### 1. Introduction

### 2. Methodology

### 2.1. Data

_{2}-Carbon dioxide emissions (kt), COPRA-Copra Oilseed Production (1000 MT), CORN-Corn Production (1000 MT), GREENCOFFEE-Green Coffee Production (1000 60 KG BAGS), MILLEDRICE-Milled Rice Production (1000 MT), MILLET-Millet Production (1000 MT), PALMKERNEL-Palm kernel oil seed Production (1000 MT) and SORGHUM-Sorghum Production (1000 MT). The selection of variables was based on the available data on Ghana’s agricultural commodity. Fig. 1 depicts the trend of the study variables. Evidence from Fig. 1 shows that all the series increase periodically.

### 2.2. Model Estimation

##### (1)

$$\begin{array}{l}LC{O}_{2t}=f(LCOPR{A}_{t},\hspace{0.17em}LCOR{N}_{t},\hspace{0.17em}LGREENCOFFE{E}_{t},\\ LMILLEDRIC{E}_{t},\hspace{0.17em}LMILLE{T}_{t},\hspace{0.17em}LPALMKERNE{L}_{t}\\ LSORGHU{M}_{t}\end{array}$$##### (2)

$$\begin{array}{l}LC{O}_{2t}={\beta}_{0}+{\beta}_{1}\hspace{0.17em}LCOPR{A}_{t}+{\beta}_{2}\hspace{0.17em}LCOR{N}_{t}+{\beta}_{3}\hspace{0.17em}LGREENCOFFE{E}_{t}+\\ {\beta}_{4}\hspace{0.17em}LMILLEDRIC{E}_{t}+{\beta}_{5}\hspace{0.17em}LMILLE{T}_{t}+{\beta}_{6}\hspace{0.17em}LPALMKERNE{L}_{T}+\\ {\beta}_{7}\hspace{0.17em}LSORGHU{M}_{T}+{\varepsilon}_{t}\end{array}$$*LCO*

_{2}

*is the logarithmic transformation of carbon dioxide emissions while*

_{t}*LCOPRA*

*,*

_{t}*LCORN*

*,*

_{t}*LGREENCOFFEE*

*,*

_{t}*LMILLEDRICE*

*,*

_{t}*LMILLET*

*,*

_{t}*LPALMKERNEL*

*, and are the logarithmic transformation of Copra Oilseed Production, Corn Production, Green Coffee Production, Milled Rice Production, Millet Production, Palm kernel oil seed Production, and Sorghum Production in year*

_{t}*t*,

*ɛ*

*is the error term and*

_{t}*β*

_{0},

*β*

_{1},

*β*

_{2},

*β*

_{3},

*β*

_{4},

*β*

_{5},

*β*

_{6}and

*β*

_{7}are the elasticities to be estimated (see Eq. (4)).

##### (3)

$$\begin{array}{l}\mathrm{\Delta}LC{O}_{2t}=\alpha +{\delta}_{1}\hspace{0.17em}LC{O}_{2t-1}+{\delta}_{2}\hspace{0.17em}LCOPR{A}_{t-1}+{\delta}_{3}\hspace{0.17em}LCOR{N}_{t-1}+\\ {\delta}_{4}\hspace{0.17em}LGREENCOFFE{E}_{t-1}+{\delta}_{5}\hspace{0.17em}LMILLEDRIC{E}_{t-1}+\\ {\delta}_{6}\hspace{0.17em}LMILLE{T}_{t-1}+{\delta}_{7}\hspace{0.17em}LPALMKERNE{L}_{t-1}+{\delta}_{8}\hspace{0.17em}LSORGHU{M}_{t-1}+\\ {\sum}_{i=1}^{p}{\beta}_{1}\hspace{0.17em}\mathrm{\Delta}LC{O}_{2t-i}+{\sum}_{i=0}^{p}{\beta}_{2}\hspace{0.17em}\mathrm{\Delta}LCOPR{A}_{t-i}+\\ {\sum}_{i=0}^{p}{\beta}_{3}\hspace{0.17em}\mathrm{\Delta}LCOR{N}_{t-i}+{\sum}_{i=0}^{p}{\beta}_{4}\hspace{0.17em}\mathrm{\Delta}LGREENCOFFE{E}_{t-i}+\\ {\sum}_{i=0}^{p}{\beta}_{5}\hspace{0.17em}\mathrm{\Delta}LMILLEDRIC{E}_{t-i}+{\sum}_{i=0}^{p}{\beta}_{6}\hspace{0.17em}\mathrm{\Delta}LMILLE{T}_{t-i}+\\ {\sum}_{i=0}^{p}{\beta}_{7}\hspace{0.17em}\mathrm{\Delta}LPALMKERNE{L}_{t-i}+{\sum}_{i=0}^{p}{\beta}_{8}\hspace{0.17em}\mathrm{\Delta}LSORGHU{M}_{t-i}+{\varepsilon}_{t}\end{array}$$*α*denotes the intercept,

*p*denotes the lag order,

*ɛ*

*denotes the error term and Δ denotes the first difference operator. The relationship between the variables is examined with F-tests based on the null hypothesis of no cointegration between LCO*

_{t}_{2}, LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM [

*H*

_{0}:

*δ*

_{1}=

*δ*

_{2}=

*δ*

_{3}=

*δ*

_{4}=

*δ*

_{5}=

*δ*

_{6}=

*δ*

_{7}=

*δ*

_{8}=0], contrary to the alternative hypothesis of cointegration between LCO

_{2}, LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM [

*H*

_{1}:

*δ*

_{1}≠

*δ*

_{2}≠

*δ*

_{3}≠

*δ*

_{4}≠

*δ*

_{5}≠

*δ*

_{6}≠

*δ*

_{7}≠

*δ*

_{8}≠ 0]. The estimated F-statistic is compared with the critical values of the lower and upper bounds [30]. According to Pesaran, Shin [30], the null hypothesis of no cointegration between series is rejected if the computed F-statistic goes beyond the upper bound otherwise, the null hypothesis of cointegration between series cannot be rejected if the F-statistic is lower than the critical values of the lower bound.

