Analysis of Profit Efficiency Among Smallholder Maize Producers

Reader Impact Factor Score
[Total: 4 Average: 5]

Published on International Journal of Economics & Business
Publication Date: May, 2019

Asrat Anye Aka
Departement of Economics, College of Business and Economics, Hawassa University
Hawassa Ethiopia

Journal Full Text PDF: Analysis of Profit Efficiency Among Smallholder Maize Producers (Evidence from Damot Pulasa District, Wolaita Zone, Ethiopia).

Abstract
Coping with increased population and running a profitable venture are major problems in developing countries of which Ethiopia is one. In Ethiopia, agriculture is leading sector in meeting these big concerns and maize is one of the most important crops in the country. Thus the main objective of this study was to analyze profit efficiency of maize production among smallholder famers and to assess the effects of socio-economic variables on the profit inefficiency in Damot pulasa district; wolayta zone of SNNPRS. Data for the study were collected using the multi-stage sampling technique, and administering structured questionnaires to a total of 246 randomly selected respondents from five kebeles. Data collected were analyzed using descriptive statistics and econometric models. The study employed translog stochastic frontier profit function model. The results showed that profit efficiencies of the farmers varied widely between 24.6% and 99% with a mean of 78.4% suggesting that an estimated 21.6% of the profit was lost due to a combination of both technical and allocative ineffiaciencies in maize production. From the inefficiency model, it was found that education; experience, extension, soil conservation practice, credit service, non-farm employment and access to markets were significant factors influencing profit efficiency. This implies that profit inefficiency in maize production can be reduced significantly with improvement in the level of education of sampled farmers. As maize is one of the most important staple foods of great socio-economic value in the study area, an improvement in the understanding of the level of profitability can greatly aid policy makers in enhancing policies that will promote profitability in production of the crop. In addition, acquisition of formal education, improving rural financial markets and strengthening the existing extension services were recommended to improve profitability in maize production in the area. Furthermore, the study will go a long way to help other researchers and research institutions in further research for more effective combinations of resources for better efficiencies as well as increase output and productivity in the farming business, it would also help the government, policy makers and other donor agencies in planning, designing and formulations of agricultural programs that would tend towards increase resource, resource availability as well as affordability.

Keywords: Maize producers, Profit efficiency, inefficiency model, translog model, Ethiopia.

1. INTRODUCTION
This chapter deals with background of the study, statement of the problem, research questions, objectives, significance, scope, organization and limitations of the Study.

1.1 Background of the study
Resource allocation influences profitability or productivity of crop enterprises, particularly among smallholder agricultural systems, yet many empirical studies tend to ignore this fact. Agricultural productivity and efficient use of scarce natural resources such as agricultural land and variable inputs remain an important focus of government policies in sub-Saharan Africa (Isaac et al, 2014). This sustainability objective of governments is even more central in recent times where population pressure and increasing urbanization are continuously generating a decline in agricultural land (Chamberlin et al, 2014; Nin-Pratt & McBride, 2014).
Agriculture is the most important sector for sustaining growth and reducing poverty in Ethiopia. It accounts for 85% of employment, 50% of exports and 43% of Gross Domestic Product (GDP) (FAO, 2010). In spite of its huge economic contribution, the sector is almost entirely dominated by subsistence, small-scale and resource poor farmers. More over lack of adequate farm management practices, low level of modern inputs usage, the depletion of soil organic matter, rain fed dependent agriculture system are major obstacles to sustain agricultural production in the country (Pender and Gebremedhin, 2007; Kassie et al., 2009). In cognizant of these problems, the government of Ethiopia launched Agricultural Development Led Industrialization (ADLI) strategy in 1993 that sets out agriculture as a primary sector to generate more output, employment and income for the people and as the spring board for the development of the other sectors of the economy (Kassa and Abebaw, 2004; Gebremedhin et al., 2009). Following ADLI, one of the major programs formulated by the Ethiopian government is the national extension package program known as Participatory Demonstration and Training Extension System (PADETES). The objective of PADETES is to achieve sustainable development in rural areas through increasing farm productivity (yield), reducing poverty, increasing the level of food security, increasing the volume and variety of industrial raw materials (primary products) and producing for the export market (Kassa, 2003; EEA/EEPRI, 2006). The PADETES program has been intended to focus on supply-driven intensification which consists of promotion of improved seeds, fertilizers and on-farm demonstrations of improved farm practices (Kassa, 2008; Gebremedhin et al., 2009; Asfaw et al., 2012).
However, the performance of the agriculture sector has been very dismal in spite of implementing the national extension package program-PADETES. The country is still vulnerable to recurrent food shortfalls and national food insecurity (Abate et al., 2011). Despite considerable technological changes, agricultural production under improved technology in developing countries including Ethiopia encounters substantial inefficiencies due to farmers’ high degree of unfamiliarity with new technology coupled with poor extension, education, credit and input supply system among others (Alene and Zeller,2005). Since the introduction of new technologies requires intensive management and information, farmers in developing countries with low literacy rates, poor extension services and inadequate physical infrastructures have great difficulty in adopting new technologies, let alone exploiting their full potentials (Alene and Hassan,2006).
Coping with increased population and running a profitable venture are major problems in developing countries of which Ethiopia is one. In Ethiopia, agriculture is leading sector in meeting these big concerns and maize (Zea mays) is one of the most important crops in the country. Annually an estimated amount of over 6 million tons of maize is produced and 75% of it is consumed by the farming households whereas the balance is supplementing the diets of most of the urban poor (Adam and Yitayal, 2014). Maize is one of Ethiopia’s major and strategic cereal crops that have important role in the country’s food security and farmers’ livelihood. According to the results from a DIIVA study titled ‘Improved maize varieties and poverty in rural Ethiopia’, from the 1960s to 2009, the calorie contributions of maize to the Ethiopian diet has doubled to around 20% while, its protein contribution to the country diet has been doubled to 16% in the same period. Maize is grown in 13 agro-ecological zones on about 1,994,813.8 ha (16.08%) of the total grain crop area of which 39% of the total maize area in Ethiopia is now planted with improved varieties. Among all cereals, maize is second to tef (Eragrostistef) in area coverage but first in productivity and total production (CSA, 2014). Maize is currently produced by more farmers than any other crops. According to the agricultural sample survey 2013/14 provided by central statistical agency of Ethiopia, at the national level, there are about 8,809,221 maize-cropping smallholder farmers.
Even though the emphasis was given on maize at looking agronomic factors, limited knowledge exists particularly on socio-economics. Therefore this study would make a contribution to the empirical research in this field. It should also be noted that, the current policy thrust with respect to agriculture in Ethiopia is modernization of the sector. This calls for increased research, on how best to increase productivity, profitability and inform policy. It is hoped that the transformation of the sector can make a significant contribution to poverty reduction efforts. Thrust of this study was therefore to augment the existing empirical body of literature on the economics of the smallholder maize production by focusing on the level of profit efficiency and factors that influence the profit efficiency of maize production on smallholder farmers in Damot pulasa district.

1.2 Statement of the Problem
Efficient use of scarce resources in fostering agricultural production has long been recognized and has motivated considerable research into the extent and sources of efficiency differentials in smallholder farmers. Empirical evidences suggest that improving the productivity of smallholder farmers is important for economic development(Bravo-Ureta and Evenson 1994). Accordingly, many researchers and policymakers have focused their attention on the impact that adoption of new technologies can have on increasing farm productivity and income (Hayami and Ruttan, 1985; Kuznets, 1966; Seligson, 1982). Technically efficient farmers are highly productive because they are able to use a minimum level of inputs to produce a given level of output or produce maximum output from a given level of inputs. Similarly, allocatively efficient farmers tend to run more profitable farming enterprises as they are able to produce a given level of output from minimum costs (Bravo-Ureta and Pinheiro, 1993).
How farmers allocate their resources in response to price incentive is an important determinant of the profitability of the farming enterprise. Both technical and allocative efficiency are important in improving the productivity gains from existing technologies Therefore an approach that can be used to solve the problem of efficient utilization of scarce resources focuses on two questions: first, whether farmers are economically (technically and allocatively) efficient in production and second, what factors determine their level of efficiency? Answers to these two questions provide a clue on how we can assist farmers to be efficient in utilizing their resources employed in production process. Farmers not only need to be more efficient in their production activities, but should also be responsive to market indicators, so that scarce resources are utilized efficiently to increase productivity as well as profitability.
In Ethiopia several studies have been carried out at examining productive efficiency of farmers that is exclusively focused on technical efficiency of the farmers. For instance, (Alene &Hassan, 2003a;Endrias, et al., 2013;Ahmed, et al.,2014).The existing studies have given little attention to measuring profit efficiency of farmers even when the prices of output and input are known in an attempt to examine the allocative efficiency of the farmers. The physical productivity considerations (Technical efficiency) are important improvement in production efficiency, but profit efficiency will lead to greater benefits to agricultural producer in the country. Computing profit efficiency therefore, constitutes a more important source of information for policy makers than the partial vision offered by analyzing cost efficiency (Maudus, et al., 2003).The estimation of a frontier profit function capture firm level production specialization, thus allowing the higher revenues reserved by the firms that produce differentiated or higher quality output to compensate for the higher cost incurred. Technical efficiency is derived from production function which is possible to achieve while realizing sub-optimal profit. Thus, a technically efficient farmer can be kicked out of the market due to failure to achieve profit. On the other hand, in profit measure, we take care of input costs and output prices. This apparent lack of empirical research on profit efficiency of smallholder farmers in Ethiopian agricultural sector drives the heart of this research. To augment profit aspect, it may in fact be entirely appropriate to consider profit efficiency given that most efficiency studies in Ethiopia have focused on technical efficiency.
Maize is largely grown as a cash crop in Damot pulasa district. According to the Woreda office of ARD about 80% of farmers produce maize. Production of the crop is therefore motivated by earning a positive economic return. Meeting this objective requires efficient utilization of scarce resources. Thus, this study was carried out to analyze profit efficiency in maize production and to identify factors that influence efficiency in the study area.

1.3 Research questions
What is the existing mean level of profit efficiency of households in maize production?
What determines profit efficiency and productivity of smallholders’ maize production?
What are the effects of socio-economic variables on the profit efficiency that may be valuable to the policy makers?
What are the distinctive characteristics of maize production system in Damot pulasa district?

1.4 Research hypotheses
Cobb-Douglas function model is the right model for analysis of the level of profit efficiency of smallholder maize farmers in damot pulasa district.
Maize farmers in damot pulasa district are operating on efficient profit frontier.
Variables included in the inefficiency effect model have no effect on the level of profit inefficiency.

1.5 Objectives of the Study
The main objective of this study was to analyze profit efficiency of maize production among smallholder famers at farm level in Damot pulasa district.

1.6 Specific objectives were:
To estimate the level of profit efficiency of rural households in the production of maize in the study area.
To determine farm specific production factors that influence the observed variability of profit efficiency levels among maize producers.
To assess the effects of socio-economic and institutional variables on the profit efficiency that may be valuable to the policy makers.To characterize maize production system in Damot pulasa district.

1.8 Significance of the Study
An understanding of profit efficiency, market indicators and farm – specific characteristics could provide the policy makers with information to design programs that can contribute to measures needed to expand the food production potential for the nation. Therefore the results of this study could be useful for different actors working in the area of maize research and development. Extension workers operating in the study area could use the results and recommendations forwarded on factors that influence profit inefficiency among maize farmers in study area. Similarly this study would contribute the understanding of profit loss with in resource use in smallholder maize producers in Damot pulasa district, while contributing to empirical literature with respect to African agriculture in general, and Ethiopian agriculture in particular as background information for those who would like to conduct related research on the same area.
1.9 Scope of Study
Geographically, this study was conducted in the Damot Pulasa district of Wolaita Zone in SNNPRS, Ethiopia. Smallholder maize producers’ profit efficiency might be related to marketing, consumption, distribution, production, etc. However this study has dealt with efficiency of production and marketing. Conceptually, this study has estimated profit loss and inefficiency scores of maize crop production for selected sample farmers. Methodologically, this study intended to use one production year for cross-sectional data and its generalization is made for Smallholder maize producers in the study area. In addition, this study has been concerned with demographic, socio-economic and institutional factors affecting profit efficiencies in maize production among maize producers.

