Ghana cocoa sector recovery

The recovery process for Ghana's cocoa sector following the 1960s’ decline started with the Economic Recovery Program in 1983, followed by: the establishment of the Producer Price Review Committee and the implementation of the Structural Adjustment Program in 1984; the introduction of Licensed Buying Companies (LBCs) in 1993; the privatization of LBCs in 1999; and the initiation of Higher Technology (“HI-TECH”), Cocoa Diseases and Pests Control (“CODAPEC”), and the concept of the net “Free On Board” between 2001 and 2004 (Kolavalli and Vigneri Reference Kolavalli and Vigneri2017). Except for the HI-TECH and CODAPEC programs, most of these policies were aimed at increasing the share of export price passed on to farmers and liberalizing the cocoa economy in Ghana. As for the HI-TECH and CODAPEC programs, the GoG via the Ghana Cocoa Board (COCOBOD) supported cocoa producers with education on good and improved agronomic practices, the provision of subsidized inputs, and mass spraying of farms with agrochemicals to control pest and diseases.

The main aim of HI-TECH and CODAPEC is to increase cocoa production without increasing its cultivated area. While each of the policies and reforms has their level of success and failure, their net effect has led to cocoa production levels that exceed that of the 1960s, peaked at one million tons in 2010, and stabilized around 850,000 tons annually between 2011 and 2016 (Kolavalli and Vigneri Reference Kolavalli and Vigneri2017; Food and Agriculture Organization (FAO) 2019). Aside from the GoG-led policies and reforms, nongovernmental organizations have also deployed several programs to improve cocoa yields and the livelihoods of cocoa-producing households (World Cocoa Foundation 2018). Several studies have shown that the NGO-led programs have also improved farmer-level yields and welfare (Opoko et al. Reference Opoko, Dzene, Caria, Teal and Zeitlin2009; Gockowski et al. Reference Gockowski, Asamoah, David, Gyamfi and Kumi2010; Norton et al. Reference Norton, Lanier Nalley, Dixon and Popp2013; Tsiboe et al. Reference Tsiboe, Dixon, Nalley, Popp and Luckstead2016, Reference Tsiboe, Luckstead, Nalley, Popp and Dixon2018b).

Previous Ghanaian studies

The implemented policies and reforms by GoG and NGOs have indeed led to improvements in Ghana's cocoa yields. However, current yields are 24 percent below global standards. The extent to which this shortfall could be attributed to productive efficiency for singleton seasons is well established by previous studies. For example, Binam et al. (Reference Binam, Gockowski and Nkamleu2008) evaluated the production TE of cocoa farmers across West and Central Africa by applying the stochastic meta-production frontier to survey data collected in 2001/2002. Their results showed that Ghanaian cocoa farmers were operating at 44 percent of their potential productive capacity and that farmer gender, access to credit and agricultural extension, and the amount of canopy shade in the farm had significant effects on TE. While Binam et al. (Reference Binam, Gockowski and Nkamleu2008) utilized a stochastic meta-production frontier as this study does, their study considered heterogeneous technology defined by country. Thus, the study does not shed light on technology gaps within Ghana as the present study does.

In their study, Ofori-Bah and Asafu-Adjaye (Reference Ofori-Bah and Asafu-Adjaye2011) investigated the extent to which crop diversity on cocoa farms affects farmers' TE, and whether the production practice offers economies of scope from the sharing of farm inputs by crops on the same plots. Their results generated by applying the prototypical Stochastic Frontier (SF) to a sample of 340 cocoa farmers for the 2008/2009 growing season showed that diversified cocoa farms were more efficient than undiversified farms. Ofori-Bah and Asafu-Adjaye (Reference Ofori-Bah and Asafu-Adjaye2011) further showed that the former exhibited possibilities for cost complementarities between the production of cocoa and other crops on the same farm. Furthermore, Ofori-Bah and Asafu-Adjaye (Reference Ofori-Bah and Asafu-Adjaye2011) showed that shade, tree age, and full-time farming had significant effects on the TE of cocoa farmers. Besseah and Kim (Reference Besseah and Kim2014) applied the prototypical SF to show that Ghanaian cocoa farmers for the 2005/2006 growing season were producing at only 48 percent of their productive potential. The main drivers of the TE of cocoa farmers put forth by Besseah and Kim (Reference Besseah and Kim2014) were (1) farmer gender, age, and migratory status, (2) production equipment, and (3) location captured by regional dummies.

