Do farm‐level technical efficiency and welfare complement each other? Insight from Ghana’s cocoa industry

Technical inefficiency persists in Ghana’s cocoa farms. Farm-level guidelines from empirical studies are essential to inform programmes dealing with this challenge and subsequently improves farmers’ welfare. This study evaluates the two-way effects of technical efficiency and welfare using Data Envelopment Analysis (DEA) and Conditional Mixed-process (CMP). The study reveals that, with no additional inputs, farmers have the potential of increasing their output by an average of 56% (overall technical efficiency) with mean pure technical and scale efficiencies estimated at 76% and 58%, respectively. Observed inefficiency in the Ghanaian cocoa farms is due to both inefficient utilization of inputs and farmers’ inability to operate at the most productive scale size. Furthermore, findings from the study indicated that improved technical efficiency and welfare of smallholder cocoa farmers are crucial for the sustainable growth of Ghana’s cocoa sector as farmers’ efficiency and welfare significantly complement each other. In other words, improved welfare enhances technical efficiency, and higher technical efficiency score translates into better welfare. Hence, farm-level policies such as inputs subsidy programmes, training farmers on the proper application of agrochemicals, among others to enhance farm efficiency should be strengthened since efficiency is tied to household welfare. Moreover, investment in education targeted at farmers to improve their managerial and technical capacities will enhance their ability to optimize the operational size of the cocoa production system, and subsequently improve their welfare.

Page 2 of 15 Danso-Abbeam and Baiyegunhi Economic Structures (2020) 9:23 In 2015, the cocoa sector contributed about US$631 million, representing about 1.9% of Ghana's GDP (Ghana Statistical Service [GSS] 2016). Further, Ghana's cocoa industry has also created many employment opportunities along its value chain through backward and forward linkages. Thus, the cocoa sector is key to the socio-economic development of the country. Despite the contribution of cocoa to rural livelihoods and macroeconomic balances, the sector is still faced with many challenges. One of the significant challenges is the over-reliance on natural land productivity and expansion in land under cultivation to increase yield (Besseah and Kim 2014). Thus, cocoa production is partly responsible for the destruction of the Ghanaian green forest. As farmlands are exhausted, and the soil loses its quality, there is a decline in agricultural output. Consequently, the industry dependence on the expansion of farmland to boost productivity is not sustainable. Moreover, the fluctuation in cocoa output over the years is an urgent call on the primary stakeholders to designed policies oriented toward sustainable industrial growth. For instance, Ghana achieved a targeted one million metric tonnes in 2010/11 cocoa production year. However, this level has been unsustainable as output has been fluctuating downwards afterwards. A low output growth relative to its potential, coupled with high prices of inputs such as agrochemicals relative to farmers' real income is partly responsible for the fluctuating growth rate in the industry. For cocoa to continue to have its significant impact on the Ghanaian economy, resources available to farmers ought to be optimized. Casteneda et al. (2018) noted that about 80% of the extreme poor live in the rural areas of developing countries and their livelihoods are tied farm activities-either from their farms or agricultural wage employment. Thus, their per capita growth and general socioeconomic welfare are also dependent on agricultural productivity. Hence, efficient use of resources to enhance total agricultural productivity is key to boosting income levels and general well-being of farmers. Although Ghana is the leading producer of cocoa next to Ivory Coast, its yield (kg/ha) is below that of its competitors in the world cocoa industry. For instance, while Ghana's average yield is about 0.4 tonnes/ha, that of Indonesia and Cote d'Ivoire are about 0.85 tonnes/ha and 0.6 tonnes/ha, respectively (FAOStat 2018). With fluctuating output levels and low yields, the efficiency of resource use has become a significant area of study in Africa's cocoa industry, in order to increase productivity and improve farmers' welfare in a sustainable manner. Many empirical studies (Besseah and Kim 2014;Binam et al. 2008;Onumah et al. 2013) have estimated the productivity and technical efficiency levels in cocoa production in Africa and identified sources of farmers' inefficiencies. However, the question these and other studies in technical efficiency fail to answer is whether farm-level technical efficiency translate into welfare gains or welfare translates into technical efficiency gains. In other words, do technically efficient farmers have better welfare or does improved welfare leads to farm-level technical efficiency? Assessing the two-way effect is critical as better welfare may not necessarily lead to efficient farm management. This is because well-endowed farmers may divert their income into other non-farm activities rather than purchasing farm inputs to improve their efficiency. Moreover, though some farmers may be technically efficient, it may not be sufficient to make them "better-off " due to their scale of operations. Therefore, the two-way quantitative effects of farmers' technical efficiency and welfare gains come into play. Building on the previous studies, this study examines the relationship between farm-level technical efficiency and farmers' welfare (proxied by consumption expenditure per capiata). To the best of the authors' knowledge, this is the first study in the Ghanaian cocoa industry to examine the effects of technical efficiency on the welfare of farmers and the effects of welfare on technical efficiency. The study aims to establish a premise on which development efforts geared towards the efficient use of resources for improved rural farm welfare are discussed. The study also hopes to fill a gap in existing agricultural literature, particularly in the African cocoa industry.

