Liberalization vis-à-vis non-liberalization trade policy: Exploring the impact of price volatility on producer share price and cocoa supply response in Nigeria and Ghana

Abstract

Cocoa producers respond differently to volatile price shocks, but the nature of these responses remains unknown, especially in the liberalized and non-liberalized markets in Nigeria and Ghana, respectively. Therefore, we assess the extent to which price volatility affects the supply of cocoa while also analyzing the effect of price volatility on Nigeria's cocoa producer price share vis-à-vis Ghana's cocoa producer price share. We further analyze how producers react given the asymmetric nature of price volatility in Nigeria and Ghana. Annual secondary data were obtained from the World Development Index, National Bureau of Statistics, International Cocoa Organization, Central Bank of Ghana, Nigeria, and so on, from 1970 to 2019. We used the Ordinary Least Squares method, generalized autoregressive conditional heteroskedastic (GARCH) model, extensions, and the Vector Error Correction Model (VECM) for this study's analysis. Our results show the presence of volatility in price series and that volatility is asymmetric in nature. The results of the supply response show that price volatility has no significant relationship with cocoa supply in Ghana. In contrast, price volatility has a significantly positive relationship with the supply of cocoa in Nigeria at the 1 % level. The results of the VECM show that, in the long run, the cocoa producer price in Ghana will be negatively affected by both international price volatility and inflation rates at 5 % and 1 %, respectively. We suggest that cocoa farmers should have licensing to sell commodities to the international market directly without interference from the marketing board.

1. Introduction

The economies of West African countries like Ghana, Nigeria, Cote d'Ivoire, Togo, and Cameroon all rely heavily on the export of cocoa, which also provides millions of people with jobs and a significant amount of their foreign exchange revenues [1]. Except for Togo, cocoa accounts for the lion's share of these nations' agricultural output. It represents the biggest portion of the entire economy in Cameroon, Cote d'Ivoire, and Ghana [1]. Prior to Nigeria's discovery and exploitation of crude oil (the 1970s oil boom), the country's economy was completely reliant on agriculture, particularly cocoa, as the main source of income from abroad [[2], [3]]. Nigeria, which ranks second to Ghana in cocoa production, provided 75 % and more of the total annual exports of goods in 1960 through agricultural export commodities [4]. This large production and export of cocoa contributed immensely to the gross domestic product of the country. Being a top exporter of agricultural goods, Nigeria has, however, lost its place and importance in the global market [4]. Despite the fact that crude oil now makes up over 90 % of Nigeria's exports, cocoa remains the country's major export crop and the country's second-largest export after crude oil [3]. Nigeria, behind Ivory Coast and Ghana is the largest African exporter of cocoa and the fourth-largest producer of cocoa commodity in the world [3]. This implies that Nigeria has an edge in production of cocoa comparatively and absolutely, making her a supplier as well as a rival on the global market. The apparent decline in cocoa production in Nigeria led the government's direct involvement in agriculture especially in the 1980's. To handle agricultural produce, for instance, the marketing board was created [4]. The cocoa board exports cocoa as a monopoly-monopsony and makes purchases at set prices. The marketing board publishes the price risk following the announcement of purchase prices due to price volatility such that if the price of cocoa rises through the year, the board can recommend payment of bonuses, however they are exposed to possible price falls in the year, hence farmers are shielded from extreme price volatility shocks at the international market as well as global competition. Conception of the Structural Adjustment Program (SAP) began a new era in production, marketing as well as exporting of agricultural commodities (especially Cocoa) in Nigeria as contrary to the pre-liberalization era where cocoa was solely marketed through the cocoa marketing board, where prices are controlled and stabilized. While Nigeria abolished its marketing boards in 1986, with limited options available as its economy deteriorated, Ghana established an Economic Recovery Program in 1983. Ghana agreed to modernize the cocoa industry without opening up both regional and export marketing, rejecting Washington Consensus-based reforms that demanded the elimination of regulatory agencies [[5], [6]]. Ghana committed that it will raise farmers price, particularly by lowering marketing expenses. The Ghana Cocoa Board (COCOBOD) started establishing producer pricing and the costs of other services in the industry using a process that was suggested by stakeholders. After reintroducing the act of utilizing buying agencies (Licensed Buying Companies (LBCs)) to obtain cocoa from farmers and privatizing its cocoa-buying subsidiary, which had previously exercised a monopoly over the purchase of cocoa from farmers, COCOBOD required producers to pay a fee that it declared every year, a price that was constant regardless of the location or the time of year [[5], [6]].

Consequently, in 1986, the cocoa sector in Nigeria was liberalized, leading to the abolishment of the cocoa marketing board [7] while that of Ghana still operates. Therefore, Nigeria's cocoa industry's liberalization offers cocoa producers the freedom to export cocoa beans directly to the world market; it also puts producers in a critical situation as a result of changes in the commodity market [8]. Rezitis and Stavropoulos [9] opined that liberalization ensures that price volatility from the global market reaches local markets. With the elimination of price stabilization following deregulation of the agricultural market, the volatility of agricultural commodity prices is much higher [10]. This exposes producers to international price volatility, because smallholder cocoa producers have a low capacity to manage price shocks. Cocoa producers face a threat from price volatility in the global market [8], which also affects the producer prices of farmers, especially in Nigeria, where the cocoa industry has been liberalized. As a result, production decisions cannot be made efficiently because prices cannot be anticipated. Agricultural prices are more prone to volatility because of the seasonal nature of agricultural production, inelasticity of demand, and uncertainty in production [11,12]. Therefore, frequent price changes result in severe price risks.

Since the liberalization of the cocoa sector in 1986 in Nigeria, smallholder cocoa farmers have seen greater price volatility, which has led to revenue declines and, subsequently, to the supply of cocoa to the world market. However, the experience of cocoa producers in Ghana may differ because of the partial liberalization of their cocoa sector. Under these conditions, determining how much the changes in global pricing affect the amounts producers are paid, which in turn influences the supply response of producers in cocoa-producing countries, is a central issue in agricultural commodity dynamics.

Several studies [8,10,13,14] [15] have been conducted on agricultural market liberalization in Nigeria and Ghana. The majority of these studies focused on other crops, whereas few focused on cocoa. Furthermore, these studies failed to evaluate the effects of price volatility on producer share prices among cocoa farmers and their subsequent effects on the supply of cocoa in Nigeria. Although independent studies have also been conducted in Ghana on the impact of non-liberalization on producer share price, none of the studies in Nigeria and Ghana have empirically compared the impact of agricultural policy (liberalization vis-à-vis non-liberalization) on producer price and cocoa supply response, thus creating a gap in knowledge. To fill this knowledge gap, this study is focused on the following objectives namely; assesses the extent to which price volatility affects the supply of cocoa, examines the nature of producer price volatility of cocoa, analyzes the effect of price volatility on Nigeria's cocoa producer price vis-à-vis Ghana's cocoa producer price, and analyzes how producers react, given the asymmetric nature of price volatility in Nigeria and Ghana.

The motivation of this study relies on the fact that the results of this study are of extreme importance to the Nigerian and Ghanaian economy given the position that cocoa holds in the both country's economy as the largest export of agricultural goods and the second-largest export after crude oil, and cocoa's position as the primary export commodity of Ghana, the world's largest producer of the commodity. Although both economies operate the cocoa industry under different policy regimes, with the Nigerian cocoa industry fully liberalized and the Ghanaian cocoa industry operating under the market board policy, there is a need to study the policy implications of such regimes on the supply of cocoa, which invariably affects the prices received by producers of cocoa and, hence, the welfare of the producers. Cocoa farmers, which are, of course, the backbone of cocoa global value chains, are exposed to the greatest price risk (due to the variability and volatility of cocoa price, input price) and production risk (due to climate and biotic factors; climate change, pests, and diseases), yet have profited the least in the value chain, receiving a very low share of the international price of cocoa. In a broad context, this study is motivated by the critical task of examining the response of cocoa supply to price volatility and the effect of price fluctuations on the producer price of cocoa farmers.

2. Literature review

African agricultural commodity markets have undergone widespread market liberalization since the early 1980s because of price shocks, changing government perceptions, and other factors. Through these initiatives, the government's intervention in marketing and setting export commodity prices was greatly reduced. According to Gilbert and Tollens [16], market liberalization involves an increased dependence on market forces to guide resource utilization and investment. Market liberalization describes actions taken to create public and private institutions that are supportive of and consistent with private markets, as well as open domestic and export markets to competition. Simply stated, liberalization is the transition from a regulated regime to one in which prices are determined by the market [17], [18].

For commodity markets such as the cocoa market, liberalization has led to a decrease in government interventions in production and marketing, boosting the involvement of the private sector and lessening disturbances in commodity prices, particularly prices received by cocoa. Although the methods used to accomplish these objectives varied, they frequently used strategies involving the dissolution of marketing organizations owned by the government, introduction of marketing competitiveness, privatization of government assets, abolition of set prices, and lowering of taxes.

