Spatial Spillover Effect of Green Water Use Efficiency and its Influence Factor: 1 New Evidence from Yellow River Economic Belt, China

47 The shortage of fresh water resources is an important factor restriction the sustainable 48 development of the Yellow River Economic Belt (YREB). Increasing Green Water-Use 49 Efficiency (GWUE) is a necessary way to ensure the sustainable development of water 50 resources. Therefore, it is of theoretical significance and practical value to measure GWUE 51 and investigate its influencing factors. Based on the panel data of 98 cities in YREB from 52 2005-2018, this paper first measures GWUE by global Malmqusit approach which contains 53 unexpected output, and decomposes the comprehensive efficiency into Technological Change 54 (TC), Pure Technical Efficiency Change (PEC) and Scale Efficiency Change (SEC). 55 Furthermore, the spatial correlation of GWUE and decompositon indexs are analyzed by 56 using the spatial Durbin model, and the influence of other interpretations on GWUE is 57 analyzed. The empirical results show that: (1) The average annual growth rate of WGUE is 58 7.86% during 2005-2018, and the average annual growth rate of TC, PEC, SEC is 2.57%, 59 3.87% and 1.84% respectively, which all contribute to the improvement of WGUE. (2) 60 GMLPI, TC, PEC, SEC all show the agglomeration characteristics of "high-high" or 61 "low-low", and the GWUE of the local city will be affected by the same direction of the 62 surrounding cities. Every 1% increase in GMLPI, TC, PEC and SEC of surrounding cities 63 will lead to the corresponding index growth of about 0.321%, 0.393%, 0.244% and 0.358% 64 respectively. (3) Industrial structure and foreign direct investment have a negative total effect 65 on GWUE. The expenditure on science and technology, education and population density 66 have significatly promoted technological progress both the local city and surrounding cities. 67 Infrastructure has a significant positive effect on the pure technical efficiency of the city. This 68 paper hodls that the government should strengthen cooperation and technical innovation, 69 optimize foreign capital structure and industrial structure. 70


Consent of publication:
Not applicable. 23 Availablity of data and materials: 24 The data that support the findings of this study are available from [www.cnki.net] but 25 restrictions apply to the availablity of these data, which were used under license for the 26 current study, and so are not publicly available. Data are however available from the authors 27 upon reasonable request and with permission of [www.cnki.net]. 28 Competing interests: 29 We declare that we have no financial and personal relationships with other people or 30 organizations that can inappropriately influence our work, there is no professional or other 31 personal interest of any nature or kind in any product, service and/or company that could be 32 construed as influencing the position presented in, or the review of, the manuscript entitled 33 "Spatial Spillover Effect of Green Water Use Efficiency and its Influence Factor: New 34 Evidence from Yellow River Economic Belt, China". 35 Funding: 36 We thank "young innovative talents" program of Harbin University of Commerce 37 including unexpected output and its decomposition index are used to measure urban water-use 176 efficiency. Thirdly, the spatial correlation and its influencing factors of green water-use 177 efficiency are analyzed empirically by using spatial Durbin model, and the 178 economy-geography nested matrix is used in spatial regression. 179 The Yellow River flows through nine provinces in China (including: Shandong, Henan, 182

Method
Shanxi, Shannxi, Inner Mongolia, Ningxia, Gansu, Qinghai, Sichuan), is called "mother river" 183 among Chinese, related to the livelihood of more than 400 million people and more than one 184 third of the country's crops output, and is also an important bond of "One Belt, One Road" 185 strategy in inland China (Wang et al,2012). Figure 1 shows the geographical location of the 186 Yellow River Economic Belt (YREB) in China. YREB includes 118 cities, due to the lack of 187 complete data, 20 cities are excluded (in white). Finally, we select 98 cities as samples for 188 empirical study (in yellow).  193 Malmquist productivity index is widely used to measure productive efficiency and has a 194 major advantage in panel dataset. Fare et al (1992) calculated Malmquist Index (MI) with 195 DEA method for the first time and decomposes it into two parts: one is the change of 196 technical efficiency change (EC) between two periods; the other is the technology change (TC) 197 between two periods, that is, the change of production frontier. MI=EC*TC. 198 Fig.2 shows the theory of output-oriented Malmquist productivity index under the assumption of constant returns of scale (CRS). X represents input, Y1 and Y2 represent output 200 (assume they are both desirable output). A 1 B 1 C 1 is the production frontier of period t, A 2 B 2 C 2 201 is the production frontier of period t+1, N (x n , y n ) and M (x m , y m ) represent the productivity 202 index of the DMU in period t and t+1 respectively. Then Malmquist Productivity Index (MI) 203 in the period from t to t+1 is: 204 reference to production frontier A 1 B 1 C 1 , The change with production frontier from A 1 B 1 C 1 to 207 A 2 B 2 C 2 represent the technology change (TC) from period t to t+1, could be measured by 208