Theoretical framework and estimation technique
This section of the study discusses the theoretical framework on which the objectives of the study are premised. The study employed the two-stage econometric technique to achieve its objectives. First, the technical, pure technical and scale efficiencies of each farm household unit were estimated with the Data Envelopment Analysis (DEA) technique. Second, the study employed Tobit regression and Ordinary Least Square (OLS) regression models with endogenous covariate (to correct for endogeneity) within the framework of Conditional Mixed-process (CMP) to estimate the two-way quantitative effects of technical efficiency and welfare, respectively. 1

Technical efficiency estimation with DEA approach
DEA is a non-parametric approach that uses linear programming technique to measure the efficiency of decision-making units (DMU) such that the observed input-output vectors are enveloped as tightly as possible (Lee et al. 2009). In DEA, multiple inputs and output can be considered at the same time, with no assumption of the empirical specification or functional form and data distribution. There are two types of DEA, namely input-oriented and the output-oriented DEA. The input-oriented DEA minimizes the input requirements for at least a given output level while the output-oriented maximizes the output levels for a given input (without requiring additional inputs). DEA can further be sub-divided in terms of return-to-scale through the addition of weight constraints. Originally, Charnes et al. (1978) proposed a constant return-to-scale (CRS) for the measurement of efficiency where all DMUs operate at their optimal scale level. Later, efforts were made to break down the efficiency of the DMUs into components in other to identify specific sources of inefficiencies. Banker et al. (1984) introduced the concept of a variable return-to-scale (VRS) measurement of efficiency where the overall efficiency can be subdivided into technical and scale efficiencies. Technical efficiency refers to the ability of DMU to produce a given output with a minimum set of inputs (input-oriented) or using a given set of inputs to produce a maximum output level (an output-oriented) (Coelli et al. 2005). A DMU is said to achieve scale efficiency when it operates at an optimal scale. The fundamental principles of calculating the efficiency of DMUs is to construct a frontier, where all efficient DMUs lie, and those found below the Danso-Abbeam and Baiyegunhi Economic Structures (2020) 9:23 frontier are considered inefficient. The efficiency index ranges between zero (fully inefficient) and one (fully efficient). DEA initially emerged as a practical technique of measuring efficiency and sustainability of industrial production systems (Ullah and Perret 2014). However, recently, DEA has been used in agricultural production sectors following the pioneer works of De Koeijer et al. (2002) and Reig-Martıńez and Picazo-Tadeo (2004). This was motivated by the heterogeneity of smallholder farmers, particularly in developing countries, who are less likely to exhibit a uniform production function rendering stochastic frontier technique of estimating efficiency less appropriate. In this vein, the study used DEA to generate technical efficiency index for smallholder cocoa farmers in Ghana. Agricultural production in general and cocoa production, in particular, is such that farmers do have less control over output but more control over the quantities of inputs used. Hence, the input-oriented efficiency model was applied in this study. As noted by Coelli et al. (2005), the decision on which orientation to use depends on which side of the production system (input or output) the DMU has more control over. Previous studies such as; Davidova and Latruffe (2003), Krasachat (2004), and Reig-Martıńez and Picazo-Tadeo (2004), and recent studies such as Ogada et al. (2014b), Ullah and Perret (2014) and Rahman and Awerije (2015) applied input-oriented DEA in agricultural production systems.
