Before building the impact model of industrial structure transformation on ecological efficiency, it is necessary to measure the industrial structure effectively. Since industrial structure change mainly consists of industrial upgrading change and industrial rationalization change, the study mainly measures from these two aspects. There is no research on the industrial structure upgrading, which is mainly measured by the product of the proportion of industrial output value and industrial labor and industrial labor productivity s t r = ∑ i = 1 n B i L i (1)

In Formula (1), s t r refers to the industrial structure upgrading, i refers to the industrial type, n refers to the total number of industries, B refers to the proportion of different industrial output value in the total output value, and L refers to the labor productivity of different industries. Industrial rationalization is measured by structural deviation degree, as shown in Formula (2). E = ∑ i = 1 n | Q i L i ′ Q L ′ − 1 | (2)

In Formula (2), Q represents the regional gross product, and L ′ represents the number of people with bad business in the region. The research selects Cobb Douglas production function and cost function as the main theoretical basis, further introduces environmental factors, analyzes the transformation of industrial structure and its impact on ecological efficiency, and explores the ways in which industrial structure affects production efficiency from different perspectives (Rahim et al., 2010; Vasyl’yeva, 2021; Mohajan, 2021). As one of the main tools to measure the performance relationship between economy and environment, production efficiency is mainly reflected in the impact of economic output on resource consumption and environmental change (Apriyanti, 2019; Kliment et al., 2020; Zhang et al., 2022). The specific calculation method is shown in Formula (3). e c o = Q C + P (3)

In Formula (1), Q = F ( A , K , L ) represents the total output, i.e. the product value and service value provided by the economic benefit provider, Q represents the production cost, i.e. the resource consumption formed by the economic benefit provider in the production of products, and K represents the environmental load, i.e. the environmental load formed by the economic benefit provider in the production of products, In general, the value of environmental load generated by economic benefits can be estimated by the way of emission trading value (Lee et al., 2019; Habibi et al., 2020; Parente et al., 2020). The C-D production function including environmental factors is mainly based on the production function under the traditional Douglas Solow model, as shown in Formula (4). Q = F ( A , K , L ) (4) In Formula (2), Q represents output, K represents capital, L represents labor, and A represents knowledge or labor efficiency. The C-D production function is shown in Formula (5). Q = A K α L β , α > 0 , β > 0 , α + β = 1 (5)

In Formula (5), α and β represent production function coefficients. Although the C-D production function effectively disassembles the economic production problem, it ignores the natural resource consumption and natural environment pollution in the process of generating economic benefits. In the study, R is used for the unified expression of other resource elements except the existing production elements. The C-D production function added with this expression is shown in Formula (6). Q = A K α R β L 1 − α − β , α > 0 , β > 0 , α + β = 1 (6)

The cost function unit factor price measurement mechanism is introduced here, and the factor price is defined as the lowest cost price under the effect of fixed output, then the cost minimization problem can be transformed into the form with production factors, as shown in Formula (7). C ( K , R , L , Q ) = min ( r K + d R + w L ) (7) In Formula (7), r represents the fixed unit price of capital element K , d represents the fixed unit price of resource element R , and w represents the fixed unit price of resource element L . Further, the Lagrangian function can be constructed, as shown in Formula (8). F ( x ) = r K + d R + w L + λ ( A K α R β L 1 − α − β − Q ) (8) Finally, the C-D production function containing the environment can be formed as shown in Formula (9). C = Q α A r α d β w 1 − α − β ( α β ) β ( α 1 − α − β ) 1 − α − β (9)