2.1. Liberalization of cocoa market

There are around 5–6 million producers of cocoa worldwide, and 40–50 million people rely on the crop for a living ([19]; Lafargue et al. [20], Renier et al. [21], and Echchabi & Azouzi [22]. The industry produces income and employment for households in exporting nations as well as export-related tax revenues for governments. For instance, from 1995 to 2014, cocoa contributed more than 30 % of the export revenues to Côte d'Ivoire and Ghana. Therefore, the cocoa industry is crucial in eliminating penury and promoting sustainable development in cocoa-producing nations. Cocoa is extensively used in the food, beverage, and confectionery industries in consuming nations. Additionally, cocoa and cocoa wastes may be processed to produce a variety of by-products such as potash, soft drinks, and animal feed [23].

West Africa produces approximately 65 percent of the world's supply of cocoa. The production and distribution of cocoa in West Africa was regulated by the government until the late 1980s. Togo, a smaller cocoa producer, as well as the four main cocoa producers in West Africa— Ghana, Nigeria, Côte d'Ivoire, and Cameroon— moved to liberalize their cocoa markets beginning in the late 1980s and continuing into the 1990s [16]. The main goals of the reforms were to enhance the producer share of FOB prices, lower domestic marketing expenses, and increase the transmission of international pricing to producers' prices [24]. These reforms were anticipated to raise cocoa producer prices by enhancing domestic and international cocoa market efficiency and competitiveness. Additionally, they were designed to lessen the distortions in national trade policies that helped shield local cocoa markets in cocoa-producing nations from global price shocks prior to the reform period, such as high levels of local taxation, including various ineffective mechanisms of government intervention.

Although cocoa has tremendous socioeconomic benefits, farmers who form the foundation of the supply chain for cocoa have not reaped many rewards. The majority of the money made throughout the value chain of cocoa goes to manufacturers and retailers, while producers get a small fraction, making it impossible for them to earn a living wage. For instance, according to Idowu et al. [25], less than 7 % of the value added to one ton of cocoa beans is paid to cocoa farmers. According to estimates from the International Labour Rights Forum (ILRF), typical cocoa farmers in Ghana and Côte d'Ivoire, the top producers of cocoa in the world, earn about US$2.07 and US$2.69 per day, respectively, which is just above the US$1.90 per person per day poverty line [26]. This terrible dilemma of cocoa producers may indicate that trade liberalization policy reforms implemented by countries that produce cocoa in the first decade of liberalization in a bid to increase cocoa growers' earnings have had less of an impact than anticipated. Trade reforms were anticipated to raise prices received by producers by enhancing competition and, as a result, the effectiveness of markets at the local and international levels.

Prior to liberalization, monopoly-monopsony marketing boards were the typical crop marketing structures used in nations with a history of British colonialism. In contrast, private companies owned the crops in the former French colonies, but the government still intervened by setting prices for producers as well as prices for exports, approving exports, and price stability. The process of liberalizing the cocoa market was anticipated to cut the costs of middlemen, which would increase farmers’ prices [27].

2.2. Impact of trade liberalization

Determining the relevant dates for before-and-after comparisons is challenging because of the diversity and intricate nature of the West African cocoa market liberalization process. Since liberalization is a legal act, it can be accurately dated: Ghana is yet to complete its process of liberalization, 1989–1991 and 1995 for Cameroon, 1986–1987 for Nigeria, and 1999 for Côte d'Ivoire (Fig. 1).

Fig. 1.

Deflated ICCO indicator price and Deflated cocoa producer prices.

Source: Gilbert and Tollens (2003).

Unexpectedly, cocoa trade liberalization has led to a considerable degree of market concentration. The intricacy of the markets for cocoa, which are characterized by ease of access to resources like risk management tools, finance and technologies, in addition to their drive to gain scale economies, serve as the primary driving force at the upstream end of the cocoa value chain. As a result, most small businesses have either abandoned the cocoa marketing industry or amalgamated with international corporations that have taken over their operations [14,28]. With advantages for smallholders, particularly small farmers, the ensuing market structure may help increase the cost effectiveness of the cocoa GVC. High concentrations, particularly in local cocoa markets, could negate the advantages for producers by resulting in oligopsonic or monopsonic structures (Lafargue et al. [20]; Renier et al. [21]; Echchabi & Azouzi [22].

The fluctuation in prices that farmers receive will also have been impacted by liberalization and has typically increased. The four (deflated) producer prices are shown in Fig. 2 along with their unconditional inter-annual logarithmic standard deviations before and after liberalization. With a surge of 32 % from 12 % to 44 %, producers in Cameroon have experienced the largest increase in price fluctuations. While volatility in Ghana has decreased, it has increased slightly in Nigeria and Côte d'Ivoire. This final, contradictory result is a result of COCOBOD's failure to achieve its stated stabilization objective during the 1980s, when rapid inflationary changes caused the ostensibly stabilized domestic price to become more volatile than the global price. The data listed in Fig. 2 may understate the increase in unpredictability that farmers experience because liberalization has also increased intra-annual price variability, with the exception of Ghana, where the nominal producer price remains fixed for the full crop year. The price variation during the same period is shown in Fig. 2. Due to the minor drop in global pricing volatility, it follows that the increases in Nigeria, Côte d'Ivoire, and Cameroon cannot be explained by increased volatility in the post-liberalization global market.

Fig. 2.

Producer price volatility before and after Liberalization.

Source: Gilbert and Tollens (2003).

3. Conceptual framework

Changes in the general level of farm prices affect the ability of farmers to repay debt, profitability, and the competitive position of one country relative to another in selling agricultural export commodities. Changes in relative prices are of even greater importance from a social and political point of view because they affect the welfare of farm families and the level and distribution of income in the farm and non-farm sectors of the economy. Prices observed over time are the result of a complex mixture of changes associated with seasonal, cyclical, trend, and regular factors. The most common regularity observed in agricultural prices was the seasonal pattern of change. Economists have devoted substantial effort to identifying empirical regularities in price and quantity behavior.

Price is a key variable that is expected to directly affect the supply of agricultural commodities. This is in line with the theory of supply, which states that the higher the price, the higher is the quantity supplied. However, a change in price (price volatility or price variability) is expected to indirectly affect agricultural export commodities. Price volatility is expected not to have a significant effect on the supply of cocoa in Ghana because of the existence of cocoa boards; however, price volatility is expected to cause a significant and indirect relationship with the supply of cocoa. Favorable rainfall conditions are expected to enhance yield and hence have a positive impact on agricultural commodity supply. Producer prices are expected to have a positive and significant relationship with the supply of cocoa, while pesticide prices are expected to have a negative relationship with the supply of cocoa. The volatility of international cocoa prices is expected to have a negative relationship with the cocoa producer prices.

4. Methodology

4.1. Theoretical framework

Following studies like Yu et al. [29], Duan et al. [30], and Celık [31], The equation model for the supply of cocoa is as follows:

$$Y_t=a_0+a_1{P}_t^e+a_2{h}_t+a_3{X}_t+{\epsilon }_t$$ (1)

Where $Y_t$ is the cocoa production over a certain period t, i.e 40 years period, ${Xi}_t$ is a vector of independent variables, $h_t$ is the expected price variance, $P_t^e$ is the measured price volatility, ${\epsilon }_t$ is a mean zero error term with a Gaussian distribution. We use the GARCH (p, q) process to generate the $h_t$ as follows:

$$h_t=C_0+\sum _{i=1}^p{C}_{1i}{e}_{t-i}^2+\sum _{i=1}^q{C}_{2i}{h}_{t-i}$$ (2)

Where $e_t|{\omega }_{t-1}$ $\sim$ N (0, $h_t$), $C_0>0;C_{1i}\ge 0;C_{2i}\ge 0;\sum C_{1i}+\sum C_{2i}<1$.

The autoregressive conditional heteroscedastic (ARCH) model permits the conditional variance $h_t$, to depend on the historical volatility measure as a linear function of the historical errors, $e_t$ , while maintaining a constant value for the unconditional variance. $e_t$ is a discrete time stochastic error, and ${\omega }_{t-1}$ is the information set of all previous states up to time t-_1. The lagged variable of _t-1 is added to control for any potential endogeneity brought by the omitted variable, in the case when a large influence on current production by its lagged value is present.

The generalized ARCH (p, q) specification [GARCH (p, q)] was created by Bollerslev in [32]. In accordance with this description, $h_t$ is defined in Equation (2), also known as the GARCH conditional variance equation. Equation (2) states that the conditional variance $h_t$ is a linear function of its own q-lagged conditional variances and p-lagged squared residuals. Because the variance is expected to be positive, the coefficients $C_0$ , $C_{1i}$, $C_{2i}$ are always positive. In addition, the stationarity of the variance was preserved by the restriction $\sum C_{1i}+\sum C_{2i}<1$.

