With the CN = 0.7 criterion, the four-year Dn ranged from 0.3221 to 0.3509, with growth rates of 11.21%, −6.78%, and 5.09% for the four time points, indicating that the development space of agricultural trade between China and B&R countries has experienced the process of "rise–fall–rise". In 2013, the "Belt and Road" initiative injected new impetus to the agricultural trade of B&R countries. With the CN = 0.8 criterion, Dn ranged from 0.4975 to 0.5426, with growth rates of 7.32%, −5.175%, and 7.17% for the four time points, indicating that, when lowering the competitive advantage criterion, the development space of the agricultural trade of the B&R countries is also in the trend of "rise–fall–rise". Comparing the CN = 0.7 and CN = 0.8 criteria, it is found that the "Belt and Road" initiative provides development opportunities for countries with different levels of competitive advantage. Compared with the CN = 0.7 criterion, Dn in 2019 is the largest under the CN = 0.8 criterion, indicating that the countries with weaker comparative advantages in agricultural trade have achieved the best development in history after the introduction of the "Belt and Road" initiative.

#### 3.2.2. Analysis of the Centrality of Trade Networks

Combining Figures 2–17 and Table 5, in terms of the De values, China, Russia, India, Turkey, Thailand, and Malaysia occupy the main centrality positions in the standard condition of trade volume, and they are the most influential countries in the agricultural trade network between China and B&R countries. Over the four years of the study sample, under the criterion of US \$10 million, China's centrality rankings are 2, 1, 1, and 1, respectively, indicating that under the criterion of small and medium trade, China has the highest centrality and the greatest influence among B&R countries. Under the US \$100 million criterion, China's De rankings over the four years are 2, 2, 2, and 2, respectively, indicating

that among B&R countries, under the large trade volume criterion, China's influence is firmly in second place, after Russia. Under the criterion of CN = 0.7, China's De rankings over the four years are 31, 11, 10, and 15, respectively, indicating that, under the condition of greater competitive advantage, China's agricultural trade development space is generally improving. Under the criterion of CN = 0.8, China's De ranking over the four years are 29, 10, 11, and 11, respectively, which indicates that China's trade development space is steadily increasing and staying stable under the smaller trade competitive advantage. The criterion of CN = 0.7 and CN = 0.8 indicates that China's trade development space with B&R countries is huge.

**Table 5.** Network centricity of trade relations of China with B&R countries.

According to Table 5, from the relative degree centrality index, under the US \$10 million criterion, the NC index between China and B&R countries grew from 40% to 59.66% in the four years of the simulation, with an overall growth rate of 49.15% and annual growth rates of 37.78%, 7.24%, and 0.95%, indicating that the centrality of agricultural trade between China and B&R countries tends to be concentrated, and that the countries have closer trade relations, but the centrality tends to slow down. Under the US \$100 million criterion, the NC index between China and B&R countries grew from 18.16% to 48.16% in the four years of the simulation and annual growth rates of 120.87%, 13.31%, and 5.96%.

Compared with the US \$10 million criterion, the US \$100 million criterion centered on a smaller base but a faster growth rate, proving that China has relatively fewer countries, with a trade volume exceeding US \$100 million along the B&R countries, but this closeness

is growing faster. Under the criterion of CN = 0.7, the NC index between China and B&R countries ranged from 47.20% to 58.28% in the four years of the simulation and annual growth rates of −13.47%, 5.40%, and 17.15%, indicating that after the financial crisis, the central tendency of China and B&R countries with large competitive advantages has increased, and the trade exchanges tended to be closer. Under the criterion of CN = 0.8, the NC index between China and B&R countries ranged from 37.63% to 41.78% in the four years of the simulation and annual growth rates of 19.21%, 11.93%, and 0.81%, indicating that the trade center potential of China and B&R countries with smaller competitive advantages in the "Belt and Road" initiative tended to disperse, and the countries with room for trade development were more widely distributed.

#### 3.2.3. Analysis of the Trade Block Model

According to the analysis in Table 6, the first plate is an internal type plate. The second plate is an internal type plate. Third plate is an isolated plate and the fourth plate is an internal plate. According to the above analysis, it can be concluded that in the early stage of China's accession to WTO, the agricultural trade between China and B&R countries is in an internal block or isolated state; a "small circle" trade. Similarly, the first, second, third, and fourth plates in 2009 are, respectively, the internal plate, isolated plate, isolated plate, and isolated plate. In 2013, the first, second, third, and fourth plates are the simultaneous plate, the internal plate, the simultaneous plate, and the internal plate, respectively. In 2019, the first, second, third, and fourth plates are the simultaneous plate, internal plate, internal plate, and internal plate, respectively.

**Table 6.** Trade volume (US\$ 100 million) in 2001, 2009, 2013, and 2019 between China and B&R country plates (%).

Due to space limitations, only the country distributions for 2001 and 2019 are listed. According to the CONCOR method analysis results, in 2001, the countries in the first plate are China, nine countries in Southeast Asia, five countries in South Asia, and four countries in Western Asia and the Middle East. The countries in the second plate are Russia, two countries in Central Asia, three countries in Western Asia and the Middle East, and seven countries in central and Eastern Europe. The countries in the third plate are Mongolia, three countries in Central Asia, two countries in Southeast Asia, three countries in South Asia, seven countries in Western Asia and the Middle East, and six countries in central and Eastern Europe. The countries in the fourth plate are four countries in Western Asia and the Middle East, and three countries in Central and Eastern Europe. In 2019, the countries in the first plate are China, Russia, 10 countries in Southeast Asia, 3 countries in South Asia, and 2 countries in Western Asia and the Middle East. The countries in the second plate are four countries in South Asia, seven countries in Western Asia and the Middle East, and one country in Central and Eastern Europe. The countries in the third plate are Mongolia, four countries in Central Asia, five countries in Western Asia and the Middle East, and six countries in Central and Eastern Europe. The countries in the fourth plate are one in Southeast Asia, one in South Asia, four in Western Asia and the Middle East, and nine in Central and Eastern Europe. China always belonged to the first plate, and most of the

countries in the first plate belonged to China's neighboring countries. The trade density of the first plate continued to increase from 2001 to 2019, rising from 0.216 to 0.591, indicating that the trade of countries in the first plate became increasingly close.

According to the analysis in Table 7, the first, second, third, and fourth plates in 2001 were, respectively, the export-oriented plate, dual-oriented plate, dual-oriented plate, and the dual-oriented plate. In 2009, they were the export-oriented plate, take into account plate, take into account plate, and the take into account plate. In 2013, they were the export-oriented plate, multi-faceted plate, multi-faceted plate, and the internal plate. In 2019, they were the simultaneous plate, simultaneous plate, simultaneous plate, and the simultaneous plate. Due to space limitations, only the country distributions in 2001 and 2019 are listed. Countries belonging to the first plate in 2001, included China, Russia, one in Southeast Asia, four in West Asia and the Middle East, and three in Central and Eastern Europe. The countries belonging to the second plate numbered three in Southeast Asia and eight in West Asia and the Middle East. The countries belonging to the third plate were Mongolia, and two in Central Asia, five in Southeast Asia, five in South Asia, three West Asia and the Middle East, and four in Central and Eastern Europe. Finally, the countries in the fourth plate numbered three in Central Asia, two in Southeast Asia, three in South Asia, three in West Asia and the Middle East, and nine in Central and Eastern Europe. The countries belonging to the first segment in 2019 were China, one in Southeast Asia, one in South Asia, eight in West Asia and the Middle East, and two in Central and Eastern Europe. The countries in the second segment were Mongolia and Russia, three in Central Asia, four in Southeast Asia, two in South Asia, one in West Asia and the Middle East, and five in Central and Eastern Europe. The countries in the third segment cinluded two in Central Asia, one in Southeast Asia, one in South Asia, two in West Asia and Middle East, and seven in Central and Eastern Europe. The countries in the fourth segment included four in Southeast Asia, four in South Asia, seven in West Asia and the Middle East, and four in Central and Eastern Europe. From 2001 to 2019, China was in the first plate, which changed from an export-oriented plate in 2001 to a balanced plate in 2019, indicating that the internal and external trade space of the plate gradually increased, and that the agricultural trade between China and B&R countries has broad prospects. From the perspective of the overall trade sector, the second, third, and fourth trade sectors had a large space for trade development. Although the fourth sector was transformed into an internal sector in 2013, and the foreign trade was not close enough, after the "Belt and Road" Initiative was proposed, the four sectors were all balanced sectors in 2019. This shows that the trade potential of agricultural products between China and B&R countries is huge.

#### *3.3. Analysis of Spatial Network Influencing Factors*

#### 3.3.1. QAP Correlation Analysis

Using the QAP correlation analysis method and Ucinet 6 software, 5000 random permutations are selected to obtain the results of correlation analysis between China's agricultural trade network F and each influencing factor with B&R countries in 2019, where P represents the probability that the random correlation coefficient is greater or less than the actual value. This is shown in Table 8. The agricultural trade network F is not significantly correlated with the per capita arable land resource matrix (PCLA), scientific research expenditure share (SCI), and economic distance (DE), and is significantly correlated with the per capita water resource matrix (PCWR), geographic location matrix (DIS), transportation (TRA), total economic output (DGDP), trade agreement matrix (TA), culture matrix (CUL), and trade structure matrix (IS). We tentatively determine that the geographical distance, transportation, GDP difference, trade agreements, cultural differences, and trade structure differences between the two countries are the main factors affecting the agricultural trade network between China and B&R countries.

**Table 8.** QAP correlation analysis results of F and influencing factors of China with B&R countries.

#### 3.3.2. QAP Regression Analysis

Based on the correlation analysis results in Table 9, we included the matrices of PCWR, DIS, TRA, DGDP, TA, CUL, and IS, which were significantly correlated with F, in the QAP regression analysis, and set the number of random permutations to 5000. The results are shown in Table 9. As seen from the table, (1) PCWR is significantly correlated with the trade network between China and B&R countries, with a regression coefficient of −0.000002, and a negative regression coefficient, indicating that the smaller the difference in water resources, the closer the trade in agricultural products. (2) The correlation of DIS to China's trade network with B&R countries is significant, with a regression coefficient of 0.360666, indicating that countries with closer geographical locations are more likely to trade agricultural products, which also verifies the fact that China has close agricultural trade with neighboring countries such as Russia, Thailand, and Vietnam. (3) The correlation of TRA with the trade network between China and B&R countries is significant, with a regression coefficient of 0.053962, indicating that the more convenient the domestic and international transportation, the greater the possibility of agricultural trade. (4) DGDP is not significantly correlated with China's trade network with B&R countries, indicating that although GDP is correlated with agricultural trade between countries, countries with a large difference in GDP between the two countries do not necessarily have close agricultural trade. (5) TA is significantly correlated with the trade network between China and B&R countries, indicating that a trade agreement between two or more countries can facilitate bilateral or multilateral trade exchanges. (6) The correlation of CUL with the trade network between China and B&R countries is significant, indicating that the two countries have

the same or similar culture, which is conducive to the economic and trade exchanges between the two countries and the expansion of bilateral agricultural trade. (7) IS is significantly correlated with the trade network between China and B&R countries, with a negative coefficient of −0.000983, indicating that the smaller the gap in the agricultural trade structure, the closer the bilateral trade between the countries.

