Examining Drivers of Technical, Allocative and Economic Efficiencies in Cocoa Farming: Empirical Evidence from Ghana.

In Ghana, cocoa production is a major economic activity among rural farmers. Its production contributes significantly to the GDP and further, livelihood security enhancement among rural folks. However, recent development has unveiled a situation of persistent low farm-level productivity among cocoa farmers which threatens their livelihood security. In view of this, we estimated the economic, technical, and allocative efficiencies among cocoa farmers and their determinants to help proffer relevant policy strategies to arrest the situation of low farm-level productivity. Using a multistage sampling procedure, we collected data from  cocoa farmers across the cocoa-growing regions of Ghana. To estimate the farm-level efficiency scores, we employed the stochastic frontier analysis and our results show that cocoa farmers generally exhibited significant levels of technical, allocative, and economic inefficiencies. We estimated the average technical, allocative, and economic efficiencies scores among the cocoa farmers to be (cid:476), (cid:476), and (cid:476) respectively. The analysis of the determinants of technical, allocative, and economic inefficiencies revealed that farmer and farm-specific variables such as sex, household size, educational level, years of farming experience, frequency of extension contact, quality of extension received, use of climate smart adaptation technologies, farm size, farm labour and access to credit facilities significantly explain cocoa farm level efficiencies. Accordingly, we recommend that extension service providers and COCOBOD develop strategies to improve upon the quality of extension service delivery as well as incorporate the promotion and adoption of climate smart adaptation technologies into its productivity enhancement programmes for farmers. field-level training to farmers on how to combine their input resources efficiently, using minimum input at the least cost possible to obtain maximum output. The results show that cocoa farmers, in general, exhibited a significant level of technical, allocative, and economic inefficiencies. The efficiency estimates revealed that cocoa farmers were fully not efficient in terms of their technical efficiency, allocative efficiency, and economic efficiency levels. This means that with the existing technology, farmers were operating far below their optimum potential,


Introduction
Cocoa is a major economic crop in Ghana, impacting greatly the socioeconomic well-being of the country. Evidence shows that cocoa contributes signi cantly to Ghana's economic performance in terms of GDP growth rate and macroeconomic balance (COCOBOD, ). The production and trading of cocoa beans represent a major economic activity for many people, especially those in the rural economy, contributing signi cantly to their livelihood security enhancement (e.g., income and food security). Given the socioeconomic importance of cocoa, the sector has seen much investment from the government all geared towards improving the sector's performance in terms of sustainable productivity growth. Despite the signi cant government investment in the sector, one key challenge that continues to bedevil the sector is the continuous decline in productivity due to the persistent low farm-level productivity (COCOBOD, ; Aneani et al., ; Onumah et al., ). Empirical evidence shows that the average farm-level productivity in Ghana is about -kg/ha compared to the potential optimum of .tons/ha (COCOBOD & Forest Initiative ; COCOBOD, ). Accordingly, it can be extrapolated that the average cocoa farmer loses about . per cent of his/her annual potential yield, thereby impacting negatively his/her potential welfare gains (e.g., income and food security).
In addressing the persistent low farm-level productivity that continues to characterised cocoa production in Ghana, policies usually resort to technological interventions, trying to make available to farmers some new technologies. This though being a step in the right direction often does not result in the anticipated outcomes. And this is largely due to the direction of the policy tilting towards increasing access to more technologies without recourse to the root course of low productivity, which is often attributed to the effi ciency of production. Production economists have argued that output growth is not necessarily a function of the quantum of technologies introduced to farmers but the effi ciency with which these technologies are utilised at the farm level (Onumah et al., ; Inkoom & Micah, ; Miao et al., ; Inkoom et al., ). We argued that to break the cycle of persistent low farm-level productivity in cocoa production, promoting farm-level effi ciency is non-negotiable as it is the most cost-eff ective way to boost farm-level productivity more sustainably. This is because estimating the farm-level effi ciencies of farmers helps to understand their economic and technical performance and the factors that limit or enhance their ability to do well technically and allocatively with respect to technology application and resource use (COCOBOD & Forest Initiative, ; COCOBOD, ; Aneani et al., ; Onumah et al., ; Kyei et al., ). We argued that given the limited ability of most developing countries concerning technological advancement, the most pragmatic way to engineer positive and sustainable productivity growth among farmers, given resource scarcity is to develop mechanisms that rather enhance the effi ciency of production at the existing technology.
