Climate Change, Factor Inputs and Cotton Yield Growth: Evidence from the Main Cotton Producing Areas in China

Abstract

Increasing the yield per unit area is crucial for achieving stable growth in China’s cotton production. Based on the transcendental logarithmic production function model and using panel data from eight major cotton-producing provinces in China from 1990 to 2022, this paper measures the elasticity of climate factors and factor inputs and calculates the contribution rate of each factor influencing cotton yield increase. The results show that accumulated temperature positively impacts cotton yield, while precipitation and sunshine duration have negative effects. Climate factors contribute 7.95% to yield growth. Among input factors, agricultural machinery and labor inputs positively affect yield, whereas fertilizer input negatively affects it. Factor inputs contribute 44.21% to yield improvement. Technological progress also plays a role in enhancing cotton yield. Finally, the paper suggests improving meteorological disaster forecasting, optimizing input structures, and promoting agricultural research and technology services based on local conditions.

1. Introduction

Global warming has become a globally recognized fact [1], and the influence of human activities on climate change has become increasingly evident. Anthropogenic greenhouse gas emissions have reached historical peaks [2]. From 1880 to 2020, the global average temperature increased by 1.09 °C, accompanied by a significant rise in climate extremes, manifested in the continuous increase in high-temperature days and the gradual decrease in low-temperature days. Since 1950, global average precipitation has been on the rise, and the spatial extent of heavy precipitation events has expanded [1]. Meanwhile, solar radiation in many regions has shown a declining trend. Collectively, these changes constitute the core features of the evolution of the global climate system [3,4].

Climate change in China is generally consistent with global trends but exhibits distinct regional characteristics [5]. Since 1951, most parts of China have experienced a significant rise in temperature [6,7]. The Third National Assessment Report on Climate Change indicates that the rate of warming in China is higher than the global average [8]. Regional disparities in precipitation are also pronounced, with annual average precipitation showing a declining trend in northern China while increasing significantly in the regions south of the Yangtze River Basin [9]. In addition, direct solar radiation in China has continued to decrease since 1961, at a rate of −6.6 W/(m²·10a) [10]. Climate change directly influences agricultural production by altering the environmental conditions for crop growth [11]. Consequently, clarifying the mechanisms and impacts of climate change on crop yield remains a key research focus at the intersection of agricultural economics and climate science.

Cotton is a major economic crop in China [12,13]. It is planted in more than 20 provinces, and nearly 200 million farmers and textile workers are directly or indirectly dependent on the cotton industry. However, the national cotton planting area has significantly decreased, dropping from 5.588 million hectares in 1990 to 2.838 million hectares in 2024. From the perspective of China’s cotton industry development, the decline in cotton planting area is the result of a combination of multiple factors, including policy changes, social and economic conditions, as well as climate change. Against this backdrop, improving yield per unit area through technological progress has become a crucial pathway to ensure stable and increased cotton production in China [14].

A large number of studies have shown that factor input is an important driving force for improving cotton yield per unit area. Among these, management measures such as fertilizer, labor, and irrigation play central roles. The role of chemical fertilizer input in improving crop yield has been widely recognized [15,16,17], but excessive application not only reduces input–output efficiency but also leads to environmental degradation and indirectly inhibits yield growth [17]. As a key management measure affecting crop growth [18], irrigation plays an irreplaceable role in improving cotton water conditions and alleviating the impacts of climate fluctuations. This role becomes even more critical in mitigating the adverse effects of high temperatures, thereby ensuring yield stability [19]. Furthermore, technological progress, as a key driver of agricultural development, not only directly increases yield levels through the promotion of new varieties and the application of agricultural machinery but also indirectly enhances production capacity by improving factor utilization efficiency [20]. However, although factor input and technological progress have improved the growth environment of cotton to a certain extent, climate factors still play a fundamental role in determining yield. Previous studies have shown that rising temperatures, changes in the spatiotemporal distribution of precipitation, and related microclimatic stresses have a direct and significant effect on cotton yield [21]. Given the increasing trend of climate change, it is difficult to offset these adverse impacts solely through factor expansion. Therefore, on the basis of the scientific allocation of factor inputs, there is an urgent need to strengthen research on and responses to climatic adaptability.

The existing literature mostly uses the yield decomposition method to evaluate the impact of climate factors on cotton yield from the perspective of meteorological yield. However, the role of technological progress and management factors cannot be ignored. Crop models (such as CERES-Wheat and CERES-Maize) have been widely used to study the combined effects of climate and management factors on crops, but their highly empirical nature requires model adaptation to regional realities, that is, by adjusting measures to local conditions [22]. Given that the production function provides a systematic framework and accounts for the adaptation of social production to climate change, this paper introduces climatic factors such as sunshine hours, accumulated temperature, and precipitation into the translog production function on the basis of factor input and technological progress and constructs a comprehensive model including factor inputs, technological progress, and climatic factors. Using the provincial-level panel data from major cotton-producing provinces in China (1990–2022), this paper analyzes the impact of various factors, including climatic factors, on cotton yield per unit area, in order to provide a theoretical basis and policy implications for the development of China’s cotton industry.

