**3. Empirical Results and Discussion**

This section analyzes and discusses the efficiency results of ASTI from the static and dynamic perspective. In addition, we further classify the ASTI level of the G20 countries through the results of efficiency measurement and capability evaluation. All of the computations were performed with the help of DEAP2.1.

#### *3.1. Comprehensive Efficiency Analysis of ASTI*

#### 3.1.1. Overall Analysis of the Comprehensive Efficiency of ASTI

Figure 2 shows the measurement results for the static comprehensive efficiency of ASTI in the G20 countries from 2008 to 2017. A value equal to 1 represents that the ASTI of a country is efficient, while smaller values mean it is more inefficient. Brazil, China, India, Indonesia, Saudi Arabia, and the United States were all efficient from 2008 to 2017, while Italy, Japan, and the Republic of Korea were inefficient during those 10 years. The other 10 countries (Argentina, Australia, Canada, France, Germany, Mexico, the Russian Federation, South Africa, Turkey, and the United Kingdom) changed alternately between efficiency and inefficiency. It is worth noting that the countries that have been efficient during the 10 years include both developed countries (the United States) and developing countries (Brazil, China, India, Indonesia, and Saudi Arabia). This means that innovation efficiency is dependent not only on more innovation investments. Optimized translation from inputs into outputs will lead to high innovation efficiency.

**Figure 2.** Comprehensive efficiency of ASTI in the period 2008–2017.

Due to the different levels of economic development and agricultural development, there are obvious differences in ASTI inputs between the G20 developed countries (Australia, Canada, France, Germany, Italy, Japan, the Republic of Korea, the United Kingdom, and the United States) and the G20 developing countries (Argentina, Brazil, China, India, Indonesia, Mexico, the Russian Federation, Saudi Arabia, South Africa, and Turkey). Figures 3 and 4 describe the efficiency range and efficient proportion of ASTI in the G20 developed countries and the G20 developing countries from 2008 to 2017.

The efficiency range refers to the difference value between the maximum and minimum values of the comprehensive efficiency, which is used to reflect the balance of the comprehensive efficiency development. The efficiency range of the G20 developed countries stabilized within 0.3–0.5, with no obvious change, reaching the highest value of 0.568 in 2016. The efficiency range of the G20 developing countries was relatively large (0.1–0.9), reaching the highest value of 0.872 in 2009. The above shows that, compared with developed countries, the development of comprehensive efficiency in developing countries is unbalanced. This is because developed countries generally attach importance to ASTI, while developing countries pay more or less attention to it.

**Figure 4.** Efficient proportion of ASTI.

The efficient proportion represents the proportion of the number of countries that were efficient to the total number of countries, which is used to reflect the overall development level of the comprehensive efficiency. It could be seen that the G20 developed countries showed a fluctuating downward trend, with the highest proportion of 56% in 2014 and the lowest proportion of 11% in 2012. The G20 developing countries showed an upward trend, from the lowest proportion of 50% in 2009 to the highest proportion of 80% in 2015 and 2017. The reason for this result is that the investment of ASTI in developed countries has been at a high level for a long time. When the increase of inputs is lower than the increase of outputs, the efficiency will decline. However, with the emphasis on ASTI in developing countries, the output increases rapidly with the increasing input, which promotes the improvement of efficiency.

#### 3.1.2. Input Redundancy and Output Deficiency of ASTI

If R&D resources are not used effectively, additional investment may be of little help in stimulating scientific and technological progress [29]. In this section, we analyze the input redundancy and output deficiency to investigate the binding constraints to higher efficiency. Table 4 shows the input redundancy frequency and output deficiency frequency of ASTI for 13 countries (Argentina, Australia, Canada, France, Germany, Italy, Japan, the Republic of Korea, Mexico, the Russian Federation, South Africa, Turkey, and the United Kingdom) during 2008–2017. Brazil, China, India, Indonesia, Saudi Arabia, and the United States all achieved efficiency in ASTI from 2008 to 2017, so there was no input redundancy and output deficiency. A frequency of 0 means that there is no input redundancy or output deficiency in the country during these 10 years; a frequency of 1–4 means that input redundancy or output deficiency happens occasionally; and a frequency of 5–10 means that input redundancy or output deficiency happens frequently.

There are input redundancy and output deficiency in both the G20 developed and developing countries. From the perspective of input indicators redundancy, R&D personnel redundancy occurred frequently (5–10) in Japan and the Russian Federation, while R&D expenditure redundancy occurred frequently (5–10) in Canada, France, Italy, the Republic of Korea, South Africa, and the United Kingdom. The output deficiency mainly focuses on the scientific and technological output, while the economic performance performs well. The countries with a higher frequency (5–10) of agricultural journal papers deficiency include Germany, Japan, the Republic of Korea, the Russian Federation, and Turkey. The countries with a higher frequency (5–10) of agricultural patents deficiency include Argentina, South Africa, and Turkey.