1.9 Limitations of the Study
According to Best and Khan (2008), limitations are conditions beyond the control of the researcher that may place limitations on the conclusion of the study and their application to other situations. Damot pulasa Woreda is one of densely populated areas with large households’ size. As a result undertaking study in this Woreda needs longer time and enough budgets. However, because of time and budget constraints only five kebels were used for sampling frame which may pose some limitations of the result of the study as representing the Woreda. The study also took one production year cross-sectional data. As a result, the effects of those factors that vary with time are not be incorporated in the study. Again there was inconvenience of respondents to give the right response for all questions because of their personal reason. Some respondents were affected by factors such as suspicion; however the researcher assured them of the confidentiality of the study.

1.10 Organization of the study
This study is organized into five chapters. The first chapter deals with introduction which contains background, statement of the problem, objectives of study, research questions, significance, limitations and scope of the study. The second chapter is concerned with theoretical and empirical review of related literatures and conceptual framework of the study. The third chapter elaborates the research methodology which includes description of the study area, the study design, sampling technique, and methods of data collection, model specification, discussion of the variables and data set that were used in the study. The fourth chapter lists the data and outlines findings and analysis and discussion on significance of the data. Finally, the summary conclusions of the major findings and recommendations, and suggestions for further research are discussed in chapter five.

2. LITERATURE REVIEW AND THEORETICAL FRAMEWORK
This chapter presents a review of literature from a number of studies that are related to this study and elaborates on the theoretical and empirical basis for the study. It presents about maize production and transformation in Ethiopia, the meaning of efficiency, theoretical and empirical literature of technical, allocative and profit efficiency as well as demographic, socio-economic, and institutional factors that affect profit efficiency of stallholder maize producers. The theoretical literature deals with concepts and methods that have been advanced to explain types of efficiencies, profit function and profit inefficiency model. The empirical literature provides evidences from past studies related to the factors that affect technical, allocative and profit efficiencies in maize production, including studies specifically carried out in Africa and Ethiopia. The last part elaborates conceptual frame work of the study.

2.1 The maize production in Ethiopia
Maize is the second most widely cultivated crop in Ethiopia and is grown under diverse agro-ecologies and socioeconomic conditions typically under rain-fed production. The maize agro-ecologies in Ethiopia can be broadly divided into six major categories (MOA 2005), including Moist and Semi-moist mid-altitudes (1700–2000 m above sea level; 1000–1200 mm rainfall), Moist upper mid-altitudes (2000– 2400 m; >1200 mm), Dry mid-altitudes (1000–1600 m; 650–900 mm), Moist lower mid-altitudes (900–1500 m; 900–1200 mm), Moist lowlands (<900 m, 900–1200 mm), and Dry lowlands (<1000 m, <700 mm)). The moist and semi-moist mid-altitude zones comprise the bulk of the national maize area in Ethiopia. These are mostly located in the South West and West Oromia, West and North West Amhara, parts of the Southern Nations Nationalities and Peoples Region (SNNPR), and Ben Shangul-Gumuz (BSG). Taken together, the Semi-moist and Moist ecologies cover about 75 % of the national maize production area whereas the dry ecologies cover the remaining 25 %.
Smallholder farms account for more than 95 % of the total maize area and production in Ethiopia. The farmers use animal traction for land preparation and cultivation; almost all production is rain fed, irrigated areas accounting for only about 1 % of the total. More than 9 million households, more than for any other crop, grow maize in Ethiopia (CSA, 2011–13 data). The annual rate of growth for the number of households cultivating maize grew at 3.5 % each year between 2004 and 2013, compared to 3.0 % for sorghum, 3.1 % for teff, 2.1 % for wheat, and 1.8 % for barley. At present, as a sub-Saharan country, Ethiopia has the fifth largest area devoted to maize but is second, only to South Africa, in yield and third, after South Africa and Nigeria, in production. It is interesting to see that the increases in maize production in Ethiopia resulted more from increases in productivity rather than area expansion – i.e., the yield grew faster than the area. On average, maize area and productivity increased by 4.0 and 6.3 % per annum, respectively, during the 10 years between 2004 and 2013. The current performance of maize in Ethiopia compares favorably with the main maize producing countries in SSA. Ethiopia is the only country in SSA outside South Africa that has attained >3 MT/ha yield; only Zambia and Uganda have achieved >2.5MT/ha, followed by Malawi, with >2 MT/ha. The SSA average is about 1.8 MT/ha. Largely because of the increasing demand (Rosegrant et al. 2001) driven by population growth and competitiveness of the crop, maize area in Ethiopia also doubled during the past two decades from 1 to 2 million ha.

2.1.1 Maize transformation in Ethiopia
The expansion and productivity change in maize production in Ethiopia is attributable to multiple factors. These include a) increased availability of modern varieties, b) increased commitment to enhance farmer access to and use of modern inputs through better research-extension linkages, c) wider adaptability of the crop and modern varieties, d) better production conditions and low production risks and e) growing consumption demand and market access for producers to support market based production to absorb surplus supply (Tsedeke et al., 2015).

2.2 Meaning of Efficiency
The analysis of efficiency dates back to Knight (1933), Debrew (1951) and Koopmans (1951). Koopmans (1951) provided a definition of technical efficiency while Debrew (1951) introduced its first measure of the ‘coefficient or resource utilization’. Following on Debrew in a seminal paper. Farrell (1957) provided a definition of frontier production functions, which embodied the idea of maximality. Farrell (1957) distinguished three types of efficiency: 1) technical efficiency 2) price or allocative efficiency and 3) economic efficiency which is the combination of the first two.
Technical efficiency is an engineering concept referring to the input-output relationship. A firm is said to be efficient if it is operating on the production frontier (Ali and Byerlee, 1991). On the other hand, a firm is said to be technically inefficient when it fails to achieve the maximum output from the given inputs, or fails to operate on the production frontier. Mbowa (1996) in his study on the sugarcane industry in South Africa defined an efficient farm as that which utilizes fewer resources than other farms to generate a given quantity of output. Yilma (1996), while studying efficiency among the smallholder coffee producers in Uganda, defined an efficient farm as that which produces more output from the same measurable inputs than that one which produces less. Fan (1999) referred to technical inefficiency as a state in which actual or observed output from a given input mix is less than the maximum possible.
Price or allocative efficiency has to do with the profit maximizing principle. Under competitive conditions, a firm is said to be allocatively efficient if it equates the marginal returns of factor inputs to the market price of output (Fan, 1999). Akinwumi and Djato (1996) in their study of relative efficiency of women farm managers in Cote d’Ivoire define allocative efficiency as the extent to which farmers make efficient decisions by using inputs up to the level at which their marginal contribution to production value is equal to factor costs. Failure to equate revenue product of some or all factors to their marginal cost is at the very core of economic theory (Timmer, 1971). Similarly, Ali and Byerlee (1991) agree with this definition in their review of economic efficiency of small farmers in a changing world. They contend that allocative inefficiency is failure to meet the marginal conditions for profit maximization. Thus allocative inefficiency is failure of a farmer to equate marginal returns of factor inputs to its price.
Economic efficiency is distinct from the other two even though it is the product of technical and allocative efficiency (Farrell, 1957). A firm that is economically efficient should by definition be both technically and allocatively efficient. However, this is not always the case as Akinwumi and Djato (1997) pointed out. It is possible for a firm to have either technical or allocative efficiency without having economic efficiency. The reason may be that the farmer, in this case, is unable to make efficient decisions as far as the use of inputs is concerned. In some cases, a farmer might fail to equate marginal input cost to marginal value of product. If technical and allocative efficiency occur together they are both a necessary and a sufficient condition for economic efficiency. This assumes that the farmer has made right decision to minimize costs and maximize profits implying operating on the profit frontier. However, one needs to recognize that in least developed countries (LDC’s) there are inherent market failures due to a number of reasons such as unwarranted government interventions, lack of information on the markets and poor infrastructure. Notwithstanding this phenomenon, this study adopts a definition of efficiency, which encompasses technical and allocative efficiency, in essence economic efficiency. Apart from these definitions, literature on efficiency distinguishes many other forms of efficiency and these are productive, scale (economies of size) and economies of scope and x-efficiency. Production is said to be efficient if it is not possible to produce more of one good without taking resources away from production of another good (Binger and Hoffman, 1998). From the discussion by Wang et al., (1996b) production efficiency is equivalent to economic efficiency because it combines two components, that is, technical and allocative efficiency. Scale efficiency can also arise from spreading the cost of production, particularly fixed costs over a large output. Taking an example of an assembly line, it would not be cost effective if the firm opts to produce a few cars a year when it is capable of producing a large number of cars to achieve low per unit cost. The assembly reaps economies of scale when it experiences substantial cost savings at relatively high output (Binger and Hoffman, 1998). But the firm can experience diseconomies of scale due to coordination problems. According to (Sadoulet and Alain de Janvry, 1995) the presence of economies of scale in agriculture is not conclusive.
Economies of scope exist when a firm decides to put two separate enterprises under one management. The enterprises share the same factors of production such as labour and in the process cut down on costs. In the process of sharing the factors, the management saves on costs and as such it is able to reap economies of scope. X-efficiency is realized through motivating staff who in turn work hard to produce maximum output.

2.3 Efficiency: One of Sources for Economic growth
Raw materials yield less satisfaction to the consumer by themselves. In order to get utility from raw materials, first they must be transformed into output. However, transforming raw materials into final products require factor inputs such as land, labor, capital and entrepreneurial ability (Zalkuwi, 2010).
Jema(2008) defined economic growth as an increase in production. Production may be increased through variety of ways. First, through increased use of inputs usually called horizontal expansion. In order for farmers to increase their input use, either output prices must increase or the input prices must fall, or both, which have little applicability for the resource poor smallholder farmers. Second source of economic growth is that attained throw improvement in efficiency in resource utilization usually referred as the improvement approach. This approach requires the improvement of conditions or the removal of some of the existing institutional constraints that hinder farmers from using existing resources efficiently. Third source of growth is what is usually referred to as the transformation approach. It is economic growth attained through in technological (technical changes) that result in shifting the production function upward. This approach is also less applicable in Ethiopia, because it is costly and demands a set of skills and knowledge. Fourth source of economic growth is the impact of the environment in which the production takes place. For example good weather tends to increase output but bad weather hinders it.
Hence productivity changes due to difference in production technology, difference in efficiency of production process, and difference in the environment in which production takes. Therefore economic growth can be attained either by increasing the inputs and or by increasing productivity. In general an increase in production inputs result in move along the frontier while increase in productivity leads to a shift in the frontier.

2.4 Theoretical Basis for Measurement of Efficiency
2.4.1 Technical, Allocative and Economic Efficiency
Measurement of economic efficiency requires an understanding of the decision making behavior of the producer. A rational producer, producing a single output from a number of inputs, x = x1……xn, that are purchased at given input prices, w = w1…wn and operating on a production frontier will be deemed to be efficient. But if the producer is using a combination of inputs in such a way that it fails to maximize output or can use less inputs to attain the same output, then the producer is not economically efficient. A given combination of input and output is therefore economically efficient if it is both technically and allocativelly efficient; that is, when the related input ratio is on both the isoquant and the expansion path. These contentions are best illustrated in the figure 1.In figure 1, AB is an isoquant, representing technically efficient combinations of inputs, x1 and x2, used in producing output Q.AB is also known as the ‘best practice’ production frontier. DD’ is an iso-cost line, which shows all combinations of inputs x1 and x2 such that input costs sum to the same total cost of production. However, any firm intending to maximize profits has to produce at Q’, which is a point of tangency and representing the least cost combination of x1 and x2 in production of Q. At point Q’ the producer is economically efficient.

