4.1. Model and Method
Based on the above description of the relationships between climate change, biased technological progress, and agricultural TFP, this paper attempts to construct an extended Cobb–Douglass production function model, which lays the foundation for an extended discussion of the impacts of climate change and biased technological progress on agricultural TFP. The agricultural production process is assumed to satisfy the Cobb–Douglass production function form and the climate factor is introduced into the function as an exogenous variable:
where
is the agricultural output;
is the agricultural TFP, which is a function of climate change
and biased technological progress
; L, K and T represent the inputs of labor, capital, and land in agricultural production, respectively; and
and
are the elasticity coefficients of the outputs of labor, capital, and land, respectively, and satisfy
.
First, the impact of climate change on agricultural TFP can be discussed and expressed through Equation (2).
The impact of climate change on agricultural TFP depends on two factors. The first component is the direct effect of climate change on agricultural TFP, and the second component is the indirect effect of climate change on agricultural TFP through biased technological progress. The direct effect of climate change on agricultural TFP may have different impacts depending on geographical differences; for example, increased precipitation in southern China will increase the risk of agricultural disasters, but increased precipitation in northwestern China may improve agricultural output. However, in terms of overall impacts, the literature finds that the direct effect of climate change on agricultural TFP is negative; that is, . The indirect effect of climate change on agricultural TFP is . Among them, theoretically biased technological progress can effectively increase agricultural TFP to satisfy . Moreover, biased technological progress can weaken the adverse effects of climate change on agricultural TFP . Therefore, the indirect effect of climate change on agricultural TFP is positive.
Second, a benchmark regression model is constructed based on the derivation of the theoretical model. Promoting agricultural TFP is a timely and inevitable choice for promoting high-quality agricultural development, and agricultural production is affected by many factors, such as climate change and technological progress. Based on the research of Huffman and Evenson (2006) [
63], the following benchmark regression model is constructed according to Equation (3):
In Equation (3), denotes the agricultural of the province (urban area) in year ; is the climatic variable of the province (urban area) in year , including the average annual temperature, sunshine hours, and annual precipitation; is the biased technological progress of province (urban area) in year ; denotes the set of control variables, including rural electric power facilities, the agricultural structure, facility agriculture, per capita net income of rural residents, and rural road density; is the parameter to be estimated; and denote the fixed effects of time and each province (urban area), respectively; and is the random error term.
On this basis, this paper further examines whether biased technological progress can weaken the impact of climate change on agricultural
, i.e., whether climate change affects agricultural
by moderating biased technological progress. Based on Equation (4), the benchmark regression model, the moderating effect model is constructed. The details are as follows:
where
is the moderating variable biased technological progress,
denotes the key coefficient used to test the moderating effect, and the remaining variables have the same meaning as in the baseline regression model.
4.2. Variable Selection
- (1)
Dependent variable
Agricultural TFP (Agr_TFP) refers to the contribution rate of other factor inputs to the growth of agricultural output excluding traditional input factors such as land, labor, and capital. The core of this paper is to examine the impact of climate change on agricultural TFP; accurately measuring the agricultural TFP of each province is the basis of this paper. The Malquist-Luenberger (ML) and Global Malquist-Luenberger (GML) are widely used in panel data efficiency research. The ML index is based on the directional distance function, and the results obtained are often not cyclic in the rate of change of the latter period relative to the former period and often suffer from the problem of unsolvable linear programming. Traditionally, agricultural TFP is measured by the ML index, but there is no solution for linear programming and the index is not transferable. The GML index is based on the construction of a global production technology set, which can effectively avoid the shortcomings of linear programming and the “technological regression” phenomenon. Because the reference of each period is the same global frontier, the GML index is transferable. Therefore, the study chooses the GML index as the measurement method of agricultural TFP. In addition, this paper adopts the non-radial, non-angular, slacks-based (slacks-based measure, SBM) efficiency evaluation model proposed by Tone (2001) [
64], which can incorporate slack variables into efficiency evaluation. Based on this, the GML index is constructed according to the non-radial, non-angular SBM directional distance function, which is called the SGM productivity index, and decomposed into technical efficiency change (SEC) and technical change (STC) under the condition of constant returns to scale.
In this paper, we use MaxDEA software 5.2 to measure the SGM index under the condition of constant returns to scale and transform it into a cumulative growth index with 2000 as the base period as the explanatory variable of the empirical analysis model. and uses data for a panel of 31 provincial units from 2000–2021. Agricultural output variables are expressed as gross agricultural product at constant prices in 2000. The agricultural input variables include six factors: land, labor, agricultural machinery, fertilizer use, irrigated area, and agricultural water use. Among them, land input is calculated by the sown area of crops; labor input is calculated by the number of employees in agriculture, forestry, animal husbandry and fishery; agricultural machinery input is calculated by the total power of agricultural machinery; fertilizer use is calculated by the actual amount of discounted pure quantity; irrigated area is calculated by the actual effective irrigated area each year; and agricultural water use input is calculated by the amount of water used by agriculture in each province.