Unlike the studies discussed so far, Onumah et al. (Reference Onumah, Onumah, Al-Hassan and Brümmer2013) in their study utilized the stochastic meta-frontier framework to differentiate cocoa production in Ghana by organic and conventional practices. They showed that the conventional frontier was relatively close to the meta-frontier than that of the organic. Onumah et al. (Reference Onumah, Onumah, Al-Hassan and Brümmer2013) also showed that mean TE relative to the meta-frontier was 0.59 for the organic and 0.71 for the conventional system. Finally, Onumah et al. (Reference Onumah, Onumah, Al-Hassan and Brümmer2013) showed that farmers using organic practices could benefit from economies of scale since their RTS were 1.209 compared with 0.923 for conventional practices.

Contrary to its predecessors, the most recent study by Danso-Abbeam and Baiyegunhi (Reference Danso-Abbeam and Baiyegunhi2019) used the stochastic meta-frontier framework to differentiate cocoa production technology along regional lines. Their results that reflected conditions for the 2015/2016 cocoa season indicated that cocoa farmers from the Western, Brong Ahafo, Ashanti, and Eastern regions do not meet their potential with mean TE estimated at 0.65, 0.76, 0.60, and 0.74, respectively. Danso-Abbeam and Baiyegunhi (Reference Danso-Abbeam and Baiyegunhi2019) also showed that each region faces a technology gap when its performances are compared with the technology available in the industry. Danso-Abbeam and Baiyegunhi (Reference Danso-Abbeam and Baiyegunhi2019) identified sources of farmers' technical inefficiency emanating from a combined effect of socioeconomic (education and experience) and farm-specific factors (farm asset, age of cocoa farm, and farm size).

Aside from the above TE-related literature, several studies have also shown that cocoa productivity (kg/ha) in Ghana is mostly driven by technology (improved and hybrid varieties), labor use, nonlabor inputs use, land tenure, and biotic and abiotic stresses (Abenyega and Gockowski Reference Abenyega and Gockowski2001; Teal, Zeitlin, and Maamah Reference Teal, Zeitlin and Maamah2006; Vigneri Reference Vigneri2007; Aneani and Ofori-Frimpong Reference Aneani and Ofori-Frimpong2013; Tsiboe and Nalley Reference Tsiboe and Nalley2016; Tsiboe et al. Reference Tsiboe, Dixon, Nalley, Popp and Luckstead2016, Reference Tsiboe, Luckstead, Dixon, Nalley and Popp2018a).

While the literature devoted to the TE of cocoa production in Ghana is limited in the possibility of heterogeneous technology, the analysis presented so far is confined to only one season. Currently, the TE of cocoa production in Ghana is known only for 2001/2002, 2005/2006, 2008/2009, and 2015/2016; values aside these seasons and annual changes thereof are unknown. Building on the previous studies, this article extends the literature by accommodating data from multiple seasons throughout Ghana to ascertain the spatiotemporal heterogeneity in Ghanaian cocoa production technology and efficiency. In doing so, the chronic nature of cocoa production technology gaps and technical inefficiency is ascertained.

Meta-frontier analysis theory

Productive efficiency is the relationship between realized and feasible output, coupled with the assumption of optimized behavior of farmers, and subject to technology and price constraints. This relationship is further categorized into technical or allocative efficiency, with the two combining to form economic efficiency (Farrell Reference Farrell1957). Due to the unavailability of reliable data on input prices at the farmer level, this study focuses on TE, which deals with how well farmers manage inputs to attain potential yields. Empirically, TE is assessed either from the output or input perspective. From the output perspective, the observed output is compared with its potential given an input set; and under the input perspective, observed input levels are compared with their minimum required to produce a given output level. In terms of their operationalization, practitioners use models that are based either on the well-known Data Envelopment Analysis (DEA) (Charnes, Cooper, and Rhodes Reference Charnes, Cooper and Rhodes1978, Reference Charnes, Cooper and Rhodes1981) or on the Stochastic Frontier Analysis (SFA) (Aigner, Lovell, and Schmidt Reference Aigner, Knox Lovell and Schmidt1977; Meeusen and van Den Broeck Reference Meeusen and van Den Broeck1977).

