The key concepts relating to this study is credit facility in form of commercial Bank credit and agricultural credit guarantee scheme fund, food security, and agricultural productivity are defined and discussed in this section.

This study tends to examine how credit facilities to agriculture in form of Commercial Bank Credit and agricultural credit guarantee scheme fund to the agricultural sector and its corresponding interest rate. Commercial banks credit to agriculture in Nigeria has been on the increase as observed in Fig. (1) [16]. From 1990 with a value of ₦4,221.4 million to ₦25,278.7 million in 1995. As at 2000, it was valued at ₦41,028.9 million which increased to ₦48,561.5 million in 2005, then ₦128,406.0 million in 2010 before reaching ₦316,364.0 million in 2012, and ₦478,911.78 million as at 2014. By 2016, commercial banks’ credit to agriculture rose to ₦525,911.78 million [16].

Fig. (1). Commercial Bank Credit to Agricultural Sector (bank credit). Source: Authors’ computation using data from CBN Statistical Bulletin, 2016.

Statistics presented in Fig. (2) indicates that lending rate was 25.3% in 1990 but fell slightly to 17.80% in 1997. The rate began an ascent in 1998 from 18.18% to 24.77% in 2002; when it began to fall slowly to 15.48% in 2008. The rate later fluctuated between 2009 and 2011 before settling around 16% as at 2016 the lending rate in Nigeria stood at 16.87%.

Fig. (2). Lending Interest Rate. Source: Authors computation using data from WDI, CBN Statistical Bulletin, 2016.

Food security, however, refers to a situation that exists when all people, always have physical, social and economic access to sufficient, safe and nutritious food that meets their dietary needs and food preferences for an active and healthy life [17]. This definition points out the fact that there are four important dimensions of food security; availability, accessibility, utilisation, and stability, these four dimensions even though they overlap explain the phenomenon of food security, in this study, Food security was measured using depth of food deficit as a proxy for utilization.

Data, as presented in Fig. (3), showed that the depth of food deficit has been on a decline from 1990 [17]. It shows a trend analysis of the performance of the food security indicator over the 27 year period which has been on the decline from 134.00 calories in 1990 to 42.00 kilocalories in 2016. The value for Depth of the food deficit (kilocalories per person per day) in Nigeria was 42.00 kilocalories as of 2016 [17].

Fig. (3). Depth of Food Deficit in Nigeria (1990 - 2016). Source: Author’s computation using data from FAO, 2016.

Obilor examined the impact of Commercial Banks Credit to agriculture on Agricultural Development in Nigeria; this study underscored the importance of credit availability to the agricultural sector for adequate development pointing out that inadequate capital is a key factor for hampering attainment of food security in Nigeria [18]. Results from the study of Obilor showed that there exists a significant positive relationship between agricultural credit guarantee scheme fund and food production in Nigeria [18]. Also, the recommended that agricultural credit facility in terms of loans and other input supply should be easily accessible to farmers to encourage their participation in the agricultural sector which will increase production.

With the application of the Ordinary Least Squares (OLS) techniques analyzed the impact of commercial banks credit on agricultural productivity in Nigeria; the study concluded that there is a positive relationship between commercial banks’ credit and agricultural productivity [19]. In a similar way Chris et al. focused on the significance of commercial banks credit on food availability [20]. The estimated results from this study showed that there exists a positive and significant relationship between agricultural credit guarantee scheme fund and agricultural production in Nigeria; their findings revealed a positive and significant relationship between commercial banks credit to the agricultural sector and food production in Nigeria. The result obtained indicated that an increase in commercial banks credit to agricultural sector will lead to an increase in agricultural production, hence food security in Nigeria. Interest rate which serves as a major factor in determining the desire for credit facilities was also examined. The authors found that a negative relationship exists between interest rate and agricultural output. This establishes that increasing interest rates may deter farmers and agricultural producers from borrowing funds, which may lead to declining output and reduced agricultural investment.