**Table 4.** Input redundancy frequency and output deficiency frequency of ASTI in the period 2008–2017.

We further investigated the factors reducing the static comprehensive efficiency of the inefficient countries over the years 2008–2017. Taking 2017 as an example (see Table 5), there are nine inefficient countries: Canada, France, Germany, Italy, Japan, the Republic of Korea, the Russian Federation, Turkey, and the United Kingdom. In terms of the input redundancy, France (0.30), Germany (0.13), the Republic of Korea (0.16), the Russian Federation (0.63), and Turkey (0.09) have R&D personnel redundancy; Canada (0.21), France (0.05), Italy (0.16), the Republic of Korea (0.26), and the United Kingdom (0.06) have R&D expenditure redundancy; therefore, these countries can appropriately reduce related R&D investments. In terms of the output deficiency, Germany (0.51), Japan (3.09), the Republic of Korea (0.11), the Russian Federation (7.00), and Turkey (2.46) are deficient in agricultural journal papers; the Russian Federation (2.90) and Turkey (0.88) are deficient in agricultural patents; therefore, these countries should pay more attention to the two scientific and technological outputs. In addition, 0.00 represents no input redundancy or output deficiency, which means these inputs and outputs of the country have already been optimized.

**Table 5.** Input redundancy and output deficiency of ASTI in G20 countries in 2017.


#### *3.2. Total Factor Productivity Analysis of ASTI*

This section applies the DEA-Malmquist index model to calculate the dynamic total factor productivity change (TFPC) of ASTI for G20 countries from 2008 to 2017 and decomposes TFPC of ASTI under time dimension and spatial dimension to investigate the sources of efficiency change.

#### 3.2.1. TFPC Decomposition of ASTI under Time Dimension

Table 6 shows the TFPC decomposition of ASTI for G20 countries at different stages. A value of less (more) than 1 represents decline (growth), and a value equal to 1 shows no change. The mean value of TFPC for G20 countries is 0.981 in the period 2008–2017, a 1.9% decline in the Total Factor Productivity (TFP). The mean value of technological change (TC) is 0.974, while the mean value of Technical Efficiency Change (TEC) is 1.008, indicating that the decline of Total Factor Productivity (TFP) of ASTI was caused by the decline of TC greater than the growth of Technical Efficiency (TE). The mean value of Pure Efficiency Change (PEC) is 1.000, that is, pure efficiency (PE) kept unchanged. Thus, a 0.8% increase in Scale Efficiency (SE) improves the TE of ASTI in G20 countries.

**Table 6.** TFPC decomposition of ASTI in the period 2008–2017 under time dimension.


The TFPC of ASTI in 2008–2017 could be divided into four stages. The first stage (2008–2009) was the decline stage: the TFP of ASTI fell by 17.4%, which was caused by the decline in TE (falling by 12.9%) and TC (falling by 5.1%) simultaneously. The second stage (2009–2011) is the growth stage with a 21.7% growth from 2009 to 2010 and a 1.7% growth from 2010 to 2011. The growth of TFP of ASTI during 2009–2010 was driven by the synchronous growth of TE (increasing 6.3%) and TC (increasing 14.4%), while it was driven by TC (increasing 14.4%) during 2010–2011. The third stage (2011–2016) was the continuous decline stage: the TFP of ASTI declined by 5.5%, 6.3%, 11%, 4.2%, and 2.4%, respectively. It was mainly caused by the decline in TC. The fourth stage (2016–2017) is to resume growth. Due to the simultaneous growth of TE (increasing by 7.9%) and TC (increasing by 3.5%), the TFP of ASTI for G20 countries rose by 11.7%. The above alternating trend of "decline–growth–continuous decline–growth recovery" of TFPC decomposition indicates that the efficiency of ASTI for G20 countries was in a period of constant adjustment.

The TFPC decomposition of ASTI in G20 developed and developing countries is presented in Table 7. The G20 developed countries experienced an increment during 2009–2012, a decline during 2013–2015, and an increment again during 2015–2017. The G20 developing countries showed a fluctuating upward trend of TFPC.

