DEA model is a method to evaluate the efficiency of decision-making units (DMU) with multiple inputs and outputs ( Banker, Charnes, & Cooper, 1984 ; Wang, Yang, & Li, 2021 ). There are many application models of DEA, among which CCR model and BCC model are the basic models of DEA and the most commonly used models. This paper uses these two models to evaluate the urban land use efficiency of Yunnan Province, and the calculation principle and process are as follows.

Let’s assume that there are n DMUs, each of which has m inputs x_ij ( $j=1,\cdots ,m$), and s outputs y_ir ( $r=1,\cdots ,s$) (x_ij ≥ 0, y_ir ≥ 0), with slack variables s^- and s⁺, then the relative efficiency of DMUs has the following CCR evaluation model:

$\{\begin{array}{l}\min \theta \left(0<\theta \le 1\right)\\ s.t.{\displaystyle \underset{i=1}{\overset{n}{\sum }}{x}_{ij}{\lambda }_i}+s^{-}=\theta x_{oj}\left(j=1,\cdots ,m\right)\\ {\displaystyle \underset{i=1}{\overset{n}{\sum }}{y}_{ij}{\lambda }_i}-s^{+}=\theta y_{or}\left(r=1,\cdots ,s\right)\\ \lambda \ge 0,s^{+}\ge 0,s^{-}\ge 0\end{array}$ (1)

In the formula, λ_i is the weight variable of each DMU on a certain index. CCR model is obtained under the assumption that the DMU is constant returns to scale (CRS). θ calculated by CCR model is the comprehensive technical efficiency (TE) of the DMUs. If the constraint of “sum of λ_i is 1” is added to the above formula, it becomes the BCC model with the DMU as variable returns to scale (VRS), and the calculated θ is the pure technical efficiency (PTE) of the DMUs. As the comprehensive technical efficiency includes pure technical efficiency and scale efficiency (SE), then:

$SE=TE/PTE$ (2)

Furthermore, when the θ of CCR is 1 and both s⁻ and s⁺ are 0, DMU is DEA efficiency, indicating that this DMU is in the optimal production frontier, and the output has reached the optimal level on the basis of the original input, and both technology and scale are efficient. When the θ of CCR is less than 1, the DMU is DEA inefficiency, and both technology and scale are inefficient. In this case, the input can be reduced to θ times of the original input by optimizing the combination without reducing the original output.

DEA model can be used to calculate the input and output efficiency of multiple DMUs at the same time section, which is essentially a static efficiency and cannot reflect the internal driving mechanism of efficiency. That is, the change of efficiency is driven by technological progress change (TC), technical efficiency change (TEC) or both. To this end, this research uses Malmquist index to analyze the internal driving mechanism for urban land use efficiency. At present, the most widely used total factor productivity (TFP) index is Malmquist index, which can calculate the TFP, TC and TEC of DMU, so as to understand the dynamic evolution results of DMU efficiency in time series more deeply and systematically ( Ding & Wu, 2019 ). Malmquist index is widely used to measure TFP in different periods, and it can be used to study the dynamic evolution laws of efficiency of different DMUs in multiple periods ( Martinho, 2017 ). Then, the characteristics of internal driving mechanism of efficiency are obtained The calculation principle of Malmquist index is as follows.

$\text{TFP}=\text{TEC}\times \text{TC}$ (3)

$\text{TFP}=\text{PTEC}\times \text{SEC}\times \text{TC}$ (4)

In Formula (3), TFP, TEC and TC are the total factor productivity, and the changes of TE and technological progress at the time t and t + 1 respectively. Under the condition that VRS is assumed, TEC can be further decomposed into pure technical efficiency change (PTEC) and scale efficiency change (SEC), thus the final Malmquist index model is obtained, as shown in Formula (4), where PTEC and SEC are the changes of PTE and SE at the time t and t + 1 respectively. In specific calculation, distance function is used to calculate the change between input and output in the period from t to t + 1. The formula is as follows:

