Efficiency of chili pepper production in the volta region of Ghana

This study investigates the overall economic efficiency of chili pepper producers in the Volta region of Ghana. The study used farm level data to examine the productivity of selected agricultural inputs, technical, allocative and economic efficiency levels and the determinants of efficiency of chili pepper production. The modified translog stochastic frontier production and cost function models were adopted for the study using the maximum likelihood estimation procedure. Data was collected on 200 chili pepper producers through a multi-stage sampling technique. The results indicate that on average, chili farms were only 65.76% economically efficient, whilst mean technical and allocative efficiencies were estimated to be 70.97% and 92.65%, respectively. The findings also reveal that chili farms in the study are characterized by decreasing returns to scale. The results further show that age, experience and gender among others significantly influence technical efficiency. Allocative efficiency is however influenced by gender, education and access to credit inter alia. The joint effect of these variables explains the variation in the economic efficiency of the chili farms. The study therefore concludes that chili farms in the study area are economically less efficient. The study recommends policies and programs that aim at attracting the teaming youth into chili pepper cultivation to be pursued by giving them incentive packages. Experienced chili farmers are advised by the study not to solely rely on their know-how but should endeavour to complement their knowledge with advisory services given by extension officers. Policy makers should also focus on policies that will facilitate chili farmers’ access to low interest bank loans in the form of inputs.


INTRODUCTION
Vegetable cultivation in both rural and urban Ghana is a germane economic activity.This is because of its importance as a major source of quick employment and income generation for both the rural and urban poor.*Corresponding author.E-mail: j.asravor@uni-hohenheim.de; djgharo@gmail.com.
Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Vegetable farming has the potential to alleviate poverty and improve food security in Ghana.According to the AVRDC (2006), vegetable farming provides smallholder farmers with much higher income and more jobs per hectare than staple crops.Chili pepper (Capsicum annuum) is an important high value cash crop in Ghana and it is largely cultivated for export and domestic consumption by both the urban and rural poor.Its cultivation and consumption has long been part of Ghana's agriculture and diet (MiDA, 2010).Chili pepper is called "green gold" by some farmers because of its economic value to them.Chilies produced in Ghana are known for their good reputation in the European markets in contrast to chilies from other parts of the world especially the Legon 18 variety which has become famous for its great taste and longer shelf-life.The Bird's Eye chili variety furthermore offers an emerging opportunity for higher value chili exports in Ghana (MiDA, 2010).Chilies are the fourth most harvested crop in Ghana after cassava, plantain and yam with about 984,586 households engaging in its cultivation (GSS, 2014).
Ghana has been identified to have both comparative and competitive advantages over other African countries in terms of chili pepper production.Despite these advantages, the country is currently ranked fourth in chili production in Africa after Egypt, Nigeria and Algeria (MiDA, 2010).The world's chili demand is on the ascendancy and this continuous increase in demand means that the world's chili production still has space for improvement, through increasing land productivity and raising its yield potentials.In fact, enormous yield gaps which are still rife on chili farms need to be improved.Presently, the average yield of chili pepper in Ghana is 8.30 Mt/ha which is far below the achievable yield of 32.30 Mt/ha (MoFA, 2014).Improvement in yield is therefore a necessity and needs to be pursued with all the resources it requires for efficient production.
Knowledge of the overall productive efficiency status and its determinants, in addition to the key drivers of productivity of chili farms are relevant from policy perspective in a country where new technologies are scarce and productive resources are inadequate.This is because, gains in the efficiency and productivity of chili farms are essential for increasing the farm income of both the rural and urban dwellers who are engaged in its cultivation.The challenge of low productivity on Ghanaian chili farms can be attributed to some key constraints militating against the attainment of the potential frontier output.Such constraints may include the attack of pests and diseases, limited land, poor prices of produce, low adoption of improved chili pepper cultivation technologies and inefficiencies arising from the allocation of production resources.This implies that efforts at improving the productivity of chili farms cannot overlook identifying and addressing these key factors.As a result of the lack of access to productive resources, coupled with the low rate of adoption of improved chili production technologies in Ghana, improvement in the efficiency of chili farms has become paramount for enhancing the productivity level of chili farms.Although a plethora of efficiency studies on Ghana's agricultural production exist in the literature, much of these studies focus on technical rather than allocative and economic efficiencies.However, it is only through substantial gains in overall economic efficiency that significant gains in output can be achieved (Bravo-Ureta and Pinheiro, 1993).The need to boost the productivity and efficiency status of chili farmers in Ghana has led to the following research questions; what are the current levels of technical, allocative and economic efficiencies and what are the major determinants of inefficiency of chili farms in the Volta region of Ghana?

