Spatial Heterogeneity in Temperature Elasticity of Agricultural Economic Production in Xinjiang Province, China

Abstract

Agricultural production is significantly impacted by climate change. Owing to its arid and warm climate, investigating the impacts of climate change on agricultural production in Xinjiang Province can help improve resilience and designate adaptive responses for the agricultural sector. On the basis of agricultural output data at the county level in Xinjiang from 1990–2019, we used the feasible generalized least squares (FGLS), panel-corrected standard errors (PCSE), and double machine learning (DML) model to study the spatial heterogeneity in temperature elasticity of agricultural economic production. The results revealed that there is an inverted U-shape of temperature impact on agricultural economic production. The presented temperature elasticity in county level showed that regions with negative temperature elasticities are primarily located in the mainstream of the Tarim basin and the Turpan basin in southern Xinjiang. The SHapley Additive exPlanations (SHAP) analysis was further incorporated to elucidate the impact of different factors on the spatial heterogeneity in temperature elasticity. The results indicated that temperature is the most substantial factor influencing temperature elasticity, with labor and precipitation following in sequence. In particular, increased precipitation in arid and hot regions could alleviate the heat stress and lead to a positive temperature elasticity prediction. These findings provide a scientific basis for spatial heterogeneity in the response of agricultural economic production to climate change, and help identify priority regions for achieving Sustainable Development Goals (SDGs) 1 and 2.

1. Introduction

Climate change is known to combine and aggregate within complex human societies, exerting an effect on overall economic productivity [1,2] by reducing labor intensity under heat stress [3], and altering the dynamics of virtually all ecological, biological, and chemical processes [4,5]. Among economic sectors, agriculture is considered to be the most vulnerable to a changing climate [6,7,8], making it a key sector for climate adaptation strategies at the global and national levels. Global- and national-scale studies have shown negative and positive impacts of increasing temperature and precipitation, respectively, on agricultural production [9,10,11]. However, national-scale data may conceal local-scale characteristics or even fail to capture the impacts of climatic elements on agricultural production [12]. Furthermore, given the disparities in regional natural conditions and socioeconomic foundations, the impact of climate factors, particularly temperature, on agricultural economic production varies across regions, manifesting as spatial heterogeneity in their elasticity [13,14]. Therefore, it is imperative to focus on studies conducted at local scales, such as the county scale, as well as the spatial heterogeneity in temperature elasticity, in order to enhance our comprehension of the mechanisms through which temperature impacts agricultural economic production, thereby contributing to the realization of SDGs 1 and 2.

Climate change affects food and nonfood agriculture systems in complex ways thus compromising agricultural production and the economy both globally and locally [15,16,17]. It is likely to reduce food production directly through changes in agroecological conditions and indirectly by affecting the growth and distribution of incomes, and thus the demand for agricultural produce [18]. Specifically, increasing temperatures are likely to reduce yields of crops at the global scale [8]. Warming by 1 °C decreases yields by 7.5 ± 5.3% (maize), 6.0 ± 3.3% (wheat), 6.8 ± 5.9% (soybean), and 1.2 ± 5.2% (rice) globally [19]. Moreover, the effects of temperature on different crops are variable in different climatic zones globally, with significant spatial heterogeneity even within countries. Temperature increases are expected to affect the relative yield of major crops more strongly in the tropics (+2% to −37%) than in temperate regions (+4% to −20%) [13]. These discrepancies are related to the nonlinear effect of temperature, which was found to peak at an annual average temperature of 13 °C and decline strongly at higher temperatures on the basis of national-level data [1]. Moreover, the temperature at which the effect peaks was estimated to be 23 °C in China on the basis of province-level data [14]. When the temperature in a region exceeds the optimal temperature for local crops, it causes yield stress. Therefore, warming at high latitudes and high altitudes provides opportunities for local agriculture and is known as warming-induced gain in cold regions [19]. This phenomenon is evident in both poleward [20] and upward directions in agricultural expansion [21]. For example, there are strong regional differences with the impacts of climate change in northern Europe being greater (+14%) than those in central (+6%) and southern (+5%) Europe [22]. In addition, the maize yield reduction caused by temperature in southern China is more severe than that in northern China [17]. Studies have demonstrated that estimates of elasticity are also affected by the scale of data. It is estimated that there will be a 0.389% decrease in maize yield for every 1% increase in temperature from 1979–2016 in China, according to province-level data [23]. However, a 1% increase in average temperature has been shown to increase maize production by 0.395% in the long term and 0.377% in the short term from 1978–2015 in China on the basis of national-level data [24]. It demonstrated that when data are aggregated at larger spatial scales, the significance of the impact from precipitation decreases and eventually vanishes [12].

The importance of temperature often dominates precipitation in the production of crops [7], because of the wide availability of water storage and irrigation [25]. In addition, warming temperatures favor the release of more meltwater from glaciers in some areas, such as Xinjiang, thus benefiting irrigated agriculture [26,27]. However, there is a lack of empirical evidence from studies on the impact of temperature on agricultural economic production in such region. An empirical study based on the province-level data in Xinjiang showed that a 1% increase in temperature caused a 0.07% increase in cotton yield [28]. Findings from regression and predictive models have also been reported on the impact of temperature on crops in Xinjiang Province. Temperature variability was found to have the greatest influence on detrended cotton yield variability in Xinjiang [29]. Furthermore, climate variables could account for up to 85.7% of the variation in cotton growth indicators [30]. Temperature and precipitation are also the most important climate factors affecting wheat in Xinjiang [31]. Benefitting from a warmer and wetter climate, the yield of irrigated winter wheat in western Xinjiang is projected to increase by between 12% and 32% under future climate change scenarios [32]. In view of this, empirical research investigating the impact of temperature on agriculture in Xinjiang Province will strengthen the causal basis for this impact.