$\begin{array}{l}\text{TEC}=\frac{D^{t+1}\left(x_{t+1},y_{t+1}\right)}{D^t\left(x_t,y_t\right)}\\ \text{PTEC}=\frac{D_{vrs}{}^t\left(x_{t+1},y_{t+1}\right)}{D_{vrs}{}^t\left(x_t,y_t\right)}\\ \text{SEC}=\frac{TEC}{PTEC}=\frac{D^{t+1}\left(x_{t+1},y_{t+1}\right)}{D^t\left(x_t,y_t\right)}\times \frac{D_{vrs}{}^t\left(x_t,y_t\right)}{D_{vrs}{}^t\left(x_{t+1},y_{t+1}\right)}\\ \text{TC}=\sqrt{\frac{D^t\left(x_{t+1},y_{t+1}\right)}{D^{t+1}\left(x_{t+1},y_{t+1}\right)}\times \frac{D^t\left(x_t,y_t\right)}{D^{t+1}\left(x_t,y_t\right)}}\end{array}$ (5)

In Formula (5), (x_t, y_t) and (x_t+1, y_t+1) are the input and output vectors of time t and t + 1 respectively. D^t and D^t+1, D_vrs^t and D_vrs^t+1 are the distance functions of the actual output and the optimal output under the ideal state of time t and t + 1 respectively based on CRS and VRS. When TFP is greater than 1, it indicates that TFP increases positively from t to t + 1; when TFP is less than 1, TFP decreases. TE increases when TEC is greater than 1, and decreases when TEC is less than 1. When PTEC is greater than 1, the level of factor allocation, utilization and management is improved, otherwise, it is decreased. When SEC is greater than 1, SE increases, otherwise, it decreases. When TC is greater than 1, the technology is progressing, otherwise it is regressive. In conclusion, TEC greater than 1 indicates that urban land use efficiency is driven by changes in technical efficiency, and TC greater than 1 indicates that urban land use efficiency is driven by changes in technological progress.

Spatial autocorrelation analysis is a spatial data analysis method to study whether the observed value of a certain position in space is correlated with the observed value of its adjacent position and the degree of correlation ( Anselin, 1995 ; Nolè, Lasaponara, Lanorte, & Murgante, 2014 ), so as to test whether an attribute of a spatial object is distributed adjacent or dislocated. Moran’s I (including global Moran’s I and local Moran’s I) is the most commonly used method to calculate spatial autocorrelation. The calculation formula of global Moran’s I is as follows:

$I=\frac{{\displaystyle \underset{i=1}{\overset{n}{\sum }}{\displaystyle \underset{j=1}{\overset{n}{\sum }}{w}_{ij}}}\left(x_i-\bar{x}\right)\left(x_j-\bar{x}\right)}{S^2{\displaystyle \underset{i=1}{\overset{n}{\sum }}{\displaystyle \underset{j=1}{\overset{n}{\sum }}{w}_{ij}}}}$ (6)

$S^2=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{\sum }}{\left(x_i-\bar{x}\right)}^2},\bar{x}=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{\sum }}{x}_i}$ (7)

where I is the global Moran’s I value, n is the number of space units, x_i and x_j are the observation values of the i-th space unit and j-th space unit, respectively. The w_ij is the spatial weight value, indicating the adjacent relation of the i and j. If it is adjacent, w = 1; otherwise, it is 0. The global Moran’s I is generally (−1, 1). When I is greater than 0, it indicates positive spatial autocorrelation, and the distribution is spatially clustered. When I is less than 0, it indicates negative spatial autocorrelation, and the spatial distribution is scattered. The value of 0 indicates that there is no spatial autocorrelation, meaning the spatial distribution is random. Global Moran’s I is a global evaluation of spatial autocorrelation, which cannot reflect the degree of autocorrelation between a local space and its surrounding local space. Therefore, local spatial autocorrelation analysis must be carried out. The local indications of spatial autocorrelation (LISA) reflects the spatial agglomeration degree of each observed value and its adjacent observed value. For the i-th space element, the calculation formula of local Moran’s I is as follows:

$I_i=\frac{\left(x_i-\bar{x}\right)}{S^2}{\displaystyle \underset{i,j=1}{\overset{n}{\sum }}{w}_{ij}}\left(x_j-\bar{x}\right)$ (8)