One major advantage of the prototypical DEA is that it imposes no functional form on the data; however, its frontier (i.e., the production function) is susceptible to outliers and measurement error, does not account for idiosyncratic shocks, and has no statistical properties for inferences. On the contrary, the SFA imposes a functional form on the data; however, its frontier (known as the SF) is less susceptible to outliers and measurement error and has statistical properties for inferences. Thus, because of its merits and the absence of reliable price information in the forgoing dataset, this study utilizes the output-oriented SFA approach.

Under the prototypical output-oriented SFA approach, farmers are assumed to utilize a homogeneous technology, coupled with best management practices, given an input set. Thus, depending on their input set, all farmers are expected to be operating at various points along the SF. Reasons for observing farmers below the SF can be attributed to technical inefficiency and/or idiosyncratic shocks. However, some farmers are also observed above the SF purely due to the latter. Under this framework, the prototypical SF is

(1)$$y_i = f( x_i) e^{v_i-u_i}, \;$$

where y _i is the total production output by the ith farmer. The function f( ⋅ ) captures the relationship between the production inputs (x _i) used in producing y _i. The terms u _i and v _i describe the deviation of the ith farmer's production output from the production frontier that is attributable to technical inefficiency and idiosyncratic shocks, respectively.

The SFA approach is motivated by the distributional assumptions of u _i and v _i (Farrell Reference Farrell1957). Based on its negative skewness, u _i is assumed to follow either half-normal, exponential, and truncated, or gamma distribution. However, due to computational difficulties (i.e., nonconvergence), this study assumes that u _i follows a half-normal distribution with mean 0 and variance $\sigma _u^2 [ {u_i\sim N^ + ( 0, \;\sigma_u^2 ) } ]$. The deviation term, v _i, on the other hand, is assumed to follow a normal distribution with zero mean and variance $\sigma _v^2 [ {v_i\sim N( 0, \;\sigma_v^2 ) } ]$ (Belotti et al. Reference Belotti, Daidone, Ilardi and Atella2013).

A superior and flexible model will allow for production variation (u _i and v _i) to be heteroscedastic. Thus, the variance of technical inefficiency is modeled as $\sigma _{u_i}^2 = \exp ( w_i\alpha )$, where w _i contains covariates that affect technical inefficiency. The variance of the idiosyncratic shocks is also assumed to be heteroscedastic with an exponential functional form $[ {\sigma_{v_i}^2 = \exp ( z_i, \;\vartheta ) } ]$, where z _i and $\vartheta$ are vectors of determinants and parameters, respectively (Just and Pope Reference Just and Pope1979; Battese, Rambaldi, and Wan Reference Battese, Prasada Rao and O'Donnell1997). The superior and flexible model is represented as

(2)$$y_i = f( x_i) e^{v_i-u_i}, \;\quad u_i\sim N^ + [ 0, \;exp( w_i\alpha ) ] , \;\quad v_i\sim N[ 0, \;exp( z_i, \;\vartheta ) ] .$$

The TE score of the ith farmer is calculated as

(3)$${\rm T}{\rm E}_i = y_i[ {\,f( {x_i} ) e^{v_i}} ] ^{{-}1} = e^{{-}u_i}$$

The main objective of this article is to ascertain the spatiotemporal heterogeneity in Ghanaian cocoa production technology and efficiency. Thus, there is the need to formulate the prototypical SF in a way that captures how cocoa farmers in different regions of Ghana adopt distinct cocoa production technologies based on their specific circumstances. These circumstances include, but are not limited to, resource availability, government regulation, input price, and the environment. Since its introduction by Hayami (Reference Hayami1969) and further developments by Hayami and Ruttan (Reference Hayami and Ruttan1970, Reference Hayami and Ruttan1971), the meta-production frontier has been used by several empirical studies to capture the specific production technology adopting behavior of subgroups of farmer populations.

