1 Introduction

Rising environmental degradation through the quest to feed the ever-increasing global population has recently received academic and policy focus [1]. Concerns are heightened about reducing the destructive environmental impact of food production because agriculture contributes about 30% of the anthropogenic greenhouse gas (GHG) emissions driving climate change [2]. According to researchers, farming now contributes significantly to atmospheric CO2, CH4, and N2O emissions. The main contributor of carbon dioxide (CO2) is the burning or destruction of soil organic materials. Particularly, fermentative digestion by grazing cattle, stockpiled manures, and grains cultivated in floods leads to the production of CH4 through compound breakdown. N2O is created when bacteria in soils and manures break down nitrogen (N) in a way that is greater than what plants need. The result is growing rates of global warming; deteriorating human health and unsustainable food supply [3,4,5]. Available studies claim that the last century’s green revolution policies have created a substantial uptake of synthetic fertilizers, development of new crop varieties and increased industrial agricultural production [6].

Experts have recognized the role of agriculture to the economies of sub-Saharan African (SSA) countries in terms of contribution to GDP, employment and foreign exchange. Ensuring sustainability of this key sector is critical for the realization of inclusive growth and development in the sub-region. Although environmental pollution is less severe in sub-Saharan Africa (SSA) countries as compared to several other regions, the ever-rising economic growth and urbanization rates have resulted in fossil energy use in agriculture leading to environmental degradation [7]. Contributing an estimated 3.2% to value addition in growth of SSA, the environmental consequence of agricultural production in SSA is also reflected in severe regional deforestation [8]. Given that policy is required to reverse this trend, the Africa Union and the Food and Agricultural Organization (FAO) seek scientific investigations towards getting insights into sustainable agricultural production. This is to ensure that human agricultural practices is able to deal with climate change, rising rate of biodiversity losses, land degradation from soil erosion and pollution of water resources. Sustainable agricultural involves producing abundant food in environmentally friendly manner [9, 10]. Experts have against this background, proposed several policy options to help address the issue, including closing the yield gap, raising crops production potential, reducing waste, and modifying diets and expanding aquaculture.

Over the last few decades, one of the most highlighted factors is the deployment of green finance in agricultural production [11,12,13]. Green finance in agricultural production refers to agricultural funding that maximizes the highest social returns [14]. Effective and green financial markets could accelerate development through smart and information-based agricultural infrastructure and renewable energy (RE) technologies for sustainable food production and reduce carbon emissions [15]. Recently, several approaches to green investment financing have been proposed having great potential to support clean energy development; and can provide sustainable finance to projects. Among these are green bonds, establishment of green banks, and investment in village development funds.

Another most cited factor to has positive effects on sustainable agriculture development across the world is digital technologies [16,17,18]. Internet, mobile phones and associated communication technologies impact millions of people as they help with collection, storage, analysis, and agricultural data dissemination [19]. There is potential for mobile phones and the Internet to improve agricultural productivity. It is found to significantly deal with agricultural sector challenges, including increasing food supply and reducing resource use. Smart technologies require corporations to review their investment in agricultural growth [20]. Critics however claim, that smart technologies require huge financial investments and new skill sets due to the complexity of technologies [21].

The lingering academic question involves whether both green finance and digital technology matter for sustainable agricultural development. To validate these claims, sub-Saharan Africa presents the best location for investigating sustainable agricultural effect of both green finance and digital technologies given their historical records in those factors. With approximately 13% of the global population, the Organization for Economic Cooperation and Development and the Food and Agricultural Organization (OECD/FAO) indicates that the sub-Saharan Africa (SSA) population is projected to reach 22% by 2050, half of whom are working in the small-scale agriculture sector, which form about 80% of total current farms. Since the early 2000s, several policy initiatives have been integral to the development of the agricultural sector. The New Partnership for Africa's Development (NEPAD) is the economic program of the African Union (AU), which was officially established in 2001. To improve agricultural policies on the continent, NEPAD developed a special initiative called the Comprehensive Africa Agriculture Development Programme (CAADP). Despite the prioritization of the agricultural sector, FAO’s Monitoring and Analyzing Food and Agricultural Policies (MAFAP) programme notes an overall decreasing trend in the share of public resources channelled to agriculture in the ten African countries reviewed in 2013. Apart from South Africa which budgets 0.9% of their gross domestic product on agricultural research, all other sub-Saharan Africa economies are reported to invest less than 0.5% on same [22].

Over the years, financial support for green food supply have been sourced from external agencies or governments of advanced economies. According to the 2019 World Bank regional report, early-stage spending in the green firms in sub-Saharan Africa has seen slow growth over the years compared to growth-stage investments. Between 2006 and 2017, green firms in SSA have raised only $1.4 billion, including grants. Of this, early-stage financing stood at $448 million, including $90 million in grants, and largely concentrated East African economies and very limited green financial activity in West Africa. In general, experts have found sub-Saharan Africa has several challenges in green financing. First, the sub-region has limited access to financial, material and human resources. This is attributed essentially to economic and political risk factors. Second, the region lacks critical technical skills in managing advanced green projects such as solar systems to improve the energy mix and large-scale farming to improve food supply. Third, available informal small and medium scale enterprises borrow from unregistered and illegal money lenders at high interest rates with no regards to green and sustainable projects.

