Study on the Impact of the Rural Population Aging on Agricultural Total Factor Productivity in China

Abstract

The rural population aging poses a great challenge to China’s agricultural production, which is dominated by small farmers. Based on the panel data of 30 provinces or cities (except Tibet) in China from 2005 to 2020, the DEA-Malmquist index is employed to measure the agricultural total factor productivity (ATFP) in each province (city), and then the mediation effect model is used to reveal the mechanism by which the rural population aging affects the ATFP through farmland transfer, agricultural social services, and agricultural machinery. The results show that the rural population aging has made a significant contribution to the ATFP, and farmland transfer, agricultural socialized services and agricultural machinery have a intermediary effect on the increase of the ATFP. Further decomposition of ATFP reveals that the rural population aging can significantly contribute to the scale efficiency and technical progress rate through farmland transfer, agricultural socialization services and agricultural machinery, but does not have a significant effect on pure technical efficiency. In order to promote the high-quality and high-efficiency development of agriculture in the context of population aging, it is necessary to optimize the market environment for farmland transfer, improve the agricultural socialized service system, and continue to strengthen agricultural science and technology innovation.

1. Introduction

Agriculture is the basic and strategic industry of the national economy, which is crucial to the stability of national life and the healthy development of the economy. Therefore, raising yield is important goal for sustainable agricultural development. Traditional agriculture is a labor-intensive industry, and labor input is an important resource for agricultural production [1,2]. With the enhancement of comprehensive national power and the development of science and technology, agriculture is gradually transitioning from a labor-intensive industry to a capital-intensive and technology-intensive industry [3,4]. At this stage, the aging of China’s rural population is fast and deep, the loss of young and strong laborers is serious, and the effective agricultural labor force continues to decline [5,6,7,8]. As one of the important input factors in agricultural production, it is worthwhile to explore in depth whether the aging of the labor force will affect the high quality and efficient development of agriculture. Supported by national policies and vigorously promoted by local governments, the rapid development of farmland transfer, agricultural machinery and agricultural socialization services, provides an important support for the transformation and upgrading of agricultural modernization [9,10]. However, due to the constraints of multiple factors, there is still a big gap in the level of modernization and development of China’s agricultural industry compared with that of developed countries. At present, in the face of the pressure of tightening resource and environmental constraints, realizing the rational allocation of production factors to improve the ATFP is crucial for the high-quality and efficient development of agriculture. In particular, in the process of accelerated rural population aging, will the growth of total factor productivity in China’s agriculture be affected?

Scholars have carried out extensive research on the relationship between the rural population aging and agricultural production, but there are differences in research viewpoints. Some scholars argue that population aging brought about by the decline in the ability to work and learn will inevitably reduce the efficiency of agricultural production; that is, the “aging effect” will have a negative impact [11,12,13]. The aging of the agricultural labor force is the inevitable result of the transfer of labor to cities under the imbalance of urban and rural development, which is detrimental to agricultural production [14]. The area of cultivated land, factor inputs and marginal output of aging farmers are lower than those of young farmers, which constrains agricultural development and threatens the sustainability of smallholder production [15,16]. The rural population aging inhibits agricultural production by reducing labor supply and down-scaling farmland operations, but it promotes agricultural production through the substitution of capital factors for labor [17,18]. One study has concluded that age and productivity have an “inverted U-shape” relationship, with farm efficiency declining with age [19].

Another group of scholars maintain that the rural population aging does not adversely affect agricultural production and assert that the proportion of the rural elderly population has a notable positive impact on changes in agricultural technical efficiency [20,21]. As age increases, workers in agricultural production activities continue to accumulate planting experience, and their labor skills gradually improve, thereby enhancing agricultural production efficiency. [22]. In a sample of elderly farmers, the positive impact of farmland inflow on farmers’ green total factor productivity is more significant [23,24]. Although aging will lead to a scarcity of labor supply, it can enhance agricultural production efficiency through induced technological change [25]. Agricultural production technology eases the constraints of declining individual physical strength on agricultural development, agricultural machinery outsourcing services have a positive effect on food production in China, and in general, the change in age has not had an adverse effect on food production [26].

In summary, the divergence between the positive and negative results of the existing research findings on the impact of the rural population aging on ATFP may be due to differences in the time frame covered by the sample data and the selection of research objects. On the one hand, because the micro-data only represent the situation in a specific region, they cannot reflect the overall situation of the country. On the other hand, over time and with a higher level of agricultural modernization, the restriction of physical labor on agricultural production may gradually weaken. In view of the problems in the existing research, it is necessary to further explore the impact of the rural population aging on ATFP in the context of the gradual deepening of the rural population aging. Therefore, this study selects nationwide data and, where possible, the most recent data available for the empirical analysis. This study aims to (1) theoretically analyze the path of the impact of the rural population aging on ATFP; (2) use provincial panel data from 2005 to 2020 to empirically test the direct impact and mechanism of the rural population aging on ATFP; and (3) further explore the regional heterogeneity of the impact of the rural population aging on ATFP.

This study may contribute in the following three aspects. Firstly, from the perspective of factor input, this paper incorporates the three elements of land, labor and capital into a unified analytical framework and examines the impact path of the rural population aging affecting ATFP through farmland transfer, agricultural socialization services and agricultural machinery. Secondly, the direct and indirect effects of the rural population aging on ATFP are verified from an empirical perspective. Finally, given that modern agricultural production exhibits variable returns to scale, the ATFP index is decomposed to reveal the impact of the rural population aging on scale efficiency and technical efficiency.