2. Theoretical Analysis

Increasing factor inputs is the primary driver of China’s agricultural production growth, especially the contribution rate of increase in fertilizer application to China’s agricultural growth, which is particularly prominent [23]. In the field of cotton production, in addition to traditional inputs like fertilizers, technological advancement has become a key driver behind the rapid growth. Empirical analysis based on data from 13 major cotton-producing provinces during 1998–2005 indicates that labor, fertilizer, other material inputs, and technological progress all have significant effects on cotton yield, with the contribution of technological progress reaching 63.37%, followed by that of labor [24]. Research employing the nonlinear parameter Malmquist index further demonstrates that technological progress has been the dominant factor promoting productivity improvement since the reform and opening-up [25]. Other studies have shown that, in addition to technological progress, inputs of agricultural machinery, fertilizers, and labor also significantly influence cotton production. Among these, the output elasticity of manual labor and chemical fertilizer inputs are negative. In contrast, agricultural mechanization has become a key factor in driving cotton yield growth in the future [26].

However, the impact of these factors is not limited to China. Comparative studies from other major cotton-producing countries provide broader insights into the global challenges facing cotton production. For instance, in India, climate change has been found to significantly impact cotton yield, with rising temperatures, changes in precipitation patterns, and extreme weather events posing severe threats to cotton production. The study emphasizes the importance of genomic methods to enhance cotton’s stress resilience and calls for interdisciplinary research and policy interventions to mitigate the negative effects of climate change on cotton production [27]. Similarly, the Arizona Low Desert of the United States, future climate projections indicate that cotton yield will significantly decline under increased temperatures and reduced precipitation, as shown by simulations using the DSSAT CSM-CROPGRO-Cotton model [28]. In Australia, climatic trends such as rising temperatures and changing precipitation patterns have been identified as major challenges to cotton production, and the need for improving water resource efficiency and developing adaptive cotton varieties is emphasized as a response to climate change impacts [29]. These studies from India, the USA, and Australia highlight that climate change and factor inputs are critical factors for cotton production globally.

The growth of cotton is closely related to climate factors, which significantly influences the growth, layout, and planting structure of cotton, thus affecting cotton yield per unit area. Analysis of climate data in northern Xinjiang from 1961 to 2007 indicates that the overall set of climatic changes (including warmer temperatures, longer frost-free period, and increased accumulated temperature) has been beneficial on balance, while the reduction in sunshine hours was explicitly listed as an adverse factor [30]. Further evidence suggests that increases in accumulated temperature enhance the thermal resources available during the growing season, reduce the likelihood of climate-related disasters, and enhance seedling photosynthesis, thereby promoting dry matter accumulation and improving yields [31]. However, the impacts of climate change differ significantly across regions. For example, analysis of meteorological data in Anhui Province from 1961 to 2010 reveals that accumulated temperature is conducive to yield growth, whereas excessive precipitation is detrimental [32].

Based on the above-mentioned literature, it is not difficult to find that climate factors primarily including accumulated temperature, precipitation, and sunshine duration; factor inputs such as fertilizer, agricultural machinery, and labor inputs; and technological progress will affect the cotton yield per unit area from different aspects. Based on this, this paper proposes the following research hypotheses:

H1. 

The input factors (fertilizer, agricultural machinery, and labor) are expected to have a positive impact on cotton yield per unit area, while excessive fertilizer input may have a negative impact.

H2. 

Accumulated temperature is expected to have a positive effect on cotton yield per unit area, whereas excessive precipitation and prolonged sunshine duration are expected to have a negative effect on cotton yield per unit area.

3. Materials and Methods

3.1. Research Methods

3.1.1. Trend Analysis

Trend analysis method was used to analyze the rate of change in climate factors such as precipitation, accumulated temperature, and sunshine duration in cotton growing season, and the statistical significance of these trends was assessed using the t-test [33,34].

Establish a linear regression equation of $Z_i$ and $t_i$ as follows:

$$Z_i=a+b{t}_i(i=1,2,\dots ,n)$$

(1)

where $Z_i$ is the climate factor, $t_i$ is the corresponding time change of $Z_i$, $n$ represents the sample size, $a$ and $b$ are regression coefficients, and $b$ indicates the rate of change in climate factors.

3.1.2. Transcendental Logarithmic Production Function

The transcendental logarithmic production function was proposed by Christensen et al. (1973) [35] It is a variable elasticity production function that includes not only the logarithmic terms of labor and capital inputs but also their squared and cross-product terms. Compared with the Cobb–Douglas production function [36] and CES production function [37], the transcendental logarithmic production function is more flexible and universal in the conversion and substitution modes and has no additional restriction on technological progress. The transcendental logarithmic production function can better measure the mutual influence and output elasticity of input factors, so it is widely used.

The basic form is as follows:

$$LnY=\alpha +{\beta }_{1}LnL+{\beta }_{2}LnK+0.5{\beta }_{11}(LnL{)}^2+0.5{\beta }_{22}(LnK{)}^2+{\beta }_{12}\left(LnL\right)\times \left(LnK\right)$$

(2)

By introducing the time trend variable and the climate variable based on the Formula (2), this paper obtains Equation (3):