Although mobile banking has recently seen a rise, for the case of digital technology and sustainable agricultural development, sub-Saharan Africa smallholder farmers have been noted to have limited access to digital solutions [23]. In their empirical study, Goedde, McCullough [24] noted that most digital applications in SSA have less than 30% active users. Trendov, Varas [25] in their study found that the enabling environment for digital solutions remains under developed in SSA. They determined that policies, regulatory institutions, digital infrastructure, high cost and skills to enable the use of digital solutions continue to remain key barriers to uptake and expansion of digital agriculture in SSA.

Based on the above, it is clear studies on sustainable agriculture effect of green finance and digital technologies have not extensively explored sub-Saharan Africa. To the best of our knowledge, this is the first study to conduct a comprehension investigation on sustainable agricultural effects of green finance and digital technologies in sub-Saharan Africa. The outcomes of this paper will be significant to broadening global knowledge foundations on effects of sustainable finance and digital technologies on sustainable agriculture. Additionally, the novelty of the paper stems from the use of second, rather than first generation methodological approaches. While the later essentially assumes cross sectional independence, the former asserts the existence of cross-sectional dependence, a direct result of globalization and other cross-national interlinkages. The chosen methodology is able to correct biases that are prone to first generational panel estimates. Besides, the approach can circumvent endogeneity issues between dependent and independent variables. Further, the approach can deal with serial correlation between co-integrated panels. Further, this study uses panel-corrected standard errors (PCSE) which has been found to generate robust and reliable scientific estimates for policy recommendations [26, 27]. Lastly, this research is motivated by the resource-based theory of organizations as collection of creative resources for considering and executing impactful initiatives [28] while the authors are motivated by diffusion of innovation theory by which once made; innovative ideas are eventually diffused across the entire population until saturation point [27, 29]. The next section is the literature. Subsequent sections include the methodology, empirical outcomes, and conclusions with policy recommendations.

2 Literature review

In this review of literature, the paper aims at broadening knowledge foundations for investigating the effects of sustainable finance and digital technologies on sustainable agriculture for sub-Saharan Africa using systematic literature appraisal tool [30].

Sustainable production refers to the development of manufacturing industry’s ability to underpin societal needs for wealth creation in a way supporting sustainable economic growth. Utilizing environmentally friendly procedures to produce products is known as sustainable production [31]. Sustainable agriculture is defined to refer to an “integrated production system that use plants and animals” to provide food and fiber needs over a long period; improve the environment; and improve farmers’ and societal livelihoods amidst current global challenges in water, food and energy supply [16, 17, 31, 32].

In recent times, sustainable production has become a critical topic in manufacturing and environmental sciences, mechanical engineering, as well as energy science [33]. Understanding material and energy systems in product supply provide insight into investment cost, technology efficiency and environmental impact. Experts claim that to control these requires green resource production and use through green financing and digitization of the processes [31, 34]. As part of the review process, two hypotheses are proposed towards accomplishing the stated objectives of determining factors of sustainable agricultural development for the case of sub-Saharan Africa.

H1

Mitigated green finance causes improvements in sustainable agriculture growth in sub-Saharan Africa.

Theoretically, financial system promotes long-term development rates, investments, innovations in technology, and the amount of money saved. The theoretical basis stems from the resource-based viewpoint, which sees business entities as aggregates of innovative resources, which enable the development and deployment of approaches to increase effectiveness and productivity [28, 31]. When these resources are green, organizations may realize better environmental outcomes [31, 35]. Besides lowering emissions and cost, green financial resources facilitate sustainable production through green procurements [36]. In this scenario, “sustainable manufacturing” entails the creation of technologically advanced manufacturing systems that are beneficial to both individuals and society [33].

In their empirical studies [37], found that because of China’s governmental green economic policies, the Chinese green funds outperform several economies in the delivery of sustainable environment and circular economy objectives. To validate this claim [38], found green finance intermediation role to substantially deliver zero-carbon economies. Mirza et al. [39] found that to reduce carbon dioxide emissions, governments must give special attention to green finance and reverse the outdated project financing styles. Several other studies on green finance have been done over the years. While some studies focused on the impacts of green finance on economic growth, others have focused on replacement aspects [40]. Green finance has been found generally as strategic and purposeful tactic to help industrial production transition to efficient use of resources and reduced low-carbon emissions towards reducing climate change while improving economic prospects across the world [34, 40,41,42,43].