Turning to measurement of technical, allocative and economic efficiency, the same figure 1 is employed. Suppose a farmer is producing its output depicted by isoquant AB with input combination level of (X1and X2) in figure1. At this point (P) of input combination the production is not technically efficient because the level of inputs needed to produce the same quantity is Q on isoquant AB. In other words, the farmer can produce at any point on AB with fewer inputs (X1 and X2) in this case at Q in an input-input space. The degree of technical efficiency of such a farm is measured as OQ/OP. OQ/OP is the proportional reduction of all inputs that could theoretically be achieved without any reduction in output.
In figure1, DD’ represent input price ratio or iso-cost line, which gives the minimum expenditure for which a firm intending to maximize profit should adopt. The same farm using (X1 and X2) to produce output P would be allocatively inefficient in relation to R. Its level of allocative efficiency is represented by OR/OQ, since the distance RQ represents the reduction in production costs if the farmer using the combination of input (X1 and X2) was to produce at any point on DD’, particularly R instead of P.
The overall (economic) efficiency is measured as the product of OQ/OP and OR/OQ, which is OR/OP. This follows from interpretation of distance RP as the reduction in costs if a technically and allocatively inefficient producer at P were to become efficient (both technically and allocatively) at Q’. These forms reflect alternative behavioral objectives (i.e. profit maximization or cost minimization) and can account for multiple outputs (Coelli, 1995).
Recent developments combine both measures (technical and allocative) into one system, which enables more efficient estimates to be obtained by simultaneous estimation of the system (e.g., Ali and Flinn, 1989; and Wang, et al., 1996). The popular approach to measure efficiency, the technical efficiency component, is the use of frontier production function (e.g., Battesse and Coelli, 1995; Tzouvelekas, et al., 2001; Wadud and White, 2000). However, Yotopolous and others argue that a production function approach to measure efficiency may not be appropriate when farmers face different prices and have different factor endowments. This led to the application of stochastic profit function models to estimate farm specific efficiency directly (e.g., Ali and Flinn, 1989; Wang et al., 1996; Hyuha et al, 2007).
The profit function approach combines the concepts of technical and allocative efficiency in the profit relationship and any errors in the production decision are assumed to be translated into lower profits or revenue for the producer (Ali et al., 1994).

2.3.2 Profit Function
A profit function is an extension and formalization of the production decisions. A farmer is assumed to choose a combination of variable inputs and outputs that maximize profit subject to technology constraint (Sadoulet and De Janvry, 1995). The underlying production function can be generalized as h (q, x, z) = 0 where q is a vector of output, x is a vector of variable inputs, z is a vector of fixed inputs and h is a technology. There for restricted profit function is specified as follows:
Max p.q-wx,……………., s.t. h(q,x,z)=0…………………………………………..(1

Where: p is a vector of prices of outputs and w is a vector of prices of variable inputs considering a set of inputs and outputs the profit maximizing input demand and output supply functions are generally respectively expressed as:
X = x (p, w, z)…………………………………………………………. (2)
Q = q (p, w, z)…………………………………………………………. (3)
Substituting equation 2 and 3 into1 gives a profit function which is the maximum profit that the farmer can obtain given prices of p and w, availability of fixed factors z and production technology h(.). The profit function can be written as:
πi=p’q(p,w,z-w’x(p,w,z)………………………………………………………… (4)
This study uses the normalized profit function outlined in equation 5 given the fact that the study is dealing with a single output, that is, maize (Sadoulet and De Janvry, 1995). Hence for maize, we have:
πi= (Pij, Zik). exp (℮i )………………………………………………………..(5)
This makes profit non-linear in its error term. However, the profit function can be loglinearized to obtain the form:
ln i = lnf(.) + ei.
Where: πi=normalized profit on firm i defined as gross revenue minus variable cost divided by the output price.
Pij= prices of variable input j on firm i divided by the output price.
Zik=level of fixed input on firm i where k are a number of fixed inputs.
i =1…n number of farms in the sample.
℮ i =error term assumed to behave in a manner consistent with the frontier concept (Ali and Flinn, 1989). Figure 2 shows the stochastic profit frontier function adopted from Ali and Flinn, (1989). The stochastic profit frontier function is an extension of incorporating farm level prices and input use in the frontier production function. The incorporation of the farm specific level prices leads to the profit function approach formulation (Wang et al., 1996a).
A production approach to measure efficiency may not be appropriate when farmers face different prices and have different factor endowment (Ali and Flinn, 1989). Hence the uses of stochastic profit function to estimate farm specific efficiency directly. The profit function approach combines the concepts of technical, allocative and scale inefficiency in the profit relationships and any errors in the production decision translate into lower profits or revenue for the producer Rahman (2003). Profit efficiency is defined as the ability of a farm to achieve highest possible profit given the prices and levels of fixed factors of that farm and profit inefficiency in this context is defined as the loss of profit from not operating on the frontier (Ali and Flinn, 1989).

Normalized input price given fixed resources Pi/Zj
Figure 2: Frontier MLE and OLS Stochastic Profit Function Source: Ali and Flinn(1989).
In the context of frontier literature, DD’ in figure 2 represents profit frontier of farms in the industry (the best practice firm in the industry with the given technology). EE’ is the average response function (profit function) that does not take into account the farm specific inefficiencies. All farms that fall below DD’ are not attaining optimal profit given the prevailing input and output prices in the product and the input markets. They are producing at allocativelly inefficient point F in relation to M in Figure 2. Profit inefficiency is defined as profit loss of not operating on the frontier. In Figure 2, a firm operating at F is not efficient and its profit inefficiency is measured as FP/MP (Ali and Flinn, 1989; Sadoulet and Janvry, 1995).

2.4 Profit Inefficiency Model
The issue of whether a farmer in a developing country is responsive to economic incentive is now a mute point. The attention has shifted to how the whole system works (Ali and Byerlee, 1991). From an engineering point of view, a system is said to be efficient if maximum output is generated from the given input keeping other factors constant. If this ideal position does not obtain, it is said to be inefficient and the sources of inefficiency could either be internal or external. In agriculture, a farmer has to pay attention to relative prices of the inputs such that the production is undertaken at the point where the isoquant is tangent to isocost line (Figure1 point Q). If that is not done, economic efficiency is not achieved. The farmer may be able to achieve technical efficiency but not allocative efficiency. This inefficiency could arise from a number of sources, which include access to appropriate information in a timely manner or lack of skills to take advantage of modern agricultural inputs. Basically, what is being referred to here is the managerial ability of the farmer. The farmer should be able to make decisions that lead to optimal utilization of resources and this requires accurate information on availability of the new varieties, the inputs, and access to markets.
Besides, the farmer’s inability to make optimal decisions may be due to external factors, which lie outside his/her capacity. These include untimely input supply, bad weather, non-conducive policies and other random shocks such as wars, floods, pests and diseases, droughts, and statistical errors. Inefficiency could also arise from the introduction of new varieties without adequate provision of back-up packages to the farmers. In this learning stage, a farmer could appear inefficient while he/she is not, due to the fact that he/she is unfamiliar with the new variety. One has to recognize that it takes time to learn new agronomic practices. During this learning stage, production functions among the farmers would differ. Therefore, it is unrealistic to attribute all inefficiency to farmer’s own inability to make rational decisions.
2.5. Technical Efficiency: Empirical Studies
Most empirical studies on productivity and efficiency of farmers indicated that demographic, socio-economic, institutional, environmental and resource factors are the major determinants of efficiency differentials among farmers (Battese&Coelli, 1995; Bravo‐Ureta&Pinheiro, 1997; Obwona, 2006; Nyagaka, et al., 2010).
For instance, in their analysis on technical efficiency of smallholder farmers in Girawa district of Ethiopia, Ahmed ,et al.,(2013) confirmed that technical efficiency of farmers is positively associated with education, extension services, livestock holdings and use of irrigation. Thus, education and extension services increases efficiency of a farmer by increasing awareness and ability on the proper use of farm inputs control of pest and crop diseases and overall management of farm productions. Livestock enhances efficiency directly through their use in farming operation; and indirectly by financing farm income in bad production years. Similarly, Asefa (2012) and (Khai & Yabe, 2011) also confirmed the importance of education, extension services and irrigation in improving technical efficiency of farmers in their respective studies on Ethiopian smallholder farmers and Vetnamise rice producers. Besides demographic and socio-economic factors, environmental conservation also plays key role in enhancing efficiency of farmers. For instance, in his study on the link between technical efficiency and environmental conservations in Ghana, Nkegbe (2012) found that those farmers adopting conservation practices are more technically efficient than non-adopters. Similarly, Solis, et al. (2007) and Jara-Rojas, et al. (2012) also confirmed the role of soil, water and environmental conservations in enhancing technical efficiency of farmers.
Seymour et al.,(1998) used two step procedure proposed by Coelli (1996a) to estimate separate stochastic frontier production function for two group of maize farmers (within and outside Sasakawa Global (SG)2000 project) in Ethiopia. The procedure involves estimating frontier profit function first and then using residuals of this function to estimate the inefficiency effects. Empirical results of the study showed that technical efficiency levels for the participating group were higher than that of the non-participants. Furthermore; the participating group also registered higher mean frontier output than those outside the project. The inefficiency model showed that there exists technical inefficiency in the production of maize. The contributing factors were education, age, and extension contact. Education and extension services had a negative influence on technical inefficiency for those participating in the project. The authors therefore concluded that in order to promote agricultural productivity the government could introduce projects such as SG2000 which appear to have had a positive impact on technical efficiency.
The following table gives an overview of the findings of selected empirical studies on technical efficiency of farmers in Ethiopia. Most of these studies found that education and trainings of the household, extension services, farm size, off-farm income, access to credit and other socio-economic variables are the major determinants of technical efficiency of farmers. The effect of farm size on productivity and efficiency has received much attention in empirical literature where bulk of the studies identifies an inverse relationship between farm size and productivity (Barrett, 2010; Manjunatha et al, 2013; Latruffe & Piet, 2014).
Barrett (2010) aimed to explain possible causes of the inverse relationship which stands in sharp contrast to economic theory, and noted that about one-third of the noise due to imperfect markets explains the significant inverse relationship between farm size and productivity. Manjunatha et al (2013) explained that the efficiency of small farms is due to the fact that owners of such farms use resources more efficiently.

2.6 Review of previous studies on allocative efficiency
According to Chiona (2011) smallholder maize farmers in Zambia experience very low levels of technical and allocative efficiency. The average technical efficiency stood at 15% with only 0.23% of the farmers being efficient while allocative efficiency stood at 12% with only 0.27% of the farmers being efficient. The results also revealed that the use of hybrid seed, farm size, household size, access to extension services and education attainment of the household head were significant determinants of economic efficiency. According to( Henderson and Kingwell,2002) Greater gains in profitability are possible by improving allocative rather than technical efficiency because technically efficient farms are not necessarily allocatively efficient.The authors analyzed the technical and allocative efficiency of broad acre farmers in a southern region of Western Australia over a three-year period. Applying Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) the results revealed some inefficiency in each year, which decreased over time. The empirical results also confirmed that farmers’ education level and farmers’ age positively influenced technical efficiency. Sauer and Mendoza (2007) investigated the well known ‘poor-but-efficient’ hypothesis formulated by Schultz (1964) assuming that small-scale farmers in developing countries were reasonably efficient in allocating their scarce resources by responding positively to price incentives. Contrary to Schultz’s findings, it was assumed that scale effects explain a considerable proportion of small-scale farmers’ relative efficiency. The discussion on theoretical consistency and functional flexibility was considered by imposing convexity on the Generalized Leontief (GL) profit framework. The empirical results confirm the revised hypothesis that purports that small-scale farmers in traditional development settings are ‘poor-but-allocatively efficient’ by clearly suggesting considerable inefficiency with respect to the scale of operations. Laha and Kuri (2011) measured allocative efficiency and its determinants in agriculture practiced in West Bengal by implementing the cost minimization principle using Data Envelopment Analysis. The variable that was found to play a significant role in influencing allocative efficiency was the choice of tenurial contracts. Among the tenurial contracts, fixed rent tenancy was observed to be the most efficient mode of cultivation. The household head’s level of education, operated land, inter-linkage of factor markets and availability of credit facilities were some of the other factors which were found to have significant bearing on the level of allocative efficiency in West Bengal agriculture.

