Technical Efficiency of Yam Producers: The Case of the Municipality of Glazoue in Benin

In Benin republic, yam plays an important role both in production systems and in people’s food security and trade. In view of the decline in agricultural yields in recent years combined with strong population growth, it is essential today to analyse the technical efficiency of yam producers in order to formulate the best recommendations for relaunching yam production. The objective of this paper is to analyse the technical efficiency of yam producers in Benin and its determinants. To achieve this objective, data were collected from 150 yam producers living in the Municipality of Glazoué. A stochastic production frontier is used to analyse the technical efficiency of the yam producer. The results revealed that the mean efficiency score of producers is around 80%. This implies that yam production could be increase by 20% through better use of available resources such as land, labour, herbicides, taking into account the state of technology. Access to credit and mobile phone ownership increase the inefficiency of actors while experience in agricultural production, age and household size reduce the inefficiency of producers.


Introduction
Yam is one of Benin's main food crops. It plays an important role both in production systems and in people's food security and trade. It also plays an important role in activating social and cultural identities. In several traditional yam-producing localities, rituals are organized to mark the release of the new yam. But the consumption of yam and its by-products goes well beyond its traditional era of production and extends to the cities (Bricas & Attaie 1998;Adanguidi, 2000). Its production, estimated at 1.45 million tonnes in 2008, increased to 2.65 million tonnes in 2015 (MAEP, 2017), an 83% increase over 8 years. On the other hand, over the same time horizon, yam yield fell from 14.48 tonnes/Ha in 2008 to 13.08 tonnes/Ha in 2015, a 10% decrease compared to its 2008 level. This means that the increase in production observed over the period would probably be due to extensive agriculture. At the same time, Benin is facing significant population growth: The country's population has tripled in 34 years, from 3 331 210 inhabitants according to the RGPH1 of 1979 to 10 008 749 inhabitants according to the RGPH4 of 2013). However, according to Bricas (1999), Benin is one of the countries where per capita yam consumption has remained high since the 1960s (more than 40 kg/person/year on average). In the Strategic Plan for the Revival of the Agricultural Sector (PSRSA 2011(PSRSA -2015, the Government of Benin had selected yams as one of the thirteen priority agricultural sectors to be promoted. However, in view of the decline in yam yields in recent years, it is vital to analyse the efficiency of yam producers in order to better formulate recommendations for policy makers. According to Farrell (1957), improving efficiency has a positive impact on productivity by saving resources. This reduces discrepancies between current and potential results (Audibert, 1997).
In Benin, few studies have struggled to analyse the technical efficiency of yam producers. This paper targets to close this gap through the case study of Glazoué, a locality of Benin which is very well known for its yam production and which also hosts the country's largest yam market. The article will be presented as follows: The first will review the empirical literature on the subject. The second part will be devoted to the methodological framework of the study. In the third part, we will discuss the results of the study. In the last part, we will draw conclusions and make some recommendations.

Literature Review
Two methods are generally used for efficiency studies: (1) the first one is the parametric method which is called stochastic production frontier; (2) and the second one is called non-parametric method and is known as DEA (Data Envelopment Analysis). Studies reveal strong potential for increasing agricultural production if the various agricultural inputs were efficiently used. Degla (2015) found, based on a sample of cashew nut producers in Benin, that the average technical efficiency score was 63%. Kpenavoun Chogou, Gandonou, and Fiogbe (2017) estimated the average technical efficiency score of pineapple producers in southern Benin at 67%. Amegnaglo (2018) and Toléba, Biaou, Zannou, and Saïdou (2016) found that growth in current maize production of about 25% and 20% respectively can be accomplished in the short term by adopting best agricultural practices and addressing socio-economic and structural constraints. Regarding yam production, the studies suggested that inputs were not being used efficiently in their respective study areas, a better level of production would have been achieved if the resources had been used efficiently all other things being equal (Ekunwe & Orewa, 2007;Ogunniyi & Ajao, 2012;Reuben & Barau, 2012). Ekunwe and Orewa (2007) found that the average technical efficiency score of yam producers in Nigeria is 62%, Ogunniyi and Ajao (2012) estimated that the mean technical efficiency score of yam producers in Oyo State in Nigeria is 54.4%. Awoniyi, Abiodun, and Titus (2006) suggested that the technical efficiency of yam producers in Ekiti State, Nigeria, varies between 76 and 80% depending on the production system.
The main factors affecting the efficiency of yam producers vary according to the authors. Ekunwe and Orewa (2007) suggested that experience and age increase the technical efficiency of yam producers in Kogi State, Nigeria. Ogunniyi and Ajao (2012) indicated that farm size, hired labour, yam variety and equipment are the main factors influencing variations in yam production in Oyo State, Nigeria. The determinants of producer inefficiency are farming experience, diversification and access to agricultural extension (Awoniyi et al., 2006;Ogunniyi & Ajao, 2012). The main determinants of yam production in Taraba State in Nigeria are the amount of seed used, farming experience and farm size (Reuben & Barau, 2012). In addition, the same authors point out the underutilization of seeds, chemical fertilizers (Note 1) and land in yam production and the overuse of hired labour, herbicides and insecticides. Market imperfections justify the inefficient use of production factors. The high cost of chemical fertilizers, labour, and the difficulties of storing yam seeds push producers to limit the area of yam cultivated.