As posited by Onumah, Brummer, and Horstgen-Schwark (), efforts to improve effi ciency as means of increasing productivity are more cost-eff ective than introducing new technologies if farmers are not optimising the use of the existing ones. Also, Inkoom and Micah, () posited that through efficiency enhancement, farm rms can increase their productivity even in the absence of technical change. They further opined that effi ciency estimation help to isolate the effi ciency component of production activity to adequately measure its contribution to productivity growth. Across the literature it has been noted that farm-level effi ciency measurement helps to identify the sources of effi ciency and productivity diff erential among farmers, guiding the proff ering of appropriate response policy initiatives (Danso-Abbeam et al., ; Danso-Abbeam, & Baiyegunhi, ; Miao et al., ; Kyei et al., ). With this, it can be posited that an understanding of farm-level effi ciency and its determinants among cocoa farmers is a requirement to comprehensively address the problem of the persistent low farm-level productivity in cocoa production.
This calls for more independent empirical studies into full-scale farm-level efficiency in cocoa production (covering technical, allocative, and economic efficiencies) to help identify the best and most cost-effective way to boost productivity. Empirical evidence shows that previous effi ciency studies in cocoa production have largely concentrated on technical efficiency estimation and as well as limited in its coverage in terms of the spatial dimension of the study areas (Aneani et al., ; Onumah et al., ; Kyei et al., ; Danso-Abbeam et al., ; Danso-Abbeam, & Baiyegunhi, ). The observed limited focus of previous effi ciency studies in cocoa production has created a signi cant knowledge gap on the full-scale effi ciency analysis (i.e., economic effi ciency) which is capable of providing a much more comprehensive empirical knowledge on the overall farm level effi ciencies among cocoa farmers and the drivers of same. Given resource constraints faced by cocoa farmers, we argue that improving economic effi ciency will provide a credible pathway for improving farm-level productivity with the existing technology and help inform appropriate policy directions. This is because economic effi ciency gives a holistic view of farm unit economic performance as it de nes the ability of a farm unit operating at a given technology set to maximise output from minimal input combination at the minimum cost (i.e., cost minimising approach).
Economic efficiency simultaneously helps to unravel the technical efficiency level (indicative of technological performance) and the allocative effi ciency level (indicative of resource-use performance) among farmers (Inkoom & Micah, ; Abdulai et al., ; Orisasona et al., ; Wollie et al., ). Thus, economic effi ciency in the technical sense is the product of technical effi ciency and allocative effi ciency. Technical effi ciency as a component of economic effi ciency measures the ability of a farm unit using a given technology set to produce maximum output using a minimal input combination. Allocative efficiency as a component of economic effi ciency de nes the ability of a farm unit to maximise output at the least cost using a cost-minimising approach. Farrell () who is credited as the pioneer of economic efficiency concepts, posited that for a better appreciation of the overall farm-level efficiency and its drivers, the estimation of economic effi ciency presents a much better option. In addition, estimating the economic effi ciency simultaneously helps to unravel the technological performance (indicates the technical effi ciency level) as well as the resource-use performance (indicates the allocative efficiency level) of cocoa farmers. From the aforementioned, the empirical analysis of economic effi ciency is important to determine the bene t that can be obtained by improving the performance in cocoa production with a given input set and the existing technology. Given the above, we, therefore, estimated the economic effi ciency and its drivers in cocoa production to lend empirical support on how to improve the productivity enhancement programme currently being run by Ghana Cocoa Board (COCOBOD).

Methodology
Study Setting, Sampling Procedure, and Data Collection The study was conducted across the major cocoa-growing regions in Ghana covering the Western region (comprising western north and south), Ashanti Region, Brong-Ahafo Region, Eastern Region, Central Region, and the Volta region. These regions are characterised by similar climatic conditions and an agro-based economy where a signi cant number of the population are into cocoa production. According to Ghana Cocoa Board data, about , farm families are estimated to be engaged in cocoa farming across these regions (COCOBOB, ). Following a crosssectional survey design, we estimated the economic effi ciency of cocoa farmers and the key internal and external variables that explain the observed effi ciency differential among farmers. In arriving at the appropriate sample size that is representative of the population, we adopted Yamane's sample size determination formula and which is given as where n represents the sample size to be estimated, N denoted the estimated population size of   cocoa farmers and "e" is the assumed margin of error (which for this study purpose was assumed to be .). accordingly, substituting the de ned parameter values into Yamane's formula gave an estimated sample size of  cocoa farmers. To cater for the eff ect of incomplete data and non-response rate as well as increased the degree of representativeness and minimise the margin of error, we increased the sample size to  by assuming a power eff ect of  per cent. This again was guided by the data requirement principle underlying the power of improving upon the accuracy and effi ciency of the estimated econometric models in the study.