Study area and data collection
The study considered a cross sectional data from four districts in the Volta region of Ghana.The Volta region is endowed with abundant water resources which make all year-round production of vegetables possible.A multi-stage sampling technique was used to select 200 chili farms from the Volta region.The first stage involved the purposive selection of the four districts based on the Millennium Development Authority's observation that the southern horticultural belt of Ghana is made up of 7 districts of the Volta region (MiDA, 2010).The second stage involved the purposive selection of the communities noted for chili pepper production and the third stage involved the random selection of chili farmers.The selected districts were South Tongu district, Ketu-South district, North Dayi district and Keta municipality.A total of 50 chili farmers were sampled from each district/municipality leading to a sample size of 200 respondents.The data was collected through personal interview whilst using a well-structured questionnaire.

Analytical framework
This study adopts the stochastic frontier production and cost function models to analyze the technical, allocative and economic efficiencies of chili farms in the Volta region of Ghana.The stochastic frontier approach is adopted because of its ability to segregate the inefficiency effect from the noise effect.The stochastic frontier approach as simultaneously proposed by Aigner et al. (1977) and Meeusen and Van den Broeck (1977) is specified as: where i Y denotes the maximum output for the i th farm.

 
; i fX represents a suitable production function of row vector of inputs Xi for the i th farm and a vector  of unknown parameters to be estimated.The stochastic frontier model specified above attributes the total variation in output to an error term which is made up of two components   ii vu  .Where Equation 2 shows that the difference between  such that the mean is defined as: where i Z is a vector of inefficiency factors and  is a vector of unknown parameters to be estimated.Based on the distributional assumptions which underpin the random error term, this study adopts the single-stage maximum likelihood estimation procedure to estimate the parameters of the stochastic frontier and the inefficiency models concurrently (Onumah et al., 2010).The farmspecific are parameterized according to Battese and Corra (1977) as: Gamma (γ) has a value which ranges between zero and one.For 0 1   , then output variability is as a result of the presence of both technical inefficiency and the stochastic errors.
According to Coelli et al. (2005), when information on prices are given and firms are assumed to be operating under the assumption of cost minimization, then the cost frontier can be used to estimate the economic characteristics of the production technology and also to predict the cost efficiency of the firms.The stochastic frontier cost function for a cross-sectional data can be stated as: where denotes the total cost of production of the i th farm,   g , ; ii YP represents a suitable cost function, is a vector of output produced by the i th farm, denotes a vector of input prices, is a vector of parameters to be estimated, i u denotes inefficiency and i v is the random noise.The composed error term,

 
ii vu  is positive because inefficiencies arising from the production process are always assumed to increase production cost (Coelli et al., 1998).This equation shows that the production cost is greater or equal to the minimum cost of production.
According to Ogundari and Ojo (2007), the farm-specific allocative efficiency ( ) of the i th farm is calculated by the ratio of the predicted minimum cost of production ( ) to the corresponding actual total cost of production ( ) and it is specified as: The measure of has a value ranging from zero to one, where one indicates a fully efficient farm and zero implies a fully inefficient farm.