The literature initially proposed a mixed approach with a two-step procedure where the SF is estimated for the different groups in the first step and then a nonparametric method is utilized to determine the meta-frontier in the second step (Battese, Rao, and O'Donnell Reference Battese, Rambaldi and Wan2004; O'Donnell, Rao, and Battese Reference O'Donnell, Prasada Prasada Rao and Battese2008). Huang et al. (Reference Huang, Huang and Liu2014) indicated that the meta-frontier from the two-step mixed approach lacks statistical properties because it is deterministic. According to Huang et al. (Reference Huang, Huang and Liu2014), this is particularly problematic since it does not fully reflect the decision-making environment of farmers and fails to account for idiosyncratic shocks. Consequently, Huang et al. (Reference Huang, Huang and Liu2014) proposed a new two-step approach based on the core idea behind the prototypical SF and has desirable statistical properties that enable inference.

Under Huang et al. (Reference Huang, Huang and Liu2014)'s approach, the SF represented by equation (2) is first estimated separately for each farmer group (e.g., by regions), and then in the second step, the predicted output levels from the group-specific SFs are used as the observation for a pooled SF that captures all groups to estimate a meta-stochastic frontier (MSF). The second step directly estimates technology gaps by treating them as a conventional one-sided error term $( {u_i^M } )$. The meta-frontier that envelops all region-specific frontiers [f ^r(x _i)] is represented as

(4)$$f^r( x_i) = f^M( x_i) e^{{-}u_i^M }, \;\quad u_i^M \sim N^ + ( {0, \;{\rm exp}( w_i\alpha ) } ) , \;$$

where $u_i^M > 0$; therefore, f ^r(x _i) ≤ f ^M(x _i), and the ratio of region r's frontier to the meta-frontier is the technology gap ratio (TGR) represented as

(5)$${\rm TG}{\rm R}_i = f^r( x_i) [ {\,f^M( x_i) } ] ^{{-}1} = e^{{-}u_i^M } \le 1$$

The TGR depends on the accessibility and extent of adoption of the available MSF, which, in turn, depends on farmers' specific circumstances, such as resource availability, government regulation, input price, and the environment. Given an input set, each farmer's output relative to the MSF—i.e., their meta-frontier technical efficiency (MTE)—is represented as

(6)$${\rm MT}{\rm E}_i = f^r( x_i) [ {\,f^M( x_i) e^{v_i}} ] ^{{-}1} = {\rm TG}{\rm R}_i \times {\rm T}{\rm E}_i.$$

Empirical model

For the empirical analysis, production information from the various surveys is likely to be incomparable because of differences in respondents, interview modes, survey contexts, sampling designs, and survey questions. Thus, it will be naive to take the value from the various surveys at face value and then harmonize them as one dataset, without considering the sources of incomparabilities. To address this issue, the study utilized a two-step research design.

For the first step of the research design, the meta-stochastic frontier analysis was estimated separately for each survey wave. By estimating survey-wave-specific meta-stochastic frontiers, the study relaxes the assumption that the production frontier remains unchanged as does the relationship between factors that are associated with technical inefficiency. The functional form f _t( ⋅ ) used by previous studies estimating cocoa SFs for Ghana was either the Translog or Cobb–Douglas. However, this study preferred the Translog because of its relative flexibility; since Cobb–Douglas functional form is a special case of the Translog, this permits testing for the former.

The stylized empirical model used in this study is

(7)$$\matrix{ \hfill {\ln y_{irt} = \beta _{0r} + \sum\nolimits_j {\beta _{\,jr}\ln x_{\,jirt}} + \displaystyle{1 \over 2}\sum\nolimits_j {\sum\nolimits_k {\beta _{\,jkr}} \ln x_{\,jirt}\ln x_{kirt}} + \displaystyle{1 \over 2}\sum\nolimits_j {\sum\nolimits_s {\beta _{\,jsr}} } \ln x_{\,jirt}{\tilde{x}}_{sirt}} & \hfill {} \cr \hfill { + \sum\nolimits_j {\beta _{\,jr}{\tilde{x}}_{\,jirt}} + \displaystyle{1 \over 2}\sum\nolimits_j {\sum\nolimits_k {\beta _{\,jkr}{\tilde{x}}_{\,jirt}{\tilde{x}}_{kirt}} } + \displaystyle{1 \over 2}\sum\nolimits_j {\sum\nolimits_s {\beta _{\,jsr}} } {\tilde{x}}_{\,jirt}\ln x_{sirt} + v_{irt}-u_{irt}} & \hfill {} \cr \hfill {{\tilde{x}}_{\,jirt} = {\rm arcsinh}[ {x_{\,jirt}} ] , \;\quad u_{irt}\sim N^ + [ {0, \;{\rm exp}( w_{irt}\alpha ) } ] , \;\quad v_{irt}\sim N[ 0, \;{\rm exp}( z_{irt}, \;\vartheta ) ] .} & \hfill {} \cr } $$