Statistical modeling based on panel data is the foremost methodology for assessing the causal effect of temperature heterogeneity on agriculture. On the basis of modeling assumptions, such as the Cobb–Douglas production function (CDF) [33] and translogarithmic production function (TPF) [34], statistical methods are able to directly calculate the impacts of climate factors on model outputs (e.g., elasticities and marginal effects) [9,16]. Numerous studies have shown that statistical modeling can achieve results that are consistent with those of process-based models [35,36]. However, studies on heterogeneity based on panel models generally involve separate modeling by partitioning time periods and different factor clusters, with differences in heterogeneity analyzed by comparing model coefficients [17]. With the emergence of machine learning (ML) models, these data-driven models have been employed to assess the impact of temperature on agriculture [19,37], and have been integrated with empirical models to improve their explanatory power and provide a better understanding of the complex mechanisms involved [38]. Nevertheless, due to the differences in the assumptions of the two models, using predictive ML models for causal inference remains controversial. Recently, causal inference machine learning models represented by the double machine learning (DML) model have been used in causal inference studies due to their ability to fit residuals from outcome and treatment variables [39,40,41]. By uniformly modeling all samples, DML models offer unique advantages for analyzing heterogeneity in causal effects. Furthermore, combining DML with the SHAP method enables the identification of nonlinear relationships and high-dimensional interactions that affect outcomes.

Given that climate characteristics at the local scale are more specific than regional averages are, large-scale studies of temperature impacts on agriculture may conceal local-scale variability. In arid and semiarid regions, agriculture is more sensitive to climate change and has more complex response mechanisms. With this in mind, we investigated the heterogeneous effects of temperature on agricultural economic production at the county level in Xinjiang, China, a region with a cold mountain climate and dry, warm irrigated oases, which highlight the heterogeneity of temperature effects in this region. Initially, the overall direction of temperature effects in the region was obtained by using an empirical model to estimate the impacts of climate and other input factors in Xinjiang on agricultural economic production from 1990–2019. To address the group-wise heteroscedasticity, cross-sectional correlation, and autocorrelation within panel data, the coefficients in the TPF model were estimated via the FGLS and PCSE. The conditional treatment effects of each sample were then assessed using the DML model, and the average treatment effects and temperature elasticity of each county were calculated. Finally, the SHAP method was employed to illustrate the influence of various factors on temperature elasticity. This study aims to determine whether spatial heterogeneity exists in the temperature elasticity of agricultural economic production in Xinjiang, and to explore the factors influencing this heterogeneity. This work could lay the groundwork for researching the regional specificity of sustainable agricultural development in the context of climate change.

2. Materials and Methods

2.1. Study Area

Xinjiang is located in northwest China (Figure 1), which is a typical arid and semiarid region with plentiful solar radiation, a great temperature difference, an uneven precipitation distribution, and an important agricultural area. The area belongs to a temperate continental climate, with an average annual temperature of 8 °C and an average annual precipitation of approximately 150 mm [42]. The geographical feature of Xinjiang is typified by a mountain–oasis–desert pattern, with altitudes ranging from −156 to 7360 m a.s.l. The region is roughly separated by three mountain ranges (the Altai Mountains, Tianshan Mountains, and Kunlun Mountains) which are sandwiched between two basins (the Junggar basin and Tarim basin). The oases are situated mainly in piedmont plains, and the irrigation water demand is always supplied by rivers originating from precipitation and meltwater from glaciers and snow cover in mountainous regions. The farmland area in Xinjiang Province reached 7.7 × 10⁴ km² in 2015, nourishing 24 million people. By the end of 2017, the growing areas of cotton, wheat, and corn had reached 2.4 × 10⁴ km², 1.2 × 10⁴ km², and 1.0 × 10⁴ km², respectively.

2.2. Data Sources and Processing

A biased selection of characteristic factors may lead to estimation bias and inadequate interpretations, and selecting the most significant factors affecting agricultural production is crucial. Previous studies have indicated that agricultural economic production or yield for specific crops is affected mainly by explanatory variables, including inputs, regions, and meteorological variables, such as temperature and precipitation [6,16,43].

Temperature and precipitation are used as climatic elements that affect agricultural production. The annual mean air temperature and annual total precipitation data were obtained from the GSEP3-W5E5 dataset [44,45], with a spatial resolution of 0.5° × 0.5°. Considering the small land areas of some counties, we used the delta downscaling method [46] to increase the spatial resolution of the climate variables to 30 arcseconds. We used the spatial average of the climate elements in a given county as the input climate factor.

In this study, agricultural production consisted mainly of the economic production of specific crops such as cereals, cotton, and vegetables; forestry, pastoralism, and fisheries were not included. Agricultural economic production per sowing area served as the dependent variable rather than the yield of various crops. The annual agricultural economic production of 84 counties in Xinjiang Province from 1990–2019 was derived from the Xinjiang Statistical Yearbook (https://www.zgtjnj.org/navisearch-2-0-3-1-xinjiang-0.html, accessed on 1 March 2025). Production input explanatory variables, such as crop sowing area, total machinery power, population employed in agriculture, fertilizer application (pure volume), and GDP per capita (GDPP) were also taken from the Xinjiang Statistical Yearbook. In the context of regions subject to administrative restructuring, a consolidation of data from the respective pre-restructuring regions was undertaken to derive the data for the recently established administrative regions. Furthermore, data with less than two years of consecutive missing values were interpolated using linear interpolation, and regions with more than two years of consecutive missing data were excluded. In the final analysis, a total of 2520 observations were obtained in 84 counties for the period of 1990–2019. The explanatory variables for the input factors for all counties were converted to inputs per hectare by dividing by the sowing area, thus facilitating the comparison of results across counties. The basic summary statistics for all the variables, including sowing area, are given in

Table 1. Descriptive statistics of the data obtained for the period of 1990–2019.

Variables	Obs	Mean	Std. Dev.	Min	Max
Agricultural production (CNY/ha)	2520	18,810.95	21,948.99	1242.58	346,688.00
Temperature (°C)	2520	7.7	4.2	−2.5	15.5
Precipitation (mm/a)	2520	89.3	64.6	4.6	366.6
Sowing area (ha)	2520	39,319.62	32,284.05	1200.60	226,750.00
Machinery (kw/ha)	2520	3.50	2.28	0.33	25.01
Labor (capita/ha)	2520	1.23	0.88	0.01	7.76
Fertilizers (kg/ha)	2520	240.30	156.69	4.83	1522.59
GDPP (CNY/capita)	2520	16,303.81	24,689.81	269.00	362,590.00

Note: ha: hectare; kw: kilowatt; kg: kilogram.

.

2.3. Modeling Approach and Setting

The methodology of this study is organized into three parts. In the initial phase, an empirical model is employed as the base model to assess the directional impact of temperature on agricultural economic production. In this step, two-way fixed effects for time and region are considered with a view to eliminating the effects of time and region. In the subsequent step, the DML model is employed to evaluate the spatial heterogeneity of temperature elasticity. Finally, we use SHAP analysis to explain the impact of different factors on the spatial heterogeneity of temperature elasticity.