Empirical model specification
Although the Cobb-Douglas functional form is easy to implement, it imposes a severe constraint on the technology of the firm by restricting the production elasticities to be constant and the elasticities of input substitution to be equal to one (Wilson et al., 1998).The translog functional form also suffers from multicollinearity problems (Dawson et al., 1991).However, Coelli (1995) observed that the translog frontier functional form is less restrictive, allowing for the combination of squared and cross product terms of the explanatory variables with the view of obtaining goodness of fit of the model.Based on the strengths and weaknesses of the two functional forms, the translog functional form is adopted for this study, after testing for the significance of the interaction terms of the model.
In this study, the translog model of the production function was modified to capture the productivity associated with the price of fertilizer (PFert), family labour (Flabour) and hired labour (Hlabour) due to the effect of zero observations.For further information on this specification, see Battese and Coelli (1995), Battese and Broca (1997), Onumah and Acquah (2011) and Villano et al. (2015).The model is stated as: where Yi denotes the total quantity of chili pepper produced in kilograms (kg), is the binary variable for family labour which have their usual meanings.This study assumes that the elasticities of chili output associated with other input factors (except family labour, hired labour and price of fertilizer) are the same for farmers who did not use family labour, hired labour or fertilizer as for those who did use these inputs.
The modified cost frontier of the translog functional form which provides the basis for estimating the AE of chili farms in the Volta region of Ghana is specified as follows: where is the total cost of chili pepper production by the i th farmer in GH¢, is the dummy variable for the price of family labour which has a value of one if family labour is used in production and zero if otherwise, is the dummy variable for the price of hired labour which has a value of one if hired labour is used and zero if otherwise, is the dummy variable for the price of fertilizer which has a value of one if fertilizer is used and zero if otherwise and is the dummy variable for the price of farm land which has a value of one if the farm land on which the chilies are cultivated is paid for and zero if otherwise.Without the inclusion of the intercept changes ( , , and ), the estimator for the responsiveness of total cost of chili production with respect to the prices of family labour, hired labour, fertilizer and farm land could be biased (Battese, 1997).PFlabour is the price of family labour used (in GH¢).In Equation 7, have their usual meanings.This study assumes that the elasticities of total cost associated with other input price factors (except for prices of family labour, hired labour, fertilizer and farm land) are the same for farmers who did not use family labour, hired labour, fertilizer and farm rent as for those who did use or pay for these inputs.Economic efficiency, which is the focus of this study is estimated from the multiplicative interaction of both technical and allocative efficiencies and specified as: where i μ denotes either technical or allocative inefficiency and δ are vectors of unknown parameters to be estimated.

Tests of hypotheses
These hypotheses were tested to ascertain the appropriateness of   , the null hypothesis that inefficiency effects are absent from the models at all levels; (3) , the null hypothesis that the inefficiency effects are non-stochastic and (4) , the null hypothesis that there are no intercept changes.

Null hypothesis
These hypotheses were validated using the generalized likelihood-ratio statistic, , which is specified as: the given null hypothesis is true with a degree of freedom equal to the number of restrictions in the model under the null hypothesis.Coelli (1995) proposed that all critical values can be obtained from the appropriate Chi-square distribution.However, if the null hypothesis involves  = 0, then has a mixed chi-square distribution and hence the critical values for should be read from Table 1 of Kodde and Palm (1986).

Tests of hypotheses
As shown in Tables 1 and 2, the first hypotheses evince that the translog rather than the Cobb-Douglas functional form is a valid representation of the data.This is shown by the rejection of the first hypotheses in both the stochastic frontier production and cost functions.The second hypotheses which specify that inefficiency effects are absent from both models at all levels are also rejected, implying that technical and allocative inefficiency effects are present in both models.The third hypotheses that the inefficiency effects are non-stochastic are also rejected implying that the traditional average response (OLS) function is not an adequate representation of the data.The fourth hypotheses that there are no intercept changes are also rejected in favour of the alternate, implying that the estimates of the parameters of the stochastic frontier production and cost functions would have been biased if these dummies to account for intercept effects in dealing with zero observations in some of the input variables had not been introduced.