To select the  individual cocoa farmers to be part of the study, we followed a multistage simple random sampling approach and the process is outlined as follows. Firstly, three cocoa-growing regions (i.e., Western Region, Brong-Ahafo Region, and Central Region) were randomly selected from the list of major cocoa-growing regions listed above. The second stage involved the simple random selection of two major cocoa-growing districts from each of the three cocoa-growing selected from the rst stage. In doing so, we rst generated a list of major cocoa-growing districts for each of the three selected cocoa-growing regions, based on which two major districts from each of the sampled regions were then selected through a simple random lottery approach. The selected districts included Agona East and Assin Fosu from the Central Region, Asunafo North and Asunafo South from Brong-Ahafo Region, and Ame West and Ellembelle from the Western Region. The next sampling stage involved the selection of major cocoa-growing communities in the six sampled cocoa-growing districts. In doing so, we rst generate a list of major cocoa-growing communities for each of the six sampled districts. From the list generated, a simple random lottery approach was then used to simple randomly select six communities from each of the sampled districts, resulting in a sample frame of thirty-six cocoa-growing communities. The nal sampling stage involved the selection of the individual cocoa farmers at the community level to constitute the  estimated sample size. At the community level, a list of all active cocoa farmers with not less than  hectares of farm size was generated for each of the thirty-six cocoa communities. This benchmarking as an inclusion and exclusion criteria were aimed at getting farmers within the category of medium to large-scale farm size. From the list, twenty farmers were then randomly selected from each community, resulting in a total sample size of seven hundred and twenty () cocoa farmers from whom data was collected for the study. In our survey, we developed a structured interview schedule as our data collection instrument to collect data from the seven hundred and twenty sampled cocoa farmers from across the cocoa-growing regions in Ghana. The structured interview schedule instrument was used to collect data on the farmer and farm-speci c variables, production, and cost data.

Data processing and analysis
The data collected from the survey were processed using Microsoft Excel software and R Programming Environment software. To analyse the farmer and farm-speci c variables, we employed descriptive statistical tools such as means, standard deviations, frequencies, and percentages. Again, we employed the Effi ciency Eff ect Stochastic Frontier model and Tobit regression model as the econometric tools to analyse the farm-level economic effi ciency and its determinants. The formal specification of the Efficiency Effect Stochastic Frontier model and Tobit model as applied in our study are discussed in the subsequent sections.

Effi ciency Eff ect Stochastic Frontier Model for Estimating Economic, Technical and Allocative Effi ciencies
To analyse cocoa farmers' farm-level economic, technical and allocative efficiencies, we employed the stochastic frontier model as originally and independently proposed by Aigner, Lovell, and Schmidt (), and Meeusen and Van den Broeck (). This was implemented under the effi ciency eff ect frontier model as proposed by Battese and Coelli, (). The efficiency effect frontier model follows a one-stage modelling approach in which variables that in uence the ineffi ciency term are implicitly and explicitly included in the stochastic frontier model speci cation directly (Schmidt, ; Wang, ; Wang & Schmidt, ; Battese & Coelli, ). In the empirical literature, the functional speci cation of the stochastic frontier models (i.e., production frontier and cost frontier) has largely followed the Cobb-Douglas or Translog functional forms respectively. The two functional forms have their strengths and weakness which demands consideration when estimating stochastic frontier models (see, Kumbhakar et  In line with this, we estimated both Cobb-Douglas and Translog functional forms for both the stochastic production frontier and cost frontier models. The two estimated models were then tested for model tness to nd out which one best ts the dataset and appropriately represents the production technology and optimising behaviour of the ith production unit. From the estimated stochastic production frontier and cost frontier functions, we determine the output and cost elasticities with respect to the inputs and input prices as employed by the ith production unit. Based on the duality concepts, the three effi ciency components (economic, technical and allocative) as proposed by Farrell () were estimated from stochastic production and cost frontier models. The formal speci cation of the effi ciency eff ect stochastic production frontier and cost frontier models as in this study are explained below.