The remainder of the paper is as follows. In Section 2, we analyze the theoretical mechanism of the rural population aging on ATFP. Section 3 introduces the variables used in the study and the method of empirical analysis. Section 4 shows the results of the empirical analysis. Section 5 discusses the main results of the article. Section 6 is the conclusion and policy recommendations.

2. Theoretical Analysis and Research Hypotheses

2.1. The Scale Operation Effect of Farmland Circulation

Agricultural land is the fundamental means of production, and the efficiency of agricultural land utilization is a visual representation of agricultural output [27]. Farmland transfer alleviates the problem of land resource waste caused by a high degree of land fragmentation and provides conditions for agricultural producers to adjust their scale of operation [28]. The decline in the physical capacity of the labor force brought about by the rural population aging has forced some aging farmers to transfer out of farmland [29]. Conversely, large agricultural growers or farmers with business capacity can expand their scale of operation by transferring into this part of the farmland, thereby facilitating the realization of economies of scale. With the increase in farmers’ age, some farmers may deepen their attachment to their land and feel a reduced willingness to transfer it, and even desire to enlarge their planting area through land acquisition [30,31]. Therefore, the positive impact of land inflow on ATFP is evident among elderly farmers [23]. Farmland transfer can promote the scale of agricultural production and operation to enhance the ATFP has also been confirmed by the development experience of advanced countries in the world [32,33]. Accordingly, Hypothesis H1 is proposed:

H1: 

The rural population aging positively affects ATFP through accelerated farmland transfer.

2.2. The Labor Division Effect of Agricultural Socialization Service

The agricultural socialization service system refers to a network system formed by economic organizations related to agriculture to meet the needs of agricultural production and development and provide various services for business entities directly engaged in agricultural production. As the core of the organic connection between small farmers and modern agricultural development, agricultural socialization services play an important role in high-quality and efficient agricultural production during the process of the rural population aging [34]. The prominent feature accompanying the aging of farm households is the declining trend of their labor capacity and learning ability [35,36], but the emergence of agricultural socialization services can mask the negative impact of declining capacity. In addition, the agricultural socialization service system can overcome the disadvantage of aging farmers’ low degree of adoption of new agricultural technologies [16], which will stimulate aging farmers to expand their demand for agricultural socialization services and drive the development of the agricultural socialization service system. From one perspective, the agricultural socialization service system can provide an organizational advantage and scale effect, while professional skilled personnel adjust the factor input structure and optimize the production mode according to the characteristics of crop production, thus improving the ATFP. From another perspective, the accumulation effect of aging farmers’ planting experience and skills is also particularly important in agricultural production [22]. The combination of this accumulation effect and the agricultural socialization service system can more effectively transform the agricultural production mode. This synergy ensures that agricultural production has the double advantage of experience and professionalism, leading to the agricultural factor allocation being more reasonable [37]. Therefore, the division of labor and professional collaboration of agricultural socialization services can optimize resource allocation, promote incremental output and ultimately enhance total factor productivity [38]. Accordingly, Hypothesis H2 is proposed:

H2: 

The rural population aging positively affects ATFP by promoting the development of agricultural socialization service systems.

2.3. Capital Substitution Effects of Agricultural Machinery

In the process of modern agricultural development, the wide application of agricultural machinery can effectively solve the current problem of the weakening of the rural labor force. First of all, from the perspective of induced innovation theory, changes in the relative price of factors will have an inducing effect on technological progress [39]. Against the background of the rapid rise in labor prices due to the shortage of labor supply, the level of research into and development of new agricultural technology and equipment is constantly improving, and the high-speed development of agricultural mechanization has realized the effective substitution of capital for labor [40]. Secondly, because agricultural production has a strong seasonality and cyclical patterns, it is essential to align activities with the diurnal cycle and geographical considerations. Given the time constraints of agricultural production, aging farmers are likely to choose to use machinery to compensate for their declining labor capacity, ensuring that agricultural activities are completed within the optimal time frame. Finally, considering external effects, farmers with a higher degree of knowledge of agricultural machinery technology and a stronger capacity for adaptation can positively influence the production behaviors of their peers. Consequently, farmers in the same area will show strong behavioral convergence when making planting decisions and choosing agricultural production technology due to the herd effect. This positive external effect offsets the drawbacks associated with aging farmers in the acquisition of information and learning the application of agricultural machinery [41]. In summary, agricultural machinery has the characteristics of high efficiency, precision and automation, providing sufficient technical conditions to promote the development of scale and intensification [42], which is conducive to promoting the ATFP growth [43]. Accordingly, Hypothesis H3 is proposed:

H3: 

The rural population aging positively affects ATFP by promoting agricultural mechanization.

Based on the above assumptions, this paper constructs a theoretical analysis framework diagram, as shown in Figure 1. That is, the aging of the rural population can affect the ATFP through farmland transfer, agricultural socialization services and agricultural machinery.

3. Materials and Methods

3.1. Data Sources

In 2004, the State Council promulgated the “Decision on Deepening the Reform of Strict Land Management” and clarified the provisions on how “the right to use collectively owned construction land for farmers can be transferred according to law”. Since then, the speed of rural land transfer has gradually accelerated. Due to the lack of data on rural land transfer in Tibet, this paper selects the panel data of 30 provinces or cities in China (except Tibet) from 2005 to 2020 for empirical analysis. Among the input–output indicators of ATFP, the data of the first industry practitioners are derived from the Statistical Yearbook of each province; other indicator data are derived from the National Bureau of Statistics. The data for rural population aging degree and per capita education years are calculated from the China Population and Employment Statistics Yearbook. The data of farmland transfer are derived from the China Rural Management Statistics Annual Report, China Rural Cooperative Economy Statistics Annual Report, China Rural Policy and Reform Statistics Annual Report. The output value of agriculture, forestry, animal husbandry and fishery service industry are derived from the China Statistical Yearbook and China Tertiary Industry Yearbook. The data for the total mechanical power per capita come from the National Bureau of Statistics and the statistical yearbooks of each province. The data for rural electricity consumption, the level of industrialization development, agricultural production structure, the degree of opening to the outside world and the intensity of financial support for agriculture are derived from the National Bureau of Statistics. Among them, the expenditure on agriculture, forestry and water affairs in 2005 and 2006 are obtained from the sum of agricultural expenditure, forestry expenditure and operating expenses of agriculture, forestry, water conservancy and meteorology, and the related data are derived from the China Statistical Yearbook.