Results of the stochastic frontier production function
The maximum likelihood estimates of the stochastic frontier production function are shown in Table 3.The results show that the estimated intercept coefficients for hired and family labour are negative and significant while that of price of fertilizer is positive but has a weak relationship.The estimates of the parameters of the stochastic frontier production function would have been biased if the combined effect of these dummies to account for zero observations in hired labour, family labour and the price of fertilizer were not incorporated in the model.This is further validated by the rejection of the fourth hypothesis in Table 1 (that is, there is no intercept change) in the test of hypotheses.The gamma value is 0.7323 and it is statistically significant at 1%, implying that about 73% of the total deviations from the efficient chili frontier output is due to inefficiencies arising from the production process while the random effects constitute about 27%.This further means that technical inefficiency effects dominate the noise effect in explaining the total variation in chili output.The findings also show that chili pepper output responded positively to all the input variables except family labour.This implies that a percentage increase in farm size, hired labour, price of fertilizer, quantity of seed and othercost will result in 0.34, 0.28, 0.21, 0.09, and 0.18% increase in chili output, respectively.However, a percentage increase in family labour may decrease chili output by 0.29%.This may be attributed to the excessive use of family labour for chili pepper cultivation which leads to diminishing returns.Since majority of the farmers are resource poor and are unable to pay for the services of hired labour, they tend to depend heavily on the services of their family members for production activities, resulting in the excessive use of family labour.The estimated elasticities for farm size, family labour, hired labour and price of fertilizer are statistically significant at 1%, whiles that of other cost is at 10%.The estimated return to scale is 0.82, implying that on average, chili farms in the Volta region of Ghana are characterized by decreasing returns to scale.This means that a proportionate increase in all the inputs will result in a less than proportionate increase in chili output.
The realized return to scale is higher than the 0.304 obtained by Wosor and Nimoh (2012) in their study of the resource use efficiency of chili farms in the Keta municipality of the Volta region.

Results of the stochastic frontier cost function
The maximum likelihood estimates of the stochastic frontier cost function for the allocative efficiency are presented in Table 4.The predicted elasticities for all the input price variables are positive and significant at 1%.This means that all the input prices contributed significantly and directly to the total cost of chili pepper production.This implies that a percentage increase in the price of farm land, price of hired labour, price of family labour, price of fertilizer, price of seed and other costs will increase the total cost of chili pepper production by 0.0398, 0.3999, 0.4087, 0.0791, 0.0370 and 0.0599%, respectively.Output however has a weak positive relationship with the total cost of chili production.This positive relationship might mean that a 1% increase in chili output will lead to a 0.0047% increase in the total cost of chili production.The findings also show that the estimated intercept coefficients for the price of farm land, price of fertilizer, prices of hired and family labours are significantly positive.These estimated parameters show that the estimates of the parameters of the cost frontier function would have been biased if these dummies to account for intercept effect in dealing with zero observations in the price of farm land, price of fertilizer, price of hired labour and price of family labour were not included in the model.This is further confirmed by the rejection of the fourth null hypothesis in Table 2 (that is, there is no intercept change) in the test of hypotheses.
The estimated gamma (γ) value of the allocative efficiency model is 0.9853 and it is significant at 1%, implying that the inability of the chili farmers to operate at the minimum cost frontier is largely due to conditions under their direct control while conditions beyond their control constitute about 1.47% of that inability.

