Introduction

Agriculture has been the foundation of the world’s economy for centuries and remains dynamic for world sustainability. The significance of the agriculture sector lies in two features that allured the attention of the researchers. One aspect is that the agriculture sector is a source of food, employment opportunities, and rural development. The second aspect is that the production practices cause greenhouse gas (GHG) emissions in the atmosphere, damaging environmental quality (Waheed et al. 2018; Reza et al. 2020). The relationship between climate change and agriculture production is bidirectional (Zafeiriou and Azam 2017). Climate and agricultural productivity are both negatively impacted by climate change (Rehman et al. 2021). The agriculture sector is the second-largest emitter. According to one assessment of FAO (Food and Agriculture Organization of the United Nations), GHG emissions from the agricultural sector accounted for 21 to 24% of the global total.

Similarly, the US emission inventory statistics indicate that the agriculture sector accounted for 8% of the GHG emissions. The main drivers of agricultural GHG emissions are deforestation, livestock, fossil fuel-based fertilizers, biomass burning, etc. According to Reynolds and Wenzlau (2012), massive use of fossil fuel, irrigation, and nitrogen-rich fertilizer are responsible for at least 14 to 30% of the total GHG emissions. However, agriculture activities contribute to increasing emissions directly and indirectly. Direct emissions originate from soils and livestock manure practices. Indirect emissions are from fertilizers, transport, and agrochemical and fertilizer production.

Besides, the agriculture sector depends on favorable weather and climate, such as temperature and rain, which affect agricultural production efficiency to produce the food and fiber necessary to sustain human life (Yohannes 2016). Kang et al. (2009), Lal et al. (2005) stated that world food security would be one of the topmost challenges in the coming centuries and sustain a clean environment. Agriculture activity is expected to be vulnerable to climate change and reduce crop production efficiency of the countries (Gornall et al. 2010). Kwakwa et al. (2022) studied the relationships between quality environment and agriculture development. They concluded that the quality of the environment is important to develop the agriculture sector. Similarly, Guo et al. (2021) stated that reducing agricultural carbon emissions is necessary to attaining green and sustainable agricultural growth. Environmental degradation is a substantial barrier to agricultural development, particularly in developing countries (Khan et al. 2021). Rehman et al. (2022) analyzed the linkages between carbon emissions and the major crops production and land use in Pakistan. They discovered a positive relationship between carbon emissions and wheat, maize, sugarcane, cotton, bajra, gram, sesamum crops, and land usage.

In contrast, a negative relationship was discovered for rice, jowar, and barley. The consequences of climate change for agriculture are more severe for the countries with higher temperatures, areas with already degraded lands, and lower levels of development with little adaptation capacity (Karki and Gurung 2012; Keane et al. 2009). Crop production strongly correlates with the change in temperature and the absorption rate of fertilizers and other minerals, determining yield productivity (Hoffmann 2013).

The interlinkages between climate and agriculture put stress to adopt such strategies that would be helpful to increase the efficiency of agriculture production function and simultaneously decrease the GHG emissions while sustaining the economic growth. Increasing agricultural production efficiency is essential to reduce the environmental impact of agricultural production while maintaining a sufficient food supply for a growing world population (Clark and Tilman 2017). By undertaking agricultural productivity growth as a long-term strategy to address the environmental impact on the one hand, and to meet the growing world demand for food on the other hand, therefore, agriculture production efficiency concept seems very promising. Agriculture production efficiency means maintaining or increasing production while using fewer resources (Gołaś et al. 2020). In other words, it shows the willingness to do “more with less: delivering more value while using fewer resources” (World Business Council for Sustainable Development 2006, p. 4). Furthermore, increased production efficiency lowers food prices, undoubtedly benefiting the consumers, particularly the poor, since food expenses occupy a larger share of their total budget (Pinstrup‐Andersen and Hazell 1985).

However, agriculture productivity growth is attributed to research and development (R&D) expenditures (Khan and Salim. 2015). Since earlier literature, Schultz (1953) acknowledged that all productivity growth in agriculture is subject to investments in agricultural research. Also, Griliches (1964) used R&D and the conventional input variables in the agriculture production function. According to Fuglie and Toole (2014); Wang et al. (2013), R&D investment is the primary source of providing new knowledge and invention of advanced technologies, which increase the efficiency of agriculture production. However, further argued, R&D would affect agricultural production efficiency only over the long term. Moreover, Voutsinas and Tsamadies (2014) stated that R&D investment in agriculture accelerates technological innovation, increasing productivity growth. Increasing agriculture production efficiency indicates the effects of technological advancement in terms of R&D, as well as investments in infrastructure (e.g., irrigation, roads, and electricity) (Mukherjee and Kuroda 2003). Higher efficiency in agriculture means higher production from the available resource and improves the environmental quality (Gołaś et al. 2020). R&D in the field of agriculture is important because it increases the efficiency of novel technology. Furthermore, through R&D, agriculture products increase and reduce pressure on natural resources.

