive effects can be attributed to pure efficiency change (LPEC, 0.05%), whereas scale efficiency change still plays a negative (LSEC, − 0.03%) role. Such a conclusion accords with that from Yu et al. (2017). Spatially, on the one hand, JS, ZJ and AH have steeper pure efficiency change than that of the national level (1.87%, 2.66% and 2.82% resp.), whereas their scale efficiency change is much lower (− 4.41%, − 3.97 and − 5.46% resp.). As a result, efficiency change in these regions is inferior to that of the average level in the nation. On the other hand, JX, SD and HUN are associated with lower pure efficiency change (− 1.45%, − 1.27% and − 1.53% resp.), whereas their higher scale efficiency change distinguishes them (2.88%, 3.87% and 2.96% resp.) in efficiency change (1.43%, 2.59 and 1.43% resp.).
Both the pure technological progress and the technological progress of scale change contribute to the technological progress (2.29%), whereas subtly positive (LPTP, 0.05%) and steep positive effects (LTPSC, 2.24%) are observed, respectively. Note that, among province-level regions relative to higher technological progress, two patterns of LPTP and LTPSC can be obtained. The first pattern is that the technological progress completely relies on LTPSC (e.g., SHX, GS and NX), while the second pattern is that technological progress depends both on LPTP and LTPSC (e.g., JS, AH and YN). Noteworthy, BJ and SH, as the mega-cities, own nil growth rates for all Luenberger indicators. Hence, the joint results of nil inefficiency scores and constant nil productivity change indicate that these regions are in the frontier and potential for improvements are limited. In the latter stage, transport management policies may promote their productivity gains.

Underlying trends of technological change
On the basis of Eqs. (19)-(22), we can further perform decomposition on technological change along time-dimension (PT) and quantity-dimension (PQ). This permits depicting the paths of technological change. Figure 4 describes the performance matrix of average annual growth rates of PT and PQ in transport sector of 30 province-level regions across 2006-2015. Specifically, in order to investigate the relationship between PT and PQ, we placed the results of these two indicators along the horizontal axis and the vertical axis, respectively. The average value of PT (− 4.18%) and PQ (21.52%) in the whole country is regarded as the base point.
We compare the relationships between PQ and PT and have an interesting finding that PQ is strictly greater than or equal to PT (i.e., PQ ≥ PT ). Note that three situations can be obtained theoretically.
(1) When PT = PQ, i.e., TG c (1) = TG max c , the initial period has the worst-performance and technological progress can be regarded as robust. Sadly, such a case is absent in the paper.
(2) When 0 < PT < PQ, i.e., TG c (1) < TG c (t) < TG max c , comparatively technological regression is obtained across certain periods, whereas technological growth can be obtained compared with that in the initial period. IN-MON, JL, GZ and SH'X are clustered in the situation.
(3) PT < 0, i.e., TG c (t) < TG c (1) < TG max c , comparatively technological regression can be observed in the whole sample, whereas technological progress may happen in some certain periods. The remaining 24 province-level regions are clustered in this situation (BJ, TJ, HEB, LN, SH, JS, ZJ, FJ, SD, GD and HAN, SHX, HLJ, AH, JX, HEN, HUB, HUN, GX, SC, CQ, YN, GS, QH, NX, and XJ). Hence, real technological progress is limited in transport sector of these regions, and promoting PT is required.

Conclusion and discussion
This paper introduced the Bounded-adjusted Measure assuming managerial disposability for energy use and natural disposability for conventional inputs. Based on the additive structure, the variable-specific decomposition is performed. This permits attributing the overall inefficiency score to an individual variable. In addition, the calculation of AAT-TFP and source-decomposition for AAT-TFP were investigated. Furthermore, we identify the channels through which technological progress affects economic growth.
The study reveals that the average inefficiency score for China's 30 provinces in transport sector is 0.12, which can be attributed to Civil vehicles, Capital stock, Labor force, and Traffic casualties (with the highest share of inefficiency scores). Hence, the government should focus on these variables and improve their efficiency. Noteworthy, the inefficiency score for energy use under managerial disposability is zero, indicating no redundancy regarding clean energy use. Region-wise, southeastern regions and part of the western provinces hold relatively lower inefficiency scores. From a time-specific perspective, the elongated left W-shaped distribution is observed for AAT-TFP during 2006-2015 in China's transport sector.
As regards the decomposition indicator, technological progress (AATP, 2.29%) promotes greatly to the productivity gains (AAT-TFP, 2.32%), whereas efficiency change is lagged (AAEC, 0.03%). Hence, the tech-transfer of transport production technology in China's 30 provinces needs to be further highlighted, and the spillover effects of management experience in transport ought not to be forgotten. Furthermore, technological progress of scale change (LTPSC, 2.24%) contributes more to AATP, rather than pure technological change (LPTP, 0.05%). Simultaneously, pure efficiency change (LPEC, 0.05%) pulls the AAEC, whereas scale efficiency (LSEC, − 0.03%) plays a negative role. This implies that the technological progress is contributed mainly by the input-output scale change, and the technovation in transport sector in the latter stage still needs to be encouraged.
Moreover, we perform the time-dimension (PT) and quantity-dimension (PQ) decomposition for technological progress and divide all 30 province-level regions into four parts in terms of the relationship between PT and PQ. Results reveal that the average values of PQ and PT are 21.52% and − 4.18%, respectively. The channels of how technological progress affects economic development in transport sector of each province can be captured in Fig. 4. Funding We acknowledge the financial support from the National Social Science Foundation of China (19BGL152).

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.