Bidisha et al. attempted to disentangle the relationship between credit, food security, and dietary diversity [21]. The study which was carried out through descriptive and econometric analysis focused on Bangladesh. The study found that access to credit facility tends to improve food security and allows households to achieve greater dietary diversity. They also find that greater calorie consumption per capita is more likely with households with access to credit.

O’Hara accessed how changes in the level of deposits in community banks influence total agricultural sales and direct-to-consumer agricultural sales of local food between 2002 and 2012, in rural states which includes North Dakota, South Dakota, Minnesota, Wyoming, and Montana [22]. The study finds that changes in community bank deposits had a positive impact on changes in direct-to-consumer agricultural sales of local foods. Also, total agricultural sales may not be impacted by changes in community bank deposits and that the consolidation of the commercial banking sector may influence the viability of farms in accessing credit.

The data for this study is obtained mainly from secondary sources, particularly from the 2016 World Bank (World Development Indicators). The time series data covered a period 1990-2016 and was used to estimate the specified model. The methods of analysis engaged in the study involve two main approaches, namely descriptive and econometric techniques.

The descriptive method was employed using tabular and graphical representations to show some indicators of food security in Nigeria. While the econometric analysis applied an econometric model that was fitted into data using the approach of the Autoregressive Distributed Lag (ARDL) Bounce testing procedure developed by Pesaran et al. to examine long-run relationship amongst population, agricultural productivity, and food security as well as short-run dynamics [23].

The bound test was adopted for four reason reasons stated thus; firstly, it does not require that the variables under study must be integrated of the same other, unlike the Johansen Cointegration approach. Secondly, the bound test is suitable for small or infinite sample data, unlike the conventional approach which requires a large sample size. Thirdly, it allows the cointegration relationship to be estimated using the Ordinary Least Square method, and lastly, the long and short run parameters of the model can be estimated simultaneously.

To investigate the association amongst credit facilities and food security in Nigeria, Depth of food deficit index is the explained variable as proxy for food security; while the explanatory variables are Agricultural Credit Guarantee Scheme Fund (AGCSF), Commercial Bank Credits to the agricultural sector (BCRED), and lending interest rate (LINTR) and total Population (POP) as shown in Table 1.

Thus, the model for this stud is closely related to the study of Osabohien et al. (2018); hence, the model is expressed implicitly as expressed as;

(1)

Where:

DFD represents food security, measured by the depth of food deficit in Nigeria; POP is the total population in Nigeria, ACGSF represents Agricultural credit guarantee scheme fund, BCRED represents Commercial bank credits in form of loans, etc made available to the agricultural sector, LINTR represents the lending interest rate, μ is stochastic term and t is time.

The model can be represented in an explicit form as

(2)

Where;

β0 is the Intercept, β1, β2, β3, and β4 are the coefficients of total population, agricultural credit scheme fund, bank credit, and lending interest rate respectively.

Thus, the expected signs of the coefficient of the explanatory variable are, β0 > 0, β1 < 0, β2 > 0, β3 > 0 and β4 < 0. Hence, increase in the explanatory variables (except POP and LINTR) is expected to enhance the rate of food security, ceteris paribus.

The model for this study is hinged on bank credit channel theory. It explains who poses interest on credits through banks capital, particularly when banks’ lending is constrained by a capital adequacy requirement [24]. Thus, an increase in interest rates will raise the cost of banks' external funding, but reduce banks' profits and capital. The tendency is for the banks to reduce their supply of loans if the capital constraint becomes binding. However, banks could also become more willing to lend during certain periods because of an improvement in their underlying financial condition.

