**1. Introduction**

The challenge of sustainable agriculture development in light of population growth, resource shortage, ecological deterioration, and climate change has led many governments to support agricultural science, technology, and innovation (ASTI). The investment of the United States government in agricultural research projects reached 3.03 billion dollars in 2018, 130 million dollars more than in 2017 [1]. The European Union has invested 10 billion euros in ASTI activities such as agriculture and forestry ecosystem restoration for the "Rural Development Project (2014–2020)" [2]. The UK adopted the "UK agricultural science and technology strategy" in 2013. In 2014, Germany's agricultural research funds reached 10% of the budget of the Federal Ministry of Food and Agriculture [3]. China issued the "Agricultural Science and Technology Development Plan (2006–2020)" [4] and "the National Agricultural Science, Technology and Innovation Capacity Building Plan (2012–2016)" [5].

**Citation:** Guo, X.; Deng, C.; Wang, D.; Du, X.; Li, J.; Wan, B. International Comparison of the Efficiency of Agricultural Science, Technology, and Innovation: A Case Study of G20 Countries. *Sustainability* **2021**, *13*, 2769. https://doi.org/10.3390/ su13052769

Academic Editor: Michael Blakeney

Received: 29 January 2021 Accepted: 28 February 2021 Published: 4 March 2021

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**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/).

However, the innovation performance is dependent not only on the available innovation resources but also and maybe most importantly on their efficient and productive use [6]. Innovation efficiency, which is "the ability to translate inputs into innovation outputs" by definition, has become very important and attractive to scholars and governments [7,8]. Because of the unique advantages in the efficiency evaluation of multi-input and multioutput [9], the Data Envelopment Analysis (DEA) has been widely used to measure the relative efficiency of Decision-Making Units (DMUs) by estimating the ratio of outputs to inputs [10–12]. Many studies investigated innovation efficiency at the national [13–15], regional [10,16,17], and institutional levels [18–20] by means of DEA. Several studies have been conducted to measure the efficiency of ASTI [21–27]. Most of these studies assess a particular nation [21,22,27] or a region [24–26], and very few studies attempt cross country comparisons for ASTI efficiency [23]. Moreover, the integration of static and dynamic ASTI efficiency analyses has been usually disregarded.

The limited attention to innovation efficiency at the national level could be a potentially significant omission from a policy-oriented perspective [28,29], since measuring the ASTI efficiency helps to both identify the best innovation practitioners for benchmarking and propose ways to improve efficiency by pinpointing areas of weakness [15]. The G20 countries account for 60% of global arable land and 80% of global agricultural trade [30]. Therefore, "G20 agriculture" has a significant effect on global agriculture development. In this context, this paper aims to address this gap by estimating the static-dynamic efficiency of ASTI for the G20 countries at the national level.

This paper proceeds as follows. Section 2 presents the DEA-BCC model and the DEA-Malmquist index model, as well as the input–output indicators and data sources. Section 3 shows the empirical results, including the static comprehensive efficiency and dynamic total factor productivity. In addition, we further classify the ASTI level of G20 countries through the results of efficiency measurement and capability evaluation. Section 4 is reserved for conclusions and implications.

#### **2. Methodology**

#### *2.1. Definition of Efficiency of ASTI*

According to Schumpeter's innovation theory, innovation is not only a technology and scientific research activity but also an economic activity [31]. In this paper, ASTI is defined as a complex innovation process in which a series of innovative actors transform input (personnel and expenditure) into output (new knowledge, new varieties, or new technologies) through cooperation and interaction to obtain economic benefits. Therefore, the efficiency of ASTI is the ability of transforming input into output in the above complex innovation process. The innovation efficiency reflects the effectiveness of innovation process from input to output. The maximum efficiency of ASTI is mainly reflected in the maximum innovation output at the given innovation input.

#### *2.2. Data Envelopment Analysis*

DEA is a non-parametric method proposed by Farrell [32] and developed by Charnes, Cooper, and Rhodes [33]. There are many unique advantages in the efficiency evaluation of multi-input and multi-output: First, the functional relationship between input and output indicators does not require a priori assumption [34]. Second, multi-input and multi-output are allowed to be processed simultaneously, without any input and output indicators dimensionless processing. Moreover, DEA does not need to verify in advance which input and output indicators are the most important in efficiency evaluation [35].

