Looking further, the yields of root and tuber crops, including yam, which is presently on the decline, are predicted to increase in Nigeria towards 2050. As a result of the increase, exports are projected to grow, indicating a projected food surplus for the country (
Jalloh et al. 2013). Moreover, impacts of climate change will vary according to location, soil type, crop, and other local factors. Consequently, it is essential to conduct enterprise-specific analysis (
Ater and Aye 2012;
Sarker et al. 2012). In a review by
Knox et al. (
2012), it was indicated that for yams, there were too few studies to comment on if there has been any significant impact of climate change on the yield in West Africa. As a result, part of this section attempts to analyze the effects of climate change on yam production in Cross River State.
3.2.2. Unit Root (Stationarity) Test
Applying the Johansen’s co-integration technique involves some preliminary testing of the time series to ensure the time series variables are integrated in order one, that is to say, testing for the presence of unit root. Given that time series data are susceptible to spurious regression outcomes, it is crucial to carry out a unit root test before estimating the econometric model (
Verter and Bečvářová 2015). In other words, the time series analysis starts by carrying out a unit root test to determine the stationarity or non-stationarity of the variables and to ascertain the suitability of the model specification. Accordingly, the Augmented Dickey–Fuller (ADF) tests were employed to check if each of the variables possesses unit root (that is, to check the stationarity of the data series).
The ADF equation is provided as follows;
where Δ = the first difference operator, δ = (φ − 1) and ϵ
t denotes a serially uncorrected white noise error term with an average of zero and a constant variance.
The ADF test reduces autocorrelation in the error term because it includes the first difference in lags such that the error term is disseminated as white noise (
Eregha et al. 2014). The result of the ADF-test is presented in
Table 1. It reveals that all the variables are integrated of order one [I(1)] at level, indicating non-stationarity (presence of unit root) of the time series data. In this circumstance, where the time-series variables under consideration are non-stationary, it, therefore, implies that the result that will be produced by the regression using these variables will be a spurious regression result, except their linear combination provides a stationary residual (
Tesso et al. 2012;
Zhang et al. 2019).
Moreover, since most of the variables follow order one [I(1)] process (that is, are integrated at the same order), the next stage is to test if there exists a long-run relationship (co-integration) among the variables. Nevertheless, the variables of integrated order one [I(1)] need to undergo first difference before an estimation can be carried out (
Sarker et al. 2012;
Moreira Campos da Cunha Amarante et al. 2018). However, the study variables became stationary after the first difference exception of the output of yam, which is confirmed by the ADF-test statistics in
Table 1. Since the weather series are integrated in the same order, the co-integration technique was employed to ascertain if a stationary long-run relationship exists between the time series. Consequently, the stationarity of the linear combination of the variables in integration order one [I(1)] was tested, and the outcome is presented in the next sub-section using Johansen’s multivariate approach.
3.2.4. Johansen Co-Integration Test Result
The results of the trace statistics from the Johansen co-integration test are shown in
Table 2, which suggests a strong rejection of the null hypothesis. The results imply that the hypothesis of no co-integration among the variables can be rejected for the model used. The results further revealed that two co-integrating vectors exist among the study variables in the model. Hence, the rejection of the hypothesis of no co-integrating relationship among the variables under investigation. The result, however, infers that there exists a co-integrating long-run relationship among the time series at 0.05% level of significance. Nevertheless, the trace test indicated that the hypothesis of one co-integrating equation could not be rejected.
As soon as co-integration between time series is recognized, it is crucial to investigate the causality of each co-integrating pair. The causality from the estimated Johansen Vector Error Correction Model (VECM) is evaluated via a likelihood ratio (LR) test by using a restricted disequilibrium error term (
Natanelov et al. 2013;
Zhang et al. 2019).
Given the presence of long-term relationships recognized among the study variables, the analysis, therefore, undertook an error correction model (ECM) estimation approach. Consequently, the outcome of the ECM is made known in the following sub-section.
In view of the presence of long-term relationships recognized among the study variables, the analysis, therefore, undertook an error correction model (ECM) estimation approach. Consequently, the outcome of the ECM is made known in the following sub-section.