From an agriculture production efficiency and environment point of view, farming should entail some such decisions and actions customized to certain conditions, limitations, and goals. Such as, the agricultural sector requires undertaking specific actions, and farming activities should be regulated to limit their adverse environmental impact. So, the government can shape the ideas of economic and social interests. Government can implement the policies effectively by controlling destabilizing factors (Ullah et al. 2018; Abid 2016). However, agricultural production is intertwined with several policy areas and market pressures, making policy and implementation a complex challenge (Lencucha et al. 2020). Despite its importance, the role of government is widely neglected while assessing agriculture production efficiency (Zylbersztajn 2009). Government can provide an incentive for the farmers. Thus, this sector can operate efficiently to improve environmental quality (Yasmeen et al. 2021) because environmental quality is affected by the quality of regulations (Shah et al. 2019). Such as political stability, government effectiveness, legal provisions, and control on corruption are crucial factors to implement policies regarding the environment and thereby reduce carbon emissions (Gani 2012; Yasmeen et al. 2018). In addition, the effective government can help promote research and development in green technologies, which eventually promote a clean environment (Salman et al. 2019). It means that the government can optimize the whole cycle of agriculture production to a clean environment through R&D investment and effective implementation of strategies.

Therefore, this study is carried out to assess the nexuses of environment, agriculture production efficiency, R&D investment, and government effectiveness for the time priod of 1996–2018. To the best of our knowledge, it would be the first comprehensive study on agriculture production efficiency and environmental nexuses. The specialty of this study is in the following research objectives. The first objective is to assess the production efficiency of the agriculture sector, considering both types of farming outcomes: positive ones (agricultural production) and negative ones (environmental impact); this has never been done for these panels. The production efficiency has been measured using data envelopment analysis (DEA). Second, we simultaneously assess the impact of the environment and agriculture on production efficiency. Third, the study includes research and development investment’s role in Agriculture production efficiency and the environment. The spillover effect of R&D investment on agriculture production efficiency is also a significant contribution. Furthermore, one contribution that makes it different from the prior literature is the moderating role of R&D investment in Agriculture production efficiency and government effectiveness. So the assessment of the government’s role with R&D investment and determining the efficiency of agriculture production would be the fourth vital contribution.

Agricultural production efficiency, R&D investment, and environment

The emphasis placed on agriculture efficiency underlines the two reasons. First, the production efficiency of agriculture needs to be targeted to achieve “Sustainable Development Goals” such as the capacity of agriculture production per labor unit, income of small-scale food producers, and sustainable agriculture (Mechri and Cachia 2017; Alston and Pardey 2014). Second, environmental problems associated with agriculture have become a severe challenge. In other words, climate change and agricultural productivity are intertwined (see Fig. 1). In this context, comprehensive measures are needed towards achieving national, regional, and global targets on agricultural efficiency and the environment.

Fig. 1
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Pictography of bi-directional relation between agriculture production and climate

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Therefore, both developed and developing countries are putting stress on improving their agriculture production efficiency. Figure 2 shows the agriculture production efficiency of each country. It has been evident from the graph that the USA, Russia, Korea, Japan, and Italy are efficient in agriculture production. In comparison, Australia and France are following efficiency with a technical efficiency score (0.974 and 0.973). According to Khan et al. (2015), Islam et al. (2014), Australia has faced slowing productivity growth in some agriculture sectors. Among BRICS countries, China (0.183), India (0.378), and Brazil (0.382) are still beyond Russia in Agriculture production efficiency. It implies that these countries still need to focus on this sector to mitigate the food security problem and carbon emission. According to Doğan (2018), China’s agricultural sector is a significant factor in carbon emissions.