Given this review action, the paper hypothesizes that for sub-Saharan Africa, mitigated green finance causes sustainable agriculture development; i.e., \(\upsilon 1 = \frac{{\upsilon {\text{LAVAit}}}}{{\upsilon {\text{LM}}GF_{it} }} > 0\), where \(\upsilon 1\) functions as the interest parameter. LAVA is the log of agriculture value added; LGFit is the log of green finance in sub-Sahara Africa because this paper investigates how both green finance and digital technology affect sustainable agricultural growth for the case of sub-Saharan Africa between 2003 and 2018. This hypothesis finds support from [31, 35].

The basis for this is that historically, digital technologies have proved to have a major effect on linking farmers to markets along with vital aspects of the value chain for agriculture. In theory, innovation mechanisms (particularly system innovations) are transformative when seen from various ‘bundles’ of critical social as well as institutional innovations including agro-ecology, vertical cultivation, the internet and cellular agriculture [44,45,46,47].

Agricultural infrastructure, in theory, is what drives the delivery of ecosystem services [48]. The utilization of digital technologies, including sensors and intelligent devices, could work as the complementary driver of the positive effects of ecosystem services and agriculture [49]. However, a new study of agricultural producers in Bangladesh, China, India, and Vietnam indicated that 80% of them owned mobile phones and had been making use of these to evaluate intermediaries and dealers along with gauging the market demand [50]. On top of that, “information disparity” often leads to price injustice, causing some farmers to lose money, while raising costs for consumers [51]. The consequences of better market data on producer prices have recently been examined in a number of empirical papers, despite conflicting outcomes [51, 52].

A number of digital tools, applications, platforms and devices are typically used in electronic extension systems. The most basic means of agricultural extension service delivery are dedicated telephone lines, radio and television programs with a question-and-answer format. A highly improved extension system that combines mobile technologies with online platforms designed to be operated via smartphones and tablets constitutes the other end of the spectrum. An e-extension system can serve as an information bank, providing access to information on global best practices about crops on different agro-climatic conditions, retailers and prices. In the case of sub-Saharan African economies [53], found that extension agents' use of mobile phones reduces operational costs by one-fourth. In developing economies seeking export markets, the adoption of digital innovations has enhanced the management of agricultural supply chains. The collection, transportation, and quality control of smallholder crops is facilitated through the deployment of digital systems by cooperatives and aggregators [54]. The internet has been found to provide information that protect consumers and improve livelihood of farmers through creating a variety of specialized market options [55]. As noted by Site and Salucci [54], improved public services and technological innovations are essential in rural areas for assisting farmers to access markets across the globe. Mishra and Sharma [56] assert that global positioning systems and computer technology have traditionally been extensively used in agricultural production. In addition, in order to determine the pH value and level of moisture of soil, intelligent devices and data-collecting sensors are now being applied through digitalization.

H2

Rising mobile cellular subscriptions [57] have positive effects on sustainable agriculture in sub-Sahara Africa.

Recent innovations in information and communication technologies have influenced most parts of life. Rajagukguk et al. [57] found ICT to positively affect the agricultural industry. Pantelimon et al. [58] claims, the rapidly rising mobile cellular use, including mobile commerce is linked to gross domestic product (GDP). Based on these findings, the study expects rising mobile cellular subscriptions to positively affect sustainable agriculture in sub-Sahara Africa, i.e., \({\varvec{\upsilon}}{\mathbf{1}} = \frac{{{\varvec{\upsilon}}{\text{LAVAit}}}}{{{\varvec{\upsilon}}{\text{L}}{\varvec{MCS}}_{{{\varvec{it}}}} }} > {\mathbf{0}}\), where \({\varvec{\upsilon}}1\) refers to interest parameter; LAVA is the log of agriculture value added; and LMCSit represents the log of mobile cellular subscriptions in sub-Sahara Africa.

H3

Increasing rates of individuals using mobile phones and internet [59] have positive effects on sustainable agriculture in sub-Sahara Africa.

Theoretically, internet and mobile communication protocols have both direct and indirect economic effect through market efficiency, stakeholder welfare and job creation [60]. In the food supply sector, the internet and mobile phone revolution has a market efficiency effect [61]. Ezeoha et al. [62] finds that African mobile phone use increased from 129 million to 1.2 billion between 2010 and 2020. Several empirical studies have indicated that the rise in mobile phone use has had a positive effect on inclusive development in Africa [60, 63] and can increase agricultural productivity due to its capacity to help reduce operational costs [60]. Based on this review, the paper expects rising rates of people using mobile phones and the Internet to have positive effects on sustainable agriculture in sub-Sahara Africa; i.e., \(\upsilon 1 = \frac{{\upsilon {\text{LAVAit}}}}{{\upsilon {\text{L}}IMU_{it} }} > 0\), where \(\upsilon 1\) is interest parameter; LAVA is the log of agriculture value added; and LIMUit is the log of internet and mobile phone use in sub-Sahara Africa. This hypothesis finds support from Aker [53].