The TPF is employed to evaluate the impact of temperature and precipitation on agricultural production in the empirical model. Several methodologies are commonly used in climate impact studies, including cross-sectional models (Richardian model), experimental models (agronomic–economic model), and simulation models [47]. However, given the nonlinear effects of climate on agricultural production, the TPF is adapted via Belloumi’s method [48]. The formula is presented as follows:

LnYA_i,t = β₀ + β₁ lnM_i,t + β₂ lnL_i,t + β₃ lnF_i,t + β₄ lnG_i,t + β₅ Trend_t + β₆ T_i,t + β₇ T_i,t² + β₈ P_i,t + β₉ P_i,t² + α_i + γ_i,t

(1)

where YA represents the agricultural economic production (CNY/ha). The production input factors include machinery (M, kw/ha), labor (L, capita/ha), fertilizers (F, kg/ha), and GDP per capita (G, CNY/capita). Additionally, climate factors, specifically temperature (T, °C) and precipitation (P, mm/a), are considered key determinants that may influence agricultural production. Ln is the natural log, t denotes observations from 1990–2019, i denotes the ith county, and YA_i,t refers to agricultural economic production for county i at time t. The quadratic terms of temperature and precipitation were integrated into the model to consider their nonlinear effects on agricultural production. Taking the existence of time fixed effects into consideration, Trend indicates the time trend (1–30). In the model, the regional fixed effect is controlled based on the county, and α_i is used as the dummy variable for the 84 counties. Finally, γ_i,t are the error terms. β₀ represents the constant term; β₁–β₉ denote the parameters to be estimated.

The partial derivation and multiplication by T/YA of both sides of Equation (1) is determined to calculate the temperature elasticity of agricultural economic production. From this calculation, we establish that the rate of change in agricultural economic production is caused by a temperature increase rate, as shown in Equation (2).

E((dYA/YA)/(dT/T)) = (β₆ + 2β₇ × E(T)) × E(T)

(2)

where β₆ and β₇ are linear and quadratic term coefficients for temperature. E(T) represents the mean value of temperature.

In this study, group-wise heteroscedasticity, cross-sectional correlation, and autocorrelation within panel were tested. The group-wise heteroscedasticity and autocorrelation within panel were tested via the Wald test by Greene [49] and Wooldridge [50], respectively. The cross-sectional correlation was tested via the Breusch–Pagan Lagrange multiplier (LM) [49] and Pesaran’s test [51]. The test results are listed in

Table 2. Test on group-wise heteroscedasticity, cross-sectional correlation, and autocorrelation within the panels.

	Group-Wise Heteroscedasticity	Autocorrelation Within Panel	Cross-Sectional Correlation
Statistic	Wald’s χ2	Wald’s F	BPLM test’s F	Pesaran’s test
Value	1800.73 ***	40.26 ***	16,010.10 ***	61.94 ***

***, 0.01 level of statistical significance.

, and indicate the existence of group-wise heteroscedasticity, cross-sectional correlation, and autocorrelation within panel. Therefore, the FGLS model was used to estimate the parameters by adjusting the group-wise heteroscedasticity, cross-sectional correlation, and autocorrelation within panel to achieve more efficient estimators [52,53]. The PCSE model was also used to estimate the parameters by adjusting the group-wise heteroscedasticity and autocorrelation within panel for comparison [52,54].

In this study, DML [40,41] is employed to estimate the heterogeneous effects in temperature elasticity of agricultural economic production, since it allows for unbiased estimation of treatment effects when all potential confounding variables are observed. Specifically, we regard agricultural economic production as the outcome Y, linear and quadratic term of temperature as the treatment TM, linear and quadratic term of precipitation and other input factors in Equation (2) as the feature X, and the time variable and dummy variable for counties as confounder W. X refers to the features that can predict the heterogeneous treatment effect (i.e., the effect of TM on Y), while W represents the fixed effects.

The model follows the following structural equation assumptions:

Y = θ(X)·TM + g(X,W) + ε, E(ε|X,W) = 0

(3)

TM = f(X,W) + η, E(η|X,W) = 0; E(ε·η|X,W) = 0

(4)

By simultaneously taking expectations of both sides of Equations (3) and (4), then subtracting them from each other, we get

Y − E(Y|X,W) = θ(X)·(TM − E(TM|X,W)) + ε

(5)

Initially, the residuals are obtained by the utilization of any ML model for fitting Y and TM:

$$\tilde{Y}=Y-E(Y|X,W), \mathrm{where} E(Y|X,W)=g(X,W)$$

(6)

$$\widetilde{TM}=TM-E(TM|X,W), \mathrm{where} E(TM|X,W)=f(X,W)$$

(7)

Secondly, by substituting Equations (6) and (7) into Equation (5), we obtain

$$\tilde{Y}=\theta (X)·\widetilde{TM}+\epsilon$$

(8)

Finally, we regress $\tilde{Y}$ on X and $\widetilde{TM}$:

$$\tilde{\theta }={argmin}_{\theta \in \Theta }{E}_n[(\tilde{Y}-\theta (X)·\widetilde{TM}{)}^2]$$

(9)

Let the temperature terms in Equation (1) be denoted by [θ₁, θ₂]·[T, T²]^T, and all other terms by g(X,W), the following equation can be obtained:

LnYA = θ(X)·TM + g(X,W) + ε

(10)

where θ(X) equals to [θ₁, θ₂], and TM equals to [T, T²]^T.

Keeping other variables constant, the elasticity is derived by taking the derivative and multiplying by T/YA of both sides of the Equation (10):

(dYA/YA)/(dT/T) = (θ₁ + 2θ₂ × T) × T

(11)

Equations (2) and (11) are similar in form, but the DML estimates θ as conditional average treatment effects, with each sample having an estimated value, which differs from the global β estimate in Equation (2). It is evident that the discrepancy in the treatment effects estimates will result in divergent elasticity expectations.

Finally, the SHAP [55] analysis, which is rooted in cooperative game theory, is used to explain the spatial heterogeneity and delve into the impacts of precipitation and other input factors on the temperature elasticity.

We used EconML package (version 0.16.0) of Python (version 3.12.3) to estimate the heterogeneous causal effects. To account for the potential high-dimensional nonlinear effects of features on the causal effect, the CausalForestDML was employed to map the data into high-dimensional space. The formula g(X,W), f(X,W), and Equation (8) were predicted by the Random Forest (RF) model [56] based on the ten-fold cross-validation method for avoiding overfitting.