In the formula, I_i is the local Moran’s I value, and the meanings of other variables are the same as those in Formula (6). By calculating the local Moran’s I, the cluster map of LISA can be obtained, which is used to show the spatial positive autocorrelation between the research index value and the average value of the adjacent index with high-high and low-low, the spatial negative autocorrelation with high-low and low-high, and no significant spatial autocorrelation (spatial randomness). In addition, the significance of global Moran’s I and local Moran’s I can be tested with the standardized statistic Z value, and the test formula is as follows:

$Z\left(I\right)=\frac{I-E\left(I\right)}{\sqrt{VAR\left(I\right)}},Z\left(I_i\right)=\frac{I_i-E\left(I_i\right)}{\sqrt{VAR\left(I_i\right)}}$ (9)

where Z is the global Moran’s I test value, E(I) is the expectation of I and VAR(I) is the variance of I. Z_i is the lacal Moran’s I test value foe the i study area, E(I_i) is the expectation of I_i and VAR(I_i) is the variance of I_i.

In order to explore the relationship between urban land use efficiency and input and output indexes, it is generally necessary to establish a regression model to reveal the quantitative relationship between each input and output index and efficiency, so as to find out the main factors affecting efficiency. Since the efficiency value obtained by DEA model ranges from 0 to 1, which is a typical bounded variable. It is likely to cause deviation by using the traditional least square method for regression estimation. Therefore, this research applies Tobit regression model to explore the main influencing factors of urban land use efficiency. Tobit regression model is an econometric model that solves the limitation or truncation of dependent variables ( Wang & Qin, 2017 ). It is applicable to dependent variables continuously distributed on non-negative values. Its basic formula is as follows:

$Y={\beta }_0+{\displaystyle \underset{i=1}{\overset{n}{\sum }}{\beta }_i{X}_i}+\epsilon$ (10)

In the formula, Y is the dependent variable, X_i is the independent variable, β₀ is the intercept, β_i is the coefficient of each independent variable, n is the number of independent variables, and ε is the random error vector, which conforms to normal distribution. Taking the comprehensive technical efficiency (TE) of urban land use as the dependent variable and each input and output index as the independent variable, the Tobit regression model is established, and then the influence degree and nature of each input and output index on the TE are judged according to the coefficient, so as to analyze the main factors affecting the efficiency.

Yunnan Province is located in the southwest border of China, with an area of 394,100 km². Yunnan Province has 16 cities under its jurisdiction, including 8 prefecture-level cities and 8 autonomous prefectures, as shown in Table 1 and Figure 2 . In recent years, 16 cities in Yunnan Province are in the critical period

of rapid development of new urbanization and industrialization, and the scale of urban land use is expanding day by day. However, there is no relevant research on the returns brought by this scale expansion. Therefore, this research analyzes the characteristics of land use efficiency in 16 cities and explores its historical evolution laws, so as to provide decision-making basis for Yunnan Province to formulate urban land use policies and coordinate the relationship between urban economic and social development and land resources, thus finally realizing the healthy and sustainable development of land use.

The index system is fundamental to comprehensive evaluation, and DEA efficiency assessment is no exception. The DEA evaluation index system comprises two main components: input indices and output indices. Input indices reflect the quantity of various resources invested by the decision-making unit in the production process, while output indices represent the quantities of various outputs obtained by the decision-making unit through the allocation and utilization of the invested resources. Selecting appropriate input and output indices is crucial for constructing an effective DEA evaluation index system.

The necessary input of land resources, human resources and capital for urban land use can obtain various outputs of urban economy, society and environment through the allocation and utilization of input resources. Based on the basic idea of input and output, this research constructs an index system for evaluating the urban land use efficiency in Yunnan Province. In accordance with the principles of target, simplicity and data availability in establishing DEA evaluation index system, in terms of input indexes, urban built-up area is selected as the land resource input index, urban employment is selected as the human resource input index, and public budget expenditure is selected as the capital input index. In terms of output indexes, the total production value of the secondary and tertiary industries is selected as the economic benefit output index, the total retail sales of consumer goods is selected as the social benefit output index, and the green coverage rate of urban built-up areas is selected as the environmental benefit output index. The constructed comprehensive evaluation index system is shown in Table 2 . According to Table 2 , relevant data of 16 cities in Yunnan Province from 2008 to 2019 are collected. In order to maintain the consistency of data, all index data are from the Yunnan Statistical Yearbook (2009-2020) published by the Yunnan Provincial Bureau of Statistics. The data can also be viewed on the official website ( https://stats.yn.gov.cn ) of Yunnan Provincial Bureau of Statistics.