H4

Rising renewable energy consumption has positive effects on sustainable agriculture in sub-Sahara Africa.

In SSA, traditional open sun drying technology has historically been used for food-reservation by local farmers at no cost. A review of sustainable technologies for drying food, including renewable energy sources [64] showed that solar energy integration with microwaves is efficient for food. Based on this review, the paper assumes rising renewable energy use to have positive effects on sustainable agriculture in sub-Sahara Africa; \(\upsilon 1 = \frac{{\upsilon {\text{LAVAit}}}}{{\upsilon {\text{L}}RE_{it} }} > 0\), where \(\upsilon 1\) refers to the parameter of interest; LAVA is log of agriculture value added; and LREit represents the log of renewable energy consumption in sub-Sahara Africa.

Given this review exercise, there is clarity that studies on sustainable agriculture effect of green finance and digital technologies have not prioritized in sub-Saharan Africa. To close this gap in the literature, the study employs panel-corrected standard errors (PCSE) in this assessment. The approach is chosen because several scholars have found it to yield reliable and efficient scientific estimates [27, 29].

3 Methodology

3.1 Data and source

This paper investigates sustainable agriculture effect of green finance and digital technologies for the case of sub-Saharan Africa between (SSA) 2003 and 2018. Renewable energy consumption and Individuals using the internet were kept under control, as they are theoretically relevant in explaining sustainable agricultural development across the world. Data for this research was collected on 30 countries in SSA (i.e., Angola, Benin, Botswana, Burkina Faso, Burundi, Cabo Verde, Cameroon, Chad, Democratic Republic of Congo, Ivory Coast, Gabon, Gambia, Ghana, Guinea, Guinea-Bissau, Kenya, Lesotho, Madagascar, Malawi, Mali, Mozambique, Namibia, Nigeria, Rwanda, Senegal, South Africa, Tanzania, Uganda, Zambia and Zimbabwe). Data was sourced on (i) Agriculture, Forestry and Fishing value added [65] as proxy for sustainable agriculture. Data was sourced from World Bank database. (ii) Mitigation-related development finance (commitment) as proxy for green finance (Steele, 2015); Climate-related development mitigation finance is funding to raise renewable energy supply and consumption with the objective to trigger a decline in greenhouse gas emissions. Data was sourced from Organization for Economic Cooperation and Development (OECD). (iii) Mobile cellular subscriptions [57]. Mobile cellular-phone subscriptions are public mobile telephone service subscriptions using cellular technology. The indicator is derived by dividing total mobile subscriptions by the total population and multiplied by 100. Data was sourced from the World Bank; (iv) individuals using the internet [59]; individual internet users are those using internet within the previous quarter; and calculated as ratio of total population. Data was sourced from World Development Indicators; (v) Data on renewable energy consumption [66] was sourced from IEA; renewable energy use is the ratio of gross inland energy utilization and annual gross energy use [67]. Historically, several sectors of agriculture have found alternative sources of energy given the rising negative environmental effect from fossil fuel use. Several renewable energy sources have been used including wind, hydro, photovoltaic and biomass. Table 1 depicts data source and description.

Table 1 Data description
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3.2 Theoretical motivations

The environmental Kuznets curve hypothesis argues that environmental pollution increases with resource exploitation for economic growth [68]. When economic growth is mainly propelled by fossil fuel use, air pollution and environmental degradation are worsened. Theoretically, improvements in financial systems help to generate saving rates, support investment decisions on relevant green technologies and assure sustainable growth. When services offered by the financial system are green, beneficiary organizations may produce better environmental outcomes [31, 35]. The theoretical foundation is hinged on resource-based theory, which recognizes organizations as collection of creative resources for conceiving and implementing projects [28]. According to Razzaq et al. [69], besides lowering emissions and costs, green financial resources are essential for realizing sustainable production through green procurements. In agriculture, it is also becoming evident that using digital technologies can address traditional information asymmetry difficulties of farmers, particularly those related to input and output market access [70]. Several economies have been found to optimize the use of mobile phones and internet to solve socioeconomic challenges, including agriculture [71, 72]. To account for agriculture value added in this paper for SSA, the model is

$$AVA = f\left( {MGF, IMU, MCS,RE} \right),$$
(1)

where “AVA is the agricultural value added; MGF is mitigation-related Green finance; RE is renewable energy consumption; IMU is individuals using the Internet; MCS represents mobile cellular subscriptions”.

Next, the data is transformed into their natural logarithms to avoid scaling and create the real elasticities among variables [73].

$$lnAVA_{it} = \beta_{0} + \beta_{1} lnMGF_{1it} + \beta_{2} lnRE_{2it} + \beta_{3} lnIMU_{3it} + \beta_{4} lnMCS_{4it} + \varepsilon_{it} ,$$
(2)

where β0 is constant, slope coefficients are denoted by β; country is represented by i; t; is time (from 2003 to 2018). LAVA is the natural log of value-added agriculture; LMGF is the natural log of Mitigation-related Green finance; LRE is the natural log of renewable energy consumption; LIMU is the log of Individuals using the Internet; MCS represents the log of Mobile cellular subscriptions and “\(\varepsilon\)” is the error term.