3.2. Variable Selection

3.2.1. Explained Variable

The explained variable in this paper is the ATFP, which is measured by using the DEA-Malmquist model. As a non-parametric frontier efficiency analysis method, the DEA-Malmquist index method does not involve the econometric estimation of a parameter equation, which can effectively avoid the disadvantages of the parameter method. It has obvious advantages in simulating input–output analyses and is widely used by scholars [44,45]. Given that the input conditions of agricultural capital and labor are relatively stable, while their outputs are variable and align with the BCC model’s criteria for multiple inputs and outputs, the ATFP is measured based on the output-oriented approach. Referring to the related research [46], this paper adopts the total agricultural output value as the output indicator. The input indicators are categorized into three dimensions, labor, land and production materials, which are measured by the primary industry employees, the total sown area of crops, the total power of agricultural machinery, the effective irrigated area and the discounted amount of agricultural fertilizer application.

3.2.2. Explanatory Variable

The explanatory variable of this study is the degree of the rural population aging. According to the classification criteria established by the United Nations “Population Aging and Its Socioeconomic Consequences” in 1956, when the number of elderly people aged 65 and over in a country or region accounts for more than 7% of the total population, it means that the country or region is aging. Referring to the related research [47,48], the proportion of the rural population aged 65 and above in the total population is used as a measure.

3.2.3. Intermediary Variable

According to the related research [9,26,48], the intermediary variables in this paper are the degree of farmland transfer, agricultural socialization services and agricultural mechanization. The farmland transfer is measured by the ratio of the total area of family-contracted arable land transferred to the area of family-contracted operated arable land. The output value of the agriculture, forestry, animal husbandry and fishery services is chosen as the proxy variable for the degree of agricultural socialization services [49]. The total output value of agriculture, forestry, animal husbandry and fishery includes the output value of agriculture, forestry, animal husbandry and fishery services in the implementation of the new National Economic Industry Classification Standard in 2003, so the output value of agriculture, forestry, animal husbandry and fishery services is obtained from the gross output value of agriculture, forestry, animal husbandry and fishery less the value of agriculture, forestry, animal husbandry and fishery output from 2005 to 2010. The level of agricultural mechanization is measured by the total power of agricultural machinery per capita, which is expressed as the ratio of the total power of agricultural machinery to the number of employees in the primary industry. The data of primary industry employees in Liaoning Province in 2019 is missing, so the total number of employed persons in 2019 is calculated according to the ratio of primary industry in 2018.

3.2.4. Control Variable

In this paper, the following control variables are selected, which may impact the ATFP: (1) Rural electric power facilities, as indicated by the related study [50], rural electricity consumption is used to measure the rural electric power facilities. (2) Education level, the per capita number of years of schooling of rural residents is used as a proxy variable for the education level of rural residents, calculated as follows: per capita number of years of schooling = (primary school population × 6 + junior high school population × 9 + senior high school population × 12 + junior college and above population × 16)/6 years of age above population × 16/total population aged 6 and above [51]. (3) Intensity of financial support for agriculture, the intensity of fiscal support for agriculture is measured by the proportion of expenditure on agriculture, forestry and water affairs to the general budget expenditure of local finance [51]. (4) Industrialization development level, to quantify the extent of industrialization, this paper uses the proportion of the value added of the secondary industry to the regional gross domestic product as a surrogate measure/proxy variable. (5) Agricultural production structure, the ratio of total agricultural output value to total agricultural, forestry, animal husbandry and fishery output value is used to measure the differences in the structure of agricultural production in each region. (6) Degree of opening to the outside world, drawing on the related research [52], this paper selects the ratio of the total amount of imports and exports of the location of the business unit to the regional gross domestic product to measure the degree of opening to the outside world. Given that the unit’s import and export figures are denominated in U.S. dollars, it will be converted into RMB according to the prevailing exchange rate.

First, in order to eliminate the effect of inflation, this paper uses the consumer price index for the base period of 2005 to deflate the indicators in monetary terms. Secondly, because the ATFP measurements are the chain change indices with the previous year as the base period, to ensure the consistency of the meaning of the indicators, this paper converts the ATFP and the decomposition index into the cumulative value with 2005 as the base period. Thirdly, to address the issue of heteroskedasticity arising from the large absolute values of the relevant data, this paper will regress the variables expressed in absolute values (including the output value of agricultural productive services, rural electricity consumption and the number of years of education of rural residents) after taking the logarithm of the variables. Descriptive statistics for the variables are displayed in

Table 1. Descriptive statistics of variables.