Global Malmquist-Luenberger Productivity Index
In eq(4), is the directional vector,  is the directional distance function 237 of y maximization and b minimization in year t. The eq(4) shows that, given the input X, the 238 expected output Y and the unexpected output B increase and decrease in the same proportion. 239  is the production possibility set of the current period.
In eq(5), 1 t t EC  represents technical efficiency change from period t to t + 1, which 246 means the city's production level and scale effect of science and technology. EC>1 reveals 247 that there has been an improvement in efficiency between t and t+1. Under Variable Returns to Scale (VRS) assumption, we can get following formula: ( , , , , , ) In eq(6), Pure Technical Efficiency Change (PEC) is the efficiency value obtained by 252 eliminating the scale effect. Finally, GMLPI can be decomposed into 255 When measuring the Global Mlamquist-Luenberger Productivity Index (GMLPI), this 256 paper takes capital, labor, water resources, technology expenditure as the input variable, and 257 GDP and water pollutant emission as the output. The specific indicators are as follows:  The First Law of Geography states that no city is isolated (Tobler, 1970). Existing 281 studies have pointed out that spatial econometric model can avoid ignoring the spatial 282 correlation among cities (Getis, 2007;Elhorst, 2003;Anselin, 2010). Water efficiency is not 283 only affected by the variables of the local cith, but also may be affected by the "spillover 284 effect" and "siphon effect" of the surrounding cities. Therefore, we employ the spatial 285 econometrics model to investigate the spatial correlation of GMLPI and its determinants. The 286 most widely used and relatively mature spatial econometric models are spatial lag model 287 (SLM) and spatial error model (SEM) and spatial Durbin model (SDM). The SLM only 288 considers the spatial correlation of the interpreted variable, while the explanatory variables 289 only affect the interpreted variable in the city, but no spatial spillover effect (Ma et al,2016;290 Wang et al,2020b). SEM is considered to be a reasonable model when the error term has 291 spatial correlation (Haining,1978;Casetti,1986 Combined with this studies, the SLM is set as follows: 296

Input and output variables
In eq(10), GMLPI represents the WGTFP of city in the YREB calculated based on DEA 298 model introduced in the previous section. Because GMLPI shows a change in efficiency 299 within two periods, this paper assumes that the GMLPI in 2007 is the base period, and 300 transforms the GMLPI in the following years. X represents the control variable, and the 301 specific calculation method and data source of each variable are discussed in the next section. 302 W represents the spatial weight matrix established in this paper.  , spatial autoregressive 303 coefficient of GMLPI, is the most concerned numerical value in this paper.  and  304 represents the explanatory variable parameter to be estimated, it  represents the error term.

305
SEM is set as follows: 306 In eq(11), the spatial correlation of error terms is the main factor different from other 308 models. The meaning of each variable is the same as eq(11). Then, SDM is set as follows: 309 The meaning of each variable is the same as eq(11). The difference is that the SDM 311 contains the spatial lag term of explanatory variables, which expressed by  . It will analyze 312 the spatial spillover effect of the explanatory variables. Elhorst (2014) proposed likehood 313 ratio (LR) test method for SLM, SEM and SDM models, the test can identify whether the 314 SDM could be simply reduced to the SEM or SLM. 315

Spatial Weight Matrix 316
The spatial weight matrix is used to measure the degree of interaction between cities. 317 The larger the corresponding elements in the matrix, the higher the degree of interaction 318 between the two cities. Most of the existing literature constructs weight matrix from two 319 aspects: geographical factor or economic factor. 320 The theoretical basis for constructing a matrix based on geographical factor is that the 321 closer the geographical distance between the two cities, the more advantages they have in raw 322 material and commodity transportation, labor mobility, industrial production, etc (Wang et 323 al,2019). Therefore, by constructing the geographic distance matrix (W1), this paper measures 324 the actual spherical distance of the earth between cities, based on the longitude and latitude of 325 each city, and it uses the reciprocal of the distance to represent the actual corresponding 326 elements in Wgeo. There is no doubt that the closer the economic level between cities, the 327 higher the degree of mutual influence (Bai et al,2012), thus the cities will tend to learn from 328 cities with similar economic level, i.e. "imitation effect". This paper uses GDP per capita to   Table 1. 379  respectively. The other years also show the same characteristics, which shows that the urban green 422 water resources utilization efficiency lacks stable growth momentum. Secondly, the driving effect 423 of technological progress on gwue is more and more obvious during the period.  gradually becoming an important driving factor of GWUE. Finally, the cities present obvious 427 "high-high" or "low-low" spatial correlation characteristics, that is, a city may be affected by the 428 same direction of the surrounding cities. This reminds the government to strengthen cooperation 429 and exchange with surrounding cities to improving the efficiency of resource utilization.