2.7 Profit Function Analysis: Empirical Studies
Maize is the main staple food in Africa such that a lot of research on its level of efficiency has been conducted. Ogunniyi (2011) used translog stochastic profit function to measure profit efficiency among maize producers in Oyo State, Nigeria. The results showed that mean profit efficiency of the farmers was 41.4% suggesting that an estimated 58.6% of the profit is lost due to a combination of both technical and allocative inefficiencies in maize production. From the inefficiency model, it was found that education, experience, extension and non-farm employment were significant factors influencing profit efficiency. Sadiq, et al (2015) using Cobb-Douglas profit function, showed that profit efficiencies of the farmers varied widely between 12% and 95% with a mean of 71% in Nigeria. The mean level of efficiency indicates that there exists room to increase profit by improving the technical and allocative efficiency.
The study conducted at Ghana used the stochastic efficiency frontier model by Bidzakin,et al (2014) showed a measure of profit efficiency of 61% was recorded in the area with a minimum and maximum efficiency of 11% and 100% respectively. This implies there is an opportunity to increase profit by 40%. The inefficiency model showed that educational level, farming experience, and household size have negative coefficients, meaning that as these variables increases the profit efficiency of the farmer increases. Whiles the variables sex of farmer and age are positive and vice versa. This implies female farmers are more efficient than their male counterparts Bidzakin, et al (2014).
Isaac et al (2014) conducted study at Ghana using farm level data from 199 respondents who cultivate maize and cowpea. They employed the stochastic frontier function to measure and compare the profit efficiencies of farmers cultivating the two crops. Results from the analysis showed that the profit efficiency of maize farmers ranges between 47% and 96.7% while that of cowpea farmers ranges between 50.3% and 100% with mean profit efficiencies of 89% and 95% for maize and cowpea respectively. The study further showed that education, farm size and on-farm labour participation were major significant factors which influence profit efficiency in the study area.

2.8 Conceptual framework
Conceptual framework is a diagrammatic representation of variables in a study, their operational definition and how they interact in the study. It shows how the independent variables influence the dependent variable of the study. According to (Dorward and Omamo, 2005) it is assumed that an exogenous set of variables influence same situations of the agents and the behavior of the agents in those situations. This leads to outcomes which provide feedback to modify the exogenous variables, the agents and their situations.
The framework is operationalized as shown in Figure 3 below, which represents how various factors inter-relate to influence maize productivity, profitability and hence the welfare of maize producers. The policy environment is characterized by the existing political and economic trends in the country which have an influence on the farming system and indirectly determine the maize output. However, within the farming system various sets of factors interrelate to determine productivity. Production factors such as seeds, fertilizers, plot size, pesticides and herbicides are used as inputs into the production process. The availability and distribution of these inputs may be influenced by the policy framework in place, which in-turn determines the extent of maze profitability.
Maize productivity is also affected by the farm profit efficiency. This is supported by the notion that for a production process to be effective, the manner in which available farm resources are utilized is crucial. But the farm’s profit efficiency is also influenced by institutional and socio-economic characteristics of the farmer. Institutional factors are expected to influence production efficiency as follows: The access to the market, group membership, and credit-access and extension service are hypothesized to have a positive influence on production efficiency. This is because access to the market increases access to inputs and credit. While group membership is expected to help farmers to mitigate problems associated with market imperfections. On the other hand, credit access provides funds necessary for farmers to overcome liquidity problems that hinder them from purchasing inputs on time. Then access to extension service provides farmers with information on better methods of farming and improved technologies that improve their productivity.
With respect to socio-economic characteristics of the farmer, it is hypothesized that age of the farmer negatively affects profit efficiency. This is because older farmers are risk averse making them late adopters of better agricultural technologies. Off-farm income is expected to have a positive effect on profit efficiency; since farmers with such incomes have a regular source of income that they can use to acquire farm inputs. Schooling is expected to have positive results since; educated farmers committed in farming may be able to take up improved technologies faster because they understand the benefits associated with the technology, hence increasing their efficiency.
In addition, farmer’s experience is expected to positively influence profit efficiency because experienced farmers are better producers, who have learned from their past mistakes; hence they make rational decisions compared to less experienced farmers. Farm size is also hypothesized to have a positive influence in profit efficiency, with larger farmers expected to portray economies of scale in their farming operations compared to smaller farms.
The best allocation of resources is a precondition for maximum household welfare, sustainable land use and food security (Isaac et al., 2014). A farm that is technically and allocatively efficient utilizes resources efficiently expected to realize higher maize output per hectare compared to one that is less efficient in production. On the other hand, such a firm is hypothesized to incur less production costs leading to higher returns from the enterprise. This therefore has positive spillover effects on the welfare of the maize producing households (HH). Improved welfare of the households then provides a feedback effect in form of increased access to production inputs and relevant lessons to policy makers.

Figure 3: Conceptual Framework of factors influencing profit efficiency
Source: adapted from Waluse (2012) and Essa (2011) with modification.

3. RESEARCH METHODOLOGY
This chapter describes the area of study, types and sources of data, Sample size determination and sampling technique, data analysis method. It also elaborates on approaches to measure efficiency, discusses theoretical advances to profit efficiency models explains, justifies and discusses the implementation of the translog model adopted in this study. The chapter concludes by describing variables and their expected signs and discusses model specification tests for data reliability and validity.

3.1 Description of the Study area
Damot pulasa is one of 12 rural Woredas found in Wolaita zone of SNNPRS. It is divided into 23 rural kebeles .Its capital is Shanto which is about 395kms south of Addis Ababa. It is bordered on the east and south by Damot GaleWoreda, on the west by the Boloso Sore, and on the north by the Hadiya Zone. Based on the Woreda finance and economic development office, this Woreda has a total population of 130,398, of which 64,209 are male and 66,189 female; 5.08% of its population is urban dweller. Agro-ecologically the Woreda is categorized into weynadega with two sub-zones; dry and humid weynadega. Geographically, it is located between 6 95’-7 11’N latitude and 37 96’-38 46’E longitude. The area receives mean annual rain fall of 1450mm and daily average temperature of 22.5 .Its altitude ranges from 1200m-1500m above sea level.
The dominant livelihood of the Woreda is agriculture and small scale traditional farming system predominates in the area. Farming system of the study area generally depends on the rain fed agriculture and mixed farming system .There are two cropping seasons in the study area ,i.e. Belg (short rainy season) which runs March to May and Meher (main rainy season) which occurs in the months from June to September. Belg rains are mainly used for land preparation and planting long cycle crops such as maize. The meher rains are used for planting potato, green pepper, haricot bean teff. The main crops grown during the two copping seasons are maize, teff, haricot-bean, potatoes, sweet potatoes, enset, and some parts sugar cane. The major cash crops are maize, teff, potato, green pepper. Among this maize is the most dominant annual crop produced for both cash as well as consumption purposes. According to Woreda office of ARD about 80% of farmers grow maize crop. In addition to crop production; animal husbandry is another livelihood activity of farmers in the area. The main livestock species are cattle, goats, sheep and poultry. Apart from these non-farm activities like petty trade, carpentry, pottery, etc are used as households’ income sources.

Figure 4: Administrative Map of Study area

3.2 Design of the Study
Research design is considered as the blue print and cornerstone of any study since it facilitates various research operations. The nature and objectives to be achieved and the means of obtaining information are the most important factors to be considered in order to choose the appropriate research design. To achieve the stated objectives, both quantitative and qualitative data methods were used to get accurate and more complete information. Using both quantitative qualitative methods at the same time is more advisable. Because quantitative data provides precise summaries and comparisons, while qualitative data provides general elaborations, explanations, meanings, and relatively new ideas. Taking all these into account, multiple approaches which combine both quantitative and qualitative methods were used for theses study. A cross-sectional survey was administered to collect both qualitative and quantitative data that are used the study. The study was completed in less than one year period; therefore cross-sectional study design is the most appropriate one which was employed by this study.

Types and Sources of Data
The study utilized both primary and secondary data to attain the stated objectives. The secondary data were collected from different sources including research papers, booklets, internet, BoFED, EEA, and CSA, from Zone and Woreda sector offices, and unpublished materials. Moreover different published sources including journals were used to collect some secondary data. The primary data were collected through household’s survey and key informant interviews from sample households using structured questionnaires. Moreover FGDs was held during the survey with 10-15 famers, local administrators and DAs. During the survey, information was gathered on issues related to factors that affect profit efficiency in maize production in the study area and farmers’ knowledge about the production of maize. The questionnaire in this study was also structured to elicit responses from the selected farmers on their households’ farming activities. These include information on farm size, material inputs and cost, labor supply and wages, and so on, as well as quantities of maize output and prices. This was expected to increase the explanatory power of the analysis significantly. Socio-economic data of the farmers such as age, level of education, farming experience, extension service and about credit service also have been collected.

3.3.1 Data Reliability and Validity
In order to control for data reliability and validity, measurement and sampling errors; a number of measurements were effected. The first measure taken was to pretest the questionnaire in two of the kebeles. The instrument was tested in Lera and tomtomementa kebeles. This was to ensure that the right questions were asked during the actual field survey. The data obtained during the pre-testing exercise were coded and analyzed to gauge the accuracy of the questions. Second, the enumerators were then trained for one week on how to administer the questionnaire through role-play. Third, while in the field, the author participated in data gathering as well as supervising the field team. Questions that appeared redundant and misplaced were removed. After data collection, field editing was done to check out response errors and if possible corrected before leaving a given location. Data were entered in the STATA computer software to obtain descriptive and necessary transformation such as log linearization conducted. Variables needed for efficiency measurement were then transferred from STATA to Frontier 4.1c program for analysis reliability.

3.4 Sample size determination and sampling technique
3.4.1 Sample size determination
The sample size for the study was determined based on the following formula given by Israel (1992).
…………………………………………………………………………… (6)
Where n is the sample size; Z is 1.96 at 95% confidence level; P is the population proportion i.e. the proportion of maize producers in the study area that was found to be 80%. While d is the margin of error (acceptable error) which was assumed to be 0.05 and q is a weighting variable computed as (1-P)

=246
Therefore the total of 246 households was selected for the study .These households were selected from selected 5 kebeles by using random sampling methods. The sample size was then proportionately disaggregated as follows below table for the five kebeles, based on the proportion of maize growers in each kebeles. The target households of the study are obtained from office of the Woreda ARD.

Table 3.1 Sample Household Distribution for Selected Kebeles

3.4.2 Sampling Techniques
A multi-stage sampling technique was used to select sample farmers in the study area. In the first stage the study Woreda was selected purposively based on the extent and potentiality of maize production. Then the Woreda was clustered into two zones; humid weinadega which includes 13kebeles and dry weinadega which includes 10 kebeles. From these 3 and 2 kebeles were selected randomly from humid and dry weinadega areas respectively. Finally 246 sample households were selected from sampled kebeles using simple random sampling method.

3.5 Methods of Data Analysis
The data collected from different sources were analyzed by using both descriptive statistics and econometric methods. The descriptive method includes percentages, tables, frequencies, standard deviations, etc. The qualitative and quantitative data were tabulated in the way that can enable to understand or compute the view of factors that affect profit efficiency in maize production. And frontier computer programming (version 4.1) software was used for estimation of farm specific profit efficiency scores of maize producers in the study area.
The purpose of using econometric method is to estimate effects of factors on maize profit efficiency by using stochastic frontier profit function with maximum likelihood estimation and factors that affect profit efficiency of smallholder maize producers by using trans log stochastic frontier profit model in the study area. The qualitative data was also summarized and presented to supplement the result of quantitative analysis.