3.3 Econometric approach

The paper uses second-generation econometric techniques to investigate the connection between LAVA, LMGF, LIMU, LMCS, and LRE in sub-Saharan Africa from 2003 to 2018. To realize this objective, the paper employs (i) Breusch–Pagan LM, Breusch–Pagan LM and Bias-corrected scaled LM Pesaran CD by [74] for cross-section dependence checks; (ii) Pesaran and Yamagata [75] and Blomquist and Westerlund [76] for homogeneity of slope tests, (iii) CIPS, CADF, Hadri and Breitung for stationarity checks; (iv) Pedroni [77] and Westerlund [78] for panel co-integration test, and (v) panel corrected standard errors (PCSE) for the model estimation. (vi) Dumitrescu Hurlin panel test is finally adopted for panel causality estimates. These techniques are explained in the proceeding paragraphs.

3.3.1 Cross-section dependence test

Recent investigations [79] demonstrate that panel data contain severe cross-sectional reliance challenges due to cross-border shocks from economic integration and prevalent risk variables. The study employs the [74] tests to determine whether cross-sectional units have equal effects through observable and hidden factors in order to achieve the objectives.

$${\mathbf{CSD}}_{{\varvec{TM}}} \frac{{{\varvec{TN}}\left( {{\varvec{N}} - {\mathbf{1}}} \right)^{{{\mathbf{1}}/{\mathbf{2}}}} }}{{\mathbf{2}}}{\overline{\varvec{\rho}}}_{{\varvec{N}}} .$$
(3)

Here \(\overline{\rho }_{N}\) represents the parameters of pairwise correlation while N and T represents cross-sectional units in relation to numbers and period respectively. Results are illustrated in Table 3.

3.3.2 Slope heterogeneity check

Panel data can selectively pool time series dimension information from cross-sections to enable efficient estimates. Nevertheless, this is possible when parameters of interest are homogeneous [80]. The paper checks for homogeneity of slope by employing approaches used by Pesaran and Yamagata [75] and Blomquist and Westerlund [76]. Results are shown in Table 4.

3.3.3 Unit root test

To prevent erroneous regression, empirical analysis has to establish the stationary behaviour of the data. A variable can become stationary at level or at the first difference, which suggests that the variable’s mean zero has a variance that remains constant [81]. Given that outcomes of the panel LM test always display cross-section dependence, the paper employs second-generation Augment Dickey–Fuller Fisher-type panel unit root tests [74] to check for the integration properties of variables. Lagged cross-section averages and their initial differences are added to the traditional ADF regression to adjust cross-sectional dependence using single-factor frameworks for residuals:

$$\Delta y_{it} = a_{i} + \beta_{i} y_{i, t - 1} + \gamma_{i} \overline{f}_{t - 1} + \varepsilon_{it} ,$$
(4)

where \(\Delta y_{it}\) = \(y_{it}\) − \(y_{i, t - 1}\), ft is the unobserved common effect, and εit is unit-specific errors; ith is time specific cross-section unit; and, H0: βi = 0 for all i, against alternatives, H1: βi < 0, i = 1, 2,…,N1, βi = 0, i = N1 + 1, N1 + 2,…,N. For a subsequent stage, the statistic associated with the bootstrapped non-standard null distribution is generated by aggregating all N t-statistics for i. The technique combines lagged levels of cross-section averages and first differences of variables to the Augmented Dickey–Fuller estimates as opposed to tests on deviations generated by common components estimates. A shortened adaptation, indicated by CADF, prevents excessively severe results from occurring in tiny T samples. The development of a modified IPS t-bar test using average individual CADF or CIPS statistics was successful in this case. The CIPS test is modelled as

$$\widehat{CIPS} = \frac{1}{N}\sum\limits_{i = 1}^{n} {CADF_{i} } .$$
(5)

The average lagged of the cross section and the first difference of its averages are is denoted by \(\overline{Y}_{t - 1}\) and \(\Delta \overline{{Y_{t - 1} }}\) respectively; CADF refers to cross-sectionally augmented Dickey–Fuller.