The CCR model and the BCC model are two basic DEA models. Both models are named after the author's initials. In 1978, Charnes, Cooper, and Rhodes created the first DEA model, which was named the CCR model [33]. Similarly, in 1984, Banker, Charnes, and Cooper proposed a new DEA model, which was named the BCC model [36]. The difference between BCC model and CCR model lies in the assumptions. The CCR model assumes that returns to scale are constant, while the BCC model assumes that returns

to scale are variable. According to the efficiency measurement, the two models can be divided into input-oriented and output-oriented [37]. Input orientation emphasizes the degree to which the various input factors should be reduced to achieve technical efficiency without reducing output. In contrast, output orientation focuses on the extent to which all kinds of output should be increased for the purpose of achieving technical efficiency without increasing input. In practice, the ASTI in most countries is not in the optimal scale state, and ASTI will produce scale efficiency with the increasing input. This means that the measurement of the efficiency of ASTI meets the assumption of BCC model, that is, variable returns to scale. The fundamental purpose of increasing the input of ASTI is to expect more output, which is consistent with the output-oriented model. Therefore, we carried out the output-oriented BCC model to measure the comprehensive efficiency of ASTI in G20 countries. The linear form of the output-oriented BCC model is as follows:

$$\mathbf{A}\left(\mathbf{B}^2\mathbf{C}\right)^{\bullet}\begin{cases} \max\left[\boldsymbol{\theta} - \boldsymbol{\varepsilon}\left(\mathbf{e}^\mathbf{t} - \mathbf{e}^\mathbf{t}\mathbf{s}^+ + \mathbf{e}^\mathbf{t}\mathbf{s}^+\right)\right],\\ \text{s.t.} \sum\_{j=1}^k \mathbf{x}\_{jl}\boldsymbol{\lambda}\_j + \mathbf{s}^- = \mathbf{x}\_1^n, \\ \quad \sum\_{j=1}^k \mathbf{y}\_{jm}\boldsymbol{\lambda}\_j - \mathbf{s}^+ = \boldsymbol{\theta}\mathbf{y}\_1^n, \\ \quad \sum\_{j=1}^k \boldsymbol{\lambda}\_j = 1, \\ \quad \mathbf{s}^- \ge 0, \mathbf{s}^+ \ge 0, \boldsymbol{\lambda}\_j \ge 0, j = 1, 2, \cdots \text{ k}. \end{cases} \tag{1}$$

^ e t <sup>=</sup> (1, 1, . . . , 1) <sup>∈</sup> Em, et <sup>=</sup> (1, 1, . . . , 1) <sup>∈</sup> Es ; xjl represents the lth inputs of the jth DMU; yjm represents the mth outputs of the jth DMU; ε is the non-Archimedes infinitesimal; λ<sup>j</sup> is the weighting factor; s<sup>−</sup> represents the relaxation variables; s<sup>+</sup> is the residual variable; and θ represents the relative efficiency of DMU.

If θ < 1, DMU is inefficient.

If <sup>θ</sup> <sup>=</sup> 1, ^ e t s<sup>−</sup> + et s<sup>+</sup> > 0, DMU is weakly efficient.

If <sup>θ</sup> <sup>=</sup> 1, ^ e t s<sup>−</sup> + e<sup>t</sup> s<sup>+</sup> = 0, DMU is efficient.

The BCC model can only use the cross-section data to reflect the efficiency value of DMU at a certain time statically. To show the dynamic changes of DMU in a specific time series, we need to use the DEA-Malmquist index model [38] to calculate the total factor productivity change (TFPC). The TFPC can be decomposed into the technical efficiency change (TEC) and technological change (TC) in two periods [39]. TEC can also be decomposed into the pure efficiency change (PEC) and scale efficiency change (SEC). The model is as follows:

$$\text{TFPC} = \mathbf{m}\_0 \left( \mathbf{x}\_{t+1}, \mathbf{y}\_{t+1}; \mathbf{x}\_{t\prime} \mathbf{y}\_t \right) \tag{2}$$

$$\mathbf{y} = \left[ \frac{\mathbf{d}\_0^t(\mathbf{x}\_{t+1}, \mathbf{y}\_{t+1})}{\mathbf{d}\_0^t(\mathbf{x}\_t, \mathbf{y}\_t)} \times \frac{\mathbf{d}\_0^{t+1}(\mathbf{x}\_{t+1}, \mathbf{y}\_{t+1})}{\mathbf{d}\_0^{t+1}(\mathbf{x}\_t, \mathbf{y}\_t)} \right]^{\frac{1}{2}} \tag{3}$$