**Table 7.** TFPC decomposition of ASTI in G20 developed and developing countries under time dimension.


#### 3.2.2. TFPC Decomposition of ASTI under Spatial Dimension

As shown in Table 8, seven G20 countries (Saudi Arabia, Japan, China, Mexico, the Republic of Korea, the Russian Federation, and Argentina) (37%) have shown growth in TFP of ASTI (TFPC > 1) during 2008–2017. Among them, Saudi Arabia, Japan, and China saw the larger growth, with increases of 11.4%, 7.5%, and 6.6% respectively; Mexico and the Republic of Korea saw growth of 3.9% and 2.8%, respectively; and the Russian Federation and Argentina saw smaller growth, with increases of 0.6% and 0.4% respectively. The TFP of ASTI for 12 countries (Australia, Turkey, the United States, South Africa, France, Indonesia, India, Italy, Germany, Brazil, the United Kingdom, and Canada) (63%) declined from 2008 to 2017 (TFPC < 1). Australia, Turkey, the United States, South Africa, and Indonesia fell 0–5%; India, Italy, Germany, and Brazil fell 5–10%; and the United Kingdom and Canada fell by more than 10%.


**Table 8.** TFPC decomposition of ASTI in the period 2008–2017 under spatial dimension.

The influencing factors of TFPC of ASTI were identified, as shown in Tables 9 and 10. As shown in Table 8, the growth for China and Saudi Arabia in TFP of ASTI was due to the improvement in TC (TC > 1, TEC ≤ 1). The growth for Japan, Mexico, the Republic of Korea, the Russian Federation, and Argentina was attributed to the improvement in TE (TEC > 1, TC ≤ 1), where two countries (the Republic of Korea and the Russian Federation) were driven by SE (SEC > 1) only and three countries (Japan, Mexico, and Argentina) by the synchronous improvements of SE and PE (SEC > 1, PEC > 1).

**Table 9.** Sources for growth of TFPC of ASTI.



**Table 10.** Sources for decline of TFPC of ASTI.

The sources for decline of TFP of ASTI is shown in Table 10. Eight countries (Australia, Turkey, the United States, France, Indonesia, India, Italy, and Brazil) were because of the decrease in TC (TC < 1, TEC ≥ 1), while four countries (South Africa, Germany, the United Kingdom, and Canada) were attributed to the synchronous decrease in TE and TC (TC < 1, TEC < 1). Among them, the source for decline in South Africa is SE (SEC < 1), Germany is PE (PEC < 1), and the United Kingdom and Canada showed declines due to the decrease of SE and PE (PEC < 1, SEC < 1).

#### *3.3. Classification and Change Analysis of National ASTI level*

The innovation efficiency and innovation capability are two important aspects of national ASTI level [50,51]. The efficiency of ASTI focuses on the relationship of transformation from input to output, that is, whether more output can be obtained under the given input or less input can be invested under the given output. The capability of ASTI is a comprehensive performance from the joint influence of input and output [46]. The efficiency of ASTI concentrates on innovation quality, while the capability of ASTI focuses on innovation quantity. This study integrated the analysis of the efficiency and capability of ASTI to locate the type of ASTI level and identify the type change for each G20 country, from both the innovation "quality" and "quantity" aspects.

According to the rankings of efficiency measurement of ASTI, countries ranked 1–10 are called "efficiency superior" and countries ranked 11–19 are called "efficiency inferior". Similarly, based on to the rankings of capability evaluation of ASTI for G20 countries, countries ranked 1–10 are called "capability superior " and countries ranked 11–19 are called "capability inferior ". Combining the rankings of the efficiency and capability of ASTI, the ASTI level of G20 countries is divided into four categories: "double superior type" ("efficiency superior" and "capability superior"), "efficiency single-superior type" ("efficiency superior" and "capability inferior"), "capability single-superior type" ("efficiency inferior" and "capability superior"), and "double inferior type" ("efficiency inferior" and "capability inferior").

This study used the evaluation system and calculation model, which were referred from Wang's methodology [46], to evaluate the capabilities of ASTI for G20 countries. For the details of the efficiency measurement, please refer to Figure 2.

As shown in Figure 5, in 2017, Australia, China, and the United States with outstanding efficiency and capability of ASTI simultaneously belong to the double superior type; Brazil, India, Indonesia, Mexico, Saudi Arabia, and South Africa are efficiency single-superior type, indicating that the capabilities of ASTI for these six countries need to be improved; the capacity single-superior type included Canada, France, Italy, Japan, and the Republic of Korea, which means that these five countries are weak in the efficiency of ASTI; and the Russian Federation and Turkey are weak in both capability and efficiency of ASTI, so they fell in the double-inferior type.