Distribution of technical, allocative and economic efficiency scores
The frequency distribution of the various estimates of technical, allocative and economic efficiencies of chili farms in the Volta region of Ghana are presented in Figure 1.Technical, allocative and economic efficiency scores varied greatly among the sampled chili farms.The predicted technical, allocative and economic efficiencies ranged from 18.62 to 92.06%, 69.76 to 99.58% and 17.40 to 91.10%, respectively with their means being 70.97, 92.65 and 65.76%, respectively.This mean TE estimate shows that on average, chili farms are operating at 29.03% below the efficient frontier output.This therefore implies that with the current level of technology and resource endowment, chili farms in the Volta region can increase chili output by 29.03% through the adoption of the best farm practices.The mean AE estimate of 92.65% implies that on average chili farms are operating at 7.35% above the minimum attainable cost frontier.Consequently, there is the possibility for the chili farmers to minimize cost by an average of 7.35% thr ou g h th e adoption of the practices of the best cost efficient farm.These high allocative efficiency estimates of the sampled chili farms confirm the hypothesis formulated by Schultz (1964) that resourcepoor farmers in developing countries are highly efficient in allocating the scarce financial resources at their disposal.The mean EE of 65.76% shows that on average, the ability of the chili farmers to produce a    predetermined level of output at the lowest attainable cost is relatively low.The findings further show that substantial gains in EE can be achieved by improving the technical and allocative efficiencies of the chili farmers.
Following the work of Bravo-Ureta and Pinheiro (1997), the efficiency scores also indicate that if the average chili farmer is to attain the efficiency level of the most technically efficient chili farm among the sampled chili farms, that farmer will have to realize a 22.91% cost savings (that is, 1-[70.97/92.06]).Also, the most technically inefficient chili farmer will have to realize a cost reduction of 79.77% (that is, 1-[18.62/92.06]) in order to achieve the technical efficiency level of the most efficient chili farm.From the allocative efficiency scores, the average and least efficient chili farms will have to realize cost reductions of 6.96% (that is, 1-[92.65/99.58])and 29.95% (that is, 1-[69.76/99.58]),respectively before they can attain the efficiency level of the most allocative efficient chili farm among the sampled chili farms.The results further show that the average and the most economically inefficient chili farms must save cost by 27.82% (that is, 1-[65.76/91.10])and 80.90% (that is, 1-[17.40/91.10]),respectively to be able to attain the efficiency status of the most economic efficient chili farm among the sampled chili farms.It is evident from these findings that substantial gains in EE can be achieved and that technical inefficiency effects pose more challenge to EE than allocative inefficiency effects.

Determinants of technical and allocative inefficiency
The results of the analysis of the technical and allocative inefficiency models are shown in Table 5.Since EE is composed of technical and allocative efficiencies, economic inefficiency also arises from the joint effects of technical and allocative inefficiencies (Bravo-Ureta and Pinheiro, 1993).Knowledge of these inefficiency factors according to Bravo-Ureta and Pinheiro (1993) is of great importance in formulating appropriate policies towards the attainment of the frontier output given the technology level.The results of the inefficiency models revealed female chili farmers to be technically more efficient than their male counterparts.Male farmers however are allocatively more efficient than their female counterparts.This finding is not surprising since much of the labour that  is required for farm operations (weeding, transplanting, harvesting, processing, etc) are supplied by women.Since chili plants are very delicate, they require care and patience in handling them and this is done better by females than males.On the other hand, male farmers who may mostly be the heads of their respective households may want to minimize cost in order to save money for the upkeep of their farm families and by so doing may end up producing at the minimum attainable cost.This finding contradicts the views of Onumah et al. (2013) who found male cocoa growers to be technically more efficient than their female counterparts.It is however in consonance with Amewu and Onumah (2015) who found male NERICA rice farmers to be allocatively more efficient than their female counterparts.The age of chili farmers has a positive relationship with technical inefficiency, implying that aged farmers are less efficient relative to their youngsters.This result agrees with the findings of Asante et al. (2014), Mariano et al. (2011) and Khan and Saeed (2011).The implication of this finding is that policies that are aimed at persuading the teaming youth to go into chili pepper cultivation should be implemented since it has the potential to boost chili production.Surprisingly, experienced chili farmers are found to be technically and allocatively less efficient than their inexperienced counterparts.This may be attributed to the fact that most experienced farmers may tend to rely solely on their knowledge and so may not seek advisory services from extension officers and this may lead to their inefficiency compared to their inexperienced counterparts who may be willing to seek extension advice.This finding concurs with the findings of Onumah and Acquah (2011) and Onumah et al. (2010) who posit that new farmers are progressive and willing to implement new farming systems, leading to high level of efficiency as opposed to their experienced counterparts.
Even though the individual effects of age and experience of the farmers are found to influence technical and allocative inefficiency positively, this study illustrates that the joint effect of these factors impact technical and allocative inefficiency negatively.This implies that aged farmers with numerous years of experience in chili pepper cultivation are relatively more efficient as opposed to aged farmers who are less experienced or experienced young farmers.This finding reveals that people who go into chili farming at old age (e.g. after retirement) are less efficient as opposed to those who enter at tender age since they tend to acquire more experience as they grow.
Onumah and Acquah (2011) also realized a similar relationship in their study of the technical efficiency and its determinants of Ghanaian fish farms.Contrary to expectations, farm families with relatively larger household sizes are found to be relatively less efficient than those with relatively smaller sizes.This finding is confirmed by the negative contribution of family labour to chili output.A summary statistic of the data revealed that more than 92% of the sampled chili farms are less than 2 hectares and increasing labour inputs on these atomized land holdings will lead to diminishing returns.This finding lends support to Effiong (2005) and Idiong (2006) who argued that larger household sizes do not necessarily ensure increased efficiency since family labour is made up of children who are always in school.Contrary to the findings of Onumah et al. (2013), Khan and Saeed (2011) and Mbanasor and Kalu (2008), but consistent with the findings of Okike et al. (2001), chili farmers who had access to credit facilities operate with less technical and allocative efficiency than those without access.This may be ascribed to the fact that majority of the farmers who had access to credit facilities may not have used the credits for the planned purposes.Since most of the chili farmers are resource poor and have large family sizes, a high possibility of credit diversion into meeting their daily needs may exist among them.Consistent with the results of Bravo-Ureta and Pinheiro (1997), Khan andSaeed (2011), andAbdulai andHuffman (2000), chili farmers with more years of education are found to be allocatively more efficient than their counterparts who are less educated.According to Khan and Saeed (2011), education helps to sharpen the managerial skills of farmers thereby enabling them to be good decision makers with regards to input usage.Chili farmers who engage in other forms of income generating activities are found to be allocatively more efficient than their counterparts who do not engage in such activities.
Engagement in off-farm activities yield returns which increase the purchasing power of the farmers, enabling them to purchase productivity enhancing inputs for chili cultivation.This result contradicts the views of Abdulai and Eberlin (2001)