**Table 9.** QAP regression analysis results of China with B&R countries.

Note: \*\*\*, \*\* indicate that the coefficients passed the significance tests of 1%, 5%.

#### **4. Discussion**

#### *4.1. Comparison to Prior Studies*

The main objective of our paper is to explore the factors influencing the evolution and trade space of agricultural trade between China and B&R countries, from a planar and spatial perspective. Our results confirm that China's agricultural trade with B&R countries has become increasingly close and highly concentrated, with high intensity areas being mainly concentrated in closer or neighboring countries, and that the trade development space shows a "rise-fall-rise " trend, with China remaining at the "power" core of the trade network, and with the centralization of trade in the B&R countries tending to be concentrated. The agricultural trade network between China and B&R countries can be divided into four major segments, with increasingly close internal and external trade in each segment. The trade network linkages are mainly influenced by water resources, geographic location, railroad convenience, trade agreements, and trade structure. The findings of this paper are consistent with previous studies on agricultural trade between China and B&R countries. For example, Yu (2016) found that China's total bilateral trade with eight South Asian countries has quadrupled, and that China's total agricultural imports from South Asia are greater than its total agricultural exports, with a widening deficit [8]. Zhan (2018) pointed out that the network density of agricultural export relations, competitive relations, and complementary relations among B&R countries is increasing day by day [32]. Su (2019) argued that the density of spatially linked networks of agricultural trade in China and B&R countries is high, and that China is at the center of this spatially linked network [33]. As expected, the empirical results of this paper show that China's agricultural trade with B&R countries is getting closer and closer, and that China is gradually becoming the center of agricultural trade. Our findings are almost consistent with those of the aforementioned scholars.

However, our study is somewhat different from previous studies, from the following perspectives. In analyzing the comprehensiveness of agricultural products and time chains, we have used all the total agricultural products and the time of WTO accession as samples, which can provide China with an overall perspective and ability to grasp the dynamics of agricultural cooperation in B&R countries; this is conducive to making comprehensive and sustainable decisions. For example, Li (2018) takes aquatic products as a sample and concludes that China is located in the middle and high end of the regional value chain of B&R countries, and has the ability to dominate the regional value chain [23], which is similar to the conclusion reached in this paper. However, the conclusion of this paper

has a greater generalization of agricultural products and is more conducive to national agricultural sector decision-making.

Second, we use a combination of planar- and spatial-shaped analysis, taking into account the quantity, specific agricultural product dynamics, and spatial national agricultural trade dynamics, each focusing on the other and complementing each other. For example, both Chen (2019) and Su (2019) analyzed the relationship model of food and agricultural trade networks between China and B&R countries from a spatial perspective [26,33], which can reflect that the density of food trade networks among B&R countries is increasing. However, they did not compare with the flat volume structure reference, and could not produce accurate figures.

Third, we improved the competitive index CS and constructed the competitive advantage index CN in the research technique of Li et al. (2017) [37], which provides a method for scholars to measure the spatial relationship. For example, Wei (2018) refers to Li Jing's (2017) method of screening nodes, and uses the total agricultural import and export trade of more than US \$100 million, and unilateral agricultural imports of more than US \$10 million as the criteria for trade flows, without further constructing the network model with the criteria of comparative advantage to derive new trade structure information [31].

Finally, regarding measurements of the influencing factors of spatial association relationships, for example, previous studies found that Wei's (2018) "proximity effect", FTAs, differences in consumer population base, and differences in total economic size all enhance the association relationships of agricultural trade between countries [31]. However, we found that trade linkages are influenced by water resources, geographic location, railroad accessibility, trade agreements, and trade structure. There were also both overlapping elements and new elements that can provide a reference for China to select sustainable cooperation partners.

#### *4.2. Sustainability Implications*

First, the types of agricultural products traded and the import and export areas between China and B&R countries are highly concentrated. China has close trade with countries that are geographically close, so China has to maintain friendly relations with neighboring countries, such as Russia, India, Vietnam, Thailand and other large agricultural countries, and actively sign trade agreements. It can not only save China's trade costs and improve its own agricultural products supply security capacity, but also promote the differentiated division of labor in agriculture between China and B&R countries, improve labor productivity, increase the export of agricultural products with comparative advantages, and achieve sustainable mutual benefits.

Second, large agricultural countries such as China, Russia, and India occupy a dominant position, and the trade network can be divided into four major segments, with increasingly close trade within and outside each segment. Therefore, China should stabilize production and trade with large agricultural countries such as Russia and India to reduce the overall trade risk and enhance sustainable agricultural production and trade. China should also actively use its dominant position as a large agricultural trading country to guide other strong agricultural trade countries to play a greater role in emphasizing their own advantages, supporting countries with weaker trade by providing agricultural production factors, and promoting sustainable cooperation among countries.

Last, the relationship between China and the agricultural trade network of B&R countries is mainly influenced by water resources, geographical location, railroad convenience, trade agreements and trade structure. Therefore, China can, based on the conditions of natural resources, public facilities, and trade agreements of the B&R countries, reduce unnecessary waste of agricultural resources and the environment in the context of the global goal of achieving carbon peaking and carbon neutrality. China should also strengthen infrastructure development and natural resource advantages of neighboring countries to complement each other, reduce trade costs and increase agricultural productivity, and

improve environmentally friendly and sustainable production between countries. Additionally, China should develop an agricultural production policy within China that suits its own resource environment and trade structure, so that both domestic and international agricultural exports and imports can take advantage of their comparative advantages and form a sustainable domestic production and international trade relationship.

#### *4.3. Limitations and Future Research Directions*

There are also some shortcomings to our research. First, when discussing the classification of specific agricultural products, this paper only explores in the plane structure, and it hardly shows the spatial structure. Therefore, although the current situation of the cooperation of specific classified agricultural products with B&R countries can be understood from the perspective of a single Chinese country, the analysis of the agricultural products classified in the spatial scope of B&R countries is lacking. The results of our study need to be supplemented and improved again by subsequent studies. Second, when discussing the factors influencing the spatial structure of trade, we only list 10 indicators, due to the length and the availability of the data, and there are other important influencing factors to be explored to further improve the indicator system for promoting bilateral trade. Third, we assumed only two significant indicators, namely the US \$10 million and US \$100 million markers, since other data were not available for the countries and years we analyzed. Fourth, we constructed indicators of comparative competitive advantage in trade without constructing indicators of trade complementarity. The conclusions drawn can only reflect a situation of competitive advantage in trade.

There are three future research directions. First, our research here mainly explores the agricultural trade structure and its influencing factors between China and B&R countries from a plane and spatial perspective. However, with the establishment of AFTA, CEFTA, and RCEP, the policies between countries are very different, and the global dual carbon initiative goals are included in the influence of the factors. These factors enrich the system of indicators affecting sustainable trade structure and help to quantify the effect of regional cooperation and the reference direction of future sustainable cooperation in the face of COVID-19, the Russia–Ukraine conflict, and climate change. Second, the spatial structure of this paper only explores the overall agricultural trade structure from different markers, so we can take global bulk agricultural products, such as soybean, wheat, corn, and rice, as the research objects, and explore the agricultural trade structure between China and B&R countries, which is conducive to exploring the targets of trade-led sustainable cooperation from the perspective of specific agricultural products. Third, future research can construct trade complementarity indexes. International trade not only has the theory of comparative advantage, but complementarity is also one of the important theories for promoting the development of international trade, and so it is beneficial to expand the criteria of trade cooperation and explore the trade network space from multiple perspectives to provide a rich reference for international agricultural sustainable cooperation.

#### **5. Conclusions**

From the perspective of plane and space, this paper analyzes the plane structure and the spatial network structure, and the influencing factors of agricultural trade between China and the B&R countries from 2001 to 2019. This paper takes all agricultural products and all countries along the B&R as research samples, classifies countries and products, and uses plane and spatial perspectives to conclude that China's agricultural product trade with B&R countries tends to be decentralized in terms of import types and regions, and concentrated in terms of export types and regions, the regions with high trade intensity are mainly concentrated in close proximity or in neighboring countries, and that trade relations are getting closer. China has always had a greater influence in the trade network, and the trade centrality of the B&R countries tends to be concentrated. China's agricultural trade network with the B&R countries can be divided into four major segments, with increasingly close internal and external trade in each segment. The results of this paper are beneficial for China and B&R countries to provide a basis for making decisions on trade cooperation from the perspective of agriculture as a whole, to promote global agricultural cooperation, and to facilitate global agricultural cooperation, the flow of global agricultural factors, world food production, and the establishment of a reference method to study global trade structure.

**Author Contributions:** Conceptualization: L.Z. and G.T.; methodology: L.Z. and G.T.; software: L.Z.; validation: L.Z. and G.T.; formal analysis: L.Z.; investigation: L.Z.; data curation: L.Z. and G.T.; writing—original draft preparation: L.Z.; writing—review and editing: L.Z. and G.T.; visualization: L.Z. and G.T.; funding acquisition: L.Z. and G.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was funded by Heilongjiang Provincial Philosophy and Social Science Office, grant number 18JLD310.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors would like to thank the anonymous reviewers for their constructive comments and valuable suggestions on this article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

**Xiangdong Guo 1,\*, Pei Lung <sup>2</sup> , Jianli Sui <sup>3</sup> , Ruiping Zhang <sup>1</sup> and Chao Wang <sup>1</sup>**

**Abstract:** Due to the weak nature of agricultural production, governments usually adopt supportive policies to protect food security. To discern the growth of agriculture from 2001 to 2018 under China's agricultural support policies, we use the nonlinear MS(M)-AR(p) model to distinguish China's agricultural economic cycle into three growth regimes—rapid, medium, and low—and analyze the probability of shifts and maintenance among the different regimes. We further calculated the average duration of each regime. Moreover, we calculated the growth regime transfers for specific times. In this study, we find that China's agricultural economy has maintained a relatively consistent growth trend with the support of China's proactive agricultural policies. However, China's agricultural economy tends to maintain a low-growth status in the long-term. Finally, we make policy recommendations for agricultural development based on our findings that continue existing agricultural policies and strengthen support for agriculture, forestry, and animal husbandry.

**Keywords:** agricultural development; agricultural economic cycle; agricultural policies

#### **1. Introduction**

Agriculture not only affects the macroeconomics of a country but is also associated with the food security and employment issues of a country, particularly for developing countries. With the majority of countries in the world still in the developing stage and a very high proportion of the population still underdeveloped, development remains a central topic in the world economy. As early as 1946, economists Burns and Mitchell emphasized that economic growth can be effectively guided only by a thorough analysis of the mechanisms of change inherent in economic growth [1].