Formal speci cation of the stochastic production frontier model Formal speci cation of the stochastic cost frontier model Following the self-duality principle of the production and cost functions, we estimated the stochastic cost frontier model, assuming a cost minimisation framework to derive the economic effi ciency scores of the ith cocoa farmer. The formal speci cation of the stochastic cost frontier dual of the stochastic production frontier model was speci ed as: As posited by Farrell (), the overall cost (economic) effi ciency is a product of technical effi ciency and allocative effi ciency. Accordingly, haven estimated the economic efficiency from the cost frontier, we decomposed it into its respective efficiency components (i.e., technical efficiency and allocative effi ciency) following the duality approach. In principle, the cost frontier as speci ed in equation  is said to be a self-dual function of the production frontier as speci ed in equation . As such the technical effi ciency estimate derived from the decomposition of economic efficiency as specified in equation  does not signi cantly deviate from that gotten from equation . Following the decomposition procedure, the allocative effi ciency of the ith farmer can be expressed as the ratio of economic effi ciency to technical effi ciency and this is mathematically stated in equation :  e estimated value of AE as speci ed in equation  lies between  and . An AE value of  means the production unit is allocatively ineffi cient and a value of  means the production unit is allocatively effi cient in production.

Parameterisation of effi ciency estimator
With the SFA model, it is assumed that ∼ (0, 2 ) and ∼ + (0, 2 ), and that these two error terms are distributed independently of each other and the regressors (Coelli et al., 2005;Battese & Coelli, 1995;Kumbhakar, & Lovell, 2003). Fundamentally, the appropriate efficiency estimator of cocoa farmers is conditioned on the conditional expectation of the inefficiency effect term (u). Accordingly, Battese and Corra (1977) posited that the firm-specific technical or cost efficiencies can be estimated following a reparameterization of the inefficiency effect term (u) based on the gamma distribution, and this is specified as: Empirical speci cation of the stochastic production and cost frontier models as applied in this study was speci ed as follows: We estimated the Cobb-Douglas and Translog functional forms of the stochastic production and cost frontier models following the maximum likelihood estimation approach.  e two models under the production and cost frontiers were then subjected to model tness test to check which of them best t the data set and appropriately represents the production technology and optimising behaviour of the ith cocoa farmer.  e empirical model speci cations for the Cobb-Douglas production (Equation 7) and cost (Equation 8) frontier models as applied in this study were speci ed as follows: log ( ) = 0 + 1 1 + 2 2 + 3 3 + 4 4 + − Eqn. 7 log ( ) = 0 + 1 1 + 2 2 + 3 3 + 4 4 + 5 y + + Eqn. 8  e empirical Translog production (Equation 9) and cost (Equation 10) functions were speci ed as follows:  e de nition of variables included in empirical models as speci ed in equations 7, 8, 9, and 10 are presented in Table 1.
Second, the drivers of allocative effi ciency were estimated under the Tobit regression model. This becomes necessary as allocative effi ciency is a derived estimate from economic and technical effi ciency, thus making it diffi cult to predict its drivers in the one-stage estimation approach. To satisfy theoretical consistency and data suitability requirement, we estimated both the Cobb-Douglas and Translog functional speci cations for the effi ciency eff ect stochastic production and cost frontier models and then tested them for model tness. From the diagnostic analysis, as indicated by the Log-Likelihood ratio test results (see, model summary in Table ), the Cobb-Douglas functional form was found to give the best model tness to the data set and appropriately represents the production technologies and the optimising behaviour at the individual farm level than the Translog functional specification. Given that the log-likelihood ratio test favoured the Cobb-Douglas functional specification as appropriately and accurately tting the data and thus producing an effi cient estimate for the stochastic production and cost frontier models, we selected to present the Cobb-Douglas Model estimates for the effi ciency eff ect stochastic production and cost frontier models as contained in Tables a and b.  The model fitness test further suggests that the efficiency effect stochastic frontier models present efficient and consistent results. Furthermore, the estimated sigma and gamma coefficients for both the production and cost frontier models were found to be statistical and significantly different from zero, suggesting a good fit of the models and the correctness of the specified distributional assumptions. Additionally, the estimated gamma coefficients of . for the production frontier and . for the cost frontier indicate that the presence of the inefficiency effect does affect the production technology and optimising behaviour of the individual cocoa farmer. Hence, we can conclude that technical, economic, and allocative inefficiencies are significant in explaining the variability in farm-level productivity among cocoa farmers in Ghana. Theoretically, gamma picks a value between zero and one, indicating the importance of the inefficiency term. A value of zero means that the inefficiency term "u" is irrelevant or absent. On the other hand, if gamma is equal to one, then the noise or stochastic term "v" is completely irrelevant and that inefficiency (i.e., Technical, economic, and inferably allocative inefficiencies) accounts for all the observed deviation from the production or cost frontier (Henningsen, ; Inkoom & Micah, ). Drawing from this, the estimated gamma coefficient of . and . for both production and cost frontier models implies that both inefficiency and stochastic noise effects are important