3.3.4 Panel co-integration test

Historically, the conventional co-integration methods have not considered cross-sectional dependence issues associated with panel data. To consider cross-section factors, the paper employs the recently developed [77] and [78] panel co-integration, which can deal with cross-sectional dependence, heteroscedasticity and serial correlation errors. Both implement different methods whether eit is nonstationary, and very comparable to combined Johansen test. Pedroni estimator relies on Engle–Granger residual-based cointegration approaches where heterogeneous intercepts and trend coefficients are considered across the cross-sections. Pedroni [77] co-integration estimator considers panel-specific vectors and AR coefficients (*i) to be compared across panels, assumes independence for the idiosyncratic error terms cross sections, and uses GLS-based error correction toward getting feedback in both within-dimension (panel) and between-dimension (group) approaches. The null hypothesis is no cointegration between yit and xit, whereas for Westerlund, some panels are co-integrated. The test equation is generally modelled as:

$$y_{it} = x_{it }^{{\wr }} \beta_{i} + z_{it}^{{\wr }} { \curlyvee }_{i} + e_{it} .$$
(6)

For every panel i, each covariate in xit is an I(1) series. Pedroni and Westerlund tests allow seven maximum covariates in xit; βi is the cointegrating vector with possible variations in the panel; γi is coefficient vector on zit; controling panel-specific effects and linear time trends; eit is error term. The estimates of this advanced co-integration test are illustrated in Table 6

3.3.5 Long-run equilibrium test

Knowing from the co-integration outcomes that long-run equilibrium linkages exist in panel data, the paper employs panel corrected standard error (PCSE) estimator found to yield robust estimates amidst cross-sectional dependence factors. In their studies [82], proved that the PCSE estimator is a robust tool for long-run co-integration analysis, although they noted the approach is limited when the number of periods (T) is less than the cross sections (N) unless relevant ECMs are inverted. To them the modified GLS (i.e., “panel-corrected standard errors” (PCSE), can preserve weights and correct inherent errors using sandwich estimators. The method uses an interleaved estimate and integrates lateral dependencies in calculating standard errors. The approach is robust to heteroskedastic, contemporaneously cross-sectionally correlated, and autocorrelated to first-order autoregression. Accepting that the blunders are autonomously time-related; and the change of errors in the covariance framework is built as

$$\cap = \sum \otimes { }1{\text{r ,}}$$
(7)

where Ʃ is the N × N lattice of error variances and concurrent co-variances; and ⨂ addresses the Kronecker item. Given that Ʃ refers to the T × N grid of the OLS residuals. E′E/T gives a predictable gauge of Σ. PCSE estimates are assessed by the square base of the askew of

$$(X^{\prime}X)^{\prime}X^{\prime} \left( {\frac{E E}{T} \otimes I_{r} } \right)X (X^{\prime}X)^{ - 1} .$$
(8)

The PCSE approach for testing co-integration properties has been confirmed as yielding robust estimates by many researchers [73, 83]. Outcomes are shown in Table 7

3.3.6 Robustness test

To check model robustness, the paper follows previous works by Raihan and Shayanmehr et al. [84, 85] who use both the dynamic ordinary least squares and fully modified ordinary least squares estimators. Both econometric tools have been found as valid for determining rates at which independent variables can explain the dependent variable. The paper concludes with Dumitrescu and Hurlin causality test to determine the direction of causality between individual variables. The results are illustrated in Tables 8 and 9.

4 Empirical outcomes and discussion

To assess the sustainable agriculture effect of green finance and digital technologies in sub-Sahara Africa, Table 2 describes the variables employed.

Table 2 Summary statistics
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The outcomes of Table 2 indicate a normally distributed panel and enable further estimates.

The outcomes of the cross-section dependence estimates using Breusch–Pagan LM, Pesaran scaled LM, Bias-corrected scaled LM, and Pesaran CD tests (Table 3) indicate the null hypothesis cross-section independence is rejected. This means the panel is cross-sectionally dependent. The cross-section dependence evidence implies that a shock in one economy is transferred easily to sub-Saharan African economies. This finding aligns with previous findings by Addai et al. [86].

Table 3 Cross-section dependence estimates (H0: there is cross-sectional independency)
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Pesaran and Yamagata [75] and Blomquist and Westerlund [76] slope homogeneity estimates (Table 4) indicate that the null hypothesis of slope homogeneity is rejected, given the p-values. This means the panel has heterogeneous slopes.

Table 4 Slope homogeneity estimates
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The outcomes of the stationarity tests (Table 5) indicates that the panel is integrated at mixed order. Our findings in the data series confirm non-stationary of variables at level. This allows choosing estimators, which can deal with cross-sectional dependence, autocorrelation and heteroscedasticity errors associated with panel data.

Table 5 Stationarity test
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The outcome of the panel co-integration estimates (Table 6) indicates that the null hypothesis of no-co-integration is rejected in both cases. This means the panel is co-integrated; and this allows conducting long-run equilibrium assessment using Panel corrected standard errors (PCSE) estimator. This finding supports previous empirical work by Kanapiyanova et al. [83].

Table 6 Panel co-integration estimates
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An important key inference of empirical research is the estimation of long-run equilibrium coefficients of the predicting variables, once panel co-integrating estimates indicate a long-run association. Given the manifestation of transverse dependence issues and heterogeneity with the model, the paper adopts panel-corrected standard error (PCSE), which is a second-generation based estimator for the long-run equilibrium assessment (see Table 7).