$$\begin{array}{l}Ln{Y}_{it}={\alpha }_o+{\alpha }_{1}Ln\left(F{T}_{it}\right)+{\alpha }_{2}Ln\left(A{M}_{it}\right)+{\alpha }_{3}Ln\left(L{A}_{it}\right)+0.5{\alpha }_{11}Ln\left(F{T}_{it}\right)\times Ln\left(F{T}_{it}\right)\\ +0.5{\alpha }_{22}Ln\left(A{M}_{it}\right)\times Ln\left(A{M}_{it}\right)+0.5{\alpha }_{33}Ln\left(L{A}_{it}\right)\times Ln\left(L{A}_{it}\right)+{\alpha }_{12}Ln\left(F{T}_{it}\right)\times Ln\left(A{M}_{it}\right)\\ +{\alpha }_{13}Ln\left(F{T}_{it}\right)\times Ln\left(L{A}_{it}\right)+{\alpha }_{23}Ln\left(A{M}_{it}\right)\times Ln\left(L{A}_{it}\right)+{\alpha }_{t}t+0.5{\alpha }_{tt}{t}^2+{\beta }_{1}Ln\left(A{T}_{it}\right)\\ +{\beta }_{2}Ln\left(R{F}_{it}\right)+{\beta }_{3}Ln\left(I{T}_{it}\right)+0.5{\beta }_{11}Ln\left(A{T}_{it}\right)\times Ln\left(A{T}_{it}\right)+0.5{\beta }_{22}Ln\left(R{F}_{it}\right)\times Ln\left(R{F}_{it}\right)\\ +0.5{\beta }_{33}Ln\left(I{T}_{it}\right)\times Ln\left(I{T}_{it}\right)+\mu \end{array}$$

(3)

In the above formula, $Y_{it}$ represents the cotton yield per unit area in the t-th year of the i-th cotton production province, $F{T}_{it}$ represents the fertilizer input per unit area of the cotton field in the t-th year of the i-th cotton production province, $A{M}_{it}$ indicates the agricultural machinery input per unit area of the cotton field in the t-th year of the i-th cotton production province, $L{A}_{it}$ means the labor input per unit area of the cotton field in the t-th year of the i-th cotton production province, $A{T}_{it}$ indicates the accumulated temperature of the t-th year of the i-th cotton production province, $R{F}_{it}$ represents the precipitation in the t-th year of the i-th cotton production province, $I{T}_{it}$ means the sunshine duration of the t-th year of the i-th cotton production province, and the time trend term t and its quadratic term represent Hicks neutral technology advancement.

3.2. Data Sources and Basic Statistics

Except for Tibet and Heilongjiang Province where the accumulated temperature is inadequate for cotton cultivation, cotton is planted in all provinces of China. Considering the continuity of data obtained, this paper selects eight major cotton growing provinces including Hunan, Anhui, Jiangsu, Hubei, Henan, Hebei, Shandong, and Xinjiang from 1990 to 2022 as the research object and comprehensively investigates the impacts of production factors and climate factors on cotton yield per unit area in China.

The data on daily average temperature, precipitation and sunshine duration in the major cotton producing provinces selected in this paper were sourced from the China Meteorological Data Network. The cotton input and output data come from China Statistical Yearbook (National Bureau of Statistics of China. (1990–2022). China Statistical Yearbook. National Bureau of Statistics of China. https://www.stats.gov.cn/, accessed on 5 January 2025), China Agricultural Yearbook (China Agricultural Press. (1990–2022). China Agricultural Yearbook. China Agricultural Press. Published on China Economic and Social Big Data Research Platform. https://www.cnki.net/, accessed on 1 January 2025) and the statistical yearbook of each province. While these yearbooks provide the most comprehensive and authoritative data for large-scale economic and agricultural research in China, we do acknowledge their potential limitations, including measurement errors, and inconsistencies in statistical standards across different periods or provinces. To minimize the impact of these potential issues on the empirical research results, we implemented rigorous data cleaning procedures and conducted a series of tests. The robustness tests performed later in the study also support the reliability of our empirical findings. To address potential endogeneity between variables, the input and output variables were processed based on the characteristics of cotton production. The specific treatments are described below.

3.2.1. Input Variables

The climate data of each province was averaged from the four meteorological observatories near the main cotton producing areas of the province. The effective accumulated temperature expression for cotton growth period is as follows:

$$AT=\sum \mathit{max}(0,T_i-T_b)$$

(4)

In Formula (4), $AT$ is the effective accumulated temperature (°C·d), and $T_i$ is the average daily temperature (°C) measured by the adjacent meteorological observatory on the i-th day of the cotton growing season; $T_b$ represents the minimum biological temperature of cotton (according to the literature, this article takes 10 °C [38]); the total amount of precipitation (RF) is the mean of total precipitation measured by the adjacent meteorological observatory during the cotton growing season, and sunshine duration (IT) represents the mean of total sunshine duration measured by the adjacent meteorological observatory during the cotton growing season; fertilizer input (FT) is calculated based on the area planted with crops, cotton planting area, and fertilizer application rate in the study area; agricultural machinery input (AM) is calculated based on the total power of agricultural machinery, cotton planting area, and crop planting area; and labor input (LA) is expressed as the number of rural population per unit area of the study area (ren/hm²).

3.2.2. Output Variables

Y is expressed as cotton yield per unit area (kg/hm²). Descriptive statistics of the main variables are shown in

Table 1. Descriptive statistics of the main variables.

Variable Name	Mean	Standard Deviation	Minimum Value	Maximum Value	Median
Cotton yield per unit area (kg/hm2)	1050.480	284.970	346.900	2056.840	485.81
Accumulated temperature (°C)	2613.990	259.980	2067.880	3756.980	2613.99
Precipitation (mm)	641.060	313.400	22.170	1531.380	641.06
Sunshine duration (h)	1376.463	249.570	831.280	2054.080	1376.46
Fertilizer input (kg/hm2)	330.560	86.330	132.570	496.420	330.56
Agricultural machinery input (kw·h/hm2)	4.830	2.810	1.490	12.700	4.83
Labor input (ren/hm2)	5.115	1.238	2.030	6.730	5.12
Time trend	17	7.807	1	33	17

. According to the descriptive statistical analysis of the sample data, the difference between the maximum and minimum values of cotton yield per unit area and each input factor is large, and the variables have large variation, reflecting significant disparities in cotton production inputs and outputs among the major cotton-producing provinces. The main reason for this is that the range of sample selection is relatively scattered, and because the production conditions, capacity, and climate of the eight sample areas differ significantly.