The input-oriented DEA is also called CCR-model named after the initials of Charnes et al. (1978) who developed the model. In the CCR-model, a jth cocoa farm household uses the input vector X = (1, 2, . . . Z), ∈ R Z + to produce a desirable output, Following Cooper et al. (2007), the technical efficiency (TE) can be calculated using the DEA model; Minimize θ subject to; where θ is a scalar and represents the TE score [also known as the overall technical efficiency (OTE)] of the jth cocoa farm household, and denotes the intensity vector of the weight of the efficient cocoa farmer. The is an indicator that helps to project an inefficient cocoa farmer to an efficient frontier. The inputs and output used and produce by the farmer, respectively, are represented by z × n input matrix X / and m × n output matrix Y / , where X j is an input vector of the jth cocoa farm and Y j is an output vector of the jth cocoa farm. If the above model satisfies the three basic assumptions (convexity, scalability, and free disposability) of the DEA, then the model exhibits a constant returnto-scale. If the assumption of scalability is not satisfied, then the model exhibits variable return-to-scale. Nonetheless, farming is an activity that exhibits a variable return-toscale (VRS) due to its potential economies of scale (Ullah and Perret 2014). Following Banker et al. (1984), adding extra constraint of j = 1 to Eq. (1) leads to a VRS frontier. The VRS is also referred to as pure technical efficiency (PTE) and the model is known as BCC model named after the initials of the authors who suggested it (Banker et al. 1984). Unfortunately, BCC model fails to indicate whether an efficient farmer is exhibiting an increasing or a decreasing return-to-scale. To resolve this problem, Cooper et al. (2007) introduced a non-increasing return-to-scale (NIRS) model where a constraint ≤ 1 is  ) and technical efficiency under non-decreasing return-to-scale (TE NIRS ) specify whether a production unit exhibits increasing return-to-scale or decreasing return-to-scale. If TE CRS < 1 and TE CRS = TE NIRS , then the farmer produces at an inefficiently small output level, and the inefficiency emanates from increasing return-to-scale. On the other hand, if TE CRS < 1 and TE NIRS > TE CRS , then the farmers' inefficiency results from decreasing return-to-scale (Wossink and Denaux 2006).

The two-way impact of welfare and technical efficiency
The study performs a regression analysis on the second stage of the efficiency analysis to estimate the impact of welfare (proxied by consumption expenditure per capita) on farm-level technical efficiency. Technical efficiency indices were regressed on a set of socioeconomic (including the welfare variable), farm-specific, and policy factors to explain the variation in technical efficiency. In many studies, a Tobit regression model has been used due to the censoring nature of the efficiency score as recently done by Ogada et al. (2014a) and previously by Wossink and Denaux (2006). A simplified farm-level technical efficiency model is specified as: where θ i denotes the ith farm efficiency score estimated from the DEA approach, W i is welfare indicator, S i is other socioeconomic variables, F i is farm-specific variables, I i is institutional variables, and L i is location-specific variables. Given the nature of the efficiency score, the following conditions will be observed: Thus, Tobit regression model could be used to estimate Eq. (2) given the conditions in Eq. (3). Again, to find out whether farmers with improved welfare are technically efficient or not, a simplified OLS model could be used where the welfare indicator ( W i ) is now the dependent variable and the technical efficiency score ( θ ) as an explanatory variable as specified in Eq. (4): where variables are as defined earlier.
However, the problem with estimating Eq.