3.6 Analytical Frame work and Empirical Model Specification
3.6.1 Approaches to Measuring Efficiency
Following Farrell’s (1957) work, there has been a proliferation of studies in the field of measuring efficiencies in all fields. But in the field of agriculture, the modeling and estimation of stochastic function, originally proposed by Aigneir et al., (1977) and Meeusen and van den Broeck (1977), has proved to be invaluable. A critical narrative of the frontier literature dealing with farm level efficiency in developing countries conducted by (Battese, 1992; Bravo-Ureta and Penheiro ,1993;Coelli ;1995 and Thiam et al., 2001), indicated that there were wide-ranging theoretical issues that had to be dealt with in measuring efficiency in the context of frontiers and these included selection of functional forms and relevant approaches (parametric as opposed to non-parametric). Parametric and non-parametric models differ in two ways. First, the two models differ on assumptions of the distribution of the error term that represents inefficiency. Second, they differ in the way the functional form is imposed on the data. Parametric methods impose functional and distributional forms on the error term whereas the non-parametric methods do not.
Nevertheless, parametric models suffer from the same criticism as the frontier deterministic models, in a sense that they do not take into account the possible influence of measurement errors and other noises in the data as do stochastic frontier models (Thiam et al., 2001). The results can also be misleading because they do not allow for random error as in stochastic parametric approaches. Besides, non-parametric methods also lack statistical tests that would tell us about the confidence of the results. For this reason, this study adopts the stochastic parametric model and profit function frontier for maize farmers.

3.6.2 Deterministic Versus Stochastic Frontier Models
According to Taylor and Shonkwiler (1986), Afriat (1972) was the first to propose the formulation and application of a deterministic production frontier model. The basic structure of the model is:
Y =ƒ (х, ß) е-μ…………………………………………………………………. (7)
Where ƒ (х, ß) denotes the frontier production function and μ is a one-sided non-negative distribution term. This model imposes constraint of μ≥0, which implies output is less than the potential or it is equal to the potential, within the given input and output prices. According to Taylor and Shonkwiler (1986), the model is in full agreement with production theory, but the main criticism against it is that all the observed variations are accounted for by the management practices as pointed out in section 3.6.1.No account is taken of statistical noise such as random errors, omitted variables and shocks.
Stochastic models begin with Aigner and Chu (1968) who proposed a composed error term, and since their work much effort has been exerted to finding an appropriate model to measure technical efficiency. The result was the development of a stochastic frontier model (Aigner, et al., 1977; Meeusen and van den Broeck, 1977; Battese and Corra, 1977). The model addressed the weaknesses of the deterministic model by introducing ν into the deterministic model to form a composed error term model (stochastic frontier). The error term of the stochastic model is assumed to have two additive components: a symmetric component accounting for pure random factors and a one-sided component that captures the effects of inefficiency relative to stochastic frontier. The model is specified as follows:
ƒ (х, ß) е ν-μ……………………………………………………………………….(8)
where ƒ ( х, ß), is as defined in (7) and ν-μ is error term, ν represents factors external to the farmer and are assumed to be independently and identically distributed (iid) as Ν(0,σν2); μ is half-normal distribution or exponential distribution. The model addresses the weaknesses of the deterministic model. It is also possible to estimate standard errors and test for hypotheses that the observed inefficiency is not due to farmer’s practices only as suggested in deterministic model (Thiam et al., 2001 and Jondrow et al., 1982) provided an explicit formula to separate the two component error term for both half normal distribution and exponential distribution cases. Though this was an improvement over the deterministic model, it was still constrained by lack of a priori justification for the selection of a particular distributional form for the one-sided inefficiency term μ (Thiam et al., 2001).

3.6.3 Theoretical Profit Function and Stochastic Frontier Model
A profit functions under mild ‘regularity conditions’ is a logical extension of the production function (Sadoulet and Alain de Janvry, 1995). Regularity conditions require that the function must be non-negative, monotonically increasing in output, convex and homogeneous of degree zero in all prices. To estimate the profit function, in the neoclassical theory, it is assumed that the farmer is operating on the frontier and the price of inputs and outputs are known. But in reality some of the farmers operate below and some above the frontier.
Furthermore, Junanker (1989) observed that farmers do not always operate in competitive input and output markets in developing countries and this violates the neoclassical assumptions. Since Junanker’s observation, there have been a number of developments to respond to this criticism. First, the assumption of output and input competitive markets is not needed in defining the firm’s profit function, especially in developing countries. What is needed is the output and input prices to be exogenous to the farm but be competitively determined (Sevilla-Siero, 1991). Secondly price variation can be handled by including district dummies (Lau and Yotopolous, 1971; Akinwumi and Djato, 1996). Third, it is currently possible to incorporate institutional and environmental factors referred to earlier such as quality of soils and rainfall as shown by (Ali and Flinn, 1989; Coelli, 1995). Fourth, profit function does not suffer from simultaneous equation bias problems as in production function. Fifth, the function has been used before in African context (Saleem, 1988; Akinwumi and Djato, 1996 and 1997). Thus, a stochastic profit function approach is deemed appropriate for this study. This study adopts the Ali and Flinn’s model specified in equation 9:
πј = ƒ (Pιј, Zκј, Dіј).expe ј…………………………………………………………………………………………..(9)
Where
π ј=normalized profit of јth farm defined as gross revenue less variable cost, divided by
Commodity prices from farm j. Pιј= prices of the variable inputs on jth farm,
Zκј=kth fixed factors on jth farm and Dіј=exogenous variables on jth farm,
eј=an error term, and ј = 1,…….n, is the number of farms in the sample.
Thus the error term can be specified in equation 10 as follows:
eј = νј- µ ј…………………………………………………………………………………………………………..(10)
Where νј and µј are random error terms and inefficiency effects of the farm ј, respectively. When µј = 0, the firm lies on the frontier but if µј>0 the farm is profit inefficient and incurring losses.
The inefficiency effects (µј) in equation (10) which are non-negative random variables are assumed to be identically and independently distributed such that µј is defined by the truncation (at zero) of the normal distribution with a mean of and variance where are the variable representing socio-economic characteristics of farm j to explain inefficiency and δ0 and δd are the unknown parameters to be estimated. The profit efficiency of the farm in the context of stochastic frontier is given by:
ηj = E [ exp(-µ ј)| eј] = E[exp(- )……………………………………… (11)
Where ηj is profit efficiency of farmer j and lies between 0 and 1 and is inversely related to the level of profit inefficiency. E is the expectation operator. This is achieved by obtaining the expressions for the conditional expectation µј upon observed value of ηj.
As pointed out by a number of researchers including Akinwumi and Djato (1996,1997), a profit function is much superior to production function because first it permits straight forward derivation of own-price and cross-price elasticities and output supply and input demand functions, second, the indirect elasticity estimates via profit function have a distinct advantage of statistical consistency, third, it avoids problems of simultaneity bias because input prices are exogenously determined. Quismbing (1994) confirm that “problems of endogeneity can be avoided by estimating the profit or cost function instead of the production function”. Besides, the profit function is extensively used in literature.
In measuring efficiency based on the stochastic profit frontier, two key assumptions are made which results in two types of the functions. Depending on whether market forces are taken into account or not, the standard and the alternative profit functions can generally be recognized (Berger & Mester, 1997). The standard profit function considers the profit gain from operating on the profit frontier, taking into consideration farm-specific prices and factors. It assumes that markets for outputs and inputs are perfectly competitive. Under the standard profit function, when given the input price ( w) and output price ( p ) vectors, the enterprise maximizes profits by adjusting the amount of inputs and output.
The alternative profit function explores how farmers are able to achieve the highest attainable profit conditional on their output levels rather than output prices (Ibid). The proponents indicate that the alternative profit function reduces scale bias that is often present in the standard profit function by holding outputs fixed and measuring farmers’ ability to generate more profit. Following the work of Berger and Mester (1997), this study adopts a translog functional form of the alternative profit efficiency model. In this model, output is held constant while output prices vary. As presented above the reasons for choice of this function in the study area include:-
-Output prices may not be measured accurately due to different measurement scales in typical rural Ethiopian markets.
-Differences in quality of labour may rather translate into different outputs realized by farmers. If output prices are used instead of output levels, it is likely that these differences in the quality of labour may remain unmeasured.
-Maize output markets are not perfectly competitive in the Damot pulasa district. As in most rural Africa, markets for crop produce are seasonal and prices that farmers receive depend on their negotiation power and skills with assemblers. Therefore, more produce can only be sold if prices are reduced, particularly during bumper harvests. Therefore, the alternative profit function is better fit to this situation than the standard profit function.

3.6.4 Empirical Model Selection criteria
Selecting an adequate model is key for any empirical analysis. Numerous methods for model choice and validation have been suggested in the literature. Well-known approaches to model selection include the usage information criteria, such as Akaike’s (1973) AIC and Schwarz’ (1978) SIC. Alternatively, Podolskij and Dette (2008) propose, among many others, goodness-of-fit tests. Common to all these tests, measures, and criteria is the idea that they provide us with a single ‘best’ model, regardless of the purpose of inference.
A number of functional forms exist in literature for estimating the profit function which includes the Cobb-Douglas (C-D) and flexible functional forms, such as normalized quadratic, normalized translog and generalized Leontif. From these the two popular functional forms that are used in most of literature are Cobb-Douglas and translog forms.
The C-D functional form is popular and is frequently used to estimate farm efficiency despite its known weaknesses (Saleem, 1988; Yilma, 1996).Rebecca (2011) showed that C-D production function model has a number of limitations. The major criticisms are firstly, that it cannot represent all the three stages of neoclassical production function, representing only one stage at a time. Secondly the elasticities of these types of function are constant irrespective of the amount of input used. The translog model has also its own weaknesses as well, but it has also been used widely (Ali and Flinn, 1989; Wang et al., 1996b). The main drawbacks of the translog model are its susceptibility to multicollinearity and potential problems of insufficient degrees of freedom due to the presence of interaction terms. The interaction terms of the translog also don’t have economic meaning (Abdulai and Huffman, 2000).
A solution to these problems would be to estimate both C-D and Translog function models and then use the results of the values of the AIC to reject or accept one model over the other. The Akaike information criterion (AIC) is a measure of the relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Hence, AIC provides a means for model selection.
AIC is founded on information theory: it offers a relative estimate of the information lost when a given model is used to represent the process that generates the data. In doing so, it deals with the trade-off between the goodness of fit of the model and the complexity of the model (Burnham, et al, 2011).
AIC is based on the maximum likelihood estimates of the model parameters. In maximum likelihood, the idea is to estimate parameters so that, under the model, the probability of the observed data would be as large as possible. The likelihood is this probability, and will always be between 0 and 1. It is common to consider likelihoods on a log scale. Logarithms of numbers between 0 and 1 are negative, so log-likelihoods are negative numbers. It is also common to multiply log-likelihoods by -2. In a regression setting, the estimates of the βi based on least squares and the maximum likelihood estimates are identical. The deference comes from estimating the common variance σ2 of the normal distribution for the errors around the true means. We have been using the best unbiased estimator of σ2, σ^2 = RSS/ (n – K) where there are K parameters for the means (K different βi parameters) and RSS is the residual sum of squares. This estimate does not tend to be too large or too small on average. The maximum likelihood estimate, on the other hand, is RSS/n. This estimate has a slight negative bias, but also has a smaller variance. Putting all of this together, we can write -2 times the log-likelihood to be:

AIC = -2*ln (likelihood) + 2*K……………………………………………….. (12)
Where ln is the natural logarithm (Likelihood) is the value of the likelihood K is the number of parameters in the model,
AIC can also be calculated using residual sums of squares from regression:
AIC = n*ln (RSS/n) + 2*K……………………………………………………. (13)
Where n is the number of data points (observations) RSS is the residual sums of squares AIC requires a bias-adjustment for small sample sizes. If ratio of n/K < 40 then uses bias adjustment:
AICc = -2*ln (likelihood) + 2*K + (2*K*(K+1))/(n-K-1)……………………..(14)
Where variables are as defined above. Notice that as the size of the dataset, n, increases relative to the number of parameters, K, the bias adjustment term on the right becomes very, very small. Therefore, it is recommended that you always use the small sample adjustment.
Hyuha (2007) tried both models and found that the translog function model was an adequate representation of the data. This study ran both the C-D and translog frontier profit function models. Both of these models have been widely used in Asia and Africa. According to the result of AIC “smaller is better”: given two models, the one with the smaller AIC fits the data better. Thus, translog production function constitutes a more flexible form and is an approximation for any production frontier. Therefore as shown on appendix-2, translog frontier profit function model was appropriate for this study than C-D function model, the one with larger value of AIC.