Fig. 2
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Average agriculture production efficiency by country

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On the other hand, efficiency could be enhanced by investing in R&D while keeping carbon emissions. Also, these are three essential elements in this research. Therefore, before proceeding with formal empirical analysis, we plot two graphs to observe the nexuses between carbon emission, agriculture production efficiency, and R&D investment. Figure 3 depicts that agriculture production efficiency would be decreased by carbon emission. It proved that carbon emission is a big hindrance to improving agriculture production. However, it is worth mentioning that R&D can play a leading role in improving the input efficiency used in agriculture production. Figure 4 indicates the positive relationship between agriculture production efficiency and R&D investment. R&D is such a variable that, though unable to produce output directly but can affect the skill of the farm to transform the inputs into outputs more efficiently.

Fig. 3
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Agriculture production efficiency and CO2 emissions

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Fig. 4
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Agriculture production efficiency and R&D investment

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Model description and data

According to the Consultative Group on International Agricultural Research, mitigating agriculture’s carbon emissions is vital to control global warming (Gilbert 2012). In this context, R&D investment is a crucial driving force for the growing agriculture sector that increasingly responds to demand change and keeps lessening the myriad environmental impact. Braun and Wield (1994), Yasmeen et al. (2021) suggested that technology is a standard process that improves agriculture production and reduces environmental pollution. Bromley (2010), Carberry et al. (2013) highlighted the importance of technology and institutions to solve increasing demand and environmental quality. Technology innovation in consequences of R&D is committed to following the “win–win” development pattern of environment and economy (Chen et al. 2006). Meanwhile, the positive externality of modern invention requires the government’s support through research funding and implementation of environmental regulations. In a nutshell, well-designed environmental regulations by the government possibly will lead to a Pareto improvement or a “win–win” situation by protecting the environment and stimulating innovation through the improvement of production processes (Esty and Porter 2005). The phenomena between environment, agriculture, R&D investment, and government, for the empirical analysis, are composed as follows:

$${{CO}_{2}}_{it}={\alpha }_{0}+{\alpha }_{1}{IN}_{it}+{\alpha }_{2}{IN}_{it}^{2}+{\alpha }_{3}{AGE}_{it}+{\alpha }_{4}{EN}_{it}+{\alpha }_{5}{RD}_{it}+ {\mathrm{Country }\_\mathrm{dummy}}_{it}+{\mathrm{Time}\_\mathrm{ dummy}}_{it}+{\mu }_{1,it }$$
(1)
$${{CO}_{2}}_{it}={\beta }_{0}+{\beta }_{1}{IN}_{it}+{\beta }_{2}{IN}_{it}^{2}+{\beta }_{3}{AGE}_{it}+{\beta }_{4}{EN}_{it}+{\beta }_{5}{RD}_{it}+{\beta }_{6}{AGE\times RD}_{it}+{\beta }_{7}{GE}_{it}+{\beta }_{8}{GE*RD}_{it}+ {\mathrm{Country }\_\mathrm{dummy}}_{it}+{\mathrm{Time}\_\mathrm{ dummy}}_{it}+{\mu }_{2,it }$$
(2)
$${AGE}_{it}={\varnothing }_{0}+{\varnothing }_{1}{IN}_{it}+{\varnothing }_{2}{IN}_{it}^{2}+{\varnothing }_{3}{{CO}_{2}}_{it}+{\varnothing }_{4}{EN}_{it}+{\varnothing }_{5}{RD}_{it}+ {\mathrm{Country }\_\mathrm{dummy}}_{it}+{\mathrm{Time}\_\mathrm{ dummy}}_{it}+{\mu }_{3,it }$$
(3)
$${AGE}_{it}={\theta }_{0}+{\theta }_{1}{IN}_{it}+{\theta }_{2}{IN}_{it}^{2}+{\theta }_{3}{{CO}_{2}}_{it}+{\theta }_{4}{EN}_{it}+{\theta }_{5}{RD}_{it}+{\theta }_{6}{GE}_{it}+{\theta }_{7}{GE\times RD}_{it}+ {\mathrm{Country }\_\mathrm{dummy}}_{it}+{\mathrm{Time}\_\mathrm{ dummy}}_{it}+{\mu }_{4,it }$$
(4)