Variable Type	Variable Name	Average Value	Standard Deviation	Minimum Value	Maximum Values	Sample Size
explained variable	Agricultural total factor productivity (atfp)	1.691	0.596	0.868	4.504	480
explanatory variables	Aging of the rural population (agi)	0.106	0.044	0.001	0.261	480
intermediary variable	Farmland transfer (land)	0.237	0.179	0.014	0.911	480
	Agricultural socialization services (ser)	92.950	93.137	2.774	552.758	480
	Agricultural machinery (sci)	4.001	2.208	0.606	15.294	480
control variable	Rural electricity consumption (ele)	246.116	364.137	2.990	1949.110	480
	Level of industrialization development (ind)	0.427	0.083	0.160	0.620	480
	Structure of agricultural production (str)	0.521	0.085	0.339	0.740	480
	Degree of openness to the outside world (open)	0.309	0.359	0.008	1.711	480
	Intensity of financial support to agriculture (fin)	0.106	0.034	0.021	0.204	480
	Years of schooling per rural inhabitant (edu)	7.574	0.685	5.149	9.797	480

.

3.3. Model Specifications

3.3.1. Benchmark Model

In order to analyze the impact of the rural population aging on the ATFP, this paper first constructs the following panel data regression model:

$$atf{p}_{it}=\alpha +\beta ag{i}_{it}+\gamma contro{l}_{it}+u_i+{\epsilon }_{it}$$

(1)

where $i$ and $t$ denote region and year, respectively; $atf{p}_{it}$ refers to total factor productivity in agriculture; $ag{i}_{it}$ refers to the degree of the rural population aging; $contro{l}_{it}$ refers to the above control variables affecting total factor productivity in agriculture; $u_{it}$ refers to unobserved individual fixed effects; and ${\epsilon }_{it}$ refers to the random error term.

3.3.2. Intermediary Effect Model Specification

On the basis of the benchmark model, this paper takes farmland transfer, agricultural socialization services and agricultural machinery as intermediary variables to test the mechanism of the impact of the rural population aging on the ATFP. The mediation effect model is constructed as follows:

$$atf{p}_{it}={\phi }_1+cag{i}_{it}+{\delta }_{1}contro{l}_{it}+e_1$$

(2)

$$M_{it}={\phi }_1+bag{i}_{it}+{\delta }_{1}contro{l}_{it}+e_2$$

(3)

$$atf{p}_{it}={\phi }_2+c^{\prime }ag{i}_{it}+aM+{\delta }_{1}contro{l}_{it}+e_3$$

(4)

where $M_{it}$ denotes the intermediary variable, which in this paper includes farmland transfer ($land$), agricultural socialization services ($\ln ser$) and agricultural machinery ($sci$), and $e$ is a random perturbation term.

4. Analysis of Empirical Results

4.1. Estimates and Hypothesis Testing

Before the regression analysis, the applicability of fixed and random effects was first determined by the Hausman test. The test results rejected the random effects model, so this study uses fixed effects for regression analysis. The estimation results are shown in

Table 2. Estimated results of the impact of the rural population aging on the ATFP.

Variable	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	atfp	land	atfp	lnser	atfp	sci	atfp
agi	3.591 ***	0.940 ***	3.031 ***	2.176 ***	2.868 ***	10.097 ***	2.237 ***
	(0.501)	(0.111)	(0.536)	(0.484)	(0.486)	(1.362)	(0.496)
lnele	0.281 ***	0.021 **	0.269 ***	0.228 ***	0.206 ***	0.564 ***	0.206 ***
	(0.045)	(0.010)	(0.045)	(0.043)	(0.044)	(0.122)	(0.043)
lnedu	3.220 ***	0.953 ***	2.652 ***	4.544 ***	1.711 ***	3.752 ***	2.717 ***
	(0.423)	(0.094)	(0.466)	(0.408)	(0.454)	(1.149)	(0.399)
fin	2.107 **	0.461 **	1.833 *	4.151 ***	0.728	10.084 ***	0.755
	(0.990)	(0.220)	(0.987)	(0.955)	(0.958)	(2.688)	(0.937)
ind	−3.341 ***	−0.770 ***	−2.882 ***	−2.105 ***	−2.641 ***	−8.546 ***	−2.195 ***
	(0.431)	(0.096)	(0.457)	(0.416)	(0.420)	(1.169)	(0.425)
str	2.832 ***	0.039	2.809 ***	−1.708 ***	3.399 ***	0.184	2.807 ***
	(0.563)	(0.125)	(0.559)	(0.544)	(0.540)	(1.530)	(0.525)
open	0.283 **	−0.148 ***	0.371 ***	0.808 ***	0.014	1.340 ***	0.103
	(0.135)	(0.030)	(0.137)	(0.130)	(0.133)	(0.365)	(0.127)
land			0.596 ***
			(0.213)
lnser					0.332 ***
					(0.047)
sci							0.134 ***
							(0.016)
cons	−6.872 ***	−1.583 ***	−5.929 ***	−5.421 ***	−5.071 ***	−5.221 **	−6.172 ***
	(0.794)	(0.176)	(0.856)	(0.766)	(0.794)	(2.155)	(0.745)
N	480	480	480	480	480	480	480
R2	0.710	0.751	0.715	0.662	0.739	0.595	0.748

Note: Standard errors are denoted in parentheses, with ** and *** indicating statistical significance at the 5% and 1% levels, respectively (with the same convention applying below).

, where the labels (1), (2) and (3), etc., represent the results under different regression equations.

As evidenced by the data presented in the table, the regression coefficient of the rural population aging on the ATFP in model (1) is significantly positive at the 1% statistical level. This indicates that the total utility of the rural population aging on the ATFP is positive, implying that the rural population aging can significantly enhance the growth of the ATFP. This is mainly attributable to the decrease in the availability of agricultural labor as the age of rural population increases. To enhance labor productivity, agricultural mechanization is advancing at a faster pace. The emergence of a large number of new types of agricultural practitioners makes up for the shortcomings of the scarcity of labor, which contributes to the effect of the accumulation of human capital in agriculture [53]. Consequently, rather than adversely affecting the overall factor productivity of agriculture, the aging rural population can actually contribute positively to it. The level of industrialization development has a negative effect on the total factor productivity of agriculture. In the control variables, this is probably because the higher the degree of industrialization, the more labor and capital will be inclined to industry. The resulting insufficient investment in agriculture makes the agricultural production conditions weaker, which has a negative effect on the growth of agricultural total factor productivity.