To estimate the above formulated model, the study used time series data from 1990 to 2016 where there is availability of data for the variables [17]. The economic view package (E –views, version 10) was used in the estimation process. The ARDL model for equation (3) is specified as:

(3)

Once cointegration is established, the long run relationship is estimated using the conditional ARDL model specified as:

(4)

The short run dynamic relationship is estimated using the error correction model specified as:

(5)

δ0: Constant term; μt means white noise, this captures other explanatory variables which are not explicitly captured in the model; δ1- δ5 represents the short-run elasticities (that is, coefficients of the first-differenced explanatory variables); β1-β5 represents the long-run elasticities (coefficients of the explanatory variables); ecm_t-1 represents error correction term lagged for one period; α represents the speed of adjustment from short-run to long-run equilibrium in the event of shock; Δ represents first difference operator and P represents Lag length.

An F-test of the joint significance of the coefficients of the lagged levels of the variables was used to test the hypothesis of no cointegration amongst the variables against the presence of cointegration. The null hypothesis of no cointegration between credit facilities and food security given as:

H0: δ1 = δ2 = δ3 = δ4 = δ5

The alternative hypothesis was given as

H1: δ1 ≠ δ2 ≠ δ3 ≠ δ4 ≠ δ5

The F-test has a non-standard distribution irrespective of whether the variables are integrated at order 0, which is [1(0)]; or order 1, that is [1(1)]. Pesaran et al. (2001) posited two sets of adjusted critical values that provide the lower and upper bounds used for inference. One set assumes that all variables are integrated at order 0, that is [1(0)]; and the other assumes that they are all integrated at order 1 that is, [1(1)].

If the calculated F-statistics falls above the upper bound critical value, then the null hypothesis of no cointegration is rejected. If it falls below the lower bound, then the null hypothesis will be accepted. Finally, if it falls between the lower and upper bound, then the result would be inconclusive. The optimal lag length for the specified ARDL model was determined based on the Akaike Information Criterion (AIC).

The stationary test was conducted for the time series data using the Augmented Dickey-Fuller to determine the level of the unit root. Although, the bounds testing procedure does not require the pre-testing of the variables included in the model for unit roots owing to its suitability irrespective of whether the regressors in the model are purely integrated of 0; ie, I(0), purely order 1 [I(1)] or mutually cointegrated. The application of unit root tests in the ARDL procedure might still be necessary in order to ensure that the variables are integrated of order one and none of the variables is integrated of order 2 or beyond because the computed F-statistics provided by [23] are valid for only variables that are I(0) or I(1). The Augmented Dickey-Fuller (ADF) test was used to investigate whether the variables used in this study have a unit root or not Table 2.

The Augmented Dickey-Fuller (ADF) unit root testing of the variables indicates that three of the variables which include DFD the depth of food deficit, POP total population, and BCRED Commercial bank loans attain their stationarity at the first difference which means that they are all integrated of order one while ACGSF Agricultural credit guarantee scheme fund and LINTR lending interest rate attain stationarity at level which means it was integrated of order zero. From the result above, the variables are not integrated at the same order, therefore, we conduct the Autoregressive Distributed Lag (ARDL) Bounce test [23].

Cointegration test is employed to ascertain the long-run equilibrium relationship between Bank Credit and Food Security.

Table 3 above presents the ARDL bounds test results. Evidence from Table 3 shows that the F-statistic goes beyond the critical value of the upper bound at 5% significance level, showing a co-integration amongst Bank Credit and Food Security meaning there exist a long run relationship between Bank credit and Food Security.

Fig. (4) depicts the ARDL model selection using the Hannan-Quinn Criteria. The study employs the Hannan-Quinn Criteria to select the optimal model [ARDL (4, 0, 1,0,1)] to estimate the long-run and the short-run equilibrium relationship between the variables. Using the optimal model [ARDL (4,0,1,0,1)], the normalized co-integration equation for the ARDL regression analysis is expressed as:

Cointeq EC= DFD-(-0.000001* POP +0.000002* ACGSF +0.081204*BCRED + 2.6498*LINTR -89.8085)

Based on the above, the results of the long-run and the short-run equilibrium relationship between Bank credit and Food Security are presented below.

Fig. (4). ARDL model selection criterion.