\({CO}_{2}\) is carbon emissions (kilotonnes) emitted by the agriculture sector. \(IN\) and \({IN}^{2}\) are per capita income and square per capita income to capture the environmental Kuznets curve effect. \(AGE\) is used for agriculture production efficiency, \(EN\) represents energy consumption in the agriculture sector, \(RD\) indicates the research and development investment made by three sectors (Government), and \(GE\) is government effectiveness. \(\mathrm{Country }\_\mathrm{dummy}\) and \(\mathrm{Year}\_\mathrm{dummy}\) are used for country effects and year effects. As described in previous sections, agriculture production efficiency can be improved by R&D. Furthermore, the government’s role is important to provide the funds for R&D and implement the regulations. Considering this, we used two interaction terms AGE ∗ RD and GE ∗ RD to capture the effect of R&D investment in improving agro-production efficiency and government effectiveness. \({\alpha }_{0}\),\({\beta }_{0}, {\varnothing }_{0}\),\(\mathrm{and} {\theta }_{0}\) are constants in Eqs. (1), (2), (3) and (4). While \({\alpha }_{1} \mathrm{to}{ \alpha }_{5}, {\beta }_{1} \mathrm{to }{\beta }_{8},{\varnothing }_{1} \mathrm{to }{\varnothing }_{5}, \mathrm{and }{\theta }_{1} \mathrm{to }{\theta }_{7}\) are explanatory coefficients in Eqs. (1), (2), (3) and (4), \({\mu }_{1 }\mathrm{to} {{\mu }_{4 }}\) indicate to error terms in Eqs. (1), (2), (3) and (4). i expression is used for each country i = 1,2,…..N (N = 17), and t shows the time. This study explores the relationships between agriculture production and carbon emissions in major (seventeen) agriculture-producing countries over the time period of 1996–2018 (for detailed data set, source, and countries, see Table 1 in Appendix).

Analysis methods

This study is based on two empirical analyses. Firstly, through data envelopment analysis (DEA), agriculture production efficiency is measured for top agriculture production countries. Secondly, the appropriate econometric methods are applied, to be precise, (1) cross-sectional dependence tests and panel unit root testing, (2) Westerlund test, and for long-run assessment Driscoll and Kraay test.

Agriculture production efficiency

Data envelopment analysis is a famous tool to quantify the relative efficiency of homogenous DMUs. DEA CCR by Charnes et al. (1978) is used to estimate the efficiency. The efficiency score range from 0 (inefficient) to 1 (efficient).

DEA model development

Considering a set of J DMUs with n input and m output in T (t = 1,…, T) periods. Suppose in time t, decision-makers are using inputs \(x^{t} \in R_{ + }^{n}\) to produce outputs \(y^{t} \in R_{ + }^{m}\). Define the input requirement set in period t, which is:

$$L^t(y^t)=\{\;x^t:x^t\;\mathrm{can}\;\mathrm{produce}\;y^t\}.$$

Assume Lt(yt) is non-empty, closed, convex, and bounded, and that it satisfies the substantial disposability property of inputs and outputs, Lt (yt) is bounded from below by the input isoquant (a constant returns to scale (CRS) production boundary), that is:

$${\text{Isoq}}L_{{}}^{t} \left( {y^{t} } \right) = \left\{ {x^{t} :x^{t} \in L^{t} \left( {y^{t} } \right),\,\lambda x^{t} \notin L^{t} \left( {y^{t} } \right){\text{ for }}\lambda < 1} \right\}.$$

Define the input distance function of period t as follows:

$$D_{{}}^{t} \left( {y^{t} ,x^{t} } \right) = \mathop {\sup }\limits_{\theta } \left\{ {\theta :\left( {x^{t} /\theta } \right) \in L^{t} \left( {y^{t} } \right)\theta > 0} \right\}.$$

Therefore, technical efficiency for period t can be defined as;

$${\text{TE}}^{t} \left( {y^{t} ,x^{t} } \right) = 1/D_{{}}^{t} \left( {y^{t} ,x^{t} } \right).$$
(5)

Understandably, model (5) attempts to specify as much input as possible for a given level of output. The detail of the used variables is given in Table 1 in Appendix.

Econometric procedure

We followed the cross-sectional dependence and panel unit root, Westerlund test for panel co-integration, and long-run assessment Driscoll and Kraay test for the empirical evaluation.