To further verify whether there is a intermediary effect between the two variables, this study analyses the role path of the impact of the rural population aging on the ATFP from the perspective of agricultural factor inputs. The analysis considers three key factors: land, labor and capital. Firstly, farmland transfer is tested as a intermediary variable. Model (2) shows that the rural population aging has a significant positive effect on the ATFP, and there is also a significant positive effect of farmland transfer on the ATFP in model (3). This indicates that the rural population aging will exert a positive effect on the ATFP through farmland transfer, with a intermediary effect of 15.60%, which accepts the null hypothesis and verifies H1 proposed in this paper. Then, we introduce the agricultural socialized service as a intermediary variable into the model for testing. From model (4) and model (5), it can be seen that the rural population aging exerts a notable positive impact on agricultural socialization services, and agricultural socialization services have a promotional effect on the ATFP. This suggests that the rural population aging can promote the growth of the ATFP through agricultural socialization services, with an intermediary effect of 20.12%; the intermediary effect on the ATFP is greater than that of farmland transfer, which accepts the null hypothesis and verifies H2 proposed in this paper. Finally, agricultural machinery is introduced into the model to test the mediation effect. From the results of model (6) and model (7), it can be seen that the rural population aging has a driving effect on the development of agricultural mechanization, and agricultural mechanization also has a significant positive effect on the ATFP. This suggests that the rural population aging can have a positive effect on the enhancement of the ATFP through the promotion of agricultural mechanization, with an intermediary effect of 37.68%, which accepts the null hypothesis and verifies H3 proposed in this paper. It is evident that the rural population aging has a greater intermediary effect on total factor productivity through agricultural machinery. Therefore, increasing the research and development, as well as the adoption of region-specific agricultural machinery, is pivotal for the sustainable enhancement of ATFP growth.

4.2. Decomposition Index Regression Analysis of the ATFP

In order to further analyze the specific enhancement paths of farmland transfer, agricultural socialization services and agricultural machinery on the ATFP, this study decomposes the total factor productivity change into scale efficiency change, pure technical efficiency change and technical progress change, and discusses the impact of the rural population aging on the ATFP. Firstly, farmland transfer is used as a intermediary variable to study its impact on the total factor productivity decomposition index, and the regression results are shown in

Table 3. Estimated results of agricultural land turnover on decomposition indices.

Variable	(2)	(9)	(10)	(11)	(12)	(13)	(14)
	land	se	se	pe	pe	tech	tech
agi	0.940 ***	0.390 ***	0.089	−0.083	0.063	3.241 ***	2.701 ***
	(0.111)	(0.145)	(0.152)	(0.158)	(0.170)	(0.342)	(0.363)
land			0.320 ***		−0.155 **		0.573 ***
			(0.060)		(0.067)		(0.144)
control variable	controlled	controlled	controlled	controlled	controlled	controlled	controlled
cons	−1.583 ***	1.592 ***	2.098 ***	−0.280	−0.526 *	−5.677 ***	−4.769 ***
	(0.176)	(0.230)	(0.243)	(0.251)	(0.271)	(0.542)	(0.579)
N	480	480	480	480	480	480	480
R2	0.751	0.322	0.362	0.091	0.101	0.755	0.763

*, ** and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.

.

The results show that the coefficient of the effect of the rural population aging on scale efficiency is significantly positive in model (9), so the intermediary effect mechanism is further tested. Model (2) and model (10) show that the rural population aging has a significant positive effect on farmland transfer, and farmland transfer has a significant positive effect on scale efficiency. However, the coefficient of the effect of the rural population aging on scale efficiency is not significant, so there is a complete mediation effect. In other words, the effect of the rural population aging on the enhancement of scale efficiency is fully realized through the pathway of farmland transfer. In model (11), the rural population aging has no significant effect on pure technical efficiency. The possible reason is that although aging farmers have some experience in agricultural cultivation, but due to their decline in physical strength, the process of agricultural production is time-consuming. Consequently, the cumulative effect of farmers’ cultivation is difficult to gauge, and the enhancement of pure technical efficiency is not obvious. Model (13) shows that the rural population aging has a facilitating effect on technical progress. Model (2) and model (14) show that the rural population aging has a positive effect on farmland transfer, and the farmland transfer also has a facilitating effect on technical progress; that is, the rural population aging can enhance the rate of technical progress through farmland transfer. The main reason is that as the age of farmers increases, the lack of labor capacity leads to farmers’ tendency to transfer land to large-scale farmers. The large-scale operation of land is more likely to increase the degree of farmers’ technology adoption and the time that agricultural machinery is used, thus accelerating the progress of agricultural technology.

Then, the agricultural socialized service is used as an intermediary variable to analyze the total factor productivity decomposition index, and the regression results are shown in

Table 4. Estimated results of agricultural socialization on decomposition indices.