The result of the estimated coefficients of the long run relationship in Table 4 indicates that Population has a negative influence on food security in Nigeria. The estimated coefficient of the population (-0.000001) implies that 1 unit increase in population will decrease food security by approximately 0.000001 unit all things being equal. Agricultural credit guarantee scheme fund was found to be positively related to food security with an estimated coefficient of 0.000002. This implies that a 1 unit increase in Agricultural credit guarantee scheme fund will lead to an increase of Food security by a magnitude of 0.000002 units.

Bank credit was found to be positively related to Food security with an estimated coefficient of (0.081204) which implies that 1unit increase in Bank credit will lead to an increase of Food security by 0.081204 units. The lending Interest rate was found to be positively related to Food security with an estimated coefficient of (2.5449793) which implies that 1 unit increase in Gross fixed capital formation will lead to an increase of Food security by 2.649793 unit. All variables were statistically significant at their respective level of significance. All variables apart from Lending Interest rate meet the a priori expectation.

The results of this study closely follow [25] in the area that improved level of credit given to farmers enhances the productivity level of the agricultural sector and thus lead to an increase in the level of food security in Nigeria as seen in ARDL result. This study is also in line with [26] where it was believed that access to agricultural credit to farmers increases their production capacity which in turn lead to food security, also aggress with [27] where it was pointed out that there exists a significant positive relationship between food security and the availability of agricultural credit to farmers. His study noted that one percent increase in the availability of agricultural credit to farmers amounted to a 2.5% and increase in agricultural productivity in Nigeria, this, of course, follows the apriori expectations. Also, the study of [28] finds that in Pakistan, small-scale farmers close to 76% of credit received from both formal and informal sources to improve their farm practices, thus, this was observed to increase agricultural productivity by 69% in the country.

From Table 5 above the coefficient of the error correction model ECM (-1) is (-0.180296 which satisfy the condition of being negative and lie between 0 and 1. This indicates in an event of disequilibrium, there is a tendency for the economy to return to equilibrium in the long run with a speed of 18%.

The ARDL model was validated and verified using a series of diagnostic and stability check to scrutinize the independence of the residuals from the fitted model. For a robust ARDL model, the residuals must exhibit the required independence during the diagnostic and stability checks, if not, the model is unacceptable statistically and requires further model modification before additional diagnostic and stability checks [23].

In this way, the ARDL model becomes unbiased and robust to make the correct statistical inferences. Diagnostic tests employed to validate the ARDL model include; Heteroskedasticity Test, Jarque-Bera Test and Ramsey RESET Test as presented in Table 6 below.

ARDL residual heteroskedasticity was tested with Breusch-Pagan-Godfrey Test statistic [29]. The result showed that the Probability value of the observed R-squared is greater than 5% this means we accept the null hypothesis which indicates no heteroskedasticity.

ARDL residual normal distribution was tested with Jarque-Bera test statistic. Evidence from Table 5 shows that the null hypothesis of multivariate normal distribution was accepted at the 5% significance level, this means that; the ARDL residuals are normally distributed. ARDL functional misspecification was estimated with Ramsey RESET Test statistic. Findings show that the probability level is greater than 5%, therefore, we accept the null hypothesis, meaning that there the ARDL model is in its functional form [29].

To estimate the structural stability of the equation in the ARDL model, the study employed the CUSUM (Cumulative Sum test) and CUSUM (Cumulative Sum of Squares residual tests).

Fig. (5) shows the CUSUM and CUSUM of Squares residual tests of the ARDL Model. Evidence from Fig. (5) shows that all the plots in CUSUM and CUSUM of Squares residual test lie within the 5% significance level. Meaning that the estimated parameters of the equation in the ARDL model are constant and stable to verify and validate the evidence of ARDL cointegration bound test, the long-run and short-run relationship. In other words, the ARDL model is robust and meets stability conditions to make unbiased statistical inferences [30].

Fig. (5). Test of Model Stability.