The agricultural surplus theory considers a highly developed agricultural economy as the fundamental condition for macroeconomic development. For this reason, the Chinese government introduced beneficial agricultural policies every year since 2004 to support agricultural development. China's economy has been increasing with a double digit high growth rate in the past few decades. The growth rate has only slowed down slightly in recent years, but it is still one of the fastest growing economies in the world. Within this historical context, what are the dynamics that drive China's agricultural economic growth? In this paper, we investigate the true underlying dynamics of China's agricultural economy during this period of time, and summarize its experience to incentivize further growth of China's agricultural economy.

The available literature focuses mainly on the factors influencing the growth of agriculture. Even though agriculture may grow rapidly in the short term, long-term growth is constrained by factors such as overconsumption of natural resources and environmental pollution [2]. The role of water use in driving agricultural growth in different regions of China was based on a panel vector autoregressive model [3]. Infrastructure development has a catalytic effect on China's agricultural GDP [4]. Agricultural production and

**Citation:** Guo, X.; Lung, P.; Sui, J.; Zhang, R.; Wang, C. Agricultural Support Policies and China's Cyclical Evolutionary Path of Agricultural Economic Growth. *Sustainability* **2021**, *13*, 6134. https://doi.org/10.3390/ su13116134

Academic Editor: Aaron K. Hoshide

Received: 14 April 2021 Accepted: 27 May 2021 Published: 29 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

development can also be influenced by other factors. For example, in Nigeria rainfall, currency exchange rate, and food exports are the most important factors driving agricultural output. Food importation, diversion of funds for agriculture, and low penetration of agricultural technology were identified as the major constraints to agricultural development in Nigeria [5].

Other studies reach the same results, in which increasing agricultural research and development expenditures will support agricultural economic growth [6–9]. However, increasing fiscal spending on agriculture, while promoting agricultural growth, can also impact the quality of agroecosystems [10]. Soil and water conservation has a significant impact on the per capita income of rural households in China [11].

To achieve sustainable long-term growth in agriculture, we need to strengthen reforms and innovation in the rural economic system [12]. In the long run, a land system that is compatible with the country's macroeconomic condition has a positive contribution to China's agricultural economic growth [13,14]. Studies in Commonwealth of Independent States (CIS) countries have shown that policy factors such as land reform contribute, to some extent, to the growth of agricultural production [15]. Studies in the EU countries show that the average farm income is already close to the average non-farm income, thanks to the Common Agricultural Policy (CAP) support [16]. Agricultural policies are important for poverty reduction and agricultural development [17–22]. On the contrary, distorted agricultural policies can hinder its agricultural development [23]. Effective monetary and fiscal policies can boost agricultural growth over time [24–26].

The studies above focus on the different factors that are related to agricultural growth, but few scholars have analyzed the historical trajectory of agricultural growth in depth. As a reflection of China's economic growth, agricultural growth has shown up-and-down cycles over the past 20 years. This is despite China's high rate of macroeconomic growth and strong support from the government's pro-agricultural policies.

Recent studies on agricultural economic cycles in Spain, Cuba, and the United Kingdom identified the causative factors driving these cycles. Studies in the Spanish regional economy show that the agricultural production cycle is constrained by the natural environment and ecological conditions, meanwhile, at the same time, benefitted from rapid economic and social development and globalization [27]. The history of agricultural development in Cuba indicates that, according to the theory of the adaptive renewal cycle, the process of agricultural development is nonlinear and is divided into four stages: Growth, maturation, collapse, and transformation [28]. Studies on the United Kingdom agriculture shows that agriculture sustainably reinforces cultural management and ecosystems and will affect cultural service assets in a broad sense [29].

Since 1952, China's agricultural economic cycle has fluctuated several times, with three classical economic cycles and three growth cycles. The agricultural economies have achieved growth and development in the midst of cyclical fluctuations, and responded to the economic policies and institutional reforms in different economic periods [30]. Changes in China's agricultural policies are the main cause of agricultural fluctuations. Institutional factors are important causes of the cyclical fluctuations of the agricultural economy [31]. The pricing mechanism and land system can promote the change of the agricultural economy to a high-growth state [32].

The magnitude of fluctuations in China's agricultural economic cycle has declined significantly and China's agricultural development has gradually stabilized from the 1980s. Overall, China's agricultural economic cycle has a high frequency of fluctuations with small magnitude [33]. China's agricultural economy is characterized by significant inertia during low-growth rates. When the agricultural growth rate is relatively high, its risk of shocks is higher, as well. When the growth rate is relatively low, its uncertainty is relatively low [34]. Agricultural economic cycles have certain spatial correlations and will amplify agricultural economic fluctuations through cyclical spatial spillover, forming cyclical synergistic effects [35]. Technological and institutional innovations in China should emphasize more on sustainable development which considers the relationship between agriculture

and the environment, rather than setting inconsistent and sometimes incompatible policy goals from different perspectives [36].

Agricultural policies implemented by the Chinese government have raised farmers' income levels and contributed to long-term food security goals. However, such policies have also led to a price gap between domestic and international markets for agricultural products leading to a sharp increase in agricultural imports and the accumulation of large stocks [37]. Previous experience in developing agriculture through institutional reform, technological change, market reform, and investment in agriculture remains the key to future success in ensuring food security and sustainable agriculture growth in China [38]. The true family farm of moderate "small and precise" scale, which has emerged quite widely in China over the past 30 years, can chart a more sustainable way forward for Chinese agriculture [39].

Agricultural economic growth should not come at the cost of damage to natural resources and pollution of the ecological environment, but should focus on the coordination and balance between the short- and long-term [2]. Environmentally friendly technological innovation is a long-term driving force for both the development and sustainable growth of agricultural economies. On the whole, every 1% increase in environmentally friendly agricultural technology innovation causes a 0.375% increase in agricultural economic growth, while every 1% increase in the extent of environmentally friendly technology diffusion causes a 0.542% increase in agricultural economic growth [40].

Attention should be paid to the phenomenon of decreasing ecological land use in the agro-pastoral zone, and the land use structure should be adjusted to provide good ecological conditions for the sustainable development of the agricultural economy in the agro-pastoral zone [41]. Soil and water conservation can contribute to agricultural economic growth and rural poverty reduction in China. Soil quality and capital inputs are now more important than farmland size and agricultural labor in poverty reduction and economic growth. Governments and farmers need to prioritize investments in soil and water conservation to boost the agricultural economy and reduce rural poverty [11]. As the use of linear measures does not allow for effective measurement of the characteristics of economic cycles, such as those found in agriculture, scholars have proposed various nonlinear econometric models to characterize the variability of economic cycles in detail, such as the Smoothed Migration Autoregressive (STAR) model, the Markov transfer (MS) model, and Threshold Autoregressive (TAR) models [42–44]. In recent years, researchers have measured the economic cycles of South Africa, Brazil, Turkey, etc. using Markov regime transfer models [45–47].

On this basis, in the existing studies on the fluctuation dynamics of the Chinese economic cycle, scholars have quantitatively measured the economic cycle based on different forms of Markov transfer (MS) models to analyze the dynamic characteristics of the economic cycle when it varies across regimes [48–50]. Sui Jianli and Song Diandian first used a Markovian regime shift model to study the Chinese agricultural economic cycle, but he chose a two-regimes Markovian shift model that could only distinguish the Chinese agricultural economic cycle into a high-growth and a low-growth regime [51].

This paper follows the previous research path but differs in that the time domain of this paper is placed in the specific context of the Chinese government's annual agricultural policies to support agricultural development from the early 21st century. Our research focuses on China's agricultural economic development under the support of agricultural policies. In this paper, we construct a Markov transfer model with three regions to analyze the agricultural development in China since 2001 and use it to initially assess the effects of agricultural policies during this period.

In addition, a nonlinear MS (M)-Autoregressive Process (AR) (p) model with "mean form" and "intercept form" was created, and the growth rate of the overall agricultural product is included in our study. The nonlinear model with the "mean form" focuses on capturing the trajectory of the mean levels as they shift across time, while the nonlinear model with the "intercept form" is able to track the dynamic path of time series means since they smoothly transition over time as they shift by regime. The model is able to more accurately and sharply capture the cyclical fluctuations in the mean of each variable's time series data. Drawing on the ideas of Krolzig, this paper provides a quantitative demonstration of the growth dynamics in the context of policy support for China's agricultural economy [52]. The specific contribution of this paper to the scientific literature on agricultural development is to empirically highlight the importance of agricultural policy for agricultural development.

The Markov transfer model has the advantage of being able to accurately distinguish the dynamic changes between different variables, which is different from other models. Therefore, the Markov transfer model is used in this paper to study the growth of China's agricultural economy. In order to accurately understand the cyclical evolutionary path of the agricultural economy, this paper takes not only the total agricultural output as the object of study, but also the total output of agriculture, forestry, fishery, and animal husbandry sub-sectors of Chinese agriculture.

#### **2. Methods and Materials**

#### *2.1. Nonlinear MS (M)-AR (p) Model Construction and Model Estimation*

In this paper, we model the growth rates of China's agriculture, forestry, livestock, fisheries, and overall agriculture, respectively, and its regime shifts. The growth rate is measured as *y<sup>t</sup>* and the regime shift in the growth rate is measured as *s<sup>t</sup>* . We consider a linear p-order Autoregressive Process (AR) as the starting point for the nonlinear model:

$$y\_t = v + A\_1 y\_{t-1} + \dots + A\_p y\_{t-p} + u\_t \tag{1}$$

where *v* is chosen as the intercept term. In addition, this paper requires the necessary assumptions regarding the smoothness of the *y<sup>t</sup>* time series. In the equation 1 − *A*1*L* − *A*2*L* <sup>2</sup> − · · · − *<sup>A</sup>p<sup>L</sup> <sup>p</sup>* = 0 of the lag operator *L*, we assumed that the characteristic roots of the equation are located outside the unit circle. We also assumed that the error term *u<sup>t</sup>* of Equation (1) follows the standard normal distribution, i.e., *u<sup>t</sup>* ∼ *N ID*(0, Σ). Based on these assumptions, the model form presented in Equation (1) is the "intercept form" of the classical AR (*p*) model. The "mean value form" of the linear p-order AR (*p*) model is presented as follows:

$$y\_t - \mu = A\_1(y\_{t-1} - \mu) + \dots + A\_p(y\_{t-p} - \mu) + u\_t \tag{2}$$

In this paper, *µ* is defined as the mean of the time series *y<sup>t</sup>* for each variable. We can clearly see that the linear AR (*p*) models in "intercept form" and "mean form" constructed in the previous section have limitations in detailing the possible *y<sup>t</sup>* nonlinear features in the time series and cannot successfully capture the "structural mutations" embedded in the time series. In light of this, we explored in depth the "structural mutation" phenomenon in China.