CONCLUSIONS AND POLICY RECOMMENDATIONS
Based on the findings of the study, the following conclusions are drawn.Chili pepper output in the study area is greatly influenced by farm size, hired labour, family labour, price of fertilizer and othercost of production.The production technology of chili farms is characterized by decreasing returns to scale.The total cost of chili pepper cultivation in the study area is significantly influenced by the price of farm land, price of hired labour, price of family labour, price of fertilizer, price of seed and othercosts.However, output does not significantly influence total cost though they are positively related.
Chili farms in the study area are economically less efficient and this is largely due to the presence of both technical and allocative inefficiencies in chili production with technical inefficiency effects constituting a more serious problem to economic efficiency than allocative inefficiency effects.This implies that economic efficiency could be improved substantially by improving both technical and allocative efficiencies, however improvement in technical efficiency offers a higher potential for enhancing economic efficiency than in allocative efficiency.This further implies that chili farmers in the study area generally make good decisions with respect to input allocation rather than good decisions regarding the perfect conversion of inputs into output.
The results also demonstrate the import of examining not only technical efficiency as a measure of productivity but also allocative and economic efficiency components.The current economic efficiency level of the farmers implies that the ability of the chili farmers to produce a potential level of output at a lower cost is relatively low on average and needs to be improved.There is the presence of both technical and allocative inefficiencies among the chili pepper producers in the study area and these inefficiencies are greatly influenced by farmers' socio-economic characteristics as well as technical and institutional factors.The joint effects of technical and allocative inefficiencies are responsible for explaining the level of variations in the economic efficiency of chili farms although the individual effects of some variables are statistically non-significant.
On the basis of the findings, the study recommends that chili farmers should rely more on the services of hired labour rather than family labour and those who desire to make efficient use of the services of their large farm families should increase their farm-sizes so as to commensurate the quantity of available family labour.The study also recommends policies that aim at attracting the teaming youth into chili pepper cultivation to be pursued by the government and other stakeholders of the chili industry.These policies should focus on giving incentive packages such as enhancing the access of the youth to improved inputs at subsidized prices, especially young female chili farmers since female farmers are found to be technically more efficient than their male counterparts.The study further recommends that experienced chili farmers should not rely solely on their know-how but should endeavour to complement their knowledge with advisory services.Furthermore, financial institutions and other credit providers should focus on providing credit to the farmers in the form of inputs rather than cash and these inputs should directly be channeled into production activities so as to avert the possible diversion of these inputs.