The supply response equation is explicitly estimated using the GARCH model's predictions of $h_t$. The Asymmetric GARCH (AGARCH) model is an alternative to the standard GARCH model and has been empirically demonstrated to provide a good depiction of the volatility process.

4.2. Supply response

In determining the effect of price vo1ati1ity on the supp1y of cocoa, the Ordinary 1east square (OLS and ARIMA) was used. The cocoa response equation (1) is specified as

$$Q_t=a_o+a_1{h}_t+a_2{RER}_t+a_3{PF}_{t-1}+a_4{PP}_{t-1}+a_5{Rain}_t+a_6{Rain}_t^2+{\epsilon }_t$$ (4)

where:

$Q_t$ is the cocoa production in time t;

$h_t$ is price variance;

${RER}_t$ is the Rea1 Exchange Rate in time t;

${PF}_{t-1}$ is the rea1 price of pesticide in time t-1;

${PP}_{t-1}$ is the Producer price of cocoa in time t-1;

${Rain}_t$ is the quantity of rainfa11 in time t;

${Rain}_t^2$ is the square of the quantity of rainfa11 in time t;

${\epsilon }_t$ is the error term.

The conditiona1 price vo1ati1ity term, $h_t$ was assumed to be a key risk factor of supp1y. ${Rain}_t$ is the quantity of rain fa11 in the year as the c1imatic factor affecting supp1y; the variab1e ${RER}_t$, the rea1 exchange rate in year t, is introduced in mode1 in other to capture the effect of internationa1 price. The lagged variable of _t-1 is added to control for any potential endogeneity brought by the omitted variable, in the case when a large influence on current production by its lagged value is present.

4.3. Vector error correction Mode1 (VECM)

Echoing on the econometric model of Lafargue et al. [20], Renier et al. [21], and Echchabi & Azouzi [22], the effect of price vo1ati1ity on the cocoa producer's price was estimated using the VECM. The fo11owing is an examp1e of a matrix containing the VECM mode1 specifications emp1oyed in this study.

$$\left|\begin{array}{c}{\Delta Y}_t\\ {\Delta X}_t\end{array}\right|=\left|\begin{array}{c}{\phi }_1\\ {\phi }_2\end{array}\right|+\left|\begin{array}{c}{\alpha }_1\\ {\alpha }_2\end{array}\right|\left[Y_{t-1}-{\beta }_0-{\beta }_1{X}_{t-1}\right]+\sum _{i=1}^k\left|\begin{array}{cc}{\delta }_{1j}& {\rho }_{1j}\\ {\delta }_{2j}& {\rho }_{2j}\end{array}\right|\left|\begin{array}{c}{\Delta Y}_{t-1}\\ {\Delta X}_{t-1}\end{array}\right|+\left|\begin{array}{c}{\epsilon }_{1t}\\ {\epsilon }_{2t}\end{array}\right|$$ (6)

$$\Delta \mathit{ln}{Pp}_t=\sigma +\sum _{i=1}^{k-1}{\psi }_i\Delta \mathit{ln}{Pp}_t+\sum _{i=1}^{k-1}{\beta }_j\Delta 1\mathrm{n}{Vol}_{t-1}+\sum _{m=1}^{k-1}{\phi }_m\Delta {lnInf}_{t-m}+{\lambda }_1{ECT}_{t-1}+u_{1t}$$

$$\Delta 1\mathrm{n}{Vol}_t=\alpha +\sum _{i=1}^{k-1}{\psi }_i\Delta \mathit{ln}{Pp}_t+\sum _{i=1}^{k-1}{\beta }_j\Delta 1\mathrm{n}{Vol}_{t-1}+\sum _{m=1}^{k-1}{\phi }_m\Delta {lnInf}_{t-m}+{\lambda }_2{ECT}_{t-1}+u_{2t}$$

$$\Delta {lnInf}_t=\delta +\sum _{i=1}^{k-1}{\psi }_i\Delta \mathit{ln}{Pp}_t+\sum _{i=1}^{k-1}{\beta }_j\Delta 1\mathrm{n}{Vol}_{t-1}+\sum _{m=1}^{k-1}{\phi }_m\Delta {lnInf}_{t-m}+{\lambda }_4{ECT}_{t-1}+u_{3t}$$

where;

K-1 is the 1 ag 1ength reduced by 1;

${\psi }_i$, ${\beta }_j$ and ${\phi }_m$ are short-run dynamics coefficients of the mode1's adjustment to 1ong-run equi1ibrium;

ƛ is the speed of adjustment parameter with a negative sign;

$ECT$ is the Error Correction Term, which is the 1agged va1ue of residua1s obtained from the cointegration regression of dependent variab1e on the regressors.

$\mathit{ln}{Pp}_t$ is the 1og of the producer price of cocoa;

$1\mathrm{n}{Vol}_t$ is the 1og of internationa1 price vo1ati1ity;

${lnInf}_t$ is the 1og inf1ation rate.

VECM is thought to be a superior technique because it has a number of advantages over ECM, which offers a so1id framework for eva1uating this purpose. The VECM does not presuppose a sing1e co-integration re1ationship, in contrast to Error Correction Mode1 which is a sing1e equation co-integrated mode1. The VECM is estimated using a system of equations rather than a sing1e equation and a1so considers the endogeneity of a11 variab1es in it.

The first step was to test for stationarity, as described above using the Phi1ip-perron unit root test and Augmented Dickey Fu11er test of stationarity. The next step emp1oyed was to obtain the optimum 1 ag 1ength, k, which was determined using a set of criteria, namely, the Schwarz Criteria (SC) and the Akaike Information Criteria (AIC). Subsequently, we performed a cointegration test to determine whether the variab1es were cointegrated. Cointegration is a 1ong-term re1ationship that exists between variab1es, despite not being stationary [33]. According to Verbeek [34], cointegration connections in a system of equations indicates that an error correction mechanism is present in the system, which imp1ies the existence of short-term dynamics in a way that is consistent with 1ong-term re1ationships and represents the 1ong-term equi1ibrium re1ationships.

The Johansen cointegration test was used in this study;

Where.

$H_0:r=0$ (no cointegration equation).

$H_1:r=0$ ($H_0$ is not true, i.e., there is a cointegration equation).

Decision criteria at 5 % 1eve1 of significance: The nu11 hypothesis of no cointegration was rejected where the Trace and Max statistic was greater than the critica1 va1ue (which in this study was 5 %). The nu11 hypothesis was rejected because the trace statistic was greater than the critica1 va1ue.

From here on, the study proceeded to estimate the vector error correction mode1, whereafter, post-estimations (diagnostics) which inc1uded fo11owing were carried out.

• i.Test for autocorre1ation using the 1-M test for residua1 autocorre1ation.
• ii.Jarque Bera Norma1ity test.
• iii.Test for stabi1ity, considering the eigenva1ue stabi1ity conditions.

4.4. Non-1inear asymmetric GARCH

The above-mentioned standard GARCH mode1 cou1d not account for the asymmetric nature of the series insofar as the error term $e_t$, which represents an unanticipated price shock, enters the conditiona1 variance equation as a square, imp1ying that it does not matter if the price is negative or positive. When a rise or dec1ine in price produces a different vo1ati1ity asymmetric effect is observed. The asymmetric GARCH mode1 accounts for distributions that are neither symmetric nor norma1 (i.e., skewed), in which the vo1ati1ity response to good and negative news differs. The EGARCH and the TGARCH Asymmetric mode1s (NAGARCH), created by Eng1e and Ng [35], is a typica1 asymmetric GARCH mode1 that was used in this study.

In this Non-1 inear asymmetric GARCH mode1, equations (2) and (3) presented ear1ier wi11 be described as follows:

$$h_t=C_0+\sum _{i=1}^p{C}_{1i}{\left({ϵ}_{t-1}+C_3\sqrt{h_{t-1}}\right)}^2+\sum _{i=1}^q{C}_{2i}{h}_{t-i}$$ (7)

Where ${ϵ}_t|{\omega }_{t-1}$ $\sim$ N (0, $h_t$), $C_0>0;C_{1i}\ge 0\text{;}$ i = 1, …, p; $C_{2i}\ge 0\text{;}$ i = 1, …, q; $\sum C_{1i}+\sum C_{2i}<1$.

This mode1 describes vo1ati1ity as a non1inear asymmetric function of past periods' shocks and vo1ati1ity; if $C_3$ is not equa1 to 0, that is, ($C_3$ $\ne 0$), there is a presence of asymmetry. Therefore, $C_3$ is the asymmetry parameter, and if $C_3$ is positive, then a positive impu1se creates greater vo1ati1ity than a negative impu1se of the equa1 magnitude.

4.5. Estimation techniques

This study use the inferentia1 methods. The first objective, which is to ana1yze the effect of price vo1ati1ity on the supp1y of cocoa, was carried out using the genera1ized auto-regressive conditiona1 heteroskedastic mode1. To ana1yse this, the expected price variance equation was first estimated before estimating the supp1y response equations. The expected variance of price $h_t$ is inc1uded in the response equation as a regressor.