4. Results

4.1. Trend Analysis of Climate Factors in Cotton Growing Season in Major Cotton Producing Provinces of China

Figure 1 shows the rate of change in climate factors during the cotton growing season in China’s major cotton producing provinces from 1990 to 2022. In terms of the accumulated temperature changes, the accumulated temperature of cotton growing seasons in Xinjiang, Shandong, Jiangsu, Anhui, Hubei, Hunan, and Henan showed an upward trend, and the accumulated temperature in Henan and Hunan increased significantly (Figure 1a). With regard to the change in precipitation, the precipitation during cotton growing season in Xinjiang, Henan, Hubei, Anhui, and Jiangsu increased, among which the precipitation in Anhui and Hubei increased greatly, while the precipitation in cotton growing season in Shandong, Hebei and Hunan decreased (Figure 1b). In terms of sunshine duration, an increasing trend was observed only in Xinjiang, while the other seven provinces showed a decrease. (Figure 1c).

4.2. Analysis of Factors Affecting the Cotton Yield per Unit Area in China

4.2.1. Model Selection

This study selects the data of 8 major cotton producing areas to analyze the influencing factors of cotton yield per unit area. Given the panel nature of the data, it is necessary to use the Hausman test to determine the specific regression model. See

Table 2. Model selection.

Estimation Method	Test Method		Test Result
Mixed OLS and fixed effect	F test: F(7, 191) = 18.87	Prob > F = 0.00	fixed effect
Mixed OLS and random effect	LM test: χ2 = 0.00	Prob > χ2 = 1.00	Mixed OLS
Fixed effect and random effect	Hausman test: χ2= 97.95	Prob > χ2 = 0.00	fixed effect

for details. Through the comparison of the above three tests results, it is found that the fixed effects model should be selected in this paper.

Subsequently, tests for between-group heteroscedasticity, autocorrelation, and cross-sectional dependence were conducted, the detailed results are shown in

Table 3. Results and Conclusions of Various Tests Used in This Study.

Test	p-Value (5% Significance Level)		Conclusion
Modified Wald Test	chi2(192) = 4089.38	Prob > chi2 = 0.0000	Reject the null hypothesis
Wooldridge Test	F(6, 191) = 64.235	Prob > F = 0.0000	Reject the null hypothesis
Pesaran CD Test	Pr = 0.0000		Reject the null hypothesis

. The Modified Wald test indicates the presence of heteroscedasticity between groups, while the Wooldridge test reveals the existence of first-order autocorrelation in the panel data. The Pesaran CD test results show the presence of cross-sectional dependence. Due to the existence of heteroscedasticity, autocorrelation, and cross-sectional dependence, the Driscoll–Kraay standard errors (referred to as “DK standard errors”) were used for the regression analysis.

To ensure the stationarity of the series and avoid spurious regression results, unit root tests were conducted on the variables in the model. Each variable series was analyzed for unit roots using EViews 7 software. Eviews 7 provides six testing methods: Common root—Levin, Lin, Chu, Individual root-Im, Pesaran, Shin, Individual root—Fisher-ADF, and Individual root—Fisher-PP, with the results shown in

Table 4. Results of the sequence unit root test.

Variable Name	Levin, Lin & Chu t	Im, Pesaran and Shin W-Stat	ADF-Fisher Chi-Square	PP-Fisher Chi-Square
Accumulated temperature	0.0000	0.0000	0.0000	0.0000
Precipitation	0.0000	0.0000	0.0000	0.0000
Sunshine duration	0.0000	0.0000	0.0000	0.0000
Fertilizer input	0.2280	0.0083	0.0158	0.0068
Agricultural machinery input	0.5849	0.4967	0.6738	0.6895
Labor input	0.6819	0.6812	0.8236	0.8265
Cotton Yield unit area	0.0000	0.0000	0.0000	0.0000

. From Table 4, it can be concluded that the series of Accumulated temperature, Precipitation, Sunshine duration, Fertilizer input, and cotton yield unit area all passed the unit root test. However, since the p-values for the six test methods of the Agricultural machinery input and Labor input series are all greater than 0.1, they failed the unit root test, indicating the presence of non-stationarity in the series. Therefore, first-order differencing is required.

The Agricultural machinery input and Labor input series were subjected to first-order differencing to ensure the stationarity of the series, thereby ensuring the reliability of the model. The first-order differenced series were then tested for unit roots (see

Table 5. Results of unit root test again.

Variable Name	Levin, Lin & Chu t	Im, Pesaran, and Shin W-Stat	ADF-Fisher Chi-Square	PP-Fisher Chi-Square
Agricultural machinery input	0.0000	0.0000	0.0000	0.0000
Labor input	0.0000	0.0000	0.0000	0.0000

). The results of the subsequent unit root test show that the p-values for the first-order differenced series of effective irrigation area changes are all 0.0000, indicating that the null hypothesis of a unit root is rejected at the 1% significance level, confirming the series are stationary and suitable for the panel data model.

4.2.2. Empirical Results

Table 6. Estimation results by fixed effects model.