Variable	(4)	(9)	(15)	(11)	(16)	(13)	(17)
	lnser	se	se	pe	pe	tech	tech
agi	2.176 ***	0.390 ***	0.305 **	−0.083	−0.107	3.241 ***	2.754 ***
	(0.484)	(0.145)	(0.148)	(0.158)	(0.162)	(0.342)	(0.332)
lnser			0.039 ***		0.011		0.224 ***
			(0.014)		(0.016)		(0.032)
control variable	controlled	controlled	controlled	controlled	controlled	controlled	controlled
cons	−5.421 ***	1.592 ***	1.803 ***	−0.280	−0.220	−5.677 ***	−4.463 ***
	(0.766)	(0.230)	(0.241)	(0.251)	(0.265)	(0.542)	(0.543)
N	480	480	480	480	480	480	480
R2	0.662	0.322	0.333	0.091	0.092	0.755	0.779

** and *** indicate statistical significance at the 5% and 1% levels, respectively.

. Model (9) and model (13) show that the rural population aging significantly affects the scale efficiency and technical progress rate. Model (4) and model (15) indicate that the rural population aging positively affects scale efficiency through socialization services. Model (4) and model (17) indicate that the rural population aging can enhance the technical progress rate through agricultural socialization services. The main reason is that elderly laborers are more willing to choose agricultural production through pre-production, in-production and post-production business services due to physical reasons. The older the farmers are, the greater the demand for agricultural production services is. Therefore, there is a positive correlation between the rural population aging and agricultural socialization services. From one perspective, the specialized division of labor in agricultural socialization services can make up for the shortage of family labor, break through the constraints of labor shortage and help farmers expand their business scale through farmland transfer. From another perspective, considering that the promotion of agricultural technology requires a large amount of capital investment and personnel training, agricultural socialization services can serve as a bridge for the promotion and use of agricultural technology among aging farmers. This not only solves the problem of the low adoption of new agricultural technologies by aging farmers but also effectively promotes the wide application of agricultural technologies, which ultimately can promote the rate of technological progress.

Finally, agricultural machinery is used as a intermediary variable to analyze the path of the total factor productivity decomposition index, and the regression results are shown in

Table 5. Estimated results of agricultural machinery on decomposition indices.

Variable	(6)	(9)	(18)	(11)	(19)	(13)	(20)
	sci	se	se	pe	pe	tech	tech
agi	10.097 ***	0.390 ***	0.048	−0.083	−0.096	3.241 ***	2.575 ***
	(1.362)	(0.145)	(0.146)	(0.158)	(0.168)	(0.342)	(0.351)
sci			0.034 ***		0.001		0.066 ***
			(0.005)		(0.006)		(0.012)
control variable	controlled	controlled	controlled	controlled	controlled	controlled	controlled
cons	−5.221 **	1.592 ***	1.769 ***	−0.280	−0.274	−5.677 ***	−5.333 ***
	(2.155)	(0.230)	(0.220)	(0.251)	(0.253)	(0.542)	(0.527)
N	480	480	480	480	480	480	480
R2	0.595	0.322	0.390	0.091	0.091	0.755	0.771

** and *** indicate statistical significance at the 5% and 1% levels, respectively.

. Model (9) and model (13) show that the rural population aging significantly affects the scale efficiency and technical progress rate. Model (6) and model (18) indicate that the rural population aging positively affects scale efficiency through agricultural machinery. Model (6) and model (20) indicate that the rural population aging can enhance the technical progress rate through agricultural machinery. The primary factor driving the adoption of agricultural machinery is the escalating cost of labor. With the growth in age, the availability of effective labor becomes increasingly constrained, leading to a greater inclination to substitute manual labor with mechanized solutions. The introduction of agricultural machinery enables the expansion of land management without altering the existing levels of labor input. Consequently, the advancement of agricultural mechanization fosters the growth of appropriately scaled farming operations. In addition, as a product of science and technology, agricultural machinery improve the productivity of land, labor and capital. It simultaneously saves labor input, maximizes the benefits of technology within agricultural economic expansion and accelerates the pace of technological advancement.

4.3. Analysis of Regional Heterogeneity

Due to the different degrees of the rural population aging and differences in the level of agricultural economic development in China’s provinces and municipalities, it is difficult to analyze the impact of the rural population aging on ATFP at the national level to reflect the inter-regional differences. Therefore, this paper adopts the regional classification method proposed by the existing research, which divides the 30 provinces and cities in China (except Tibet) into three regions: eastern, central and western. The aim is to explore the impact of the rural population aging on ATFP within each region.

From the regional heterogeneity results in

Table 6. Estimated results of the impact of the rural population aging on the ATFP in the Eastern region.

Variable	(21)	(22)	(23)	(24)	(25)	(26)	(27)
	tfp	land	tfp	lnser	tfp	sci	tfp
agi	3.296 ***	0.520 ***	2.501 ***	2.344 ***	2.285 ***	8.605 ***	1.802 ***
	(0.679)	(0.164)	(0.651)	(0.735)	(0.619)	(1.886)	(0.631)
land			1.529 ***
			(0.294)
lnser					0.431 ***
					(0.062)
sci							0.174 ***
							(0.024)
control variable	controlled	controlled	controlled	controlled	controlled	controlled	controlled
cons	−6.504 ***	−0.360	−5.954 ***	−3.687 **	−4.913 ***	−10.497 **	−4.681 ***
	(1.469)	(0.355)	(1.374)	(1.591)	(1.323)	(4.082)	(1.315)
N	192	192	192	192	192	192	192
R2	0.678	0.824	0.722	0.593	0.749	0.556	0.753

** and *** indicate statistical significance at the 5% and 1% levels, respectively.

,

Table 7. Estimated results of the impact of the rural population aging on the ATFP in the Central region.