The total cocoa output for the ith farmer in region r for the t season was taken as the outcome variable (y _irt), and the inputs (x _jirt) included the total amounts of land, family, and hired labor, fertilizer, and pesticide. In terms of production variance drivers, the vector for the inefficiency function (w _i) contained covariates that control for farmer characteristics (gender, age, and education) and access to credit and extension.

It is worth noting that farmer-level data for developing countries do not come without shortcomings. Particularly, only a handful of farmers report nonzero values for nonland production inputs. The study faced a comparable situation. Consequently, in order not to lose observation due to zeros reported for at least one nonland input, the log function was replaced with an inverse hyperbolic sine function $( {{\tilde{x}}_{jirt} = arcsinh [ {x_{jirt}} ] } )$ for such inputs (Bellemare and Wichman Reference Bellemare and Wichman2020). The outcome and the input variables were also normalized by dividing each observation by its survey-specific mean.

For each survey wave, parameters of the regional- and overall meta-frontier were obtained via maximum-likelihood estimation, utilizing the “frontier” command in Stata 16.1. Given the maximum-likelihood parameters, farmer-level elasticities for each input were estimated as the first derivative f _t( ⋅ ) with respect to that input and evaluated at every observation. The elasticity for the inputs without and with zeroes is given by ${\in} _{jirt} = \beta _{jr} + \sum\nolimits_k {\beta _{jkr}\ln x} _{kirt} + \sum\nolimits_s {\beta _{jsr}\tilde{x}} _{sirt}$ and ${\in} _{jirt} = \left({\beta_{jr} + {\sum\nolimits_k {\beta_{jkr}\ln x} }_{kirt} + {\sum\nolimits_s {\beta_{jsr}\tilde{x}} }_{sirt}} \right)\cdot \left({x_{jirt}/\sqrt {x_{jirt}^2 + 1} } \right)$, respectively. Consequently, farmer-level production RTS were estimated as the summation of all the input elasticities. Given the estimated frontiers, each farmer's TE relative to the regional SF (TE) and MSF (MTE) and their technology gap ratio (TGR) were estimated as outlined in equations (3), (5), and (6).

Since the farmer-level elasticities and scores (TGR, TE, and MTE) are all unitless, the second step of the research design pools them across all surveys into one sample to assess their spatiotemporal heterogeneity. To that end, the regression framework in equation (8) was utilized.

(8)$$\tau _h = \theta _0 + \theta _sS_h + \theta _rR_h + \vartheta _h.$$

In equation (8), τ _h is the elasticities/score of interest for household h; S _h and R _h are categorical variables for six regions and 20 seasons, respectively. For the case of elasticities and RTS, equation (8) was estimated as a linear regression model. However, since the range of the scores (TGR, TE, and MTE) is [0,1], a fractional regression model was utilized for them.

By omitting the category Ashanti (r = 1) and 198719/88 (s = 1) for region and season, respectively, the parameter θ ₀ serves as the average elasticity/score for the Ashanti region during the 1987/1988 growing season, ceteris paribus. Consequently, the marginal changes in elasticities/scores for a given region–season combination, {r, s} ≠ {1, 1}, over the omitted categories, is equal to their respective parameters in vectors θ _s and θ _r. Furthermore, the mean of the elasticities/scores for a given region/season was taken as the mean of the seasonal/regional estimates for that region/season. The resulting region-specific elasticities/scores from Equation (8) were plotted on regional maps to show their spatial heterogeneity, and the seasonal-specific elasticities/scores were plotted on a scatterplot to show their temporal dynamics.