According to the endogenous and neoclassical growth model, capital inflows (Private and Public inflows) enhance the growth of the economy. Also, according to the two-gap model, capital inflows bridge the savings and foreign exchange gap that exist in a developing economy. The saving gap is the gap between savings and investment; while the foreign exchange gap is the gap between import and export. Majority of the developing economy relies on the inflow of foreign capital to enhance agricultural output in a bid to eradicate/reduce poverty, provide employment opportunities and ensure sustainability in the agricultural sector. The neoclassical growth theory postulates that the inflow of foreign capital provides the developing economies an opportunity to be able to acquire the required technology that will enhance and promote productivity, stimulate growth and ensure sustainable development in the agricultural sector [3, 30, 34, 37, 42].
Several studies have shown that the inflow of foreign capital has positively influenced the growth of agricultural output in developing economies. Findings by Zingwena [43] showed that FDI has positively affected the growth of agricultural output in Zimbabwe. Likewise, Gameli Djokoto et al. [17] also confirmed that FDI exerts a positive effect on Ghana agricultural output. Other studies conducted have also shown that FDI plays a significant role in terms of increasing welfare and reducing unemployment problem in a country, and hence advocate for the need of FDI to be directed to the agricultural sector of less developed countries [10, 28, 35].
Several other studies have been conducted in Nigeria to examine the link between capital flows and agricultural output. Research study in Nigeria conducted by Akpokodje and Omojmite [6], Ajuwon and Ogwumike [5], Oloyede [32], Yusuf [40], Kareem et al. [24], Yusuff et al. [41] and Eke (2016); all showed that FDI has positively influenced the growth of the agricultural sector in the economy. However, despite the positive impacts of capital inflows on agricultural output, some scholars still have opposing views based on their research finding. Larson and Vogel [25], Massoud [26], Djokoto [12, 13], Iddrisu et al. [20], Epaphra [15], Epaphra and Mwakalasya [16]; documented that the inflow of foreign capital affects agricultural output negatively.
Furthermore, on the link between exchange rate and agricultural output, Oyinbo et al. [33] concluded that that exchange rate affects the agricultural share of GDP negatively. Wondemu and Potts [38] research findings revealed that exchange rate appreciation affects export, while exchange rate depreciation raised the supply of export and boost the diversification of export. Abdullahi [1] research findings indicate that agricultural output positively responds to exchange rate, inflation and interest rate in the long run. Yaqub [39] using a two-stage least square technique showed that while exchange rate affects fishery and crop output negatively, it affects forestry and livestock positively. Iddrisu et al. [20] concluded that the depreciation of the country currency (cedi) negatively affects Ghana agricultural output.
Theoretical framework
The study adopts the conventional neo-classical growth production function. The neo-classical production function links the aggregate output in period t with inputs or factors of production.
Expressing the neo-classical production function in the form of Cobb–Douglas production
$$Y_{t} = A_{t} K_{t}^{\alpha } L_{t}^{\beta } ,$$
(1)
where \(Y_{t}\) represents agricultural output (AO) at time t, while \(A_{t}\) represents total factor productivity, \(K_{t}\) capital stock (domestic investment) and \(L_{t}\) labor stock, \(\alpha\) and \(\beta\) are the output elasticities of capital and labor, respectively.
According to the endogenous and neoclassical growth model, capital inflow (Private and Public inflows) operates through the total factor productivity (A) since capital inflows can stimulate growth provided there is an increasing return to production that would enhance output [42]. Hence, total factor productivity is a function of capital inflow.
$$A_{t} = f\left( {\text{CAPI}} \right)$$
(2)
Thus, combining Eqs. 1 and 2, the Cobb–Douglas production function is expressed as
$$Y_{t} = {\text{CAPI}}_{t} K_{t}^{\alpha } L_{t}^{\beta }$$
(3)
where CAPI is capital inflows (Private and Public inflows).
Following similar studies, additional variable such as real effective exchange rate was employed to capture the efficiency of economic activity. Empirical studies have shown that real effective exchange rate affects agricultural output [1, 20, 33, 38]. Hence, the Cobb–Douglas production function is modified and, thus, expressed as
$$Y_{t} = {\text{CAPI}}_{t} K_{t}^{\alpha } L_{t}^{\beta } {\text{REXR}}_{t}$$
(4)
Decomposing capital inflow into private and public capital inflows, the study expressed two models:
$$\begin{aligned} \log Y_{t } &= \alpha_{0} + \alpha_{1} \log {\text{PRCI}} + \alpha_{2} \log K \\ &\quad+ \alpha_{3} \log L + \alpha_{4} {\text{REXR}} + \mu_{t} , \end{aligned}$$
(5)
$$\begin{aligned} \log Y_{t } &= \alpha_{0} + \alpha_{1} \log {\text{PUBCI}} + \alpha_{2} \log K \\ &\quad+ \alpha_{3} \log L + \alpha_{4} {\text{REXR}} + \mu_{t} , \end{aligned}$$
(6)
where Y is the Agricultural output; PRCI is the Private capital inflow; PUBCI is the Public capital inflow; K is the Domestic investment; L is the Labor force; REXR is the Real effective exchange rate; µ is the Error term.
In summary, the review of the literature has shown a mixed result. While some researchers claimed that capital inflows influence agricultural output positively [17, 24, 32, 40, 43], others have divergent views that capital inflows exert a negative effect on agricultural output [13, 14, 15, 26]. Also, most of the studies focused on the effect of FDI on agricultural output thus ignoring other components of private and public capital inflows. In addition, the effect of capital inflows and exchange rate on agricultural output, however, remains open to question. Hence, this study fills the gap in the literature by investigating the effect of both private and public capital inflows, and exchange rate on agricultural output in Nigeria using an ARDL technique.