Table 7 Panel corrected standard errors (PCSE) long-run estimates
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The outcomes of the panel corrected standard errors (PCSE) long-run estimates indicates that the coefficient of the LMGF, LRE, LIMU and LMCS are all positive, indicating that they exert positive effect on LAVA in sub-Sahara Africa. This implies that any changes in LMGF, LRE, LIMU and LMCS have direct or indirect effect on LAVA in SSA.

For the case of LMGF effects on LAVA, the coefficient of the PCSE estimates is 0.062783 (Table 7) and statistically significant. This means that, for the case of sub-Sahara Africa, a unit rise in LMGF results in 06.2783% expansion in LAVA. This finding validates the hypothesis 1 established for the enquiry, (H1: mitigated green finance causes improvements in sustainable agriculture development in sub-Sahara Africa); and aligns with recent investigative outcomes by [37, 38, 83]. This outcome implies that governments in sub-Sahara Africa should ensure budgetary allocations, or mitigated green finance policies should be implemented to attain the benefits of improvements in sustainable agriculture development.

On the effect of LMCS on LAVA, the coefficient of the PCSE estimates is 0.2187013 (Table 7) and is statistically significant. This means that, for the case of SSA, a unit rise in LMCS results in a 21.87013% increase in LAVA. The implication is that investments are needed in LMCS through deliberate and purpose-driven policies in countries under study, given that such actions would cause improvements in LAVA. This finding validates hypothesis 2 established for the enquiry (i.e., H2: rising mobile cellular subscriptions has positive effects on sustainable agriculture in sub-Sahara Africa). This finding supports previous research outcomes [57].

Regarding the impact of LIMU on LAVA, the coefficient of the PCSE estimates is 0.0002144 (Table 7) although not statistically significant. This means that, for the case of SSA, a unit rise in LIMU results in a 00.02144% increase in LAVA. This implication is that although the effect of LIMU on LAVA is not too significant, given that such effect is positive on LAVA, policies should be implemented to increased improvements on LAVA. To realize this, governments could prioritize investments in research and development so that in the medium to long term, real significant effects of LIMU on LAVA could be realized. This finding validates hypothesis 3 established for the enquiry (i.e., H3: increasing rates of individuals using mobile phones and Internet [59] have positive effects on sustainable agriculture in sub-Sahara Africa). This finding supports previous research outcomes [53].

On LRE, the coefficient of the PCSE estimates is 0.8024883 (Table 7) and is statistically significant. This indicates a unit rise in LRE results in an 80.24883% increase in LAVA for the case of SSA. The implication of this finding is that the governments across SSA should prioritize investments in LRE towards ensuring improvements in LAVA. They can do this through tax incentives on LRE projects and budgetary allocations for LRE development. This finding validates hypothesis 4 established for the study (H4: rising renewable energy consumption has positive effects on sustainable agriculture in sub-Sahara Africa). The finding also supports [64].

4.1 Model robustness check

Model robustness assessment is relevant in econometric approaches. Historically [87], claimed that annoyance constraints in regressions could create endogeneity and serial correlation problems leading to biased estimates. However, by focusing on nonparametric processes, both the DOLS and the FMOLS estimators are effective in getting rid of endogeneity and autocorrelation errors in heterogeneous panels.

According to Frank et al. [88], to invalidate a model outcome, 60.701% of the estimates would have to be attributable to bias, based on a threshold of 0.786 for statistical significance (alpha = 0.05). This means, to invalidate an inference in the model estimates of 480 observations, 2 covariates, and a standard error of 0.4 for a minimum of 2 estimated effects, 291 observations would have to be replaced with cases for which the effect is 0 (RIR = 291) as illustrated in Figs. 1 and 2 for Robustness of Inference to Replacement (RIR).

Fig. 1
figure 1

Threshold plot

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Fig. 2
figure 2

Correlation plot

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The minimum effect of omitted variables to invalidate an inference for a null hypothesis of 0 impact is hinged on 0.383 correlation with both the outcome and the predictor of interest (i.e., conditioning on observed covariates) on the basis of 0.09 threshold for statistical significance (alpha = 0.05). Similarly, the effect of an omitted variable must equally be 0.383 to invalidate an inference for a null hypothesis of 0 effect.

The outcomes of both the FMOLS and DOLS tests for model robustness (Table 8) indicate positive coefficients and the p-values are statistically significant. This means for FMOLS estimates, the independent variables (i.e., LMGF, LIMU, LMCS, and LRE) can collectively explain 96.7190% of the dependent variable (i.e., LAVA) in sub-Saharan Africa. Similarly, for DOLS estimates, the independent variables (i.e., LMGF, LIMU, LMCS, and LRE) can collectively explain 95.5099% of the dependent variable (i.e., LAVA) in sub-Saharan Africa.