The first step in estimating this was to p1ot the series for visua1ization, this was done in order to observe vo1ati1ity c1ustering of the series and a1so see the nature of the data (via Histogram). The next step was to test for the ARCH effect. The study proceeded to the GARCH estimation, as the ARCH effect was present in series. A diagnostic test was performed as soon as the estimation was completed. The second objective, whose concern is to eva1uate the effect of price vo1ati1ity and wor1d price on cocoa producer share price was eva1uated using the vector error correction mode1 (VECM), which is a system of equations where each dependent variab1es is exp1ained by a11 the 1 ags of other variab1es and the 1 ag of the dependent variab1e. Precise1y, this study estimated equation (6) using VECM. Taking after some ear1ier studies, in adopting this mode1, the fundamenta1 step was to examine the nature of the series or examine the stationarity of the data using unit root tests for stationarity, as described above using the Phi1ip-perron unit root test and the Augmented Dickey Fu11er test of stationarity.

The next step was to determine the optimum 1 ag 1ength, k, which was determined using a set of criteria, namely, the Schwarz Criteria (SC) and the Akaike Information Criteria (AIC).

The cointegration test was then run to determine if the variab1es were actua11y cointegrated. According to Daryanto, Sofia, Sahara, and Sinaga [33], cointegration is a 1ong-term re1ationship between variab1es that, despite not being non-stationary, might resu1t in 1 inear combinations that is stationary. According to Verbeek [34], cointegration connections in a system of equations indicate the presence of an error correction mode1 that imp1ies that a 1ong-term equi1ibrium re1ationship exists among variab1es whi1e a1so describing short-term dynamics in a way that is consistent with 1ong-term re1ationship.

In this study, the Johansen cointegration test was used;

Where;

$H_0:r=0$ (no cointegration equation).

$H_1:r=0$ ($H_0$ is not true, i.e., there is a cointegration equation).

Decision criteria at 5 % 1eve1 of significance: The nu11 hypothesis of no cointegration was rejected where the Trace and Max statistic was greater than the critica1 va1ue (which in this study was 5 %). The nu11 hypothesis was rejected because the trace statistic was greater than the critica1 va1ue.

The study estimated the vector error correction mode1. Diagnostic tests were then performed as described above. The third objective, whose concern is to examine how producers react given the asymmetric nature of price vo1ati1ity in Nigeria and Ghana was eva1uated using the non-1 inear asymmetric GARCH mode1 whose operation is a1most identica1 to that of the standard GARCH mode1.

4.6. Data source and description

This study used annua1 secondary data spanning 1970 to 2019 from various sources which inc1ude the internationa1 Cocoa Organization (ICCO), the Food and Agricu1ture Organization (FAO), Nationa1 Bureau of Statistics (NBS), Wor1d Deve1opment Index (WDI), Centra1 Bank of Nigeria, Centra1 Bank of Ghana, and a11 maintain an on1ine database that has these statistics for various years. In addition, the c1imatic data for precipitation (mm/season) were obtained from the Wor1d bank. The selection of a long-time span were based on the fact that this study covers pre-liberalization period, liberalization period and post liberalization period especially the Nigerian case.

5. Results and discussion

5.1. Volatility analysis

The result of the plot of the log of the price of cocoa indicates that there is a trend in the series of data, as displayed in Fig. 3. However, the result of the plot of changes in the log of price indicates volatility clustering, which explains that certain periods of higher volatilities are followed by periods of higher volatility, which could be positive or negative (and therefore riskier), followed by intervals of smaller volatilities, which could also be positive or negative, as shown in Fig. 4.

Fig. 3.

The plot of log of price (ln price).

Source: Author's Computation, 2023.

Fig. 4.

The plot of changes in log of price (% ln price).

Source: Author's Computation, 2023.

Fig. 5 is a histogram of the changes in the log of price (% ln price) which clearly shows a leptokurtic behavior (having fat tails) of the series implying that the data are not following normal distribution (are not normally distributed). From these results, it is clear that the assumption of homoscedasticity is very limited, and in such instances, it is recommended to model after patterns that permit the variance to depend on its lagged values. Hence, the use of certain methods is also feasible to see or capture the variance (volatility) in the series.

Fig. 5.

Histogram of the changes in the log of price (% ln price).

Source: Author's Computation, 2023.

5.2. Testing for ARCH effects (test for heteroskedasticity)

This study employs the LM test to test for heteroskedasticity (ARCH effect) in the series because the above results are not sufficient to justify the presence of heteroskedasticity in the series. The results of the LM test with the null hypothesis that there is no ARCH effect and the alternative hypothesis that there is an ARCH effect are presented in Table 1. From these results, the Chi-square coefficient (LM-statistic or), which is 42.16429, is significant at the 1 % level of probability, as observed from the observed R-squared, and b1 is 0.264614 and significant at the 1 % level. We reject the null hypothesis and accept the alternative hypothesis that the ARCH effect is present in the series.

Table 1.

LM test for heteroskedasticity.

Variable	Coefficient	Standard error	t-statistic	Prob
C	26827.75	3044.905	8.810699	0.0000
RESID^2(-1)	0.264614	0.039364	6.722297	0.0000
F- statistic	45.18928		Prob. F	0.0000
Obs*R-squared	42.16429		Prob. Chi-Squared	0.0000

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

With the arch effect being present and the LM-statistic significant, it implies that the data exhibits a heteroskedastic behavior (i.e., non-constant variance) as well as an autoregressive behavior (i.e., the heteroskedasticity observed over different time periods may be autocorrelated); hence, we can perform ARCH- models on this series.

In addition, the result of the LM test clearly shows that the Durbin-Watson statistic of 2.083292 is greater than the R-squared value of 0.070040; hence, it is not a spurious regression.

5.3. Generalized auto-regressive conditional heteroskedastic models

GARCH models were estimated to analyze the nature of the price volatility of cocoa commodities. From Table 2, it is observed that not only does the ARCH-term tend toward zero and the GARCH-term tends towards one, but also that all variance equation coefficients are statistically significant even at the 1 % level of probability. It is evident that the GARCH effect is stronger than the ARCH effect, implying that volatility impacts last longer than the past shocks.

Table 2.

Result of the standard GARCH estimation.

Variables	Coefficients	Standard error	t-statistic	Prob
C	49.34364***	14.52243	3.397754	0.0007
Price (−1)	0.970478***	0.006946	139.7198	0.0000
Variance Equation
C	954.5366	366.8761	2.601796	0.0093
ARCH effect	0.234215***	0.044247	5.293353	0.0000
GARCH effect	0.761777***	0.039560	19.25615	0.0000

Source: Author's computation, 2023; ***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively

Furthermore, as the sum of the GARCH and ARCH terms is less than one, it is evident that the conditional variance is stable. However, this result shows that shocks in the variance are the same regardless of whether it is a positive or negative shock; that is, it does not capture the asymmetry of the series. The significant GARCH term implies past volatility, and we can predict the current volatility and that current volatility will persist in the second period as well, while the significant ARCH term simply means that past volatility has a positive effect on the current volatility of the data.

T-GARCH is an asymmetric GARCH model that captures the asymmetry of a series, if present. The results of the T-GARCH in Table 3 show that the variance equation coefficients are significant at the 1 % level of probability. The ARCH-term tends toward zero, and the GARCH-term tends towards one. It is evident that the effect of GARCH is stronger than that of ARCH, implying that the volatility effect is more persistent than that of past shocks.

Table 3.

Result of the standard T-GARCH estimation.

Variables	Coefficients	Standard error	t-statistic	Prob
C	52.41025***	14.57348	3.596277	0.0003
Price(-1)	0.972421***	0.007499	129.6693	0.0000
Variance Equation
C	1040.285	324.7909	3.202936	0.0014
ARCH effect	0.278824***	0.059190	4.710659	0.0000
Asymmetric coefficient	−0.181338***	0.052840	−3.431835	0.0006
GARCH effect	0.790741***	0.040099	19.71965	0.0000

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Alongside the GARCH and ARCH terms, the asymmetry term is significant at the 1 % level of probability and is equal to −0.181338 and not equal to zero. The significance of this asymmetry term confirms the presence of asymmetry in the series (i.e., the influence of good news on price volatility is not equal to that of bad news of equal magnitude). If the asymmetry coefficient is equal to zero, it implies that there is no leverage or asymmetry effect in the series.

A negative and significant asymmetry term implies that positive impulses will have greater effects on the volatility of prices than negative shocks, implying that if there is a gain in the current period, farmers are more likely to produce more, and that if there is a loss in the current period, farmers are less likely to produce more; hence, this behavior decreases the volatility of the data.

From Table 4, C(3) is the constant of the variance equation, C(4) is the ARCH term, C(5) is the asymmetry term, and C(6) is the GARCH term of the variance equation. It is clear that all the variance equation coefficients are statistically significant at the 1 % probability level. The asymmetry-Garch term, which is the coefficient of interest, is positively significant at the 1 % probability level. This implies that positive shocks have a stronger impact than negative shocks.