Results without spatial interaction effects 435
Before the spatial analysis, it is necessary to use the model without spatial factors to 436 investigate the impress of the influencing factors on the city.

Result of spatial econometric model 451
Before spatial econometric modelempirical analysis, it is necessary to carry out the 452 following two types of tests: spatial autocorrelation test and likehood ratio test. Global Moran 453 Index is a widely used method to test the spatial correlation among variable (Moran,1950 Table 4 reports the regression results of the spatial econometric model with GMLPI as 468 the explanatory variable. The LR test results show that SDM is the optimal model regardless 469 of the spatial weight matrix. Since the matrix WX considers the influence of economic factors 470 and geographical factors. Therefore, this section will mainly discuss the SDM regression 471 results based on the matrix WX. 472 Firstly, the spatial lag coefficient of GMLPI is positive and significant at the level of 1%. 473 The 1% rise in the GMLPI in the surrounding cities will lead to an increase of 0.321% in the 474 local city. It indicates that the improvement of water efficiency in surrounding cities also promotes the sustainable development of water resources in the local city, which may be due 476 to the "technology spillover effect" and "political competition" occupying the dominant 477 position. The technological progress and environmental protection achievements of the 478 surrounding cities will stimulate the environment-friendly development of the local city. 479 Secondly, among the other explanatory variables, TS and EDU have positive effects on the 480 local city and significantly. Every 1% increase in TS and EDU will promote the GWUE by 481 about 0.498% and 0.225% respectively, implying that industrial agglomeration and education 482 expenditure will significantly improve the water resources efficiency of YREB. In addition, 483 the coefficients of TEC, INV and PEO are also positive but unsignificantly, which indicates 484 that increasing science and technology expenditure, strengthening water supply and drainage 485 infrastructure, and increasing population density have positive effects on GWUE of the local 486 city. The spatial lag coefficients of TS and FDI are negative and significant at 1% level. Every 487 1% increase in the TS and FDI in surrounding cities will lead to the decline of GWUE by 488 1.003% and 0.486% respectively. This may be because the industrial development and foreign 489 investment in surrounding cities have a more significant "siphon effect" on the local city, 490 which weakening the water sustainable development ability. In addition, the spatial lag 491 coefficient of PEO is positive and significant at the level of 10%. The increase of population 492 density in surrounding cities by 1% will lead to the improvement of water resource efficiency 493 by about 4.9%. 494 Table 4 Table 5 reports the regression results of the spatial econometric model with TC as the 498 explanatory variable. Firstly, the spatial lag coefficient of TC is positive and significant at 1%, 499 indicating the increase of technical progress of surrounding cities by 1% will contribute the 500 TC of the local city by 0.393%. This proves the existence of technology spillover effect. This 501 enlightens us that the cooperation between cities in science and technology can achieve 502 win-win situation and promote the sustainable development of both sides. The coefficients of 503 TEC, EDU and PEO are positive and significant. Every 1% increase in TEC, EDU and PEO 504 will contribute to TC of the local city by 2.206%, 0.771% and 3.265% respectively. This 505 shows that higher expenditure on science and technology and education can improve the level 506 of scientific and technological innovation and promote technological progress. The significant 507 impact of population density on technological progress may be due to that city with higher 508 population density have more advantages in talent reserve and R&D personnel, which is more 509 conducive to urban technological innovation. The spatial lag coefficients of TS, FDI and INV 510 are negative and statistically significant. The increase of TS, FDI and INV in surrounding 511 cities by 1% will lead to the decrease of TC in the local city by 1.572%, 0.320% and 4.275% 512 respectively. On the contrary, the spatial lag coefficient of EDU is significantly positive, 513 means the increase of education expenditure in surrounding cities by 1% will promote the 514 technological progress of the local city by 0.934%. Indicates that the education expenditure of 515 the city may improve the technical level of water resources utilization in the surrounding 516 cities through the flow of talents and technology spillover. 