Table 8 Robustness check
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Given that the coefficients of the PCSE estimates establishes a long-term association only between the variable, the paper unearths the direction of causality using Dumitrescu and Hurlin panel causality test. The outcomes of the [89] panel causality estimates (Table 9) indicate (i) a uni-direction causality between LMGF and LAVA. (ii) A uni-direction causality running from LIMU towards LAVA, and there is no rebound effect.

Table 9 Pairwise Dumitrescu Hurlin panel causality tests
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5 Conclusions and policy suggestions

Many of the environmental problems associated with the recent phase of agriculture come from the excessive and unscientific use of chemical pesticides, mineral fertilizers, and increasing abuse of land and groundwater resources. Governments and FAO seek alternative policies to minimize the environmental and economic costs in food supply for the case of case of SSA. This study sought to investigate the effect of both green finance and digital technologies on sustainable agricultural development in SSA, while controlling renewable energy consumption and individuals using the internet.

Analysis of Pedroni [77] and Westerlund [78] panel co-integration estimates indicates all variables are integrated. The long-run equilibrium examination using the panel corrected standard errors (PCSE) indicates that the coefficients of the LMGF, LRE, LIMU and LMCS are all positive, indicating that the variables individually and collectively exert positive effects on LAVA in sub-Saharan Africa. The outcomes of the panel causality estimates indicate (i) a unit-direction causality between LMGF and LAVA. (ii) A unit-direction causality runs from LIMU towards LAVA, and there is no rebound effect.

5.1 Policy implications

For purposes of policymaking, the African Union could support member states to implement macro-policies towards increasing green agricultural credits to farmers to sustain food production. Increase employment generation and improve environmental quality. For instance, member government could promote green finance through the establishment of mandatory agricultural-related emissions trading system; promote agriculture green bonds, grants and other financial investment instruments. Given the limitations to credit access for sustainable food supply in SSA, agricultural improvement policies could target foreign direct investments (FDI) and official development assistance (ODA) towards ensuring sustainable agricultural financing. Individual economies could deliberately design their domestic policy and regulations to provide alternative sources of green finance to small-scale farmers who largely depend on unregulated moneylenders for insufficient funding at high-interest rates. Policy options on green agricultural development in sub-Saharan Africa could provide revenue-neutral feebates for industrial farming to provide emissions reduction incentives and competitiveness. Such policy-feebate schemes could be made to consider variations in emissions-intensity, covering all agricultural products and directly linked subsidies. Alternatively, such feebates could be implemented at the product level or across the entire sector.

It has now been evident based on findings of the study and the literature review that agriculture in SSA is predominantly small and medium-scaled due to inadequate digital infrastructure, skilled workforce and relevant investment facilitating policies. Given this fact, the agriculture sector in SSA is limited in witnessing the uptake of green financing and digital technology investments. Based on this, the governments in SSA are advised to prioritize budgetary allocations for the development of necessary infrastructure and services to ensure the growth of agricultural green financing and digital technology investments. In particular, the Ministries of Communications could ensure speedy licensing of applications for cellular and fibre optic projects, especially those targeting rural and farming communities.

Furthermore, the African Union could provide technical support in digital agricultural research and value chains to ensure sustainable agriculture development. Globally, green technology and innovations facilitated by huge investments in research and development are found to reduce climate change. Investments in advanced technologies including satellite imaging could control land grabbing and support bio-economy delivery across the sub-Saharan region.

5.2 Academic implications

It is worth noting that the outcomes of this paper on the positive effect of green finance and digital technologies on sustainable agricultural development have implications of the resource-based theory, which recognizes organizations as collections of creative resources for conceiving and implementing projects to propel economic growth. By confirming the implications of the EKC hypothesis which investments in technology after economic expansion tend to reduce environmental degradation, it appears the findings are consistent with the variety of frameworks or models identified in the literature review, or specified in the analysis. Given these observations, scholars could use evidence of the long-run asymmetries in the relationships between the dependent and independent to improve forecasting on global sustainable agriculture and food supply.

5.3 Management implications

The outcomes of this paper indicate that green finance and digital technologies have positive effect on sustainable agricultural development. This provides significant insights into management decision-making. For instance, green and digital technology corporations could prioritize investments in research and development in the agricultural sector towards finding economically viable investment opportunities. Additionally, given that in SSA in particular, there exist infrastructural deficits to aid financing of green agricultural production, corporations interested in the sector could partner governments to raise the necessary funding towards putting in place the infrastructure required. Digital technology corporations could invest in simple agriculture technologies and services that benefits the small-scale farmers in SSA, especially in mobile telephony.

5.4 Limitations and future research

The study is limited for not addressing possible negative effects of green financing strategies on agricultural productivity or ecological sustainability, and future research could gather pertinent data for such assessment. Additionally, no comparative assessment on a regional basis was done due to the sole concentration of the distinct characteristics of sub-Saharan Africa in terms of green finance, digital technologies, and ecological pollution. Future study is advised to examine other regional contexts on green financing and digital technologies to enable comparison of their collective effects on agriculture value added.