When establishing the impact model of industrial structure transformation on production efficiency, three basic assumptions should be followed first. Hypothesis 1 is that all labor forces in the economic environment are homogeneous; Hypothesis 2 refers to that both the first and second industries are willing to pay for environmental pollution, which is reflected in the form of right price, and the proportion of the cost to the total industrial output value is expressed in P 1 and P 2 respectively; Assumption 3 is that the value of unit output is defined as 1. The output value of the primary industry is expressed as Q 1 , the output value of the secondary industry is expressed as Q 2 , the total output value of the two industries is expressed as Q , the number of labor forces in the primary industry is expressed as L 1 , the number of labor forces in the primary industry is expressed as L 2 , and the total output value of the two industries is expressed as L . On this basis, the model is divided into two main parts: the impact model of industrial structure upgrading on production efficiency and the impact model of industrial structure rationalization on production efficiency. In the part of the impact model of industrial structure upgrading on production efficiency, the measurement of industrial structure upgrading is the product of industrial proportion and labor productivity. Under the assumption that it is true, industrial structure upgrading can be defined as: a d v = Q 2 Q (10) When the measurement value increases, it proves that the primary industry is constantly transferring to the secondary industry, which is the process of industrial structure upgrading. The constructed Lagrangian function is shown in Formula (9). F ( X ) = r 1 K 1 + d 1 R 1 + w 1 L 1 + r 2 K 2 + d 2 R 2 + w 2 L 2 + λ ( A K 1 α R 1 β L 1 1 − α − β + B K 2 ρ R 2 τ L 2 1 − ρ − τ − Q ) (11)

In Formula (11), A K 1 α R 1 β L 1 1 − α − β represents the production function and corresponding elements of the primary industry, and B K 2 ρ R 2 τ L 2 1 − ρ − τ represents the production factors and corresponding elements of the secondary industry. r 1 K 1 + d 1 R 1 + w 1 L 1 and r 2 K 2 + d 2 R 2 + w 2 L 2 represent the cost functions of the primary and secondary industries respectively. The ecological efficiency finally calculated is shown in Formula (12). e c o = 1 [ A ( α / r 1 ) α ( β / d 1 ) β ( 1 − α − β / w 1 ) 1 − α − β ] − 1 + p 1 ( 1 − a d v ) + p 2 a d v (12)

In this case, you can: ∂ e c o ∂ a d v = P 1 − P 2 Δ 2 (13)

Δ in Formula (11) is calculated as shown in Formula (14). Δ = 1 e c o (14)

At this time, if P 1 > P 2 is used, it means that the environmental cost of the first type of industry is relatively high, and the upgrading of industrial structure promotes the improvement of ecological efficiency. If P 1 < P 2 is used, it means that the environmental cost of the second industry is relatively high, and the upgrading of industrial structure has led to the reduction of ecological efficiency. As shown in Figure 2.

It can be seen that under the two environments of low and advanced industrial structure, the rise and fall of production efficiency depends on the size of P 1 and P 2 . Industrial upgrading refers to the upgrading of industrial transfer, that is, the primary industry transfers to the secondary industry and the tertiary industry, and the secondary industry transfers to the tertiary industry. At this time, a d v 1 , a d v 2 and a d v 3 are used to represent the proportion of the output value of the secondary industry, the proportion of the output value of the tertiary industry, and the proportion of the output value of the secondary and tertiary industries. The evolution of industrial structure is shown in Figure 3.

It can be seen from Figure 3 that when the ratio of the output value of the secondary industry to that of the tertiary industry is equal to 1, the highly U-shaped relationship of the ecological efficiency language industry institutions is at the bottom, while the first half of the stage is the industrialization stage when the proportion of the secondary industry rises, and the second stage of the later version is the post industrialization stage when the proportion of the tertiary industry rises. In the impact model of industrial structure rationalization on production efficiency, industrial structure rationalization refers to the deviation between the per capita output value in the industry and the per capita output value of the economy. The smaller the deviation value, the more reasonable the structure will be. The definition of industrial structure rationalization index is shown in Formula (15). E = ∑ i = 1 3 | Q i / L i Q / L − 1 | (15) In Formula (15), Q and Q i respectively represent the total output value and the output value of an industry, and L and L i respectively represent the total labor force and the labor force of an industry. In addition, l = L 2 L is defined as the indicator of labor structure upgrading. The higher the l , the higher the proportion of labor in the secondary industry, the higher the labor structure. At this time, if a d v > l is used, the level of industrial structure upgrading will be higher than that of labor structure upgrading, and the index of industrial structure rationalization will be converted into Formula (16). E = a d v l − 1 − a d v 1 − l (16)

If a d v < l is used, there will be a level of industrial structure upgrading below the level of labor structure upgrading, and the index of industrial structure rationalization will be converted into Formula (17). E = 1 − a d v 1 − l − a d v l (17) When the upgrading of power structure and industrial structure are in convergence, the industrial structure is the most reasonable. The specific change process is shown in Figure 4.