DEA model is used to calculate the TE and PTE of urban land use in different cities of Yunnan Province from 2008 to 2019, and then the SE is calculated, thus obtaining the dynamic change results of urban land use efficiency in Yunnan Province in nearly 12 years, as shown in Table 3 . On the whole, the overall average values of TE, PTE and SE of urban land use in Yunnan Province during the research period are 0.8686, 0.8959 and 0.9698 respectively. TE and PTE are all less than 0.9, while SE is significantly higher, showing the characteristics of “two low and one high”. In terms of the TE, it is greater than 0.9 only in 2010, and less than 0.9 in the rest years. Meanwhile, it is less than the average value for 5 consecutive years from 2015 to 2019. In terms of the PTE, it is greater than 0.9 in 2008~2011, 2013 and 2019, and is less than the average value for 5 consecutive years from 2014 to 2018. The SE is greater than 0.9 in 12 years, and is less than the average value only in 2012, 2013, 2015 and 2019. The overall characteristics of “two low and one high” indicate that the low TE of urban land use in Yunnan Province is due to the low PTE. That is, there are deficiencies in the allocation, utilization and management of input resources, and there is a large space for improvement in the future. High SE indicates that under the overall technical level, urban land use in Yunnan Province has reached a relatively high level in terms of scale agglomeration of input and output, but there is limited space for future improvement. Obviously, the key to improve the TE of urban land use in Yunnan Province is to vigorously improve the PTE. That is, it is necessary to improve the technical level of the development and utilization of the input resources, and fully improve the reasonable utilization of the input resources, so as to catch up with the level of scale agglomeration, thus improving the TE of urban land use.

The change trend of urban land use efficiency in Yunnan Province in nearly 12 years is shown in Figure 3 . According to Figure 3 , the SE value is the maximum in each year, followed by the PTE value, while the TE value is the minimum. The change of TE shows a downward trend in fluctuation, which can be divided into three stages, namely the W-shaped change stage from 2008 to 2013, the continuous decrease stage from 2013 to 2017, and the slow increase stage after 2017. In the W-shaped change stage, the TE shows an obvious fluctuation and reaches 0.9083 in 2010, the maximum value in nearly 12 years. In the continuous decrease stage, the TE decreases from 0.8921 in 2013 to 0.8401 in 2017, a decrease of 5.83%, reaching the minimum value in nearly 12 years. After 2017, the TE value shows a slow upward trend, reaching 0.8585 in 2019, an increase of 2.19%. On the whole, the TE value decreases from 0.8855 in 2008 to 0.8585 in 2019, a decrease of 0.027 or 3.05%. Obviously, there is still a large space for improvement and optimization of urban land use efficiency in Yunnan Province. The change trend of PTE is basically the same as that of TE, which shows a fluctuation in three stages. The change of SE is relatively gentle. Except in 2013 and 2019, it basically shows a gentle change trend in small fluctuation. Furthermore, from the beginning and end of the research period, the TE and SE both show a downward trend, with a decrease of 3.05% and 4.41% respectively, while the PTE increases slightly, with an increase of 1.49%. Obviously, the sharp decrease of SE is the main reason for the decrease of TE at the end of the research period. To sum up, the SE of urban land use in Yunnan Province shows a high-value change, the PTE shows a mid-value change, and the TE shows a low-value change in nearly 12 years. This also shows once again that the key to improve the TE of urban land use in Yunnan Province is to improve the PTE and convert the input resources into output as much as possible, thus improving the efficiency.

