In the new normal period of China′s current economic growth slow down, structural optimization and upgrading, it is not a perfect strategy to develop the economy blindly or protect the environment unilaterally. The key to China′s economic transformation and development is to improve the environmental total factor productivity (ETFP) of each city. In recent years, domestic scholars have found that the level of ETFP in the eastern coastal areas of China is generally higher than that in the central and western regions, and the regional differences are very large. At the same time, some scholars have found that the regional distribution of FDI also presents a "high in the eastern regions and low in the western regions" agglomeration difference. The question is: why is the level of ETFP high in the eastern regions and low in the western regions? Is this related to the agglomeration difference of FDI between the eastern regions and the western regions? In other words, does the spatial agglomeration of FDI affect the ETFP in different regions? Based on these problems, this paper examines the net effect of FDI on ETFP in 285 cities in China from the perspective of spatial agglomeration, hoping to provide policy reference for accelerating the realization of high-quality economic development and promoting the coordinated, healthy and sustainable development among cities according to local conditions.
    First of all, through the study of domestic and foreign literature, we find that most of the literature use ML index to measure and study ETFP at national, regional and industrial levels. However, ML index is limited to the shortcomings of linear programming, which cannot effectively overcome the evaluation deviation. In addition, these research literature on the impact of FDI on ETFP does not include geographical and spatial factors into the analysis of ETFP. Ignoring the spatial agglomeration characteristics of FDI may lead to a deviation in the evaluation of ETFP. Therefore, this paper uses SBM direction distance function and GML index to measure the environmental total factor productivity at the "micro" level of China′s cities, which overcomes the defects of ML to a certain extent, which is different from other provincial level or industry level measurement. And this paper constructs a spatial weight matrix, and uses spatial analysis method to divide FDI into four kinds of urban samples of different agglomeration types from the perspective of spatial agglomeration.
    Secondly, we analyze the channels through which FDI influences ETFP, and puts forward three hypotheses about the impact of spatial agglomeration of FDI on urban ETFP. On this basis, we set a spatial panel model and selected human capital, economic development level, human capital, endowment structure, industrial structure, marketization degree as control variables. In addition, in order to investigate the impact of spatial agglomeration of FDI on ETFP, this paper constructs a nested spatial weight matrix of economic geography including geographical and economic factors, and divides FDI into four agglomeration samples with local Moran index.
    Thirdly, according to the spatial autocorrelation analysis, the global Moran index of per capita FDI and ETFP is significantly greater than zero from 2003 to 2016, which shows that the distribution of per capita FDI and ETFP in China′s cities shows a strong spatial clustering feature, and there is a significant spatial positive correlation between them. In addition, the local Moran scatter diagram shows that there are 30 cities with the overlapping of FDI per capita and ETFP high-high agglomeration types, most of which belong to the eastern developed cities, 25 cities with the overlapping of low-high agglomeration types, 119 cities with the overlapping of low-low agglomeration types, most of which are located in the western and northeast regions, 16 cities with the overlapping of high-low agglomeration types, most of which belong to some provincial capitals in the central and western regions or some more developed cities. This further shows that the economic geography of ETFP is closely related to the spatial agglomeration of FDI in a region.
    Fourthly, we have screened the spatial econometric model and found that the sample is suitable for SAR model regression. Then, we use SAR model to regress the whole city sample and four cluster samples respectively. The results show that the spatial agglomeration of FDI has a positive effect on ETFP, and the effect of agglomeration FDI is more obvious than that of decentralized FDI, and the robustness test also supports the empirical results.
   At the end of this paper, the research conclusions and policy suggestions are given．This study shows that the economic geography of ETFP is closely related to the spatial agglomeration of FDI in a region. In addition, the regression results show that the positive effect of FDI spatial agglomeration on ETFP comes from two aspects. On the one hand, FDI mainly promotes the improvement of ETFP through technological progress, which brings positive technological spillover. On the other hand, the FDI of high-high and high-low agglomeration type cities can enhance the ETFP of cities, and the technology spillover effect of high value agglomeration FDI is more obvious than that of scattered FDI, producing agglomeration effect, further promoting the promotion and agglomeration of ETFP of itself and surrounding cities, and then have a more positive effect on the ETFP of cities. In addition, FDI in low-high and low-low agglomeration cities has no significant impact on ETFP, which may be due to the existence of "threshold" of FDI, including the agglomeration scale of FDI, investment motivation of FDI, absorption capacity of technology, etc.
     Through the conclusion of the study, we propose some policy recommendations. First of all, in the process of improving ETFP, China should consider the spatial correlation and spillover effect of ETFP, and give full play to the positive effect between cities. Secondly, China should not only expand the opening up, actively attract investment, but also combine the characteristics of the agglomeration types of FDI in various regions, break the shackles of urban administrative areas, adopt the differentiated strategy of "private customization", and promote ETFP according to local conditions. Finally, local governments should draw on the "dividend" brought by FDI, build a matching "urban allocation", give full play to the positive role of other economic factors in improving ETFP, further improve the technology spillover ability of FDI, and promote the improvement of ETFP.