3. Results

3.1. Changes in Annual Mean Temperature and Precipitation

The climate of Xinjiang Province is cold and arid, as shown in Figure 2. The average annual air temperature was 7.3 °C and the average annual precipitation was 59.4 mm/a from 1990–2019. Owing to the varied climate and complicated topography, there is considerable spatial heterogeneity in both temperature and precipitation. The temperature is typically higher in southern Xinjiang, especially in the Taklamakan Desert, where the average annual temperature exceeds 10 °C. Conversely, the mountainous areas are obviously cooler, with the majority of counties reporting average annual temperatures below 5 °C. There are also notable spatial differences in the distribution of precipitation. Southern Xinjiang is particularly arid, with average annual precipitation remaining below 100 mm/a, whereas the western slopes of the Tianshan Mountains have much more precipitation, exceeding 250 mm annually. These variations highlight the critical influence of topography and regional climate patterns in determining the thermal and hydrological regimes of Xinjiang.

From 1990–2019, both air temperature and precipitation in Xinjiang showed increasing trends, a phenomenon known as the “warming and wetting” of the region’s climate. As shown in Figure 2, the increasing trends of air temperature and precipitation were 0.03 ± 0.02 °C/a and 0.31 ± 0.39 mm/a, respectively. Nevertheless, there was no statistically significant increase in precipitation. The air temperature tended to increase in all counties, with the central and southern regions showing the most significant increase. Among these areas, the mountainous areas in the western part of southern Xinjiang warmed the most, with temperatures rising faster than the provincial average. Significant spatial variability was found in the changes in precipitation, with precipitation decreasing in the eastern part of southern Xinjiang, and increasing most significantly in the Altai Mountains in the north and the western Tianshan Mountains in the central region, which were greater than the provincial average. Mountainous areas were found to be more sensitive to climate change when temperature and precipitation changes were combined. The Tianshan Mountains were the most sensitive to regional climate variability, with the largest and most statistically significant changes.

3.2. Results for the Empirical Model

We adjusted the group-wise heteroscedasticity, autocorrelation within panel, and cross-sectional correlation in the stochastic disturbance term via the FGLS model.

Table 3. The FGLS model and PCSE model estimation results showing the impacts of input and climatic factors on agricultural economic production.

Variables	Model (1) 1		Model (2) 2		Model (3) 3		Model (4) 4
	Coef.	z-Value	Coef.	z-Value	Coef.	z-Value	Coef.	z-Value
Input factors
Ln(machinery)	0.2601 *** (0.0037)	71.05	0.2556 *** (0.0029)	88.41	0.2599 *** (0.0527)	4.93	0.2566 *** (0.0519)	4.95
Ln(labor)	0.0663 *** (0.0021)	30.94	0.0676 *** (0.0011)	63.74	0.0660 *** (0.0581)	1.13	0.0671 (0.0569)	1.18
Ln(fertilizers)	0.1627 *** (0.0011)	150.23	0.1643 *** (0.0011)	150.97	0.1631 *** (0.0233)	7.00	0.1647 *** (0.0231)	7.12
Ln(GDPP)	0.2902 *** (0.0013)	220.47	0.2869 *** (0.0022)	128.14	0.2909 *** (0.0524)	5.55	0.2894 *** (0.0509)	5.68
Climatic factors
Temperature			0.0138 *** (0.0022)	6.36			0.0138 (0.0401)	0.34
Temperature 2			−0.0005 *** (0.0001)	−3.55			−0.0005 (0.0017)	−0.29
Precipitation			−0.0002 *** (<0.0001)	−5.58			−0.0002 (0.0008)	−0.21
Precipitation 2			<0.0001 (<0.0001)	0.79			<0.0001 (<0.0001)	0.02
Trend	0.0212 *** (0.0003)	62.89	0.0217 *** (0.0004)	52.84	0.0211 *** (0.0080)	2.63	0.0213 *** (0.0079)	2.71
Cons	5.4359 *** (0.0109)	497.9	5.4039 *** (0.0206)	261.72	5.4229 *** (0.3949)	13.73	5.3747 *** (0.4510)	11.92
Chi-square	504,844.89 ***		434,121.07 ***		331.75 ***		315.92 ***
R-squared					0.8692		0.8666

¹ Model (1) reports the coefficients of the input factors estimated by the FGLS model. ² Model (2) reports the coefficients of the input and climate factors estimated by the FGLS model. ³ Model (3) reports the coefficients of the input factors estimated by the PCSE model. ⁴ Model (4) reports the coefficients of the input and climate factors estimated by the PCSE model. ***, 0.01 level of statistical significance. The values in parentheses are the parameter standard deviations.

shows the estimation results of Model (2) for the FGLS model and Model (4) for the PCSE model, including input and climatic factors. To assess the impacts of climate variables, Model (1) for the FGLS model and Model (3) for the PCSE model used only input factors for comparison. Most of the estimated coefficients related to the input and climatic factors were statistically significant.

Models (1) and (3) indicated that all of the input factors had positive impacts on agricultural production at the 1% level of significance (Table 3). Among all the input factors in the models, GDP per capita had the greatest impact on agricultural production. A 10% increase in GDP per capita would lead to a 2.90% increase in agricultural production for Model (1) and a 2.91% increase for Model (3), with other factors remaining constant. Machinery was the second largest impact factor on agricultural production. Under the conditions of other factors being constant, agricultural production increased by 2.60% for Model (1) and Model (3) when machinery increased by 10%. Fertilizers had the third greatest impact on agricultural production. A 10% increase in fertilizers would lead to a 1.63% increase in agricultural production for Models (1) and (3), with other factors remaining constant. Furthermore, labor had a comparatively limited impact on agricultural economic production, indicating agriculture in Xinjiang Province is a sector in which labor input is less significant than other input factors. Hence, technological development, infrastructure, investments in machinery and fertilizers assume greater importance in increasing agricultural economic production.