In order to further analyze the spatial pattern characteristics of urban land use efficiency in Yunnan Province, based on the interval distribution of TE values, 16 cities in Yunnan Province are divided into four echelons according to the classification criteria of equal to 1 (high efficiency), 0.9 - 1 (relatively high efficiency), 0.8 - 0.9 (medium efficiency) and less than 0.8 (low efficiency). The results are shown in Figure 4 . In 2008, the first echelon consists of 5 cities with DEA efficiency, including Kunming, Yuxi, Wenshan, Xishuangbanna and Nujiang, with efficiency value of 1. The second echelon consists of 3 cities, including Chuxiong,

Qujing and Baoshan. The third echelon consists of 5 cities, including Diqing, Dali, Lijiang, Dehong and Lincang. The fourth echelon consists of 3 cities, including Zhaotong, Honghe and Pu’er. In 2019, the first echelon consists of 5 cities including Kunming, Yuxi, Xishuangbanna, Dali and Diqing, the second echelon consists of 2 cities including Wenshan and Nujiang, the third echelon consists of 3 cities including Lijiang, Dehong and Zhaotong, and the fourth echelon consists of 6 cities including Honghe, Baoshan, Chuxiong, Lincang, Qujing and Pu’er.

In terms of spatial distribution, Yunnan Province forms an obvious spatial agglomeration area of efficient urban land use with Kunming and Yuxi as the center and Chuxiong, Qujing and Wenshan as the two wings in 2008, while the cities with medium and low efficiency are mainly distributed in the western and southern regions of Yunnan Province. Yunnan Province forms a spatial agglomeration area of efficient urban land use with Kunming and Yuxi as the center in 2019, while Xishuangbanna, Dali and Diqing shows a dotted distribution. The cities with relatively high and medium efficiency are distributed in the eastern and western border regions of Yunnan Province, while the cities with low efficiency form the largest and contiguous spatial agglomeration area. On the whole, the spatial distribution for urban land use efficiency in Yunnan Province has two obvious characteristics. First, Kunming, Yuxi and Xishuangbanna are always the agglomeration areas of urban land use with high efficiency in Yunnan Province; Second, the number of cities with low efficiency increases from 3 in 2008 to 6 in 2019. In terms of spatial distribution, the cities with low efficiency are mainly distributed in southern regions in 2008, while that in southern and central regions in 2019, forming an obvious trend of spatial diffusion.

Based on the TE data of 16 cities, the global Moran’s I of urban land use efficiency in Yunnan Province from 2008 to 2019 is calculated. The results are shown in Table 4 and Figure 5 . On the whole, the global Moran’s I values of all the years during the research period are negative, and the land use efficiency of the 16 cities may have a negative spatial autocorrelation, which may be a discrete spatial pattern. In terms of specific values, the minimum value of global Moran’s I in 2010 is −0.3726, which is closest to −1, and the possible negative spatial autocorrelation is the most obvious. In 2012, the maximum value of the global Moran’s I is −0.1100, close to 0, indicating that the spatial distribution of that year is more random. According to Figure 5 , the global Moran’s I fluctuates during the research period, which can be divided into three stages, including the gentle change stage from 2008 to 2010, the sharp change stage from 2010 to 2015, and the gentle change stage after 2015. In the first stage, the global Moran’s I values are all less than −0.3000. In the second stage, the global Moran’s I values fluctuate sharply. Firstly, it sharply increases from −0.3726 in 2010 to −0.1735 in 2011, an increase of 53.43%, showing an obvious V-shaped trend; Secondly, from 2012 to 2015, the global Moran’s I shows an inverted N-shaped trend, experiencing repeated fluctuations of “high-low-high-low”, from the maximum value of −0.1100 in 2012 to −0.2809 in 2015. In the third stage, the global Moran’s I shows a stable trend, which basically fluctuates slightly around −0.2700, indicating that the spatial distribution of urban land use efficiency in Yunnan Province tends to be stable.

Negative values may indicate a negative spatial autocorrelation, but it still needs to pass a significance test. According to Table 4 , only the Z value of 2010 is −1.7096 and p value is 0.0873, passing the significance test of Z value less than -1.65 and p value less than 0.1. The remaining years fail to pass the significance test with confidence level of 0.1. Therefore, except in 2010, there is no significant difference between global Moran’s I and E(I) in other years, which accept the null hypothesis (land use efficiency is randomly distributed in space), and there is no significant global spatial autocorrelation, showing that the overall spatial distribution of urban land use efficiency in Yunnan Province is neither aggregated nor discrete, but a random spatial pattern.