Independent Variable	Coefficient	Independent Variable	Coefficient
Ln (AT)	30.805 ** (2.248)	Ln2(FT)	−0.616 (−1.256)
Ln (RF)	0.216 (1.354)	Ln2(AM)	0.254 * (1.955)
Ln (IT)	12.626 ** (2.347)	Ln2(LA)	0.961 ** (2.418)
Ln (FT)	3.624 (1.477)	Ln (FT) × Ln (AM)	0.223 (0.933)
Ln (AM)	1.349 (−1.106)	Ln (FT) × Ln (LA)	−0.325 (−1.325)
Ln (LA)	0.585 (0.356)	Ln (AM) × Ln (LA)	−0.029 (−0.147)
Ln2(AT)	−3.786 ** (−2.00)	t	0.027 ** (2.015)
Ln2(RF)	−0.050 * (−1.725)	t2	−0.002 ** (−2.845 )
Ln2(IT)	−1.787 ** (−2.374)	c	−173.337 *** (−2.848)
R2 = 0.6249		F(17, 191) = 26.71 Prob > F = 0.000

Note: ***, **, and * indicate significant levels at 1%, 5%, and 10%, respectively.

shows the estimation results of panel data by fixed effect model. The model’s goodness-of-fit, indicated by an R² value of 0.639, and the F test result is {F(17, 191) = 19.150, Prob > F = 0.000}, indicating that the explanatory variables in the model have a significant combined impact on the explained variables. Among the 17 variables, 9 variables passed the significance tests. These empirical results demonstrate that both input factors and climate factors provide a sound explanation for the variation in cotton yield per unit area.

The regression results indicate that sunshine duration has a significant impact on cotton yield, while precipitation does not. This can be explained from an agronomic perspective. Cotton is a photosynthesis-driven crop, and sunshine duration is crucial for its photosynthesis, directly affecting the synthesis of carbohydrates, which in turn influence boll development and lint production. In regions where water is sufficiently available, such as China’s major cotton-producing areas, sunlight becomes the primary limiting factor for growth, while water availability plays a lesser role. Therefore, the significant effect of sunshine duration on cotton yield reflects its decisive role in cotton growth. On the other hand, the insignificance of precipitation may be attributed to the irrigation infrastructure in China’s cotton-growing regions. Irrigation systems effectively ensure a stable water supply, reducing the impact of irregular rainfall. As a result, cotton growth depends more on artificial irrigation rather than natural precipitation, which explains why precipitation was not significant in the regression results.

In summary, these findings suggest that in regions with advanced irrigation systems, sunshine duration has a more significant impact on cotton yield, while the effect of precipitation is relatively minor, highlighting the importance of maximizing solar radiation utilization.

a. Output elasticity of cotton production factors

Since in Equation (3) there are quadratic terms in the explanatory variables, the coefficients of which are difficult to directly explain, the output elasticity at the mean of the samples needs to be calculated. Taking the accumulated temperature, fertilizer input, and time trend as examples, the calculation formula of output elasticity is as follows:

$${\displaystyle \frac{\partial Y/Y}{\partial AT/AT}}={\displaystyle \frac{\partial LnY}{\partial Ln(AT)}}={\beta }_1+{\beta }_{11}Ln(AT)$$

(5)

$${\displaystyle \frac{\partial Y/Y}{\partial FT/FT}}={\displaystyle \frac{\partial LnY}{\partial Ln(FT)}}={\alpha }_1+{\alpha }_{11}Ln(FT)+{\alpha }_{12}Ln(AM)+{\alpha }_{13}L\mathrm{n}(LA)$$

(6)

$${\displaystyle \frac{\partial Y/Y}{\partial t/t}}=({\alpha }_t+{\alpha }_{tt}t)·t$$

(7)

This section presents an analysis of the output elasticity of climate factors on cotton yield per unit area. Among the climate factors, the accumulated temperature and sunshine duration during the cotton growing season passed the 5% significance level test, and the output elasticity was 1.016 and −0.288 (Table 4), respectively; the output elasticity of precipitation was −0.110, which was not statistically significant at the 10% level. According to the regression results of climate factors, the quadratic coefficients of accumulated temperature, precipitation, and sunshine duration are negative, indicating that the impact of the three on cotton yield per unit area is “inverted U-shaped”. Based on the calculations, the turning points for accumulated temperature (AT) is 58.56 °C, for rainfall (RF) is 8.67 mm, and for insolation time (IT) is 34.47 h. These calculated turning points help further explain the impact of climate factors on cotton yield and provide specific thresholds for optimizing climate conditions to increase yield.

Accumulated temperature, precipitation, and sunshine duration are indispensable climate factors in the whole growing season of cotton, which directly affect cotton growth. The cotton growing season is generally divided into five periods: emergence stage, seedling stage, bud stage, flowering and boll-setting stage, and boll-opening stage. Cotton requires favorable climatic conditions throughout its life cycle, from seed germination to flowering, boll setting, and boll opening [39]. In general, the higher accumulated temperature during sowing and emergence periods is beneficial to the germination and growth of cotton seedlings, but extreme weather affects the germination of cotton seeds and the growth of roots, making the growth of cotton seedlings slower [40]; the more precipitation, the more it is not conducive to the hardening and strengthening of seedling, and as a result, the cotton seedlings are prone to premature decay [41]; an increase in sunshine hours will advance the cotton emergence period [42]. The bud period requires higher temperature and longer sunshine hours. The increase in accumulated temperature and sunshine time tend to increase the budding speed of cotton and shorten the flowering period; excessive precipitation during the growing period increases the incidence of pests and adversely affects cotton yield and quality. The suitable temperature for cotton flowering and boll setting is 25–30 °C. If the temperature is too low, the pistil will be abnormal and the fertilization rate will be reduced; and if the temperature is too high, the pollen will develop abnormally, thus hindering the photosynthesis of the plants and reducing the single boll weight. During the boll opening period, cotton growth slows down. Excessive or low accumulated temperature is likely to cause problems such as premature decay, stay-green, and rotten cotton boll. At the same time, if there is too much precipitation and insufficient sunshine hours during this period, it is easy to cause diseases, resulting in falling of cotton boll and rotten cotton boll, which will have an adverse impact on cotton yield per unit area.