Variable	(28)	(29)	(30)	(31)	(32)	(33)	(34)
	tfp	land	tfp	lnser	tfp	sci	tfp
agi	1.562 ***	0.490 **	1.567 ***	−0.463	1.664 ***	5.383	1.206 **
	(0.582)	(0.226)	(0.595)	(1.010)	(0.541)	(3.472)	(0.542)
land			−0.009
			(0.229)
lnser					0.219 ***
					(0.047)
sci							0.066 ***
							(0.014)
control variable	controlled	controlled	controlled	controlled	controlled	controlled	controlled
cons	−4.309 ***	−2.546 ***	−4.333 ***	−7.113 ***	−2.748 ***	2.139	−4.450 ***
	(0.899)	(0.348)	(1.075)	(1.559)	(0.900)	(5.361)	(0.830)
N	144	144	144	144	144	144	144
R2	0.906	0.845	0.906	0.774	0.919	0.746	0.920

** and *** indicate statistical significance at the 5% and 1% levels, respectively.

and

Table 8. Estimated results of the impact of the rural population aging on the ATFP in the Western region.

Variable	(35)	(36)	(37)	(38)	(39)	(40)	(41)
	tfp	land	tfp	lnser	tfp	sci	tfp
agi	3.196 **	0.185	3.183 **	0.632	3.077 **	5.185 ***	1.559
	(1.241)	(0.162)	(1.252)	(1.129)	(1.229)	(1.589)	(1.186)
land			0.073
			(0.679)
lnser					0.189 *
					(0.096)
sci							0.316 ***
							(0.063)
control variable	controlled	controlled	controlled	controlled	controlled	controlled	controlled
cons	−8.156 ***	−1.270 ***	−8.063 ***	−5.130 ***	−7.184 ***	−7.484 ***	−5.793 ***
	(1.307)	(0.171)	(1.570)	(1.189)	(1.384)	(1.673)	(1.291)
N	144	144	144	144	144	144	144
R2	0.806	0.808	0.806	0.698	0.812	0.796	0.838

*, ** and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.

, it can be seen that the impact of the rural population aging on ATFP is significantly positive in the Eastern, Central and Western regions, but the degree of the impact is decreasing. The Eastern region is significant and has the largest impact coefficient, while the Central region is more significant than the western region. Among them, in the Eastern region, farmland transfer, agricultural socialization services and agricultural machinery are all intermediary variables of the rural population aging on ATFP, while in the Western region only agricultural machinery is a intermediary variable of the rural population aging on ATFP. The reason may be that the aging of the population in the Eastern region is serious, and the level of agricultural modernization is high. As the age of the elderly farmers increases, the physical fitness of the farmers is worse, and they are more inclined to take measures to replace labor input to cope with the aging problem. Therefore, they are more inclined to reduce labor demand through farmland transfer, agricultural socialization services and agricultural machinery, exerting a driving force on ATFP. The Central region is an important agricultural production base, the development of agricultural infrastructure is perfect, and farmland transfer, agricultural socialization services and agricultural machinery development may have been at a high level. Moreover, the aging of the rural population is less serious compared to the Eastern region, which means that the impact of this demographic shift on the aforementioned factors is not as evident. The Western region, conversely, has a late start in agricultural development and a complex and varied terrain, with a low degree of agricultural mechanization. The deepening of the aging of the rural population will increase the demand for agricultural machinery, thereby increasing the ATFP, but the intensity of improvement is relatively low.

4.4. Robustness Test

Referring to another measurement index of the rural population aging in the existing research, this paper replaces the core explanatory variable to test the robustness of the rural elderly dependency ratio. The regression results of the main variables are shown in

Table 9. Robustness test results.

Variable	(42)	(43)	(44)	(45)	(46)	(47)	(48)
	atfp	land	atfp	lnser	atfp	sci	atfp
dep	0.051 ***	0.011 ***	0.048 ***	0.034 ***	0.043 ***	0.142 ***	0.037 ***
	(0.004)	(0.001)	(0.005)	(0.004)	(0.005)	(0.012)	(0.005)
land			0.323 *
			(0.195)
lnser					0.237 ***
					(0.046)
sci							0.103 ***
							(0.017)
control variable	controlled	controlled	controlled	controlled	controlled	controlled	controlled
cons	−8.102 ***	−1.878 ***	−7.496 ***	−6.833 ***	−6.480 ***	−9.658 ***	−7.105 ***
	(0.728)	(0.177)	(0.813)	(0.737)	(0.773)	(1.926)	(0.720)
N	480	480	480	480	480	480	480
R2	0.760	0.759	0.761	0.702	0.774	0.654	0.778

* and *** indicate statistical significance at the 10% and 1% levels, respectively.

. Model (42) in Table 9 provides the benchmark regression results, in which the rural old-age dependency ratio has a significant positive effect on the ATFP. The regression results of model (43) to model (48) are based on the intermediary variables of agricultural land transfer, agricultural socialization services and agricultural machinery, and the results are consistent with the previous analysis. This substantiates the hypotheses put forward by this study, indicating that the estimation results of this paper have a strong robustness.

5. Discussions

We integrate the three factors of land, labor and capital into a unified analytical framework. Building upon the hypothesis of variable returns to scale, we incorporate the effect of economies of scale into the decomposition index of total factor productivity and comprehensively investigate the impact of the rural population aging on the ATFP. This research is of great value for improving agricultural production efficiency against the background of national aging.

Firstly, the rural population aging shows a significant contribution to ATFP, which is consistent with the existing studies [34,48,53]. On the one hand, this positive impact may be due to the accumulation of planting experience of aging farmers, a factor that significantly contributes to the enhancement of human capital in agricultural production [22,54]. During long-term agricultural production, aging farmers have accumulated a lot of practical experience, which can better cope with the impact of climate change and the market environment on agricultural production, to effectively manage and optimize the production process. On the other hand, it may be due to the fact that agricultural technological progress has reduced the excessive demand for labor, so the decline in physical fitness caused by aging has not had a negative impact on agricultural production [1]. Furthermore, in the context of the rural population aging, the state actively develops the production mode of “old-age agriculture”. It encourages the construction of high-standard farmland to increase the adoption rate of agricultural machinery, thus reducing the intensity of agricultural manual labor.