Table 4.

Result of the E-GARCH estimation.

Variables	Coefficient	Standard error	t-statistic	Prob
C	52.41025	14.57348	3.596277	0.0003
Price(-1)	0.972421	0.007499	129.6693	0.0000
Variance Equation
C(3)	0.321126**	0.132458	2.424356	0.0153
C(4)	0.274983***	0.061023	4.506189	0.0000
C(5)	0.111774***	0.026964	4.145291	0.0000
C(6)	0.947084***	0.014883	63.63398	0.0000

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

5.4. Supply response of cocoa to price volatility in Ghana and Nigeria

The supply response regression is analyzed to capture the effect of price volatility on the supply of cocoa in both Nigeria and Ghana. To evaluate the effect of price volatility on the supply of cocoa, the expected variance price of cocoa was estimated with different GARCH models (asymmetric and non-asymmetric models) before performing the supply response equation using the expected price variances as independent variables of the equation.

Regressions for the cocoa sector in Ghana (using the expected price variance generated by different GARCH models); Table 5, Table 6, Table 7 show that price volatility has a positive relationship with the quantity of cocoa supplied in the international market, but this relationship is statistically insignificant, implying that the effect of price volatility in the international market on the supply of cocoa is not statistically different from zero. This could be a result of the interference of the cocoa market board, which insulates cocoa producers from international market shocks, thereby mitigating the effect of price volatility.

Table 5.

Ghana supply response regression with standard GARCH conditional variance.

Variables	Coefficients	Standard error	t-statistic	Prob
C	−229.3108	144.6603	−1.585167	0.1206
Garch	8.664252	9.119695	0.950059	0.3476
G_exchange_rate	0.202003***	0.039794	5.076261	0.0000
G-pesticide(-1)	−0.069641***	0.026697	−2.608618	0.0126
G_rainfall	68.50665*	41.19619	1.662937	0.1040
G_rainfall^2	−4.876038*	2.933672	−1.662094	0.1041
Producer_price(-1)	0.178689	0.112720	1.585245	0.1206

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Table 6.

Ghana supply response regression with T-GARCH conditional variance.

Variables	Coefficients	Standard error	t-statistic	Prob
C	−229.3345	144.6377	−1.585578	0.1205
Garch	8.723480	9.121039	0.956413	0.3445
G_exchange_rate	0.201918***	0.039784	5.075425	0.0000
G-pesticide(-1)	−0.069696***	0.026696	−2.610706	0.0126
G_rainfall	68.51346	41.18971	1.663363	0.1039
G_rainfall^2	−4.876472	2.933209	−1.662504	0.1040
Producer_price(-1)	0.178352	0.112705	1.582470	0.1212

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Table 7.

Ghana supply response regression with E-GARCH conditional variance.

Variables	Coefficients	Standard error	t-statistic	Prob
C	−227.3987	146.3368	−1.553941	0.1279
Garch	4.517912	10.48917	0.430722	0.6689
G_exchange_rate	0.210121***	0.039946	5.260072	0.0000
G-pesticide(-1)	−0.068385***	0.026902	−2.542001	0.0149
G_rainfall	67.92045	41.67646	1.629708	0.1108
G_rainfall^2	−4.835691	2.967855	−1.629356	0.1109
Producer_price(-1)	0.208020*	0.112142	1.854973	0.0708

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

However, the exchange rate of the Ghanaian economy showed a positive relationship with the cocoa quantity supplied in the international market, and this is significant at the 1 % level of probability with a coefficient of 0.210121. This result conforms with Boansi's [13] finding that exchange rates allowed local farmers to increase production even when international prices fell. This implies that if the exchange rate of Ghana increases, the quantity of cocoa supplied in the international market increases, and if the exchange rate decreases, the quantity of cocoa supplied in the global market also decreases.

The price of pesticides in the previous production year was negatively significant at the 1 % level of probability, with a coefficient of −0.068385. This implies that cocoa producers in Ghana are very responsive to the prices of pesticides (i.e., when the price of pesticides in the previous production year is low, they tend to apply more pesticides, thus leading to an increase in the quantity of cocoa supplied), making the prices of pesticides a key determinant in the quantity of cocoa supplied in Ghana. This result agrees with the findings of Yovo [8], who observed that the coefficient of pesticide prices for cocoa production and supply in Togo is negative and significant.

The price received by cocoa producers in the previous year also has a positive but not statistically significant relationship with the quantity of cocoa supplied. However, using the conditional variance of the exponential-volatility model, the price received by cocoa producers in the previous year with a coefficient of 0.208020 is a significant variable in determining the quantity of cocoa supplied. This implies that if the price received by cocoa producers in the previous year increases, the quantity of cocoa supplied to the international market also increases, and vice versa, making the producer price a motivation for cocoa producers in Ghana to supply more cocoa for export.

Rainfall amount, which is an abiotic (environmental) factor affecting cocoa production, has a positive relationship with the quantity of cocoa supplied but is significant at the 10 % level of probability. However, this implies that in Ghana, with an increase in the amount of rainfall, the quantity of cocoa supplied in the global market will increase, and with a decrease in rainfall amount, the quantity of cocoa supplied in the international market will decline.

Contrary to what is experienced in Ghana, the supply response regression to analyze the effect of price volatility on the supply of cocoa in Nigeria presented in Table 8, Table 9 and Table 10 shows that, using expected conditional price variances generated by different GARCH models, price volatility has a positive relationship with the quantity of cocoa that is supplied at the international market, an effect that is statistically significant, For the three GARCH-models, at the 1 % level of probability. This implies that price volatility in the international market has a marked effect on the quantity of cocoa supplied at time (t). As the volatility of prices in the international market increases, the quantity of cocoa supplied by Nigeria at the international market also increases. This could be a result of the absence of a cocoa market board that insulates cocoa producers from international market shocks. This coefficient is expected to be negative, but positive. This could be a result of market intermediaries (which mostly have private information) that hoard a cocoa commodity only to sell when the price of cocoa experiences a positive shock, as previously stated in the asymmetric regression that positive shocks bear a stronger marked impact as negative shocks. This agrees with Thiyagarajan et al. [36], who find that the agricultural commodities market responds more favorably to positive shocks than to negative shocks in situations of speculative hoarding.

Table 8.

Nigeria supply response regression with standard GARCH conditional variance.

Variable	Coefficient	Standard error	t-statistic	Prob
C	−53.64573	105.1121	−0.510367	0.6125
Garch	34.94669***	11.99274	2.913986	0.0058
N_exchange_rate	0.040815***	0.016611	2.457175	0.0183
N-pesticide(-1)	0.261861***	0.031358	8.350739	0.0000
N_rainfall	17.09323	29.84814	0.572673	0.5700
N_rainfall^2	−1.202320	2.118680	−0.567486	0.5735
N_Producer_price(-1)	0.394487***	0.115581	3.413094	0.0015

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Table 9.

Nigeria supply response regression with T-GARCH conditional variance.

Variable	Coefficient	Standard error	t-statistic	Prob
C	−53.78072	105.1052	−0.511685	0.6116
Garch	34.95460***	11.99454	2.914209	0.0058
N_exchange_rate	0.040888***	0.016614	2.461104	0.0181
N-pesticide(-1)	0.261831***	0.031352	8.351230	0.0000
N_rainfall	17.12975	29.84627	0.573933	0.5691
N_rainfall^2	−1.204837	2.118552	−0.568708	0.5727
N_Producer_price(-1)	0.394856***	0.115562	3.416849	0.0014

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Table 10.

Nigeria supply response regression with E-GARCH conditional variance.

Variable	Coefficient	Standard error	t-statistic	Prob
C	−68.94949	106.6523	−0.646488	0.5216
Garch	36.02907***	13.94342	2.583947	0.0134
N_exchange_rate	0.039470***	0.016889	2.337027	0.0244
N-pesticide(-1)	0.254565***	0.031390	8.109620	0.0000
N_rainfall	21.42792	30.28706	0.707494	0.4833
N_rainfall^2	−1.508473	2.150067	−0.701594	0.4869
N_Producer_price(-1)	0.399071***	0.117753	3.389063	0.0016

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Furthermore, the exchange rate of the Nigerian currency showed a positive relationship with the cocoa quantity supplied in the international market with a coefficient of 0.039470, which is significant at the 1 % level of probability. This result also conforms to Boansi's [13] findings that exchange rates allowed local farmers to increase production even when international prices fell. This implies that the quantity of cocoa supplied in the international market increases by one unit with a 0.039470 increase in the exchange rate and vice versa. Cocoa producers appear to benefit more from foreign exchange earnings. The exchange rate could be a reason why cocoa producers want to supply more cocoa commodities in the international market. One lagged price of pesticides (i.e., the price of pesticides in the previous year) is also an important factor that contributes positively to the quantity of cocoa supplied in a given period, and it is statistically significant at the 1 % level of probability.