This section analyzes the output elasticity of factor inputs on cotton yield per unit area is as follows. The output elasticity of chemical fertilizer input, agricultural machinery input, and labor input at the mean of samples is −0.127, 0.298, and 0.221, respectively. The quadratic coefficients of agricultural machinery input and labor input were both positive, indicating that the impact of the two on cotton yield per unit area was positive U-shaped. The quadratic coefficient of fertilizer input was negative, but it did not pass the 10% significance test. The output elasticity of chemical fertilizer input is negative, indicating that the average chemical fertilizer input of cotton planting in China has been overused for many years, and the increase in chemical fertilizer input will inhibit the cotton yield per unit area in China. A large number of studies have pointed out that the application of chemical fertilizers in cotton fields has the effects of improving soil physical and chemical properties, increasing the quantity of soil microorganisms, enhancing soil enzyme activities, increasing soil fertility, and increasing soil effective nutrients [43], but inappropriate application of fertilizer will not only adversely affect the growth of cotton, but also change the soil environment, thereby reducing soil enzyme activities and destroying the ecological environment [44]. Studies have shown that the marginal benefits of China’s fertilizer input are declining [45,46], and most of the fertilizer inputs have not played a role [47,48]. The output elasticity of agricultural machinery input is 0.298, indicating that the increase in agricultural machinery input will promote the increase in cotton yield per unit area, but there are some problems in the input of agricultural machinery such as structural imbalance [49,50] and low efficiency [51,52]. The output elasticity of labor input is 0.221, which explains that the increase in labor input will promote the increase in cotton yield per unit area, but there is still a problem of relatively surplus labor input in cotton production, indicating that there are problems in the allocation of labor input factors in China’s cotton production. The scale elasticity is 0.478, which indicates that currently the cotton yield per unit area is in the stage of diminishing returns to scale. That is, when the input factors such as fertilizer, agricultural machinery, and labor increase by the same proportion, the increased proportion of cotton yield per unit area is far less than the increased proportion of each factor, which also indicates the factor productivity is reduced. The output elasticity of technological progress is 0.065 and passed the 1% significance test, which shows that the average annual contribution rate of technological progress is 6.5%. Its quadratic coefficient is negative, indicating that the future contribution of technological advances to productivity growth may decline.

b. Estimation of the marginal influence range and contribution rate of each factor

In order to explore the influence range of various factors on cotton yield per unit area, this paper referred to the practice of He Yaqin et al. (2015) [53]. Marginal effects were calculated using the annual maximum and minimum values of each input factor to determine their impact range. (The annual value of each input factor is the average of accumulated temperature, precipitation, sunshine hours, fertilizer input, agricultural machinery input, and labor input in the eight provinces of the year.) The marginal effect means the percentage of changes in cotton yield per unit area caused by 1% change in a single variable when other input factors remain unchanged. Taking the accumulated temperature as an example, the calculation formula of the marginal effect is as follows:

$${\displaystyle \frac{\partial Y/Y}{\partial AT}}={\displaystyle \frac{\partial Y/Y}{\partial AT/AT}}\times {\displaystyle \frac{1}{AT}}$$

(8)

Referring to Formula (8), the maximum and minimum values of accumulated temperature, precipitation, sunshine hours, fertilizer input, agricultural machinery input, and labor input are substituted into the formula, and the numerical interval obtained is used to explain the marginal effect range of each input factor on cotton yield per unit area. During cotton growing season, the accumulated temperature range is 2067.880~3756.980 °C, the range of precipitation is 22.170~1531.380 mm, the range of sunshine hours is 831.280~2054.080 h, the range of chemical fertilizer input is 132.570~496.420 (kg/hm²), the range of agricultural machinery input is 1.490~12.700 (kw·h/hm²), and the labor input varies from 2.030 to 6.730 (persons/hm²). By putting these values into the formula, it can be calculated that for every 1% increase in the accumulated temperature during cotton growing season, the yield per unit of cotton changes between −0.0001% and 0.0009%, that is, the accumulated temperature increase results in a decrease in cotton yield per unit area in regions with higher accumulated temperature and a higher yield per unit area in regions with lower accumulated temperature; for every 1% increase in the precipitation during cotton growing season, the yield per unit of cotton changes between −0.0001% and 0.0027%, that is, the increase in the precipitation results in a decrease in cotton yield per unit area in regions with more precipitation and a higher cotton yield per unit area in regions with insufficient precipitation; for every 1% increase in sunshine hours during cotton growing season, the yield per unit of cotton changes between −0.0005% and 0.0007%, that is, the increase in sunshine duration results in a higher cotton yield per unit area in regions with less sunshine hours and a decrease in cotton yield per unit area in regions with longer sunshine hours; for every 1% increase in fertilizer input, the yield per unit of cotton changes between −0.0008% and 0.0033%, that is, the increase in chemical fertilizer input was not conducive to the increase in cotton yield per unit area in regions with a large amount of chemical fertilizer application but conducive to the increase in cotton yield per unit area in regions with less fertilizer application; for every 1% increase in agricultural machinery input, the yield per unit area of cotton changes between −0.0008% and 0.0428%, that is, the increase in agricultural machinery input hinders the increase in cotton yield per unit area in regions with a large amount of agricultural machinery input, but promotes the cotton yield per unit area in regions with small agricultural machinery input; for every 1% increase in labor input, the yield per unit area of cotton changes between −0.0329% and 0.0719%, that is, the increase in agricultural machinery input hinders the increase in cotton yield per unit area in regions with rich labor but promotes the cotton yield per unit area in regions with insufficient labor.