This paper follows the approach of Hamilton and Krolzig [43,52] to add random *s<sup>t</sup>* variables to the time series *y<sup>t</sup>* to deeply explore the potential nonlinear "Markovian shifts" in China's agricultural economic growth process, where M different regimes *s<sup>t</sup>* can be characterized, *s<sup>t</sup>* ∈ {1, . . . , *M*}. By introducing *s<sup>t</sup>* into the time series data generation process, we are able to more accurately examine the dynamic changes in the nonlinear AR (*p*) model. At the same time, this paper further assumes *s<sup>t</sup>* that it is possible for the Markov process to be followed to traverse all *M* regimes, based on which, the specific transfer matrix can be expressed in the following form:

$$P = \begin{bmatrix} P\_{11} & P\_{12} & \cdots & P\_{1M} \\ P\_{21} & P\_{22} & \cdots & P\_{2M} \\ \vdots & \vdots & \ddots & \vdots \\ P\_{M1} & P\_{M2} & \cdots & P\_{MM} \end{bmatrix} \tag{3}$$

In Equation (3), *pij* = Pr(*st*+<sup>1</sup> = *j s<sup>t</sup>* = *i*), Σ *M j*=1 *pij* = 1, ∀*i*, *j* ∈ {1, . . . , *M*}.

In the following sections of this paper, we construct nonlinear MS (*M*)-AR (*p*) models with reference to the "mean-form" linear AR (*p*) models. The MSM (*M*)-AR (*p*) model containing the variable parameter function *µ*(*st*) can be constructed by introducing the regime state variable *s<sup>t</sup>* into the mean *µ* shown in Equation (2).

$$y\_t - \mu(s\_t) = A\_1[y\_{t-1} - \mu(s\_{t-1})] + \dots + A\_p[y\_{t-p} - \mu(s\_{t-p})] + u\_t, \quad u\_t \sim NID(0, \Sigma) \tag{4}$$

It is known that

$$\mu(s\_t) = \begin{cases} \mu\_{1\prime} & s\_t = 1 \\ \vdots & \vdots \\ \mu\_{M\prime} & s\_t = M \end{cases} \tag{5}$$

The variable-parameter functions *A*1(*st*), . . . , *Ap*(*st*), Σ(*st*), and, *v*(*st*) have very similar expressions to *µ*(*st*) as defined above and, therefore, will not be repeated in the following section.

The average duration *D*[*st*(*i*)] with regime variables *s<sup>t</sup>* using the following formula:

$$D[\mathbf{s}\_t(i)] = E[\mathbf{s}\_t = i] = \frac{1}{1 - p\_{ii}}, i = 1, 2, 3 \tag{6}$$

The unique approach of this paper is to create a nonlinear MS (M)-AR (p) model that includes both "mean form" and "intercept form." The nonlinear MS (M)-AR (p) model is further explored using the Expectation Maximization (EM) algorithm and the Maximum Likelihood (ML) technique [43,52].

When we use these nonlinear MS (M)-AR (p) models for economic analysis, we need to first verify the stationarity of the variable data. In this paper, we will use ADF (Augmented Dickey–Fuller) test, PP (Phillips–Perron) test, and KPSS (Kwiatkowski–Phillips–Schmidt– Shin) test to check the stability of the variable data. In addition, for the multiple nonlinear models created in this paper, it is necessary to calculate the AIC (Akaike Information Criterion), HQ (Hannan Quinn), and SC (Schwarz Criterion) values under different model settings according to the AIC information criterion, HQ information criterion, and SC information criterion to analyze the reliability and validity of the model.

#### *2.2. Data Selection for China's Agricultural Economic Growth*

Based on the quarterly data of China's gross product of agriculture, forestry, livestock, fishery, and overall gross agricultural product from Q1 2001 to Q1 2018, this paper further calculated the quarterly data of the growth rate of each variable to examine the cyclical dynamic change process of China's agricultural economic growth in detail. The growth rate is calculated by the year-on-year method and takes into account price inflation. The data in this paper were obtained from the China Economy Internet (CEI) data (http://db.cei.cn, accessed on 24 May 2021) and the China Statistical Yearbook.

To further explore the dynamic paths of the growth rates of China's gross product of agriculture, forestry, livestock, fishery, and overall agricultural product over time, this paper uses the H-P filtering technique [52,53] to capture the *trend component* and the *volatility component* of the time series of each variable to provide a clearer picture of the dynamic evolution of the aggregate value of each variable within the time domain under study. Specifically, the "trend component" can clearly depict the trend state and the change process of each variable time series over a long period of time. The "volatility component" can more carefully depict the fluctuation magnitude and uncertainty of each variable time series data in different economic periods. The "volatility component" can provide a more detailed picture of the volatility and uncertainty of the time series of each variable in different economic periods.

#### **3. Results 3. Results**  *3.1. Growth Rate Dynamic Trajectory Analysis*

#### *3.1. Growth Rate Dynamic Trajectory Analysis* In this paper, we first depict the time fluctuation paths of the growth rates of the

variable in different economic periods.

*Sustainability* **2021**, *13*, 6134 6 of 29

In this paper, we first depict the time fluctuation paths of the growth rates of the gross product value in China's agriculture, forestry, livestock, fishery, and agriculture industries. We can see that, on the one hand, the growth rates of the gross product value of China's agriculture, livestock, fishery, and agriculture time series have generally similar time dynamic trajectories, while the growth rates of China's forestry industry alone show relatively different trend changes (Figures 1–5). On the whole, the fluctuations and oscillations of the time series of the growth rates of the gross product value of China's agriculture, forestry, fishery, and agriculture are relatively small, while the fluctuations of the growth rate of the gross product value of China's livestock are more drastic—showing steep fluctuations with steep increases and decreases. gross product value in China's agriculture, forestry, livestock, fishery, and agriculture industries. We can see that, on the one hand, the growth rates of the gross product value of China's agriculture, livestock, fishery, and agriculture time series have generally similar time dynamic trajectories, while the growth rates of China's forestry industry alone show relatively different trend changes (Figures 1–5). On the whole, the fluctuations and oscillations of the time series of the growth rates of the gross product value of China's agriculture, forestry, fishery, and agriculture are relatively small, while the fluctuations of the growth rate of the gross product value of China's livestock are more drastic—showing steep fluctuations with steep increases and decreases.

paper uses the H-P filtering technique [52,53] to capture the *trend component* and the *volatility component* of the time series of each variable to provide a clearer picture of the dynamic evolution of the aggregate value of each variable within the time domain under study. Specifically, the "trend component" can clearly depict the trend state and the change process of each variable time series over a long period of time. The "volatility component" can more carefully depict the fluctuation magnitude and uncertainty of each variable time series data in different economic periods. The "volatility component" can provide a more detailed picture of the volatility and uncertainty of the time series of each

**Figure 1.** Time series of the growth rate of the gross agriculture product. **Figure 1.** Time series of the growth rate of the gross agriculture product.

The "trend component" of the growth rate of China's gross agriculture product shows that China's agriculture started to achieve significant growth in the early 21st century and showed an increasing trend year by year, reaching its highest "peak" roughly around 2010 and declining from 2010–2018 (Figure 1). In addition, looking at the "fluctuating components" of the growth rate of China's gross agriculture product depicted in Figure 1, the growth rate of China's gross agriculture product has been characterized by weak fluctuations since 2010, with more significant fluctuations clustering in the sample interval before 2010. However, in recent years, the volatility of the growth rate of China's The "trend component" of the growth rate of China's gross agriculture product shows that China's agriculture started to achieve significant growth in the early 21st century and showed an increasing trend year by year, reaching its highest "peak" roughly around 2010 and declining from 2010–2018 (Figure 1). In addition, looking at the "fluctuating components" of the growth rate of China's gross agriculture product depicted in Figure 1, the growth rate of China's gross agriculture product has been characterized by weak fluctuations since 2010, with more significant fluctuations clustering in the sample interval before 2010. However, in recent years, the volatility of the growth rate of China's gross agriculture product has increased.

gross agriculture product has increased. The "trend component" of the growth rate of China's gross forestry product as depicted shows that China's gross forestry product has generally grown steadily over the time horizon selected for this paper, rising year by year at the beginning of the 2000s and peaking in 2003 (Figure 2). Subsequently, the growth rate of the gross forestry product moves down from the "peak" at a very slow pace. In the rest of the sample period, the fluctuation of the growth rate of China's gross forestry product is small, and, especially in recent years, the fluctuation of the growth rate of China's gross forestry product is extremely weak.

*Sustainability* **2021**, *13*, 6134 7 of 29

**Figure 2.** Time series of growth rate of the gross forestry product. **Figure 2.** Time series of growth rate of the gross forestry product. tremely weak.

**Figure 3.** Time series of growth rate of the gross livestock product. **Figure 3.** Time series of growth rate of the gross livestock product.

The "trend component" shown in Figure 3 shows that the growth rate of China's gross livestock product changes slowly and appears to hover between "peaks" and "troughs" several times. The growth rate of the gross livestock product in general gradually shifts downward, particularly in recent years. Industry livestock growth rates are The "trend component" shown in Figure 3 shows that the growth rate of China's gross livestock product changes slowly and appears to hover between "peaks" and "troughs" several times. The growth rate of the gross livestock product in general gradually shifts downward, particularly in recent years. Industry livestock growth rates are lower than the initial levels during the early 21st century.

**Figure 3.** Time series of growth rate of the gross livestock product. The "trend component" shown in Figure 3 shows that the growth rate of China's gross livestock product changes slowly and appears to hover between "peaks" and "troughs" several times. The growth rate of the gross livestock product in general gradually shifts downward, particularly in recent years. Industry livestock growth rates are lower than the initial levels during the early 21st century. lower than the initial levels during the early 21st century. At the same time, the "fluctuation component" in Figure 3 reflects that the time series of the growth rate of China's gross livestock product contains significant fluctuation clustering characteristics, and shows higher fluctuation than the growth rate of gross product At the same time, the "fluctuation component" in Figure 3 reflects that the time series of the growth rate of China's gross livestock product contains significant fluctuation clustering characteristics, and shows higher fluctuation than the growth rate of gross product of agriculture, forestry, and fishery industries. In other words, there is relatively more volatility and uncertainty in the time series of the growth rate of China's gross product value of livestock. However, it is also clear that the volatility of the growth rate of China's gross livestock product has significantly decreased in the recent years. In recent years, the Chinese government has implemented policies to curb the development of animal husbandry in order to protect the environment, resulting in negative growth in the animal husbandry industry.

At the same time, the "fluctuation component" in Figure 3 reflects that the time series of the growth rate of China's gross livestock product contains significant fluctuation clustering characteristics, and shows higher fluctuation than the growth rate of gross product

**Figure 4.** Time series of growth rate of the gross fishery product. **Figure 4.** Time series of growth rate of the gross fishery product.

husbandry industry.