CD and panel unit root tests

After estimating the efficiency score of agriculture production efficiency, we apply the cross-sectional dependence test for empirical assessment. The cross-sectional dependence test presented by Pesaran (2021) is applied for each variable to avoid deceptive results and forecasting errors. Pesaran (2021) provided a modification of the LM test as follows:

$$CD=\sqrt{\frac{2T}{N(N-1)}}{\sum }_{i=1}^{N-1}{\sum }_{j=i+1}^{N}{\partial }_{ij}N\left(\mathrm{0,1}\right)$$
(6)

And, the \({\partial }_{ij}\) is the estimate of

$${\partial }_{ij }=\frac{\sum_{t=1}^{T}{\in }_{it}{\in }_{jt}}{\left(\sqrt{\sum_{t=1}^{T}{{\in }^{2}}_{it}}\right)\sqrt{\sum_{t=1}^{T}{{\in }^{2}}_{jt}}}$$
(7)

The null hypothesis is known as \({\partial }_{ij}\)= corr \(\left({\in }_{it}{\in }_{jt}\right)\)=0 for i ≠ j. The alternative is \({\partial }_{ij }\ne 0\) for \(i \ne j\).

The next test is applied to confirm the unit root level of each variable. A unit root test indorses the order of each variable’s integration. Existing dependence in the panel series, the CIPS unit root test developed by (Pesaran 2007) is appropriate since it is more robust against cross-sectional dependence cases. The test can be specified as:

The average of the t-ratios, indicated by CIPS is;

$$\mathrm{CIPS}\left(N,{T}_{m}\right)=\frac{\sum_{i=1}^{N}{t}_{i}\left(N,{T}_{m}\right)}{N}$$
(8)

Panel co-integration and long-run estimates

The purpose of panel co-integration is to authenticate whether a long-run symmetry exists among the variables. The study found evidence of cross-sectional dependence between the concerned series; therefore, the Westerlund (2007) test for co-integration is applied. The statistics of Westerlund co-integration comprise two sets of statistics. The first set is residual-based group statistics, while the second set is panel statistics.

The panel co-integration test is merely used to explore the long-run co-integrating relationship between the variables. However, this test cannot calculate long-run estimates. Accordingly, it is compulsory to apply a suitable method to analyze the long-run parameters. We applied the Driscoll and Kraay (1998) (D&K) standard error approach to the results above. This method of approach is suitable in cross-sectional dependence cases to avoid biased estimators for consistent coefficient analysis. Furthermore, the average values are used in the hetro-autocorrelation to produce a robust estimator. They are equally applicable for balanced and unbalanced panel data as they can efficiently fix the missing values (Baloch et al. 2019).

Results and discussion

The descriptive statistics for each variable are summarized in Table 2. The maximum agriculture production efficiency is 1 (technical efficiency score), and the average efficiency is 0.800. At the same time, the maximum and minimum values of carbon emission from the agriculture sector are (5651.282, 17202), respectively. Similarly, energy consumption and per capita income have ranged from the highest (1940193, 56832.05) to the lowest (17199.71, 711.9288). However, government effectiveness and R&D are on average values. For instance, the highest and lowest values of R&D are between (4.810, 0.047) with an average of 1.293954. On the other hand, the maximum and minimum values of government effectiveness are 2.006 and −0.8178, respectively, and the average of the entire panel is 0.4586.

Table 2 Descriptive statistics
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Following Pesaran (2021), cross-sectional dependence identification results are given in Table 3 in Appendix. The results indicate that each cross-section is inter-reliant as the null hypothesis is rejected at 5% and 1% significance levels. These results suggest that the countries on earth have become global villages, and their economic and social decisions possibly affect each other. Increasing CO2 in one country defiantly would affect global warming. Similarly, if one government is involved in inventing advanced environmental technology resulting from R&D investment, it would be spread worldwide through trade and foreign direct investment. So, decisions regarding goods production procedures, technological advancement, etc. are interrelated, especially when countries enter the global value chain.

Furthermore, in the presence of cross-dependence, the second-generation panel unit root test is highly recommended. Therefore, the CIPS panel unit root test is applied to each panel unit to sort the stationary level and the order of integration (Table 3 in Appendix). The results confirmed that all six time-panel have unit roots and assume that the data is unstable. While it has become stationary at the first difference, thus the alternative hypothesis of no unit root in the panel is accepted. Underlying the variables appears to be integrated at first-order, so the hypothetical co-integration test can be determined to diagnose long-term relationships among the variables. The systematic results of the panel co-integration tests are presented in Table 4 in Appendix. The results by Westerlund prove the existence of panel co-integration among the CO2, per capita income, agriculture production efficiency, energy consumption, R&D, and government effectiveness.