Models (2) and (4) reveal that agricultural economic production in Xinjiang Province was much less affected by climate factors than by input factors (Table 3). In addition, it was also observed that the elasticity in precipitation was lower than in temperature in related studies. This is due to the use of drainage and groundwater irrigation in many areas [57,58]. The machinery and fertilizers’ inputs and GDP per capita increased significantly throughout the 30-year period. As shown in Figure 3, the average annual growth rates for machinery, fertilizers’ input, and GDP per capita reached 3.1%, 3.6%, and 9.9%, respectively. The temperature and precipitation change rates, however, were only 0.4% and 0.6%, respectively. Differences in the variation in inputs and climate factors lead to differences in agricultural economic production elasticities. Importantly, the labor input showed an inverted U-shaped change, suggesting that agricultural economic production in Xinjiang Province underwent a labor-intensive transition during the 30-year period.

By controlling the traditional input factors, the elasticities of temperature and precipitation can be derived from Equation (2). As shown in

Table 4. Elasticities of annual mean air temperature on agricultural economic production based on the FGLS and PCSE model.

	Temperature
	Model (2) 1	Model (4) 2
Elasticities	0.0447 (0.0258)	0.0491 (0.3667)

¹ Model (2) reports the results for the FGLS model. ² Model (4) reports the results for the PCSE model. The values in parentheses are the standard deviations.

, we established that for every 10% increase in temperature, the agricultural production increased by 0.48% for the FGLS model and 0.49% for the PCSE model, respectively.

There is consistency among the four models’ input factor coefficients and significance. The FGLS model, however, estimated more significant climate factor coefficients and smaller standard deviations of the estimated coefficients for all factors than the PCSE model. Cross-section correlation adjustments can enhance model performance, as seen by the superior estimation results obtained by FGLS over PCSE.

3.3. Assessing the Spatial Heterogeneity in Temperature Elasticiy

The causal inference machine learning model is conducted to estimate conditional average causal effects, revealing a nonlinear impact of temperature on agricultural economic production (as illustrated in Figure 4). As shown in Figure 4a,b, the linear term of the temperature effect coefficients (coefficient θ₁) for 76.71% of all samples are positive (the average value is 0.0336, and the 95% confidence interval is [−0.0356, 0.1211]), while the quadratic term of the temperature effect coefficients (coefficient θ₂) for 72.42% of all samples are negative (the average value is −0.0016, and the 95% confidence interval is [−0.0062, 0.0029]), indicating that the temperature elasticity increases and then decreases with the increase in temperature.

The prediction of agricultural economic production is crucial for sustainable development of agriculture, which is often realized by regression models. Here, we propose a more accurate prediction method that considers spatial heterogeneity. Specifically, the agricultural economic production in a given county at an assumed temperature condition can be predicted through the counterfactual prediction model generated based on the causal inference machine learning model. The performance of the counterfactual predictive model is evaluated on all samples (Figure 4c), and the results show that the predictive performance (R² = 0.95) is better than conventional regression (OLS, R² = 0.83).

To facilitate the application of the model, the map illustrating the county-level average temperature elasticity is also provided (Figure 4d). The average temperature elasticity of all samples is −0.0085, and the 95% confidence interval is [−0.4881, 0.2870]. Figure 4d demonstrates the spatial heterogeneity of temperature elasticities, with 66.67% of all counties revealing positive values. The regions where the temperature elasticities are negative primarily locate in the mainstream of the Tarim basin and the Turpan basin within southern Xinjiang. However, the Junggar basin within northern Xinjiang, which also has high temperatures, exhibits a positive temperature elasticity. This implies that the temperature elasticity may be affected by climate and other input factors.

3.4. Explaining Spatial Heterogeneity in Temperature Elasticity

The trained causal inference machine learning model has revealed spatial heterogeneity in the impacts of temperature on agricultural economic production. The temperature elasticities are smaller (i.e., more negative, indicating less agricultural economic production per hectare with rising temperature), and are concentrated in the mainstream of the Tarim basin and Turpan basin where the temperature is high (see Figure 4d). To explore the underlying factors that lead to the observed variations, we conducted a comprehensive assessment of the diverse influential factors related to climate and other input factors using the SHAP method. The analytical approach enabled us to quantify the individual contribution of the features to the value of temperature elasticity. Since temperature elasticity indicates the percentage change in agricultural economic production due to a 1% increase in temperature, a positive temperature elasticity represents that temperature rising favors agricultural economic production. Features that yield positive SHAP values strengthen the temperature elasticity, while features with negative SHAP values weaken it.

As shown in Figure 5a, the SHAP values of temperature appear more negative (shown in blue) in the mainstream of the Tarim basin and Turpan basin, implying that the high temperatures in these regions lead to a prediction of weaker temperature elasticity. Shaya has the lowest SHAP value of temperature, a finding that may be attributable to the high heat accumulation and diminishing marginal impacts. In contrast, some of the northern and southern mountainous regions have positive SHAP values, indicating that the relatively low air temperatures in these regions are predicted to contribute to their temperature elasticities. On the other hand, Figure 5b shows that the northern region and the Tianshan Mountains also have higher precipitation and positive SHAP values of precipitation, which reinforces the temperature elasticity. In addition, despite less precipitation in Fukang (warmer) compared to Zhaosu (colder), the SHAP value of precipitation in the former exceeds that of the latter. This suggests that precipitation plays an important role in buffering temperature shocks. Nevertheless, the negative SHAP values of precipitation in the southern arid regions amplify the negative temperature sensitivity, implying that extreme water scarcity makes the agriculture system more vulnerable to high-temperature stress.

The SHAP values of the other input factors (Figure 5c–f) do not demonstrate the regular spatial heterogeneity of distribution patterns exhibited by the climate factors (Figure 5a,b), suggesting that the effect of input factors on temperature elasticity varies from place to place. As shown in Figure 5c and Figure S1c, the southwestern regions with lower machinery input have lower SHAP values of machinery, and the more mechanized regions have positive SHAP values in most counties. A positive correlation has been suggested between higher machinery inputs and more positive SHAP values, indicating that agricultural mechanization enhances adaptation to high temperatures and thus amplifies the effect of temperature on agricultural economic production. However, Urumqi and Korla have the strongest positive effect of machinery input on temperature elasticity, even though they do not have the highest levels of machinery input. The lowest SHAP values of machinery are found in the Shanshan and Gaochang counties, which have the highest machinery inputs. This may be related to the fact that excessively high summer temperatures in these two regions reduce mechanical efficiency. The distribution of labor (Figure S1d) and the SHAP values (Figure 5d) demonstrate a positive correlation analogous to that observed in the context of machinery, with the exception of Shanshan and Gaochang.