The dynamic trajectory of the growth rate of China's gross fishery product over time is shown in Figure 4. It can be seen from the "trend component" of the figure that, during the initial period in 2001, the growth rate of gross fishery product was at a low level. Subsequently, the growth rate of the gross fishery product shows a "cyclical-like" pattern of gradually climbing from a lower growth level to a higher "peak" level, and then slowly falling back to a lower "trough" level. In recent years, the growth rate of China's gross fishery product has been moving downward. In addition, the "volatility component" of the time series of the gross fishery product growth rate shows that during the global financial crisis from 2007 to 2010, China's gross fishery product growth rate exhibited a highly volatile clustering characteristic. However, in recent years, the volatility of China's The dynamic trajectory of the growth rate of China's gross fishery product over time is shown in Figure 4. It can be seen from the "trend component" of the figure that, during the initial period in 2001, the growth rate of gross fishery product was at a low level. Subsequently, the growth rate of the gross fishery product shows a "cyclical-like" pattern of gradually climbing from a lower growth level to a higher "peak" level, and then slowly falling back to a lower "trough" level. In recent years, the growth rate of China's gross fishery product has been moving downward. In addition, the "volatility component" of the time series of the gross fishery product growth rate shows that during the global financial crisis from 2007 to 2010, China's gross fishery product growth rate exhibited a highly volatile clustering characteristic. However, in recent years, the volatility of China's gross fishery product growth rate has significantly weakened.

of agriculture, forestry, and fishery industries. In other words, there is relatively more volatility and uncertainty in the time series of the growth rate of China's gross product value of livestock. However, it is also clear that the volatility of the growth rate of China's gross livestock product has significantly decreased in the recent years. In recent years, the Chinese government has implemented policies to curb the development of animal husbandry in order to protect the environment, resulting in negative growth in the animal

gross fishery product growth rate has significantly weakened. The growth rate of China's gross agricultural product for all four agricultural sectors aggregated together is depicted in Figure 5. Since 2001, this aggregated growth rate has shown a gradual increase in development momentum and, after reaching the highest "peak" in succession, has been declining. In addition, looking at the "fluctuating component" of the growth rate of China's agricultural product depicted in Figure 5, we can see that, since 2001, China's gross agricultural product has shown more obvious fluctuations and a certain clustering of fluctuations. During the subsequent period of 2012–2018, the volatility of the growth rate of China's gross agricultural product decreased. The growth rate of China's gross agricultural product for all four agricultural sectors aggregated together is depicted in Figure 5. Since 2001, this aggregated growth rate has shown a gradual increase in development momentum and, after reaching the highest "peak" in succession, has been declining. In addition, looking at the "fluctuating component" of the growth rate of China's agricultural product depicted in Figure 5, we can see that, since 2001, China's gross agricultural product has shown more obvious fluctuations and a certain clustering of fluctuations. During the subsequent period of 2012–2018, the volatility of the growth rate of China's gross agricultural product decreased. *Sustainability* **2021**, *13*, 6134 9 of 29

> ment of the long-term dynamic changes in China's agricultural economy. The next part of this paper is based on a nonlinear MS (M)-AR (p) model with time series data on the growth rates of China's gross product of agriculture, forestry, livestock, fishery, and agriculture. The results show that the growth rates of China's gross product of agriculture, forestry, livestock, fishery, and overall agriculture were stationary at the 5% significance level, while the growth rates of all variables were first-order single integers at the 1% sig-

> The study shows that the AIC, HQ, and SC values of the time series of the growth rate of China's gross agriculture product were the smallest when the model was set to the MSM (3)-AR (3) form. The AIC, HQ, and SC values of the time series of the growth rate of China's gross forestry product were the smallest when the model was set to the MSM (3)- AR (1) form. The AIC, HQ, and SC values of the time series of the growth rate of China's livestock, fishery, and China's agricultural output are all minimized when the model is set in the form of MSM (3)—AR (4). Thus, it is reasonable and reliable to use the MSM (3)—AR (p) model constructed in this paper to investigate the dynamic evolution of China's agricultural economy in terms of the growth region system and its changing dy-

> The parameter estimation results of the MSM (M)-AR (p) model calculated by different variables are presented in Tables 1 and 2, respectively. The results of the t-statistical test indicate that all values were significant at the 1% or 5% level, except for the growth rate of the total fishery output in the zone system 1 ( 1 *<sup>t</sup> s* = ). This indicates that the model

> of China's agriculture, forestry, livestock, fishery, and agricultural industries are all con-

growth rates of each variable are considered as the low-growth regime, medium-growth regime, and rapid-growth regime for regime 1, regime 2, and regime 3, respectively.

μμμ

estimates of the growth rates of the gross product

<sup>123</sup> < < (Tables 1 and 2). Therefore, the

μ

**Figure 5.** Time series of growth rate of the gross agricultural product. **Figure 5.** Time series of growth rate of the gross agricultural product.

nificance level.

namics.

we chose is appropriate. The mean

sistent with the parameter constraints

*3.2. The Parameter Estimation of the MSM (M)-AR (p) Model*

#### *3.2. The Parameter Estimation of the MSM (M)-AR (p) Model*

The growth rates of China's gross product of agriculture, forestry, livestock, fishery, and agriculture, depicted in Figures 1–5, can be used to make a preliminary visual judgment of the long-term dynamic changes in China's agricultural economy. The next part of this paper is based on a nonlinear MS (M)-AR (p) model with time series data on the growth rates of China's gross product of agriculture, forestry, livestock, fishery, and agriculture. The results show that the growth rates of China's gross product of agriculture, forestry, livestock, fishery, and overall agriculture were stationary at the 5% significance level, while the growth rates of all variables were first-order single integers at the 1% significance level.

The study shows that the AIC, HQ, and SC values of the time series of the growth rate of China's gross agriculture product were the smallest when the model was set to the MSM (3)-AR (3) form. The AIC, HQ, and SC values of the time series of the growth rate of China's gross forestry product were the smallest when the model was set to the MSM (3)-AR (1) form. The AIC, HQ, and SC values of the time series of the growth rate of China's livestock, fishery, and China's agricultural output are all minimized when the model is set in the form of MSM (3)-AR (4). Thus, it is reasonable and reliable to use the MSM (3)-AR (p) model constructed in this paper to investigate the dynamic evolution of China's agricultural economy in terms of the growth region system and its changing dynamics.

The parameter estimation results of the MSM (M)-AR (p) model calculated by different variables are presented in Tables 1 and 2, respectively. The results of the t-statistical test indicate that all values were significant at the 1% or 5% level, except for the growth rate of the total fishery output in the zone system 1 (*s<sup>t</sup>* = 1). This indicates that the model we chose is appropriate. The mean *µ* estimates of the growth rates of the gross product of China's agriculture, forestry, livestock, fishery, and agricultural industries are all consistent with the parameter constraints *µ*<sup>1</sup> < *µ*<sup>2</sup> < *µ*<sup>3</sup> (Tables 1 and 2). Therefore, the growth rates of each variable are considered as the low-growth regime, medium-growth regime, and rapid-growth regime for regime 1, regime 2, and regime 3, respectively.

Note: "\*\*\*", "\*\*", and "\*" indicate significance at the 1%, 5%, and 10% levels, respectively.

**Table 2.** *Cont.*

Note: "\*\*\*" and "\*\*" indicate significance at the 1% and 5% levels, respectively.

#### *3.3. The Dynamic Shift Probabilities of China's Agricultural Growth Regime*

Based on the time series data of the growth rates of total output value of Chinese agriculture, forestry, livestock, fishery and overall agricultural in China, we calculated the dynamic shift probabilities of China's agricultural economic growth regimes using Equation (3). The results are presented in Tables 3–7, respectively. We can see that the probability of staying at a low-growth rate for the agriculture sector is 0.9133 (*p*<sup>11</sup> = 0.9133), and the probability of shifting to the medium or fast growth range is very low, corresponding to A and B, which respectively, indicates that the agriculture sector is likely to maintain a low-growth state (Table 3). The probability of staying in the medium-growth range for agriculture is only 0.0548, while the probability of shifting to the low-growth range is as high as 0.9452 (*p*<sup>21</sup> = 0.9452), and there is almost no possibility of shifting to the high-growth range. This reinforces the high probability of maintaining a low-growth rate for the agriculture sector.

The probability of maintaining a high-growth range for the agriculture is relatively high at 0.5588 (*p*<sup>33</sup> = 0.5588), but the probability of falling back to a medium-growth state is also relatively high (0.4421). Since the probability of agriculture maintaining the medium-growth state is very low and the probability of shifting to the low-growth state is very high 0.9452 (*p*<sup>21</sup> = 0.9452), the probability of falling back from the fast-growth state to the medium-growth state through the medium-growth state to the low-growth state is also very high. Again, the result shows that the probability of maintaining the low-growth rate in the agriculture sector is high.

Overall, the probability of staying at the low-growth state for the agriculture sector is very high, while the probability of shifting to the medium or fast rate range is very low. Moreover, the probability of falling from a medium to a low-speed state and of falling from a fast state to a low-speed state through a medium-speed state is very high. Therefore, agriculture in China clearly tends to maintain a low-growth rate.

**Table 3.** Transfer probability matrix of the regime for the growth rate of the gross agriculture product.

The probability of forestry maintaining the low and medium speed states are both very high at 0.8937 (*p*<sup>11</sup> = 0.8937) and 0.9774 (*p*<sup>22</sup> = 0.9774), respectively, and the probability of shifting to other states is very small (Table 4). The probability of maintaining forestry in the fast-growth state is close to zero, while the probability of shifting to the low and medium speed states is very high, 0.6109 (*p*<sup>31</sup> = 0.6109) and 0.3891 (*p*<sup>32</sup> = 0.3891), respectively. This indicates that forestry will likely maintain a low to medium-growth state and has the highest probability of staying in the medium-growth state.

**Table 4.** Transfer probability matrix of the regime of the growth rate of the gross forestry product.

The probability of maintaining a low-growth state in the livestock sector is very high 0.9063 (*p*<sup>11</sup> = 0.9063), while the probability of shifting to either the medium or high growth range is low 0.0937 (*p*<sup>12</sup> = 0.0937) and close to zero, respectively (Table 5). Therefore, it is relatively easy for the livestock industry to maintain a low-growth range. At the same time, the probability that the livestock sector maintains a fast-growth state is relatively high 0.6609 (*p*<sup>33</sup> = 0.6609), but the probability of maintaining a medium-growth range is very low.

**Table 5.** Transfer probability matrix of the regime of the growth rate of the gross livestock production.

The probability of shifting China's total fishery output from the low-growth range to the medium-growth range and the fast-growth range is *p*<sup>12</sup> = 0.5515 and *p*<sup>13</sup> = 0.4464, respectively. The probability of maintaining a particular growth rate is highest sustaining fast-growth (*p*<sup>33</sup> = 0.8026) followed by keeping at medium (*p*<sup>22</sup> = 0.7345) and low (*p*<sup>11</sup> = 0.0020) growth (Table 6). It can be seen that the probability of maintaining the total fishery output value in the low-growth range is very low, and it is easy to climb from the low-growth state to the medium- and high-growth state. There is a high probability of maintaining the medium-growth state and high-growth state, and it is easy to maintain the medium- and high-growth state, so China's fishery industry has a very good developmental trend.

The probability of transferring China's total fishery output value from the mediumgrowth regime back to the low-growth regime is *p*<sup>21</sup> = 0.2646, and the probability of transferring from the fast-growth regime to the medium-growth regime is *p*<sup>32</sup> = 0.1974. The probability of shifting from the "fast-growth regime" to the "medium-growth regime" is close to zero. Therefore, the probability of shifting from a higher growth state to a lower growth state is low, which indicates a more stable development trend of fisheries.