Alternatively, the long run co-integrating relationship was tested using the Engle and Granger technique. The results are shown in
Table 3 below. It reveals that the R-squared value of 0.981 (98%) is exceptionally high. Still, the Durbin–Watson statistics are low (1.188), implying that using variables with an ordinary level regression (OLS) will lead to spuriousness.
Furthermore, in examining the residual, which is the Error Correction Model (ECM), the ADF was used to perform unit root on ECM. The result of the test is shown in
Table 4 below. The outcome revealed that since the ADF test statistics of −3.37 is significant at 1% level of significance, the null hypothesis of the presence of unit root in ECM was rejected. It, therefore, means that a linear combination of the three non-stationary series is stationary. In other words, the variables are co-integrated. Thus, the study proceeds to the error correction model.
3.2.5. The Outcome from the Error Correction Model
By employing the lag length of three as determined by the information criteria,
Table 5 below presents the error correction model result (parsimonious model).
The error correction model results presented in
Table 5 specifiy that the model is devoid of any critical econometric hitches. This is so because the Durbin–Watson value of 1.186 indicated the unit root test statistically addressed the existence of positive autocorrelation. Therefore, the Durbin–Watson statistics show the nonappearance of serial correction. The F-statistics value of 2.718, however, conceded the significant test. Simply put, the value of F-statistics suggests that there exists a considerable congruence between each of the climate change variables in the model as the dependent variable and the independent variables are placed together. This implies that the model was statistically fitted at 1% level of probability, which confirms the general explanatory power of the model.
Furthermore, the value of the coefficient of determination of the model clearly showed the goodness of fit. The explanatory variables explained 40% of the variation in output of yam, which was used as the dependent variable in the model. In other words, the R-squared value of 0.404 implied that 40% of the total variation in yam production (dependent variable) was explained by the climate variables (independent variables) included in the model. Thus, the results of the error correction model analysis are reliable and can be used to draw inferences.
Specifically, it can be deduced from the ECM result in line with the theory that climate variables, such as temperature, played a significant role in yam production in the study area. Rainfall was seen to have a positive coefficient but was not statistically significant. The temperature, on the other hand, had a negative impact on yam production in the study area. This implies that a rise in the amount of temperature could result in a decline in yam output in Cross River State. The coefficient (−2.8747) was statistically significant at a 5% probability level, meaning that a 1% increase in temperature will lead to a 28% decrease in yam production. This is true because an increase in temperature encourages the proliferation of pests and diseases, which could be a threat to yam production and yield at the growth and developmental stages. This finding corresponds with the a priori expectation since the temperature has shown a downward trend. In contrast, yam output showed an upward trend during the period under study, implying that as temperature decreases, the quantity of yam produced increases. Hence, the lower the temperature, the higher the quantity of yam produced and vice versa.
However, the Error Correction Model (ECM-1), which signifies the long-run adjustment of the model after disequilibrium, was seen to be statistically significant. The coefficient (−0.477128) of this term specified that, annually, about 48% of the deviation from the equilibrium was adjusted back to stability. In other words, the result from the ECM implies that about 48% of the variation of yam production from its long-run value is corrected. This outcome demonstrates the presence of a strong co-integration, which, in turn, indicates that there is a long-run equilibrium relationship between the study variables.
From previous studies, the assessment of the impact of climate change on China’s rice production was done using the Cobb–Douglas function by
Wang et al. (
2018). They utilized the daily weather information over the whole growing season for the period 1979–2011. They reported that the minimum temperatures (Tmin), maximum temperatures (Tmax), temperature difference (TD), and precipitation (RP) are the four significant climatic factors that affect rice production in China. They added that except for maximum temperatures, all the factors have positive effects. Similarly, another study was carried out by
Samuel et al. (
2017) in southwest Nigeria on the impacts of climate variability on agricultural productivity of smallholder farmers. The study discovered that crop yield had reduced tremendously as a result of erratic rainfall, an increase in the number of hours of sunshine, a rise in temperature and pest outbreak.
This finding implies that as the temperature continues to increase over time, it may lead to a decrease in yam production in Cross River State.