In order to further analyze the comprehensive impacts of input factors on cotton yield per unit area in China, this paper quantifies the comprehensive contribution rate of input factors by calculating the contribution of accumulated temperature, precipitation, sunshine duration, fertilizer input, agricultural machinery input, and labor input to the growth rate of cotton yield per unit area. Taking accumulated temperature as an example, the contribution rate of accumulated temperature to the growth rate of cotton yield is the product of its output elasticity and its own percentage change from 1990 to 2022. Similarly, this paper calculates the percentage change in each factor and its contribution rate to cotton yield per unit area (see

Table 7. The marginal impact of various factors on cotton productivity and its percentage contribution rate to the cotton productivity growth in 1990–2022.

	Output Elasticity (1)	Marginal Effect (%) (2)	Percentage of Change (%) (3)	Contribution Rate (%) (4) = (1) × (3)
Accumulated temperature	1.0155	−0.0001~0.0009	4.8945	4.9704
Precipitation	−0.1103	−0.0001~0.0027	16.0355	−1.7689
Sunshine hours	−0.2882	−0.0005~0.0007	−16.4800	4.7490
Fertilizer input	−0.1272	−0.0008~0.0033	111.9093	−14.2298
Agricultural Machinery input	0.2979	−0.0008~0.0428	226.3900	67.4489
Labor input	0.2206	−0.0329~0.0719	−40.8269	−9.0058

Note: Output elasticity is the regression coefficient of climate variables; data of marginal effect is the calculation result (calculation formula refers to Formula (8)); taking the accumulated temperature as an example, the formula for calculating the percentage of factors change is 100 × (AT2022 − AT1990)/AT1990, where AT1990 and AT2022 represent the average accumulated temperature of cotton growing season in the eight major cotton producing provinces in 1990 and 2022, respectively.

for details). The results show that the comprehensive contribution rate of climate factors is 7.951%, indicating that the climate change during the period of 1990–2022 led to an increase of 7.951% in cotton yield per unit area; the comprehensive contribution rate of chemical fertilizer input, agricultural machinery input, and labor input was 44.213%, which shows that such factors as fertilizer input led to an increase of 44.213% in cotton yield per unit area during the period of 1990–2022.

Table 8. Interpretation of elasticity results.

Factor	Elasticity Result	Interpretation	Inverted U-Shape Interpretation
Accumulated Temperature (AT)	+ve (1.0155)	Positive impact on cotton yield; higher temperature generally promotes growth.	Negative U-shape: After a certain temperature threshold, the impact becomes negative.
Precipitation (RF)	−ve (−0.1103)	Negative impact on cotton yield; excessive rainfall hampers growth.	Negative U-shape: More precipitation has a diminishing or negative effect on yield.
Sunshine Duration (IT)	−ve (−0.2882)	Negative impact on cotton yield; excess sunlight may damage plants.	Negative U-shape: Increasing sunshine hours beyond a threshold reduces yield.
Agricultural Machinery Input (AM)	+ve (0.2979)	Positive impact on cotton yield; better machinery improves efficiency.	Positive U-shape: Optimal use of machinery leads to higher yield.
Labor Input (LA)	+ve (0.2206)	Positive impact on cotton yield; more labor increases production efficiency.	Positive U-shape: Optimal labor input enhances yield, but excessive labor beyond a certain point may reduce efficiency.
Fertilizer Input (FT)	−ve (−0.1272)	Negative impact on cotton yield; excessive fertilizer can harm plant health.	Negative U-shape: Over-fertilization reduces yield after a certain point.

explains the elasticity results for key climatic and input factors affecting cotton yield. First, Positive Elasticity (+ve): A positive elasticity indicates that an increase in the factor leads to an increase in cotton yield. For example, accumulated temperature, agricultural machinery, and labor input all have positive elasticities, meaning that higher levels of these factors typically result in higher cotton yields. Second, Negative Elasticity (−ve): A negative elasticity means that an increase in the factor results in a decrease in cotton yield. Factors such as precipitation, sunshine duration, and fertilizer input show negative elasticities, suggesting that excessive amounts of these factors are detrimental to cotton yield. Third, Inverted U-Shape Relationship: Some factors exhibit an inverted U-shape relationship, meaning their impact on cotton yield is positive up to a certain threshold, beyond which the effect becomes negative. For example, accumulated temperature and sunshine duration exhibit an inverted U-shaped relationship, where their impact increases up to an optimal level (turning point), beyond which further increases negatively affect yield. On the other hand, precipitation and fertilizer input show an inverted U-shaped relationship, where moderate amounts of these factors initially have a positive effect, but beyond a certain level, they begin to reduce yield.

5. Discussion

5.1. Similarities and Differences with Existing Studies

This study empirically analyzed the effects of climate factors and factor inputs on cotton yield growth in China’s major production regions during 1990–2022. The results highlight that accumulated temperature has a significant positive impact on yield, whereas precipitation and sunshine duration exert negative effects, consistent with prior studies indicating the sensitivity of cotton to climatic variability [41,54]. Moreover, the “inverted U-shaped” relationship between climate factors and yield observed in this study echoes earlier findings in crop science that excessive temperature or rainfall may reduce yield potential [54].