**Table 6.** Transfer probability matrix of regimes for the growth rate of the gross fishery product.

From the results of the transfer probability matrix of China's gross agricultural product, the maintaining probabilities of the low-, medium-, and rapid-growth regime of the gross agricultural product are *p*<sup>11</sup> = 0.8425, *p*<sup>22</sup> = 0.5909, and *p*<sup>33</sup> = 0.8020, respectively (Table 7). This indicates that China's gross agricultural product does not easily change its growth

status when it is in different regimes, and it has certain inertia characteristics. When China's gross agricultural product is in the low-growth regime, it does not easily change to a higher growth rate, but when the level of agricultural development increases significantly, the gross agricultural product easily stays in the medium-growth regime and the rapid-growth regime and does not decline significantly.

It is clear that the probability of gross agricultural product climbing from the lowgrowth regime to the medium-growth regime is low (*p*<sup>12</sup> = 0.1575), and essentially does little to possibly jump from the low-growth regime to the rapid-growth regime, while the probability of transferring the gross agricultural product from the medium-growth regime to the rapid-growth regime is relatively high (*p*<sup>23</sup> = 0.3999). Thus, when the gross agricultural product is in the low-growth regime, it is difficult to achieve a significant increase due to the limitation of resources and technical facilities. When the gross agricultural product is in the medium-growth regime, the existing capital and technology advantages can be fully utilized to achieve a smooth transition from the medium-growth regime to the rapid-growth regime. The rise from the medium-growth regime to the rapid-growth regime is smooth.

The probability of change of China's gross agricultural product falling back from the medium-growth regime is *p*<sup>21</sup> = 0.0092, while the probability of change from the fastgrowth regime to the low-growth regime is relatively low (*p*<sup>31</sup> = 0.1980). At the same time, the probability of change of gross agricultural product falling back from the rapid-growth regime to the medium-growth regime is close to zero. Thus, it is clear that the probability of a decline in gross agricultural product from the medium-growth regime is not high, and the gross agricultural product has a relatively stable development trend. In addition, when the gross agricultural product is in the rapid-growth regime, it does not decrease to the medium-growth regime. Therefore, the national strategy of modernizing agricultural development has achieved significant results during the sample period.

The overall improvement of China's agricultural production conditions and mechanization level in recent years has laid a good foundation for the development of agricultural facilities. Coupled with the Chinese government's rational planning and allocation of resources and active financial support policies, China's agricultural production modernization level has maintained steady and rapid growth. China's existing agricultural policies have achieved positive results.

**Table 7.** Transfer probability matrix of growth rate regime of China's gross agricultural product.

#### *3.4. Estimated Average Duration of Each Regime of China's Agricultural Economy*

We calculated the average durations of the growth rates of China's agriculture, forestry, livestock, fisheries, and overall agriculture for each growth rate (Table 8). Combining the maintenance probabilities given in Tables 3–7, and considering the average duration presented in Table 8, we further examined the dynamic characteristics of the variables in different regimes. The probability that China's gross agriculture product is in the lowgrowth regime is *p*<sup>11</sup> = 0.9133 maintained with an average duration of 11.54 quarters. This indicates that the lower level of development of the agriculture is more inclined to maintain a low rate of growth and will not make a significant leap to a state of rapid growth.

At the same time, the probability of maintaining a fast-growth state for the gross agriculture product is *p*<sup>33</sup> = 0.5588, and 2.27 quarters of average duration. The gross agriculture product can be stabilized in the rapid-growth regime with a moderate probability of maintenance in the short-term. When the gross agriculture product is in the

medium-growth regime, the maintenance probability is *p*<sup>22</sup> = 0.0548 with an average duration of 1.06 quarters. The probability and average duration of sustaining agriculture in the medium-growth regime are low. Overall, China's agriculture is most likely to remain in the low-growth regime and is the least likely to be in the medium-growth regime among all regimes.

The probability that China's gross forestry product is in the low-growth regime is *p*<sup>11</sup> = 0.8937 with an average duration of 9.41 quarters and has the inertia characteristic of maintaining a low-growth rate. The probability of maintaining the medium-growth rate of forestry product is higher *p*<sup>22</sup> = 0.9774 with an average duration of 44.19 quarters, and the gross forestry product tends to maintain the medium-growth regime. The probability of maintaining the forestry product in the rapid-growth regime is close to zero with an average duration of 1.00 quarter. On balance, the gross forestry product tends to maintain a medium-growth rate over a longer time horizon, with a possible shift to a low-growth regime but a difficult shift to a rapid-growth regime.

The probabilities of maintaining medium- and fast-growth in the gross livestock product are *p*<sup>22</sup> = 0.0066 and *p*<sup>33</sup> = 0.6609 with 1.01 and 2.95 quarters of average duration, respectively. The probability that the gross product of livestock is in the low-growth regime is the highest among all regimes (*p*<sup>11</sup> = 0.9063) and has an average duration of 10.67 quarters. Overall, the gross product of the livestock sector is more likely to remain in the low-growth regime, the least likely to remain in the medium-growth regime, and moderately likely to be in the rapid-growth regime.

The probability of maintaining low growth in China's gross fishery product was the lowest among all regimes (*p*<sup>11</sup> = 0.0020) and only showed an average duration of 1.00 quarter. The probabilities of maintaining medium- and rapid-growth rates were *p*<sup>22</sup> = 0.7345 and *p*<sup>33</sup> = 0.8026, with 3.77 and 5.07 quarters average duration, respectively. This indicates that the gross fishery product is more likely to achieve medium- and highgrowth rates and has the highest probability of being in a fast-growth state and the lowest probability of being in a low-growth state.

**Table 8.** Estimated average duration of each regime (quarters).

The average duration of the gross agricultural product in the low-growth regime was relatively long, with an average duration of 6.35 quarters, while the average duration in the rapid-growth regime was also relatively long (Table 8). However, the average duration in the medium-growth regime was relatively short, at 2.44 quarters. At the same time, the probability that China's gross agricultural product will remain in the low-growth regime and rapid-growth regime was high (*p*<sup>11</sup> = 0.8425, *p*<sup>33</sup> = 0.8020), and the probability of medium-growth was lower (*p*<sup>22</sup> = 0.5909). This indicates that China's gross agricultural product is more likely to be in the low-growth regime and rapid-growth regime, and less likely to be in the medium-growth regime.

#### *3.5. Filter Probability and Smoothing Probability*

In the next section, the dynamic paths of the time series trajectories of the growth rates of each variable are clarified by depicting the smoothed probabilities of the gross

product value of China's agriculture, forestry, livestock, fishery, and overall agriculture industries in each growth regime. In the smoothed probabilities of the low-growth regime (probability of *s<sup>t</sup>* = 1:Pr(*s<sup>t</sup>* = 1 *<sup>ξ</sup>t*|*<sup>t</sup>* ) > 0.5), medium-growth regime (probability of: *s<sup>t</sup>* = 2:Pr(*s<sup>t</sup>* = 2 *<sup>ξ</sup>t*|*<sup>t</sup>* ) > 0.5), and rapid-growth regime (probability of *s<sup>t</sup>* = 3: Pr(*s<sup>t</sup>* = 3 *<sup>ξ</sup>t*|*<sup>t</sup>* ) > 0.5), *<sup>ξ</sup>t*|*<sup>t</sup>* refers to all information sets based on past *t* periods. *Sustainability* **2021**, *13*, 6134 15 of 29 Overall, we found that China's gross agriculture product generally fluctuated between the rapid-growth regime and the medium-growth regime but was able to maintain

The growth rates of China's gross product of agriculture, forestry, livestock, fishery, and overall agricultural industries changed frequently and dynamically among various regimes during the development of China's agricultural economic growth, and the dynamic paths of the growth rates of each variable in each regime will be further detailed in this paper. Within the sample interval studied, the gross agriculture product was in the rapidgrowth regime during (a) Q2 to Q4 2004, (b) Q1 2006, (c) Q4 2007 to Q1 2008, and (d) Q1 to Q4 2010 (Figure 6). Looking back at history, it is easy to see that these particular timeframes correspond to the launch of relevant policies in China (Appendix A, Table A1). For example in 2004, the first "Document No. 1" of the century was issued, which introduced the "three subsidies" policy, namely "direct subsidies for farmers, subsidies for good seeds, and subsidies for the purchase of agricultural machinery, and minimum purchase price for rice." a relatively stable growth rate when it was in the low-growth regime. However, when in the low-growth regime, the growth rate remained relatively stable and had a more consistent smoothing probability. In the time domain selected in this paper, the gross agriculture product in the low-growth regime basically coincided with the occurrence of natural disasters, such as floods and snowstorms. This judgment is consistent with the phenomena revealed in Tables 3 and 8. That is, it is difficult for China's gross agriculture product to remain in the rapid-growth regime or medium-growth regime in general, but it tends to stay in the low-growth regime. Unlike prior literature, the model in this paper captures the rapid-growth regime of Chinese agriculture around 2006 and 2008, suggesting that the model in this paper is more accurate in modeling real fluctuations in economic development.

**Figure 6.** Filter probability and smoothing probability of gross agriculture product located in different growth regimes. Note: The green arrows mark the times when important policies were in-**Figure 6.** Filter probability and smoothing probability of gross agriculture product located in different growth regimes. Note: The green arrows mark the times when important policies were introduced.

troduced. We can see from Figure 7 that in the early part of this century, China's agricultural development, including forestry, was greatly affected by the *soft landing* of China's macroeconomics. In the case of forestry, the gross forestry product showed more dramatic fluctuations at the beginning of the 20th century, with more frequent cyclical fluctuations. Coupled with the sudden impact of natural disasters on forestry development, the process of change in gross forestry product showed a direct fall from the rapid-growth regime to the low-growth regime and was less often in the medium-growth regime. In 2006, China completely abolished all agricultural taxes except the tobacco tax nationwide. In 2009, the Chinese government implemented the property rights policy of giving farmers fuller and more secure rights to contracted land management, and indicated that the existing land contract relationship would remain stable and unchanged for a long time. This injected confidence and vitality into the agricultural economy. In 2010, the government clearly proposed to give full play to the effective allocation of resources to promote agricultural development, and to improve the efficiency of agricultural development by improving the allocation of resource factors.

Under a series of effective policy measures, China's agriculture has achieved remarkable results and has been in the rapid-growth regime for a long period of time. However, China's gross agriculture product still fell into the medium-growth regime during Q1 2005, Q2 2006, and Q2 2008. It was in the low-growth rate during the periods from (a) Q4 2001 to Q1 2004, (b) Q2 to Q4 2005, (c) Q3 2006 to Q3 2007, (d) Q3 2008 to Q4 2009, and (e) Q1 2011 to Q1 2018.

Overall, we found that China's gross agriculture product generally fluctuated between the rapid-growth regime and the medium-growth regime but was able to maintain a relatively stable growth rate when it was in the low-growth regime. However, when in the low-growth regime, the growth rate remained relatively stable and had a more consistent smoothing probability. In the time domain selected in this paper, the gross agriculture product in the low-growth regime basically coincided with the occurrence of natural disasters, such as floods and snowstorms.