3.6.5. Trans-log Stochastic Frontier Profit Function Model
This study employed translog frontier profit function model for data analysis. Profit efficiency in this study is defined as profit gain from operating on the profit frontier, taking into consideration farm-specific prices and factors. And, considering a farm that maximizes profit and a singular output technology that is quasi-concave in the (n x 1) vector of variable inputs, and the (m x 1) vector of fixed factors. The actual normalized profit function which is assumed to be well behaved can be derived as follows:
Farm profit is measured in term of Gross Margin (GM) which equals the difference between the Total Revenue (TR) and Total Variable Cost (TVC).That is:
GM (π) = Σ (TR-TVC) = Σ (PQ-WXi) ……………………………………….. (15)
To normalize the profit function, gross margin (π) is divided on the both side of the equation above by P which is the market price of the output (maize). That is:

Where: TR represents total revenue, TVC represents total variable cost , P represents price of output (Q),X represents the quantity of optimized input used represents price of fixed inputs used pi= W/P which represents normalized price of input Xi while f(Xi,Z) represents production function.
The choice of normalized translog profit function for this study is based on the fact that it is the best-investigated second order flexible functional form and certainly one with most applications (Sauer et al., 2004 cited in Endrias et al., 2013). Another reason is that this functional form is convenient to estimate and proven to be a statistically significant specification for economic analysis as well as a flexible approximation of the effect of input interaction on yield.
The general form of the translog profit frontier model, dropping the jth subscript for the farm, is defined as:

for all
=restricted normalized profit computed for farm defined as gross revenue less variable costs divided by farm specific maize price
ln=natural log
=price of variable inputs normalized by price of output where (for i =1, 2, and 3) so that:
=the cost of hired labor normalized by price of maize output ( )
=the cost of “other inputs” normalized by price of maize ( )
=Imputed cost of family labor normalized by the price of maize output ( )
= the quantity of fixed input ( =1, 2)
Where: =land under maize (hectares under maize) for each farm j , =capital used in farm j (sum of total cost of hoes, sickles and plough),μ=inefficiency effects =truncated random variable =constant in equation 18;
=variables explaining inefficiency effects and are defined as follows: =non-farm employment , =education, =extension services, =credit access,
=experience, =degree of specialization, = age, =soil conservation, = access to market.α0, αi ,rik, ø , β , φ , δ0 and d, are the parameters to be estimated.

3.7 Description of Variables and Expected signs
Normalized profit( ) of the th farm defined as gross revenue less variable cost divided by farm specific price (dependent). Note the j is suppressed.
Labor is included in the model because it is one of the primary factors of production. It has been disaggregated into cost of hired labor ( ) and imputed cost of family labor ( ) as done in a number of profit efficiency studies (Ali and Flinn, 1989; Saleem 1988).
Land ( ) is defined as net area covered by maize and was treated as fixed input.
Capital ( ) in this study is derived as the sum total of the cost (using the prevailing prices) of hoes, sickles and ploughs. It was also treated as fixed.
Variable ( ) costs (fertilizer, seed and insecticide) used in production enhance productivity. Fertilizer used on the farm is a variable factor of production.
Non-farm employment ( ) one of the variables included in the model to capture access to extra income, which can then be used to buy, among other items, agricultural inputs.
Education ( ) through education the quality of labor is improved and with it the propensity to adopt new technologies. However, education has varying impacts depending on the environments, and has been proposed to be more effective in a rapidly changing technological or economic environment (Shultz, 1964 and 1975).
Access to extension services ( ) is a conduit for the diffusion of new technology among farmers. Thus it should reduce inefficiency levels among maize farmers through improvement in managerial ability.
Credit ( ) plays a crucial role in inefficiency improvement and should have a negative relationship with profit inefficiency.
Experience ( ) in maize production should have a direct relationship with profit inefficiency. As one gets proficient in the methods of production, optimal allocation of resources at his/her disposal should be achieved. Thus the more experienced one is the higher the profit and the lower the profit inefficiency.
Specialization ( ) implies optimal allocation of resources (time, money and human) in the enterprise to improve productivity. In this case specialization in maize production by maize farmers should lead them to seek better methods of production and hence improvement in profits efficiency.
Age ( ) number of years of the maize producing farmer.
Soil conservation ( ) Lu et al (2000) states that soil conservation is a set of management strategies for prevention of soil being eroded from the earth’s surface or becoming chemically altered by overuse, acidification, salinization or other chemical soil contamination. Households practice different soil conservation mechanisms to sustain the productivity of their farm land. It is obvious that conserved farm land produces more output than non-conserved lands. Hence, those households practicing soil conservation are expected to be more efficient. Soil conservation is a dummy variable that assumes 1 if the farmer conserves soil and 0 otherwise.
Access of market ( ) availability and nearness of input and output markets. It is a dummy variable that assumes 1 for accessibility and 0 other wise.

Table: 3.2 Variables Included in the Frontier Profit Function Models and their expected signs.

3.8 Operational Definitions of Some Terms
Development agents/extension agents:-Agricultural extension service providers assigned by government and are the sources of agricultural information in the study area.
Economic efficiency:-is distinct from the other two even though it is the product of technical and allocative efficiency (Farrell, 1957). A firm that is economically efficient should by definition be both technically and allocatively efficient.
Household: -it comprises either one person living in alone or a group of people who may or may not be related, live in the same address, who either share at least one meal a day or share common living accommodation.
Output: – the total quantity of maize harvested of one season.
Price or allocative efficiency: – has to do with the profit maximizing principle. Under competitive conditions, a firm is said to be allocatively efficient if it equates the marginal returns of factor inputs to the market price of output (Fan, 1999).
Production efficiency: – is equivalent to economic efficiency because it combines two components, that is, technical and allocative efficiency.
Profit efficiency is defined as the ability of a farm to achieve highest possible profit given the prices and levels of fixed factors of that farm and profit inefficiency in this context is defined as the loss of profit from not operating on the frontier (Ali and Flinn, 1989).
Profit function: – is an extension and formalization of the production decisions taken by a farmer. According to production theory, a farmer is assumed to choose a combination of variable inputs and outputs that maximize profit subject to technology constraint (Sadoulet and De Janvry, 1995).
Scale efficiency: – can also arise from spreading the cost of production, particularly fixed costs over a large output.
Technical efficiency: – is an engineering concept referring to the input-output relationship. A firm is said to be efficient if it is operating on the production frontier (Ali and Byerlee, 1991).
Yield:-the total quantity of maize harvested per hectare.

3.9 Model Specification Tests
A test of the appropriateness of the model and the explanatory variables included in the model is critical step before analysis and drawing implications. Taking into account the varying nature of the cross-sectional data which were used, multi-colinearity, heteroscedasticity, normality and indogeneity problems were checked. The variables included were tested for multicollinearity using Variance Inflation Factor (VIF). In addition, Breusch Pagan (BP) test was used to test safety of heteroskedasticity.

Multicollinearity Test
Multicollinearity refers to a situation with a high correlation among the explanatory variables with in multiple regressions and it is a sample problem and a state of nature that results in relatively large standard errors for the estimated regression coefficients, but not biased estimates (Andren, 2007). The data were tested for multicollinearity. It is expected that no single explanatory variable should be a linear function of another. The results showed that there is no indication of any trouble of multicollinearity. It can be investigated by calculating by variance inflation factor (VIF) for each of the explanatory variables. If a mean value of VIF are larger than 10; there is evidence of multicollinearity problem that calls for serious concern.VIF values were computed for all variables and they were ranging between 1.77 and 8.94. Moreover, the mean value of the factors (VIF) was 5.32 as shown on (Appendix-2).Hence mullticollireaty was not a problem among the explanatory variables.

Heteroskedasticity Test
Heteroskedasticity is a violation of one of the requirements of ordinary least squares (OLS) in which the error variance is not constant. The consequences of heteroscedasticity are that the estimated coefficients are unbiased but inefficient. Colin and pravin (2009) showed that the maximum likelihood estimators of regression result are inconsistent if there is heteroscedasticity problem. Heteroscedasticity is mainly prevalent in cross-sectional data set such as the one used in this study. Some of the main causes are: variance of dependent variable increase with increase in the level of dependent variable, variance of dependent variables increases or decreases with changes in independent variables and outliers in the data set. The first step in addressing the problem of heteroscedasticity is to determine whether or not heteroscedasticity actually exists. Therefore following the techniques mentioned by Andren (2007) to identify the problem of heteroskedasticity, the Breusch-Pagan is popular test procedure presented in most econometrics textbooks. And it is slightly more general than the Goldfeld-Qaunt test, since it allows for the test the chi-square. Some of the methods used to correct for heteroskedasticity are transformation of data into natural logarithms, the Weighted Least Squares(WLS) and robustness of the weighted of standard errors (Gujarati,2004). Andren (2007) illustrated the effects heteroskedasticity on estimates for various models and provided the robustness of the standard error of the estimators as the best remedial way of correcting heteroskedasticity. Heterokedasticity-robust methods are valid at least in large samples whether or not the errors have constant variance. So, variance matrix estimator should be robust in the presence of heteroskedastiy of unknown form (Wooldridge, 2000). According to the Breusch-Pagan, the chi-square was 6.18 with prob>chi2 equals 0.0861 at 10 percent level of confidence (Appendix2). Since the prob>chi2 was 0.0861 which less than 10 percent level of confidence the null hypothesis of homoskedasticity is rejected and researcher conclude that there is heteroscedasticity in the data even though as such not problematic in this case. For this study, transformation of data into natural logarithms and robust standard errors methods were used to address heteroskedasticity.

Endogenity test
Endogenity problem exists when an independent variable in the model is explained by other variables and correlated with error terms with in the equation. Neglecting the problem of endogenity in the equation introduces a simultaneity bias. A more difficult problem arises when a model excludes a key variable, because of data unavailability. One possibility is to obtain a proxy variable for the omitted variable. Loosely speaking a proxy variable is something that is related to unobserved variable (Wooldridge, 2000).Although researcher explicitly recognizes that human capital affect farm profit efficiency researcher can never estimate it since human capital is a vague and not observed. The omitted variable bias can be solved or at least mitigated, by obtaining a proxy variable for the omitted variables. Consequently in model specification one possibility was using education variable as a proxy for human capital.
Therefore in this study the independent variables were not explained within the model in which it appeared in stochastic frontier profit function models. And to solve the potential endogenity in the two-limit Tobit model, few variables suspected of causing the problem were added in model and consistency was achieved. Therefore the independent variables and the error are not linearly related, ensuring that variables measuring efficiency are independent from the variables in the error term.

Normality test
It is important to note that profit efficiency can only be estimated if the inefficiency effects are stochastic and has a particular distributional specification (Battese and Coelli, 1996).If the underlying disturbances are not normally distributed, the estimator is inconsistent. And unifying treatment includes several distributions such as exponential, lognormal and Weibull (Greene 2003).one of the assumptions made in this study is inefficiency component (μ) is half-normal distribution or one-sided non-negative distribution of which is independent on ν that represents factors external to the farmer and is assumed to be independently and identically distributed (iid) with zero mean and constant variance as Ν (0, σ 2μ). In order to confirm the assumed distribution, skweness/kurtosis test is one of used method in stata (Colin and Pravin, 2009).According to sketests, the joint chi-square was 4.40 with prob>chi2 equals 0.1107 at 10 percent level of confidence (Appendix Table 2E). Since the prob>chi2 was 0.1107 which is greater than 10 percent level of confidence, the null hypothesis of normality in the distribution of inefficiency is accepted and the researcher concluded that this was an indication of assumption that μ is non-negative half normal distribution at least 10 percent level of significance.

4. DATA ANALYSIS, INTERPRETATIONS AND DISCUSSIONS
This chapter provides an analysis, interpretation and discussion of the results for the study on socio-economic and institutional characteristics of the farmers in a study area, the econometric results from the frontier profit function and the results of the inefficiency model. The first part of the chapter presents descriptive statistic results of socio-demographic and institutional characteristics of the respondents. The next part deals with econometric results of the model.