The global Moran’s I only reveals the global comprehensive characteristics, but cannot show the local spatial relationship between each city and its adjacent cities. This research adopts local Moran’s I to obtain the local spatial relationship of urban land use efficiency in Yunnan Province. The results are shown in Figure 6 and Table 5 . The local Moran’s I scatter plot ( Figure 6 ) portrays the spatial aggregation types of urban land use efficiency in each year. According to Figure 6 , during the study period, most cities in Yunnna Province are in II and IV quadrants (spatial negative autocorrelation) belonging to low-high and high-low types, and only a few cities are in I and III quadrants (spatial positive autocorrelation) belonging to high-high and low-low types. In 2008, the number of cities in I to IV quadrants is 2, 5, 1 and 8 respectively, and in 2019, the number of cities in I to IV quadrants is 3, 5, 3 and 5 respectively. The number of cities with high-high and low-low types increased, indicating that the agglomeration effect of local space has been enhanced. According to Table 5 , during the research period, Xishuangbanna, Zhaotong, Dali and Lijiang show a discrete spatial pattern, forming a heterogeneous area of spatial distribution of land use efficiency with Xishuangbanna, Zhaotong, Dali and Lijiang as the core. In particular, Xishuangbanna shows a stable and continuous local negative spatial autocorrelation, becoming the only city in Yunnan Province with significant local spatial autocorrelation in each year. Lincang shows a positive spatial autocorrelation in three years, which indicates that a certain degree of spatial pattern of agglomeration has been formed with Lincang as the core.

Note: “—” represent local Moran’s I can not pass the significance test at the level of 5%.

In order to more clearly reveal the spatial distribution pattern characteristics of urban land use efficiency in Yunnan Province, the cluster map of local spatial autocorrelation is drawn, as shown in Figure 7 . According to Figure 7 , Xishuangpana shows a high-low pattern of local spatial distribution in all years, while Dali shows a high-low pattern of local spatial distribution in 2017. Both of them show an obvious discrete spatial pattern with high and low values adjacent to each other. Zhaotong shows a low-high pattern in 2009, 2011 and 2014, while Lijiang shows low-high only in 2018. Both of them show a discrete spatial pattern with low and high values adjacent to each other. Lincang shows a low-low pattern in 2011, 2012 and 2015, showing an obvious spatial agglomeration pattern with low values adjacent to each other. On the whole, there is no “hot spot” area with high value agglomeration in urban land use efficiency in Yunnan Province, and only one “cold spot” area with low value agglomeration, namely Lincang. The rest of the local spatial autocorrelation shows a local discrete distribution pattern with heterogeneous high and low values, indicating that there is a certain degree of local spatial heterogeneity.

The TFP changes for urban land use in Yunnan Province based on Malmquist index are shown in Table 6 and Figure 8 . On the whole, the average TFP of urban land use in Yunnan Province from 2008 to 2019 is 1.0661, which means an average annual increase of 6.61% in TFP, achieving positive growth and showing an upward trend. Among them, only the TFP values in 2014-2015 are less than 1, indicating that TFP in this period shows a downward trend, while TFP in other periods are all greater than 1, showing a positive growth trend. As can be seen from the time trajectory in Figure 8 , on the whole, TFP shows an increase in fluctuation, reaching a minimum value in 2014-2015, a maximum value of 1.2477 in 2018-2019, and a second extreme value of 1.2221 in 2013-2014, thus forming two significant peaks.