The rationalization of industrial structure, the upgrading of industrial structure and the upgrading of labor force will maintain a dynamic interaction relationship, as shown in Figure 5.

It can be seen that the relationship between the rationalization of industrial structure, the upgrading of industrial structure and the upgrading of labor force is interactive and balanced.

Spatial econometric model refers to the interaction of different regions in economic space to a certain extent, which includes both correlation and heterogeneity. The study mainly uses two models, SAR model and SEM model. SAR model is shown in Formula (18). Y = ρ W y + X β ′ + ε (18) In Formula (18), Y represents dependent variable, X represents exogenous explanatory variable matrix, ρ represents spatial regression coefficient, W y represents spatial lag dependent variable of spatial weight matrix, ε represents random deviation vector, μ represents normal distribution random deviation vector, β ′ represents influence parameter, and SEM model is shown in Formula (19). Y = X β ′ + ε (19) When applying the spatial measurement method, it is necessary to test the spatial correlation of the explained variables. MoranI method is mainly used for the study, as shown in Formula (20). M o r a n Ι = ∑ i = 1 n ∑ j n W i j ( x i − x ¯ ) ( x j − x ¯ ) ( S 2 ∑ I = 1 n ∑ j = 1 n W i j ) (20)

In Formula (18), n represents the number of units in the space, i and j represent the serial number of the current research unit, x i represents the observation data of the i research unit, x j represents the observation data of the j research unit, x ¯ represents the average value obtained in group observation, W i j represents the weight of the research unit i and j , and S represents the sum of the weight elements in the space area. The spatial econometric model established by the theory of basic industrial structure transformation and ecological efficiency is shown in Formula (21). e c o i , t = α i + δ i + ρ ∑ j W i j ( e c o i , t ) + β ′ X i , t + μ i , t (21) In Formula (21), i represents the city, i represents the year, e c o i , t represents the ecological efficiency level, α i represents the fixed effect of the region, δ i represents the fixed effect of time, μ i , t represents the random deviation, and X i t represents the combination of explanatory variables and control variables. ρ is the spatial auto regressive coefficient.

When selecting indicators, the study takes into account both feasibility and scientificity, that is, to ensure comprehensive theoretical interpretation and comprehensive collection of relevant indicator data. On this basis, the study divides model indicator variables into three main variable categories: control variable, explanatory variable and explained variable. Specific indicator symbols and indicator meanings are shown in Table 1.

It can be seen from Table 1 that the explained variables of the study are expressed by ecological efficiency as the main indicator, which represents the comparison between the value formed by economic development and the environmental pollution measurement value and resource consumption measurement value formed in the process of value formation. The evaluation system of ecological efficiency mainly includes two main dimensions: input and output. The input dimension mainly refers to the relevant variables of input in the production process, while the output mainly refers to the total value of products or services produced by the region. In terms of input, the research is mainly expressed in terms of environmental impact and resource consumption, while output is mainly expressed in the form of GDP. The explanatory variables are the rationalization of industrial structure and the upgrading of industrial structure. The rationalization of industrial structure is measured by the improved Theil index, and the upgrading of industrial structure is measured by multiplying the proportion of each industry in the total industry by the labor productivity of the corresponding industry. The control variables are mainly divided into urbanization rate, logarithmic representation of capital stock, logarithmic representation of the number of employees, logarithmic representation of the amount of actually utilized foreign capital, energy structure (ratio expression), logarithmic expression of per capita GDP, and logarithmic square expression of per capita GDP. Among them, the urbanization ratio, as an important symbol of the transformation of small-scale peasant economy in rural areas towards the development of urbanization and socialized cooperative economy, may also cause excessive resource consumption and environmental pollution in the rough development process while generating economic benefits. Therefore, the urbanization ratio is selected as one of the control variables in the study; The logarithm of capital stock represents the measurement of changes in investment and depreciation of urban fixed assets, that is, stock changes; The logarithm of the number of employees mainly measures the level of industrial input labor from the perspective of industry input employees, and labor input will also have a certain impact on ecological efficiency; The logarithm of the amount of actually utilized foreign capital is mainly measured against the resource consumption and environmental pollution caused by the inflow of foreign capital from the transfer of highly polluting industries from countries with higher economic development levels. To attract this inflow of foreign capital, countries with low economic development levels tend to formulate more preferential policies, which leads to the neglect of the environment and the resource burden of industrial development. The study converts the average exchange rate of each year into RMB during calculation, and then uses the CPI index to assist measurement; The energy structure mainly measures the energy consumption in the process of economic development. Since the energy consumption and environmental pollution caused by different types of energy, such as traditional energy and new energy, are different, the use of energy structure as a control variable can best reflect the impact of energy elements on ecological efficiency; Both the logarithm of GDP per capita and the logarithm square of GDP per capita are important factors to measure the level of economic development, so they are also important to control variables to explore the impact of economic development and industrial structure changes on ecological benefits.