Results for full panel

Co-integration among the panel series induces us to use Driscoll and Kraay, which is more effective in cross-dependence cases. The long-run parameters concerning CO2 (dependent variable) are given in Table 5. Three regressions have been estimated for judging the environmental impact. In the first regression, agriculture production efficiency on carbon emission has been considered without the time and country effects. The results indicated that the bonding between agriculture production efficiency and carbon emission is significantly negative at the level of 1%. The subsequent two regressions controlled the time and country-specific effects to avoid the misspecification of the results. The results of column (2) in Table 5 indicated that income significantly degrades the environmental quality at the initial stage of the country’s growth. However, environmental quality does not remain a secondary priority at the second phase of the development. Because when the country’s production (per capita income) increases, people/government become conscious about health (Gozgor 2017).

Table 5 Carbon emissions full panel long-run estimates
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Furthermore, technological advancement decline environmental pollution in the latter phase of income growth (Zerbo 2017; Dogan and Turkekul 2016). In the third regression, income and income square impact on carbon emissions are significantly positive and negative at the level of 1% and 10%, respectively. The results reported in Table 5 are indorsed the cogency of inverted U-shaped EKC hypothesis in considered countries. Moreover, the results could be validated by Managi et al. (2008) and Yasmeen et al. (2018). Again, agriculture production efficiency positively reduced carbon emissions (see columns 2 and 3). These results can be justified by Gołaś et al. (2020), who stated that technological progress in the agriculture sector increases the production intensity and lowers the negative environmental impact of production. However, efficiency may be characterized by larger or small areas of production. So the economic goals (production augmentation) can be achieved simultaneously with environmental goals if the agriculture sector can use the input efficiently. In contrast, Ullah et al. (2015) mentioned that “most farms cannot combine high economic performance and low environmental impacts.”

Agriculture’s efficiency could be enhanced if enough investment is made in R&D for technological advancement. If a country wants to produce on a large scale with less emission, it may need to pay more attention to input use, technology, and energy source. Given this, we incorporated the R&D to see its impact on carbon emissions. The results proved that investment in R&D is beneficial for the country’s environmental health as carbon emissions are significantly positive in columns 2 and 3 of Table 5. The results are in line with Petrović and Lobanov (2020). According to Guo et al. (2018), Yu and Wu (2018), the association between R&D and carbon emissions is a long-term phenomenon. Furthermore, the interaction terms of R&D investment and agriculture production efficiency are included for comprehensive analysis. The aim of this term is to find whether R&D investment could have the ability to improve the agriculture sector and that could reduce the carbon emission from the agriculture sector. The regression results significantly support the role of R&D investment in the agriculture sector to promote a cleaner environment by reducing carbon emissions. The use of energy is important for the production process. Therefore, including an energy indicator is imperative, and the regression outcomes are not beyond the expectations. The impact of energy on emitting carbon emission is significant at the level of 1%. The second two significant results that make the study necessary are the government’s effectiveness in improving the environment and its moderating role to encourage R&D investment in R&D for technological advancement. The results endorsed that government effectiveness plays a positive role in diminishing carbon emissions and supporting research and development activities to improve the environment. The results are supported by Yasmeen et al. (2018), Gani (2012). The government can use a robust device mechanism of monitoring illegal activities such as bribery and black market. These constraints by the government would encourage foreign investment, which eventually would invent the new technologies with mutual corporation.

Carbon emissions possibly have reverse causality. Therefore, the study used carbon emission as an explanatory variable to capture the simultaneous effect between environment and agriculture production efficiency. The results of column 1 in Table 6 indicated that carbon emission lessens the production efficiency of agriculture as the coefficient impact is significantly negative. The results for CO2 are similar in columns 2 and 3. The results are validated by Zafeiriou and Azam (2017), who recommended that the agriculture output decreases with increasing carbon emissions. Agriculture production efficiency does not seem to be increased with income at an early stage of economic growth as the coefficient impacts on improving agriculture production efficiency are insignificant and negative. It may imply that countries do not have advanced technologies or lack access to advanced production methods in the starting phase of economic growth. However, the second development phase (square of per capita income) positively increased production efficiency. These two results are not astonishing as in previous regression; we found that the environmental quality improves in the later income stage. So, in line with the EKC hypothesis, we can say that production methods improve due to technique effects, which is primarily possible in the second phase of the country’s development.