517 Table 5 Table 6 reports the regression results of spatial econometric model with pure technical 519 efficiency (PEC) as the explanatory variable. Firstly, the spatial lag coefficient of PEC is 520 positive and significant at the level of 1%. The increase of PEC in surrounding cities by 1% 521 will lead to a 0.244% increase of the local city. This shows that the improvement of 522 management level and utilization level of existing technologies in surrounding cities will also 523 promote the pure technical efficiency of the city. The coefficients of TS and INV are 524 significantly positive, the increase of the TS and INV by 1% will increase the pure technical 525 efficiency of the city by 0.856% and 2.135%, respectively. Conversely, the coefficients of 526 TEC and EDU are significantly negative. The increase of TEC and EDU by 1% will lead to 527 the decrease of PEC by 2.97% and 0.81% respectively. In the spatial regression results of 528 variables, the coefficient of TEC is significantly positive. The increase of 1% in science and 529 technology expenditure of surrounding cities will promote the pure technical efficiency of the 530 city by 4.872%. In addition, the spatial lag coefficients of TS, INV and PEO are significantly 531 negative. The increase of TS, INV and PEO in surrounding cities by 1% will lead to the 532 decrease of pure technical efficiency of the local city by 1.085%, 2.085% and 12.936% 533 respectively. 534  Table 7 reports the regression results of spatial econometric model with the scale 536 efficiency change (SEC) as the explanatory variable. The spatial lag coefficient of SEC is 537 positive and significant at the level of 1%. A 1% increase in the scale efficiency of 538 surrounding cities will promote the scale efficiency of the city by about 0.358%. In the 539 influence of control variables on SEC, the coefficient of TS is negative and significant. An 540 increase of 1% in the proportion of the secondary industry in GDP will lead to a decrease of 541 about 0.319% in the local city's scale efficiency, indicating that the rapid expansion of the 542 secondary industry is not conducive to the formation of scale effect. The coefficient of EDU 543 is positive and significant at the level of 1%. The increase of education expenditure by 1% 544 will increase the scale efficiency of the city by 0.549%. In the spatial lag coefficient of 545 variables, only the coefficient of INV is significant. If the investment of water supply and 546 drainage facilities in surrounding cities increases by 1%, the scale efficiency of the city will 547 be increased by about 7.406%. 548  Table 8 reports the direct effect, spatial spillover effect (i.e. indirect effect) and total effect of 550 each variable. Direct effect refers to the influence of variables on the city, including both the direct 551 impact on the city and the spatial feedback effect. Spatial feedback effect refers to the effect of 552 spatial spillover effect of variables on surrounding cities, and the influence of surrounding cities 553 on the local city. Spatial spillover effect refers to the impact of variables on surrounding cities. 554 The total effect is the sum of direct effect and spatial spillover effect, which represents the impact 555 of variable change on all sample cities. 556 TS shows a significant negative total effect on GMLPI. An increase of 1% in the proportion 557 of the secondary industry in GDP will reduce the GWUE of YREB by about 0.714%, which is 558 mainly due to the inhibition of technological progress. TEC and EDU promote the technical 559 progress of the city and surrounding cities at the same time. The increase of TEC and EDU by 1% 560 will increase the technical level of YREB by 5.241% and 1.719% respectively. The restraining 561 effect of FDI on GWUE is that it leads to the technology retrogression both the local city and the 562 surrounding cities. The increase of FDI by 1% will lead to the technology retrogression of YREB 563 about 0.417%. INV can inhibit technological progress and improve scale efficiency. PEO has 564 significantly promoted the technical progress of YREB. 565

567
In the empirical analysis, we use the two-way fixed model and spatial Durbin model to 568 investigate the spatial correlation and influencing factors of GWUE. This section will analyze 569 the reasons for these results. 570 GMLPI, TC, PEC and SEC are all characterized by "high-high" or "low-low". The local 571 city is affected by the technological changes of the surrounding cities in the same direction, 572 which verifies the existence of "technology spillover effect", that is, the technological 573 progress of the surrounding cities may contribute to the technological progress of the local 574 city through enterprise exchange, labor flow, government cooperation and other channels 575 INV and PEO have a negative spatial imapct on PEC, which confirms the siphon effect. On 584 the other hand, the government has the characteristics of "political competition" and 585 "conpetition to the bottom" in sustainable development. The city will imitate other cities that 586 have performed well in resources utilization efficiency, that is, the "imitation effect" (Yang et 587 al, 2020). The imitation effect will make cities strengthen environmental regulations and force 588 companies to improve their management capabilities and technology utilization. The reason 589 that may lead to the "high-high" agglomeration characteristics of scale efficiency is that the