### 2.3. Descriptive Analysis

_{2}, CORN, GREENCOFEE, MILLEDRICE, MILLET, PALMKERNEL and SORGHUM exhibit a positive skewness while COPRA exhibits a negative skewness. Furthermore, while CO

_{2}, COPRA, CORN, MILLET and SORGHUM exhibit a platykurtic distribution, GREENCOFEE, MILLEDRICE and PALMKERNEL exhibit a leptokurtic distribution. Evidence from the Jarque-Bera test statistic shows that CO

_{2}, GREENCOFEE, MILLEDRICE and PALMKERNEL do not fit the normal distribution based on 5% significance level. In order to have a stable variance in the ARDL model, the study applies a logarithmic transformation to the study variables.

*τ*

*= 0.104,*

_{b}*ρ*= 0.288), CORN (

*τ*

*= 0.771,*

_{b}*ρ*= 0.000), GREENCOFFEE (

*τ*

*= 0.332,*

_{b}*ρ*= 0.000), MILLEDRICE (

*τ*

*= 0.752,*

_{b}*τ*

*= 0.000), MILLET (*

_{b}*τ*

*= 0.564,*

_{b}*ρ*= 0.000), PALMKERNEL (

*τ*

*= 0.638,*

_{b}*ρ*= 0.000) and SORGHUM (

*τ*

*= 0.558,*

_{b}*τ*= 0.000) have a significant positive relation with CO

_{2}. Nevertheless, statistical inferences cannot be made from descriptive statistics since Kendall’s tau-b correlation and bootstrapping do not provide evidence of causation, therefore, the study estimates the validity of the relationship and causation using econometric techniques.

### 3. Results and Discussion

### 3.1. Unit Root

### 3.2. ARDL Cointegration and Regression Analysis

_{2}, LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM.

_{2}, LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM is estimated using the ARD

*L*regression analysis based on the model specifications in Eq. (2), expressed as:

##### (4)

$$\begin{array}{l}Cointeq=LC{O}_{2}-(0.0909\times LCOPRA+0.9576\times LCORN-0.0522\times \\ LGREENCOFFEE+0.3665\times LMILLEDRICE-1.6174\times \\ LMILLET-0.5245\times LPALMKERNEL+0.2000\times \\ LSORGHUM+4.6984)\end{array}$$*β*

_{0}=4.6984,

*β*

_{1}=0.0909,

*β*

_{2}=0.9576,

*β*

_{3}=−0.0522,

*β*

_{4}= 0.3665,

*β*

_{5}=−0.6174,

*β*

_{6}=−0.5245 and

*β*

_{7}=0.2000

*ρ*=0.000] is negative and significant at 1% level, showing evidence of a long-run equilibrium relationship running from LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM to LCO

_{2}. There is no evidence of long-run elasticities from LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM to LCO

_{2}due to statistical insignificance. Nevertheless, evidence from Table 5 shows that the joint effect of the variables at constant will increase carbon dioxide emissions by 4.7% in the long-run.

_{2}by 0.22%, a 1% increase in LGREENCOFFEE will increase LCO

_{2}by 0.03%, a 1% increase in LMILLET will decrease LCO

_{2}by 0.13% and a 1% increase in LSORGHUM will decrease LCO

_{2}by 0.11% in the short-run.

### 3.3. Diagnostic Test

### 3.4. Granger-causality

_{2}, LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM using the Granger-causality test since the ARDL model only estimates the long-run and short-run equilibrium relationships existing between variables [25, 31]. Table 7 presents a summary of the Granger causality test. The null hypothesis that LCORN does not Granger Cause LCO

_{2}, LMILLEDRICE does not Granger Cause LCO

_{2}, LCO

_{2}does not Granger Cause LMILLEDRICE, LMILLET does not Granger Cause LCO

_{2}, LCO

_{2}does not Granger Cause LMILLET, LCO

_{2}does not Granger Cause LPALMKERNEL, LSORGHUM does not Granger Cause LCO

_{2}and LCO

_{2}does not Granger Cause LSORGHUM is rejected at the 5% significance level. Evidence from Table 7 shows bidirectional causality between; LMILLEDRICE ↔ LCO

_{2}, LMILLET ↔ LCO

_{2}and LSORGHUM ↔ LCO

_{2}, and a unidirectional causality running from; LCORN → LCO

_{2}and LCO

_{2}→ LPALMKERNEL.

### 3.5. Impulse-response Analysis

_{2}, LCOPRA, LCORN, LGREENCOFFEE, LMILLEDRICE, LMILLET, LPALMKERNEL and LSORGHUM to random innovations in each other that is not explained by the Granger-causality test. Significantly, the impulse-response analysis avoids the orthogonal problems related with out-of-sample Granger-causality tests. Fig. 5 depicts the Impulse-Response of carbon dioxide emissions to Cholesky One S.D. Innovations in other variables.