This judgment is consistent with the phenomena revealed in Tables 3 and 8. That is, it is difficult for China's gross agriculture product to remain in the rapid-growth regime or medium-growth regime in general, but it tends to stay in the low-growth regime. Unlike prior literature, the model in this paper captures the rapid-growth regime of Chinese agriculture around 2006 and 2008, suggesting that the model in this paper is more accurate in modeling real fluctuations in economic development.

We can see from Figure 7 that in the early part of this century, China's agricultural development, including forestry, was greatly affected by the *soft landing* of China's macroeconomics. In the case of forestry, the gross forestry product showed more dramatic fluctuations at the beginning of the 20th century, with more frequent cyclical fluctuations. Coupled with the sudden impact of natural disasters on forestry development, the process of change in gross forestry product showed a direct fall from the rapid-growth regime to the low-growth regime and was less often in the medium-growth regime. *Sustainability* **2021**, *13*, 6134 16 of 29

**Figure 7.** Filter probability and smoothing probability of gross forestry product located in different growth regimes. Note: The green arrows mark the times when important policies were intro-**Figure 7.** Filter probability and smoothing probability of gross forestry product located in different growth regimes. Note: The green arrows mark the times when important policies were introduced.

duced. During the periods from Q2 2001 to Q4 2001 and Q2 2002 to Q4 2002, China's gross forestry product was in the low-growth regime, and, during Q1 2002 and Q1 2003, China's gross forestry product was in the rapid-growth regime. In 2002, the Chinese government promulgated the *Regulations on Returning Farmland to Forestry* to promote the development of forestry, which solved the inherent problems in forestry development while expanding the area of forestland and laid the policy foundation for sustainable development of for-During the periods from Q2 2001 to Q4 2001 and Q2 2002 to Q4 2002, China's gross forestry product was in the low-growth regime, and, during Q1 2002 and Q1 2003, China's gross forestry product was in the rapid-growth regime. In 2002, the Chinese government promulgated the *Regulations on Returning Farmland to Forestry* to promote the development of forestry, which solved the inherent problems in forestry development while expanding the area of forestland and laid the policy foundation for sustainable development of forestry (Appendix A, Table A1).

estry (Appendix A, Table A1). In 2003, the Chinese government further promulgated the *Decision on Accelerating the Development of Forestry*, which provided concrete measures for forestry development by adjusting the structure of forestry industry and strengthening the construction of forestry bases (refer to the attachment for details). This series of policies and measures strongly promoted the development of forestry and the process of forestry modernization. The In 2003, the Chinese government further promulgated the *Decision on Accelerating the Development of Forestry*, which provided concrete measures for forestry development by adjusting the structure of forestry industry and strengthening the construction of forestry bases (refer to the attachment for details). This series of policies and measures strongly promoted the development of forestry and the process of forestry modernization. The gross forestry product entered the medium-growth regime from Q2 2003 to Q3 2014.

gross forestry product entered the medium-growth regime from Q2 2003 to Q3 2014. However, China's gross forestry product was in the low-growth regime from Q4 2014 to Q1 2018. From the smoothed probability time dynamics trajectory shown in Figure 7, However, China's gross forestry product was in the low-growth regime from Q4 2014 to Q1 2018. From the smoothed probability time dynamics trajectory shown in Figure 7, whether in the low-growth regime, medium-growth regime or rapid-growth regime, the

whether in the low-growth regime, medium-growth regime or rapid-growth regime, the smoothed probability of China's gross forestry product in different regimes were all close

At the beginning of this century, the gross livestock product, which has a certain scale but is still immature in general, was basically in the low-growth regime due to the influence of the soft landing of China's economy (Figure 8). Several factors caused China's grow livestock product to drop from a rapid-growth to a low-growth regime. In 2004, the No. 1 Document encouraged the continuous improvement of feed, technology, equipment, and other inputs. In addition, there was increasing industry maturity in the pro-

In 2006, under the influence of the policy of abolishing agricultural tax and benefiting farmers, China's gross livestock product stepped into the rapid-growth regime again, fluctuating back and forth until falling back to a low-growth regime in 2009. In 2011, stimulated by the policy of accelerating the construction of water resources and infrastructure, it again entered the rapid-growth regime. From 2001 to 2012, there was an interaction between the rapid-growth regime and the low-growth regime, with a long-term low-growth regime after 2012. Unlike previous studies, our model sensitively captures the rapid-

product was more effective.

cessing of both dairy and meat products.

smoothed probability of China's gross forestry product in different regimes were all close to the 1.00 level. This shows that the risk prevention and control of China's gross forestry product was more effective.

At the beginning of this century, the gross livestock product, which has a certain scale but is still immature in general, was basically in the low-growth regime due to the influence of the soft landing of China's economy (Figure 8). Several factors caused China's grow livestock product to drop from a rapid-growth to a low-growth regime. In 2004, the No. 1 Document encouraged the continuous improvement of feed, technology, equipment, and other inputs. In addition, there was increasing industry maturity in the processing of both dairy and meat products. *Sustainability* **2021**, *13*, 6134 17 of 29 growth regime of China's livestock industry from (a) 2003–2005, (b) 2007–2008, (c) 2008– 2009, and (d) 2010–2012, indicating that our model can more accurately simulate agricultural economic development.

**Figure 8.** Filter probability and smoothing probability when the gross livestock product is in different growth regimes. Note: The green arrows mark the times when important policies were introduced. **Figure 8.** Filter probability and smoothing probability when the gross livestock product is in different growth regimes. Note: The green arrows mark the times when important policies were introduced.

China's fisheries industry was also affected by the *soft landing* of China's economy and was developing at a low rate in the early 2000s. However, fisheries entered a rapidgrowth phase starting in 2004 under the influence of the first Document No. 1 (Figure 9). In 2008, the Chinese government introduced policies to strengthen the safety of fishery production, improve regulatory efforts, strengthen fishery production measures, and optimize departmental cooperation to ensure safe fishery production, while establishing a long-term mechanism to maintain sustainable fishery development (Appendix A, Table A1). This series of comprehensive requirements as well as specific initiatives have greatly In 2006, under the influence of the policy of abolishing agricultural tax and benefiting farmers, China's gross livestock product stepped into the rapid-growth regime again, fluctuating back and forth until falling back to a low-growth regime in 2009. In 2011, stimulated by the policy of accelerating the construction of water resources and infrastructure, it again entered the rapid-growth regime. From 2001 to 2012, there was an interaction between the rapid-growth regime and the low-growth regime, with a long-term low-growth regime after 2012. Unlike previous studies, our model sensitively captures the rapid-growth regime of China's livestock industry from (a) 2003–2005, (b) 2007–2008, (c) 2008–2009, and (d) 2010–2012, indicating that our model can more accurately simulate agricultural economic development.

improved the pattern of fishery production, and under the new management mechanism, China's gross fishery production climbed to the medium-growth regime during the periods from Q3 2008 to Q1 2009 and from Q2 2010 to Q4 2012, while China's gross fishery production was in the rapid-growth regime during the periods from Q3 2008 to Q1 2009 and from Q2 2010 to Q4 2012. In general, China's fishery industry has been developing at a medium to high speed for a long time and has achieved a very good development trend. The possibility of China's fishery product moving into a low-growth regime still requires China's fisheries industry was also affected by the *soft landing* of China's economy and was developing at a low rate in the early 2000s. However, fisheries entered a rapid-growth phase starting in 2004 under the influence of the first Document No. 1 (Figure 9). In 2008, the Chinese government introduced policies to strengthen the safety of fishery production, improve regulatory efforts, strengthen fishery production measures, and optimize departmental cooperation to ensure safe fishery production, while establishing a long-term mechanism to maintain sustainable fishery development (Appendix A, Table A1).

special attention. Finally, we can see the basic overview of China's gross agricultural product in the low-growth regime, medium-growth regime, and rapid-growth regime. Specifically, China's agricultural economy was in the rapid-growth regime for 24 quarters in stages throughout the sample period (Figure 10). Looking back at history, during the period when China's gross agricultural product was in rapid growth, the Chinese government had major policies benefiting agriculture (Appendix A, Table A1). This series of comprehensive requirements as well as specific initiatives have greatly improved the pattern of fishery production, and under the new management mechanism, China's gross fishery production climbed to the medium-growth regime during the periods from Q3 2008 to Q1 2009 and from Q2 2010 to Q4 2012, while China's gross fishery production was in the rapid-growth regime during the periods from Q3 2008 to Q1 2009 and from Q2 2010 to Q4 2012. In general, China's fishery industry has been developing at a medium to high speed for a long time and has achieved a very good development trend. The possibility of China's fishery product moving into a low-growth regime still requires special attention.

*Sustainability* **2021**, *13*, 6134 18 of 29

**Figure 9.** Filter probability and smoothing probability when the gross fishery product is in different growth regimes. Note: The green arrows mark the times when important policies were intro-**Figure 9.** Filter probability and smoothing probability when the gross fishery product is in different growth regimes. Note: The green arrows mark the times when important policies were introduced.

duced. Finally, we can see the basic overview of China's gross agricultural product in the lowgrowth regime, medium-growth regime, and rapid-growth regime. Specifically, China's agricultural economy was in the rapid-growth regime for 24 quarters in stages throughout the sample period (Figure 10). Looking back at history, during the period when China's gross agricultural product was in rapid growth, the Chinese government had major policies benefiting agriculture (Appendix A, Table A1). **Figure 9.** Filter probability and smoothing probability when the gross fishery product is in different growth regimes. Note: The green arrows mark the times when important policies were introduced.

In 2004, the Chinese government issued the first No. 1 Document, which introduced direct subsidies for farmers, subsidies for good seeds and agricultural machinery, and subsidies for the purchase of agricultural machinery, and a minimum purchase price for rice, which greatly motivated farmers. In 2006, the agricultural tax regulations were abol-**Figure 10.** Filter probability and smoothing probability when the overall agricultural product is in different growth regimes. Note: The green arrows mark the times when important policies were introduced. **Figure 10.** Filter probability and smoothing probability when the overall agricultural product is in different growth regimes. Note: The green arrows mark the times when important policies were introduced.

ished. The agricultural tax regulations, which had been implemented for nearly 50 years in New China, became historical records, and the system of taxing farmers by the area of land, which had lasted for 2600 years, was retired from the historical precedence. The burden of farmers nationwide was reduced by CNY 133.5 billion per year, and the per capita burden was reduced by about CNY 140. After 2009, the Chinese government implemented the property rights policy of giving farmers fuller and more secure rights to In 2004, the Chinese government issued the first No. 1 Document, which introduced direct subsidies for farmers, subsidies for good seeds and agricultural machinery, and subsidies for the purchase of agricultural machinery, and a minimum purchase price for rice, which greatly motivated farmers. In 2006, the agricultural tax regulations were abolished. The agricultural tax regulations, which had been implemented for nearly 50 years In 2004, the Chinese government issued the first No. 1 Document, which introduced direct subsidies for farmers, subsidies for good seeds and agricultural machinery, and subsidies for the purchase of agricultural machinery, and a minimum purchase price for rice, which greatly motivated farmers. In 2006, the agricultural tax regulations were abolished. The agricultural tax regulations, which had been implemented for nearly 50 years in New

contracted land management and indicated that the existing land contracting relationship would remain stable and unchanged for a long time. In 2010, the Chinese government

in New China, became historical records, and the system of taxing farmers by the area of

implemented the property rights policy of giving farmers fuller and more secure rights to contracted land management and indicated that the existing land contracting relationship would remain stable and unchanged for a long time. In 2010, the Chinese government

land, which had lasted for 2600 years, was retired from the historical precedence.