(2) directly with Tobit model is that welfare as one of the explanatory variables is assumed to be exogenous while it is potentially endogenous. Thus, while welfare explains variation in technical efficiency, it is by itself been explained by other variables. Hence, estimating without accounting for such endogeneity leads to biased and inconsistent estimates. Likewise, Eq. (4), where estimating with OLS directly could also lead to bias estimates due to endogenous nature of the efficiency score ( θ ) as an explanatory variable. (2)

The Conditional Mixed-process (CMP)
The endogeneity nature of welfare and efficiency variables can lead to under or over-estimation of the true impact of welfare on efficiency and the other way round. To account for this possibility, the study employed the Conditional Mixed-process (CMP) estimator proposed by Roodman (2011) to estimate Eqs. (2) and (4) separately. 2 The CMP is an empire of multi-equation systems with the ability to take a different format of dependent variables. It also controls for both simultaneity and endogeneity where consistent estimates are produced for a recursive system in which all endogenous variables are observed at the right-hand side of the equation (Asfaw and Lipper 2015). Moreover, the CMP has its foundation from the seemingly unrelated regression framework where cross-equations of the error terms are correlated (Makate et al. 2016). From Eq. (2), assuming the determinants of welfare (as an endogenous variable) is given by: where X i is a vector of variables (excluding efficiency score in this case) explaining the variation in welfare. Allowing for potential endogeneity of the welfare variable W i , Eqs. (2) and (5) can jointly be estimated, and the joint marginal likelihoods can be expressed as follows; where L 2 and L 5 are conditional likelihood functions of Eqs. (2) and (5), respectively; f (η 5 , η 2 ) is the joint estimation of the unobserved heterogeneity components. The joint distribution of the unobserved effects f (η 5 , η 2 ) is assumed to be a two-dimensional normal distribution characterized as follows: Similarly, the endogenous efficiency score ( θ ) in the welfare Eq. (4) is given by: where Z i is a vector of explanatory variables (excluding the welfare variable in this case), then Eqs. (4) and (8) could also be jointly estimated by the CMP estimator as elaborated above. The full model is jointly estimated through the conditional mixed process, which utilizes the Geweke, Hajivassiliou, and Keane (GHK) algorithm to consistently estimate the likelihood function in Eq. (6) (Roodman 2011).The main objective for jointly estimating Eqs.
(2) and (5), and Eqs. (4) and (8) (with correlated errors) allows selectivity bias to be derived from the estimates of the two-way impact of welfare and technical efficiency. Following the arguments of (5) Chamberlin et al. (1975) as cited in Makate et al. (2016), a system of equations does not necessarily require a set of instruments for identification. However, for the purpose of a 'good practice' , the study included some instrumental variables for the identification of welfare in Eq.
(2) and TE in Eq. (4). Instruments for identification must satisfy two conditions. First, they must have a direct correlation with the endogenous variable and second, they must not have a direct correlation with the error term of the outcome variable. In this study, income from other crops and engagement of spouse in non-farm activities were used as instrumental variables for the endogenous variable, welfare in Eq. (5). Thus, these two variables significant influence welfare but redundant in explaning farm efficiency. For Eq. (8), location-specific variables, and frequency of pesticides application were used to instruments the endogenous variable, TE. Similarly, the location-specific variables and frequency of pesticides explain the variation in farm efficiency score but not welfare,

Data collection procedure and description of variables
The data used for the study was collected from the four-principal cocoa-producing regions in Ghana: Western, Brong-Ahafo, Eastern, and Ashanti regions. These four regions produce about 90% of Ghana's cocoa (COCOBOD 2016). The regions are deciduous and semi-deciduous rainforest with an annual rainfall varying from an average of 1250 mm in the Brong-Ahafo to about 1600 mm in the Western region. All the regions are predominantly rural, the populace depends on agriculture for their livelihoods, and cocoa is the dominant cash crop contributing significantly to the household income. A wide variety of other food crops such as maize, yam, plantain, cassava, cocoyam, and other cash crops such as palm tree, cashew, and rubber are also grown. Questionnaire administration and interview with the key informants were the two main techniques used for the data collection. The use of two or more techniques in data collection help to triangulate the information gathered (Bless