In contrast to the existing literature, however, this study integrates climate variables and factor inputs within a transcendental logarithmic production function, thus simultaneously capturing the nonlinear effects of both natural and socio-economic drivers. The decomposition results reveal that factor inputs, especially agricultural machinery, contribute more substantially to yield growth than climate factors, which enriches the current theoretical framework emphasizing technological and input-driven growth paths in cotton production [39].

5.2. Mechanisms and Heterogeneity

From a mechanism perspective, the findings suggest that agricultural machinery and labor input enhance yield, while fertilizer input shows diminishing and even negative returns, consistent with concerns over over-fertilization and ecological risks in Chinese agriculture [45,47]. The positive contribution of mechanization implies that improvements in machinery structure and efficiency are critical to sustaining productivity growth [49]. Meanwhile, climate factors such as accumulated temperature and sunshine duration demonstrate threshold effects: moderate levels are beneficial, while excessive levels may harm yield, reflecting the fragile balance between crop physiology and environmental stress [40].

Heterogeneity across regions also matters. For instance, Xinjiang’s longer sunshine duration and more advanced irrigation infrastructure offset adverse climatic stress more effectively than do the conditions in central and eastern provinces, aligning with previous findings on the role of local agro-ecological conditions in shaping climate impacts [39,41]. Moreover, differences in cultivated land quality may moderate the effect of inputs: higher-quality land mitigates the negative impact of aging labor and excessive fertilizer, underscoring the importance of promoting high-standard farmland construction [44].

5.3. Limitations and Future Recommendations

Despite these contributions, several limitations remain.

First, the analysis is based on provincial-level panel data, which may mask intra-regional heterogeneity in farm practices and micro-level decision-making. Future research should incorporate household- or plot-level data to better capture farmers’ adaptive strategies. Second, this paper focuses mainly on climate and factor inputs, while other institutional and policy factors (e.g., subsidies, cooperative participation, extension services) were not explicitly considered. Future studies that include including these variables could provide a more comprehensive explanation of yield dynamics [47,48]. Especially important is that, due to challenges in data accessibility and measurement, issues such as soil health, pesticide input, and irrigation were not explicitly considered. Additionally, the use of rural population per unit area (LA) as a proxy for labor input in cotton production has limitations, as it does not distinguish between individuals directly involved in cotton farming and those engaged in other activities. Third, the static decomposition framework employed in this study may not fully capture future uncertainties under climate change. Further research could adopt crop models or integrated assessment approaches to simulate yield responses under alternative climate and management scenarios [22,55]. Furthermore, the use of annual averages for climate variables and input factors may mask important seasonal variations that are crucial to cotton growth. For example, fluctuations in water availability during the flowering and boll stages can significantly impact cotton yield, yet annual averages may not capture such seasonality. This temporal aggregation issue may reduce the accuracy of yield predictions and limit the interpretability of the results.

In summary, this paper contributes by combining climate and input perspectives within a unified analytical framework, revealing both the opportunities and challenges of sustaining cotton yield growth in China. Future studies should place greater emphasis on policy design, technological innovation, and adaptive management strategies to ensure the long-term resilience of cotton production under climate change. Additionally, incorporating factors like soil health, pesticide use, and irrigation, along with more detailed data collection, will be crucial for developing more accurate models and improving agricultural practices. Furthermore, future research should aim to disaggregate data at a more granular level, such as using household-level surveys or local agricultural cooperatives’ information, as well as monthly or seasonal data, to more accurately estimate labor input, capture seasonal variations, and enhance the robustness of the findings.

6. Conclusions and Recommendations

6.1. Conclusions

Based on the panel data of eight major cotton-producing provinces in China from 1990 to 2022 and the transcendental logarithmic production function model, this paper evaluates the elasticity of climate factors and input factors and calculates the contribution rates of each factor to cotton yield growth. The key findings are as follows: (1) accumulated temperature has a positive impact on cotton yield, while precipitation and sunshine duration show negative effects; (2) climate factors contribute significantly to yield growth, with a contribution rate of approximately 7.95%; (3) among input factors, agricultural machinery and labor inputs have a positive impact on yield, while fertilizer input shows a negative effect; (4) factor inputs collectively contribute around 44.21% to yield growth; (5) technological progress also plays a significant role in enhancing cotton productivity. These findings highlight the importance of managing climate factors and optimizing input usage, while also recognizing the role of technological innovation in sustaining cotton production.

6.2. Recommendations

Based on the above conclusions, this paper proposes the following recommendations: (1) Strengthen climate risk management: Strengthen climate forecasting, early warning, and prevention systems to improve the accuracy of meteorological data and assist farmers in adapting to climate change. Ensure timely communication of weather forecasts to farmers for better decision-making and mitigation strategies. (2) Optimize factor input efficiency: Improve the input structure by advancing high-standard farmland construction, promoting efficient use of fertilizers and pesticides, and enhancing agricultural machinery integration into production. This will optimize labor and material inputs for better cotton yield. (3) Targeted agricultural research and localized technology promotion: Adapt agricultural practices to local conditions. For instance, in regions like Xinjiang, where high temperatures prevail, select early-maturing cotton varieties. In areas with limited sunlight, such as Hunan and Henan, implement rational close planting to maximize light usage, thus boosting productivity.