Table 6 Agriculture production efficiency full panel long-run estimates
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In contrast to Table 2, the impact of energy consumption on agriculture production efficiency is negative. Energy consumption in oil is not beneficial to improving production efficiency and the environment. The role of R&D investment is positive given the agriculture production efficiency. The findings can be verified by Ahearn et al. (2002), who believe that agricultural research institutes are critical to increasing agricultural output. However, the direct effect of government to improve agriculture efficiency is positive. Also, the moderating role raises the positive aspects of the government to improve agriculture production. Government can be a bridge to improve agriculture production efficiency if it efficiently regulates the R&D relevant activities. The investment in R&D is for creative work, which increases the stock of knowledge. This knowledge can devise new applications (Ouru et al. 2018).

Results for developed and developing countries

The study divided the panel into developed and developing countries for further wide-ranging results. Because developed and developing countries are different in their economic level, the relationships between the concerned indicators can be heterogeneous. Therefore, first, to know whether the statistical difference exists between the divided groups, we applied the Mann–Whitney U test proposed by Frank Wilcoxon (1992). The summary for Mann–Whitney U test is given in Table 7, and the mean ranking of both groups (developed and developing) is presented in Fig. 5. The results showed a significant statistical difference between average agriculture production efficiencies of developed and developing countries, rejecting the null hypothesis “the distribution of average agriculture production efficiency is the same across categories of type of countries” as the significance level is less than 5%.

Table 7 Mann–Whitney U test summary
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Fig. 5
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Mann–Whitney U test (mean ranking)

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After difference identification, analysis for developed and developing panels is statistically rational. The results for the developing panel are given in Tables 8 and 9. Table 8 shows that agriculture production efficiency increased the environmental quality by lowering the carbon emission intensity. The impact of income on emitting carbon emission is positive in the first phase of the growth due to the scale effect. However, the subsequent growth stage showed that pollution is intended to be lower on technique effects as income grows, ignoring significance level. The study fails to validate the EKC hypothesis in true words. Yet, these results might be possible in developing countries as low-income countries are not very competitive and have fewer sources to access advanced technologies.

Table 8 Carbon emissions long-run estimates for developing countries
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Table 9 Agriculture production efficiency long-run estimates for developing countries
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Furthermore, developing countries continue to engage in dirty production by polluting industries with less demanding environmental policies. These results could be supported by the positive impact of government effectiveness on carbon emission. In contrast, investment in R&D is a positive tool to reduce carbon emissions. The positive connection between government and carbon emission showed less government’s effectiveness in reducing emission. In other words, the environment is the second priority in developing countries, so the direct impact is not much encouraging. However, it enhances the agriculture production efficiency by innovating new methods that are helpful to keep the environment clean (see interaction terms effect). Even government can be a source to promote R&D investment in all economic dimensions. R&D investment by the government means promoting technological innovation behavior to touch the optimum level of efficiency (Guo et al. 2018). Government through incentive effect can stimulate modernization and control the cost and risk element in R&D investment. The use of energy is a significant source of increasing pollution into the air.

In Table 9, agriculture production efficiency is used as a dependent variable to gauge the environmental impact on the agriculture sector. The results indicate that carbon emission is consistent with previous results and shows a deleterious effect on improving agriculture efficiency. Similarly, developing countries are not much advanced to improve the efficiency of agriculture sector production at starting economic growth. However, it can promote agriculture efficiency in the later development phase, possibly having invented or access to advanced production methods. As research related to economic sectors speeds up, it also positively promotes its efficiency. Therefore, R&D activities are important to develop the agriculture sector as the co-efficient impact is positive and significant in Table 9.

In contrast, government effectiveness is positive on agriculture production efficiency, indicating the government priority towards the economic decision. Developing countries’ governments are more concerned with production expansion and comparative advantages than the environment. Therefore, government effects on carbon emission and agriculture efficiency can be dissimilar. Furthermore, government support for R&D investment to increase the efficiency of agriculture production is positive.

The results of developed countries group are for CO2 and agriculture which are given in Tables 10 and 11. The results in Table 10 indicate that increasing the level of production efficiency can lower the carbon emission as the coefficient impact on CO2 is negative. Research and development activities improve the level of efficiency of the agriculture sector to decrease emissions. Developed countries’ governments are more successful in implementing the rules and policies. Accordingly, government effectiveness and moderating effect (interaction term) positively reduce carbon emissions. However, we find the U-shaped EKC in the case of developed countries as the income decreases the carbon emissions at an earlier stage of growth and increases by the expansion of growth. As the level of the industrial sector increases with growth expansion, demand for energy consumption also increases. These two parallel augmentations in industrial growth and energy consumption drive pollution even in development. According to World Energy Statistics 2019, oil consumption demand is rising day by day, including developing (India, China) and developed countries (USA).