4.1 Questionnaire Return Rate
The study sample was 246 subjects, all of which were small scale maize farmers. The response rate was 100%, this was possible since researcher worked closely with agricultural extension officers and assistant data collectors who also helped in collection of the questionnaires. According to Frankel and Wallen (2004), a response rate of above 95% of the respondent can adequately represent the study sample and offer adequate information for the study analysis and thus conclusion and recommendations.

4.2. Descriptive Results
4.2.1 Characteristics of the respondents
The average statistics of the sampled maize producers are presented in Table 4.1. On the average, a typical maize farmer in the study district was 52 years old, with about 5.98 years of education, 16.3 years of farming experience and an average household size of 6.51 persons. The average maize farmer cultivated 0.75 ha of land, produced an output of 2093.98 kg of maize per annum.

Table 4.1: Characteristics of the respondents

According to respondents shown on Table 4.2 maize production in the Damot pulasa district is dominated by male (88.6%) with very few female 11.4%. The distribution of sex in the survey may be explained by the socio-cultural pattern of the study area where most women are involved in domestic and household chores, and do petty-trading, dressmaking as well as activities that support their husbands. This distribution, according to the respondents, helps diversify family sources of income. Few of the respondents were below age 30 (3.3%) while respondents aging between 41 and 50 years accounted for the majority (29.2%). Approximately 46% of respondents aged above 50 years. In the survey, 87.4% of the respondents had primary to secondary education while the remaining 12.6% had no formal education at all. Through education, the quality of labour could be improved and the propensity to adopt new and improved farming techniques could increase (Hyuha, et al., 2007). Thus, farmers in the study area may easily adopt new technologies due to enhanced educational outlook of majority of the respondents. This could improve productivity and therefore level of profit earned from the respective enterprise.

Table 4.2: Demographic and Socio-economic Characteristics of Respondents

4.2.2 Institutional characteristics of sample households
Table 4.3 presents the summary statistics of some of institutional characteristics of households the in study area. Membership of cooperatives was one of the channels through which new technologies were transferred to farmers. The farmers’ membership to cooperatives included those established to facilitate the agricultural production of farmers such as input supply cooperatives and farmers associations. It was observed that about 69.11 % of smallholder maize producers were members of agricultural production oriented cooperatives. Such participation in cooperatives facilitated communication between farmers and other bodies such as researchers, extension officers and government. According to the result almost all smallholder maize producers were members of various non-agriculture oriented institutions and organizations such as religious groups (churches), Idir, Ikub and others. About 79.24% of smallholder maize producers needed credit to undertake maize production. In addition to this from those who needed credit only 36.59% got credit services for agricultural activities (Table 4.3). The remaining 63.41% of households could not get the services for intended purposes and to high interest rate imposed money lenders.
Trainings were the best tool to pass on new information and to correct misconceptions concerning wise and efficient production input usage. In the study area about 18.69% of the sample farmers did not attend training and 81.31% of respondents had training on farm practices (Table 4.3).

4.2.3 Distribution of respondents by usage of inputs
Since most of farmers in the study area were smallholder maize producers, they did not have enough capital to hire labor and as a consequence relied on family labour for most of the farming activities. However, some of farmers hire a few daily workers to supplement family labor. Farmers with small family size are the ones who usually hire labour. As shown in (Table 4.4) about 71.5% of the sample farmers did not hire labour and mainly depend on family lobour while about 28.5% of the sample farmers used both family labour and hired labour.
In addition to labor improved maize seed usage play important in maize production. Most smallholder maize producers used the same seed they used previously. The result showed that 69.1% of farmers used improved maize seed (Table 4.4). In addition about 18.3% farmers used both local and improved maize seeds. Due to limitation of cash to buy improved seeds, about 2.8% of the farmers did not purchase seed at all; they used recycled seed instead. According to Focus Group Discussion, smallholder maize producers bought improved seeds extension centers, kebele administration and local markets. In addition to this, some farmers bought seed from their fellow farmers, more over as FGD, result indicated farmers complain that the price of seed become beyond their capacity and sometimes timely unavailability and shortage of required quantity challenged maize production and profitability.
Almost all of the sample farmers applied fertilizer for maize production (Table 4.4). As the FGD indicated although most of them applied fertilizers on maize farm ,but they did not use required quantity of fertilizer due to expensive and timely unavailability of it. And only 10.6% and 11% of the sample farmers applied manure and agrochemicals in their maize farm respectively. Farmers who undertake soil conservation on their farm were 69.9% of the respondents (Table 4.4).
In general, according to focus group discussion there is limited knowledge among respondents on wise and efficient utilization of production resources like family labor, inputs like improved maize seed, chemical fertilizers and other farm implements. Other ideas raised during this period were almost all of farmers complained that inputs were expensive. For some of respondents, absence of suppliers in their area was one of the major problems in accessing production inputs. In addition, some of them had transport problem to access the input markets. As response of extension agents those who were one of key informants, most of the time farmers resist to use full package (improved maize seed, urea, DAP) according to their plot of maize hectare and hence, this would have high contribution on observed profit inefficiency in the study area.

Table 4.4: Distribution of respondents by usage of inputs

4.3 Econometric Results
4.3.1 Testing for the hypothesis
The AIC value, sigma-squared and gamma parameters are results on the behavior of the error term outlined in equation 15. Basically, the statistics are designed to test the appropriateness of the model to represent the data and for efficiency effects in the model. The gamma () and the Akaike Information Criterion (AIC) parameters are employed to test for efficiency and the appropriateness of the model, respectively. The gamma () tests whether the observed variations in efficiency are simply random or systematic. The parameter is defined as the ratio of the unexplained inefficiency error term of ( ) to the total sum of errors, explained ( ) and random ) or  = / ( + ). The gamma () is bounded by 0 and 1, where if  is zero inefficiency effects are not present in the model, and if it is one inefficiency exists and is not random (Battese and Coelli, 1995 cited in Hyuha, 2007).
The results in Table 4.5 show that gamma (=0.6702) is significantly different from zero in all the estimated samples implying that there is profit inefficiency in maize production. The observed variations in profit efficiency among the maize farmers are due mainly to differences in farm practices and characteristics of sampled maize farmers rather than random factors.

The first null hypothesis was set to find out whether a C-D model can be employed in estimating the level of profit efficiency in the study area or a translog specification. The Display information criterion for this hypothesis is conducted using the AIC values of the estimated stochastic frontier function and the values of the corresponding C-D profit function. The rejection in general is, “smaller is better”: given two models, the one with the smaller AIC fits the data better than the one with the larger AIC. The null hypothesis is rejected in favor of the alternate (the translog specification) because of larger AIC values of C-D model. When this happens, it implies that the C-D model is not adequate, necessitating the need to use the alternative model, in this case the translog specification model.
The second hypothesis tests various restrictions on joint and inefficiency effects included within the two models 14 and 15. In the first instance, we test whether farmers individually are operating at the frontier. If they are, then we reject null hypothesis at the fixed critical confidence level, in this case 5% and accept the alternate. This would imply that farmers are profit inefficient or are not operating on the frontier.
The third hypothesis is designed to test the contribution of factors included in model 15 to observed inefficiency levels (Table 4.7), in case hypothesis 3 is rejected. The null hypothesis to test is that factors included in model equation 15 contribute significantly to observed profit inefficiency levels. Hence the null hypothesis is rejected. Rejecting the null hypothesis implies that these factors contribute significantly to explaining the observed profit inefficiency of smallholder maize producers in the study area.
To conclude this section, the three hypotheses tested show that first, the C-D model is not an adequate representation of the data, second, that all farmers are not operating on the efficient profit frontier and third, that in general the variables included in inefficiency model adequately explain the observed variations. Therefore, the next section concentrates on estimating the translog profit function using MLE method.

4.3.2 Estimation of Frontier Profit Function: Translog Model
The stochastic translog frontier profit function model was adopted for analysis in this study. The translog function shows some interactions among variables and it is also known to have several possible interpretations. It can also approximate arbitrary twice continuously differentiable functions. As a result, recent advances in econometric theory and in applied production economics explain its popularity.
As explained in chapter 3, the estimation of the stochastic frontier profit function was undertaken. The dependent variable was normalized profit from an output of one season.
The study identified key factors that influence the profit of maize as well as efficiency of farms cultivating the crop. The results of the maximum likelihood estimates (MLE) are presented in (Table 4.5).All the estimated coefficients of sampled farmers carry the theoretically expected signs in the MLE except costs of capital and are statistically significant. The direction of most of the input prices meet theoretical expectation, indicating that the average profit function of farmers in the study area is convex in input prices. This implies that in its property profit is non-increasing in input prices like costs of other inputs, wages of hired labors and wages of family labors. A stochastic translog frontier profit function model analysis of coefficient estimates for the study area showed that costs of “other inputs”, area under maize and capital are the most influential variables in maize production (Table 4.5). The estimates associated with these three variables were statistically significant. Costs of “other inputs” affect profit efficiency negatively whereas area under maize and capital had the opposite influence

4.2.3 Determinants of Farm-Specific Profit Inefficiency in Maize: Inefficiency model
In line with objective number 3, estimated results based on model equation 16 are presented in Table 4.7. The purpose was to determine factors that explain profit inefficiency. The variables included in the model were in line with hypothesized sign as explained in chapter 3 except age of farmers. These were: non-farm employment, education, experience in maize growing, degree of specialization, access to credit, extension services, age of household head, market access and soil conservation practices.
The results this research revealed that the estimated coefficient on education is negative and statistically significant at 5% level, indicating reduction in profit inefficiency. This implies that to an extent more education brings about decrease inefficiency (increase in efficiency) in maize production. This also indicates that farmers with more years of schooling incur significantly higher profit efficiency than farmers with less years of schooling. These results are consistent with (Nganga et al, 2010; Ogunniyi, 2011; Oladeebo and Oluwaranti, 2012). Thus, giving education to maize farmers in particular would be very beneficial in terms of reducing inefficiency in maize production. Reduction in profit inefficiency will enhance the Government’s policy on commercialization of agriculture and poverty eradication. Therefore, an effort to improve farmer education is an important thing that one way is to increase investment on education through allocating a larger budget for education.
The ability of a farmer to manage his/her farm not only depends on formal education level, but also on non-formal education. Non-formal education includes involvement in extension activities, communication with extension workers, training in farmers training centers (FTC), and others. Those forms of non-formal education deliver practical and specific knowledge, and skills according to the farmer’s needs. Therefore, farmers with non-formal education have higher managerial skills, so they manage their farms more efficiently. Previous research has also proved that non-formal education, with various terms, significantly increase profit efficiently (Hyuha et al., 2007; Ogunniyi, 2011; Abu and Asember, 2011).
The estimated coefficient associated with experience, in this study carries the expected negative sign and is statistically significant at 10% level. This finding agrees with the result of (Bidzakin, et al., 2014) .Probably, this could be explained that those farmers with experience are better performers than those without. In other words, maize farmers with more years of experience tend to operate at significantly higher level of profit efficiency. Whereas this is so, education and quality of extension services given to the farmers would supplement or in some cases substitute it.
The estimated coefficient associated with the extension services is significant in the study area. This result reveals that farmers who have access to extension services perform significantly better in operating at higher level of efficiency. This result is also consistent with findings obtained by other researchers (Rahman, 2002; Hyuha, et al., 2007; Ogunniyi, 2011). This result therefore would serve to emphasize the role of extension services in reducing profit inefficiency in maize production.