From the change of decomposition efficiency of TFP for urban land use in Yunnan Province, TEC from 2008 to 2019 has a negative growth of less than 1 in 7 periods, and a positive growth of greater than 1 in 4 periods, while the overall average value is less than 1, that is, 0.9970, indicating that TE presents a trend of regression on the whole. This also shows that the efficiency of factors allocation, utilization and management operation for urban land use in Yunnan Province is insufficient, the structure of urban land use is unreasonable, and the way of urban land use is extensive. TC of urban land use in Yunnan Province only shows negative growth of less than 1 in 2012-2013 and 2014-2015, and positive growth of greater than 1 in the other 9 periods. The overall average value is 1.0694, greater than 1, and the annual TC increases by 6.94% on average. On the whole, TC shows an upward trend, indicating that Yunnan Province pays more attention to technological progress of urban land use. By comparing the change characteristics of TEC and TC, it can be seen that TEC shows a downward trend, and TC shows an upward trend, while TFP shows an upward trend. Obviously, TFP of urban land use in Yunnan Province is mainly driven by TC. However, due to the negative growth of TEC, the positive promoting effect of TC on TFP is delayed, indicating that there is still a large space to improve the resource allocation, utilization, management and scale agglomeration of urban land use in Yunnan Province in the future.

TE of urban land use is the integration of all input and output indexes, which reflects the overall efficiency of the DMUs in the allocation and utilization of factors and scale agglomeration. In order to further reveal the relationship between efficiency and input and output indexes, this research establishes a Tobit regression model to explore the main factors affecting efficiency, so as to provide more detailed decision-making information for the formulation and regulation of urban land use policies. This paper takes the TE of each year in each city of Yunnan Province from 2008 to 2019 as the dependent variable and the 6 input and output indexes of each year as the independent variable to establish the Tobit regression model. The formula is as follows:

$\begin{array}{l}0<T{E}_i\le 1\\ T{E}_i={\beta }_0+{\beta }_1\ln X_1+{\beta }_2\ln X_2+{\beta }_3\ln X_3+{\beta }_4\ln X_4+{\beta }_5\ln X_5+{\beta }_6\ln X_6+\epsilon \end{array}$ (11)

In the formula, TE_i is the TE of each year, X₁ to X₆ are input and output indexes, β₁ to β₆ are regression coefficients of each variable, β₀ is the intercept term, ε is the residual term, and i represent different years. Tobit regression results are shown in Table 7 .

According to Table 7 , all input and output indexes pass the significance test of 5% at least once and then enter the model. On the whole, at 5% confidence level, only the urban built-up area in 2009 and 2018 passes the significance test. In 2009, the coefficient affecting the TE is 0.0777, which has a positive effect on efficiency, while in 2018, the coefficient is −0.2118, which has a negative effect on efficiency. The remaining 10 annual urban built-up areas fail to pass the test, indicating that although they have an impact on efficiency, it is not significant. This clearly suggests that blindly expanding urban scale cannot always improve efficiency, and the development model of “urban sprawl” is not desirable. Urban employment personnel only fails to pass the significance test in 2013 and 2015, public budget expenditure only fails to pass the significance test in 2019, and they all pass the significance test in other years. However, the coefficients of urban employment personnel and public budget expenditure are negative in all years, which have a negative effect. The total output value of the secondary and tertiary industries passes the significance test in all years, and the total retail sales of consumer goods fail to pass the significance test only in 2019. Both coefficients are positive, indicating that they have a positive effect on efficiency. The green coverage rate of urban built-up area fails to pass the significance test in 2008 and 2011-2015. It has a positive effect on efficiency in 2009 and 2010, while has a negative effect in 2016-2019.

From the number of years passing the significance test, the urban built-up area has the least influence on efficiency, followed by the green coverage rate and urban employment personnel. The total output value of secondary and tertiary industries has the biggest impact on efficiency, followed by public budget expenditure and total retail sales of consumer goods, both of which fail to pass

Note: ^* represent significance at 5% statistical level.

the test only in 2019. In terms of their relationship with efficiency, the total output value of the secondary and tertiary industries and the total retail sales of consumer goods are positively correlated with efficiency, while the urban employment personnel and the public budget expenditure are negatively correlated with efficiency. The other two indexes have positive and negative correlations with efficiency, but they are mainly negative. On the whole, there is a significant negative correlation between the input resource index and the efficiency of urban land use in Yunnan Province, which suggests that the input scale should be carefully controlled. Blindly expanding the input scale can not improve the efficiency, but cause the waste of resources and reduce the efficiency due to the excessively large input scale. At the same time, on the premise of a certain input scale, Yunnan Province should pay more attention to improving output indexes such as the total output value of secondary and tertiary industries and the total retail sales of consumer goods, so as to improve efficiency.