iv
is the random error which captures the effects of the conditions beyond the control of the farmer and i u is the non-negative error term which accounts for technical inefficiency (conditions under the direct control of the farmer).The i th farm's technical efficiency ( ) measure is given by the ratio of the realized output ( i Y ) given the values of its inputs and inefficiency effects to the corresponding maximum potential output ( * i Y ) assuming there were no inefficiencies arising from the production process.Thus the technical efficiency of the i th farm is given as: that the output lies on the frontier and thus the farm is technically efficient and obtains its maximum potential output given the level of inputs.However, if i u > 0, the production lies below the frontier and the farm is technically less efficient.Following Battese and has a value of one if family labour is used and zero if otherwise, is the binary variable for hired labour which has a value of one if hired labour is used and zero if otherwise and is the dummy variable for the price of fertilizer which has the value of one if the farmer uses fertilizer and zero if otherwise.According toBattese (1997), without the inclusion of , and , the estimator for the responsiveness of chili output with respect to the use of family labour, hired labour and price of fertilizer could be biased.Flabour represents the number of family labour used (in man-days).In Equation6, is expressed aswhichdenotes zero usage of family labour.Hlabour denotes the number of hired labour used (in man-days) and in Equation 6 is expressed as which represents zero usage of hired labour.PFert denotes the price of the quantity of fertilizer used (GH¢) and in Equation 6 is expressed as Farm size denotes the quantity of land (hectares) cultivated to chili pepper.Quantity of seed is the total quantity of chili pepper seed (kg) that is used in the planting process.Othercost comprises of the price of chemicals, price of capital inputs and price of irrigation water (GH¢) used during the cropping season under consideration.
expressed as which denotes zero usage of family labour.PHlabour denotes the price of hired labour used (in GH¢) and in Equation 7 is expressed as which represents zero usage of hired labour.PFert denotes the price of the quantity of fertilizer used (in GH¢) and in Equation 7 is expressed as which represents zero usage of fertilizer.Rent represents the price of farm land used (in GH¢) and in equation (7) is expressed as which represents no payment for the farm land.PSeed is the price of the quantity of chili pepper seed (GH¢) used in the planting process.Othercost comprises of the prices of chemicals, capital inputs and irrigation water that were used during the planting period (in GH¢).
efficiency, technical efficiency and allocative efficiency of the i th producer respectively.The various farm-specific and operational factors hypothesized to influence the technical and allocative inefficiencies of chili farms in the Volta region are defined by the model: is a dummy variable (value of 1 if the chili farmer is a male and 0 if otherwise), 2 Z is the age of the farmer in years, 3 Z is the experience of the farmer in years, 4 Z is the interaction term for age and experience in years, 5 Z denotes the household size of respondents in number of persons, 6 Z is the dummy variable for access to credit (value of 1 if yes and 0 if otherwise), 7 Z is the number of years of education of the farmer, 8 Z is the dummy variable for access to off-farm income (value of 1 if yes and 0 if otherwise) and 9 Z is the dummy variable for access to chili cultivation related training (value of 1 if yes and 0 if otherwise).
1 ofKodde and Palm (1986, p. 1246), ***Corresponds to 1% significance level.the specified frontier function and the presence of inefficiency effects and the relevance of farm-specific and socio-economic factors in explaining the inefficiency of the chili farms.The tested hypotheses are: (1), the null hypothesis that the coefficients of the second-order variables in the translog models are zero; (2) *, ***Statistically significant at leve ls of 0.1, 0.05, and 0.01 respectively.

Table 1 .
Hypotheses test for the stochastic frontier production function.

Table 2 .
Hypotheses test for the stochastic frontier cost function.

Table 3 .
Maximum likelihood estimates of the stochastic frontier production function.

Table 4 .
Maximum likelihood estimates of the stochastic frontier cost function.

Table 5 .
Technical and allocative inefficiency models.
Mariano et al. (2011)ano et al. (2011).Contrary to expectations, chili farmers who had access to some form of training in chili cultivation operate with less allocative efficiency than those who do not have access to such forms of training.This can be attributed to the infrequent nature of the training since majority of those who were trained could not remember the last time they received such forms of training.