in explaining any observed deviations from the production and cost frontiers. Nonetheless, inefficiency effects are considered the most important factor. This is because a composite analysis of the gamma values following Henningsen () in the R Programming Environment Language revealed that, about  per cent of the observed total inefficiency variance is attributable to technical, allocative and economic inefficiencies effect, with stochastic noise effect accounting for about  per cent of the total inefficiency variance. The model estimates as presented in Table a reflect the contributions of the production inputs to changes in output elasticity and their cost implications on the performance of cocoa farmers in Ghana. The result from the stochastic production frontier model as presented in Table a shows that the estimated output elasticities were monotonically increasing for labour, fertilizer, and capital inputs utilisation per hectare of land, but monotonically nonincreasing for agrichemical input utilisation per hectare of land. Furthermore, it was observed that all the input variables were significant in defining the production technology at the farm level. This implies that for meaningful productivity growth in cocoa production, optimal and efficient use of labour, fertiliser, capital, and agrochemicals are critical. In technical terms, the results suggest that a percentage increase in fertiliser, labour and capital inputs would lead to a . per cent, . per cent, and . per cent increase respectively in output. The observed input-output relationship suggests that there is some level of optimal allocation of labour and fertiliser inputs by farmers. Accordingly, an optimal upward adjustment in their utilisation would strengthen the potential of attaining maximum farm-level productivity in cocoa production. The negative and significant coefficient of agrochemical inputs suggests that a percentage increase in the agrochemical input usage leads to a . per cent decrease in output, thereby impacting negatively farm-level productivity. This suggests a potential misallocation or excessive use of agrochemicals by farmers. Thus, a radial reduction in agrochemical usage to an optimal level will lead to a positive output elasticity of production. Furthermore, the elasticity of scale was estimated to be ., which means that the production technology exhibits an increasing return to scale and this suggests that total factor productivity increases at an increasing rate when there is an optimal proportional increase in all input quantities. Accordingly, a relative increase in the output quantity of cocoa is almost more than double the relative increase of the aggregate input quantity. This consequently implies that ensuring efficient and optimal use of labour, fertiliser, capital, and agrochemical per hectare of land at the given technology can significantly increase productivity in cocoa production.
For the cost frontier model, Table b reveals that the estimated cost elasticity coefficients were all monotonically nondecreasing for Labour, fertiliser, and Capital input prices except for agrochemical input prices. Additionally, the coefficient of the output quantity was found to be non-negative, suggesting that the cost function is monotonically nondecreasing in output quantities. The estimated coefficients of the explanatory variables in the stochastic cost frontier model were all found to be significant. The estimated positive cost elasticities of labour, capital, and fertiliser imply the total cost of production increases by . per cent, . per cent, and . per cent as the cost share of these variable inputs increases by one per cent. Furthermore, the estimated negative coefficient of agrochemical input, suggests the total cost of production decreases by . per cent as the cost share of agrochemicals increases by one per cent. One probable reason that could account for the observed costshare behaviour of agrochemical input price is the potential impact of the cocoa mass spraying programme which absorbs a greater percentage of the cost incurred in the control of disease and pests on the average cocoa farm across the country. Again, the estimated positive coefficient of output quantity reflecting the cost flexibility, suggests that a per cent increase in output quantity contributes to the marginal increase in the cost build-up by . per cent. Following the cost flexibility concept, an inverse of . gives an elasticity of size value of .. This means that achieving a cost minimisation of one per cent increases the output quantity of cocoa by . per cent.

Distribution of Farm-level Technical, Allocative, and Economic Efficiencies among Cocoa Farmers
Figure  presents summary statistics on the farm-level efficiency estimates covering economic, technical, and allocative efficiencies respectively. The summary statistics estimated include the mean efficiency estimates with their standard deviations as well as the maximum and minimum estimates across the three efficiency components. Besseah & Kim, ) The estimated technical efficiency estimates range between . to ., with a mean of . and a standard deviation of .. The mean technical efficiency of . indicates that farmers produce about . per cent of potential output given the level of farm production technology available. The mean estimate also indicates a . technological efficiency, implying that farmers exhibit a moderate ability to achieve the minimum input combination to produce maximum output. The mean estimate of technical efficiency further suggests that farmers were about . (i.e.,  per cent) below the efficient and optimal frontier that maximises output and utility (i.e., profit). This means that there is about  per cent technical inefficiency in cocoa production. The technical efficiency performance as observed from our study when compared to other study findings in cocoa production shows some differentials. For instance, the mean technical efficiency of . was found to be higher than the mean technical efficiency estimates of . and . as observed by Besseah and Kim, () and Danso-Abbeam et al.
