## 2 Literature Review
Working from an input-output perspective, [PERSON] et al. used the three-stage DEA model to measure the integrated transport efficiency of China's provinces in 2013 and further analyzed the spatial cluster characteristics, which mainly focuses on the impact of random environments on efficiency [38]. However, all of the aforementioned studies have ignored the fact that transport not only brings significant economic benefits to society but can also lead to environmental and social problems (e.g., excessive energy consumption, air pollution, carbon emissions, accidents and congestion) [39]. According to the relevant statistics, the total energy consumption required by the global transport system rose from 23% in 1973 to 28% in 2012. Moreover, in 2050, as much as 30-50% of total CO\({}_{2}\) emissions are predicted to come from the transport sector [40]. With the rapid growth of energy consumption and increasing emissions of pollutants brought about by transport, numerous scholars have paid much attention to the negative effects of undesirable outputs. For instance, [PERSON] et al. analyzed urban transport efficiency in 285 cities across the world from 2009 to 2012, exploring efficiency levels with a focus on productive capacity slacks including two undesirable output indicators [41]. [PERSON] et al. attempted to evaluate regional integrated transport efficiency and explored the factors influencing transport efficiency in China, in particular considering undesirable outputs during the period 1995-2012 [42]. However, this study merely incorporated CO\({}_{2}\) emissions as an undesirable output and ignored other undesirable transport outputs. [PERSON] et al. evaluated the efficiency of road transport in China's provinces using the number of traffic accidents and carbon dioxide emissions from the energy consumption of road transport as undesired outputs, finding the level of road transport efficiency to be generally low [43]. The limitation of this study is that it only discussed the efficiency of road transport, ignoring the measurement of the efficiency of other modes of transport. With advances being made in the construction of China's transport powerhouse, the development of high-speed railways and the gradual improvement of the country's road network infrastructure have grown increasingly rapidly. Therefore, a measurement of transport efficiency should consider all modes of transport. Combining the above analysis, some scholars have introduced undesirable outputs into their DEA models for the purpose of evaluating transport efficiency. However, there still exist certain deficiencies in the selection of indicators and evaluation methods that make it impossible to measure the efficiency of transport resource allocation accurately. In addition, the aforementioned studies have mostly focused on evaluating the efficiency of certain types of transport, and ignore the efficiency measuring of integrated transport system. To date, there have been few significant attempts to study the effect of differences in the efficiency of various transport modes over time in different areas, and the impact of the geographic spatial effect on this efficiency. In fact, some studies have considered the convergence of spatial effects in other fields of research. For example, spatial panel data models were utilized to investigate the stochastic convergence and \(\beta\)-convergence of carbon intensity [44]. [PERSON] et al. analyzed the convergence of innovation capabilities on different space-scales by applying the spatial panel of the \(\beta\)-convergence model [45]. In addition, studies of convergence in this context have also included economic growth [46] and per capita energy consumption [47], among other factors. These studies of convergence provide a methodology reference for considering the convergence of spatial effects. Integrated transport efficiency is a key performance metric for measuring the development of the transport industry.