and Higson-Smith 2000). A multi-stage proportionate random sampling technique was followed in selecting districts and villages from each region and farm household from each village. The proportionate sampling was based on the production intensities of the regions under study. In the first stage, four districts from Western region and three districts each from Eastern, Brong-Ahafo, and Ashanti regions were randomly selected from a list of cocoa-producing districts in respect of the production capacities of the regions. Western region produces about 53% of Ghana's cocoa, while Ashanti, Brong-Ahafo, and Eastern regions produce about 17%, 10% and 9%, respectively, in the 2015/16 cocoa production season (COCO-BOD 2016). Hence, the selection of the four regions for the study. In the second stage, a random sampling was used to select 3-5 villages from the selected districts and 10-16 farm households from each village. The districts and villages were selected with the help of the regional and district offices of COCOBOD, and was also based on production intensities. In total, 183, 121, 110 and 91 farm households were randomly sampled from Western, Ashanti, Brong-Ahafo, and Eastern regions, respectively. The total sample size for the study was 505 cocoa farm households. Some slight modifications were made during pre-testing of the questionnaire to get more pertinent information and upsurge reliability. Key informants such as some heads of departments of COCOBOD district offices and community leaders were approached to discuss the cocoa production system, challenges, and opportunities regarding efficient use of resources and rural farm welfare. The selected variables hypothesized to influence farm-level technical efficiency and welfare was based on the review of past and recent theoretical and empirical efficiency and welfare-related literature.  Table 1. Table 1 also provides the summary descriptive statistics of the sampled farm households. The average quantity of cocoa output is 425 kg/ha, and the mean consumption expenditure per capita is GH¢2040.91 ($US 477.75). 34 The average farm size, labour/ ha, the quantity of fertilizer used/ha, and pesticides used/ha are 7, 110, 81, and 1026, respectively. On the average, farmers received GH¢8335 (US$ 2142) and GH¢801 ($206) as revenue from cocoa and other crops, respectively. A household head had an average of 6 years of schooling, and there is an average of 6 persons per household. About 71% of households are male headed, 44% had their spouses engaged in nonfarm income activities, 39% visited cocoa demonstration farms, and 49% attended cocoa farm seminar. On the average, farmers are managing approximately 2 plots and had their farms sprayed about 5 times with pesticides per cocoa season. 5 A farmer received an average of 2 extension services in the last cocoa season.

Efficiency analysis
The distribution and the summary statistics of the technical efficiency under CRS(TE CCR ), technical efficiency under VRS(TE BCC ) and scale efficiency are presented in Table 2. As stated earlier, a farmer who fails to achieve technical efficiency of one (1) is considered to be relatively inefficient.
TE under the assumption of CRS represents the overall technical efficiency (OTE) measuring inefficiency resulting from input/output configuration and the size of operation (Kumar and Gulati 2008). The pure technical efficiency (PTE) measures inefficiency The frequency distribution in Table 2 reveals that most cocoa farmers are inefficient. The number of efficient farmers under constant-to-scale (OTE) is 29 representing about 6%; thus the majority (94%) of the farmers were inefficient. The 29 efficient farmers together define the efficient frontier and, hence, set the standard for inefficient farmers. These farmers are utilizing their resources very well without or with minimal waste. They are referred to as peers, and their practices are good examples for their inefficient counterparts to replicate. The mean OTE efficiency is about 44% implying that, by adopting best practices, cocoa farmers can still achieve their output level with the existing technology by potentially reducing their inputs by a substantial average of 56%. Alternatively, cocoa farmers have the scope of producing as much as 2.27 times (1/0.44) of their current production level without altering the quantities of inputs. Using stochastic frontier approach, Onumah et al. (2013) obtained a mean efficiency of 68% among cocoa farmers in the Eastern Region of Ghana while Ullah and Perret (2014) reported an average OTE of 54% among small and large cotton farms in Pakistan with DEA approach. However, Kabwe et al. (2016) reported a lower OTE level of 43% and 31% among cotton farmers in Zambia using DEA and stochastic frontier, respectively. A large proportion (64%) of cocoa farmers achieve OTE of 50% and below while only 30% of them had more than 50% efficiency, albeit, they are still inefficient.