Table 4.7: Determinants of Demographic, Socio-economic and Institutional factors on farm-Specific Inefficiency in maize Production in the study District: Tobit regression

The result of this study showed that access to credit in the study area may increase profit efficiency. Credit access is expected to ease the financial constraint, enhance the acquisition of the much-needed inputs, and improve revenue and, subsequently, profits. The finding of this study imply that institutional arrangements that aim at reducing transaction costs of providing farmers greater access to credit would have the potential of increasing profit efficiency. This result is consistent with the findings of (Mohammed et al., 2013). From the findings of this study, it is apparent that policy makers need to introduce appropriate legislation that encourages commercial and microfinance institutions like Omo microfinance that are operating in the area to accommodate small agricultural producers.
The estimated coefficient associated with farmer’s age, carries positive sign and statistically significant at 5 percent level. This is due to the fact that aged farmers are risk averse when compared to their contemporary young ones. This result is contrary to the findings of (Sunday et al., 2012), but it agrees with (Maganga et al., 2012).
The coefficient of non-farm employment variable entered into the profit inefficiency effect model indicated that the variable affects level of profit inefficiency in maize production negatively. In other words, those farmers engaged in some off-farm activities were less profit inefficient relative to those who were not engaged in off-farm activities other than their farm operation. Abdulai and Huffman (2000) reported similar results for farmers in Northern Ghana. (Ali and Flinn, 1989; Wang et al., 1996b; Rahman, 2002, 2003) reported similar results for farmers in Pakistan, China and Bangladesh, respectively. The results indicated that having non-farm work provides the income to buy inputs needed to raise productivity, and hence reducing inefficiency.
When a farmer specializes in maize production, all his/her efforts in terms of accessing information on new technology should translate into improvement of efficiency in the production of the crop. In this study a negative and statistically significant relationship between the degree of specialization in the maize crop production and profit inefficiency was observed in study area implying that efficient allocation of resources is important for reducing inefficiency in maize production.
Soil conservation practice would have the potential of increasing profit efficiency. In the study area maize farmers practicing soil conservation are more profitable than those who could not. This result is also consistent with findings obtained by other researchers (Job and Cebile, 2013). Results of their study showed that maize farmers operating under conservation agriculture are experiencing an increase in yields with subsequent higher profit level compared with maize farmers who operated under conventional agriculture. This calls for a coordinated effort to promote effective soil fertility management, for example through moderating crop mixes, input use adjustments, particularly chemicals, and directly undertaking soil conservation practices. This again points towards justification in favour of strengthening extension services equipped with skills that can address a broader development agenda.
Access to input markets tend to help farmers to purchase input at the right quantity, time, and price. Thus improved access to input markets and services enables farmers to adjust their resources relatively more effectively, such as timely availability of fertilizers and pesticides at competitive prices, thereby positively influencing profitability. Purchasing input correctly leads to an increase in input utilization efficiency. Therefore, an access to improved input market is predicted to affect farming profit efficiency. This research proves that access to input market has a significant effect on profit efficiency. Other studies support this conclusion, such as (Wadud and Ar Rashid, 2011; Dwi, R., et al., 2014).

4.2.4 Marginal effects
Quantification of marginal effects of these variables on profit efficiency is possible by partial differentiation of the profit efficiency predictor with respect to each variables in the efficiency function to indicate that the effects of a unit change in those variables on the unconditional expected value of profit efficiency expected value of profit efficiency conditional up on being between 0 and 1, and probability of being between 0 and 1. For variables constructed as a dummy variable, the coefficient estimated represents a one-off shift in efficiency rather than a true marginal effect. The marginal effects of changes in explanatory variables from Tobit Regression analysis were computed following the procedure proposed by (Greene, 2003; Waluse, 2012; and Endrias, et al.2013).
The results showed that, other variables keep constant; a one year increase in age of the farmer decreases the expected value of profit efficiency by about 1.3% (Table 4.8).One year increase in education of the house hold head increases expected value of profit efficiency of farmers by about 9.4% keeping other variables constant. Specifically, it was also found an increase in utilization of credit increases farmers’ expected value of profit efficiency by about 5.4%.
A unit increase in access of near market increases profit efficiency of smallholder maize producers by about 8.9%. This result is attributed to the fact a farmer located far from the market incurs more costs to transport far inputs from the market ,compared to the one closer to the market. In similar manner a unit increase in distance farmers from extension centers decreases profit efficiency of smallholder maize producers by about 3.2% with other variables kept constant by implying that efficient utilization of one the most precious resources ;time is affected (Table 4.8). In the same manner a unit increase in soil conservation practice increases profit efficiency of smallholder farmer by 4.7%.

Table 4.8: The marginal effects of explanatory variables on profit efficiency

5. SUMMARY, CONCLUSION AND RECOMMENDATIONS
This chapter begins with the study summary where the key findings of study are summarized. Based on the key findings, policy recommendations are then highlighted. The chapter concludes with areas of focus for future research.

5.1 Summary
Maize is influential for food security of Ethiopian households as a source of both food and income. Much of the existing studies have been focused on physical productivity (technical) efficiency. More importantly efficient resource use is the basis for achieving food security and poverty reduction. As such the objective of this was, to analyze profit efficiency of maize production among smallholder famers and to assess the effects of socio-economic variables on the profit inefficiency in Damot pulasa district; wolayta zone of SNNPRS. Data for the study were collected using the multi-stage sampling technique, and administering structured questionnaires to a total of 246 randomly selected respondents from five kebeles. Data collected were analyzed using descriptive statistics and econometric models.
Descriptive statistics indicated that the mean age of all the sampled farmers was about 52 years. The respondents in the study area had about 16 years of maze growing experience on average in the study area. This showed that maize production has been in existence for a number of years as the majority of smallholder maize producers. An experience for farmers in production helped to capture the knowledge of the production practices. Additionally, most of farmers depend mainly on family labor. The average family size of respondents was found to be about 7 members per household. This shows that farmers can have easy access to additional labor from family members.
The results of the AIC value showed that the C-D model was not the right model for this study necessitating the adoption of a frontier translog model. Thus the stochastic profit frontier translog model was estimated in this study.
The analysis from the translog model showed that the variables maize hectarage and capital had a positive influence on the profit levels while imputed cost of family labor, costs of hired labor and costs of “other inputs” had a negative effect on profit efficiency levels in study area.
The analysis of profit efficiency levels revealed that the sampled farmers from the study district were not operating at the profit frontier. They had different levels of efficiency, with a wide variation (24.6%-99%) and a mean of 78.4%.
In analyzing the sources of inefficiency of maize farmers, nine factors were identified. These were non-farm employment, education, experience, access to credit, access to extension service, soil conservation practice, access to market, age of respondents and degree of specialization in maize growing.
Lack of education was found to have an impact on profit inefficiency levels in area. Lack of it contributed to the loss of profit efficiency. The significant differences were observed between those who are illiterate and those who have at least primary education. The implication is that to improve efficiency in maize production at least primary level of education is need to be necessary.
Extension services were found to be statistically significant and influencing profit inefficiency negatively in the area of study. These results reinforce the already acknowledged view that extension access is a necessary lubricant to adoption of new technology, which has positive impact on profit efficiency. The most crucial point is to pass on the relevant messages to farmers. In the crop under study case, such information was found to be limited as the crop has in the past received very low priority in terms of budget allocation (research and human). It is recommended that research institutions that are charged with the responsibility to carry out research on crops such as maize to refocus its efforts on crop. In addition, the organization should foster linkages with private sector to come in where they are weak, particularly in providing credit.
The degree of specialization in maize production was found to be an important variable in influencing profit inefficiency levels. The results tend to suggest that specialization in maize production reduces profit inefficiency in the study district implying efficient use of resources on specialization is necessary that it would pay for the farmers to specialize the crop. Experience as a factor was important in the study area. Farmers with experience in maize production were more efficient than those without.
Generally, development of market and other important infrastructures like road could promote resource use efficiency and productivity and hence, profitability by reducing extra unnecessary costs on maize production. Therefore policy makers should focus on market and road infrastructure so as to facilitate market participation and integration of far distant resident smallholder maize producers. Consequently policies targeting and encouraging education and trainings to enhance farmer’s capacity building, facilitating enough access to credit, practices of soil conservation and providing regular extension services to smallholder maize producers would promote profit efficiency of maize production in the study area.

5.2 Conclusion
This study employed Trans-log stochastic profit frontier function model to analyze profit efficiency among smallholder maize farmers in Damot pulasa district, Wolayta zone of SNNPRS using farm level data obtained from 246 maize farmers. The main objective of the study was to analyze profit efficiency of maize production among smallholder maize famers and to assess the effects of socio-economic variables on the profit inefficiency in the study area.
The study results from the frontier profit function showed that the major farm specific production factors affecting profit efficiency were imputed wage of family labor and costs of ‘’other inputs’’ such as seed, fertilizer and agro-chemicals which had a negative influence on profits, whereas area under maize that had the opposite effect.
The study also has shown that profit efficiency varied widely among the sampled farmers with ranging from 24.6% to 99% with a mean of 78.4%. The mean level of profit efficiency indicates that there exists room to increase profit by improving the technical and allocative efficiency. Least profit efficient farmer needs an efficiency gain of 74.4% to attain the profit efficiency of the best farmer in the study area, an average efficient farmer needs an efficiency gain of 20.6% to attain the level of the most profit efficient farmer, while the most profit efficient farmer needs about 1% gains in profit efficiency to be on the frontier.
All the parameters of variables included in the inefficiency model have significant impacts on profit efficiency. The Tobit regression of inefficiency model estimation revealed that profit efficiency was positively influenced by education (at 1% level ), extension services(at 1% level), Experience of the farmer ( at 10% level), degree of specialization( at 5% level), soil conservation(at1% level), access to markets(at 1% level ), non-farm employment( at 5% level), credit access( at 10% level) and negatively influenced by ages of farmers ( at 10% level).
Finally, the policy implication in maize production is that inefficiency in maize production can be reduced significantly by improving the level of education among the farmers and awareness by extension agents. Most important are the extension services and the existing technological packages that need to be critically examined. Furthermore, the study will go a long way to help other researchers and research institutions in further research for more effective combinations of resources for better efficiencies as well as increase output and productivity in the farming business, it would also help the government, policy makers and other donor agencies in planning, designing and formulations of agricultural programs that would tend towards increase resource, resource availability as well as affordability.

5.3 Recommendations
– In order to improve profit levels in maize production there is need to increase area under maize and reduce excess family labor in maize production. Currently, maize farmers in the study area are operating an average of 0.75 hectares. But area expansion may imply increasing family labor, which negatively affects profit efficiency. Thus, this suggests that land-augmenting technologies such as improved seeds would be the most appropriate approach. This serves to re-emphasize the need for research stations to strengthen the breeding programs in order to come up with high yielding varieties for release to maize farmers. The recently released high yielding varieties like (Jabi PHB3253 and BH540) are hence very encouraging.
-Acquisition of formal and informal education, improving rural financial markets and strengthening the existing extension services by training extension agents in order to fill skill gap on wise utilization of resources were recommended to improve profitability in maize production in the study area.
-Younger farmers were comparatively more educated than the older farmers in the study area. Therefore, by increasing the education status of older farmers through Adult Based Education and Training government can increase the efficiency level of farmers.
-To reduce profit inefficiency levels in the study area the issue of off-farm and non-farm employment would be tackled. One way could be creating employment opportunities outside the farm. This would enable some of the farmers to access jobs from which they can earn income. The income would be used to purchase inputs to use on the farm and hence improve on productivity. Alternatively, they need stay on the farm, but could combine non-farm activities effectively by employing labor-saving technologies to ease the weeding and bird-scaring burdens. This implies that the concerned organizations should come up with varieties which are less palatable to the birds. This would help to reduce on the drop out of school going as these are the ones who are mainly employed to perform this ardors task.
-The homegrown research, institutional support and sustained commitment to agricultural research and development are the key drivers of the change. Hence, it is essential to progressively improve access to and effectiveness of extension and marketing services and continue to increase the critical mass of researchers and retain highly skilled and qualified scientists by providing appropriate incentives if further advances are going to be made in improving the productivity profitability of maize and other crops in a sustainable manner.

5.4 Areas of further research
-The study failed to look at marketing challenges faced by maize producers, yet the current strategy for improving agricultural productivity and profitability is through a market-led production approach. Therefore future research can venture into this area not only in the study area but also in the other parts of the country producing maize and other cash crops.
-Moreover, it was observed that the literature available on efficiency analysis in Ethiopia is majorly on technical efficiency. Technical efficiency is derived from production function which is possible to achieve while realizing sub-optimal profit. Thus, a technically efficient farmer can be kicked out of the market due to failure to achieve profit. On the other hand, in profit measure, we take care of input costs and output prices. Therefore, future research should consider measuring not only technical efficiency, but also profit efficiency so as to give accurate policy recommendations.

6. REFERENCES