Table 10 Carbon emissions long-run estimates for developed countries
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Table 11 Agriculture production efficiency long-run estimates for developed countries
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The results conveyed in Table 11 showed that carbon emission has a reverse adverse impact on agriculture production efficiency. If weather is not compatible, agriculture production will remain lower. However, agriculture production efficiency increases with economic growth as the impact of income on agriculture production efficiency is negative and positive, respectively. Investment in R&D is positive to improve the efficiency in developed countries, and government can facilitate to promote R&D investment because the R&D process geared the production process and invented green technologies. Governments can pay more attention to the “emission reduction technologies” for reducing the amount of sewage commendably through a regeneration process, equipment modification, or modernism. However, oil energy consumption is not beneficial for improving agriculture production efficiency. However, through the R&D process, energy-saving technologies would positively increase production efficiency and the environment.

Conclusion and policy implications

The agriculture sector has been transformed over time by the forces of globalization. Still, management practices to agriculture production need to be utilized efficiently for economic and environmental advantages. The production efficiency is subject to research and development for green technologies. Therefore, the study investigates the nexuses between agriculture production efficiency, carbon emissions, R&D investment, and government effectiveness over 1996–2018 for the major agriculture-producing countries. Based on empirical findings, we have reached the following conclusions.

Firstly, the DEA application suggested that the USA, Russia, Korea, Japan, and Italy are efficient countries in agriculture production. In comparison, Australia and France are near to efficient. Among BRICS countries, China (0.183), India (0.378), and Brazil (0.382) are far off to Russia in Agriculture production efficiency. Secondly, agriculture production efficiency is a significant determining factor in improving environmental quality. In comparison, carbon emission has a reverse effect and lowers the efficiency of agriculture production. These results indicated bidirectional causality between agri-production and the environment. Thirdly, full panel results supported inverted U-shaped EKC curve, however different by developed and developing case. R&D investment is favorable to invent the advanced production methods as the impact is positive. Government effectiveness plays a significant role in improving the environment by encouraging investment in R&D for technological advancement. The results certified that government effectiveness is important to reduce carbon emissions by supporting R&D activities. Agriculture production efficiency is less efficient than starting economic growth as the coefficient impacts on improving agriculture production efficiency are insignificant and negative. At the later stage of the development, agriculture production efficiency increased. Countries may have access to advanced technologies which increase production efficiency.

We divided the sample into developed and developing groups for the comprehensive analysis. The statistical differences have been identified by employing the Mann–Whitney U test proposed by Frank Wilcoxon. The results showed a significant difference between the mean agriculture production efficiency of developed and developing countries. The study could not capture a significant inverted U-shaped EKC curve in developing countries’ cases. However, U-shaped EKC has been found in developed countries. Furthermore, two important results have emerged; one is that developed countries’ governments are concerned about improving agriculture production efficiency and the environment. In contrast, environmental quality is the second priority for developing countries compared to agriculture production. The impact of oil energy consumption is not beneficial to improving the environment and agriculture efficiency.

According to the results, some significant policies could be drawn easily. First, though developed nations are comparatively efficient in agriculture production, they still need to improve the efficiency of the available resources. R&D activities could achieve this. Such as, Australia experienced a continuous upward trend in crop yield based on its modern agriculture initiated during the 20th epoch, but the gap remains between potential and actual farm yield for many reasons. Therefore, the agricultural sector has been an ongoing concern for the Australian government, investing in R&D to optimize this sector. Developing countries’ governments have less concern to improve environmental quality. To improve the environment quality is in favor of human lives and improving crop yield efficiency. Therefore, the government needs to invest a significant amount in R&D. For instance, the US government has started R&D programs; the focus is on the reduction of carbon capture and storage. CO2 would be captured and safely stored in geological formations by this program. R&D activities have several other positive consequences. For instance, from investment in R&D, green products with improved performance can be produced. The agriculture production cost would be reduced; green innovation would overcome global warming. The efficiency of existing raw resources can be improved, help create jobs, and many other benefits. However, all these would be possible if the government is committed and reforms its policies to prevent carbon activities and improvisation of the agriculture sector on a priority basis. Special attention is required from the developing countries. Though the present study tried to carry out comprehensive research on agriculture production efficiency and environment, many important factors still need to be incorporated and researched, such as other institutional and social factors that can improve the agriculture structure and environment. In this way, future study on agriculture production efficiency and the environment tends to grow and become more in-depth and comprehensive.