**Figure 5.** Classification for the national ASTI level for G20 countries.

Compared with 2008, in 2017, the types of ASTI levels in 15 countries, including Australia, Brazil, Canada, China, France, India, Indonesia, Italy, Japan, the Republic of Korea, the Russian Federation, Saudi Arabia, South Africa, Turkey, and the United States, remained unchanged. There were only four countries (Argentina, Germany, Mexico, and the United Kingdom) whose types of ASTI levels changed. Argentina and Mexico changed from the double inferior type to the efficiency single-superior type due to efficiency improvement. On the contrary, the ASTI types of Germany and the United Kingdom transformed from the double superior type to capacity single-superior type caused by a drop in efficiency. The results indicate that the ASTI levels of G20 countries were in a stable status on the whole during the period 2008–2017.

#### **4. Conclusions and Implications**

In this study, we estimated the static-dynamic efficiency of ASTI and identified the efficiency determinants across the G20 countries. First, we measured the static comprehensive efficiency of ASTI by means of the DEA-BCC model. The results show that one developed country (the United States) and five developing countries (Brazil, China, India, Indonesia, and Saudi Arabia) have been efficient in the period 2008–2017. The values of the G20 developing countries were relatively larger than the G20 developed countries from the perspective of efficiency range. The G20 developed countries showed a fluctuating downward trend, while the G20 developing countries showed an upward trend from the perspective of efficient proportion. The major binding constraints to the higher efficiency of ASTI included the R&D expenditure redundancy and the agricultural journal papers deficiency. Second, we applied the DEA-Malmquist index model to calculate the dynamic total factor productivity change (TFPC) of ASTI in the periods 2008–2017. The TFPC of ASTI for G20 countries showed "decline–growth–continuous decline–growth recovery" trend, where the G20 developed countries showed a "growth–decline–growth" trend, while

the G20 developing countries experienced a fluctuating upward trend. The technological change (TC) was the main cause of the TFTC of ASTI in most G20 countries. Finally, we further classified the ASTI level of G20 countries based on efficiency and capability. The G20 developed countries usually had higher capacity, while the G20 developing countries had advantages in efficiency.

The theoretical contributions of this study are as follows. First, although measuring innovation efficiency is not a novel concept, the empirical evidence in ASTI is limited and most studies have taken a cross-sectional sample of one region or one country. In this study, we went beyond the range of single-country studies. We collected the G20 countries data during a 10-year period (2008–2017) and performed a comparative study of countries at different stages of development. Our second contribution is the integration of static and dynamic ASTI efficiency analyses, contrary to the previous studies only conducting static or dynamic efficiency analyses. Here, we investigated the efficiency determinants from static and dynamic perspectives. Third, this study is pioneering in classification and change analysis of the national ASTI level based on the rankings of efficiency measurement and capability evaluation of ASTI.

This study has important implications for the design and implementation of agricultural innovation strategies for policymakers. Firstly, developed countries should optimize the investment structure of ASTI, while developing countries should pay more attention to the scale of investment. The ASTI in developed countries started earlier, but most developed countries in G20 had R&D personnel and R&D expenditure investment redundancy during 2008–2017. Thus, policymakers in developed countries should pay more attention to the optimization of investment structure of ASTI, instead of focusing only on inputs. Although the efficiency of ASTI of developing countries is higher than that of developed countries on the whole, this is mainly based on the premise of low input–low output in ASTI of developing countries. Policymakers in developing countries should appropriately expand the scale of investment in ASTI while maintaining current efficiency. Secondly, the role of technological progress in promoting the efficiency of ASTI must be taken seriously. The empirical results show that the reason for the decline in the TFP of ASTI in G20 countries from 2008 to 2017 was that the decline in technological progress was greater than the increase in technological efficiency. All countries should strengthen the development and transformation of agricultural technology continuously. Finally, in 2008, there were four "double superior type" countries of G20 but only three in 2017. Therefore, the efficiency and capability of ASTI should be taken into consideration when implementing different policies simultaneously.

This research is not free of limitations and these could be addressed in future research. First, a national agriculture innovation system is a complex system, including various input and output indicators. Concerning the future work, it would be interesting and valuable to investigate more detailed indicators for a better simulation of the national agriculture innovation system, which can more effectively reflect the real process of ASTI activities at the national level. Second, due to the lack of data, our empirical research was not able to include more countries. Hence, a direction for our future research is to conduct comparative studies between more countries.

**Author Contributions:** Conceptualization, D.W., X.G., and C.D.; methodology, D.W., X.G., C.D., and X.D.; validation, D.W.; formal analysis, D.W.; investigation, D.W., C.D., X.D., J.L., and B.W.; writing—original draft preparation, D.W. and C.D.; writing—review and editing, D.W.; supervision, X.G.; and funding acquisition, D.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Chinese Postdoctoral Science Foundation (2017M621239) and the Postdoctoral Science Foundation of Heilongjiang Province (LBH-Z17007).

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

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** We are grateful for the helpful insights and suggestions from the editor of this journal, as well as the anonymous referees.

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

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