As illustrated in Figure 5e, the lowest SHAP values of fertilizers are observed in Tuoli and Fuyun, which have comparatively low levels of fertilizers’ input, while the highest SHAP values are recorded in Aksu and Yuli, which have relatively high levels of fertilizers’ input. This suggests that fertilizers’ input has a positive impact on temperature elasticity. However, the distribution of SHAP values of fertilizers is found to be more heterogeneous in other regions, implying the presence of more complex nonlinear effects of fertilizers on temperature elasticity. GDPP represents factors such as the regional technological levels, industrial structures, and infrastructures. However, as shown in Figure 5f and Figure S1f, the distribution of GDPP does not correspond to its high SHAP values. Counties with high GDPP such as Shanshan and Korla instead predicted negative SHAP values, while Moyu, which has a low GDPP, predicted the highest SHAP values. This does not imply that a high GDPP exacerbates the sensitivity of agricultural economic production to rising temperature. Precipitation is scarce and glacier cover is also rare in eastern Xinjiang, and the middle reaches of the Tarim River, which are susceptible to upstream water stress. Therefore, the temperature elasticity is difficult to alleviate by high GDPP in terms of water access. The southwestern regions with lower GDPP are close to the upper Tarim River, and the economic production in these regions is dominated by agriculture. Despite the high temperatures and scarce precipitation, these regions have relatively easy access to water resources, thus mitigating the sensitivity of temperature elasticity.

3.5. Impacts of Factors on Temperature Elasticity

While SHAP values decompose the temperature elasticity into the contribution of different predictor features and explain the spatial heterogeneity of elasticity, the dependence plot better illustrates the change in the temperature elasticity with respect to individual factors (Figure 6). Figure 6a illustrates the importance of features in relation to temperature elasticity. The results suggest that temperature is the most significant factor influencing temperature elasticity, followed by labor, precipitation, and GDPP, while fertilizers and machinery have the least impact.

Figure 6b shows the SHAP summary plot, where higher values of the features are represented by red dots, and lower values are represented by blue dots. Additionally, a positive SHAP value suggests that the feature contributes positively to the predicted temperature elasticity, and a negative SHAP value suggests that the feature contributes negatively to the predicted temperature elasticity. The SHAP values for temperature demonstrate a skewed distribution, with SHAP values for low temperatures (blue dots) closer to the center of the distribution than those for high temperatures (red dots). It is indicated that the impact of extreme high temperatures on temperature elasticity gradually increases. Warmer temperatures have been shown to contribute to temperature elasticity when temperatures are lower, but when temperatures exceed a certain threshold, temperature elasticity will decline and agricultural economic production will become more vulnerable to rising temperature (Figure 6c). As corroborated by the positive SHAP contribution of higher precipitation in Figure 6b and the corresponding trend in Figure 6d, an increase in precipitation leads to a more positive temperature elasticity, indicating the benefit of rising temperature in humid regions. Specifically, in hot conditions (red dots), the temperature elasticity is observed to be more sensitive to increased precipitation. This finding indicates that increased water inputs may serve as a mitigating factor against the impact of heat stress on agricultural economic production.

In terms of other input factors, the majority of samples characterized by high labor input (red dots) yield positive SHAP values, signifying that greater labor and machinery inputs amplify the prediction of temperature elasticity. However, the SHAP value distributions for GDPP and fertilizers are more complex, suggesting that these factors exert complex nonlinear effects on temperature elasticity and may be influenced by interdependencies with other factors. The patterns of influence on temperature elasticity for labor and machinery are quite similar (Figure 6e,f). In circumstances where input levels are relatively constrained, the impact on temperature elasticity is found to be minimal. Furthermore, it has been demonstrated that, once their input levels exceed a certain threshold, they significantly enhance the prediction of temperature elasticity. In addition, it has been shown that temperature elasticity is more sensitive to labor. However, the SHAP values for samples with the highest labor and machinery inputs (Shanshan, as shown in Figure 5c,d) decrease to negative values, which may be related to the extreme high temperatures in the Turpan basin during summer. The region under consideration is the lowest-altitude region in Xinjiang, where the number of days with temperatures above 35 °C reaches 100 days per year. It is hypothesized that extreme high temperatures may impede the efficiency of labor and machinery inputs, thereby amplifying the vulnerability of temperature elasticity to rising temperature.

As illustrated in Figure 6g, an increase in fertilizers use has the potential to enhance temperature elasticity. However, the distribution range of its SHAP values is wide, suggesting that fertilizer is only capable of explaining a limited proportion of temperature elasticity anomaly. This phenomenon may be attributable to differences in soil properties and agronomic practices across different regions. When fertilizer use is minimal, an increase in use can enhance temperature elasticity, but when fertilizer application exceeds a certain threshold, an increase in use reduces temperature elasticity. Figure 6h shows the variation between GDPP and its SHAP value. Samples exposed to conditions of high temperature and moderate to low temperature show significant differences. In conditions of moderate-to-low temperature, GDPP has been observed to yield marginal enhancements in the predictions of temperature elasticity, provided that the threshold for GDPP is attained. However, in regions where temperatures are high, an increase in GDPP has been shown to actually weaken temperature elasticity. These regions, characterized by high temperatures, are also typically associated with low precipitation. It is evident that these regions characterized by higher temperatures are also typically associated with lower precipitation levels. It is noteworthy that discrepancies emerge in the geographical distribution of these regions within the context of the watershed. Regions such as Moyu, which are closer to the upstream, have lower GDPP levels but are more likely to obtain water resources (Figure 5f). Therefore, the use of GDPP to represent irrigation facilities in order to explain the impact of temperature elasticity is subject to certain limitations. Indeed, our model is insufficiently sophisticated to explain the impact of water resource shortages in areas with high water pressure on temperature elasticity.