() among cocoa farming households in Ghana. The study results as portrayed in Figure  again revealed that the allocative efficiency estimates among cocoa farmers range between . to ., with a mean of . and a standard deviation of .. The estimated mean allocative efficiency of . indicates that farmers were about . per cent efficient in their allocative potential, thereby operating at . . (i.e.,  per cent) below the optimal frontier that maximises profit at the minimum cost. It can thus be inferred that farmers exhibited on average a  per cent resource-use efficiency among cocoa farmers, which suggests a moderate ability of farmers in producing maximum output using a cost-minimising input proportion. The estimated mean allocative efficiency by implication reveals that farmers are relatively efficient in producing a given level of cocoa output using the cost-minimising input ratio. Further, the mean allocative efficiency estimate means that the average farmer's cost-shaving potential in relation to the most efficient farmer stands at about . per cent [i.e., (-(./.) *)]. In comparison to the empirical literature on cocoa production, the mean allocative efficiency of . from our study is found to be consistent with similar findings by Ogunya and Tijani, (), who also found that the average allocative efficiency among cocoa farmers in Nigeria was about .. On the state of economic efficiency, as shown in Figure , the estimated economic efficiency of cocoa farmers ranges between . to ., with a mean of . and a standard deviation of .. The mean economic efficiency of . indicates that farmers on average were operating about . below their optimum frontier output which maximises profit from the best cost minimising input combination. Additionally, the mean estimate indicates a  per cent technological and resource-use efficiency potential among cocoa farmers. This by inference suggests a moderate ability of farmers to produce maximum output from a minimal input combination at the least cost possible. In other words, farmers' ability to maximise output with minimal input combination at the least cost possible was reduced by a  per cent point deviation. In relation to similar empirical findings on the estimation of economic efficiency among cocoa farmers, the mean economic efficiency of . as estimated from our study was found to be lower than the average economic efficiency score of about . among cocoa farmers in Nigeria as estimated by Ogunya and Tijani, (). Figure  presents the percentage distribution of farmers according to their farm-level efficiency estimates. Following the quartile distribution principle, the efficiency score was quarterised. The quarterisation led to four efficiency profile categories. The description of the categories is as follows: low-efficiency profile ( -.), moderately low-efficiency profile (. -.), moderately high-efficiency profile (. -.), and High-efficiency profile (. -.). As illustrated in Figure , the percentage distribution shows that the majority (i.e., about . ) of the farmers exhibited a moderately high to a high level of technical efficiency profile, with few of them (. ) showing a low level of technical efficiency profile at the farm level. From this it can be inferred that majority of the farmers when given the needed technical training can significantly be improved their farm-level performance given the existing technology. We further observed from the results that when it comes to allocative efficiency, the majority (i.e., about . ) of the farmers exhibited a moderately low to moderately high level of allocative efficiency profile. In addition, we observed that about similar situation happened for economic efficiency, where about . per cent of the farmers exhibited a moderately low to a moderatelyhigh level of farm-level economic efficiency profile. This means, there is a need for urgent technical and farm-management economic training for cocoa farmers to help improve their technological and economic performance in production. The significant variations in efficiency distribution among farmers as observed in Figure

Drivers of Farm-level Technical, Allocative, and Economic Efficiencies of Cocoa Farmers
In empirical efficiency analysis, the estimated level of farm-level efficiencies is often not enough to guide appropriate policy intervention. Thus, it becomes necessary to identify the sources of efficiency differentials among farmers. This helps to identify factors contributing to the technical, allocative, and economic inefficiencies among farmers, which when addressed help position farmers to achieve sustainable and higher productivity growth. To ascertain the potential sources of the variation in the technical, allocative, and economic efficiencies among cocoa farmers, we estimated two separate models in line with theoretical soundness and consistency. First, in estimating the drivers of technical and economic efficiency, the one-stage efficiency effect stochastic production and cost frontier models were employed. After that, the Tobit regression model was used to analyse the drivers of allocative inefficiency. The two model results are accordingly presented in Table . In empirical efficiency analysis, the estimated level of farm-level efficiencies is often not enough to guide appropriate policy intervention. Thus, it becomes necessary to identify the sources of efficiency differentials among farmers. This helps to identify