The price received by cocoa producers in the previous year also has a positive relationship with the quantity of cocoa supplied in the present period, and this coefficient is significant at the 1 % level of probability. This implies that as the price received by cocoa producers in the previous period (t) increases, the quantity of cocoa supplied in the international market increases, and as the price received by cocoa producers in the previous period (t) decreases, the quantity of cocoa supplied in the international market decreases this might be attributed to factors such as economic incentives, market demand, and supply-demand relationships. This corroborates the findings of Ogunleye [37], who used the Error Correction Model (ECM) and concluded that producer price had a positive effect on cocoa output, and farmers were encouraged to improve production and hence supply. If there is an increase in the price received by producers in the previous period, it could be a motivation for producers to supply more in the international market and vice versa. In other words, price incentives are an important motivation for the quantity of cocoa offered in the international market.

5.5. Vector error correction model

The vector error correction model (VECM) was used to analyze the effect of price volatility on cocoa producer prices in countries of interest. To perform the VECM, a number of analyses, including the stationarity test (unit root test) and cointegration tests (Johansen cointegration test), were carried out.

5.6. Stationarity test (group)

This section presents the unit root test of stationarity, also known as the stationarity test. The null hypothesis of non-stationarity was tested on the variables of interest to be used in the Vector Error Correction Model to establish whether they were stationary (non-trending) or non-stationary (trending). When a variable is stationary, it implies that the variables’ covariance, variance, and mean are constant over time, and hence do not have a unit root. When non-stationary variables are regressed together, it results in a spurious regression, which has a high $R^2$ that is greater than the Durbin-Watson statistic. The results of the unit root test are presented in Table 11, Table 12, respectively.

Table 11.

Philip-perron And Augmented Dickey Fuller Unit root tests for Ghana.

	With Constant		With Constant & Trend		Without Constant & Trend
At Level (Philip-Perron)
Variables	t-stat	Prob	t-stat	Prob	t-stat	Prob
Volatility	−5.8969***	0.0000	−5.7212***	0.0001	−1.8691*	0.0593
Inflation	−3.8434***	0.0047	−3.7817**	0.0259	−0.6507	0.4304
Exchange Rate	−0.7093	0.8349	−1.5038	0.8151	1.4355	0.9607
Producers Price	−0.9995	0.7466	−2.3622	0.3941	−3.0423***	0.0030
At First Difference (PP)
Volatility	−13.3625***	0.0000	−14.5684***	0.0000	−13.3664***	0.0000
Inflation	−18.1994***	0.0000	−17.7636***	0.0000	−17.9554***	0.0000
Exchange Rate	−6.2048***	0.0000	−6.1686***	0.0000	−5.2379***	0.0000
Producers Price	−6.8431***	0.0000	−6.7995***	0.0000	−6.1684***	0.0000
	At Level	(ADF)
Volatility	−5.8182***	0.0000	−5.6977***	0.0001	−1.4824	0.1277
Inflation	−4.0660***	0.0025	−4.6359***	0.0027	−0.2858	0.5777
Exchange Rate	−0.7018	0.8368	−1.3242	0.8703	1.9299	0.9861
Producers Price	−1.0406	0.7317	−2.3622	0.3941	−2.4105**	0.0168
	At First	difference	(ADF)
Volatility	−10.1757***	0.0000	−10.2003***	0.0000	−10.2568***	0.0000
Inflation	−7.7457***	0.0000	−7.7014***	0.0000	−7.8270***	0.0000
Exchange Rate	−6.2079***	0.0000	−6.1730***	0.0000	−5.1524***	0.0000
Producers Price	−6.7059***	0.0000	−6.6570***	0.0000	−6.1684***	0.0000

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Table 12.

Philip-perron And Augmented Dickey Fuller Unit root tests for Nigeria.

	With Constant		With Constant & Trend		Without Constant & Trend
At Level (Philip-Perron)
Variables	t-stat	Prob	t-stat	Prob	t-stat	Prob
Volatility	−5.8969***	0.0000	−5.7212***	0.0001	−1.8691*	0.0593
Inflation	−4.2283***	0.0015	−5.3869***	0.0003	−0.5572	0.4708
Exchange Rate	−1.6695	0.4403	−1.5225	0.8085	−0.8689	0.3346
Producers Price	−0.3019	0.1970	−1.0554	0.9263	0.7012	0.8637
At First Difference (PP)
Volatility	−13.3625***	0.0000	−14.5684***	0.0000	−13.3664***	0.0000
Inflation	−11.7964***	0.0000	−11.8587***	0.0000	−11.9615***	0.0000
Exchange Rate	−6.9080***	0.0000	−7.0228***	0.0000	−6.9794***	0.0000
Producers Price	−6.4785***	0.0000	−8.7410***	0.0000	−6.4832***	0.0000
	At Level	(ADF)
Volatility	−5.8182	0.0000	−5.6977	0.0001	−1.4824	0.1277
Inflation	−4.2156***	0.0016	−5.3632***	0.0003	−0.3984	0.5350
Exchange Rate	−1.6165	0.4668	−1.5170	0.8105	−0.8652	0.3362
Producers Price	−4680	0.8886	−1.2948	0.8779	−2.4105	0.5726
	At First	difference	(ADF)
Volatility	−10.1757***	0.0000	−10.2003***	0.0000	−10.2568***	0.0000
Inflation	−4.0465***	0.0000	−4.0408***	0.0000	−7.5822***	0.0000
Exchange Rate	−6.9080***	0.0000	−7.0228***	0.0000	−6.9794***	0.0000
Producers Price	−6.5551***	0.0000	−7.4009***	0.0000	−6.5290***	0.0000

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

The stationarity of the variables of interest, as given by the results of both the Philip-Perron test (PP) and the Augmented Dickey Fuller test (ADF) using the Schwarz Criterion, are presented in Table 11, which shows that the series of the conditional variance (E_GARCH) and inflation are I(0) and hence both stationary (i.e., has no unit root) at level, while the producer price and the local exchange rate both have unit roots at level, implying that they are trending at level.

Nevertheless, not all variables have a unit root at the first difference, as shown in the first difference section of Table 11, with the conditional variance (E_GARCH) and inflation being I(0) (i.e., integrated in order 0), and the producer price and the local exchange rate being I(1) (i.e., integrated in order 1). Hence, this series is said to be integrated of different orders; that is, it has a combination of variables that are stationary at level I(0) and variables that are stationary at the first difference I(1) series.

These results are consistent for both the PP test and the ADF when carried out for Nigeria, as shown in Table 12, having all variables not to have a unit root at first difference, with the conditional variance (E_GARCH) and inflation being I(0) (i.e., integrated in order 0) and the producer price and the local exchange rate being I(1) (i.e., integrated in order 1). Hence, this series is said to be integrated of different orders, implying that the series has a combination of variables that are stationary at level I(0) and variables that are stationary at the first difference I(1) series.

5.7. VAR lag order selection criteria

Prior to performing the cointegration test, it was imperative to determine the optimum lag length for use in the Vector Error Correction equation as well as the cointegration equation. The results of this selection criterion, as shown in Table 13 for Ghana and Table 14 for Nigeria (using both the Akaike Information Criteria (AIC) and the Schwarz Criterion (SC)), show that the optimum lag length, k, for use in the cointegration equations is 1 (i.e., k = 1).

Table 13.

Lag order selection criteria (Ghana).

Lag	Log L	LR	FPE	AIC	SC	HQ
0	62.01945	NA	8.41e-07	−2.637248	−2.475049	−2.577097
1	186.2219	220.1770*	6.17e-09*	−7.555540*	−6.744545*	−7.254784*
2	198.8006	20.01160	7.35e-09	−7.400027	−5.940236	−6.858666
3	213.3330	20.47746	8.26e-09	−7.333318	−5.224730	−6.551352
4	220.6452	8.974078	1.35e-08	−6.928418	−4.181034	−5.915847

Source: Author's computation, 2023

Table 14.

Lag order selection criteria (Nigeria).

Lag	Log L	LR	FPE	AIC	SC	HQ
0	27.51445	NA	4.04e-06	−1.068839	−0.906640	−1.008687
1	104.7307	136.8833*	2.51e-07*	−3.851395*	−3.040399*	−3.550638*
2	107.8987	5.039955	4.58e-07	−3.268121	−1.808329	−2.726759
3	118.8774	15.47004	6.05e-07	−3.039881	−0.931294	−2.257915
4	138.4844	24.06321	5.65e-07	−3.203838	−0.446454	−2.181268

Source: Author's computation, 2023

5.8. Cointegration test

This study adopts the Johansen cointegration test. If the maximum eigenvalue and trace statistic are greater than the critical value, the null hypothesis of no cointegrating equation will be rejected; hence, accepting the alternative hypothesis of there is a cointegrating equation.