However, the number of efficient farmers increased significantly when PTE was used. The mean PTE was estimated to be 76%, high above that of OTE. This is expected because, as noted by Kumar and Gulati (2008) "BCC model forms a convex hull of intersecting planes which envelopes the data points more tightly than CRS conical hull and provides efficiency scores which are greater than or equal to those obtained using CCR model. " In addition to 29 farmers that are technically efficient, 181 farmers that were not efficient under CRS have become efficient under VRS. Thus, the total efficient farmers under VRS is 210 representing about 42%. This suggests that technical inefficiency under CRS may be caused by inappropriate scale size rather than poor utilization of resources (managerial inefficiency). However, for those inefficient farmers under VRS, managerial inefficiencies exist. Table 2 further indicates that apart from the 42% of farmers that are BCC-efficient, about 7% also achieve scale efficiency with the mean scale efficiency of about 58%.
One of the fundamental objectives of every production unit is to operate with constant return-to-scale (most productive scale size) to maximize profit. DMUs may operate in the region of increasing return-to-scale (IRS) or decreasing return-to-scale (DRS) in the short run. However, in the long-term, they will try to manipulate their operating strategies to move towards CRS where costs and revenue can be optimized. As indicated in Table 2, the 6% TE CCR -efficient farmers operate at the most productive scale size, hence, experience CRS. About 69% of the cocoa farmers operate below their optimal scale size Page 11 of 15 Danso-Abbeam and Baiyegunhi Economic Structures (2020) 9:23 and thus, experience IRS. These farmers can improve their level of TE CCR by increasing their scale size. The remaining 25% of farmers operate above their optimal scale level (DRS), hence, downsizing their scale of operation is a better option to enhance their efficiency level. Generally, it is observed that Ghanaian cash crop farmers exhibit increasing return-to-scale. Onumah et al. (2013) and Mensah and Brümmer (2016) reported similar results in Ghana's cocoa and oil palm industry, respectively.

Factors explaining variation in farmers' efficiency: OTE and PTE
The variation in farmers' OTE and PTE could be explained by some socioeconomic, farm-specific and policy or institutional factors. The results are presented in Table 3. From the results, gender gap exists in measuring farmers' performance under the assumption of VRS. Male farmers were observed to be technically more efficient than their female counterparts.
This could partly be attributed to the tedious nature of cocoa farming which, in principle, is more suitable for male farmers than female farmers. It contradicts the results of Kabwe et al. (2016) where female-headed cotton farmers are more technically efficient

Table 3 Determinants of technical efficiency and the two-way impacts of efficiency and welfare
The superscripts "1-4" indicates the various models estimated a,b,c Denote significance level at 1%, 5% and 10%. ME and SE indicate marginal effects and standard errors, respectively. OTE and PTE denote overall technical efficiency and pure technical efficiency under the assumption of constant-return scale and variable-return scale, respectively than male-headed farmers. However, it is in line with Rahman and Awerije (2015) where male farmers are more technically efficient than female farmers under VRS assumption. A visit to farm demonstration correlates positively and significantly with OTE, but have no influence on PTE. Demonstration farms offer an excellent opportunity to farmers to learn new ways of farming to improve their technical and managerial skills. Similarly, the frequency of pesticides application positively and significantly influences OTE and PTE. Pests and diseases have the potential to reduce output considerably. Hence, Cocoa Research Institute of Ghana (CRIG) recommends an application of insecticides and fungicides at least 3 and 6 times per cocoa season, respectively. Thus, farmers that have their farms sprayed more frequently tend to have 2.8% and 2% higher OTE and PTE score than those that sprayed their farms less frequently, respectively. Moreover, while the number of farm plots negatively influence OTE, farm size positively and significantly affect PTE. Linh et al. (2017) reported a negative effect of farm size on OTE. The location variables in the two models indicate that farmers located in the Eastern, Brong-Ahafo, and Ashanti regions are less technically efficient under both OTE and PTE assumption than their counterparts in the Western region. 7 This may partially be attributed to differences in regional climatic features (e.g., an intensity of rainfall, soil conditions, and topography) and market conditions such as input prices.