factors contributing to the technical, allocative, and economic inefficiencies among farmers, which when addressed help position farmers to achieve sustainable and higher productivity growth. To ascertain the potential sources of the variation in the technical, allocative, and economic efficiencies among cocoa farmers, we estimated two separate models in line with theoretical soundness and consistency. First, in estimating the drivers of technical and economic efficiency, the one-stage efficiency effect stochastic production and cost frontier models were employed. After that, the Tobit regression model was used to analyse the drivers of allocative inefficiency. The two model results are accordingly presented in Table . The results as portrayed in Table  shows that the sex of the farmer was a significant driver of the observed technical and allocative inefficiencies at . and . signi cance level respectively. In particular, the estimated coeffi cient of sex was negative in both technical and allocative inefficiency models. This means that the average female cocoa farmer was more technically and allocatively ineffi cient than her male counterpart. In other words, compared to the average male farmer, the average female farmer was less technically and allocatively effi cient in production. This could probably to attributed to the socio-cultural and economic factors that favour men but limit women when it comes to access to information and production resources. This observed influence of sex on farm-level effi ciency diff erentials among cocoa farmers as witnessed in our study con rms similar study ndings where male cocoa farmers were found to be more effi cient in production as compared to female farmers (see, for example, Danso-Abbeam & Baiyegunhi, ; Besseah & Kim, ; Danso-Abbeam et al., ). Another important variable that signi cantly explained the variation in farm-level ineffi ciency was household size. Farm household size as a variable was found to be negative and signi cantly in uenced technical ineffi ciency variation among farmers at a signi cant level of .. This means that cocoa farmers with more household members were less technically ineffi cient in production. Accordingly, it can be inferred that farmers with a higher number of household members had the bene t of social capital which contributed to the number of available farm hands to carry out timely and eff ective production activity. From the three model results, years of farming experience were found to have a negative and significant relationship with technical, allocative, and economic inefficiencies. This suggests that an increase in years of farming experience increases the likelihood of farmers attaining a higher level of efficiency. That is more experienced farmers were less inefficient as compared to their counterparts. This can be attributed to the potential experiential knowledge acquisition that comes with years of experience. The observed impact of farming experience on farm-level efficiency in our study affirms similar findings by other studies (see, for example, Ogunya & Tijani, ; Onumah et al., ). We further observed from our study that, education as a farmer-specific variable negatively and significantly influenced the technical, allocative, and economic inefficiencies among cocoa farmers. The results as indicated in Table  suggest that receiving some level of education increases the likelihood of cocoa farmers being technically, allocatively, and economically more efficient (i.e., less inefficient) in production. As such, it can be adduced that education enhances the cognitive ability of farmers to carry out their production active efficiently, hence given reducing the probability of higher levels of technical, allocative, and economic inefficiencies among cocoa farmers. Again, extension service as an important institutional variable significantly and negatively influenced economic, technical and allocative inefficiencies among farmers. Accordingly, efficient and effective utilisation of extension services would increase the propensity of farmers to achieve higher productivity growth. Another novel finding from our study was that not only is the frequency of extension contact important in predicting farm-level efficiency deferential but the quality of the extension service received by the farmers. for instance, our results as portrayed in Table  shows that access to quality extension service increases the propensity of cocoa farmers to be technically, allocatively, and economically more efficient (i.e., less inefficient) production. It is therefore important for cocoa extension service providers to ensure that they provide frequent and quality extension service to farmers to increase the likelihood of achieving higher productivity growth. In comparison to other efficiency studies in cocoa production, our study findings on the significant and positive impact of education and extension contact on farm-level efficiency confirm findings by Ogunya and Tijani, () who likewise observed a positive impact of education and extension contact on the economic, technical and allocative efficiency level among cocoa farmers in Nigeria. Furthermore, we observed that the observed impact of education on the technical efficiency of cocoa farmers deviates from that of Onumah et al., () who observed that farmers with a higher level of education were more inefficient or less efficient in production.