3.6. Robust Check

Alternative estimation methods, such as pooled OLS, fixed effect, and random effect models, were employed in agreement with Equation (1) to validate the results obtained from FGLS and PCSE (Table S1). Our findings suggests that there is a relationship between agricultural production and climate variables. The FGLS model achieved more accurate estimations than traditional regression models did, as the panels have group-wise heteroscedasticity, cross-sectional correlation, and autocorrelation. The direction of the effect of the input factors and the trend term on agricultural economic production is consistent across all models and is found to be highly significant. However, the direction of the climate term varies considerably, and the coefficients of the temperature term in the fixed effects and random effects models are opposite to those of the other models. As demonstrated in Table S2, the between-group deviations in temperature are an order of magnitude higher than the within-group deviations when compared to the other factors. Consequently, a within-group deviation that is too insignificant may have a significant effect on the direction and significance of the temperature coefficients. The region was then divided into northern and southern Xinjiang based on the Tianshan Mountains (Figure 1). And the coefficients of Equation (1) were estimated using FGLS and PCSE in groups to validate the effect of climatic discrepancies on the model outcomes. As demonstrated in Table S3, the coefficients of the temperature terms are more significant in southern Xinjiang, whereas the directions of the precipitation terms are reversed and the coefficients are more significant in northern Xinjiang. It is suggested that the agricultural economic production in northern and southern Xinjiang is primarily impacted by the climatic variables of precipitation and temperature, respectively.

In addition, the robustness of the causal inference machine learning model results was also tested. As detailed in

Table 5. The results of the validation by refuting for causal inference machine learning model.

Name	Original Effects		New Effects		Result
	θ1	θ2	θ1	θ2
Add random common cause	0.0336	−0.0016	0.0327	−0.0015	Pass (Not changed effect)
Data subsets validation			0.0380	−0.0018	Pass (Partially sensitive to data subsets)
Add unobserved common cause			0.0440	−0.0023	Fail (Sensitive to confounder)
Placebo treatment			0.0002	<0.0001	Pass (Almost zero effect)
Dummy outcome			0.0014	<0.0001	Pass (Almost zero effect)

, the results of the validation by a refuting approach demonstrate the robustness of the estimated effects. The addition of a random common cause factor does not significantly alter the estimated effects, implying that the model successfully passed the add random common cause refutation test. In the placebo treatment and dummy outcome refutation tests, the newly estimated effects are significantly diminished compared to the true causal effect and are insignificantly different from 0, suggesting that the model effectively passes the placebo treatment and dummy outcome refutation tests. Nevertheless, the new effects are partially comparable to the original effects in the data subsets validation, indicating the model is partially sensitive to sample heterogeneity. This is attributable to the cross-validation process, which prevents samples from the same county from being allocated to both the training and validation sets, suggesting the presence of spatial heterogeneity in treatment effects. Nonetheless, in an add unobserved common cause refutation test, the effects are significantly impacted.

4. Discussion

4.1. Spatial Heterogeneity in Temperature Elasticity

The causal inference machine learning model is employed to estimate the spatial heterogeneity of temperature elasticity of agricultural economic production in Xinjiang Province, which has received limited investigation. The FGLS and PCSE empirical models provide directional references to temperature impacts, and the results show that the directions of the linear and quadratic terms of temperature impacts for most samples in the DML model are in the same direction as the results of the empirical models. It is suggested that there is an inverted U-shape of temperature impacts on agricultural economic production. The nonlinearity of temperature effects is evidenced in economic development [14], maize, soybean, cotton, and rice yields [23,59,60] in China. This study presents a quantitative demonstration of the temperature elasticity of agricultural economic production. In addition, the estimator is simplified into a county-level temperature elasticity expression (Figure 4d). The regions with negative temperature elasticities are primarily located in the mainstream of the Tarim basin and the Turpan basin in southern Xinjiang. In addition, the temperature elasticity is predicted to be positive in northern Xinjiang and the mountainous regions of southern Xinjiang. This spatial heterogeneity is also predicted by the FGLS and PCSE model, as demonstrated in Table S3 and Equation (2), which yielded average temperature elasticities of 0.0382 and 0.0304 for northern and southern Xinjiang, respectively.

4.2. The Impacts of Factors on the Spatial Heterogeneity in Temperature Elasticity

The SHAP analysis was incorporated to elucidate the impact of different factors on the spatial heterogeneity in temperature elasticity. The results indicate that temperature is the most substantial factor influencing temperature elasticity, with labor, precipitation, and GDP per capita following in sequence. Conversely, fertilizers and machinery exhibit the least significant impact. The distribution of SHAP values for temperature and precipitation is highly similar to the distribution of temperature elasticity, suggesting that counties with negative temperature elasticity tend to have high temperatures and low precipitation (Figure 5a,b). It has been indicated that elevated temperatures have a positive effect on temperature elasticity when temperatures are lower, but when temperatures exceed a certain threshold, temperature elasticity will decline and agricultural economic production will become more vulnerable to rising temperature. As summarized by Ye et al. [61], when rising temperature exceeds the crop optimal temperature, the impacts of temperature increase on physiological processes and yield formation could be detrimental. Although there are discrepancies in temperature thresholds for distinct crops [62], research has demonstrated that agricultural yields in tropical regions experience amplified temperature stress compared to temperate zones [13]. Moreover, while in cooler growing regions, increasing growing season temperature could be beneficial for crop yield, owing to its enhancement on leaf photosynthesis and biomass accumulation [63]. The relatively cooler temperatures in northern Xinjiang and the mountainous regions of southern Xinjiang have been found to be conducive to warming gain, a phenomenon consistent with the characteristics of higher latitudes [1,22].

It has been noted that the impact of precipitation on yield is obscured by irrigation [17]. However, group simulation of FGLS and PCSE in northern Xinjiang illustrates the positive effect of precipitation on yield. Lin et al. determined that the optimal irrigation levels for cotton in northern and southern Xinjiang are 345.59 mm/a and 675.61 mm/a, respectively [64]. The arid climate in southern Xinjiang is associated with a high rate of evapotranspiration, which can limit the availability of water for agricultural purposes. Even a slight increase in precipitation may not be sufficient to adequately recharge soil moisture, thereby affecting crop productivity. However, the SHAP values illustrated in Figure 5b and Figure 6d indicate a positive impact of precipitation on temperature elasticity. As demonstrated by the positive SHAP contribution of higher precipitation in Figure 5b and the corresponding trend for hot conditions (red dots) in Figure 6d, increased precipitation in arid and hot regions could alleviate the heat stress and lead to a positive temperature elasticity prediction. It has been proposed that the interaction of temperature and precipitation together has a stronger explanatory power than other joint drivers for cotton yield in Xinjiang [29]. Therefore, irrigation is considered to be an effective measure to minimize yield loss due to high temperatures [65]. Xinjiang is the primary cotton-producing region in China. Although the natural condition in southern Xinjiang is potentially capable of achieving higher cotton yields than in the northern part [64,66], southern Xinjiang is confronted with more severe water shortages. In such conditions, the resilience of temperature can be enhanced by measures to improve water use efficiency. For example, the application of high-reflective mulch drip irrigation has been shown to reduce daytime soil temperatures and retain moisture [67]. Alternatively, a higher-density drip irrigation program can also be used to cool the soil [68].