China, became historical records, and the system of taxing farmers by the area of land, which had lasted for 2600 years, was retired from the historical precedence.

The burden of farmers nationwide was reduced by CNY 133.5 billion per year, and the per capita burden was reduced by about CNY 140. After 2009, the Chinese government implemented the property rights policy of giving farmers fuller and more secure rights to contracted land management and indicated that the existing land contracting relationship would remain stable and unchanged for a long time. In 2010, the Chinese government made it clear that it was committed to giving full play to the role of efficient allocation of resources in promoting agricultural development, and to achieving increased efficiency in agricultural development by improving the allocation of resource factors. This injected confidence and vitality into the agricultural economy, and China's agricultural economy once again entered a high-speed growth regime. As the above-mentioned policy dividend receded, China's total agricultural output value shifts to a low-growth regime after a brief transition to a medium-growth regime.

Overall, China's gross agricultural product generally fluctuated frequently between the rapid-growth regime and the low-growth regime. The medium-growth regime occurred over shorter time periods. After 2012, except for 2016 when it was in the medium-highgrowth range for a short time, China's gross agricultural product was in the low-growth regime for a long time and was able to maintain relative stability (Tables 7 and 8).

The Chinese government has introduced beneficial agricultural policies every year since 2004. However, the growth of China's agricultural economy fluctuated between fast and low growth. After 2012, despite active fiscal policy, and, except for one quarter of fast growth in 2016, it has been in a low growth trend for a long time. This fully illustrates the vulnerability of agricultural economic growth and indicates that the government should pay attention to agricultural development in the long-term and increase policy support.

Comparing Figures 6–10 with Figures 1–5, we can see that the changes in the total output value of the agriculture, forestry, livestock, fishery, and overall agriculture industries show some similarities. Specifically, the time range of the "fast-growth regime" for each industry shown in Figures 5–8 corresponds to the period when the "fluctuation component" is relatively strong as shown in Figures 1–5, and the time range of the low-growth regime for each industry shown in Figures 6–10 corresponds to the period when the "fluctuation component" is relatively calm as shown in Figures 1–5. This implies that the risk of shocks is higher when the growth rate of the total output of each industry was relatively high in the agriculture, forestry, livestock, fishery, and overall agriculture industries and less uncertain when the growth rate of the total output of each industry was relatively low.

#### **4. Discussion**

#### *4.1. Contrast to Prior Studies*

Since China is still a developing country, the level of development of China's rural areas still lags behind that of the developed world, and agricultural production is still the main source of income for many Chinese farmers. Development remains a major issue for the Chinese government now and in the future. Therefore, in order to better understand the implications of our results, we need to compare and contrast our results to previous studies.

First, based on the above-mentioned empirical findings, we found that China's agricultural economy maintained a relatively good development with the support of the benefit agriculture policy during the sample period, i.e., the probability of maintaining China's agricultural economy in the fast-growth regime was *p*<sup>33</sup> = 0.8020 and had an average duration of 5.05 quarters, which is only slightly lower than the average duration of 6.65 quarters in the low-growth regime. This indicates that China's agricultural economy developed relatively well during periods following the agricultural support policies, which is consistent with prior studies [13–15].

Second, we found that the agricultural economy tended to maintain a low-growth rate, with the highest maintenance probability of *p*<sup>11</sup> = 0.8425 and the longest average duration of 6.35 quarters, which is consistent with the results of another study [34], demonstrating

that China's agricultural economy is not easy to move into the expansion phase of its economic cycle. Our results are also consistent with research showing that maintaining rapid long-term growth in the agricultural economy is not easy due to factors such as excessive consumption of natural resources and environmental pollution [2].

A possible reason for this phenomenon is that the law of diminishing marginal returns is particularly evident in traditional agriculture due to natural conditions. Since the amount of resources invested in agriculture, such as land, is fixed, increasing the labor force will not increase the agricultural output significantly, resulting in slow agricultural growth. This pattern is particularly evident in developing countries where technological progress in agriculture is slow. Another possible reason is that since the demand for agricultural products typically lacks elasticity, an increase in the supply of agricultural products will cause the prices of agricultural products to fall, and hence an increase in production will not lead to an increase in income, which will, in turn, lead to a slow growth in agricultural output.

Third, based on the results of our empirical tests, we distinguished three growth statuses of China's agricultural economy—low, medium, and rapid—and we show their specific transfer paths in Figures 6–10. Specifically, China's agricultural economy was in the rapid-growth regime for 24 quarters in stages throughout the sample period. These rapid- growth states are clearly synchronized with the timing of important agricultural policies. Our analysis suggests that the possible reasons for the shifts to the rapid-growth regime are the introduction of major pro-agricultural policies by the Chinese government.

For example, in 2004, the Chinese government issued the first "Document No. 1" in the time period under examination, which introduced "direct subsidies for farmers, subsidies for good seeds and agricultural machinery purchases, and a minimum purchase price for rice," that greatly motivated farmers to produce more agricultural products. China's total agricultural output value also entered a high-growth zone. In 2006, when the agricultural tax regulations were abolished, China changed from an agricultural tax-raising country to an agricultural subsidy country, and the total agricultural output value entered a high-growth zone at the same time. In 2009, the Chinese government implemented the property rights policy of "granting farmers more complete and more secure rights to contracted land management and the existing land contract relationship should remain stable and unchanged for a long time."

From 2009 to 2010, a series of major initiatives for the benefit of farmers were proposed, including improving the policy system for the benefit of farmers, focusing on promoting the allocation of resources to rural areas, promoting the transformation of agricultural development, and improving the level of modern agricultural equipment. It also includes accelerating the improvement of rural people's livelihood, narrowing the gap between the development of urban and rural public utilities, coordinating the reform of urban and rural areas, and enhancing the vitality of agricultural and rural development. This was intended to enhance the vitality of agricultural and rural development, to promote urbanization actively and steadily, with the development of small and medium-sized cities and small towns as the focus, and to deepen the reform of the household registration system, etc. This has injected confidence, capital, technology, and vitality into China's agricultural economy, which has once again stepped into a high-speed growth regime. The above results support the findings of Qiao et al. [12], Jin and Deininger [13], Deininger et al. [14], and Xi et al. [32] that demonstrated agricultural growth is influenced by policies and institutions.

In addition, our research results show that China's agriculture, forestry, and animal husbandry tended to grow at a low rate. It was in the low-growth regime for a long time after 2011. The recent low-growth rate of the Chinese agricultural economy has been previously documented [34]. Policymakers should pay attention to this issue and continue to rely on agricultural support policies to avoid food shortages in China as well as adverse macroeconomic outcomes.

In this paper, the causal explanation of the correlation between agricultural economic cycles and government support policies is based on the common sense judgment of temporal synchronization and is not the result of empirical studies constructed using specialized

models, such as Data Envelopment Analysis (DEA), Common Agricultural Policy Regionalized Impact (CAPRI), Propensity Score Matching (PSM), and other modeling methods. Hence, the generalizability of our results may be limited. Using specialized policy efficiency assessment models to evaluate the efficiency of agricultural support policies in China may be a fruitful, future research direction.

#### *4.2. Policy Recommendations*

Since China is still a developing country. The level of development of China's rural areas still lags behind that of the developed world, and agricultural production is still the main source of income for many Chinese farmers. Development remains a major issue for the Chinese government now and for the foreseeable future. Therefore, based on the results of our study, we propose the following policy recommendations.

First, there is a large body of theoretical and empirical research that shows a strong correlation between agricultural policy and agricultural development. China's current agricultural policies have achieved relatively good results. Therefore the current agricultural policy in the form of the annual Central Government Document No. 1 should be continued.

Secondly, agriculture, forestry, animal husbandry, and fisheries each have their own industry characteristics. Past research results show that the impacts of policies are rather limited with the exception of fisheries. Therefore, the formulation of agricultural policies in line with the development characteristics and stages of each industry may achieve better policy results.

Finally, China is a vast country with a wide range of regional development levels, and the geographical characteristics of agricultural development vary. Therefore policymakers should consider this situation and delegate policy-making authority to provincial governments or lower institutions. This is especially true for autonomous regions, autonomous prefectures, and even autonomous counties that are less developed. These institutions may be able to develop policies in their own regions that are more in line with the level of local agricultural development. Financial and policy supports from the central government could be channeled to allow for more local control if policy makers can be convinced that this improves productivity. Thus, it may be possible to promote the development of Chinese agriculture better than the current grand unified agricultural policy.

Because this study is not an assessment of the effectiveness of current agricultural policies in China, the above policy recommendations may be somewhat biased. Our next research aims to specifically assess the policy efficiency of China's current agricultural policies. Therefore it may be possible to make more nuanced policy recommendations that are more in line with China's agricultural development after completing this additional research.

#### **5. Conclusions**

Based on the above findings and discussion, it can be concluded that China's agricultural economy has achieved relatively good development in the context of the country's rapid macroeconomic development and agricultural policies, especially the fishery industry, which has been able to maintain medium to high-growth rates. However, in the long-term, China's agricultural economy tends to maintain a low-growth rate. Since 2011, China's agriculture, forestry, and livestock industries have mostly maintained low-growth rates. In order to maintain agricultural development in China, the Chinese government should continue its current agricultural support policies, especially increasing support for the agriculture, forestry, and livestock industries. Future research should focus on using specialized policy assessment models to evaluate the efficiency of agricultural support policies in China.

**Author Contributions:** Conceptualization, X.G., J.S., R.Z., and C.W.; methodology, X.G., J.S., and P.L.; formal analysis, X.G., J.S., and C.W.; writing—original draft preparation, X.G. and J.S.; writing reviewing and editing, X.G., P.L., and R.Z.; supervision, P.L. and C.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable for studies not involving humans or animals.

**Informed Consent Statement:** Not applicable for studies not involving humans.

**Data Availability Statement:** The data presented in this study are available in article.

**Acknowledgments:** We gratefully acknowledge Yu Zhu for his comments and suggestions for improvement, and Yudong Chen for checking the paper. Similarly, we also thank Qiusheng Zhang, Li Li, Changsheng Gao, Zisheng Fang, Xinsheng Deng, Qing Chang, Dehong Liu, and Zizheng Wu for their advice and help with the paper. Finally, we are particularly grateful to Aaron K. Hoshide for his editorial comments and to the two anonymous reviewers for their review comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** Summary of the Chinese government's main agricultural support policies from 2002–2018.

are protected. The contracted land plots are identified, registered, and certified.

#### **References**