Methodology
Two main families of methods are used to measure efficiency according to the Farrell conception: parametric and non-parametric methods. The parametric methods assume that the frontier function is represented by a function with explicit parameters (Cobb-Douglas or Translog) while the non-parametric methods consider that the production process studied does not a priori have a well-defined functional form. The non-parametric approach uses the DEA (Data Envelopment Analysis, DEA) method introduced by Charnes, Cooper, and Rhodes (1978). The DEA method consists in using mathematical programming to construct a fragmented production frontier from all the data of the production units. The DEA approach allows the model to be estimated by constant returns to scale (Constant Returns to Scale, CRS) or variable returns to scale (Variable Returns to Scale, VRS). In addition, the DEA approach allows the estimation of multi-product and multi-input production frontiers without the imposition of additional restrictions. However, non-parametric methods do not take into account random variations (weather conditions, parasitic episodes, etc.) that are not under the control of farmers, which could influence the efficiency or inefficiency of a farm. Also, non-parametric methods do not allow to test the statistical properties. Finally, non-parametric methods are very sensitive to extreme observations, which are largely responsible for determining this function, and recent developments in parametric approaches make them more robust, less sensitive to extreme values, measurement errors and statistical noise and allow statistical testing (Cazals, Florens, & Simar, 2002;Simar & Wilson, 2007, 2011. Parametric methods are most commonly used in sectors with low random variations or in multi-product and multi-input production sectors. non-parametric methods. The SFA approach makes it possible to consider exogenous factors (climatic conditions, pest outbreaks, etc.) that are out of farmers' control, but which can affect the producers' performance. SFA approach can also control for measurement errors, statistical noise and differential technological adoption rate (Aigner, Lovell, & Schmidt, 1977;Meeusen & van Den Broeck, 1977).
Based on Farrell's (1957) conception of technical efficiency, Aigner, Lovell, and Schmidt (1977) and Meeusen and van Den Broeck (1977) suggested that the production technology of an agricultural product can be represented by a stochastic frontier production function. The model is as follows: where Y is the level of production of a producer i; f X , β is a Cobb-Douglas or Translog production function and represent the maximum feasible quantity of production possible X (input vector) and β is a vector of parameters. ε is the error term composed of two independent elements v and u as ε v u .
Production may differ from the deterministic frontier due to random shocks v which may be positive or negative, or due to a non-negative inefficiency error term, and u which reduces production (u 0). v is identically distributed with a zero mean and constant variance assumed to be independent of u .
The technical efficiency (TE) of the i th producer is: TE is the relationship between real and potential output. The maximum value the TE can take is 1 while the minimum is 0, reflecting the inefficiency. The imposition of an appropriate distribution form for the inefficiency error term u is required in order to estimate correctly the parameters of the production function. Assuming that the inefficiency terms follow a semi-normal distribution which means ~ 0, ), the technical efficiency is defined as follows: ( 3) where is a vector of independents variables associated with the technical inefficiency and θ is the error term of inefficiency.

Model Specification
A Cobb-Douglas production was chosen because it is flexible, and its returns to scale and is easily interpreted (Bravo-Ureta & Evenson, 1994).
where we simultaneously model the average of the subsequent distribution of inefficiency at the farm level as exp ∑ . Y i is the production of yam (tons) produced during the 2018 season by the i th producer; X is a set of inputs, namely: land size, labour, seeds, weedicides, capital, fertilizers, β represents parameters to be estimated; v i denotes random shocks; u i is the non-negative unilateral error representing inefficiency terms. The model specification used is described in equation (5) below.

_ _
(5) where Output corresponds to the yam production (tons) and ε corresponds to the error term of the equation. Table  1 provides details on the variables used in the regression analysis and their measures.