$$\mathbf{y} = \text{TEC}(\mathbf{x}\_{\mathbf{t}+1}, \mathbf{y}\_{\mathbf{t}+1}; \mathbf{x}\_{\mathbf{t}}, \mathbf{y}\_{\mathbf{t}}) \times \text{TC}(\mathbf{x}\_{\mathbf{t}+1}, \mathbf{y}\_{\mathbf{t}+1}; \mathbf{x}\_{\mathbf{t}}, \mathbf{y}\_{\mathbf{t}}) \tag{4}$$

$$\mathbf{y} = \text{SEC}(\mathbf{x}\_{\text{t}+1}, \mathbf{y}\_{\text{t}+1}; \mathbf{x}\_{\text{t}}, \mathbf{y}\_{\text{t}}) \times \text{PEC}(\mathbf{x}\_{\text{t}+1}, \mathbf{y}\_{\text{t}+1}; \mathbf{x}\_{\text{t}}, \mathbf{y}\_{\text{t}}) \times \text{TC}(\mathbf{x}\_{\text{t}+1}, \mathbf{y}\_{\text{t}+1}; \mathbf{x}\_{\text{t}}, \mathbf{y}\_{\text{t}}) \tag{5}$$

where d0 refers to the input and output matrix and xt, xt+<sup>1</sup> represent the input vectors of the t and t + 1 periods, respectively. The relationship between variables satisfies the following conditions: TFPC = TEC × TC, EC = SEC × PEC. Thus, TFPC = SEC × PEC × TC.

#### *2.3. Indicators Selection*

The discriminatory power of DEA would be decreased when many input–output indicators are introduced [40]; the principle is as follows:

$$\mathbf{d} \ge \mathbf{3} \* (\mathbf{m} + \mathbf{n}) \tag{6}$$

where d represents the number of DMUs, m represents the number of input indicators, and n represents the number of output indicators.

Following this restriction, only a few critical indicators can be selected. In this study, the number of DMUs is 19; therefore, the total number of indicators cannot be greater than 6.

As shown in Table 1, based on previous research experience [9,19,20,24,26,41,42], the definition of efficiency of ASTI and data availability, the input and output indicators are selected as follows.

**Table 1.** List of the innovation efficiency evaluation studies using DEA met.


Input indicators: The innovation inputs mainly include the research and development (R&D) personnel and expenditure [9,19,20,44–46]. The R&D personnel served as the inputs in the brainwork for the upstream technological creation process in an innovation system, representing a basic element for the realization of the technological creation process. As a proxy for this indicator, we employ the number of agricultural researchers to measure R&D personnel [22,24,26,46]. As a supporting input, R&D expenditure is also needed, which is used to complete various R&D activities [47], including the payment of R&D employees' wages and the purchase of R&D equipment and facilities [48]. Percentage shares of R&D expenditure in agricultural value added is used as a proxy indicator to measure R&D expenditure.

Output indicators: The output indicators could be divided into two general categories: (1) scientific and technological output; and (2) economic performance. The scientific and technological output captured the extent to which a country produced some type of scientific and technological output. The commonly accepted measures of this are the number of agricultural journal papers [9,49] and the number of agricultural patents [19,25,47]. The agricultural value added (annual percent growth) is an appropriate proxy for economic performance generated by ASTI [49].

#### *2.4. Data Sources*

The study was limited to G20 countries and covered the period between 2008 and 2017. The G20 countries include Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, the Republic of Korea, Mexico, the Russian Federation, Saudi Arabia, South Africa, Turkey, the United Kingdom, and the United States (note: the European Union (EU) is a political and economic union, and its major member states are already within the G20, so the EU was not included in this empirical analysis). The specific sources of each indicator are shown in Table 2 and its notes. The descriptive statistics of the input and output indicators are shown in Table 3.

#### **Table 2.** Index system for measuring ASTI efficiency.


Notes: United Nations Educational, Scientific and Cultural Organization-Institute for Statistics (UNESCO-UIS): http://uis.unesco.org/ (accessed on 10 September 2020); The Food and Agriculture Organization (FAO): http://www.fao.org/home/en/ (accessed on 10 September 2020); World Intellectual Property Organization (WIPO): https://www3.wipo.int/ipstats/index.htm?lang=en (accessed on 10 September 2020); Web of Science (WOS): http://apps.webofknowledge.com/RAMore.do?product=WOS&search\_mode=AdvancedSearch&SID= 5BeAM2moXj26NR13wVH&qid=13&ra\_mode=more&ra\_name=CountryTerritory&colName=WOS&viewType=raMore (accessed on 10 September 2020); World Bank (WB): https://data.worldbank.org/indicator/NV.AGR.TOTL.ZS?view=chart (accessed on 10 September 2020).


The empirical research framework of this paper is shown as Figure 1.

**Figure 1.** Empirical research framework.