Although not to the same degree, machinery and labor exert a favorable effect on temperature elasticity. It is evident that inputs will have a substantial impact on temperature elasticity, particularly when they exceed a predetermined threshold. However, the Turpan basin, despite having the highest machinery and labor inputs, predicts a negative temperature elasticity contribution. This may be attributed to the fact that the present study did not consider the effect of extreme heat, which has been demonstrated to significantly reduce the efficiency of machinery and labor [69,70]. The enhancement of agricultural productivity could be achieved through the optimization of operational timing, the management of shading and cooling, and the integration of mechanical thermal management techniques, complemented by scientific and technological inputs [69,71]. It has been shown that fertilizers contribute the most to cotton yield in Xinjiang [29], which is only supported by the OLS in this study (Table S1). However, the DML results indicated that when fertilizers’ input exceeds a certain threshold, it might reduce temperature elasticity prediction, and the regions with negative effects were mostly those with high temperatures. It is evident that rising temperature has a detrimental effect on the nitrogen use efficiency [72]. High temperature promotes the occurrence of microbial processes and increases the rate of NH₃ volatilization, resulting in effective nitrogen loss and reduced fertilizer utilization [73,74]. GDPP represents the level of technology, water facilities, and other impact factors that are difficult to quantify. In the regions with low and medium temperature, GDPP increase will enhance temperature elasticity. However, the direction of GDPP impact reverses in the regions with high temperature. Indeed, disparities in water availability conditions are evident in the high-temperature regions. Regions such as Moyu, with comparatively lower GDPP levels but higher temperatures, are located in proximity to the headwaters of the basin and consequently benefit from more favorable access to water resources. In contrast, in eastern Xinjiang with high temperature and low precipitation, it is difficult to access water resources, thus leading to a negative temperature elasticity prediction. This suggests that representing irrigation conditions in terms of GDPP is inadequate.

4.3. Limitations and Uncertainties

The impacts of temperature on agricultural economic production in Xinjiang were revealed to be positive and negative at the county scale. Despite their differences in how they assess temperature elasticity, all three models demonstrate significant explanatory power and achieve consistency in the direction of temperature effects. Research on the predictability of agricultural yields shows that ML models are more effective than traditional panel data models [37,75,76]. But the reasons for this discrepancy have not been well addressed beyond the explanation of the difference in nonlinear structure. This is despite the fact that panel models are able to assess the average treatment effect of temperature at the group level by introducing a quadratic term for temperature to capture potential non-linear relationships. In contrast, the CausalForestDML approach enables the consideration of heterogeneity in treatment effects by estimating the individualized conditional treatment effects conditional on observed covariates. Consequently, average elasticities calculated based on individual-level heterogeneity effects may differ significantly from those derived in panel models using fixed-average coefficients. This discrepancy underscores the efficacy of the CausalForestDML approach in discerning heterogeneity in treatment effects that may be overlooked in conventional parametric models. Our results suggest that the Turpan basin shows unique temperature elasticity differences, likely due to the model not accounting for temperature extremes. Temperature extremes impact crop production [77] and play an important role in the productivity of input factors [71]. Additionally, temperature impacts vary across growing periods [30], potentially obscuring differences in crop response when using annual average data. Furthermore, we used agricultural economic production as an explanatory variable to mitigate the impact of variations in input factor allocation across crops. However, this introduces uncertainty regarding the differences in response across crops. For example, winter wheat may benefit more from warming than spring wheat [78], and cotton may be more resilient to drought than wheat and maize [79].

Notably, the study area is characterized by glaciers in mountainous regions, as illustrated in Figure 1. Glaciers play an instrumental role in the hydrological cycles of the region, thereby serving as a crucial source of freshwater. Studies have shown that glacier water resources account for 31% of the total water resources in Xinjiang [15] and up to 41% in the Tarim River basin, and this proportion increases with increasing temperature [80]. Consequently, the observed increase in temperature is expected to positively impact water resources and agricultural production. The model structure of this study does not consider the effects of temperature on glacier water resources, and the resulting temperature elasticity may be overestimated. Moreover, water resources in Xinjiang are derived from glaciers and snowpack in the headwaters of the mountains [81]. Due to the importance of irrigation for agricultural production in Xinjiang, the explanation of precipitation on cotton yields is still unclear [30]. Snowpack constitutes an essential water resource in the study area [82], and the impact of the previous year’s snowfall on the following year’s water resources is a significant yet unconsidered factor in this study. In summary, the spatial and temporal heterogeneity of water resources in this study area contributes to significant uncertainties in the assessment of the impact from precipitation and temperature on agricultural production. However, irrigation at the county level is often not included in statistics, and the intersection of watershed and administrative boundaries makes irrigation reconstruction difficult. Although the process-based model produced acceptable results for irrigation reconstruction at provincial and national scales, errors remain significant at more detailed scales [83,84].

5. Conclusions

Our study explored the impacts of temperature on agricultural production in Xinjiang Province at the county level, examining spatial heterogeneity via the DML model. The findings of the study indicated an inverted U-shaped relationship between temperature and agricultural economic production from 1990–2019. In addition, the estimator is simplified into a county-level temperature elasticity expression. The presented temperature elasticity at the county level demonstrated that regions exhibiting negative temperature elasticities are predominantly situated in the mainstream of the Tarim basin and the Turpan basin in southern Xinjiang. As demonstrated by SHAP analysis, temperature is the most significant factor influencing temperature elasticity, followed by labor, precipitation, and GDPP, while fertilizers and machinery have the least impact. The findings of this study indicate that implementing countermeasures, such as reducing the temperature in hot regions and preventing extreme droughts, can enhance temperature elasticity in a direct manner. Additionally, these countermeasures can also exert an indirect influence on temperature elasticity by promoting the productivity of input factors.

Given the significant impact of the cryosphere on water resources and irrigation on crop yield, it is important to consider the role of temperature and irrigation in this context. In future research initiatives, it is imperative to emphasize the necessity for the reinforcement of basin scale and administrative scale water resource linkages. Furthermore, it is essential to undertake the quantification of the contribution made by cryospheric water resources at the administrative scale.