The Inefficiency Model
The inefficiency model of yam producers is defined as follows: ∑ (6) Where δ is a vector of parameters to be estimated; Z is the vector of variables that are possible source of inefficiency for the yam producer i. It is composed of the age of the yam producer (Z 1 ), the squared age of the producer (Z 2 ), the producer's experience (Z 3 ), the size of the producer's household (Z 4 ), the access to agricultural credit (Z 5 ), the area of yam cultivated (Z 6 ), the producer's education level (Z 7 ), hired labour' use (Z 8 ), and finally the possession of a mobile phone (Z 9 ).The variables that explain the farmer inefficiency equation are explained in Table 1. This study adopts a two-step procedure to estimate the technical efficiency of yam producers. Fractional Regression Model proposed by Papke and Wooldridge (1996) is used for the second step estimation since efficiency scores are proportions. Maximum likelihood method was used to estimate the production functions and inefficiencies of yam producers. The estimate was made in a single step on STATA from the FRONTIER program.

Study Area and Sampling Techniques
First, we chose the study region. The area that can be described as Benin's "Yam belt" consists of the departments of Alibori, Atacora, Borgou, Donga, Zou and Collines, which, according to statistics from the Ministry of Agriculture, Livestock and Fisheries, account for nearly 99% of national yam production over the period 1997-2017. In this area, the Municipality of Glazoué located in the department of Collines is known to be a large yam production area (table 2) and also has the largest yam market in Benin. We have therefore selected this municipality for this study. The second step of the selection process was the random selection of 12 villages in Glazoué. The choice of villages was based on interviews with several resource persons, extension agents and producers in the commune. The third step was the random selection of farmers. The sample size for the study is 150 yam producers.

Descriptive Statistics
Yam producers are almost entirely male (Table 3). On average, the producer is 43 years old and has been growing yams since 19.42 years.

Stochastic Production Function
The estimated parameters of the stochastic production function are summarised in Table 4. The results of the estimation indicate the presence of technical inefficiency among yam producers in the municipality of Glazoué. The estimated lambda coefficient is significant and well above zero. The hypothesis of no inefficiency is therefore rejected at 1%.
The estimation of the stochastic production model reveals that only land and herbicide factors have a significant and positive effect on yam production in the municipality of Glazoué. Yam production is very poorly mechanized (use of hoe and cutting) and very few producers use fertilizers. The few producers who use fertilizers use very small amounts of fertilizer. The increase in the area cultivated by one percent will contribute to an increase in yam yields by 0.82 percent. The increase in areas cultivated is generally on new land that is generally rich, justifying the positive effect of cultivated areas on yam yields. Also the low use of the market inputs (off-farm inputs such as seeds, fertilizers, herbicides, equipment, etc.) is another reason for the positive effect of land. Also, the increased use of herbicides contributes to higher yields. The parameters estimated in the technical inefficiency model revealed that age, agricultural production experience, access to credit, household size and mobile phone ownership affect significantly yam producers' technical inefficiency (Table 5). Age, experience in agricultural production and household size affect significantly and negatively technical inefficiency of yam producers. The results imply that older producers are less inefficient than younger ones. This result is in line with the experience result. Experience allows producers to make rational use of all available resources to the best of the available information. Household size also reduces producer inefficiency. Producers with large households will then have more manpower at their disposal, which will allow them to take better care of their agricultural activities.
Access to agricultural credit and mobile phone ownership increase producers' inefficiency. The positive effect of credit on inefficiency may be due to insufficient access to credit (Diagne & Zeller, 2001) or credit diversion (Feder, Lau, Lin & Luo, 1990). The credit obtained for production reasons is then used in part or totally to smooth consumption. Mobile phone ownership affect positively inefficiency of yam producers, which may be due to a diversion of productive resources to this medium.

Technical Efficiency of Yam Producers
The technical efficiency of yam producers varies from 0.39 to 0.94 (Table 6). The mean technical efficiency is estimated at 0.80, which means that about 20% of potential technical output is not achieved. Cross-analysis of efficiency scores with producer yields reveals that 64 percent of producers have an efficiency level below 80% and this majority has an average yield of 2.3 tonnes per hectare. Also the 36% with an above-average level of technical efficiency have an average yield of 3.6 tonnes of yams per hectare. The correlation rate between the efficiency level and the producer's performance is 0.72, indicating a strong positive correlation between the two variables. So the most efficient producers have a better yield. Improving the level of efficiency would therefore lead to an increase in the producer's yield.

Conclusion
This study analysed the technical efficiency of yam producers in the Municipality of Glazoué in Benin based on a sample of 150 producers. The results revealed that yam production is very poorly mechanized with little use of off-farm inputs. Production depends mainly on land and labour factors. The average efficiency score of producers is 80%, meaning that yam production could be increased by 20% through better use of available resources such as land, labour, herbicides and taking into account the state of technology. Producers with low yields have the lowest efficiency scores. Access to credit and mobile phone ownership increase the inefficiency of actors while experience in agricultural production, age and household size reduce the inefficiency of yam producers. Based on the results, decision-makers could improve yam production through better and reliable access to key inputs such as fertilizers, labour, seeds and equipment. An improvement of the institutional environment can also contribute to a reliable access to markets and extension services for farmers.