Secondly, farmland transfer, agricultural socialization services and agricultural machinery play a significant intermediary role in the impact of population aging on the ATFP. Agricultural machinery exerts the most significant intermediary effect on the ATFP, and the intermediary effects of the three are 15.60%, 20.12% and 37.68%, respectively. This study has confirmed that farmland transfer can reduce production costs, improve production efficiency [55,56] and also provide conditions for the widespread promotion of agricultural machinery and socialization services. Agricultural machinery can improve and modernize smallholder agriculture and play an important role in ensuring food security [57,58]. Compared with previous studies, this paper reveals that agricultural machinery plays a prominent role in the process of population aging, which shows that machinery can effectively make up for the physical decline of aging farmers and is crucial for fostering the efficient development of agriculture.

Thirdly, through the index decomposition of total factor productivity, it is found that the rural population aging can significantly promote the scale efficiency and technological progress rate through farmland transfer, agricultural socialization services and agricultural machinery, but it has no significant impact on pure technical efficiency. Related research indicates that the aging of the workforce does not notably affect the technical efficiency of agricultural production, but it exerts a considerable negative influence on technological advancement [47]. The reason for the difference between the two may be that on the one hand, this paper decomposes total factor productivity based on variable returns to scale, so it considers the positive impact of economies of scale. On the other hand, it may be that the data used in the study are different. The macro data of the provinces used in this paper are highly aggregated, more comprehensive and general, while the micro data focus on reflecting the specific individual situation. In addition, studies have shown that farmland transfer can concentrate scattered land resources to form a larger contiguous farming area, so as to achieve large-scale production [59,60]. Agricultural mechanization makes large-scale production possible, improving agricultural production efficiency by increasing operational efficiency and reducing labor costs. Social service institutions usually have strong technology research and development and promotion capabilities, which can quickly transfer the latest agricultural technology and management concepts to farmers and promote the popularization and application of technology [61]. Therefore, the combination of farmland transfer, agricultural socialization services and agricultural machinery has promoted the scale effect and technological progress of agricultural production.

Fourth, the impact of the rural population aging on ATFP has a regional heterogeneity, and the degree of impact is decreasing from east to west. This conclusion is consistent with the existing studies [48,62]. Due to the deep aging of the population in the Eastern region and the high level of agricultural technology, elderly farmers tend to reduce labor expenditure through farmland transfer, agricultural socialization services and agricultural machinery, In doing so, they contribute to the enhancement of ATFP. However, the terrain in the Western region is complex and diverse, and the level of agricultural technology development is low. Hence, the improvement in ATFP resulting from aging is lower than that in the Eastern region.

6. Conclusions

Based on the panel data of 30 provinces (cities), except Tibet, in China from 2005 to 2020, this study explores the impact of the rural population aging on ATFP and its mechanism. The conclusions are as follows:

The rural population aging makes a significant contribution to the ATFP, and farmland transfer, agricultural socialization services and agricultural machinery have a intermediary effect on the increase in the ATFP. Further decomposition of the total factor productivity reveals that the rural population aging can have a significant promotion effect on the scale efficiency and technical progress rate through farmland transfer, agricultural socialization services and agricultural machinery, but it has no significant effect on pure technical efficiency. Finally, the impact of the rural population aging on ATFP is regionally heterogeneous, with a decreasing trend from east to west.

Based on the conclusions, we propose the following agricultural policy implications.

Firstly, it is essential to enhance the market conditions for farmland transfer, thereby facilitating farmland transfer and large-scale operations. It is necessary to focus on establishing a sound market for farmland transfer transactions and providing transparent transaction channels. This will encourage farmers to actively participate in land transfer behavior and reduce the phenomenon of agricultural land abandonment. In addition, we should strengthen the information service system for farmland transfer, improve the construction of the service platform for the farmland transfer and make its process concise and convenient.

Secondly, the agricultural social service system should be improved and the level of socialization services upgraded. Skills training in all aspects of agricultural production should be carried out in a categorical manner to solidify the talent base of agricultural socialized service subjects. The development of new agricultural business entities should be actively encouraged, giving full play to their ability to drive aging farmers, which is conducive to promoting changes in agricultural efficiency and realizing the integration of small-scale farming with agricultural modernization.

Thirdly, focusing on cutting-edge areas and key issues in agricultural production, the applicability of agricultural machinery and equipment research and development should be strengthened by increasing the Government’s investment in agricultural research, so as to solve the problem of mismatches between agricultural machinery and agricultural land during the production process. In addition, it is imperative to improve the agricultural technology promotion system and guide farmers to apply new technologies and products in practice. This can promote the effective transformation of agricultural technology achievements and enhance the effectiveness of technology as a substitute for labor.

Due to limitations in the availability of public data, future studies should be further expanded and improved. At the macro level, the measurement index system of ATFP is more complex, including a variety of factor inputs. This study calculates ATFP from three aspects: labor, land and means of production. But the inputs of means of production include many kinds, such as seeds, fertilizers, pesticides and agricultural films, etc. In view of the limitations in data availability of some variables, some factor inputs are not included in the index system. In the future, it can be further comprehensively calculated according to data releases. In addition, the samples used in this study are data at the provincial level, which ignore regional differences and particularities to a certain extent. If data availability conditions permit, the study area can be refined in the future, such as through narrowing to the city or county level.