Another important variable that was found to significantly and negatively influence farmers' technical, allocative and economic inefficiencies was the use of climate smart adaptation strategies. The results from the three models as presented in Table  show that adopting more climate smart adaptation technologies increases the likelihood of cocoa farmers being more technically, allocatively, and economically efficient in production. That is, a higher climate smart adaptation drive among farmers makes them less inefficient in production. This finding is revealing, pointing to the significance of climate smart adaptation in the presence of the increasing trend of climate change and its adverse consequences on cocoa production. The observed significant impact of climate smart adaptation on farm-level efficiency improvement among cocoa lay credence to other study findings that observed that the adoption of climate smart adaptation technologies enhances farm-level productivity and performance of farmers in Ghana (see, for example, Adzawla & Alhassan, ; Issahaku & Abdulai, ; Mzyece & Ng'ombe, ). It is generally accepted that credit is an important factor when it comes to production due to its impact on production efficiency. Studies have reported that access to credit accounts for variation in farmlevel efficiency among farmers (for example, Inkoom & Micah, ; Onumah et al., ). To validate this, we tested the impact of credit access on cocoa farmers' technical, allocative and economic efficiencies. From the three model results as presented in Table , we observed that access to credit has a significant and negative impact on the technical, allocative, and economic inefficiencies among cocoa farmers. This implies that having access to external credit facilities increases the likelihood of cocoa farmers attaining a higher level of technical efficiency, allocative efficiency, and economic efficiency. This could largely be attributed to the enhanced liquidity preference that access to credit presents to farmers, facilitating timely production decision-making and operational activities. The observed finding of credit access calls for the development of appropriate credit facilities for farmers and the reengineering of existing credit conditions by banks to make it more flexible for farmers to access credit to fund their farm business. In addition, we observed that farm size and farm labour both significantly accounted for the observed inefficiency variation among cocoa farmers.
In particular, land size had a significant negative impact on the economic, technical, and allocative inefficiencies among farmers. This suggests that an increase in farm size tends to reduce the level of inefficiencies among farmers. hence it can be concluded that farmers with large farm sizes were more economically, technically, and allocatively efficient than their counter. On the contrary, farm labour was found to increase the level of economic, technical, and allocative inefficiencies among farmers. this could imply that there was possible misallocation as well as ineffective deployment of farm labour use on the cocoa farmers. The observed impact of farm size and farm labour use on farm-level efficiency is found to be consistent with that of Orisasona et al, () who observed that whereas farm size positively impacts the input use efficiency, farm labour negatively impacts the level of input efficiency among cocoa farmers in Nigeria.

Conclusions and Policy Implications
Our paper considered the Efficiency-Effect Stochastic Frontier Analysis and the Tobit regression analysis to estimate cocoa farmers' farm-level technical, allocative, and economic efficiencies and their driving factors. The stochastic production results showed that the production function was monotonically increasing for labour, fertilizer, and capital inputs except for agrochemical input and that the observed productivity increases with more than the proportionate increases in the level of the aggregate inputs. In addition, the cost frontier model revealed that the cost function was monotonically non-decreasing for labour, capital, and fertilizer inputs except for agrochemical and that achieving a cost minimisation of one per cent increases the output quantity of cocoa significantly. Given this, by ensuring minimal input combination and effective cost-minimising production strategies, farmers could significantly maximise their utility of achieving higher productivity and profit. Policy intervention can therefore be framed to provide extensive education that provides appropriate field-level training to farmers on how to combine their input resources efficiently, using minimum input at the least cost possible to obtain maximum output. The results show that cocoa farmers, in general, exhibited a significant level of technical, allocative, and economic inefficiencies. The efficiency estimates revealed that cocoa farmers were fully not efficient in terms of their technical efficiency, allocative efficiency, and economic efficiency levels. This means that with the existing technology, farmers were operating far below their optimum potential, hence the need for stringent effort to build farmers' ability to generate maximum productivity without necessarily providing them with new technologies. Again, by engaging farmers in efficient and effective farm management and best agronomic practices, the cocoa productivity of farmers can significantly be increased at the least cost possible. Having established that farmers were not fully efficient in production, suggesting a gab, it became necessary to find out the driving forces of the observed efficiency differentials among the farmers. From the analysis of determinants of economic, technical, and allocative inefficiencies, we identified that key significant drivers of farm-level (in)efficiencies differentials include sex, household size, educational level, years of farming experience, frequency of extension contact, quality of extension received, use of climate smart adaptation technologies, farm size, farm labour and access to credit facilities. From this, cocoa extension service providers must ensure that they render frequent extension services which will help ensure access to timely technical information and identification and redress of farmers' problems. Again, our finding supports the position that by providing quality extension service delivery to farmers, the derived service utility which is a function of service quality will generate higher confidence and trust in farmers, influencing them to efficiently utilise the technological information and advice delivered to them. We further recommend that the government working with the relevant banking institutions and cocoa institutional authorities develop appropriate credit schemes for cocoa farmers to increase their liquidity preference in production. We further proposed that efforts be made by the government and other socio-cultural institutions to appropriately change the socio-cultural and economic factors that hinder the productivity of female cocoa farmers. Given that education significantly explains farm-level efficiency differential among cocoa farmers, we recommend to the Ghana Cocoa Board (COCOBOARD) to enhance and improve upon its extension education and farmer field school initiatives as well as develop some kind of adult education model for the less endowed cocoa farmer to help bring them up to speed in terms of educational abilities.