Table 15 shows the results of the cointegration test of the variables in Ghana. The first line in Table 15 shows significance, indicating that there are more than 0 cointegrating relationships in selected variables, with a trace statistic of 77.93680 being greater than the 5 % critical value of 55.24578, thus rejecting the null hypothesis of no cointegrating equation at a significance level of 1 %. The second line in Table 15 shows insignificance, which implies that there is no more than one cointegrating relationship in the selected variables, with a trace statistic of 34.74050 being less than the 5 % critical value of 35.01090, thus accepting the null hypothesis. Since exists cointegration, it implies that there is a long-run relationship between variables of interest, and individual series would converge back to equilibrium in the long run if a short-term shock occurred that could have an impact on their individual movement. The result, using both the maximum eigenvalue and trace statistic, shows that the test contains one cointegrating equation.

Table 15.

Johansen Cointegration test (Ghana).

Cointegrating equations	Eigen value	Trace stat	Critical value	Prob
(Trace) None*	0.609001	43.19629	30.81507	0.0010
At most 1	0.401325	23.59968	24.25202	0.0608
At most 2	0.176057	8.908066	17.14769	0.5052
At most 3	0.047379	2.232761	3.841466	0.1351
(Maximum Eigenvalue)	Eigen value	Max-Eigen statistic	Critical value	Prob
None*	0.609001	43.19629	30.81507	0.0010
At most 1	0.401325	23.59968	24.25202	0.0608
At most 2	0.176057	8.908066	17.14769	0.5052
At most 3	0.047379	2.232761	3.841466	0.1351

Source: Author's computation, 2023

From the normalized cointegrating equation I shown in Table 17 (which shows the relationship between variables in the long run), it is evident that price volatility will have a negative impact on the producers' price of cocoa; in the long run, at the 5 % level of significance, inflation rate will have a negative effect on cocoa producers’ price at the 1 % level of significance.

Table 17.

Normalized cointegrating equation (Ghana).

1 Cointegrating Equation(s):		Log likelihood	200.7878
Normalized cointegrating coefficients
G_PRODUCERS_PRICE_USD	E_GARCH01	G_INFLATION	G_LOCAL_EXCHANGE_RATE
1.000000	62.74228**	0.752624***	0.001330
	(27.8503)	(0.10504)	(0.09473)
Adjustment coefficients
D(G_PRODUCERS_PRICE_USD)	−0.057348
	(0.06311)
D(E_GARCH01)	−0.002311
	(0.00100)
D(G_INFLATION)	−0.908865
	(0.20267)
D(G_LOCAL_EXCHANGE_RATE)	−0.294421
	(0.08987)

***& ** represents significance at the 1 %& 5 % level of probability respectively.

Source: Author's computation, 2023

The cointegration test of the variables in Nigeria is presented in Table 16. The first line of Table 16 shows significance, indicating that there are more than 0 cointegrating relationships in selected variables, with a trace statistic of 74.83535 being greater than the 5 % critical value of 63.87610, thus rejecting the null hypothesis of no cointegrating equation at a significance level of 1 %. The second line in Table 16 shows insignificance, which implies that there is no more than one cointegrating relationship in the selected variables, with a trace statistic of 35.62558 being less than the 5 % critical value of 42.91525, thus accepting the null hypothesis. Since exists cointegration, it implies that there is a long-run relationship between variables of interest, and individual series would converge back to equilibrium in the long run if a short-term shock occurred that could have an impact on their individual movement.

Table 16.

Johansen Cointegration test (Nigeria).

Cointegrating equations	Eigen value	Trace stat	Critical value	Prob
(Trace) None*	0.567171	70.70075	55.24578	0.0012
At most 1	0.392977	32.17981	35.01090	0.0974
At most 2	0.154330	9.217119	18.39771	0.5580
At most 3	0.032216	1.506315	3.841466	0.2197
(Maximum Eigenvalue)	Eigen value	Max-Eigen statistic	Critical value	Prob
None*	0.567171	38.52094	30.81507	0.0047
At most 1	0.392977	22.96269	24.25202	0.0733
At most 2	0.154330	7.710804	17.14769	0.6348
At most 3	0.032216	1.506315	3.841466	0.2197

Source: Author's computation, 2023

From the normalized cointegrating equation in Table 18 (which shows the relationship between variables in the long run), it is evident that price volatility will have a negative effect on the producers' price of cocoa in Nigeria. In the long run, at the1% level of probability, the inflation rate will have a negative effect on cocoa producers' price at the 1 % level of significance, and the exchange rate will have a negative effect on the producers’ price of cocoa in Nigeria at the 1 % level of probability.

Table 18.

Normalized cointegrating equation (Nigeria).

1 Cointegrating Equation(s):		Log likelihood	116.4641
Normalized coefficients
NN_PRODUCERS_PRICE_USD	E_GARCH01	NN_INFLATION	NN_LOCAL_EXCHANGE_RATE
1.000000	−146.1507a	−1.280018a	0.107628a
	(43.2861)	(0.20356)	(0.02835)
Adjustment coefficients
D(NN_PRODUCERS_PRICE_USD)	−0.172310
	(0.04091)
D(E_GARCH01)	0.000792
	(0.00074)
D(NN_INFLATION)	0.661808
	(0.15536)
D(NN_LOCAL_EXCHANGE_RATE)	−0.492025
	(0.35707)

^aRepresents significance at the 1 % level of probability.

Source: Author's computation, 2023

5.9. Vector error correction model

The Error Correction Term (ECT) or the cointegration equation captures the convergence back to the long-run equilibrium. The cointegration equation from the two VECM in Table 19, Table 20 had negative coefficients, as expected, where only the coefficient for Nigeria (Table 20) is significant. If these coefficients are positive, the model will be explosive and will not converge to equilibrium.

Table 19.

Vector error correction model (Ghana).

E-C	(G_producers_price)	(E_Garch01)	(G_inflation)	(G_Exchange_rate)
CointEq1	−0.057348 (0.06311) [-0.90869]	−0.002311 (0.00100) [-2.31914]	−0.908865 (0.20267) [-4.48456]	−0.294421 (0.08987) [-3.27606]
D(Gproducer_price(-1))	0.159798 (0.15287) [1.04534]	0.004299 (0.00241) [1.78087]	1.091857** (0.49090) [2.22420]	−0.046942 (0.21769) [-0.21564]
D(E_Garch01(-1))	−22.26925** (9.16927) [-2.42868]	−0.357654*** (0.14479) [-2.47019]	1.421066 (29.4452) [0.04826]	8.641844 (13.0572) [0.66184]
D(G_inflation(-1))	0.088069* (0.04619) [1.90670]	0.000814 (0.00073) [1.11563]	0.339846** (0.14833) [2.29120]	0.138496** (0.06577) [2.10563]
D(G_Exchange_rate(-1))	0.036361 (0.10725) [0.33904]	−0.001302 (0.00169) [-0.76880]	−0.131063 (0.34440) [-0.38056]	−0.040563 (0.15272) [-0.26560]
C	−0.109268* (0.06385) [-1.71133]	−0.000516 (0.00101) [-0.51165]	0.095504 (0.20504) [0.46578]	0.168599* (0.09092) [1.85429]
TREND	0.001767 (0.00197) [0.89514]	2.67E-05 (3.1E-05) (0.85580)	−0.000641 (0.00634) [-0.10103]	−0.001023 (0.00281) [-0.36]

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Table 20.

Vector error correction model (Nigeria).

E-C	(N_producers_price)	(N_Inflation)	(N_Exchange_rate)	(E_Garch)
CointEq1	−0.172310*** (0.04091) [-4.21193]	0.661808*** (0.15536) [4.25992]	−0.492025 (0.35707) [-1.37795]	0.000792 (0.00074) [1.07763]
D(G_producers_price(-1))	−0.020543 (0.14042) [-0.14630]	−0.490026 (0.53325) [-0.91894]	0.190075 (1.22563) [0.15508]	0.000315 (0.00252) [0.12471]
D(N_Inflation(-1))	−0.095209*** (0.04538) [-2.09823]	0.090047 (0.17232) [0.52257]	−0.337279 (0.39605) [-0.85160]	0.000161 (0.00082) [0.19756]
D(N_Exchange_rate(-1))	0.013250 (0.01896) [0.69901]	−0.095793 (0.07198) [-1.33077]	−0.024758 (0.16544) [-0.14964]	8.17E-06 (0.00034) [0.02399]
D(E_Garch(-1))	−17.32110* (8.83589) [-1.96031]	36.01145 (33.5546) [1.07322]	−62.2483 (77.1216) [-0.80707]	−0.336256** (0.15881) [-2.11738]
C	−0.092958 (0.05730) [-1.62226]	0.099999 (0.21760) [0.45955]	0.463597 (0.50014) [0.92693]	−0.000954 (0.00103) [-0.92644]
TREND	0.003879* (0.00190) [2.04125]	−0.003377 (0.00722) [-0.46793]	−0.017522 (0.01658) [-1.05653]	2.76E-05 (3.4E-05) [0.80893]

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

The result of the VECM shows both short- and long-run relationships between the variables of interest. The result in Table 19 has an ECT of −0.057348, implying that the previous period deviation from long-run equilibrium is corrected at an adjustment speed of 5.7 %, that is, it indicates feedback of about 5.7 % of the previous year's disequilibrium from the long-run values of the explanatory variables. The results also showed that the producer price of the Ghanaian cocoa sector will be negatively affected, in the long run, by price volatility in the international market at a 5 % (t-statistic of 2.25284) significance level, while the inflation rate with a coefficient of 0.752626 will also negatively affect the producer price of cocoa producers at the 1 % significance level.