The original data used in the study are mainly from China Urban Statistical Yearbook and China Regional Economic Statistical Yearbook. In addition, it also includes the conceptual statistical annual reports of the regions involved. The missing data is supplemented by the moving average method. At the same time, the average exchange rate of each year shall be used to calculate the exchange rate.

In the empirical analysis of the impact of industrial structure on the ecological efficiency of regionalized urban agglomeration, three models, the OLS model (ordinary panel model), SAR model (spatial lag model), and SEM model (spatial error model), are also used for analysis. The difference is that in this part of the study, the Yangtze River Ecological Economic Zone is divided into four main regions: the Yangtze River Delta, the middle reaches of the Yangtze River, Chengdu Chongqing, and central Guizhou and Yunnan. The Yangtze River Delta region includes 26 prefecture-level cities, the middle reaches of the Yangtze River region include 28 prefecture-level cities, the Chengdu Chongqing region includes 16 prefecture-level cities, and the central Guizhou Yunnan region includes 7 prefecture-level cities. In the four regions, the OLS model, SAR model, and SEM model are used to analyze the regions that pass the significance test of the regression coefficient, while the OLS model is used to analyze the regions that do not pass the significance test of the regression coefficient. Among them, the Yangtze River Delta region and the middle reaches of the Yangtze River passed the significance test of the regression coefficient, while the Chengdu Chongqing region and central Guizhou and Yunnan region failed to pass the significance test of the regression coefficient. The empirical analysis results of the Yangtze River Delta region and Chengdu Chongqing region are shown in Table 5.

It can be seen from Table 5 that in the Yangtze River Delta region, the two regression coefficients pass the significance test at the level of 10% and 5%, respectively. It can be seen that the ecological efficiency of the Yangtze River Delta region has a high spatial role relationship and spatial dependence, and the spatial spillover benefits of ecological efficiency are relatively significant. From the perspective of the two explanatory variables of industrial structure upgrading and industrial structure rationalization, the model values of the OLS model, SAR model, and SEM model in the industrial structure upgrading variables are 0.092, 0.107, and 0.107 respectively, while the significance level is at the level of 1%, which shows that industrial structure upgrading is conducive to the improvement of ecological efficiency in the region. At the same time, the model values of the OLS model, SAR model, and SEM model in the variables of industrial structure rationalization are -0.053, -0.047, and -0.075 respectively. The significance level of the OLS model and SAR model is more than 10%, lacking statistical significance, while the significance level of the SEM model is 10%. It can be seen that the impact of industrial structure rationalization on regional ecological efficiency is mainly reflected in the spatial spillover effect. From the comparison of coefficients, the value of industrial structure upgrading is relatively higher, which shows that the impact of industrial structure upgrading is more significant. From the perspective of control variables, the logarithmic expression of GDP per capita is a significant positive impact, and the logarithmic square value of GDP per capita is a significant negative impact; The logarithmic representation of the number of employees and the logarithmic representation of the capital stock show a significant positive correlation, and the regression results of the energy structure are not significant, which indicates that the labor and capital variables have a positive significant impact on the ecological efficiency, but the impact of the energy variables on the ecological efficiency is not significant; The logarithm of the actual amount of foreign capital used shows a 1% significance in the OLS model, which shows that foreign investment can promote the ecological efficiency in the local area. The urbanization ratio shows significant positive performance in the OLS model and SAR model. It can be seen that urbanization variables have a significant positive impact on ecological efficiency, which is conducive to the improvement of ecological efficiency. In the Chengdu Chongqing region, the two regression coefficients have not passed the significance level test, which shows that the cooperation effect of urban groups within the region has not yet appeared, but from the perspective of the OLS model, the industrial structure upgrading still has a significant positive impact on ecological efficiency, and among the control variables, the labor variable and foreign capital variable have more significant effects. On the whole, the industrial structure of the Chengdu Chongqing region still needs to develop in an environmentally friendly direction. The empirical analysis results of the middle and long reaches and central Guizhou and Yunnan are shown in Table 6.