The impact of welfare on efficiency and of efficiency on welfare
For farm-level policy formulation, it is critical to know the quantitative effects of welfare on efficiency, i.e., if farmers with improved welfare are technically efficient. The consumption expenditure per capita was used as a proxy for farmers' welfare. In Table 3, welfare is included as explanatory variables in OTE and PTE models (1 and 2) after accounting for endogeneity. The second part of Table 3 contains welfare regression models (3 and 4) where OTE and PTE scores are used as explanatory variables. The reported atanhrho_12 at the bottom of the table indicates a primary measure of endogeneity resulting from selectivity bias. A significant value of atanhrho_12 is an evidence of self-selection bias, and this is observed in all the four models. A significant positive value indicates that some unobserved covariates positively affect the endogenous and the outcome variables.
The reverse applies to a negative significant value. In this study, some omitted variables impact negatively on welfare and OTE while others have positive effects on welfare and PTE. For instance, in the welfare models (3 and 4), the negative values of atanhrho_12 are evidence that some unobserved factors are negatively affecting both the outcome variable (welfare) and the endogenous variables (OTE and PTE scores). The positive coefficient of OTE and PTE of models 1 and 2, respectively, in Table 3 indicates that better welfare improves both OTE and PTE of farmers. Thus, farmers with improved welfare are "better-off " by 0.22% and 0.94% regarding efficiency under CRS and VRS, respectively. A plausible explanation for this is that households with better welfare can purchase the right quantity of inputs at the right time, and subsequently improves their efficiency level. Another attributable reason is that, in a typical African society, wealthy households have better access to information and other services such as extension services than the poorer households. Similarly, the positive and significant values of OTE and PTE in both models (3 and 4) confirm that high scores of efficiencies (i.e., OTE and PTE) translate into better welfare. This is not surprising as efficient use of resources enables farmers to save cash resources to be used for other productive goods and services, which are vital to their welfare development. In sum, the principle that improvement in farm households' welfare translate into increasing efficiency and increasing efficiency also make farmers' better-off regarding welfare holds, at least, in Ghana's cocoa industry. However, the magnitude of the effects of technical efficiency on welfare is larger than that of welfare on technical efficiency as revealed by the study. Kabwe et al. (2016) found no significant effect of welfare (proxied by productive assets) on technical efficiency probably because of the weak econometric technique used where the study fails to account for potential endogeneity. Other variables such as engagement of spouse in non-farm activities, income from cocoa farm, income from other crops, extension contacts and farm size also exert positive and significant effects on welfare in both models (3 and 4).

Conclusions and recommendations
This study endeavors to evaluate the extent of technical efficiency and the two-way effects of farm-level efficiency and welfare of smallholder cocoa farmers in Ghana. Improved technical efficiency and welfare of smallholder cocoa farmers are vital for the sustainable growth of the Ghanaian cocoa industry as technical efficiency and welfare significantly complement each other. Results from the study revealed that only 6% of cocoa farmers are on the frontier in the cocoa production system. On average, farmers have the potential to increase their output by 56% without increasing their input levels.
The primary source of inefficiency emanates from farmers operating below their optimal level (IRS). Hence, farmers can improve their standard of efficiency by up-scaling their size of the operation. The study further revealed that higher technical efficiency score leads to better farm households' welfare and an improved welfare translates into higher efficiency score. Thus, technical efficiency and welfare significantly complement each other. One of the policy implication of the study's findings is that increasing farm-level efficiency is crucial to sustaining Ghana's target of achieving one million metric tonne of cocoa per year. There will be a concomitant impact on farm households' welfare since efficiency and welfare are complementary. Thus, an urgent call on Ghana Cocoa Board (COCOBOD) to strengthen her existing cocoa farm-level policies such as cocoa Hi-tech programme, payment of better producer prices and bonus payment schemes as means of encouraging farmers to enhance productivity. Creating awareness on the unproductive use of resources can also be the surest avenue to improving farmers' level of efficiency. If farm households are conscious of inefficient use of resources and/or inappropriate farm management practices, then through technical and managerial skill development programs, they could effectively combine inputs to optimize their output.