However, the inflation rate has a negative relationship with the producers' price in the short run at the 10 % level, and the volatility of price in the international market has a positive relationship with the producers' price at the 5 % level. Thus, a percentage change in the inflation rate is associated with a 0.09 % decrease in the producer's price on average ceteris paribus in the short run, whereas a percentage change in price volatility is associated with a 22.26 % decrease in the producer's price on average ceteris paribus in the short run.

The results in Table 20 have an ECT of −0.172310, implying that the previous period deviation from long-run equilibrium is corrected at an adjustment speed of 17.2 %, that is, it indicates feedback of approximately 17.2 % of the previous year's disequilibrium from the long-run values of the explanatory variables. The result also showed that in the long run, producers' price of the Nigerian cocoa sector will positively affect price volatility in the international market at the 1 % (t-statistic of 3.37639) significance level, while the inflation rate with a t-statistic of 6.28817 and the exchange rate with a t-statistic of 3.79628 will positively affect the cocoa producers' price at the 1 % level of significance.

However, in the short run, the inflation rate and price volatility in the international market have positive relationships with producers' prices at the 5 % and 10 % levels, respectively. Thus, a percentage change in the inflation rate is associated with a 0.10 % decrease in the producer's price on average ceteris paribus in the short run, whereas a percentage change in price volatility is associated with a 17.32 % decrease in the producer's price on average ceteris paribus in the short run.

5.10. Residual tests

LM autocorrelation test.

This study used the LM test to test for autocorrelation, with the null hypothesis of no autocorrelation. Hence, the null hypothesis of no autocorrelation is rejected if the statistic is significant and the alternative hypothesis is accepted. The results of the LM test in Table 21 (for Ghana) and Table 22 (for Nigeria) show that there is no autocorrelation in the model from the first to fifth lags.

Table 21.

LM-Autocorrelation test (Ghana)

Null hypothesis: No serial correlation at lag h.

Lag	LRE*stat	df	Prob	F-stat	df	Prob
1	17.15945	16	0.3754	1.087351	(16, 98.4)	0.3774
2	16.46322	16	0.4211	1.039701	(16, 98.4)	0.4231
3	9.705669	16	0.8815	0.593211	(16, 98.4)	0.8822
4	22.05896	16	0.1413	1.431721	(16, 98.4)	0.1428
5	12.18885	16	0.7309	0.753964	(16, 98.4)	0.7322

Lag	LRE*stat	df	Prob	F-stat	df	Prob
1	17.15945	16	0.3754	1.087351	(16, 98.4)	0.3774
2	32.45327	32	0.4444	1.018978	(32, 104.9)	0.4536
3	39.88562	48	0.7913	0.795721	(48, 94.5)	0.8076
4	57.99281	64	0.6876	0.858163	(64, 80.6)	0.7365
5	64.81400	80	0.8911	0.703664	(80, 65.5)	0.9331

Null hypothesis: No serial correlation at lag 1 to h.

Source: Author's computation, 2023

Table 22.

LM-Autocorrelation test (Nigeria)

Null hypothesis: No serial correlation at lag h.

Lag	LRE*stat	df	Prob	F-stat	Df	Prob
1	12.50359	16	0.7086	0.774611	(16, 98.4)	0.7101
2	32.69831	16	0.0081	2.237000	(16, 98.4)	0.0083
3	15.57997	16	0.4826	0.979704	(16, 98.4)	0.4846
4	22.18744	16	0.1372	1.440968	(16, 98.4)	0.1387
5	18.26854	16	0.3084	1.163909	(16, 98.4)	0.3104

Lag	LRE*stat	df	Prob	F-stat	Df	Prob
1	12.50359	16	0.7086	0.774611	(16, 98.4)	0.7101
2	38.93823	32	0.1858	1.257807	(32, 104.9)	0.1931
3	49.74199	48	0.4038	1.037623	(48, 94.5)	0.4308
4	69.39588	64	0.3006	1.085982	(64, 80.6)	0.3607
5	79.20301	80	0.5042	0.928391	(80, 65.5)	0.6264

Null hypothesis: No serial correlation at lag 1 to h.

Source: Author's computation, 2023

5.10.1. Normality test

This study used the Jarque–Bera normality test to check the normality of the standard error of the model. Table 23 shows that the residuals of producers’ prices in Ghana and the exchange rate in Ghana are not normally distributed, while the residuals of price volatility in Ghana and the inflation rate in Ghana are normally distributed. However, the overall normality test shows that the residuals of the model are not normally distributed, although it is assumed that these errors are asymptotically normally distributed.

Table 23.

Jarque Bera Normality test (Ghana).

Component	J-B	Degree of freedom	Prob
1	72.04912***	2	0.0000
2	2.537042	2	0.2812
3	1.362038	2	0.5061
4	60.60575***	2	0.0000
Joint	136.5539***	8	0.0000

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

Table 24 shows that the residuals of the residuals of the producers’ price in Nigeria and the inflation rate in Nigeria are not normally distributed while the residuals of the price volatility and the exchange rate in Nigeria are normally distributed. However, the overall normality test shows that the residual of the model is not normally distributed but it is assumed that these errors are asymptotically normally distributed.

Table 24.

Jarque Bera Normality test (Nigeria).

Component	J-B	Degree of freedom	Prob
1	9.985885***	2	0.0068
2	0.346634	2	0.8409
3	1561.618***	2	0.0000
4	1.257689	2	0.5332
Joint	1573.209***	8	0.0000

***, ** & * represents significance at the 1 %, 5 % and 10 % level of probability respectively.

Source: Author's computation, 2023

5.10.2. Stability test

The stability test was carried out using the AR root graph, which shows that the series and the model are stable as the dotted points lie within the perimeter of the circle, as shown in Fig. 6, Fig. 7 for Ghana and Nigeria, respectively.

Fig. 6.

AR stability graph (Ghana).

Fig. 7.

AR stability graph (Nigeria).

6. Conclusions

This study contributes to existing knowledge by establishing a detailed comparative study of the effect of price volatility on the supply of cocoa commodities in Ghana and Nigeria using annual data obtained from local and international sources, such as the Food and Agricultural Organization, World Development Index, International Cocoa Organization ICCO, and Central Bank of Ghana from 1970 to 2019. These data were analyzed using different GARCH models, the Vector Error Correction Model (VECM), and the least squares method using the EVIEWS 10. All variables were linearized (logged) for normalization before being used for the analysis. This was to de-emphasize the outliers from the set of data. After carefully examining price volatility and its effect on the supply of cocoa and producers' price of cocoa for farmers in Ghana and Nigeria, it can be concluded that price volatility does not significantly affect the cocoa supply of Ghana; however, it significantly affects the producers' price of farmers in the long run. In contrast, while price volatility significantly affects the supply of cocoa in Nigeria, it significantly affects the producers’ price of cocoa farmers in the long run. Finally, the study concludes that cocoa price volatility in the international market is a significant factor in cocoa supply and influences the producer share price of cocoa. Based on the findings of this study, we suggest that cocoa farmers should have the licensing to sell commodities to the international market directly without the interference of the marketing board where farmers bear the risk themselves. Policies regarding free trade should not be implemented in isolation but also with respect to the current exchange rate and inflation rate. Since the past price of pesticides is a significant factor determining the supply of cocoa, price incentives through pesticide price subsidies can be considered in other ways to encourage farmers to supply more cocoa in the market. Finally, governments of Nigeria and Ghana should pursue a realistic exchange rate because they affect the prices of producers as well as their output.

6.1. Limitations, and future research directions

The study considered only cocoa crop during the liberalization and non-liberalization periods. Future study should consider food crops covered during the liberalization and non-liberalization periods. Future study should also consider both food crops and cash crops to present a holistic and comprehensive policy framework. In addition, this study discussion mainly focuses on the liberalization and non-liberalization policy; future study should focus on the analysis of comprehensive agricultural policies in Nigeria and Ghana to date. Also, we recommend that future studies should integrate the latest dynamics of cocoa price surges to update the data and enhance the timeliness of the empirical results.

Data avai1abi1ity statement

Data will be made available on request.

CRediT authorship contribution statement

Emmanuel Adebayo Adegunsoye: Writing – review & editing, Writing – original draft, Validation, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Akeem Abiade Tijani: Validation, Supervision, Project administration, Methodology, Investigation, Data curation. Adetomiwa Kolapo: Writing – review & editing, Visualization, Validation, Supervision, Methodology, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.