It can be seen from Table 5 that in the long and middle reaches, the two regression coefficients pass the significance test at the 5% level. It can be seen that the ecological efficiency in the long and middle reaches has a high spatial role relationship and spatial dependence, and the spatial spillover benefit of the ecological efficiency is relatively significant. From the two explanatory variables of industrial structure upgrading and industrial structure rationalization, the model values of the OLS model, SAR model, and SEM model in the industrial structure upgrading variables are 0.061, 0.054, and 0.052 respectively, and the significance level is at 5% and 10% significance levels respectively. It can be seen that industrial structure upgrading is conducive to the improvement of ecological efficiency in the region. At the same time, the model values of the OLS model, SAR model, and SEM model in the variables of industrial structure rationalization are 0.055, 0.052, and 0.052 respectively. The significance level of the OLS model and SAR model is at the 5% significance level. As the rationalization of industrial structure is a deviation from the value of the equilibrium state, it can be seen that the rationalization of industrial structure has a significant negative impact on the ecological efficiency in the region. From the comparison of coefficients, the value of industrial structure upgrading is relatively higher, which shows that the impact of industrial structure upgrading is more significant. From the perspective of control variables, the logarithmic expression of GDP per capita and the logarithmic square value of GDP per capita have no significant statistical significance; The logarithmic representation of the number of employees also lacks statistical significance, while the logarithmic representation of the capital stock shows a significant positive correlation in the OLS model, and a significant negative correlation in the SAR model and the SEM model, which shows that the capital variable has a more significant impact on the lag and spillover effects; The logarithm of the utilized foreign capital quota lacks significant statistical significance. The urbanization rate also lacks significant statistical significance. It can be seen that capital stock and foreign capital play a significant role in the improvement of ecological efficiency in the long and middle reaches. In the area of central Guizhou and central Yunnan, the two regression coefficients have not passed the significance level test, which shows that the cooperation effect of urban groups within the region has not yet appeared. However, from the perspective of the OLS model, the upgrading and rationalization of the industrial structure have not had a significant impact on the ecological efficiency, and in the control variables, all control variables except urbanization have not shown a significant impact, It can be seen that only urbanization will have a significant positive impact on production efficiency. In general, the industrial structure and urban cooperation effect in the central Guizhou Yunnan region have not yet taken shape. In general, the urban cooperation effect between the Yangtze River Delta and the middle reaches of the Yangtze River is relatively obvious, Under this kind of inter-city cooperation effect, the ecological efficiency has a significant spatial spillover effect, and Hypothesis 2 is valid. At the same time, in terms of industrial upgrading and industrial rationalization, industrial upgrading will have a significant positive impact on ecological efficiency in the regions that form the scale of ecological efficiency and ecological benefits, while in the regions that form a significant impact on industrial structure rationalization, industrial structure rationalization will have a significant negative impact on ecological efficiency. Once the assumption is established.