- (2)
Independent variables
Climate change is an important concept in climatology and a hot topic of international discussion in recent years; furthermore, its terminology in the field of climate and agricultural research is becoming more complex. Climate change is defined as a statistically significant change in the mean state of the climate or a change in weather that lasts for a longer period. The United Nations Framework Convention on Climate Change (UNFCCC) defines climate change as a change in the state of the climate over a period caused by human activities that directly or indirectly alter the composition of the atmosphere. The IPCC considers climate change as a change in climatic conditions over time, whether caused by the natural environment or human activities. Combined with existing academic research, climate change is a change in the long-term average trend of climate elements (e.g., precipitation, average temperature, sunshine hours, etc.); the greater the magnitude of climate change is, the greater the risk of unstable climate conditions and the greater the sensitivity of the environment to climate change. Drawing on the relevant research of Yin et al. (2016) [
65], this paper selects the average annual temperature (AAT), annual precipitation (AP), and sunshine duration (SD) as the specific characteristics of climate change; the data of each province (urban area) are the average of the monitoring data of all the meteorological stations in that jurisdiction. The average annual temperature is the arithmetic mean of the average daily temperature at all meteorological stations in the province (urban area); sunshine duration refers to the length of time that the sun’s rays irradiate the ground in a year; and annual precipitation is the average of the total annual precipitation at all meteorological stations in the province (urban area).
- (3)
Moderator variable
Addressing the constraints of factors such as land and labor on agricultural production is a basic feature of agricultural modernization and agricultural technological progress. Therefore, this paper uses labor productivity and land productivity indicators to construct a biased technological progress index to further elaborate on the impact of regional factor endowments on TFP in agriculture.
denotes the agricultural output,
is the labor input, and
is the land (sown area) input; the biased technological progress index (
) can be expressed as follows:
- (4)
Control variables
In addition to climate change and agricultural technology, spatial changes in agricultural production areas due to markets, natural environments, and policies, as well as factors such as the substitution of agricultural products, infrastructure, and service systems, are likely to affect TFP in agriculture. Among them, public infrastructure plays an important role in mitigating the adverse effects of climate change and promoting new agricultural technologies. To avoid missing data, in this paper, we add socio-economic variables such as rural electric power facilities, agricultural structure, facility agriculture, per capita net income of rural residents, and rural road density as control variables in the empirical model.
Rural electricity facilities (REF). Rural electricity consumption is taken as a proxy variable for rural electric power facilities. With the advancement of agricultural production scales and digitalization, electric power facilities have become important guarantees for rural development and sources of power for improving agricultural TFP.
Agricultural structure (AS). The structure of agriculture is expressed as the percentage of area sown to grain over the total area sown to crops. Agricultural restructuring indicates the development of cropping structures in the direction of factor endowment advantages.
Facility agriculture (FA). This paper uses agricultural production equipment inputs to indicate the situation of facility agriculture. The development of facility agriculture is an important symbol of agricultural modernization. Greater levels of agricultural production equipment inputs support the progress and improve the content of agricultural technology.
Per capita net income of rural residents (IRR). The per capita net income of rural residents is the total income of rural residents for the year after deducting productive and unproductive expenditures and agricultural taxes; it reflects the level of economic development in each province (urban area). To a certain extent, the per capita net income of rural residents affects the choice of agricultural production methods.
Rural road density (RRD). Rural road density can reflect the infrastructure stock of rural roads and the degree of rural road access. Considering the differences in the geographical area of each province (urban area), this paper uses the ratio of the mileage of rural roads in each province (urban area) to the land area of the corresponding region to express the density of rural roads.
4.3. Data
This paper is based on China, so the data used are all variables related to the Chinese region. The data for the measurement of agricultural TFP were taken from the China Rural Statistical Yearbook of past years. Meteorological data were obtained from the annual value dataset of China’s ground-based climate data in the China Meteorological Science Data Sharing Service Network, which covers the climate data of 752 basic and benchmark ground-based meteorological observation stations and automatic stations in China for the years 2000–2021. Notably, in this paper, the 752 baseline points are grouped according to the province (urban area) in which they are located, and the climatic variables in the region are expressed as the average value of the province (urban area). The data for the indicators selected for the control variables are taken from the China Statistical Yearbook and the China Rural Statistical Yearbook of the past years.
Table 1 shows the descriptive statistics of the relevant variables. With the agricultural TFP in 2000 as the base period, i.e., a minimum value of 1, the agricultural TFP in 2000–2021 shows an upward trend, and the maximum value is 2.8611, indicating a large gap in agricultural TFP in different periods and between different provinces (municipalities). The descriptive statistics of climate variables have obvious regional variability, and the specific representations of climate factors, annual average temperature, and sunshine hours have more significant time-series evolution characteristics. The average annual temperature and sunshine hours increase annually, and the annual precipitation exhibits spatial characteristics of increasing in the southern region and decreasing in the northern region. Biased technological progress also has more obvious regional characteristics; it gradually moves from an initially imbalanced structure to a relatively balanced one. Although studies have shown that climate change has a significant impact on agricultural TFP, it is unknown whether biased technological progress will mitigate the impact of climate change on agricultural TFP. For this reason, this paper tests whether biased technological progress mitigates the impact of climate change on agricultural TFP based on existing theories.
Before the baseline regression, the Pearson Correlation Coefficients between the explanatory variables, the explained variables, the moderating variables, and the control variables were analyzed, as shown in
Table 2. The correlation analysis shows that there is a significant negative correlation between climate change and agricultural TFP, indicating that climate change is detrimental to agricultural TFP, which is basically in line with the expectation and is to be further analyzed in the empirical test. In addition, in order to avoid the problem of multicollinearity between the variables, this paper carried out the analysis of variance inflation factor VIF, as can be seen in
Table 2, the VIF is significantly less than 10, indicating that there is no problem of multicollinearity.